Clone Assignment Repo

Clone the repo & start new RStudio project

• Go to the sta210-sp20 organization on GitHub (http://www.github.com/sta210-sp20). Click on the repo with the prefix lab-01-review-r-. It contains the starter documents you need to complete the lab.

• Click on the green Clone or download button, select Use HTTPS (this might already be selected by default, and if it is, you’ll see the text Clone with HTTPS as in the image below). Click on the clipboard icon to copy the repo URL.

• Go to https://vm-manage.oit.duke.edu/containers and login with your Duke NetId and Password.

• Click to log into the Docker container STA 210 - Regression Analysis. You should now see the RStudio environment.

• Go to File ➡️ New Project ➡️ Version Control ➡️ Git.

• Copy and paste the URL of your assignment repo into the dialog box Repository URL. You can leave Project Directory Name empty. It will default to the name of the GitHub repo.

• Click Create Project, and the files from your GitHub repo will be displayed the Files pane in RStudio.

Configure git

If you are unable to push to GitHub, it may be because you need to configure git. Follow the steps below to configure git.

To do so, you will use the use_git_config() function from the usethis package.

Type the following lines of code in the console in RStudio filling in your name and email address.

⊕The email address is the one tied to your GitHub account.

library(usethis)
use_git_config(user.name = "GitHub username", user.email="your email")

For example, mine would be

library(usethis)
use_git_config(user.name="matackett", user.email="maria.tackett@duke.edu")

If you get the error message

Error in library(usethis) : there is no package called ‘usethis’

then you need to install the usethis package. Run the following code in the console to install the package. Then, rerun the use_git_config function with your GitHub username and email address associated with your GitHub account.

install.package("usethis")

Once you run the configuration code, your values for user.name and user.email will display in the console. If your user.name and user.email are correct, you’re good to go! Otherwise, run the code again with the necessary changes.

Packages

We will use the following packages in today’s lab.

library(tidyverse)
library(knitr)
library(broom)
library(modelr)
library(openintro) #package containing dataset

YAML:

Open the R Markdown (Rmd) file in your project, change the author name to your team name, and knit the document.

Committing and pushing changes:

• Go to the Git pane in your RStudio.
• View the Diff and confirm that you are happy with the changes.
• Add a commit message like “Update team name” in the Commit message box and hit Commit.
• Click on Push. This will prompt a dialogue box where you first need to enter your user name, and then your password.

Pulling changes:

Now, the remaining team members who have not been concurrently making these changes on their projects should click on the Pull button in their Git pane and observe that the changes are now reflected on their projects as well.

If you need a more detailed review on committing and pushing changes, see Getting Starte from Lab 01.

Exploratory Data Analysis

Team Member 1: Your turn to type!

1. Plot a histogram to examine the distribution of gift_aid. What is the approximate shape of the distribution? Also note if there are any outliers in the dataset.

2. To better understand the distribution of gift_aid, we would like calculate measures of center and spread of the distribution. Use the summarise function to calculate the appropriate measures of center (mean or median) and spread (standard deviation or IQR) based on the shape of the distribution from Exercise 1. Show the code and output, and state the measures of center and spread in your narrative. Be sure to report your conclusions for this exercise and the remainder of the lab in dollars.

3. Plot the distribution of family_income and calculate the appropriate summary statistics. Describe the distribution of family_income (shape, center, and spread, outliers) using the plot and appropriate summary statistics.

4. Create a scatterplot to display the relationship between gift_aid (response variable) and family_income (predictor variable). Use the scatterplot to describe the relationship between the two variables. Be sure the scatterplot includes informative axis labels and title.

Simple Linear Regression

Team Member 1: Knit, commit, and push your work.

All team members: Pull to see the updated .Rmd and .pdf files.

Team Member 2: Your turn to type!

5. Use the lm function to fit a simple linear regression model using family_income to explain variation in gift_aid. Complete the code below to assign your model a name, and use the tidy and kable functions to neatly display the model output. Replace X and Y with the appropriate variable names.

