pull out p-values and r-squared from a linear regression

How do you pull out the p-value (for the significance of the coefficient of the single explanatory variable being non-zero) and R-squared value from a simple linear regression model? For example...

x = cumsum(c(0, runif(100, -1, +1)))
y = cumsum(c(0, runif(100, -1, +1)))
fit = lm(y ~ x)
summary(fit)

I know that summary(fit) displays the p-value and R-squared value, but I want to be able to stick these into other variables.

r-squared: You can return the r-squared value directly from the summary object summary(fit)$r.squared. See names(summary(fit)) for a list of all the items you can extract directly.

Model p-value: If you want to obtain the p-value of the overall regression model, this blog post outlines a function to return the p-value:

lmp <- function (modelobject) {
	if (class(modelobject) != "lm") stop("Not an object of class 'lm' ")
	f <- summary(modelobject)$fstatistic
	p <- pf(f[1],f[2],f[3],lower.tail=F)
	attributes(p) <- NULL
	return(p)
}

> lmp(fit)
[1] 1.622665e-05

In the case of a simple regression with one predictor, the model p-value and the p-value for the coefficient will be the same.

Coefficient p-values: If you have more than one predictor, then the above will return the model p-value, and the p-value for coefficients can be extracted using:

summary(fit)$coefficients[,4]  

Alternatively, you can grab the p-value of coefficients from the anova(fit) object in a similar fashion to the summary object above.

Notice that summary(fit) generates an object with all the information you need. The beta, se, t and p vectors are stored in it. Get the p-values by selecting the 4th column of the coefficients matrix (stored in the summary object):

summary(fit)$coefficients[,4] 
summary(fit)$r.squared

Try str(summary(fit)) to see all the info that this object contains.

Edit: I had misread Chase's answer which basically tells you how to get to what I give here.

You can see the structure of the object returned by summary() by calling str(summary(fit)). Each piece can be accessed using $. The p-value for the F statistic is more easily had from the object returned by anova.

Concisely, you can do this:

rSquared <- summary(fit)$r.squared
pVal <- anova(fit)$'Pr(>F)'[1]

I came across this question while exploring suggested solutions for a similar problem; I presume that for future reference it may be worthwhile to update the available list of answer with a solution utilising the broom package.

Sample code

x = cumsum(c(0, runif(100, -1, +1)))
y = cumsum(c(0, runif(100, -1, +1)))
fit = lm(y ~ x)
require(broom)
glance(fit)

Results

>> glance(fit)
  r.squared adj.r.squared    sigma statistic    p.value df    logLik      AIC      BIC deviance df.residual
1 0.5442762     0.5396729 1.502943  118.2368 1.3719e-18  2 -183.4527 372.9055 380.7508 223.6251          99

---

Side notes

I find the glance function is useful as it neatly summarises the key values. The results are stored as a data.frame which makes further manipulation easy:

>> class(glance(fit))
[1] "data.frame"

While both of the answers above are good, the procedure for extracting parts of objects is more general.

In many cases, functions return lists, and the individual components can be accessed using str() which will print the components along with their names. You can then access them using the $ operator, i.e. myobject$componentname.

In the case of lm objects, there are a number of predefined methods one can use such as coef(), resid(), summary() etc, but you won't always be so lucky.

Extension of @Vincent 's answer:

For lm() generated models:

summary(fit)$coefficients[,4]   ##P-values 
summary(fit)$r.squared          ##R squared values

For gls() generated models:

summary(fit)$tTable[,4]         ##P-values
##R-squared values are not generated b/c gls uses max-likelihood not Sums of Squares

To isolate an individual p-value itself, you'd add a row number to the code:

For example to access the p-value of the intercept in both model summaries:

summary(fit)$coefficients[1,4]
summary(fit)$tTable[1,4]  

• Note, you can replace the column number with the column name in each of the above instances:

   summary(fit)$coefficients[1,"Pr(>|t|)"]  ##lm 
   summary(fit)$tTable[1,"p-value"]         ##gls 
  

If you're still unsure of how to access a value form the summary table use str() to figure out the structure of the summary table:

str(summary(fit))

This is the easiest way to pull the p-values:

coef(summary(modelname))[, "Pr(>|t|)"]

I used this lmp function quite a lot of times.

And at one point I decided to add new features to enhance data analysis. I am not in expert in R or statistics but people are usually looking at different information of a linear regression :

• p-value
• a and b
• r²
• and of course the aspect of the point distribution

Let's have an example. You have here

Here a reproducible example with different variables:

Ex<-structure(list(X1 = c(-36.8598, -37.1726, -36.4343, -36.8644, 
-37.0599, -34.8818, -31.9907, -37.8304, -34.3367, -31.2984, -33.5731
), X2 = c(64.26, 63.085, 66.36, 61.08, 61.57, 65.04, 72.69, 63.83, 
67.555, 76.06, 68.61), Y1 = c(493.81544, 493.81544, 494.54173, 
494.61364, 494.61381, 494.38717, 494.64122, 493.73265, 494.04246, 
494.92989, 494.98384), Y2 = c(489.704166, 489.704166, 490.710962, 
490.653212, 490.710612, 489.822928, 488.160904, 489.747776, 490.600579, 
488.946738, 490.398958), Y3 = c(-19L, -19L, -19L, -23L, -30L, 
-43L, -43L, -2L, -58L, -47L, -61L)), .Names = c("X1", "X2", "Y1", 
"Y2", "Y3"), row.names = c(NA, 11L), class = "data.frame")


library(reshape2)
library(ggplot2)
Ex2<-melt(Ex,id=c("X1","X2"))
colnames(Ex2)[3:4]<-c("Y","Yvalue")
Ex3<-melt(Ex2,id=c("Y","Yvalue"))
colnames(Ex3)[3:4]<-c("X","Xvalue")

ggplot(Ex3,aes(Xvalue,Yvalue))+
          geom_smooth(method="lm",alpha=0.2,size=1,color="grey")+
          geom_point(size=2)+
          facet_grid(Y~X,scales='free')


