3_chemometrics_linearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chemometrics\n",
    "<br>\n",
    "Julien Wist / 2017 / Universidad del Valle\n",
    "\n",
    "\n",
    "An up-to-date version of this notebook can be found here: https://github.com/jwist/chemometrics/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.plot.width=4, repr.plot.height=4) # change these setting to plot larger figures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A first example - simple linear regression\n",
    "\n",
    "we make repeated measurement of an observable Y as a function of X. You might think of a calibration curve where you measure the transmitted intensity as a function of the concentration of a solution.\n",
    "\n",
    "### create data and visualize it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rm(list=ls(all=TRUE)) # we clear the variable space\n",
    "\n",
    "N <- 20 # we define the number of observations\n",
    "\n",
    "# we create a fake dataset using a quadratic\n",
    "#equation and adding some noise\n",
    "# first create a vector of x repeated rep times\n",
    "rep <- 2 # number of replicates\n",
    "X <- rep(seq(from=43, to=96, length.out=N),rep)\n",
    "# then create the Y vector according to the equation:\n",
    "Y <- (0.075 * X + -1.874 + 0.01* X^2)\n",
    "# create some noise\n",
    "noise <-runif(length(Y), -1, 1) \n",
    "# add some noise to Y\n",
    "Y <- Y + 1*noise\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we take a look to the data that we just created."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AgQIECAQIcEWi+QXpixfNAyxvP1+R4F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\nQIAAAQIECBAgQIAAAQLTIfD/J0inLu+BdZ0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to prepare a nice dataset for R we need to sort the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_sorted <- sort(X,index.return=TRUE)\n",
    "x <-x_sorted$x\n",
    "y <- Y[x_sorted$ix]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and now we can create a data.frame with columns x,y and $x^2$. \n",
    "\n",
    "<span style=\"background-color: #DDEBF6\">consider data.frame is equivalent to an excel spreadsheet, with columns headers, and data of the same length, however data could be of different kind, such as strings, numbers (numeric), factors, etc.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data <- data.frame(x=x, y=y, x2=x^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "to access the data within the data frame, use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<ol class=list-inline><li>1</li><li>21</li><li>2</li><li>22</li><li>3</li><li>23</li><li>4</li><li>24</li><li>5</li><li>25</li><li>6</li><li>26</li><li>7</li><li>27</li><li>8</li><li>28</li><li>9</li><li>29</li><li>10</li><li>30</li><li>11</li><li>31</li><li>12</li><li>32</li><li>13</li><li>33</li><li>14</li><li>34</li><li>15</li><li>35</li><li>16</li><li>36</li><li>17</li><li>37</li><li>18</li><li>38</li><li>19</li><li>39</li><li>20</li><li>40</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 21\n",
       "\\item 2\n",
       "\\item 22\n",
       "\\item 3\n",
       "\\item 23\n",
       "\\item 4\n",
       "\\item 24\n",
       "\\item 5\n",
       "\\item 25\n",
       "\\item 6\n",
       "\\item 26\n",
       "\\item 7\n",
       "\\item 27\n",
       "\\item 8\n",
       "\\item 28\n",
       "\\item 9\n",
       "\\item 29\n",
       "\\item 10\n",
       "\\item 30\n",
       "\\item 11\n",
       "\\item 31\n",
       "\\item 12\n",
       "\\item 32\n",
       "\\item 13\n",
       "\\item 33\n",
       "\\item 14\n",
       "\\item 34\n",
       "\\item 15\n",
       "\\item 35\n",
       "\\item 16\n",
       "\\item 36\n",
       "\\item 17\n",
       "\\item 37\n",
       "\\item 18\n",
       "\\item 38\n",
       "\\item 19\n",
       "\\item 39\n",
       "\\item 20\n",
       "\\item 40\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 21\n",
       "3. 2\n",
       "4. 22\n",
       "5. 3\n",
       "6. 23\n",
       "7. 4\n",
       "8. 24\n",
       "9. 5\n",
       "10. 25\n",
       "11. 6\n",
       "12. 26\n",
       "13. 7\n",
       "14. 27\n",
       "15. 8\n",
       "16. 28\n",
       "17. 9\n",
       "18. 29\n",
       "19. 10\n",
       "20. 30\n",
       "21. 11\n",
       "22. 31\n",
       "23. 12\n",
       "24. 32\n",
       "25. 13\n",
       "26. 33\n",
       "27. 14\n",
       "28. 34\n",
       "29. 15\n",
       "30. 35\n",
       "31. 16\n",
       "32. 36\n",
       "33. 17\n",
       "34. 37\n",
       "35. 18\n",
       "36. 38\n",
       "37. 19\n",
       "38. 39\n",
       "39. 20\n",
       "40. 40\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  1 21  2 22  3 23  4 24  5 25  6 26  7 27  8 28  9 29 10 30 11 31 12 32 13\n",
       "[26] 33 14 34 15 35 16 36 17 37 18 38 19 39 20 40"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_sorted$ix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<ol class=list-inline><li>20.4783508372344</li><li>19.2814728882946</li><li>22.2089451545413</li><li>23.0793450058932</li><li>25.5041246974011</li><li>25.5055203522657</li><li>28.6812712757451</li><li>27.425585733035</li><li>32.3191569752922</li><li>32.0947720881482</li><li>35.8238555264812</li><li>35.0441807426665</li><li>37.5169131635027</li><li>38.711251522907</li><li>42.3900862156695</li><li>42.8184555091246</li><li>45.6361008904131</li><li>46.4362982598322</li><li>49.1468464418304</li><li>48.7935643673864</li><li>54.4168888420484</li><li>53.5658678819111</li><li>57.7611024080984</li><li>57.6194509471974</li><li>61.6741868467695</li><li>61.9639067897267</li><li>67.5091162422677</li><li>66.8770791768102</li><li>72.5828872868071</li><li>71.9922641404185</li><li>76.1817281943127</li><li>75.5075319882795</li><li>80.5949458945851</li><li>81.4514370556298</li><li>85.7993929531624</li><li>86.6101693065105</li><li>92.2302901978589</li><li>91.5897079781614</li><li>96.7220842707567</li><li>97.6709730988033</li></ol>\n"
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       "\\item 27.425585733035\n",
       "\\item 32.3191569752922\n",
       "\\item 32.0947720881482\n",
       "\\item 35.8238555264812\n",
       "\\item 35.0441807426665\n",
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       "\\item 49.1468464418304\n",
       "\\item 48.7935643673864\n",
       "\\item 54.4168888420484\n",
       "\\item 53.5658678819111\n",
       "\\item 57.7611024080984\n",
       "\\item 57.6194509471974\n",
       "\\item 61.6741868467695\n",
       "\\item 61.9639067897267\n",
       "\\item 67.5091162422677\n",
       "\\item 66.8770791768102\n",
       "\\item 72.5828872868071\n",
       "\\item 71.9922641404185\n",
       "\\item 76.1817281943127\n",
       "\\item 75.5075319882795\n",
       "\\item 80.5949458945851\n",
       "\\item 81.4514370556298\n",
       "\\item 85.7993929531624\n",
       "\\item 86.6101693065105\n",
       "\\item 92.2302901978589\n",
       "\\item 91.5897079781614\n",
       "\\item 96.7220842707567\n",
       "\\item 97.6709730988033\n",
       "\\end{enumerate*}\n"
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       "1. 20.4783508372344\n",
       "2. 19.2814728882946\n",
       "3. 22.2089451545413\n",
       "4. 23.0793450058932\n",
       "5. 25.5041246974011\n",
       "6. 25.5055203522657\n",
       "7. 28.6812712757451\n",
       "8. 27.425585733035\n",
       "9. 32.3191569752922\n",
       "10. 32.0947720881482\n",
       "11. 35.8238555264812\n",
       "12. 35.0441807426665\n",
       "13. 37.5169131635027\n",
       "14. 38.711251522907\n",
       "15. 42.3900862156695\n",
       "16. 42.8184555091246\n",
       "17. 45.6361008904131\n",
       "18. 46.4362982598322\n",
       "19. 49.1468464418304\n",
       "20. 48.7935643673864\n",
       "21. 54.4168888420484\n",
       "22. 53.5658678819111\n",
       "23. 57.7611024080984\n",
       "24. 57.6194509471974\n",
       "25. 61.6741868467695\n",
       "26. 61.9639067897267\n",
       "27. 67.5091162422677\n",
       "28. 66.8770791768102\n",
       "29. 72.5828872868071\n",
       "30. 71.9922641404185\n",
       "31. 76.1817281943127\n",
       "32. 75.5075319882795\n",
       "33. 80.5949458945851\n",
       "34. 81.4514370556298\n",
       "35. 85.7993929531624\n",
       "36. 86.6101693065105\n",
       "37. 92.2302901978589\n",
       "38. 91.5897079781614\n",
       "39. 96.7220842707567\n",
       "40. 97.6709730988033\n",
       "\n",
       "\n"
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       " [1] 20.47835 19.28147 22.20895 23.07935 25.50412 25.50552 28.68127 27.42559\n",
       " [9] 32.31916 32.09477 35.82386 35.04418 37.51691 38.71125 42.39009 42.81846\n",
       "[17] 45.63610 46.43630 49.14685 48.79356 54.41689 53.56587 57.76110 57.61945\n",
       "[25] 61.67419 61.96391 67.50912 66.87708 72.58289 71.99226 76.18173 75.50753\n",
       "[33] 80.59495 81.45144 85.79939 86.61017 92.23029 91.58971 96.72208 97.67097"
      ]
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     "metadata": {},
     "output_type": "display_data"
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   "source": [
    "data$y"
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  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<ol class=list-inline><li>43</li><li>45.7894736842105</li><li>45.7894736842105</li><li>48.5789473684211</li><li>48.5789473684211</li><li>51.3684210526316</li><li>51.3684210526316</li><li>54.1578947368421</li><li>54.1578947368421</li><li>56.9473684210526</li><li>56.9473684210526</li><li>59.7368421052632</li><li>59.7368421052632</li><li>62.5263157894737</li><li>62.5263157894737</li><li>65.3157894736842</li><li>65.3157894736842</li><li>68.1052631578947</li><li>68.1052631578947</li><li>70.8947368421053</li><li>70.8947368421053</li><li>73.6842105263158</li><li>73.6842105263158</li><li>76.4736842105263</li><li>76.4736842105263</li><li>79.2631578947368</li><li>79.2631578947368</li><li>82.0526315789474</li><li>82.0526315789474</li><li>84.8421052631579</li><li>84.8421052631579</li><li>87.6315789473684</li><li>87.6315789473684</li><li>90.4210526315789</li><li>90.4210526315789</li><li>93.2105263157895</li><li>93.2105263157895</li><li>96</li><li>96</li></ol>\n"
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       "\\begin{enumerate*}\n",
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       "\\item 51.3684210526316\n",
       "\\item 51.3684210526316\n",
       "\\item 54.1578947368421\n",
       "\\item 54.1578947368421\n",
       "\\item 56.9473684210526\n",
       "\\item 56.9473684210526\n",
       "\\item 59.7368421052632\n",
       "\\item 59.7368421052632\n",
       "\\item 62.5263157894737\n",
       "\\item 62.5263157894737\n",
       "\\item 65.3157894736842\n",
       "\\item 65.3157894736842\n",
       "\\item 68.1052631578947\n",
       "\\item 68.1052631578947\n",
       "\\item 70.8947368421053\n",
       "\\item 70.8947368421053\n",
       "\\item 73.6842105263158\n",
       "\\item 73.6842105263158\n",
       "\\item 76.4736842105263\n",
       "\\item 76.4736842105263\n",
       "\\item 79.2631578947368\n",
       "\\item 79.2631578947368\n",
       "\\item 82.0526315789474\n",
       "\\item 82.0526315789474\n",
       "\\item 84.8421052631579\n",
       "\\item 84.8421052631579\n",
       "\\item 87.6315789473684\n",
       "\\item 87.6315789473684\n",
       "\\item 90.4210526315789\n",
       "\\item 90.4210526315789\n",
       "\\item 93.2105263157895\n",
       "\\item 93.2105263157895\n",
       "\\item 96\n",
       "\\item 96\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 43\n",
       "2. 45.7894736842105\n",
       "3. 45.7894736842105\n",
       "4. 48.5789473684211\n",
       "5. 48.5789473684211\n",
       "6. 51.3684210526316\n",
       "7. 51.3684210526316\n",
       "8. 54.1578947368421\n",
       "9. 54.1578947368421\n",
       "10. 56.9473684210526\n",
       "11. 56.9473684210526\n",
