Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 05 Aug 2010 15:06:05 +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/05/t1281020784pabbe0oyop8dv8a.htm/, Retrieved Sun, 05 May 2024 20:28:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78417, Retrieved Sun, 05 May 2024 20:28:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPhilippe De Vocht
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Omzet product X] [2010-08-05 15:06:05] [181f2439255053cc457d7672472fa443] [Current]
Feedback Forum

Post a new message
Dataseries X:
73
72
71
69
89
88
73
63
64
64
65
67
69
71
70
72
88
83
76
70
75
71
75
81
87
90
80
85
105
104
98
94
107
112
121
118
120
122
109
112
132
127
116
113
123
125
137
127
123
128
114
120
143
135
119
117
132
139
158
141
139
150
142
149
166
150
139
140
158
169
186
177
175
187
176
185
204
188
171
171
182
185
200
192
185
195
190
195
213
194
171
171
186
182
193
185
172
185
179
182
193
173
155
164
188
186
200
185
173
190
190
193
195
178
163
165
188
182
200
177




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=78417&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=78417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78417&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
alpha0.691910685724984
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.691910685724984 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78417&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]0.691910685724984[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78417&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
alpha0.691910685724984
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
27273-1
37172.308089314275-1.30808931427501
46971.4030083398455-2.40300833984546
58969.740341191620119.2596588083799
68883.06630492455554.93369507544452
77386.4799812673643-13.4799812673643
86377.1530381851023-14.1530381851023
96467.3603998293563-3.36039982935628
106465.0353032791162-1.03530327911625
116564.31896587732960.681034122670397
126764.79018066414862.20981933585141
136966.31917827614592.68082172385414
147168.17406747340422.82593252659578
157070.1293603856936-0.129360385693644
167270.03985455252271.96014544747729
178871.396100133207416.6038998667926
188382.88451587574890.115484124251140
197682.9644205753498-6.96442057534982
207078.1456635593823-8.14566355938234
217572.50959190032512.49040809967491
227174.2327318763062-3.23273187630622
237571.99597014700623.00402985299382
248174.07449050252956.92550949747054
258778.86632452791928.13367547208081
269084.49410150127115.5058984987289
278088.3036915070588-8.30369150705877
288582.5582786223612.441721377639
2910584.247731735112620.7522682648874
3010498.60644790061975.39355209938034
3198102.338304232195-4.33830423219534
329499.3365851760135-5.33658517601346
3310795.644144867448211.3558551325518
34112103.5013823792068.4986176207943
35121109.38166672492411.6183332750761
36118117.4205156682630.579484331736779
37120117.8214670696022.17853293039789
38122119.3288172833482.67118271665183
39109121.177037148523-12.1770371485235
40112112.75161502499-0.751615024990002
41132112.23156455764819.7684354423520
42127125.9095562802761.09044371972415
43116126.664045942135-10.6640459421347
44113119.285478601710-6.28547860170954
45123114.9364887922918.06351120770901
46125120.5157183613684.48428163863198
47137123.61844074493813.3815592550622
48127132.877284585177-5.87728458517742
49123128.810728577646-5.81072857764642
50128124.7902233829253.20977661707468
51114127.011102123069-13.0111021230695
52120118.0085815310591.99141846894132
53143119.38646524946923.6135347505307
54135135.724922271100-0.724922271099729
55119135.223340805406-16.2233408054058
56117123.998237943987-6.99823794398733
57132119.15608232929612.8439176707035
58139128.04292621222810.9570737877718
59158135.62424265026522.3757573497354
60141151.106268261736-10.1062682617359
61139144.113633258638-5.11363325863758
62150140.5754557641089.42454423589243
