The following sample moments for x = [1, x₁, x₂, x₃] were computed from 100 observations produced using a random number generator:

The true model underlying these data is y = x₁ + x₂ + x₃ + ε.

a. Compute the simple correlations among the regressors.

b. Compute the ordinary least squares coefficients in the regression of y on a constant x₁, x₂, and x₃.

c. Compute the ordinary least squares coefficients in the regression of y on a constant, x₁ and x₂, on a constant, x₁ and x₃, and on a constant, x₂ and x₃.

d. Compute the variance inflation factor associated with each variable.

e. The regressors are obviously collinear. Which is the problem variable?

460] [100 123 123 252 125 189 96 109] 810 X'y = 3 3924. 712] X'X = 96 125 167 146 615 109 189 146 168