A family physician is interested in predicting the adult heights of boys who are 10 years old. He...

A family physician is interested in predicting the adult
heights of boys who are 10 years old. He collects data on each child's height
at age 10 (Xi), the mother's height (X2), and the father's height (X3). Eight
years later, the same boys return to the physician's office, and he measures
their adult heights (Y). All of the data are given in inches. A multiple linear
regression is fit with 20 subjects with the following results.

(a) Test the null hypothesis that each of
the three predictor values are 0. Use a = 0.05 and two-sided hypothesis tests.

(b) Tim Thompson is 4'8", Josh Jones
is 5'2", and both boys are 10 years old. Tim's mom is 5'9", and his
dad is 6'0". Josh's mom is 5'2", and his dad is 5'10". According
to the estimated model above, which boy will most likely be the taller of the
two in eight years? How much taller will he be?

(c) The physician has his height scale
inspected, and he learns that the height scale used to measure the boys when
they were 18 is off by 1 inch. Every boy's reported height is 1 inch more than
it should be. Could this error affect which predictor variables are considered
statistically significant? Explain.