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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 13:03:28 +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/2010/Aug/19/t1282223215fg3ame2ox2mf9wr.htm/, Retrieved Fri, 03 May 2024 05:03:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79288, Retrieved Fri, 03 May 2024 05:03:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQuaglia Laura
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [Tijdreeks B - Stap 6] [2010-08-17 13:31:24] [af95ebf906227b9d031fe2c98e4f0d3b]
- RMP     [Exponential Smoothing] [Tijdreeks B - Sta...] [2010-08-19 13:03:28] [f9e29edf9cfe01f572cce0cb5a360ea2] [Current]
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Dataseries X:
93
92
91
89
87
86
87
89
90
90
91
93
93
87
89
92
98
92
92
87
92
98
101
102
102
90
87
92
105
90
88
83
98
109
118
118
115
107
101
111
128
115
111
105
120
132
135
142
139
127
113
130
143
139
137
134
139
157
152
153
147
132
117
123
139
134
134
128
118
144
140
151
144
135
122
124
146
146
147
148
132
161
159
173




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79288&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79288&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.980528379652752
beta0.0160501661027135
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.980528379652752 \tabularnewline
beta & 0.0160501661027135 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79288&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]0.980528379652752[/C][/ROW]
[ROW][C]beta[/C][C]0.0160501661027135[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79288&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
alpha0.980528379652752
beta0.0160501661027135
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
391910
48990-1
58788.0037339769854-1.00373397698540
68685.98801027620770.0119897237923254
78784.96842117992552.03157882007453
88985.9610687707173.03893122928294
99087.98927960293672.01072039706328
109089.0409445344080.959055465592002
119189.07651542756791.92348457243214
129390.08800754436062.91199245563942
139392.11458759288780.885412407112241
148792.1679826948873-5.16798269488729
158986.2045202375732.79547976242705
169288.09345298348093.9065470165191
179891.13329854745126.86670145254875
189297.1837252426362-5.18372524263619
199291.33678695711270.663213042887264
208791.2333750049651-4.23337500496513
219286.26209616238475.73790383761535
229891.15824029062646.84175970937362
2310197.2444196024473.75558039755299
24102100.3636164992441.63638350075622
25102101.4306335165970.569366483402618
2690101.460370553521-11.4603705535213
278789.5142498014155-2.51424980141554
289286.30048596785265.69951403214738
2910591.230247596037313.7697524039627
3090104.289810430864-14.2898104308641
318889.6112876452242-1.61128764522421
328387.3390583926644-4.33905839266441
339882.323885955542915.6761140444571
3410997.18086320879411.8191367912061
35118108.4419701652229.55802983477786
36118117.6364184462240.363581553776100
37115117.821171169280-2.82117116928025
38107114.838784879479-7.8387848794786
39101106.813121947869-5.8131219478692
40111100.68219416827910.3178058317211
41128110.53047681516217.4695231848377
42115127.666150415616-12.6661504156162
43111115.053605452864-4.05360545286425
44105110.822111050179-5.82211105017912
45120104.76492041243115.2350795875688
46132119.59466703989212.4053329601081
