Notes

No, the average height of fathers of 72-inch sons should not be 74 inches. This is due to the difference between the regression line fitting heights of sons to heights of fathers, and the regression line fitting heights of fathers to heights of sons. In both cases, we expect regression to the mean, and since 72 inches is above the mean for sons, the average height of fathers of 72-inch sons should be less than 72 (but greater than 68). If the question were about 68-inch fathers whose sons average 68 inches, then the answer would be yes, since both heights are already at the mean, so both regression lines intersect that point.

Grading Rubric
Please grade this question out of 6 points following these guidelines.

4 points for concluding "no" in part (a) and explaining that there is a difference between regressing y on x and regressing x on y, or applying regression to the mean to answer the question.
2 points for concluding "yes" in part (b) and explaining that there is no regression when x and y are already at the mean (or equivalent).
Feel free to give partial credit or to use your good judgement if you think the case merits it