Consider the following data of expenses (in lakhs) of an organization year wise

Then expected expenses trends for the year 2006 using method of least square is:

Rs. 519.5 lakh

The correct answer is Option (4) → Rs. 519.5 lakh **

Given years: 2001–2005 and corresponding expenses:

$160,\;185,\;220,\;300,\;510$

Assign coded time values (least squares standard coding):

$t=-2,-1,0,1,2$ for years 2001–2005.

Compute required sums:

$\sum t = 0$

$\sum y = 160+185+220+300+510 = 1375$

$\bar{y} = 1375/5 = 275$

$\sum t^2 = 4+1+0+1+4 = 10$

$\sum ty = (-2)(160) + (-1)(185) + 0 + (1)(300) + (2)(510)$

$= -320 -185 + 0 + 300 + 1020 = 815$

Slope:

$b = \frac{\sum ty}{\sum t^2} = \frac{815}{10} = 81.5$

Intercept:

$a = \bar{y} = 275$

Trend equation:

$y = 275 + 81.5\,t$

For year 2006, $t=3$:

$y_{2006} = 275 + 81.5(3) = 275 + 244.5 = 519.5$

Expected expenses in 2006 ≈ ₹520 lakhs