Question

1. Write notes on Multicollinearity
2. 1. define what the issue is
   2. explain whether, or under what circumstances, it causes a problem for inference in OLS regression
3. 3. explain how it can be detected (if it can)
   4. state what action, if any, you should take to deal with the issue

Answer 1

(i)

Multi-collinearity is defined as a situation in which two or more

independent variables are highly related.

(ii)

Multi-collinearity causes a problem for inference in Ordinary Least

Square (OLS) regression because Multi-collinearity undermines the

statistical significance of the independent variable. Multi-collinearity

leads to wider confidence intervals and less reliable probability values

for the independent variables.

(i)

Multi-collinearity can be detected as follows:

(a) Large changes in the estimated regression coefficients when an

independent variable is added or deleted.

(b) The individual outcome of a statistic is not significant but overall

outcome of the statistic is significant.

(c) Multi-collinearity can be detected by calculating correlation

coefficients for all pairs of independent variables and checking whether

the values are near - 1 or + 1.

(ii)

We should take the following actions to deal with the issue :

(a) Remove highly correlated independent variables from the regression

model.

(b) Use Partial Least Squares Regression (PL) or Principal Components

Analysis that cut the number of independent variables to a smaller set of

uncorrelated components.