Suppose you have four potential independent variables, x1, x2, x3, and x4, from which you want to develop a multiple regression model. Using stepwise regression, x2 and x4 entered the model.

a. Why did only two variables enter the model?

Discuss.

b. Suppose a full regression with only variables x2 and x4 had been run. Would the resulting model be different from the stepwise model that included only these two variables? Discuss.

c. Now, suppose a full regression model had been developed, with all four independent variables in the model. Which would have the higher R2 value, the full regression model or the stepwise model? Discuss.

15-39. You are given the following data:

y x1 x2 x3 y x1 x2 x3 33 9 192 40 45 12 296 52 44 11 397 47 25 9 235 27 34 10 235 37 53 10 295 57 60 13 345 61 45 13 335 50 20 11 245 23 37 11 243 41 30 7 235 35 44 13 413 51

a. Determine the appropriate correlation matrix and use it to predict which variable will enter in the first step of a stepwise regression model.

b. Use standard stepwise regression to construct a model, entering all significant variables.

c. Construct a full regression model. What are the differences in the model? Which model explains the most variation in the dependent variable?