Data available for profit (Rs. Thousands) of a company as
| Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
| Profit(Rs. 000) | 114 | 130 | 126 | 144 | 138 | 156 | 164 |
Based on the above data using least square method the trend value for the year '2007' is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 138.86
The least squares straight-line trend is \(y = a + bX\). With 7 years (an odd number), take the origin at the middle year 2007, so \(X = \text{year} - 2007\) runs from \(-3\) to 3 and \(\sum X = 0\). The normal equations then give
\( \displaystyle a = \frac{\sum y}{n}, \quad b = \frac{\sum Xy}{\sum X^2} \)
\(\sum y = 114 + 130 + 126 + 144 + 138 + 156 + 164 = 972\)
\( \displaystyle a = \frac{972}{7} = 138.857 \)
For 2007, \(X = 0\), so the bX term vanishes and b is not needed:
\(y_{2007} = a = 138.86\)
(For completeness, \(\sum Xy = 214\) and \(\sum X^2 = 28\), so the trend line is \(y = 138.86 + 7.64X\).)