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.

summary(fit)

r <- summary(lm(rnorm(10)~runif(10)))

11 Answers
11

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.

summary(fit)$r.squared

names(summary(fit))

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.

anova(fit)

inherits

class

unname(pf(f[1],f[2],f[3],lower.tail=F))

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)

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


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

str(summary(fit))

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

summary(fit)$coefficients[1,4]

lm()

gls()

lm()

gls()

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.

summary()

str(summary(fit))

$

anova

Concisely, you can do this:

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


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.

str()

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.

coef()

resid()

summary()

Extension of @Vincent 's answer:

For lm() generated models:

lm()

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


For gls() generated models:

gls()

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()

str(summary(fit))


I cam 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.

broom

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)


>> 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 useful as it neatly summarises the useful values. As an added benefit the results are stored as a data.frame which makes further manipulation easy:

glance

data.frame

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


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 :

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.

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 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.

num

num

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


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