a. Compute the least-squares regression line for predicting son’s height (y) from father’s height (x). b. Construct a 95% confidence interval for the slope. c. Test H0: β1 = 0 versus H1: β1 ≠ 0. Can you conclude that father’s height is useful in predicting son’s height? Use the α = 0.05 level of significance.
1. 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 16 pairs, with height measured in inches, simulated from the distribution specified by Pearson.
|
Father’s height |
Son’s height |
Father’s height |
Son’s height |
|---|---|---|---|
|
70.8 |
69.8 |
72.4 |
69.1 |
|
65.4 |
66.0 |
65.7 |
65.3 |
|
65.7 |
70.9 |
69.1 |
71.8 |
|
69.0 |
69.1 |
70.7 |
71.0 |
|
73.6 |
74.9 |
72.3 |
71.9 |
|
66.7 |
68.8 |
73.6 |
76.5 |
|
70.1 |
73.3 |
69.3 |
71.4 |
|
68.3 |
68.3 |
64.5 |
68.5 |
|
a. |
Compute the least-squares regression line for predicting son’s height (y) from father’s height (x). |
|
b. |
Construct a 95% confidence interval for the slope. |
|
c. |
Test H0: β1 = 0 versus H1: β1 ≠ 0. Can you conclude that father’s height is useful in predicting son’s height? Use the α = 0.05 level of significance. |
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