Chapter 13, Problem 5PS

Zagat’s publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, decor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, decor, and service.

a. Construct a scatter plot, For these data, $b_0=-46.7718\text{ and }{b}_1=\mathrm{1.4963.}$

b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients $b_0\text{ and }{b}_1$ .

c. Interpret the meaning of the Y intercept. $b_0$ , and the slope, $b_1$ , in this problem.

d. Predict the mean cost per person for a restaurant with a summated rating of 50.

e. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal?