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.