Question

Using the scatterplot matrix for the seven regressors,?identify the most severe multicollinearity existing between regressors. Is there a possible simple way to mitigate that multicollinearity in this case?

Multivariate Correlations X1 X1 1.0000 X2 -0.2118 X3 0.4649 X4 0.6586 X5 -0.8085 X6 -0.8085 X7 -0.1817 X2 -0.2118 1.0000 0.6310 0.1651 0.1546 0.1546 0.2559 Х3 0.4649 0.6310 1.0000 0.8047 -0.5306 -0.5306 0 .0752 X4 0.6586 0.1651 0.8047 1.0000 -0.6457 -0.6457 -0.1166 X5 -0.8085 0.1546 -0.5306 -0.6457 1.0000 1.0000 0.1472 X6 -0.8085 0.1546 -0.5306 -0.6457 1.0000 1.0000 0.1472 X7 -0.1817 0.2559 0.0752 -0.1166 0.1472 0.1472 1.0000 The correlations are estimated by Row-wise method. Scatterplot Matrix 1000 500 0 2000 1500 1000

Answer 1

(first part) answer is x5 and x6

Multicollinearity is the occurrence of high linear correlation/inter-correlations among independent variables/predictors in a multiple regression model. Here the correlation between x5 and x6 is 1, which is perfect correlation between the two variable. So the most severe multicollinearity existing between regressors are x5 and x6.

(second) either remove x5 or x6 from the model

There a possible simple way to mitigate that multicollinearity in this case is to remove one of the two variable x5 and x6. i.e. either remove x5 or x6 from the multiple regression model