Linear Regression with TensorFlow

2.1 What is Linear Regression?

Linear regression aims to find the best-fit line through data points in a plot, represented by the equation:

y = mx + b

Where:

• y: Dependent variable
• x: Independent variable
• m: Slope of the line
• b: Intercept of the line

2.2 Cost Function

The cost function measures the accuracy of the linear regression model by calculating the difference between predicted and actual values. The most common cost function used is Mean Squared Error (MSE):

MSE = (1/n) Σ(y_i - ŷ_i)^2

2.3 Gradient Descent

Gradient descent is an optimization algorithm used to minimize the cost function by iteratively adjusting the parameters (weights) of the model.

3.1 Setup

To start implementing linear regression with TensorFlow, ensure you have TensorFlow installed. You can install it using pip:

pip install tensorflow

3.2 Code Example

Below is a simple implementation of linear regression using TensorFlow:

import numpy as np
import tensorflow as tf
from sklearn.model_selection import train_test_split

# Generate some linear data
np.random.seed(0)
X = 2 * np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)

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

# Build the TensorFlow model
model = tf.keras.Sequential([
    tf.keras.layers.Dense(1, input_shape=(1,))
])

# Compile the model
model.compile(optimizer='sgd', loss='mean_squared_error')

# Train the model
model.fit(X_train, y_train, epochs=100)

# Evaluate the model
loss = model.evaluate(X_test, y_test)
print(f"Test Loss: {loss}")

# Make predictions
y_pred = model.predict(X_test)
print(y_pred)