correlation
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| Both sides previous revisionPrevious revision | |||
| correlation [2023/10/05 08:18] – [e.g. 1,] hkimscil | correlation [2023/10/05 08:19] (current) – [e.g. 1,] hkimscil | ||
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| Line 186: | Line 186: | ||
| & = E[XY - X \overline{Y} - \overline{X} Y - \overline{X} \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 \\ | & = 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 \\ | + | & \because |
| & = E[XY] - E[X]E[Y] - E[X]E[Y] + E[X]E[Y] \nonumber \\ | & = E[XY] - E[X]E[Y] - E[X]E[Y] + E[X]E[Y] \nonumber \\ | ||
| & = E[XY] - E[X]E[Y] \nonumber \\ | & = E[XY] - E[X]E[Y] \nonumber \\ | ||
| & = \frac{\Sigma{XY}}{n} - \frac{\Sigma{X}}{n} \frac{\Sigma{Y}}{n} | & = \frac{\Sigma{XY}}{n} - \frac{\Sigma{X}}{n} \frac{\Sigma{Y}}{n} | ||
| & \therefore | & \therefore | ||
| - | SP & = \Sigma{XY} - \frac{\Sigma{X} \Sigma{Y}}{n} | + | SP & = \Sigma{XY} - \frac{\Sigma{X} \Sigma{Y}}{n} |
| \end{align} | \end{align} | ||
correlation.1696493919.txt.gz · Last modified: by hkimscil