       "12. 59.7368421052632\n",
       "13. 59.7368421052632\n",
       "14. 62.5263157894737\n",
       "15. 62.5263157894737\n",
       "16. 65.3157894736842\n",
       "17. 65.3157894736842\n",
       "18. 68.1052631578947\n",
       "19. 68.1052631578947\n",
       "20. 70.8947368421053\n",
       "21. 70.8947368421053\n",
       "22. 73.6842105263158\n",
       "23. 73.6842105263158\n",
       "24. 76.4736842105263\n",
       "25. 76.4736842105263\n",
       "26. 79.2631578947368\n",
       "27. 79.2631578947368\n",
       "28. 82.0526315789474\n",
       "29. 82.0526315789474\n",
       "30. 84.8421052631579\n",
       "31. 84.8421052631579\n",
       "32. 87.6315789473684\n",
       "33. 87.6315789473684\n",
       "34. 90.4210526315789\n",
       "35. 90.4210526315789\n",
       "36. 93.2105263157895\n",
       "37. 93.2105263157895\n",
       "38. 96\n",
       "39. 96\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 43.00000 45.78947 45.78947 48.57895 48.57895 51.36842 51.36842 54.15789\n",
       " [9] 54.15789 56.94737 56.94737 59.73684 59.73684 62.52632 62.52632 65.31579\n",
       "[17] 65.31579 68.10526 68.10526 70.89474 70.89474 73.68421 73.68421 76.47368\n",
       "[25] 76.47368 79.26316 79.26316 82.05263 82.05263 84.84211 84.84211 87.63158\n",
       "[33] 87.63158 90.42105 90.42105 93.21053 93.21053 96.00000 96.00000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['x'][data['y']>20.10071]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### linear model with ```lm()```\n",
    "\n",
    "Now that we have defined a ```data.frame``` we can use it as input into most pre-built functions of R. Here we would like to test a simple linear regression. Therefore we use the ```lm()``` function and store the results in the ```fit.lm``` object. The linear model function accept a data.frame as input (here data) and allows you to define a model, in this case the function $y=ax$. <mark>Therefore it is important to define your data.frame properly so that lm will find the $x$ and $y$ columns in data.</mark>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "fit.lm = lm(y ~ x, data=data) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'coefficients'</li><li>'residuals'</li><li>'effects'</li><li>'rank'</li><li>'fitted.values'</li><li>'assign'</li><li>'qr'</li><li>'df.residual'</li><li>'xlevels'</li><li>'call'</li><li>'terms'</li><li>'model'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'coefficients'\n",
       "\\item 'residuals'\n",
       "\\item 'effects'\n",
       "\\item 'rank'\n",
       "\\item 'fitted.values'\n",
       "\\item 'assign'\n",
       "\\item 'qr'\n",
       "\\item 'df.residual'\n",
       "\\item 'xlevels'\n",
       "\\item 'call'\n",
       "\\item 'terms'\n",
       "\\item 'model'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'coefficients'\n",
       "2. 'residuals'\n",
       "3. 'effects'\n",
       "4. 'rank'\n",
       "5. 'fitted.values'\n",
       "6. 'assign'\n",
       "7. 'qr'\n",
       "8. 'df.residual'\n",
       "9. 'xlevels'\n",
       "10. 'call'\n",
       "11. 'terms'\n",
       "12. 'model'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"coefficients\"  \"residuals\"     \"effects\"       \"rank\"         \n",
       " [5] \"fitted.values\" \"assign\"        \"qr\"            \"df.residual\"  \n",
       " [9] \"xlevels\"       \"call\"          \"terms\"         \"model\"        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names(fit.lm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this stage we can have a look to the coefficient found, in this case of a linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>-46.8714333268893</dd><dt>x</dt><dd>1.45470303677099</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] -46.8714333268893\n",
       "\\item[x] 1.45470303677099\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   -46.8714333268893x\n",
       ":   1.45470303677099\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)           x \n",
       " -46.871433    1.454703 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# have a look to the coefficients\n",
    "fit.lm$coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You find a lot of information about your optimization by using the ```summary()``` function of R. It allows you to get some information about any object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x, data = data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-3.4079 -1.7411 -0.3978  1.7080  4.8909 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -46.87143    1.65550  -28.31   <2e-16 ***\n",
       "x             1.45470    0.02321   62.68   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 2.361 on 38 degrees of freedom\n",
       "Multiple R-squared:  0.9904,\tAdjusted R-squared:  0.9902 \n",
       "F-statistic:  3929 on 1 and 38 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(fit.lm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case you need to access one of the data shown here to use it further in your script, you can find the name of the objects displayed by ```summary()```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'call'</li><li>'terms'</li><li>'residuals'</li><li>'coefficients'</li><li>'aliased'</li><li>'sigma'</li><li>'df'</li><li>'r.squared'</li><li>'adj.r.squared'</li><li>'fstatistic'</li><li>'cov.unscaled'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'call'\n",
       "\\item 'terms'\n",
       "\\item 'residuals'\n",
       "\\item 'coefficients'\n",
       "\\item 'aliased'\n",
       "\\item 'sigma'\n",
       "\\item 'df'\n",
       "\\item 'r.squared'\n",
       "\\item 'adj.r.squared'\n",
       "\\item 'fstatistic'\n",
       "\\item 'cov.unscaled'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'call'\n",
       "2. 'terms'\n",
       "3. 'residuals'\n",
       "4. 'coefficients'\n",
       "5. 'aliased'\n",
       "6. 'sigma'\n",
       "7. 'df'\n",
       "8. 'r.squared'\n",
       "9. 'adj.r.squared'\n",
       "10. 'fstatistic'\n",
       "11. 'cov.unscaled'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"call\"          \"terms\"         \"residuals\"     \"coefficients\" \n",
       " [5] \"aliased\"       \"sigma\"         \"df\"            \"r.squared\"    \n",
       " [9] \"adj.r.squared\" \"fstatistic\"    \"cov.unscaled\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names(summary(fit.lm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So if you want to use the $r^2$ coefficient you can use the following command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.99"
      ],
      "text/latex": [
       "0.99"
      ],
      "text/markdown": [
       "0.99"
      ],
      "text/plain": [
       "[1] 0.99"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(summary(fit.lm)$r.squared,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maybe you want a nice picture of your data and the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Gzqsm0EEEAAAQQQQACBXAmUakefV+qUfZQ3FStifq28oQy6LZo6fdSw8KibPdcp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CfhWYqTNFnbWRa3TWaEtnqD55T7RkdV/U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\nIIAAAkUj8P8BSS8vyOheh6IAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$x,data$y); lines(data$x, fitted(fit.lm), col=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want more control on what you do, you can display the regression by ploting a line that crosses 0 at \"intercept\" and with a slope of \"x\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3L6f19lVBzbOSuT8tfqOecujKhVIMbk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\nQQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “linear regression”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$x,data$y,main=\"linear regression\",ylab=\"intensity\",xlab=\"concentration\",ylim=c(-50,100),xlim=c(0,100));\n",
    "abline(fit.lm$coefficients[1],fit.lm$coefficients[2],col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may have noticed that the data look to have some quadratic component (that we included intentionally at the beginning). You might want to see how good it fits if you use a quadratic function to fit your data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'the coefficient $r^2$ =  0.999'</span>"
      ],
      "text/latex": [
       "'the coefficient \\$r\\textasciicircum{}2\\$ =  0.999'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'the coefficient $r^2$ =  0.999'</span>"
      ],
      "text/plain": [
       "[1] \"the coefficient $r^2$ =  0.999\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+nwIU/PfjvR52P1arf1Hpl4v1SvLyWGeWlFgAKpFRwmIYAAAggggAACCCAQZoH6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AgC8FOIPky26lUQgggEC7BOySulcmO87s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\nDRneVqxEXnvp440e/JkAAQZICUBkExknYG+qrURO57fmRdmupaakjoD1md0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ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCPhP4P8DAhyic6R2AuQAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “linear regression”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.lm = lm(y ~ x + x2, data=data)\n",
    "plot(data$x,data$y, main=\"linear regression\",ylab=\"intensity\",xlab=\"concentration\")\n",
    "lines(data$x, fitted(fit.lm), col=2)\n",
    "paste(\"the coefficient $r^2$ = \",round(summary(fit.lm)$r.squared,3))\n",
    "text(60,80,paste(\"r2 = \",round(summary(fit.lm)$r.squared,3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimental design\n",
    "\n",
    "### linear regression\n",
    "Use the data of Table 2.2 in Brereton, R. G. (2003). Chemometrics. Technometrics. Chichester, UK: John Wiley & Sons, Ltd. http://doi.org/10.1002/0470863242\n",
    "\n",
    "Or import the table from the dataset section provided in this course.\n",
    "\n",
    "#### import dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in read.table(file = file, header = header, sep = sep, quote = quote, :\n",
      "“incomplete final line found by readTableHeader on './datasets/table2.2.csv'”\n"
     ]
    }
   ],
   "source": [
    "data <- read.csv(\"./datasets/table2.2.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 3 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>q</th><th scope=col>q.1</th><th scope=col>q.2</th><th scope=col>q.3</th><th scope=col>q.4</th><th scope=col>q.5</th><th scope=col>q.6</th><th scope=col>q.7</th><th scope=col>q.8</th><th scope=col>q.9</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1.000</td><td>1.000</td><td>2.000</td><td>3.000</td><td> 3.000</td><td> 4.000</td><td> 4.000</td><td> 5.000</td><td> 6.000</td><td> 6.000</td></tr>\n",
       "\t<tr><td>3.803</td><td>3.276</td><td>5.181</td><td>6.948</td><td> 8.762</td><td>10.672</td><td> 8.266</td><td>13.032</td><td>15.021</td><td>16.426</td></tr>\n",
       "\t<tr><td>4.797</td><td>3.878</td><td>6.342</td><td>9.186</td><td>10.136</td><td>12.257</td><td>13.252</td><td>14.656</td><td>17.681</td><td>15.071</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 10\n",
       "\\begin{tabular}{llllllllll}\n",
       " q & q.1 & q.2 & q.3 & q.4 & q.5 & q.6 & q.7 & q.8 & q.9\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 1.000 & 1.000 & 2.000 & 3.000 &  3.000 &  4.000 &  4.000 &  5.000 &  6.000 &  6.000\\\\\n",
       "\t 3.803 & 3.276 & 5.181 & 6.948 &  8.762 & 10.672 &  8.266 & 13.032 & 15.021 & 16.426\\\\\n",
       "\t 4.797 & 3.878 & 6.342 & 9.186 & 10.136 & 12.257 & 13.252 & 14.656 & 17.681 & 15.071\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 10\n",
       "\n",
       "| q &lt;dbl&gt; | q.1 &lt;dbl&gt; | q.2 &lt;dbl&gt; | q.3 &lt;dbl&gt; | q.4 &lt;dbl&gt; | q.5 &lt;dbl&gt; | q.6 &lt;dbl&gt; | q.7 &lt;dbl&gt; | q.8 &lt;dbl&gt; | q.9 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1.000 | 1.000 | 2.000 | 3.000 |  3.000 |  4.000 |  4.000 |  5.000 |  6.000 |  6.000 |\n",
       "| 3.803 | 3.276 | 5.181 | 6.948 |  8.762 | 10.672 |  8.266 | 13.032 | 15.021 | 16.426 |\n",
