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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 13:46:08 +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/2014/Nov/30/t14173551831zes4c5061x716a.htm/, Retrieved Sun, 19 May 2024 12:58:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261422, Retrieved Sun, 19 May 2024 12:58:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 13:46:08] [959220cfe8d8b51f3b8cc01ba011fecd] [Current]
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Dataseries X:
123
146
156
127
128
147
128
139
130
118
147
98
141
138
130
145
123
116
90
110
102
109
111
93
120
81
84
87
110
90
108
101
87
118
82
86
103
93
83
91
69
95
96
105
121
101
111
130
134
161
186
244
145
170
164
124
154
126
173
140
142
129
171
107
98
185
142
135
126
126
134
119
134
133
129
96
150
113
99
164
127
148
166
115
199
141
149
131
171
178
181
129
112
186
153
116
190
169
165
160
202
155
257
171
168
202
189
132




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261422&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261422&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.392962210112437
beta0.246240970712897
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.392962210112437 \tabularnewline
beta & 0.246240970712897 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261422&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]0.392962210112437[/C][/ROW]
[ROW][C]beta[/C][C]0.246240970712897[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261422&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
alpha0.392962210112437
beta0.246240970712897
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3156169-13
4127185.633567119608-58.6335671196079
5128178.661283770297-50.6612837702967
6147169.919648638614-22.919648638614
7128169.861644721371-41.8616447213706
8139158.309477251125-19.3094772511247
9130153.751008757627-23.7510087576268
10118145.148957959536-27.1489579595363
11147132.58461616124414.4153838387555
1298137.748371473791-39.7483714737915
13141117.78163037861223.2183696213877
14138124.80512732358313.1948726764172
15130129.1665494469050.833450553095474
16145128.75104731848816.2489526815117
17123135.965558820517-12.9655588205168
18116130.445279811914-14.445279811914
1990122.945752040377-32.9457520403771
20110104.9882949602615.01170503973918
21102102.431633704349-0.431633704349139
2210997.694179682078111.3058203179219
2311198.663091102828912.3369088971711
2493101.230942572419-8.230942572419
2512094.919951715077325.0800482849227
2681104.12575209176-23.1257520917599
278492.1507683030745-8.15076830307446
288785.27169121879071.72830878120928
2911082.441955126548427.5580448734516
309092.4289392267825-2.42893922678253
3110890.397139371947217.6028606280528
3210197.94039243554293.05960756445707
3387100.064754651627-13.0647546516267
3411894.588661825691523.4113381743085
3582105.711655641228-23.7116556412283
368696.0226733335722-10.0226733335722
3710390.743115858250312.2568841417497
389395.4046002635694-2.40460026356938
398394.0719980657477-11.0719980657477
409188.26207193751882.73792806248125
416988.1438561196535-19.1438561196535
429577.5745014963317.42549850367
439683.061671701628312.9383282983717
4410588.037510171541316.9624898284587
4512196.236040171797924.7639598282021
46101109.896497918436-8.89649791843635
47111109.4688124438281.5311875561721
48130113.28697620763716.7130237923633
49134124.6882368331589.31176316684171
50161134.08211955309526.9178804469055
51186152.99920655799533.0007934420055
52244177.49991734387666.5000826561244
53145221.599356693379-76.5993566933794
54170202.054110199703-32.0541101997025
