## What is a Multiple Regression Formula?

Multiple regression formula is used in the analysis of relationship between dependent and multiple independent variables and formula is represented by the equation Y is equal to a plus bX1 plus cX2 plus dX3 plus E where Y is dependent variable, X1, X2, X3 are independent variables, a is intercept, b, c, d are slopes, and E is residual value.

**y = mx1 + mx2+ mx3+ b**

Where,

- Y= the dependent variable of the regression
- M= slope of the regression
- X1=first independent variable of the regression
- The x2=second independent variable of the regression
- The x3=third independent variable of the regression
- B= constant

### Explanation of Regression Analysis Formula

Multiple Regressions are a method to predict the dependent variable with the help of two or more independent variables. While running a multiple regression analysis, the main purpose of the researcher is to find out the relationship between the dependent variable and the independent variables. In order to predict the dependent variable, multiple independent variables are chosen which can help in predicting the dependent variable. It is used when linear regression is not able to do serve the purpose. Regression analysis helps in the process of validating whether the predictor variables are good enough to help in predicting the dependent variable. Now you can take look at the below-given formula of Multiple Regression.

While running a multiple 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, 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 multiple regressions analysis with the help of an example. Let us try to find out what is the relation between the distance covered by an UBER driver and the age of the driver and the number of years of experience of the driver.**

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

The regression formula for the above example will be

**y = MX + MX + b****y= 604.17*-3.18+604.17*-4.06+0****y= -4377**

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 UBER driver and the independent variables are the age of the driver and the number of experiences he has in driving.

#### Example #2

**Let us try and understand the concept of multiple regressions analysis with the help of another example. Let us try to find out what is the relation between the GPA of a class of students and the number of hours of study and the height of the students.**

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

The regression equation for the above example will be

**y = MX + MX + b**

**y= 1.08*.03+1.08*-.002+0**

**y= .0325**

** **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 is the GPA and the independent variables are study hours and height of the students.

#### Example #3

**Let us try and understand the concept of multiple regressions analysis with the help of another example. Let us try to find out what is the relation between the salary of a group of employees in an organization and the number of years of experience and the age of the employees.**

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

The regression equation for the above example will be

**y = MX + MX + b****y= 41308*.-71+41308*-824+0****y= -37019**

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 salary and the independent variables are the experience and age of the employees.

### Relevance and Use

Multiple regressions is a very useful statistical method. Regression plays a very role in the world of finance. A lot of forecasting is done using regression analysis. 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.

### Recommended Articles

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

- Relative Change | Definition
- What is Standard Deviation Formula?
- Formula of Adjusted R Squared
- Formula of Correlation
- FORECAST Function in Excel
- Regression vs ANOVA – Compare
- R Squared Formula
- Relative Standard Deviation Formula

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