47135131.8449974978123.15500250218807
48142135.0747687247606.92523127523967
49139142.110343081477-3.11034308147725
50127139.256802505169-12.2568025051685
51113127.242005704005-14.2420057040052
52130113.05652522047816.943474779522
53143129.71594374754713.2840562524532
54139142.996258295498-3.99625829549751
55137139.269842332020-2.26984233201986
56134137.200504246709-3.20050424670862
57139134.1682573477704.83174265222971
58157139.08789672829617.9121032717042
59152157.115095205459-5.11509520545908
60153152.4829725277620.517027472238311
61147153.381442767199-6.38144276719882
62132147.415338290274-15.4153382902737
63117132.348641777841-15.3486417778411
64123117.1057916382845.89420836171597
65139122.78491987437016.2150801256298
66134138.839142925832-4.83914292583168
67134134.172946058252-0.172946058252222
68128134.079365880996-6.0793658809956
69118128.098698553294-10.0986985532942
70144118.01803175688825.9819682431121
71140143.724377661202-3.72437766120177
72151140.24419542317810.7558045768222
73144151.131513828580-7.13151382857978
74135144.367575680336-9.36757568033582
75122135.263691862564-13.2636918625639
76124122.1308163054981.8691836945015
77146123.86557124425122.134428755749
78146145.8193178319510.180682168049259
79147146.2496363622290.750363637771272
80148147.2503526962540.749647303745604
81132148.262164326352-16.2621643263521
82161132.33748372137228.6625162786277
83159160.913807855457-1.91380785545707
84173159.47905960511813.5209403948819

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 91 & 91 & 0 \tabularnewline
4 & 89 & 90 & -1 \tabularnewline
5 & 87 & 88.0037339769854 & -1.00373397698540 \tabularnewline
6 & 86 & 85.9880102762077 & 0.0119897237923254 \tabularnewline
7 & 87 & 84.9684211799255 & 2.03157882007453 \tabularnewline
8 & 89 & 85.961068770717 & 3.03893122928294 \tabularnewline
9 & 90 & 87.9892796029367 & 2.01072039706328 \tabularnewline
10 & 90 & 89.040944534408 & 0.959055465592002 \tabularnewline
11 & 91 & 89.0765154275679 & 1.92348457243214 \tabularnewline
12 & 93 & 90.0880075443606 & 2.91199245563942 \tabularnewline
13 & 93 & 92.1145875928878 & 0.885412407112241 \tabularnewline
14 & 87 & 92.1679826948873 & -5.16798269488729 \tabularnewline
15 & 89 & 86.204520237573 & 2.79547976242705 \tabularnewline
16 & 92 & 88.0934529834809 & 3.9065470165191 \tabularnewline
17 & 98 & 91.1332985474512 & 6.86670145254875 \tabularnewline
18 & 92 & 97.1837252426362 & -5.18372524263619 \tabularnewline
19 & 92 & 91.3367869571127 & 0.663213042887264 \tabularnewline
20 & 87 & 91.2333750049651 & -4.23337500496513 \tabularnewline
21 & 92 & 86.2620961623847 & 5.73790383761535 \tabularnewline
22 & 98 & 91.1582402906264 & 6.84175970937362 \tabularnewline
23 & 101 & 97.244419602447 & 3.75558039755299 \tabularnewline
24 & 102 & 100.363616499244 & 1.63638350075622 \tabularnewline
25 & 102 & 101.430633516597 & 0.569366483402618 \tabularnewline
26 & 90 & 101.460370553521 & -11.4603705535213 \tabularnewline
27 & 87 & 89.5142498014155 & -2.51424980141554 \tabularnewline
28 & 92 & 86.3004859678526 & 5.69951403214738 \tabularnewline
29 & 105 & 91.2302475960373 & 13.7697524039627 \tabularnewline
30 & 90 & 104.289810430864 & -14.2898104308641 \tabularnewline
31 & 88 & 89.6112876452242 & -1.61128764522421 \tabularnewline
32 & 83 & 87.3390583926644 & -4.33905839266441 \tabularnewline
