Supposed that you were asked to examine the relationship between the height of children and their parents. To conduct such a study you have collected data from 110 college students, and estimated the following relationship:

Student_hat = 19.6 + 0.73 Midparh,R2= 0.45,SER= 2.0

(7.2)(0.10)

whereStudenthis the height of students in inches, andMidparhis the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. Both variables were adjusted so that the average female height was equal to the average male height.

(a) Interpret the estimated coefficients.

(b) What is the meaning of the regressionR2?

(c)What is the prediction for the height of a child whose parents have an average height of 70.06 inches?

(d)What is the interpretation of theSERhere?

(e)Given the positive intercept and the fact that the slope lies between zero and one, what can you say about the height of students who have quite tall parents? Those who have quite short parents?

(f) Test for the statistical significance of the slope coefficient.

(g) If children, on average, were expected to be of the same height as their parents, then this would imply two hypotheses, one for the slope and one for the intercept.

(i) What should the null hypothesis be for the intercept? Calculate the relevantt-statistic and carry out the hypothesis test at the 1%level. For full credit make sure that you show ALL the steps including a graphical representation of your test.

(ii) What should the null hypothesis be for the slope? Calculate the relevantt-statistic and carry out the hypothesis test at the 5% level.For full credit make sure that you show ALL the steps including a graphical representation of your test.

(h) Can you reject the null hypothesis that the regressionR2is zero?