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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 05 Jan 2015 13:09:35 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/05/t1420463422ubfjtyrnvqpf6o0.htm/, Retrieved Mon, 13 May 2024 20:39:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271958, Retrieved Mon, 13 May 2024 20:39:47 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

116

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

-       [Exponential Smoothing] [] [2015-01-05 13:09:35] [bdca4dcc63d0690a1e5c4820657ce42d] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271958&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271958&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999936379665509
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999936379665509 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271958&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]0.999936379665509[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271958&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	0.999936379665509
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	59.2	55.7	3.5
3	59.8	59.1997773288293	0.600222671170712
4	61.6	59.7999618136329	1.80003818636711
5	65.8	61.5998854809685	4.20011451903151
6	64.2	65.7997327873094	-1.59973278730939
7	67	64.200101775535	2.79989822446497
8	62.8	66.9998218695384	-4.19982186953843
9	65.5	62.8002671940721	2.69973280592787
10	75.2	65.4998282420958	9.70017175790416
11	80.9	75.1993828718281	5.70061712817186
12	83.2	80.8996373248315	2.3003626751685
13	83.7	83.1998536501572	0.500146349842836
14	86.4	83.6999681805219	2.70003181947807
15	85.9	86.3998282230725	-0.499828223072512
16	80.4	85.9000317992387	-5.50003179923874
17	81.8	80.4003499138628	1.39965008613721
18	87.5	81.7999109537933	5.70008904620666
19	83.7	87.4996373584283	-3.79963735842826
20	87	83.7002417341997	3.29975826580031
21	99.7	86.9997900682754	12.7002099317246
22	101.4	99.699192008396	1.70080799160397
23	101.9	101.399891794027	0.500108205973333
24	115.7	101.899968182949	13.8000318170513
25	123.2	115.69912203736	7.50087796264019
26	136.9	123.199522791635	13.700477208365
27	146.8	136.899128371057	9.9008716289427
28	149.6	146.799370103235	2.80062989676478
29	146.5	149.599821822989	-3.09982182298918
30	157	146.500197211701	10.4998027882988
31	147.9	156.999331999035	-9.09933199903452
32	133.6	147.900578902545	-14.3005789025454
33	128.7	133.600909807613	-4.9009098076132
34	100.8	128.700311797521	-27.9003117975213
35	91.8	100.801775027169	-9.00177502716896
36	89.3	91.8005726959382	-2.50057269593823
37	96.7	89.3001590872713	7.39984091272868
38	91.6	96.699529219646	-5.09952921964596
39	93.3	91.6003244337547	1.6996755662453
40	93.3	93.2998918660719	0.000108133928051757
41	101	93.2999999931205	7.70000000687952
42	100.4	100.999510123424	-0.599510123423968
43	86.9	100.400038141035	-13.5000381410346
44	83.9	86.9008588769422	-3.00085887694216
45	80.3	83.9001909156455	-3.60019091564551
46	87.7	80.3002290453503	7.39977095464972
47	92.7	87.6995292240967	5.00047077590328
48	95.5	92.6996818683766	2.80031813162337
49	92	95.4998218428238	-3.49982184282379
50	87.4	92.0002226598363	-4.60022265983629
51	86.8	87.4002926677043	-0.600292667704352
52	83.7	86.8000381908203	-3.10003819082031
53	85	83.7001972254666	1.29980277453336
54	81.7	84.9999173061127	-3.29991730611272
55	90.9	81.7002099418428	9.19979005815721
56	101.5	90.8994147062793	10.6005852937207
57	113.8	101.499325587218	12.3006744127822
58	120.1	113.799217426979	6.3007825730206
59	122.1	120.099599142105	2.00040085789485
60	132.5	122.099872733828	10.4001272661717
