Implications of Multicollinearity in Regression Analysis

Very Hard Multiple Regression Analysis Multicollinearity

During a quantitative analysis, an analyst is investigating the relationship between several independent variables and a dependent variable. The model is formulated as:

$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \epsilon$

Where:

- $Y$ is the dependent variable.

- $X_1$, $X_2$, and $X_3$ are independent variables representing different predictors.

Upon analyzing the regression results, the analyst notices high variance inflation factors (VIFs) for $X_1$ and $X_2$. Given that the VIF for $X_1$ and $X_2$ exceeds 10, the analyst suspects multicollinearity might be influencing the regression model's results.

In light of this analysis, which of the following statements best represents the implications of multicollinearity in this regression model?

Multicollinearity implies that the regression coefficients of $X_1$ and $X_2$ will be biased and inconsistent.

Multicollinearity results in inflated standard errors for the coefficients of $X_1$ and $X_2$, making it difficult to determine their significance.

The presence of multicollinearity affects the overall model fit but does not significantly alter individual coefficient estimates.

Hint

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