A public relation firm wishes to estimate the trend in their sales on the basis of the given data :
| Year(x) | 2001 | 2002 | 2003 | 2004 | 2005 |
| Sales (y) (in Lakh Rupees) | 15 | 20 | 25 | 22 | 43 |
The trend analysis team is using method of least squares to fix the straight line trend. Then for the best fitted trend line equation $y_c=a+bx,$ the value of a is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 25
$y_c=a+bx$
x here represents the year, $y_c$ represents predicted sales.
For simple calculations, let us define x as deviation from 2003 (middle year).
| Year | x = Year - 2003 | Sales (y) |
| 2001 | -2 | 15 |
| 2002 | -1 | 20 |
| 2003 | 0 | 25 |
| 2004 | 1 | 22 |
| 2005 | 2 | 43 |
$a=\frac{∑y}{y}$
$∴a=\frac{15+20+25+22+43}{5}=\frac{125}{5}=25$