Multicollinearity in Multiple Regression

Multicollinearity in Multiple Regression#

Multicollinearity occurs when two or more explanatory variables in a regression model are highly correlated. This condition can affect the precision of our coefficient estimates and make it difficult to determine the individual effect of each variable on the dependent variable.

1. Effects of Multicollinearity:

  • Increased variance of coefficient estimates

  • Reduced precision in identifying individual variable effects

  • Potential instability in coefficient estimates

  • Wider confidence intervals

2. Detection and Assessment:

  • High correlation between explanatory variables

  • Large standard errors of coefficient estimates

  • Significant F-test but insignificant t-tests

  • Variance Inflation Factors (VIF)

3. Solutions and Considerations:

  • Collect more data

  • Remove highly correlated variables

  • Use principal components analysis

  • Consider ridge regression

The following simulation allows you to explore how different levels of correlation between explanatory variables affect the precision of coefficient estimates: