The program below learns a linear relationship between a three-dimensional input and an output.

It downloads and operates on a dataset from Helmut Spaeth, Mathematical Algorithms for Linear Regression, Academic Press, 1991, ISBN 0-12-656460-4.

The data concerns pasture rent structure and grass variety and includes 67 examples. The inputs are

• the rent per acre of arable land,
• the number of milk cows per square mile, and
• the difference between pasturage and arable land

The output is the rental price per acre for this variety of grass. The program includes a loss function as well as a function that calculates the partial derivative of the loss with respect to a specified element of $\vec{\theta}$.

Note:

• This program depends on the numpy library, which can generally be installed using the command pip install numpy.

• This program will generally take a few minutes to complete execution and output the best-fit $\theta$ vector.