Remember the definition of 'mean' as '[SUM from i=1 to n](x) / n'. So we can rewrite this... = [1/(n-1)] * ({SUM from i=1 to n} (yi - mean(y))^2) = [1/(n-1)] * n * mean((yi - mean(y))^2) = [n/(n-1)] * mean((yi - mean(y))^2)
Some rules about means...
1)When finding the mean, if all the numbers contain a common factor, this number can be factored out before finding the mean. mean(k*y) = k*mean(y)
2)Also, the mean of two addends is equal to the sum of the mean of each addend mean(y+z) = mean(y) + mean(z)
3)And the mean of a constant equals the constant mean(k^2) = k^2
Multiply out the term inside the ^2 and you get = [n/(n-1)] * mean((yi - mean(y))^2) = [n/(n-1)] * mean(yi^2 - 2*yi*mean(y) + mean(y)^2)
Applying the above rules and remembering that 2, mean(y) and mean(y)^2 are all constant for a given problem, and that mean(yi) = mean(y)
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