55164196.911797657209-32.9117976572086
56124188.247789043695-64.2477890436954
57154161.053085740926-7.05308574092624
58126155.651258925662-29.6512589256623
59173138.50004751977634.4999524802237
60140149.896170495632-9.89617049563168
61142142.888707801211-0.888707801210813
62129139.334843169734-10.3348431697344
63171131.06896978385139.9310302161488
64107146.419547189268-39.4195471892676
6598126.773977066117-28.7739770661165
66185108.52744596706376.4725540329371
67142139.0385683698542.9614316301456
68135140.949155827166-5.94915582716575
69126138.782558622256-12.7825586222563
70126132.693808569626-6.69380856962613
71134128.349991544655.65000845535027
72119129.403542145004-10.4035421450043
73134123.14197195216710.8580280478325
74133126.2860550413176.7139449586829
75129128.4513341961050.548665803895318
7696128.24698239476-32.2469823947601
77150112.03485266562537.9651473343753
78113127.087073199983-14.0870731999832
7999120.321625068361-21.3216250683611
80164108.65011859398955.3498814060113
81127132.46345925344-5.46345925344011
82148131.85079229137116.1492077086286
83166141.29373888689324.7062611131065
84115156.489945829825-41.4899458298245
85199141.65883693008257.3411630699183
86141171.213144684784-30.2131446847839
87149163.438391673632-14.4383916736324
88131160.465412657569-29.4654126575686
89171148.73620886885522.2637911311453
90178159.48894736758818.5110526324118
91181170.55819376945710.4418062305429
92129179.466915903294-50.4669159032944
93112159.557461800234-47.5574618002336
94186136.18949169939849.8105083006024
95153155.903288266765-2.90328826676523
96116154.621622799136-38.6216227991358
97190135.56684226829154.433157731709
98169158.34621115739410.6537888426056
99165164.9528392799480.0471607200519486
100160167.396026805056-7.3960268050557
101202166.19865823892235.8013417610778
102155185.440482508299-30.4404825082989
103257175.70624864534181.2937513546586
104171217.745605726866-46.7456057268662
105168204.947070506705-36.9470705067053
106202192.4238653253999.57613467460124
107189199.109140986006-10.109140986006
108132197.080652403176-65.0806524031762

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 156 & 169 & -13 \tabularnewline
4 & 127 & 185.633567119608 & -58.6335671196079 \tabularnewline
5 & 128 & 178.661283770297 & -50.6612837702967 \tabularnewline
6 & 147 & 169.919648638614 & -22.919648638614 \tabularnewline
7 & 128 & 169.861644721371 & -41.8616447213706 \tabularnewline
8 & 139 & 158.309477251125 & -19.3094772511247 \tabularnewline
9 & 130 & 153.751008757627 & -23.7510087576268 \tabularnewline
10 & 118 & 145.148957959536 & -27.1489579595363 \tabularnewline
11 & 147 & 132.584616161244 & 14.4153838387555 \tabularnewline
12 & 98 & 137.748371473791 & -39.7483714737915 \tabularnewline
13 & 141 & 117.781630378612 & 23.2183696213877 \tabularnewline
14 & 138 & 124.805127323583 & 13.1948726764172 \tabularnewline
15 & 130 & 129.166549446905 & 0.833450553095474 \tabularnewline
16 & 145 & 128.751047318488 & 16.2489526815117 \tabularnewline
17 & 123 & 135.965558820517 & -12.9655588205168 \tabularnewline
18 & 116 & 130.445279811914 & -14.445279811914 \tabularnewline
19 & 90 & 122.945752040377 & -32.9457520403771 \tabularnewline
20 & 110 & 104.988294960261 & 5.01170503973918 \tabularnewline
21 & 102 & 102.431633704349 & -0.431633704349139 \tabularnewline
22 & 109 & 97.6941796820781 & 11.3058203179219 \tabularnewline
23 & 111 & 98.6630911028289 & 12.3369088971711 \tabularnewline
24 & 93 & 101.230942572419 & -8.230942572419 \tabularnewline
25 & 120 & 94.9199517150773 & 25.0800482849227 \tabularnewline
