Data available for profit (₹ Thousands) of a company as

Based on the above data using least square method the trend value for the year '2007' is

138.86

The correct answer is Option (2) → 138.86 **

Least Squares Trend for 2007

Given 7 years: 2004–2010

Profits (₹000):

114, 130, 126, 144, 138, 156, 164

Let 2007 be the central year → assign:

$\begin{aligned} 2004 &\to x=-3\\ 2005 &\to x=-2\\ 2006 &\to x=-1\\ 2007 &\to x=0\\ 2008 &\to x=1\\ 2009 &\to x=2\\ 2010 &\to x=3 \end{aligned}$

Sum of $y$:

$114+130+126+144+138+156+164=972$

Sum of $xy$:

$-3(114)=-342$ $-2(130)=-260$ $-1(126)=-126$ $0(144)=0$ $1(138)=138$ $2(156)=312$ $3(164)=492$

Total:

$-342-260-126+0+138+312+492=214$

Trend equation:

$\hat{y}=a+bx$

where

$a=\frac{\sum y}{n}=\frac{972}{7}=138.857$

$b=\frac{\sum xy}{\sum x^{2}}=\frac{214}{28}=7.643$

For year 2007, $x=0$:

$\hat{y}=a+bx=138.857+7.643(0)=138.857$

Trend value for 2007 ≈ 138.86 (₹ thousand)