Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Aug 2013 00:14:52 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/21/t13770585940fw5q47nkqwe1b3.htm/, Retrieved Sat, 27 Apr 2024 10:34:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211283, Retrieved Sat, 27 Apr 2024 10:34:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsRaedts Mathias
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2013-08-21 04:14:52] [e2e43c39163d7563005e2a800525cced] [Current]
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Dataseries X:
58896
57616
56232
53708
79784
78524
58896
45848
47112
47112
48372
51040
54968
53708
45848
47112
83716
91572
70664
58896
61548
62828
69404
75856
77260
64088
65476
48372
96888
111200
78524
68016
74596
82452
94220
108656
108656
99412
95484
71928
111200
129564
113848
96888
99412
108656
121704
137420
126896
120444
120444
99412
129564
149188
133492
116516
121704
142612
151856
164888
154380
137420
133492
102080
122968
145260
120444
106008
120444
134756
142612
163624
153120
126896
129564
104744
125636
144000
122968
108656
121704
137420
134756
166168
160976
140068
141332
113848
130824
157048
137420
125636
145260
157048
147928
189724
179340
155784
149188
119056
136140
151856
132212
132212
154380
166168
159696
205420
193652
171484
162240
129564
141332
162240
146524
142612
160976
176672
159696
200228




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211283&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211283&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.204033093693474
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.204033093693474 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211283&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]0.204033093693474[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211283&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
alpha0.204033093693474
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135496854443.9853201372524.014679862841
145370852959.627205834748.372794165982
154584844971.5030092609876.496990739121
164711245942.88122236951169.11877763054
178371680921.13621018622794.86378981383
189157287411.69319351214160.30680648793
197066464328.46940697946335.53059302064
205889651914.37357442166981.62642557844
216154855950.12236389045597.8776361096
226282858388.29328256514439.70671743492
236940461582.40177505127821.59822494876
247585666420.49586186489435.50413813522
257726073460.6325509793799.36744902103
266408872108.4660315167-8020.4660315167
276547659757.83026743915718.1697325609
284837262107.7126362952-13735.7126362952
2996888104407.580670731-7519.58067073095
30111200111219.615458363-19.615458362663
317852483973.8922393961-5449.8922393961
326801667116.058656684899.941343315964
337459668837.53566707845758.46433292162
348245270294.548838090912157.4511619091
359422078260.701437393215959.2985626068
3610865686468.390373991722187.6096260083
3710865691578.183478296917077.8165217031
389941280556.753957132218855.2460428678
399548484403.096845977811080.9031540222
407192866911.78124921845016.2187507816
41111200137752.242055786-26552.2420557861
42129564151528.192428078-21964.1924280776
43113848105005.6234582518842.37654174869
449688892048.85783215614839.14216784394
4599412100089.333352422-677.333352421672
46108656106481.8913179282174.10868207221
47121704117087.228290194616.77170980973
48137420129139.314556528280.68544348024
49126896125877.2562266811018.74377331862
50120444109993.88361697410450.116383026
51120444104807.28523117315636.7147688265
529941280069.33408484419342.665915156
53129564135082.93700153-5518.93700152956
54149188160658.28259315-11470.2825931504
55133492136599.198601315-3107.19860131497
56116516114361.5082709982154.49172900188
57121704117837.1175262513866.88247374864
58142612128986.01105715213625.9889428477
59151856146250.0558484555605.94415154509
