I never said that no multicollinearity is a formal algebraic *assumption* of Ordinary Least Squares. Obviously, solution (X'X)^{-1} * X'Y exists whenever matrix (X'X) is invertable. This is trivial. We are not passing a midterm in Statistics 102 here. Our task is somewhat bigger. bc1212 is asking for an accurate framework for comparing relative predictive power of predictors A and B. Read his/her post. He/she is not building a black-box data mining model, where out-of-sample prediction is the only concern. He/she wants to use the model for *inference*. Therefore, "inflated standard errors" are a huge concern, contrary to your statement above. Removing multicollinearity is likely to improve the accuracy of inference by an order of magnitude.

You quoted my post where I said absence of MC is not an assumption, then you went on to say you can't agree-- seemed much like you were saying you disagree and that absence of MC is an assumption. Maybe I misunderstood that part. If you reread post #3, you'll see that I'm clarifying for OP that your post isn't a generally true statement and that the OP should investigate the degree of MC in his or her model. It may be a huge problem or it may be negligible, even for inferential purposes. You'll also notice that I introduced the OP to both sides of the potential issue.

Without having seen any output, we can take a guess based on the Pearson correlation or make a VIF, but without seeing the actual output and looking at some other information, it's hard to judge how problematic MC is for this case. I'm open to the possibility that OP has different independent variables beyond A and B, which would be useful to know. Again, no one is disagreeing with you on variance inflation, possibly inappropriate inferences, and potential issues with parameter estimate instability.

Again, nobody is talking about "assumptions" which are *formally* violated. I am just drawing attention to bad statistical practices.

It's a lot more clear in this post what you are doing than the several prior where it seems you were doing the former.

I would not say "traditionally". Some resources use β as notation for unstandardized regression coefficients. But many others use B, A, φ or something else. Separately, many resources use word "beta" to refer to standardized regression coefficients (see an SPSS example below). That is why I said: "One useful metric is the *standardized regression coefficient *(**often** called "beta")." Did I say "always"?.... But I agree: this is a minor point. Your tolerance to multicollinearity is the truly dangerous element here.

For the "often" and "always" debate, sure you said "often", but again, it was possibly unclear for the OP who admitted to be less familiar with statistics. SPSS isn't also what I would call a resource for learning statistics (nor would I call any statistical software). Also, the "B" in SPSS is the capital Greek letter beta-- just another point that illustrates a benefit of clarification.

I think you're grabbing at straws in a defensive effort and jumping to the conclusion that I have an unreasonable "tolerance to multicollinearity." Before jumping to further incorrect positions, reread again what I wrote in post #3. I encouraged the OP to look into the degree of MC because it may or may not actually be problematic for inferences. I'd be curious to see how that indicates a "truly dangerous" "tolerance" regarding multicollinearity.

It seems, overall, that a few of these points of discussion could be avoided with increased clarification in the responses:

Almost everything in life is correlated. Allowing several correlated predictors into a linear model is totally fine **in cases of prediction**, **but for inferences on the betas as you want, you'll want to minimize the issues of multicollinearity**.

To see which predictor has the highest predictive power, you can look at a number of metrics. One useful metric is the *standardized regression coefficient* (called "beta" **in SPSS, not to be confused with the unstandardized coefficient which may also be called beta**).

My intention wasn't any sort of argument, but rather, clarification for OP. I think this is apparent in my initial few replies.

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