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> First, it's not necessarily wrong to fit a linear regression to data that might not be from a linear model, or that you know to be nonlinear. The data could b
by fractionalhare 6y ago
> First, it's not necessarily wrong to fit a linear regression to data that might not be from a linear model, or that you know to be nonlinear. The data could be linear enough in the region of interest for the line to nonetheless be useful, for example.
Yes, very good point! Likewise regression is not robust to log transformations, but we still use log transformations (depending on the data) because we may be able to tolerate some loss of information. If the nonlinear correlation is bounded below some tolerable amount it's okay to use the linear relationship on its own.
- gbrown 6y agoWhat do you mean it’s not robust to log transformations? A log transformation changes the inference to be about the conditional geometric mean, certainly (the log of an average of x is not equal to the average of a log(x)), but this is often quite sensible.