AE 17: Multicollinearity

Rail Trail

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-17”.

  • Go to the Canvas and locate your AE-17 assignment to get started.

  • Upload the ae-17.qmd and rail_trail.csv files 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(GGally)
library(broom)
library(knitr)
library(mosaic)
library(mosaicData)

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

The data for this AE is based on data from the Pioneer Valley Planning Commission (PVPC) and is included in the mosaicData package. The PVPC collected data 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. More information can be found here.

Analysis goal

The goals of this activity are to:

  • Detect and remedy multicollinearity in our data

Exercise 0

Fit a linear model to predict volume from ALL of the other predictors. The resulting model is called the “full model”.

Exercise 1

Create a new data frame called rail_trail_new with two new columns, hightemp_c and avgtemp_c. These two new columns should store the hightemp and avgtemp measured in Celsius rather than Fahrenheit. Note that the formula to convert between Fahrenheit and Celsius is \(C = (F-32)\times \frac{5}{9}\). Make sure hightemp and avgtemp are still in your data set.

Exercise 2

Try to refit the full model on your data. Do you notice anything odd about your coefficients? If so, what do you think is happening?

Exercise 3

Add a comment next to each line of code explaining what that line of code is doing.

library(corrplot)

rail_trail |> # Take the rail_trail data set and then
  select(-volume) |> # What do I do
  select(where(is.numeric)) |> # What do I do
  cor() |>   # What do I do
  corrplot(method="number") # What do I do

rail_trail |> 
  select(-volume) |> # What do I do
  ggpairs()

Exercise 4

Based on the output from the previous exercise, do you have reason to believe that our data is exhibiting multicollinearity?

Exercise 5

Pipe the model you fit in Exercise 0 (i.e. not including the variable measured in Celcius) into the function vif. Are any of the vif’s concerning? If so, which ones.

Exercise 6

Fit two models:

  • m1: use all predictors except for avgtemp
  • m2: use all predictors except for hightemp
  • m3: average avgtemp and hightemp together and use it instead of either avgtemp and hightemp

Exercise 7

Use glance to compute the \(R^2_{adj}\), AIC, and BIC for both of these models. Which should we choose?

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.