# summary Function in R (3 Examples)

This article shows how to **compute descriptive statistics using the summary function** in the R programming language.

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## Definition & Basic R Syntax of summary Function
##

**Definition:** The summary R function computes summary statistics of data and model objects.

**Basic R Syntax:** Please find the basic R programming syntax of the summary function below.

summary(data) # Basic R syntax of summary function |

summary(data) # Basic R syntax of summary function

In the following, I’ll show three examples for the application of the summary function in R.

## Example 1: Applying summary Function to Vector

Example 1 illustrates how to apply the summary function to a numeric vector. First, we have to create a numeric vector in R:

vec <- 1:10 # Create example vector vec # Print example vector # 1 2 3 4 5 6 7 8 9 10 |

vec <- 1:10 # Create example vector vec # Print example vector # 1 2 3 4 5 6 7 8 9 10

As you can see based on the previous RStudio console output, our example vector ranges from 1 to 10.

Now, we can use the summary command to calculate summary statistics of our vector:

summary(vec) # Apply summary function to vector # Min. 1st Qu. Median Mean 3rd Qu. Max. # 1.00 3.25 5.50 5.50 7.75 10.00 |

summary(vec) # Apply summary function to vector # Min. 1st Qu. Median Mean 3rd Qu. Max. # 1.00 3.25 5.50 5.50 7.75 10.00

The summary function returned descriptive statistics such as the minimum, the first quantile, the median, the mean, the 3rd quantile, and the maximum value of our input data.

## Example 2: Applying summary Function to Data Frame

We can also apply the summary function to other objects. The following R programming syntax shows how to compute descriptive statistics of a data frame. First, we have to construct a data frame in R:

data <- data.frame(x1 = 1:5, # Create example data frame x2 = letters[1:5], x3 = 3) data # Print example data frame # x1 x2 x3 # 1 1 a 3 # 2 2 b 3 # 3 3 c 3 # 4 4 d 3 # 5 5 e 3 |

data <- data.frame(x1 = 1:5, # Create example data frame x2 = letters[1:5], x3 = 3) data # Print example data frame # x1 x2 x3 # 1 1 a 3 # 2 2 b 3 # 3 3 c 3 # 4 4 d 3 # 5 5 e 3

Our data frame contains five rows and three columns. We can now use the summary function to return summary statistics for each of the variables of this data frame to the RStudio console:

summary(data) # Apply summary function to data frame # x1 x2 x3 # Min. :1 a:1 Min. :3 # 1st Qu.:2 b:1 1st Qu.:3 # Median :3 c:1 Median :3 # Mean :3 d:1 Mean :3 # 3rd Qu.:4 e:1 3rd Qu.:3 # Max. :5 Max. :3 |

summary(data) # Apply summary function to data frame # x1 x2 x3 # Min. :1 a:1 Min. :3 # 1st Qu.:2 b:1 1st Qu.:3 # Median :3 c:1 Median :3 # Mean :3 d:1 Mean :3 # 3rd Qu.:4 e:1 3rd Qu.:3 # Max. :5 Max. :3

## Example 3: Applying summary Function to Linear Regression Model

A very common application of the summary function it the computation of summary statistics of statistical models. In this Example, I’ll explain how to create summary statistics of a linear regression model. Again, we have to create some example data first:

set.seed(93274) # Create random data my_x <- rnorm(1000) my_y <- rnorm(1000) + my_x |

set.seed(93274) # Create random data my_x <- rnorm(1000) my_y <- rnorm(1000) + my_x

Our example data consists of two randomly distributed numeric vectors.

We can estimate a linear regression model using the lm function as shown below:

mod <- lm(my_y ~ my_x) # Estimate linear regression model |

mod <- lm(my_y ~ my_x) # Estimate linear regression model

The data object mod contains the output of our linear regression.

Now, we can apply the summary function to this model object to print summary statistics for this model:

summary(mod) # Apply summary function to model # Call: # lm(formula = my_y ~ my_x) # # Residuals: # Min 1Q Median 3Q Max # -3.7337 -0.6964 -0.0047 0.7333 3.3489 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) -0.02159 0.03292 -0.656 0.512 # my_x 1.00156 0.03262 30.707 <2e-16 *** # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # # Residual standard error: 1.041 on 998 degrees of freedom # Multiple R-squared: 0.4858, Adjusted R-squared: 0.4853 # F-statistic: 942.9 on 1 and 998 DF, p-value: < 2.2e-16 |

summary(mod) # Apply summary function to model # Call: # lm(formula = my_y ~ my_x) # # Residuals: # Min 1Q Median 3Q Max # -3.7337 -0.6964 -0.0047 0.7333 3.3489 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) -0.02159 0.03292 -0.656 0.512 # my_x 1.00156 0.03262 30.707 <2e-16 *** # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # # Residual standard error: 1.041 on 998 degrees of freedom # Multiple R-squared: 0.4858, Adjusted R-squared: 0.4853 # F-statistic: 942.9 on 1 and 998 DF, p-value: < 2.2e-16

The previous output shown descriptive statistics such as regression coefficients, standard errors, p-values, significance levels, the intercept, the R-squared, and the F-statistic.

## Video, Further Resources & Summary

If you need more explanations on the R codes of this tutorial, I can recommend to watch the following video of my YouTube channel. I’m explaining the content of this article in the video.

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Furthermore, you might read the other articles that I have published on this homepage.

- mean Function in R
- Median in R
- R max and min Functions
- Extract Regression Coefficients of Linear Model
- Specify Reference Factor Level in Linear Regression
- R Functions List (+ Examples)
- The R Programming Language

You learned in this article how to **calculate object summaries** in the R programming language. Don’t hesitate to let me know in the comments section, if you have additional questions.

### Statistics Globe Newsletter

## 4 Comments. Leave new

Jim, This is a wonderful thing you have done/are doing. Thank you very much. Arch Turner, Ph.D.

Hey Arch,

Thanks a lot for the very kind words! I assume that you wanted to post this comment below Jim’s guest post though?

Here is the link: https://statisticsglobe.com/introduction-to-hypothesis-testing

Regards

Joachim

Hi , Good evening

I have a set of data in the form of matrix

When the function “Summary” is turned on, Just lets me the 10 first Variables

How can I view all results?

Thanks

As reference for future readers, the problem was solved in the Statistics Globe Facebook group: https://www.facebook.com/groups/statisticsglobe/posts/793016191377710/