Meade Image Processing Specifikace stáhnout pdf (Strana 95)

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

* y

) – Σ x

* Σ y

N * Σ x

– (Σ x

)

Y-Intercept a = y

iavg

– b * x

iavg

Where:

Data points are x

and y

The variables x

iavg

and y

iavg

are the average vales for the

and y

data, respectively.

The sigma (Σ) symbol means the sum.

Table F-1 lists sample data to demonstrate a least squares fit.

1 2 ... 90 91 92 93 94 95 96 97 98 99 100 ... 127 128

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Meade Image Processing Specifikace Strana 95