AE 11: Inference for Multiple Linear Regression

Credit Cards

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-11”.

  • Go to the Canvas and locate your AE-11 assignment to get started.

  • Upload the ae-11.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 activity are to:

  • Perform inference for multiple linear regression
  • Conduct/interpret hypothesis tests
  • Construct/interpret confidence intervals

Exercise 0

Fit and display two linear regression models predicting Limit from Income and Rating. In one, include an interaction term between the two variables and in the other, do not.

Exercise 1

Consider the model without an interaction term. Perform a hypothesis test on Rating (fill in the blanks where appropriate:

  1. Set hypothesis: \(H_0: \beta_{Rating} [fill in]\) vs. \(\beta_{Rating} [fill in]\). Restate these hypothesis in words: [fill in]
  2. Calculate test statistics and p-value: The test statistic is \([fill in]\). The p-value is \([fill in]\).
  3. State the conclusion: [fill in]

Exercise 2

Consider the model with an interaction term. Interpret the p-value associated with Income and the p-value associated with the interaction term.

Exercise 3

Generate 95% confidence intervals for the model without an interaction term. Hint: use the tidy function with the argument conf.int = TRUE. Interpret the confidence interval for Income and explain why the combination of p-value and confidence interval makes sense.

Exercise 4

What does it mean for two things to be independent in statistics (feel free to use google)? Do we think our p-values/confidence intervals are independent across variables?

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.