The nature of multicollinearity and its practical consequences

Question 1

What is multicollinearity?

Answer 1

Refers to the existence of perfect or exact linear relationship among some or all explanatory variables of a regression model.

Question 2

What are the two types of multicollinearity and what does each mean?

Answer 2

1. Perfect multicollinearity
   in multiple linear regression models, we assume that no exact linear relationships exist between sample values of explanatory variables (X1, X2,Xp)
2. Near multicollinearity
   occurs when 2+ independent variables in the analysis are significantly correlated

Question 3

What is the first practical consequence of multicollinearity?

Answer 3

Although OLS estimators have the large variance and covarianbce, making precise estimations is difficult

Question 4

What is the second practical consequence of multicollinearity?

Answer 4

The confidence intervals tend to be much wider, leading to the acceptance of the ‘zero null hypothesis’ more readily

Question 5

What is the third practical consequence of multicollinearity?

Answer 5

The t ratio of one or more coeffcients tends to be statistically insignifcant

Question 6

What is the fourth practical consequence of multicollinearity?

Answer 6

Although t-ratio of one or more coeffeicnts is statistcially insignifcant, (R2) the overall measure of goodness of fit can be very high

Question 7

What is the fifth practical consequence of multicollinearity?

Answer 7

OLS estimates and their standard errors can be sensitive to small changes in the data