In A Regression Of Weight On Height Involving 51 Students

In a regression of weight on height involving 51 students, 36 males and 15 females, the following regression results were obtained:15
1.
In a regression of weight on height involving 51 students,

2.

In a regression of weight on height involving 51 students,

3.

In a regression of weight on height involving 51 students,

where weight is in pounds, height is in inches, and where
Dum sex = 1 if male
= 0 if otherwise
Dumht. = the interactive or differential slope dummy
a. Which regression would you choose, 1 or 2? Why?
b. If 2 is in fact preferable but you choose 1, what kind of error are you committing?
c. What does the dum sex coefficient in 2 suggest?
d. In Model 2 the differential intercept dummy is statistically significant whereas in Model 3 it is statistically insignificant. What accounts for this change?
e. Between Models 2 and 3, which would you choose? Why?
f. In Models 2 and 3 the coefficient of the height variable is about the same, but the coefficient of the dummy variable for sex changes dramatically. Do you have any idea what is going on?
To answer questions (d), (e), and (/) you are given the following correlation matrix.

In a regression of weight on height involving 51 students,

The interpretation of this table is that the coefficient of correlation between height and dum sex is 0.6276 and that between dum sex and dumht. is 0.9971.

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