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### ElasticNet Regression Example in Python

ElasticNet regularization applies both L1-norm and L2-norm regularization to penalize the coefficients in a regression model. In this tutorial, we'll learn how to use sklearn's ElasticNet and ElasticNetCV models to analyze regression data. The post covers:
1. Preparing data
2. Best alpha
3. Defining model and checking the results
4. Cross-validation with ElasticNetCV
5. Source code listing

```from sklearn.datasets import load_boston
from sklearn.linear_model import ElasticNet,ElasticNetCV
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
import numpy as np```

Preparing data

We use Boston house-price dataset as regression data in this tutorial. After loading the dataset, first, we'll separate it into the x - feature and y - label, then split into the train and test parts. Here, we'll extract 15 percent of the dataset as test data.

```boston = load_boston()
x, y = boston.data, boston.target
xtrain, xtest, ytrain, ytest = train_test_split(x, y, test_size=0.15)```

Best alpha

To figure out what alpha value is good for our model, we'll define multiple values and check the performance accuracy.

`alphas = [0.0001, 0.001, 0.01, 0.1, 0.3, 0.5, 0.7, 1]`

We define ElasticNet model by setting alpha and train it with x and y data. Then, we'll check the R-squared, MSE, and RMSE metrics for each alpha.

```for a in alphas:
model = ElasticNet(alpha=a).fit(x,y)
score = model.score(x, y)
pred_y = model.predict(x)
mse = mean_squared_error(y, pred_y)
print("Alpha:{0:.4f}, R2:{1:.2f}, MSE:{2:.2f}, RMSE:{3:.2f}"
.format(a, score, mse, np.sqrt(mse)))```
` `
```Alpha:0.0001, R2:0.74, MSE:21.90, RMSE:4.68
Alpha:0.0010, R2:0.74, MSE:21.92, RMSE:4.68
Alpha:0.0100, R2:0.74, MSE:22.32, RMSE:4.72
Alpha:0.1000, R2:0.73, MSE:23.16, RMSE:4.81
Alpha:0.3000, R2:0.71, MSE:24.08, RMSE:4.91
Alpha:0.5000, R2:0.71, MSE:24.85, RMSE:4.99
Alpha:0.7000, R2:0.70, MSE:25.55, RMSE:5.05
Alpha:1.0000, R2:0.69, MSE:26.50, RMSE:5.15 ```

The result shows that we can use 0.01 value for our model.

Defining model and checking the results

Now, we can define ElasticNet regression model with an alpha value taken above and fit it with xtrain and ytrain data. Then we'll predict xtest data and check the model accuracy.

```elastic=ElasticNet(alpha=0.01).fit(xtrain, ytrain)
ypred = elastic.predict(xtest)
score = elastic.score(xtest, ytest)
mse = mean_squared_error(ytest, ypred)
print("R2:{0:.3f}, MSE:{1:.2f}, RMSE:{2:.2f}"
.format(score, mse, np.sqrt(mse)))```
` `
`R2:0.738, MSE:20.24, RMSE:4.50 `

Finally, we'll visualize the model in a plot.

```x_ax = range(len(xtest))
plt.scatter(x_ax, ytest, s=5, color="blue", label="original")
plt.plot(x_ax, ypred, lw=0.8, color="red", label="predicted")
plt.legend()
plt.show()```

Cross-validation with ElasticNetCV

ElasticNetCV is a cross-validation class that can search multiple alpha values and applies the best one. We'll define the model with alphas value and fit it with xtrain and ytrain data.

```elastic_cv=ElasticNetCV(alphas=alphas, cv=5)
model = elastic_cv.fit(xtrain, ytrain)
print(model.alpha_)```
`0.0001 `
`print(model.intercept_)`
`40.95939049160889 `

We can predict xtest data and check the accuracy metrics.

```ypred = model.predict(xtest)
score = model.score(xtest, ytest)
mse = mean_squared_error(ytest, ypred)
print("R2:{0:.3f}, MSE:{1:.2f}, RMSE:{2:.2f}"
.format(score, mse, np.sqrt(mse)))```
` `
`R2:0.743, MSE:19.87, RMSE:4.46 `

In this post, we've briefly learned how to use ElasticNet and ElasticNetCV models to analyze regression data. The full source code is listed below. Thank you for reading!

Source code listing

```from sklearn.datasets import load_boston
from sklearn.linear_model import ElasticNet,ElasticNetCV
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
import numpy as np

x, y = boston.data, boston.target
xtrain, xtest, ytrain, ytest = train_test_split(x, y, test_size=0.15)

alphas = [0.0001, 0.001, 0.01, 0.1, 0.3, 0.5, 0.7, 1]

for a in alphas:
model = ElasticNet(alpha=a).fit(x,y)
score = model.score(x, y)
pred_y = model.predict(x)
mse = mean_squared_error(y, pred_y)
print("Alpha:{0:.4f}, R2:{1:.2f}, MSE:{2:.2f}, RMSE:{3:.2f}"
.format(a, score, mse, np.sqrt(mse)))

elastic=ElasticNet(alpha=0.01).fit(xtrain, ytrain)
ypred = elastic.predict(xtest)
score = elastic.score(xtest, ytest)
mse = mean_squared_error(ytest, ypred)
print("R2:{0:.3f}, MSE:{1:.2f}, RMSE:{2:.2f}"
.format(score, mse, np.sqrt(mse)))

x_ax = range(len(xtest))
plt.scatter(x_ax, ytest, s=5, color="blue", label="original")
plt.plot(x_ax, ypred, lw=0.8, color="red", label="predicted")
plt.legend()
plt.show()

# --- ElasticNetCV ----
elastic_cv=ElasticNetCV(alphas=alphas, cv=5)
model = elastic_cv.fit(xtrain, ytrain)
print(model.alpha_)
print(model.intercept_)

ypred = model.predict(xtest)
score = model.score(xtest, ytest)
mse = mean_squared_error(ytest, ypred)
print("R2:{0:.3f}, MSE:{1:.2f}, RMSE:{2:.2f}"
.format(score, mse, np.sqrt(mse)))

x_ax = range(len(xtest))
plt.scatter(x_ax, ytest, s=5, color="blue", label="original")
plt.plot(x_ax, ypred, lw=0.8, color="red", label="predicted")
plt.legend()
plt.show()```