Which of the following is used to calculate the R-squared for a regression model?
Question
Which of the following is used to calculate the R-squared for a regression model?
Solution
The R-squared for a regression model is calculated using the following formula:
R-squared = 1 - (SSR/SST)
Where:
- SSR (Sum of Squared Residuals) is the sum of the squares of the model's residual errors.
- SST (Total Sum of Squares) is the total variation in the dependent variable.
Here are the steps to calculate R-squared:
-
Calculate the residuals: The residuals of a model are the difference between the observed values of the dependent variable and the predicted values from the model.
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Square the residuals: To calculate SSR, square each of the residuals.
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Sum the squared residuals: Add up all the squared residuals to get the SSR.
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Calculate the total sum of squares: Subtract the mean of the dependent variable from each of the observed values, square the result, and then sum these squares to get the SST.
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Substitute SSR and SST in the R-squared formula: Finally, substitute the SSR and SST values into the R-squared formula and calculate the result.
The resulting value, R-squared, represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It ranges from 0 to 1, with 1 indicating that the independent variables perfectly predict the dependent variable.
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