Consider the following data:

A straight line trend by the method of least square is:

$y = 23+ 6.9$ (x-2012)

The correct answer is Option (2) → $y = 23+ 6.9$ (x-2012)

Given data:

Year (x): 2010, 2011, 2012, 2013, 2014

Sales (y): 9, 18, 21, 29, 38

Let x' = x - 2012 (central year) to simplify calculations:

x': -2, -1, 0, 1, 2

Compute sums:

$Σx' = -2 -1 + 0 +1 +2 = 0$

$Σy = 9 + 18 + 21 + 29 + 38 = 115$

$Σx'y = (-2)(9) + (-1)(18) + (0)(21) + 1(29) + 2(38) = -18 -18 +0 +29 +76 = 69$

$Σx'^2 = 4 +1 +0 +1 +4 = 10$

Slope: $b = Σx'y / Σx'^2 = 69 / 10 = 6.9$

Intercept: $a = mean(y) = Σy / n = 115 / 5 = 23$

Trend line equation: $y = a + b x' = 23 + 6.9 x'$

Substitute x' = x - 2012:

$y = 23 + 6.9(x - 2012)$