Two actuaries are analyzing dental claims for a group of n = 100 participants. The predictor variable is sex, with 0 and 1 as possible values.

Actuary 1 uses the following regression model:

[[math]] Y = \beta + \epsilon. [[/math]]

Actuary 2 uses the following regression model:

[[math]] Y = \beta_0 + \beta_1 \times \textrm{Sex} + \epsilon. [[/math]]

The residual sum of squares for the regression of Actuary 2 is 250,000 and the total sum of squares is 490,000.

Calculate the F-statistic to test whether the model of Actuary 2 is a significant improvement over the model of Actuary 1.

• 92
• 93
• 94
• 95
• 96

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: C

The model of Actuary 1 is the null model and hence values from it are not needed. The solution is

[[math]] F = \frac{(TSS-RSS)/1}{RSS/(n-2)} = \frac{490,000 − 250,000}{250,000/98} = 94.08. [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.