Question

To plan staffing for the credit department, Mr. Browne, the department manager of a discount store, would like to predict the number of credit transactions the company will have to process next year. The number of credit card transactions processed has been increasing over time. The data for the last ten years are shown in Table 3.

   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) number of transactions(Y) XY X^2

1 20 20 1

2 25 50 4

3 28 84 9

4 32 128 16

5 40 200 25

X = 1+2+3+4+5 = 15

Y = 20+25+28+32+40 = 145

XY = 20+50+84+128+200 = 482

X^2 = 1+4+9+16+25 = 55

n = Number of periods = 5

X-bar = X / n = 15/5 = 3

Y-bar = Y/n = 145/5 = 29

b = ( XY - nX-bar .Y-bar ) / ( X^2 - n. Square of X-bar)

= [482 - (5)(3)(29) ] / [55 - (5)(3)(3)]

= (482 - 435) / (55 - 45)

= 47/ 10

= 4.7

a = Y-bar - b(X-bar) = 29 - 4.7(3) = 29 - 14.1 = 14.9

Y = a + bx => Y = 14.9 + 4.7x

So the regression equation is Y = 14.9 + 4.7x

where, x = sequential number of year

So ,

For year 6 , x = 6 and forecast for year 6 = 14.9 + (4.7 × 6) = 14.9 + 28.2 = 43.1

For year 7 , x = 7 and forecast for year 6 = 14.9 + (4.7 × 7) = 14.9 + 32.9 = 47.8