60164888164100.570335284787.429664715659
61154380151281.1595251093098.84047489078
62137420141307.003753054-3887.00375305364
63133492136248.347868433-2756.34786843302
64102080106663.625942772-4583.62594277241
65122968138909.849418299-15941.849418299
66145260158474.709179782-13214.7091797819
67120444140006.752809418-19562.7528094178
68106008118251.889109582-12243.8891095816
69120444120107.907671192336.092328808125
70134756137860.17554093-3104.17554093018
71142612145017.355863356-2405.35586335565
72163624156816.822576356807.17742365022
73153120147538.7903014065581.209698594
74126896133116.723209659-6220.72320965934
75129564128637.066402608926.933597391602
7610474499401.6343978545342.36560214598
77125636123967.0956322191668.90436778148
78144000149375.726477762-5375.72647776231
79122968126541.667212985-3573.66721298486
80108656113097.083772999-4441.083772999
81121704127358.093880544-5654.09388054394
82137420141817.730854175-4397.73085417479
83134756149606.953539353-14850.9535393528
84166168166672.383223793-504.383223792887
85160976154667.9846704786308.01532952164
86140068130477.2514701859590.74852981538
87141332134990.3134957266341.68650427437
88113848108953.7135773734894.2864226274
89130824131489.854181933-665.85418193342
90157048151633.7630602585414.23693974232
91137420131147.6844344876272.31556551266
92125636117916.4587201857719.54127981534
93145260135001.27160721810258.7283927815
94157048155693.3612954691354.63870453121
95147928156012.158798715-8084.15879871545
96189724190336.034784657-612.03478465692
97179340182626.824235558-3286.82423555767
98155784155891.384555919-107.384555919038
99149188155703.246378045-6515.24637804463
100119056123172.623563024-4116.62356302395
101136140140671.437351599-4531.43735159931
102151856166494.268612942-14638.2686129416
103132212141662.635253736-9450.63525373637
104132212126058.0828342756153.91716572538
105154380144943.4140751169436.58592488355
106166168158498.0168048617669.98319513898
107159696152365.8389619537330.16103804708
108205420197428.6049562217991.39504377855
109193652188817.3319738644834.66802613574
110171484164855.1607654786628.83923452205
111162240160495.3156882651744.6843117346
112129564129202.307034594361.692965405513
113141332148751.010224441-7419.01022444057
114162240167176.723033743-4936.72303374289
115146524146611.773009848-87.7730098477623
116142612145081.560358411-2469.56035841058
117160976166540.272262484-5564.27226248448
118176672176240.993212215431.006787785154
119159696167770.80739427-8074.80739426997
120200228211901.134221201-11673.1342212011

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 54968 & 54443.9853201372 & 524.014679862841 \tabularnewline
14 & 53708 & 52959.627205834 & 748.372794165982 \tabularnewline
15 & 45848 & 44971.5030092609 & 876.496990739121 \tabularnewline
16 & 47112 & 45942.8812223695 & 1169.11877763054 \tabularnewline
17 & 83716 & 80921.1362101862 & 2794.86378981383 \tabularnewline
18 & 91572 & 87411.6931935121 & 4160.30680648793 \tabularnewline
19 & 70664 & 64328.4694069794 & 6335.53059302064 \tabularnewline
20 & 58896 & 51914.3735744216 & 6981.62642557844 \tabularnewline
21 & 61548 & 55950.1223638904 & 5597.8776361096 \tabularnewline
22 & 62828 & 58388.2932825651 & 4439.70671743492 \tabularnewline
23 & 69404 & 61582.4017750512 & 7821.59822494876 \tabularnewline
24 & 75856 & 66420.4958618648 & 9435.50413813522 \tabularnewline
25 & 77260 & 73460.632550979 & 3799.36744902103 \tabularnewline
26 & 64088 & 72108.4660315167 & -8020.4660315167 \tabularnewline
27 & 65476 & 59757.8302674391 & 5718.1697325609 \tabularnewline
28 & 48372 & 62107.7126362952 & -13735.7126362952 \tabularnewline
29 & 96888 & 104407.580670731 & -7519.58067073095 \tabularnewline
30 & 111200 & 111219.615458363 & -19.615458362663 \tabularnewline
