Test questions on detecting and mitigating multicollinearity with VIF

📚 Quick Study Guide

• 📈 Multicollinearity occurs when independent variables in a regression model are highly correlated.
• 🔎 Variance Inflation Factor (VIF) measures the inflation of the variance of the estimated regression coefficients due to multicollinearity.
• 🔢 VIF is calculated as: $VIF_i = \frac{1}{1 - R_i^2}$, where $R_i^2$ is the R-squared value when regressing the $i$-th independent variable on the remaining independent variables.
• 🔥 A VIF of 1 indicates no multicollinearity.
• 🌡️ A VIF between 1 and 5 suggests moderate multicollinearity.
• 🚨 A VIF above 5 (or 10, depending on the source) indicates high multicollinearity.
• 🛠️ To mitigate multicollinearity, you can remove one of the correlated variables, combine them into a single variable, or use regularization techniques.

Practice Quiz

1. What does a VIF of 1 indicate?
   1. No multicollinearity
   2. Perfect multicollinearity
   3. Moderate multicollinearity
   4. Severe multicollinearity
2. Which of the following VIF values suggests the highest degree of multicollinearity?
   1. 1.5
   2. 3
   3. 6
   4. 1
3. The $R^2$ value obtained from regressing an independent variable on other independent variables is 0.8. What is the VIF?
   1. 1.25
   2. 5
   3. 0.2
   4. 2
4. Which of the following is NOT a method to mitigate multicollinearity?
   1. Removing one of the correlated variables
   2. Adding more correlated variables
   3. Combining correlated variables
   4. Using regularization techniques
5. What does VIF stand for?
   1. Variance Inflation Form
   2. Variance Inflation Factor
   3. Variable Influence Factor
   4. Variable Inflation Form
6. A regression model has two independent variables, $X_1$ and $X_2$. When $X_1$ is regressed on $X_2$, the $R^2$ is 0.9. What is the VIF for $X_1$?
   1. 10
   2. 0.1
   3. 5
   4. 2
7. If all independent variables in a regression model are perfectly uncorrelated, what would be the VIF for each variable?
   1. 0
   2. Infinity
   3. 1
   4. Varies depending on the variable