(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)
Andrew Dolman writes:
Just in case you need another example of why it is important to consider what the intercepts in a model represent, here is a short comment I [Dolman] just got published correcting a misinterpretation of a simple linear model, that would not have happened if they had centered their predictor around a sensible value.
The actual topic here is “Macrophyte effects on algal turbidity in subtropical versus temperate lakes.” That is so cool! I google-imaged “algal turbidity” and found the above pretty picture, which is on a webpage with a full discussion of turbidity. Surprisingly interesting stuff.
Back to Dolman and interpreting the intercept: Here’s his graph:
You can perhaps already see what happened. The other researchers noticed that the two lines had essentially the same intercept, and they concluded that the two groups differed only in the slopes, not the level of the lines. But this was a mistake in the context of the data. It’s similar to the example that Jennifer and I give in our book with the regressions of earnings on height. The intercept of such a regression doesn’t have much meaning, as it corresponds to the earnings of someone with a height of zero inches.
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