26 & 81 & 104.12575209176 & -23.1257520917599 \tabularnewline
27 & 84 & 92.1507683030745 & -8.15076830307446 \tabularnewline
28 & 87 & 85.2716912187907 & 1.72830878120928 \tabularnewline
29 & 110 & 82.4419551265484 & 27.5580448734516 \tabularnewline
30 & 90 & 92.4289392267825 & -2.42893922678253 \tabularnewline
31 & 108 & 90.3971393719472 & 17.6028606280528 \tabularnewline
32 & 101 & 97.9403924355429 & 3.05960756445707 \tabularnewline
33 & 87 & 100.064754651627 & -13.0647546516267 \tabularnewline
34 & 118 & 94.5886618256915 & 23.4113381743085 \tabularnewline
35 & 82 & 105.711655641228 & -23.7116556412283 \tabularnewline
36 & 86 & 96.0226733335722 & -10.0226733335722 \tabularnewline
37 & 103 & 90.7431158582503 & 12.2568841417497 \tabularnewline
38 & 93 & 95.4046002635694 & -2.40460026356938 \tabularnewline
39 & 83 & 94.0719980657477 & -11.0719980657477 \tabularnewline
40 & 91 & 88.2620719375188 & 2.73792806248125 \tabularnewline
41 & 69 & 88.1438561196535 & -19.1438561196535 \tabularnewline
42 & 95 & 77.57450149633 & 17.42549850367 \tabularnewline
43 & 96 & 83.0616717016283 & 12.9383282983717 \tabularnewline
44 & 105 & 88.0375101715413 & 16.9624898284587 \tabularnewline
45 & 121 & 96.2360401717979 & 24.7639598282021 \tabularnewline
46 & 101 & 109.896497918436 & -8.89649791843635 \tabularnewline
47 & 111 & 109.468812443828 & 1.5311875561721 \tabularnewline
48 & 130 & 113.286976207637 & 16.7130237923633 \tabularnewline
49 & 134 & 124.688236833158 & 9.31176316684171 \tabularnewline
50 & 161 & 134.082119553095 & 26.9178804469055 \tabularnewline
51 & 186 & 152.999206557995 & 33.0007934420055 \tabularnewline
52 & 244 & 177.499917343876 & 66.5000826561244 \tabularnewline
53 & 145 & 221.599356693379 & -76.5993566933794 \tabularnewline
54 & 170 & 202.054110199703 & -32.0541101997025 \tabularnewline
55 & 164 & 196.911797657209 & -32.9117976572086 \tabularnewline
56 & 124 & 188.247789043695 & -64.2477890436954 \tabularnewline
57 & 154 & 161.053085740926 & -7.05308574092624 \tabularnewline
58 & 126 & 155.651258925662 & -29.6512589256623 \tabularnewline
59 & 173 & 138.500047519776 & 34.4999524802237 \tabularnewline
60 & 140 & 149.896170495632 & -9.89617049563168 \tabularnewline
61 & 142 & 142.888707801211 & -0.888707801210813 \tabularnewline
62 & 129 & 139.334843169734 & -10.3348431697344 \tabularnewline
63 & 171 & 131.068969783851 & 39.9310302161488 \tabularnewline
64 & 107 & 146.419547189268 & -39.4195471892676 \tabularnewline
65 & 98 & 126.773977066117 & -28.7739770661165 \tabularnewline
66 & 185 & 108.527445967063 & 76.4725540329371 \tabularnewline
67 & 142 & 139.038568369854 & 2.9614316301456 \tabularnewline
68 & 135 & 140.949155827166 & -5.94915582716575 \tabularnewline
69 & 126 & 138.782558622256 & -12.7825586222563 \tabularnewline
70 & 126 & 132.693808569626 & -6.69380856962613 \tabularnewline
71 & 134 & 128.34999154465 & 5.65000845535027 \tabularnewline
72 & 119 & 129.403542145004 & -10.4035421450043 \tabularnewline
73 & 134 & 123.141971952167 & 10.8580280478325 \tabularnewline
74 & 133 & 126.286055041317 & 6.7139449586829 \tabularnewline
75 & 129 & 128.451334196105 & 0.548665803895318 \tabularnewline
76 & 96 & 128.24698239476 & -32.2469823947601 \tabularnewline
77 & 150 & 112.034852665625 & 37.9651473343753 \tabularnewline
78 & 113 & 127.087073199983 & -14.0870731999832 \tabularnewline
79 & 99 & 120.321625068361 & -21.3216250683611 \tabularnewline
80 & 164 & 108.650118593989 & 55.3498814060113 \tabularnewline
81 & 127 & 132.46345925344 & -5.46345925344011 \tabularnewline
82 & 148 & 131.850792291371 & 16.1492077086286 \tabularnewline