63142147.096398629009-5.09639862900934
64149143.5701459588845.42985404111639
65166147.32711999185918.6728800081410
66150160.247085202752-10.2470852027522
67139153.157017453434-14.1570174534336
68140143.361625799408-3.36162579940776
69158141.03568098738916.9643190126113
70169152.77347458826216.226525411738
71186164.00078091283221.9992190871685
72177179.222275676848-2.22227567684845
73175177.684659389410-2.68465938941029
74187175.82711487034511.1728851296546
75176183.557753481931-7.55775348193117
76185178.3284630877086.6715369122922
77204182.94457076753121.0554292324686
78188197.513047246003-9.51304724600266
79171190.930868202687-19.9308682026868
80171177.140487517471-6.14048751747148
81182172.8918185885729.10818141142792
82185179.1938666346615.80613336533926
83200183.21119235288316.7888076471166
84192194.827547764505-2.82754776450469
85185192.871137251846-7.8711372518461
86195187.4250132784867.5749867215142
87190192.666227535326-2.66622753532633
88195190.8214362130604.17856378694017
89213193.71262914822719.2873708517728
90194207.057767140109-13.0577671401094
91171198.022958524159-27.0229585241592
92171179.325484761390-8.32548476139038
93186173.56499289114412.4350071088562
94182182.168907186828-0.168907186827568
95193182.05203849936610.9479615006342
96185189.627050048560-4.62705004856036
97172186.425544676577-14.4255446765771
98185176.4443561674508.55564383254975
99179182.364097558448-3.36409755844849
100182180.0364425099371.96355749006335
101193181.39504891934711.6049510806532
102173189.424638579366-16.4246385793665
103155178.060255637132-23.060255637132
104164162.1046183462511.89538165374944
105188163.41605316600724.5839468339931
106186180.4259486777425.57405132225838
107200184.28269435039215.7173056496083
108185195.157666080161-10.1576660801613
109173188.129468377272-15.1294683772715
110190177.66122753769912.3387724623009
111190186.1985560530943.80144394690575
112193188.8288157411434.17118425885712
113195191.7149027019743.28509729802602
114178193.987896626124-15.9878966261244
115163182.925700108243-19.9257001082425
116165169.138895282798-4.13889528279805
117188166.27514940953321.7248505904666
118182181.3068056788560.693194321144034
119200181.78643423693918.2135657630606
120177194.388595013556-17.3885950135557

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 72 & 73 & -1 \tabularnewline
3 & 71 & 72.308089314275 & -1.30808931427501 \tabularnewline
4 & 69 & 71.4030083398455 & -2.40300833984546 \tabularnewline
5 & 89 & 69.7403411916201 & 19.2596588083799 \tabularnewline
6 & 88 & 83.0663049245555 & 4.93369507544452 \tabularnewline
7 & 73 & 86.4799812673643 & -13.4799812673643 \tabularnewline
8 & 63 & 77.1530381851023 & -14.1530381851023 \tabularnewline
9 & 64 & 67.3603998293563 & -3.36039982935628 \tabularnewline
10 & 64 & 65.0353032791162 & -1.03530327911625 \tabularnewline
11 & 65 & 64.3189658773296 & 0.681034122670397 \tabularnewline
12 & 67 & 64.7901806641486 & 2.20981933585141 \tabularnewline
13 & 69 & 66.3191782761459 & 2.68082172385414 \tabularnewline
14 & 71 & 68.1740674734042 & 2.82593252659578 \tabularnewline
15 & 70 & 70.1293603856936 & -0.129360385693644 \tabularnewline
16 & 72 & 70.0398545525227 & 1.96014544747729 \tabularnewline
17 & 88 & 71.3961001332074 & 16.6038998667926 \tabularnewline
18 & 83 & 82.8845158757489 & 0.115484124251140 \tabularnewline
19 & 76 & 82.9644205753498 & -6.96442057534982 \tabularnewline
20 & 70 & 78.1456635593823 & -8.14566355938234 \tabularnewline
21 & 75 & 72.5095919003251 & 2.49040809967491 \tabularnewline
22 & 71 & 74.2327318763062 & -3.23273187630622 \tabularnewline
23 & 75 & 71.9959701470062 & 3.00402985299382 \tabularnewline
24 & 81 & 74.0744905025295 & 6.92550949747054 \tabularnewline
25 & 87 & 78.8663245279192 & 8.13367547208081 \tabularnewline
26 & 90 & 84.4941015012711 & 5.5058984987289 \tabularnewline
27 & 80 & 88.3036915070588 & -8.30369150705877 \tabularnewline
28 & 85 & 82.558278622361 & 2.441721377639 \tabularnewline
