0) Introduction

Random Forests are supervised machine learning algorithms used for both classification and regression. In scikit-learn, the main classes are RandomForestClassifier and RandomForestRegressor. A random forest is a meta-estimator that fits many decision trees on different subsamples of the data and uses averaging to improve predictive accuracy and reduce overfitting compared with a single tree.

1) What a Random Forest does

A Random Forest builds many decision trees instead of relying on just one.

For classification:

• each tree predicts a class
• the forest combines the trees by voting
• the final class is the majority vote

For regression:

• each tree predicts a number
• the forest averages those predictions
• the final prediction is the average

This averaging is the main reason Random Forests are usually more stable and more accurate than a single decision tree. Scikit-learn explicitly describes random forests as ensembles that use averaging to improve predictive accuracy and control overfitting.

2) Why Random Forests are useful

Random Forests are popular because they are:

• powerful on tabular data
• less likely to overfit than a single tree
• usable for both classification and regression
• able to model nonlinear patterns
• not very sensitive to feature scaling

They are often a strong baseline for many practical machine learning problems. They belong to scikit-learn’s ensemble methods family, which combines multiple predictors to improve robustness and generalization.

3) Why it is called “Random Forest”

The method is “random” for two main reasons.

1. Random sampling of training data

Each tree is trained on a different subsample of the data. In scikit-learn, this is controlled by bootstrap=True by default, and the sub-sample size can also be controlled with max_samples.

2. Random subset of features

At each split, the tree considers only a subset of features rather than all of them. This randomness helps the trees become less correlated with each other, which improves the ensemble effect. The main control for this is max_features.

So the forest becomes strong because:

• each tree is different
• the errors of individual trees are less correlated
• averaging reduces variance

4) Random Forest vs Decision Tree

A Decision Tree is one tree.

A Random Forest is many trees combined together.

A single Decision Tree

• easy to interpret
• can overfit easily
• unstable to small data changes

A Random Forest

• harder to interpret directly
• usually more accurate
• more robust and stable
• less likely to overfit than one tree

Scikit-learn’s documentation emphasizes that random forests improve predictive accuracy and control overfitting by averaging many trees.

5) Why Random Forests usually do not need feature scaling

Random Forests are based on decision trees, and trees split on thresholds such as:

• feature <= value
• feature > value

They do not rely on geometric distances like KNN or margin geometry like SVM. Because of this, feature scaling is usually not necessary for Random Forests. This follows from the tree-based structure described in scikit-learn’s ensemble and tree documentation.

That is one of the practical advantages of tree-based models.

Part I — First Classification Example

6) Install required libraries

pip install numpy pandas matplotlib scikit-learn

7) A simple Random Forest classification example

We will use the Breast Cancer dataset from scikit-learn.

import numpy as np
import pandas as pd

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score, classification_report, confusion_matrix

# Load dataset
data = load_breast_cancer()
X = data.data
y = data.target

# Split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# Build model
model = RandomForestClassifier(
    n_estimators=100,
    random_state=42
)

# Train
model.fit(X_train, y_train)

# Predict
y_pred = model.predict(X_test)

# Evaluate
print("Accuracy:", accuracy_score(y_test, y_pred))
print("\nConfusion Matrix:\n", confusion_matrix(y_test, y_pred))
print("\nClassification Report:\n", classification_report(y_test, y_pred))

What this code does

• loads the dataset
• splits it into train and test sets
• trains a forest with 100 trees
• predicts on the test set
• evaluates the model

In scikit-learn, n_estimators is the number of trees in the forest, and RandomForestClassifier fits multiple decision tree classifiers on different sub-samples of the dataset.

8) Predicting class probabilities

Random Forests can also output probabilities with predict_proba.

proba = model.predict_proba(X_test[:5])
print(proba)

For classification, the forest combines information from its trees to produce class probabilities and class predictions. The classifier API in scikit-learn includes predict, predict_proba, and score.

