Introduction

In today’s lab, you’ll use simple linear regression to analyze the relationship between the admissions rate and total cost for colleges and universities in the United States.

Getting started

• Go to the sta210-fa21 organization on GitHub. Click on the repo with the prefix lab-02. It contains the starter documents you need to complete the lab.

• Clone the repo and start a new project in RStudio. See the Lab 01 instructions for details on cloning a repo, starting a new R project and configuring git.

library(tidyverse)
library(broom)
library(knitr)

scorecard <- read_csv("data/scorecard.csv")

Exercises

Note: Include axis labels and an informative title for all plots. Use the kable function to neatly print tables and regression output.

1. Create a histogram to examine the distribution of admrate and calculate summary statistics for the center (mean and median) and the spread (standard deviation and IQR).

2. Use the results from the previous exercise to describe the distribution of admrate. Include the shape, center, spread, and if there are potential outliers.

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

4. The goal of this analysis is to fit a regression model that can be used to understand the variability in the cost of college based on the admission rate. Before fitting the model, let’s look at the relationship between the two variables. Create a scatterplot to display the relationship between cost and admissions rate. Describe the relationship between the two variables based on the plot.

5. Does the relationship between cost and admissions rate differ by type of college? Modify the plot from the previous exercise visualize the relationship by type of college.

6. Describe two new observations from the scatterplot in Exercise 5 that you didn’t see in the scatterplot from Exercise 4.

7. Fit the linear regression model. Display the confidence interval for the coefficients in the output. Use the kable function to neatly display the results.

8. Consider the model from the previous exercise.

   • Interpret the slope in the context of the problem.
   • Does the intercept have a meaningful interpretation? If so, write the interpretation in the context of the problem. Otherwise, explain why the interpretation is not meaningful.

9. Does the data provide evidence of a statistically significant linear relationship between cost and admissions rate? Conduct a hypothesis test to answer this question. In your response

   • State the null and alternative hypotheses used to answer this question in words and in mathematical notation.
   • What is the test statistic? State with the test statistic means in context.
   • What distribution was used to calculate the p-value?
   • State your conclusion for the test in context.

10. Interpret the 95% confidence interval for the slope in context. Then indicate whether or not it is consistent with the results of the hypothesis test from the previous exercise. Briefly explain your response.

Submission

Before you wrap up the assignment, make sure all documents are updated on your GitHub repo. We will be checking these to make sure you have been practicing how to commit and push changes.

Remember – you must turn in a PDF file to the Gradescope page before the submission deadline for full credit.

To submit your assignment:

• Go to http://www.gradescope.com and click Log in in the top right corner.

• Click School Credentials ➡️ Duke NetID and log in using your NetID credentials.

• Click on your STA 210 course.

• Click on the assignment, and you’ll be prompted to submit it.

• Mark the pages associated with each exercise. All of the pages of your lab should be associated with at least one question (i.e., should be “checked”).

• Select the first page of your .PDF submission to be associated with the “Workflow & formatting” section.

Grading (50 pts)

Grading notes:

• The “Workflow & formatting” grade is to assess the reproducible workflow. This includes having at least 3 informative commit messages and updating the name and date in the YAML.