Question: Based on the data in Zagat.mtp, build three regression models for Cost (the dependent variable) using the independent variables as given in parts (a) — (c). The definition of the variables can be found on page 137 of the course packet.

(a) Model #1: use Food as the independent variable.

(b) Model #2: use Decor as the independent variable.

(c) Model #3: use Service as the independent variable.

(d) Which of the three models is the best model? Provide the criteria that your choice is based on. What is the practical implication of your finding?

(e) Use the best model you found in part (d) to predict the cost for dinner at a restaurant with ratings of 21 on Food, 18 on Decor, and 20 on Service.

The following parts all refer to Model #1.

(f) Interpret the slope for Food. Does the sign of the slope make sense in the real world?

(g) Produce the Fitted Line Plot, and check if there are any outliers and/or influential points. Briefly explain the practical meaning of outliers and influential points in the context of this data set.

(h) If you are looking for a restaurant that costs less than the predicted cost (i.e., a bargain restaurant), should you search among the restaurants that are above or below the line on the Fitted Line Plot? Briefly explain.

(i) What proportion of the variation in Cost is explained by the regression model? Flow is this proportion related to the improved accuracy of the predicted cost of a restaurant using the regression model as opposed to not using the regression model?