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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 01:59:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/20/t1305856500av3rvfhfxhdgoei.htm/, Retrieved Mon, 13 May 2024 10:59:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122353, Retrieved Mon, 13 May 2024 10:59:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-20 01:59:07] [7ec7c2b78d31d17737f91280a6e28d4a] [Current]
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Dataseries X:
90
51
47
59
54
79
59
80
46
62
55
77
72
72
71
50
66
78
59
52
71
98
70
84
90
98
98
78
59
0
58
55
62
80
91
86
61
49
61
56
73
85
82
32
39
30
51
48
57
59
32
56
54
74
62
78
72
48
59
61
80
69
58
63
27
23
34
45
51
51
73
37
35
66
54
30
66
61
37
55
64
53
63
70
72
52
53
50
60
73
66
78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122353&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122353&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.439852181310189
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.439852181310189 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122353&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]0.439852181310189[/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=122353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122353&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
ParameterValue
alpha0.439852181310189
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25190-39
34772.8457649289026-25.8457649289026
45961.4774488472944-2.47744884729442
55460.3877375677276-6.38773756772756
67957.578077264925521.4219227350745
75967.0005567078064-8.00055670780638
88063.481494388181916.5185056118181
94670.7471951135247-24.7471951135247
106259.8620873615322.137912638468
115560.8024528990128-5.80245289901277
127758.250231334432418.7497686655676
137266.49735798104375.50264201895628
147268.91770707605073.08229292394925
157170.27346034208680.726539657913207
165070.5930303954283-20.5930303954283
176661.53514105621214.46485894378788
187863.499019001879514.5009809981205
195969.8773071250404-10.8773071250404
205265.0928998593105-13.0928998593105
217159.333959296516911.6660407034831
229864.465292747197433.5347072528026
237079.2156068819412-9.21560688194124
248475.16210209282228.8378979071778
259079.049470765491110.9505292345089
269883.866084935790814.1339150642092
279890.08291830723627.91708169276382
287893.5652639594093-15.5652639594093
295986.7188486541942-27.7188486541942
30074.5266526102399-74.5266526102399
315841.745941893879216.2540581061208
325548.8953248069996.10467519300101
336251.580479506830710.4195204931693
348056.163528323957423.8364716760426
359166.648052385403324.3519476145967
368677.35930966283518.6406903371649
376181.159936155663-20.159936155663
384972.2925442625205-23.2925442625205
396162.0472678603867-1.04726786038671
405661.5866248075796-5.58662480757956
417359.129335699804113.8706643001959
428565.230377648466619.7696223515334
438273.92608916346728.07391083653276
443277.4774164566201-45.4774164566201
453957.4740756278239-18.4740756278239
463049.3482131652361-19.3482131652361
