Refer to the International Journal of Foresting Engineering (Vol. 19, 2008) study of neck muscle activity patterns among forestry vehicle operators, Exercise 12.23. Recall that 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 reproduced below:

a. Write a model for E(y) as a function of the seven independent variables that (1) hypothesizes straight-line relationships between each quantitative x and y, and (2) allows for interactions among all possible pairs of independent variables.

b. Refer to the model, part a. Specify the null hypothesis to test to determine if the impact of any of the four qualitative independent variables on E(y) depends on the levels of the three qualitative variables.

c. How would you conduct the test, part b. Identify the reduced model as part of your answer.

d. The researchers collected data for n = 13 forestry vehicle operators. Is this sufficient to fit the model, part a, and carry out the test, part c? Explain.

Data from Exercise 12.23

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 the number of sustained low-level muscle activity (SULMA) periods exhibited by an operator that exceed 8 minutes.

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x1 = Age of operator (years) x2 = Duration of lunch break (minutes) X3 = Dominant hand power level (percentage) X4 = Perceived stress at work (5-point scale) X5 = {1 if married, 0 if not} {1 if day shift, 0 if night shift} (1 if operating a Timberjack vehicle, 0 if operating a Valmet vehicle) %3! !3! %3D %3! X7