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+---
+title: 'Correlation and Linear regression pre-lab'
+author: "Professor Amelia McNamara"
+format:
+  html:
+    toc: true
+    toc-depth: 2
+    toc-location: left
+    code-tools: true
+editor: visual
+---
+
+
+<a href="https://github.com/tidy-MN/R-camp-penguins/raw/main/content/data/stat220_regression_prelab.qmd" download>
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+https://github.com/tidy-MN/R-camp-penguins/raw/main/content/page/videos/day6/stat220_regression_prelab.qmd
+
+## Setup and packages
+
+We use three packages in this course: `Lock5Data`, `tidyverse` and `infer`. To load a package, you use the `library()` function, wrapped around the name of a package. I've put the code to load one package into the chunk below. Add the other two you need.
+
+```{r}
+#| label: install-load-packages
+#| warning: false
+
+# Install if needed
+#install.packages("Lock5Data")
+#install.packages("infer")
+
+# Load
+library(Lock5Data)
+library(tidyverse)
+library(infer)
+```
+
+## Load the data
+
+Let's load the example dataset I have for this course, `GSS_clean.csv`. It should be inside the `data` folder in your RStudio Cloud. We'll use the `read_csv()` function to read in the data.
+
+```{r}
+#| label: data-load
+
+GSS <- read_csv("https://tidy-mn.github.io/R-camp-penguins/data/GSS_clean.csv")
+```
+
+## Data visualization for two quantitative variables
+
+Our main data visualization for two quantitative variables is a scatterplot.
+
+To make our visualization, we will use the `ggplot()` function, with our data inside, and then use a `+` to add on a `geom_` to tell R what kind of plot we want. In this case, we want a `geom_point()` to make a scatterplot. Inside the `geom_` function, we use the `aes()` function and tell R how to map between variables in our dataset and variables in the plot. Here's an example:
+
+```{r}
+#| label: scatterplot
+
+ggplot(GSS) +
+  geom_point(aes(x = highest_year_school_completed_spouse, y = highest_year_of_school_completed))
+```
+
+As with our plots in the last lab, we get a warning message about missing values being removed.
+
+Does this plot show a positive association, negative association, or no association? If it shows an association, how strong would you say it is?
+
+## Summary statistics for two quantitative variables
+
+One way to quantify the strength and direction of the relationship is with correlation. To find this, we use the `cor()` function inside our `summarize()` in a data pipeline.
+
+```{r}
+GSS %>%
+  summarize(correlation = cor(y = highest_year_of_school_completed, 
+                              x = highest_year_school_completed_spouse))
+```
+
+Much like with our other summary statistics, this gives an `NA` value, because there are `NA` values in one or more of the variables in the dataset. We can use `drop_na()` on those two variables,
+
+```{r}
+GSS %>%
+  drop_na(highest_year_of_school_completed, highest_year_school_completed_spouse) %>%
+  summarize(correlation = cor(
+    y = highest_year_of_school_completed,
+    x = highest_year_school_completed_spouse))
+```
+
+## Linear models
+
+Another way to study the relationship between two quantitative variables is to fit a linear model. R has a function that does least squares regression, called `lm()` for linear model. This uses the formula syntax, which we're not focusing on in this class. The syntax requires you to write $y~x$ to specify your response and explanatory variable, with a "tilde" in between. (The tilde is up above your Tab key on the keyboard, along with the "tick" \`\``).  You can run the`lm()\` function in your Console or RMarkdown document and get a little information about your model,
+
+```{r}
+lm(highest_year_of_school_completed ~ highest_year_school_completed_spouse, data = GSS)
+```
+
+but, it's better practice to assign your model object to a name, so you can refer back to it later, and get more information about it. Recall that the assignment operator in R is `<-`. I usually call my models `m1`, `m2`, etc., but you could think of a better name to use (like `schoolmodel` or similar) to remind you what it's about.
+
+```{r}
+m1 <- lm(highest_year_of_school_completed ~ highest_year_school_completed_spouse, data = GSS)
+```
+
+When we run this code, nothing prints out. But, a new object should appear in our RStudio Environment pane. Now, we can run R functions on that model object. The most useful one is `summary()`,
+
+```{r}
+m1 %>%
+  summary()
+```
+
+The same model coefficients are shown here, but there is also a lot more information about things like the $R^2$ value.
+
+### Interpreting coefficients
+
+Let's interpret our model coefficients. Here are the generic sentences I prefer:
+
+**Intercept** If the value of \[explanatory variable\] was zero, our model would predict \[response variable\] to be \[intercept value\].
+
+**Slope** For a one-\[unit\] increase in \[explanatory variable\], our model would predict a \[slope value\]-\[unit\] \[increase/decrease\] in \[response variable\].
+
+Let's apply that to this model:
+
+## Predicting values
+
+Models are also useful for prediction. There are more programmatic ways to do prediction in R, but for now I recommend you just use R as a big calculator. Let's see what the model would predict for a person whose spouse had completed 12 years of school (high school):
+
+```{r}
+
+```
+
+Does that make sense?
+
+## Residuals
+
+We are also interested in whether our model overpredicts or underpredicts certain points. We can compute a residual, which is $observed - expected$ or $y_i-\hat{y}_i$. Look at row 21 in the dataset. It represents a 34-year-old person with one child whose spouse completed 12 years of school. What is the observed value of `highest_year_of_school_completed` for this person? What is their residual?
+
+```{r}
+
+```