Consider the following data :
| Year | 2008 | 2009 | 2010 | 2011 | 2012 |
| Profit (in lakh ₹) | 10 | 12 | 15 | 20 | 25 |
The best fitted trend line equation by the method of least squares is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $y=8.8+3.8x$
The linear regression equation is,
$y=a+bx$
$∑X=0+1+2+3+4=10$
$∑Y=10+12+15+20+25=82$
$∑X^2=0^2+1^2+2^2+3^2+4^2=30$
$∑XY=(0×10)+(1×12)+(2×15)+(3×20)+(4×25)=202$
$b=\frac{n∑XY-(∑X)(∑Y)}{n∑X^2-(∑X)^2}=\frac{190}{50}=3.8$
$a=\frac{∑Y-b∑X}{n}=\frac{82-3.8×10}{5}=8.8$