How can I fit a curve to x, y points and obtain the regression?

I have plotted x vs y and obtained a plot of points, now I'm trying to fit a curve to my data using a nonlinear polynomial of order 4, the coeficiants are unknown.

I aim to obtain the regression coefficient as well.

Any idea how it is possible to do this? what are the suitable matlab functions to plot the fitting curve and to obtain the regression coeficient?

I already tried polyfit, but is it correct? if yes then how to proceed?

Answer 1

[KSSV]

Yes polyfit is the function you need.

x = linspace(0,4*pi,50);
y = sin(x);
% Use polyfit to fit a 4th-degree polynomial to the points.

p = polyfit(x,y,7);
% Evaluate the polynomial on a finer grid and plot the results.

x1 = linspace(0,4*pi);
y1 = polyval(p,x1);
figure
plot(x,y,'o')
hold on
plot(x1,y1)
hold off

In the above p has your coefficients. YOu can use poly2sym to see the polynomial obtained.

[Luna]

+1. but you fit a 7th degree :)

[Sarah]

will this work if my x and y are vectors of equal size ?

woukd the code change in anyway ? if yes then how ?

[KSSV]

YOu need to have equal number of x and y.

[Sarah]

the fitting curve in this case appears to be connecting the points, i want to obtain smooth fitting curve. any idea why that is happening ?a

[KSSV]

What data you have? How many points? Attach your data and your expectations.

[Luna]

When you fit 7th degree polynomial, it might looks like it is connecting the points.

But if you put 5 like below (5th degree) you can see actually it is making a fit for that sinusoidal function.

p = polyfit(x,y,5);

[Sarah]

i have x and y as vectors of 6 values. i am plotting x vs y. this method is not resng in a smooth curve fitting even if i change n frkm 4 to 5. it looks more like it is connecting the data.

also, how can i get the regression coeficient from this?ulti

[KSSV]

What you want to do? HAve a smooth curve? or fit a polynomial?

[Sarah]

i want to fit the polynomial curve to the plotted data points and obtain the regression coeficient..

[KSSV]

Then using polyfit is apt.

[Sarah]

so i tried this as below, but the resulting fitting does not apear same as it is when done on excel.

x =[6 values input by the user ]

y = [6 values calculated ]

so x and y are the same size

then:

p = polyfit(x, y, 4);

val = polyval(p, x);

plot(x, y, 'o');

hold on;

plot(x, val);

hold off

Answer 2

[madhan ravi]

Read interp1 and use appropriate method you want

x = linspace(0,4*pi,50);
y = sin(x);
xx = linspace(x(1),x(end),1000);
yy = interp1(x,y,xx,'spline')
plot(x,y,'o',xx,yy)

[Sarah]

this worked perfectly!

but what is the difference between using interp1 or using polyfit and polyval?

[madhan ravi]

Anytime :) , polyfit is for polynomials

[Sarah]

then how can i get the regression coeficient if I am sing the interp1 method?

Answer 3

[Luna]

Hello Sarah,

you can use polyfit. It uses least squares, here is the link you can read about it:

polyfit