Consider the following data:
|
Year |
2012 |
2013 |
2014 |
2015 |
2016 |
|
Sales (in ₹ crores) |
8 |
10 |
7 |
9 |
12 |
The equation of the straight line trend by the method of least squares is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - $y=9.2+0.7 x$
$\text{Take } x = -2,-1,0,1,2 \text{ for years } 2012,2013,2014,2015,2016$
$y = 8,10,7,9,12$
$\sum y = 46,\;\; \sum x = 0,\;\; \sum x^2 = 10$
$\sum xy = (-2)(8)+(-1)(10)+0(7)+1(9)+2(12)$
$= -16 -10 + 9 + 24 = 7$
$b = \frac{\sum xy}{\sum x^2} = \frac{7}{10} = 0.7$
$a = \frac{\sum y}{n} = \frac{46}{5} = 9.2$
$y = a + bx$
$y = 9.2 + 0.7x$
$x = \text{Year} - 2014$
$y = 9.2 + 0.7(\text{Year} - 2014)$
The trend equation is $y = 9.2 + 0.7(\text{Year} - 2014)$.