(a)
The linear regression model is,
where H is categorical variable with value 1 for High School degree only (iii) and 0 for College degree (i) and High School degree plus some college (ii)
HC is categorical variable with value 1 for High School degree plus some college (ii) and 0 for College degree (i) and High School degree only (iii)
For category (i), HC = H = 0, the linear model becomes,
For category (iii), HC = 0 and H = 1, the linear model becomes,
Thus, is the parameter that measure between categories (iii) and (i) with age.
(b)
Now, if the slope of the regression lines with age are equal in categories (i) and (ii), then HC * age parameter in the previous linear model should be omitted.
Then for category (ii), HC = 1, H = 0
thus, the slopes for both categories (i) and (ii) is
Again here, is the parameter that measure between categories (iii) and (i) with age.
For category (i), HC = H = 0, the linear model becomes,
For category (iii), HC = 0 and H = 1, the linear model becomes,
Thus, is the parameter that measure between categories (iii) and (i) or (ii) with age.
R. A. Miech and M. J. Shanahan investigated the association of de- pression with age and...
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