Description
In this project we will see some of the challenges of working with a “real-world” dataset, and see
the importance of exploratory data analysis to understand the features.
The project may be completed individually, or in a group of no more than three (3) people. 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 previous projects.
Libraries
You will need scikit-learn to obtain the data and build models, pandas to analyze the data, and
seaborn to visualize the data.
You may reuse code from the Jupyter notebooks accompanying the textbook and from the
documentation for the libraries. All other code and the results of experiments should be your
own.
Dataset
While they are not included directly with scikit-learn, the sklearn.datasets module includes
the ability to fetch some larger “real-world” datasets for experimentation. In this project we will
continue our earlier task of trying to predict median values of homes, but this time from the
California Housing dataset.
Note that in newer versions of scikit-learn, fetch_california_housing() includes an
as_frame parameter that will add a .frame attribute containing a pandas DataFrame.
Experiments
Run the following experiments in a Jupyter notebook, performing each action in a code cell and
answering each question in a Markdown cell.
1. Load and examine the California dataset’s features, target values, and description.
2. Recall that when we originally discussed housing prices, we suggested that the price of
a house might depend on how many bedrooms it has. Create and fit() an
sklearn.linear_model.LinearRegression model using AveBedrms as a predictor of
MedHouseVal. How well does the model score()?
3. Let’s take a closer look at the data. Seaborn’s pairplot() function can be used to plot
pairs of features against each other. Plot MedHouseVal as a function of each of the
features.
Note that older versions of Seaborn (including Google Colab) may have a bug that
displays the first plot incorrectly. You can work around this by passing the additional
parameter diag_kind=None.
4. Because of the size of the dataset, graphs produced by Seaborn are rather crowded. Try
the plot again using a sample() of 1%. How does the distribution of AveBedrms seem to
affect MedHouseVal?
5. Which features seem to have a linear relationship with MedHouseVal?
6. What interesting relationship do you see between MedHouseVal and the Latitude and
Longitude? Look these values up on a map of the state.
(If you are feeling particularly ambitious, you might try plotting the values on a map.)
7. Recall that the covariance matrix shows how pairs of features in a dataset co-vary. What
patterns (if any) do you observe? (Hint: use describe() to examine the distribution of
the features before attempting to interpret the results.)
8. Covariance is difficult to interpret because the features are on very different scales.
While you could standardize the features yourself, the correlation matrix is the
covariance matrix of the standardized variables. Based on the correlation matrix, which
features is the best predictor of MedHouseVal?
9. Repeat experiment (2) using the feature you found in experiment (8) instead of
AveBedrms. How well does this model score?
10. Another way to visualize the predictive value of the two features is to compare the
variance. The seaborn.regplot() function can be used to create a scatter plot, add a
regression line, and plot a 95% confidence interval in a single step. (Recall that 95%
corresponds to ±2𝜎.)
Plot AveBedrms as a predictor of MedHouseVal, then use the feature you found in
experiment (8). What difference do you see? (Don’t forget to use the sample you created
in experiment (4), or your graph will be difficult to interpret.)
11. Other than the feature you found in experiment (8), there appears to be only a very weak
relationship between MedHouseVal and the other features. Nevertheless, fit and score a
model to predict MedHouseVal using all the features at once. Are you surprised by the
result? What accounts for the difference from experiment (9)?
Submission
Submit your Jupyter .ipynb notebook file through Canvas before class on the due date. Your
notebook should include the usual identifying information found in a README.TXT file.
If the assignment is completed by a team, only one submission is required. Be certain to identify
the names of all students on your team at the top of the notebook.