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?

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[100 123 96 109 123 252 125 189 96 125 167 146 109 189 146 168 0.03767 -0.06263 -06247 -0.06263 1.129 1.107 -0.06247 1.107 1.110 0.1003 -2.192 -2.170 generator: X'X= (X'X)¹= X'y = 460 810 615 [712] 0.1003 -2.102 - 2.170 4.292 ,y'y=3924