%%

n = 6;
a = 0;
b = 60;
M = b - a;

xx = a:0.001:b;
x = a:M/n:b
yl = 2*x - 0.25;
%y = yl + randn(1, length(yl))
y = [-10 3 -30 6 10 -2 15]

pc = polyfit(x,y,n);
yp = polyval(pc, xx);

pcl = polyfit(x,y,1);
yl = polyval(pcl, xx);

hold off
figure(1000)
plot(x,y,'bo')
XLIM([-10 70])
YLIM([-40 40])

figure(3000)
plot(x,y,'bo')
hold on
plot(xx,yp,'r')
plot(xx,yl,'k')
XLIM([-10 70])
YLIM([-40 40])
hold off

%%
n = 6;
a = 0;
b = 10;
M = b - a;

%n+1 datapoints
x = a:M/n:b;  
xx = a-1:.25:b+1;

y =  exp((-1*((x-5).^2))/4);
        yy = exp((-1*((xx-5).^2))/4);
        ys = spline(x,y,xx);
        pc = polyfit(x,y,n);
        yp = polyval(pc, xx);
        
        figure(100);
        hold off
        plot(x,y,'ko')
        hold on
        %plot(xx,ys, 'g')
        plot(xx,yp, 'r')
        plot(xx,yy, 'b')
        XLIM([a-1,b+1])
        YLIM([-1 1.2])
        hold off
        
%%



for i=1:5

n = i*4;
a = -1;
b = 1;
M = b - a;

%n+1 datapoints
x = a:M/n:b;  
xx = a:.01:b;        
        
y = 1./(1+16*x.^2);
        yy = 1./(1+16*xx.^2);
        ys = spline(x,y,xx);
        pc = polyfit(x,y,n);
        yp = polyval(pc, xx);
        
        figure(100+i);
        
        hold off
        plot(x,y,'ko')
        hold on
        plot(xx,ys,'g')
        plot(xx,yp,'r')
        plot(xx,yy,'b')
        XLIM([-1 1]);
        YLIM([-0.7, 1.2]);
        hold off
        
end %for
        
        
%%


xx = -1:0.001:1;

n = 6;
a = -1;
b = 1;
M = b - a;


x = a:M/n:b;
yl = 2*x - 0.25;
y = yl + randn(1, length(yl))

figure(2)
hold off
%plot(x,yl,'k')

plot(x,y,'ko')
hold on
pc = polyfit(x,y,n);
yp = polyval(pc, xx);
ys = spline(x,y,xx);
plot(xx,ys,'b');
plot(xx,yp,'r');

hold off




%%

xx = -1:0.001:1;

n = 6;
a = -1;
b = 1;
M = b - a;


x = a:M/n:b;
yl = 2*x - 0.25;
y = yl + randn(1, length(yl))

figure(2)
hold off

plot(x,y,'ko')
hold on

yp = zeros(6,length(xx));

for i=1:n
pc = polyfit(x,y,i);
yp(i,:) = polyval(pc, xx);
end %for

plot(xx,yp(1,:),'k');
plot(xx,yp(2,:),'b');
plot(xx,yp(3,:),'m');
plot(xx,yp(4,:),'c');
plot(xx,yp(5,:),'g');
plot(xx,yp(6,:),'r');


hold off


%%