Statistical Analysis on seasonal index, production, base year production, Plot the original data and Decentralized data

The quarterly production of pine lumber, in millions of board feet, by Northwest lumber since 1998 is:

Productions in different quarters of several years

Year	Quarter	Production	Year	Production	Sales	Year	Quarter	Production
1998	Winter	90	2001	Winter	201	2004	Winter	265
	Spring	85		Spring	142		Spring	185
	Summer	56		Summer	110		Summer	142
	Fall	102		Fall	274		Fall	333
1999	Winter	115	2002	Winter	251	2005	Winter	282
	Spring	89		Spring	165		Spring	175
	Summer	61		Summer	125		Summer	157
	Fall	110		Fall	305		Fall	350
2000	Winter	165	2003	Winter	241	2006	Winter	290
	Spring	110		Spring	158		Spring	201
	Summer	98		Summer	132		Summer	187
	Fall	248		Fall	299		Fall	400

Note: Add last three digits of your ID with number of Productions

i)                    Develop a seasonal index for each quarter and interpret.

ii)                  Project the production for 2007 and also find the base year production.

iii)                Plot the original data and Decentralized data and interpret.

Computations needed for specific seasonal indexes 

Year	Quarter(Q)	Production + ID(047)	4Q total	4Q moving average	Centered moving average	Specific seasonal
1998	winter	137
	spring	132	521	130.25
	summer	103	546	136.5	133.375	0.772258669
	Fall	149	550	137.5	137	1.087591241
1999	winter	162	555	138.75	138.125	1.172850679
	spring	136	563	140.75	139.75	0.973166369
	summer	108	613	153.25	147	0.734693878
	Fall	157	634	158.5	155.875	1.007217322
2000	winter	212	671	167.75	163.125	1.299616858
	spring	157	809	202.25	185	0.848648649
	summer	145	845	211.25	206.75	0.701330109
	Fall	295	877	219.25	215.25	1.370499419
2001	winter	248	889	222.25	220.75	1.123442809
	spring	189	915	228.75	225.5	0.838137472
	summer	157	965	241.25	235	0.668085106
	Fall	321	988	247	244.125	1.314900154
2002	winter	298	1003	250.75	248.875	1.197388247
	spring	212	1034	258.5	254.625	0.832596956
	summer	172	1024	256	257.25	0.668610301
	Fall	352	1017	254.25	255.125	1.379715826
2003	winter	288	1024	256	255.125	1.128858403
	spring	205	1018	254.5	255.25	0.803134182
	summer	179	1042	260.5	257.5	0.695145631
	Fall	346	1069	267.25	263.875	1.311226907
2004	winter	312	1079	269.75	268.5	1.162011173
	spring	232	1113	278.25	274	0.846715328
	summer	189	1130	282.5	280.375	0.674097191
	Fall	380	1120	280	281.25	1.351111111
2005	winter	329	1135	283.75	281.875	1.167184035
	spring	222	1152	288	285.875	0.776563183
	summer	204	1160	290	289	0.705882353
	Fall	397	1186	296.5	293.25	1.353793691
2006	winter	337	1216	304	300.25	1.122398002
	spring	248	1266	316.5	310.25	0.799355359
	summer	234
	Fall	447

Seasonal index for quarter (winter, spring, summer& fall)

Year	Winter	Spring	Summer	Fall
1998			0.772259	1.087591241
1999	1.1728507	0.973166369	0.734694	1.007217322
2000	1.2996169	0.848648649	0.70133	1.370499419
2001	1.1234428	0.838137472	0.668085	1.314900154
2002	1.1973882	0.832596956	0.66861	1.379715826
2003	1.1288584	0.803134182	0.695146	1.311226907
2004	1.1620112	0.846715328	0.674097	1.351111111
2005	1.167184	0.776563183	0.705882	1.353793691
2006	1.122398	0.799355359
total	9.3737502	6.718317498	5.620103	10.17605567
Seasonal mean	1.1717188	0.839789687	0.702513	1.272006959	total of seasonal mean=	3.986028327
Correction Factor	1.0035052
Adjusted	1.1758258	0.842733286	0.704975	1.276465549	total of adjusted     =	4
Seasonal index	117.5	84.2	70.4	127.6

 Interpretation 

·         Production in winter is 17.5% more than the annual average production.

·         Production in spring is 15.8% less than the annual average production.

·         Production in summer is 29.6% lower than the annual average production. 

·         Production in fall is 27.6 % greater than the annual average production.

 

Year	Quarter(Q)	Production	SI	Time (t)	Decentralized  Production Y)
1998	winter	137	1.175	1	116.5957447
	spring	132	0.842	2	156.7695962
	summer	103	0.704	3	146.3068182
	Fall	149	1.276	4	116.7711599
1999	winter	162	1.175	5	137.8723404
	spring	136	0.842	6	161.52019
	summer	108	0.704	7	153.4090909
	Fall	157	1.276	8	123.0407524
2000	winter	212	1.175	9	180.4255319
	spring	157	0.842	10	186.4608076
	summer	145	0.704	11	205.9659091
	Fall	295	1.276	12	231.1912226
2001	winter	248	1.175	13	211.0638298
	spring	189	0.842	14	224.4655582
	summer	157	0.704	15	223.0113636
	Fall	321	1.276	16	251.5673981
2002	winter	298	1.175	17	253.6170213
	spring	212	0.842	18	251.7814727
	summer	172	0.704	19	244.3181818
	Fall	352	1.276	20	275.862069
2003	winter	288	1.175	21	245.106383
	spring	205	0.842	22	243.4679335
	summer	179	0.704	23	254.2613636
	Fall	346	1.276	24	271.1598746
2004	winter	312	1.175	25	265.5319149
	spring	232	0.842	26	275.5344418
	summer	189	0.704	27	268.4659091
	Fall	380	1.276	28	297.8056426
2005	winter	329	1.175	29	280
	spring	222	0.842	30	263.6579572
	summer	204	0.704	31	289.7727273
	Fall	397	1.276	32	311.1285266
2006	winter	337	1.175	33	286.8085106
	spring	248	0.842	34	294.5368171
	summer	234	0.704	35	332.3863636
	Fall	447	1.276	36	350.3134796

 

So the production equation Y'= 129.42 – 5.5896 * t

Projection of the production for 2007 

Plot of original and deseasonalized Production

 

 Interpretation 

The graph of original data showing a constant fluctuation which cannot provide any meaningful information or idea about improvement or diss-improvement of production but the graph of De-seasonal data provides us a meaningful clarification about production whether it is improving or demolishing.