Consider the following data:
|
Year (x) |
2010 |
2011 |
2012 |
2013 |
2014 |
|
Sale (in crore Rs.) (y) |
9 |
18 |
21 |
29 |
38 |
A straight line trend by the method of least square is:
Answer & explanation
Correct answer: option 2
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:
$y = 23 + 6.9(x - 2012)$