Based on the data available for the production ($y_i$ in thousand tons) of a cloth factory for 7 years ($x_i$) using the method of least squares, the straight line trend is given by $y = a + bx$ with $∑y_i=608,∑x_i=0,∑x_iy_i= 116,∑{x_i}^2= 28$. Then, the increase in production per year is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4,143 tons **
Least–squares trend: $y = a + bx$.
Increase per year = slope $b$.
Formula: $b = \frac{\sum x_i y_i}{\sum x_i^2}$ (since $\sum x_i = 0$).
$b = \frac{116}{28} = \frac{29}{7} = 4.142857\ldots$
Increase in production per year = $\frac{29}{7}$ thousand tons