AE 12: Categorical Predictors

Pee-to-Peer Loans

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-12”.

  • Go to the Canvas and locate your AE-12 assignment to get started.

  • Upload the ae-12.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(mosaic)
library(broom)
library(knitr)
library(openintro)

loan50 <- loan50 |>
  mutate(annual_income_k = annual_income / 1000)

The data for this AE is is a sample of 10,000 loans made through a peer-to-peer lending club. The data is in the loan50 data frame in the openintro R package.

Variables

  • annual_income_k: Annual income in $1,000’s
  • verified_income: Whether borrower’s income source and amount have been verified (Not Verified, Source Verified, Verified)

Response: interest_rate: Interest rate for the loan

Analysis goal

  • Predict interest_rate using the categorical variable verified_income as a predictor
  • Include other quantitative variables and understand how they interact with verified_income

Exercise 1

Generate side-by-side boxplots of interest_rate vs. verified_income. Does it appear that there is a relationship between the two variables?

Exercise 2

Based on the output of the code below, what do you think would be the best predictions for the interest rate of a borrow with Not Verified, Source Verified, and Verified income, respectively.

favstats(interest_rate ~ verified_income, data = loan50) |> 
  kable()
verified_income min Q1 median Q3 max mean sd n missing
NA NA NA NA NA NaN NA 0 0
Not Verified 5.31 7.9600 9.44 9.9300 18.45 9.541429 2.984269 21 0
Source Verified 6.08 7.8075 10.91 16.2875 19.42 11.765500 4.270998 20 0
Verified 5.32 11.9800 14.08 21.4500 26.30 15.853333 7.694652 9 0

Exercise 3

Fit a linear model predicting interest_rate from verified_income. What is the reference level for verified_income?

Exercise 4

WITHOUT WRITING ANY CODE except for addition, subtraction, multiplication, and addition, what would the model predict the average interest_rate for each of the three levels of verified_income? How do these answers compare to your answers from Exercise 2?

Exercise 5

The linear model below predicts interest_rate from annual_income_k. Add verified_income as a predictor to this model. Do not include an interaction term. Be prepared to discuss how and why the plot changes when you add in verified_income.

ex5_model <- lm(interest_rate ~ annual_income_k, data = loan50) 
ex5_model |> 
  tidy() |> 
  kable()
term estimate std.error statistic p.value
(Intercept) 12.994265 1.2851395 10.111171 0.0000000
annual_income_k -0.016561 0.0124397 -1.331308 0.1893763 
plotModel(ex5_model) # nifty function from the mosaic package

Exercise 6

How do you think the plot above will change if you add in an interaction term between verified_income and interest_rate? AFTER thinking about it, add in an interaction term between verified_income and annual_income_k.

ex6_model <- lm(interest_rate ~ annual_income_k, data = loan50) 
ex6_model |> 
  tidy() |> 
  kable()
term estimate std.error statistic p.value
(Intercept) 12.994265 1.2851395 10.111171 0.0000000
annual_income_k -0.016561 0.0124397 -1.331308 0.1893763 
plotModel(ex6_model) # nifty function from the mosaic package

Exercise 7

Based on the model above (and the equation on the slides):

  • Write the equation of the model to predict interest rate for applicants with Not Verified income.
  • Write the equation of the model to predict interest rate for applicants with Verified income.
  • Our degrees of freedom will be \(n-p-1\). What is \(p\) in this case? Hint: it isn’t 2.

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.