475140.837859400052510.1621405999475
484845.30769910972022.69230089027975
495746.491913529053210.5080864709468
505951.11391828469527.88608171530479
513254.5826285291624-22.5826285291624
525644.649610110892611.3503898891074
535449.64210386233764.35789613766238
547451.558933984411722.4410660155883
556261.42968582229410.570314177705853
567861.680539757390216.3194602426098
577268.8586899429073.14131005709298
584870.240402023691-22.240402023691
595960.457912680355-1.45791268035497
606159.8166466077411.18335339225894
618060.33714717858719.662852821413
626968.98589588286670.0141041171333001
635868.9920996095532-10.9920996095532
646364.1572006191124-1.15720061911237
652763.6482034025823-36.6482034025823
662347.528411194857-24.528411194857
673436.7395360267259-2.73953602672587
684535.53454512959279.46545487040735
695139.697946101434511.3020538985655
705144.66917916200396.33082083799615
717347.453804517080525.5461954829195
723758.6903543244191-21.6903543244191
733549.1498046614325-14.1498046614325
746642.925982215988323.0740177840117
755453.0751392698760.924860730124045
763053.4819412794292-23.4819412794292
776643.153358186274522.8466418137255
786153.20250342365427.79749657634578
793756.6322493015186-19.6322493015186
805547.99696162222027.00303837777977
816451.077263328485612.9227366715144
825356.7613572419484-3.7613572419484
836355.10691605439057.89308394560948
847058.578706245131311.4212937548687
857263.60238721659478.39761278340527
865267.2960955171739-15.2960955171739
875360.5680745384159-7.56807453841594
885057.2392404443756-7.23924044437558
896054.0550447438885.94495525611196
907356.669946281080416.3300537189196
916663.85275603025972.14724396974027
927864.797225974155113.2027740258449

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 51 & 90 & -39 \tabularnewline
3 & 47 & 72.8457649289026 & -25.8457649289026 \tabularnewline
4 & 59 & 61.4774488472944 & -2.47744884729442 \tabularnewline
5 & 54 & 60.3877375677276 & -6.38773756772756 \tabularnewline
6 & 79 & 57.5780772649255 & 21.4219227350745 \tabularnewline
7 & 59 & 67.0005567078064 & -8.00055670780638 \tabularnewline
8 & 80 & 63.4814943881819 & 16.5185056118181 \tabularnewline
9 & 46 & 70.7471951135247 & -24.7471951135247 \tabularnewline
10 & 62 & 59.862087361532 & 2.137912638468 \tabularnewline
11 & 55 & 60.8024528990128 & -5.80245289901277 \tabularnewline
12 & 77 & 58.2502313344324 & 18.7497686655676 \tabularnewline
13 & 72 & 66.4973579810437 & 5.50264201895628 \tabularnewline
14 & 72 & 68.9177070760507 & 3.08229292394925 \tabularnewline
15 & 71 & 70.2734603420868 & 0.726539657913207 \tabularnewline
16 & 50 & 70.5930303954283 & -20.5930303954283 \tabularnewline
17 & 66 & 61.5351410562121 & 4.46485894378788 \tabularnewline
18 & 78 & 63.4990190018795 & 14.5009809981205 \tabularnewline
19 & 59 & 69.8773071250404 & -10.8773071250404 \tabularnewline
20 & 52 & 65.0928998593105 & -13.0928998593105 \tabularnewline
21 & 71 & 59.3339592965169 & 11.6660407034831 \tabularnewline
22 & 98 & 64.4652927471974 & 33.5347072528026 \tabularnewline
23 & 70 & 79.2156068819412 & -9.21560688194124 \tabularnewline
