Hello Mohammd,

The answer depends on your research goal/s. If your primary goal was to determine the combined explanatory power of the four independent variables you used, then collinearity won't have much impact on that result.

Excessive collinearity can yield biased values for individual (predictor) regression coefficients, however (both standardized and unstandardized), so that could make interpretation of the contribution of individual variables challenging.

Bivariate plots (and correlations) are one place to start, but do not necessarily explain whether one variable is largely redundant with the remainder of the IV ensemble.

How high or how low the overall R-squared turns out to be is not the trigger for deciding to be concerned about collinearity.

Good luck with your work.

Hello Mohammd,

Conduct VIF test, remove the variable with VIF greater than 10, reestimate your model.

Best regards

As David Morse said, it depends on your objective. If your objective is generalizable prediction accuracy -- generating an OLS model that manifests accuracy in predicting the criterion in the population or an alternate sample from the population, multicollinearity, actually up to close to machine precision (going beyond that will create a singular predictor variable matrix yielding an insoluble OLS solution), will have no effect. [As I am apparently without Greek symbols here I will have to improvise.] The criterion that I intend is MSE=SIGMA[(y-yhat)2]/N for "absolute" accuracy, or ry,yhat, for "relative" accuracy, where y is the population criterion value and yhat is the sample estimated value.

I assume that 125.8 is the typically used CI from the predictor variable matrix, and, although 30 is often recommended as the point at which you should worry, as I say, it depends on your goal, if prediction accuracy, worry not.

On the other hand, if explanation is you goal (estimation of population Betas from sample Betas) then increasing multicollinearity will do damage to SIGMA[(Beta-Betahat)2]/p, where Beta is the vector of p population weights, and Betahat is the corresponding vector of sample estimated weights.

I can also share a publication (full-test on RG) that shows through simulation exactly what I have said. Multicollinearity as evidenced by CIs or VIFs that are what would normally be considered enormous are shown to have no effect on prediction accuracy. But, of course, this is relevant only if prediction accuracy is your goal. It is:

Article Multicollinearity's Effect on Regression Prediction Accuracy...

You may also find interest in some other pieces in my "Multicollinearity, Validity Concentration, and Prediction Accuracy" project.

My best on your research.

John