Impact of Multicollinearity on Multiple Regression Coefficients

Very Hard Multiple Regression Analysis Multicollinearity

Consider a multiple regression model that investigates the relationship between a dependent variable, Y, and two independent variables, X₁ and X₂. The estimated regression equation is given by:

Y = β₀ + β₁X₁ + β₂X₂ + ε

During the analysis, it was found that X₁ and X₂ exhibit a high degree of correlation with a correlation coefficient of 0.95. The variance inflation factor (VIF) for both variables was calculated and resulted in values well above 10. The researcher expressed concerns regarding the model’s reliability due to potential multicollinearity.

Which of the following statements accurately describes the impact of multicollinearity on the coefficients estimated by this regression model?

Multicollinearity reduces the precision of the estimated coefficients, increasing the standard errors, but does not affect the overall predictive power of the model.

Multicollinearity inflates the test statistics for the coefficients, leading to misleading inferences about their significance.

Multicollinearity eliminates the ability to identify the specific effect of each independent variable on the dependent variable.

Hint

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