Biology, images, analysis, design...
Use/Abuse Principles How To Related
"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

Search this site



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:

 Σ Yi / n

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|

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