61	140	132.499338340425	7.50066165957543
62	149.4	139.999522805396	9.4004771946037
63	144.3	149.399401938497	-5.0994019384965
64	154.4	144.300324425657	10.099675574343
65	151.4	154.399357455262	-2.9993574552617
66	145.5	151.400190820125	-5.90019082012458
67	136.8	145.500375372114	-8.70037537211354
68	146.6	136.800553520791	9.79944647920863
69	145.1	146.599376555937	-1.49937655593715
70	133.6	145.100095390838	-11.500095390838
71	131.4	133.600731639915	-2.20073163991543
72	127.5	131.400140011283	-3.90014001128307
73	130.1	127.500248128212	2.59975187178792
74	131.1	130.099834602916	1.00016539708369
75	132.3	131.099936369143	1.20006363085713
76	128.6	132.29992365155	-3.69992365155042
77	125.1	128.60023539038	-3.50023539038031
78	128.7	125.100222686146	3.59977731385365
79	156.1	128.699770980963	27.4002290190368
80	163.2	156.098256788265	7.10174321173528
81	159.8	163.199548184721	-3.39954818472137
82	157.4	159.800216280393	-2.40021628039261
83	156.2	157.400152702563	-1.20015270256263
84	152.5	156.200076354116	-3.70007635411636
85	149.4	152.500235400095	-3.1002354000953
86	145.9	149.400197238013	-3.50019723801316
87	144.8	145.900222683719	-1.10022268371907
88	135.9	144.800069996535	-8.90006999653514
89	137.6	135.90056622543	1.6994337745698
90	136	137.599891881455	-1.59989188145482
91	117.7	136.000101785657	-18.3001017856566
92	111.5	117.701164258597	-6.20116425859682
93	107.8	111.500394520144	-3.70039452014437
94	107.3	107.800235420337	-0.50023542033712
95	102.6	107.300031825145	-4.70003182514476
96	101	102.600299017597	-1.60029901759683
97	98.3	101.000101811559	-2.70010181155878
98	102.7	98.3001717813804	4.39982821861959
99	110.8	102.699720081457	8.10027991854295
100	112.8	110.799484657482	2.00051534251789
101	113.4	112.799872726545	0.600127273455243
102	104.3	113.399961819702	-9.09996181970213
103	93.8	104.300578942615	-10.5005789426148
104	90.5	93.8006680503447	-3.30066805034467

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 59.2 & 55.7 & 3.5 \tabularnewline
3 & 59.8 & 59.1997773288293 & 0.600222671170712 \tabularnewline
4 & 61.6 & 59.7999618136329 & 1.80003818636711 \tabularnewline
5 & 65.8 & 61.5998854809685 & 4.20011451903151 \tabularnewline
6 & 64.2 & 65.7997327873094 & -1.59973278730939 \tabularnewline
7 & 67 & 64.200101775535 & 2.79989822446497 \tabularnewline
8 & 62.8 & 66.9998218695384 & -4.19982186953843 \tabularnewline
9 & 65.5 & 62.8002671940721 & 2.69973280592787 \tabularnewline
10 & 75.2 & 65.4998282420958 & 9.70017175790416 \tabularnewline
11 & 80.9 & 75.1993828718281 & 5.70061712817186 \tabularnewline
12 & 83.2 & 80.8996373248315 & 2.3003626751685 \tabularnewline
13 & 83.7 & 83.1998536501572 & 0.500146349842836 \tabularnewline
14 & 86.4 & 83.6999681805219 & 2.70003181947807 \tabularnewline
15 & 85.9 & 86.3998282230725 & -0.499828223072512 \tabularnewline
16 & 80.4 & 85.9000317992387 & -5.50003179923874 \tabularnewline
17 & 81.8 & 80.4003499138628 & 1.39965008613721 \tabularnewline
18 & 87.5 & 81.7999109537933 & 5.70008904620666 \tabularnewline
19 & 83.7 & 87.4996373584283 & -3.79963735842826 \tabularnewline
20 & 87 & 83.7002417341997 & 3.29975826580031 \tabularnewline
21 & 99.7 & 86.9997900682754 & 12.7002099317246 \tabularnewline
22 & 101.4 & 99.699192008396 & 1.70080799160397 \tabularnewline
23 & 101.9 & 101.399891794027 & 0.500108205973333 \tabularnewline
24 & 115.7 & 101.899968182949 & 13.8000318170513 \tabularnewline
25 & 123.2 & 115.69912203736 & 7.50087796264019 \tabularnewline
26 & 136.9 & 123.199522791635 & 13.700477208365 \tabularnewline
27 & 146.8 & 136.899128371057 & 9.9008716289427 \tabularnewline
