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DMTN
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AFAIK, there are two basic type of linear regression:
y=ax+b and y=a2 + bx + c
But I have to do the same with the function y = asin(x)+bcos(x).
Here is what I have done:
We have:
[tex]
\begin{array}{l}
\frac{{\partial L}}{{\partial a}} = 0
\frac{{\partial L}}{{\partial b}} = 0[/tex]Continue:
[tex]
\begin{array}{l}
\frac{{\partial L}}{{\partial a}} = \sum\limits_{i = 1}^n {2\left[ {fi - \left( {a\sin (\frac{{\pi x}}{2}) + b\cos (\frac{{\pi x}}{2})} \right)} \right]\left( { - \sin (\frac{{\pi x}}{2})} \right)}
\frac{{\partial L}}{{\partial b}} = \sum\limits_{i = 1}^n {2\left[ {fi - \left( {a\sin (\frac{{\pi x}}{2}) + b\cos (\frac{{\pi x}}{2})} \right)} \right]\left( {\cos (\frac{{\pi x}}{2})} \right)}
\end{array}[/tex]
At last, I have:
[tex]
\left( {\begin{array}{*{20}c}
{\sin ^2 \left( {\frac{{\pi x}}{2}} \right)} & {\sin \left( {\frac{{\pi x}}{2}} \right)\cos \left( {\frac{{\pi x}}{2}} \right)} \\
{\sin \left( {\frac{{\pi x}}{2}} \right)\cos \left( {\frac{{\pi x}}{2}} \right)} & {\cos ^2 \left( {\frac{{\pi x}}{2}} \right)} \\
\end{array}} \right)\left( \begin{array}{l}
a \\
b \\
\end{array} \right) = \left( \begin{array}{l}
fi\sin \left( {\frac{{\pi x}}{2}} \right) \\
fi\cos \left( {\frac{{\pi x}}{2}} \right) \\
\end{array} \right)
[/tex]
What I have to do now? Please suggest me with this situation.
y=ax+b and y=a2 + bx + c
But I have to do the same with the function y = asin(x)+bcos(x).
Here is what I have done:
We have:
[tex]
\begin{array}{l}
\frac{{\partial L}}{{\partial a}} = 0
\frac{{\partial L}}{{\partial b}} = 0[/tex]Continue:
[tex]
\begin{array}{l}
\frac{{\partial L}}{{\partial a}} = \sum\limits_{i = 1}^n {2\left[ {fi - \left( {a\sin (\frac{{\pi x}}{2}) + b\cos (\frac{{\pi x}}{2})} \right)} \right]\left( { - \sin (\frac{{\pi x}}{2})} \right)}
\frac{{\partial L}}{{\partial b}} = \sum\limits_{i = 1}^n {2\left[ {fi - \left( {a\sin (\frac{{\pi x}}{2}) + b\cos (\frac{{\pi x}}{2})} \right)} \right]\left( {\cos (\frac{{\pi x}}{2})} \right)}
\end{array}[/tex]
At last, I have:
[tex]
\left( {\begin{array}{*{20}c}
{\sin ^2 \left( {\frac{{\pi x}}{2}} \right)} & {\sin \left( {\frac{{\pi x}}{2}} \right)\cos \left( {\frac{{\pi x}}{2}} \right)} \\
{\sin \left( {\frac{{\pi x}}{2}} \right)\cos \left( {\frac{{\pi x}}{2}} \right)} & {\cos ^2 \left( {\frac{{\pi x}}{2}} \right)} \\
\end{array}} \right)\left( \begin{array}{l}
a \\
b \\
\end{array} \right) = \left( \begin{array}{l}
fi\sin \left( {\frac{{\pi x}}{2}} \right) \\
fi\cos \left( {\frac{{\pi x}}{2}} \right) \\
\end{array} \right)
[/tex]
What I have to do now? Please suggest me with this situation.