Fit a trend line to the following data by the least squares method

Question: Fit a trend line to the following data by the least squares method

Year: 1991 1993 1995 1997 1999
Production(in ’000 tons): 36 42 46 54 32

Estimate the production in 1996 and 2002.

Solution:

Let the trend line be given by the equation :
Y = a+bx
Where origin is at 1995.
Computation for Straight Line Trend

Substituting values of a and b in the least square equation we get.

Y_c = 42 + 0.2X

By substituting X = -4, -2, 0, 2, 4, in the above equation we will obtain the estimated values for the years 1991, 1993, 1995, 1997 and 1999 respectively.

Thus