Question

4.2 A random sample of 200 20-year-old men is selected from a population and these men's height and weight are recorded. A regression of weight on height yields -------Weight = -99.41 + 3.94 x Height, R2 = 0.81, SER = 10.2,
where Weight is measured in pounds and Height is measured in inches.
a. What is the regression's weight prediction for someone who is 70 in. tall? 65 in. tall? 74 in. tall?
b. A man has a late growth spurt and grows 1.5 in. over the course of a year. What is the regression's prediction for the increase in this man's weight?

Answer 1

Given regression equation is

Weight = -0.9941+3.94 * Height

a) For height = 70 inch,

Weight = -0.9941+3.94 * 70

            = -0.9941 + 275.8

            = 274.81                 (Round to 2 decimal)

Regression's weight prediction for someone who is 70 in. tall is 274.81 pounds

For height = 65 inch,

Weight = -0.9941+3.94 * 65

            = -0.9941 + 256.1

            = 255.11                 (Round to 2 decimal)

Regression's weight prediction for someone who is 65 in. tall is 255.11 pounds

For height = 74 inch,

Weight = -0.9941+3.94 * 74

            = -0.9941 + 291.56

            = 290.57                 (Round to 2 decimal)

Regression's weight prediction for someone who is 70 in. tall is 290.57 pounds.

b)

For 1.5 inch increase in height,

Weight = -0.9941+3.94 * 1.5

            = -0.9941 + 5.91

            = 4.92                 (Round to 2 decimal)

Regression's prediction for the increase in this man's weight is 4.92 pounds