Software tutorial/Least squares modelling (linear regression)

One of the best packages for fitting least squares models, in addition to all sorts of other statistical manipulation of data is the R language. The following pages from the 4C3 (Statistics for Engineering) website will help you:

• Installing R
• Building a least squares model in R
• Importing data into R from other sources

However, here is a tutorial on how you can use MATLAB or Python to fit a least squares model.

• MATLAB: use the regress.m and regstats.m function
• Python: use the numpy.linalg.lstsq

http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html

x = np.array([0, 1, 2, 3])

   >>> y = np.array([-1, 0.2, 0.9, 2.1])
   
   By examining the coefficients, we see that the line should have a
   gradient of roughly 1 and cut the y-axis at, more or less, -1.
   
   We can rewrite the line equation as ``y = Ap``, where ``A = x 1``
   and ``p = [[m], [c]]``.  Now use `lstsq` to solve for `p`:
   
   >>> A = np.vstack([x, np.ones(len(x))]).T
   >>> A
   array([[ 0.,  1.],
          [ 1.,  1.],
          [ 2.,  1.],
          [ 3.,  1.]])
   
   >>> m, c = np.linalg.lstsq(A, y)[0]
   >>> print m, c
   1.0 -0.95
   
   Plot the data along with the fitted line:
   
   >>> import matplotlib.pyplot as plt
   >>> plt.plot(x, y, 'o', label='Original data', markersize=10)
   >>> plt.plot(x, m*x + c, 'r', label='Fitted line')
   >>> plt.legend()
   >>> plt.show()