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 7 pairs, with height measured in inches, simulated from the distribution specified by Pearson. The least-squares regression line y=b0+b1x, se=2.3624697, E(x-x)^ 2=33.51, and x=70.02 are known for this data. Compute a point estimate of the mean height of sons whose fathers are 70 inches tall.

Father's height	Son's height
69	69.1
73.6	74.9
66.7	68.8
70.1	73.3
68.3	68.3
72.4	69.1

The point estimate is 70.572. Construct a 98% confidence interval for the mean height of sons whose fathers are 70 inches tall.

Answer 1

EXCEL (Mega Stat) output:

Regression Analysis 0.425 r 0.652 Std. Error 2.362 Dep. Var. Son's height ANOVA table Source Regression df 1 16.4833 P-value 1608 MS 16.4833 Residual 22.3250 Total 38.8083 2.95 5.5813 4 Regression out vanables Intercept Father's height confidence interval coefficients std. error 21.4759 28.5916 0.7014 0.4081 t (df-4) 0.751 p-value 98% lower 98% upper std. coeff 4944 -85.6553 128.6071 0.000 8278 2.2306 0.652 Predictedvaluesfor Son's 98% confidence intenal 98%Prediction leer Leverage Father's height Predicted lower upper Leverage 0.167 r upper lower 70 70.5716 66.9577 74.1856 61.0103 80.1330 The 98% confidence interval for the mean height of sons whose fathers are 70 inches tall is (66.9577,74.1856.