See:
http://en.wikipedia.org/wiki/Coefficient_of_determination#Adjusted_R2
and the implementation in summary.lm :
ans$adj.r.squared <- 1 - (1 - ans$r.squared) * ((n -
df.int)/rdf)
Brian Smith wrote:> Hi,
>
> Sorry for the naive question, but what exactly does the 'Adjusted
R-squared'
> coefficient in the summary of linear model adjust for?
>
> Sample code:
>
>> x <- rnorm(15)
>> y <- rnorm(15)
>> lmr <- lm(y~x)
>> summary(lmr)
>
> Call:
> lm(formula = y ~ x)
>
> Residuals:
> Min 1Q Median 3Q Max
> -1.7828 -0.7379 -0.4485 0.7563 2.1570
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) -0.13084 0.28845 -0.454 0.658
> x 0.01923 0.25961 0.074 0.942
>
> Residual standard error: 1.106 on 13 degrees of freedom
> Multiple R-squared: 0.0004217, Adjusted R-squared: -0.07647
> F-statistic: 0.005485 on 1 and 13 DF, p-value: 0.942
>
>> cor(x,y)
> [1] 0.02053617
>
>
> - What factors are included in the adjustment?
>
> many thanks!
>
> [[alternative HTML version deleted]]
>
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