       "| 4.797 | 3.878 | 6.342 | 9.186 | 10.136 | 12.257 | 13.252 | 14.656 | 17.681 | 15.071 |\n",
       "\n"
      ],
      "text/plain": [
       "  q     q.1   q.2   q.3   q.4    q.5    q.6    q.7    q.8    q.9   \n",
       "1 1.000 1.000 2.000 3.000  3.000  4.000  4.000  5.000  6.000  6.000\n",
       "2 3.803 3.276 5.181 6.948  8.762 10.672  8.266 13.032 15.021 16.426\n",
       "3 4.797 3.878 6.342 9.186 10.136 12.257 13.252 14.656 17.681 15.071"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you may notice, the data are not in the way we want. We would like to have two columns and we also would like the index of the row to be correct. We can solve this readily.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "data <- t(data) # we transpose the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "rownames(data) <- seq(1,10)\n",
    "colnames(data) <- c(\"conc\",\"A\",\"B\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 10 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>conc</th><th scope=col>A</th><th scope=col>B</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td> 3.803</td><td> 4.797</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>1</td><td> 3.276</td><td> 3.878</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2</td><td> 5.181</td><td> 6.342</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>3</td><td> 6.948</td><td> 9.186</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>3</td><td> 8.762</td><td>10.136</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>4</td><td>10.672</td><td>12.257</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>4</td><td> 8.266</td><td>13.252</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>5</td><td>13.032</td><td>14.656</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>6</td><td>15.021</td><td>17.681</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>6</td><td>16.426</td><td>15.071</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 10 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & conc & A & B\\\\\n",
       "\\hline\n",
       "\t1 & 1 &  3.803 &  4.797\\\\\n",
       "\t2 & 1 &  3.276 &  3.878\\\\\n",
       "\t3 & 2 &  5.181 &  6.342\\\\\n",
       "\t4 & 3 &  6.948 &  9.186\\\\\n",
       "\t5 & 3 &  8.762 & 10.136\\\\\n",
       "\t6 & 4 & 10.672 & 12.257\\\\\n",
       "\t7 & 4 &  8.266 & 13.252\\\\\n",
       "\t8 & 5 & 13.032 & 14.656\\\\\n",
       "\t9 & 6 & 15.021 & 17.681\\\\\n",
       "\t10 & 6 & 16.426 & 15.071\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 10 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | conc | A | B |\n",
       "|---|---|---|---|\n",
       "| 1 | 1 |  3.803 |  4.797 |\n",
       "| 2 | 1 |  3.276 |  3.878 |\n",
       "| 3 | 2 |  5.181 |  6.342 |\n",
       "| 4 | 3 |  6.948 |  9.186 |\n",
       "| 5 | 3 |  8.762 | 10.136 |\n",
       "| 6 | 4 | 10.672 | 12.257 |\n",
       "| 7 | 4 |  8.266 | 13.252 |\n",
       "| 8 | 5 | 13.032 | 14.656 |\n",
       "| 9 | 6 | 15.021 | 17.681 |\n",
       "| 10 | 6 | 16.426 | 15.071 |\n",
       "\n"
      ],
      "text/plain": [
       "   conc A      B     \n",
       "1  1     3.803  4.797\n",
       "2  1     3.276  3.878\n",
       "3  2     5.181  6.342\n",
       "4  3     6.948  9.186\n",
       "5  3     8.762 10.136\n",
       "6  4    10.672 12.257\n",
       "7  4     8.266 13.252\n",
       "8  5    13.032 14.656\n",
       "9  6    15.021 17.681\n",
       "10 6    16.426 15.071"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<mark>Although the table looks good there is a problem **may be** a problem with it. R sees each data in the table as characters and not as number. This means that we cannot use these data because they are not \"numbers\". We should change this. It is done very simply, but it is sometime annoying because it is not something we are used to think of. In order to \"see\" what R \"sees\", use the following command.</mark>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'numeric'</li><li>'vector'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'numeric'\n",
       "\\item 'vector'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'numeric'\n",
       "2. 'vector'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"numeric\" \"vector\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>1</dt><dd>1</dd><dt>2</dt><dd>1</dd><dt>3</dt><dd>2</dd><dt>4</dt><dd>3</dd><dt>5</dt><dd>3</dd><dt>6</dt><dd>4</dd><dt>7</dt><dd>4</dd><dt>8</dt><dd>5</dd><dt>9</dt><dd>6</dd><dt>10</dt><dd>6</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[1] 1\n",
       "\\item[2] 1\n",
       "\\item[3] 2\n",
       "\\item[4] 3\n",
       "\\item[5] 3\n",
       "\\item[6] 4\n",
       "\\item[7] 4\n",
       "\\item[8] 5\n",
       "\\item[9] 6\n",
       "\\item[10] 6\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "1\n",
       ":   12\n",
       ":   13\n",
       ":   24\n",
       ":   35\n",
       ":   36\n",
       ":   47\n",
       ":   48\n",
       ":   59\n",
       ":   610\n",
       ":   6\n",
       "\n"
      ],
      "text/plain": [
       " 1  2  3  4  5  6  7  8  9 10 \n",
       " 1  1  2  3  3  4  4  5  6  6 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is(data[1])\n",
    "data[,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Putting this altogether in something nicer, it gives:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in read.table(file = file, header = header, sep = sep, quote = quote, :\n",
      "“incomplete final line found by readTableHeader on './datasets/table2.2.csv'”\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 10 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>conc</th><th scope=col>A</th><th scope=col>B</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td> 3.803</td><td> 4.797</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>1</td><td> 3.276</td><td> 3.878</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2</td><td> 5.181</td><td> 6.342</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>3</td><td> 6.948</td><td> 9.186</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>3</td><td> 8.762</td><td>10.136</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>4</td><td>10.672</td><td>12.257</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>4</td><td> 8.266</td><td>13.252</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>5</td><td>13.032</td><td>14.656</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>6</td><td>15.021</td><td>17.681</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>6</td><td>16.426</td><td>15.071</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 10 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & conc & A & B\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1 &  3.803 &  4.797\\\\\n",
       "\t2 & 1 &  3.276 &  3.878\\\\\n",
       "\t3 & 2 &  5.181 &  6.342\\\\\n",
       "\t4 & 3 &  6.948 &  9.186\\\\\n",
       "\t5 & 3 &  8.762 & 10.136\\\\\n",
       "\t6 & 4 & 10.672 & 12.257\\\\\n",
       "\t7 & 4 &  8.266 & 13.252\\\\\n",
       "\t8 & 5 & 13.032 & 14.656\\\\\n",
       "\t9 & 6 & 15.021 & 17.681\\\\\n",
       "\t10 & 6 & 16.426 & 15.071\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 10 × 3\n",
       "\n",
       "| <!--/--> | conc &lt;dbl&gt; | A &lt;dbl&gt; | B &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 | 1 |  3.803 |  4.797 |\n",
       "| 2 | 1 |  3.276 |  3.878 |\n",
       "| 3 | 2 |  5.181 |  6.342 |\n",
       "| 4 | 3 |  6.948 |  9.186 |\n",
       "| 5 | 3 |  8.762 | 10.136 |\n",
       "| 6 | 4 | 10.672 | 12.257 |\n",
       "| 7 | 4 |  8.266 | 13.252 |\n",
       "| 8 | 5 | 13.032 | 14.656 |\n",
       "| 9 | 6 | 15.021 | 17.681 |\n",
       "| 10 | 6 | 16.426 | 15.071 |\n",
       "\n"
      ],
      "text/plain": [
       "   conc A      B     \n",
       "1  1     3.803  4.797\n",
       "2  1     3.276  3.878\n",
       "3  2     5.181  6.342\n",
       "4  3     6.948  9.186\n",
       "5  3     8.762 10.136\n",
       "6  4    10.672 12.257\n",
       "7  4     8.266 13.252\n",
       "8  5    13.032 14.656\n",
       "9  6    15.021 17.681\n",
       "10 6    16.426 15.071"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "remove(data)\n",
    "data <- t(read.csv2(\"./datasets/table2.2.csv\",header=TRUE,sep=\",\",dec=\".\"))\n",
    "rownames(data) <- seq(1:10)\n",
    "data <- data.frame(\"conc\"=(data[,1]), \"A\"=data[,2],\"B\"=data[,3])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis of variance (ANOVA)\n",
    "\n",
    "In order to estimate the quality of our regression we perform an analysis of variance. Here we will perform this analysis step by step as described in Chapter 2 of Brereton, R. G. (2003). Chemometrics. Technometrics. Chichester, UK: John Wiley & Sons, Ltd. http://doi.org/10.1002/0470863242\n",
    "\n",
    "One of the most important feature of ANOVA is to compare the lack of fit to the replicate error. The error on replicate gives a estimation of the experimental error of the data, while the lack of fit gives an estimation of how good is our model for our data.\n",
    "\n",
    "##### with intercept\n",
    "We first find duplicated data in our table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>FALSE</li><li>TRUE</li><li>FALSE</li><li>FALSE</li><li>TRUE</li><li>FALSE</li><li>TRUE</li><li>FALSE</li><li>FALSE</li><li>TRUE</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. TRUE\n",
       "3. FALSE\n",
       "4. FALSE\n",
       "5. TRUE\n",
       "6. FALSE\n",
       "7. TRUE\n",
       "8. FALSE\n",
       "9. FALSE\n",
       "10. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] FALSE  TRUE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "duplicated(data[,1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "4"
      ],
      "text/latex": [
       "4"
      ],
      "text/markdown": [
       "4"
      ],
      "text/plain": [
       "[1] 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Rep <- duplicated(data$conc) # find replicates\n",
    "R <- sum( Rep ) # enumerate replicates\n",
    "N <- dim(data)[1] # find out dimension of data\n",
    "P <- 2 # if our model is y = ax + b\n",
    "# find out the degree of freedom for our experiment\n",
    "D <- N - P - R\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "4"
      ],
      "text/latex": [
       "4"
      ],
      "text/markdown": [
       "4"
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      "text/plain": [
       "[1] 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "10"
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       "10"
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       "[1] 10"
      ]
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     "metadata": {},
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   ],
   "source": [
    "R\n",
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Sum.Replicate</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>5.665593</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 1\n",
       "\\begin{tabular}{l}\n",
       " Sum.Replicate\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 5.665593\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 1\n",
       "\n",
       "| Sum.Replicate &lt;dbl&gt; |\n",
       "|---|\n",
       "| 5.665593 |\n",
       "\n"
      ],
      "text/plain": [
       "  Sum.Replicate\n",
       "1 5.665593     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(plyr) # this library helps a lot\n",
    "\n",
    "meanRep <- aggregate(A ~ conc, data = data, mean) # this calculates the mean for all replicates\n",
    "\n",
    "sumRep=0\n",
    "sumRep2=0\n",
    "for (i in seq(1,nrow(data))) {\n",
    "    sumRep[i] <- meanRep$A[ meanRep$conc == data$conc[i] ] - data$A[i] \n",
    "    sumRep2[i] <- ( meanRep$A[ meanRep$conc == data$conc[i] ] - data$A[i] )^2\n",
    "}\n",
    "S_replicate <- sum(sumRep2) # R degrees of freedom\n",