31 & 78524 & 83973.8922393961 & -5449.8922393961 \tabularnewline
32 & 68016 & 67116.058656684 & 899.941343315964 \tabularnewline
33 & 74596 & 68837.5356670784 & 5758.46433292162 \tabularnewline
34 & 82452 & 70294.5488380909 & 12157.4511619091 \tabularnewline
35 & 94220 & 78260.7014373932 & 15959.2985626068 \tabularnewline
36 & 108656 & 86468.3903739917 & 22187.6096260083 \tabularnewline
37 & 108656 & 91578.1834782969 & 17077.8165217031 \tabularnewline
38 & 99412 & 80556.7539571322 & 18855.2460428678 \tabularnewline
39 & 95484 & 84403.0968459778 & 11080.9031540222 \tabularnewline
40 & 71928 & 66911.7812492184 & 5016.2187507816 \tabularnewline
41 & 111200 & 137752.242055786 & -26552.2420557861 \tabularnewline
42 & 129564 & 151528.192428078 & -21964.1924280776 \tabularnewline
43 & 113848 & 105005.623458251 & 8842.37654174869 \tabularnewline
44 & 96888 & 92048.8578321561 & 4839.14216784394 \tabularnewline
45 & 99412 & 100089.333352422 & -677.333352421672 \tabularnewline
46 & 108656 & 106481.891317928 & 2174.10868207221 \tabularnewline
47 & 121704 & 117087.22829019 & 4616.77170980973 \tabularnewline
48 & 137420 & 129139.31455652 & 8280.68544348024 \tabularnewline
49 & 126896 & 125877.256226681 & 1018.74377331862 \tabularnewline
50 & 120444 & 109993.883616974 & 10450.116383026 \tabularnewline
51 & 120444 & 104807.285231173 & 15636.7147688265 \tabularnewline
52 & 99412 & 80069.334084844 & 19342.665915156 \tabularnewline
53 & 129564 & 135082.93700153 & -5518.93700152956 \tabularnewline
54 & 149188 & 160658.28259315 & -11470.2825931504 \tabularnewline
55 & 133492 & 136599.198601315 & -3107.19860131497 \tabularnewline
56 & 116516 & 114361.508270998 & 2154.49172900188 \tabularnewline
57 & 121704 & 117837.117526251 & 3866.88247374864 \tabularnewline
58 & 142612 & 128986.011057152 & 13625.9889428477 \tabularnewline
59 & 151856 & 146250.055848455 & 5605.94415154509 \tabularnewline
60 & 164888 & 164100.570335284 & 787.429664715659 \tabularnewline
61 & 154380 & 151281.159525109 & 3098.84047489078 \tabularnewline
62 & 137420 & 141307.003753054 & -3887.00375305364 \tabularnewline
63 & 133492 & 136248.347868433 & -2756.34786843302 \tabularnewline
64 & 102080 & 106663.625942772 & -4583.62594277241 \tabularnewline
65 & 122968 & 138909.849418299 & -15941.849418299 \tabularnewline
66 & 145260 & 158474.709179782 & -13214.7091797819 \tabularnewline
67 & 120444 & 140006.752809418 & -19562.7528094178 \tabularnewline
68 & 106008 & 118251.889109582 & -12243.8891095816 \tabularnewline
69 & 120444 & 120107.907671192 & 336.092328808125 \tabularnewline
70 & 134756 & 137860.17554093 & -3104.17554093018 \tabularnewline
71 & 142612 & 145017.355863356 & -2405.35586335565 \tabularnewline
72 & 163624 & 156816.82257635 & 6807.17742365022 \tabularnewline
73 & 153120 & 147538.790301406 & 5581.209698594 \tabularnewline
74 & 126896 & 133116.723209659 & -6220.72320965934 \tabularnewline
75 & 129564 & 128637.066402608 & 926.933597391602 \tabularnewline
76 & 104744 & 99401.634397854 & 5342.36560214598 \tabularnewline
77 & 125636 & 123967.095632219 & 1668.90436778148 \tabularnewline
78 & 144000 & 149375.726477762 & -5375.72647776231 \tabularnewline
79 & 122968 & 126541.667212985 & -3573.66721298486 \tabularnewline
80 & 108656 & 113097.083772999 & -4441.083772999 \tabularnewline
81 & 121704 & 127358.093880544 & -5654.09388054394 \tabularnewline
82 & 137420 & 141817.730854175 & -4397.73085417479 \tabularnewline
83 & 134756 & 149606.953539353 & -14850.9535393528 \tabularnewline
84 & 166168 & 166672.383223793 & -504.383223792887 \tabularnewline
85 & 160976 & 154667.984670478 & 6308.01532952164 \tabularnewline
86 & 140068 & 130477.251470185 & 9590.74852981538 \tabularnewline
87 & 141332 & 134990.313495726 & 6341.68650427437 \tabularnewline
88 & 113848 & 108953.713577373 & 4894.2864226274 \tabularnewline
