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My understanding is that even regression does not give causality. It can only give association between y variable and x variables and possibly a direction. Am I correct? I've often found phrases similar to "x predicts y" even in most course textbooks and on various course pages online. And you often call the regressors as predictors and the y as the response.

  1. How fair is it to use it for linear regression?
  2. How about logistic regression? (if I do have a threshold t with which I can compare the probability?)
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    $\begingroup$ It's fine to use as long as you realize that there's no way to predict the error part, it's completely random. $\endgroup$
    – Aksakal
    Jan 18, 2015 at 18:14
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    $\begingroup$ There is no error part, random or otherwise. $\endgroup$
    – Frank Harrell
    Jan 18, 2015 at 20:53

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There is no problem with using the word "predict".

It is important to recognize that predictions are unrelated to causality. Consider a case where most people who die in a hospital emergency room die of a heart attack. If you hear that a patient died, but didn't know the cause, you could predict that it was probably from a heart attack, because you know that heart attacks are responsible for >50%. You are making a prediction, but you are predicting an unknown cause from a known effect. Also, the prediction in this example is categorical, so it is analogous to logistic regression. (The analogy is probably stronger to multinomial logistic regression, but that doesn't matter here.)

For what it's worth, predictions don't have to be related to any direct causal connection at all. You can make a prediction based on a spurious correlation, so long as the relationship is reliable. Consider predicting the unknown height of an identical twin based on the twin's sibling. In this case, both heights are effects of a set of common causes (shared genetics and environment). The height of neither twin is a cause or an effect of the other. Nonetheless, you can make very good predictions in this situation.

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  • $\begingroup$ 'spurious regression' example +1! $\endgroup$
    – PatrickT
    Jan 19, 2015 at 9:08

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