Example of Interpolation and extrapolation:
The MATLAB has a function to do this, known as polyfit. The function polyfit finds the coefficients of the polynomial of the particular degree which best fits the data by using a least squares algorithm. There are 3 arguments passed to the function: the vectors which represent the data, and the degree of the preferred polynomial. For illustration, to fit a straight line (degree 1) through the earlier data points, the call to the polyfit function would be:
>> polyfit(x,y,1)
ans =
0.0000 67.6000
that says that the best straight line is of the form 0x + 67.6. Though, from the plot as shown in figure, it appears like a quadratic would be a much better fit. The following would generate the vectors and then fit a polynomial of degree 2 through the data points, storing the values in a vector known as coefs.
>> x = 2:6;
>> y = [65 67 72 71 63];
>> coefs = polyfit(x,y,2)
coefs =
-1.8571 14.8571 41.6000
This says that the MATLAB has determined that the best quadratic which fits these data points are:
-1.8571x^{2 }+ 14.8571x + 41.6. So, the variable coefs now stores a vector which represents this polynomial.