Problem 258. linear least squares fitting

Inputs:

• f: cell-array of function handles
• x: column vector of x values
• y: column vector of y values, same length as x

Output:

• a: column vector of coefficients, same length as f

In a correct answer the coefficients a take values such that the function

   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)

minimizes the sum of the squared deviations between fit(x) and y, i.e. sum((fit(x)-y).^2) is minimal.

Remarks:

• The functions will all be vectorized, so e.g. f{1}(x) will return results for the whole vector x
• The absolute errors of a must be smaller than 1e-6 to pass the tests