29 & 105 & 84.2477317351126 & 20.7522682648874 \tabularnewline
30 & 104 & 98.6064479006197 & 5.39355209938034 \tabularnewline
31 & 98 & 102.338304232195 & -4.33830423219534 \tabularnewline
32 & 94 & 99.3365851760135 & -5.33658517601346 \tabularnewline
33 & 107 & 95.6441448674482 & 11.3558551325518 \tabularnewline
34 & 112 & 103.501382379206 & 8.4986176207943 \tabularnewline
35 & 121 & 109.381666724924 & 11.6183332750761 \tabularnewline
36 & 118 & 117.420515668263 & 0.579484331736779 \tabularnewline
37 & 120 & 117.821467069602 & 2.17853293039789 \tabularnewline
38 & 122 & 119.328817283348 & 2.67118271665183 \tabularnewline
39 & 109 & 121.177037148523 & -12.1770371485235 \tabularnewline
40 & 112 & 112.75161502499 & -0.751615024990002 \tabularnewline
41 & 132 & 112.231564557648 & 19.7684354423520 \tabularnewline
42 & 127 & 125.909556280276 & 1.09044371972415 \tabularnewline
43 & 116 & 126.664045942135 & -10.6640459421347 \tabularnewline
44 & 113 & 119.285478601710 & -6.28547860170954 \tabularnewline
45 & 123 & 114.936488792291 & 8.06351120770901 \tabularnewline
46 & 125 & 120.515718361368 & 4.48428163863198 \tabularnewline
47 & 137 & 123.618440744938 & 13.3815592550622 \tabularnewline
48 & 127 & 132.877284585177 & -5.87728458517742 \tabularnewline
49 & 123 & 128.810728577646 & -5.81072857764642 \tabularnewline
50 & 128 & 124.790223382925 & 3.20977661707468 \tabularnewline
51 & 114 & 127.011102123069 & -13.0111021230695 \tabularnewline
52 & 120 & 118.008581531059 & 1.99141846894132 \tabularnewline
53 & 143 & 119.386465249469 & 23.6135347505307 \tabularnewline
54 & 135 & 135.724922271100 & -0.724922271099729 \tabularnewline
55 & 119 & 135.223340805406 & -16.2233408054058 \tabularnewline
56 & 117 & 123.998237943987 & -6.99823794398733 \tabularnewline
57 & 132 & 119.156082329296 & 12.8439176707035 \tabularnewline
58 & 139 & 128.042926212228 & 10.9570737877718 \tabularnewline
59 & 158 & 135.624242650265 & 22.3757573497354 \tabularnewline
60 & 141 & 151.106268261736 & -10.1062682617359 \tabularnewline
61 & 139 & 144.113633258638 & -5.11363325863758 \tabularnewline
62 & 150 & 140.575455764108 & 9.42454423589243 \tabularnewline
63 & 142 & 147.096398629009 & -5.09639862900934 \tabularnewline
64 & 149 & 143.570145958884 & 5.42985404111639 \tabularnewline
65 & 166 & 147.327119991859 & 18.6728800081410 \tabularnewline
66 & 150 & 160.247085202752 & -10.2470852027522 \tabularnewline
67 & 139 & 153.157017453434 & -14.1570174534336 \tabularnewline
68 & 140 & 143.361625799408 & -3.36162579940776 \tabularnewline
69 & 158 & 141.035680987389 & 16.9643190126113 \tabularnewline
70 & 169 & 152.773474588262 & 16.226525411738 \tabularnewline
71 & 186 & 164.000780912832 & 21.9992190871685 \tabularnewline
72 & 177 & 179.222275676848 & -2.22227567684845 \tabularnewline
73 & 175 & 177.684659389410 & -2.68465938941029 \tabularnewline
74 & 187 & 175.827114870345 & 11.1728851296546 \tabularnewline
75 & 176 & 183.557753481931 & -7.55775348193117 \tabularnewline
76 & 185 & 178.328463087708 & 6.6715369122922 \tabularnewline
77 & 204 & 182.944570767531 & 21.0554292324686 \tabularnewline
78 & 188 & 197.513047246003 & -9.51304724600266 \tabularnewline
79 & 171 & 190.930868202687 & -19.9308682026868 \tabularnewline
80 & 171 & 177.140487517471 & -6.14048751747148 \tabularnewline
81 & 182 & 172.891818588572 & 9.10818141142792 \tabularnewline
82 & 185 & 179.193866634661 & 5.80613336533926 \tabularnewline
83 & 200 & 183.211192352883 & 16.7888076471166 \tabularnewline
84 & 192 & 194.827547764505 & -2.82754776450469 \tabularnewline
85 & 185 & 192.871137251846 & -7.8711372518461 \tabularnewline
86 & 195 & 187.425013278486 & 7.5749867215142 \tabularnewline
87 & 190 & 192.666227535326 & -2.66622753532633 \tabularnewline
88 & 195 & 190.821436213060 & 4.17856378694017 \tabularnewline
89 & 213 & 193.712629148227 & 19.2873708517728 \tabularnewline
90 & 194 & 207.057767140109 & -13.0577671401094 \tabularnewline