83 & 166 & 141.293738886893 & 24.7062611131065 \tabularnewline
84 & 115 & 156.489945829825 & -41.4899458298245 \tabularnewline
85 & 199 & 141.658836930082 & 57.3411630699183 \tabularnewline
86 & 141 & 171.213144684784 & -30.2131446847839 \tabularnewline
87 & 149 & 163.438391673632 & -14.4383916736324 \tabularnewline
88 & 131 & 160.465412657569 & -29.4654126575686 \tabularnewline
89 & 171 & 148.736208868855 & 22.2637911311453 \tabularnewline
90 & 178 & 159.488947367588 & 18.5110526324118 \tabularnewline
91 & 181 & 170.558193769457 & 10.4418062305429 \tabularnewline
92 & 129 & 179.466915903294 & -50.4669159032944 \tabularnewline
93 & 112 & 159.557461800234 & -47.5574618002336 \tabularnewline
94 & 186 & 136.189491699398 & 49.8105083006024 \tabularnewline
95 & 153 & 155.903288266765 & -2.90328826676523 \tabularnewline
96 & 116 & 154.621622799136 & -38.6216227991358 \tabularnewline
97 & 190 & 135.566842268291 & 54.433157731709 \tabularnewline
98 & 169 & 158.346211157394 & 10.6537888426056 \tabularnewline
99 & 165 & 164.952839279948 & 0.0471607200519486 \tabularnewline
100 & 160 & 167.396026805056 & -7.3960268050557 \tabularnewline
101 & 202 & 166.198658238922 & 35.8013417610778 \tabularnewline
102 & 155 & 185.440482508299 & -30.4404825082989 \tabularnewline
103 & 257 & 175.706248645341 & 81.2937513546586 \tabularnewline
104 & 171 & 217.745605726866 & -46.7456057268662 \tabularnewline
105 & 168 & 204.947070506705 & -36.9470705067053 \tabularnewline
106 & 202 & 192.423865325399 & 9.57613467460124 \tabularnewline
107 & 189 & 199.109140986006 & -10.109140986006 \tabularnewline
108 & 132 & 197.080652403176 & -65.0806524031762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261422&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]156[/C][C]169[/C][C]-13[/C][/ROW]
[ROW][C]4[/C][C]127[/C][C]185.633567119608[/C][C]-58.6335671196079[/C][/ROW]
[ROW][C]5[/C][C]128[/C][C]178.661283770297[/C][C]-50.6612837702967[/C][/ROW]
[ROW][C]6[/C][C]147[/C][C]169.919648638614[/C][C]-22.919648638614[/C][/ROW]
[ROW][C]7[/C][C]128[/C][C]169.861644721371[/C][C]-41.8616447213706[/C][/ROW]
[ROW][C]8[/C][C]139[/C][C]158.309477251125[/C][C]-19.3094772511247[/C][/ROW]
[ROW][C]9[/C][C]130[/C][C]153.751008757627[/C][C]-23.7510087576268[/C][/ROW]
[ROW][C]10[/C][C]118[/C][C]145.148957959536[/C][C]-27.1489579595363[/C][/ROW]
[ROW][C]11[/C][C]147[/C][C]132.584616161244[/C][C]14.4153838387555[/C][/ROW]
[ROW][C]12[/C][C]98[/C][C]137.748371473791[/C][C]-39.7483714737915[/C][/ROW]
[ROW][C]13[/C][C]141[/C][C]117.781630378612[/C][C]23.2183696213877[/C][/ROW]
[ROW][C]14[/C][C]138[/C][C]124.805127323583[/C][C]13.1948726764172[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]129.166549446905[/C][C]0.833450553095474[/C][/ROW]
[ROW][C]16[/C][C]145[/C][C]128.751047318488[/C][C]16.2489526815117[/C][/ROW]
[ROW][C]17[/C][C]123[/C][C]135.965558820517[/C][C]-12.9655588205168[/C][/ROW]
[ROW][C]18[/C][C]116[/C][C]130.445279811914[/C][C]-14.445279811914[/C][/ROW]
[ROW][C]19[/C][C]90[/C][C]122.945752040377[/C][C]-32.9457520403771[/C][/ROW]
[ROW][C]20[/C][C]110[/C][C]104.988294960261[/C][C]5.01170503973918[/C][/ROW]
[ROW][C]21[/C][C]102[/C][C]102.431633704349[/C][C]-0.431633704349139[/C][/ROW]
[ROW][C]22[/C][C]109[/C][C]97.6941796820781[/C][C]11.3058203179219[/C][/ROW]
[ROW][C]23[/C][C]111[/C][C]98.6630911028289[/C][C]12.3369088971711[/C][/ROW]
[ROW][C]24[/C][C]93[/C][C]101.230942572419[/C][C]-8.230942572419[/C][/ROW]
[ROW][C]25[/C][C]120[/C][C]94.9199517150773[/C][C]25.0800482849227[/C][/ROW]
