Question

3. The quarterly sales for a product line for last 3 years is as follows: Quarters: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 600, 1550, 1500, 1500, 2400, 3100, 2600, 2900, 3800, 4500, 4000, 4900 Forecast sales for the next 4 quarters (13, 14, 15, 16)

Answer 1

Since the sales is increasing over time, we can use trend line forecasting to forecast the sales

Let the quarters be denoted by x and sales by y

Let the Regression line be y = b_o + b₁x

where,

b_o = ( Σy Σx² - Σx Σxy ) / ( nΣx² - (Σx)² )

b₁ = ( nΣxy - ΣxΣy ) / ( nΣx² - (Σx)² )

	Quarter (x)	Sales (y)	x2	xy
	1	600	1	600
	2	1550	4	3100
	3	1500	9	4500
	4	1500	16	6000
	5	2400	25	12000
	6	3100	36	18600
	7	2600	49	18200
	8	2900	64	23200
	9	3800	81	34200
	10	4500	100	45000
	11	4000	121	44000
	12	4900	144	58800
sum	78	33350	650	268200

b_o = ( 33350*650 - 78*268200 ) / ( 12*650 - 78² ) = 441.67

b₁ = ( 12*268200 - 78*33350 ) / ( 12*650 - 78² ) = 359.62

Hence, y = 441.67 + 359.62x

For Quarter 13, x = 13 => Sales = y = 441.67 + 359.62*13 = 5116.73

For Quarter 14, x = 14 => Sales = y = 441.67 + 359.62*14 = 5476.35

For Quarter 15, x = 15 => Sales = y = 441.67 + 359.62*15 = 5835.97

For Quarter 16, x = 16 => Sales = y = 441.67 + 359.62*16 = 6195.59