Originally Posted by

**SammyS** ... to be the model of a an arbitrary data set defined by vector f (function values) and vector x (data points) for $\displaystyle x_i > 0 \text{ for All }i = 0,1,2,.....,n$

And we're asked to find the best fit in the least squares sense for this model -- Find the normal equation?

$\displaystyle h(x)=a + b\,x + c\,e^{\arctan (x)}+ d\,(\cos(\sin(T_{14}(x)))),$ (corrected) where $\displaystyle T_{14}(x)$ is the 14th degree Chebyshev polynomial (of the first kind).

You certainly can show HOW to get the normal matrix, and normal equation for this, but you have no specific values for the $\displaystyle \displaystyle x_i$ and no observed dependent values $\displaystyle \displaystyle y_i,$ so you certainly can't give a numerical answer.