Extract Multiple & Adjusted R-Squared from Linear Regression Model in R (2 Examples)
In this tutorial you’ll learn how to return multiple and adjusted R-squared in the R programming language.
The tutorial is structured as follows:
Let’s get started!
Example Data
First, we have to create some example data:
set.seed(96149) # Create randomly distributed data x1 <- rnorm(300) x2 <- rnorm(300) - 0.1 * x1 x3 <- rnorm(300) + 0.1 * x1 - 0.5 * x2 x4 <- rnorm(300) - 0.4 * x2 - 0.1 * x3 x5 <- rnorm(300) + 0.1 * x1 - 0.2 * x3 y <- rnorm(300) + 0.5 * x1 + 0.5 * x2 + 0.15 * x3 - 0.4 * x4 - 0.25 * x5 data <- data.frame(y, x1, x2, x3, x4, x5) head(data) # Show first six lines # y x1 x2 x3 x4 x5 # 1 -0.2553708 0.4399836 0.2144276 -0.24921404 0.7626867 -0.000145643 # 2 0.9582395 0.1866435 -0.8674311 0.56741079 0.2266811 -0.482339176 # 3 0.5354913 0.5123466 0.8521783 -0.15192973 -0.5772924 1.598023729 # 4 -0.1751357 -0.2642710 -0.6622039 0.91587607 -0.8784139 0.175314482 # 5 0.4741015 -1.2264237 1.1414974 -0.02544234 -1.4704185 2.154123548 # 6 -2.4687764 -0.4832017 -0.6963652 -0.27676098 3.5740767 1.535050595
The previous output of the RStudio console illustrates the structure of our example data – It consists of six variables, whereby the column y is containing our outcome and the remaining columns are used as predictors.
Let’s use our data to fit a linear regression model in R:
mod_summary <- summary(lm(y ~ ., data)) # Run linear regression model mod_summary # Summary of linear regression model
The previous image shows the output of our linear regression analysis. I have marked the values we are interested in in this example in red.
Example 1: Extracting Multiple R-squared from Linear Regression Model
This Example shows how to pull out the multiple R-squared from our output.
mod_summary$r.squared # Returning multiple R-squared # 0.4131335
The RStudio console shows our result: The multiple R-squared of our model is 0.4131335.
Example 2: Extracting Adjusted R-squared from Linear Regression Model
Alternatively to the multiple R-squared, we can also extract the adjusted R-squared:
mod_summary$adj.r.squared # Returning adjusted R-squared # 0.4031528
The adjusted R-squared of our linear regression model is 0.4031528.
Video, Further Resources & Summary
Do you need further info on the R programming codes of this tutorial? Then you may want to watch the following video of my YouTube channel. In the video, I’m explaining the R programming code of this tutorial.
The YouTube video will be added soon.
In addition to the video, you might read the other tutorials of this homepage. I have published numerous tutorials about linear regression models already.
- Extract F-Statistic, Number of Predictor Variables/Categories & Degrees of Freedom
- Extract Regression Coefficients of Linear Model
- R Programming Examples
This page illustrated how to pull out multiple and adjusted R-squared from regressions in the R programming language. Don’t hesitate to let me know in the comments below, in case you have any further questions or comments. Furthermore, don’t forget to subscribe to my email newsletter in order to receive updates on new tutorials.
I’m Joachim Schork. On this website, I provide statistics tutorials as well as code in Python and R programming.
16 Comments. Leave new
hello i want to extract feature by using r square with R studio kindly guide the codding and procedure as well..thanks
Hi Aroosa,
I’m not sure if I get your question. Could you please tell some more details?
Thanks!
Joachim
Hi, Joachim,
Do you have any idea how to derive outcome from summary(stan_glm). Thanks
Hey Jason,
Could you explain what exactly you mean with “outcome”?
Regards,
Joachim
And how can I pull if I have a list with 24 results of lm inside?
Hey Lais,
So your list contains 24 different model outputs? Please clarify your question 🙂
Regards,
Joachim
Hi Joachim,
Can i get a coeficient of determination for the test predictions?
Hey Fernando,
The coefficient of determination (i.e. R-Squared) is extracted in Example 1 of this tutorial. Or am I misinterpreting your question?
Regards,
Joachim
Hey Joachim,
I would like to know how can I get an adjusted regression. Is it the adjusted R-square?
Thanks,
Christian
Hi Christian,
Could you please explain what exactly you mean with “adjusted regression”?
Regards,
Joachim
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .567a .321 .309 .11806
a. Predictors: (Constant), X4, X2, X1, X3
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 1.504 4 .376 26.975 .000b
Residual 3.178 228 .014
Total 4.682 232
a. Dependent Variable: WPI
b. Predictors: (Constant), X4, X2, X1, X3
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) 3.200 .008 413.317 .000
X1 .040 .008 .284 5.101 .000
X2 .067 .008 .473 8.599 .000
X3 .010 .008 .069 1.231 .220
X4 .007 .008 .050 .902 .368
a. Dependent Variable: WPI
Hello,
What is your question about?
Best,
Cansu
hello,
interpretation of the findings
Hello,
This source of Scribbr could be useful for you to interpret the results in case you are using ANOVA model.
Best,
Cansu
Thank you
Welcome!