🏠 Sales using Linear Regression from Scratch

This project demonstrates how to build a simple Linear Regression model from scratch in Python using Pandas and Numpy, without using any machine learning libraries. The model is trained using Gradient Descent to predict hMonthly Sales based on the Five Features.

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📁 Dataset Feature Description – Monthly Sales Dataset

This dataset simulates the monthly sales performance of a single product across different time periods or markets. It includes five features that influence the number of units sold (monthly_sales), which is the target variable.

🔍 Features:

• ad_spend
  Monthly advertising budget (in $1000s). Higher ad spend typically boosts sales.

• product_price
  Selling price of one unit of the product (in $) in 300 months. It can vary due to promotions, seasonality, or market testing and discounts. The company is constantly adjusting the price of their same product for various business reasons.

• market_trend_index
  Index reflecting overall market demand (scaled from 40 to 100). A higher value means stronger demand of customer.

• seasonality_index
  Seasonal multiplier (range: 0.5 to 1.5). Shows how seasonal effects boost or reduce sales. 1.0 is normal, above 1.0 is a seasonal boost, below 1.0 is a seasonal dip. eg ==> Like how ice cream sells more in summer or coats sell more in winter

• social_media_mentions
  Total number of times the product was mentioned on social platforms in that month. More mentions often indicate higher customer awareness or virality.

🎯 Target:

• monthly_sales
  The number of units sold in a given month. This is the value you're predicting in a regression model.

Example row:
2104, 399900

📊 Objective

• Implement Linear Regression using only NumPy (no sklearn or ML libraries)
• Use Gradient Descent to optimize parameters (weights and bias)
• Visualize the loss (RSS), learned regression line, and predictions vs actual values

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Linear Regression Formula
y = b0 + w1x1 + w2x2 + w3 * x3 + w4 * x4 + w5 * x5

Where:
ŷ: Predicted sales x₁: Advertising spend (ad_spend) x₂: Product price (product_price) x₃: Market trend index (market_trend_index) x₄: Seasonality index (seasonality_index) x₅: Social media mentions (social_media_mentions) w₁ to w₅: Weights (slopes) learned for each feature b₀: Bias (intercept)

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🚀 How It Works

1. Preprocessing

• Input features and targets are standardized (scaled to mean 0, std 1)

2. Initialize Parameters

• Start with b0 = 0, w1 = 0 , w2 = 0, w3 = 0, w4 = 0, w5 = 0
• Define learning rate and number of epochs

3. Training

• For each epoch:
  • Predict sales using current weights
  • Calculate errors
  • Compute gradients
  • Update parameters using gradient descent