#Use the lmp function

lmp <- function (modelobject) {
  if (class(modelobject) != "lm") stop("Not an object of class 'lm' ")
  f <- summary(modelobject)$fstatistic
	p <- pf(f[1],f[2],f[3],lower.tail=F)
	attributes(p) <- NULL
	return(p)
	}

# create function to extract different informations from lm

lmtable<-function (var1,var2,data,signi=NULL){
  #var1= y data : colnames of data as.character, so "Y1" or c("Y1","Y2") for example
  #var2= x data : colnames of data as.character, so "X1" or c("X1","X2") for example
  #data= data in dataframe, variables in columns
  # if signi TRUE, round p-value with 2 digits and add *** if <0.001, ** if < 0.01, * if < 0.05.
  
  if (class(data) != "data.frame") stop("Not an object of class 'data.frame' ")
  Tabtemp<-data.frame(matrix(NA,ncol=6,nrow=length(var1)*length(var2)))
  for (i in 1:length(var2))
       {
  Tabtemp[((length(var1)*i)-(length(var1)-1)):(length(var1)*i),1]<-var1
  Tabtemp[((length(var1)*i)-(length(var1)-1)):(length(var1)*i),2]<-var2[i]
  colnames(Tabtemp)<-c("Var.y","Var.x","p-value","a","b","r^2")
  
  for (n in 1:length(var1))
  {
  Tabtemp[(((length(var1)*i)-(length(var1)-1))+n-1),3]<-lmp(lm(data[,var1[n]]~data[,var2[i]],data))
  
  Tabtemp[(((length(var1)*i)-(length(var1)-1))+n-1),4]<-coef(lm(data[,var1[n]]~data[,var2[i]],data))[1]
  
  Tabtemp[(((length(var1)*i)-(length(var1)-1))+n-1),5]<-coef(lm(data[,var1[n]]~data[,var2[i]],data))[2]
  
  Tabtemp[(((length(var1)*i)-(length(var1)-1))+n-1),6]<-summary(lm(data[,var1[n]]~data[,var2[i]],data))$r.squared
  }
  }
  
  signi2<-data.frame(matrix(NA,ncol=3,nrow=nrow(Tabtemp)))
  signi2[,1]<-ifelse(Tabtemp[,3]<0.001,paste0("***"),ifelse(Tabtemp[,3]<0.01,paste0("**"),ifelse(Tabtemp[,3]<0.05,paste0("*"),paste0(""))))
  signi2[,2]<-round(Tabtemp[,3],2)
  signi2[,3]<-paste0(format(signi2[,2],digits=2),signi2[,1])
  
  for (l in 1:nrow(Tabtemp))
    {
  Tabtemp$"p-value"[l]<-ifelse(is.null(signi),
         Tabtemp$"p-value"[l],
         ifelse(isTRUE(signi),
                paste0(signi2[,3][l]),
                Tabtemp$"p-value"[l]))
  }
      
   Tabtemp
}

# ------- EXAMPLES ------

lmtable("Y1","X1",Ex)
lmtable(c("Y1","Y2","Y3"),c("X1","X2"),Ex)
lmtable(c("Y1","Y2","Y3"),c("X1","X2"),Ex,signi=TRUE)

There is certainly a faster solution than this function but it works.

For the final p-value displayed at the end of summary(), the function uses pf() to calculate from the summary(fit)$fstatistic values.

fstat <- summary(fit)$fstatistic
pf(fstat[1], fstat[2], fstat[3], lower.tail=FALSE)

Source: [1], [2]

Another option is to use the cor.test function, instead of lm:

> x <- c(44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1)
> y <- c( 2.6,  3.1,  2.5,  5.0,  3.6,  4.0,  5.2,  2.8,  3.8)

> mycor = cor.test(x,y)
> mylm = lm(x~y)

# r and rsquared:
> cor.test(x,y)$estimate ** 2
      cor 
0.3262484 
> summary(lm(x~y))$r.squared
[1] 0.3262484

# P.value 

> lmp(lm(x~y))  # Using the lmp function defined in Chase's answer
[1] 0.1081731
> cor.test(x,y)$p.value
[1] 0.1081731

x = cumsum(c(0, runif(100, -1, +1)))
y = cumsum(c(0, runif(100, -1, +1)))
fit = lm(y ~ x)
> names(summary(fit))
[1] "call"          "terms"        
 [3] "residuals"     "coefficients" 
 [5] "aliased"       "sigma"        
 [7] "df"            "r.squared"    
 [9] "adj.r.squared" "fstatistic"   
[11] "cov.unscaled" 
    summary(fit)$r.squared

Use:

(summary(fit))$coefficients[***num***,4]

where num is a number which denotes the row of the coefficients matrix. It will depend on how many features you have in your model and which one you want to pull out the p-value for. For example, if you have only one variable there will be one p-value for the intercept which will be [1,4] and the next one for your actual variable which will be [2,4]. So your num will be 2.