The following data are the heights of fathers and their sons in inches. The fath

Question

The following data are the heights of fathers and their sons in inches. The father's height is his height when he was the same age as the son.

Father's Height

Son's Height

a. A geneticist might wonder if there is a tendency for tall fathers to have tall sons and short fathers to have short sons. Answer this question by computing the appropriate statistic and testing it for statistical significance. (Hint: The statistic will be much easier to compute if you subtract 40 from each of the scores. Doing so will not affect the value of the statistic.)

b. Can you use the height of a father to predict the height of his son? Compute the regression equation for predicting sons’ heights from fathers’ heights. Use this equation to predict the height of a son whose father is 46 inches tall.

c. If you had a father who had a height of 25" when he was the same age as his son, should you use the regression equation to predict the son’s height? Why or why not?

d. An environmentalist might wonder if there is a tendency for generations to get taller. Are sons taller than their fathers were at the same age? What statistical test would be most appropriate for answering this question. (Hint: You will need to recall some previous lessons to get this one correct.)

Father's Height

Son's Height

44 44 47 47 43 46 41 42 45 47 44 44 44 45 44 45

Explanation / Answer

SOl)

The Regression equation is

y=a+bx

where x is father's age

a)

The fitted regression is

y=9.8+0.8 (father height)

b)

Now when father height is 46

then son;s height is

y=9.8+0.8 (father height)

y=46.6

c)

Now when father height is 25

then son;s height is

y=9.8+0.8 (father height)

y=29.8

SUMMARY OUTPUT Regression Statistics Multiple R 0.8 R Square 0.64 Adjusted R Square 0.58 Standard Error 1.095445 Observations 8 ANOVA df SS MS F Significance F Regression 1 12.8 12.8 10.66667 0.01712 Residual 6 7.2 1.2 Total 7 20 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 9.8 10.78471 0.908694 0.39854 -16.5892 36.18924 Father's Height 0.8 0.244949 3.265986 0.01712 0.200631 1.399369

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