AE 05: Multicollinearity

Published

October 22, 2024

Important

Go to the course GitHub organization and locate your ae-05 repo to get started.

Render, commit, and push your responses to GitHub by the end of class to submit your AE.

library(tidyverse)
library(knitr)
library(tidymodels)
library(rms) #calculate VIF

Introduction

The Pioneer Valley Planning Commission (PVPC) collected data at the beginning a trail in Florence, MA for ninety days from April 5, 2005 to November 15, 2005. Data collectors set up a laser sensor, with breaks in the laser beam recording when a rail-trail user passed the data collection station. The data were collected from by Pioneer Valley Planning Commission via the mosaicData package.

We will use the following variables in this analysis:

Outcome:

  • volume estimated number of trail users that day (number of breaks recorded)

Predictors

  • hightemp daily high temperature (in degrees Fahrenheit)

  • avgtemp average of daily low and daily high temperature (in degrees Fahrenheit)

  • season one of “Fall”, “Spring”, or “Summer”

  • precip measure of precipitation (in inches)

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

Part 1

Exercise 1

  • Fit the regression model using high temperature, average temperature, season, and precipitation to predict volume.

  • Are there any coefficients that may be not what you expected?

# add code here

Exercise 2

  • Use the formula

\[ VIF_j = \frac{1}{1 - R^2_j} \]

to calculate the VIF for avgtemp.

# add code here

Exercise 3

Based on the VIF from the previous exercise, does avgtemp have a linear dependency with one or more other predictors? Explain.

Exercise 4

  • Fill in the name of the model from Exercise 1 to calculate VIF for all predictors. (Remove #| eval: false after you’ve filled in the code.)

  • Are there predictors with linear dependencies? If so, which ones?

vif(____)

Part 2

Exercise 5

Let’s try to deal with the mulitcollinearity by removing one of the predictors that are linearly dependent. Choose a final model using this strategy.

# add code here

Submission

To submit the AE:

Render the document to produce the PDF with all of your work from today’s class.

Push all your work to your AE repo on GitHub. You’re done! 🎉