Choose the following data: Year 2008 2009 2010 2011 2012 Production (…

The correct answer is Option (4) → $y=23.6+7.4 x$

$\text{Take } x = -2,-1,0,1,2 \text{ for years } 2008,2009,2010,2011,2012$

$y = 9,17,23,29,40$

$\sum y = 118,\;\; \sum x = 0,\;\; \sum x^2 = 10$

$\sum xy = (-2)(9)+(-1)(17)+0(23)+1(29)+2(40)$

$\sum xy = -18 -17 + 29 + 80 = 74$

$b = \frac{\sum xy}{\sum x^2} = \frac{74}{10} = 7.4$

$a = \frac{\sum y}{n} = \frac{118}{5} = 23.6$

$y = a + bx$

$y = 23.6 + 7.4x$

$x = \text{Year} - 2010$

$y = 23.6 + 7.4(\text{Year} - 2010)$

The straight line trend is $y = 23.6 + 7.4(\text{Year} - 2010)$.