Based on the data available for the sales of an item in a district for the period 2004 to 2010. We have \(\sum x=0,\ \sum x^2=28,\ \sum y=972,\ \sum xy=214\). A straight line trend by the method of least squares is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(y=138.86+7.64x\)
The years 2004 to 2010 give n = 7 values. \(\sum x = 0\) means x is measured from the middle year 2007.
For the trend line \(y = a + bx\), the normal equations of the least squares method are
\(\sum y = na + b\sum x\)
\(\sum xy = a\sum x + b\sum x^2\)
With \(\sum x = 0\) they separate:
\( \displaystyle a = \frac{\sum y}{n} = \frac{972}{7} = 138.86 \)
\( \displaystyle b = \frac{\sum xy}{\sum x^2} = \frac{214}{28} = 7.64 \)
So the trend line is \(y = 138.86 + 7.64x\).