28 & 149.6 & 146.799370103235 & 2.80062989676478 \tabularnewline
29 & 146.5 & 149.599821822989 & -3.09982182298918 \tabularnewline
30 & 157 & 146.500197211701 & 10.4998027882988 \tabularnewline
31 & 147.9 & 156.999331999035 & -9.09933199903452 \tabularnewline
32 & 133.6 & 147.900578902545 & -14.3005789025454 \tabularnewline
33 & 128.7 & 133.600909807613 & -4.9009098076132 \tabularnewline
34 & 100.8 & 128.700311797521 & -27.9003117975213 \tabularnewline
35 & 91.8 & 100.801775027169 & -9.00177502716896 \tabularnewline
36 & 89.3 & 91.8005726959382 & -2.50057269593823 \tabularnewline
37 & 96.7 & 89.3001590872713 & 7.39984091272868 \tabularnewline
38 & 91.6 & 96.699529219646 & -5.09952921964596 \tabularnewline
39 & 93.3 & 91.6003244337547 & 1.6996755662453 \tabularnewline
40 & 93.3 & 93.2998918660719 & 0.000108133928051757 \tabularnewline
41 & 101 & 93.2999999931205 & 7.70000000687952 \tabularnewline
42 & 100.4 & 100.999510123424 & -0.599510123423968 \tabularnewline
43 & 86.9 & 100.400038141035 & -13.5000381410346 \tabularnewline
44 & 83.9 & 86.9008588769422 & -3.00085887694216 \tabularnewline
45 & 80.3 & 83.9001909156455 & -3.60019091564551 \tabularnewline
46 & 87.7 & 80.3002290453503 & 7.39977095464972 \tabularnewline
47 & 92.7 & 87.6995292240967 & 5.00047077590328 \tabularnewline
48 & 95.5 & 92.6996818683766 & 2.80031813162337 \tabularnewline
49 & 92 & 95.4998218428238 & -3.49982184282379 \tabularnewline
50 & 87.4 & 92.0002226598363 & -4.60022265983629 \tabularnewline
51 & 86.8 & 87.4002926677043 & -0.600292667704352 \tabularnewline
52 & 83.7 & 86.8000381908203 & -3.10003819082031 \tabularnewline
53 & 85 & 83.7001972254666 & 1.29980277453336 \tabularnewline
54 & 81.7 & 84.9999173061127 & -3.29991730611272 \tabularnewline
55 & 90.9 & 81.7002099418428 & 9.19979005815721 \tabularnewline
56 & 101.5 & 90.8994147062793 & 10.6005852937207 \tabularnewline
57 & 113.8 & 101.499325587218 & 12.3006744127822 \tabularnewline
58 & 120.1 & 113.799217426979 & 6.3007825730206 \tabularnewline
59 & 122.1 & 120.099599142105 & 2.00040085789485 \tabularnewline
60 & 132.5 & 122.099872733828 & 10.4001272661717 \tabularnewline
61 & 140 & 132.499338340425 & 7.50066165957543 \tabularnewline
62 & 149.4 & 139.999522805396 & 9.4004771946037 \tabularnewline
63 & 144.3 & 149.399401938497 & -5.0994019384965 \tabularnewline
64 & 154.4 & 144.300324425657 & 10.099675574343 \tabularnewline
65 & 151.4 & 154.399357455262 & -2.9993574552617 \tabularnewline
66 & 145.5 & 151.400190820125 & -5.90019082012458 \tabularnewline
67 & 136.8 & 145.500375372114 & -8.70037537211354 \tabularnewline
68 & 146.6 & 136.800553520791 & 9.79944647920863 \tabularnewline
69 & 145.1 & 146.599376555937 & -1.49937655593715 \tabularnewline
70 & 133.6 & 145.100095390838 & -11.500095390838 \tabularnewline
71 & 131.4 & 133.600731639915 & -2.20073163991543 \tabularnewline
72 & 127.5 & 131.400140011283 & -3.90014001128307 \tabularnewline
73 & 130.1 & 127.500248128212 & 2.59975187178792 \tabularnewline
74 & 131.1 & 130.099834602916 & 1.00016539708369 \tabularnewline
75 & 132.3 & 131.099936369143 & 1.20006363085713 \tabularnewline
76 & 128.6 & 132.29992365155 & -3.69992365155042 \tabularnewline
77 & 125.1 & 128.60023539038 & -3.50023539038031 \tabularnewline
78 & 128.7 & 125.100222686146 & 3.59977731385365 \tabularnewline
79 & 156.1 & 128.699770980963 & 27.4002290190368 \tabularnewline
80 & 163.2 & 156.098256788265 & 7.10174321173528 \tabularnewline
81 & 159.8 & 163.199548184721 & -3.39954818472137 \tabularnewline
82 & 157.4 & 159.800216280393 & -2.40021628039261 \tabularnewline
