Learning goals

By the end of the lab you will be able to…

• Use model selection to identify candidate models
• Use the appropriate model summary statistics to select the best fit model
• Interpret main effects and interactions in the multiple linear regression model

The data

The data from this lab comes from the the article FiveThirtyEight The Ultimate Halloween Candy Power Ranking by Walt Hickey. To collect data, Hickey and collaborators at FiveThirtyEight set up an experiment people could vote on a series of randomly generated candy matchups (e.g. Reeses vs. Skittles). Click here to check out some of the match ups.

The data set contains the characteristics and win percentage from 85 candies in the experiment. The variables are

Use the code below to load the data from the candy_rankings data frame in the fivethirtyeight R package.

candy <- fivethirtyeight::candy_rankings

Exercises

The goal of this analysis is to use linear regression to determine what makes the best candy. We’ll define “best” as the candy that can win the highest percentage of match ups.

1. Before fitting our model, let’s take a look at the model used by author Walt Hickey in the FiveThirtyEight article. He fits a model using nine candy characteristics. The output can be found within the text of the article.

   • On average, how far are the win percentages predicted from his model from the actual win percentages? Show the calculation or briefly explain how you obtain this value.

Now it’s your turn to build a model. For the model selection, consider all relevant variables in the data set as potential predictors, regardless of whether they’re in the model in the FiveThirtyEight article.

1. Use backward model selection with AIC as the selection criteria to choose a candidate model. Add include = FALSE in the header of the code chunk with the model selection code, so the step-by-step output does not print in the knitted PDF.

   • Which variable was removed in the first step of the selection process?
   • Neatly display the model selected by backward selection using 3 digits.

2. Next, use forward model selection with BIC as the selection criteria to choose a candidate model. Add include = FALSE in the header of the code chunk with the model selection code, so the step-by-step output does not print in the knitted PDF.

   • Which 2 variables are included in the model after the second step?
   • Neatly display the final model selected by forward selection using 3 digits.

3. There are some variables selected by the model selection procedure in Exercise 2 that were not included in the selection procedure in Exercise 3. Use a Nested F test to determine if there is evidence that at least one of the additional variables selected in Exercise 2 are useful predictors of win percentage. Use \(\alpha = 0.05\).

   • State the null and alternative hypotheses in statistical notation.
   • Display the output from the Nested F test.
   • State your conclusion in the context of the data.

4. Let’s use model summary statistics to choose the model that is the best fit for the data - either the model selected in Exercise 2 or the model selected in Exercise 3. Briefly explain your choice using appropriate model summary statistic, \(R^2\) or Adjusted \(R^2\), to support your response.

5. Use the model chosen in the previous exercise:

   • Describe the type of candy whose expected win percentage is represented by the intercept.
   • Interpret the coefficient of chocolate in the context of the data.

6. Plot the relationship between the sugar percentile and win percentage with the points colored based on whether the candy has crisped rice, wafers or cookie. Include lines on the plot to more clearly see the relationship between sugar percentile and win percentage based on whether the candy has crisped rice, wafers or cookie.

   • Does there appear to be an interaction between sugar percentile and whether the candy has crisped rice, wafers or cookie? Briefly explain your response.

7. Add the interaction between sugarpercent and crispedricewafer to the model selected in Exercise 5. Neatly display the updated model using 3 digits.

   • Interpret the effect of sugar percentile on win percentage for candy that does have crisped rice, wafers or cookie.

8. Is there evidence that the effect of sugar percentile differs based on whether candy has crisped rice, wafers or cookie? Briefly explain, including the results used to make the determination.

9. Use the model to describe what generally makes a good candy, i.e. one with a high win percentage.

Submission

• Select one team member to upload the team’s PDF submission to Gradescope.
• Be sure to mark every team member’s name on Gradescope.
• Associate the “Workflow & formatting” graded section with the first page of your PDF, and mark the page associated with each exercise. If any answer spans multiple pages, then mark all pages.

There should only be one submission per team on Gradescope.

Grading (50 pts)

Grading notes:

• The “Workflow & formatting” grade is to assess the reproducible workflow and team work. This includes having at least one meaningful commit by each team member and updating the name and date in the YAML.

There should only be one submission per team on Gradescope.