24 & 84 & 75.1621020928222 & 8.8378979071778 \tabularnewline
25 & 90 & 79.0494707654911 & 10.9505292345089 \tabularnewline
26 & 98 & 83.8660849357908 & 14.1339150642092 \tabularnewline
27 & 98 & 90.0829183072362 & 7.91708169276382 \tabularnewline
28 & 78 & 93.5652639594093 & -15.5652639594093 \tabularnewline
29 & 59 & 86.7188486541942 & -27.7188486541942 \tabularnewline
30 & 0 & 74.5266526102399 & -74.5266526102399 \tabularnewline
31 & 58 & 41.7459418938792 & 16.2540581061208 \tabularnewline
32 & 55 & 48.895324806999 & 6.10467519300101 \tabularnewline
33 & 62 & 51.5804795068307 & 10.4195204931693 \tabularnewline
34 & 80 & 56.1635283239574 & 23.8364716760426 \tabularnewline
35 & 91 & 66.6480523854033 & 24.3519476145967 \tabularnewline
36 & 86 & 77.3593096628351 & 8.6406903371649 \tabularnewline
37 & 61 & 81.159936155663 & -20.159936155663 \tabularnewline
38 & 49 & 72.2925442625205 & -23.2925442625205 \tabularnewline
39 & 61 & 62.0472678603867 & -1.04726786038671 \tabularnewline
40 & 56 & 61.5866248075796 & -5.58662480757956 \tabularnewline
41 & 73 & 59.1293356998041 & 13.8706643001959 \tabularnewline
42 & 85 & 65.2303776484666 & 19.7696223515334 \tabularnewline
43 & 82 & 73.9260891634672 & 8.07391083653276 \tabularnewline
44 & 32 & 77.4774164566201 & -45.4774164566201 \tabularnewline
45 & 39 & 57.4740756278239 & -18.4740756278239 \tabularnewline
46 & 30 & 49.3482131652361 & -19.3482131652361 \tabularnewline
47 & 51 & 40.8378594000525 & 10.1621405999475 \tabularnewline
48 & 48 & 45.3076991097202 & 2.69230089027975 \tabularnewline
49 & 57 & 46.4919135290532 & 10.5080864709468 \tabularnewline
50 & 59 & 51.1139182846952 & 7.88608171530479 \tabularnewline
51 & 32 & 54.5826285291624 & -22.5826285291624 \tabularnewline
52 & 56 & 44.6496101108926 & 11.3503898891074 \tabularnewline
53 & 54 & 49.6421038623376 & 4.35789613766238 \tabularnewline
54 & 74 & 51.5589339844117 & 22.4410660155883 \tabularnewline
55 & 62 & 61.4296858222941 & 0.570314177705853 \tabularnewline
56 & 78 & 61.6805397573902 & 16.3194602426098 \tabularnewline
57 & 72 & 68.858689942907 & 3.14131005709298 \tabularnewline
58 & 48 & 70.240402023691 & -22.240402023691 \tabularnewline
59 & 59 & 60.457912680355 & -1.45791268035497 \tabularnewline
60 & 61 & 59.816646607741 & 1.18335339225894 \tabularnewline
61 & 80 & 60.337147178587 & 19.662852821413 \tabularnewline
62 & 69 & 68.9858958828667 & 0.0141041171333001 \tabularnewline
63 & 58 & 68.9920996095532 & -10.9920996095532 \tabularnewline
64 & 63 & 64.1572006191124 & -1.15720061911237 \tabularnewline
65 & 27 & 63.6482034025823 & -36.6482034025823 \tabularnewline
66 & 23 & 47.528411194857 & -24.528411194857 \tabularnewline
67 & 34 & 36.7395360267259 & -2.73953602672587 \tabularnewline
68 & 45 & 35.5345451295927 & 9.46545487040735 \tabularnewline
69 & 51 & 39.6979461014345 & 11.3020538985655 \tabularnewline
70 & 51 & 44.6691791620039 & 6.33082083799615 \tabularnewline
71 & 73 & 47.4538045170805 & 25.5461954829195 \tabularnewline
72 & 37 & 58.6903543244191 & -21.6903543244191 \tabularnewline
73 & 35 & 49.1498046614325 & -14.1498046614325 \tabularnewline
