Library fpp R PROGRAMMING You can find the data set file in R UNDER THE FPP PACKAGE TYPE IN 'fancy' The data below (data set fancy) concern the monthly sales figures of a shop which opened in January 1987 and sells gifts, souvenirs, and novelties The shop is situated on the wharf at a beach resort town in Queensland, Australia The sales volume varies with the seasonal population of tourists There is a large influx of visitors to the town at Christmas and for the local surfing festival, held every March since 1988 Over time, the shop has expanded its premises, range of products, and staff 1987 1988 1989 1990 1991 1992 1993 Jan 1664 81 2499 81 4717 02 5921 10 4826 64 7615 03 10243 24 Feb 2397 53 5198 24 5702 63 5814 58 6470 23 9849 69 11266 88 Mar 2840 71 7225 14 9957 58 12421 25 9638 77 14558 40 21826 84 Apr 3547 29 4806 03 5304 78 6369 77 8821 17 11587 33 17357 33 May 3752 96 5900 88 6492 43 7609 12 8722 37 9332 56 15997 79 Jun 3714 74 4951 34 6630 80 7224 75 10209 48 13082 09 18601 53 Jul 4349 61 6179 12 7349 62 8121 22 11276 55 16732 78 26155 15 Aug 3566 34 4752 15 8176 62 7979 25 12552 22 19888 61 28586 52 Sep 5021 82 5496 43 8573 17 8093 06 11637 39 23933 38 30505 41 Oct 6423 48 5835 10 9690 50 8476 70 13606 89 25391 35 30821 33 Nov 7600 60 12600 08 15151 84 17914 66 21822 11 36024 80 46634 38 Dec 19756 21 28541 72 34061 01 30114 41 45060 69 80721 71 104660 67 a) Produce a time plot of the data and describe the patterns in the graph Identify any unusual or unexpected fluctuations in the time series Explain why it is necessary to take logarithms of these data before fitting a model b) Use R to fit a regression model to the logarithms of these sales data with a linear trend, seasonal dummies and a surfing festival dummy variable c) Plot the residuals against time and against the fitted values Do these plots reveal any problems with the model d) Draw boxplots of the residuals for each month Does this reveal any problems with the model e) What does the Durbin Watson statistic tell you about your model f) Regardless of your answers to the above questions, use your regression model to predict the monthly sales for 1994, 1995, and 1996 Produce prediction intervals for each of your forecasts g) Do you need to transform your predictions and intervals to obtain predictions and intervals for the raw data

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Question: Library : fpp ; R PROGRAMMING You can find the data set file in R UNDER THE FPP PACKAGE TYPE IN 'fancy' The data below

Library : fpp ; R PROGRAMMING You can find the data set file in R UNDER THE FPP PACKAGE TYPE IN 'fancy'

The data below (data set fancy) concern the monthly sales figures of a shop which opened in January 1987 and sells gifts, souvenirs, and novelties. The shop is situated on the wharf at a beach resort town in Queensland, Australia. The sales volume varies with the seasonal population of tourists. There is a large influx of visitors to the town at Christmas and for the local surfing festival, held every March since 1988. Over time, the shop has expanded its premises, range of products, and staff.


	1987	1988	1989	1990	1991	1992	1993

Jan	1664.81	2499.81	4717.02	5921.10	4826.64	7615.03	10243.24
Feb	2397.53	5198.24	5702.63	5814.58	6470.23	9849.69	11266.88
Mar	2840.71	7225.14	9957.58	12421.25	9638.77	14558.40	21826.84
Apr	3547.29	4806.03	5304.78	6369.77	8821.17	11587.33	17357.33
May	3752.96	5900.88	6492.43	7609.12	8722.37	9332.56	15997.79
Jun	3714.74	4951.34	6630.80	7224.75	10209.48	13082.09	18601.53
Jul	4349.61	6179.12	7349.62	8121.22	11276.55	16732.78	26155.15
Aug	3566.34	4752.15	8176.62	7979.25	12552.22	19888.61	28586.52
Sep	5021.82	5496.43	8573.17	8093.06	11637.39	23933.38	30505.41
Oct	6423.48	5835.10	9690.50	8476.70	13606.89	25391.35	30821.33
Nov	7600.60	12600.08	15151.84	17914.66	21822.11	36024.80	46634.38
Dec	19756.21	28541.72	34061.01	30114.41	45060.69	80721.71	104660.67

a).Produce a time plot of the data and describe the patterns in the graph. Identify any unusual or unexpected fluctuations in the time series. Explain why it is necessary to take logarithms of these data before fitting a model.

b).Use R to fit a regression model to the logarithms of these sales data with a linear trend, seasonal dummies and a surfing festival dummy variable.

c).Plot the residuals against time and against the fitted values. Do these plots reveal any problems with the model?

d).Draw boxplots of the residuals for each month. Does this reveal any problems with the model?

e).What does the Durbin-Watson statistic tell you about your model?

f).Regardless of your answers to the above questions, use your regression model to predict the monthly sales for 1994, 1995, and 1996. Produce prediction intervals for each of your forecasts.

g).Do you need to transform your predictions and intervals to obtain predictions and intervals for the raw data?

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