Consider the following data :
| Year | 2010 | 2011 | 2012 | 2013 | 2014 |
| Production (in tonnes) | 3 | 6 | 9 | 16 | 24 |
A straight line trend by the method of least square is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $y=11.6+5.2x$
The straight line trend equations,
$y=a+bx$
$∑x=(-2)+(-1)+0+1+2=0$
$∑y=3+6+9+16+24=58$
$∑xy=(-2)(3)+(-1)(6)+(0)(9)+(1)(16)+(2)(24)=52$
$∑x^2=(-2)^2+(-1)^2+0^2+1^2+2^2=10$
$b=\frac{∑xy}{∑x^2}=\frac{52}{10}=5.2$
$a=\frac{∑y}{n}=\frac{58}{5}=11.6$
$y=11.6+5.2x$