Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Aug 2010 08:38:17 +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/17/t1282034269efn9dnf9b0jytil.htm/, Retrieved Sat, 27 Apr 2024 11:25:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79060, Retrieved Sat, 27 Apr 2024 11:25:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B Stap ...] [2010-08-17 08:38:17] [5e78ed906b09bab42b8ec3dd93b6358a] [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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79060&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79060&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79060&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.980528379652785
beta0.0160501661027114
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.980528379652785 \tabularnewline
beta & 0.0160501661027114 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79060&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]0.980528379652785[/C][/ROW]
[ROW][C]beta[/C][C]0.0160501661027114[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79060&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79060&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
alpha0.980528379652785
beta0.0160501661027114
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
391910
48990-1
58788.0037339769854-1.00373397698537
68685.98801027620760.0119897237923539
78784.96842117992552.03157882007453
88985.96106877071713.03893122928288
99087.98927960293682.0107203970632
109089.04094453440810.95905546559193
119189.07651542756791.92348457243213
129390.08800754436062.91199245563938
139392.11458759288780.88541240711217
148792.1679826948873-5.16798269488729
158986.20452023757282.79547976242723
169288.0934529834813.90654701651901
179891.13329854745146.86670145254864
189297.1837252426364-5.18372524263637
199291.33678695711250.663213042887463
208791.233375004965-4.23337500496511
219286.26209616238455.73790383761552
229891.15824029062656.84175970937348
2310197.24441960244723.75558039755281
24102100.3636164992441.63638350075617
25102101.4306335165970.569366483402618
2690101.460370553521-11.4603705535213
278789.5142498014151-2.51424980141513
289286.30048596785255.69951403214748
2910591.230247596037513.7697524039625
3090104.289810430865-14.2898104308645
318889.6112876452237-1.61128764522371
328387.3390583926643-4.3390583926643
339882.323885955542715.6761140444573
3410997.180863208794411.8191367912056
35118108.4419701652229.55802983477753
36118117.6364184462240.363581553775873
37115117.82117116928-2.82117116928018
38107114.838784879478-7.83878487947842
39101106.813121947869-5.81312194786888
40111100.68219416827910.3178058317213
41128110.53047681516317.4695231848374
42115127.666150415617-12.6661504156166
43111115.053605452864-4.05360545286376
44105110.822111050179-5.8221110501789
45120104.76492041243115.2350795875691
46132119.59466703989212.4053329601077
47135131.8449974978123.15500250218773
48142135.074768724766.92523127523967
49139142.110343081477-3.11034308147734
50127139.256802505168-12.2568025051683
51113127.242005704005-14.2420057040047
52130113.05652522047716.9434747795226
53143129.71594374754713.2840562524527
54139142.996258295498-3.99625829549785
55137139.26984233202-2.26984233201961
56134137.200504246708-3.20050424670845
57139134.168257347774.83174265222991
58157139.08789672829617.9121032717041
59152157.11509520546-5.11509520545954
60153152.4829725277610.517027472238595
61147153.381442767199-6.3814427671987
62132147.415338290273-15.4153382902734
63117132.34864177784-15.3486417778405
64123117.1057916382835.89420836171654
65139122.7849198743716.2150801256297
66134138.839142925832-4.83914292583214
67134134.172946058252-0.172946058251995