33 & 98 & 82.3238859555429 & 15.6761140444571 \tabularnewline
34 & 109 & 97.180863208794 & 11.8191367912061 \tabularnewline
35 & 118 & 108.441970165222 & 9.55802983477786 \tabularnewline
36 & 118 & 117.636418446224 & 0.363581553776100 \tabularnewline
37 & 115 & 117.821171169280 & -2.82117116928025 \tabularnewline
38 & 107 & 114.838784879479 & -7.8387848794786 \tabularnewline
39 & 101 & 106.813121947869 & -5.8131219478692 \tabularnewline
40 & 111 & 100.682194168279 & 10.3178058317211 \tabularnewline
41 & 128 & 110.530476815162 & 17.4695231848377 \tabularnewline
42 & 115 & 127.666150415616 & -12.6661504156162 \tabularnewline
43 & 111 & 115.053605452864 & -4.05360545286425 \tabularnewline
44 & 105 & 110.822111050179 & -5.82211105017912 \tabularnewline
45 & 120 & 104.764920412431 & 15.2350795875688 \tabularnewline
46 & 132 & 119.594667039892 & 12.4053329601081 \tabularnewline
47 & 135 & 131.844997497812 & 3.15500250218807 \tabularnewline
48 & 142 & 135.074768724760 & 6.92523127523967 \tabularnewline
49 & 139 & 142.110343081477 & -3.11034308147725 \tabularnewline
50 & 127 & 139.256802505169 & -12.2568025051685 \tabularnewline
51 & 113 & 127.242005704005 & -14.2420057040052 \tabularnewline
52 & 130 & 113.056525220478 & 16.943474779522 \tabularnewline
53 & 143 & 129.715943747547 & 13.2840562524532 \tabularnewline
54 & 139 & 142.996258295498 & -3.99625829549751 \tabularnewline
55 & 137 & 139.269842332020 & -2.26984233201986 \tabularnewline
56 & 134 & 137.200504246709 & -3.20050424670862 \tabularnewline
57 & 139 & 134.168257347770 & 4.83174265222971 \tabularnewline
58 & 157 & 139.087896728296 & 17.9121032717042 \tabularnewline
59 & 152 & 157.115095205459 & -5.11509520545908 \tabularnewline
60 & 153 & 152.482972527762 & 0.517027472238311 \tabularnewline
61 & 147 & 153.381442767199 & -6.38144276719882 \tabularnewline
62 & 132 & 147.415338290274 & -15.4153382902737 \tabularnewline
63 & 117 & 132.348641777841 & -15.3486417778411 \tabularnewline
64 & 123 & 117.105791638284 & 5.89420836171597 \tabularnewline
65 & 139 & 122.784919874370 & 16.2150801256298 \tabularnewline
66 & 134 & 138.839142925832 & -4.83914292583168 \tabularnewline
67 & 134 & 134.172946058252 & -0.172946058252222 \tabularnewline
68 & 128 & 134.079365880996 & -6.0793658809956 \tabularnewline
69 & 118 & 128.098698553294 & -10.0986985532942 \tabularnewline
70 & 144 & 118.018031756888 & 25.9819682431121 \tabularnewline
71 & 140 & 143.724377661202 & -3.72437766120177 \tabularnewline
72 & 151 & 140.244195423178 & 10.7558045768222 \tabularnewline
73 & 144 & 151.131513828580 & -7.13151382857978 \tabularnewline
74 & 135 & 144.367575680336 & -9.36757568033582 \tabularnewline
75 & 122 & 135.263691862564 & -13.2636918625639 \tabularnewline
76 & 124 & 122.130816305498 & 1.8691836945015 \tabularnewline
77 & 146 & 123.865571244251 & 22.134428755749 \tabularnewline
78 & 146 & 145.819317831951 & 0.180682168049259 \tabularnewline
79 & 147 & 146.249636362229 & 0.750363637771272 \tabularnewline
80 & 148 & 147.250352696254 & 0.749647303745604 \tabularnewline
81 & 132 & 148.262164326352 & -16.2621643263521 \tabularnewline
82 & 161 & 132.337483721372 & 28.6625162786277 \tabularnewline
83 & 159 & 160.913807855457 & -1.91380785545707 \tabularnewline
