Question

The Annual production of a commodity is given as follows:

Year	1995	1996	1997	1998	1999	2000	2001
Production (in tones)	155	162	171	182	158	180	178

Fit a straight line trend by the method of least squares.

Answer 1

Computation of trend values by the method of least squares. (ODD years)

Therefore, the required equation of the straight line trend is given by Y = a + bX 

(i.e) Y = 169.429 + 3.286 X (or) Y = 169.429 + 3.286 (x – 1998) 

The trends values are obtained by 

When x = 1995, Y_t = 169.429 + 3.286 (1995 – 1998) = 159.57 

When x = 1996, Y_t = 169.429 + 3.286 (1996 – 1998) = 162.86 

When x = 1997, Y_t = 169.429 + 3.286 (1997 – 1998) = 166.14 

When x = 1998, Y_t = -169.429 + 3.286 (1998 – 1998) = 169.43 

When x = 1999, Y_t = 169.429 + 3.286 (1999 – 1998) = 172:72 

When x = 2000, Y_t = 169.429 + 3.286 (2000 – 1998) = 176.00 

When x = 2001, Y_t = 169.429 + 3.286 (2001 – 1998) = 179.29