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May 17, 2011 at 14:13 comment added whuber @mp re Note 2: Ah, Taylor's Theorem! But real data aren't even continuous, much less differentiable. The model might enjoy these mathematical properties. Especially in explanations for the uninitiated, it may be worthwhile to distinguish the model's behavior from the behavior we expect of the data. Also, Taylor's Theorem says little about the range of $X$ values over which near-linearity holds. The regression model says this range is infinite!
May 17, 2011 at 6:06 comment added mpiktas @whuber, yes induce was a poor choice. I'll leave the explanation of interaction terms for somebody else :)
May 17, 2011 at 6:03 history edited mpiktas CC BY-SA 3.0
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May 17, 2011 at 5:52 comment added whuber @mp "Best" isn't necessarily a problem. I'm just trying to give you a hard time :-) (But "induce" did get my attention...) If you're truly after the "best" explanation, recall that a common point of confusion among the uninitiated is how to interpret interaction coefficients: after all, you can't independently vary (say) $X Y$; you do so by varying either $X$ or $Y$ or both. So an explanation that handles that situation would be most welcome.
May 17, 2011 at 5:49 comment added mpiktas @whuber, I knew that putting the word best was not a wise choice:) Thanks for your comment, I'll try to rephrase the answer.
May 17, 2011 at 5:44 comment added whuber ...assuming the behavior is truly linear across the entire range of $X$ values! (A more cautious answer might couch the same idea in terms of average changes and also avoid any hint of suggesting the relationship is causal.)
May 17, 2011 at 5:36 history answered mpiktas CC BY-SA 3.0