QUESTION FOUR A researcher estimates a multiple regression model with Y as the dependent variable and 3 independent variables, X, X and X3. The following estimation results are obtained, with t-ratios in parenthesis under each coefficient: Y = t=242.71 +0.29X +13.02X +0.53X3t (1) (2.26) (0.19) (10.15) (0.32) (a) After estimating model (1) above, the researcher suspects that there may be a multicollinearity problem. Explain what the problem of multicollinearity is and describe what the likely effects of the problem are. (15 MARKS) (b) In order to investigate this problem in more detail, the researcher also computes the sample correlation coefficients between each pair of independent variables: Table 1: Correlation Coefficients Between Independent Variables X X X3 X 1.00 0.39 0.44 X 0.39 1.00 0.95 X3 0.44 0.95 1.00 They also estimate the following three auxiliary regressions: X = +X +X + (2) X = V0 + X + 7 X 3+ & (3) X=+X +X + (4) The R values obtained for these three auxiliary regressions are 0.19 for model (2), 0.90 for model (3) and 0.91 for model (4). Use all of the above information to determine whether there is evidence of a multicollinearity problem when fitting model (1). (20 MARKS) (c) In the case where the presence of multicollinearity is confirmed in model (1), what possible actions could the researcher take to remedy this problem? (15 MARKS) QUESTION FOUR A researcher estimates a multiple regression model with Y as the dependent variable and 3 independent variables, X, X and X3. The following estimation results are obtained, with t-ratios in parenthesis under each coefficient: Y = t=242.71 +0.29X +13.02X +0.53X3t (1) (2.26) (0.19) (10.15) (0.32) (a) After estimating model (1) above, the researcher suspects that there may be a multicollinearity problem. Explain what the problem of multicollinearity is and describe what the likely effects of the problem are. (15 MARKS) (b) In order to investigate this problem in more detail, the researcher also computes the sample correlation coefficients between each pair of independent variables: Table 1: Correlation Coefficients Between Independent Variables X X X3 X 1.00 0.39 0.44 X 0.39 1.00 0.95 X3 0.44 0.95 1.00 They also estimate the following three auxiliary regressions: X = +X +X + (2) X = V0 + X + 7 X 3+ & (3) X=+X +X + (4) The R values obtained for these three auxiliary regressions are 0.19 for model (2), 0.90 for model (3) and 0.91 for model (4). Use all of the above information to determine whether there is evidence of a multicollinearity problem when fitting model (1). (20 MARKS) (c) In the case where the presence of multicollinearity is confirmed in model (1), what possible actions could the researcher take to remedy this problem? (15 MARKS)
