HOW to implement the Weighted Linear Least Squares
Estimation (Weighted LSE) algorithm. Apply your algorithm to the following
data sets (x1, y1, w1), …, (xN, yN, wN) where xi, yi are the
coordinates of the point
and wi is the weight of the corresponding point. 
x 1 2 3 4 5
y 2.67 5.89 7.03 9.47 10.01
w 1.0 0.5 0.4 0.3 0.1

Hello,

Put all your y samples in a column vector 5x1 y5.
Put all your x samples in a column vector 5x1 h5.
Put all your weights in the diagonal elements of a 5x5 matrix W5. In the ii position put the
weight that corresponds to the i-th entry of y5 and x5. Then the optimal coefficient c in the
weighted least squares sense is given by 

c = inv(h5'*W5*h5)*h5'*W5*y5

where * denotes multiplication and ' denotes transpose (MATLAB notation)

and your y estimates become

y=c*x

If you have questions tell me.

Manolis

HOW to implement the Weighted Linear Least Squares
>Estimation (Weighted LSE) algorithm. Apply your algorithm to the following
>data sets (x1, y1, w1), ?, (xN, yN, wN) where xi, yi are the
>coordinates of the point
>and wi is the weight of the corresponding point. 
>x 1 2 3 4 5
>y 2.67 5.89 7.03 9.47 10.01
>w 1.0 0.5 0.4 0.3 0.1