Looks like your data are indeed quite distant from the origin, so that the non-intercept regression is explaining lots by simply joining the means to the origin. In addition, the regression with intercept is not significant, and reduces the uncertainty hardly at all (r**2=0.05). You're not going to be able to use this to predict anything with any precision.
Brian G Miller, BSc, PhD, CStat
Director of Research Operations
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-----Original Message-----
From: Alain Zuur [mailto:[log in to unmask]]
Sent: 18 March 2006 01:32
To: [log in to unmask]
Subject: Re: [ENVSTAT] Regression through the origin
On Fri, 17 Mar 2006 18:38:23 +0000, Sion Roberts <[log in to unmask]>
wrote:
>Dear List,
>I have a question regarding interpretations of equivalent R2 for
regression
>through the origin.
>
See the regression chapter in Quinn and Keough (2002) for a discussion on
keeping in the intercept, even if it is not significant.
>I have two variables, river discharge (x) and pesticide concentration
(y), for
>which I wish to explore the relationship between concentration and
discharge,
>with a view to regressing y on x. It is my assumption that any regression
>should be forced through the origin on the basis that zero discharge
(m3/s)
>corresponds to zero concentration.
>
>I am using R 2.1.1, and have excluded the origin with lm(y ~ x -1).
>
>How do I assess the 'goodness of fit' other than using R2, as this is
>considerably larger in the model with no intercept, and makes me
sceptical when
>compared with the plotted data.
>
>Could anyone also recommend some literature that would help explain this?
>
>Thanks in advance and best wishes,
>Sion
>
># WITH INTERCEPT
>Call:
>lm(formula = p$logatz ~ p$Q)
>
>Residuals:
> Min 1Q Median 3Q Max
>-0.4786 -0.2557 -0.1291 0.1292 0.8178
>
>Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>(Intercept) 2.0094 0.7203 2.790 0.0087 **
>p$Q 0.2746 0.2078 1.322 0.1954
>---
>Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Can't say from this....but (i) is the majority of your p$Q values far away
from zero, and (ii) is it really a linear relationship? Your intecept
doesn't seem to be zero.....hence the model below starts to do funny
things.
Kind regards
Alain Zuur
www.brodgar.com
>
>Residual standard error: 0.3551 on 33 degrees of freedom
>Multiple R-Squared: 0.05026, Adjusted R-squared: 0.02148
>F-statistic: 1.746 on 1 and 33 DF, p-value: 0.1954
>
>
># WITHOUT INTERCEPT
>Call:
>lm(formula = p$logatz ~ p$Q - 1)
>
>Residuals:
> Min 1Q Median 3Q Max
>-0.56836 -0.24188 -0.07718 0.18188 0.92652
>
>Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>p$Q 0.85236 0.01896 44.95 <2e-16 ***
>---
>Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>Residual standard error: 0.3889 on 34 degrees of freedom
>Multiple R-Squared: 0.9834, Adjusted R-squared: 0.983
>F-statistic: 2020 on 1 and 34 DF, p-value: < 2.2e-16
>
>
>--
>Siôn Roberts
>
>Department of Geography,
>Queen Mary, University of London,
>London,
>E1 4NS.
>
>Tel: +44 20 7882 5400
>http://www.geog.qmul.ac.uk/postgraduate/student/roberts.html
>
>
>
>
>_____________________________________________________________________
>
>
>
> Homepage for envstat list: http://www.jiscmail.ac.uk/files/envstat
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