74 & 66 & 42.9259822159883 & 23.0740177840117 \tabularnewline
75 & 54 & 53.075139269876 & 0.924860730124045 \tabularnewline
76 & 30 & 53.4819412794292 & -23.4819412794292 \tabularnewline
77 & 66 & 43.1533581862745 & 22.8466418137255 \tabularnewline
78 & 61 & 53.2025034236542 & 7.79749657634578 \tabularnewline
79 & 37 & 56.6322493015186 & -19.6322493015186 \tabularnewline
80 & 55 & 47.9969616222202 & 7.00303837777977 \tabularnewline
81 & 64 & 51.0772633284856 & 12.9227366715144 \tabularnewline
82 & 53 & 56.7613572419484 & -3.7613572419484 \tabularnewline
83 & 63 & 55.1069160543905 & 7.89308394560948 \tabularnewline
84 & 70 & 58.5787062451313 & 11.4212937548687 \tabularnewline
85 & 72 & 63.6023872165947 & 8.39761278340527 \tabularnewline
86 & 52 & 67.2960955171739 & -15.2960955171739 \tabularnewline
87 & 53 & 60.5680745384159 & -7.56807453841594 \tabularnewline
88 & 50 & 57.2392404443756 & -7.23924044437558 \tabularnewline
89 & 60 & 54.055044743888 & 5.94495525611196 \tabularnewline
90 & 73 & 56.6699462810804 & 16.3300537189196 \tabularnewline
91 & 66 & 63.8527560302597 & 2.14724396974027 \tabularnewline
92 & 78 & 64.7972259741551 & 13.2027740258449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122353&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]51[/C][C]90[/C][C]-39[/C][/ROW]
[ROW][C]3[/C][C]47[/C][C]72.8457649289026[/C][C]-25.8457649289026[/C][/ROW]
[ROW][C]4[/C][C]59[/C][C]61.4774488472944[/C][C]-2.47744884729442[/C][/ROW]
[ROW][C]5[/C][C]54[/C][C]60.3877375677276[/C][C]-6.38773756772756[/C][/ROW]
[ROW][C]6[/C][C]79[/C][C]57.5780772649255[/C][C]21.4219227350745[/C][/ROW]
[ROW][C]7[/C][C]59[/C][C]67.0005567078064[/C][C]-8.00055670780638[/C][/ROW]
[ROW][C]8[/C][C]80[/C][C]63.4814943881819[/C][C]16.5185056118181[/C][/ROW]
[ROW][C]9[/C][C]46[/C][C]70.7471951135247[/C][C]-24.7471951135247[/C][/ROW]
[ROW][C]10[/C][C]62[/C][C]59.862087361532[/C][C]2.137912638468[/C][/ROW]
[ROW][C]11[/C][C]55[/C][C]60.8024528990128[/C][C]-5.80245289901277[/C][/ROW]
[ROW][C]12[/C][C]77[/C][C]58.2502313344324[/C][C]18.7497686655676[/C][/ROW]
[ROW][C]13[/C][C]72[/C][C]66.4973579810437[/C][C]5.50264201895628[/C][/ROW]
[ROW][C]14[/C][C]72[/C][C]68.9177070760507[/C][C]3.08229292394925[/C][/ROW]
[ROW][C]15[/C][C]71[/C][C]70.2734603420868[/C][C]0.726539657913207[/C][/ROW]
[ROW][C]16[/C][C]50[/C][C]70.5930303954283[/C][C]-20.5930303954283[/C][/ROW]
[ROW][C]17[/C][C]66[/C][C]61.5351410562121[/C][C]4.46485894378788[/C][/ROW]
[ROW][C]18[/C][C]78[/C][C]63.4990190018795[/C][C]14.5009809981205[/C][/ROW]
[ROW][C]19[/C][C]59[/C][C]69.8773071250404[/C][C]-10.8773071250404[/C][/ROW]
[ROW][C]20[/C][C]52[/C][C]65.0928998593105[/C][C]-13.0928998593105[/C][/ROW]
[ROW][C]21[/C][C]71[/C][C]59.3339592965169[/C][C]11.6660407034831[/C][/ROW]
[ROW][C]22[/C][C]98[/C][C]64.4652927471974[/C][C]33.5347072528026[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]79.2156068819412[/C][C]-9.21560688194124[/C][/ROW]
[ROW][C]24[/C][C]84[/C][C]75.1621020928222[/C][C]8.8378979071778[/C][/ROW]
[ROW][C]25[/C][C]90[/C][C]79.0494707654911[/C][C]10.9505292345089[/C][/ROW]
