Suppose that you are interested in the relationship between the height of childr

Question

Suppose that you are interested in the relationship between the height of children and that of their parents. To do some research on this problem, you collect data from 110 college students and estimate the following linear regression

With ESS = 2.0 and where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are the standard errors.

(a) Test the null hypothesis that average parental height has no effect on the height of their children versus the alternative hypothesis that there is a non?zero effect. Carefully state the null and alternative hypotheses in terms of hypotheses concerning the parameters of the linear model, and carry out a test at the 5% significance level.

(b) Construct a 95% confidence interval for the slope coefficient of the regression above. (c) Is the result in part (b) consistent with the test result obtained in part (a)?

Explanation / Answer

a) let beta1 is the average parental height

Null hypothesis beta1=0

alternative hypothesis beta1 not equal to 0

significance level alpha =0.05

talpha/2 =1.982 from student t table corresponding to 0.05 probability and 108 degrees of freedom

test statistic t = 0.73/0.1=7.3

Since the value of teh test statistic is in teh critical region, we reject the null hypothesis.

Therefore, we conclude that the average parental height has a non zero effect on the height of their children.

b) 95% confidence interval = (0.73-1.982*0.01, 0.73+1.982*0.01) =(0.710,0.750)

c) Yes. since the 95% confidence interval doesnot include the point zero. hence, the average parental height has a non zero effect on the height of their children.

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