Part II — Important Parameters

9) Key parameters for RandomForestClassifier

Important parameters include:

• n_estimators
• criterion
• max_depth
• min_samples_split
• min_samples_leaf
• max_features
• bootstrap
• max_samples
• oob_score
• n_jobs
• random_state
• class_weight 

n_estimators

Number of trees in the forest.

• small value → faster but less stable
• larger value → more stable predictions but slower training

max_depth

Maximum depth of each tree.

• smaller depth → simpler trees
• larger depth → more complex trees

max_features

Number of features considered at each split.

This is one of the key sources of randomness in the forest.

bootstrap

Whether each tree is trained on a bootstrap sample. Default is True.

oob_score

Whether to use out-of-bag samples for validation. This is only available when bootstrapping is enabled.

10) What is out-of-bag evaluation

When bootstrap sampling is used, each tree is trained on a sample drawn with replacement from the training set. That means some training points are left out for that tree. These are called out-of-bag samples.

You can use them to estimate performance without needing a separate validation set for every tree.

model = RandomForestClassifier(
    n_estimators=200,
    oob_score=True,
    random_state=42
)

model.fit(X_train, y_train)
print("OOB Score:", model.oob_score_)

Scikit-learn exposes oob_score directly in the Random Forest API when bootstrapping is enabled.

Part III — Why Random Forests work well

11) Bagging intuition

Random Forests are a form of bagging.

Bagging means:

• train many models on different bootstrap samples
• average the predictions

Averaging reduces variance. This is especially helpful for decision trees because single trees can vary a lot from one sample to another. Random forests add extra randomness through feature subsampling on top of bagging.

12) Why more trees usually help

In a Random Forest:

• one bad tree is not a disaster
• noisy trees can be corrected by the others
• more trees usually make predictions more stable

Adding trees usually helps until performance levels off, though training and prediction become slower. n_estimators is therefore one of the most important practical controls in scikit-learn’s API.

Part IV — Feature Importance

13) Built-in feature importance

Random Forests in scikit-learn expose feature_importances_.

import pandas as pd

importance = pd.Series(model.feature_importances_, index=data.feature_names)
print(importance.sort_values(ascending=False))

Scikit-learn’s forest importance example shows how a forest of trees can be used to evaluate feature importance, and it also visualizes variability across trees.

Why this is useful

Feature importance helps you understand which variables the forest relied on the most.

14) Plot feature importance

import matplotlib.pyplot as plt

importance = importance.sort_values(ascending=True)

plt.figure(figsize=(8, 6))
importance.plot(kind="barh")
plt.title("Random Forest Feature Importance")
plt.xlabel("Importance")
plt.ylabel("Feature")
plt.show()

The scikit-learn example on forest importances uses impurity-based importances and shows inter-tree variability with error bars.

15) Important caution about feature importance

Scikit-learn also provides an example comparing impurity-based Random Forest importances with permutation importance, and it warns that impurity-based importance can inflate the importance of numerical features in some settings.

So built-in feature importance is useful, but it should be interpreted carefully.

Permutation importance example

from sklearn.inspection import permutation_importance

result = permutation_importance(
    model, X_test, y_test, n_repeats=10, random_state=42, n_jobs=-1
)

perm_importance = pd.Series(result.importances_mean, index=data.feature_names)
print(perm_importance.sort_values(ascending=False))

Permutation importance is often a better diagnostic when you want a more reliable picture of feature influence. This is an inference grounded in scikit-learn’s comparison example.

