Regression-Oriented Exam Questions
Answer the following questions on the basis of what you learn from the data collected by the "Eating Marvelously Pub (EMP)" restaurant group. For questions (1)-(13), use only the four variables provided in the dataset.
- Give a 95%-confidence interval for your estimate of average customer satisfaction.
- (Session 3) Roughly how large a sample would be required to estimate mean customer satisfaction with a margin of error (at the 95%-confidence level) of only 1 point?
- Give a 95%-confidence interval for the average satisfaction of customers who end up waiting 15 minutes before being seated.
- Which of the maitres d’hotel is currently being assigned the larger parties (on average)?
- Give a 95%-confidence interval for the percentage of all parties currently being assigned to Franz.
- Predict how satisfied a guest will be if his group must wait 10 minutes to be seated, and is then assigned to Hans.
- What is the margin of error for your prediction in (6)?
- (Session 4) In the model incorporating all three explanatory variables, the patron appearing in row 403 of the “Data” tab (with a satisfaction score of 17) has the highest leverage. This is because his party (a) ___________, and (b) ___________ . (Fill in two explanations.)
- In the dataset description, I noted that larger parties have, on average, been less satisfied than smaller parties. Cite a number which justifies this statement.
- Still, I observed that there's no real evidence that party-size plays a role as a determinant of customer satisfaction once waiting time and maitre d' identity are taken into account. Cite a number which justifies this statement.
For the next few questions ((11)-(16)), please leave the party-size variable out of your analyses. (Which of the other original variables to use in each question is up to you.)
- How much of the variation in customer-to-customer satisfaction levels can be explained by the facts that waiting times vary, and that some parties are put in Hans’ care while others are assigned to Franz?
- Estimate the average decrease in customer satisfaction associated with each incremental minute of waiting.
- What is the margin of error in your estimate in (12)?
Session 3: (14)-(16)
- You suspect that a customer’s satisfaction decreases more and more rapidly as his or her waiting time grows. What new variable would you add to your model to explore whether this is so?
- Add that variable to your model (continuing, for now, to ignore party-size). How strong is the evidence that this variable belongs in your model? (Cite a relevant significance level.)
- Taking this new variable into account, how much less satisfied would you expect a party assigned to Franz to be if they had to wait 16 minutes rather than 15 before being seated?
Resume Session 2: Now, ignore the variable you introduced in (14-(16), but resurrect party-size in your analysis.
- You want to explore whether Hans and Franz have differing abilities to satisfy customers, as the party size varies. What new variable would you add to your model to explore this possibility?
- Add this variable to your model. You should find overwhelmingly strong evidence that it does play a role in the relationship. With respect to this new model, what appears to be the optimal (i.e., customer satisfaction maximizing) assignment-of-maitres-d’-to-parties-of-varying-sizes policy?