89 & 130824 & 131489.854181933 & -665.85418193342 \tabularnewline
90 & 157048 & 151633.763060258 & 5414.23693974232 \tabularnewline
91 & 137420 & 131147.684434487 & 6272.31556551266 \tabularnewline
92 & 125636 & 117916.458720185 & 7719.54127981534 \tabularnewline
93 & 145260 & 135001.271607218 & 10258.7283927815 \tabularnewline
94 & 157048 & 155693.361295469 & 1354.63870453121 \tabularnewline
95 & 147928 & 156012.158798715 & -8084.15879871545 \tabularnewline
96 & 189724 & 190336.034784657 & -612.03478465692 \tabularnewline
97 & 179340 & 182626.824235558 & -3286.82423555767 \tabularnewline
98 & 155784 & 155891.384555919 & -107.384555919038 \tabularnewline
99 & 149188 & 155703.246378045 & -6515.24637804463 \tabularnewline
100 & 119056 & 123172.623563024 & -4116.62356302395 \tabularnewline
101 & 136140 & 140671.437351599 & -4531.43735159931 \tabularnewline
102 & 151856 & 166494.268612942 & -14638.2686129416 \tabularnewline
103 & 132212 & 141662.635253736 & -9450.63525373637 \tabularnewline
104 & 132212 & 126058.082834275 & 6153.91716572538 \tabularnewline
105 & 154380 & 144943.414075116 & 9436.58592488355 \tabularnewline
106 & 166168 & 158498.016804861 & 7669.98319513898 \tabularnewline
107 & 159696 & 152365.838961953 & 7330.16103804708 \tabularnewline
108 & 205420 & 197428.604956221 & 7991.39504377855 \tabularnewline
109 & 193652 & 188817.331973864 & 4834.66802613574 \tabularnewline
110 & 171484 & 164855.160765478 & 6628.83923452205 \tabularnewline
111 & 162240 & 160495.315688265 & 1744.6843117346 \tabularnewline
112 & 129564 & 129202.307034594 & 361.692965405513 \tabularnewline
113 & 141332 & 148751.010224441 & -7419.01022444057 \tabularnewline
114 & 162240 & 167176.723033743 & -4936.72303374289 \tabularnewline
115 & 146524 & 146611.773009848 & -87.7730098477623 \tabularnewline
116 & 142612 & 145081.560358411 & -2469.56035841058 \tabularnewline
117 & 160976 & 166540.272262484 & -5564.27226248448 \tabularnewline
118 & 176672 & 176240.993212215 & 431.006787785154 \tabularnewline
119 & 159696 & 167770.80739427 & -8074.80739426997 \tabularnewline
120 & 200228 & 211901.134221201 & -11673.1342212011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211283&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]54968[/C][C]54443.9853201372[/C][C]524.014679862841[/C][/ROW]
[ROW][C]14[/C][C]53708[/C][C]52959.627205834[/C][C]748.372794165982[/C][/ROW]
[ROW][C]15[/C][C]45848[/C][C]44971.5030092609[/C][C]876.496990739121[/C][/ROW]
[ROW][C]16[/C][C]47112[/C][C]45942.8812223695[/C][C]1169.11877763054[/C][/ROW]
[ROW][C]17[/C][C]83716[/C][C]80921.1362101862[/C][C]2794.86378981383[/C][/ROW]
[ROW][C]18[/C][C]91572[/C][C]87411.6931935121[/C][C]4160.30680648793[/C][/ROW]
[ROW][C]19[/C][C]70664[/C][C]64328.4694069794[/C][C]6335.53059302064[/C][/ROW]
[ROW][C]20[/C][C]58896[/C][C]51914.3735744216[/C][C]6981.62642557844[/C][/ROW]
[ROW][C]21[/C][C]61548[/C][C]55950.1223638904[/C][C]5597.8776361096[/C][/ROW]
[ROW][C]22[/C][C]62828[/C][C]58388.2932825651[/C][C]4439.70671743492[/C][/ROW]
[ROW][C]23[/C][C]69404[/C][C]61582.4017750512[/C][C]7821.59822494876[/C][/ROW]
[ROW][C]24[/C][C]75856[/C][C]66420.4958618648[/C][C]9435.50413813522[/C][/ROW]
[ROW][C]25[/C][C]77260[/C][C]73460.632550979[/C][C]3799.36744902103[/C][/ROW]
[ROW][C]26[/C][C]64088[/C][C]72108.4660315167[/C][C]-8020.4660315167[/C][/ROW]
[ROW][C]27[/C][C]65476[/C][C]59757.8302674391[/C][C]5718.1697325609[/C][/ROW]
[ROW][C]28[/C][C]48372[/C][C]62107.7126362952[/C][C]-13735.7126362952[/C][/ROW]
[ROW][C]29[/C][C]96888[/C][C]104407.580670731[/C][C]-7519.58067073095[/C][/ROW]
[ROW][C]30[/C][C]111200[/C][C]111219.615458363[/C][C]-19.615458362663[/C][/ROW]
[ROW][C]31[/C][C]78524[/C][C]83973.8922393961[/C][C]-5449.8922393961[/C][/ROW]
[ROW][C]32[/C][C]68016[/C][C]67116.058656684[/C][C]899.941343315964[/C][/ROW]