68128134.079365880996-6.07936588099551
69118128.098698553294-10.0986985532939
70144118.01803175688825.9819682431125
71140143.724377661203-3.72437766120251
72151140.24419542317810.7558045768224
73144151.13151382858-7.13151382858004
74135144.367575680335-9.36757568033548
75122135.263691862564-13.2636918625635
76124122.1308163054981.869183694502
77146123.86557124425122.134428755749
78146145.8193178319510.180682168048605
79147146.2496363622290.750363637771358
80148147.2503526962540.74964730374569
81132148.262164326352-16.262164326352
82161132.33748372137228.6625162786283
83159160.913807855458-1.91380785545789
84173159.47905960511813.5209403948821

\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 & -1.00373397698537 \tabularnewline
6 & 86 & 85.9880102762076 & 0.0119897237923539 \tabularnewline
7 & 87 & 84.9684211799255 & 2.03157882007453 \tabularnewline
8 & 89 & 85.9610687707171 & 3.03893122928288 \tabularnewline
9 & 90 & 87.9892796029368 & 2.0107203970632 \tabularnewline
10 & 90 & 89.0409445344081 & 0.95905546559193 \tabularnewline
11 & 91 & 89.0765154275679 & 1.92348457243213 \tabularnewline
12 & 93 & 90.0880075443606 & 2.91199245563938 \tabularnewline
13 & 93 & 92.1145875928878 & 0.88541240711217 \tabularnewline
14 & 87 & 92.1679826948873 & -5.16798269488729 \tabularnewline
15 & 89 & 86.2045202375728 & 2.79547976242723 \tabularnewline
16 & 92 & 88.093452983481 & 3.90654701651901 \tabularnewline
17 & 98 & 91.1332985474514 & 6.86670145254864 \tabularnewline
18 & 92 & 97.1837252426364 & -5.18372524263637 \tabularnewline
19 & 92 & 91.3367869571125 & 0.663213042887463 \tabularnewline
20 & 87 & 91.233375004965 & -4.23337500496511 \tabularnewline
21 & 92 & 86.2620961623845 & 5.73790383761552 \tabularnewline
22 & 98 & 91.1582402906265 & 6.84175970937348 \tabularnewline
23 & 101 & 97.2444196024472 & 3.75558039755281 \tabularnewline
24 & 102 & 100.363616499244 & 1.63638350075617 \tabularnewline
25 & 102 & 101.430633516597 & 0.569366483402618 \tabularnewline
26 & 90 & 101.460370553521 & -11.4603705535213 \tabularnewline
27 & 87 & 89.5142498014151 & -2.51424980141513 \tabularnewline
28 & 92 & 86.3004859678525 & 5.69951403214748 \tabularnewline
29 & 105 & 91.2302475960375 & 13.7697524039625 \tabularnewline
30 & 90 & 104.289810430865 & -14.2898104308645 \tabularnewline
31 & 88 & 89.6112876452237 & -1.61128764522371 \tabularnewline
32 & 83 & 87.3390583926643 & -4.3390583926643 \tabularnewline
33 & 98 & 82.3238859555427 & 15.6761140444573 \tabularnewline
34 & 109 & 97.1808632087944 & 11.8191367912056 \tabularnewline
35 & 118 & 108.441970165222 & 9.55802983477753 \tabularnewline
36 & 118 & 117.636418446224 & 0.363581553775873 \tabularnewline
37 & 115 & 117.82117116928 & -2.82117116928018 \tabularnewline
38 & 107 & 114.838784879478 & -7.83878487947842 \tabularnewline
39 & 101 & 106.813121947869 & -5.81312194786888 \tabularnewline
40 & 111 & 100.682194168279 & 10.3178058317213 \tabularnewline
41 & 128 & 110.530476815163 & 17.4695231848374 \tabularnewline
42 & 115 & 127.666150415617 & -12.6661504156166 \tabularnewline
43 & 111 & 115.053605452864 & -4.05360545286376 \tabularnewline
44 & 105 & 110.822111050179 & -5.8221110501789 \tabularnewline
45 & 120 & 104.764920412431 & 15.2350795875691 \tabularnewline
46 & 132 & 119.594667039892 & 12.4053329601077 \tabularnewline
47 & 135 & 131.844997497812 & 3.15500250218773 \tabularnewline
48 & 142 & 135.07476872476 & 6.92523127523967 \tabularnewline
49 & 139 & 142.110343081477 & -3.11034308147734 \tabularnewline
50 & 127 & 139.256802505168 & -12.2568025051683 \tabularnewline
51 & 113 & 127.242005704005 & -14.2420057040047 \tabularnewline
52 & 130 & 113.056525220477 & 16.9434747795226 \tabularnewline
