MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 23: Correlation And Dependence, Dependent And Independent Variables, Linear Independence

• School: Indian Institute of Technology - IIT Kanpur
• Department: Mathematics
• Course: MTH-416, REGRESSION ANALYSIS

Document Summary

The standard errors of 1b and becomes non-singular. 2b rise sharply as r and they break down at. If r is close to 0, then multicollinearity does not harm, and it is termed as non-harmful multicollinearity. If r is close to +1 or -1 then multicollinearity inflates the variance, and it rises terribly. There is no clear cut boundary to distinguish between the harmful and non-harmful multicollinearity. Generally, if r is low, the multicollinearity is considered as non-harmful, and if r is high, the multicollinearity is regarded as harmful. In case of near or high multicollinearity, the following possible consequences are encountered: the olse remains an unbiased estimator of , but its sampling variance becomes very large. Olse becomes imprecise, and property of blue does not hold anymore: due to large standard errors, the regression coefficients may not appear significant. 1 we use t ratio as t. Var b is large, so 0t is small and consequently.