[ROW][C]33[/C][C]74596[/C][C]68837.5356670784[/C][C]5758.46433292162[/C][/ROW]
[ROW][C]34[/C][C]82452[/C][C]70294.5488380909[/C][C]12157.4511619091[/C][/ROW]
[ROW][C]35[/C][C]94220[/C][C]78260.7014373932[/C][C]15959.2985626068[/C][/ROW]
[ROW][C]36[/C][C]108656[/C][C]86468.3903739917[/C][C]22187.6096260083[/C][/ROW]
[ROW][C]37[/C][C]108656[/C][C]91578.1834782969[/C][C]17077.8165217031[/C][/ROW]
[ROW][C]38[/C][C]99412[/C][C]80556.7539571322[/C][C]18855.2460428678[/C][/ROW]
[ROW][C]39[/C][C]95484[/C][C]84403.0968459778[/C][C]11080.9031540222[/C][/ROW]
[ROW][C]40[/C][C]71928[/C][C]66911.7812492184[/C][C]5016.2187507816[/C][/ROW]
[ROW][C]41[/C][C]111200[/C][C]137752.242055786[/C][C]-26552.2420557861[/C][/ROW]
[ROW][C]42[/C][C]129564[/C][C]151528.192428078[/C][C]-21964.1924280776[/C][/ROW]
[ROW][C]43[/C][C]113848[/C][C]105005.623458251[/C][C]8842.37654174869[/C][/ROW]
[ROW][C]44[/C][C]96888[/C][C]92048.8578321561[/C][C]4839.14216784394[/C][/ROW]
[ROW][C]45[/C][C]99412[/C][C]100089.333352422[/C][C]-677.333352421672[/C][/ROW]
[ROW][C]46[/C][C]108656[/C][C]106481.891317928[/C][C]2174.10868207221[/C][/ROW]
[ROW][C]47[/C][C]121704[/C][C]117087.22829019[/C][C]4616.77170980973[/C][/ROW]
[ROW][C]48[/C][C]137420[/C][C]129139.31455652[/C][C]8280.68544348024[/C][/ROW]
[ROW][C]49[/C][C]126896[/C][C]125877.256226681[/C][C]1018.74377331862[/C][/ROW]
[ROW][C]50[/C][C]120444[/C][C]109993.883616974[/C][C]10450.116383026[/C][/ROW]
[ROW][C]51[/C][C]120444[/C][C]104807.285231173[/C][C]15636.7147688265[/C][/ROW]
[ROW][C]52[/C][C]99412[/C][C]80069.334084844[/C][C]19342.665915156[/C][/ROW]
[ROW][C]53[/C][C]129564[/C][C]135082.93700153[/C][C]-5518.93700152956[/C][/ROW]
[ROW][C]54[/C][C]149188[/C][C]160658.28259315[/C][C]-11470.2825931504[/C][/ROW]
[ROW][C]55[/C][C]133492[/C][C]136599.198601315[/C][C]-3107.19860131497[/C][/ROW]
[ROW][C]56[/C][C]116516[/C][C]114361.508270998[/C][C]2154.49172900188[/C][/ROW]
[ROW][C]57[/C][C]121704[/C][C]117837.117526251[/C][C]3866.88247374864[/C][/ROW]
[ROW][C]58[/C][C]142612[/C][C]128986.011057152[/C][C]13625.9889428477[/C][/ROW]
[ROW][C]59[/C][C]151856[/C][C]146250.055848455[/C][C]5605.94415154509[/C][/ROW]
[ROW][C]60[/C][C]164888[/C][C]164100.570335284[/C][C]787.429664715659[/C][/ROW]
[ROW][C]61[/C][C]154380[/C][C]151281.159525109[/C][C]3098.84047489078[/C][/ROW]
[ROW][C]62[/C][C]137420[/C][C]141307.003753054[/C][C]-3887.00375305364[/C][/ROW]
[ROW][C]63[/C][C]133492[/C][C]136248.347868433[/C][C]-2756.34786843302[/C][/ROW]
[ROW][C]64[/C][C]102080[/C][C]106663.625942772[/C][C]-4583.62594277241[/C][/ROW]
[ROW][C]65[/C][C]122968[/C][C]138909.849418299[/C][C]-15941.849418299[/C][/ROW]
[ROW][C]66[/C][C]145260[/C][C]158474.709179782[/C][C]-13214.7091797819[/C][/ROW]
[ROW][C]67[/C][C]120444[/C][C]140006.752809418[/C][C]-19562.7528094178[/C][/ROW]
[ROW][C]68[/C][C]106008[/C][C]118251.889109582[/C][C]-12243.8891095816[/C][/ROW]
[ROW][C]69[/C][C]120444[/C][C]120107.907671192[/C][C]336.092328808125[/C][/ROW]
[ROW][C]70[/C][C]134756[/C][C]137860.17554093[/C][C]-3104.17554093018[/C][/ROW]
[ROW][C]71[/C][C]142612[/C][C]145017.355863356[/C][C]-2405.35586335565[/C][/ROW]
[ROW][C]72[/C][C]163624[/C][C]156816.82257635[/C][C]6807.17742365022[/C][/ROW]
[ROW][C]73[/C][C]153120[/C][C]147538.790301406[/C][C]5581.209698594[/C][/ROW]
[ROW][C]74[/C][C]126896[/C][C]133116.723209659[/C][C]-6220.72320965934[/C][/ROW]
[ROW][C]75[/C][C]129564[/C][C]128637.066402608[/C][C]926.933597391602[/C][/ROW]
[ROW][C]76[/C][C]104744[/C][C]99401.634397854[/C][C]5342.36560214598[/C][/ROW]
[ROW][C]77[/C][C]125636[/C][C]123967.095632219[/C][C]1668.90436778148[/C][/ROW]
[ROW][C]78[/C][C]144000[/C][C]149375.726477762[/C][C]-5375.72647776231[/C][/ROW]
[ROW][C]79[/C][C]122968[/C][C]126541.667212985[/C][C]-3573.66721298486[/C][/ROW]
[ROW][C]80[/C][C]108656[/C][C]113097.083772999[/C][C]-4441.083772999[/C][/ROW]
