Day 01 — Linear Regression. CONCEPT | by Ime Eti-mfon | Jan, 2025

30 Days of Knowledge Science Sequence

• Idea: Predict steady values
• Implementation: Atypical Least Squares
• Analysis: R-squared, RMSE

CONCEPT

Linear regression is a statistical methodology employed to mannequin the connection between a dependent variable (goal) and a number of unbiased variables (options). The intention is to establish the linear equation that the majority precisely predicts the goal variable primarily based on the characteristic variables.

The equation of a easy linear regression mannequin is:

[y = mx + c]

the place:

• {y} is the expected worth
• {x} is the unbiased variable
• {m} is the slope of the road (co-efficient)
• {c} is the y-intercept

IMPLEMENTATION

Let’s think about an instance utilizing Python and its libraries.

Instance

Suppose we’ve got a dataset with home costs and their corresponding dimension (in sq. ft):

# Import essential 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
import warnings                  # To take away warnings from my output
warnings.simplefilter(motion = 'ignore')

# Instance Knowledge
knowledge = {
'Measurement': [1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400],
'Worth': [300000, 320000, 340000, 360000, 380000, 400000, 420000, 440000, 460000, 480000]
}
df = pd.DataFrame(knowledge)
df

# Defining Unbiased variable (characteristic) and Dependent variable (goal)
X = df[['Size']]
y = df['Price']

# Splitting the info into coaching and testing units
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 42)

# Creating and coaching the linear regression mannequin
mannequin = LinearRegression()
mannequin.match(X_train, y_train)

# Making predictions
y_pred = mannequin.predict(X_test)

# Evaluating the mannequin
mse = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)
print(f'Imply Squared Error: {mse}')
print(f'R-squared: {r2}')

# Plotting the outcomes
plt.scatter(X, y, shade = 'blue')                          # Authentic knowledge factors
plt.plot(X_test, y_pred, shade = 'purple', linewidth = 2).    # Regression line
plt.xlabel('Measurement (sq ft)')
plt.ylabel('Worth ($)')
plt.title('Linear Regression: Home Costs vs Measurement')
plt.present()

# Predicting with new values
# Right here, we need to predict the value of a home when given the scale
X_new = np.array([[3600]])
y_pred = mannequin.predict(X_new)
print(f'Predicted worth for X = 3600: {y_pred[0]:.0f}')

EXPLANATION OF THE CODE

1. Libraries: We import essential libraries like numpy, pandas, sklearn, and matplotlib.
2. Knowledge Preparation: We create a DataFrame containing the scale and worth of homes.
3. Characteristic and Goal: We separate the characteristic (Measurement) and the goal (Worth).
4. Prepare-Take a look at-Cut up: We break up the info into coaching and testing units.
5. Mannequin Coaching: We create and practice a LinearRegression mannequin utilizing the coaching knowledge.
6. Predictions: We use the educated mannequin to foretell home costs for the take a look at set.
7. Analysis: We consider the mannequin utilizing Imply Squared Error (MSE) and R-squared (R²)metrics.
8. Visualization: We plot the unique knowledge factors and the regression line to visualise the mannequin’s efficiency.

EVALUATION METRICS

• Imply Squared Error (MSE): Measures the common squared distinction between the precise and predicted values. Decrease values point out higher efficiency.
• R-squared (R²): Represents the proportion of the variance within the dependent variable that’s predictable from the unbiased variable(s). Values nearer to 1 point out a greater match.