91 & 171 & 198.022958524159 & -27.0229585241592 \tabularnewline
92 & 171 & 179.325484761390 & -8.32548476139038 \tabularnewline
93 & 186 & 173.564992891144 & 12.4350071088562 \tabularnewline
94 & 182 & 182.168907186828 & -0.168907186827568 \tabularnewline
95 & 193 & 182.052038499366 & 10.9479615006342 \tabularnewline
96 & 185 & 189.627050048560 & -4.62705004856036 \tabularnewline
97 & 172 & 186.425544676577 & -14.4255446765771 \tabularnewline
98 & 185 & 176.444356167450 & 8.55564383254975 \tabularnewline
99 & 179 & 182.364097558448 & -3.36409755844849 \tabularnewline
100 & 182 & 180.036442509937 & 1.96355749006335 \tabularnewline
101 & 193 & 181.395048919347 & 11.6049510806532 \tabularnewline
102 & 173 & 189.424638579366 & -16.4246385793665 \tabularnewline
103 & 155 & 178.060255637132 & -23.060255637132 \tabularnewline
104 & 164 & 162.104618346251 & 1.89538165374944 \tabularnewline
105 & 188 & 163.416053166007 & 24.5839468339931 \tabularnewline
106 & 186 & 180.425948677742 & 5.57405132225838 \tabularnewline
107 & 200 & 184.282694350392 & 15.7173056496083 \tabularnewline
108 & 185 & 195.157666080161 & -10.1576660801613 \tabularnewline
109 & 173 & 188.129468377272 & -15.1294683772715 \tabularnewline
110 & 190 & 177.661227537699 & 12.3387724623009 \tabularnewline
111 & 190 & 186.198556053094 & 3.80144394690575 \tabularnewline
112 & 193 & 188.828815741143 & 4.17118425885712 \tabularnewline
113 & 195 & 191.714902701974 & 3.28509729802602 \tabularnewline
114 & 178 & 193.987896626124 & -15.9878966261244 \tabularnewline
115 & 163 & 182.925700108243 & -19.9257001082425 \tabularnewline
116 & 165 & 169.138895282798 & -4.13889528279805 \tabularnewline
117 & 188 & 166.275149409533 & 21.7248505904666 \tabularnewline
118 & 182 & 181.306805678856 & 0.693194321144034 \tabularnewline
119 & 200 & 181.786434236939 & 18.2135657630606 \tabularnewline
120 & 177 & 194.388595013556 & -17.3885950135557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78417&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]72[/C][C]73[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]71[/C][C]72.308089314275[/C][C]-1.30808931427501[/C][/ROW]
[ROW][C]4[/C][C]69[/C][C]71.4030083398455[/C][C]-2.40300833984546[/C][/ROW]
[ROW][C]5[/C][C]89[/C][C]69.7403411916201[/C][C]19.2596588083799[/C][/ROW]
[ROW][C]6[/C][C]88[/C][C]83.0663049245555[/C][C]4.93369507544452[/C][/ROW]
[ROW][C]7[/C][C]73[/C][C]86.4799812673643[/C][C]-13.4799812673643[/C][/ROW]
[ROW][C]8[/C][C]63[/C][C]77.1530381851023[/C][C]-14.1530381851023[/C][/ROW]
[ROW][C]9[/C][C]64[/C][C]67.3603998293563[/C][C]-3.36039982935628[/C][/ROW]
[ROW][C]10[/C][C]64[/C][C]65.0353032791162[/C][C]-1.03530327911625[/C][/ROW]
[ROW][C]11[/C][C]65[/C][C]64.3189658773296[/C][C]0.681034122670397[/C][/ROW]
[ROW][C]12[/C][C]67[/C][C]64.7901806641486[/C][C]2.20981933585141[/C][/ROW]
[ROW][C]13[/C][C]69[/C][C]66.3191782761459[/C][C]2.68082172385414[/C][/ROW]
[ROW][C]14[/C][C]71[/C][C]68.1740674734042[/C][C]2.82593252659578[/C][/ROW]
[ROW][C]15[/C][C]70[/C][C]70.1293603856936[/C][C]-0.129360385693644[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]70.0398545525227[/C][C]1.96014544747729[/C][/ROW]
[ROW][C]17[/C][C]88[/C][C]71.3961001332074[/C][C]16.6038998667926[/C][/ROW]
[ROW][C]18[/C][C]83[/C][C]82.8845158757489[/C][C]0.115484124251140[/C][/ROW]
[ROW][C]19[/C][C]76[/C][C]82.9644205753498[/C][C]-6.96442057534982[/C][/ROW]
[ROW][C]20[/C][C]70[/C][C]78.1456635593823[/C][C]-8.14566355938234[/C][/ROW]
[ROW][C]21[/C][C]75[/C][C]72.5095919003251[/C][C]2.49040809967491[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]74.2327318763062[/C][C]-3.23273187630622[/C][/ROW]
[ROW][C]23[/C][C]75[/C][C]71.9959701470062[/C][C]3.00402985299382[/C][/ROW]
[ROW][C]24[/C][C]81[/C][C]74.0744905025295[/C][C]6.92550949747054[/C][/ROW]
[ROW][C]25[/C][C]87[/C][C]78.8663245279192[/C][C]8.13367547208081[/C][/ROW]
[ROW][C]26[/C][C]90[/C][C]84.4941015012711[/C][C]5.5058984987289[/C][/ROW]
