How to plot best fit line with polyfit?

I just want to plot a best fit line based on 6 points. The coordinates are given. After entering the six points, how do I use the polyfit command? Can someone explain in detail to me?

Answer 1

[Friedrich]

Hi,

%generate some points, here of the function y = x^2
x = 1:6;
y = x.^2;

%fit second order polynomial
coefs = polyfit(x,y,2)

%plot it, use polyval to calcualte function values of that fit
 plot(x,y,'*',1:0.1:6,polyval(coefs,1:0.1:6),'-')

So if you don't know which order matches best you can try it out and use the second return value if polyfit which is a struct.

x = (0: 0.1: 2.5)';
y = erf(x); 

for i=1:10
    [p,S] = polyfit(x,y,i);
    f = polyval(p,x);
    subplot(5,2,i)
    plot(x,y,'*',x,f,'-')
    axis([0  3  0  1.5])
    title(['Order is: ',num2str(i),' norm is: ',num2str(S.normr)])
end

Smaller S.normr means better fit for the given values. But this isn't a measure for the behavior between the given points!

[Wong]

Still dont get it. But I used the basic fitting tool, and tick linear under plot ticks. Now another problem is that the best fit line isn't exactly straight. It is somehow not smooth, having small curves along the line. What is the problem?

[Friedrich]

Can you gives us your x and y values so we can better understand your problem?

[Wong]

x=[9 16 25 49 64 80 ]

y=[18.1 22.8 30 47.5 61.2 74]

Can you give me the command for the best fit based on these values?

[Friedrich]

I wouldn't go for polyfit with that values, since you won't get a nice fit. Best to get with polyfit is:

>> [p,S] = polyfit(x,y,4);

>> f = polyval(p,x);

>> plot(x,y,'*',x,f,'-')

I would rather go for splines (needs curve fitting toolbox):

pp=csapi(x,y)

hold on

fnplt(pp)

plot(x,y,'r*')

hold off

[Wong]

I used the solines command you gave me

pp=csapi(x,y)

hold on

fnplt(pp)

plot(x,y,'r*')

hold off

But I still don't get a best fit line.

[Friedrich]

What do you expect? What is the best fit line for you?

[Wong]

Nevermind, thats okay with me. Now how do I insert the x-axis and y-axis

[Friedrich]

What do you mean with insert x-axis? the axis is already there. Do you mean labeling it?

pp = spapi(2,x,y);

fnplt(pp)

xlabel('text for x-axis')

ylabel('text for y-axis')

[Wong]

I mean when I set the limit of the x-axis and y-axis to less than zero, both of the axis will move to the border of the graph. I want them to intersect at the origin.

[Friedrich]

MATLAB doesn't provide a feature like that. Maybe this from the FileExchange helps:

http://www.mathworks.com/matlabcentral/fileexchange/3245

[Wong]

Oh, thanks. I have another problem. How do I draw more grid lines between boxes? For example, the scale of my x-axis is 1:10. So how do I insert 10 more lines between the two boxes?

[Friedrich]

I modified the example so it works in 2D:

x=[9 16 25 49 64 80 ]

y=[18.1 22.8 30 47.5 61.2 74]

hold on

pp = spapi(2,x,y);

fnplt(pp)

axis([-10,80,-10,80])

plot(get(gca,'XLim'),[0 0],'k');

plot([0 0],get(gca,'YLim'),'k');

X=get(gca,'Xtick');

Y=get(gca,'Ytick');

XL=get(gca,'XtickLabel');

YL=get(gca,'YtickLabel');

set(gca,'Xtick',[]);

set(gca,'Ytick',[]);

Xoff=diff(get(gca,'XLim'))./30;

Yoff=diff(get(gca,'YLim'))./30;

for i=1:length(X)

plot([X(i) X(i)],[-Yoff, Yoff],'k');

end;

for i=1:length(Y)

plot([-Xoff Xoff],[Y(i) Y(i)],'k');

end;

text(X,zeros(size(X))-5,zeros(size(X))-3.*Zoff,XL);

text(zeros(size(Y))-3.*Xoff,Y,zeros(size(Y)),YL);

hold off

[Wong]

I get this error

??? Undefined function or variable 'Zoff'.

[Friedrich]

Sorry small typo. instead of

text(X,zeros(size(X))-5,zeros(size(X))-3.*Zoff,XL);

use

text(X,zeros(size(X))-5,zeros(size(X))-3,XL);

Regarding the grid. There is no ML functionality available. You have to plot this lines by your own, e.g.:

plot(1:10)

hold on

for i=1:10

plot(ones(10,1)*0.1*i,1:10,'MarkerSize',4,'LineStyle',':','Color',[0 0 0]);

end

grid