You are given the following set of data:

y x1 x2 x3 45 40 41 39 41 31 41 35 43 45 49 39 38 43 41 41 50 42 42 51 39 48 40 42 50 44 44 41 y x1 x2 x3 45 42 39 37 43 37 52 41 34 40 47 40 49 35 44 44 45 39 40 45 40 43 30 42 43 53 34 34

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?