Data from a random sample of 100 college students were used to estimate the following multiple regression equation:

where Y is the student’s height (inches), X₁ is a dummy variable equal to 1 if the student is female and 0 if male, X₂ is the biological mother’s height (inches), X₃ is the biological father’s height (inches), and the standard errors are in parentheses.

a. Which (if any) of the coefficients other than the intercept are statistically significant at the 5 percent level?

b. Interpret each of the coefficients other than the intercept. Does the magnitude of each seem plausible or implausible?

c. Interpret the value of R₂.

d. Explain why this conclusion is misleading: “The student’s gender is important in determining height. In these data, females are taller than males, which is shown in the t value for the coefficient of X₁.”

Transcribed Image Text:

Y = 4.589-4.608X+0.405X2+0.568X3, R2 = 0.74 (0.402) (0.080) (0.079)