53 & 143 & 129.715943747547 & 13.2840562524527 \tabularnewline
54 & 139 & 142.996258295498 & -3.99625829549785 \tabularnewline
55 & 137 & 139.26984233202 & -2.26984233201961 \tabularnewline
56 & 134 & 137.200504246708 & -3.20050424670845 \tabularnewline
57 & 139 & 134.16825734777 & 4.83174265222991 \tabularnewline
58 & 157 & 139.087896728296 & 17.9121032717041 \tabularnewline
59 & 152 & 157.11509520546 & -5.11509520545954 \tabularnewline
60 & 153 & 152.482972527761 & 0.517027472238595 \tabularnewline
61 & 147 & 153.381442767199 & -6.3814427671987 \tabularnewline
62 & 132 & 147.415338290273 & -15.4153382902734 \tabularnewline
63 & 117 & 132.34864177784 & -15.3486417778405 \tabularnewline
64 & 123 & 117.105791638283 & 5.89420836171654 \tabularnewline
65 & 139 & 122.78491987437 & 16.2150801256297 \tabularnewline
66 & 134 & 138.839142925832 & -4.83914292583214 \tabularnewline
67 & 134 & 134.172946058252 & -0.172946058251995 \tabularnewline
68 & 128 & 134.079365880996 & -6.07936588099551 \tabularnewline
69 & 118 & 128.098698553294 & -10.0986985532939 \tabularnewline
70 & 144 & 118.018031756888 & 25.9819682431125 \tabularnewline
71 & 140 & 143.724377661203 & -3.72437766120251 \tabularnewline
72 & 151 & 140.244195423178 & 10.7558045768224 \tabularnewline
73 & 144 & 151.13151382858 & -7.13151382858004 \tabularnewline
74 & 135 & 144.367575680335 & -9.36757568033548 \tabularnewline
75 & 122 & 135.263691862564 & -13.2636918625635 \tabularnewline
76 & 124 & 122.130816305498 & 1.869183694502 \tabularnewline
77 & 146 & 123.865571244251 & 22.134428755749 \tabularnewline
78 & 146 & 145.819317831951 & 0.180682168048605 \tabularnewline
79 & 147 & 146.249636362229 & 0.750363637771358 \tabularnewline
80 & 148 & 147.250352696254 & 0.74964730374569 \tabularnewline
81 & 132 & 148.262164326352 & -16.262164326352 \tabularnewline
82 & 161 & 132.337483721372 & 28.6625162786283 \tabularnewline
83 & 159 & 160.913807855458 & -1.91380785545789 \tabularnewline
84 & 173 & 159.479059605118 & 13.5209403948821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79060&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]-1.00373397698537[/C][/ROW]
[ROW][C]6[/C][C]86[/C][C]85.9880102762076[/C][C]0.0119897237923539[/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]85.9610687707171[/C][C]3.03893122928288[/C][/ROW]
[ROW][C]9[/C][C]90[/C][C]87.9892796029368[/C][C]2.0107203970632[/C][/ROW]
[ROW][C]10[/C][C]90[/C][C]89.0409445344081[/C][C]0.95905546559193[/C][/ROW]
[ROW][C]11[/C][C]91[/C][C]89.0765154275679[/C][C]1.92348457243213[/C][/ROW]
[ROW][C]12[/C][C]93[/C][C]90.0880075443606[/C][C]2.91199245563938[/C][/ROW]
[ROW][C]13[/C][C]93[/C][C]92.1145875928878[/C][C]0.88541240711217[/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]86.2045202375728[/C][C]2.79547976242723[/C][/ROW]
[ROW][C]16[/C][C]92[/C][C]88.093452983481[/C][C]3.90654701651901[/C][/ROW]
[ROW][C]17[/C][C]98[/C][C]91.1332985474514[/C][C]6.86670145254864[/C][/ROW]
[ROW][C]18[/C][C]92[/C][C]97.1837252426364[/C][C]-5.18372524263637[/C][/ROW]
[ROW][C]19[/C][C]92[/C][C]91.3367869571125[/C][C]0.663213042887463[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]91.233375004965[/C][C]-4.23337500496511[/C][/ROW]
[ROW][C]21[/C][C]92[/C][C]86.2620961623845[/C][C]5.73790383761552[/C][/ROW]
[ROW][C]22[/C][C]98[/C][C]91.1582402906265[/C][C]6.84175970937348[/C][/ROW]
[ROW][C]23[/C][C]101[/C][C]97.2444196024472[/C][C]3.75558039755281[/C][/ROW]
[ROW][C]24[/C][C]102[/C][C]100.363616499244[/C][C]1.63638350075617[/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]89.5142498014151[/C][C]-2.51424980141513[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]86.3004859678525[/C][C]5.69951403214748[/C][/ROW]
