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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 09 Dec 2014 15:35:16 +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/Dec/09/t14181393290wjtum7qukwuudk.htm/, Retrieved Thu, 16 May 2024 13:02:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=264703, Retrieved Thu, 16 May 2024 13:02:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-09 15:35:16] [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=264703&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=264703&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264703&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
alpha0.322634551106305
beta0.0205844386272427
gamma0.257499917249435

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.322634551106305 \tabularnewline
beta & 0.0205844386272427 \tabularnewline
gamma & 0.257499917249435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264703&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]0.322634551106305[/C][/ROW]
[ROW][C]beta[/C][C]0.0205844386272427[/C][/ROW]
[ROW][C]gamma[/C][C]0.257499917249435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264703&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264703&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
alpha0.322634551106305
beta0.0205844386272427
gamma0.257499917249435







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13141146.903388361255-5.90338836125545
14138143.365146880029-5.36514688002879
15130134.323881587174-4.32388158717421
16145148.220536245983-3.22053624598291
17123125.129299713449-2.12929971344914
18116117.440908338987-1.4409083389868
1990112.480574622663-22.4805746226634
20110112.026435255693-2.02643525569329
21102103.482634269071-1.48263426907097
2210992.08893912149716.911060878503
23111119.119844612986-8.11984461298586
249377.240297660115515.7597023398845
25120118.4790215722521.52097842774789
2681117.333601093189-36.3336010931887
278499.5831425923733-15.5831425923733
2887104.709496826634-17.7094968266344
2911083.28425349178826.715746508212
309086.18192711348693.81807288651315
3110880.552670366506427.4473296334936
3210198.52209843764952.47790156235048
338792.3637118714482-5.3637118714482
3411883.658727729938634.3412722700614
3582111.159038814706-29.1590388147058
368670.551786402805315.4482135971947
37103105.418119472793-2.41811947279336
389396.7381255083114-3.7381255083114
398393.3547819011328-10.3547819011328
409199.81506173173-8.81506173173
416988.9572867809021-19.9572867809021
429574.065403955265620.9345960447344
439677.958259034822718.0417409651773
4410587.993977212725717.0060227872743
4512185.814775262613635.1852247373864
4610197.01526515825133.98473484174875
47111103.3516793189727.64832068102827
4813080.541505563747349.4584944362527
49134130.7738555986393.22614440136121
50161122.78913529832638.2108647016744
51186132.03674588380353.9632541161967
52244169.41803392423274.5819660757682
53145176.554396217859-31.5543962178591
54170166.9580613243463.04193867565434
55164164.258554333691-0.258554333690967
