What is Multicollinearity?

A linear relationship between two explanatory variables is known as collinearity. These variables can be said to be collinear if there exists an exact linear relationship between both of them. 

When three or more explanatory variables in a multiple regression model are strongly correlated linearly, this is referred to as multicollinearity. However, attaining multicollinearity of a data collection is uncommon in the real world. The problem of multicollinearity more frequently appears when there is an approximately linear relationship between all the independent variables.

What is Multicollinearity?

Multicollinearity is a technique in statistics when one predictor variable in a multiple regression model may be linearly predicted with a high level of precision. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably. Multicollinearity only impacts statistics pertaining to specific predictors; it has no impact on the predictive capability or the model's reliability. In other words, a multivariate regression model with collinear predictors can show how effectively the complete set of predictors predicts the outcome variable, but it could not provide accurate information about any particular predictor or those that may be duplicate in relation to others.

High intercorrelations between two or more independent variables in a multiple regression model are referred to as multicollinearity. If an analyst tries to figure out how efficiently each independent variable can be utilized to predict or comprehend the dependent variable in a predictive model, multicollinearity can result in distorted or inaccurate conclusions.

A multiple regression model's multicollinearity suggests that collinear independent variables are related somehow, whether or not the connection is coincidental. For instance, market capitalization and previous performance may be associated since rising market values are indicative of prior performance for companies.

The regression estimates are not affected by multicollinearity, but it renders them unclear, uncertain, and unreliable. As a result, it may be challenging to isolate the specific effects of the independent variables on the dependent variable. 

Generally speaking, multicollinearity can cause broader confidence intervals, which might result in odds that are less trustworthy when predicting the impact of independent variables in a model.

Detecting Multicollinearity

The level of collinearity in a multiple regression model can be detected and measured using a statistical technique known as the variance inflation factor (VIF). Once the predictor variables are not linearly connected, VIF quantifies the extent to which the variation of the estimated regression coefficients is exaggerated. A VIF of 1 indicates no correlation between the variables; a VIF between 1 and 5 indicates moderate correlation; and a VIF between 5 and 10 indicates strong correlation between the variables.

Also, whenever a predictor variable is included or removed, the predicted regression coefficients undergo significant modifications. When all other independent variables are held constant, a regression coefficient is interpreted as the average change in the dependent variable for each change in an independent variable of 1 unit.

The concept is that just one independent variable's value can be altered, not the others. When independent variables, on the other hand, are correlated, it means that variations in one variable are related to shifts in another one. It is more challenging to alter one variable without also changing another when there is a high link between the two. Because the independent variables frequently change simultaneously, it becomes challenging for the model to calculate the link between each independent variable and the dependent variable separately.