84 & 173 & 159.479059605118 & 13.5209403948819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79288&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]3[/C][C]91[/C][C]91[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]89[/C][C]90[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]87[/C][C]88.0037339769854[/C][C]-1.00373397698540[/C][/ROW]
[ROW][C]6[/C][C]86[/C][C]85.9880102762077[/C][C]0.0119897237923254[/C][/ROW]
[ROW][C]7[/C][C]87[/C][C]84.9684211799255[/C][C]2.03157882007453[/C][/ROW]
[ROW][C]8[/C][C]89[/C][C]85.961068770717[/C][C]3.03893122928294[/C][/ROW]
[ROW][C]9[/C][C]90[/C][C]87.9892796029367[/C][C]2.01072039706328[/C][/ROW]
[ROW][C]10[/C][C]90[/C][C]89.040944534408[/C][C]0.959055465592002[/C][/ROW]
[ROW][C]11[/C][C]91[/C][C]89.0765154275679[/C][C]1.92348457243214[/C][/ROW]
[ROW][C]12[/C][C]93[/C][C]90.0880075443606[/C][C]2.91199245563942[/C][/ROW]
[ROW][C]13[/C][C]93[/C][C]92.1145875928878[/C][C]0.885412407112241[/C][/ROW]
[ROW][C]14[/C][C]87[/C][C]92.1679826948873[/C][C]-5.16798269488729[/C][/ROW]
[ROW][C]15[/C][C]89[/C][C]86.204520237573[/C][C]2.79547976242705[/C][/ROW]
[ROW][C]16[/C][C]92[/C][C]88.0934529834809[/C][C]3.9065470165191[/C][/ROW]
[ROW][C]17[/C][C]98[/C][C]91.1332985474512[/C][C]6.86670145254875[/C][/ROW]
[ROW][C]18[/C][C]92[/C][C]97.1837252426362[/C][C]-5.18372524263619[/C][/ROW]
[ROW][C]19[/C][C]92[/C][C]91.3367869571127[/C][C]0.663213042887264[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]91.2333750049651[/C][C]-4.23337500496513[/C][/ROW]
[ROW][C]21[/C][C]92[/C][C]86.2620961623847[/C][C]5.73790383761535[/C][/ROW]
[ROW][C]22[/C][C]98[/C][C]91.1582402906264[/C][C]6.84175970937362[/C][/ROW]
[ROW][C]23[/C][C]101[/C][C]97.244419602447[/C][C]3.75558039755299[/C][/ROW]
[ROW][C]24[/C][C]102[/C][C]100.363616499244[/C][C]1.63638350075622[/C][/ROW]
[ROW][C]25[/C][C]102[/C][C]101.430633516597[/C][C]0.569366483402618[/C][/ROW]
[ROW][C]26[/C][C]90[/C][C]101.460370553521[/C][C]-11.4603705535213[/C][/ROW]
[ROW][C]27[/C][C]87[/C][C]89.5142498014155[/C][C]-2.51424980141554[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]86.3004859678526[/C][C]5.69951403214738[/C][/ROW]
[ROW][C]29[/C][C]105[/C][C]91.2302475960373[/C][C]13.7697524039627[/C][/ROW]
[ROW][C]30[/C][C]90[/C][C]104.289810430864[/C][C]-14.2898104308641[/C][/ROW]
[ROW][C]31[/C][C]88[/C][C]89.6112876452242[/C][C]-1.61128764522421[/C][/ROW]
[ROW][C]32[/C][C]83[/C][C]87.3390583926644[/C][C]-4.33905839266441[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]82.3238859555429[/C][C]15.6761140444571[/C][/ROW]
[ROW][C]34[/C][C]109[/C][C]97.180863208794[/C][C]11.8191367912061[/C][/ROW]
[ROW][C]35[/C][C]118[/C][C]108.441970165222[/C][C]9.55802983477786[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]117.636418446224[/C][C]0.363581553776100[/C][/ROW]
[ROW][C]37[/C][C]115[/C][C]117.821171169280[/C][C]-2.82117116928025[/C][/ROW]
[ROW][C]38[/C][C]107[/C][C]114.838784879479[/C][C]-7.8387848794786[/C][/ROW]
[ROW][C]39[/C][C]101[/C][C]106.813121947869[/C][C]-5.8131219478692[/C][/ROW]
[ROW][C]40[/C][C]111[/C][C]100.682194168279[/C][C]10.3178058317211[/C][/ROW]
[ROW][C]41[/C][C]128[/C][C]110.530476815162[/C][C]17.4695231848377[/C][/ROW]
[ROW][C]42[/C][C]115[/C][C]127.666150415616[/C][C]-12.6661504156162[/C][/ROW]
[ROW][C]43[/C][C]111[/C][C]115.053605452864[/C][C]-4.05360545286425[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]110.822111050179[/C][C]-5.82211105017912[/C][/ROW]
