Given the data for the sales of a product in a state is as follows:
| Year | 2005 | 2006 | 2007 | 2008 | 2009 |
| Sales (In lakh ₹) | 150 | 130 | 160 | 170 | 200 |
The equation of the straight-line trend by method of least squares is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $162+14x$
To find the equation of straight line trend,
$y=a+bx$
$∑x=(-2)+(-1)+0+1+2=0$
$∑y=150+150+160+170+200=810$
$∑xy=(-300)+(-150)+0+170+400=140$
$∑x^2=4+1+0+1+4=10$
$a=\frac{∑y}{n}=\frac{810}{5}=162$
$b=\frac{∑xy}{x^2}=\frac{140}{10}=14$
$y=162+14x$