In this notebook we express the cost function and the gradient of a linear regressor in a vectorized form. We analitically solve the normal equation for the best fit parameters, and show how the model can be applied to the non-linear fit of atmospheric CO2 levels over time.
We cast the gradient of a linear regressor in a vectorized form, and test the result of a gradient descent optimization algorithm by comparing our result the analytical solution found in the previous notebook. We review the importance of feature normalization.
This time we cannot derive an analytical solution to test our numerical algorithm. Therefore, we test our classifier on a simple data set with only two features that we can easily visualize.
We use the algorithm developed and tested in our previous notebook to reproduce cancer diagnosis classification results found in the medical literature.