1. Sum Of Squares Due To Error

對于第i個觀察點, 真實數據的Yi與估算出來的Yi-head的之間的差稱為第i個residual, SSE 就是所有觀察點的residual的和
2. Total Sum Of Squares

3. Sum Of Squares Due To Regression

通過以上我們能得到以下關于他們三者的關系

決定系數: 判斷 回歸方程 的擬合程度

(coefficient of determination)決定系數也就是說: 通過回歸方程得出的 dependent variable 有 number% 能被 independent variable 所解釋. 判斷擬合的程度

(Correlation coefficient) 相關系數 : 測試dependent variable 和 independent variable 他們之間的線性關系有多強. 也就是說, independent variable 產生變化時 dependent variable 的變化有多大.

可以反映是正相關還是負相關

參考鏈接：http://blog.csdn.net/ytdxyhz/article/details/51730995

注意此決定系數不能用來衡量非線性回歸的擬合優度

Why Is It Impossible to Calculate a Valid R-squared for Nonlinear Regression?

R-squared is based on the underlying assumption that you are fitting a linear model. If you aren’t fitting a linear model, you shouldn’t use it. The reason why is actually very easy to understand.

For linear models, the sums of the squared errors always add up in a specific manner: SS Regression + SS Error = SS Total.

This seems quite logical. The variance that the regression model accounts for plus the error variance adds up to equal the total variance. Further, R-squared equals SS Regression / SS Total, which mathematically must produce a value between 0 and 100%.

In nonlinear regression, SS Regression + SS Error do not equal SS Total! This completely invalidates R-squared for nonlinear models, and it no longer has to be between 0 and 100%.

參考鏈接：http://blog.minitab.com/blog/adventures-in-statistics-2/why-is-there-no-r-squared-for-nonlinear-regression

更新：

For cases other than fitting by ordinary least squares, theR²statistic can be calculated as above and may still be a useful measure. If fitting is byweighted least squaresorgeneralized least squares, alternative versions of R²can be calculated appropriate to those statistical frameworks, while the "raw"R²may still be useful if it is more easily interpreted. Values forR²can be calculated for any type of predictive model, which need not have a statistical basis.

參考鏈接：https://en.wikipedia.org/wiki/Coefficient_of_determination

更新：

https://stats.stackexchange.com/questions/7357/manually-calculated-r2-doesnt-match-up-with-randomforest-r2-for-testing

這篇回答中給了兩個信息：

（1）線性回歸的R方等于實際值與預測值的相關系數的平方

（2）randomForest is reporting variation explained as opposed to variance explained.

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