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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 18 May 2014 06:18:17 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/18/t1400408317rmt18d5jwaq90nh.htm/, Retrieved Wed, 15 May 2024 13:52:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234915, Retrieved Wed, 15 May 2024 13:52:42 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

171

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2014-05-18 10:18:17] [9093db98244a413fd54e2b1bc98c9896] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234915&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234915&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.862126953202547
beta	0
gamma	0.898783821824626

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.862126953202547 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.898783821824626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234915&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.862126953202547[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.898783821824626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234915&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.862126953202547
beta	0
gamma	0.898783821824626

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	76.23	75.6774679487179	0.552532051282071
14	76.97	76.4359856410514	0.534014358948582
15	78.4	77.8718720650464	0.528127934953574
16	78.6	78.4547669775907	0.145233022409329
17	80.08	79.9913078657864	0.088692134213602
18	81.12	81.1870199969773	-0.0670199969772511
19	80.31	78.3193218362612	1.99067816373882
20	84.59	77.2860373881204	7.30396261187958
21	81.34	87.4005620060871	-6.06056200608707
22	80.95	84.0098364008324	-3.05983640083237
23	80.48	79.3061172190328	1.17388278096725
24	75.26	81.0465681228199	-5.7865681228199
25	76.32	77.6763620647284	-1.35636206472839
26	78.92	76.7868760122571	2.13312398774286
27	80.47	79.6006685140965	0.869331485903487
28	83.14	80.430276608193	2.70972339180697
29	85.42	84.1707273276769	1.24927267232312
30	81.53	86.3477116763071	-4.81771167630713
31	87.31	79.6393001447082	7.67069985529176
32	86.01	84.1613274135386	1.8486725864614
33	85.1	87.9165934470891	-2.81659344708913
34	79.91	87.6944246792682	-7.78442467926818
35	78.6	79.4421448840644	-0.842144884064382
36	78.6	78.581998399368	0.0180016006320045
37	79.37	80.7650509091252	-1.39505090912515
38	82.89	80.2746205168345	2.61537948316551
39	84.43	83.3475717595741	1.08242824042591
40	85.32	84.5889541112313	0.731045888768733
41	87.71	86.4425573980308	1.26744260196921
42	84.68	87.8833975783877	-3.20339757838769
43	80.62	84.1142695200621	-3.49426952006212
44	84.79	78.289221411434	6.50077858856605
45	85.49	85.4770826839712	0.0129173160287621
46	81.68	87.0787073812021	-5.39870738120212
47	77.69	81.7434926428453	-4.05349264284534
48	78.31	78.2213443862747	0.0886556137253365
49	79.18	80.2902068938349	-1.1102068938349
50	80.91	80.542312974312	0.367687025688042
51	83.91	81.4875076168551	2.42249238314494
52	86.3	83.840652764255	2.45934723574499
53	89.76	87.2507404677358	2.50925953226424
54	85.11	89.2081666353654	-4.09816663536543
55	83.81	84.6315897682647	-0.821589768264673
56	85.36	82.3492979214204	3.0107020785796
57	85.89	85.7243069580381	0.16569304196193
58	82.59	86.7870456712094	-4.19704567120944
59	80.87	82.6545122876124	-1.78451228761236
60	80.27	81.6018001440289	-1.33180014402889
61	81.36	82.2974887361457	-0.937488736145667
62	84.81	82.8816375488712	1.92836245112883
63	90.3	85.426960042531	4.87303995746903
64	95.43	89.8973552858414	5.53264471415864
65	97.59	95.9632006158228	1.62679938417722
66	97.8	96.3410546464248	1.45894535357522
67	99.48	96.9614408686346	2.51855913136538
68	97.52	98.0336716019363	-0.513671601936267
69	104.39	98.0176750837504	6.37232491624957
70	97.74	103.890696289595	-6.15069628959469
71	91.37	98.372824516802	-7.00282451680199
72	92.42	92.8773639625569	-0.457363962556869
73	96.9	94.3757898618255	2.5242101381745
74	101.58	98.2994933086039	3.28050669139607
75	105.46	102.375434531891	3.08456546810859
76	110.06	105.385674657215	4.67432534278484
77	107.9	110.227534931389	-2.32753493138888
78	102.87	107.175450620073	-4.30545062007302
79	96.28	102.957500992323	-6.67750099232283
80	98.59	95.7258122678704	2.86418773212965
81	103.22	99.4752586824527	3.74474131754727
82	98.6	101.531140703715	-2.93114070371504
83	91.79	98.6833404987097	-6.89334049870973
84	93.83	94.0933698668009	-0.2633698668009
85	95.17	96.1285141948011	-0.958514194801083
86	95.19	97.1433859281769	-1.95338592817693
87	99.44	96.6827665969293	2.75723340307069
88	109.18	99.6078048921155	9.5721951078845
89	109.15	107.804593734993	1.34540626500704
90	109.72	107.673951543865	2.04604845613498
91	108.41	108.637860573288	-0.227860573287799
92	102.96	108.14896828588	-5.18896828588034
93	107.64	105.06468833448	2.57531166551988
94	97.28	105.285111157774	-8.00511115777398
95	97.25	97.5719161370826	-0.321916137082553
96	91.84	99.4689206928648	-7.62892069286481
97	94.12	95.0678841892562	-0.947884189256243
98	97.86	95.9686377578691	1.89136224213087
99	98.83	99.4064102799464	-0.576410279946401
100	102.29	100.301921363829	1.98807863617118
101	104.49	100.940791234467	3.5492087655326
102	102.11	102.796928802408	-0.686928802407991
103	102.14	101.122886070279	1.01711392972145
104	101.28	101.092548995286	0.187451004713566
105	101.21	103.605559565392	-2.39555956539181
106	94.2	98.2293548078236	-4.02935480782362
107	88.47	94.8958531475299	-6.42585314752991
108	88.08	90.625019228295	-2.54501922829502
109	88.02	91.4348523132722	-3.41485231327225
110	92.95	90.5606000902692	2.38939990973083
111	97.05	94.1219427161459	2.9280572838541
112	101.44	98.3565362448529	3.08346375514709
113	100.34	100.133219373867	0.206780626133494
114	99.98	98.5828255877399	1.39717441226006
115	94.17	98.9167060864467	-4.74670608644665
116	94.54	93.8144141987285	0.725585801271507
117	95.12	96.4712836124516	-1.35128361245162
118	98.04	91.7929205571988	6.24707944280119
119	93.72	97.0220404127214	-3.30204041272135
120	93.83	95.9252350746169	-2.09523507461695
121	93.03	97.0150511697732	-3.98505116977321
122	95.81	96.3684668419152	-0.558466841915191
123	99.1	97.4551234656697	1.64487653433028
124	100.12	100.602709953426	-0.482709953425982
125	100.67	98.948425604597	1.72157439540301
126	103.87	98.8514876487887	5.01851235121126
127	102.39	101.54608341492	0.843916585079697
128	107.21	101.941733833481	5.26826616651908
129	105.71	108.25760879309	-2.54760879308974
130	99.79	103.489435993637	-3.69943599363692
131	96.12	98.9600883562557	-2.84008835625565
132	96.17	98.4110893181526	-2.2410893181526
133	97.23	99.1409781870275	-1.91097818702754
134	98.08	100.707123776295	-2.62712377629528
135	99.84	100.283369545343	-0.443369545342577
