I am interested in the effect of age on outcome Y.
I have two nested linear regression models to test linear and quadratic effects of age:
- Y= $\beta_0$ + $\beta_1$ some_covariate + $\beta_2$ Age + error
- Y= $\beta_0$ + $\beta_1$ some_covariate + $\beta_2$ Age + $\beta_3$ Age$^2$ + error
I have calculated η2 (not partial η2) as measures of effect size for the individual predictors.
Let's assume that the effect sizes are as follows:
- $\eta^2$ age= .05
- $\eta^2$ age= .03 & age$^2$= .04
For model (1) I could state that the effect size of age is .05.
If I want to make a statement about the effect size of age in the second model, am I allowed to add the two effect sizes up? E.g. the $η^2$ for age in model two is .07?