Hour 1 Linear Regression Model

#### 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).

#pip install numpy

#pip install pandas

#pip install scikit-learn

#pip install matplotlip

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()

Results:

Mean Squared Error: 0.0

R-squared: 1.0

#### Explanation of the Code

1. Libraries: We import necessary libraries like numpy, pandas, scikit-learn, 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. this channel with your real friends: https://t.me/datasciencefun

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