[R] linear model - lm (Adjusted R-squared)?

[Erik Iverson]

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]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.