Diagnostics and Inferences for a Simple Linear Regression:

Download this Minitab project. The data consists of the average ratings of 4808 beers along with their ABV (alcohol by volume) and their bitterness in IBU (international bittering units). The data were downloaded from the Rich Data guide to beer.

Perform two simple linear regressions in Minitab to predict the average rating of a beer based on (a) its ABV and (b) its IBU value. For each predictor:

1. Use Minitab to generate a scatter plot with a line of best fit:
   • From the top menu bar, select Stat > Regression > Fitted Line Plot....
   • Select the appropriate response and predictor.
   • Select Linear for the Type of Regression Model.
2. Print out the scatter plot.
3. Annotate the printout with a description of the trend and its strength.
4. Use Minitab to estimate the linear regression model using Stat > Regression > Regression > Fit Regression Model....
   • Important: Be sure to also generate the diagnostic plots by clicking the Graphs... button in the dialog box, and selecting the Four in one radio button from the resulting window.
5. Print the session window and the diagnostic plots.
6. Annotate the printout with the estimate of the linear regression model.
7. Annotate the printout with your interpretation of the slope and intercept of the linear regression model.
8. Give your interpretation of the diagnostic plots. Does it appear that the last four assumptions of the simple linear model with normal residuals hold? If not, how do the diagnostic plots show deviation from the violated assumption(s)?
9. Regardless of your conclusion from the diagnostic plots, test the hypothesis that the predictor is linearly associated with the average beer rating at the \(\alpha = 0.01\) significance level.
10. Is the predictor associated with the average beer rating? Does this mean that the predictor caused the average beer rating? Explain your reasoning.