Pizza ratings, part 3.

In Exercise 19, we raised questions about two gourmet pizzas. After removing them, the resulting regression looks like this.

A plot of the residuals against the predicted values for this regression looks like this. It has been colored according to the Type of pizza.

a) What does this plot say about how the regression model deals with these two types of pizza?
We constructed another variable consisting of the indicator variable Type multiplied by Calories. Here’s the resulting regression.

b) Interpret the coefficient of Type*Cals in this regression model.

c) Is this a better regression model than the one in Exercises 17 and 19?

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Dependent variable is: Score R-squared = 64.4% R-squared (adjusted) = 59.8% s = 14.41 with 27-4 = 23 degrees of freedom Sum of Squares df Mean Square Source Regression Residual 8649.29 3 2883.10 F-ratio 13.9 4774.56 23 207.590 Variable Coeff SE(Coeff) t-ratio P-value Intercept -363.109 72.15 -5.03 0.0001 Calories 1.56772 0.2824 5.55 0.0001 25.1540 6.214 4.05 0.0005 Fat -8.82748 1.887 -4.68 0.0001