136	99.72	101.366976404493	-1.64697640449286
137	99.92	98.9820972163416	0.937902783658402
138	102.7	98.6180850099606	4.08191499003942
139	102.06	99.9879071217097	2.07209287829029
140	102.36	101.990658260201	0.369341739799253
141	102.43	103.11451033694	-0.684510336940079
142	100.6	99.8098327363334	0.790167263666547
143	98.4	99.2575817717242	-0.857581771724156
144	98.61	100.491981896143	-1.88198189614324
145	103.03	101.572373684877	1.45762631512262
146	104.7	105.953940635216	-1.25394063521614
147	107.45	106.984651198264	0.465348801736354
148	109.67	108.702540005585	0.96745999441508
149	110.54	108.891950128847	1.64804987115255
150	112.05	109.529774772912	2.52022522708829
151	113.19	109.304168782554	3.8858312174459
152	114.2	112.659591004856	1.54040899514366
153	112.56	114.662460417426	-2.1024604174258
154	107.36	110.318069027321	-2.95806902732072
155	103.93	106.330176658976	-2.40017665897579
156	103.83	106.107722473118	-2.27772247311799
157	104.74	107.260773427782	-2.5207734277818
158	107.5	107.876442602454	-0.376442602453551
159	109.53	109.876718889286	-0.346718889285569
160	109.42	110.956722899225	-1.53672289922483
161	108.6	109.071546833985	-0.471546833985443
162	110.72	107.990088310144	2.72991168985649
163	105.1	108.114481921473	-3.01448192147261
164	105.19	105.230318020296	-0.0403180202959561
165	102.55	105.418982742454	-2.86898274245421
166	101.25	100.307726433293	0.942273566706987
167	101.56	99.7515574841484	1.8084425158516
168	101.62	103.172641610306	-1.55264161030561
169	101.7	104.920685916314	-3.22068591631373
170	102.94	105.198662994033	-2.25866299403317
171	104.37	105.579909654405	-1.20990965440545
172	106.93	105.768270647002	1.16172935299798
173	107.82	106.34149755608	1.47850244391988
174	110.83	107.337947616811	3.49205238318868
175	106.86	107.407569127243	-0.547569127242781
176	109.46	107.018749869608	2.44125013039208
177	108.8	108.996318724814	-0.196318724814248
178	108.69	106.661521605077	2.02847839492328
179	107.77	107.149133094248	0.62086690575201
180	108.64	109.129877240362	-0.489877240362475
181	108.5	111.587458533657	-3.08745853365654
182	113.84	112.099506546852	1.74049345314802
183	114.59	116.058493253797	-1.46849325379678
184	116.27	116.317811269834	-0.0478112698336872
185	113.63	115.887514515106	-2.25751451510648
186	112.29	113.912558867934	-1.6225588679342
187	110.31	109.072154087048	1.2378459129518
188	108.47	110.592957954053	-2.12295795405279
189	110.67	108.308757573622	2.36124242637767
190	109.1	108.4545954085	0.645404591500181
191	107.02	107.575393202972	-0.555393202971857
192	108.12	108.404410541274	-0.28441054127353
193	106.69	110.717242969079	-4.02724296907917
194	109.87	111.017347953235	-1.14734795323491
195	110.82	112.08899732727	-1.26899732726986
196	114.14	112.696354319529	1.44364568047129
197	113.31	113.278060653193	0.0319393468072207
198	115.16	113.355587362967	1.80441263703278
199	111.06	111.824122906866	-0.764122906865907
200	111.13	111.202511186396	-0.0725111863962411
201	115.96	111.241729659874	4.71827034012581
202	117.57	113.207001486134	4.36299851386639
203	114.69	115.38403666428	-0.694036664280475
204	119.42	116.127105384498	3.29289461550179
205	118.4	121.060224459733	-2.6602244597326
206	123.32	122.895743961	0.424256039000113
207	123.39	125.307240941593	-1.91724094159299
208	127.04	125.691875111347	1.34812488865256
209	129.35	126.016294480092	3.33370551990809
210	127.12	129.160004259356	-2.04000425935649
211	122.1	123.995876425803	-1.89587642580254
212	120.22	122.484252677666	-2.26425267766574
213	121.53	121.227576108533	0.3024238914672
214	119.01	119.341803093322	-0.331803093321938
215	114.27	116.844665257485	-2.57466525748532
216	114.46	116.460446183739	-2.00044618373926

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 76.23 & 75.6774679487179 & 0.552532051282071 \tabularnewline
14 & 76.97 & 76.4359856410514 & 0.534014358948582 \tabularnewline
15 & 78.4 & 77.8718720650464 & 0.528127934953574 \tabularnewline
16 & 78.6 & 78.4547669775907 & 0.145233022409329 \tabularnewline
17 & 80.08 & 79.9913078657864 & 0.088692134213602 \tabularnewline
18 & 81.12 & 81.1870199969773 & -0.0670199969772511 \tabularnewline
19 & 80.31 & 78.3193218362612 & 1.99067816373882 \tabularnewline
20 & 84.59 & 77.2860373881204 & 7.30396261187958 \tabularnewline
21 & 81.34 & 87.4005620060871 & -6.06056200608707 \tabularnewline
22 & 80.95 & 84.0098364008324 & -3.05983640083237 \tabularnewline
23 & 80.48 & 79.3061172190328 & 1.17388278096725 \tabularnewline
24 & 75.26 & 81.0465681228199 & -5.7865681228199 \tabularnewline
25 & 76.32 & 77.6763620647284 & -1.35636206472839 \tabularnewline
26 & 78.92 & 76.7868760122571 & 2.13312398774286 \tabularnewline
27 & 80.47 & 79.6006685140965 & 0.869331485903487 \tabularnewline
28 & 83.14 & 80.430276608193 & 2.70972339180697 \tabularnewline
29 & 85.42 & 84.1707273276769 & 1.24927267232312 \tabularnewline
30 & 81.53 & 86.3477116763071 & -4.81771167630713 \tabularnewline
31 & 87.31 & 79.6393001447082 & 7.67069985529176 \tabularnewline
32 & 86.01 & 84.1613274135386 & 1.8486725864614 \tabularnewline
33 & 85.1 & 87.9165934470891 & -2.81659344708913 \tabularnewline
34 & 79.91 & 87.6944246792682 & -7.78442467926818 \tabularnewline
35 & 78.6 & 79.4421448840644 & -0.842144884064382 \tabularnewline
36 & 78.6 & 78.581998399368 & 0.0180016006320045 \tabularnewline
37 & 79.37 & 80.7650509091252 & -1.39505090912515 \tabularnewline
38 & 82.89 & 80.2746205168345 & 2.61537948316551 \tabularnewline
39 & 84.43 & 83.3475717595741 & 1.08242824042591 \tabularnewline
40 & 85.32 & 84.5889541112313 & 0.731045888768733 \tabularnewline
41 & 87.71 & 86.4425573980308 & 1.26744260196921 \tabularnewline
42 & 84.68 & 87.8833975783877 & -3.20339757838769 \tabularnewline
43 & 80.62 & 84.1142695200621 & -3.49426952006212 \tabularnewline
44 & 84.79 & 78.289221411434 & 6.50077858856605 \tabularnewline
45 & 85.49 & 85.4770826839712 & 0.0129173160287621 \tabularnewline
46 & 81.68 & 87.0787073812021 & -5.39870738120212 \tabularnewline
47 & 77.69 & 81.7434926428453 & -4.05349264284534 \tabularnewline
48 & 78.31 & 78.2213443862747 & 0.0886556137253365 \tabularnewline
49 & 79.18 & 80.2902068938349 & -1.1102068938349 \tabularnewline
50 & 80.91 & 80.542312974312 & 0.367687025688042 \tabularnewline
51 & 83.91 & 81.4875076168551 & 2.42249238314494 \tabularnewline
52 & 86.3 & 83.840652764255 & 2.45934723574499 \tabularnewline
53 & 89.76 & 87.2507404677358 & 2.50925953226424 \tabularnewline
54 & 85.11 & 89.2081666353654 & -4.09816663536543 \tabularnewline
55 & 83.81 & 84.6315897682647 & -0.821589768264673 \tabularnewline
56 & 85.36 & 82.3492979214204 & 3.0107020785796 \tabularnewline
57 & 85.89 & 85.7243069580381 & 0.16569304196193 \tabularnewline
