[R] Coefficient of determination when intercept is zero

From: endeitz <endeitz_at_yahoo.com>
Date: Wed 17 Jan 2007 - 22:18:53 GMT

I am curious as to the "lm" calculation of R2 (multiple coefficient of determination, I assume) when intercept is zero. I have 18 data points, two independent variables:

First, a model with an intercept:

> mod0=lm(Div~Rain+Evap,data=test)
> summary(mod0)$r.squared

[1] 0.6257541
> cor(predict(mod0),test$Div)^2

[1] 0.6257541

The $r.squared and the result from "cor" are the same, as I would expect.

Now we try a model with zero intercept:

> mod1=lm(Div~0+Rain+Evap,data=test)
> summary(mod1)$r.squared

[1] 0.9099358
> cor(predict(mod1),test$Div)^2

[1] 0.5813659

Why has the $r.squared value increased to 0.9? And now the result from "cor" is not the same? Is there a special way to calculate the coefficient of determination when the intercept is zero?

Cheers,

Ed.

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