In Problem, you used the summated rating of a restaurant to predict the cost of a meal. Th...

In Problem, you used the summated rating of a restaurant to predict the cost of a meal. The data are stored in Restaurants. Using the results of that problem, b1 = 1.2409 and

a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?

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b. Construct a 95% confidence interval estimate of the population slope, β1.

Problem

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 price per person, based on a variable that represents the sum of the ratings for food, décor, and service.

Sources: Extracted from Zagat Survey 2010, New York City Restaurants; and Zagat Survey 2009–2010, Long Island Restaurants.

a. Construct a scatter plot. For these data, b0 = - 28.1975 and b1 = 1.2409.

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b. Assuming a linear cost relationship, use the least-squares method to compute the regression coefficientsb0 and b1.

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c. Interpret the meaning of the Y intercept, b0 and the slope, b1, in this problem.

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