58 & 82.59 & 86.7870456712094 & -4.19704567120944 \tabularnewline
59 & 80.87 & 82.6545122876124 & -1.78451228761236 \tabularnewline
60 & 80.27 & 81.6018001440289 & -1.33180014402889 \tabularnewline
61 & 81.36 & 82.2974887361457 & -0.937488736145667 \tabularnewline
62 & 84.81 & 82.8816375488712 & 1.92836245112883 \tabularnewline
63 & 90.3 & 85.426960042531 & 4.87303995746903 \tabularnewline
64 & 95.43 & 89.8973552858414 & 5.53264471415864 \tabularnewline
65 & 97.59 & 95.9632006158228 & 1.62679938417722 \tabularnewline
66 & 97.8 & 96.3410546464248 & 1.45894535357522 \tabularnewline
67 & 99.48 & 96.9614408686346 & 2.51855913136538 \tabularnewline
68 & 97.52 & 98.0336716019363 & -0.513671601936267 \tabularnewline
69 & 104.39 & 98.0176750837504 & 6.37232491624957 \tabularnewline
70 & 97.74 & 103.890696289595 & -6.15069628959469 \tabularnewline
71 & 91.37 & 98.372824516802 & -7.00282451680199 \tabularnewline
72 & 92.42 & 92.8773639625569 & -0.457363962556869 \tabularnewline
73 & 96.9 & 94.3757898618255 & 2.5242101381745 \tabularnewline
74 & 101.58 & 98.2994933086039 & 3.28050669139607 \tabularnewline
75 & 105.46 & 102.375434531891 & 3.08456546810859 \tabularnewline
76 & 110.06 & 105.385674657215 & 4.67432534278484 \tabularnewline
77 & 107.9 & 110.227534931389 & -2.32753493138888 \tabularnewline
78 & 102.87 & 107.175450620073 & -4.30545062007302 \tabularnewline
79 & 96.28 & 102.957500992323 & -6.67750099232283 \tabularnewline
80 & 98.59 & 95.7258122678704 & 2.86418773212965 \tabularnewline
81 & 103.22 & 99.4752586824527 & 3.74474131754727 \tabularnewline
82 & 98.6 & 101.531140703715 & -2.93114070371504 \tabularnewline
83 & 91.79 & 98.6833404987097 & -6.89334049870973 \tabularnewline
84 & 93.83 & 94.0933698668009 & -0.2633698668009 \tabularnewline
85 & 95.17 & 96.1285141948011 & -0.958514194801083 \tabularnewline
86 & 95.19 & 97.1433859281769 & -1.95338592817693 \tabularnewline
87 & 99.44 & 96.6827665969293 & 2.75723340307069 \tabularnewline
88 & 109.18 & 99.6078048921155 & 9.5721951078845 \tabularnewline
89 & 109.15 & 107.804593734993 & 1.34540626500704 \tabularnewline
90 & 109.72 & 107.673951543865 & 2.04604845613498 \tabularnewline
91 & 108.41 & 108.637860573288 & -0.227860573287799 \tabularnewline
92 & 102.96 & 108.14896828588 & -5.18896828588034 \tabularnewline
93 & 107.64 & 105.06468833448 & 2.57531166551988 \tabularnewline
94 & 97.28 & 105.285111157774 & -8.00511115777398 \tabularnewline
95 & 97.25 & 97.5719161370826 & -0.321916137082553 \tabularnewline
96 & 91.84 & 99.4689206928648 & -7.62892069286481 \tabularnewline
97 & 94.12 & 95.0678841892562 & -0.947884189256243 \tabularnewline
98 & 97.86 & 95.9686377578691 & 1.89136224213087 \tabularnewline
99 & 98.83 & 99.4064102799464 & -0.576410279946401 \tabularnewline
100 & 102.29 & 100.301921363829 & 1.98807863617118 \tabularnewline
101 & 104.49 & 100.940791234467 & 3.5492087655326 \tabularnewline
102 & 102.11 & 102.796928802408 & -0.686928802407991 \tabularnewline
103 & 102.14 & 101.122886070279 & 1.01711392972145 \tabularnewline
104 & 101.28 & 101.092548995286 & 0.187451004713566 \tabularnewline
105 & 101.21 & 103.605559565392 & -2.39555956539181 \tabularnewline
106 & 94.2 & 98.2293548078236 & -4.02935480782362 \tabularnewline
107 & 88.47 & 94.8958531475299 & -6.42585314752991 \tabularnewline
108 & 88.08 & 90.625019228295 & -2.54501922829502 \tabularnewline
109 & 88.02 & 91.4348523132722 & -3.41485231327225 \tabularnewline
110 & 92.95 & 90.5606000902692 & 2.38939990973083 \tabularnewline
111 & 97.05 & 94.1219427161459 & 2.9280572838541 \tabularnewline
112 & 101.44 & 98.3565362448529 & 3.08346375514709 \tabularnewline
113 & 100.34 & 100.133219373867 & 0.206780626133494 \tabularnewline
114 & 99.98 & 98.5828255877399 & 1.39717441226006 \tabularnewline
115 & 94.17 & 98.9167060864467 & -4.74670608644665 \tabularnewline
116 & 94.54 & 93.8144141987285 & 0.725585801271507 \tabularnewline
117 & 95.12 & 96.4712836124516 & -1.35128361245162 \tabularnewline
118 & 98.04 & 91.7929205571988 & 6.24707944280119 \tabularnewline
119 & 93.72 & 97.0220404127214 & -3.30204041272135 \tabularnewline
120 & 93.83 & 95.9252350746169 & -2.09523507461695 \tabularnewline
121 & 93.03 & 97.0150511697732 & -3.98505116977321 \tabularnewline
122 & 95.81 & 96.3684668419152 & -0.558466841915191 \tabularnewline
123 & 99.1 & 97.4551234656697 & 1.64487653433028 \tabularnewline
124 & 100.12 & 100.602709953426 & -0.482709953425982 \tabularnewline
125 & 100.67 & 98.948425604597 & 1.72157439540301 \tabularnewline
126 & 103.87 & 98.8514876487887 & 5.01851235121126 \tabularnewline
127 & 102.39 & 101.54608341492 & 0.843916585079697 \tabularnewline
128 & 107.21 & 101.941733833481 & 5.26826616651908 \tabularnewline
129 & 105.71 & 108.25760879309 & -2.54760879308974 \tabularnewline
130 & 99.79 & 103.489435993637 & -3.69943599363692 \tabularnewline
131 & 96.12 & 98.9600883562557 & -2.84008835625565 \tabularnewline
132 & 96.17 & 98.4110893181526 & -2.2410893181526 \tabularnewline
133 & 97.23 & 99.1409781870275 & -1.91097818702754 \tabularnewline
134 & 98.08 & 100.707123776295 & -2.62712377629528 \tabularnewline
135 & 99.84 & 100.283369545343 & -0.443369545342577 \tabularnewline
136 & 99.72 & 101.366976404493 & -1.64697640449286 \tabularnewline
137 & 99.92 & 98.9820972163416 & 0.937902783658402 \tabularnewline
138 & 102.7 & 98.6180850099606 & 4.08191499003942 \tabularnewline
139 & 102.06 & 99.9879071217097 & 2.07209287829029 \tabularnewline
140 & 102.36 & 101.990658260201 & 0.369341739799253 \tabularnewline
141 & 102.43 & 103.11451033694 & -0.684510336940079 \tabularnewline
142 & 100.6 & 99.8098327363334 & 0.790167263666547 \tabularnewline
143 & 98.4 & 99.2575817717242 & -0.857581771724156 \tabularnewline
144 & 98.61 & 100.491981896143 & -1.88198189614324 \tabularnewline
145 & 103.03 & 101.572373684877 & 1.45762631512262 \tabularnewline
146 & 104.7 & 105.953940635216 & -1.25394063521614 \tabularnewline
147 & 107.45 & 106.984651198264 & 0.465348801736354 \tabularnewline
148 & 109.67 & 108.702540005585 & 0.96745999441508 \tabularnewline
149 & 110.54 & 108.891950128847 & 1.64804987115255 \tabularnewline
150 & 112.05 & 109.529774772912 & 2.52022522708829 \tabularnewline
151 & 113.19 & 109.304168782554 & 3.8858312174459 \tabularnewline
152 & 114.2 & 112.659591004856 & 1.54040899514366 \tabularnewline
153 & 112.56 & 114.662460417426 & -2.1024604174258 \tabularnewline
154 & 107.36 & 110.318069027321 & -2.95806902732072 \tabularnewline
155 & 103.93 & 106.330176658976 & -2.40017665897579 \tabularnewline
156 & 103.83 & 106.107722473118 & -2.27772247311799 \tabularnewline
157 & 104.74 & 107.260773427782 & -2.5207734277818 \tabularnewline
158 & 107.5 & 107.876442602454 & -0.376442602453551 \tabularnewline
