Matlab polynomial fitting

In MATLAB, the function polyfit does the polynomial regression. The statement polyfit(X, Y, N) evaluates the coefficients of the Mh order polynomial fitted to the data points given in the vectors X (independent variable) and Y (dependent variable). Note that polyfit returns the coefficients in the descending order, which is the opposite of what is shown in Eq. (7.126). 

The example below shows a short Matlab program that fits the function y =tan(x) with a polynomial of degree 3 defined by 4 linear parameters, i.e. the elements of a. 

To use nonlinear regression, you minimize Eq. (E.3) with respect to the unknown parameters. Polynomial and multiple regression do this too (behind the scenes), but for nonlinear curve fits it is necessary to use functions such as Solver in Excel and fminsearch in MATLAB. This is demonstrated using the same example given above for multiple regression. 

In Secdon 14.8, plots of data points revealed that the teladonship between y and x is qua-dradc (second order polynomial). To obtain the coefficients of the second order polynomial that best fits the given data, we will type the following sequence of commands. The MATLAB Command Window for Example 14.11 (Revisited) is shown in F jire 15.27. 

A surface response fitting of second-order polynomial fimction with = 0.71 was plotted in MATLAB to fiuther explore the coupling effects of T. Thus, the thermal conductivity for the GSA-SDS/FMWNT composites can be expressed as cn =f T(, Tc, Aabuik( i , Tm), Agd) and can be evaluated as shown in Eq. 6.14. The fuU polynomial equation for (Tf Tc) is given in Appendix 6B. 

A polynomial fnnction is the first approach suggested by most of the curve-fitting tools available (e.g.. Excel, graphing calculators, MATLAB). Usually, it is a univariate (single-variable) polynomial function with constant parameters given by... 

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