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)
With the middle year 2012 as origin, let \(u = x - 2012\), so u = −2, −1, 0, 1, 2 and \(\sum u = 0\).
For the trend \(y = a + bu\), the normal equations with \(\sum u = 0\) give
\( \displaystyle a = \frac{\sum y}{n},\quad b = \frac{\sum uy}{\sum u^2} \)
The sums:
\(\sum y = 9 + 18 + 21 + 29 + 38 = 115\)
\(\sum uy = -18 - 18 + 0 + 29 + 76 = 69\)
\(\sum u^2 = 4 + 1 + 0 + 1 + 4 = 10\)
So
\( \displaystyle a = \frac{115}{5} = 23,\quad b = \frac{69}{10} = 6.9 \)
The trend line is \(y = 23 + 6.9(x - 2012)\).