The model corresponding to the analysis for Table 7.7 has an intercept, a dummy variable for the fifth birth, a continuous predictor of centered age (age minus the average age), and the product of the...

The model corresponding to the analysis for Table 7.7 has an intercept, a dummy variable for the fifth birth, a continuous predictor of centered age (age minus the average age), and the product of the dummy variable and centered age.

(1) Write down a model equation.

(2) Verify that the intercept is the average for the first-born, and that the coefficient for the dummy variable is the difference between the two groups, both of these when age is equal to its average.

(3) Verify that the coefficient for the product measures how the change in birthweight from first to last birth depends on age.