Let x and y be the year and production.
The straight line equations y = a+bx
Normal equations are. na + b Σx = Σ y ……..(1)
a Σx + b Σx2 = Σxy……..(2)
Here x = X – x̄( odd time points) x̄ = 1996
From (1) 5a + b. 0 = 289
\(∴ a = \frac{289}{5} = 57.8\)
From (2) a.0 + b.10 = 35
\(∴b = \frac{35}{10} = 3.5\)
Hence the fitted straight line trend equation is ŷ = 57.8 + 3.5x
Note: The trend values for the given years can be obtained by substituting the
values of x as -2, -1, 0, 1, 2 if n is odd and -5, -3, -1, 1, 3, 5 if n is even.
