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If I have a dataset which contains two variables having a high negative correlation coefficient , should I delete one of the variables.

Consider the following scenario: If I have two columns, test_type_online and test_type_offline, which are (obviously) having a high negative correlation of-1, is it safe to say I can delete one of the two variables?

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    $\begingroup$ Do you know how you would proceed in the case of a high positive correlation coefficient? If so, simply negate one of the variables. $\endgroup$ – whuber Jul 7 '18 at 1:47
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Probably not if you only have two covariates. If you had 50 covariates and two were essentially replicates (like in your example), then yes, you could probably eliminate one without risking losing explanatory value of your covariate set.

Run regression in both scenarios. Compare the Multiple R-Squared value (an output of lm() in R. This will tell you if adding the additional covariate does anything to explain the variance in your response variable.

Also, you could try running regression using training/testing datasets, to better understand the predictive ability of a model with/without the highly collinear covariate. This could give you important insights (i.e. maybe one is better at prediction, but it may also have an extremely heavy tail and occasionally make horrendously erroneous predictions).

If the correlation coefficient is exactly 1 or -1, then delete it.

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