📃 Solution for Exercise M4.03

In all previous notebooks, we only used a single feature in data. But we have already shown that we could add new features to make the model more expressive by deriving new features, based on the original feature.

The aim of this notebook is to train a linear regression algorithm on a dataset with more than a single feature.

We will load a dataset about house prices in California. The dataset consists of 8 features regarding the demography and geography of districts in California and the aim is to predict the median house price of each district. We will use all 8 features to predict the target, the median house price.

Note

If you want a deeper overview regarding this dataset, you can refer to the Appendix - Datasets description section at the end of this MOOC.

from sklearn.datasets import fetch_california_housing

data, target = fetch_california_housing(as_frame=True, return_X_y=True)
target *= 100  # rescale the target in k$
data.head()

	MedInc	HouseAge	AveRooms	AveBedrms	Population	AveOccup	Latitude	Longitude
0	8.3252	41.0	6.984127	1.023810	322.0	2.555556	37.88	-122.23
1	8.3014	21.0	6.238137	0.971880	2401.0	2.109842	37.86	-122.22
2	7.2574	52.0	8.288136	1.073446	496.0	2.802260	37.85	-122.24
3	5.6431	52.0	5.817352	1.073059	558.0	2.547945	37.85	-122.25
4	3.8462	52.0	6.281853	1.081081	565.0	2.181467	37.85	-122.25

Now it is your turn to train a linear regression model on this dataset. First, create a linear regression model.

# solution
from sklearn.linear_model import LinearRegression

linear_regression = LinearRegression()

Execute a cross-validation with 10 folds and use the mean absolute error (MAE) as metric. Be sure to return the fitted estimators.

# solution
from sklearn.model_selection import cross_validate

cv_results = cross_validate(
    linear_regression,
    data,
    target,
    scoring="neg_mean_absolute_error",
    return_estimator=True,
    cv=10,
    n_jobs=2,
)

Compute the mean and std of the MAE in thousands of dollars (k$).

# solution
print(
    "Mean absolute error on testing set: "
    f"{-cv_results['test_score'].mean():.3f} k$ ± "
    f"{cv_results['test_score'].std():.3f}"
)

Mean absolute error on testing set: 54.452 k$ ± 9.109

Inspect the fitted model using a box plot to show the distribution of values for the coefficients returned from the cross-validation. Hint: use the function df.plot.box() to create a box plot.

# solution
import pandas as pd

weights = pd.DataFrame(
    [est.coef_ for est in cv_results["estimator"]], columns=data.columns
)

import matplotlib.pyplot as plt

color = {"whiskers": "black", "medians": "black", "caps": "black"}
weights.plot.box(color=color, vert=False)
_ = plt.title("Value of linear regression coefficients")