March 21, 2013

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.






 







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