83 & 156.2 & 157.400152702563 & -1.20015270256263 \tabularnewline
84 & 152.5 & 156.200076354116 & -3.70007635411636 \tabularnewline
85 & 149.4 & 152.500235400095 & -3.1002354000953 \tabularnewline
86 & 145.9 & 149.400197238013 & -3.50019723801316 \tabularnewline
87 & 144.8 & 145.900222683719 & -1.10022268371907 \tabularnewline
88 & 135.9 & 144.800069996535 & -8.90006999653514 \tabularnewline
89 & 137.6 & 135.90056622543 & 1.6994337745698 \tabularnewline
90 & 136 & 137.599891881455 & -1.59989188145482 \tabularnewline
91 & 117.7 & 136.000101785657 & -18.3001017856566 \tabularnewline
92 & 111.5 & 117.701164258597 & -6.20116425859682 \tabularnewline
93 & 107.8 & 111.500394520144 & -3.70039452014437 \tabularnewline
94 & 107.3 & 107.800235420337 & -0.50023542033712 \tabularnewline
95 & 102.6 & 107.300031825145 & -4.70003182514476 \tabularnewline
96 & 101 & 102.600299017597 & -1.60029901759683 \tabularnewline
97 & 98.3 & 101.000101811559 & -2.70010181155878 \tabularnewline
98 & 102.7 & 98.3001717813804 & 4.39982821861959 \tabularnewline
99 & 110.8 & 102.699720081457 & 8.10027991854295 \tabularnewline
100 & 112.8 & 110.799484657482 & 2.00051534251789 \tabularnewline
101 & 113.4 & 112.799872726545 & 0.600127273455243 \tabularnewline
102 & 104.3 & 113.399961819702 & -9.09996181970213 \tabularnewline
103 & 93.8 & 104.300578942615 & -10.5005789426148 \tabularnewline
104 & 90.5 & 93.8006680503447 & -3.30066805034467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271958&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]2[/C][C]59.2[/C][C]55.7[/C][C]3.5[/C][/ROW]
[ROW][C]3[/C][C]59.8[/C][C]59.1997773288293[/C][C]0.600222671170712[/C][/ROW]
[ROW][C]4[/C][C]61.6[/C][C]59.7999618136329[/C][C]1.80003818636711[/C][/ROW]
[ROW][C]5[/C][C]65.8[/C][C]61.5998854809685[/C][C]4.20011451903151[/C][/ROW]
[ROW][C]6[/C][C]64.2[/C][C]65.7997327873094[/C][C]-1.59973278730939[/C][/ROW]
[ROW][C]7[/C][C]67[/C][C]64.200101775535[/C][C]2.79989822446497[/C][/ROW]
[ROW][C]8[/C][C]62.8[/C][C]66.9998218695384[/C][C]-4.19982186953843[/C][/ROW]
[ROW][C]9[/C][C]65.5[/C][C]62.8002671940721[/C][C]2.69973280592787[/C][/ROW]
[ROW][C]10[/C][C]75.2[/C][C]65.4998282420958[/C][C]9.70017175790416[/C][/ROW]
[ROW][C]11[/C][C]80.9[/C][C]75.1993828718281[/C][C]5.70061712817186[/C][/ROW]
[ROW][C]12[/C][C]83.2[/C][C]80.8996373248315[/C][C]2.3003626751685[/C][/ROW]
[ROW][C]13[/C][C]83.7[/C][C]83.1998536501572[/C][C]0.500146349842836[/C][/ROW]
[ROW][C]14[/C][C]86.4[/C][C]83.6999681805219[/C][C]2.70003181947807[/C][/ROW]
[ROW][C]15[/C][C]85.9[/C][C]86.3998282230725[/C][C]-0.499828223072512[/C][/ROW]
[ROW][C]16[/C][C]80.4[/C][C]85.9000317992387[/C][C]-5.50003179923874[/C][/ROW]
[ROW][C]17[/C][C]81.8[/C][C]80.4003499138628[/C][C]1.39965008613721[/C][/ROW]
[ROW][C]18[/C][C]87.5[/C][C]81.7999109537933[/C][C]5.70008904620666[/C][/ROW]
[ROW][C]19[/C][C]83.7[/C][C]87.4996373584283[/C][C]-3.79963735842826[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]83.7002417341997[/C][C]3.29975826580031[/C][/ROW]
[ROW][C]21[/C][C]99.7[/C][C]86.9997900682754[/C][C]12.7002099317246[/C][/ROW]
[ROW][C]22[/C][C]101.4[/C][C]99.699192008396[/C][C]1.70080799160397[/C][/ROW]
[ROW][C]23[/C][C]101.9[/C][C]101.399891794027[/C][C]0.500108205973333[/C][/ROW]
[ROW][C]24[/C][C]115.7[/C][C]101.899968182949[/C][C]13.8000318170513[/C][/ROW]
[ROW][C]25[/C][C]123.2[/C][C]115.69912203736[/C][C]7.50087796264019[/C][/ROW]
[ROW][C]26[/C][C]136.9[/C][C]123.199522791635[/C][C]13.700477208365[/C][/ROW]
[ROW][C]27[/C][C]146.8[/C][C]136.899128371057[/C][C]9.9008716289427[/C][/ROW]