[ROW][C]81[/C][C]121704[/C][C]127358.093880544[/C][C]-5654.09388054394[/C][/ROW]
[ROW][C]82[/C][C]137420[/C][C]141817.730854175[/C][C]-4397.73085417479[/C][/ROW]
[ROW][C]83[/C][C]134756[/C][C]149606.953539353[/C][C]-14850.9535393528[/C][/ROW]
[ROW][C]84[/C][C]166168[/C][C]166672.383223793[/C][C]-504.383223792887[/C][/ROW]
[ROW][C]85[/C][C]160976[/C][C]154667.984670478[/C][C]6308.01532952164[/C][/ROW]
[ROW][C]86[/C][C]140068[/C][C]130477.251470185[/C][C]9590.74852981538[/C][/ROW]
[ROW][C]87[/C][C]141332[/C][C]134990.313495726[/C][C]6341.68650427437[/C][/ROW]
[ROW][C]88[/C][C]113848[/C][C]108953.713577373[/C][C]4894.2864226274[/C][/ROW]
[ROW][C]89[/C][C]130824[/C][C]131489.854181933[/C][C]-665.85418193342[/C][/ROW]
[ROW][C]90[/C][C]157048[/C][C]151633.763060258[/C][C]5414.23693974232[/C][/ROW]
[ROW][C]91[/C][C]137420[/C][C]131147.684434487[/C][C]6272.31556551266[/C][/ROW]
[ROW][C]92[/C][C]125636[/C][C]117916.458720185[/C][C]7719.54127981534[/C][/ROW]
[ROW][C]93[/C][C]145260[/C][C]135001.271607218[/C][C]10258.7283927815[/C][/ROW]
[ROW][C]94[/C][C]157048[/C][C]155693.361295469[/C][C]1354.63870453121[/C][/ROW]
[ROW][C]95[/C][C]147928[/C][C]156012.158798715[/C][C]-8084.15879871545[/C][/ROW]
[ROW][C]96[/C][C]189724[/C][C]190336.034784657[/C][C]-612.03478465692[/C][/ROW]
[ROW][C]97[/C][C]179340[/C][C]182626.824235558[/C][C]-3286.82423555767[/C][/ROW]
[ROW][C]98[/C][C]155784[/C][C]155891.384555919[/C][C]-107.384555919038[/C][/ROW]
[ROW][C]99[/C][C]149188[/C][C]155703.246378045[/C][C]-6515.24637804463[/C][/ROW]
[ROW][C]100[/C][C]119056[/C][C]123172.623563024[/C][C]-4116.62356302395[/C][/ROW]
[ROW][C]101[/C][C]136140[/C][C]140671.437351599[/C][C]-4531.43735159931[/C][/ROW]
[ROW][C]102[/C][C]151856[/C][C]166494.268612942[/C][C]-14638.2686129416[/C][/ROW]
[ROW][C]103[/C][C]132212[/C][C]141662.635253736[/C][C]-9450.63525373637[/C][/ROW]
[ROW][C]104[/C][C]132212[/C][C]126058.082834275[/C][C]6153.91716572538[/C][/ROW]
[ROW][C]105[/C][C]154380[/C][C]144943.414075116[/C][C]9436.58592488355[/C][/ROW]
[ROW][C]106[/C][C]166168[/C][C]158498.016804861[/C][C]7669.98319513898[/C][/ROW]
[ROW][C]107[/C][C]159696[/C][C]152365.838961953[/C][C]7330.16103804708[/C][/ROW]
[ROW][C]108[/C][C]205420[/C][C]197428.604956221[/C][C]7991.39504377855[/C][/ROW]
[ROW][C]109[/C][C]193652[/C][C]188817.331973864[/C][C]4834.66802613574[/C][/ROW]
[ROW][C]110[/C][C]171484[/C][C]164855.160765478[/C][C]6628.83923452205[/C][/ROW]
[ROW][C]111[/C][C]162240[/C][C]160495.315688265[/C][C]1744.6843117346[/C][/ROW]
[ROW][C]112[/C][C]129564[/C][C]129202.307034594[/C][C]361.692965405513[/C][/ROW]
[ROW][C]113[/C][C]141332[/C][C]148751.010224441[/C][C]-7419.01022444057[/C][/ROW]
[ROW][C]114[/C][C]162240[/C][C]167176.723033743[/C][C]-4936.72303374289[/C][/ROW]
[ROW][C]115[/C][C]146524[/C][C]146611.773009848[/C][C]-87.7730098477623[/C][/ROW]
[ROW][C]116[/C][C]142612[/C][C]145081.560358411[/C][C]-2469.56035841058[/C][/ROW]
[ROW][C]117[/C][C]160976[/C][C]166540.272262484[/C][C]-5564.27226248448[/C][/ROW]
[ROW][C]118[/C][C]176672[/C][C]176240.993212215[/C][C]431.006787785154[/C][/ROW]
[ROW][C]119[/C][C]159696[/C][C]167770.80739427[/C][C]-8074.80739426997[/C][/ROW]
[ROW][C]120[/C][C]200228[/C][C]211901.134221201[/C][C]-11673.1342212011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211283&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
135496854443.9853201372524.014679862841
145370852959.627205834748.372794165982
154584844971.5030092609876.496990739121
164711245942.88122236951169.11877763054
178371680921.13621018622794.86378981383
189157287411.69319351214160.30680648793
197066464328.46940697946335.53059302064
205889651914.37357442166981.62642557844
216154855950.12236389045597.8776361096
226282858388.29328256514439.70671743492
236940461582.40177505127821.59822494876
247585666420.49586186489435.50413813522