[ROW][C]45[/C][C]120[/C][C]104.764920412431[/C][C]15.2350795875688[/C][/ROW]
[ROW][C]46[/C][C]132[/C][C]119.594667039892[/C][C]12.4053329601081[/C][/ROW]
[ROW][C]47[/C][C]135[/C][C]131.844997497812[/C][C]3.15500250218807[/C][/ROW]
[ROW][C]48[/C][C]142[/C][C]135.074768724760[/C][C]6.92523127523967[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]142.110343081477[/C][C]-3.11034308147725[/C][/ROW]
[ROW][C]50[/C][C]127[/C][C]139.256802505169[/C][C]-12.2568025051685[/C][/ROW]
[ROW][C]51[/C][C]113[/C][C]127.242005704005[/C][C]-14.2420057040052[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]113.056525220478[/C][C]16.943474779522[/C][/ROW]
[ROW][C]53[/C][C]143[/C][C]129.715943747547[/C][C]13.2840562524532[/C][/ROW]
[ROW][C]54[/C][C]139[/C][C]142.996258295498[/C][C]-3.99625829549751[/C][/ROW]
[ROW][C]55[/C][C]137[/C][C]139.269842332020[/C][C]-2.26984233201986[/C][/ROW]
[ROW][C]56[/C][C]134[/C][C]137.200504246709[/C][C]-3.20050424670862[/C][/ROW]
[ROW][C]57[/C][C]139[/C][C]134.168257347770[/C][C]4.83174265222971[/C][/ROW]
[ROW][C]58[/C][C]157[/C][C]139.087896728296[/C][C]17.9121032717042[/C][/ROW]
[ROW][C]59[/C][C]152[/C][C]157.115095205459[/C][C]-5.11509520545908[/C][/ROW]
[ROW][C]60[/C][C]153[/C][C]152.482972527762[/C][C]0.517027472238311[/C][/ROW]
[ROW][C]61[/C][C]147[/C][C]153.381442767199[/C][C]-6.38144276719882[/C][/ROW]
[ROW][C]62[/C][C]132[/C][C]147.415338290274[/C][C]-15.4153382902737[/C][/ROW]
[ROW][C]63[/C][C]117[/C][C]132.348641777841[/C][C]-15.3486417778411[/C][/ROW]
[ROW][C]64[/C][C]123[/C][C]117.105791638284[/C][C]5.89420836171597[/C][/ROW]
[ROW][C]65[/C][C]139[/C][C]122.784919874370[/C][C]16.2150801256298[/C][/ROW]
[ROW][C]66[/C][C]134[/C][C]138.839142925832[/C][C]-4.83914292583168[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]134.172946058252[/C][C]-0.172946058252222[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]134.079365880996[/C][C]-6.0793658809956[/C][/ROW]
[ROW][C]69[/C][C]118[/C][C]128.098698553294[/C][C]-10.0986985532942[/C][/ROW]
[ROW][C]70[/C][C]144[/C][C]118.018031756888[/C][C]25.9819682431121[/C][/ROW]
[ROW][C]71[/C][C]140[/C][C]143.724377661202[/C][C]-3.72437766120177[/C][/ROW]
[ROW][C]72[/C][C]151[/C][C]140.244195423178[/C][C]10.7558045768222[/C][/ROW]
[ROW][C]73[/C][C]144[/C][C]151.131513828580[/C][C]-7.13151382857978[/C][/ROW]
[ROW][C]74[/C][C]135[/C][C]144.367575680336[/C][C]-9.36757568033582[/C][/ROW]
[ROW][C]75[/C][C]122[/C][C]135.263691862564[/C][C]-13.2636918625639[/C][/ROW]
[ROW][C]76[/C][C]124[/C][C]122.130816305498[/C][C]1.8691836945015[/C][/ROW]
[ROW][C]77[/C][C]146[/C][C]123.865571244251[/C][C]22.134428755749[/C][/ROW]
[ROW][C]78[/C][C]146[/C][C]145.819317831951[/C][C]0.180682168049259[/C][/ROW]
[ROW][C]79[/C][C]147[/C][C]146.249636362229[/C][C]0.750363637771272[/C][/ROW]
[ROW][C]80[/C][C]148[/C][C]147.250352696254[/C][C]0.749647303745604[/C][/ROW]
[ROW][C]81[/C][C]132[/C][C]148.262164326352[/C][C]-16.2621643263521[/C][/ROW]
[ROW][C]82[/C][C]161[/C][C]132.337483721372[/C][C]28.6625162786277[/C][/ROW]
[ROW][C]83[/C][C]159[/C][C]160.913807855457[/C][C]-1.91380785545707[/C][/ROW]
[ROW][C]84[/C][C]173[/C][C]159.479059605118[/C][C]13.5209403948819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79288&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79288&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
391910
