Linear Interpolation and Regression for given data points in MATLAB

Question:

Find Linear Interpolation and Linear Regression for given \(X\) and \(Y\) data points in MATLAB?

Answer:

Linear Interpolation for given \(X\) and \(Y\) data points can be evalued in MATLAB by using built-in command "interp1" and Linear Regression can be obtainbed by solving system of Linear Equations.

x = [0.023 0.05 0.072 0.055 0.013 0.096 0.011]
y = [0.050623 0.0925 0.112608 0.098175 0.030303 0.120192 0.025927]
xi = linspace(min(x),max(x));
yi = interp1(x,y,xi);
A = [numel(x) sum(x);
    sum(x) sum(x.^2)];
b = [sum(y);
    sum(x.*y)];
var = fliplr((A\b)')
poly2sym(var)
xr = xi;
yr = polyval(var,xi);
yu = polyval(var,x);
err = immse(y,yu)
plot(x,y,'o',xi,yi,':.',xr,yr,'b--',x,yu,'go');
legend('Data Points','Interpolation','Linear Regression','$y = ax + b$','Interpreter','latex')

OUTPUT

x =

    0.0230    0.0500    0.0720    0.0550    0.0130    0.0960    0.0110


y =

    0.0506    0.0925    0.1126    0.0982    0.0303    0.1202    0.0259


var =

    1.1889    0.0214


ans =
 
(5354402693154885*x)/4503599627370496 + 771401281570945/36028797018963968


err =

   9.3126e-05