Question

5. The quarterly sales in units for “Retailsale Sports” for the last two years are as follows:

Quarter	Year 1	Year 2
I	440	560
II	460	490
III	420	500
IV	390	400

Using linear regression, a straight line was fitted to the sales data. Assume that the equation of the fitted line is Y = 420 + 6 × t. The first quarter in the data is labeled t = 1.

1. Calculate seasonal indexes for this product using the fitted line approach.
2. Using the fitted line and seasonal indexes you have just calculated, forecast sales in
3. each quarter of year 3.

Answer 1

a.

Year	Qtr	t	Sales (St)	Trend (Tt)= 420 + 6 * t	Seasonal index (St / Tt)	Seasonal index (avg.)	Seasonal index (normalized)
1	I	1	440	426	1.0329	1.139	1.112
	II	2	460	432	1.0648	1.070	1.045
	III	3	420	438	0.9589	1.021	0.997
	IV	4	390	444	0.8784	0.867	0.846
2	I	5	560	450	1.2444
	II	6	490	456	1.0746	1.024	1.000
	III	7	500	462	1.0823
	IV	8	400	468	0.8547

b.

Year	Qtr	t	Sales (St)	Trend (Tt)= 420 + 6 * t	Seasonal index (St / Tt)	Seasonal index (avg.)	Seasonal index (normalized)	Forecast
1	I	1	440	426	1.0329	1.139	1.112
	II	2	460	432	1.0648	1.070	1.045
	III	3	420	438	0.9589	1.021	0.997
	IV	4	390	444	0.8784	0.867	0.846
2	I	5	560	450	1.2444		1.112
	II	6	490	456	1.0746	1.024	1.045
	III	7	500	462	1.0823		0.997
	IV	8	400	468	0.8547		0.846
3	I	9		474			1.112	527.1
	II	10		480			1.045	501.5
	III	11		486			0.997	484.4
	IV	12		492			0.846	416.4

All calculations: