The standard deviation of a single batch of numbers is a typical value
for the residuals (deviations from the mean). If you divide by n, it
is the RMS mean of the residuals. You can check your calculation of
the s.d. by comparing it to the residuals. The mean is the measure of
center that minimizes the sum of the squared residuals, so the s.d. is
the measure of variability that goes with the mean in particular, and
with least squares in general. For simple linear regression, s is a
typical value for the residuals (deviations from the regression line).
For multiple regression, s is a typical value for the residuals
(deviations from the model). There's a pattern here!-)
Least squares methods are in some sense optimal when the "errors"
estimated by the residuals are normally distributed. They are
questionable when the errors are multimodal, strongly skewed, or
afflicted with outliers.
_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College MSC#29
| | Plymouth, New Hampshire 03264 USA
| * | 82 River Street
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
L_____/ fax (603) 535-2943 (work)
[EMAIL PROTECTED]
http://mathpc04.plymouth.edu
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