Based on what you know about the least square linear approximation, apply these

Question

Based on what you know about the least square linear approximation, apply
these ideas to fit a function of the form y = a ln(x) + b cos(x) + c ex to the
following table of values. This may be done with or without MATLAB.
- If you choose to do this without MATLAB: you may solve for the coefficients
in terms of sums of xi and yi.
- If you choose to use MATLAB you must solve for the coefficients exactly,
label each coefficient, and plot the original data overlaid with your model
predictions indicating which values are predicted and which are data.

*MATLAB is preferred

xi 0.24 0.65 0.95 1.24 1.73 2.01 2.23 2.52 2.77 2.99 yi 0.23 -0.26 -1.10 -0.45 0.27 0.10 -0.29 0.24 0.56 1.00

Explanation / Answer

Following table shows the various tranformed values of X needed to find regression line:

Folloiwng is the output of regression analysis generated by excel:

So required regression line is

y' = -0.2926 -0.8663 ln(x) +-0.8302 cos(x) + 0.0641 e^(x)

xi yi ln(xi) Cos(xi) e^(xi) 0.24 0.23 -1.42712 0.971338 1.271249 0.65 -0.26 -0.43078 0.796084 1.915541 0.95 -1.1 -0.05129 0.581683 2.58571 1.24 -0.45 0.215111 0.324796 3.455613 1.73 0.27 0.548121 -0.15853 5.640654 2.01 0.1 0.698135 -0.42522 7.463317 2.23 -0.29 0.802002 -0.61249 9.299866 2.52 0.24 0.924259 -0.81295 12.4286 2.77 0.56 1.018847 -0.93175 15.95863 2.99 1 1.095273 -0.98853 19.88568

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