    "result <- data.frame(\"Sum Replicate\"=S_replicate)\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can verify our result by computing the strait sum of the replicate that gives 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0"
      ],
      "text/latex": [
       "0"
      ],
      "text/markdown": [
       "0"
      ],
      "text/plain": [
       "[1] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(sum(sumRep),3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the models proposed in Chapter 2 of Brereton, we can compute the sum of residuals, that is the sum of the difference between the experimental data and the predicted ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Sum Residual</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>8.371165</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 1\n",
       "\\begin{tabular}{l}\n",
       " Sum Residual\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 8.371165\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 1\n",
       "\n",
       "| Sum Residual &lt;dbl&gt; |\n",
       "|---|\n",
       "| 8.371165 |\n",
       "\n"
      ],
      "text/plain": [
       "  Sum Residual\n",
       "1 8.371165    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predicted <- 0.6113 + 2.4364 * as.numeric(data$conc)\n",
    "S_residual <- sum( (data$A - predicted)^2 )\n",
    "result[\"Sum Residual\"] <- S_residual # N-P degrees of freedom (# or S_total - S_predicted)\n",
    "result[\"Sum Residual\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Sum Total</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1024.58</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 1\n",
       "\\begin{tabular}{l}\n",
       " Sum Total\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 1024.58\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 1\n",
       "\n",
       "| Sum Total &lt;dbl&gt; |\n",
       "|---|\n",
       "| 1024.58 |\n",
       "\n"
      ],
      "text/plain": [
       "  Sum Total\n",
       "1 1024.58  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Sum Predicted</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1016.208</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 1\n",
       "\\begin{tabular}{l}\n",
       " Sum Predicted\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 1016.208\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 1\n",
       "\n",
       "| Sum Predicted &lt;dbl&gt; |\n",
       "|---|\n",
       "| 1016.208 |\n",
       "\n"
      ],
      "text/plain": [
       "  Sum Predicted\n",
       "1 1016.208     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S_total <- sum( data$A^2 ) # N degrees of freedom \n",
    "result[\"Sum Total\"] <- S_total; result[\"Sum Total\"]\n",
    "\n",
    "S_predicted <- sum( predicted^2 ) # P degrees of freedom\n",
    "result[\"Sum Predicted\"] <- S_predicted; result[\"Sum Predicted\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Sum Lack Of Fit</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2.705572</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 1\n",
       "\\begin{tabular}{l}\n",
       " Sum Lack Of Fit\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 2.705572\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 1\n",
       "\n",
       "| Sum Lack Of Fit &lt;dbl&gt; |\n",
       "|---|\n",
       "| 2.705572 |\n",
       "\n"
      ],
      "text/plain": [
       "  Sum Lack Of Fit\n",
       "1 2.705572       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>F</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.4775444</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 1\n",
       "\\begin{tabular}{l}\n",
       " F\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.4775444\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 1\n",
       "\n",
       "| F &lt;dbl&gt; |\n",
       "|---|\n",
       "| 0.4775444 |\n",
       "\n"
      ],
      "text/plain": [
       "  F        \n",
       "1 0.4775444"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S_lackOfFit <- S_residual - S_replicate # N-P-R degrees of freedom\n",
    "result[\"Sum Lack Of Fit\"] <- S_lackOfFit; result[\"Sum Lack Of Fit\"]\n",
    "result[\"F\"] <- (S_lackOfFit / D) / (S_replicate / R); result[\"F\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Call:\n",
       "   aov(formula = A ~ conc, data = data)\n",
       "\n",
       "Terms:\n",
       "                     conc Residuals\n",
       "Sum of Squares  181.05083   8.37116\n",
       "Deg. of Freedom         1         8\n",
       "\n",
       "Residual standard error: 1.022935\n",
       "Estimated effects may be unbalanced"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 2 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>conc</th><td>1</td><td>181.050833</td><td>181.050833</td><td>173.0233</td><td>1.061953e-06</td></tr>\n",
       "\t<tr><th scope=row>Residuals</th><td>8</td><td>  8.371165</td><td>  1.046396</td><td>      NA</td><td>          NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 2 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
       "  & <int> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tconc & 1 & 181.050833 & 181.050833 & 173.0233 & 1.061953e-06\\\\\n",
       "\tResiduals & 8 &   8.371165 &   1.046396 &       NA &           NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 2 × 5\n",
       "\n",
       "| <!--/--> | Df &lt;int&gt; | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| conc | 1 | 181.050833 | 181.050833 | 173.0233 | 1.061953e-06 |\n",
       "| Residuals | 8 |   8.371165 |   1.046396 |       NA |           NA |\n",
       "\n"
      ],
      "text/plain": [
       "          Df Sum Sq     Mean Sq    F value  Pr(>F)      \n",
       "conc      1  181.050833 181.050833 173.0233 1.061953e-06\n",
       "Residuals 8    8.371165   1.046396       NA           NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BAgQIAAAQIECBAgUEuBvXNUl2dMZXxv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\nw7/ZT9oeOZMAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$conc, data$A)\n",
    "abline(0.6113, 2.4364, col=\"red\")\n",
    "fit <- lm(A ~ conc, data)\n",
    "aov(A ~ conc, data)\n",
    "anova(fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### lack of fit\n",
    "\n",
    "We can now put this in order and run the four cases, for both datasets A and B and with or without intercept. Table of comparison is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MAgBW6UUX0uuSZ5RzPCvfJYF6nVsrr/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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(as.numeric(data$conc), as.numeric(data$A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "#var.test((data$A - predicted),sumRep2[c(1,4,6,9)])\n",
    "#sumRep2[c(1,4,6,9)]\n",
    "#to be tested. Should be possible to use this command in this context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rep <- duplicated(data$conc) # find replicates\n",
    "R <- sum( Rep ) # enumerate replicates\n",
    "N <- dim(data)[1] # find out dimension of data\n",
    "P <- 2\n",
    "D <- N - P - R\n",
    "meanRep <- aggregate(A ~ conc, data = data, mean)\n",
    "result <- data.frame(\"Number Replicate\"=R)\n",
    "result[\"Number of Data\"] <- N\n",
    "result[\"Number of Parameters\"] <- P\n",
    "\n",
    "sumRep=0\n",
    "sumRep2=0\n",
    "for (i in seq(1,nrow(data))) {\n",
    "    sumRep[i] <- meanRep$A[ meanRep$conc == data$conc[i] ] - data$A[i] \n",
    "    sumRep2[i] <- ( meanRep$A[ meanRep$conc == data$conc[i] ] - data$A[i] )^2\n",
    "}\n",
    "S_replicate <- sum(sumRep2) # R degrees of freedom \n",
    "result[\"Sum Replicate\"] <- S_replicate\n",
    "\n",
    "predicted <- 0.6113 + 2.4364 * as.numeric(data$conc)\n",
    "S_residual <- sum( (data$A - predicted)^2 ) # N-P degrees of freedom (# or S_total - S_predicted)\n",
    "result[\"Sum Residual\"] <- S_residual\n",
    "\n",
    "S_total <- sum( data$A^2 ) # N degrees of freedom\n",
    "result[\"Sum Total\"] <- S_total\n",
    "\n",
    "S_predicted <- sum( predicted^2 ) # P degrees of freedom\n",
    "result[\"Sum Predicted\"] <- S_predicted\n",
    "\n",
    "S_lackOfFit <- S_residual - S_replicate # N-P-R degrees of freedom\n",
    "result[\"Sum Lack Of Fit\"] <- S_lackOfFit\n",
    "\n",
    "result[\"Mean Residuals\"] <- S_residual / (N-P)\n",
    "result[\"Mean Total\"] <- S_total / N\n",
    "result[\"Mean Predicted\"] <- S_predicted / P\n",
    "result[\"Mean Replicate\"] <- S_replicate / R\n",
    "result[\"Lack Of Fit\"] <- S_lackOfFit / D\n",
    "A2 <- t(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rep <- duplicated(data$conc) # find replicates\n",
    "R <- sum( Rep ) # enumerate replicates\n",
    "N <- dim(data)[1] # find out dimension of data\n",
    "P <- 1\n",
    "D <- N - P - R\n",
    "meanRep <- aggregate(A ~ conc, data = data, mean)\n",
    "result <- data.frame(\"Number Replicate\"=R)\n",
    "result[\"Number of Data\"] <- N\n",
    "result[\"Number of Parameters\"] <- P\n",
    "\n",
    "sumRep=0\n",
    "sumRep2=0\n",
    "for (i in seq(1,nrow(data))) {\n",
    "    sumRep[i] <- meanRep$A[ meanRep$conc == data$conc[i] ] - data$A[i] \n",
    "    sumRep2[i] <- ( meanRep$A[ meanRep$conc == data$conc[i] ] - data$A[i] )^2\n",
    "}\n",
    "S_replicate <- sum(sumRep2) # R degrees of freedom \n",
    "result[\"Sum Replicate\"] <- S_replicate\n",
    "\n",
    "predicted <- 2.576 * as.numeric(data$conc)\n",
    "S_residual <- sum( (data$A - predicted)^2 ) # N-P degrees of freedom (# or S_total - S_predicted)\n",
    "result[\"Sum Residual\"] <- S_residual\n",
    "\n",
    "S_total <- sum( data$A^2 ) # N degrees of freedom\n",
    "result[\"Sum Total\"] <- S_total\n",
    "\n",
    "S_predicted <- sum( predicted^2 ) # P degrees of freedom\n",
    "result[\"Sum Predicted\"] <- S_predicted\n",
    "\n",
    "S_lackOfFit <- S_residual - S_replicate # N-P-R degrees of freedom\n",
    "result[\"Sum Lack Of Fit\"] <- S_lackOfFit\n",
    "\n",
    "result[\"Mean Residuals\"] <- S_residual / (N-P)\n",
    "result[\"Mean Total\"] <- S_total / N\n",
    "result[\"Mean Predicted\"] <- S_predicted / P\n",
    "result[\"Mean Replicate\"] <- S_replicate / R\n",
    "result[\"Lack Of Fit\"] <- S_lackOfFit / D\n",
    "A1 <- t(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rep <- duplicated(data$conc) # find replicates\n",
    "R <- sum( Rep ) # enumerate replicates\n",
    "N <- dim(data)[1] # find out dimension of data\n",
    "P <- 2\n",
    "D <- N - P - R\n",
    "meanRep <- aggregate(B ~ conc, data = data, mean)\n",
    "result <- data.frame(\"Number Replicate\"=R)\n",
    "result[\"Number of Data\"] <- N\n",
    "result[\"Number of Parameters\"] <- P\n",
    "\n",
    "sumRep=0\n",
    "sumRep2=0\n",
    "for (i in seq(1,nrow(data))) {\n",
    "    sumRep[i] <- meanRep$B[ meanRep$conc == data$conc[i] ] - data$B[i] \n",
    "    sumRep2[i] <- ( meanRep$B[ meanRep$conc == data$conc[i] ] - data$B[i] )^2\n",
    "}\n",
    "S_replicate <- sum(sumRep2) # R degrees of freedom \n",
    "result[\"Sum Replicate\"] <- S_replicate\n",
    "\n",
    "predicted <- 2.032 + 2.484 * as.numeric(data$conc)\n",
    "S_residual <- sum( (data$B - predicted)^2 ) # N-P degrees of freedom (# or S_total - S_predicted)\n",
    "result[\"Sum Residual\"] <- S_residual\n",
    "\n",
    "S_total <- sum( data$B^2 ) # N degrees of freedom\n",
    "result[\"Sum Total\"] <- S_total\n",
    "\n",
    "S_predicted <- sum( predicted^2 ) # P degrees of freedom\n",
    "result[\"Sum Predicted\"] <- S_predicted\n",
    "\n",
    "S_lackOfFit <- S_residual - S_replicate # N-P-R degrees of freedom\n",
    "result[\"Sum Lack Of Fit\"] <- S_lackOfFit\n",
    "\n",
    "result[\"Mean Residuals\"] <- S_residual / (N-P)\n",
    "result[\"Mean Total\"] <- S_total / N\n",
    "result[\"Mean Predicted\"] <- S_predicted / P\n",
    "result[\"Mean Replicate\"] <- S_replicate / R\n",
