There are six independent variables, x₁, x₂, x₃, x₄, x₅, and x₆, that might be useful in predicting a response y. A total of n = 50 observations are available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful.

a. How many models are fit to the data in step 1? Give the general form of these models.

b. The table gives the estimate of β₁ and standard error for each independent variable fit in the model in step 1. Use the results to determine which independent variable is declared the best one-variable predictor of y.

c. How many models are fit to the data in step 2? Give the general form of these models.

d. Explain how the procedure determines when to stop adding independent variables to the model.

e. Give two major drawbacks to using the final stepwise model as the “best” model for E(y).

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Independent Variable SB, 1.6 42 X2 -.9 .01 X3 3.4 1.14 X4 2.5 2.06 X5 -4.4 .73 X6 .3 .35