[ROW][C]29[/C][C]105[/C][C]91.2302475960375[/C][C]13.7697524039625[/C][/ROW]
[ROW][C]30[/C][C]90[/C][C]104.289810430865[/C][C]-14.2898104308645[/C][/ROW]
[ROW][C]31[/C][C]88[/C][C]89.6112876452237[/C][C]-1.61128764522371[/C][/ROW]
[ROW][C]32[/C][C]83[/C][C]87.3390583926643[/C][C]-4.3390583926643[/C][/ROW]
[ROW][C]33[/C][C]98[/C][C]82.3238859555427[/C][C]15.6761140444573[/C][/ROW]
[ROW][C]34[/C][C]109[/C][C]97.1808632087944[/C][C]11.8191367912056[/C][/ROW]
[ROW][C]35[/C][C]118[/C][C]108.441970165222[/C][C]9.55802983477753[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]117.636418446224[/C][C]0.363581553775873[/C][/ROW]
[ROW][C]37[/C][C]115[/C][C]117.82117116928[/C][C]-2.82117116928018[/C][/ROW]
[ROW][C]38[/C][C]107[/C][C]114.838784879478[/C][C]-7.83878487947842[/C][/ROW]
[ROW][C]39[/C][C]101[/C][C]106.813121947869[/C][C]-5.81312194786888[/C][/ROW]
[ROW][C]40[/C][C]111[/C][C]100.682194168279[/C][C]10.3178058317213[/C][/ROW]
[ROW][C]41[/C][C]128[/C][C]110.530476815163[/C][C]17.4695231848374[/C][/ROW]
[ROW][C]42[/C][C]115[/C][C]127.666150415617[/C][C]-12.6661504156166[/C][/ROW]
[ROW][C]43[/C][C]111[/C][C]115.053605452864[/C][C]-4.05360545286376[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]110.822111050179[/C][C]-5.8221110501789[/C][/ROW]
[ROW][C]45[/C][C]120[/C][C]104.764920412431[/C][C]15.2350795875691[/C][/ROW]
[ROW][C]46[/C][C]132[/C][C]119.594667039892[/C][C]12.4053329601077[/C][/ROW]
[ROW][C]47[/C][C]135[/C][C]131.844997497812[/C][C]3.15500250218773[/C][/ROW]
[ROW][C]48[/C][C]142[/C][C]135.07476872476[/C][C]6.92523127523967[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]142.110343081477[/C][C]-3.11034308147734[/C][/ROW]
[ROW][C]50[/C][C]127[/C][C]139.256802505168[/C][C]-12.2568025051683[/C][/ROW]
[ROW][C]51[/C][C]113[/C][C]127.242005704005[/C][C]-14.2420057040047[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]113.056525220477[/C][C]16.9434747795226[/C][/ROW]
[ROW][C]53[/C][C]143[/C][C]129.715943747547[/C][C]13.2840562524527[/C][/ROW]
[ROW][C]54[/C][C]139[/C][C]142.996258295498[/C][C]-3.99625829549785[/C][/ROW]
[ROW][C]55[/C][C]137[/C][C]139.26984233202[/C][C]-2.26984233201961[/C][/ROW]
[ROW][C]56[/C][C]134[/C][C]137.200504246708[/C][C]-3.20050424670845[/C][/ROW]
[ROW][C]57[/C][C]139[/C][C]134.16825734777[/C][C]4.83174265222991[/C][/ROW]
[ROW][C]58[/C][C]157[/C][C]139.087896728296[/C][C]17.9121032717041[/C][/ROW]
[ROW][C]59[/C][C]152[/C][C]157.11509520546[/C][C]-5.11509520545954[/C][/ROW]
[ROW][C]60[/C][C]153[/C][C]152.482972527761[/C][C]0.517027472238595[/C][/ROW]
[ROW][C]61[/C][C]147[/C][C]153.381442767199[/C][C]-6.3814427671987[/C][/ROW]
[ROW][C]62[/C][C]132[/C][C]147.415338290273[/C][C]-15.4153382902734[/C][/ROW]
[ROW][C]63[/C][C]117[/C][C]132.34864177784[/C][C]-15.3486417778405[/C][/ROW]
[ROW][C]64[/C][C]123[/C][C]117.105791638283[/C][C]5.89420836171654[/C][/ROW]
[ROW][C]65[/C][C]139[/C][C]122.78491987437[/C][C]16.2150801256297[/C][/ROW]
[ROW][C]66[/C][C]134[/C][C]138.839142925832[/C][C]-4.83914292583214[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]134.172946058252[/C][C]-0.172946058251995[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]134.079365880996[/C][C]-6.07936588099551[/C][/ROW]
[ROW][C]69[/C][C]118[/C][C]128.098698553294[/C][C]-10.0986985532939[/C][/ROW]
[ROW][C]70[/C][C]144[/C][C]118.018031756888[/C][C]25.9819682431125[/C][/ROW]
[ROW][C]71[/C][C]140[/C][C]143.724377661203[/C][C]-3.72437766120251[/C][/ROW]
[ROW][C]72[/C][C]151[/C][C]140.244195423178[/C][C]10.7558045768224[/C][/ROW]
[ROW][C]73[/C][C]144[/C][C]151.13151382858[/C][C]-7.13151382858004[/C][/ROW]
[ROW][C]74[/C][C]135[/C][C]144.367575680335[/C][C]-9.36757568033548[/C][/ROW]
[ROW][C]75[/C][C]122[/C][C]135.263691862564[/C][C]-13.2636918625635[/C][/ROW]
