Where
The value of the coefficient ranges from 0 to 1, where a value of 0 indicates that the independent variable does not explain the variation of the dependent variable, and a value of 1 indicates that the independent variable perfectly explains the variation in the dependent variable. ExamplesExample #1Let us try and understand the coefficient 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. 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. 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. 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 presented in the excel sheet attached. Solution: Below is given data for 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 #2Let us try and understand the concept of coefficient of determination 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. 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. We can find the correlation with the help of the formula and square that to get the R^2 of the regression equation. The data set and the variables are presented in the excel sheet attached. Solution: Below is given data for calculation of the coefficient of determination. Therefore, the calculation is as follows, R = 34.62/√(169204*3245) R = 0.000467045 R^2 = 0.000000218 InterpretationThe coefficient of determination is a critical output to find out whether the data set is a good fit or not. Someone actually does a regression 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 better the regression equation as it implies that the independent variable chosen to determine the dependent variable is chosen properly. Ideally, a researcher will look for the coefficient of determination, which is closest to 100%. Recommended ArticlesThis article has been 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 – |
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