In: Statistics and Probability
Your answer should
a problem for inference in OLS regression
(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.
(iii)
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.
(iv)
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 (PLS) or Principal Components Analysis that cut the number of independent variables to a smaller set of uncorrelated components.