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09/21/00 14:23
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#5222 - RE: Least Squares Algorithm
Ryan

I'm not clear on the two-dimensionality
of your task. Are you looking for an
average speed? If so, George's response
would cover your needs. The data can be collected on an ongoing basis in
three variables: sum-of-squares, sum-of-values and count. Sum-of-squares is the
sum of the squares of individual measurements, Sigma(X^2). Sum-of-values is as the name implies, Sigma(X).
Count is the count of the measurements, N.
Now Mean, or Average, = Sigma(X)/N.
Standard Deviation, or SD, given by the
equation:
/ Sigma(X^2) - (Sigma(X)^2)/N
SD = Sqrt|-----------------------------|
N-1 /

where Sqrt is the Square Root function.

If loss of precision is too large, because X and/or N is very large, replace X with x = X - C, where is a
(carefully chosen) constant. Then the
mean = Sigma(x)/N + C, and the SD is

/ Sigma(x^2) - (Sigma(x)^2)/N
SD = Sqrt|-----------------------------|
N-1 /


If you need more, for example a regression of speed versus time, or moving averages for speed, finding a statistician to help you is your best bet.

Chris


List of 10 messages in thread
TopicAuthorDate
Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm for Nihat S            01/01/70 00:00      
RE: Least Squares Algorithm for Nihat S            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      
RE: Least Squares Algorithm            01/01/70 00:00      

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