[ROW][C]26[/C][C]98[/C][C]83.8660849357908[/C][C]14.1339150642092[/C][/ROW]
[ROW][C]27[/C][C]98[/C][C]90.0829183072362[/C][C]7.91708169276382[/C][/ROW]
[ROW][C]28[/C][C]78[/C][C]93.5652639594093[/C][C]-15.5652639594093[/C][/ROW]
[ROW][C]29[/C][C]59[/C][C]86.7188486541942[/C][C]-27.7188486541942[/C][/ROW]
[ROW][C]30[/C][C]0[/C][C]74.5266526102399[/C][C]-74.5266526102399[/C][/ROW]
[ROW][C]31[/C][C]58[/C][C]41.7459418938792[/C][C]16.2540581061208[/C][/ROW]
[ROW][C]32[/C][C]55[/C][C]48.895324806999[/C][C]6.10467519300101[/C][/ROW]
[ROW][C]33[/C][C]62[/C][C]51.5804795068307[/C][C]10.4195204931693[/C][/ROW]
[ROW][C]34[/C][C]80[/C][C]56.1635283239574[/C][C]23.8364716760426[/C][/ROW]
[ROW][C]35[/C][C]91[/C][C]66.6480523854033[/C][C]24.3519476145967[/C][/ROW]
[ROW][C]36[/C][C]86[/C][C]77.3593096628351[/C][C]8.6406903371649[/C][/ROW]
[ROW][C]37[/C][C]61[/C][C]81.159936155663[/C][C]-20.159936155663[/C][/ROW]
[ROW][C]38[/C][C]49[/C][C]72.2925442625205[/C][C]-23.2925442625205[/C][/ROW]
[ROW][C]39[/C][C]61[/C][C]62.0472678603867[/C][C]-1.04726786038671[/C][/ROW]
[ROW][C]40[/C][C]56[/C][C]61.5866248075796[/C][C]-5.58662480757956[/C][/ROW]
[ROW][C]41[/C][C]73[/C][C]59.1293356998041[/C][C]13.8706643001959[/C][/ROW]
[ROW][C]42[/C][C]85[/C][C]65.2303776484666[/C][C]19.7696223515334[/C][/ROW]
[ROW][C]43[/C][C]82[/C][C]73.9260891634672[/C][C]8.07391083653276[/C][/ROW]
[ROW][C]44[/C][C]32[/C][C]77.4774164566201[/C][C]-45.4774164566201[/C][/ROW]
[ROW][C]45[/C][C]39[/C][C]57.4740756278239[/C][C]-18.4740756278239[/C][/ROW]
[ROW][C]46[/C][C]30[/C][C]49.3482131652361[/C][C]-19.3482131652361[/C][/ROW]
[ROW][C]47[/C][C]51[/C][C]40.8378594000525[/C][C]10.1621405999475[/C][/ROW]
[ROW][C]48[/C][C]48[/C][C]45.3076991097202[/C][C]2.69230089027975[/C][/ROW]
[ROW][C]49[/C][C]57[/C][C]46.4919135290532[/C][C]10.5080864709468[/C][/ROW]
[ROW][C]50[/C][C]59[/C][C]51.1139182846952[/C][C]7.88608171530479[/C][/ROW]
[ROW][C]51[/C][C]32[/C][C]54.5826285291624[/C][C]-22.5826285291624[/C][/ROW]
[ROW][C]52[/C][C]56[/C][C]44.6496101108926[/C][C]11.3503898891074[/C][/ROW]
[ROW][C]53[/C][C]54[/C][C]49.6421038623376[/C][C]4.35789613766238[/C][/ROW]
[ROW][C]54[/C][C]74[/C][C]51.5589339844117[/C][C]22.4410660155883[/C][/ROW]
[ROW][C]55[/C][C]62[/C][C]61.4296858222941[/C][C]0.570314177705853[/C][/ROW]
[ROW][C]56[/C][C]78[/C][C]61.6805397573902[/C][C]16.3194602426098[/C][/ROW]
[ROW][C]57[/C][C]72[/C][C]68.858689942907[/C][C]3.14131005709298[/C][/ROW]
[ROW][C]58[/C][C]48[/C][C]70.240402023691[/C][C]-22.240402023691[/C][/ROW]
[ROW][C]59[/C][C]59[/C][C]60.457912680355[/C][C]-1.45791268035497[/C][/ROW]
[ROW][C]60[/C][C]61[/C][C]59.816646607741[/C][C]1.18335339225894[/C][/ROW]
[ROW][C]61[/C][C]80[/C][C]60.337147178587[/C][C]19.662852821413[/C][/ROW]
[ROW][C]62[/C][C]69[/C][C]68.9858958828667[/C][C]0.0141041171333001[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]68.9920996095532[/C][C]-10.9920996095532[/C][/ROW]
[ROW][C]64[/C][C]63[/C][C]64.1572006191124[/C][C]-1.15720061911237[/C][/ROW]
[ROW][C]65[/C][C]27[/C][C]63.6482034025823[/C][C]-36.6482034025823[/C][/ROW]