[ROW][C]26[/C][C]81[/C][C]104.12575209176[/C][C]-23.1257520917599[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]92.1507683030745[/C][C]-8.15076830307446[/C][/ROW]
[ROW][C]28[/C][C]87[/C][C]85.2716912187907[/C][C]1.72830878120928[/C][/ROW]
[ROW][C]29[/C][C]110[/C][C]82.4419551265484[/C][C]27.5580448734516[/C][/ROW]
[ROW][C]30[/C][C]90[/C][C]92.4289392267825[/C][C]-2.42893922678253[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]90.3971393719472[/C][C]17.6028606280528[/C][/ROW]
[ROW][C]32[/C][C]101[/C][C]97.9403924355429[/C][C]3.05960756445707[/C][/ROW]
[ROW][C]33[/C][C]87[/C][C]100.064754651627[/C][C]-13.0647546516267[/C][/ROW]
[ROW][C]34[/C][C]118[/C][C]94.5886618256915[/C][C]23.4113381743085[/C][/ROW]
[ROW][C]35[/C][C]82[/C][C]105.711655641228[/C][C]-23.7116556412283[/C][/ROW]
[ROW][C]36[/C][C]86[/C][C]96.0226733335722[/C][C]-10.0226733335722[/C][/ROW]
[ROW][C]37[/C][C]103[/C][C]90.7431158582503[/C][C]12.2568841417497[/C][/ROW]
[ROW][C]38[/C][C]93[/C][C]95.4046002635694[/C][C]-2.40460026356938[/C][/ROW]
[ROW][C]39[/C][C]83[/C][C]94.0719980657477[/C][C]-11.0719980657477[/C][/ROW]
[ROW][C]40[/C][C]91[/C][C]88.2620719375188[/C][C]2.73792806248125[/C][/ROW]
[ROW][C]41[/C][C]69[/C][C]88.1438561196535[/C][C]-19.1438561196535[/C][/ROW]
[ROW][C]42[/C][C]95[/C][C]77.57450149633[/C][C]17.42549850367[/C][/ROW]
[ROW][C]43[/C][C]96[/C][C]83.0616717016283[/C][C]12.9383282983717[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]88.0375101715413[/C][C]16.9624898284587[/C][/ROW]
[ROW][C]45[/C][C]121[/C][C]96.2360401717979[/C][C]24.7639598282021[/C][/ROW]
[ROW][C]46[/C][C]101[/C][C]109.896497918436[/C][C]-8.89649791843635[/C][/ROW]
[ROW][C]47[/C][C]111[/C][C]109.468812443828[/C][C]1.5311875561721[/C][/ROW]
[ROW][C]48[/C][C]130[/C][C]113.286976207637[/C][C]16.7130237923633[/C][/ROW]
[ROW][C]49[/C][C]134[/C][C]124.688236833158[/C][C]9.31176316684171[/C][/ROW]
[ROW][C]50[/C][C]161[/C][C]134.082119553095[/C][C]26.9178804469055[/C][/ROW]
[ROW][C]51[/C][C]186[/C][C]152.999206557995[/C][C]33.0007934420055[/C][/ROW]
[ROW][C]52[/C][C]244[/C][C]177.499917343876[/C][C]66.5000826561244[/C][/ROW]
[ROW][C]53[/C][C]145[/C][C]221.599356693379[/C][C]-76.5993566933794[/C][/ROW]
[ROW][C]54[/C][C]170[/C][C]202.054110199703[/C][C]-32.0541101997025[/C][/ROW]
[ROW][C]55[/C][C]164[/C][C]196.911797657209[/C][C]-32.9117976572086[/C][/ROW]
[ROW][C]56[/C][C]124[/C][C]188.247789043695[/C][C]-64.2477890436954[/C][/ROW]
[ROW][C]57[/C][C]154[/C][C]161.053085740926[/C][C]-7.05308574092624[/C][/ROW]
[ROW][C]58[/C][C]126[/C][C]155.651258925662[/C][C]-29.6512589256623[/C][/ROW]
[ROW][C]59[/C][C]173[/C][C]138.500047519776[/C][C]34.4999524802237[/C][/ROW]
[ROW][C]60[/C][C]140[/C][C]149.896170495632[/C][C]-9.89617049563168[/C][/ROW]
[ROW][C]61[/C][C]142[/C][C]142.888707801211[/C][C]-0.888707801210813[/C][/ROW]
[ROW][C]62[/C][C]129[/C][C]139.334843169734[/C][C]-10.3348431697344[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]131.068969783851[/C][C]39.9310302161488[/C][/ROW]
[ROW][C]64[/C][C]107[/C][C]146.419547189268[/C][C]-39.4195471892676[/C][/ROW]
[ROW][C]65[/C][C]98[/C][C]126.773977066117[/C][C]-28.7739770661165[/C][/ROW]
[ROW][C]66[/C][C]185[/C][C]108.527445967063[/C][C]76.4725540329371[/C][/ROW]
[ROW][C]67[/C][C]142[/C][C]139.038568369854[/C][C]2.9614316301456[/C][/ROW]
[ROW][C]68[/C][C]135[/C][C]140.949155827166[/C][C]-5.94915582716575[/C][/ROW]
[ROW][C]69[/C][C]126[/C][C]138.782558622256[/C][C]-12.7825586222563[/C][/ROW]
[ROW][C]70[/C][C]126[/C][C]132.693808569626[/C][C]-6.69380856962613[/C][/ROW]
[ROW][C]71[/C][C]134[/C][C]128.34999154465[/C][C]5.65000845535027[/C][/ROW]
