# What is binary logistic regression

## Logistic regression

You wonder what the **logistic regression** is and when do you use it? Then this post is the right place for you.

Would you like to clarify your questions even faster? Then check out our **Video** and find out everything there is to know about the **logistic regression** need to know.

### Logistic regression explained in simple terms

Logistic regression is a form of **Regression analysis**that you use to be a **nominally scaled, categorical criterion ** to predict. This means that you always use logistic regression when the dependent variable is only a few **few, equal values** Has. An example of a categorical criterion would be the outcome of an entrance examination, in which one only has either **"accepted"** or **"declined"** can be.

If the criterion in the logistic regression has only two values, then one speaks of one **binary logistic regression**. If, on the other hand, the criterion has more than two categories, the method is referred to as **multinomial logistic regression**. In this article we will mainly focus on binary logistic regression with one predictor.

### Logistic regression and probabilities

In contrast to **linear regression** do you not predict the concrete values of the criterion in logistic regression? Instead, you guess how **probably** it is that a person falls into one category or the other of the criterion. For example, you could predict how likely it is that a person with an IQ of 112 will pass the entrance exam. You also use a for the prediction in logistic regression **Regression equation**. Do you translate this regression equation into **Coordinate system**, so you get the **characteristic curve of logistic regression**. You can use it to estimate how likely a characteristic value of the criterion is for a person with a certain predictor value and how well the model fits your data.

The **Logistic regression function** looks like:

### Logistic regression versus linear regression

Let's take a closer look at how the **logistic regression** of the** linear regression** differs. In both linear and logistic regression, you use a predictor variable to predict a criterion variable. However, the two forms of regression analysis differ in the **Type of your criterion**.

In the **linear regression** do you use a **continuous, interval-scaled criterion**. An example of this would be the **height**. Body size has an infinite number of characteristics in an ascending order of rank, all of which are equidistant from one another. It looks different with the** logistic regression** from: Here you use a **nominally scaled criterion**. This criterion only has a few characteristics that do not have a natural sequence. An example would be that **Favorite school subject** one person. Here it is not automatically clear whether "Math" or "German" should be assigned the higher value, but both options are **equivalent to**.

### Logistic regression prediction

You probably know that you are with the **linear regression** try that **Values of your criterion** to estimate as accurately as possible. This means that you are trying to predict, for example, how tall a person is as precisely as possible. In the **logistic regression** is that a little different. Here you are not directly predicting the values of the criterion. Instead, you estimate which of the two expressions of the criterion is how **probably** is. As a result of the regression equation, you don't get a criterion value, but one **Probability for one of the two criterion values**.

In order to be able to include the two expressions of your categorical criterion in the regression analysis, you assign one of them to each **value** to (mostly 0 and 1). If a person is rejected at the entrance exam, for example, they have the criterion value and is she accepted the value . If you now carry out the logistic regression, you will always get a value for as the result , that is, how likely it is that a person was accepted with a certain value of the predictor.

In purely mathematical terms, you could also use a criterion with two expressions **linear regression** predict. However, the linear regression equation can also be used to predict values that **way below 0 or way above 1 or somewhere in between** lie. This is not very conclusive in terms of content, after all, only either level 0 or level 1 can occur. Therefore it is more clever to use a logistic regression, because here it is not the expression itself, but yours **Probability of occurrence** predicted.

### Regression equation

Logistic regression has one too **Regression equation**. On the one hand, this equation describes the regression graph, which you can draw in a coordinate system. On the other hand, you can use the regression equation **Predictor values** deploy. If you then calculate the regression equation, you get an estimate of how **probably one of the two expressions of the criterion** is.

To the different **Regression parameters** the regression equation will get the **Maximum likelihood method** applied. This method tries to find those parameters for which the **Most likely occurrence of the available data** is. The implementation of the Maximum Likelihood Method is comparatively complicated and is usually carried out with the help of a computer program.

Use the regression equation to estimate how **it is likely that your criterion is 1** accepts. If you have assigned the values “1” for accepted and “0” for rejected to the results of the entrance exams, then you use the regression equation to calculate the probability that a person will pass the entrance examination .

The **Regression equation of logistic regression** looks like:

### Interpretation of the logistic regression

The interpretation of the **Regression coefficients ** is not quite as simple in logistic regression as it is in linear regression. First, however, you can see which one **sign** the regression coefficient Has. Is the coefficient** positive,** then the probability that the criterion assumes the value 1 increases the higher the value of the predictor is. On the other hand, is the regression coefficient **negative**, the probability decreases with increasing predictor values.

You can also use the so-called **Odds ratios** consider. A **Odd** looks at the ratio of the probability for one characteristic to the probability of the other characteristic. If you put different odds in a ratio in the next step, you can collect information about how much the probabilities change between the predictor values under consideration.

You can also use a for logistic regression **Coefficient of determination** to calculate. The coefficient of determination of logistic regression is also called **pseudo** denotes and exists in two variants: On the one hand there is that **Cox & Snell ** and on the other **Nagelkerkes **. It is best to always include both parameters.

### Coefficient of determination

You can find out what the coefficient of determination is and how to calculate it in our video. Check it out right now!

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