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 77 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 YearlySales15215132744142931135163541297225051910133577(a)Deseasonalize the data. (Round your answers to four decimal places.) YearQuarter Sales AdjustedDeseasonalized SeasonalSales Index 11 51.3407 12 20.5998 13 10.4842 14 51.5753 21 71.3407 22 40.5998 23 40.4842 24 141.5753 31 111.3407 32 30.5998 33 50.4842 34 161.5753 41 121.3407 42 90.5998 43 70.4842 44 221.5753 51 191.3407 52 100.5998 53 130.4842 54 351.5753 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___

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly sales 1 5 2 1 5 13 2 7 4 4 14 29 3…

Answered: A company that sells musical…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

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 77 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	7	4	4	14	29
3	11	3	5	16	35
4	12	9	7	22	50
5	19	10	13	35	77

(a)

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

Year	Quarter	Sales	Adjusted	Deseasonalized
	Seasonal	Sales
	Index
1	1	5	1.3407
1	2	2	0.5998
1	3	1	0.4842
1	4	5	1.5753
2	1	7	1.3407
2	2	4	0.5998
2	3	4	0.4842
2	4	14	1.5753
3	1	11	1.3407
3	2	3	0.5998
3	3	5	0.4842
3	4	16	1.5753
4	1	12	1.3407
4	2	9	0.5998
4	3	7	0.4842
4	4	22	1.5753
5	1	19	1.3407
5	2	10	0.5998
5	3	13	0.4842
5	4	35	1.5753

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___

Expert Solution