What R-squared is
R-squared is a statistical measure that represents the proportion of the variance for a dependent variable that’s explained by an independent variable or variables in a regression model. It is also known as the coefficient of determination.
Steps for calculating R-squared:
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Calculate the regression line: The first step is to calculate the regression line by using the least squares method. This method consists of finding the line that minimizes the sum of the squares of the vertical distances between each data point and the regression line.
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Calculate the sum of the squares of the vertical distances: The second step is to calculate the sum of the squares of the vertical distances between each data point and the regression line.
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Calculate the total sum of squares: The third step is to calculate the total sum of squares. This is done by calculating the sum of the squared differences between each data point and the mean of all the data points.
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Calculate the R-squared value: The final step is to calculate the R-squared value. This is done by dividing the sum of the squares of the vertical distances by the total sum of squares. The result is the R-squared value, which is a measure of how much of the variance in the dependent variable is explained by the independent variable(s).
Examples
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R-squared is used to measure the strength of the relationship between an independent variable and a dependent variable in a linear regression model.
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R-squared is used to measure the proportion of variation in a dependent variable that can be explained by the independent variables in a multiple regression model.
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R-squared can be used to compare and evaluate the performance of different models in predicting a dependent variable.
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R-squared can be used to assess the accuracy of a model for predicting a dependent variable.