Data available for profit (₹ Thousands) of a company as
|
Year |
2004 |
2005 |
2006 |
2007 |
2008 |
2009 |
2010 |
|
Profit(₹ 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 **
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)