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Topic: Explanation for why linear regression is a poor fit
Replies: 8   Last Post: Feb 15, 2013 10:36 AM

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Richard Ulrich

Posts: 2,961
Registered: 12/13/04
Re: Explanation for why linear regression is a poor fit
Posted: Feb 4, 2013 6:13 PM
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On Mon, 4 Feb 2013 12:55:36 -0800 (PST), wrote:

>I haven't taken stats in a few years and recently there have been a lot thrown around my work place, including the attached graph (and raw data). I realize that low R2 mean that the linear regression is not a good fit, but it produces a p-value 0.025. I can't formulate a solid argument because I don't understand the material well enough. Am I incorrect in saying this is a poor fit? Even visually to me it looks like a poor fit. Additionally, he says things like: "FC Count at Samish River/Thomas Road: N = 498, r2 = 0.01, p = 0.025, meaning it is significant at 97.5% confidence" I know you can't use P-values to describe stats like this. I need help explaining why this data isn't showing a significant declining trend with a linear regression (in less of course I am incorrect.)
>Thanks for clarification and help.
>Data and Graph:

Oh, there's a declining trend, of sorts. I'm tempted to say
that Nobody calls R^2 of 0.01 a large effect -- but that's
not really true. Context rules.

The highest 5 outcome scores are all in the first half of the graph,
and the very highest one is near the beginning. Does that
seem important? That's most of the effect.

On the other hand, very few people would say that any
time series is properly tested by a simply linear regression
when there are autocorrelation effects... which there almost
always are.

As to the size of the effect, and how few cases it depends
on -- I'm "pretty sure" that the trend becomes n.s. if you
remove the top 5 points; "probably" for the top 3, and
"maybe" for removing the top one alone.

Rich Ulrich

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