257726073460.6325509793799.36744902103
266408872108.4660315167-8020.4660315167
276547659757.83026743915718.1697325609
284837262107.7126362952-13735.7126362952
2996888104407.580670731-7519.58067073095
30111200111219.615458363-19.615458362663
317852483973.8922393961-5449.8922393961
326801667116.058656684899.941343315964
337459668837.53566707845758.46433292162
348245270294.548838090912157.4511619091
359422078260.701437393215959.2985626068
3610865686468.390373991722187.6096260083
3710865691578.183478296917077.8165217031
389941280556.753957132218855.2460428678
399548484403.096845977811080.9031540222
407192866911.78124921845016.2187507816
41111200137752.242055786-26552.2420557861
42129564151528.192428078-21964.1924280776
43113848105005.6234582518842.37654174869
449688892048.85783215614839.14216784394
4599412100089.333352422-677.333352421672
46108656106481.8913179282174.10868207221
47121704117087.228290194616.77170980973
48137420129139.314556528280.68544348024
49126896125877.2562266811018.74377331862
50120444109993.88361697410450.116383026
51120444104807.28523117315636.7147688265
529941280069.33408484419342.665915156
53129564135082.93700153-5518.93700152956
54149188160658.28259315-11470.2825931504
55133492136599.198601315-3107.19860131497
56116516114361.5082709982154.49172900188
57121704117837.1175262513866.88247374864
58142612128986.01105715213625.9889428477
59151856146250.0558484555605.94415154509
60164888164100.570335284787.429664715659
61154380151281.1595251093098.84047489078
62137420141307.003753054-3887.00375305364
63133492136248.347868433-2756.34786843302
64102080106663.625942772-4583.62594277241
65122968138909.849418299-15941.849418299
66145260158474.709179782-13214.7091797819
67120444140006.752809418-19562.7528094178
68106008118251.889109582-12243.8891095816
69120444120107.907671192336.092328808125
70134756137860.17554093-3104.17554093018
71142612145017.355863356-2405.35586335565
72163624156816.822576356807.17742365022
73153120147538.7903014065581.209698594
74126896133116.723209659-6220.72320965934
75129564128637.066402608926.933597391602
7610474499401.6343978545342.36560214598
77125636123967.0956322191668.90436778148
78144000149375.726477762-5375.72647776231
79122968126541.667212985-3573.66721298486
80108656113097.083772999-4441.083772999
81121704127358.093880544-5654.09388054394
82137420141817.730854175-4397.73085417479
83134756149606.953539353-14850.9535393528
84166168166672.383223793-504.383223792887
85160976154667.9846704786308.01532952164
86140068130477.2514701859590.74852981538
87141332134990.3134957266341.68650427437
88113848108953.7135773734894.2864226274
89130824131489.854181933-665.85418193342
90157048151633.7630602585414.23693974232
91137420131147.6844344876272.31556551266
92125636117916.4587201857719.54127981534
93145260135001.27160721810258.7283927815
94157048155693.3612954691354.63870453121
95147928156012.158798715-8084.15879871545
96189724190336.034784657-612.03478465692
97179340182626.824235558-3286.82423555767
98155784155891.384555919-107.384555919038
99149188155703.246378045-6515.24637804463
100119056123172.623563024-4116.62356302395
101136140140671.437351599-4531.43735159931
102151856166494.268612942-14638.2686129416
103132212141662.635253736-9450.63525373637
104132212126058.0828342756153.91716572538
105154380144943.4140751169436.58592488355
106166168158498.0168048617669.98319513898
107159696152365.8389619537330.16103804708
108205420197428.6049562217991.39504377855
109193652188817.3319738644834.66802613574
110171484164855.1607654786628.83923452205
111162240160495.3156882651744.6843117346
112129564129202.307034594361.692965405513
113141332148751.010224441-7419.01022444057
114162240167176.723033743-4936.72303374289
115146524146611.773009848-87.7730098477623
116142612145081.560358411-2469.56035841058
