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 in the table. The researchers collected data for n = 13 forestry vehicle operators and applied the stepwise regression method (using α = .10) in order to determine the best subset of predictor variables.

a. The stepwise regression identified x₇ as the best one variable predictor of y. How many one-variable models were fit and tested to arrive at this result?

b. The stepwise regression method did not select an other variables as “significant” predictors of y. How many more models were fit and tested to arrive at this result?

c. The model identified by stepwise regression took the form, E(y) = β₀ + β₁x₇. The p-value for testing H₀: β₁ = 0 was p = .067, with R² = .30. Would you advise the researchers to use this model for predicting y = the number of sustained low-level muscle activity (SULMA) periods exhibited by an operator that exceed 8 minutes. Fully 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. (See Exercise 7.38.) 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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Age of operator (years) %3! X2 Duration of lunch break (minutes) %3! X3 Dominant hand power level (percentage) %3D X4 = Perceived stress at work (5-point scale) X5 = (1 if married, 0 if not) X6 = (1 if day shift, 0 if night shift} X7 {l if operating a Timberjack vehicle, O if operating a Valmet vehicle}