📈 Sales Forecast Engine

Calculus-Based Time-Series Sales Predictor

Applies linear regression, differentiation, and integration to a real monthly sales dataset (2019–2023) to predict future sales, analyze rates of change, and compute cumulative revenue - all in an interactive CLI.

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📌 Overview

This project bridges pure calculus and applied machine learning by building a sales prediction pipeline on 60 months of real product sales data (Jan 2019 – Dec 2023).

Given the time-series dataset, the program:

• Fits a linear regression model (S(t) = mt + b) to the sales trend
• Applies differentiation (dS/dt) to measure the instantaneous rate of change of sales
• Applies integration (∫S dt) to compute cumulative/total sales over any time window
• Predicts sales for any future year entered by the user

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✨ Features

Part 1 - Data Exploration & Visualization

• Loads and summarizes sales_dataset.csv (60 monthly records, 2019–2023)
• Prints dataset overview, missing-value check, and summary statistics
• Line plot - sales trend over time
• Histogram - sales frequency distribution

Part 2 - Predictive Model (Linear Regression)

• Encodes each month as a sequential time index
• Splits data 80/20 (train/test, no shuffle - respects time order)
• Trains sklearn.LinearRegression and evaluates with MSE and R²
• Predicts sales for any user-specified future year (e.g. 2025, 2050, 2100)

Part 3 - Derivative Analysis (Rate of Change)

• Computes first-order finite differences (Sales.diff()) as the discrete derivative dS/dt
• Applies a 3-month rolling average to smooth out noise
• Plots raw rate of change vs. smoothed rate side-by-side

Part 4 - Integration (Cumulative Sales)

• Uses the regression coefficients (m, b) to derive the antiderivative analytically:

  ∫(mt + b) dt = (m·t²)/2 + b·t

• Computes total cumulative sales from t = 0 up to any time index

Interactive CLI Flow

Welcome screen (team info)
    ↓
Enter year for prediction
    ↓  [press any key]
Part 1: Data visualization
    ↓  [press any key]
Part 2: Model training + prediction
    ↓  [press any key]
Part 3: Derivative analysis
    ↓
Part 4: Cumulative sales + final summary
    ↓
Continue or terminate?

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📂 Repository Structure

sales-forecast-engine/
├── python-pr.py          # Main interactive Python program
├── sales_dataset.csv     # Monthly sales dataset (Jan 2019 – Dec 2023, 60 records)
└── README.md

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⚙️ Setup & Run

Prerequisites

pip install pandas numpy matplotlib scikit-learn

Run

python python-pr.py

When prompted, enter a year (e.g. 2025, 2050, or 2100) to get a future sales prediction. Follow the on-screen prompts to step through each part of the analysis.

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🗃 Dataset

sales_dataset.csv - 60 monthly sales records:

Column	Description
Date	End-of-month date (DD/MM/YYYY)
Sales	Monthly sales figure (USD)

Date range: January 2019 – December 2023
Sales range: ~$406 – $637 per month with a mild upward trend

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📊 Sample Output

Predicted Sales for the year 2025: 574.83
Cumulative Sales up to December 2023: 31,204.17
Model R²: 0.87  |  MSE: 412.6

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🧮 Calculus Applied

Concept	Application
Linear Model	S(t) = mt + b fitted to monthly sales
Differentiation	dS/dt - rate of sales growth/decline per month
Integration	∫S(t) dt - total cumulative revenue over a period
Analytical Solution	Closed-form antiderivative derived from regression coefficients

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📄 License

Feel free to use or learn from this. Credit Appreciated but not required.