[ROW][C]28[/C][C]149.6[/C][C]146.799370103235[/C][C]2.80062989676478[/C][/ROW]
[ROW][C]29[/C][C]146.5[/C][C]149.599821822989[/C][C]-3.09982182298918[/C][/ROW]
[ROW][C]30[/C][C]157[/C][C]146.500197211701[/C][C]10.4998027882988[/C][/ROW]
[ROW][C]31[/C][C]147.9[/C][C]156.999331999035[/C][C]-9.09933199903452[/C][/ROW]
[ROW][C]32[/C][C]133.6[/C][C]147.900578902545[/C][C]-14.3005789025454[/C][/ROW]
[ROW][C]33[/C][C]128.7[/C][C]133.600909807613[/C][C]-4.9009098076132[/C][/ROW]
[ROW][C]34[/C][C]100.8[/C][C]128.700311797521[/C][C]-27.9003117975213[/C][/ROW]
[ROW][C]35[/C][C]91.8[/C][C]100.801775027169[/C][C]-9.00177502716896[/C][/ROW]
[ROW][C]36[/C][C]89.3[/C][C]91.8005726959382[/C][C]-2.50057269593823[/C][/ROW]
[ROW][C]37[/C][C]96.7[/C][C]89.3001590872713[/C][C]7.39984091272868[/C][/ROW]
[ROW][C]38[/C][C]91.6[/C][C]96.699529219646[/C][C]-5.09952921964596[/C][/ROW]
[ROW][C]39[/C][C]93.3[/C][C]91.6003244337547[/C][C]1.6996755662453[/C][/ROW]
[ROW][C]40[/C][C]93.3[/C][C]93.2998918660719[/C][C]0.000108133928051757[/C][/ROW]
[ROW][C]41[/C][C]101[/C][C]93.2999999931205[/C][C]7.70000000687952[/C][/ROW]
[ROW][C]42[/C][C]100.4[/C][C]100.999510123424[/C][C]-0.599510123423968[/C][/ROW]
[ROW][C]43[/C][C]86.9[/C][C]100.400038141035[/C][C]-13.5000381410346[/C][/ROW]
[ROW][C]44[/C][C]83.9[/C][C]86.9008588769422[/C][C]-3.00085887694216[/C][/ROW]
[ROW][C]45[/C][C]80.3[/C][C]83.9001909156455[/C][C]-3.60019091564551[/C][/ROW]
[ROW][C]46[/C][C]87.7[/C][C]80.3002290453503[/C][C]7.39977095464972[/C][/ROW]
[ROW][C]47[/C][C]92.7[/C][C]87.6995292240967[/C][C]5.00047077590328[/C][/ROW]
[ROW][C]48[/C][C]95.5[/C][C]92.6996818683766[/C][C]2.80031813162337[/C][/ROW]
[ROW][C]49[/C][C]92[/C][C]95.4998218428238[/C][C]-3.49982184282379[/C][/ROW]
[ROW][C]50[/C][C]87.4[/C][C]92.0002226598363[/C][C]-4.60022265983629[/C][/ROW]
[ROW][C]51[/C][C]86.8[/C][C]87.4002926677043[/C][C]-0.600292667704352[/C][/ROW]
[ROW][C]52[/C][C]83.7[/C][C]86.8000381908203[/C][C]-3.10003819082031[/C][/ROW]
[ROW][C]53[/C][C]85[/C][C]83.7001972254666[/C][C]1.29980277453336[/C][/ROW]
[ROW][C]54[/C][C]81.7[/C][C]84.9999173061127[/C][C]-3.29991730611272[/C][/ROW]
[ROW][C]55[/C][C]90.9[/C][C]81.7002099418428[/C][C]9.19979005815721[/C][/ROW]
[ROW][C]56[/C][C]101.5[/C][C]90.8994147062793[/C][C]10.6005852937207[/C][/ROW]
[ROW][C]57[/C][C]113.8[/C][C]101.499325587218[/C][C]12.3006744127822[/C][/ROW]
[ROW][C]58[/C][C]120.1[/C][C]113.799217426979[/C][C]6.3007825730206[/C][/ROW]
[ROW][C]59[/C][C]122.1[/C][C]120.099599142105[/C][C]2.00040085789485[/C][/ROW]
[ROW][C]60[/C][C]132.5[/C][C]122.099872733828[/C][C]10.4001272661717[/C][/ROW]
[ROW][C]61[/C][C]140[/C][C]132.499338340425[/C][C]7.50066165957543[/C][/ROW]
[ROW][C]62[/C][C]149.4[/C][C]139.999522805396[/C][C]9.4004771946037[/C][/ROW]
[ROW][C]63[/C][C]144.3[/C][C]149.399401938497[/C][C]-5.0994019384965[/C][/ROW]
[ROW][C]64[/C][C]154.4[/C][C]144.300324425657[/C][C]10.099675574343[/C][/ROW]
[ROW][C]65[/C][C]151.4[/C][C]154.399357455262[/C][C]-2.9993574552617[/C][/ROW]
[ROW][C]66[/C][C]145.5[/C][C]151.400190820125[/C][C]-5.90019082012458[/C][/ROW]
[ROW][C]67[/C][C]136.8[/C][C]145.500375372114[/C][C]-8.70037537211354[/C][/ROW]
[ROW][C]68[/C][C]146.6[/C][C]136.800553520791[/C][C]9.79944647920863[/C][/ROW]
[ROW][C]69[/C][C]145.1[/C][C]146.599376555937[/C][C]-1.49937655593715[/C][/ROW]
[ROW][C]70[/C][C]133.6[/C][C]145.100095390838[/C][C]-11.500095390838[/C][/ROW]
[ROW][C]71[/C][C]131.4[/C][C]133.600731639915[/C][C]-2.20073163991543[/C][/ROW]
[ROW][C]72[/C][C]127.5[/C][C]131.400140011283[/C][C]-3.90014001128307[/C][/ROW]
[ROW][C]73[/C][C]130.1[/C][C]127.500248128212[/C][C]2.59975187178792[/C][/ROW]
