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"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

## Notation of residuals

Let us look at a list of observations 1 to n of variable Y:
 Responses to Epsom salt synergist List item( i = ) 1 2 3 4 5 6 . . . n % Original bodyweight( Y = ) 9.4 11.2 13.5 10.1 14.7 13.2 . . . 12.0

This list is represented algebraically as:
Y(i=1) + Y(i=2) + Y(i=3) + ... Y(i=n)

The mean, written out completely, is:

 i=n Σ Yi / n i=1

If we represent the deviation of each observation from its mean as yi

Then   yi =   Yi - Or more briefly as   y =   Y -  In which case :

the square of each deviation is y2
their sum is Σy2
which makes their mean   Σy2 / n

Which is the variance.

Incidentally, the Mean Absolute Deviation (MAD), could be written like this :
 MAD = Σ |y| n

Where |y| is the 'absolute' value of y
(In other words all the negative deviations from the mean are rendered positive)