[ROW][C]76[/C][C]124[/C][C]122.130816305498[/C][C]1.869183694502[/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]0.180682168048605[/C][/ROW]
[ROW][C]79[/C][C]147[/C][C]146.249636362229[/C][C]0.750363637771358[/C][/ROW]
[ROW][C]80[/C][C]148[/C][C]147.250352696254[/C][C]0.74964730374569[/C][/ROW]
[ROW][C]81[/C][C]132[/C][C]148.262164326352[/C][C]-16.262164326352[/C][/ROW]
[ROW][C]82[/C][C]161[/C][C]132.337483721372[/C][C]28.6625162786283[/C][/ROW]
[ROW][C]83[/C][C]159[/C][C]160.913807855458[/C][C]-1.91380785545789[/C][/ROW]
[ROW][C]84[/C][C]173[/C][C]159.479059605118[/C][C]13.5209403948821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79060&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79060&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
58788.0037339769854-1.00373397698537
68685.98801027620760.0119897237923539
78784.96842117992552.03157882007453
88985.96106877071713.03893122928288
99087.98927960293682.0107203970632
109089.04094453440810.95905546559193
119189.07651542756791.92348457243213
129390.08800754436062.91199245563938
139392.11458759288780.88541240711217
148792.1679826948873-5.16798269488729
158986.20452023757282.79547976242723
169288.0934529834813.90654701651901
179891.13329854745146.86670145254864
189297.1837252426364-5.18372524263637
199291.33678695711250.663213042887463
208791.233375004965-4.23337500496511
219286.26209616238455.73790383761552
229891.15824029062656.84175970937348
2310197.24441960244723.75558039755281
24102100.3636164992441.63638350075617
25102101.4306335165970.569366483402618
2690101.460370553521-11.4603705535213
278789.5142498014151-2.51424980141513
289286.30048596785255.69951403214748
2910591.230247596037513.7697524039625
3090104.289810430865-14.2898104308645
318889.6112876452237-1.61128764522371
328387.3390583926643-4.3390583926643
339882.323885955542715.6761140444573
3410997.180863208794411.8191367912056
35118108.4419701652229.55802983477753
36118117.6364184462240.363581553775873
37115117.82117116928-2.82117116928018
38107114.838784879478-7.83878487947842
39101106.813121947869-5.81312194786888
40111100.68219416827910.3178058317213
41128110.53047681516317.4695231848374
42115127.666150415617-12.6661504156166
43111115.053605452864-4.05360545286376
44105110.822111050179-5.8221110501789
45120104.76492041243115.2350795875691
46132119.59466703989212.4053329601077
47135131.8449974978123.15500250218773
48142135.074768724766.92523127523967
49139142.110343081477-3.11034308147734
50127139.256802505168-12.2568025051683
51113127.242005704005-14.2420057040047
52130113.05652522047716.9434747795226
53143129.71594374754713.2840562524527
54139142.996258295498-3.99625829549785
55137139.26984233202-2.26984233201961
56134137.200504246708-3.20050424670845
57139134.168257347774.83174265222991
58157139.08789672829617.9121032717041
59152157.11509520546-5.11509520545954
60153152.4829725277610.517027472238595
61147153.381442767199-6.3814427671987
62132147.415338290273-15.4153382902734
63117132.34864177784-15.3486417778405
64123117.1057916382835.89420836171654
65139122.7849198743716.2150801256297
66134138.839142925832-4.83914292583214
67134134.172946058252-0.172946058251995
68128134.079365880996-6.07936588099551
69118128.098698553294-10.0986985532939
70144118.01803175688825.9819682431125
71140143.724377661203-3.72437766120251
72151140.24419542317810.7558045768224
73144151.13151382858-7.13151382858004
74135144.367575680335-9.36757568033548
75122135.263691862564-13.2636918625635
76124122.1308163054981.869183694502
77146123.86557124425122.134428755749
78146145.8193178319510.180682168048605
79147146.2496363622290.750363637771358
80148147.2503526962540.74964730374569