[ROW][C]74[/C][C]131.1[/C][C]130.099834602916[/C][C]1.00016539708369[/C][/ROW]
[ROW][C]75[/C][C]132.3[/C][C]131.099936369143[/C][C]1.20006363085713[/C][/ROW]
[ROW][C]76[/C][C]128.6[/C][C]132.29992365155[/C][C]-3.69992365155042[/C][/ROW]
[ROW][C]77[/C][C]125.1[/C][C]128.60023539038[/C][C]-3.50023539038031[/C][/ROW]
[ROW][C]78[/C][C]128.7[/C][C]125.100222686146[/C][C]3.59977731385365[/C][/ROW]
[ROW][C]79[/C][C]156.1[/C][C]128.699770980963[/C][C]27.4002290190368[/C][/ROW]
[ROW][C]80[/C][C]163.2[/C][C]156.098256788265[/C][C]7.10174321173528[/C][/ROW]
[ROW][C]81[/C][C]159.8[/C][C]163.199548184721[/C][C]-3.39954818472137[/C][/ROW]
[ROW][C]82[/C][C]157.4[/C][C]159.800216280393[/C][C]-2.40021628039261[/C][/ROW]
[ROW][C]83[/C][C]156.2[/C][C]157.400152702563[/C][C]-1.20015270256263[/C][/ROW]
[ROW][C]84[/C][C]152.5[/C][C]156.200076354116[/C][C]-3.70007635411636[/C][/ROW]
[ROW][C]85[/C][C]149.4[/C][C]152.500235400095[/C][C]-3.1002354000953[/C][/ROW]
[ROW][C]86[/C][C]145.9[/C][C]149.400197238013[/C][C]-3.50019723801316[/C][/ROW]
[ROW][C]87[/C][C]144.8[/C][C]145.900222683719[/C][C]-1.10022268371907[/C][/ROW]
[ROW][C]88[/C][C]135.9[/C][C]144.800069996535[/C][C]-8.90006999653514[/C][/ROW]
[ROW][C]89[/C][C]137.6[/C][C]135.90056622543[/C][C]1.6994337745698[/C][/ROW]
[ROW][C]90[/C][C]136[/C][C]137.599891881455[/C][C]-1.59989188145482[/C][/ROW]
[ROW][C]91[/C][C]117.7[/C][C]136.000101785657[/C][C]-18.3001017856566[/C][/ROW]
[ROW][C]92[/C][C]111.5[/C][C]117.701164258597[/C][C]-6.20116425859682[/C][/ROW]
[ROW][C]93[/C][C]107.8[/C][C]111.500394520144[/C][C]-3.70039452014437[/C][/ROW]
[ROW][C]94[/C][C]107.3[/C][C]107.800235420337[/C][C]-0.50023542033712[/C][/ROW]
[ROW][C]95[/C][C]102.6[/C][C]107.300031825145[/C][C]-4.70003182514476[/C][/ROW]
[ROW][C]96[/C][C]101[/C][C]102.600299017597[/C][C]-1.60029901759683[/C][/ROW]
[ROW][C]97[/C][C]98.3[/C][C]101.000101811559[/C][C]-2.70010181155878[/C][/ROW]
[ROW][C]98[/C][C]102.7[/C][C]98.3001717813804[/C][C]4.39982821861959[/C][/ROW]
[ROW][C]99[/C][C]110.8[/C][C]102.699720081457[/C][C]8.10027991854295[/C][/ROW]
[ROW][C]100[/C][C]112.8[/C][C]110.799484657482[/C][C]2.00051534251789[/C][/ROW]
[ROW][C]101[/C][C]113.4[/C][C]112.799872726545[/C][C]0.600127273455243[/C][/ROW]
[ROW][C]102[/C][C]104.3[/C][C]113.399961819702[/C][C]-9.09996181970213[/C][/ROW]
[ROW][C]103[/C][C]93.8[/C][C]104.300578942615[/C][C]-10.5005789426148[/C][/ROW]
[ROW][C]104[/C][C]90.5[/C][C]93.8006680503447[/C][C]-3.30066805034467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271958&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
2	59.2	55.7	3.5
3	59.8	59.1997773288293	0.600222671170712
4	61.6	59.7999618136329	1.80003818636711
5	65.8	61.5998854809685	4.20011451903151
6	64.2	65.7997327873094	-1.59973278730939
7	67	64.200101775535	2.79989822446497
8	62.8	66.9998218695384	-4.19982186953843
9	65.5	62.8002671940721	2.69973280592787
10	75.2	65.4998282420958	9.70017175790416
11	80.9	75.1993828718281	5.70061712817186
12	83.2	80.8996373248315	2.3003626751685
13	83.7	83.1998536501572	0.500146349842836
14	86.4	83.6999681805219	2.70003181947807
15	85.9	86.3998282230725	-0.499828223072512
16	80.4	85.9000317992387	-5.50003179923874
17	81.8	80.4003499138628	1.39965008613721
18	87.5	81.7999109537933	5.70008904620666
19	83.7	87.4996373584283	-3.79963735842826
20	87	83.7002417341997	3.29975826580031
21	99.7	86.9997900682754	12.7002099317246
22	101.4	99.699192008396	1.70080799160397
23	101.9	101.399891794027	0.500108205973333
24	115.7	101.899968182949	13.8000318170513
25	123.2	115.69912203736	7.50087796264019
