AE 13: Conditions for Multiple Linear Regression

Rail Trail

Author

Driver: ____, Reporter: _____, Gopher: _____

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-13”.

  • Go to the Canvas and locate your AE-13 assignment to get started.

  • Upload the ae-13.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(broom)
library(knitr)
library(mosaic)
library(mosaicData)

rail_trail <- read_csv("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:

  • Determine whether the conditions for inference are satisfied in this multi-predictor setting.

Exercise 0

Fit a linear model to predict volume from ALL of the other predictors. The resulting model is called the “full model”. Hint: if you use the formula volume ~ . in your lm command, it will automatically include all predictors. Once you have fit your model, use tidy to print it out. Have the reporter for you group write down the model on the white board. Does the model include any interaction terms?

Exercise 1

Augment the model you created above using the augment function. Generate a scatter plot of the residuals vs. the fitted values for this model.

Exercise 2

Make two plots:

  1. Residuals vs. precip.
  2. Residuals vs. day_type.

Exercise 3

Based on the three plots you’ve made and the four on the screen, do you think the linearity condition is satisfied?

Exerise 4

We check the constant variance assumption in the same way we do with SLR. Does the constant variance condition seems to be satisfied?

Exercise 5

Generate a histogram of the residuals. If you have time, also generate a QQ-plot of the residuals. Do you believe the normality condition is satisfied?

Exercise 6

How do you think would you go about checking the independence condition?

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.