117160976166540.272262484-5564.27226248448
118176672176240.993212215431.006787785154
119159696167770.80739427-8074.80739426997
120200228211901.134221201-11673.1342212011







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121196473.367571372179549.761376867213396.973765877
122172555.965936601155365.053499006189746.878374197
123162888.58974299145424.318005553180352.861480426
124130005.517478921112521.703967512147489.330990331
125143269.538819453125270.066660761161269.010978145
126165451.628962589146693.490982071184209.766943106
127149430.49275225130748.765953176168112.219551324
128145935.802045275127044.046499345164827.557591204
129165842.533535248146044.463508507185640.603561989
130181899.716554507161245.906647997202553.526461016
131166031.978746147145731.936018257186332.021474037
132210504.508989474195692.303693579225316.714285369

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 196473.367571372 & 179549.761376867 & 213396.973765877 \tabularnewline
122 & 172555.965936601 & 155365.053499006 & 189746.878374197 \tabularnewline
123 & 162888.58974299 & 145424.318005553 & 180352.861480426 \tabularnewline
124 & 130005.517478921 & 112521.703967512 & 147489.330990331 \tabularnewline
125 & 143269.538819453 & 125270.066660761 & 161269.010978145 \tabularnewline
126 & 165451.628962589 & 146693.490982071 & 184209.766943106 \tabularnewline
127 & 149430.49275225 & 130748.765953176 & 168112.219551324 \tabularnewline
128 & 145935.802045275 & 127044.046499345 & 164827.557591204 \tabularnewline
129 & 165842.533535248 & 146044.463508507 & 185640.603561989 \tabularnewline
130 & 181899.716554507 & 161245.906647997 & 202553.526461016 \tabularnewline
131 & 166031.978746147 & 145731.936018257 & 186332.021474037 \tabularnewline
132 & 210504.508989474 & 195692.303693579 & 225316.714285369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211283&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]121[/C][C]196473.367571372[/C][C]179549.761376867[/C][C]213396.973765877[/C][/ROW]
[ROW][C]122[/C][C]172555.965936601[/C][C]155365.053499006[/C][C]189746.878374197[/C][/ROW]
[ROW][C]123[/C][C]162888.58974299[/C][C]145424.318005553[/C][C]180352.861480426[/C][/ROW]
[ROW][C]124[/C][C]130005.517478921[/C][C]112521.703967512[/C][C]147489.330990331[/C][/ROW]
[ROW][C]125[/C][C]143269.538819453[/C][C]125270.066660761[/C][C]161269.010978145[/C][/ROW]
[ROW][C]126[/C][C]165451.628962589[/C][C]146693.490982071[/C][C]184209.766943106[/C][/ROW]
[ROW][C]127[/C][C]149430.49275225[/C][C]130748.765953176[/C][C]168112.219551324[/C][/ROW]
[ROW][C]128[/C][C]145935.802045275[/C][C]127044.046499345[/C][C]164827.557591204[/C][/ROW]
[ROW][C]129[/C][C]165842.533535248[/C][C]146044.463508507[/C][C]185640.603561989[/C][/ROW]
[ROW][C]130[/C][C]181899.716554507[/C][C]161245.906647997[/C][C]202553.526461016[/C][/ROW]
[ROW][C]131[/C][C]166031.978746147[/C][C]145731.936018257[/C][C]186332.021474037[/C][/ROW]
[ROW][C]132[/C][C]210504.508989474[/C][C]195692.303693579[/C][C]225316.714285369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211283&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
121196473.367571372179549.761376867213396.973765877
122172555.965936601155365.053499006189746.878374197
123162888.58974299145424.318005553180352.861480426
124130005.517478921112521.703967512147489.330990331
125143269.538819453125270.066660761161269.010978145
126165451.628962589146693.490982071184209.766943106
127149430.49275225130748.765953176168112.219551324
128145935.802045275127044.046499345164827.557591204
129165842.533535248146044.463508507185640.603561989
130181899.716554507161245.906647997202553.526461016
131166031.978746147145731.936018257186332.021474037
132210504.508989474195692.303693579225316.714285369



Parameters (Session):
par1 = 22 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')