Extract Standard Error, t-Value & p-Value from Linear Regression Model in R (4 Examples)

This post illustrates how to pull out the standard errors, t-values, and p-values from a linear regression in the R programming language.

The article consists of this information:

1) Creation of Example Data

2) Example 1: Extracting Standard Errors from Linear Regression Model

3) Example 2: Extracting t-Values from Linear Regression Model

4) Example 3: Extracting p-Values of Predictors from Linear Regression Model

5) Example 4: Extracting p-Value of F-statistic from Linear Regression Model

6) Video, Further Resources & Summary

Let’s just jump right in…

Creation of Example Data

First, we need to create some example data:

set.seed(1234421234)                       # Drawing randomly distributed data
x1 <- round(rnorm(1500), 2)
x2 <- round(rnorm(1500) - 0.1 * x1, 2)
x3 <- round(rnorm(1500) + 0.1 * x1 - 0.5 * x2, 2)
x4 <- round(rnorm(1500) - 0.4 * x2 - 0.1 * x3, 2)
x5 <- round(rnorm(1500) + 0.1 * x1 - 0.2 * x3, 2)
x6 <- round(rnorm(1500) - 0.3 * x4 - 0.1 * x5, 2)
y <- round(rnorm(1500) + 0.5 * x1 + 0.5 * x2 + 0.15 * x3 - 0.4 * x4 - 0.25 * x5 - 0.1 * x6, 2)
data <- data.frame(y, x1, x2, x3, x4, x5, x6)
head(data)                                 # Showing head of example data
#       y    x1    x2    x3    x4    x5    x6
# 1 -2.16 -0.15 -2.07  0.47  0.27 -0.62 -2.55
# 2  1.93  0.53  0.44  0.15 -0.53 -0.30  0.05
# 3 -0.34 -0.55 -0.63  1.94  0.56 -0.66  1.33
# 4 -0.37  1.81  0.20  0.13  1.10  0.76  0.50
# 5  0.37 -0.35  0.93 -1.43  0.65 -0.58 -0.19
# 6  1.74  1.68  1.61 -0.63 -3.16 -0.21  0.31

As you can see based on the previous RStudio console output, our example data is a data frame containing seven columns. The variable y is our target variable and the variables x1-x6 are the predictors.

Let’s fit a linear regression model based on these data in R:

mod_summary <- summary(lm(y ~ ., data))    # Estimate linear regression model
mod_summary                                # Summary of linear regression model

standard errors, t-values and p-values of linear regression model r

As you can see in Figure 1, the previous R code created a linear regression output in R. As indicated by the red squares, we’ll focus on standard errors, t-values, and p-values in this tutorial.

Let’s do this!

Example 1: Extracting Standard Errors from Linear Regression Model

This Example explains how to extract standard errors of our regression estimates from our linear model. For this, we have to extract the second column of the coefficient matrix of our model:

mod_summary$coefficients[ , 2]             # Returning standard error
# (Intercept)          x1          x2          x3          x4          x5          x6 
#  0.02616978  0.02606729  0.03166610  0.02639609  0.02710072  0.02551936  0.02563056

The output of the previous R syntax is a named vector containing the standard errors of our intercept and the regression coefficients.

Example 2: Extracting t-Values from Linear Regression Model

Example 2 illustrates how to return the t-values from our coefficient matrix.

mod_summary$coefficients[ , 3]             # Returning t-value
# (Intercept)          x1          x2          x3          x4          x5          x6 
#   0.1932139  20.1345274  15.6241787   5.6212606 -15.0215850  -8.0582917  -4.7656111

Again, the output is a named vector containing the values of interest.

Example 3: Extracting p-Values of Predictors from Linear Regression Model

Similar to the code of Example 2, this example extracts the p-values for each of our predictor variables.

mod_summary$coefficients[ , 4]             # Returning p-value
#  (Intercept)           x1           x2           x3           x4           x5           x6 
# 8.468177e-01 5.866428e-80 4.393611e-51 2.258705e-08 1.325589e-47 1.569553e-15 2.066174e-06

The previous result shows a named vector containing the p-values for our model intercept and the six independent variables.

Example 4: Extracting p-Value of F-statistic from Linear Regression Model

Be careful! The output of regression models also shows a p-value for the F-statistic. This is a different metric as the p-values that we have extracted in the previous example.

We can use the output of our linear regression model in combination with the pf function to compute the F-statistic p-value:

pf(mod_summary$fstatistic[1],              # Applying pf() function
   mod_summary$fstatistic[2],
   mod_summary$fstatistic[3],
   lower.tail = FALSE)
# 2.018851e-176

Note that this p-value is basically zero in this example.

Video, Further Resources & Summary

Do you want to learn more about linear regression analysis? Then you may have a look at the following video of my YouTube channel. In the video, I explain the R code of this tutorial in a live session.

The YouTube video will be added soon.

Besides the video, you may have a look at the other tutorials of this homepage:

In summary: At this point you should know how to return linear regression stats such as standard errors or p-values in R programming. Don’t hesitate to let me know in the comments section, in case you have further questions.