    "result[\"Lack Of Fit\"] <- S_lackOfFit / D\n",
    "B2 <- t(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rep <- duplicated(data$conc) # find replicates\n",
    "R <- sum( Rep ) # enumerate replicates\n",
    "N <- dim(data)[1] # find out dimension of data\n",
    "P <- 1\n",
    "D <- N - P - R\n",
    "meanRep <- aggregate(B ~ conc, data = data, mean)\n",
    "result <- data.frame(\"Number Replicate\"=R)\n",
    "result[\"Number of Data\"] <- N\n",
    "result[\"Number of Parameters\"] <- P\n",
    "\n",
    "sumRep=0\n",
    "sumRep2=0\n",
    "for (i in seq(1,nrow(data))) {\n",
    "    sumRep[i] <- meanRep$B[ meanRep$conc == data$conc[i] ] - data$B[i] \n",
    "    sumRep2[i] <- ( meanRep$B[ meanRep$conc == data$conc[i] ] - data$B[i] )^2\n",
    "}\n",
    "S_replicate <- sum(sumRep2) # R degrees of freedom \n",
    "result[\"Sum Replicate\"] <- S_replicate\n",
    "\n",
    "predicted <- 2.948 * as.numeric(data$conc)\n",
    "S_residual <- sum( (data$B - predicted)^2 ) # N-P degrees of freedom (# or S_total - S_predicted)\n",
    "result[\"Sum Residual\"] <- S_residual\n",
    "\n",
    "S_total <- sum( data$B^2 ) # N degrees of freedom\n",
    "result[\"Sum Total\"] <- S_total\n",
    "\n",
    "S_predicted <- sum( predicted^2 ) # P degrees of freedom\n",
    "result[\"Sum Predicted\"] <- S_predicted\n",
    "\n",
    "S_lackOfFit <- S_residual - S_replicate # N-P-R degrees of freedom\n",
    "result[\"Sum Lack Of Fit\"] <- S_lackOfFit\n",
    "\n",
    "result[\"Mean Residuals\"] <- S_residual / (N-P)\n",
    "result[\"Mean Total\"] <- S_total / N\n",
    "result[\"Mean Predicted\"] <- S_predicted / P\n",
    "result[\"Mean Replicate\"] <- S_replicate / R\n",
    "result[\"Lack Of Fit\"] <- S_lackOfFit / D\n",
    "B1 <- t(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 13 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A1</th><th scope=col>A2</th><th scope=col>B1</th><th scope=col>B2</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Number.Replicate</th><td>   4.000000</td><td>   4.000000</td><td>   4.000000</td><td>   4.0000000</td></tr>\n",
       "\t<tr><th scope=row>Number of Data</th><td>  10.000000</td><td>  10.000000</td><td>  10.000000</td><td>  10.0000000</td></tr>\n",
       "\t<tr><th scope=row>Number of Parameters</th><td>   1.000000</td><td>   2.000000</td><td>   1.000000</td><td>   2.0000000</td></tr>\n",
       "\t<tr><th scope=row>Sum Replicate</th><td>   5.665593</td><td>   5.665593</td><td>   4.774593</td><td>   4.7745930</td></tr>\n",
       "\t<tr><th scope=row>Sum Residual</th><td>   9.116023</td><td>   8.371165</td><td>  15.472464</td><td>   7.2399200</td></tr>\n",
       "\t<tr><th scope=row>Sum Total</th><td>1024.580375</td><td>1024.580375</td><td>1345.792840</td><td>1345.7928400</td></tr>\n",
       "\t<tr><th scope=row>Sum Predicted</th><td>1015.273728</td><td>1016.207748</td><td>1329.677712</td><td>1338.6635680</td></tr>\n",
       "\t<tr><th scope=row>Sum Lack Of Fit</th><td>   3.450430</td><td>   2.705572</td><td>  10.697871</td><td>   2.4653270</td></tr>\n",
       "\t<tr><th scope=row>Mean Residuals</th><td>   1.012891</td><td>   1.046396</td><td>   1.719163</td><td>   0.9049900</td></tr>\n",
       "\t<tr><th scope=row>Mean Total</th><td> 102.458038</td><td> 102.458038</td><td> 134.579284</td><td> 134.5792840</td></tr>\n",
       "\t<tr><th scope=row>Mean Predicted</th><td>1015.273728</td><td> 508.103874</td><td>1329.677712</td><td> 669.3317840</td></tr>\n",
       "\t<tr><th scope=row>Mean Replicate</th><td>   1.416398</td><td>   1.416398</td><td>   1.193648</td><td>   1.1936483</td></tr>\n",
       "\t<tr><th scope=row>Lack Of Fit</th><td>   0.690086</td><td>   0.676393</td><td>   2.139574</td><td>   0.6163318</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 13 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & A1 & A2 & B1 & B2\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tNumber.Replicate &    4.000000 &    4.000000 &    4.000000 &    4.0000000\\\\\n",
       "\tNumber of Data &   10.000000 &   10.000000 &   10.000000 &   10.0000000\\\\\n",
       "\tNumber of Parameters &    1.000000 &    2.000000 &    1.000000 &    2.0000000\\\\\n",
       "\tSum Replicate &    5.665593 &    5.665593 &    4.774593 &    4.7745930\\\\\n",
       "\tSum Residual &    9.116023 &    8.371165 &   15.472464 &    7.2399200\\\\\n",
       "\tSum Total & 1024.580375 & 1024.580375 & 1345.792840 & 1345.7928400\\\\\n",
       "\tSum Predicted & 1015.273728 & 1016.207748 & 1329.677712 & 1338.6635680\\\\\n",
       "\tSum Lack Of Fit &    3.450430 &    2.705572 &   10.697871 &    2.4653270\\\\\n",
       "\tMean Residuals &    1.012891 &    1.046396 &    1.719163 &    0.9049900\\\\\n",
       "\tMean Total &  102.458038 &  102.458038 &  134.579284 &  134.5792840\\\\\n",
       "\tMean Predicted & 1015.273728 &  508.103874 & 1329.677712 &  669.3317840\\\\\n",
       "\tMean Replicate &    1.416398 &    1.416398 &    1.193648 &    1.1936483\\\\\n",
       "\tLack Of Fit &    0.690086 &    0.676393 &    2.139574 &    0.6163318\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 13 × 4\n",
       "\n",
       "| <!--/--> | A1 &lt;dbl&gt; | A2 &lt;dbl&gt; | B1 &lt;dbl&gt; | B2 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| Number.Replicate |    4.000000 |    4.000000 |    4.000000 |    4.0000000 |\n",
       "| Number of Data |   10.000000 |   10.000000 |   10.000000 |   10.0000000 |\n",
       "| Number of Parameters |    1.000000 |    2.000000 |    1.000000 |    2.0000000 |\n",
       "| Sum Replicate |    5.665593 |    5.665593 |    4.774593 |    4.7745930 |\n",
       "| Sum Residual |    9.116023 |    8.371165 |   15.472464 |    7.2399200 |\n",
       "| Sum Total | 1024.580375 | 1024.580375 | 1345.792840 | 1345.7928400 |\n",
       "| Sum Predicted | 1015.273728 | 1016.207748 | 1329.677712 | 1338.6635680 |\n",
       "| Sum Lack Of Fit |    3.450430 |    2.705572 |   10.697871 |    2.4653270 |\n",
       "| Mean Residuals |    1.012891 |    1.046396 |    1.719163 |    0.9049900 |\n",
       "| Mean Total |  102.458038 |  102.458038 |  134.579284 |  134.5792840 |\n",
       "| Mean Predicted | 1015.273728 |  508.103874 | 1329.677712 |  669.3317840 |\n",
       "| Mean Replicate |    1.416398 |    1.416398 |    1.193648 |    1.1936483 |\n",
       "| Lack Of Fit |    0.690086 |    0.676393 |    2.139574 |    0.6163318 |\n",
       "\n"
      ],
      "text/plain": [
       "                     A1          A2          B1          B2          \n",
       "Number.Replicate        4.000000    4.000000    4.000000    4.0000000\n",
       "Number of Data         10.000000   10.000000   10.000000   10.0000000\n",
       "Number of Parameters    1.000000    2.000000    1.000000    2.0000000\n",
       "Sum Replicate           5.665593    5.665593    4.774593    4.7745930\n",
       "Sum Residual            9.116023    8.371165   15.472464    7.2399200\n",
       "Sum Total            1024.580375 1024.580375 1345.792840 1345.7928400\n",
       "Sum Predicted        1015.273728 1016.207748 1329.677712 1338.6635680\n",
       "Sum Lack Of Fit         3.450430    2.705572   10.697871    2.4653270\n",
       "Mean Residuals          1.012891    1.046396    1.719163    0.9049900\n",
       "Mean Total            102.458038  102.458038  134.579284  134.5792840\n",
       "Mean Predicted       1015.273728  508.103874 1329.677712  669.3317840\n",
       "Mean Replicate          1.416398    1.416398    1.193648    1.1936483\n",
       "Lack Of Fit             0.690086    0.676393    2.139574    0.6163318"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tableOfResult1 <- data.frame(A1,A2,B1,B2)\n",
    "tableOfResult1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<mark>Both datasets are similar. However, for the second set, excluding the intercept increase the lack of fit. It is important to note that it is not possible to judge the lack of fit other than by comparing it to the Mean Sum of Replicates. In all cases the LOF is smaller than the MSR, except for B1. The conclusion is that we need 2 parameters to best fit our data.</mark>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.25605650216089"
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      "text/latex": [
       "6.25605650216089"
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      "text/markdown": [
       "6.25605650216089"
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      "text/plain": [
       "[1] 6.256057"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.79246662332614"
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      "text/latex": [
       "1.79246662332614"
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      "text/markdown": [
       "1.79246662332614"
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      "text/plain": [
       "[1] 1.792467"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "0.487211927720881"
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       "0.487211927720881"
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      "text/markdown": [
       "0.487211927720881"
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      "text/plain": [
       "[1] 0.4872119"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "0.704083882026608"
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       "0.704083882026608"
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       "0.704083882026608"
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      "text/plain": [
       "[1] 0.7040839"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "0.225084202869423"
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       "0.225084202869423"
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       "0.225084202869423"
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      "text/plain": [
       "[1] 0.2250842"
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     "metadata": {},
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   ],
   "source": [
    "# Brereton p.42\n",
    "qf(0.95,5,4)  # this would be the F-ratio for 95% confidence.\n",
    "# above this number we can conclude with 95% confidence that intercept is useful.\n",
    "2.1395742/1.193648\n",
    "0.6900860/1.416398\n",
    "pf(1.792,5,4,lower.tail = TRUE)\n",
    "pf(0.48721,5,4,lower.tail = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can conclude with 70.4% of confidence that intercept is useful in the case of the B dataset. It is not possible to conclude in the case of the dataset A, since the value for F-ratio is very low."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### programing a function\n",
    "\n",
    "The way we performed the calculation above is not very efficient. We copy and paste 4 time the same code. If we want to make a modification we would have to propagate in all four pieces. In this case, a better practise consists in creating a funcion. If we are interested in more flexibility we can program a function to perform the calculation. This is done like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "lof <- function(x, y, fit.lm) {\n",
    "    \n",
    "    data=data.frame(\"x\"=as.numeric(x), \"y\"=y)\n",
    "    #fit.lm <- lm( y ~ x, data=data )\n",
    "    \n",
    "    Rep <- duplicated(data$x) # find replicates\n",
    "    R <- sum(Rep) # enumerate replicates\n",
    "    N <- dim(data)[1] # find out dimension of data\n",
    "    P <- length(fit.lm$coefficients)\n",
    "    D <- N - P - R\n",
    "    result <- data.frame(\"Number Replicate\"=R)\n",
    "    result[\"Number of Data\"] <- N\n",
    "    result[\"Number of Parameters\"] <- P\n",
    "    result[\"Degrees of Freedom\"] <- D\n",
    "    \n",
    "    meanRep <- aggregate(y ~ x, data = data, mean)\n",
    "    \n",
    "    sumRep=0\n",
    "    sumRep2=0\n",
    "    for (i in seq(1,nrow(data))) {\n",
    "        sumRep[i] <- meanRep$y[ meanRep$x == data$x[i] ] - data$y[i] \n",
