A public relation firm wishes to estimate the trend in their sales on the basis of the given data :

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 :

25

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).

$a=\frac{∑y}{y}$

$∴a=\frac{15+20+25+22+43}{5}=\frac{125}{5}=25$