Tuddenham and Snyder obtained the following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped): average height at 6 ≈ 3 feet 10 inches, SD ≈ 1.7 inches average height at 18 ≈ 5 feet 10 inches, SD ≈ 2.5 inches, r≈0.80 a) Find the r.m.s. error for the regression prediction of height at 18 from height at 6. b) Find the r.m.s. error for the regression prediction of height at 6 from height at 18.

Question
Analyzing categorical data
asked 2021-02-24
Tuddenham and Snyder obtained the following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped):
average height at 6 ≈ 3 feet 10 inches, SD ≈ 1.7 inches
average height at 18 ≈ 5 feet 10 inches, SD ≈ 2.5 inches, r≈0.80
a) Find the r.m.s. error for the regression prediction of height at 18 from height at 6. b) Find the r.m.s. error for the regression prediction of height at 6 from height at 18.

Answers (1)

2021-02-25
\(\sqrt{(1-r^{2})} * SD_{y}\)
a) The r.m.s. error for the regression prediction of height at 18 from height at 6: in this case:
\(\sqrt{1-0.8^2} * 2.5 = \sqrt{1-0.64} * 2.5 = \sqrt{0.36} * 2.5 = 0.6 * 2.5 = 1.5\)
b) The r.m.s. error for the regression prediction of height at 6 from height at 18:
\(\sqrt{1-0.8^2} * 1.7 = \sqrt{1-0.64} * 1.7 = \sqrt{0.36} * 1.7 = 0.6 * 1.7 = 1.02\)
Answer: a) 1.5, b)1.02
0

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