Question

10. Assume that you work in a fitness center and have created a method of estimating one's maximum bench press based on body weight. Based on your linear regression results from SPSS, you have learned that the slope of the line for predicting maximum bench press from body weight is.50, and the y-intercept is 50. The correlation between weight and bench press is .60. The standard deviation of bench press is 100. Answer the following two questions based on what you have learned about the relationship between body weight and maximum bench press. a. You next client weighs 300 pounds. What do you predict the maximum bench press is? b. How much error (in pounds) is there in predicting maximum bench press?

Answer 1

a)

The regression equation is defined as,

Y abX

where

Y = maximum bench press

X = body weight

a = intercept = 50

b = slope = 0.50

Now, for body weight = 300 pounds

Y500.50 x 300 200

Maximum bench press = 200

b)

The standard error of prediction is obtained using the following formula,

SE = Sy 1-r2

where

s_Y = standard deviation for maximum bench press = 100

r = correlation between two variable = 0.60

SE 100 1-0.602

SD 80

The standard error of prediction = 80 pounds