[ROW][C]27[/C][C]80[/C][C]88.3036915070588[/C][C]-8.30369150705877[/C][/ROW]
[ROW][C]28[/C][C]85[/C][C]82.558278622361[/C][C]2.441721377639[/C][/ROW]
[ROW][C]29[/C][C]105[/C][C]84.2477317351126[/C][C]20.7522682648874[/C][/ROW]
[ROW][C]30[/C][C]104[/C][C]98.6064479006197[/C][C]5.39355209938034[/C][/ROW]
[ROW][C]31[/C][C]98[/C][C]102.338304232195[/C][C]-4.33830423219534[/C][/ROW]
[ROW][C]32[/C][C]94[/C][C]99.3365851760135[/C][C]-5.33658517601346[/C][/ROW]
[ROW][C]33[/C][C]107[/C][C]95.6441448674482[/C][C]11.3558551325518[/C][/ROW]
[ROW][C]34[/C][C]112[/C][C]103.501382379206[/C][C]8.4986176207943[/C][/ROW]
[ROW][C]35[/C][C]121[/C][C]109.381666724924[/C][C]11.6183332750761[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]117.420515668263[/C][C]0.579484331736779[/C][/ROW]
[ROW][C]37[/C][C]120[/C][C]117.821467069602[/C][C]2.17853293039789[/C][/ROW]
[ROW][C]38[/C][C]122[/C][C]119.328817283348[/C][C]2.67118271665183[/C][/ROW]
[ROW][C]39[/C][C]109[/C][C]121.177037148523[/C][C]-12.1770371485235[/C][/ROW]
[ROW][C]40[/C][C]112[/C][C]112.75161502499[/C][C]-0.751615024990002[/C][/ROW]
[ROW][C]41[/C][C]132[/C][C]112.231564557648[/C][C]19.7684354423520[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]125.909556280276[/C][C]1.09044371972415[/C][/ROW]
[ROW][C]43[/C][C]116[/C][C]126.664045942135[/C][C]-10.6640459421347[/C][/ROW]
[ROW][C]44[/C][C]113[/C][C]119.285478601710[/C][C]-6.28547860170954[/C][/ROW]
[ROW][C]45[/C][C]123[/C][C]114.936488792291[/C][C]8.06351120770901[/C][/ROW]
[ROW][C]46[/C][C]125[/C][C]120.515718361368[/C][C]4.48428163863198[/C][/ROW]
[ROW][C]47[/C][C]137[/C][C]123.618440744938[/C][C]13.3815592550622[/C][/ROW]
[ROW][C]48[/C][C]127[/C][C]132.877284585177[/C][C]-5.87728458517742[/C][/ROW]
[ROW][C]49[/C][C]123[/C][C]128.810728577646[/C][C]-5.81072857764642[/C][/ROW]
[ROW][C]50[/C][C]128[/C][C]124.790223382925[/C][C]3.20977661707468[/C][/ROW]
[ROW][C]51[/C][C]114[/C][C]127.011102123069[/C][C]-13.0111021230695[/C][/ROW]
[ROW][C]52[/C][C]120[/C][C]118.008581531059[/C][C]1.99141846894132[/C][/ROW]
[ROW][C]53[/C][C]143[/C][C]119.386465249469[/C][C]23.6135347505307[/C][/ROW]
[ROW][C]54[/C][C]135[/C][C]135.724922271100[/C][C]-0.724922271099729[/C][/ROW]
[ROW][C]55[/C][C]119[/C][C]135.223340805406[/C][C]-16.2233408054058[/C][/ROW]
[ROW][C]56[/C][C]117[/C][C]123.998237943987[/C][C]-6.99823794398733[/C][/ROW]
[ROW][C]57[/C][C]132[/C][C]119.156082329296[/C][C]12.8439176707035[/C][/ROW]
[ROW][C]58[/C][C]139[/C][C]128.042926212228[/C][C]10.9570737877718[/C][/ROW]
[ROW][C]59[/C][C]158[/C][C]135.624242650265[/C][C]22.3757573497354[/C][/ROW]
[ROW][C]60[/C][C]141[/C][C]151.106268261736[/C][C]-10.1062682617359[/C][/ROW]
[ROW][C]61[/C][C]139[/C][C]144.113633258638[/C][C]-5.11363325863758[/C][/ROW]
[ROW][C]62[/C][C]150[/C][C]140.575455764108[/C][C]9.42454423589243[/C][/ROW]
[ROW][C]63[/C][C]142[/C][C]147.096398629009[/C][C]-5.09639862900934[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]143.570145958884[/C][C]5.42985404111639[/C][/ROW]
[ROW][C]65[/C][C]166[/C][C]147.327119991859[/C][C]18.6728800081410[/C][/ROW]
[ROW][C]66[/C][C]150[/C][C]160.247085202752[/C][C]-10.2470852027522[/C][/ROW]
[ROW][C]67[/C][C]139[/C][C]153.157017453434[/C][C]-14.1570174534336[/C][/ROW]
[ROW][C]68[/C][C]140[/C][C]143.361625799408[/C][C]-3.36162579940776[/C][/ROW]
[ROW][C]69[/C][C]158[/C][C]141.035680987389[/C][C]16.9643190126113[/C][/ROW]
[ROW][C]70[/C][C]169[/C][C]152.773474588262[/C][C]16.226525411738[/C][/ROW]
[ROW][C]71[/C][C]186[/C][C]164.000780912832[/C][C]21.9992190871685[/C][/ROW]
[ROW][C]72[/C][C]177[/C][C]179.222275676848[/C][C]-2.22227567684845[/C][/ROW]
[ROW][C]73[/C][C]175[/C][C]177.684659389410[/C][C]-2.68465938941029[/C][/ROW]
[ROW][C]74[/C][C]187[/C][C]175.827114870345[/C][C]11.1728851296546[/C][/ROW]
[ROW][C]75[/C][C]176[/C][C]183.557753481931[/C][C]-7.55775348193117[/C][/ROW]
[ROW][C]76[/C][C]185[/C][C]178.328463087708[/C][C]6.6715369122922[/C][/ROW]
