How to Perform
Binary Logistic
Regression in R

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What is a Logistic Regression?

With the logistic regression model, we describe the relationship between predictors that can be continuous, binary, categorical, and categorical dependent variables. For example, the dependent variable can be binary, and we predict whether something will happen or not. We estimate the probabilities of belonging to each category for a given set of predictors. Binary logistic regression implies that we have one dependent binary variable that takes the values 1 or 0 (e.g. 1 – yes, 0 – no).

What is binary logistic regression used for?

Logistic Regression is a classification algorithm that is used when we want to predict a categorical variable (Yes/No, Pass/Fail) based on a set of the independent variable(s). In the Logistic Regression model, the log of odds of the dependent variable is modeled as a linear combination of the independent variables.

An Example Of Logistic Regression Analysis

For example, a researcher wants to examine whether levels of stress, anxiety, and happiness predict success in an English language exam. So, we have one dependent variable – passed English language exam (1 – yes, 0 – no) and three independent variables – level of stress, anxiety, and happiness.

Therefore, we test the following hypotheses:

Null hypothesis: Levels of stress, anxiety, and happiness do not significantly predict the probability of passing the English language exam.

Alternative hypothesis: Level of stress, anxiety, and happiness significantly predict the probability of passing the English language exam.

R function to Compute Logistic Regression

The code to run a Logistic Regression using R is as follows:

glm (DV~ IV1 +IV2,…+IVx, family=binomial, data = dataframe)

DV: dependent variable (two-group categorical variable)

IV: Independent variables

Running Logistic Regression in Rstudio

In this section, we will show you how to run the logistic regression using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the logistic regression analysis. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the binary logistic regression in APA format.

# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
anxiety <- data$anxiety
stress <- data$stress
happy <- data$happy
english <- data$english

# PERFORM LOGISTIC REGRESSION
model <- glm(english ~ happy + stress + anxiety, data = data, family = binomial)
summary(model)

> model <- glm(english ~ happy + stress + anxiety, data = data, family = binomial)
> summary(model)

## 
## Call:
## glm(formula = english ~ happy + stress + anxiety, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.5099  -1.0529  -0.8585   1.0861   1.5323  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept) -1.506139   1.581910  -0.952   0.3410  
## happy        0.139650   0.332618   0.420   0.6746  
## stress       0.177930   0.076332   2.331   0.0198 *
## anxiety     -0.004323   0.076120  -0.057   0.9547  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 137.23  on 98  degrees of freedom
## Residual deviance: 131.39  on 95  degrees of freedom
## AIC: 139.39
## 
## Number of Fisher Scoring iterations: 4

Reporting Logistic Regression in R

Logistic regression was conducted to determine whether the level of stress, anxiety, and happiness predict the probability of passing the English language exam. The results indicate that only the level of stress is a significant positive predictor of the probability of passing the English language exam (p = 0.019). If the level of stress increases by 0.18 units, it means a 19% increase in the odds of passing the English language exam (assuming that all other variables remain fixed). Level of anxiety is a non-significant negative predictor of the probability of passing the English language exam (p = 0.955). Level of happiness is a non-significant positive predictor of the probability of passing the English language exam (p = 0.675).

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How to Perform Binary Logistic Regression in R