Exam MAS-I Practice Question 108
Study guide: Exam MAS-I
An insurer regresses annual operating expense y ($000s) on the number of policies x (hundreds) for its 8 branch offices. Management believes expenses are almost entirely variable with the number of policies. Two models are fitted in R.
Model 1, with an intercept:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.0425 2.6175 0.780 0.465
policies 2.4229 0.1072 22.607 4.9e-07 ***
Residual standard error: 2.267 on 6 degrees of freedom
Multiple R-squared: 0.9884, Adjusted R-squared: 0.9865
Model 2, through the origin:
Estimate Std. Error t value Pr(>|t|)
policies 2.50251 0.03189 78.47 1.4e-11 ***
Residual standard error: 2.203 on 7 degrees of freedom
Multiple R-squared: 0.9989, Adjusted R-squared: 0.9987
Which choice is best supported, for the reason given?
- A) Model 2, because its R-squared of 0.9989 is higher than Model 1's 0.9884
- B) Model 1, because its residual sum of squares is smaller than Model 2's
- C) Model 1, because Model 2's residuals do not sum to zero, so its slope is biased
- D) Model 2, because dropping a parameter always lowers the residual standard error
- E) Model 2, because the intercept is not significant and Model 2's residual standard error is lower
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