81132148.262164326352-16.262164326352
82161132.33748372137228.6625162786283
83159160.913807855458-1.91380785545789
84173159.47905960511813.5209403948821







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85173.391307784884154.584681314348192.19793425542
86174.045890187874147.498913051365200.592867324384
87174.700472590865142.035915484475207.365029697255
88175.355054993855137.400367725492213.309742262218
89176.009637396846133.281752146574218.737522647117
90176.664219799836129.520925825548223.807513774124
91177.318802202826126.023700576816228.613903828837
92177.973384605817122.729025355153233.217743856481
93178.627967008807119.594750086864237.66118393075
94179.282549411798116.590388314421241.974710509174
95179.937131814788113.693086674405246.18117695517
96180.591714217778110.885220549797250.29820788576

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 173.391307784884 & 154.584681314348 & 192.19793425542 \tabularnewline
86 & 174.045890187874 & 147.498913051365 & 200.592867324384 \tabularnewline
87 & 174.700472590865 & 142.035915484475 & 207.365029697255 \tabularnewline
88 & 175.355054993855 & 137.400367725492 & 213.309742262218 \tabularnewline
89 & 176.009637396846 & 133.281752146574 & 218.737522647117 \tabularnewline
90 & 176.664219799836 & 129.520925825548 & 223.807513774124 \tabularnewline
91 & 177.318802202826 & 126.023700576816 & 228.613903828837 \tabularnewline
92 & 177.973384605817 & 122.729025355153 & 233.217743856481 \tabularnewline
93 & 178.627967008807 & 119.594750086864 & 237.66118393075 \tabularnewline
94 & 179.282549411798 & 116.590388314421 & 241.974710509174 \tabularnewline
95 & 179.937131814788 & 113.693086674405 & 246.18117695517 \tabularnewline
96 & 180.591714217778 & 110.885220549797 & 250.29820788576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79060&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]192.19793425542[/C][/ROW]
[ROW][C]86[/C][C]174.045890187874[/C][C]147.498913051365[/C][C]200.592867324384[/C][/ROW]
[ROW][C]87[/C][C]174.700472590865[/C][C]142.035915484475[/C][C]207.365029697255[/C][/ROW]
[ROW][C]88[/C][C]175.355054993855[/C][C]137.400367725492[/C][C]213.309742262218[/C][/ROW]
[ROW][C]89[/C][C]176.009637396846[/C][C]133.281752146574[/C][C]218.737522647117[/C][/ROW]
[ROW][C]90[/C][C]176.664219799836[/C][C]129.520925825548[/C][C]223.807513774124[/C][/ROW]
[ROW][C]91[/C][C]177.318802202826[/C][C]126.023700576816[/C][C]228.613903828837[/C][/ROW]
[ROW][C]92[/C][C]177.973384605817[/C][C]122.729025355153[/C][C]233.217743856481[/C][/ROW]
[ROW][C]93[/C][C]178.627967008807[/C][C]119.594750086864[/C][C]237.66118393075[/C][/ROW]
[ROW][C]94[/C][C]179.282549411798[/C][C]116.590388314421[/C][C]241.974710509174[/C][/ROW]
[ROW][C]95[/C][C]179.937131814788[/C][C]113.693086674405[/C][C]246.18117695517[/C][/ROW]
[ROW][C]96[/C][C]180.591714217778[/C][C]110.885220549797[/C][C]250.29820788576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79060&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79060&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
85173.391307784884154.584681314348192.19793425542
86174.045890187874147.498913051365200.592867324384
87174.700472590865142.035915484475207.365029697255
88175.355054993855137.400367725492213.309742262218
89176.009637396846133.281752146574218.737522647117
90176.664219799836129.520925825548223.807513774124
91177.318802202826126.023700576816228.613903828837
92177.973384605817122.729025355153233.217743856481
93178.627967008807119.594750086864237.66118393075
94179.282549411798116.590388314421241.974710509174
95179.937131814788113.693086674405246.18117695517
96180.591714217778110.885220549797250.29820788576



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')