Zagat’s publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, décor, 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, décor, and service. Sources: Extracted from Zagat Survey 2013, New York City Restaurants; and Zagat Survey 2012–2013, Long Island Restaurants.

a. Construct a scatter plot. For these data, b₀ = 46.7718 and b₁ = 1.4963.

b. Assuming a linear relationship, use the least squares method to compute the regression coefficients b₀ and b₁.

c. Interpret the meaning of the Y intercept, b₀, and the slope, b₁, 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?