correlation
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| correlation [2023/10/05 16:29] – [e.g. 1,] hkimscil | correlation [2023/10/05 17:19] (current) – [e.g. 1,] hkimscil | ||
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| Line 172: | Line 172: | ||
| & \therefore \nonumber \\ | & \therefore \nonumber \\ | ||
| SS_{\small{X}} & = \Sigma {X^2} - \frac{(\Sigma{X})^2}{n} | SS_{\small{X}} & = \Sigma {X^2} - \frac{(\Sigma{X})^2}{n} | ||
| + | \end{align} | ||
| + | </ | ||
| + | |||
| + | <WRAP box> | ||
| + | 또한 | ||
| + | \begin{align} | ||
| + | SP & = & \sum XY - \frac{\sum X \sum Y}{n} \label{sp.simplified} \tag{SP simplified} \\ | ||
| + | \end{align} | ||
| + | |||
| + | |||
| + | \begin{align} | ||
| + | Cov[X,Y] & = E[(X-\overline{X})(Y-\overline{Y})] \nonumber \\ | ||
| + | & = E[XY - X \overline{Y} - \overline{X} Y - \overline{X} \overline{Y}] \nonumber \\ | ||
| + | & = E[XY] - E[X] \overline{Y} - \overline{X} E[Y] + \overline{X} \overline{Y} \nonumber \\ | ||
| + | & \because \;\;\; E[c] = c \;\;\; \text{and, } \overline{X} = E[X] \nonumber \\ | ||
| + | & = E[XY] - E[X]E[Y] - E[X]E[Y] + E[X]E[Y] \nonumber \\ | ||
| + | & = E[XY] - E[X]E[Y] \nonumber \\ | ||
| + | & = \frac{\Sigma{XY}}{n} - \frac{\Sigma{X}}{n} \frac{\Sigma{Y}}{n} | ||
| + | & \therefore | ||
| + | SP & = \Sigma{XY} - \frac{\Sigma{X} \Sigma{Y}}{n} | ||
| + | |||
| \end{align} | \end{align} | ||
| </ | </ | ||
correlation.txt · Last modified: 2023/10/05 17:19 by hkimscil