Regression Analysis Formula

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

Regression is a statistical tool to predict the dependent variable with the help of one or more independent variables. While running a regression analysis, the main purpose of the researcher is to find out the relationship between the dependent and independent variables. One or multiple independent variables are chosen, which can help predict the dependent variable to predict the dependent variable. In addition, it helps validate whether the predictor variables are good enough to help predict 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:

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Where,

  • Y= the dependent variable of the regression equationM= slope of the regression equationx=dependent variable of the regression equationB= constant of the equation

Explanation

While running a regression, the main purpose of the researcher is to find out the relationship between the dependent and independent variables. Then, one or multiple independent variables chose to help predict 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. First, let us try to find out the relation between the distance covered by the truck driver and the age of the truck driver. Then, someone 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 further calculation procedure, refer to the given article here – 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

The regression analysis formula for the above example will be

  • y = MX + by= 575.754*-3.121+0y= -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 determinationCoefficient Of DeterminationCoefficient of determination, also known as R Squared determines the extent of the variance of the dependent variable which can be explained by the independent variable. Therefore, the higher the coefficient, the better the regression equation is, as it implies that the independent variable is chosen wisely.read more. In addition, the analysis helps validate 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 present 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 the relation between the height of the students of a class and the GPA grade of those students. Then, someone 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

For regression analysis calculation, go to the “Data” tab in Excel and select the “Data Analysis” option.

The regression for the above example will be

  • y = MX + by= 2.65*.0034+0y= 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 student’s GPA, and the independent variable is the student’s height. 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 another predictor variable 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 present in the Excel sheet attached.

Relevance and Uses

Regression is a very useful statistical method. One can validate any business decision to validate a hypothesis that a particular action will increase a division’s profitability based on the 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 between the dependent and independent variables. Therefore, the regression analysis equation plays a very important role in finance. In addition, a lot of forecasting is performed using regression. 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. Both linear and multiple regressionsMultiple RegressionsMultiple regression formula is used in the analysis of the relationship between dependent and numerous independent variables. Formula = y = mx1 + mx2+ mx3+ bread more are useful for practitioners to make predictions of the dependent variables and validate the independent variables as a predictor of the dependent variables.

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

  • Definition of Gini CoefficientDefinition Of Gini CoefficientGini Coefficient or Gini Index is statistical dispersion depicting the income dispersions amongst the population of a country i.e. it represents the wealth inequalities of the citizens of a particular country. read moreRegression Analysis ExcelRegression Analysis ExcelRegression is done to define relationships between two or more variables in a data set in statistics regression is done by some complex formulas. Still, excel has provided us with tools for regression analysis. So the study took the park of the excel, clicked on data analysis, and then on regression analysis on excel.read moreFormula of R SquaredFormula Of R SquaredR 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 moreExamplesExamplesLinear regression represents the relationship between one dependent variable and one or more independent variable. Examples of linear regression are relationship between monthly sales and expenditure, IQ level and test score, monthly temperatures and AC sales, population and mobile sales.read more of Linear Regression