please see the attached file for the complet solution.

The response (y) variable is weight in pounds, and the predictor (x) variables are HT (height in inches), WAIST (waist circumference in cm) and CHOL (cholesterol in mg).

Predictor (x) Variables P-Value R² Adjusted R² Regression Equation
HT, WAIST, CHOL 0.000 0.880 0.870 Y = -199 + 2.55 HT + 2.18 WAIST - 0.00534 CHOL
HT, WAIST 0.000 0.877 0.870 Y = -206 + 2.66 HT + 2.15 WAIST
HT, CHOL 0.002 0.277 0.238 Y = -148 + 4.65 HT + 0.00589 CHOL
WAIST, CHOL 0.000 0.804 0.793 Y = -42.8 + 2.41 WAIST - 0.0106 CHOL
HT 0.001 0.273 0.254 Y = -139 + 4.55 HT
WAIST 0.000 0.790 0.785 Y = -44.1 + 2.37 WAIST
CHOL 0.874 0.001 0.000 Y = 173 - 0.00233 CHOL

1. If exactly two predictor (x) variables are to be used to predict weight, which two variables should be chosen and why?

2. If a male has a height of 72in., a weight circumference of 105cm, and a cholesterol level of 250 mg, what is the best predicted value of his weight? Is that predicted value likely to be a good estimate? Is that predicated value likely to be very accurate?

Answer

1. Select that model for which R2 is ,maximum .The model Y = -206 + 2.66 HT + 2.15 WAIST explain 87.7 % variability in weight.

2. When

Height =72in
Waist circumference =105cm
Cholesterol level = 250 mg

Weight = -199 + 2.55 *72 + 2.18 *105 - 0.00534* 250 =212.165 pounds

The R2 suggests that 88% variability in weight can be explained by Height, Waist circumference, Cholesterol level. Thus above predicted value is likely to be a good estimate and accurate upto 88%