# Extract Regression Coefficients of Linear Model in R (Example)

This tutorial illustrates how to **return the regression coefficients of a linear model estimation** in R programming.

The content of the tutorial looks like this:

So without further ado, let’s get started:

## Constructing Example Data

We use the following data as basement for this tutorial:

set.seed(87634) # Create random example data x1 <- rnorm(1000) x2 <- rnorm(1000) + 0.3 * x1 x3 <- rnorm(1000) + 0.1 * x1 + 0.2 * x2 x4 <- rnorm(1000) + 0.2 * x1 - 0.3 * x3 x5 <- rnorm(1000) - 0.1 * x2 + 0.1 * x4 y <- rnorm(1000) + 0.1 * x1 - 0.2 * x2 + 0.1 * x3 + 0.1 * x4 - 0.2 * x5 data <- data.frame(y, x1, x2, x3, x4, x5) head(data) # Head of data # y x1 x2 x3 x4 x5 # 1 -0.6441526 -0.42219074 -0.12603789 -0.6812755 0.9457604 -0.39240211 # 2 -0.9063134 -0.19953976 -0.35341624 1.0024131 1.3120547 0.05489608 # 3 -0.8873880 0.30450638 -0.58551780 -1.1073109 -0.2047048 0.44607502 # 4 0.4567184 1.33299913 -0.05512412 -0.5772521 0.3476488 1.65124595 # 5 0.6631039 -0.36705475 -0.26633088 1.0520141 -0.3281474 0.77052209 # 6 1.3952174 0.03528151 -2.43580550 -0.6727582 1.8374260 1.06429782 |

set.seed(87634) # Create random example data x1 <- rnorm(1000) x2 <- rnorm(1000) + 0.3 * x1 x3 <- rnorm(1000) + 0.1 * x1 + 0.2 * x2 x4 <- rnorm(1000) + 0.2 * x1 - 0.3 * x3 x5 <- rnorm(1000) - 0.1 * x2 + 0.1 * x4 y <- rnorm(1000) + 0.1 * x1 - 0.2 * x2 + 0.1 * x3 + 0.1 * x4 - 0.2 * x5 data <- data.frame(y, x1, x2, x3, x4, x5) head(data) # Head of data # y x1 x2 x3 x4 x5 # 1 -0.6441526 -0.42219074 -0.12603789 -0.6812755 0.9457604 -0.39240211 # 2 -0.9063134 -0.19953976 -0.35341624 1.0024131 1.3120547 0.05489608 # 3 -0.8873880 0.30450638 -0.58551780 -1.1073109 -0.2047048 0.44607502 # 4 0.4567184 1.33299913 -0.05512412 -0.5772521 0.3476488 1.65124595 # 5 0.6631039 -0.36705475 -0.26633088 1.0520141 -0.3281474 0.77052209 # 6 1.3952174 0.03528151 -2.43580550 -0.6727582 1.8374260 1.06429782

The previously shown RStudio console output shows the structure of our example data – It’s a data frame consisting of six numeric columns. The first variable y is the outcome variable. The remaining variables x1-x5 are the predictors.

## Example: Extracting Coefficients of Linear Model

In this Example, I’ll illustrate how to estimate and save the regression coefficients of a linear model in R. First, we have to estimate our statistical model using the lm and summary functions:

summary(lm(y ~ ., data)) # Estimate model # Call: # lm(formula = y ~ ., data = data) # # Residuals: # Min 1Q Median 3Q Max # -2.9106 -0.6819 -0.0274 0.7197 3.8374 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) -0.01158 0.03204 -0.362 0.717749 # x1 0.10656 0.03413 3.122 0.001847 ** # x2 -0.17723 0.03370 -5.259 1.77e-07 *** # x3 0.11174 0.03380 3.306 0.000982 *** # x4 0.09933 0.03295 3.015 0.002638 ** # x5 -0.24871 0.03323 -7.485 1.57e-13 *** # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # # Residual standard error: 1.011 on 994 degrees of freedom # Multiple R-squared: 0.08674, Adjusted R-squared: 0.08214 # F-statistic: 18.88 on 5 and 994 DF, p-value: < 2.2e-16 |

summary(lm(y ~ ., data)) # Estimate model # Call: # lm(formula = y ~ ., data = data) # # Residuals: # Min 1Q Median 3Q Max # -2.9106 -0.6819 -0.0274 0.7197 3.8374 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) -0.01158 0.03204 -0.362 0.717749 # x1 0.10656 0.03413 3.122 0.001847 ** # x2 -0.17723 0.03370 -5.259 1.77e-07 *** # x3 0.11174 0.03380 3.306 0.000982 *** # x4 0.09933 0.03295 3.015 0.002638 ** # x5 -0.24871 0.03323 -7.485 1.57e-13 *** # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # # Residual standard error: 1.011 on 994 degrees of freedom # Multiple R-squared: 0.08674, Adjusted R-squared: 0.08214 # F-statistic: 18.88 on 5 and 994 DF, p-value: < 2.2e-16

