14.3 A number of investigations have focused on the problem of assessing loads that can be manually handled in a safe manner. The article “Anthropometric, Muscle Strength, and Spinal Mobility Characteristics as Predictors in the Rating of Acceptable Loads in Parcel Sorting” (Ergonomics [1992]: 1033–1044) proposed using a regression model to relate the dependent variable y  individual’s rating of acceptable load (kg)

to k  3 independent (predictor) variables:

x1  extent of left lateral bending (cm)

x2  dynamic hand grip endurance (seconds)

x3  trunk extension ratio (N/kg)

Suppose that the model equation is y  30  .90x1  .08x2  4.50x3  e and that s  5.

a. What is the population regression function?

b. What are the values of the population regression coefficients?

c. Interpret the value of b1.

d. Interpret the value of b3.

e. What is the mean rating of acceptable load when extent of left lateral bending is 25 cm, dynamic hand grip endurance is 200 seconds, and trunk extension ratio is 10 N/kg?

f. If repeated observations on rating are made on different individuals, all of whom have the values of x1, x2, and x3 specified in Part (e), in the long run approximately what percentage of ratings will be between 13.5 kg and 33.5 kg?