Question:

Regress Y against X_1, X_2, and X₃ with the following sample data:

Y X₁ X₂ X₃

13.79 76.45 44.47 8.00

21.23 24.37 37.45 7.56

66.49 98.46 95.04 19.00

35.97 49.21 2.17 0.44

37.88 76.12 36.75 7.50

72.70 82.93 42.83 8.74

81.73 23.04 82.17 16.51

58.91 80.98 7.84 1.59

30.47 47.45 88.58 17.86

8.51 65.09 25.59 5.12

39.96 44.82 74.93 15.05

67.85 85.17 55.70 11.16

10.77 27.71 30.60 6.23

72.30 62.32 12.97 2.58

a. What is the regression equation?

b. Change the first observation of X₃, from 8.00 to 9.00. Repeat the regression. What is the new regression equation?

c. Compare the old and the new regression equations. Does the comparison prove multicollinearity in the data. What is your suggestion for getting rid of the multicollinearity?

d. Looking at the results of the original regression only, could you have figured out that there is a multicollinearity problem? HOW?