Specifications

AUTOSTAR CCD PHOTOMETRY 85
APPENDIX F
Least Squares Method
Introduction
While it is possible to graphically plot data for extinction and color
transformation coefficient determination, sometimes it is difficult
to decide exactly where to draw the straight line plot. By using the
method of least squares or linear regression analysis, one can
mathematically determine the slope and Y-intercept of data that are
in the form of a straight line without having to make a graph and
physically draw a line between points.
While the results can be calculated by hand, a calculator or
computer program can speed the calculations and provide more
accurate results.
Equations
There are basically two equations used, one for the Slope, b and
one for the Y-intercept, a.
Slope b = N * Σ (x
i
* y
i
) – Σ x
i
* Σ y
i
N * Σ x
i
2
– (Σ x
i
)
2
Y-Intercept a = y
iavg
– b * x
iavg
Where:
Data points are x
i
and y
i
.
The variables x
iavg
and y
iavg
are the average vales for the
x
i
and y
i
data, respectively.
The sigma (Σ) symbol means the sum.
Table F-1 lists sample data to demonstrate a least squares fit.