Regression Output

[jimjohn]

can someone plz help me with this:

I just conducted a simple linear regression and my output looks like this:
R^2 = .004, R^2adj = .004

Under ANOVA, the F* = 91.462, SIG = 0.000

Under Coefficients
beside my independent variable, it gives me:
Unstandardized = 0.112 , StdError = 0.012, T* = 9.564 , Sig = 0.000

I don't understand how can the tests be significant if the R^2 is so low? Since my test results are significant, that means I can conclude there is a relationship between the two variables right? Can someone please explain. thanks.

[jimjohn]

hey just to follow up when i do analyze - correlate - bivariate, I get r = .061 and significant. i guess because the sample size is so large (24,000), that maybe thats why even a small correlation becomes significant? any ideas. thanks.

jimjohn wrote

can someone plz help me with this:

I just conducted a simple linear regression and my output looks like this:
R^2 = .004, R^2adj = .004

Under ANOVA, the F* = 91.462, SIG = 0.000

Under Coefficients
beside my independent variable, it gives me:
Unstandardized = 0.112 , StdError = 0.012, T* = 9.564 , Sig = 0.000

I don't understand how can the tests be significant if the R^2 is so low? Since my test results are significant, that means I can conclude there is a relationship between the two variables right? Can someone please explain. thanks.

[Ornelas, Fermin-2]

I think you are asking two different questions. You are not mentioning what your dependent variable is. If by any chance you happen to fit a dependent variable that is binary your results will look somewhat similar to your results.
If you look at the definition of R^2 which is the proportion of variability that in Y explained by the linear model, this would suggest that you have a very poor fit. Ideally when fitting a linear model one would like to have a high R^2 and a set of statistically significant parameters, but obviously that is not the case in your exercise.

Another case that you will find is that when variables are collinear you will have a high R^2 but many of your parameter estimates will not be statistically significant.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
1789 W. Jefferson Street
Phoenix, AZ 85032
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of jimjohn
Sent: Friday, January 25, 2008 12:04 PM
To: [hidden email]
Subject: Regression Output

can someone plz help me with this:

I just conducted a simple linear regression and my output looks like this:
R^2 = .004, R^2adj = .004

Under ANOVA, the F* = 91.462, SIG = 0.000

Under Coefficients
beside my independent variable, it gives me:
Unstandardized = 0.112 , StdError = 0.012, T* = 9.564 , Sig = 0.000

I don't understand how can the tests be significant if the R^2 is so low?
Since my test results are significant, that means I can conclude there is a
relationship between the two variables right? Can someone please explain.
thanks.
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[Swank, Paul R]

Yes, it is because you have 24,000 observations on each measure. T = r /
sqrt[(1-r**2) / (n-2)] so the t for a correlation of .05 is 7.755. Even
a correlation of .01 has a t of 1.55 with a sample size that large. So
the next question is, can such a correlation ever be of real importance.
Examples could probably be given for the practical significance of such
a small correlation but it would be unlikely for most problems.

Paul R. Swank, Ph.D.
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center - Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
jimjohn
Sent: Friday, January 25, 2008 1:29 PM
To: [hidden email]
Subject: Re: Regression Output

hey just to follow up when i do analyze - correlate - bivariate, I get r
=
.061 and significant. i guess because the sample size is so large
(24,000),
that maybe thats why even a small correlation becomes significant? any
ideas. thanks.



jimjohn wrote:
>
>
> can someone plz help me with this:
>
> I just conducted a simple linear regression and my output looks like
this:
> R^2 = .004, R^2adj = .004
>
> Under ANOVA, the F* = 91.462, SIG = 0.000
>
> Under Coefficients
> beside my independent variable, it gives me:
> Unstandardized = 0.112 , StdError = 0.012, T* = 9.564 , Sig = 0.000
>
> I don't understand how can the tests be significant if the R^2 is so
low?
> Since my test results are significant, that means I can conclude there
is
> a relationship between the two variables right? Can someone please
> explain. thanks.
>

--
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[jimjohn]

thanks guys. so how would i go about deciding if the two variables are correlated in this case. im guessing that since the sample size is so high, a lot of my variables will be significantly correlated and that i shouldnt pay much attention to this particular significant correlation. does that sound rigiht? thx.

Swank, Paul R wrote

Yes, it is because you have 24,000 observations on each measure. T = r /
sqrt[(1-r**2) / (n-2)] so the t for a correlation of .05 is 7.755. Even
a correlation of .01 has a t of 1.55 with a sample size that large. So
the next question is, can such a correlation ever be of real importance.
Examples could probably be given for the practical significance of such
a small correlation but it would be unlikely for most problems.

Paul R. Swank, Ph.D.
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center - Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[e-mail]] On Behalf Of
jimjohn
Sent: Friday, January 25, 2008 1:29 PM
To: [e-mail]
Subject: Re: Regression Output

hey just to follow up when i do analyze - correlate - bivariate, I get r
=
.061 and significant. i guess because the sample size is so large
(24,000),
that maybe thats why even a small correlation becomes significant? any
ideas. thanks.



jimjohn wrote:
>
>
> can someone plz help me with this:
>
> I just conducted a simple linear regression and my output looks like
this:
> R^2 = .004, R^2adj = .004
>
> Under ANOVA, the F* = 91.462, SIG = 0.000
>
> Under Coefficients
> beside my independent variable, it gives me:
> Unstandardized = 0.112 , StdError = 0.012, T* = 9.564 , Sig = 0.000
>
> I don't understand how can the tests be significant if the R^2 is so
low?
> Since my test results are significant, that means I can conclude there
is
> a relationship between the two variables right? Can someone please
> explain. thanks.
>

--
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http://www.nabble.com/Regression-Output-tp15094660p15095024.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

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