Consider the following data:

A straight line trend by the method of least squares is:

$y=11.6+5.2 x$

$\text{Years: }2012,2013,2014,2015,2016.$

$\text{Production }(y): 3,6,9,16,24.$

$\text{Take }x=-2,-1,0,1,2.$

$\sum y = 3+6+9+16+24 = 58.$

$\sum x = 0.$

$\sum x^2 = 4+1+0+1+4 = 10.$

$\sum xy = (-2)(3)+(-1)(6)+0(9)+1(16)+2(24) = -6-6+0+16+48 = 52.$

$a=\frac{\sum y}{n}=\frac{58}{5}=11.6.$

$b=\frac{\sum xy}{\sum x^2}=\frac{52}{10}=5.2.$

$\text{Trend line } y = a+bx.$

$y = 11.6 + 5.2x.$

$\text{Straight line trend: } y = 11.6 + 5.2x.$