Multicollinearity occurs when two or more independent variables are highly (but not perfectly) correlated across observations, even though the regression equation seems to fit rather well. With Multicollinearity, the regression coefficients may not be individually statistically significant even when the overall regression is significant as judged by the F-statistic.

The existence of multicollinearity causes great problems in the field of statistical inference, as correcting for this form of estimation bias is often not possible. One way to check for multicollinearity is to find the sample correlation coefficients between all pairs of potential explanatory variables in the model. When the sample correlation coefficient between two variables is large in absolute value, it may be difficult to separate the effects of these two variables on the dependent variable Y. One remedy for mitigating multicollinearity involves the removal of select regression coefficients.

For example, a multivariate regression is defined by three independent variables. The t-statistics for these three independent variables, as well as the intercept, are as follows:

• t-intercept: 0.87
• t-independent variable one: -0.26
• t-independent variable two: 0.32
• t-independent variable three: -0.47
• R²: 0.95

When α is equal to 0.05, the critical value for the t-statistic is 1.735.

The regression profiled in this example appears to suffer from multicollinearity bias. This is indicated by the low t-statistics for the regression coefficients and the suspiciously high R². These two indicators occurring in conjunction should raise red flags as a possible indication of multicollinearity bias.