[ROW][C]77[/C][C]204[/C][C]182.944570767531[/C][C]21.0554292324686[/C][/ROW]
[ROW][C]78[/C][C]188[/C][C]197.513047246003[/C][C]-9.51304724600266[/C][/ROW]
[ROW][C]79[/C][C]171[/C][C]190.930868202687[/C][C]-19.9308682026868[/C][/ROW]
[ROW][C]80[/C][C]171[/C][C]177.140487517471[/C][C]-6.14048751747148[/C][/ROW]
[ROW][C]81[/C][C]182[/C][C]172.891818588572[/C][C]9.10818141142792[/C][/ROW]
[ROW][C]82[/C][C]185[/C][C]179.193866634661[/C][C]5.80613336533926[/C][/ROW]
[ROW][C]83[/C][C]200[/C][C]183.211192352883[/C][C]16.7888076471166[/C][/ROW]
[ROW][C]84[/C][C]192[/C][C]194.827547764505[/C][C]-2.82754776450469[/C][/ROW]
[ROW][C]85[/C][C]185[/C][C]192.871137251846[/C][C]-7.8711372518461[/C][/ROW]
[ROW][C]86[/C][C]195[/C][C]187.425013278486[/C][C]7.5749867215142[/C][/ROW]
[ROW][C]87[/C][C]190[/C][C]192.666227535326[/C][C]-2.66622753532633[/C][/ROW]
[ROW][C]88[/C][C]195[/C][C]190.821436213060[/C][C]4.17856378694017[/C][/ROW]
[ROW][C]89[/C][C]213[/C][C]193.712629148227[/C][C]19.2873708517728[/C][/ROW]
[ROW][C]90[/C][C]194[/C][C]207.057767140109[/C][C]-13.0577671401094[/C][/ROW]
[ROW][C]91[/C][C]171[/C][C]198.022958524159[/C][C]-27.0229585241592[/C][/ROW]
[ROW][C]92[/C][C]171[/C][C]179.325484761390[/C][C]-8.32548476139038[/C][/ROW]
[ROW][C]93[/C][C]186[/C][C]173.564992891144[/C][C]12.4350071088562[/C][/ROW]
[ROW][C]94[/C][C]182[/C][C]182.168907186828[/C][C]-0.168907186827568[/C][/ROW]
[ROW][C]95[/C][C]193[/C][C]182.052038499366[/C][C]10.9479615006342[/C][/ROW]
[ROW][C]96[/C][C]185[/C][C]189.627050048560[/C][C]-4.62705004856036[/C][/ROW]
[ROW][C]97[/C][C]172[/C][C]186.425544676577[/C][C]-14.4255446765771[/C][/ROW]
[ROW][C]98[/C][C]185[/C][C]176.444356167450[/C][C]8.55564383254975[/C][/ROW]
[ROW][C]99[/C][C]179[/C][C]182.364097558448[/C][C]-3.36409755844849[/C][/ROW]
[ROW][C]100[/C][C]182[/C][C]180.036442509937[/C][C]1.96355749006335[/C][/ROW]
[ROW][C]101[/C][C]193[/C][C]181.395048919347[/C][C]11.6049510806532[/C][/ROW]
[ROW][C]102[/C][C]173[/C][C]189.424638579366[/C][C]-16.4246385793665[/C][/ROW]
[ROW][C]103[/C][C]155[/C][C]178.060255637132[/C][C]-23.060255637132[/C][/ROW]
[ROW][C]104[/C][C]164[/C][C]162.104618346251[/C][C]1.89538165374944[/C][/ROW]
[ROW][C]105[/C][C]188[/C][C]163.416053166007[/C][C]24.5839468339931[/C][/ROW]
[ROW][C]106[/C][C]186[/C][C]180.425948677742[/C][C]5.57405132225838[/C][/ROW]
[ROW][C]107[/C][C]200[/C][C]184.282694350392[/C][C]15.7173056496083[/C][/ROW]
[ROW][C]108[/C][C]185[/C][C]195.157666080161[/C][C]-10.1576660801613[/C][/ROW]
[ROW][C]109[/C][C]173[/C][C]188.129468377272[/C][C]-15.1294683772715[/C][/ROW]
[ROW][C]110[/C][C]190[/C][C]177.661227537699[/C][C]12.3387724623009[/C][/ROW]
[ROW][C]111[/C][C]190[/C][C]186.198556053094[/C][C]3.80144394690575[/C][/ROW]
[ROW][C]112[/C][C]193[/C][C]188.828815741143[/C][C]4.17118425885712[/C][/ROW]
[ROW][C]113[/C][C]195[/C][C]191.714902701974[/C][C]3.28509729802602[/C][/ROW]
[ROW][C]114[/C][C]178[/C][C]193.987896626124[/C][C]-15.9878966261244[/C][/ROW]
[ROW][C]115[/C][C]163[/C][C]182.925700108243[/C][C]-19.9257001082425[/C][/ROW]
[ROW][C]116[/C][C]165[/C][C]169.138895282798[/C][C]-4.13889528279805[/C][/ROW]
[ROW][C]117[/C][C]188[/C][C]166.275149409533[/C][C]21.7248505904666[/C][/ROW]
[ROW][C]118[/C][C]182[/C][C]181.306805678856[/C][C]0.693194321144034[/C][/ROW]
[ROW][C]119[/C][C]200[/C][C]181.786434236939[/C][C]18.2135657630606[/C][/ROW]
[ROW][C]120[/C][C]177[/C][C]194.388595013556[/C][C]-17.3885950135557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78417&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
27273-1
37172.308089314275-1.30808931427501
46971.4030083398455-2.40300833984546
58969.740341191620119.2596588083799
68883.06630492455554.93369507544452
77386.4799812673643-13.4799812673643
86377.1530381851023-14.1530381851023
96467.3603998293563-3.36039982935628
106465.0353032791162-1.03530327911625
116564.31896587732960.681034122670397
126764.79018066414862.20981933585141
