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Need help Using Linear Correlation as a Predictor

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12-04-2016 , 03:18 PM

Ted4242

centurion

Join Date: Feb 2006 Posts: 127

Hi, I'm building a predictive model. I have 3 variables and an output, so I'm using a linear regression, which gives me a linear equation in the form of:

X-Intercept+c1*Variable1+c2*Variable2+c3*variable3 = Output

This equation gives me a Correlation Coefficient of between 0 and 1.

My issue is when I remove the X-Intercept the Correlation Coefficient doesn't change. Also, if I multiply c1,c2,and c3 by the same constant the Correlation Coefficient doesn't change.

So, I could multiply the c1,c2,c3 by a huge number and still have the same correlation, but the equation's predictive value is worthless.

Any thoughts? Thanks!

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12-04-2016 , 10:07 PM

dessin d'enfant

Guest

Posts: n/a

I'm not sure I get the question. But maybe you care more about Mean Squared Error than correlation coefficient?

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12-05-2016 , 01:48 AM

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Quote:

Originally Posted by Ted4242

I think that you might be making the mistake of thinking that 1km isn't the same as 1,000,000,000,000nm.

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12-05-2016 , 04:23 AM

Ted4242

centurion

Join Date: Feb 2006 Posts: 127

Thanks for the response.

My goal for running the regression is to produce an equation that best predicts performance. My understanding is that the higher the correlation coefficient - the higher the predictive value of the linear equation. But, when you can simply multiply each variable in the equation by a billion and get the same correlation coefficient...what's the use of the linear equation as a predictor?

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12-05-2016 , 04:25 AM

Ted4242

centurion

Join Date: Feb 2006 Posts: 127

Quote:

Originally Posted by BrianTheMick2

I think that you might be making the mistake of thinking that 1km isn't the same as 1,000,000,000,000nm.

I may be. Care to explain?

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12-05-2016 , 10:33 AM

dessin d'enfant

Guest

Posts: n/a

Quote:

Originally Posted by Ted4242

Its the definition of correlation. y=x is perfectly correlated, but so is y=10000000x. Telling you x gives you 100% information about what y is in both cases.

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12-05-2016 , 03:05 PM

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Quote:

Originally Posted by Ted4242

I may be. Care to explain?

Multiplying by a huge constant doesn't affect the predictive value at all. You are just changing the units

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