Question: 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

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. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE DATASETA

(a) Find the correlations between the response variable Y and each of the explanatory variables X1 and X2. 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 X1 and X2 could be useful in predicting Y .

(b) Analyze the data using X1 and X2 in a multiple regression to predict Y . The fit is quite good. Summarize the results of this analysis.

(c) 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?

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