# Regression Analysis Examples

## What is a Regression Analysis?

An analysis of regression is the method of analysis used to measure the connection between two or more variables. If a single variable is used in the analysis, it is called univariate regression; on the other side if there is more than one variable it is called multivariable regression analysis. The analysis variables have a cause and effect relationship. This analysis generally targets to define this relationship and so the estimations and predictions related to the analysis subjects can be made. It is possible to find cause-effect relationships in many cases. But there may be no a cause-effect relationship in every cases because regression mainly interested in the structure and the level of the relationship between the variables.

### Dependent and Independent Variables

A mathematical model is used to explain the relationship between the variables in regression models. Y is the dependent variable and X is the independent variable. We can say this in other words; Y is the result and X is the cause.

**The dependent variable (Y)**: This variable is the explained or predicted variance in the regression model. It is assumed that the variable is connected with the independent variable.

**The independent variable (X): **This variable is the explanatory variable in the regression model. X variable is used to estimate the value of the dependent variable.

**Regression analysis **allows estimates to be made from known findings to unknown future events. Regression develops a prediction equation using the concept of linear curves and relation between the dependent and independent variables. There may be a linear relationship between variables or a non-linear relationship.

### Simple and Multiple Regression Model

There are 2 types of regression models;

- Simple Regression Model
- Multiple Regression Model

**Simple Model**: An analysis of univariate regression examines the relationship between the one dependent variable and one independent variable. Simple model is used to formulate a linear equation representing the linear relationship between dependent and independent variables.

**Multiple Model: **Regression models in which one dependent variable and several independent variables are present are called as multivariate regression.

An analysis of regression is an important statistical tool for many field data analysis technique is used to explain the connection between the variables. There is a linear relationship between the variables in the simple and multiple models. If there is curvilinear relationship between the two dependent and independent variables; this can be explained by curvilinear regression model.

### **Examples for Regression Models**

There are too many examples for the regression models; below you can see some of them:

**Simple regression example**: The relationship between the income and expenditure; x=income y=expenditure In this example; income is the independent variable because you will spend less if you have less income and if you have more income, you can spend more. Normally, the expenditure is the dependent variable; changes according to the income.

**Multiple regression example: **The relationship between the success of the student and the factors. The factors are more than one; intelligence, study time, family etc. This model is commonly used in social areas.

**Regression analysis** examines how the other changes when one of the variables changes a certain unit.