Implications of Multicollinearity in a Regression Model

Hard Multiple Regression Analysis Multicollinearity

Consider a multiple regression model used to predict the annual sales of a company based on various independent variables: the company’s advertising budget, average customer income, and the number of sales representatives. The model is specified as follows:

$$ ext{Sales} = eta_0 + eta_1 ext{Advertising} + eta_2 ext{Income} + eta_3 ext{SalesReps} + heta $$

After running the regression analysis, the following results were obtained: high Variance Inflation Factors (VIFs) for the independent variables and the R-squared value was found to be excessively high, near 0.95.

Given your understanding of multicollinearity, which of the following statements best describes the implications of this model?

The high VIF values indicate that the estimates of the regression coefficients may be unreliable due to multicollinearity, leading to possible incorrect conclusions about the significance of each independent variable.

The R-squared value is high, therefore, despite the VIFs, multicollinearity is not a concern because the model is explained well by its variables.

The presence of multicollinearity suggests that one of the independent variables can be entirely omitted from the model without affecting its predictive ability.

Hint

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