# [R] Coefficient of determination when intercept is zero

endeitz endeitz at yahoo.com
Wed Jan 17 23:18:53 CET 2007

```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
 0.6257541
> cor(predict(mod0),test\$Div)^2
 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
 0.9099358
> cor(predict(mod1),test\$Div)^2
 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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