[ROW][C]66[/C][C]23[/C][C]47.528411194857[/C][C]-24.528411194857[/C][/ROW]
[ROW][C]67[/C][C]34[/C][C]36.7395360267259[/C][C]-2.73953602672587[/C][/ROW]
[ROW][C]68[/C][C]45[/C][C]35.5345451295927[/C][C]9.46545487040735[/C][/ROW]
[ROW][C]69[/C][C]51[/C][C]39.6979461014345[/C][C]11.3020538985655[/C][/ROW]
[ROW][C]70[/C][C]51[/C][C]44.6691791620039[/C][C]6.33082083799615[/C][/ROW]
[ROW][C]71[/C][C]73[/C][C]47.4538045170805[/C][C]25.5461954829195[/C][/ROW]
[ROW][C]72[/C][C]37[/C][C]58.6903543244191[/C][C]-21.6903543244191[/C][/ROW]
[ROW][C]73[/C][C]35[/C][C]49.1498046614325[/C][C]-14.1498046614325[/C][/ROW]
[ROW][C]74[/C][C]66[/C][C]42.9259822159883[/C][C]23.0740177840117[/C][/ROW]
[ROW][C]75[/C][C]54[/C][C]53.075139269876[/C][C]0.924860730124045[/C][/ROW]
[ROW][C]76[/C][C]30[/C][C]53.4819412794292[/C][C]-23.4819412794292[/C][/ROW]
[ROW][C]77[/C][C]66[/C][C]43.1533581862745[/C][C]22.8466418137255[/C][/ROW]
[ROW][C]78[/C][C]61[/C][C]53.2025034236542[/C][C]7.79749657634578[/C][/ROW]
[ROW][C]79[/C][C]37[/C][C]56.6322493015186[/C][C]-19.6322493015186[/C][/ROW]
[ROW][C]80[/C][C]55[/C][C]47.9969616222202[/C][C]7.00303837777977[/C][/ROW]
[ROW][C]81[/C][C]64[/C][C]51.0772633284856[/C][C]12.9227366715144[/C][/ROW]
[ROW][C]82[/C][C]53[/C][C]56.7613572419484[/C][C]-3.7613572419484[/C][/ROW]
[ROW][C]83[/C][C]63[/C][C]55.1069160543905[/C][C]7.89308394560948[/C][/ROW]
[ROW][C]84[/C][C]70[/C][C]58.5787062451313[/C][C]11.4212937548687[/C][/ROW]
[ROW][C]85[/C][C]72[/C][C]63.6023872165947[/C][C]8.39761278340527[/C][/ROW]
[ROW][C]86[/C][C]52[/C][C]67.2960955171739[/C][C]-15.2960955171739[/C][/ROW]
[ROW][C]87[/C][C]53[/C][C]60.5680745384159[/C][C]-7.56807453841594[/C][/ROW]
[ROW][C]88[/C][C]50[/C][C]57.2392404443756[/C][C]-7.23924044437558[/C][/ROW]
[ROW][C]89[/C][C]60[/C][C]54.055044743888[/C][C]5.94495525611196[/C][/ROW]
[ROW][C]90[/C][C]73[/C][C]56.6699462810804[/C][C]16.3300537189196[/C][/ROW]
[ROW][C]91[/C][C]66[/C][C]63.8527560302597[/C][C]2.14724396974027[/C][/ROW]
[ROW][C]92[/C][C]78[/C][C]64.7972259741551[/C][C]13.2027740258449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122353&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122353&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
tObservedFittedResiduals
25190-39
34772.8457649289026-25.8457649289026
45961.4774488472944-2.47744884729442
55460.3877375677276-6.38773756772756
67957.578077264925521.4219227350745
75967.0005567078064-8.00055670780638
88063.481494388181916.5185056118181
94670.7471951135247-24.7471951135247
106259.8620873615322.137912638468
115560.8024528990128-5.80245289901277
127758.250231334432418.7497686655676
137266.49735798104375.50264201895628
147268.91770707605073.08229292394925
157170.27346034208680.726539657913207
165070.5930303954283-20.5930303954283
176661.53514105621214.46485894378788
187863.499019001879514.5009809981205
195969.8773071250404-10.8773071250404
205265.0928998593105-13.0928998593105
217159.333959296516911.6660407034831
229864.465292747197433.5347072528026
237079.2156068819412-9.21560688194124
248475.16210209282228.8378979071778
259079.049470765491110.9505292345089
