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