Consider the following data:
|
year |
2012 |
2013 |
2014 |
2015 |
2016 |
|
Production (in tonnes) |
3 |
6 |
9 |
16 |
24 |
A straight line trend by the method of least squares is:
Answer & explanation
Correct answer: option 3
$\text{Years: }2012,2013,2014,2015,2016.$
$\text{Production }(y): 3,6,9,16,24.$
$\text{Take }x=-2,-1,0,1,2.$
$\sum y = 3+6+9+16+24 = 58.$
$\sum x = 0.$
$\sum x^2 = 4+1+0+1+4 = 10.$
$\sum xy = (-2)(3)+(-1)(6)+0(9)+1(16)+2(24) = -6-6+0+16+48 = 52.$
$a=\frac{\sum y}{n}=\frac{58}{5}=11.6.$
$b=\frac{\sum xy}{\sum x^2}=\frac{52}{10}=5.2.$
$\text{Trend line } y = a+bx.$
$y = 11.6 + 5.2x.$
$\text{Straight line trend: } y = 11.6 + 5.2x.$