Question

TABLE 3

YEAR	1	2	3	4	5	6	7	8	9	10
NO.OF(‘000)	20	25	28	32	40	45	48	52	56	60

(i). Compute the Trend Projection equation expressing the number of credit card transactions as a function of time.

(ii) Use that equation to predict the number of credit card transactions in each of the next two years.

Answer 1

	Year (x)	No.of ('000)(y)	x^2	xy
	1	20	1	20
	2	25	4	50
	3	28	9	84
	4	32	16	128
	5	40	25	200
	6	45	36	270
	7	48	49	336
	8	52	64	416
	9	56	81	504
	10	60	100	600
Sum	55	406	385	2608

here to find trend equation, we require the above table

here if the equation is

y^ = a + bt

a = [(Σy) (Σx2 ) - (Σx) (Σxy)]/ [ n (Σx2 ) - (Σx)2 ]

a = [(406 * 385 - 55 * 2608)]/ [10 * 385 - 55 * 55]

a = 15.6

b = [ n(Σxy) - (Σx)((Σy)]/ [ n (Σx2 ) - (Σx)2 ]

b = [10 * 2608 - 55 * 406]/[10 * 385 - 55 * 55]

b = 4.5454

y^ = 15.6 + 4.5454 t

(b) So here forecast equation is y^ = 15.6 + 4.5454 t

y^(11) = 15.6 + 4.5454 * 11 = 65.6

y^(12) = 15.6 + 4.5454 * 12 = 70.145