Question

What is the meaning of the term "multicollinearity? Why is it important in assessing the strength of a multiple regression model?

Answer 1

Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results.

A key goal of regression analysis is to isolate the relationship between each independent variable and the dependent variable. The interpretation of a regression coefficient is that it represents the mean change in the dependent variable for each 1 unit change in an independent variable when you hold all of the other independent variables constant.

Multicollinearity reduces the precision of the estimated coefficients, which weakens the statistical power of your regression model. You might not be able to trust the p-values to identify independent variables that are statistically significant.

So if Multicollinearity exits in the data then we get higher R^2(% of the variation in data explain by the model) value. Or can get the highest precision but actual it is not true.so removing Multicollinearity is necessary before we go for the model fitting in regression analysis.