48990-1
58788.0037339769854-1.00373397698540
68685.98801027620770.0119897237923254
78784.96842117992552.03157882007453
88985.9610687707173.03893122928294
99087.98927960293672.01072039706328
109089.0409445344080.959055465592002
119189.07651542756791.92348457243214
129390.08800754436062.91199245563942
139392.11458759288780.885412407112241
148792.1679826948873-5.16798269488729
158986.2045202375732.79547976242705
169288.09345298348093.9065470165191
179891.13329854745126.86670145254875
189297.1837252426362-5.18372524263619
199291.33678695711270.663213042887264
208791.2333750049651-4.23337500496513
219286.26209616238475.73790383761535
229891.15824029062646.84175970937362
2310197.2444196024473.75558039755299
24102100.3636164992441.63638350075622
25102101.4306335165970.569366483402618
2690101.460370553521-11.4603705535213
278789.5142498014155-2.51424980141554
289286.30048596785265.69951403214738
2910591.230247596037313.7697524039627
3090104.289810430864-14.2898104308641
318889.6112876452242-1.61128764522421
328387.3390583926644-4.33905839266441
339882.323885955542915.6761140444571
3410997.18086320879411.8191367912061
35118108.4419701652229.55802983477786
36118117.6364184462240.363581553776100
37115117.821171169280-2.82117116928025
38107114.838784879479-7.8387848794786
39101106.813121947869-5.8131219478692
40111100.68219416827910.3178058317211
41128110.53047681516217.4695231848377
42115127.666150415616-12.6661504156162
43111115.053605452864-4.05360545286425
44105110.822111050179-5.82211105017912
45120104.76492041243115.2350795875688
46132119.59466703989212.4053329601081
47135131.8449974978123.15500250218807
48142135.0747687247606.92523127523967
49139142.110343081477-3.11034308147725
50127139.256802505169-12.2568025051685
51113127.242005704005-14.2420057040052
52130113.05652522047816.943474779522
53143129.71594374754713.2840562524532
54139142.996258295498-3.99625829549751
55137139.269842332020-2.26984233201986
56134137.200504246709-3.20050424670862
57139134.1682573477704.83174265222971
58157139.08789672829617.9121032717042
59152157.115095205459-5.11509520545908
60153152.4829725277620.517027472238311
61147153.381442767199-6.38144276719882
62132147.415338290274-15.4153382902737
63117132.348641777841-15.3486417778411
64123117.1057916382845.89420836171597
65139122.78491987437016.2150801256298
66134138.839142925832-4.83914292583168
67134134.172946058252-0.172946058252222
68128134.079365880996-6.0793658809956
69118128.098698553294-10.0986985532942
70144118.01803175688825.9819682431121
71140143.724377661202-3.72437766120177
72151140.24419542317810.7558045768222
73144151.131513828580-7.13151382857978
74135144.367575680336-9.36757568033582
75122135.263691862564-13.2636918625639
76124122.1308163054981.8691836945015
77146123.86557124425122.134428755749
78146145.8193178319510.180682168049259
79147146.2496363622290.750363637771272
80148147.2503526962540.749647303745604
81132148.262164326352-16.2621643263521
82161132.33748372137228.6625162786277
83159160.913807855457-1.91380785545707
84173159.47905960511813.5209403948819







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85173.391307784884154.584681314348192.197934255419
86174.045890187874147.498913051365200.592867324383
87174.700472590865142.035915484475207.365029697254
88175.355054993855137.400367725493213.309742262217