    "        sumRep2[i] <- ( meanRep$y[ meanRep$x == data$x[i] ] - data$y[i] )^2\n",
    "    }\n",
    "\n",
    "    S_replicate <- sum(sumRep2) # R degrees of freedom \n",
    "    result[\"Sum Replicate\"] <- round(S_replicate,3)\n",
    " \n",
    "    S_residual <- sum ( resid(fit.lm)^2 ) # N-P degrees of freedom (# or S_total - S_predicted)\n",
    "    result[\"Sum Residual\"] <- round(S_residual,3)\n",
    "\n",
    "    S_total <- sum( data$y^2 ) # N degrees of freedom\n",
    "    result[\"Sum Total\"] <- round(S_total,3)\n",
    "\n",
    "    S_predicted <- sum( fitted(fit.lm)^2 ) # P degrees of freedom\n",
    "    result[\"Sum Predicted\"] <- round(S_predicted,3)\n",
    "\n",
    "    S_lackOfFit <- S_residual - S_replicate # N-P-R degrees of freedom\n",
    "    result[\"Sum Lack Of Fit\"] <- round(S_lackOfFit,3)\n",
    "\n",
    "    result[\"Mean Residuals\"] <- round(S_residual / (N-P),3)\n",
    "    \n",
    "    result[\"Mean Total\"] <- round(S_total / N,3)\n",
    "    \n",
    "    result[\"Mean Predicted\"] <- round(S_predicted / P,3)\n",
    "    \n",
    "    result[\"Mean Replicate\"] <- round(S_replicate / R,3)\n",
    "    \n",
    "    result[\"Lack Of Fit\"] <- round(S_lackOfFit / D,3)\n",
    "    \n",
    "    result[\"F-value\"] <- round(result[\"Lack Of Fit\"] / result[\"Mean Replicate\"],3)\n",
    "    \n",
    "    result[\"p-value\"] <- df(as.numeric(result[\"F-value\"]),D,R)\n",
    "    \n",
    "    result[\"r2\"] <- round(summary(fit.lm)$r.squared,3)\n",
    "    \n",
    "    result[\"a(slope)\"] <- round(fit.lm$coefficients[2],3)\n",
    "    \n",
    "    result[\"b(intercept)\"] <- round(fit.lm$coefficients[1],3)\n",
    "    \n",
    "    return( t(result) )\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use this function on our dataset A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dQWUZPD6PPjvWOiFkRlm80+E3su+Z/3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\nTkSuQmCC",
      "text/plain": [
       "Plot with title “linear regression”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.lm <- lm( A ~ conc, data=data.frame(\"conc\"=as.numeric(data$conc), \"A\"=data$A) )\n",
    "r1 <- lof(data$conc, data$A, fit.lm)\n",
    "\n",
    "plot(data$conc,data$A, main=\"linear regression\",ylab=\"intensity\",xlab=\"concentration\")\n",
    "#lines(data$conc, fitted(fit.lm), col=2)\n",
    "abline(fit.lm$coefficients[1],fit.lm$coefficients[2],col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We repeated the calculation for the A dataset, but this time we use ```lm()``` to fit the data. It means that we are not using the models from the book, but the one we are optimizing here. In addition we computed the p-value. A p-value higher than 0.05 means that we cannot conclude that our model doesn't fit our data acurrately.\n",
    "\n",
    "We repeat the same calculation but this time we concatenate A and B datasets to see the effect of a larger dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DftuefOrKxy0zJQ0i7Ad5DSTkqFCCCAAAIIIIAAAgikV+DBB3epTo6uumq+HX30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\nRK5CYII=",
      "text/plain": [
       "Plot with title “linear regression”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.lm <- lm( A ~ conc, data=data.frame(\"conc\"=as.numeric(c(data$conc,data$conc)), \"A\"=c(data$A, data$B)) )\n",
    "r2 <- lof(c(data$conc,data$conc), c(data$A, data$B), fit.lm)\n",
    "\n",
    "plot(as.factor(c(data$conc,data$conc)), c(data$A, data$B), main=\"linear regression\",ylab=\"intensity\",xlab=\"concentration\")\n",
    "abline(fit.lm$coefficients[1],fit.lm$coefficients[2],col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next table shows the comparison. The first thing to note is that the degree of freedom is not changed because we added more points, but also more replicates. Maybe there are too many replicates in this case. The next thing to note is that the lack of fit is smaller which is good, but the MSR is larger. p-values for both are larger than 0.05 and we cannot rule out that our model is not accurate, which is ok. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 19 × 2 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Number.Replicate</th><td>   4.0000000</td><td>  14.0000000</td></tr>\n",
       "\t<tr><th scope=row>Number of Data</th><td>  10.0000000</td><td>  20.0000000</td></tr>\n",
       "\t<tr><th scope=row>Number of Parameters</th><td>   2.0000000</td><td>   2.0000000</td></tr>\n",
       "\t<tr><th scope=row>Degrees of Freedom</th><td>   4.0000000</td><td>   4.0000000</td></tr>\n",
       "\t<tr><th scope=row>Sum Replicate</th><td>   5.6660000</td><td>  27.5520000</td></tr>\n",
       "\t<tr><th scope=row>Sum Residual</th><td>   8.3710000</td><td>  28.2370000</td></tr>\n",
       "\t<tr><th scope=row>Sum Total</th><td>1024.5800000</td><td>2370.3730000</td></tr>\n",
       "\t<tr><th scope=row>Sum Predicted</th><td>1016.2090000</td><td>2342.1370000</td></tr>\n",
       "\t<tr><th scope=row>Sum Lack Of Fit</th><td>   2.7060000</td><td>   0.6850000</td></tr>\n",
       "\t<tr><th scope=row>Mean Residuals</th><td>   1.0460000</td><td>   1.5690000</td></tr>\n",
       "\t<tr><th scope=row>Mean Total</th><td> 102.4580000</td><td> 118.5190000</td></tr>\n",
       "\t<tr><th scope=row>Mean Predicted</th><td> 508.1050000</td><td>1171.0680000</td></tr>\n",
       "\t<tr><th scope=row>Mean Replicate</th><td>   1.4160000</td><td>   1.9680000</td></tr>\n",
       "\t<tr><th scope=row>Lack Of Fit</th><td>   0.6760000</td><td>   0.1710000</td></tr>\n",
       "\t<tr><th scope=row>F-value</th><td>   0.4770000</td><td>   0.0870000</td></tr>\n",
       "\t<tr><th scope=row>p-value</th><td>   0.6013782</td><td>   0.3188609</td></tr>\n",
       "\t<tr><th scope=row>r2</th><td>   0.9560000</td><td>   0.9290000</td></tr>\n",
       "\t<tr><th scope=row>a(slope)</th><td>   2.4360000</td><td>   2.4600000</td></tr>\n",
       "\t<tr><th scope=row>b(intercept)</th><td>   0.6110000</td><td>   1.3220000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 19 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "\tNumber.Replicate &    4.0000000 &   14.0000000\\\\\n",
       "\tNumber of Data &   10.0000000 &   20.0000000\\\\\n",
       "\tNumber of Parameters &    2.0000000 &    2.0000000\\\\\n",
       "\tDegrees of Freedom &    4.0000000 &    4.0000000\\\\\n",
       "\tSum Replicate &    5.6660000 &   27.5520000\\\\\n",
       "\tSum Residual &    8.3710000 &   28.2370000\\\\\n",
       "\tSum Total & 1024.5800000 & 2370.3730000\\\\\n",
       "\tSum Predicted & 1016.2090000 & 2342.1370000\\\\\n",
       "\tSum Lack Of Fit &    2.7060000 &    0.6850000\\\\\n",
       "\tMean Residuals &    1.0460000 &    1.5690000\\\\\n",
       "\tMean Total &  102.4580000 &  118.5190000\\\\\n",
       "\tMean Predicted &  508.1050000 & 1171.0680000\\\\\n",
       "\tMean Replicate &    1.4160000 &    1.9680000\\\\\n",
       "\tLack Of Fit &    0.6760000 &    0.1710000\\\\\n",
       "\tF-value &    0.4770000 &    0.0870000\\\\\n",
       "\tp-value &    0.6013782 &    0.3188609\\\\\n",
       "\tr2 &    0.9560000 &    0.9290000\\\\\n",
       "\ta(slope) &    2.4360000 &    2.4600000\\\\\n",
       "\tb(intercept) &    0.6110000 &    1.3220000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 19 × 2 of type dbl\n",
       "\n",
       "| Number.Replicate |    4.0000000 |   14.0000000 |\n",
       "| Number of Data |   10.0000000 |   20.0000000 |\n",
       "| Number of Parameters |    2.0000000 |    2.0000000 |\n",
       "| Degrees of Freedom |    4.0000000 |    4.0000000 |\n",
       "| Sum Replicate |    5.6660000 |   27.5520000 |\n",
       "| Sum Residual |    8.3710000 |   28.2370000 |\n",
       "| Sum Total | 1024.5800000 | 2370.3730000 |\n",
       "| Sum Predicted | 1016.2090000 | 2342.1370000 |\n",
       "| Sum Lack Of Fit |    2.7060000 |    0.6850000 |\n",
       "| Mean Residuals |    1.0460000 |    1.5690000 |\n",
       "| Mean Total |  102.4580000 |  118.5190000 |\n",
       "| Mean Predicted |  508.1050000 | 1171.0680000 |\n",
       "| Mean Replicate |    1.4160000 |    1.9680000 |\n",
       "| Lack Of Fit |    0.6760000 |    0.1710000 |\n",
       "| F-value |    0.4770000 |    0.0870000 |\n",
       "| p-value |    0.6013782 |    0.3188609 |\n",
       "| r2 |    0.9560000 |    0.9290000 |\n",
       "| a(slope) |    2.4360000 |    2.4600000 |\n",
       "| b(intercept) |    0.6110000 |    1.3220000 |\n",
       "\n"
      ],
      "text/plain": [
       "                     [,1]         [,2]        \n",
       "Number.Replicate        4.0000000   14.0000000\n",
       "Number of Data         10.0000000   20.0000000\n",
       "Number of Parameters    2.0000000    2.0000000\n",
       "Degrees of Freedom      4.0000000    4.0000000\n",
       "Sum Replicate           5.6660000   27.5520000\n",
       "Sum Residual            8.3710000   28.2370000\n",
       "Sum Total            1024.5800000 2370.3730000\n",
       "Sum Predicted        1016.2090000 2342.1370000\n",
       "Sum Lack Of Fit         2.7060000    0.6850000\n",
       "Mean Residuals          1.0460000    1.5690000\n",
       "Mean Total            102.4580000  118.5190000\n",
       "Mean Predicted        508.1050000 1171.0680000\n",
       "Mean Replicate          1.4160000    1.9680000\n",
       "Lack Of Fit             0.6760000    0.1710000\n",
       "F-value                 0.4770000    0.0870000\n",
       "p-value                 0.6013782    0.3188609\n",
       "r2                      0.9560000    0.9290000\n",
       "a(slope)                2.4360000    2.4600000\n",
       "b(intercept)            0.6110000    1.3220000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tableOfResult2 <- cbind(r1,r2)\n",
    "tableOfResult2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Replicates\n",
    "\n",
    "If we are curious to understand the effect of the replicates we can remove them and apply the test again. Clearly we will have no estimation of the experimental error to compare with. We can compute the LOF but we have no MRS to compute a p-value. \n",
    "\n",
    "<mark>Finally it is important to look at the coefficient. After all we are interested in a calibration curve, how the different experimental designs affect the value of the coefficients?</mark>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 19 × 1 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Number.Replicate</th><td>  0.000</td></tr>\n",
       "\t<tr><th scope=row>Number of Data</th><td>  4.000</td></tr>\n",
       "\t<tr><th scope=row>Number of Parameters</th><td>  2.000</td></tr>\n",
       "\t<tr><th scope=row>Degrees of Freedom</th><td>  2.000</td></tr>\n",
       "\t<tr><th scope=row>Sum Replicate</th><td>  0.000</td></tr>\n",
       "\t<tr><th scope=row>Sum Residual</th><td>  6.486</td></tr>\n",
       "\t<tr><th scope=row>Sum Total</th><td>425.645</td></tr>\n",
       "\t<tr><th scope=row>Sum Predicted</th><td>419.159</td></tr>\n",
       "\t<tr><th scope=row>Sum Lack Of Fit</th><td>  6.486</td></tr>\n",
       "\t<tr><th scope=row>Mean Residuals</th><td>  3.243</td></tr>\n",
       "\t<tr><th scope=row>Mean Total</th><td>106.411</td></tr>\n",
       "\t<tr><th scope=row>Mean Predicted</th><td>209.580</td></tr>\n",
       "\t<tr><th scope=row>Mean Replicate</th><td>    NaN</td></tr>\n",
       "\t<tr><th scope=row>Lack Of Fit</th><td>  3.243</td></tr>\n",
       "\t<tr><th scope=row>F-value</th><td>    NaN</td></tr>\n",
       "\t<tr><th scope=row>p-value</th><td>    NaN</td></tr>\n",
       "\t<tr><th scope=row>r2</th><td>  0.927</td></tr>\n",
       "\t<tr><th scope=row>a(slope)</th><td>  2.510</td></tr>\n",
       "\t<tr><th scope=row>b(intercept)</th><td>  0.398</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 19 × 1 of type dbl\n",
       "\\begin{tabular}{r|l}\n",
       "\tNumber.Replicate &   0.000\\\\\n",
       "\tNumber of Data &   4.000\\\\\n",
