Author Topic: Least Squares Method  (Read 2012 times)

Offline Alberto Dominguez

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Least Squares Method
« on: July 12, 2011, 05:09:15 PM »
Linear Least Squares aproximation by y=mx+b:

m=\frac{\overset{N}{\underset{j=1}{\sum}}x_{j}y_{j}-NX_{c}Y_{c}}{\overset{N}{\underset{j=1}{\sum}}x_{j}^{2}-NX_{c}^{2}}

b=\frac{\overset{N}{Y_{c}\underset{j=1}{\sum}}x_{j}^{2}-X_{c}\overset{N}{\underset{j=1}{\sum}}x_{j}y_{j}}{\overset{N}{\underset{j=1}{\sum}}x_{j}^{2}-NX_{c}^{2}}

X_{c}=\frac{1}{N}\overset{N}{\underset{j=1}{\sum}}x_{j}

Y_{c}=\frac{1}{N}\overset{N}{\underset{j=1}{\sum}}y_{j}

Errors:

\epsilon_{m}=\sqrt{\frac{\sum(y_{j}-mx_{j}-b)^{2}}{(N-2)\sum(x_{j}-X_{c})^{2}}}

\epsilon_{b}=\sqrt{\frac{\sum(y_{j}-mx_{j}-b)^{2}}{N(N-2)}}

Correlation coeficient:

r=\frac{N\sum x_{i}y_{i}-(\sum x_{i})(\sum y_{i})}{\sqrt{\left[N\sum x_{i}^{2}-(\sum x_{i})^{2}\right]\left[N\sum y_{i}^{2}-(\sum y_{i})^{2}\right]}}



*Source: Documents about Experimental Techniques I of Physics Undergraduate course from UNED.
« Last Edit: July 16, 2011, 08:32:10 AM by Alberto Dominguez »
Kind regards,

Alberto Domínguez
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