If for the following data:
| Year | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 |
| Production (in lakh tonnes) | 30 | 35 | 36 | 32 | 37 | 40 | 36 |
Using straight line trend by the method of least squares, the trend value for the year 2009 is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 40.32
There are 7 years (odd), so take the middle year 2004 as origin: u = year − 2004, giving u = −3, −2, −1, 0, 1, 2, 3 and \( \sum u=0 \). The trend line is \( y=a+bu \) with
\( \displaystyle a=\frac{\sum y}{n},\quad b=\frac{\sum uy}{\sum u^2} \)
\( \displaystyle \sum y=30+35+36+32+37+40+36=246 \)
\( \displaystyle \sum uy=-90-70-36+0+37+80+108=29 \)
\( \displaystyle \sum u^2=9+4+1+0+1+4+9=28 \)
\( \displaystyle a=\frac{246}{7}=35.143 \)
\( \displaystyle b=\frac{29}{28}=1.036 \)
For 2009, u = 5:
\( \displaystyle y=35.143+5\times 1.036 \)
\( \displaystyle =35.143+5.179 \)
\( \displaystyle =40.32 \)
The trend value for 2009 is 40.32 lakh tonnes.