If y = a+b (x- 2005) fits the time series date x(year): 2003 2004 200…

The correct answer is Option (2) → 20.3

The equations for a  and b in a simple regression model.

$b=\frac{∑ty}{∑t^2},a=\frac{∑y}{n}$

$∑y=6+13+17+20+24=80$

$∑t=(-2)+(-1)+0+1+2=0$

$∑ty=(-2)(6)+(-1)(13)+(0)(17)+(1)(20)+(2)(24)=43$

$∑t=(-2)^2+(-1)^2+(0)^2+(1)^2+(2)^2=10$

$b=\frac{∑ty}{∑t^2}=\frac{43}{10}=4.3$

$a=\frac{∑y}{n}=\frac{80}{5}=16$

$∴a+b=20.3$