Research in the International Journal of Foresting Engineering (Vol. 19, 2008) investigated the muscle activity patterns in the neck and upper extremities exhibited during a work day among forestry vehicle operators. For one portion of the study, the researchers compared the muscle activity of operators of two types of harvesting vehicles—Timber jack and Valmet. In another part of the study, the researchers identified the key explanatory variables of y = the number of sustained low-level muscle activity (SULMA) periods exhibited by an operator that exceed 8 minutes. A list of the potential predictors is provided below:

a. Write the equation of a first-order model for E(y) as a function of the four quantitative independent variables.

b. Which of the β’s in the model, part a represents the change in E(y) for every 1 percent increase in dominant hand power when the operator is 50 years old, takes a 30 minute lunch break, and has a perceived work stress of 2 points?

c. Add terms to the model, part a that allow for interactions between all possible pairs of the quantitative variables.

d. What function of the β’s in the model, part c represents the change in E(y) for every 1 percent increase in dominant hand power, when the operator is 50 years old, takes a 30 minute lunch break, and has a perceived work stress of 2 points?

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x = Age of operator (years) x2 = Duration of lunch break (minutes) !! X3 = Dominant hand power level (percentage) X4 = Perceived stress at work (5-point scale) %3! I5 = {1 if married, 0 if not} {1 if day shift, 0 if night shift} x7 = {1 if operating a Timberjack vehicle, O if operating a Valmet vehicle} X6