- 2066 Magh · 8 marks
Forecast Panchakanya sales for 2020
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.
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 |
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.)
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Forecast sales for year 2010 · Engineering Economics, chapter 1
- Forecast CFL demand for next five years · Engineering Economics, chapter 1
- Log-Pearson III 50-year flood, 1990-2006 · Engineering Hydrology, chapter 6
- Gumbel 30-year flood, Lothar River 1989-2009 · Engineering Hydrology, chapter 6
- Pre-qualifying contractors for Rs 500 million complex · Construction Management, chapter 5
- Sales of products by sales-persons · Computer Programming, chapter 7