159 & 109.53 & 109.876718889286 & -0.346718889285569 \tabularnewline
160 & 109.42 & 110.956722899225 & -1.53672289922483 \tabularnewline
161 & 108.6 & 109.071546833985 & -0.471546833985443 \tabularnewline
162 & 110.72 & 107.990088310144 & 2.72991168985649 \tabularnewline
163 & 105.1 & 108.114481921473 & -3.01448192147261 \tabularnewline
164 & 105.19 & 105.230318020296 & -0.0403180202959561 \tabularnewline
165 & 102.55 & 105.418982742454 & -2.86898274245421 \tabularnewline
166 & 101.25 & 100.307726433293 & 0.942273566706987 \tabularnewline
167 & 101.56 & 99.7515574841484 & 1.8084425158516 \tabularnewline
168 & 101.62 & 103.172641610306 & -1.55264161030561 \tabularnewline
169 & 101.7 & 104.920685916314 & -3.22068591631373 \tabularnewline
170 & 102.94 & 105.198662994033 & -2.25866299403317 \tabularnewline
171 & 104.37 & 105.579909654405 & -1.20990965440545 \tabularnewline
172 & 106.93 & 105.768270647002 & 1.16172935299798 \tabularnewline
173 & 107.82 & 106.34149755608 & 1.47850244391988 \tabularnewline
174 & 110.83 & 107.337947616811 & 3.49205238318868 \tabularnewline
175 & 106.86 & 107.407569127243 & -0.547569127242781 \tabularnewline
176 & 109.46 & 107.018749869608 & 2.44125013039208 \tabularnewline
177 & 108.8 & 108.996318724814 & -0.196318724814248 \tabularnewline
178 & 108.69 & 106.661521605077 & 2.02847839492328 \tabularnewline
179 & 107.77 & 107.149133094248 & 0.62086690575201 \tabularnewline
180 & 108.64 & 109.129877240362 & -0.489877240362475 \tabularnewline
181 & 108.5 & 111.587458533657 & -3.08745853365654 \tabularnewline
182 & 113.84 & 112.099506546852 & 1.74049345314802 \tabularnewline
183 & 114.59 & 116.058493253797 & -1.46849325379678 \tabularnewline
184 & 116.27 & 116.317811269834 & -0.0478112698336872 \tabularnewline
185 & 113.63 & 115.887514515106 & -2.25751451510648 \tabularnewline
186 & 112.29 & 113.912558867934 & -1.6225588679342 \tabularnewline
187 & 110.31 & 109.072154087048 & 1.2378459129518 \tabularnewline
188 & 108.47 & 110.592957954053 & -2.12295795405279 \tabularnewline
189 & 110.67 & 108.308757573622 & 2.36124242637767 \tabularnewline
190 & 109.1 & 108.4545954085 & 0.645404591500181 \tabularnewline
191 & 107.02 & 107.575393202972 & -0.555393202971857 \tabularnewline
192 & 108.12 & 108.404410541274 & -0.28441054127353 \tabularnewline
193 & 106.69 & 110.717242969079 & -4.02724296907917 \tabularnewline
194 & 109.87 & 111.017347953235 & -1.14734795323491 \tabularnewline
195 & 110.82 & 112.08899732727 & -1.26899732726986 \tabularnewline
196 & 114.14 & 112.696354319529 & 1.44364568047129 \tabularnewline
197 & 113.31 & 113.278060653193 & 0.0319393468072207 \tabularnewline
198 & 115.16 & 113.355587362967 & 1.80441263703278 \tabularnewline
199 & 111.06 & 111.824122906866 & -0.764122906865907 \tabularnewline
200 & 111.13 & 111.202511186396 & -0.0725111863962411 \tabularnewline
201 & 115.96 & 111.241729659874 & 4.71827034012581 \tabularnewline
202 & 117.57 & 113.207001486134 & 4.36299851386639 \tabularnewline
203 & 114.69 & 115.38403666428 & -0.694036664280475 \tabularnewline
204 & 119.42 & 116.127105384498 & 3.29289461550179 \tabularnewline
205 & 118.4 & 121.060224459733 & -2.6602244597326 \tabularnewline
206 & 123.32 & 122.895743961 & 0.424256039000113 \tabularnewline
207 & 123.39 & 125.307240941593 & -1.91724094159299 \tabularnewline
208 & 127.04 & 125.691875111347 & 1.34812488865256 \tabularnewline
209 & 129.35 & 126.016294480092 & 3.33370551990809 \tabularnewline
210 & 127.12 & 129.160004259356 & -2.04000425935649 \tabularnewline
211 & 122.1 & 123.995876425803 & -1.89587642580254 \tabularnewline
212 & 120.22 & 122.484252677666 & -2.26425267766574 \tabularnewline
213 & 121.53 & 121.227576108533 & 0.3024238914672 \tabularnewline
214 & 119.01 & 119.341803093322 & -0.331803093321938 \tabularnewline
215 & 114.27 & 116.844665257485 & -2.57466525748532 \tabularnewline
216 & 114.46 & 116.460446183739 & -2.00044618373926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234915&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]76.23[/C][C]75.6774679487179[/C][C]0.552532051282071[/C][/ROW]
[ROW][C]14[/C][C]76.97[/C][C]76.4359856410514[/C][C]0.534014358948582[/C][/ROW]
[ROW][C]15[/C][C]78.4[/C][C]77.8718720650464[/C][C]0.528127934953574[/C][/ROW]
[ROW][C]16[/C][C]78.6[/C][C]78.4547669775907[/C][C]0.145233022409329[/C][/ROW]
[ROW][C]17[/C][C]80.08[/C][C]79.9913078657864[/C][C]0.088692134213602[/C][/ROW]
[ROW][C]18[/C][C]81.12[/C][C]81.1870199969773[/C][C]-0.0670199969772511[/C][/ROW]
[ROW][C]19[/C][C]80.31[/C][C]78.3193218362612[/C][C]1.99067816373882[/C][/ROW]
[ROW][C]20[/C][C]84.59[/C][C]77.2860373881204[/C][C]7.30396261187958[/C][/ROW]
[ROW][C]21[/C][C]81.34[/C][C]87.4005620060871[/C][C]-6.06056200608707[/C][/ROW]
[ROW][C]22[/C][C]80.95[/C][C]84.0098364008324[/C][C]-3.05983640083237[/C][/ROW]
[ROW][C]23[/C][C]80.48[/C][C]79.3061172190328[/C][C]1.17388278096725[/C][/ROW]
[ROW][C]24[/C][C]75.26[/C][C]81.0465681228199[/C][C]-5.7865681228199[/C][/ROW]
[ROW][C]25[/C][C]76.32[/C][C]77.6763620647284[/C][C]-1.35636206472839[/C][/ROW]
[ROW][C]26[/C][C]78.92[/C][C]76.7868760122571[/C][C]2.13312398774286[/C][/ROW]
[ROW][C]27[/C][C]80.47[/C][C]79.6006685140965[/C][C]0.869331485903487[/C][/ROW]
[ROW][C]28[/C][C]83.14[/C][C]80.430276608193[/C][C]2.70972339180697[/C][/ROW]
[ROW][C]29[/C][C]85.42[/C][C]84.1707273276769[/C][C]1.24927267232312[/C][/ROW]
[ROW][C]30[/C][C]81.53[/C][C]86.3477116763071[/C][C]-4.81771167630713[/C][/ROW]
[ROW][C]31[/C][C]87.31[/C][C]79.6393001447082[/C][C]7.67069985529176[/C][/ROW]
[ROW][C]32[/C][C]86.01[/C][C]84.1613274135386[/C][C]1.8486725864614[/C][/ROW]
[ROW][C]33[/C][C]85.1[/C][C]87.9165934470891[/C][C]-2.81659344708913[/C][/ROW]
[ROW][C]34[/C][C]79.91[/C][C]87.6944246792682[/C][C]-7.78442467926818[/C][/ROW]
[ROW][C]35[/C][C]78.6[/C][C]79.4421448840644[/C][C]-0.842144884064382[/C][/ROW]
[ROW][C]36[/C][C]78.6[/C][C]78.581998399368[/C][C]0.0180016006320045[/C][/ROW]
[ROW][C]37[/C][C]79.37[/C][C]80.7650509091252[/C][C]-1.39505090912515[/C][/ROW]
[ROW][C]38[/C][C]82.89[/C][C]80.2746205168345[/C][C]2.61537948316551[/C][/ROW]
[ROW][C]39[/C][C]84.43[/C][C]83.3475717595741[/C][C]1.08242824042591[/C][/ROW]
[ROW][C]40[/C][C]85.32[/C][C]84.5889541112313[/C][C]0.731045888768733[/C][/ROW]
[ROW][C]41[/C][C]87.71[/C][C]86.4425573980308[/C][C]1.26744260196921[/C][/ROW]
[ROW][C]42[/C][C]84.68[/C][C]87.8833975783877[/C][C]-3.20339757838769[/C][/ROW]
[ROW][C]43[/C][C]80.62[/C][C]84.1142695200621[/C][C]-3.49426952006212[/C][/ROW]
[ROW][C]44[/C][C]84.79[/C][C]78.289221411434[/C][C]6.50077858856605[/C][/ROW]
[ROW][C]45[/C][C]85.49[/C][C]85.4770826839712[/C][C]0.0129173160287621[/C][/ROW]
[ROW][C]46[/C][C]81.68[/C][C]87.0787073812021[/C][C]-5.39870738120212[/C][/ROW]