Part V — Tuning a Random Forest

16) Tune with GridSearchCV

from sklearn.model_selection import GridSearchCV
from sklearn.ensemble import RandomForestClassifier

param_grid = {
    "n_estimators": [100, 200, 300],
    "max_depth": [None, 5, 10, 20],
    "min_samples_split": [2, 5, 10],
    "min_samples_leaf": [1, 2, 4],
    "max_features": ["sqrt", "log2"]
}

grid = GridSearchCV(
    estimator=RandomForestClassifier(random_state=42),
    param_grid=param_grid,
    cv=5,
    scoring="accuracy",
    n_jobs=-1
)

grid.fit(X_train, y_train)

print("Best Parameters:", grid.best_params_)
print("Best CV Score:", grid.best_score_)

best_model = grid.best_estimator_
y_pred = best_model.predict(X_test)
print("Test Accuracy:", accuracy_score(y_test, y_pred))

Why this helps

Instead of guessing the best forest size or depth, you let cross-validation search for a stronger combination.

The most influential tuning parameters in practice are usually:

• n_estimators
• max_depth
• min_samples_split
• min_samples_leaf
• max_features 

17) A good practical starting point

A strong default starting point for classification is often something like:

model = RandomForestClassifier(
    n_estimators=200,
    max_depth=None,
    min_samples_split=2,
    min_samples_leaf=1,
    max_features="sqrt",
    random_state=42,
    n_jobs=-1
)

This is not universally optimal, but it is a sensible baseline built from the core parameters exposed in the current scikit-learn API.

Part VI — Random Forest Regression

18) Example with RandomForestRegressor

Now let us use a Random Forest for regression.

import numpy as np
import matplotlib.pyplot as plt

from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, r2_score

# Synthetic data
rng = np.random.RandomState(42)
X = np.sort(5 * rng.rand(200, 1), axis=0)
y = np.sin(X).ravel()

# Add noise
y[::5] += 0.5 - rng.rand(40)

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

model = RandomForestRegressor(
    n_estimators=200,
    random_state=42
)

model.fit(X_train, y_train)
y_pred = model.predict(X_test)

print("MSE:", mean_squared_error(y_test, y_pred))
print("R²:", r2_score(y_test, y_pred))

Scikit-learn defines RandomForestRegressor analogously to the classifier: it fits many decision tree regressors on different subsamples and uses averaging to improve predictive accuracy and control overfitting.

19) Plot regression predictions

X_plot = np.linspace(X.min(), X.max(), 500).reshape(-1, 1)
y_plot = model.predict(X_plot)

plt.figure(figsize=(8, 6))
plt.scatter(X, y, label="Data")
plt.plot(X_plot, y_plot, linewidth=2, label="Random Forest prediction")
plt.xlabel("X")
plt.ylabel("y")
plt.title("Random Forest Regression")
plt.legend()
plt.show()

Random Forest regression often gives smoother and more robust predictions than a single decision tree regressor because it averages many trees. That is an inference directly supported by the ensemble definition in the scikit-learn API.

20) Important regression parameters

RandomForestRegressor shares many structural parameters with the classifier version, including:

• n_estimators
• criterion
• max_depth
• min_samples_split
• min_samples_leaf
• max_features
• bootstrap
• max_samples
• oob_score
• n_jobs 

Example:

model = RandomForestRegressor(
    n_estimators=300,
    max_depth=10,
    min_samples_leaf=2,
    random_state=42,
    n_jobs=-1
)

Part VII — A Full Real Workflow

21) End-to-end classification workflow

Step 1: Load data

import pandas as pd

df = pd.read_csv("your_data.csv")

Step 2: Separate features and target

X = df.drop("target", axis=1)
y = df["target"]

Step 3: Split data

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

Step 4: Build model

from sklearn.ensemble import RandomForestClassifier

model = RandomForestClassifier(random_state=42)

Step 5: Tune parameters

from sklearn.model_selection import GridSearchCV

param_grid = {
    "n_estimators": [100, 200],
    "max_depth": [None, 5, 10],
    "min_samples_split": [2, 5, 10],
    "min_samples_leaf": [1, 2, 4],
    "max_features": ["sqrt", "log2"]
}

grid = GridSearchCV(
    model,
    param_grid=param_grid,
    cv=5,
    scoring="accuracy",
    n_jobs=-1
)

grid.fit(X_train, y_train)

