An independent variable X; is not considered highly correlated with the other independent variables if O VIF < 5 R-squared > 0 R-squared > .5 VIF > 5
An independent variable X; is not considered highly correlated with the other independent variables if O VIF < 5 R-squared > 0 R-squared > .5 VIF > 5
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Correlation of Independent Variables
**Question:**
An independent variable \(X_j\) is not considered highly correlated with the other independent variables if
- [ ] VIF < 5
- [ ] R-squared > 0
- [ ] R-squared > .5
- [ ] VIF > 5
**Explanation:**
In the context of multicollinearity in regression analysis, the Variance Inflation Factor (VIF) is a metric used to evaluate the extent of correlation between independent variables. A commonly accepted threshold is that a VIF less than 5 suggests that the variable \(X_j\) is not highly correlated with the other independent variables. If the VIF exceeds this threshold, it indicates a higher degree of multicollinearity which can affect the stability and interpretability of the regression coefficients.
- **VIF (Variance Inflation Factor)**: This measures how much the variance of a regression coefficient is inflated due to multicollinearity with other predictors. A VIF value less than 5 is generally accepted as an indicator that multicollinearity is not a concern.
- **R-squared**: This represents the proportion of the variance for the dependent variable that's explained by the independent variables in a regression model. Although useful, R-squared alone does not provide information about multicollinearity between independent variables.
When addressing multicollinearity, utilizing VIF is more direct and relevant than R-squared values. Hence, the correct answer to the question is:
- **VIF < 5**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9045e4c-214a-4ed5-8350-6a40e5f22583%2Fdca14795-4546-4858-9229-3e28aba843ca%2Fjfuwojm_processed.png&w=3840&q=75)
Transcribed Image Text:### Correlation of Independent Variables
**Question:**
An independent variable \(X_j\) is not considered highly correlated with the other independent variables if
- [ ] VIF < 5
- [ ] R-squared > 0
- [ ] R-squared > .5
- [ ] VIF > 5
**Explanation:**
In the context of multicollinearity in regression analysis, the Variance Inflation Factor (VIF) is a metric used to evaluate the extent of correlation between independent variables. A commonly accepted threshold is that a VIF less than 5 suggests that the variable \(X_j\) is not highly correlated with the other independent variables. If the VIF exceeds this threshold, it indicates a higher degree of multicollinearity which can affect the stability and interpretability of the regression coefficients.
- **VIF (Variance Inflation Factor)**: This measures how much the variance of a regression coefficient is inflated due to multicollinearity with other predictors. A VIF value less than 5 is generally accepted as an indicator that multicollinearity is not a concern.
- **R-squared**: This represents the proportion of the variance for the dependent variable that's explained by the independent variables in a regression model. Although useful, R-squared alone does not provide information about multicollinearity between independent variables.
When addressing multicollinearity, utilizing VIF is more direct and relevant than R-squared values. Hence, the correct answer to the question is:
- **VIF < 5**
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