How to find the equation of a graph after getting Xdata and Ydata ?

x = [0 1 2 3 4 5 6 7 8 9 10];

y = [4 3 4 7 12 19 28 39 52 67 84];

% How to find the function y = F(x) ??

% because I need for example to know

% if x = 1.5

% y = ??

% the solution should be something regarding regression.

Answer 1

[Azzi Abdelmalek]

You can find yi by interpolation

x = [0 1 2 3 4 5 6 7 8 9 10];
y = [4 3 4 7 12 19 28 39 52 67 84];
xi= 1.5
yi=interp1(x,y,xi)

[Joel Sande]

GREAT !! perfect

Answer 2

[Brendan Hamm]

The easiest way would be to use the polynomial fitting functions. For this you need to know what order polynomial to fit, so visualize the data:

plot(x,y)

The data you gave looks quadratic, so let's find the coefficients for a second order polynomial:

coeff = polyfit(x,y,2);

Now evaluate the polynomial at a new value of x:

xNew = 1.5;
yNew = polyval(coeff,xNew);
plot(xNew,yNew,'r*');

[Brendan Hamm]

For more complex linear models you can take a look at fitlm in the Statistics and Machine Learning Toolbox.

[Joel Sande]

Yes this solution works too. But the first one is more simple. Thinks.

[Brendan Hamm]

If you want to assume the data you had was from a one dimensional polynomial, then this works fine (as interp1 is doing a 1 dimensional linear interpolation). On the other hand if you want the requirement that, "the solution should be something regarding regression", then polyfit or fitlm would be the appropriate choice.

[Joel Sande]

Thanks for the advice.

[Joel Sande]

Yes, Finally I used Polyfit

Answer 3

[Walter Roberson]

one of the infinite number of solutions is:

x = [0 1 2 3 4 5 6 7 8 9 10];
y = [4 3 4 7 12 19 28 39 52 67 84];
pp = polyfit(x, y, length(x)-1);
y1_5 = polyval(pp, 1.5)

Another of the infinite solutions is:

x = [0 1 2 3 4 5 6 7 8 9 10];
y = [4 3 4 7 12 19 28 39 52 67 84];
y1_5 = 19;

It is not mathematically possible to distinguish between these two solutions as to which one is "more correct".

[Joel Sande]

Thanks !

[Joel Sande]

It is exactelly what I used, because I didn t know the order of the polynom.