AE 14: Model Comparison

Tips Data

Author

Driver: ____, Reporter: _____, Gopher: _____

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-14”.

  • Go to the Canvas and locate your AE-14 assignment to get started.

  • Upload the ae-14.qmd and tip-data.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(broom)
library(yardstick)
library(ggformula)
library(patchwork)
library(knitr)
library(kableExtra)

tips <- read_csv("data/tip-data.csv")

What factors are associated with the amount customers tip at a restaurant? To answer this question, we will use data collected in 2011 by a student at St. Olaf who worked at a local restaurant.1

The variables we’ll focus on for this analysis are

  • Tip: amount of the tip
  • Meal: which meal this was (Lunch, Dinner, Late Night)
  • Party: number of people in the party
  • Age: Age category of person paying the bill (Yadult, Middle, SenCit)

Analysis goal

The goals of this activity are to:

  • Use ANOVA to determine whether our model is useful as a whole
  • Begin thinking about \(R^2\) in a multivariate setting

Exercise 0

Complete the following to clean and then observe your data:

  1. Use drop_na to remove any rows where Party is missing.
tips <- tips |> 
  _______   # drop missing values from party
  1. Generate a bar chart of the variable Meal.
# insert code here
  1. Run the following code and generate the same bar chart as above. You can even copy and paste your code. What’s the difference between the two plots? What do you think fct_relevel does?
tips <- tips |> 
  mutate(
    Meal = fct_relevel(Meal, "Lunch", "Dinner", "Late Night"),
    Age  = fct_relevel(Age, "Yadult", "Middle", "SenCit")
  )

# Generate plot here

Exercise 1

Fit a linear model to predict Tips from Party and Age.

Exercise 2

Pipe the model you generated in the previous Exercise into the function anova.

Exercise 3

Based on the output above, compute \(SSTotal\), \(SSError\), and \(SSModel\). You should only need to use addition and/or subtraction.

Exercise 4

Pipe your model into the glance function. Identify, the F-statistic and p-value for an F-test of this model. Interpret the outcome of your test in the context of the problem. Be prepared to discuss the difference between this p-value and the p-values from the individual model coefficients.

Exercise 5

What is the \(R^2\) value for this model?

Exercise 6

Fit the full model. What is it’s \(R^2\)? Does this model have a higher or lower \(R^2\) than the previous model? Does this mean it is a better model? Be prepared to discuss.

Exercise 7

The following code converts the numerical variable Bill into a new categorical variable Bill_factor. Essentially, each different number in Bill is treated as it’s own category. Fit a model predicting Tip from Bill_factor. What is your R^2? Think about the implications of this and what it means for the usefullness of \(R^2\).

tips <- tips |> 
  mutate(Bill_factor = factor(Bill))

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.

Footnotes

  1. Dahlquist, Samantha, and Jin Dong. 2011. “The Effects of Credit Cards on Tipping.” Project for Statistics 212-Statistics for the Sciences, St. Olaf College.↩︎