Consider the following data:
| Year(xi) | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
| Profit (Rs. 000)(yi) | 26 | 26 | 44 | 42 | 108 | 120 | 166 |
Using method of least squares, the trend value for year 2004 will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
There are 7 years (odd), so take the middle year 2007 as origin: u = x − 2007, which gives u = −3, −2, −1, 0, 1, 2, 3 and \( \sum u=0 \). The trend line is y = a + bu with
\( \displaystyle a=\frac{\sum y}{n},\qquad b=\frac{\sum uy}{\sum u^2} \)
\( \displaystyle \sum y=26+26+44+42+108+120+166=532 \)
\( \displaystyle a=\frac{532}{7}=76 \)
\( \displaystyle \sum uy=-78-52-44+0+108+240+498=672 \)
\( \displaystyle \sum u^2=9+4+1+0+1+4+9=28 \)
\( \displaystyle b=\frac{672}{28}=24 \)
\( \displaystyle y=76+24u \)
For 2004, u = −3:
\( \displaystyle y=76+24(-3)=76-72=4 \)