A statistical program is recommended.A company that sells musical instruments has been in business for five years. During that time, sales of pianos increased from 13 units in the first year to 76 units in the most recent year. The firm's owner wants to develop a forecast of piano sales for the coming year. The quarterly sales data follow.YearQuarter 1Quarter 2Quarter 3Quarter 4Total YearlySales15215132644142831035163441297225051810133576(a)Deseasonalize the data. (Round your answers to four decimal places.)YearQuarterSalesAdjustedSeasonalIndexDeseasonalizedSales1151.2726 220.6125 310.4953 451.6197 2161.2726 240.6125 340.4953 4141.6197 31101.2726 230.6125 350.4953 4161.6197 41121.2726 290.6125 370.4953 4221.6197 51181.2726 2100.6125 3130.4953 4351.6197 Use the deseasonalized time series to identify the trend. (Lett = 1denote the time series value in quarter 1 of year 1;t = 2denote the time series value in quarter 2 of year 1; andt = 20denote the time series value in quarter 4 of year 5. Round your numerical values to two decimal places.)Tt = (b)Use the results of part (a) to develop a quarterly forecast for next year based on trend. (Round your answers to two decimal places.)forecast for quarter 1 forecast for quarter 2 forecast for quarter 3 forecast for quarter 4(c)Use the adjusted seasonal indexes given in part (a) to adjust the forecasts developed in part (b) to account for the effect of season. (Round your answers to one decimal place.)forecast for quarter 1 forecast for quarter 2 forecast for quarter 3 forecast for quarter 4

From the given information, Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 5…

Answered: A statistical program is recommended. A…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Question

A statistical program is recommended.

A company that sells musical instruments has been in business for five years. During that time, sales of pianos increased from 13 units in the first year to 76 units in the most recent year. The firm's owner wants to develop a forecast of piano sales for the coming year. The quarterly sales data follow.

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4	Total Yearly Sales
1	5	2	1	5	13
2	6	4	4	14	28
3	10	3	5	16	34
4	12	9	7	22	50
5	18	10	13	35	76

(a)

Deseasonalize the data. (Round your answers to four decimal places.)

Year	Quarter	Sales	Adjusted Seasonal Index
1	1	5	1.2726
2	2	0.6125
3	1	0.4953
4	5	1.6197
2	1	6	1.2726
2	4	0.6125
3	4	0.4953
4	14	1.6197
3	1	10	1.2726
2	3	0.6125
3	5	0.4953
4	16	1.6197
4	1	12	1.2726
2	9	0.6125
3	7	0.4953
4	22	1.6197
5	1	18	1.2726
2	10	0.6125
3	13	0.4953
4	35	1.6197

Use the deseasonalized time series to identify the trend. (Let

t = 1

denote the time series value in quarter 1 of year 1;

t = 2

denote the time series value in quarter 2 of year 1;

and

t = 20

denote the time series value in quarter 4 of year 5. Round your numerical values to two decimal places.)

T_t =

(b)

Use the results of part (a) to develop a quarterly forecast for next year based on trend. (Round your answers to two decimal places.)

forecast for quarter 1 forecast for quarter 2 forecast for quarter 3 forecast for quarter 4

(c)

Use the adjusted seasonal indexes given in part (a) to adjust the forecasts developed in part (b) to account for the effect of season. (Round your answers to one decimal place.)

forecast for quarter 1 forecast for quarter 2 forecast for quarter 3 forecast for quarter 4

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