Step 6: Evaluate

from sklearn.metrics import classification_report, confusion_matrix, accuracy_score

best_model = grid.best_estimator_
y_pred = best_model.predict(X_test)

print("Best Params:", grid.best_params_)
print("Accuracy:", accuracy_score(y_test, y_pred))
print(confusion_matrix(y_test, y_pred))
print(classification_report(y_test, y_pred))

Step 7: Predict on new samples

new_samples = X_test.iloc[:5]
predictions = best_model.predict(new_samples)
print(predictions)

This workflow follows scikit-learn’s standard estimator and model selection pattern for ensemble estimators.

Part VIII — How to Read the Results

22) Classification metrics

For classification, common metrics are:

• accuracy
• precision
• recall
• F1-score
• confusion matrix

from sklearn.metrics import confusion_matrix, classification_report

print(confusion_matrix(y_test, y_pred))
print(classification_report(y_test, y_pred))

Random forests support binary and multiclass classification through the same RandomForestClassifier API.

23) Regression metrics

For regression, common metrics are:

• MAE
• MSE
• RMSE
• R²

from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
import numpy as np

mae = mean_absolute_error(y_test, y_pred)
mse = mean_squared_error(y_test, y_pred)
rmse = np.sqrt(mse)
r2 = r2_score(y_test, y_pred)

print("MAE:", mae)
print("MSE:", mse)
print("RMSE:", rmse)
print("R²:", r2)

Random forest regressors also support multi-output regression natively, as shown in scikit-learn’s example comparing random forest regression with a multi-output meta-estimator.

Part IX — Strengths and Weaknesses

24) Strengths of Random Forests

Random Forests are strong because they are:

• usually more accurate than a single decision tree
• robust to overfitting compared with one tree
• good at modeling nonlinear relationships
• useful without feature scaling
• able to provide feature importance estimates

These strengths follow directly from scikit-learn’s description of random forests as ensembles of trees that improve predictive accuracy and control overfitting.

25) Weaknesses of Random Forests

They also have limitations:

• less interpretable than a single decision tree
• can be slower than one tree
• large forests use more memory
• impurity-based feature importance can be misleading in some cases

Scikit-learn’s comparison examples also show that computation time matters when comparing forest methods with alternatives such as Histogram Gradient Boosting.

Part X — Common Mistakes

26) Using too few trees

Bad:

model = RandomForestClassifier(n_estimators=10, random_state=42)

This may work, but the predictions can be less stable.

Better:

model = RandomForestClassifier(n_estimators=200, random_state=42, n_jobs=-1)

Because the forest prediction is an average across trees, too few trees can leave performance unnecessarily noisy. This is a practical inference grounded in the ensemble formulation.

27) Ignoring max_depth and leaf controls

Even though Random Forests reduce overfitting compared with a single tree, forests can still become unnecessarily complex.

Good parameters to tune:

• max_depth
• min_samples_split
• min_samples_leaf
• max_features 

28) Treating built-in feature importance as absolute truth

Impurity-based importance is convenient, but scikit-learn’s permutation importance comparison shows it can overstate the importance of some feature types. Use it carefully, and compare with permutation importance when interpretability matters.

Part XI — Practical Advice

29) When should you use Random Forests?

Use Random Forests when:

• you want a strong tabular-data baseline
• you expect nonlinear relationships
• you want something robust and practical
• interpretability of a single rule tree is not your top priority

30) When should you avoid them?

Be careful with Random Forests when:

• you need maximum interpretability
• you need very fast lightweight models
• your dataset is extremely large and training cost matters a lot

In those cases, simpler models or other ensemble methods may be worth comparing. Scikit-learn’s ensemble examples include comparisons with Histogram Gradient Boosting specifically on score and computation time.

