Run Multiple Regression Models in for-Loop in R (Example)

In this article, I’ll show how to estimate multiple regression models in a for-loop in the R programming language.

Table of contents:

2) Example: Running Multiple Linear Regression Models in for-Loop

If you want to know more about these topics, keep reading…

Introducing Example Data

The following data is used as basement for this R programming tutorial:

set.seed(98274)                          # Creating example data
y <- rnorm(1000)
x1 <- rnorm(1000) + 0.2 * y
x2 <- rnorm(1000) + 0.2 * x1 + 0.1 * y
x3 <- rnorm(1000) - 0.1 * x1 + 0.3 * x2 - 0.3 * y
data <- data.frame(y, x1, x2, x3)
head(data)                               # Head of data
#            y         x1         x2          x3
# 1  0.5587036 -0.3779533 -0.5320515 -0.92069263
# 2  0.8422515 -1.3835572  1.2782521  0.87967960
# 3 -0.5395343 -0.9729798 -0.1515273 -0.05973894
# 4 -0.3522260  1.2977564 -0.3512013 -0.77239810
# 5  1.5848675 -1.3152806 -2.3644414 -1.14651812
# 6  0.2207957  1.8860636  0.1967851 -0.04963894

As you can see based on the previous RStudio console output, our example data consists of four numeric columns. The first variable is our regression outcome and the three other variables are our predictors.

Example: Running Multiple Linear Regression Models in for-Loop

In this Example, I’ll show how to run three regression models within a for-loop in R. In each for-loop iteration, we are increasing the complexity of our model by adding another predictor variable to the model.

First, we have to create a list in which we will store the outputs of our for-loop iterations:

mod_summaries <- list()                  # Create empty list

Now, we can write a for-loop that runs multiple linear regression models as shown below:

for(i in 2:ncol(data)) {                 # Head of for-loop
 
  predictors_i <- colnames(data)[2:i]    # Create vector of predictor names
  mod_summaries[[i - 1]] <- summary(     # Store regression model summary in list
    lm(y ~ ., data[ , c("y", predictors_i)]))
 
}

Let’s have a look at the output of our previously executed for-loop:

mod_summaries                            # Return summaries of all models

multiple linear regressions executed in a for-loop in r

As you can see in Figure 1, we have created a list containing three different summary statistics of three different linear regressions.

Video, Further Resources & Summary

If you need further explanations on the content of this tutorial, I can recommend having a look at the following video that I have published on my YouTube channel.

In the video, I’m explaining how top loop and repeat the estimation of multiple regression models using the R programming syntax of this tutorial in RStudio.

The YouTube video will be added soon.

In addition, you may want to read the other R programming tutorials of my homepage.

Summary: At this point you should know how to write a for-loop executing several linear regressions in R programming. Please let me know in the comments below, in case you have further questions. Furthermore, please subscribe to my email newsletter to receive updates on new articles.

18 Comments. Leave new

Fernando Ramires
March 1, 2021 1:46 pm

the procedure can follow the stepwise line….

Reply
- Joachim
  March 1, 2021 2:31 pm
  
  Hey Fernando,
  
  Could you explain what you mean? I’m afraid I don’t get it.
  
  Thanks!
  
  Joachim
  
  Reply
Farieda Hassanen
July 24, 2021 5:22 pm

Very good

Reply
- Joachim
  August 2, 2021 10:03 am
  
  Thanks a lot Farieda, glad you like it! 🙂
  
  Reply
Anu
August 7, 2021 8:07 am

Thanks for the excellent explanation. If you can provide steps on how to use PCA (principal component analysis) on series of images, that would be great!

Reply
- Joachim
  August 9, 2021 6:17 am
  
  Hey Anu,
  
  Thanks a lot for the nice feedback, and for the topic suggestion! I’ve noted it on my to-do list.
  
  Regards
  
  Joachim
  
  Reply
Helen
August 28, 2021 9:14 pm

How can I modify this to have models for each variable by itself? For example I want the the second model to just have x2 and the third model to just have x3 so on, rather than them building onto each other. Also could I change this to do and OddsRatio with each predictor?

Reply
- Joachim
  August 30, 2021 5:52 am
  Hey Helen,
  
  To change the predictor variables as you want, you only have to change
  predictors_i <- colnames(data)[2:i]
  predictors_i <- colnames(data)[2:i]
  to
  predictors_i <- colnames(data)[i]
  predictors_i <- colnames(data)[i]
  (i.e. remove the “2:”).
  
  I don’t have a tutorial on Odds Ratios yet. However, I think this article explains it nicely: https://jarrettmeyer.com/2019/07/23/odds-ratio-in-r
  
  Regards
  
  Joachim
  Reply
Hussein Ali
October 25, 2021 8:22 pm

Hi Mr Joachim
I need your help because till now no one answered my question and I hope to find the solution with you,

How can find the range (minimum, maximum) values for Intercept, slope and R-square in r programming?

Best Regards
Hussein Ali

Reply
- Joachim
  October 26, 2021 5:46 am
  
  Hey Hussein,
  
  Could you specify what you mean with range values?
  
  The following tutorial shows how to extract R-squared values from a regression model: https://statisticsglobe.com/r-extract-multiple-adjusted-r-squared-from-linear-regression-model
  
  Regards
  
  Joachim
  
  Reply
  - Hussein Ali
    November 8, 2021 12:23 pm
    
    I mean range for Intercept, Slope and R-square, I have paper (article) they found range (minimum, maximum) for intercept, slope and r-square.
    can you send to me your email to show you the paper?
    
    Reply
    - Joachim
      November 8, 2021 1:22 pm
      
      I’m not an expert on this topic. However, I have recently created a Facebook discussion group where people can ask questions about R programming and statistics. Could you post your question there? This way, others can contribute/read as well: https://www.facebook.com/groups/statisticsglobe
      
      Reply
Simon von Zahn
October 28, 2021 7:31 pm

Hello Joachim,
will this example provide me knowing which of the tested models to use for a maximised adj. R squared?
And which packages are required to run it?
Best Regards
Simon

Reply
- Joachim
  October 29, 2021 5:39 am
  
  Hey Simon,
  
  You may combine the for-loop with the code shown in this tutorial: https://statisticsglobe.com/r-extract-multiple-adjusted-r-squared-from-linear-regression-model
  
  This way, you could obtain a vector of R squared after running the for-loop.
  
  You don’t have to load any additional packages for this.
  
  Regards,
  Joachim
  
  Reply
Alexandre
April 14, 2022 8:42 pm

Hi Joachim,

I’m trying to use this method to run regressions on “n” independent variables, so up to every combination available from my columns. Is there a way I can do this with this code? Thanks for your help!

Reply
- Joachim
  April 18, 2022 8:49 am
  
  Hey Alexandre,
  
  This is definitely possible. I would find all combinations of your columns as explained here, and then I would convert each of the combinations to a formula as explained in Example 4 here.
  
  I don’t know if there is a more efficient way, though.
  
  Let me know in case you need further help.
  
  Regards,
  Joachim
  
  Reply
Simone
May 10, 2022 2:14 pm

Hi Joachim,
thank you for sharing this guide. I run several linear regression models with it. How can I extract all p-values and estimates of the list of models I created? I would like to store them in one dataframe.

Reply
- Joachim
  May 10, 2022 2:44 pm
  
  Hey Simone,
  
  Glad you find the tutorial helpful!
  
  You may extract p-values from regression models as explained here, and you may extract regression coefficients as explained here.
  
  Regards,
  Joachim
  
  Reply