The previous output of the RStudio console shows all the estimates we need. However, the coefficient values are not stored in a handy format. Let’s therefore convert the summary output of our model into a data matrix:

matrix_coef <- summary(lm(y ~ ., data))$coefficients # Extract coefficients in matrix matrix_coef # Return matrix of coefficients # Estimate Std. Error t value Pr(>|t|) # (Intercept) -0.01158450 0.03203930 -0.3615716 7.177490e-01 # x1 0.10656343 0.03413045 3.1222395 1.846683e-03 # x2 -0.17723211 0.03369896 -5.2592753 1.770787e-07 # x3 0.11174223 0.03380415 3.3055772 9.817042e-04 # x4 0.09932518 0.03294739 3.0146597 2.637990e-03 # x5 -0.24870659 0.03322673 -7.4851370 1.572040e-13 |

matrix_coef <- summary(lm(y ~ ., data))$coefficients # Extract coefficients in matrix matrix_coef # Return matrix of coefficients # Estimate Std. Error t value Pr(>|t|) # (Intercept) -0.01158450 0.03203930 -0.3615716 7.177490e-01 # x1 0.10656343 0.03413045 3.1222395 1.846683e-03 # x2 -0.17723211 0.03369896 -5.2592753 1.770787e-07 # x3 0.11174223 0.03380415 3.3055772 9.817042e-04 # x4 0.09932518 0.03294739 3.0146597 2.637990e-03 # x5 -0.24870659 0.03322673 -7.4851370 1.572040e-13

The previous R code saved the coefficient estimates, standard errors, t-values, and p-values in a typical matrix format.

Now, we can apply any matrix manipulation to our matrix of coefficients that we want. For instance, we may extract only the coefficient estimates by subsetting our matrix:

my_estimates <- matrix_coef[ , 1] # Matrix manipulation to extract estimates my_estimates # Print estimates # (Intercept) x1 x2 x3 x4 x5 # -0.01158450 0.10656343 -0.17723211 0.11174223 0.09932518 -0.24870659 |

my_estimates <- matrix_coef[ , 1] # Matrix manipulation to extract estimates my_estimates # Print estimates # (Intercept) x1 x2 x3 x4 x5 # -0.01158450 0.10656343 -0.17723211 0.11174223 0.09932518 -0.24870659

That’s it. Now you can do whatever you want with your regression output!

## Video & Further Resources

I have recently released a video on my YouTube channel, which shows the R codes of this tutorial. Please find the video below:

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Besides the video, you might have a look at the related articles of this website.

- Specify Reference Factor Level in Linear Regression
- Add Regression Line to ggplot2 Plot
- summary Function in R
- The R Programming Language

This tutorial explained how to **extract the coefficient estimates of a statistical model** in R. Please let me know in the comments section, in case you have additional questions.

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## 8 Comments. Leave new

Hi,

How do I do the same with a simple linear regression output to compare both tables?

Thank you

Hi Brent,

This depends on the values/estimates you want to compare. You may run the code shown in this tutorial to as many different linear regression models as you want.

Regards

Joachim

Hi Joachim,

I want to use those intercepts in an expression, how do I do that?

Hey Kunal,

Do you still need help with this question? I just got back from vacation and couldn’t reply earlier.

Regards,

Joachim

Hi Joachim,

How do you extract the information at the bottom of the summary() output:

Residual standard error: 1.011 on 994 degrees of freedom

Multiple R-squared: 0.08674

Adjusted R-squared: 0.08214

F-statistic: 18.88 on 5 and 994 DF, p-value: < 2.2e-16

?

Is there a way to view the structure of functions like summary() to ascertain how the numbers are stored in them, in general?

Thanks,

Eric

Hey Eric,

Please have a look at the following three tutorials. They explain how to extract those values:

https://statisticsglobe.com/extract-residuals-and-sigma-from-regression-in-r

https://statisticsglobe.com/r-extract-multiple-adjusted-r-squared-from-linear-regression-model

https://statisticsglobe.com/r-extract-f-statistic-predictors-degrees-of-freedom-regression-model

Regards,

Joachim

Hey Eric,

Do you know how I can use the estimated regression coefficients to predict another dataset?

Hey Christian,

I don’t know who Eric is 🙂 but I would need to get some more information on what you would like to do.

Could you please provide some example data and explain your problem in some more detail?

Regards,

Joachim