Let's start with Day 1 today

Let's learn Linear Regression in detail

30 Days of Data Science Series: https://t.me/datasciencefun/1709

#### Concept
Linear regression is a statistical method used to model the relationship between a dependent variable (target) and one or more independent variables (features). The goal is to find the linear equation that best predicts the target variable from the feature variables.

The equation of a simple linear regression model is:
\[ y = \beta_0 + \beta_1 x \]
Where:
- \( y) is the predicted value.
- \( \beta_0) is the y-intercept.
- \( \beta_1) is the slope of the line (coefficient).
- \( x) is the independent variable.

#### Implementation

Let's consider an example using Python and its libraries.

##### Example
Suppose we have a dataset with house prices and their corresponding size (in square feet).

# Import necessary libraries
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
import matplotlib.pyplot as plt

# Example data
data = {
    'Size': [1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400],
    'Price': [300000, 320000, 340000, 360000, 380000, 400000, 420000, 440000, 460000, 480000]
}
df = pd.DataFrame(data)

# Independent variable (feature) and dependent variable (target)
X = df[['Size']]
y = df['Price']

# Splitting the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

# Creating and training the linear regression model
model = LinearRegression()
model.fit(X_train, y_train)

# Making predictions
y_pred = model.predict(X_test)

# Evaluating the model
mse = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)

print(f"Mean Squared Error: {mse}")
print(f"R-squared: {r2}")

# Plotting the results
plt.scatter(X, y, color='blue')  # Original data points
plt.plot(X_test, y_pred, color='red', linewidth=2)  # Regression line
plt.xlabel('Size (sq ft)')
plt.ylabel('Price ($)')
plt.title('Linear Regression: House Prices vs Size')
plt.show()

#### Explanation of the Code

1. Libraries: We import necessary libraries like numpy, pandas, sklearn, and matplotlib.
2. Data Preparation: We create a DataFrame containing the size and price of houses.
3. Feature and Target: We separate the feature (Size) and the target (Price).
4. Train-Test Split: We split the data into training and testing sets.
5. Model Training: We create a LinearRegression model and train it using the training data.
6. Predictions: We use the trained model to predict house prices for the test set.
7. Evaluation: We evaluate the model using Mean Squared Error (MSE) and R-squared (R²) metrics.
8. Visualization: We plot the original data points and the regression line to visualize the model's performance.

#### Evaluation Metrics

- Mean Squared Error (MSE): Measures the average squared difference between the actual and predicted values. Lower values indicate better performance.
- R-squared (R²): Represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). Values closer to 1 indicate a better fit.

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