I have 7 independent variables and 1 dependent variables. In one-way ANOVA, the difference for all the 7 independent variables are significant. However, the 7 independent variables are highly correlated. So I wonder what should I do in the next analysis to find the real effective variable.
I tried to put all 7 variables into stepwise regression. The coefficient of determination is low. And the residuals are not normally distributed.
Dear Tao,
In terms of multiple linear regression, it is advised that you should only include variables with bivariate correlation coefficients less than 0.8. The real issue to watch out for, however, is multicollinearity, not bivariate correlation. The cut off rule is a Variance Inflation Factor of 5.
You have at least 2 problems. The correlation among the IVs (called colinearity) messes things up and stepwise regression is very unstable. I would recommend doing the variable selection step by lasso, See the attached papers for guidance. Best, David
You can do a cluster analysis between the independent variables taking as a distance matrix the correlation matrix and then selecting a variable as representative of each group of highly correlated variables identified from a correlation coefficient value that indicates that there is no colinearity between them.
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