Graphics Programs Reference
In-Depth Information
sigma = 0;
fori=1:n
y = polyEval(coeff,xData(i));
sigma = sigma + (yData(i) - y)ˆ2;
end
sigma =sqrt(sigma/(n - m));
functiony=polyEval(coeff,x)
% Returns the value of the polynomial at x.
m = length(coeff);
y = coeff(1);
forj=1:m-1
y = y*x + coeff(j+1);
end
Weighting of Data
There are occasionswhenconfidence inthe accuracy of datavaries frompointtopoint.
For example, the instrumenttaking the measurements may be moresensitive in a
certain rangeofdata. Sometimes the datarepresent the results of severalexperiments,
each carried out underdifferentcircumstances. Under these conditions we may want
to assign a confidence factor,or weight ,toeach datapoint and minimize the sum of
the squares of the weighted residuals r i =
W i [ y i
f ( x i )], where W i are the weights.
Hence the function to be minimizedis
n
W 2
i
f ( x i )] 2
S ( a 1 ,
a 2 ,...,
a m )
=
[ y i
(3.24)
i
=
1
This procedureforces the fitting function f ( x ) closer to the datapoints thathave
higherweights.
Weighted linear regression
If the fitting functionis the straight line f ( x )
=
+
a
bx , Eq. (3.24) becomes
n
W i ( y i
bx i ) 2
S ( a
,
b )
=
a
(3.25)
=
i
1
The conditionsfor minimizing S are
n
S
W 2
i
a =−
2
( y i
a
bx i )
=
0
i
=
1
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