Dear List,
I have a question regarding interpretations of equivalent R2 for regression
through the origin.
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$Q 0.2746 0.2078 1.322 0.1954
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.3551 on 33 degrees of freedom
Multiple R-Squared: 0.05026, Adjusted R-squared: 0.02148
F-statistic: 1.746 on 1 and 33 DF, p-value: 0.1954
# WITHOUT INTERCEPT
Call:
lm(formula = p$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
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