[ROW][C]47[/C][C]77.69[/C][C]81.7434926428453[/C][C]-4.05349264284534[/C][/ROW]
[ROW][C]48[/C][C]78.31[/C][C]78.2213443862747[/C][C]0.0886556137253365[/C][/ROW]
[ROW][C]49[/C][C]79.18[/C][C]80.2902068938349[/C][C]-1.1102068938349[/C][/ROW]
[ROW][C]50[/C][C]80.91[/C][C]80.542312974312[/C][C]0.367687025688042[/C][/ROW]
[ROW][C]51[/C][C]83.91[/C][C]81.4875076168551[/C][C]2.42249238314494[/C][/ROW]
[ROW][C]52[/C][C]86.3[/C][C]83.840652764255[/C][C]2.45934723574499[/C][/ROW]
[ROW][C]53[/C][C]89.76[/C][C]87.2507404677358[/C][C]2.50925953226424[/C][/ROW]
[ROW][C]54[/C][C]85.11[/C][C]89.2081666353654[/C][C]-4.09816663536543[/C][/ROW]
[ROW][C]55[/C][C]83.81[/C][C]84.6315897682647[/C][C]-0.821589768264673[/C][/ROW]
[ROW][C]56[/C][C]85.36[/C][C]82.3492979214204[/C][C]3.0107020785796[/C][/ROW]
[ROW][C]57[/C][C]85.89[/C][C]85.7243069580381[/C][C]0.16569304196193[/C][/ROW]
[ROW][C]58[/C][C]82.59[/C][C]86.7870456712094[/C][C]-4.19704567120944[/C][/ROW]
[ROW][C]59[/C][C]80.87[/C][C]82.6545122876124[/C][C]-1.78451228761236[/C][/ROW]
[ROW][C]60[/C][C]80.27[/C][C]81.6018001440289[/C][C]-1.33180014402889[/C][/ROW]
[ROW][C]61[/C][C]81.36[/C][C]82.2974887361457[/C][C]-0.937488736145667[/C][/ROW]
[ROW][C]62[/C][C]84.81[/C][C]82.8816375488712[/C][C]1.92836245112883[/C][/ROW]
[ROW][C]63[/C][C]90.3[/C][C]85.426960042531[/C][C]4.87303995746903[/C][/ROW]
[ROW][C]64[/C][C]95.43[/C][C]89.8973552858414[/C][C]5.53264471415864[/C][/ROW]
[ROW][C]65[/C][C]97.59[/C][C]95.9632006158228[/C][C]1.62679938417722[/C][/ROW]
[ROW][C]66[/C][C]97.8[/C][C]96.3410546464248[/C][C]1.45894535357522[/C][/ROW]
[ROW][C]67[/C][C]99.48[/C][C]96.9614408686346[/C][C]2.51855913136538[/C][/ROW]
[ROW][C]68[/C][C]97.52[/C][C]98.0336716019363[/C][C]-0.513671601936267[/C][/ROW]
[ROW][C]69[/C][C]104.39[/C][C]98.0176750837504[/C][C]6.37232491624957[/C][/ROW]
[ROW][C]70[/C][C]97.74[/C][C]103.890696289595[/C][C]-6.15069628959469[/C][/ROW]
[ROW][C]71[/C][C]91.37[/C][C]98.372824516802[/C][C]-7.00282451680199[/C][/ROW]
[ROW][C]72[/C][C]92.42[/C][C]92.8773639625569[/C][C]-0.457363962556869[/C][/ROW]
[ROW][C]73[/C][C]96.9[/C][C]94.3757898618255[/C][C]2.5242101381745[/C][/ROW]
[ROW][C]74[/C][C]101.58[/C][C]98.2994933086039[/C][C]3.28050669139607[/C][/ROW]
[ROW][C]75[/C][C]105.46[/C][C]102.375434531891[/C][C]3.08456546810859[/C][/ROW]
[ROW][C]76[/C][C]110.06[/C][C]105.385674657215[/C][C]4.67432534278484[/C][/ROW]
[ROW][C]77[/C][C]107.9[/C][C]110.227534931389[/C][C]-2.32753493138888[/C][/ROW]
[ROW][C]78[/C][C]102.87[/C][C]107.175450620073[/C][C]-4.30545062007302[/C][/ROW]
[ROW][C]79[/C][C]96.28[/C][C]102.957500992323[/C][C]-6.67750099232283[/C][/ROW]
[ROW][C]80[/C][C]98.59[/C][C]95.7258122678704[/C][C]2.86418773212965[/C][/ROW]
[ROW][C]81[/C][C]103.22[/C][C]99.4752586824527[/C][C]3.74474131754727[/C][/ROW]
[ROW][C]82[/C][C]98.6[/C][C]101.531140703715[/C][C]-2.93114070371504[/C][/ROW]
[ROW][C]83[/C][C]91.79[/C][C]98.6833404987097[/C][C]-6.89334049870973[/C][/ROW]
[ROW][C]84[/C][C]93.83[/C][C]94.0933698668009[/C][C]-0.2633698668009[/C][/ROW]
[ROW][C]85[/C][C]95.17[/C][C]96.1285141948011[/C][C]-0.958514194801083[/C][/ROW]
[ROW][C]86[/C][C]95.19[/C][C]97.1433859281769[/C][C]-1.95338592817693[/C][/ROW]
[ROW][C]87[/C][C]99.44[/C][C]96.6827665969293[/C][C]2.75723340307069[/C][/ROW]
[ROW][C]88[/C][C]109.18[/C][C]99.6078048921155[/C][C]9.5721951078845[/C][/ROW]
[ROW][C]89[/C][C]109.15[/C][C]107.804593734993[/C][C]1.34540626500704[/C][/ROW]
[ROW][C]90[/C][C]109.72[/C][C]107.673951543865[/C][C]2.04604845613498[/C][/ROW]
[ROW][C]91[/C][C]108.41[/C][C]108.637860573288[/C][C]-0.227860573287799[/C][/ROW]
[ROW][C]92[/C][C]102.96[/C][C]108.14896828588[/C][C]-5.18896828588034[/C][/ROW]
[ROW][C]93[/C][C]107.64[/C][C]105.06468833448[/C][C]2.57531166551988[/C][/ROW]
[ROW][C]94[/C][C]97.28[/C][C]105.285111157774[/C][C]-8.00511115777398[/C][/ROW]
[ROW][C]95[/C][C]97.25[/C][C]97.5719161370826[/C][C]-0.321916137082553[/C][/ROW]
[ROW][C]96[/C][C]91.84[/C][C]99.4689206928648[/C][C]-7.62892069286481[/C][/ROW]
[ROW][C]97[/C][C]94.12[/C][C]95.0678841892562[/C][C]-0.947884189256243[/C][/ROW]
[ROW][C]98[/C][C]97.86[/C][C]95.9686377578691[/C][C]1.89136224213087[/C][/ROW]
[ROW][C]99[/C][C]98.83[/C][C]99.4064102799464[/C][C]-0.576410279946401[/C][/ROW]
[ROW][C]100[/C][C]102.29[/C][C]100.301921363829[/C][C]1.98807863617118[/C][/ROW]
[ROW][C]101[/C][C]104.49[/C][C]100.940791234467[/C][C]3.5492087655326[/C][/ROW]
[ROW][C]102[/C][C]102.11[/C][C]102.796928802408[/C][C]-0.686928802407991[/C][/ROW]
[ROW][C]103[/C][C]102.14[/C][C]101.122886070279[/C][C]1.01711392972145[/C][/ROW]
[ROW][C]104[/C][C]101.28[/C][C]101.092548995286[/C][C]0.187451004713566[/C][/ROW]
[ROW][C]105[/C][C]101.21[/C][C]103.605559565392[/C][C]-2.39555956539181[/C][/ROW]
[ROW][C]106[/C][C]94.2[/C][C]98.2293548078236[/C][C]-4.02935480782362[/C][/ROW]
[ROW][C]107[/C][C]88.47[/C][C]94.8958531475299[/C][C]-6.42585314752991[/C][/ROW]
[ROW][C]108[/C][C]88.08[/C][C]90.625019228295[/C][C]-2.54501922829502[/C][/ROW]
[ROW][C]109[/C][C]88.02[/C][C]91.4348523132722[/C][C]-3.41485231327225[/C][/ROW]
[ROW][C]110[/C][C]92.95[/C][C]90.5606000902692[/C][C]2.38939990973083[/C][/ROW]
[ROW][C]111[/C][C]97.05[/C][C]94.1219427161459[/C][C]2.9280572838541[/C][/ROW]
[ROW][C]112[/C][C]101.44[/C][C]98.3565362448529[/C][C]3.08346375514709[/C][/ROW]
[ROW][C]113[/C][C]100.34[/C][C]100.133219373867[/C][C]0.206780626133494[/C][/ROW]
[ROW][C]114[/C][C]99.98[/C][C]98.5828255877399[/C][C]1.39717441226006[/C][/ROW]
[ROW][C]115[/C][C]94.17[/C][C]98.9167060864467[/C][C]-4.74670608644665[/C][/ROW]
[ROW][C]116[/C][C]94.54[/C][C]93.8144141987285[/C][C]0.725585801271507[/C][/ROW]
[ROW][C]117[/C][C]95.12[/C][C]96.4712836124516[/C][C]-1.35128361245162[/C][/ROW]
[ROW][C]118[/C][C]98.04[/C][C]91.7929205571988[/C][C]6.24707944280119[/C][/ROW]
[ROW][C]119[/C][C]93.72[/C][C]97.0220404127214[/C][C]-3.30204041272135[/C][/ROW]
[ROW][C]120[/C][C]93.83[/C][C]95.9252350746169[/C][C]-2.09523507461695[/C][/ROW]
[ROW][C]121[/C][C]93.03[/C][C]97.0150511697732[/C][C]-3.98505116977321[/C][/ROW]
[ROW][C]122[/C][C]95.81[/C][C]96.3684668419152[/C][C]-0.558466841915191[/C][/ROW]
[ROW][C]123[/C][C]99.1[/C][C]97.4551234656697[/C][C]1.64487653433028[/C][/ROW]
[ROW][C]124[/C][C]100.12[/C][C]100.602709953426[/C][C]-0.482709953425982[/C][/ROW]
[ROW][C]125[/C][C]100.67[/C][C]98.948425604597[/C][C]1.72157439540301[/C][/ROW]
[ROW][C]126[/C][C]103.87[/C][C]98.8514876487887[/C][C]5.01851235121126[/C][/ROW]
[ROW][C]127[/C][C]102.39[/C][C]101.54608341492[/C][C]0.843916585079697[/C][/ROW]
[ROW][C]128[/C][C]107.21[/C][C]101.941733833481[/C][C]5.26826616651908[/C][/ROW]
[ROW][C]129[/C][C]105.71[/C][C]108.25760879309[/C][C]-2.54760879308974[/C][/ROW]