31) A good default starting point

For classification:

RandomForestClassifier(
    n_estimators=200,
    max_features="sqrt",
    random_state=42,
    n_jobs=-1
)

For regression:

RandomForestRegressor(
    n_estimators=200,
    max_features=1.0,
    random_state=42,
    n_jobs=-1
)

These are sensible baseline starting points based on the current parameterized API for the stable scikit-learn random forest estimators.

Part XII — Mini Project Example

32) Predicting iris species with a Random Forest

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import classification_report, confusion_matrix, accuracy_score

# Load
data = load_iris()
X, y = data.data, data.target

# Split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, stratify=y, random_state=42
)

# Model
model = RandomForestClassifier(random_state=42)

# Search space
param_grid = {
    "n_estimators": [100, 200, 300],
    "max_depth": [None, 3, 5, 10],
    "min_samples_split": [2, 5, 10],
    "min_samples_leaf": [1, 2, 4],
    "max_features": ["sqrt", "log2"]
}

# Grid search
grid = GridSearchCV(
    model,
    param_grid=param_grid,
    cv=5,
    scoring="accuracy",
    n_jobs=-1
)

grid.fit(X_train, y_train)

# Evaluate
best_model = grid.best_estimator_
y_pred = best_model.predict(X_test)

print("Best Parameters:", grid.best_params_)
print("Accuracy:", accuracy_score(y_test, y_pred))
print("\nConfusion Matrix:\n", confusion_matrix(y_test, y_pred))
print("\nClassification Report:\n", classification_report(y_test, y_pred))

Why this mini-project is good

• uses a train/test split
• tunes the most important forest parameters
• evaluates on held-out data
• stays close to real practice

This matches scikit-learn’s general estimator, ensemble, and cross-validation workflow.

Part XIII — Summary

33) What you should remember

Random Forests are one of the most practical and powerful classical machine learning algorithms.

The core idea is:

• train many decision trees
• make them different through randomness
• combine their predictions by voting or averaging

For classification, they vote.
For regression, they average.
This improves predictive accuracy and helps control overfitting compared with a single decision tree.

The most important practical rules are:

• feature scaling is usually not needed
• tune n_estimators
• tune max_depth, min_samples_split, and min_samples_leaf
• tune max_features
• use cross-validation
• interpret built-in feature importance carefully

These recommendations align with the current scikit-learn Random Forest API, user guide, and feature-importance examples.

34) Final ready-to-use template

from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import classification_report

# X, y = your data

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

model = RandomForestClassifier(random_state=42)

param_grid = {
    "n_estimators": [100, 200],
    "max_depth": [None, 5, 10],
    "min_samples_split": [2, 5, 10],
    "min_samples_leaf": [1, 2, 4],
    "max_features": ["sqrt", "log2"]
}

grid = GridSearchCV(
    model,
    param_grid=param_grid,
    cv=5,
    scoring="accuracy",
    n_jobs=-1
)

grid.fit(X_train, y_train)

print("Best params:", grid.best_params_)
print("Test score:", grid.best_estimator_.score(X_test, y_test))

y_pred = grid.best_estimator_.predict(X_test)
print(classification_report(y_test, y_pred))

35) Practice exercises

Exercise 1

Train a RandomForestClassifier on the Iris dataset and report accuracy.

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score, classification_report, confusion_matrix

# Load Iris dataset
iris = load_iris()
X = iris.data
y = iris.target

# Split data
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# Build model
model = RandomForestClassifier(
    n_estimators=100,
    random_state=42
)

# Train
model.fit(X_train, y_train)

# Predict
y_pred = model.predict(X_test)

# Evaluate
acc = accuracy_score(y_test, y_pred)

print("Accuracy:", acc)
print("\nConfusion Matrix:\n", confusion_matrix(y_test, y_pred))
print("\nClassification Report:\n", classification_report(y_test, y_pred))

Exercise 2

Train a Random Forest on the Breast Cancer dataset and display feature importances.

import pandas as pd
import matplotlib.pyplot as plt

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score

# Load dataset
data = load_breast_cancer()
X = data.data
y = data.target

# Split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# Build model
model = RandomForestClassifier(
    n_estimators=200,
    random_state=42
)