26	136.9	123.199522791635	13.700477208365
27	146.8	136.899128371057	9.9008716289427
28	149.6	146.799370103235	2.80062989676478
29	146.5	149.599821822989	-3.09982182298918
30	157	146.500197211701	10.4998027882988
31	147.9	156.999331999035	-9.09933199903452
32	133.6	147.900578902545	-14.3005789025454
33	128.7	133.600909807613	-4.9009098076132
34	100.8	128.700311797521	-27.9003117975213
35	91.8	100.801775027169	-9.00177502716896
36	89.3	91.8005726959382	-2.50057269593823
37	96.7	89.3001590872713	7.39984091272868
38	91.6	96.699529219646	-5.09952921964596
39	93.3	91.6003244337547	1.6996755662453
40	93.3	93.2998918660719	0.000108133928051757
41	101	93.2999999931205	7.70000000687952
42	100.4	100.999510123424	-0.599510123423968
43	86.9	100.400038141035	-13.5000381410346
44	83.9	86.9008588769422	-3.00085887694216
45	80.3	83.9001909156455	-3.60019091564551
46	87.7	80.3002290453503	7.39977095464972
47	92.7	87.6995292240967	5.00047077590328
48	95.5	92.6996818683766	2.80031813162337
49	92	95.4998218428238	-3.49982184282379
50	87.4	92.0002226598363	-4.60022265983629
51	86.8	87.4002926677043	-0.600292667704352
52	83.7	86.8000381908203	-3.10003819082031
53	85	83.7001972254666	1.29980277453336
54	81.7	84.9999173061127	-3.29991730611272
55	90.9	81.7002099418428	9.19979005815721
56	101.5	90.8994147062793	10.6005852937207
57	113.8	101.499325587218	12.3006744127822
58	120.1	113.799217426979	6.3007825730206
59	122.1	120.099599142105	2.00040085789485
60	132.5	122.099872733828	10.4001272661717
61	140	132.499338340425	7.50066165957543
62	149.4	139.999522805396	9.4004771946037
63	144.3	149.399401938497	-5.0994019384965
64	154.4	144.300324425657	10.099675574343
65	151.4	154.399357455262	-2.9993574552617
66	145.5	151.400190820125	-5.90019082012458
67	136.8	145.500375372114	-8.70037537211354
68	146.6	136.800553520791	9.79944647920863
69	145.1	146.599376555937	-1.49937655593715
70	133.6	145.100095390838	-11.500095390838
71	131.4	133.600731639915	-2.20073163991543
72	127.5	131.400140011283	-3.90014001128307
73	130.1	127.500248128212	2.59975187178792
74	131.1	130.099834602916	1.00016539708369
75	132.3	131.099936369143	1.20006363085713
76	128.6	132.29992365155	-3.69992365155042
77	125.1	128.60023539038	-3.50023539038031
78	128.7	125.100222686146	3.59977731385365
79	156.1	128.699770980963	27.4002290190368
80	163.2	156.098256788265	7.10174321173528
81	159.8	163.199548184721	-3.39954818472137
82	157.4	159.800216280393	-2.40021628039261
83	156.2	157.400152702563	-1.20015270256263
84	152.5	156.200076354116	-3.70007635411636
85	149.4	152.500235400095	-3.1002354000953
86	145.9	149.400197238013	-3.50019723801316
87	144.8	145.900222683719	-1.10022268371907
88	135.9	144.800069996535	-8.90006999653514
89	137.6	135.90056622543	1.6994337745698
90	136	137.599891881455	-1.59989188145482
91	117.7	136.000101785657	-18.3001017856566
92	111.5	117.701164258597	-6.20116425859682
93	107.8	111.500394520144	-3.70039452014437
94	107.3	107.800235420337	-0.50023542033712
95	102.6	107.300031825145	-4.70003182514476
96	101	102.600299017597	-1.60029901759683
97	98.3	101.000101811559	-2.70010181155878
98	102.7	98.3001717813804	4.39982821861959
99	110.8	102.699720081457	8.10027991854295
100	112.8	110.799484657482	2.00051534251789
101	113.4	112.799872726545	0.600127273455243
102	104.3	113.399961819702	-9.09996181970213
103	93.8	104.300578942615	-10.5005789426148
104	90.5	93.8006680503447	-3.30066805034467

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
105	90.5002099896054	75.9461235756662	105.054296403545
106	90.5002099896054	69.9182783201642	111.082141659047
107	90.5002099896054	65.2928620301971	115.707557949014
