Cross validated predictions

    %matplotlib inline
    from matplotlib import rcParams

    # figure size in inches
    rcParams['figure.figsize'] = 20,8
    from sklearn import datasets
    from sklearn.model_selection import cross_val_predict
    from sklearn import linear_model
    import matplotlib.pyplot as plt

    lr = linear_model.LinearRegression()
    boston = datasets.load_boston()
    y = boston.target

    # cross_val_predict returns an array of the same size as `y` where each entry
    # is a prediction obtained by cross validation:
    predicted = cross_val_predict(lr, boston.data, y, cv=10)

    fig, ax = plt.subplots()
    ax.scatter(y, predicted, color=(0.1,0.7,0.1,0.28))
    ax.plot([y.min(), y.max()], [y.min(), y.max()], 'k--', lw=1)
    ax.set_xlabel('Measured')
    ax.set_ylabel('Predicted')
    plt.show()

    # compare this to the usual approach
    lr.fit(boston.data,y)
    p = lr.predict(boston.data)

    fig, ax = plt.subplots()
    ax.scatter(y, p, color = (0.1,0.1,0.71,0.28))
    ax.plot([y.min(), y.max()], [y.min(), y.max()], 'k--', lw=1)
    ax.set_xlabel('Measured')
    ax.set_ylabel('Predicted')
    plt.show()