- 2067 Mangsir · 6 marks
Forecast CFL demand for next five years
Short answer
Using least-squares linear trend with origin mid-2008.5, Y = 181,250 + 67,500X. Forecast demand: 2011 – 350,000; 2012 – 417,500; 2013 – 485,000; 2014 – 552,500; 2015 – 620,000 nos.
Based on the following data, forecast the demand of CFL for next five years.
| Year | 2007 | 2008 | 2009 | 2010 |
|---|---|---|---|---|
| Demand (Nos.) | 1,00,000 | 1,25,000 | 2,00,000 | 3,00,000 |
Method
The demand is rising steadily, so fit a straight-line trend by least squares: Y = a + bX. Take the mid-point of the years as the origin, so ΣX = 0 and a = ΣY / n, b = ΣXY / ΣX².
Mid-year = 2008.5. Let X = (year − 2008.5), so X = −1.5, −0.5, 0.5, 1.5.
| Year | X | Y (nos.) | XY | X² |
|---|---|---|---|---|
| 2007 | −1.5 | 100,000 | −150,000 | 2.25 |
| 2008 | −0.5 | 125,000 | −62,500 | 0.25 |
| 2009 | 0.5 | 200,000 | 100,000 | 0.25 |
| 2010 | 1.5 | 300,000 | 450,000 | 2.25 |
| Total | 0 | 725,000 | 337,500 | 5.00 |
a = 725,000 / 4 = 181,250 b = 337,500 / 5 = 67,500
Trend line: Y = 181,250 + 67,500 X
Forecast
| Year | X | Demand = 181,250 + 67,500 X |
|---|---|---|
| 2011 | 2.5 | 350,000 |
| 2012 | 3.5 | 417,500 |
| 2013 | 4.5 | 485,000 |
| 2014 | 5.5 | 552,500 |
| 2015 | 6.5 | 620,000 |
Answer: Forecast demand of CFL is 3,50,000; 4,17,500; 4,85,000; 5,52,500 and 6,20,000 nos. for 2011 to 2015. (The straight line adds about 67,500 per year. The data are growing slightly faster than linear, so this forecast may be on the low side.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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