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sackerpint1

Member

Registered: 2009-09-24

Posts: 5

General question about linear regression

Let's say you are fitting a linear regression function to a set of data. 

Let's say you get a positive relation when plotting the residuals against the actual outcomes and no relation when you plot the residuals against the fitted values.  In what event would this difference occur?  Also, which would be the more meaningful plot?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: General question about linear regression

Hi sackerpint1;

Do you mean a positive correlation? You can have a positive, negative and no correaltion between two sets of data or two variables. Positve correlation would imply that when one increases so does the other. Negative correlation , when one decreases so does the other. 0 correlation means there is no relationship between the data or variables. A correlation of .89 would mean a strong relationship exists between the variables or data.

Neither plot really is more meaningful in the sense that 2 variables can be strongly correlated but have no real relation. It is possible the rise of  some disease and  an increase in sales of Britney Spears' albums could have a high correlation but it is obvious that there is probably no connection between them.

In statitistics you have to very careful as to what conclusions you form from the data.

Last edited by bobbym (2009-09-26 10:28:05)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: General question about linear regression

Let's say you get a positive relation when plotting the residuals against the actual outcomes and no relation when you plot the residuals against the fitted values.  In what event would this difference occur?

The only way I could see this occurring is if your model is not accurate.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."