56124174.705567404946-50.7055674049456
57154152.0201422025061.97985779749368
58126145.955044133264-19.9550441332636
59173148.91314093604124.0868590639593
60140129.59617378777110.4038262122291
61142167.018047940787-25.0180479407869
62129155.3758061483-26.3758061483004
63171145.49513419786125.5048658021387
64107174.831845426143-67.831845426143
6598125.643487047998-27.6434870479981
66185120.65721928855564.3427807114453
67142137.3720842438944.62791575610555
68135139.114758692082-4.11475869208175
69126140.225704615371-14.2257046153715
70126125.8726863818040.127313618196254
71134141.343769413788-7.3437694137879
72119113.1574919437555.84250805624545
73134138.251268200597-4.2512682005968
74133132.9859046271170.0140953728829629
75129139.816797799784-10.8167977997838
7696138.648797642096-42.6487976420961
77150106.35180850734243.6481914926583
78113140.532755490021-27.5327554900206
7999118.835634949479-19.8356349494795
80164110.90071785549153.0992821445095
81127128.488551957068-1.48855195706801
82148121.02003707929826.9799629207015
83166144.46843350423521.5315664957649
84115125.89919514483-10.8991951448302
85199145.26852219745953.7314778025415
86141159.546538767806-18.5465387678058
87149159.796186126666-10.796186126666
88131152.190312852669-21.1903128526694
89171140.72329551940230.2767044805978
90178159.75496144717818.2450385528223
91181151.33549221551729.6645077844829
92129177.140981057294-48.1409810572942
93112151.463539238146-39.4635392381456
94186136.43199170545849.5680082945416
95153168.282485828353-15.2824858283531
96116130.593259912624-14.5932599126239
97190160.64974787029729.3502521297026
98169154.43851115881114.5614888411891
99165167.276424634789-2.27642463478878
100160160.158297586883-0.158297586883123
101202164.99928647266237.0007135273385
102155185.340060961071-30.3400609610708
103257162.49581080528194.504189194719
104171195.580373617775-24.5803736177746
105168176.883625082258-8.88362508225811
106202191.19821000994810.8017899900515
107189200.649053050797-11.6490530507971
108132157.266283828934-25.2662838289338

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 141 & 146.903388361255 & -5.90338836125545 \tabularnewline
14 & 138 & 143.365146880029 & -5.36514688002879 \tabularnewline
15 & 130 & 134.323881587174 & -4.32388158717421 \tabularnewline
16 & 145 & 148.220536245983 & -3.22053624598291 \tabularnewline
17 & 123 & 125.129299713449 & -2.12929971344914 \tabularnewline
18 & 116 & 117.440908338987 & -1.4409083389868 \tabularnewline
19 & 90 & 112.480574622663 & -22.4805746226634 \tabularnewline
20 & 110 & 112.026435255693 & -2.02643525569329 \tabularnewline
21 & 102 & 103.482634269071 & -1.48263426907097 \tabularnewline
22 & 109 & 92.088939121497 & 16.911060878503 \tabularnewline
23 & 111 & 119.119844612986 & -8.11984461298586 \tabularnewline
24 & 93 & 77.2402976601155 & 15.7597023398845 \tabularnewline
25 & 120 & 118.479021572252 & 1.52097842774789 \tabularnewline
26 & 81 & 117.333601093189 & -36.3336010931887 \tabularnewline
27 & 84 & 99.5831425923733 & -15.5831425923733 \tabularnewline