[ROW][C]72[/C][C]119[/C][C]129.403542145004[/C][C]-10.4035421450043[/C][/ROW]
[ROW][C]73[/C][C]134[/C][C]123.141971952167[/C][C]10.8580280478325[/C][/ROW]
[ROW][C]74[/C][C]133[/C][C]126.286055041317[/C][C]6.7139449586829[/C][/ROW]
[ROW][C]75[/C][C]129[/C][C]128.451334196105[/C][C]0.548665803895318[/C][/ROW]
[ROW][C]76[/C][C]96[/C][C]128.24698239476[/C][C]-32.2469823947601[/C][/ROW]
[ROW][C]77[/C][C]150[/C][C]112.034852665625[/C][C]37.9651473343753[/C][/ROW]
[ROW][C]78[/C][C]113[/C][C]127.087073199983[/C][C]-14.0870731999832[/C][/ROW]
[ROW][C]79[/C][C]99[/C][C]120.321625068361[/C][C]-21.3216250683611[/C][/ROW]
[ROW][C]80[/C][C]164[/C][C]108.650118593989[/C][C]55.3498814060113[/C][/ROW]
[ROW][C]81[/C][C]127[/C][C]132.46345925344[/C][C]-5.46345925344011[/C][/ROW]
[ROW][C]82[/C][C]148[/C][C]131.850792291371[/C][C]16.1492077086286[/C][/ROW]
[ROW][C]83[/C][C]166[/C][C]141.293738886893[/C][C]24.7062611131065[/C][/ROW]
[ROW][C]84[/C][C]115[/C][C]156.489945829825[/C][C]-41.4899458298245[/C][/ROW]
[ROW][C]85[/C][C]199[/C][C]141.658836930082[/C][C]57.3411630699183[/C][/ROW]
[ROW][C]86[/C][C]141[/C][C]171.213144684784[/C][C]-30.2131446847839[/C][/ROW]
[ROW][C]87[/C][C]149[/C][C]163.438391673632[/C][C]-14.4383916736324[/C][/ROW]
[ROW][C]88[/C][C]131[/C][C]160.465412657569[/C][C]-29.4654126575686[/C][/ROW]
[ROW][C]89[/C][C]171[/C][C]148.736208868855[/C][C]22.2637911311453[/C][/ROW]
[ROW][C]90[/C][C]178[/C][C]159.488947367588[/C][C]18.5110526324118[/C][/ROW]
[ROW][C]91[/C][C]181[/C][C]170.558193769457[/C][C]10.4418062305429[/C][/ROW]
[ROW][C]92[/C][C]129[/C][C]179.466915903294[/C][C]-50.4669159032944[/C][/ROW]
[ROW][C]93[/C][C]112[/C][C]159.557461800234[/C][C]-47.5574618002336[/C][/ROW]
[ROW][C]94[/C][C]186[/C][C]136.189491699398[/C][C]49.8105083006024[/C][/ROW]
[ROW][C]95[/C][C]153[/C][C]155.903288266765[/C][C]-2.90328826676523[/C][/ROW]
[ROW][C]96[/C][C]116[/C][C]154.621622799136[/C][C]-38.6216227991358[/C][/ROW]
[ROW][C]97[/C][C]190[/C][C]135.566842268291[/C][C]54.433157731709[/C][/ROW]
[ROW][C]98[/C][C]169[/C][C]158.346211157394[/C][C]10.6537888426056[/C][/ROW]
[ROW][C]99[/C][C]165[/C][C]164.952839279948[/C][C]0.0471607200519486[/C][/ROW]
[ROW][C]100[/C][C]160[/C][C]167.396026805056[/C][C]-7.3960268050557[/C][/ROW]
[ROW][C]101[/C][C]202[/C][C]166.198658238922[/C][C]35.8013417610778[/C][/ROW]
[ROW][C]102[/C][C]155[/C][C]185.440482508299[/C][C]-30.4404825082989[/C][/ROW]
[ROW][C]103[/C][C]257[/C][C]175.706248645341[/C][C]81.2937513546586[/C][/ROW]
[ROW][C]104[/C][C]171[/C][C]217.745605726866[/C][C]-46.7456057268662[/C][/ROW]
[ROW][C]105[/C][C]168[/C][C]204.947070506705[/C][C]-36.9470705067053[/C][/ROW]
[ROW][C]106[/C][C]202[/C][C]192.423865325399[/C][C]9.57613467460124[/C][/ROW]
[ROW][C]107[/C][C]189[/C][C]199.109140986006[/C][C]-10.109140986006[/C][/ROW]
[ROW][C]108[/C][C]132[/C][C]197.080652403176[/C][C]-65.0806524031762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261422&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261422&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
3156169-13
4127185.633567119608-58.6335671196079
5128178.661283770297-50.6612837702967
6147169.919648638614-22.919648638614
7128169.861644721371-41.8616447213706
8139158.309477251125-19.3094772511247
9130153.751008757627-23.7510087576268
10118145.148957959536-27.1489579595363
11147132.58461616124414.4153838387555
1298137.748371473791-39.7483714737915
13141117.78163037861223.2183696213877
14138124.80512732358313.1948726764172
15130129.1665494469050.833450553095474
16145128.75104731848816.2489526815117
17123135.965558820517-12.9655588205168
