What is a Multiple Regression Formula?

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Where,

  • Y= the dependent variable of the regressionM= slope of the regressionX1=first independent variable of the regressionThe x2=second independent variable of the regressionThe x3=third independent variable of the regressionB= 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 this analysis, the main purpose of the researcher is to find out the relationship between the dependent and independent variables. The multiple independent variables are chosen, which can help predict the dependent variable to predict the dependent variable. One may use it when linear regression cannot serve the purpose. The 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 regression analysis with the help of an example. But, first, let us try to find out 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.

To calculate multiple regression, go to the “Data” tab in Excel and select the “Data Analysis” option. For further procedure and calculation, refer to the: Analysis ToolPak in ExcelAnalysis ToolPak In ExcelExcel’s data analysis toolpak can be used by users to perform data analysis and other important calculations. It can be manually enabled from the addins section of the files tab by clicking on manage addins, and then checking analysis toolpak.read more article.

The regression formulaRegression FormulaThe regression formula is used to evaluate the relationship between the dependent and independent variables and to determine how the change in the independent variable affects the dependent variable. Y = a + b X +read more for the above example will be

  • y = MX + MX + by= 604.17*-3.18+604.17*-4.06+0y= -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 regression analysis with the help of another example. Let us try to find the relation between the GPA of a class of students, the number of hours of study, and the student’s height.

Go to the “Data” tab in Excel and select the “Data Analysis” option for the calculation.

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 the height of the students.

Example #3

Let us try and understand the concept of multiple regression analysis with the help of another example. Now, let us find out the relation between the salary of a group of employees in an organization, the number of years of experience, and the age of the employees.

  • y = MX + MX + by= 41308*.-71+41308*-824+0y= -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 are a very useful statistical method. Regression plays a very important role in the world of finance. A lot of forecasting is done using regressionRegressionRegression Analysis is a statistical approach for evaluating the relationship between 1 dependent variable & 1 or more independent variables. It is widely used in investing & financing sectors to improve the products & services further. read more analysis. For example, one can predict the sales of a particular segment in advance with the help of macroeconomic indicators that have a very good correlation with that segment.

This article has been a guide to the Multiple Regression Formula. Here, we discuss performing multiple regression using data analysis, examples, and a downloadable Excel template. You can learn more about statistical modeling from the following articles: –

  • Relative ChangeRelative ChangeRelative change shows the change of a value of an indicator in the first period and in percentage terms, i.e. Relative change is calculated by subtracting the value of the indicator in the first period from the value of the indicator in the second period which is then divided by the value of the indicator in the first period and the result is taken out in percentage terms.read moreFormula of CorrelationFormula Of CorrelationCorrelation is a statistical measure between two variables that is defined as a change in one variable corresponding to a change in the other. It is calculated as (x(i)-mean(x))(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2.read moreANOVA vs RegressionFormulaFormulaR Squared formula depicts the possibility of an event’s occurrence within an expected outcome. It is “r = n (∑xy) – ∑x ∑y / √ [n (∑x2 – (∑x)2)] * [n* (∑y2 – (∑y)2)]”, where r is the Correlation coefficient, n is the number in the given dataset, x is the first variable in the context and y is the second variable. read more of R Squared