Question

Determine the equation of a straight line which best fits the following data 

Year	2000	2001	2002	2003	2004
Sales (₹ '000)	35	36	79	80	40

Compute the trend values for all years from 2000 to 2004

Answer 1

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

Year (x)	Sales (y) (₹ 000)	X = (x - 2002)	X2	XY	Tred Value (Yt)
2000	335	– 2	4	– 70	43.2
2001	36	– 1	1	– 36	48.6
2002	79	0	0	0	54
2003	80	1	1	80	59.4
2004	40	2	4	80	64.8
N = 5	`sum"Y"` = 270	`sum"X"` = 0	`sum"X"^2` = 10	`sum"XY"` = 54	`sum"Y""t"`  270

a = `(sum"Y")/"n" = 270/5` = 54

b =  `(sum"XY")/(sum"X"^2) = 54/10` = 5.4

Therefore, the required equation of the straight line trend is given by

Y = a + bX

Y = 54 + 5.4X

Y = 54 + 5.4(x – 2002)

The trend value can be obtained by when x = 2000

Yt = 54 + 5.4(2000 – 2002)

Y = 54+ 5.4(– 2)

= 54 – 10.8

= 43.2

When x = 2001

Yt = 54 + 5.4(2001 – 2002)

Y = 54 + 5.4(– 1)

= 54 – 5.4

= 48.6

When x = 2002

Yt = 54 + 5.4(2002 – 2002)

V = 54 + 5.4(0)

= 54

When x = 2003

Yt = 54 + 5.4(2003 – 2002)

Y = 54 + 5.4(1)

= 54 + 5.4

= 59.4

When x = 2004

Yt = 54 + 5.4(2004 – 2002)

Y = 54 + 5.4(2)

= 54 + 10.8

= 64.8