The following problem is based on information taken from the pediatrics section of The Merck Manual (a commonly used reference in medical schools and nursing programs). Let x be the body weight of a child (in kilograms), and let y be the metabolic rate of the child (in 100 kcal/24 h).

ˆ‘x = 100; ˆ‘y = 47.1; ˆ‘x2 = 1552; ˆ‘y2 = 327.83; ˆ‘xy = 710.3
(a) Verify that Se ‰ˆ 0.518.
(b) Verify that r ‰ˆ 0.984. Test that r is positive. Use α = 0.01.
(c) Verify that b ‰ˆ 0.402. Test that b is positive. Use α = 0.01.
(d) Verify that Å· ‰ˆ 0.856 + 0.402x. Find a 90% confidence interval for the predicted metabolic rate for a child weighing 10 kg.

X 3.0 5.0 9.0 1.0 15.0 170 9.0 21.0 y 1.4 2.7 5.0 6.0 7.1 7.8 8.3 8.8