a) An analyst is using the regression model below to investigate the effects of the three independent variables, 1, 2 and 3 on the dependent variable Y:

= 0 + 11 + 22 + 33 + (1)

Based on relevant theory, all three of the included independent variables should be relevant for explaining variation in the dependent variable. However, the analyst is concerned that there may be multicollinearity between some of the independent variables. To check this, they compute the sample correlation coefficients between each pair of independent variables:

Table 1: Correlation Coefficients Between Independent Variables

X1 X2 X3

X1 1.00 0.89 0.47

X2 0.89 1.00 0.26

X3 0.47 0.26 1.00

They also estimate the following three auxiliary regressions:

X1t =a 0 +a 1 X2t +a 2 X3t +e 1t (2)

X2t =g 0 +g 1 X1t +g 2 X3t +e 2t (3)

X3t =d 0 +d 1 X1t +d 2 X2t +e 3t (4)

The R2 values obtained for these three auxiliary regressions are 0.882 for model (2), 0.766 for model (3) and 0.134 for model (4).

i) Based on the information above and any other relevant calculations, do you think the analyst is correct to be concerned about possible multicollinearity in model (1)? Clearly explain and justify your answer. (15 marks)

ii) In situations in which multicollinearity is identified, in what ways could the model or analysis be changed to minimise the level of multicollinearity? Is it always correct to regard multicollinearity as a problem which needs to be solved in order to obtain reliable results from the model? Explain your answer.