       "\tNumber of Parameters &   2.000\\\\\n",
       "\tDegrees of Freedom &   2.000\\\\\n",
       "\tSum Replicate &   0.000\\\\\n",
       "\tSum Residual &   6.486\\\\\n",
       "\tSum Total & 425.645\\\\\n",
       "\tSum Predicted & 419.159\\\\\n",
       "\tSum Lack Of Fit &   6.486\\\\\n",
       "\tMean Residuals &   3.243\\\\\n",
       "\tMean Total & 106.411\\\\\n",
       "\tMean Predicted & 209.580\\\\\n",
       "\tMean Replicate &     NaN\\\\\n",
       "\tLack Of Fit &   3.243\\\\\n",
       "\tF-value &     NaN\\\\\n",
       "\tp-value &     NaN\\\\\n",
       "\tr2 &   0.927\\\\\n",
       "\ta(slope) &   2.510\\\\\n",
       "\tb(intercept) &   0.398\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 19 × 1 of type dbl\n",
       "\n",
       "| Number.Replicate |   0.000 |\n",
       "| Number of Data |   4.000 |\n",
       "| Number of Parameters |   2.000 |\n",
       "| Degrees of Freedom |   2.000 |\n",
       "| Sum Replicate |   0.000 |\n",
       "| Sum Residual |   6.486 |\n",
       "| Sum Total | 425.645 |\n",
       "| Sum Predicted | 419.159 |\n",
       "| Sum Lack Of Fit |   6.486 |\n",
       "| Mean Residuals |   3.243 |\n",
       "| Mean Total | 106.411 |\n",
       "| Mean Predicted | 209.580 |\n",
       "| Mean Replicate |     NaN |\n",
       "| Lack Of Fit |   3.243 |\n",
       "| F-value |     NaN |\n",
       "| p-value |     NaN |\n",
       "| r2 |   0.927 |\n",
       "| a(slope) |   2.510 |\n",
       "| b(intercept) |   0.398 |\n",
       "\n"
      ],
      "text/plain": [
       "                     [,1]   \n",
       "Number.Replicate       0.000\n",
       "Number of Data         4.000\n",
       "Number of Parameters   2.000\n",
       "Degrees of Freedom     2.000\n",
       "Sum Replicate          0.000\n",
       "Sum Residual           6.486\n",
       "Sum Total            425.645\n",
       "Sum Predicted        419.159\n",
       "Sum Lack Of Fit        6.486\n",
       "Mean Residuals         3.243\n",
       "Mean Total           106.411\n",
       "Mean Predicted       209.580\n",
       "Mean Replicate           NaN\n",
       "Lack Of Fit            3.243\n",
       "F-value                  NaN\n",
       "p-value                  NaN\n",
       "r2                     0.927\n",
       "a(slope)               2.510\n",
       "b(intercept)           0.398"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XrPLHtnsndS2yTb/H7Lbf97fhbVub3Y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\nP5YXFSNSUYiqAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “linear regression”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "F <- duplicated(data$conc)\n",
    "fit.lm <- lm( A ~ conc, data=data.frame(\"conc\"=as.numeric(data$conc[F]), \"A\"=data$A[F]) )\n",
    "lof(data$conc[F], data$A[F], fit.lm)\n",
    "\n",
    "plot(data$conc[F], data$A[F], main=\"linear regression\",ylab=\"intensity\",xlab=\"concentration\")\n",
    "abline(fit.lm$coefficients[1],fit.lm$coefficients[2],col=\"blue\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p-values, model and noise\n",
    "\n",
    "As already mentionned, the p-value can be used to decide if we can conclude that our model is not appropriate. We can go back to the data of the first example to check demonstrate how p-value help us decide if our model is accurate or not and to illustrate the effect of noise in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "N <- 20 # we define the number of observations\n",
    "\n",
    "# we create a fake dataset using a quadratic\n",
    "#equation and adding some noise\n",
    "# first create a vector of x repeated rep times\n",
    "rep <- 2 # number of replicates\n",
    "X <- rep(seq(from=43, to=96, length.out=N),rep)\n",
    "# then create the Y vector according to the equation:\n",
    "Y <- (0.075 * X + -1.874 + 0.01* X^2)\n",
    "# create some noise\n",
    "noise <-runif(length(Y), -1, 1) \n",
    "# add some noise to Y\n",
    "Y <- Y + 1*noise\n",
    "x_sorted <- sort(X,index.return=TRUE)\n",
    "x <-x_sorted$x\n",
    "y <- Y[x_sorted$ix]\n",
    "data <- data.frame(\"x\"=x, \"y\"=y, x2=x^2)\n",
    "\n",
    "# we fit the data and evaluate the goodness of it\n",
    "fit.lm <- lm( y ~ x, data=data )\n",
    "noQuadLowNoise <- lof(data$x, data$y, fit.lm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.99"
      ],
      "text/latex": [
       "0.99"
      ],
      "text/markdown": [
       "0.99"
      ],
      "text/plain": [
       "[1] 0.99"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6pqNlxYArMhOBAgpwiV0B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\nenACdopdh2Kn0u2mVCr2PUhlio74OK3KoJuOHH3FCXnXagWXl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tvjumMvuvZLn8l0XgpMUq+s0BmlHKOcotg7kr9RbL9bsWRHBW2fpje7\nz/5NFymM6Wnq5peVLym2f62xjzc6FOq/z6rjdkTwdKVMsZ9f28d2ZH++Ym1P5S3lBbvT3eyN\njw5l/9QMbvNWYCf1LNajd7bvrE3YeOPwt7gbgpuhC4SGvgrWgICvBezIkZ1mt0SZrnxbsXex\nfqyk2jhNvJ26032bukCDvfCi5bfALuqevdMcV+yo0C2KnU7XoFizF1bWeu7jdzXPiqot7UFa\nwQj8XD2dpzyQ1mP2cRpGAU7az+9hir1h8brysvJVZYryhmLN9nGqIN4wo/sf+znm93S6SH5O\n2xGkz/Xo2gnd97fuvh2n256/p/lb3I3DzcAEKJAG5sXSwROw03Calb0UO7pgn124XrlQmaRY\nG6t8tGHq//+xdybtj/YW/z+LqTwUsHeb7Vz2byr/qdj+tRdSDyt2GpYVT9sp1lZtvPm/f1P7\nnH38fyR5PxFRD8uVq3v0lH3cA6TA7toRXrvQiv283q7MUZLKt5TUi2fbxz1/hjVrw8V1trQJ\nWl4LXKne7aP8UZmqfE+xNyxXK6nXsvwtFgYNAQQQGC4BOx3Dip8fdnfA3q38Sfd06maMJmyZ\n9HPiU49xm18Ca9WdZ3p0qU73bf+drlghbNM9P4d2huatV1J/nDVJy3OBG9W/VxQ7Kpze2Mfp\nGoU3PVNdtp9Ru2JhqtkpWZ3Kxd0z7A2Q57qn028e0B170U3LfwEriuyIkO3rZYqd7v6BYsWx\nNf4Wb3Tg3wwI8Ic9A4iswtcCIzW6nu8uvqh565TUkQM7973nVZDsnSxryzf8yz/5LGAvmBf0\n6OAS3bd3oLdS7CiitdQ+3Xhv4z63P8i2HC3/BezntV75b6WrR3fZxz1ACuzuMervC4qd/pxq\nr2viPuXY7hn2ezp1pLB71oYb+7m23+m0/BewIte+18zegKxS/q7YGQCpwpe/xcKgZUaAAikz\njqzFvwIdGtq9PYZ3gu6XKvYi2tp8xf5Au3anu9kHwe3IxD9SM7jNW4FW9cyOIKT/Pjyq+74V\nTvbiebli+zS92QuvePoMpvNaoFq9szc8Huqll+zjXlAKaNa76qsVP8Vpfbbfx3Y65fvd8+z3\ntL3hUdt93252VuyFNj/HppHfzY4S/VKxo0d25UFr9jlRm261O2r8Ld7owL8IIIBA1gUu1Bbs\nF7Id2t9WsVM5/qbY4X27UpK13RU7leMyxT60P1Gxd7IuUGj5L7CvumhHFH6j2LvJU5QnlceV\nIsXatxT7Q2xFkX1u6RuKFcB2uiWtMATOVDftZ9leJPfW2Me9qRTGPPsZts+iNCm7KXsodrTB\n9vd0JdXsBfRCxX5nW0E1V1mkpH6Xa5KWpwJ16pcdrY8q9kbHcYqdXvd5JdX4W5yS4BYBBBDI\nsoAdVbhcsVPq7I+tvZC+W7FiKb3ZH+G3FfsF/o7yWyX14lqTtDwXOEL9e0mx/WfF7sOKFUup\nZvvySsUes2WeVr6o0ApHwN59/udmuss+3gxOATz0GfXxecV+T9vPqP0+/rKS3nbXnTbFllmv\nPKDwJocQCqRdrH4uV2z/2tkZP1R6Nv4W9xThPgIIIJBFgRKte2/F3rnaVLNTOvZUKIw2JZT/\n83dVF0dvppsj9Ji9yKL5V4B9XNj7did1f5xiv4831ezNj2029SDz817AjhJurvG3eHM6PIYA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCHxSoESzQp+cPag5I9KetYem\nz1PGpM1jEgEEEEAAAQQQQAABBBDIW4H91LNnlFEZ6OGXtY7mtPUcpWlP+VTaPCYRQAABBApA\noKgA+kgXEUAAAQQQyIbAgVrpvhla8Qlajx2NSrWYJvZX/pmawS0CCCCAQGEIhAujm/QSAQQQ\nQCCPBLZXX45XqpRXlLVKettbd05UahQ7ivK6kmpjNXG48pwSUWy5nZXlSpeS3vrazjgtPF2x\n9SSV9O1Y32y9q5RjFTuiY6fSWX+t7abYtu25TyrrlPeUacqHymRlkmIFjo3Pih/rtz1+gFKs\nvKpYm6hElS0V64M9Z6RifXhZ6VSsjVamK0cr2ygvKQkl1Y7RxEfKdsoMxQq4d5SVCg0BBBBA\nAAEEEEAAAQTyUKBRfbJi5E1libJe+bqSahdqwgqdFcrzihVINyhWnFizIsCKgmsUKzyeUqyA\nsHWlf4anr+2creXt+W8o87qnr9Ztqv1OE48o7YoVLf9QrC+XKNasUHlBsXlPKl9QrFmB8j+K\nzbecooxTlilWqMxTbGz22C8Va1cpVly9ryxSdlKsILNlPqVYq1WsrzZWW8Yes3WmHtek84Fi\n/V6tdCi2PtumFXE0BBBAAAEEEEAAAQQQyDOBKvXHjrTMUlLFzPmathfyY5UpihVPFyj2uBVF\nVnhYMfA1xZoVSHb/z8rWirXjFJt3st1R62s7duqaFRo/VexIjjUrQGzbDXZHzQoNW+c5Sups\niRs1bcVHqu+natqWGaWkmhVIdtSmXNlVKVV+q1hxY0eIrNm4bF3WhzLF2h3K3RumNv6TXiCN\n1Cwr0B5Qdtv4sFOhWyvQHu6+bzdWIL2t2LatmY8djWq2OzQEEEAAAQQQQAABBBDIL4Fz1Z03\nlVTBYb2zAsJOGRuj2FGhZ5WezYqDBd0zUwXSlLSF7POwVmx8p3teX9v5Dy1np87ZNtNbq+6k\nihQrkKyv6S2qO1YQ7dI9c1MFkj03vdny6Ud6rL/nKbauHRVrmyuQpupxW7ZaSW+X647NTxVN\nViBdnb6Apq04snHREEAAAQRyJGDvgtEQQAABBBDoj8ABWsiKnUTawus0bUdG7MX9vopdFa5n\ns6JlfI+Zr6bd79K0Hdkp6Z7X13b20nJ25MaOrtgpaKkcoun07byi++nN+mgttZ2N9z75r40x\nvdkpdYcpVqzYqW9WnF2kWEsvFjfO+eS/5mKF0N96PGQu1vrqc1/93bgW/kUAAQQQyIhAUUbW\nwkoQQAABBIIgYIXRiF4G6mqeFQBrlNQpZ+mL2fNeT5+haSuKNtX62s56PdEKrJN7WYE9lmq2\nnsE0+2xTerMjY6crdmRpjmJHdA5VblX602x9ZmRH26ygTLWUQbpNal5qGW4RQAABBHIswBGk\nHIOzOQQQQKCABezokB29ST+1bQ/d/0g5SnlaOUhJ/0yP7m64ItwSm+hn62s7ca1nN8UKj8fT\nMkPTE5T+NivqrFnxsqlmR2++qPxc+YbSpNiRqUrFWuoIkq1rU39TzcWaFVXpzY5K2ZGzv6fP\nZBoBBBBAYHgFNvXLfHh7xdYRQAABBPJRwI6g2BEaO9WsRvm08gvFTh17UPkvxY4g2edxJiv7\nKb9XrJi4Qelv62s7v9GK7MIQdmTnM8q2ykXK95VUMaLJPpudKmdtpmIFV2/NxrtMmarsqIxU\nTlXOVazZfWtWJNqpdFYE9TyKZkWc+Vh/v6xsr1hfL1B+qyQVGgIIIIAAAggggAACCBSgwCHq\ns30Ox46YWOzoh81LtTpN2BEge8xe+NuyxymplrpIw7jUjO5b+3yQFQ2p1td27EiRHZVKbecJ\nTZ+derJurchalHbfJo9WbPk97Y7aVkpqHb/eMGdjofPd7unUzZGasCInodgpcvOVKUqX8kXF\nmhVqNgZbvz1mR9Rs+lOKte2UFsXWYfNXKJcr6Uev7PnnK+ntOt3pOY70x5lGAAEEEEAAAQQQ\nQACBPBAYqz7YUZf0F/jp3bLHLUNtfW1na23AjuwMpVmhVNSPFdh2Rm9mObPYZjOP20N2dClV\noPWxKA8jgAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAApkQ+F+zJduhEkspzQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “low noise data / linear model”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$x,data$y, cex=0.7, cex.axis=0.8, cex.main=0.8, cex.lab=0.8, main=\"low noise data / linear model\", xlab=\"concentration\", ylab=\"intensity\")\n",
    "lines(data$x, fitted(fit.lm), col=2)\n",
    "noQuadLowNoise[17]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although the correlation coefficient is high, we can see that there is a trend in the data that is not correctly described by the model, the model is linear and we know that there is a quadratic term in the data. If we only look at the lack of fit and at the correlation coefficient we can conclude that the model is not bad. \n",
    "\n",
    "However the LOF is bigger than the MSR, which indicates a problem with our model. If we compute the p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "7.704008904192e-13"
      ],
      "text/latex": [
       "7.704008904192e-13"
      ],
      "text/markdown": [
       "7.704008904192e-13"
      ],
      "text/plain": [
       "[1] 7.704009e-13"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "noQuadLowNoise[16] # p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.15112442712183"
      ],
      "text/latex": [
       "2.15112442712183"
      ],
      "text/markdown": [
       "2.15112442712183"
      ],
      "text/plain": [
       "[1] 2.151124"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "43.314"
      ],
      "text/latex": [
       "43.314"
      ],
      "text/markdown": [
       "43.314"
      ],
      "text/plain": [
       "[1] 43.314"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.999999999996513"
      ],
      "text/latex": [
       "0.999999999996513"
      ],
      "text/markdown": [
       "0.999999999996513"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Brereton p.42\n",
    "qf(0.95,noQuadLowNoise[4],noQuadLowNoise[1])  # this would be the F-ratio for 95% confidence.\n",
    "# above this number we can conclude with 95% confidence that intercept is useful.\n",
    "noQuadLowNoise[15]\n",
    "pf(noQuadLowNoise[15],noQuadLowNoise[4],noQuadLowNoise[1],lower.tail = TRUE)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "we find a very small number that means that we can conclude that our model is not accurate. Let's repeat this but this time we include a quadratic term in the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.164273827118837"
      ],
      "text/latex": [
       "0.164273827118837"
      ],
      "text/markdown": [
       "0.164273827118837"
      ],
      "text/plain": [
