Quarterly demand for jaguar auto gallery is forecasted with equation y=10+3x whe
ID: 3283382 • Letter: Q
Question
Quarterly demand for jaguar auto gallery is forecasted with equation y=10+3x where x is the index for quarters.The next years first quarter index is 8.Jaguar sales have seasonality factors of 0.8,1.0,1.3 and 0.9 for 4 quarters.find the next years quarterly sales forecast. Quarterly demand for jaguar auto gallery is forecasted with equation y=10+3x where x is the index for quarters.The next years first quarter index is 8.Jaguar sales have seasonality factors of 0.8,1.0,1.3 and 0.9 for 4 quarters.find the next years quarterly sales forecast.Explanation / Answer
We know that the equation for the trend line of quarterly demand for Jaguar is the following: Y = 10 + 3X where X indicates the index of each quarter. I'm assuming here, in order for the rest of the question to make sense, that this trend line was calculated over deseasonalized data. Thus this trend line implies that in the first quarter of the last year (X=0), deseasonalized demand was approximately 10+3*0=10; in the 2nd quarter (X=1), deseasonalized demand was approximately 10+3*1=13, and so on. In order to find the deseasonalized demand for the next year, we must first know the the numbers that correspond to each of next year's quarters. This is easy to do: This year, 1st quarter: 4 This year, 2nd quarter: 5 This year, 3rd quarter: 6 This year, 4th quarter: 7 Next year, 1st quarter: 8 Next year, 2nd quarter: 9 Next year, 3rd quarter: 10 Next year, 4th quarter: 11 So the numbers are 8, 9, 10 and 11. Therefore, following the trend line, deseasonalized demand for each quarter of the next year is simply: Demand next year, 1st quarter: 10 + 3*8 = 34 Demand next year, 2nd quarter: 10 + 3*9 = 37 Demand next year, 3rd quarter: 10 + 3*10 = 40 Demand next year, 4th quarter: 10 + 3*11 = 43 As you can see, the fact that the equation is 10+3X implies that deseasonalized demand increases by 3 each quarter. We must know seasonalize the data. Seasonal indices show the effect the time of the year has on sales. So for example, we can see that in the 1st quarter of each year, sales are usually substantially lower than sales in the 3rd quarter of each year. In order to seasonalize the data, we must simply multiply each trend forecast by its seasonal index. So we get: Demand next year, 1st quarter: 34*0.8 = 27.2 Demand next year, 2nd quarter: 37*1.0 = 37 Demand next year, 3rd quarter: 40*1.3 = 52 Demand next year, 4th quarter: 43*0.9 = 38.7 Note how despite the fact that the trend line indicates that demand is always increasing (by 3 each quarter), we have that in the 4th quarter sales are lower then in the 3rd one. This is so because of the seasonal effect: apparently, for some reason, sales in the 3rd quarter are higher than normal, and in the 4th quarter they are lower than normal.