Question

Collinearity

Discuss the problems that result when collinearity is present in a regression analysis.

How can you detect collinearity?

What remedial measures are available when collinearity is detected?

Answer 1

Discuss the problems that result when collinearity is present in a regression analysis.

Collinearity or multicollinearity:

When there are near linear dependencies among the regressors, the problem of collinearity is said to exist. If there is collinearity present in the model then the inferences based on the regression model can be misleading or erroneous.

The regressors are the columns of the design matrix ( X ) , so an exact linear dependence would result in a singular ( X'X ) . The presence of near linear dependencies can dramatically impact the ability to estimate regression coefficient.

How can you detect collinearity?

We can detect collinearity by the following methods.

1) Examination of correlation matrix

2) Variance inflation factors

3) Eigensystem Analysis of X'X

What remedial measures are available when collinearity is detected?

Some of the remedial measures are available when collinearity is detected are as follows:

1) Collecting additional data.

2) Model respecification

3) Ridge regression.method

4) principle component method.