28 & 87 & 104.709496826634 & -17.7094968266344 \tabularnewline
29 & 110 & 83.284253491788 & 26.715746508212 \tabularnewline
30 & 90 & 86.1819271134869 & 3.81807288651315 \tabularnewline
31 & 108 & 80.5526703665064 & 27.4473296334936 \tabularnewline
32 & 101 & 98.5220984376495 & 2.47790156235048 \tabularnewline
33 & 87 & 92.3637118714482 & -5.3637118714482 \tabularnewline
34 & 118 & 83.6587277299386 & 34.3412722700614 \tabularnewline
35 & 82 & 111.159038814706 & -29.1590388147058 \tabularnewline
36 & 86 & 70.5517864028053 & 15.4482135971947 \tabularnewline
37 & 103 & 105.418119472793 & -2.41811947279336 \tabularnewline
38 & 93 & 96.7381255083114 & -3.7381255083114 \tabularnewline
39 & 83 & 93.3547819011328 & -10.3547819011328 \tabularnewline
40 & 91 & 99.81506173173 & -8.81506173173 \tabularnewline
41 & 69 & 88.9572867809021 & -19.9572867809021 \tabularnewline
42 & 95 & 74.0654039552656 & 20.9345960447344 \tabularnewline
43 & 96 & 77.9582590348227 & 18.0417409651773 \tabularnewline
44 & 105 & 87.9939772127257 & 17.0060227872743 \tabularnewline
45 & 121 & 85.8147752626136 & 35.1852247373864 \tabularnewline
46 & 101 & 97.0152651582513 & 3.98473484174875 \tabularnewline
47 & 111 & 103.351679318972 & 7.64832068102827 \tabularnewline
48 & 130 & 80.5415055637473 & 49.4584944362527 \tabularnewline
49 & 134 & 130.773855598639 & 3.22614440136121 \tabularnewline
50 & 161 & 122.789135298326 & 38.2108647016744 \tabularnewline
51 & 186 & 132.036745883803 & 53.9632541161967 \tabularnewline
52 & 244 & 169.418033924232 & 74.5819660757682 \tabularnewline
53 & 145 & 176.554396217859 & -31.5543962178591 \tabularnewline
54 & 170 & 166.958061324346 & 3.04193867565434 \tabularnewline
55 & 164 & 164.258554333691 & -0.258554333690967 \tabularnewline
56 & 124 & 174.705567404946 & -50.7055674049456 \tabularnewline
57 & 154 & 152.020142202506 & 1.97985779749368 \tabularnewline
58 & 126 & 145.955044133264 & -19.9550441332636 \tabularnewline
59 & 173 & 148.913140936041 & 24.0868590639593 \tabularnewline
60 & 140 & 129.596173787771 & 10.4038262122291 \tabularnewline
61 & 142 & 167.018047940787 & -25.0180479407869 \tabularnewline
62 & 129 & 155.3758061483 & -26.3758061483004 \tabularnewline
63 & 171 & 145.495134197861 & 25.5048658021387 \tabularnewline
64 & 107 & 174.831845426143 & -67.831845426143 \tabularnewline
65 & 98 & 125.643487047998 & -27.6434870479981 \tabularnewline
66 & 185 & 120.657219288555 & 64.3427807114453 \tabularnewline
67 & 142 & 137.372084243894 & 4.62791575610555 \tabularnewline
68 & 135 & 139.114758692082 & -4.11475869208175 \tabularnewline
69 & 126 & 140.225704615371 & -14.2257046153715 \tabularnewline
70 & 126 & 125.872686381804 & 0.127313618196254 \tabularnewline
71 & 134 & 141.343769413788 & -7.3437694137879 \tabularnewline
72 & 119 & 113.157491943755 & 5.84250805624545 \tabularnewline
73 & 134 & 138.251268200597 & -4.2512682005968 \tabularnewline
74 & 133 & 132.985904627117 & 0.0140953728829629 \tabularnewline
75 & 129 & 139.816797799784 & -10.8167977997838 \tabularnewline
76 & 96 & 138.648797642096 & -42.6487976420961 \tabularnewline
