## Regression Analysis Formula

Regression analysis is the analysis of relationship between dependent and independent variable as it depicts how dependent variable will change when one or more independent variable changes due to factors, formula for calculating it is Y = a + bX + E, where Y is dependent variable, X is independent variable, a is intercept, b is slope and E is residual.

Regression is a statistical tool to predict the dependent variable with the help of one or more than one independent variable. While running a regression analysis, the main purpose of the researcher is to find out the relationship between the dependent variable and the independent variable. In order to predict the dependent variable one or multiple independent variables are chosen which can help in predicting the dependent variable. It helps in the process of validating whether the predictor variables are good enough to help in predicting the dependent variable.

A regression analysis formula tries to find the best fit line for the dependent variable with the help of the independent variables. The regression analysis equation is the same as the equation for a line which is

**y = MX + b**

Where,

- Y= the dependent variable of the regression equation
- M= slope of the regression equation
- x=dependent variable of the regression equation
- B= constant of the equation

### Explanation

While running a regression, the main purpose of the researcher is to find out the relationship between the dependent variable and the independent variable. In order to predict the dependent variable one or multiple independent variables are chosen which can help in predicting the dependent variable. Regression analysis helps in the process of validating whether the predictor variables are good enough to help in predicting the dependent variable.

### Examples

#### Example #1

**Let us try and understand the concept of regression analysis with the help of an example. Let us try to find out what is the relation between the distance covered by the truck driver and the age of the truck driver. Someone actually does a regression equation to validate whether what he thinks of the relationship between two variables, is also validated by the regression equation. **

Below is given data for calculation

For the calculation of Regression Analysis go to the Data tab in excel and then select the data analysis option. For the further procedure of calculation refer to the given article here – Analysis ToolPak in Excel

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The regression analysis formula for the above example will be

- y = MX + b
- y= 575.754*-3.121+0
**y= -1797**

In this particular example, we will see which variable is the dependent variable and which variable is the independent variable. The dependent variable in this regression equation is the distance covered by the truck driver and the independent variable is the age of the truck driver. The regression for this set of dependent and independent variables proves that the independent variable is a good predictor of the dependent variable with a reasonably high coefficient of determination. The analysis helps in validating that the factors in the form of the independent variable are selected correctly. The snapshot below depicts the regression output for the variables. The data set and the variables are presented in the excel sheet attached.

#### Example #2

**Let us try and understand regression analysis with the help of another example. Let us try to find out what is the relation between the height of the students of a class and the GPA grade of those students. Someone actually does a regression equation to validate whether what he thinks of the relationship between two variables, is also validated by the regression equation.**

In this example, Below is given data for calculation in excel

Regression analysis calculation, go to the Data tab in excel and then select the data analysis option.

The regression for the above example will be

- y = MX + b
- y= 2.65*.0034+0
**y= 0.009198**

In this particular example, we will see which variable is the dependent variable and which variable is the independent variable. The dependent variable in this regression equation is the GPA of the students and the independent variable is the height of the students. The regression analysis for this set of dependent and independent variables proves that the independent variable is not a good predictor of the dependent variable as the value for the coefficient of determination is negligible. In this case, we need to find out another predictor variable in order to predict the dependent variable for the regression analysis. The snapshot below depicts the regression output for the variables. The data set and the variables are presented in the excel sheet attached.

### Relevance and Uses

Regression is a very useful statistical method. For any business decision in order to validate a hypothesis that a particular action will lead to the increase in the profitability of a division can be validated based on the result of the regression between the dependant and independent variables. The regression analysis equation plays a very important role in the world of finance. A lot of forecasting is done using regression. For example, the sales of a particular segment can be predicted in advance with the help of macroeconomic indicators that has a very good correlation with that segment. Both linear and multiple regressions are useful for practitioners in order to make predictions of the dependent variables and also validate the independent variables as a predictor of the dependent variables.

### Recommended Articles

This has been a guide to Regression Analysis Formula. Here we discuss how to perform Regression Analysis calculation using data analysis along with examples and downloadable excel template. You can learn more about statistical modeling from the following articles –

- Definition of Gini Coefficient
- Regression Analysis Excel
- Formula of R Squared
- Examples of Linear Regression

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