Description
In this project you will use NumPy to implement vectorized linear and polynomial regression
models and compare their performance using separate training and test sets.
The project may be completed individually, or in a group of no more than three (3) students. All
students on the team must be enrolled in the same section of the course.
Platforms
The platform requirements for this project are the same as for Project 1.
Libraries and Code
Vector and matrix operations for this project must be implemented in NumPy and results
visualized with Matplotlib’s pyplot framework. You may not use any other library except the
Python Standard Library.
Code from A Whirlwind Tour of Python, the Jupyter notebooks accompanying the textbook, and
from the library documentation may be reused. All other code and the results of experiments
must be your own original work or the original work of other members of your team.
Dataset
The file boston.npz contains a version of the Boston house-price dataset in NumPy .npz
format. See http://lib.stat.cmu.edu/datasets/boston at the CMU StatLib Datasets Archive for a
description of the data.
Experiments
Run the following experiments in a Jupyter notebook, performing actions in code cells and
reporting results in Markdown cells.
1. Use the NumPy load() method to read the dataset. The data contains two arrays:
‘features’, which contains the variables CRIM through LSTAT, and ‘target’, which
contains the variable MEDV.
2. Set aside the first 102 items (20% of the total) as a test set, and the remaining 404 items
for training.
3. Create a scatterplot of the training data showing the relationship between the number of
rooms and the median value of a home. Does the relationship appear to be linear?
4. With RM as X and MEDV as t, use np.linalg.inv() to compute w for the training set.
What is the equation for MEDV as a linear function of RM?
5. Use w to add a line representing the least squares fit to your scatter plot from
experiment (3). How well does the model appear to fit the training set?
6. Use w to find the predicted response for each value of the RM attribute in the training
set, then compute the average loss 𝓛 for the model.
7. Repeat experiment (6) for the test set. How do the training and test MSE values
compare? What accounts for the difference?
8. Repeat experiments (4), (6), and (7) using all 13 input features as X. How do the training
and test MSEs for this model compare to the values you found for experiment (7)? What
accounts for the difference?
9. Using the value that you found for w for this new model, determine for each feature how
much a one unit increase in that feature would change the median value of a home.
Based on the description of the dataset provided by StatLib, convert your answer to
dollars.
10. Based on the amount of change in the value of a home, which features are most
important?
Submission
A Markdown cell at the top of the notebook should include project summary information as
described in the Syllabus for README files.
Since you may be actively editing and making changes to the code cells in your notebook, be
certain that each of your code cells still runs correctly before submission. You may wish to do
this by selecting Run All from the drop-down menu bar.
Submit your Jupyter .ipynb notebook file through Canvas before class on the due date.
If the assignment is completed by a team, only one submission is required. Be certain to identify
the names of both students at the top of the notebook. See the following sections of the Canvas
documentation for instructions on group submission:
● How do I join a group as a student?
● How do I submit an assignment on behalf of a group?
