Question

Like father, like son: In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 7pairs, with height measured in inches, simulated from the distribution specified by Pearson.

Father's height	Son's height
69.0	69.1
66.7	68.8
70.1	73.3
68.3	68.3
70.7	71.0
73.6	76.5
69.3	71.4

Use the P-value method to test H0:β1=0 versus H1:β1>0. Can you conclude that father's height is useful in predicting son's height? Use the =α0.05 level of significance and the TI-84 calculator.

Compute the least-squares regression line for predicting son's height y from father's height x. Round the slope and y-intercept values to at least four decimal places.

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put Father's height in X input range and Son's height in Y input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.898
R Square	0.806
Adjusted R Square	0.767
Standard Error	1.410
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	41.226	41.226	20.751	0.006
Residual	5	9.934	1.987
Total	6	51.160
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-13.3792	18.575	-0.720	0.504	-61.127	34.368	-61.127	34.368
Father's height	1.2140	0.266	4.555	0.006	0.529	1.899	0.529	1.899

H0:β1=0 versus H1:β1>0

p-value = 0.006

Since p-value is less than 0.05, we reject the null hypothesis.

So,  father's height is useful in predicting son's height.

Regression line: -13.37922+1.2140x

Slope = 1.2140

Intercept = -13.3792