Description
In this project you will use scikit-learn, which is a higher-level machine learning library that works
with NumPy, to compare the performance of linear and polynomial regression models.
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
In addition to NumPy and pyplot, you will need scikit-learn. 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
This project uses the same boston.npz file as Project 2.
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. Use sklearn.model_selection.train_test_split() to split the features and target
values into separate training and test sets. Use 80% of the original data as a training set,
and 20% for testing. To make sure that your results are reproducible, pass
random_state=(2021-3-11).
3. Create a scatterplot of the training data showing the relationship between the
percentage of the population that is lower status and the median value of a home. Does
the relationship appear to be linear?
(Note that “status” here refers to socioeconomic status and is not a value judgement on
the residents.)
4. With LSTAT as X and MEDV as y, create and fit() an
sklearn.linear_model.LinearRegression model. Using the coef_ and intercept_
attributes of the model, what is the equation for MEDV as a linear function of LSTAT?
5. Use the coef_ and intercept_ attributes of the model 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 data?
6. Use the predict() method of the model to find the response for each value of the
LSTAT attribute in the training set. Using sklearn.metrics.mean_squared_error(),
find the average loss 𝓛 for the training set.
7. Repeat experiment (6) for the test set. How do the training and test MSE values
compare?
8. Let’s see if we can fit the data better with a more flexible model. Use np.hstack() to
add a degree-2 polynomial feature to X, then fit a new linear model. How do the training
and test MSE values for this model compare to the previous model?
9. Repeat experiment (5) for your polynomial model.
10. Repeat experiments (4), (6), and (7) using all 13 input features as X. How do the training
and test MSEs for this model (which is a linear model including all features) compare to
the values you found for experiment (8) (which was a degree-2 polynomial model
including a single feature)? What accounts for the difference?
11. Combine experiments (8) and (10), using np.hstack() to add the squares of all 13 input
features to X. How do this model’s training and test MSE scores compare to the previous
model using all 13 features?
12. Scikit-learn is also capable of constructing polynomial features for us using
sklearn.preprocessing.PolynomialFeatures, but those features also include
interaction features, where the feature terms are multiplied together.
Use the fit_transform() method to create degree-2 polynomial and interaction terms
for the original set of 13 features, then fit a new linear model. Compare the training and
test MSE to the previous model. What is the effect of adding interaction terms in this
case? Do we seem to be overfitting?
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?