89176.009637396846133.281752146576218.737522647116
90176.664219799836129.520925825549223.807513774123
91177.318802202827126.023700576817228.613903828836
92177.973384605817122.729025355155233.21774385648
93178.627967008808119.594750086866237.66118393075
94179.282549411798116.590388314423241.974710509173
95179.937131814789113.693086674408246.18117695517
96180.591714217779110.885220549799250.298207885760

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 173.391307784884 & 154.584681314348 & 192.197934255419 \tabularnewline
86 & 174.045890187874 & 147.498913051365 & 200.592867324383 \tabularnewline
87 & 174.700472590865 & 142.035915484475 & 207.365029697254 \tabularnewline
88 & 175.355054993855 & 137.400367725493 & 213.309742262217 \tabularnewline
89 & 176.009637396846 & 133.281752146576 & 218.737522647116 \tabularnewline
90 & 176.664219799836 & 129.520925825549 & 223.807513774123 \tabularnewline
91 & 177.318802202827 & 126.023700576817 & 228.613903828836 \tabularnewline
92 & 177.973384605817 & 122.729025355155 & 233.21774385648 \tabularnewline
93 & 178.627967008808 & 119.594750086866 & 237.66118393075 \tabularnewline
94 & 179.282549411798 & 116.590388314423 & 241.974710509173 \tabularnewline
95 & 179.937131814789 & 113.693086674408 & 246.18117695517 \tabularnewline
96 & 180.591714217779 & 110.885220549799 & 250.298207885760 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79288&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]85[/C][C]173.391307784884[/C][C]154.584681314348[/C][C]192.197934255419[/C][/ROW]
[ROW][C]86[/C][C]174.045890187874[/C][C]147.498913051365[/C][C]200.592867324383[/C][/ROW]
[ROW][C]87[/C][C]174.700472590865[/C][C]142.035915484475[/C][C]207.365029697254[/C][/ROW]
[ROW][C]88[/C][C]175.355054993855[/C][C]137.400367725493[/C][C]213.309742262217[/C][/ROW]
[ROW][C]89[/C][C]176.009637396846[/C][C]133.281752146576[/C][C]218.737522647116[/C][/ROW]
[ROW][C]90[/C][C]176.664219799836[/C][C]129.520925825549[/C][C]223.807513774123[/C][/ROW]
[ROW][C]91[/C][C]177.318802202827[/C][C]126.023700576817[/C][C]228.613903828836[/C][/ROW]
[ROW][C]92[/C][C]177.973384605817[/C][C]122.729025355155[/C][C]233.21774385648[/C][/ROW]
[ROW][C]93[/C][C]178.627967008808[/C][C]119.594750086866[/C][C]237.66118393075[/C][/ROW]
[ROW][C]94[/C][C]179.282549411798[/C][C]116.590388314423[/C][C]241.974710509173[/C][/ROW]
[ROW][C]95[/C][C]179.937131814789[/C][C]113.693086674408[/C][C]246.18117695517[/C][/ROW]
[ROW][C]96[/C][C]180.591714217779[/C][C]110.885220549799[/C][C]250.298207885760[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79288&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79288&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
85173.391307784884154.584681314348192.197934255419
86174.045890187874147.498913051365200.592867324383
87174.700472590865142.035915484475207.365029697254
88175.355054993855137.400367725493213.309742262217
89176.009637396846133.281752146576218.737522647116
90176.664219799836129.520925825549223.807513774123
91177.318802202827126.023700576817228.613903828836
92177.973384605817122.729025355155233.21774385648
93178.627967008808119.594750086866237.66118393075
94179.282549411798116.590388314423241.974710509173
95179.937131814789113.693086674408246.18117695517
96180.591714217779110.885220549799250.298207885760



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')