Implications of Multicollinearity in Regression Analysis

Very Hard Multiple Regression Analysis Multicollinearity

In a certain multiple regression analysis conducted to evaluate the impact of several macroeconomic variables on economic growth, the analyst detects evidence of multicollinearity among the independent variables. The independent variables included in the analysis are inflation rate ($X_1$), interest rate ($X_2$), and exchange rate ($X_3$). The variance inflation factor (VIF) of these variables is computed, and the VIF values are as follows:

VIF($X_1$) = 12
VIF($X_2$) = 15
VIF($X_3$) = 25

Based on this analysis, which of the following statements is true regarding the implications of multicollinearity in this regression model?

The high VIF values indicate that the independent variables are highly correlated, and therefore, any interpretations regarding the coefficients of these variables will be unreliable.

The presence of multicollinearity suggests that the estimated regression coefficients will be unbiased, but their standard errors will be smaller, leading to inflated t-statistics.

The presence of multicollinearity will not affect the overall model fit (R-squared), but it may distort the coefficients, leading to possible wrong economic interpretations.

Hint

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