Understanding Multicollinearity in Regression Analysis

Hard Multiple Regression Analysis Multicollinearity

As a financial analyst at a mid-size investment firm, you have been tasked with building a multiple regression model to predict the expected return of a portfolio based on three independent variables: the market return, the interest rate, and inflation rate. After testing your model, you discover high variance inflation factors (VIFs) for the interest rate and inflation rate. This raises concerns about multicollinearity.

The variance inflation factor for a variable $X_j$ is calculated as:

$$ VIF(X_j) = \frac{1}{1 - R^2_j} $$

where $R^2_j$ is the coefficient of determination obtained by regressing $X_j$ on all other independent variables.

Which of the following statements correctly describes the implications of multicollinearity in your regression analysis?

Multicollinearity indicates that a linear relationship exists among the independent variables, leading to biased coefficient estimates.

Multicollinearity inflates the standard errors of the coefficient estimates, making them less reliable but does not affect the overall fit of the model.

Multicollinearity is beneficial in regression as it allows for more flexibility in understanding the relationships among the predictors.

Hint

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