18116130.445279811914-14.445279811914
1990122.945752040377-32.9457520403771
20110104.9882949602615.01170503973918
21102102.431633704349-0.431633704349139
2210997.694179682078111.3058203179219
2311198.663091102828912.3369088971711
2493101.230942572419-8.230942572419
2512094.919951715077325.0800482849227
2681104.12575209176-23.1257520917599
278492.1507683030745-8.15076830307446
288785.27169121879071.72830878120928
2911082.441955126548427.5580448734516
309092.4289392267825-2.42893922678253
3110890.397139371947217.6028606280528
3210197.94039243554293.05960756445707
3387100.064754651627-13.0647546516267
3411894.588661825691523.4113381743085
3582105.711655641228-23.7116556412283
368696.0226733335722-10.0226733335722
3710390.743115858250312.2568841417497
389395.4046002635694-2.40460026356938
398394.0719980657477-11.0719980657477
409188.26207193751882.73792806248125
416988.1438561196535-19.1438561196535
429577.5745014963317.42549850367
439683.061671701628312.9383282983717
4410588.037510171541316.9624898284587
4512196.236040171797924.7639598282021
46101109.896497918436-8.89649791843635
47111109.4688124438281.5311875561721
48130113.28697620763716.7130237923633
49134124.6882368331589.31176316684171
50161134.08211955309526.9178804469055
51186152.99920655799533.0007934420055
52244177.49991734387666.5000826561244
53145221.599356693379-76.5993566933794
54170202.054110199703-32.0541101997025
55164196.911797657209-32.9117976572086
56124188.247789043695-64.2477890436954
57154161.053085740926-7.05308574092624
58126155.651258925662-29.6512589256623
59173138.50004751977634.4999524802237
60140149.896170495632-9.89617049563168
61142142.888707801211-0.888707801210813
62129139.334843169734-10.3348431697344
63171131.06896978385139.9310302161488
64107146.419547189268-39.4195471892676
6598126.773977066117-28.7739770661165
66185108.52744596706376.4725540329371
67142139.0385683698542.9614316301456
68135140.949155827166-5.94915582716575
69126138.782558622256-12.7825586222563
70126132.693808569626-6.69380856962613
71134128.349991544655.65000845535027
72119129.403542145004-10.4035421450043
73134123.14197195216710.8580280478325
74133126.2860550413176.7139449586829
75129128.4513341961050.548665803895318
7696128.24698239476-32.2469823947601
77150112.03485266562537.9651473343753
78113127.087073199983-14.0870731999832
7999120.321625068361-21.3216250683611
80164108.65011859398955.3498814060113
81127132.46345925344-5.46345925344011
82148131.85079229137116.1492077086286
83166141.29373888689324.7062611131065
84115156.489945829825-41.4899458298245
85199141.65883693008257.3411630699183
86141171.213144684784-30.2131446847839
87149163.438391673632-14.4383916736324
88131160.465412657569-29.4654126575686
89171148.73620886885522.2637911311453
90178159.48894736758818.5110526324118
91181170.55819376945710.4418062305429
92129179.466915903294-50.4669159032944
93112159.557461800234-47.5574618002336
94186136.18949169939849.8105083006024
95153155.903288266765-2.90328826676523
96116154.621622799136-38.6216227991358
97190135.56684226829154.433157731709
98169158.34621115739410.6537888426056
99165164.9528392799480.0471607200519486
100160167.396026805056-7.3960268050557
101202166.19865823892235.8013417610778
102155185.440482508299-30.4404825082989
103257175.70624864534181.2937513546586
104171217.745605726866-46.7456057268662
105168204.947070506705-36.9470705067053
106202192.4238653253999.57613467460124
107189199.109140986006-10.109140986006
108132197.080652403176-65.0806524031762







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109167.153012255549108.213272682499226.092751828599
