Consider the following data
|
Year (x) |
2010 |
2011 |
2012 |
2013 |
2014 |
|
Profit (Rs. in thousands) (y) |
10 |
12 |
14 |
16 |
13 |
The equation of straight line trend by method of least square for the above data is given by
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $y=x-1999$
$n=5,\ \sum x=10060,\ \sum y=65,\ \sum xy=130790,\ \sum x^{2}=20240730$
$b=\frac{n\sum xy - (\sum x)(\sum y)}{n\sum x^{2} - (\sum x)^{2}} =\frac{5\times130790 - 10060\times65}{5\times20240730 - (10060)^{2}}=1$
$a=\frac{\sum y - b\sum x}{n}=\frac{65 - 1\times10060}{5}=-1999$
${\,\text{Trend line: }y = 1\! \cdot x - 1999\,}$