108	90.5002099896054	61.39342605445	119.606993924761
109	90.5002099896054	57.9579397714881	123.042480207723
110	90.5002099896054	54.852014651691	126.14840532752
111	90.5002099896054	51.9958165941598	129.004603385051
112	90.5002099896054	49.3373287657118	131.663091213499
113	90.5002099896054	46.8404199013158	134.160000077895
114	90.5002099896054	44.4787829098782	136.521637069333
115	90.5002099896054	42.2325579817048	138.767861997506
116	90.5002099896054	40.0863159696338	140.914104009577

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
105 & 90.5002099896054 & 75.9461235756662 & 105.054296403545 \tabularnewline
106 & 90.5002099896054 & 69.9182783201642 & 111.082141659047 \tabularnewline
107 & 90.5002099896054 & 65.2928620301971 & 115.707557949014 \tabularnewline
108 & 90.5002099896054 & 61.39342605445 & 119.606993924761 \tabularnewline
109 & 90.5002099896054 & 57.9579397714881 & 123.042480207723 \tabularnewline
110 & 90.5002099896054 & 54.852014651691 & 126.14840532752 \tabularnewline
111 & 90.5002099896054 & 51.9958165941598 & 129.004603385051 \tabularnewline
112 & 90.5002099896054 & 49.3373287657118 & 131.663091213499 \tabularnewline
113 & 90.5002099896054 & 46.8404199013158 & 134.160000077895 \tabularnewline
114 & 90.5002099896054 & 44.4787829098782 & 136.521637069333 \tabularnewline
115 & 90.5002099896054 & 42.2325579817048 & 138.767861997506 \tabularnewline
116 & 90.5002099896054 & 40.0863159696338 & 140.914104009577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271958&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]105[/C][C]90.5002099896054[/C][C]75.9461235756662[/C][C]105.054296403545[/C][/ROW]
[ROW][C]106[/C][C]90.5002099896054[/C][C]69.9182783201642[/C][C]111.082141659047[/C][/ROW]
[ROW][C]107[/C][C]90.5002099896054[/C][C]65.2928620301971[/C][C]115.707557949014[/C][/ROW]
[ROW][C]108[/C][C]90.5002099896054[/C][C]61.39342605445[/C][C]119.606993924761[/C][/ROW]
[ROW][C]109[/C][C]90.5002099896054[/C][C]57.9579397714881[/C][C]123.042480207723[/C][/ROW]
[ROW][C]110[/C][C]90.5002099896054[/C][C]54.852014651691[/C][C]126.14840532752[/C][/ROW]
[ROW][C]111[/C][C]90.5002099896054[/C][C]51.9958165941598[/C][C]129.004603385051[/C][/ROW]
[ROW][C]112[/C][C]90.5002099896054[/C][C]49.3373287657118[/C][C]131.663091213499[/C][/ROW]
[ROW][C]113[/C][C]90.5002099896054[/C][C]46.8404199013158[/C][C]134.160000077895[/C][/ROW]
[ROW][C]114[/C][C]90.5002099896054[/C][C]44.4787829098782[/C][C]136.521637069333[/C][/ROW]
[ROW][C]115[/C][C]90.5002099896054[/C][C]42.2325579817048[/C][C]138.767861997506[/C][/ROW]
[ROW][C]116[/C][C]90.5002099896054[/C][C]40.0863159696338[/C][C]140.914104009577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271958&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
105	90.5002099896054	75.9461235756662	105.054296403545
106	90.5002099896054	69.9182783201642	111.082141659047
107	90.5002099896054	65.2928620301971	115.707557949014
108	90.5002099896054	61.39342605445	119.606993924761
109	90.5002099896054	57.9579397714881	123.042480207723
110	90.5002099896054	54.852014651691	126.14840532752
111	90.5002099896054	51.9958165941598	129.004603385051
112	90.5002099896054	49.3373287657118	131.663091213499
113	90.5002099896054	46.8404199013158	134.160000077895
114	90.5002099896054	44.4787829098782	136.521637069333
115	90.5002099896054	42.2325579817048	138.767861997506
116	90.5002099896054	40.0863159696338	140.914104009577

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 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

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