Calibration
Many Things Are Not Absolute
Calibration Graph
•
line through center
of distribution
•
dN/N  normal
distribution eqn.
•
fraction of universe
between
x and (x + dx) is the
probability that x will
lie between
x and (x + dx)
Method of Least Squares
•
It can be shown:
•
best straight line through a series of
experimental points:
•
the line for which the sum of the squares
of the deviations of the points from the
line is a minimum
•
quadratic summation allows for sign of
deviation to be ignored
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View Full DocumentSum of Squares of Differences
•
equation of line y = mx + b
•
square of sum of differences, S is
•
assumes no error in x  independent variable
•
y
l
is the value on the line
Minimize S by Differentiation
•
Best straight line occurs when S goes
through a minium
•
Differentiate and set the derivatives of S
wrt
m and b equal to zero and solve for m
and b
•
The result is:
•
where
is the mean of all the values of
x
i
and
is the mean of all the values of
y
i
x
y
Easier Form of Least Squares
Equations
•
n
is the number of data points
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 Fall '08
 Michel, R
 Least Squares, Normal Distribution, Standard Deviation, pH, Calculation, Auld Reekie

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