77 & 150 & 106.351808507342 & 43.6481914926583 \tabularnewline
78 & 113 & 140.532755490021 & -27.5327554900206 \tabularnewline
79 & 99 & 118.835634949479 & -19.8356349494795 \tabularnewline
80 & 164 & 110.900717855491 & 53.0992821445095 \tabularnewline
81 & 127 & 128.488551957068 & -1.48855195706801 \tabularnewline
82 & 148 & 121.020037079298 & 26.9799629207015 \tabularnewline
83 & 166 & 144.468433504235 & 21.5315664957649 \tabularnewline
84 & 115 & 125.89919514483 & -10.8991951448302 \tabularnewline
85 & 199 & 145.268522197459 & 53.7314778025415 \tabularnewline
86 & 141 & 159.546538767806 & -18.5465387678058 \tabularnewline
87 & 149 & 159.796186126666 & -10.796186126666 \tabularnewline
88 & 131 & 152.190312852669 & -21.1903128526694 \tabularnewline
89 & 171 & 140.723295519402 & 30.2767044805978 \tabularnewline
90 & 178 & 159.754961447178 & 18.2450385528223 \tabularnewline
91 & 181 & 151.335492215517 & 29.6645077844829 \tabularnewline
92 & 129 & 177.140981057294 & -48.1409810572942 \tabularnewline
93 & 112 & 151.463539238146 & -39.4635392381456 \tabularnewline
94 & 186 & 136.431991705458 & 49.5680082945416 \tabularnewline
95 & 153 & 168.282485828353 & -15.2824858283531 \tabularnewline
96 & 116 & 130.593259912624 & -14.5932599126239 \tabularnewline
97 & 190 & 160.649747870297 & 29.3502521297026 \tabularnewline
98 & 169 & 154.438511158811 & 14.5614888411891 \tabularnewline
99 & 165 & 167.276424634789 & -2.27642463478878 \tabularnewline
100 & 160 & 160.158297586883 & -0.158297586883123 \tabularnewline
101 & 202 & 164.999286472662 & 37.0007135273385 \tabularnewline
102 & 155 & 185.340060961071 & -30.3400609610708 \tabularnewline
103 & 257 & 162.495810805281 & 94.504189194719 \tabularnewline
104 & 171 & 195.580373617775 & -24.5803736177746 \tabularnewline
105 & 168 & 176.883625082258 & -8.88362508225811 \tabularnewline
106 & 202 & 191.198210009948 & 10.8017899900515 \tabularnewline
107 & 189 & 200.649053050797 & -11.6490530507971 \tabularnewline
108 & 132 & 157.266283828934 & -25.2662838289338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264703&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]141[/C][C]146.903388361255[/C][C]-5.90338836125545[/C][/ROW]
[ROW][C]14[/C][C]138[/C][C]143.365146880029[/C][C]-5.36514688002879[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]134.323881587174[/C][C]-4.32388158717421[/C][/ROW]
[ROW][C]16[/C][C]145[/C][C]148.220536245983[/C][C]-3.22053624598291[/C][/ROW]
[ROW][C]17[/C][C]123[/C][C]125.129299713449[/C][C]-2.12929971344914[/C][/ROW]
[ROW][C]18[/C][C]116[/C][C]117.440908338987[/C][C]-1.4409083389868[/C][/ROW]
[ROW][C]19[/C][C]90[/C][C]112.480574622663[/C][C]-22.4805746226634[/C][/ROW]
[ROW][C]20[/C][C]110[/C][C]112.026435255693[/C][C]-2.02643525569329[/C][/ROW]
[ROW][C]21[/C][C]102[/C][C]103.482634269071[/C][C]-1.48263426907097[/C][/ROW]
[ROW][C]22[/C][C]109[/C][C]92.088939121497[/C][C]16.911060878503[/C][/ROW]
[ROW][C]23[/C][C]111[/C][C]119.119844612986[/C][C]-8.11984461298586[/C][/ROW]
