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correlation [2023/10/05 17:18] – [e.g. 1,] hkimscilcorrelation [2023/10/05 17:19] (current) – [e.g. 1,] hkimscil
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  & = 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[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] - 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}  \nonumber \\  & =  \frac{\Sigma{XY}}{n} - \frac{\Sigma{X}}{n} \frac{\Sigma{Y}}{n}  \nonumber \\
  & \therefore  \nonumber \\  & \therefore  \nonumber \\
-SP & = \Sigma{XY} - \frac{\Sigma{X} \Sigma{Y}}{n}  \;\;\;\;\; \text{That is,  } \; \ref{sp.simplified} +SP & = \Sigma{XY} - \frac{\Sigma{X} \Sigma{Y}}{n}  \;\;\;\;\; \text{That is,  } \; \ref{sp.simplified} \nonumber \\
  
 \end{align} \end{align}
correlation.txt · Last modified: 2023/10/05 17:19 by hkimscil

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