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Adjusted coefficient of determination

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There is a potential problem with using as an overall measure of the quality of a fitted equation. The value of generally increases as we add more and more explanatory variables to the regression model. Therefore, by adding a large number of variables to our regression model (even if they are not included in the model) we can make the value of very close to 1. Such a value of will be misleading, and it will not represent the true explanatory power of the regression model. To eliminate this shortcoming of , it is preferable to use the adjusted coefficient of determination, which is denoted by . The value of may increase, decrease, or stay the same as we add more explanatory variables to our regression model. If a new variable added to the regression model contributes significantly to explain the variation in y, then increases; otherwise it decreases. The value of is calculated as follows

 

or

 


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Читайте в этой же книге: Covariance | Exercises | The binomial distribution | Exercises | The hypergeometric probability distribution | Exercises | The Poisson probability distribution | Exercises | Multiple regression model | Standard assumptions for the multiple regression models |
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The coefficient of determination| Exercises

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