# Logistic Regression in R With Example | Logistic Regression Model

## 1. Logistic Regression in R – Objective

In this blog, we will discuss what does exactly logistic regression in R mean. Along with learning syntax, derivation and applications of R logistic regression also. Also, we will see the performance of the R Logistic Regression Model.

So, let’s start Logistic Regression in R Tutorial.

## 2. What is Logistic Regression in R?

Logistic regression is a method for fitting a regression curve, y = f(x) when y is a categorical variable. This model is used to predict that y has given a set of predictors x. Hence, if the predictors can be continuous, categorical or a mix of both.

It is a classification algorithm which comes under** nonlinear regression**. We use it to predict a binary outcome (1 / 0, Yes / No, True / False) given a set of independent variables. Moreover, it helps to represent binary / categorical outcome, we use dummy variables.

It is a regression model in which the response variable has categorical values such as True/False or 0/1. Thus, it actually measures the probability of a binary response.

### a. Syntax and Expression of R Logistic regression

The general mathematical equation for logistic regression is −

y = 1/(1+e^-(a+b1x1+b2x2+b3x3+…))

**Following is the description of the parameters used** −

- y is the response variable.
- x is the predictor variable.
- a and b are the coefficients which are numeric constants.

We use the glm() function to create the regression model and also get its summary for analysis.

**The syntax of logistic Regression in R**

The basic syntax for glm() function in logistic regression is −

glm(formula,data,family)

**Description of the parameters used** −

**Formula-**Presenting the relationship between the variables.- Data is the dataset giving the values of these variables.
- The family is the R object to specify the details of the model. Also, its value is binomial for logistic regression.

## 3. Derivation of Logistic Regression in R

We use a Generalized model as a larger class of algorithms. Basically, this model was proposed by Nelder and Wedderburn in 1972.

The fundamental equation of generalized linear model is:

**g(E(y)) = α + βx1 + γx2**

Here, g() is the link function;

E(y) is the expectation of target variable, and

α + βx1 + γx2 is the linear predictor.

The role of the link function is to ‘link’ the expectation of y to linear predictor.

## 4. Performance of Logistic Regression Model

To test the performance of this model, we must consider a few metrics. Irrespective of a tool (SAS or R vs Python) you would work on, always look for:

### i. AIC (Akaike Information Criteria)

In logistic regression, AIC is the analogous metric of adjusted R². Thus, we always prefer the model with the smallest AIC value.

### ii. Null Deviance and Residual Deviance

**Null Deviance**–

In this deviance, it shows that the response predicted by a model with nothing but an intercept.

**Residual Deviance**–

It indicates the response predicted by a model of adding independent variables.

### iii. Confusion Matrix

It is a type of matrix in which we represent a tabular representation of Actual vs Predicted values. Also, this helps us to find the accuracy of the model and avoid overfitting.

Any Doubt yet in Logistic Regression in R? Please Comment.

## 5. Applications of Logistic Regression with R

**a**. It helps in Image Segmentation and Categorization.

**b**. Generally, we use logistic regression in Geographic Image Processing.

**c**. Basically, it needs Handwriting recognition.

**d**. We use logistic regression in healthcare. That is an application area of logistic regression.

**e**. To make Predictions about something we use in logistic regression.

This was all in logistic regression in R.

So, this was all in Logistic Regression in R. Hope you like our explanation.

## 6. Conclusion

As a result, we have seen that logistic regression in R plays a very important role in R Programming. So, it is an important algorithm which helps in concluding binary results. As we have discussed its syntax, parameters, derivations as well as examples. Also, we looked at the Logistic Regression Model in R with its performance. Still, if you feel any confusion regarding R Logistic Regression, ask in the comment tab.