Zagat's publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, décor, service, and cost per person for a sample of 50 restaurants located in a city and 50 restaurants located in a suburb. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service and a dummy variable concerning location (city vs. suburban). For (a) through (m), do not include an interaction term.
Sources: Extracted from Zagat Survey 2010, New York City Restaurants; and Zagat Survey 2009-2010, Long Island Restaurants.
a. State the multiple regression equation.
b. Interpret the regression coefficients in (a).
c. Predict the cost for a restaurant with a summated rating of 60 that is located in a city and construct a 95\% confidence interval estimate and a $95 \%$ prediction interval.
d. Perform a residual analysis on the results and determine whether the regression assumptions are satisfied.
e. Is there a significant relationship between price and the two independent variables (summated rating and location) at the 0.05 level of significance?
f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.
g. Construct a $95 \%$ confidence interval estimate of the population slope for the relationship between cost and summated rating.
h. Compare the slope in (b) with the slope for the simple linear regression model of Problem 13.5 on page 531. Explain the difference in the results.
i. Compute and interpret the meaning of the coefficient of multiple determination.
j. Compute and interpret the adjusted $r^2$.
k. Compare $r^2$ with the $r^2$ value computed in Problem 13.17 (b) on page 537 .
1. Compute the coefficients of partial determination and interpret their meaning.
m. What assumption about the slope of cost with summated rating do you need to make in this problem?
n. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.
o. On the basis of the results of (f) and (n), which model is most appropriate? Explain.