# linear model - lm (Adjusted R-squared)?

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## linear model - lm (Adjusted R-squared)?

 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]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: linear model - lm (Adjusted R-squared)?

 See: http://en.wikipedia.org/wiki/Coefficient_of_determination#Adjusted_R2and 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]] > > ______________________________________________ > [hidden email] 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. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.