Explain what is meant by the notion of \"trimming\" a multiple regression result

Question

Explain what is meant by the notion of "trimming" a multiple regression result. Use the following example to illustrate your understanding of this concept.

A bicycle manufacturer maintains records over 20 years of the following: retail price in dollars, co-operative advertising amount in dollars, competitors' average retail price in dollars, number of retail locations selling the bicycle manufacturer's brand, and whether or not the winner of the Tour de France was riding the manufacturers' brand (coded as a dummy variable where 0=no, and 1-yes).
The initial multiple regression result determines the following:

Variable Significance Level

Average retail price in dollars .001

Cooperative advertising amount in dollars .202

Competitors' average retail price in dollars .028

Number of retail locations .591

Tour de France    .032
Using the "enter" method in SPSS, what would be the trimming steps you would expect to undertake to identify the significant multiple regression result? Explain.

Explanation / Answer

“Trimming” refers to the iterative process of eliminating nonsignificant independentvariables and rerunning the multiple regression until only statistically significant onesremain.In the bicycle example, the process would be to next eliminate the “numberof retail locations” for the next multiple regression run.If “cooperative advertising...”is again nonsignificant and the largest significance value, eliminate it and rerun thetrimmed multiple regression.Continue until only statistically significant betas areleft.The logic is based on the null hypothesis that says that any nonsignificantindependent variable in the multiple regression equation has a beta of zero.Thus, inorder to make it take on a zero beta, the independent variable must be removed.Otherwise, the statistical analysis will still compute a nonzero value for that independent variable.

With stepwise regression, the first independent variable to be included is the one thatis most significant and explains the most variance. The multiple regression equationis then recomputed with the remaining independent variables and the most significantone in that set is added.This process is repeated until only those independentvariables with statistically significant coefficients are in the equation.

There is no explained variance information in question, so we must work with the significance levels. Assuming that the significance levels do not differ with each iteration from those given in the bicycle example, the order of entry would be (1) average price in dollars, (2) competitors’ average retail price in dollars, and (3)Tourde France. At this point, the stepwise procedure would stop and compute a multiple regression result for these three independent variables.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.