Consider the following data :
| Year | 2008 | 2009 | 2010 | 2011 | 2012 |
| Production (in tons) | 60 | 75 | 80 | 70 | 85 |
The equation of the straight line trend by the method of least squares is ,
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $y=74+4.5x$
The equation of the straight line trend is,
$y=a+bx$
$∑x=(-2)+(-1)+0+1+2=0$
$∑y=60+75+80+70+85=370$
$∑xy=(-2)(60)+(-1)(75)+(0)(80)+(1)(70)+(2)(85)=45$
$∑x^2=(-2)^2+(-1)^2+0^2+1^2+2^2=10$
$a=\frac{∑y}{n}=\frac{370}{5}=74$
$b=\frac{∑xy}{∑x^2}=\frac{45}{10}=4.5$
$⇒y=74+4.5x$