136966.31917827614592.68082172385414
147168.17406747340422.82593252659578
157070.1293603856936-0.129360385693644
167270.03985455252271.96014544747729
178871.396100133207416.6038998667926
188382.88451587574890.115484124251140
197682.9644205753498-6.96442057534982
207078.1456635593823-8.14566355938234
217572.50959190032512.49040809967491
227174.2327318763062-3.23273187630622
237571.99597014700623.00402985299382
248174.07449050252956.92550949747054
258778.86632452791928.13367547208081
269084.49410150127115.5058984987289
278088.3036915070588-8.30369150705877
288582.5582786223612.441721377639
2910584.247731735112620.7522682648874
3010498.60644790061975.39355209938034
3198102.338304232195-4.33830423219534
329499.3365851760135-5.33658517601346
3310795.644144867448211.3558551325518
34112103.5013823792068.4986176207943
35121109.38166672492411.6183332750761
36118117.4205156682630.579484331736779
37120117.8214670696022.17853293039789
38122119.3288172833482.67118271665183
39109121.177037148523-12.1770371485235
40112112.75161502499-0.751615024990002
41132112.23156455764819.7684354423520
42127125.9095562802761.09044371972415
43116126.664045942135-10.6640459421347
44113119.285478601710-6.28547860170954
45123114.9364887922918.06351120770901
46125120.5157183613684.48428163863198
47137123.61844074493813.3815592550622
48127132.877284585177-5.87728458517742
49123128.810728577646-5.81072857764642
50128124.7902233829253.20977661707468
51114127.011102123069-13.0111021230695
52120118.0085815310591.99141846894132
53143119.38646524946923.6135347505307
54135135.724922271100-0.724922271099729
55119135.223340805406-16.2233408054058
56117123.998237943987-6.99823794398733
57132119.15608232929612.8439176707035
58139128.04292621222810.9570737877718
59158135.62424265026522.3757573497354
60141151.106268261736-10.1062682617359
61139144.113633258638-5.11363325863758
62150140.5754557641089.42454423589243
63142147.096398629009-5.09639862900934
64149143.5701459588845.42985404111639
65166147.32711999185918.6728800081410
66150160.247085202752-10.2470852027522
67139153.157017453434-14.1570174534336
68140143.361625799408-3.36162579940776
69158141.03568098738916.9643190126113
70169152.77347458826216.226525411738
71186164.00078091283221.9992190871685
72177179.222275676848-2.22227567684845
73175177.684659389410-2.68465938941029
74187175.82711487034511.1728851296546
75176183.557753481931-7.55775348193117
76185178.3284630877086.6715369122922
77204182.94457076753121.0554292324686
78188197.513047246003-9.51304724600266
79171190.930868202687-19.9308682026868
80171177.140487517471-6.14048751747148
81182172.8918185885729.10818141142792
82185179.1938666346615.80613336533926
83200183.21119235288316.7888076471166
84192194.827547764505-2.82754776450469
85185192.871137251846-7.8711372518461
86195187.4250132784867.5749867215142
87190192.666227535326-2.66622753532633
88195190.8214362130604.17856378694017
89213193.71262914822719.2873708517728
90194207.057767140109-13.0577671401094
91171198.022958524159-27.0229585241592
92171179.325484761390-8.32548476139038
93186173.56499289114412.4350071088562
94182182.168907186828-0.168907186827568
95193182.05203849936610.9479615006342
96185189.627050048560-4.62705004856036
97172186.425544676577-14.4255446765771
98185176.4443561674508.55564383254975
99179182.364097558448-3.36409755844849
100182180.0364425099371.96355749006335
101193181.39504891934711.6049510806532
102173189.424638579366-16.4246385793665
103155178.060255637132-23.060255637132
104164162.1046183462511.89538165374944
105188163.41605316600724.5839468339931
106186180.4259486777425.57405132225838
107200184.28269435039215.7173056496083
108185195.157666080161-10.1576660801613
109173188.129468377272-15.1294683772715
110190177.66122753769912.3387724623009
111190186.1985560530943.80144394690575
112193188.8288157411434.17118425885712
113195191.7149027019743.28509729802602
114178193.987896626124-15.9878966261244
115163182.925700108243-19.9257001082425
