\(\sqrt{(1-r^{2})} * SD_{y}\)

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

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