AE 10: Multiple Linear Regression

Credit Cards

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-10”.

  • Go to the Canvas and locate your AE-10 assignment to get started.

  • Upload the ae-10.qmd file into the folder you just created. The .qmd and PDF responses are due in Canvas. You can check the due date on the Canvas assignment.

Packages + data

library(tidyverse)
library(ggformula)
library(broom)
library(knitr)
library(ISLR2)
library(GGally)
library(yardstick)

The data for this AE is from the Credit data set in the ISLR2 R package. It is a simulated data set of 400 credit card customers. We will focus on the following variables:

Predictors

  • Income: Annual income (in 1000’s of US dollars)
  • Rating: Credit Rating

Response

  • Limit: Credit limit

Analysis goal

The goals of this analysis are to fit a linear regression model that has the following predictors:

  • Income
  • Rating
  • An interaction term between the two

Exercise 0

What is a credit rating and what is a credit limit as it applies to a credit card? The primary credit rating in the US is called a FICO score. Based on the data, do you think that Rating corresponds to the borrower’s FICO score?

Exercise 1

Use the function ggpairs from the GGally package (already loaded) to create a matrix of plots and correlations for our three variables of interest. Note that you will have to use select to select the four columns you are interested in. Which variable do you think will be the best predictor of Limit?

Exercise 1B (Optional)

If you have extra time, examine the variables individually and comment on anything that you think is relevant.

Exercise 2

Fit a linear model with just Income as the predictor and get the p-value associated with it’s coefficient. Is it statistically significant?

Exercise 3

Fit a linear model with just Rating as the predictor and get the p-value associated with it’s coefficient. Is it statistically significant?

Exercise 4

Fit a model with both Income and Rating as predictors. Find a spot on the white board to write down an equation representing the fitted model. How do the coefficients and p-values of Income and Rating compare to those in the two models above? Discuss what you see and the possible reasons you see them.

Exercise 5

Interpret all coefficients in the model.

Exercise 6

What is the predicted credit limit for an single borrower with a credit rating of 700 and an annual income of $59,000? Include a 90% confidence interval. Hint: make a new tibble and use the predict function. How would you interpret this interval in context?

Exercise 7

Add an interaction term between Rating and Income. Interpret all coefficients in context. What do you notice about the p-values now?

Exercise 8

What is the predicted credit limit for an single borrower with a credit rating of 700 and an annual income of $59,000? Include a 90% confidence interval. How does it compare to your answer to Exercise 6.

Exercise 9 (Optional)

Note that this data set only considers borrowers who have actually been granted loans. How does this impact the generalizability of our analysis?

To submit the AE

Important
  • Render the document to produce the PDF with all of your work from today’s class.
  • Upload your QMD and PDF files to the Canvas assignment.