Question 11.96

11.96 Correlations may not be a good way to screen for multiple regression predictors.

We use a constructed data set in this problem to illustrate this point.

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  1. Find the correlations between the response variable and each of the explanatory variables and . Plot the data and run the two simple linear regressions to verify that no evidence of a relationship is found by this approach. Some researchers would conclude at this point that there is no point in further exploring the possibility that and could be useful in predicting .
  2. Analyze the data using and in a multiple regression to predict . The fit is quite good. Summarize the results of this analysis.
  3. What do you conclude about an analytical strategy that first looks at one candidate predictor at a time and selects from these candidates for a multiple regression based on some threshold level of significance?