Pizza ratings
Manufacturers of frozen foods often refor- mulate their products to maintain and increase customer satisfaction and sales. So they pay particular attention to evaluations of their products in comparison to their com- petitors' products. Frozen pizzas are a major sector of the frozen food market, accounting for $2.84 billion in sales in 2007 (www.aibonline.org/resources/statistics/2007pizza.htm). The prestigious Consumer's Union rated frozen pizzas for flavor and quality, assigning an overall score to each brand tested. A regression model to predict the Consumer's Union score from Calories, Type (1 = cheese, 0 = pepperoni), and fat content gives the following result:
Dependent variable is: Score
R-squared = 28.7% R-squared (adjusted) = 20.2% s = 19.79 with 29 - 4 = 25 degrees of freedom
Source Sum of Squares df Mean Square F-ratio
Regression 3947.34 3 1315.78 3.36
Residual 9791.35 25 391.654
Variable Coeff SE(Coeff) t-ratio P-value
Large 5.00967 2.104 2.38 0.0203
Very Large 3.41058 3.230 1.06 0.2951
a) Why is there no coefficient for Medium?
b) Explain how the coefficients of Small, Large, and Very Large account for the size of the city in this model.