Question

(b) The following code and output is reproduced from the STATA package. #delimit; regress Y XRP; Number of obs - F( 3, 46) R-squared Adj R-squared 50 186.93 0.92 0.91 Y Coefficient Standard Errort-statistic 13.15 -36.47 60.76 0.008 2.77 5.92 1.43 2.70 10.28 0.04 0.000 0.06 389.57 0.159 0.010 144.43 cons vif; VIF 1/VIF Variable 24.80 0.040 0.044 22.60 1.50 16.30 0.667 Mean VIF Explain with the aid of equations how the VIF scores are calculated. 8 Marks (c) Give an interpretation of the VIF test results contained above, ensuring to outline any econometric problems that the results may highlight. 4 Marks (d) Given the VIF scores presented above, outline what options are available to a researcher wishing to estimate the model 6 Marks (e) Briefly explain with the aid of equations and diagrams the role of the adjusted R2 in econometric modelling. 3 Marks

Answer 1

b) When the R squared value is given the VIF is calculated using the equation

1- R2

c) The VIF scores for X, R and P are 24.8, 22.6 and 1.5 in which the scores for X and R are large. This may reduces the precision of the estimate coefficients, which weakens the statistical power of your regression model.

d) Since the VIF scores of X and R are high, which indicates the presence of multicollinearity, To remove multicollinearity problem one may remove some of the highly correlated independent variables or Linearly combine the independent variables, such as adding them together.

e) the Adjusted R squared formula is

2 n-(k +1 *7

which is a statistical measure that shows the proportion of variation explained by the estimated regression line.

Here the adjusted R squared value is 0.91