Statistical Foundations

• 相关系数\(r\)(皮尔逊相关系数)

\[r = \frac{cov(X,Y)}{\sigma _{X} \sigma _{Y}} = \frac{\sum_{i=1}^{n}{(X _{i} - \overline{X})(Y _{i} - \overline{Y})}} {\sqrt{\sum _{i=1} ^{n} {(X _{i} - \overline{X}) ^{2}}} \sqrt{\sum _{i=1} ^{n} {(Y _{i} - \overline{Y}) ^{2}}}}\]

• 决定系数\(R ^{2}\)

\[R ^{2} = \frac{ESS}{TSS} = 1 - \frac{RSS}{TSS} \]

其中\(TSS=\sum _{i=1} ^{n} {(y _{i} - \overline{y}) ^{2}}\), \(RSS=\sum _{i=1} ^{n} {(y _{i} - \hat{y} _{i}) ^{2}}\), \(ESS=\sum _{i=1} ^{n} {(\hat y _{i} - \overline{y}) ^{2}}\)