       "[1] 0.1642738"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BDZ7B9rkABVKfHwI6gAAC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\noqG4dIrrhG5VK/pHHff8/FnT/9RBi/6t9V/o4DFWI4AAAgggg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Pt0071NfW5/kG07SvoL2M9rmfJbpbVNdenjNiAZdvdY1fctxU5/jpcP\ntPB35bjYCvs9HZ8pjK3aeGM/1/Y7nZL+AjbIte81szcgC5TXFDsDID7w5W+xMCjJEWCAlBxH\n9uJfgUY17Yk2zTtJ93sp9iLayvOK/YF27U6s2AfBbWbizfgKbtNWYJZqZjMIib8Pj47dt4GT\nvXhepFifJhZ74dWUuILltBYoVO3sDY9/tlNL+rgdlAxa9YnqaoOf7IQ62+9jO53y09g6+z1t\nb3gUxe7bze6KvdDm59g00rvYLNHNis0e2ZUHrdjnRG15lt1R4W/xJgf+RQABBLpd4EodwX4h\n29T+ToqdyvGKYtP7dqUkK3srdirHdYp9aH+CYu9kXaFQ0l/gQFXRZhTuUOzd5MOVucoLSpZi\n5SLF/hDboMg+t/QtxQbAdrolJTMEzlU17WfZXiS3V+jj9lQyY539DNtnUSqVvZTPKTbbYP19\nshIv9gK6XrHf2Tag+psyW4n/LtciJU0FSlQvm60vVeyNjhMUO73uy0q88Lc4LsEtAggg0M0C\nNqtwvWKn1NkfW3sh/Zhig6XEYn+EP1LsF/jHyp1K/MW1FilpLnCk6veOYv1ng91nFBssxYv1\n5S2KPWbbLFTOViiZI2DvPi/eSnXp463gZMBDR6mObyj2e9p+Ru338deUxLK37tQqtk2z8qTC\nmxxCyJByjeq5SLH+tbMzrlLaFv4WtxXhPgIIINCNAjna9/6KvXPVUbFTOvZRGBh1JJT+6/dU\nFQdupZq99Zi9yKL4V4A+zuy+3U3VH6HY7+OOir35MbSjB1mf9gI2S7i1wt/irenwGAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggsKVAjlaFtlzdpTW9E571OS1fqgxK\nWMciAggggAACCCCAAAIIIJC2AgepZi8r/ZJQw69pH1UJ+zlay56yb8I6FhFAAAEEMkAgKwPq\nSBURQAABBBDoDoHR2umBSdrxSdqPzUbFS40WDlYWx1dwiwACCCCQGQLhzKgmtUQAAQQQSCOB\n4arLFKVAeVdZrySW/XXnFGWiYrMoHyjxMkwLRyivK8WKbbe7skhpVRLLto4zQhufrNh+okri\ncaxutt/VynGKzejYqXRWXyt7KXZse+5cZYOyXDleWaUcokxSbIBj7bPBj9XbHh+lZCvvKVYm\nKKXKAMXqYM/pq1gd/qO0KFYGKicrxyhDlXeUiBIvx2phjbKzcqpiA7iPlZUKBQEEEEAAAQQQ\nQAABBNJQoEJ1ssHIMmWe0qx8U4mXK7VgA52lyhuKDZDuVmxwYsUGATYo+LViA4+XFBtA2L4S\nP8OzreNcoO3t+UuUmbHl23UbL7/TwrNKg2KDljcVq8uPFSs2UHlLsXVzla8oVmyAcr9i6y1n\nKCOUBYoNVGYq1jZ77GbFyi8VG1x9qsxWdlNsQGbb7KtYKVKsrtZW28Yes33GH9eis0Kxeq9V\nGhXbnx3TBnEUBBBAAAEEEEAAAQQQSDOBAtXHZlqmKfHBzGVathfyw5TDFRs8XaHY4zYosoGH\nDQYuVKzYAMnu/1UZolg5QbF1p9sdlW0dx05ds4HGzxSbybFiAxA7drndUbGBhu3zG0r8bIk/\naNkGH/G6n6ll26afEi82QLJZm1xlT6WXcqdigxubIbJi7bJ9WR36KFYeVh7buLTpn8QBUl+t\nsgHak8pemx528nRrA7RnYvftxgZIHyl2bCvmY7NRVXaHggACCCCAAAIIIIAAAuklcImqs0yJ\nDzisdjaAsFPGBik2K/Sq0rbY4KAutjI+QDo8YSP7PKwNNr4bW7et4/xc29mpc3bMxDJLd+KD\nFBsgWV0TS6nu2IBoj9jKjgZI9tzEYtsnzvRYfS9VbF+7Kla2NkCarMdt20IlsVyvO7Y+Pmiy\nAdLtiRto2QZH1i4KAggggECKBOxdMAoCCCCAAAKdERiljWywE0nYeIOWbWbEXtwfqNhV4doW\nG7Ts12blewn3W7VsMzs5sXXbOs7ntZ3N3Njsip2CFs94LSce513dTyxWRyvx42y6t+W/1sbE\nYqfUHabYYMVOfbPB2dWKlcTB4qY1W/5rLjYQeqXNQ+ZiZVt13lZ9N+2FfxFAAAEEkiKQlZS9\nsBMEEEAAgSAI2MCodzsNdbXOBgDrlPgpZ4mb2fM+SFyhZRsUdVS2dZxmPdEGWKe3swN7LF5s\nP10p9tmmxGIzY2cpNrM0Q7EZnUOVPyudKbY/M7LZNhtQxkvcINEmvi6+DbcIIIAAAikWYAYp\nxeAcDgEEEMhgAZsdstmbxFPbPqf7a5SjlYXKGCXxMz26u/GKcPNsoZNlW8dp0n72Umzg8UJC\nTtXyWKWzxQZ1Vmzw0lGx2ZuzlV8o31IqFZuZylesxGeQbF8d/U01Fys2qEosNitlM2evJa5k\nGQEEEECgZwU6+mXes7Xi6AgggAAC6ShgMyg2Q2Onmk1URio3KXbq2NPKrYrNINnncQ5RDlL+\nqNhg4m6ls2Vbx7lDO7ILQ9jMzlHKTsrVyuVKfDCixW0WO1XOylTFBlztFWvvAmWysqvSVzlT\nuUSxYvet2CDRTqWzQVDbWTQbxJmP1fdrynDF6nqFcqcSVSgIIIAAAggggAACCCCQgQLjVWf7\nHI7NmFhs9sPWxUuJFmwGyB6zF/627QlKvMQv0jAiviJ2a58PskFDvGzrODZTZLNS8ePM0fIF\n8Sfr1gZZsxPu2+Ixim2/j91RGazE93HbxjWbBjoXx5bjN1/Qgg1yIoqdIve8crjSqpytWLGB\nmrXB9m+P2YyaLe+rWNlZqVZsH7Z+qXK9kjh7Zc+/TEksd+lO23YkPs4yAggggAACCCCAAAII\npIHAMNXBZl0SX+AnVsset+xo2dZxhugANrOzI8UGSlmd2IEdZ+BWtjOLoVt53B6y2aX4AG0b\nm/IwAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIJAMgf8HR9Psv/27BpQAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “low noise data / quadratic model”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.lm <- lm( y ~ x + x2, data=data )\n",
    "QuadLowNoise <- lof(data$x, data$y, fit.lm)\n",
    "plot(data$x,data$y, cex=0.7, cex.axis=0.8, cex.main=0.8, cex.lab=0.8, main=\"low noise data / quadratic model\", xlab=\"concentration\", ylab=\"intensity\")\n",
    "lines(data$x, fitted(fit.lm), col=2)\n",
    "QuadLowNoise[16]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.16670099681198"
      ],
      "text/latex": [
       "2.16670099681198"
      ],
      "text/markdown": [
       "2.16670099681198"
      ],
      "text/plain": [
       "[1] 2.166701"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.923"
      ],
      "text/latex": [
       "1.923"
      ],
      "text/markdown": [
       "1.923"
      ],
      "text/plain": [
       "[1] 1.923"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.918570767119768"
      ],
      "text/latex": [
       "0.918570767119768"
      ],
      "text/markdown": [
       "0.918570767119768"
      ],
      "text/plain": [
       "[1] 0.9185708"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Brereton p.42\n",
    "qf(0.95,QuadLowNoise[4],QuadLowNoise[1])  # this would be the F-ratio for 95% confidence.\n",
    "# above this number we can conclude with 95% confidence that intercept is useful.\n",
    "QuadLowNoise[15]\n",
    "pf(QuadLowNoise[15],QuadLowNoise[4],QuadLowNoise[1],lower.tail = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly the model is more accurate and we obtain a p-value that is larger than 0.05.\n",
    "\n",
    "Now let's see what happens if the noise is large."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.553610438205782"
      ],
      "text/latex": [
       "0.553610438205782"
      ],
      "text/markdown": [
       "0.553610438205782"
      ],
      "text/plain": [
       "[1] 0.5536104"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aARQr1OQkJila8vxMUBnQ7378Pw4VRXNBDhWBJCqDOPHoGJCTAYkJaG6UwVDGiE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\nQBQKGgCAKBQ0AABRKGgAAKL+DymCcZqC2gYrAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “high noise data / quadratic model”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N <- 20 \n",
    "rep <- 2 \n",
    "X <- rep(seq(from=43, to=96, length.out=N),rep)\n",
    "Y <- (0.075 * X + -1.874 + 0.01* X^2)\n",
    "noise <-runif(length(Y), -1, 1) \n",
    "Y <- Y + 4*noise # we increment the noise \n",
    "x_sorted <- sort(X,index.return=TRUE)\n",
    "x <-x_sorted$x\n",
    "y <- Y[x_sorted$ix]\n",
    "data <- data.frame(\"x\"=x, \"y\"=y, x2=x^2)\n",
    "\n",
    "fit.lm <- lm( y ~ x + x2, data=data )\n",
    "QuadHighNoise <- lof(data$x, data$y, fit.lm)\n",
    "\n",
    "plot(data$x,data$y, cex=0.7, cex.axis=0.8, cex.main=0.8, cex.lab=0.8, main=\"high noise data / quadratic model\", xlab=\"concentration\", ylab=\"intensity\")\n",
    "lines(data$x, fitted(fit.lm), col=2)\n",
    "\n",
    "QuadHighNoise[16]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.16670099681198"
      ],
      "text/latex": [
       "2.16670099681198"
      ],
      "text/markdown": [
       "2.16670099681198"
      ],
      "text/plain": [
       "[1] 2.166701"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.3"
      ],
      "text/latex": [
       "1.3"
      ],
      "text/markdown": [
       "1.3"
      ],
      "text/plain": [
       "[1] 1.3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.715217234887876"
      ],
      "text/latex": [
       "0.715217234887876"
      ],
      "text/markdown": [
       "0.715217234887876"
      ],
      "text/plain": [
       "[1] 0.7152172"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Brereton p.42\n",
    "qf(0.95,QuadHighNoise[4],QuadHighNoise[1])  # this would be the F-ratio for 95% confidence.\n",
    "# above this number we can conclude with 95% confidence that intercept is useful.\n",
    "QuadHighNoise[15]\n",
    "pf(QuadHighNoise[15],QuadHighNoise[4],QuadHighNoise[1],lower.tail = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We repeat now the same operation but without the quadratic term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0114897700714444"
      ],
      "text/latex": [
       "0.0114897700714444"
      ],
      "text/markdown": [
       "0.0114897700714444"
      ],
      "text/plain": [
       "[1] 0.01148977"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gUNAMBSYraL49SpU5cvX657zNq1a4UT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\nsJMAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “high noise data / linear model”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.lm <- lm( y ~ x, data=data )\n",
    "noQuadHighNoise <- lof(data$x, data$y, fit.lm)\n",
    "\n",
    "plot(data$x,data$y, cex=0.7, cex.axis=0.8, cex.main=0.8, cex.lab=0.8, main=\"high noise data / linear model\", xlab=\"concentration\", ylab=\"intensity\")\n",
    "lines(data$x, fitted(fit.lm), col=2)\n",
    "\n",
    "noQuadHighNoise[16]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.15112442712183"
      ],
      "text/latex": [
       "2.15112442712183"
      ],
      "text/markdown": [
       "2.15112442712183"
      ],
      "text/plain": [
       "[1] 2.151124"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.227"
      ],
      "text/latex": [
       "3.227"
      ],
      "text/markdown": [
       "3.227"
      ],
      "text/plain": [
       "[1] 3.227"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.99347154530691"
      ],
      "text/latex": [
       "0.99347154530691"
      ],
      "text/markdown": [
       "0.99347154530691"
      ],
      "text/plain": [
       "[1] 0.9934715"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Brereton p.42\n",
    "qf(0.95,noQuadHighNoise[4],noQuadHighNoise[1])  # this would be the F-ratio for 95% confidence.\n",
    "# above this number we can conclude with 95% confidence that intercept is useful.\n",
    "noQuadHighNoise[15]\n",
    "pf(noQuadHighNoise[15],noQuadHighNoise[4],noQuadHighNoise[1],lower.tail = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be observed than both p-values are larger than 0.05 and thus we cannot rule out a model and must **statistically** accept both model as acceptable for our data. This is the effect of noise, it increase the MSR resulting in larger p-values.\n",
    "\n",
    "<mark>You may have to re-run the last cells several time, this because the data are generated randomly and the p-value may vary largely.</mark>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may be interesting to plot the residual. Here we clearly distinguish the quadratic behavior that is not taken into account by our linear model. Plotting residual is always a good idea to help validating a model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7F8owvFnQVTFZiZvKnPgniXhMWBYWUDX4/q72NZulIwbi14ko5ug8yJH6XE0Uzo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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot( resid(fit.lm) )\n",
    "abline(0,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we may want to add the 95% confidence interval for our calibration curve. This can be achieved with a single command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "interval <- confint(fit.lm)\n",
    "interval90 <- confint(fit.lm, level=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BOVmZnZsmXLpkyZ0vetQsiYkbn2HR0d4+Li6EwNDg4O7uopTp06ZW5u/s0330yZ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\nErBaVfv27fP29p4wYQL+kpjVHjhwwMnJafDgwSY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      "text/plain": [
       "Plot with title “high noise data / linear model”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$x,data$y, cex=0.7, cex.axis=0.8, cex.main=0.8, cex.lab=0.8, main=\"high noise data / linear model\", xlab=\"concentration\", ylab=\"intensity\")\n",
    "lines(data$x, fitted(fit.lm), col=\"red\")\n",
    "abline(interval[1,1], interval[2,1], col=\"gray\")\n",
    "abline(interval[1,2], interval[2,2], col=\"gray\")\n",
    "abline(interval90[1,1], interval90[2,1], col=\"gray\", lty=2)\n",
    "abline(interval90[1,2], interval90[2,2], col=\"gray\", lty=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a calibration curve with confidence interval at 80% (gray dashed line) and 95% (gray line). More concrete information can be found here for calibration curves (https://raw.githubusercontent.com/jwist/chemometrics/master/pdf/Calibration-curve-guide.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the decision tree, in this simple decision tree we have 1 IV (X, causes) and 1 DV (Y, effect). Since both are continuous variable we are in the domain of regression. Because we only have a single DV and it is continuous we speak about simple linear regression. In the next example we will study the effect of pH, temperature and concentration on the yield of a reaction, thus we will have more than one IV but a single DV and we speaks about multiple regression or multivariable regression.\n",
    "\n",
    "for more about this read: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3518362/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}