Question :

Write down the normal equations for estimating the constant A and B in the least-square fit of the model

$\displaystyle y = A + Bx,$

using n data points i.e. $\displaystyle (x,y),(x_2,y_2),.....,(x_n,y_n).$

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- Dec 4th 2009, 09:36 PMzorroWrite down the normal eq for estmiating the constant A and B
Question :

Write down the normal equations for estimating the constant A and B in the least-square fit of the model

$\displaystyle y = A + Bx,$

using n data points i.e. $\displaystyle (x,y),(x_2,y_2),.....,(x_n,y_n).$ - Dec 4th 2009, 09:38 PMmatheagle
take the sum of squares and differentiate wrt A and B.

- Dec 13th 2009, 03:45 PMzorroIs this correct?

$\displaystyle y \ = \ A + Bx$

$\displaystyle q \ = \ \sum_{i} [y - (A+Bx)]^2$

Differentiating partuall wrt to A and B weget

$\displaystyle \frac{\partial q}{\partial A} \ = \ (-2)[y_i -(A + Bx_i)] \ = \ 0$

and

$\displaystyle \frac{\partial q}{\partial B} \ = \ (-2) x_i[y_i -(A + Bx_i)] \ = \ 0$

normal equation is

$\displaystyle \sum_{i} y_i \ = \ An + B \sum_{i} x_i$

$\displaystyle \sum_{i} x_i y_i \ = A \sum_{i} x_i + B \sum_{i} x_i ^2$

Is this correct?? - Dec 13th 2009, 05:21 PMmatheagle
Impressive, we got you to do some decent work.

The normal equations look good,

but you left out the sums in the partial derivatives

in the previous set of equations. - Dec 13th 2009, 05:24 PMmatheagle