For the multiple regression model in Exercise 14.55, the estimated standard deviations for each of the coefficients (excluding the constant) are (in order) .01, .01, .03, .06, .01, .01, .03, .04, and .05.
a. If a backward elimination variable selection process were to be used, which of the nine predictors would be the first candidate for elimination? Would it be eliminated?
b. Based on the information given, can you tell what the second candidate for elimination would be? Explain.
Ref prb:
The following statement is from the article “Blood Cadmium Levels in Nonexposed Male Subjects Living in the Rome Area: Relationship to Selected Cardiovascular Risk Factors” (Microchemical Journal [1998]: 173– 179):
A multiple regression analyzed ln(blood cadmium level) as a dependent variable, with a model including age, alcohol consumption, daily cigarette consumption, driving habits, body mass index, skinfold thickness, high density lipoprotein cholesterol, nonhigh density lipoprotein cholesterol, and ln(triglyceride level) as possible predictors. This model explained 30.92% of the total variance in ln(blood cadmium level).
a. A total of n = 1856 men participated in this study. Perform a model utility test to determine whether the predictor variables, taken as a group are useful in predicting ln(blood cadmium level).
b. The article went on to state: Smoking habits, the most important predictor of ln(blood cadmium level), explained 30.26% of the total variation, and alcohol consumption was the only other variable influencing ln(blood cadmium level).
These statements were based on the result of a forward stepwise regression. In forward stepwise regression, variables are added to the model one at a time. At each step, the variable that results in the largest improvement is added to the model. This continues until there is no variable whose addition will result in a significant improvement. Describe what you think happened at each step of the stepwise procedure.
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