What is the Coefficient of Determination?

Detailed Explanation

  • R= CorrelationR^2= Coefficient of determination of the regression equationN= Number of observations in the regression equationXi= Independent variable of the regression equationX= Mean of the independent variable of the regression equationYi= Dependent variable of the regression equationY= Mean of the dependent variable of the regression equationσx = Standard deviation of the independent variableσy = Standard deviation of the dependent variable

The coefficient value ranges from 0 to 1, where a value of 0 indicates that the independent variable does not explain the variation of the dependent variable. Conversely, a value of 1 indicates that the independent variable perfectly explains the variation in the dependent variable.

Where

Examples

Example #1

Let us try and understand the coefficient of determination formulaCoefficient Of Determination FormulaCoefficient 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 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. In this example, we will see the dependent and independent variables.

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. Therefore, we can find the correlation with the help of the formula and square that to get the coefficient of the regression equation. The data set and the variables are present in the Excel sheet attached.

Solution:

Below is given data for the calculation of the coefficient of determination.

Therefore, the calculation of the coefficient of determination is as follows:

R = -424520/√(683696*81071100)

R will be –

R = -0.057020839

R^2 will be –

R^2 = 0.325%

Example #2

Let us try and understand the concept of coefficient of determination 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. In this example, we will see the dependent and independent variables.

The dependent variable in this regression equation is the student’s GPA, and the independent variable is the height of the students. We can find the correlation with the help of the formula and square to get the R^2 of the regression equation. The data set and the variables are presented in the Excel sheet attached.

Therefore, the calculation is as follows:

R = 34.62/√(169204*3245)

R = 0.000467045

R^2 = 0.000000218

Interpretation

The coefficient of determination is a critical output to determine whether the data set is a good fit. Someone does a regression analysisRegression AnalysisRegression analysis depicts how dependent variables will change when one or more independent variables change due to factors, and it is used to analyze the relationship between dependent and independent variables. Y = a + bX + E is the formula.read more to validate whether what he thinks of the relationship between two variables is also validated by the regression equation. The higher the coefficient, the better the regression equation as it implies that the independent variable chosen to determine the dependent variable chooses properly. Ideally, a researcher will look for the coefficient of determination closest to 100%.

This article is a guide to the Coefficient of Determination. Here, we learn how to calculate the coefficient of determination using its formula with examples and a downloadable excel template. You can learn more about financing from the following articles: –

  • Gini CoefficientFormula of Multiple RegressionFormula for Coefficient of VariationFormula for Correlation CoefficientPayback Period Advantages and Disadvantages