| 0
|
The algorithm used is a Least Squares method of
data smoothing. This method allows for the smoothing of
data to any polynomial function. The polynomial used here
(since we want the slope) is simply a linear function ax
+ b - y + 0. This will give us a straight line
approximation of the data points. We don't need to solve
the entire equation. We are only interested in the 'a'
coefficient (slope). The formula using the least squares
method is:
n = number of data
points.
| |
n |
|
n |
|
n |
|
| a = 1/d (n
|
å |
XkYk - |
å |
Xk |
å |
Yk) |
| |
k=1 |
|
k=1 |
|
k=1 |
|
| |
n |
2 |
|
n |
2 |
|
| d = n |
å |
X |
k - ( |
å |
X |
k) |
| |
k=1 |
|
|
k=1 |
|
|
Reference:
Numerical Mathematics and Computing, 2nd Ed.,Cheney
and Kincaid, page 364 "Smoothing of data and the
method of Least Squares".
|