[ROW][C]24[/C][C]93[/C][C]77.2402976601155[/C][C]15.7597023398845[/C][/ROW]
[ROW][C]25[/C][C]120[/C][C]118.479021572252[/C][C]1.52097842774789[/C][/ROW]
[ROW][C]26[/C][C]81[/C][C]117.333601093189[/C][C]-36.3336010931887[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]99.5831425923733[/C][C]-15.5831425923733[/C][/ROW]
[ROW][C]28[/C][C]87[/C][C]104.709496826634[/C][C]-17.7094968266344[/C][/ROW]
[ROW][C]29[/C][C]110[/C][C]83.284253491788[/C][C]26.715746508212[/C][/ROW]
[ROW][C]30[/C][C]90[/C][C]86.1819271134869[/C][C]3.81807288651315[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]80.5526703665064[/C][C]27.4473296334936[/C][/ROW]
[ROW][C]32[/C][C]101[/C][C]98.5220984376495[/C][C]2.47790156235048[/C][/ROW]
[ROW][C]33[/C][C]87[/C][C]92.3637118714482[/C][C]-5.3637118714482[/C][/ROW]
[ROW][C]34[/C][C]118[/C][C]83.6587277299386[/C][C]34.3412722700614[/C][/ROW]
[ROW][C]35[/C][C]82[/C][C]111.159038814706[/C][C]-29.1590388147058[/C][/ROW]
[ROW][C]36[/C][C]86[/C][C]70.5517864028053[/C][C]15.4482135971947[/C][/ROW]
[ROW][C]37[/C][C]103[/C][C]105.418119472793[/C][C]-2.41811947279336[/C][/ROW]
[ROW][C]38[/C][C]93[/C][C]96.7381255083114[/C][C]-3.7381255083114[/C][/ROW]
[ROW][C]39[/C][C]83[/C][C]93.3547819011328[/C][C]-10.3547819011328[/C][/ROW]
[ROW][C]40[/C][C]91[/C][C]99.81506173173[/C][C]-8.81506173173[/C][/ROW]
[ROW][C]41[/C][C]69[/C][C]88.9572867809021[/C][C]-19.9572867809021[/C][/ROW]
[ROW][C]42[/C][C]95[/C][C]74.0654039552656[/C][C]20.9345960447344[/C][/ROW]
[ROW][C]43[/C][C]96[/C][C]77.9582590348227[/C][C]18.0417409651773[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]87.9939772127257[/C][C]17.0060227872743[/C][/ROW]
[ROW][C]45[/C][C]121[/C][C]85.8147752626136[/C][C]35.1852247373864[/C][/ROW]
[ROW][C]46[/C][C]101[/C][C]97.0152651582513[/C][C]3.98473484174875[/C][/ROW]
[ROW][C]47[/C][C]111[/C][C]103.351679318972[/C][C]7.64832068102827[/C][/ROW]
[ROW][C]48[/C][C]130[/C][C]80.5415055637473[/C][C]49.4584944362527[/C][/ROW]
[ROW][C]49[/C][C]134[/C][C]130.773855598639[/C][C]3.22614440136121[/C][/ROW]
[ROW][C]50[/C][C]161[/C][C]122.789135298326[/C][C]38.2108647016744[/C][/ROW]
[ROW][C]51[/C][C]186[/C][C]132.036745883803[/C][C]53.9632541161967[/C][/ROW]
[ROW][C]52[/C][C]244[/C][C]169.418033924232[/C][C]74.5819660757682[/C][/ROW]
[ROW][C]53[/C][C]145[/C][C]176.554396217859[/C][C]-31.5543962178591[/C][/ROW]
[ROW][C]54[/C][C]170[/C][C]166.958061324346[/C][C]3.04193867565434[/C][/ROW]
[ROW][C]55[/C][C]164[/C][C]164.258554333691[/C][C]-0.258554333690967[/C][/ROW]
[ROW][C]56[/C][C]124[/C][C]174.705567404946[/C][C]-50.7055674049456[/C][/ROW]
[ROW][C]57[/C][C]154[/C][C]152.020142202506[/C][C]1.97985779749368[/C][/ROW]
[ROW][C]58[/C][C]126[/C][C]145.955044133264[/C][C]-19.9550441332636[/C][/ROW]
[ROW][C]59[/C][C]173[/C][C]148.913140936041[/C][C]24.0868590639593[/C][/ROW]
[ROW][C]60[/C][C]140[/C][C]129.596173787771[/C][C]10.4038262122291[/C][/ROW]
[ROW][C]61[/C][C]142[/C][C]167.018047940787[/C][C]-25.0180479407869[/C][/ROW]
[ROW][C]62[/C][C]129[/C][C]155.3758061483[/C][C]-26.3758061483004[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]145.495134197861[/C][C]25.5048658021387[/C][/ROW]
