clear

clc

%% DATA INPUT

filename = input('Enter file name, including its extension: ', 's'); D = load(filename);

%or load('Mphi.out');

%%

%Trendline

%Evaluates the polynomial c at the values in X. c is a vector of

%coefficients in descending powers.

c=polyfit(x,y,1);

yhat=polyval(c,x);

c=polyfit(x,y,2);

yhat=polyval(c,x);

c=polyfit(x,y,3);

yhat=polyval(c,x);

c=polyfit(x,y,4);

yhat=polyval(c,x);

c=polyfit(x,y,5);

yhat=polyval(c,x);

c=polyfit(x,y,6);

yhat=polyval(c,x);

c=polyfit(x,y,7);

yhat=polyval(c,x);

c=polyfit(x,y,8);

yhat=polyval(c,x);

c=polyfit(x,y,9);

yhat=polyval(c,x);

c=polyfit(x,y,10);

yhat=polyval(c,x);

c=polyfit(x,y,11);

yhat=polyval(c,x);

c=polyfit(x,y,12);

yhat=polyval(c,x);

c=polyfit(x,y,13);

yhat=polyval(c,x);

c=polyfit(x,y,14);

yhat=polyval(c,x);

c=polyfit(x,y,15);

yhat=polyval(c,x);

%Correlation coefficient

R=corrcoef(x,y);

R=R(1,2);

%Coefficient of determination

%{

mx=mean(x);

my=mean(y);

syy=sum(y.^2)-length(x)*my^2;

sse=syy-c(1)*(sum(x.*y)-length(x)*mx*my);

R2=1-sse/syy;

%}

%or

R2=R^2;

%%

%PLOT

figure(1)

plot(x,y,'o')

holdon

plot(x,yhat,'k')

title('\fontname{Arial} \bf Performance of racing motorcycles equipped with Tire-X

tires','FontSize', 12);

xlabel('Lap time [s]');

ylabel('Ambient temperature [F]');

axis([65 68 0 100])

text(65.2,90,['Coefficient of determination R^2= ' num2str(R2,3)])

text(65.2,85,['Correlation coefficient R= ' num2str(R,3)] )

legend('Data points',['Trendline y=' num2str(c(1),5) 'x' num2str(c(2),

5)],'location','best')