[ROW][C]130[/C][C]99.79[/C][C]103.489435993637[/C][C]-3.69943599363692[/C][/ROW]
[ROW][C]131[/C][C]96.12[/C][C]98.9600883562557[/C][C]-2.84008835625565[/C][/ROW]
[ROW][C]132[/C][C]96.17[/C][C]98.4110893181526[/C][C]-2.2410893181526[/C][/ROW]
[ROW][C]133[/C][C]97.23[/C][C]99.1409781870275[/C][C]-1.91097818702754[/C][/ROW]
[ROW][C]134[/C][C]98.08[/C][C]100.707123776295[/C][C]-2.62712377629528[/C][/ROW]
[ROW][C]135[/C][C]99.84[/C][C]100.283369545343[/C][C]-0.443369545342577[/C][/ROW]
[ROW][C]136[/C][C]99.72[/C][C]101.366976404493[/C][C]-1.64697640449286[/C][/ROW]
[ROW][C]137[/C][C]99.92[/C][C]98.9820972163416[/C][C]0.937902783658402[/C][/ROW]
[ROW][C]138[/C][C]102.7[/C][C]98.6180850099606[/C][C]4.08191499003942[/C][/ROW]
[ROW][C]139[/C][C]102.06[/C][C]99.9879071217097[/C][C]2.07209287829029[/C][/ROW]
[ROW][C]140[/C][C]102.36[/C][C]101.990658260201[/C][C]0.369341739799253[/C][/ROW]
[ROW][C]141[/C][C]102.43[/C][C]103.11451033694[/C][C]-0.684510336940079[/C][/ROW]
[ROW][C]142[/C][C]100.6[/C][C]99.8098327363334[/C][C]0.790167263666547[/C][/ROW]
[ROW][C]143[/C][C]98.4[/C][C]99.2575817717242[/C][C]-0.857581771724156[/C][/ROW]
[ROW][C]144[/C][C]98.61[/C][C]100.491981896143[/C][C]-1.88198189614324[/C][/ROW]
[ROW][C]145[/C][C]103.03[/C][C]101.572373684877[/C][C]1.45762631512262[/C][/ROW]
[ROW][C]146[/C][C]104.7[/C][C]105.953940635216[/C][C]-1.25394063521614[/C][/ROW]
[ROW][C]147[/C][C]107.45[/C][C]106.984651198264[/C][C]0.465348801736354[/C][/ROW]
[ROW][C]148[/C][C]109.67[/C][C]108.702540005585[/C][C]0.96745999441508[/C][/ROW]
[ROW][C]149[/C][C]110.54[/C][C]108.891950128847[/C][C]1.64804987115255[/C][/ROW]
[ROW][C]150[/C][C]112.05[/C][C]109.529774772912[/C][C]2.52022522708829[/C][/ROW]
[ROW][C]151[/C][C]113.19[/C][C]109.304168782554[/C][C]3.8858312174459[/C][/ROW]
[ROW][C]152[/C][C]114.2[/C][C]112.659591004856[/C][C]1.54040899514366[/C][/ROW]
[ROW][C]153[/C][C]112.56[/C][C]114.662460417426[/C][C]-2.1024604174258[/C][/ROW]
[ROW][C]154[/C][C]107.36[/C][C]110.318069027321[/C][C]-2.95806902732072[/C][/ROW]
[ROW][C]155[/C][C]103.93[/C][C]106.330176658976[/C][C]-2.40017665897579[/C][/ROW]
[ROW][C]156[/C][C]103.83[/C][C]106.107722473118[/C][C]-2.27772247311799[/C][/ROW]
[ROW][C]157[/C][C]104.74[/C][C]107.260773427782[/C][C]-2.5207734277818[/C][/ROW]
[ROW][C]158[/C][C]107.5[/C][C]107.876442602454[/C][C]-0.376442602453551[/C][/ROW]
[ROW][C]159[/C][C]109.53[/C][C]109.876718889286[/C][C]-0.346718889285569[/C][/ROW]
[ROW][C]160[/C][C]109.42[/C][C]110.956722899225[/C][C]-1.53672289922483[/C][/ROW]
[ROW][C]161[/C][C]108.6[/C][C]109.071546833985[/C][C]-0.471546833985443[/C][/ROW]
[ROW][C]162[/C][C]110.72[/C][C]107.990088310144[/C][C]2.72991168985649[/C][/ROW]
[ROW][C]163[/C][C]105.1[/C][C]108.114481921473[/C][C]-3.01448192147261[/C][/ROW]
[ROW][C]164[/C][C]105.19[/C][C]105.230318020296[/C][C]-0.0403180202959561[/C][/ROW]
[ROW][C]165[/C][C]102.55[/C][C]105.418982742454[/C][C]-2.86898274245421[/C][/ROW]
[ROW][C]166[/C][C]101.25[/C][C]100.307726433293[/C][C]0.942273566706987[/C][/ROW]
[ROW][C]167[/C][C]101.56[/C][C]99.7515574841484[/C][C]1.8084425158516[/C][/ROW]
[ROW][C]168[/C][C]101.62[/C][C]103.172641610306[/C][C]-1.55264161030561[/C][/ROW]
[ROW][C]169[/C][C]101.7[/C][C]104.920685916314[/C][C]-3.22068591631373[/C][/ROW]
[ROW][C]170[/C][C]102.94[/C][C]105.198662994033[/C][C]-2.25866299403317[/C][/ROW]
[ROW][C]171[/C][C]104.37[/C][C]105.579909654405[/C][C]-1.20990965440545[/C][/ROW]
[ROW][C]172[/C][C]106.93[/C][C]105.768270647002[/C][C]1.16172935299798[/C][/ROW]
[ROW][C]173[/C][C]107.82[/C][C]106.34149755608[/C][C]1.47850244391988[/C][/ROW]
[ROW][C]174[/C][C]110.83[/C][C]107.337947616811[/C][C]3.49205238318868[/C][/ROW]
[ROW][C]175[/C][C]106.86[/C][C]107.407569127243[/C][C]-0.547569127242781[/C][/ROW]
[ROW][C]176[/C][C]109.46[/C][C]107.018749869608[/C][C]2.44125013039208[/C][/ROW]
[ROW][C]177[/C][C]108.8[/C][C]108.996318724814[/C][C]-0.196318724814248[/C][/ROW]
[ROW][C]178[/C][C]108.69[/C][C]106.661521605077[/C][C]2.02847839492328[/C][/ROW]
[ROW][C]179[/C][C]107.77[/C][C]107.149133094248[/C][C]0.62086690575201[/C][/ROW]
[ROW][C]180[/C][C]108.64[/C][C]109.129877240362[/C][C]-0.489877240362475[/C][/ROW]
[ROW][C]181[/C][C]108.5[/C][C]111.587458533657[/C][C]-3.08745853365654[/C][/ROW]
[ROW][C]182[/C][C]113.84[/C][C]112.099506546852[/C][C]1.74049345314802[/C][/ROW]
[ROW][C]183[/C][C]114.59[/C][C]116.058493253797[/C][C]-1.46849325379678[/C][/ROW]
[ROW][C]184[/C][C]116.27[/C][C]116.317811269834[/C][C]-0.0478112698336872[/C][/ROW]
[ROW][C]185[/C][C]113.63[/C][C]115.887514515106[/C][C]-2.25751451510648[/C][/ROW]
[ROW][C]186[/C][C]112.29[/C][C]113.912558867934[/C][C]-1.6225588679342[/C][/ROW]
[ROW][C]187[/C][C]110.31[/C][C]109.072154087048[/C][C]1.2378459129518[/C][/ROW]
[ROW][C]188[/C][C]108.47[/C][C]110.592957954053[/C][C]-2.12295795405279[/C][/ROW]
[ROW][C]189[/C][C]110.67[/C][C]108.308757573622[/C][C]2.36124242637767[/C][/ROW]
[ROW][C]190[/C][C]109.1[/C][C]108.4545954085[/C][C]0.645404591500181[/C][/ROW]
[ROW][C]191[/C][C]107.02[/C][C]107.575393202972[/C][C]-0.555393202971857[/C][/ROW]
[ROW][C]192[/C][C]108.12[/C][C]108.404410541274[/C][C]-0.28441054127353[/C][/ROW]
[ROW][C]193[/C][C]106.69[/C][C]110.717242969079[/C][C]-4.02724296907917[/C][/ROW]
[ROW][C]194[/C][C]109.87[/C][C]111.017347953235[/C][C]-1.14734795323491[/C][/ROW]
[ROW][C]195[/C][C]110.82[/C][C]112.08899732727[/C][C]-1.26899732726986[/C][/ROW]
[ROW][C]196[/C][C]114.14[/C][C]112.696354319529[/C][C]1.44364568047129[/C][/ROW]
[ROW][C]197[/C][C]113.31[/C][C]113.278060653193[/C][C]0.0319393468072207[/C][/ROW]
[ROW][C]198[/C][C]115.16[/C][C]113.355587362967[/C][C]1.80441263703278[/C][/ROW]
[ROW][C]199[/C][C]111.06[/C][C]111.824122906866[/C][C]-0.764122906865907[/C][/ROW]
[ROW][C]200[/C][C]111.13[/C][C]111.202511186396[/C][C]-0.0725111863962411[/C][/ROW]
[ROW][C]201[/C][C]115.96[/C][C]111.241729659874[/C][C]4.71827034012581[/C][/ROW]
[ROW][C]202[/C][C]117.57[/C][C]113.207001486134[/C][C]4.36299851386639[/C][/ROW]
[ROW][C]203[/C][C]114.69[/C][C]115.38403666428[/C][C]-0.694036664280475[/C][/ROW]
[ROW][C]204[/C][C]119.42[/C][C]116.127105384498[/C][C]3.29289461550179[/C][/ROW]
[ROW][C]205[/C][C]118.4[/C][C]121.060224459733[/C][C]-2.6602244597326[/C][/ROW]
[ROW][C]206[/C][C]123.32[/C][C]122.895743961[/C][C]0.424256039000113[/C][/ROW]
[ROW][C]207[/C][C]123.39[/C][C]125.307240941593[/C][C]-1.91724094159299[/C][/ROW]
[ROW][C]208[/C][C]127.04[/C][C]125.691875111347[/C][C]1.34812488865256[/C][/ROW]
[ROW][C]209[/C][C]129.35[/C][C]126.016294480092[/C][C]3.33370551990809[/C][/ROW]
[ROW][C]210[/C][C]127.12[/C][C]129.160004259356[/C][C]-2.04000425935649[/C][/ROW]
[ROW][C]211[/C][C]122.1[/C][C]123.995876425803[/C][C]-1.89587642580254[/C][/ROW]
