AE 07: Multiple Linear Regression

Credit Cards

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-07”.

  • Go to the Canvas and locate your AE-07 assignment to get started.

  • Upload the ae-07.qmd file into the folder you just created.

Packages + data

library(tidyverse)
library(ggformula)
library(broom)
library(mosaic)
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:

Response

  • Limit: Credit limit

Predictors

  • Everyone:

    • Rating: Credit Rating

  • Group 1:

    • Age
    • Own

  • Group 2:

    • Balance
    • Student

  • Group 3:

    • Education
    • Region

  • Group 4:

    • Income
    • Married

Analysis goal

The goals of this analysis is to fit a multiple linear regression model that that predicts a person’s credit limit.

Exercise 0

Look at the documentation for the data using ?Credit and Google to figure out what each of your variables represents. 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. Use favstats on Rating. Do you think that Rating corresponds to the borrower’s FICO score?

Without writing any more code (i.e. just using what you know about the world):

  • Do you think Rating will be a good predictor of Limit?
  • In addition to Limit, everyone has been assigned two additional variables, one quantitative and one categorical. Do you think these two variables will be predictive of Limit?

Exercise 1

Use the function ggpairs from the GGally package (already loaded) to create a matrix of plots and correlations for your four 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?

Credit |> 
  select(Limit, Rating) |> # add your extra variables here.
  ggpairs()

Exercise 2

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 3

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

Exercise 4

Fit a model with both Income and your second quantitative variable 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

Use head to look at the first observation in the data set. Use addition, subtraction, multiplication, and division to figure out what credit limit your model would predict for a person with the same characteristics of this person.

Exercise 7

Now use the predict function to verify the value you computed in the previous exercise and compute a 90% prediction interval. How would you interpret this interval in context?

Exercise 8

Fit a linear model predicting Limit from ONLY your categorical variable. What is the reference level?

Exercise 9

WITHOUT WRITING ANY CODE except for addition, subtraction, multiplication, and addition, what would the model predict the average Limit to be for each of the level of your categorical variable?

Exercise 10

Compute the average Limit for each level in your categorical variable. Hint: you can use “formulas” (i.e. repsonse ~ explanatory) in the mean function from the mosaic package. How do these answers compare to your answers from Exercise 9?

Exercise 11

Fit a linear model using your quantitative and your categorical variable as predictors (don’t use Rating). Use the function plotModel to make a nifty plot for your model. Your syntax should look like plotModel(model_name).

Exercise 12

Your model contains one line for every level of your categorical variable. On the board, write out the equations for two of them.

Exercise 13

How do you think the plot above will change if you add in an interaction term between your variables? AFTER thinking about it, add in an in the interaction term and plot the model using plotModel.

Exercise 14

Your model contains one line for every level of your categorical variable. On the board, write out the equations for two of them.

Exercise 15

Fit a model with your quantitative predictor, Rating, and an interaction term. Write your model on the board.

Exercise 16 (Optional)

Look back at all of the models that you’ve fit. If you compare the p-values for the same variable across multiple models, what do you notice?

Exercise 17 (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 HTML file with all of your work from today’s class.
  • Upload your QMD and HTML files to the Canvas assignment.