269883.866084935790814.1339150642092
279890.08291830723627.91708169276382
287893.5652639594093-15.5652639594093
295986.7188486541942-27.7188486541942
30074.5266526102399-74.5266526102399
315841.745941893879216.2540581061208
325548.8953248069996.10467519300101
336251.580479506830710.4195204931693
348056.163528323957423.8364716760426
359166.648052385403324.3519476145967
368677.35930966283518.6406903371649
376181.159936155663-20.159936155663
384972.2925442625205-23.2925442625205
396162.0472678603867-1.04726786038671
405661.5866248075796-5.58662480757956
417359.129335699804113.8706643001959
428565.230377648466619.7696223515334
438273.92608916346728.07391083653276
443277.4774164566201-45.4774164566201
453957.4740756278239-18.4740756278239
463049.3482131652361-19.3482131652361
475140.837859400052510.1621405999475
484845.30769910972022.69230089027975
495746.491913529053210.5080864709468
505951.11391828469527.88608171530479
513254.5826285291624-22.5826285291624
525644.649610110892611.3503898891074
535449.64210386233764.35789613766238
547451.558933984411722.4410660155883
556261.42968582229410.570314177705853
567861.680539757390216.3194602426098
577268.8586899429073.14131005709298
584870.240402023691-22.240402023691
595960.457912680355-1.45791268035497
606159.8166466077411.18335339225894
618060.33714717858719.662852821413
626968.98589588286670.0141041171333001
635868.9920996095532-10.9920996095532
646364.1572006191124-1.15720061911237
652763.6482034025823-36.6482034025823
662347.528411194857-24.528411194857
673436.7395360267259-2.73953602672587
684535.53454512959279.46545487040735
695139.697946101434511.3020538985655
705144.66917916200396.33082083799615
717347.453804517080525.5461954829195
723758.6903543244191-21.6903543244191
733549.1498046614325-14.1498046614325
746642.925982215988323.0740177840117
755453.0751392698760.924860730124045
763053.4819412794292-23.4819412794292
776643.153358186274522.8466418137255
786153.20250342365427.79749657634578
793756.6322493015186-19.6322493015186
805547.99696162222027.00303837777977
816451.077263328485612.9227366715144
825356.7613572419484-3.7613572419484
836355.10691605439057.89308394560948
847058.578706245131311.4212937548687
857263.60238721659478.39761278340527
865267.2960955171739-15.2960955171739
875360.5680745384159-7.56807453841594
885057.2392404443756-7.23924044437558
896054.0550447438885.94495525611196
907356.669946281080416.3300537189196
916663.85275603025972.14724396974027
927864.797225974155113.2027740258449







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9370.604494928768535.3862506134328105.822739244104
9470.604494928768532.129954177741109.079035679796
9570.604494928768529.128527919544112.080461937993
9670.604494928768526.3301073813604114.878882476177
9770.604494928768523.6983445213232117.510645336214
9870.604494928768521.2065951819808120.002394675556
9970.604494928768518.8346383253212122.374351532216
10070.604494928768516.5666969898323124.642292867705
10170.604494928768514.3901803866779126.818809470859
10270.604494928768512.2948498193623128.914140038175
10370.604494928768510.2722459558295130.936743901708
