For the following data:
| Year (xi) | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 |
| Production (in tonnes) (yi) | 40 | 45 | 46 | 42 | 47 | 50 | 46 |
The equation of the straight line trend is \( y=a+b\,(x_{i}-2003) \), then the trend value for the year 2007 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 49.28
Let \( u=x-2003 \), so u runs from −3 to 3 and \( \sum u=0 \). Then the least squares constants are
\( \displaystyle a=\frac{\sum y}{n}=\frac{316}{7}\approx 45.14 \)
\( \displaystyle b=\frac{\sum uy}{\sum u^{2}}=\frac{29}{28}\approx 1.036 \)
For 2007, u = 4:
\( \displaystyle y=45.14+1.036\times 4 \)
\( \displaystyle \approx 49.28 \)