_____ <- lm(Y ~ X, data = _____)
tidy(_____) %>% # output model
  kable(digits = 3) # format model output

6. Interpret the slope in the context of the problem.

7. When we fit a linear regression model, we make assumptions about the underlying relationship between the response and predictor variables. In practice, we can check that the assumptions hold by analyzing the residuals. Over the next few questions, we will examine plots of the residuals to determine if the assumptions are met.

   See Checking Model Assumptions for more details. We will also discuss these in class.

   Let’s begin by calculating the residuals and adding them to the dataset. Fill in the model name in the code below to add residuals to the original dataset using the resid() and mutate() functions.

_____<- _____ %>%
  mutate(resid = residuals(_____))

8. One of the assumptions for regression is that there is a linear relationship between the predictor and response variables. To check this assumption, we will examine a scatterplot of the residuals versus the predictor variable.

   Create a scatterplot with the predictor variable on the x axis and residuals on the y axis. Be sure to include an informative title and properly label the axes.

Team Member 2: Knit, commit, and push your work.

All team members: Pull to see the updated .Rmd and .pdf files.

Team Member 3: Your turn to type!

9. Examine the plot from the previous question to assess the linearity condition.

   • Ideally, there would be no discernible shape in the plot. This is an indication that the linear model adequately describes the relationship between the response and predictor, and all that is left is the random error that can’t be accounted for in the model, i.e. other things that affect gift aid besides family income.
   • If there is an obvious shape in the plot (e.g. a parabola), this means that the linear model does not adequately describe the relationship between the response and predictor variables.

   Based on this, is the linearity condition is satisfied? Briefly explain your reasoning.

10. Recall that when we fit a regression model, we assume for any given value of \(x\), the \(y\) values follow the Normal distribution with mean \(\beta_0 + \beta_1 x\) and variance \(\sigma^2\). We will look at two sets of plots to check that this assumption holds.

    We begin by checking the constant variance assumption, i.e that the variance of \(y\) is approximately equal for each value of \(x\). To check this, we will use the scatterplot of the residuals versus the predictor variable \(x\). Ideally, as we move from left to right, the spread of the \(y\)’s will be approximately equal, i.e. there is no “fan” pattern.

    Using the scatterplot from Exercise 8 , is the constant variance assumption satisfied? Briefly explain your reasoning. Note: You don’t need to know the value of \(\sigma^2\) to answer this question.

11. Next, we will assess with Normality assumption, i.e. that the distribution of the \(y\) values is Normal at every value of \(x\). In practice, it is impossible to check the distribution of \(y\) at every possible value of \(x\), so we can check whether the assumption is satisfied by looking at the overall distribution of the residuals. The assumption is satisfied if the distribution of residuals is approximately Normal, i.e. unimodal and symmetric.

    Make a histogram of the residuals. Based on the histogram, is the Normality assumption satisfied? Briefly explain your reasoning.

Team Member 3: Knit, commit, and push your work.

All team members: Pull to see the updated .Rmd and .pdf files.

Team Member 4: Your turn to type!

12. The final assumption is that the observations are independent, i.e. one observation does not affect another. We can typically make an assessment about this assumption using a description of the data. Do you think the independence assumption is satisfied? Briefly explain your reasoning.

Using the Model

13. Calculate \(R^2\) for this model and interpret it in the context of the data.

⊕Next week, we will discuss how to account for the uncertainty in the prediction using a prediction interval.

14. Suppose a high school senior is considering Elmhurst College, and she would like to use your regression model to estimate how much gift aid she can expect to receive. Her family income is $90,000. Based on your model, about how much gift aid should she expect to receive? Show the code or calculations you use to get the prediction.

15. Another high school senior is considering Elmhurst College, and her family income is about $310,000. Do you think it would be wise to use your model calculate the predicted gift aid for this student? Briefly explain your reasoning.

Team Member 4: Knit, commit, and push your work.

All team members: Pull to see the updated .Rmd and .pdf files.

You’re done and ready to submit your work! Knit, commit, and push all remaining changes. You can use the commit message “Done with Lab 2!”, and make sure you have pushed all the files to GitHub (your Git pane in RStudio should be empty) and that all documents are updated in your repo on GitHub. Then submit the assignment on Gradescope following the instructions below.