DOC: simplify and improve example in quick_start.rst and plot_toy_model.py

Author: Valentin-Laurent

doc/images/quickstart_1.png

@@ -37,7 +37,7 @@ Let us start with a basic regression problem.
 Here, we generate one-dimensional noisy data that we fit with a linear model.
 
 ..
-    Comment to developers: the following piece of code is duplicated in `examples/regression/1-quickstart/plot_toy_model.py`.
+    Comment to developers: the following piece of code is heavily inspired by `examples/regression/1-quickstart/plot_toy_model.py`.
     When updating it, please replicate the changes to this other file.
 
 .. testcode::
@@ -46,25 +46,18 @@ Here, we generate one-dimensional noisy data that we fit with a linear model.
     from sklearn.datasets import make_regression
     from sklearn.model_selection import train_test_split
 
-    RANDOM_STATE = 42
-    X, y = make_regression(n_samples=500, n_features=1, noise=20, random_state=RANDOM_STATE)
-    X_train_conformalize, X_test, y_train_conformalize, y_test = train_test_split(
-        X, y, test_size=0.5, random_state=RANDOM_STATE
-    )
-    X_train, X_conformalize, y_train, y_conformalize = train_test_split(
-        X_train_conformalize, y_train_conformalize, test_size=0.5, random_state=RANDOM_STATE
-    )
+    X, y = make_regression(n_samples=500, n_features=1, noise=20)
+
+    X_train, X_temp, y_train, y_temp = train_test_split(X, y)
+    X_test, X_conformalize, y_test, y_conformalize = train_test_split(X_temp, y_temp)
 
     #  We follow a sequential ``fit``, ``conformalize``, and ``predict`` process.
     #  We set the confidence level to estimate prediction intervals at approximately one and two
     #  standard deviation from the mean.
 
     from mapie_v1.regression import SplitConformalRegressor
 
-    mapie_regressor = SplitConformalRegressor(
-        confidence_level=[0.95, 0.68],
-        prefit=False,
-    )
+    mapie_regressor = SplitConformalRegressor(confidence_level=[0.95, 0.68], prefit=False)
     mapie_regressor.fit(X_train, y_train)
     mapie_regressor.conformalize(X_conformalize, y_conformalize)
 

doc/quick_start.rst

@@ -14,12 +14,14 @@
 from mapie_v1.regression import SplitConformalRegressor
 
 RANDOM_STATE = 42
+
 X, y = make_regression(n_samples=500, n_features=1, noise=20, random_state=RANDOM_STATE)
-X_train_conformalize, X_test, y_train_conformalize, y_test = train_test_split(
-    X, y, test_size=0.5, random_state=RANDOM_STATE
+
+X_train, X_test_conformalize, y_train, y_test_conformalize = train_test_split(
+    X, y, test_size=0.4,  random_state=RANDOM_STATE
 )
-X_train, X_conformalize, y_train, y_conformalize = train_test_split(
-    X_train_conformalize, y_train_conformalize, test_size=0.5, random_state=RANDOM_STATE
+X_test, X_conformalize, y_test, y_conformalize = train_test_split(
+    X_test_conformalize, y_test_conformalize, test_size=0.5, random_state=RANDOM_STATE
 )
 
 confidence_level = [0.95, 0.68]