[ROW][C]212[/C][C]120.22[/C][C]122.484252677666[/C][C]-2.26425267766574[/C][/ROW]
[ROW][C]213[/C][C]121.53[/C][C]121.227576108533[/C][C]0.3024238914672[/C][/ROW]
[ROW][C]214[/C][C]119.01[/C][C]119.341803093322[/C][C]-0.331803093321938[/C][/ROW]
[ROW][C]215[/C][C]114.27[/C][C]116.844665257485[/C][C]-2.57466525748532[/C][/ROW]
[ROW][C]216[/C][C]114.46[/C][C]116.460446183739[/C][C]-2.00044618373926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234915&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234915&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	76.23	75.6774679487179	0.552532051282071
14	76.97	76.4359856410514	0.534014358948582
15	78.4	77.8718720650464	0.528127934953574
16	78.6	78.4547669775907	0.145233022409329
17	80.08	79.9913078657864	0.088692134213602
18	81.12	81.1870199969773	-0.0670199969772511
19	80.31	78.3193218362612	1.99067816373882
20	84.59	77.2860373881204	7.30396261187958
21	81.34	87.4005620060871	-6.06056200608707
22	80.95	84.0098364008324	-3.05983640083237
23	80.48	79.3061172190328	1.17388278096725
24	75.26	81.0465681228199	-5.7865681228199
25	76.32	77.6763620647284	-1.35636206472839
26	78.92	76.7868760122571	2.13312398774286
27	80.47	79.6006685140965	0.869331485903487
28	83.14	80.430276608193	2.70972339180697
29	85.42	84.1707273276769	1.24927267232312
30	81.53	86.3477116763071	-4.81771167630713
31	87.31	79.6393001447082	7.67069985529176
32	86.01	84.1613274135386	1.8486725864614
33	85.1	87.9165934470891	-2.81659344708913
34	79.91	87.6944246792682	-7.78442467926818
35	78.6	79.4421448840644	-0.842144884064382
36	78.6	78.581998399368	0.0180016006320045
37	79.37	80.7650509091252	-1.39505090912515
38	82.89	80.2746205168345	2.61537948316551
39	84.43	83.3475717595741	1.08242824042591
40	85.32	84.5889541112313	0.731045888768733
41	87.71	86.4425573980308	1.26744260196921
42	84.68	87.8833975783877	-3.20339757838769
43	80.62	84.1142695200621	-3.49426952006212
44	84.79	78.289221411434	6.50077858856605
45	85.49	85.4770826839712	0.0129173160287621
46	81.68	87.0787073812021	-5.39870738120212
47	77.69	81.7434926428453	-4.05349264284534
48	78.31	78.2213443862747	0.0886556137253365
49	79.18	80.2902068938349	-1.1102068938349
50	80.91	80.542312974312	0.367687025688042
51	83.91	81.4875076168551	2.42249238314494
52	86.3	83.840652764255	2.45934723574499
53	89.76	87.2507404677358	2.50925953226424
54	85.11	89.2081666353654	-4.09816663536543
55	83.81	84.6315897682647	-0.821589768264673
56	85.36	82.3492979214204	3.0107020785796
57	85.89	85.7243069580381	0.16569304196193
58	82.59	86.7870456712094	-4.19704567120944
59	80.87	82.6545122876124	-1.78451228761236
60	80.27	81.6018001440289	-1.33180014402889
61	81.36	82.2974887361457	-0.937488736145667
62	84.81	82.8816375488712	1.92836245112883
63	90.3	85.426960042531	4.87303995746903
64	95.43	89.8973552858414	5.53264471415864
65	97.59	95.9632006158228	1.62679938417722
66	97.8	96.3410546464248	1.45894535357522
67	99.48	96.9614408686346	2.51855913136538
68	97.52	98.0336716019363	-0.513671601936267
69	104.39	98.0176750837504	6.37232491624957
70	97.74	103.890696289595	-6.15069628959469
71	91.37	98.372824516802	-7.00282451680199
72	92.42	92.8773639625569	-0.457363962556869
73	96.9	94.3757898618255	2.5242101381745
74	101.58	98.2994933086039	3.28050669139607
75	105.46	102.375434531891	3.08456546810859
76	110.06	105.385674657215	4.67432534278484
77	107.9	110.227534931389	-2.32753493138888
78	102.87	107.175450620073	-4.30545062007302
79	96.28	102.957500992323	-6.67750099232283
80	98.59	95.7258122678704	2.86418773212965
81	103.22	99.4752586824527	3.74474131754727
82	98.6	101.531140703715	-2.93114070371504
83	91.79	98.6833404987097	-6.89334049870973
84	93.83	94.0933698668009	-0.2633698668009
85	95.17	96.1285141948011	-0.958514194801083
86	95.19	97.1433859281769	-1.95338592817693
87	99.44	96.6827665969293	2.75723340307069
88	109.18	99.6078048921155	9.5721951078845
89	109.15	107.804593734993	1.34540626500704
90	109.72	107.673951543865	2.04604845613498
91	108.41	108.637860573288	-0.227860573287799
92	102.96	108.14896828588	-5.18896828588034
93	107.64	105.06468833448	2.57531166551988
94	97.28	105.285111157774	-8.00511115777398
95	97.25	97.5719161370826	-0.321916137082553
96	91.84	99.4689206928648	-7.62892069286481
97	94.12	95.0678841892562	-0.947884189256243
98	97.86	95.9686377578691	1.89136224213087
99	98.83	99.4064102799464	-0.576410279946401
100	102.29	100.301921363829	1.98807863617118
101	104.49	100.940791234467	3.5492087655326
102	102.11	102.796928802408	-0.686928802407991
103	102.14	101.122886070279	1.01711392972145
104	101.28	101.092548995286	0.187451004713566
105	101.21	103.605559565392	-2.39555956539181
106	94.2	98.2293548078236	-4.02935480782362
107	88.47	94.8958531475299	-6.42585314752991
108	88.08	90.625019228295	-2.54501922829502
109	88.02	91.4348523132722	-3.41485231327225
110	92.95	90.5606000902692	2.38939990973083
111	97.05	94.1219427161459	2.9280572838541
112	101.44	98.3565362448529	3.08346375514709
113	100.34	100.133219373867	0.206780626133494
114	99.98	98.5828255877399	1.39717441226006
115	94.17	98.9167060864467	-4.74670608644665
116	94.54	93.8144141987285	0.725585801271507
117	95.12	96.4712836124516	-1.35128361245162
118	98.04	91.7929205571988	6.24707944280119
119	93.72	97.0220404127214	-3.30204041272135
120	93.83	95.9252350746169	-2.09523507461695
121	93.03	97.0150511697732	-3.98505116977321
122	95.81	96.3684668419152	-0.558466841915191
123	99.1	97.4551234656697	1.64487653433028
124	100.12	100.602709953426	-0.482709953425982
125	100.67	98.948425604597	1.72157439540301
126	103.87	98.8514876487887	5.01851235121126
127	102.39	101.54608341492	0.843916585079697
128	107.21	101.941733833481	5.26826616651908
129	105.71	108.25760879309	-2.54760879308974
130	99.79	103.489435993637	-3.69943599363692
131	96.12	98.9600883562557	-2.84008835625565
132	96.17	98.4110893181526	-2.2410893181526
133	97.23	99.1409781870275	-1.91097818702754
134	98.08	100.707123776295	-2.62712377629528
135	99.84	100.283369545343	-0.443369545342577
136	99.72	101.366976404493	-1.64697640449286
137	99.92	98.9820972163416	0.937902783658402
138	102.7	98.6180850099606	4.08191499003942
139	102.06	99.9879071217097	2.07209287829029
140	102.36	101.990658260201	0.369341739799253
141	102.43	103.11451033694	-0.684510336940079
142	100.6	99.8098327363334	0.790167263666547
143	98.4	99.2575817717242	-0.857581771724156
144	98.61	100.491981896143	-1.88198189614324
145	103.03	101.572373684877	1.45762631512262
146	104.7	105.953940635216	-1.25394063521614
147	107.45	106.984651198264	0.465348801736354
148	109.67	108.702540005585	0.96745999441508
149	110.54	108.891950128847	1.64804987115255
150	112.05	109.529774772912	2.52022522708829
151	113.19	109.304168782554	3.8858312174459
