Curve fitting

In this project, I have shown graph value of the polynomial curve-fitting by 1-3 degree . Greater the degree of the polynomial, better will be the fit, however, with higher orders, shows error. Calculating the RMS value between the estimated and the original plot gives a rough idea of the best-suited curve within a particular error range. 

In this code, I have plotted a graph between the degree of a polynomial and the RMS value for each polynomial. I found that higher the order of the polynomial, lower is the RMS ERROR and and values which lies within the range of 0.5 are shown which depicts the accuracy of polynomial with increase in degree

%Preparing the data
cp_data=load(\'data\');
temp=cp_data(:,1);
cp=cp_data(:,2);

j=1;
while j<4 %find upto polynomial of 3
% curve fit
coeff=polyfit(temp,cp,(j));
predicated_cp = polyval(coeff,temp);

%compare curve fit with original data
figure(j)
plot(temp,cp,\'linewidth\',3)
xlabel(\'temperature[k]\');
ylabel(\'specific heat[KJ/Kmol-k]\');

hold on 
plot (temp,predicated_cp,\'linewidth\',3)
legend(\'original data set \', \'predicated data set\');
pause(0.5)

%Root Mean Square Error Calculation
Error(j) = sqrt((sum(abs(predicated_cp - cp).^2))); %stores the root mean sqaure error of each degree polynomial in Error matrix

fprintf(\'RMS value is %d\',Error(j));
figure(4)
plot(Error,\'-ko\') % plots the curve as well as highlights the points
grid on           %turns grid on
xlabel(\'Degree of Polynomial\')
ylabel(\'RMS Error\')

 while i<3200
    if(abs(cp(i,1)-predicated_cp(i,1))<0.5)
        c=c+1;
    end    
        i=i+1;

end 
fprintf(\'no of values lies within diff of 0.5 is %d out of %d\',c,i); 

j=j+1;
end

polynomial of degree 1

polynomial of degree 2

polynomial of degree 3

3

RMS graph

Results to show accuracy of polynomial with increase in degree

RMS value is 1.470731e+03
no of values lies within diff of 0.5 is 43 out of 3200
RMS value is 7.349201e+02
no of values lies within diff of 0.5 is 69 out of 3200  
RMS value is 3.070375e+02
no of values lies within diff of 0.5 is 143 out of 3200>>