Train-Test Split & Linear Regression

Now let's build your first real ML model. We will predict house prices based on house size using Linear Regression with Scikit-Learn.

---

1. Why Split Data into Train and Test?

Imagine studying for an exam. If you practice with 100 questions and then the exam has the same 100 questions, of course you will score 100%. But that does not mean you actually learned the subject.

ML works the same way. If you train a model on all your data and test it on the same data, it will look perfect — but it has just memorized, not learned.

The Solution: Train-Test Split

Split your data into two parts:

• Training Data (80%): Used to teach the model
• Testing Data (20%): Used to check if the model actually learned

from sklearn.model_selection import train_test_split

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

• test_size=0.2 → 20% for testing, 80% for training
• random_state=42 → Makes the split the same every time you run it (for consistency)

---

2. Installing Scikit-Learn

pip install scikit-learn

Already installed in Google Colab.

---

3. Building Your First Model — Step by Step

Let's predict house prices based on house size (in square feet):

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression

# Step 1: PREPARE DATA
# House sizes in sq ft (feature)
X = np.array([[600], [800], [1000], [1200], [1500], [1800], [2000], [2200], [2500], [3000]])
# House prices in lakhs (target)
y = np.array([30, 40, 50, 60, 75, 90, 100, 110, 125, 150])

# Split: 80% train, 20% test
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

print(f"Training samples: {len(X_train)}")  # Output: 8
print(f"Testing samples: {len(X_test)}")    # Output: 2

# Step 2: CHOOSE MODEL
model = LinearRegression()

# Step 3: TRAIN MODEL
model.fit(X_train, y_train)
print("Model trained!")

# Step 4: PREDICT
predictions = model.predict(X_test)
print("Predictions:", predictions)
print("Actual values:", y_test)

---

4. What is Linear Regression?

Linear Regression finds the best straight line that fits your data.

Price = (slope × size) + intercept

# See the learned values
print("Slope:", model.coef_[0])        # How much price increases per sq ft
print("Intercept:", model.intercept_)  # Base price when size is 0

If slope = 0.05 and intercept = 0:

• 1000 sq ft house → Price = 0.05 × 1000 + 0 = ₹50 Lakhs
• 2000 sq ft house → Price = 0.05 × 2000 + 0 = ₹100 Lakhs

---

5. Checking Your Model — Is It Good?

R² Score (0 to 1)

• 1.0 = Perfect predictions
• 0.5 = Okay predictions
• 0.0 = Terrible (model is useless)

from sklearn.metrics import r2_score

# Score on test data
score = model.score(X_test, y_test)
print(f"R² Score: {score:.2f}")

# Or calculate manually
y_pred = model.predict(X_test)
r2 = r2_score(y_test, y_pred)
print(f"R² Score: {r2:.2f}")

Rule of thumb: R² above 0.7 is good. Above 0.9 is great.

---

6. Predicting New Values

# Predict the price of a 1100 sq ft house
new_house = np.array([[1100]])
predicted_price = model.predict(new_house)
print(f"Predicted price for 1100 sq ft: ₹{predicted_price[0]:.1f} Lakhs")

# Predict multiple houses at once
new_houses = np.array([[1100], [1500], [2500]])
predictions = model.predict(new_houses)
for size, price in zip([1100, 1500, 2500], predictions):
    print(f"{size} sq ft → ₹{price:.1f} Lakhs")

---

Summary

Concept	What it Means
Train-Test Split	Divide data into training (80%) and testing (20%) to check if model actually learned
Linear Regression	Finds the best straight line through your data to make predictions
.fit(X, y)	Train the model — it learns the pattern
.predict(X_new)	Use the trained model to predict new values
R² Score	How good the model is (0 = bad, 1 = perfect)

• Always split your data before training. Never test on training data!
• Linear Regression is the simplest ML algorithm — but it is powerful and widely used.
• Next, we will learn Classification — predicting categories (pass/fail, spam/not spam) instead of numbers.