110162.79960911183497.1715610106159228.427657213052
111158.44620596811884.2710525818862232.62135935435
112154.09280282440369.690882574096238.49472307471
113149.73939968068753.6285981134628245.850201247912
114145.38599653697236.2630718975948254.508921176349
115141.03259339325617.7430283525615264.322158433951
116136.679190249541-1.81215197164821275.17053247073
117132.325787105825-22.3075564617047286.959130673355
118127.97238396211-43.6674344367103299.61220236093
119123.618980818394-65.8306800830159313.068641719804
120119.265577674679-88.7473171276057327.278472476963

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 167.153012255549 & 108.213272682499 & 226.092751828599 \tabularnewline
110 & 162.799609111834 & 97.1715610106159 & 228.427657213052 \tabularnewline
111 & 158.446205968118 & 84.2710525818862 & 232.62135935435 \tabularnewline
112 & 154.092802824403 & 69.690882574096 & 238.49472307471 \tabularnewline
113 & 149.739399680687 & 53.6285981134628 & 245.850201247912 \tabularnewline
114 & 145.385996536972 & 36.2630718975948 & 254.508921176349 \tabularnewline
115 & 141.032593393256 & 17.7430283525615 & 264.322158433951 \tabularnewline
116 & 136.679190249541 & -1.81215197164821 & 275.17053247073 \tabularnewline
117 & 132.325787105825 & -22.3075564617047 & 286.959130673355 \tabularnewline
118 & 127.97238396211 & -43.6674344367103 & 299.61220236093 \tabularnewline
119 & 123.618980818394 & -65.8306800830159 & 313.068641719804 \tabularnewline
120 & 119.265577674679 & -88.7473171276057 & 327.278472476963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261422&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]109[/C][C]167.153012255549[/C][C]108.213272682499[/C][C]226.092751828599[/C][/ROW]
[ROW][C]110[/C][C]162.799609111834[/C][C]97.1715610106159[/C][C]228.427657213052[/C][/ROW]
[ROW][C]111[/C][C]158.446205968118[/C][C]84.2710525818862[/C][C]232.62135935435[/C][/ROW]
[ROW][C]112[/C][C]154.092802824403[/C][C]69.690882574096[/C][C]238.49472307471[/C][/ROW]
[ROW][C]113[/C][C]149.739399680687[/C][C]53.6285981134628[/C][C]245.850201247912[/C][/ROW]
[ROW][C]114[/C][C]145.385996536972[/C][C]36.2630718975948[/C][C]254.508921176349[/C][/ROW]
[ROW][C]115[/C][C]141.032593393256[/C][C]17.7430283525615[/C][C]264.322158433951[/C][/ROW]
[ROW][C]116[/C][C]136.679190249541[/C][C]-1.81215197164821[/C][C]275.17053247073[/C][/ROW]
[ROW][C]117[/C][C]132.325787105825[/C][C]-22.3075564617047[/C][C]286.959130673355[/C][/ROW]
[ROW][C]118[/C][C]127.97238396211[/C][C]-43.6674344367103[/C][C]299.61220236093[/C][/ROW]
[ROW][C]119[/C][C]123.618980818394[/C][C]-65.8306800830159[/C][C]313.068641719804[/C][/ROW]
[ROW][C]120[/C][C]119.265577674679[/C][C]-88.7473171276057[/C][C]327.278472476963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261422&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261422&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
109167.153012255549108.213272682499226.092751828599
110162.79960911183497.1715610106159228.427657213052
111158.44620596811884.2710525818862232.62135935435
112154.09280282440369.690882574096238.49472307471
113149.73939968068753.6285981134628245.850201247912
114145.38599653697236.2630718975948254.508921176349
115141.03259339325617.7430283525615264.322158433951
116136.679190249541-1.81215197164821275.17053247073
117132.325787105825-22.3075564617047286.959130673355
118127.97238396211-43.6674344367103299.61220236093
119123.618980818394-65.8306800830159313.068641719804
120119.265577674679-88.7473171276057327.278472476963



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')