---
title: "Forecast Panchakanya sales for 2020"
subject: "Engineering Economics"
chapter: 1
key: "semester_6/engineering_economics:forecast-panchakanya-sales-2020"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/forecast-panchakanya-sales-2020
site: BCT Engineering
---

# Forecast Panchakanya sales for 2020

Engineering Economics · Chapter 1: Introduction

- Asked in: 2066 Magh, 8 marks
- Video: [Unit:9 | Demand Analysis & Sales Forecasting | Regression equation | Engineering Economics |](https://www.youtube.com/watch?v=k4ewp2LhYMM) — Prashant YT
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/forecast-panchakanya-sales-2020
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-1

## Question

Panchakanya has recorded the sales of its products in different years as below. Forecast the sales for year 2020.
| Year | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 |
|---|---|---|---|---|---|---|---|
| Sales (Rs. in Million) | 500 | 550 | 575 | 675 | 650 | 700 | 780 |

## Short answer

Fit linear trend Y = 632.857 + 43.393X (origin 2004). For 2020, X = 16, forecast sales = 632.857 + 43.393 × 16 = Rs 1,327.1 million.

## Answer

#### Method
Sales are growing roughly in a straight line, so fit a linear trend Y = a + bX by least squares. Take 2004 (middle year) as the origin: X = year − 2004. Then ΣX = 0, a = ΣY/n, b = ΣXY/ΣX².

| Year | X | Y (Rs million) | XY | X² |
|---|---|---|---|---|
| 2001 | −3 | 500 | −1,500 | 9 |
| 2002 | −2 | 550 | −1,100 | 4 |
| 2003 | −1 | 575 | −575 | 1 |
| 2004 | 0 | 675 | 0 | 0 |
| 2005 | 1 | 650 | 650 | 1 |
| 2006 | 2 | 700 | 1,400 | 4 |
| 2007 | 3 | 780 | 2,340 | 9 |
| Total | 0 | 4,430 | 1,215 | 28 |

a = 4,430 / 7 = 632.857
b = 1,215 / 28 = 43.393

**Trend equation: Y = 632.857 + 43.393 X**

#### Forecast for 2020
X = 2020 − 2004 = 16
Y = 632.857 + 43.393 × 16 = 632.857 + 694.286 = **1,327.1**

**Answer: Forecast sales for 2020 = about Rs 1,327 million.** (Sales grow by about Rs 43.4 million a year. The forecast is 13 years beyond the data, so it is only indicative.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Taking 2004 as origin gives ΣX =
   A. 1,215
   B. 28
   C. 0, so a = ΣY/n and b = ΣXY/ΣX^2
   D. 4,430
   Answer: C. Years are symmetric about 2004. (Key point: Origin)

2. a equals:
   A. 1,215 / 28 = 43.39
   B. 4,430 / 28
   C. 675
   D. 4,430 / 7 = 632.857
   Answer: D. a = ΣY/n. (Key point: Intercept)

3. b equals:
   A. 1,215 / 28 = 43.393
   B. 4,430 / 7
   C. 1,215 / 7
   D. 28 / 1,215
   Answer: A. Sales grow about Rs 43.4 million a year. (Key point: Slope)

4. For 2020, X is and Y is about:
   A. X = 13, Y = 1,197
   B. X = 16, Y = 1,327
   C. X = 16, Y = 694
   D. X = 20, Y = 1,500
   Answer: B. 632.857 + 43.393 x 16. (Key point: 2020)

## Related in Engineering Economics

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