# Train
model.fit(X_train, y_train)

# Predict
y_pred = model.predict(X_test)

# Accuracy
print("Accuracy:", accuracy_score(y_test, y_pred))

# Feature importance
importance = pd.Series(model.feature_importances_, index=data.feature_names)
importance = importance.sort_values(ascending=False)

print("\nFeature Importances:\n")
print(importance)

# Plot feature importances
plt.figure(figsize=(10, 8))
importance.sort_values().plot(kind="barh")
plt.title("Random Forest Feature Importances")
plt.xlabel("Importance")
plt.ylabel("Feature")
plt.show()

Exercise 3

Tune n_estimators, max_depth, and max_features using GridSearchCV.

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score

# Load data
iris = load_iris()
X = iris.data
y = iris.target

# Split data
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# Base model
model = RandomForestClassifier(random_state=42)

# Parameter grid
param_grid = {
    "n_estimators": [100, 200, 300],
    "max_depth": [None, 3, 5, 10],
    "max_features": ["sqrt", "log2"]
}

# Grid search
grid = GridSearchCV(
    estimator=model,
    param_grid=param_grid,
    cv=5,
    scoring="accuracy",
    n_jobs=-1
)

# Train grid search
grid.fit(X_train, y_train)

# Best model
best_model = grid.best_estimator_

# Predict
y_pred = best_model.predict(X_test)

# Results
print("Best Parameters:", grid.best_params_)
print("Best Cross-Validation Score:", grid.best_score_)
print("Test Accuracy:", accuracy_score(y_test, y_pred))

Exercise 4

Compare a single DecisionTreeClassifier with a RandomForestClassifier.

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score

# Load data
iris = load_iris()
X = iris.data
y = iris.target

# Split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# Model 1: single Decision Tree
tree_model = DecisionTreeClassifier(random_state=42)

# Model 2: Random Forest
forest_model = RandomForestClassifier(
    n_estimators=200,
    random_state=42
)

# Train both
tree_model.fit(X_train, y_train)
forest_model.fit(X_train, y_train)

# Predict
y_pred_tree = tree_model.predict(X_test)
y_pred_forest = forest_model.predict(X_test)

# Accuracy
acc_tree = accuracy_score(y_test, y_pred_tree)
acc_forest = accuracy_score(y_test, y_pred_forest)

print("Accuracy of Decision Tree:", acc_tree)
print("Accuracy of Random Forest:", acc_forest)

Exercise 5

Train a RandomForestRegressor on a nonlinear synthetic regression dataset.

import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_squared_error, r2_score

# Create synthetic nonlinear data
rng = np.random.RandomState(42)
X = np.sort(5 * rng.rand(200, 1), axis=0)
y = np.sin(X).ravel()

# Add noise
y[::5] += 0.5 - rng.rand(40)

# Split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

# Build regressor
model = RandomForestRegressor(
    n_estimators=200,
    random_state=42
)

# Train
model.fit(X_train, y_train)

# Predict
y_pred = model.predict(X_test)

# Evaluate
mse = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)

print("Mean Squared Error:", mse)
print("R² Score:", r2)

# Plot prediction curve
X_plot = np.linspace(X.min(), X.max(), 500).reshape(-1, 1)
y_plot = model.predict(X_plot)

plt.figure(figsize=(8, 6))
plt.scatter(X, y, label="Data")
plt.plot(X_plot, y_plot, linewidth=2, label="Random Forest prediction")
plt.xlabel("X")
plt.ylabel("y")
plt.title("Random Forest Regression on Nonlinear Data")
plt.legend()
plt.show()

Final summary

What each exercise teaches

• Exercise 1: basic Random Forest classification
• Exercise 2: feature importance analysis
• Exercise 3: hyperparameter tuning
• Exercise 4: comparison between a single tree and a forest
• Exercise 5: nonlinear regression with Random Forest