116165169.138895282798-4.13889528279805
117188166.27514940953321.7248505904666
118182181.3068056788560.693194321144034
119200181.78643423693918.2135657630606
120177194.388595013556-17.3885950135557







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121182.357240313932160.436308701556204.278171926309
122182.357240313932155.700626768136209.013853859728
123182.357240313932151.687665020079213.026815607786
124182.357240313932148.142175624811216.572305003054
125182.357240313932144.931066923427219.783413704438
126182.357240313932141.974493284643222.739987343222
127182.357240313932139.220086251489225.494394376376
128182.357240313932136.631297310180228.083183317685
129182.357240313932134.181419962247230.533060665618
130182.357240313932131.850236150814232.864244477051
131182.357240313932129.622002829792235.092477798073
132182.357240313932127.484177017957237.230303609907

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 182.357240313932 & 160.436308701556 & 204.278171926309 \tabularnewline
122 & 182.357240313932 & 155.700626768136 & 209.013853859728 \tabularnewline
123 & 182.357240313932 & 151.687665020079 & 213.026815607786 \tabularnewline
124 & 182.357240313932 & 148.142175624811 & 216.572305003054 \tabularnewline
125 & 182.357240313932 & 144.931066923427 & 219.783413704438 \tabularnewline
126 & 182.357240313932 & 141.974493284643 & 222.739987343222 \tabularnewline
127 & 182.357240313932 & 139.220086251489 & 225.494394376376 \tabularnewline
128 & 182.357240313932 & 136.631297310180 & 228.083183317685 \tabularnewline
129 & 182.357240313932 & 134.181419962247 & 230.533060665618 \tabularnewline
130 & 182.357240313932 & 131.850236150814 & 232.864244477051 \tabularnewline
131 & 182.357240313932 & 129.622002829792 & 235.092477798073 \tabularnewline
132 & 182.357240313932 & 127.484177017957 & 237.230303609907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78417&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]182.357240313932[/C][C]160.436308701556[/C][C]204.278171926309[/C][/ROW]
[ROW][C]122[/C][C]182.357240313932[/C][C]155.700626768136[/C][C]209.013853859728[/C][/ROW]
[ROW][C]123[/C][C]182.357240313932[/C][C]151.687665020079[/C][C]213.026815607786[/C][/ROW]
[ROW][C]124[/C][C]182.357240313932[/C][C]148.142175624811[/C][C]216.572305003054[/C][/ROW]
[ROW][C]125[/C][C]182.357240313932[/C][C]144.931066923427[/C][C]219.783413704438[/C][/ROW]
[ROW][C]126[/C][C]182.357240313932[/C][C]141.974493284643[/C][C]222.739987343222[/C][/ROW]
[ROW][C]127[/C][C]182.357240313932[/C][C]139.220086251489[/C][C]225.494394376376[/C][/ROW]
[ROW][C]128[/C][C]182.357240313932[/C][C]136.631297310180[/C][C]228.083183317685[/C][/ROW]
[ROW][C]129[/C][C]182.357240313932[/C][C]134.181419962247[/C][C]230.533060665618[/C][/ROW]
[ROW][C]130[/C][C]182.357240313932[/C][C]131.850236150814[/C][C]232.864244477051[/C][/ROW]
[ROW][C]131[/C][C]182.357240313932[/C][C]129.622002829792[/C][C]235.092477798073[/C][/ROW]
[ROW][C]132[/C][C]182.357240313932[/C][C]127.484177017957[/C][C]237.230303609907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78417&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78417&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
121182.357240313932160.436308701556204.278171926309
122182.357240313932155.700626768136209.013853859728
123182.357240313932151.687665020079213.026815607786
124182.357240313932148.142175624811216.572305003054
125182.357240313932144.931066923427219.783413704438
126182.357240313932141.974493284643222.739987343222
127182.357240313932139.220086251489225.494394376376
128182.357240313932136.631297310180228.083183317685
129182.357240313932134.181419962247230.533060665618
130182.357240313932131.850236150814232.864244477051
131182.357240313932129.622002829792235.092477798073
132182.357240313932127.484177017957237.230303609907



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
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')