10470.60449492876858.31528382860682132.89370602893

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
93 & 70.6044949287685 & 35.3862506134328 & 105.822739244104 \tabularnewline
94 & 70.6044949287685 & 32.129954177741 & 109.079035679796 \tabularnewline
95 & 70.6044949287685 & 29.128527919544 & 112.080461937993 \tabularnewline
96 & 70.6044949287685 & 26.3301073813604 & 114.878882476177 \tabularnewline
97 & 70.6044949287685 & 23.6983445213232 & 117.510645336214 \tabularnewline
98 & 70.6044949287685 & 21.2065951819808 & 120.002394675556 \tabularnewline
99 & 70.6044949287685 & 18.8346383253212 & 122.374351532216 \tabularnewline
100 & 70.6044949287685 & 16.5666969898323 & 124.642292867705 \tabularnewline
101 & 70.6044949287685 & 14.3901803866779 & 126.818809470859 \tabularnewline
102 & 70.6044949287685 & 12.2948498193623 & 128.914140038175 \tabularnewline
103 & 70.6044949287685 & 10.2722459558295 & 130.936743901708 \tabularnewline
104 & 70.6044949287685 & 8.31528382860682 & 132.89370602893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122353&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]93[/C][C]70.6044949287685[/C][C]35.3862506134328[/C][C]105.822739244104[/C][/ROW]
[ROW][C]94[/C][C]70.6044949287685[/C][C]32.129954177741[/C][C]109.079035679796[/C][/ROW]
[ROW][C]95[/C][C]70.6044949287685[/C][C]29.128527919544[/C][C]112.080461937993[/C][/ROW]
[ROW][C]96[/C][C]70.6044949287685[/C][C]26.3301073813604[/C][C]114.878882476177[/C][/ROW]
[ROW][C]97[/C][C]70.6044949287685[/C][C]23.6983445213232[/C][C]117.510645336214[/C][/ROW]
[ROW][C]98[/C][C]70.6044949287685[/C][C]21.2065951819808[/C][C]120.002394675556[/C][/ROW]
[ROW][C]99[/C][C]70.6044949287685[/C][C]18.8346383253212[/C][C]122.374351532216[/C][/ROW]
[ROW][C]100[/C][C]70.6044949287685[/C][C]16.5666969898323[/C][C]124.642292867705[/C][/ROW]
[ROW][C]101[/C][C]70.6044949287685[/C][C]14.3901803866779[/C][C]126.818809470859[/C][/ROW]
[ROW][C]102[/C][C]70.6044949287685[/C][C]12.2948498193623[/C][C]128.914140038175[/C][/ROW]
[ROW][C]103[/C][C]70.6044949287685[/C][C]10.2722459558295[/C][C]130.936743901708[/C][/ROW]
[ROW][C]104[/C][C]70.6044949287685[/C][C]8.31528382860682[/C][C]132.89370602893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122353&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122353&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
tForecast95% Lower Bound95% Upper Bound
9370.604494928768535.3862506134328105.822739244104
9470.604494928768532.129954177741109.079035679796
9570.604494928768529.128527919544112.080461937993
9670.604494928768526.3301073813604114.878882476177
9770.604494928768523.6983445213232117.510645336214
9870.604494928768521.2065951819808120.002394675556
9970.604494928768518.8346383253212122.374351532216
10070.604494928768516.5666969898323124.642292867705
10170.604494928768514.3901803866779126.818809470859
10270.604494928768512.2948498193623128.914140038175
10370.604494928768510.2722459558295130.936743901708
10470.60449492876858.31528382860682132.89370602893



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')