152	114.2	112.659591004856	1.54040899514366
153	112.56	114.662460417426	-2.1024604174258
154	107.36	110.318069027321	-2.95806902732072
155	103.93	106.330176658976	-2.40017665897579
156	103.83	106.107722473118	-2.27772247311799
157	104.74	107.260773427782	-2.5207734277818
158	107.5	107.876442602454	-0.376442602453551
159	109.53	109.876718889286	-0.346718889285569
160	109.42	110.956722899225	-1.53672289922483
161	108.6	109.071546833985	-0.471546833985443
162	110.72	107.990088310144	2.72991168985649
163	105.1	108.114481921473	-3.01448192147261
164	105.19	105.230318020296	-0.0403180202959561
165	102.55	105.418982742454	-2.86898274245421
166	101.25	100.307726433293	0.942273566706987
167	101.56	99.7515574841484	1.8084425158516
168	101.62	103.172641610306	-1.55264161030561
169	101.7	104.920685916314	-3.22068591631373
170	102.94	105.198662994033	-2.25866299403317
171	104.37	105.579909654405	-1.20990965440545
172	106.93	105.768270647002	1.16172935299798
173	107.82	106.34149755608	1.47850244391988
174	110.83	107.337947616811	3.49205238318868
175	106.86	107.407569127243	-0.547569127242781
176	109.46	107.018749869608	2.44125013039208
177	108.8	108.996318724814	-0.196318724814248
178	108.69	106.661521605077	2.02847839492328
179	107.77	107.149133094248	0.62086690575201
180	108.64	109.129877240362	-0.489877240362475
181	108.5	111.587458533657	-3.08745853365654
182	113.84	112.099506546852	1.74049345314802
183	114.59	116.058493253797	-1.46849325379678
184	116.27	116.317811269834	-0.0478112698336872
185	113.63	115.887514515106	-2.25751451510648
186	112.29	113.912558867934	-1.6225588679342
187	110.31	109.072154087048	1.2378459129518
188	108.47	110.592957954053	-2.12295795405279
189	110.67	108.308757573622	2.36124242637767
190	109.1	108.4545954085	0.645404591500181
191	107.02	107.575393202972	-0.555393202971857
192	108.12	108.404410541274	-0.28441054127353
193	106.69	110.717242969079	-4.02724296907917
194	109.87	111.017347953235	-1.14734795323491
195	110.82	112.08899732727	-1.26899732726986
196	114.14	112.696354319529	1.44364568047129
197	113.31	113.278060653193	0.0319393468072207
198	115.16	113.355587362967	1.80441263703278
199	111.06	111.824122906866	-0.764122906865907
200	111.13	111.202511186396	-0.0725111863962411
201	115.96	111.241729659874	4.71827034012581
202	117.57	113.207001486134	4.36299851386639
203	114.69	115.38403666428	-0.694036664280475
204	119.42	116.127105384498	3.29289461550179
205	118.4	121.060224459733	-2.6602244597326
206	123.32	122.895743961	0.424256039000113
207	123.39	125.307240941593	-1.91724094159299
208	127.04	125.691875111347	1.34812488865256
209	129.35	126.016294480092	3.33370551990809
210	127.12	129.160004259356	-2.04000425935649
211	122.1	123.995876425803	-1.89587642580254
212	120.22	122.484252677666	-2.26425267766574
213	121.53	121.227576108533	0.3024238914672
214	119.01	119.341803093322	-0.331803093321938
215	114.27	116.844665257485	-2.57466525748532
216	114.46	116.460446183739	-2.00044618373926

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
217	116.09233449333	110.232874965706	121.951794020954
218	120.603528054526	112.867126552014	128.339929557037
219	122.359108696311	113.119490172786	131.598727219836
220	124.801285769295	114.270892010632	135.331679527957
221	124.209499642845	112.530123162712	135.888876122978
222	123.813232327404	111.088198841519	136.538265813288
223	120.425707192581	106.73464735526	134.116767029901
224	120.502921139142	105.909643175597	135.096199102687
225	121.51637542346	106.07349991488	136.95925093204
226	119.291282440078	103.043173435467	135.539391444688
227	116.802269857111	99.7869917671734	133.817547947049
228	118.708895213206	100.959576050767	136.458214375645

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
217 & 116.09233449333 & 110.232874965706 & 121.951794020954 \tabularnewline
218 & 120.603528054526 & 112.867126552014 & 128.339929557037 \tabularnewline
219 & 122.359108696311 & 113.119490172786 & 131.598727219836 \tabularnewline
220 & 124.801285769295 & 114.270892010632 & 135.331679527957 \tabularnewline
221 & 124.209499642845 & 112.530123162712 & 135.888876122978 \tabularnewline
222 & 123.813232327404 & 111.088198841519 & 136.538265813288 \tabularnewline
223 & 120.425707192581 & 106.73464735526 & 134.116767029901 \tabularnewline
224 & 120.502921139142 & 105.909643175597 & 135.096199102687 \tabularnewline
225 & 121.51637542346 & 106.07349991488 & 136.95925093204 \tabularnewline
226 & 119.291282440078 & 103.043173435467 & 135.539391444688 \tabularnewline
227 & 116.802269857111 & 99.7869917671734 & 133.817547947049 \tabularnewline
228 & 118.708895213206 & 100.959576050767 & 136.458214375645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234915&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]217[/C][C]116.09233449333[/C][C]110.232874965706[/C][C]121.951794020954[/C][/ROW]
[ROW][C]218[/C][C]120.603528054526[/C][C]112.867126552014[/C][C]128.339929557037[/C][/ROW]
[ROW][C]219[/C][C]122.359108696311[/C][C]113.119490172786[/C][C]131.598727219836[/C][/ROW]
[ROW][C]220[/C][C]124.801285769295[/C][C]114.270892010632[/C][C]135.331679527957[/C][/ROW]
[ROW][C]221[/C][C]124.209499642845[/C][C]112.530123162712[/C][C]135.888876122978[/C][/ROW]
[ROW][C]222[/C][C]123.813232327404[/C][C]111.088198841519[/C][C]136.538265813288[/C][/ROW]
[ROW][C]223[/C][C]120.425707192581[/C][C]106.73464735526[/C][C]134.116767029901[/C][/ROW]
[ROW][C]224[/C][C]120.502921139142[/C][C]105.909643175597[/C][C]135.096199102687[/C][/ROW]
[ROW][C]225[/C][C]121.51637542346[/C][C]106.07349991488[/C][C]136.95925093204[/C][/ROW]
[ROW][C]226[/C][C]119.291282440078[/C][C]103.043173435467[/C][C]135.539391444688[/C][/ROW]
[ROW][C]227[/C][C]116.802269857111[/C][C]99.7869917671734[/C][C]133.817547947049[/C][/ROW]
[ROW][C]228[/C][C]118.708895213206[/C][C]100.959576050767[/C][C]136.458214375645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234915&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234915&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
217	116.09233449333	110.232874965706	121.951794020954
218	120.603528054526	112.867126552014	128.339929557037
219	122.359108696311	113.119490172786	131.598727219836
220	124.801285769295	114.270892010632	135.331679527957
221	124.209499642845	112.530123162712	135.888876122978
222	123.813232327404	111.088198841519	136.538265813288
223	120.425707192581	106.73464735526	134.116767029901
224	120.502921139142	105.909643175597	135.096199102687
225	121.51637542346	106.07349991488	136.95925093204
226	119.291282440078	103.043173435467	135.539391444688
227	116.802269857111	99.7869917671734	133.817547947049
228	118.708895213206	100.959576050767	136.458214375645

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code