Insurance (life expectancy). Insurance companies base their premiums on many factors, but basically all the factors are variables that predict life expectancy. Life expectancy varies from place to place. Here’s a regression that models Life Expectancy in terms of other demographic variables that we saw in Exercise 44 of Chapter 18.

(Refer to that exercise for variable definitions and units.)

Here’s another regression with a dummy variable for Alaska added to the regression model.

b) What does the coefficient for the dummy variable for Alaska mean? Is there evidence that Alaska is an outlier in this model?

c) Which model would you prefer for understanding or predicting Life Expectancy? Explain.

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Dependent variable is: Life exp R-squared = 67.0% R-squared (adjusted) = 64.0% s = 0.8049 with 50-5 = 45 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 59.1430. 22.8 4 14.7858 Residual 29.1560. 45 0.647910 Variable Coeff SE(Coeff) t-ratio P-value Intercept 69.4833 1.325 52.4 0.0001 Murder -0.261940 0.0445 -5.89 0.0001 HSGrad 0.046144 0.0218 2.11 0.0403 Income 1.24948e-4 0.0002 0.516 0.6084 Illiteracy 0.276077 0.3105 0.889 0.3787 a) The state with the highest leverage and largest Cook's Distance is Alaska. It is plotted with an X in the residuals plot. Here are a scatterplot of the residuals and a normal probability plot of the leverage values. What evidence do you have from these diagnostic plots that Alaska might be an influential point? 69 70 71 72 Predicted