Dear List,
Many thanks for all of the responses, thoughts and suggestions. Very helpful.
To put the analysis into context and understand the application, the data
concerns pesticide concentrations from chalk river catchments taken during the
post-application flush period (April-July). Initial observations of the plots
suggest that concentration does decline with decreasing flow. However, how I
should approach and model any relationship is less straightforward, but
considerably clearer after posting to the list. The work aim(ed) to establish
if a CQ relationship existed, and if so, to then use a rating curve to predict
concentrations (and subsequently load) for un-sampled days.
Many of the x data is far away from the origin, and I now have an appreciation
of issues concerning inclusion/exclusion of the origin. I am now combining
other CQ data from my fieldwork to further investigate any possible
relationship between pesticide concentrations and discharge.
Many thanks,
Sion
Quoting [log in to unmask]:
> 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
>
--
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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