how can we derive the formula of karl pearson's cefficient of correlation in shortcut method?

The following steps are involved in the computation of Karl Pearson's coefficient of correlation using the short-cut method.

Step 1: Decide an assumed mean for the X-series and calculate deviations of each item of the series from it. Total the deviations and denote as ∑dx.

Step 2: Similarly, calculate the deviations in Y-series from an assumed mean and determine the summation as Σdy.

Step 3: Now, square the deviations of X-series and the Y-series and obtain their total as Σdx2 and Σdy2 respectively.

Step 4: Multiply the deviations obtained in the step 1 and step 2 and obtain the total as Σdx·dy.

Step 5: The following formula is applied to compute Karl Pearson's coefficient of correlation.

 

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