[ROW][C]64[/C][C]107[/C][C]174.831845426143[/C][C]-67.831845426143[/C][/ROW]
[ROW][C]65[/C][C]98[/C][C]125.643487047998[/C][C]-27.6434870479981[/C][/ROW]
[ROW][C]66[/C][C]185[/C][C]120.657219288555[/C][C]64.3427807114453[/C][/ROW]
[ROW][C]67[/C][C]142[/C][C]137.372084243894[/C][C]4.62791575610555[/C][/ROW]
[ROW][C]68[/C][C]135[/C][C]139.114758692082[/C][C]-4.11475869208175[/C][/ROW]
[ROW][C]69[/C][C]126[/C][C]140.225704615371[/C][C]-14.2257046153715[/C][/ROW]
[ROW][C]70[/C][C]126[/C][C]125.872686381804[/C][C]0.127313618196254[/C][/ROW]
[ROW][C]71[/C][C]134[/C][C]141.343769413788[/C][C]-7.3437694137879[/C][/ROW]
[ROW][C]72[/C][C]119[/C][C]113.157491943755[/C][C]5.84250805624545[/C][/ROW]
[ROW][C]73[/C][C]134[/C][C]138.251268200597[/C][C]-4.2512682005968[/C][/ROW]
[ROW][C]74[/C][C]133[/C][C]132.985904627117[/C][C]0.0140953728829629[/C][/ROW]
[ROW][C]75[/C][C]129[/C][C]139.816797799784[/C][C]-10.8167977997838[/C][/ROW]
[ROW][C]76[/C][C]96[/C][C]138.648797642096[/C][C]-42.6487976420961[/C][/ROW]
[ROW][C]77[/C][C]150[/C][C]106.351808507342[/C][C]43.6481914926583[/C][/ROW]
[ROW][C]78[/C][C]113[/C][C]140.532755490021[/C][C]-27.5327554900206[/C][/ROW]
[ROW][C]79[/C][C]99[/C][C]118.835634949479[/C][C]-19.8356349494795[/C][/ROW]
[ROW][C]80[/C][C]164[/C][C]110.900717855491[/C][C]53.0992821445095[/C][/ROW]
[ROW][C]81[/C][C]127[/C][C]128.488551957068[/C][C]-1.48855195706801[/C][/ROW]
[ROW][C]82[/C][C]148[/C][C]121.020037079298[/C][C]26.9799629207015[/C][/ROW]
[ROW][C]83[/C][C]166[/C][C]144.468433504235[/C][C]21.5315664957649[/C][/ROW]
[ROW][C]84[/C][C]115[/C][C]125.89919514483[/C][C]-10.8991951448302[/C][/ROW]
[ROW][C]85[/C][C]199[/C][C]145.268522197459[/C][C]53.7314778025415[/C][/ROW]
[ROW][C]86[/C][C]141[/C][C]159.546538767806[/C][C]-18.5465387678058[/C][/ROW]
[ROW][C]87[/C][C]149[/C][C]159.796186126666[/C][C]-10.796186126666[/C][/ROW]
[ROW][C]88[/C][C]131[/C][C]152.190312852669[/C][C]-21.1903128526694[/C][/ROW]
[ROW][C]89[/C][C]171[/C][C]140.723295519402[/C][C]30.2767044805978[/C][/ROW]
[ROW][C]90[/C][C]178[/C][C]159.754961447178[/C][C]18.2450385528223[/C][/ROW]
[ROW][C]91[/C][C]181[/C][C]151.335492215517[/C][C]29.6645077844829[/C][/ROW]
[ROW][C]92[/C][C]129[/C][C]177.140981057294[/C][C]-48.1409810572942[/C][/ROW]
[ROW][C]93[/C][C]112[/C][C]151.463539238146[/C][C]-39.4635392381456[/C][/ROW]
[ROW][C]94[/C][C]186[/C][C]136.431991705458[/C][C]49.5680082945416[/C][/ROW]
[ROW][C]95[/C][C]153[/C][C]168.282485828353[/C][C]-15.2824858283531[/C][/ROW]
[ROW][C]96[/C][C]116[/C][C]130.593259912624[/C][C]-14.5932599126239[/C][/ROW]
[ROW][C]97[/C][C]190[/C][C]160.649747870297[/C][C]29.3502521297026[/C][/ROW]
[ROW][C]98[/C][C]169[/C][C]154.438511158811[/C][C]14.5614888411891[/C][/ROW]
[ROW][C]99[/C][C]165[/C][C]167.276424634789[/C][C]-2.27642463478878[/C][/ROW]
[ROW][C]100[/C][C]160[/C][C]160.158297586883[/C][C]-0.158297586883123[/C][/ROW]
[ROW][C]101[/C][C]202[/C][C]164.999286472662[/C][C]37.0007135273385[/C][/ROW]
[ROW][C]102[/C][C]155[/C][C]185.340060961071[/C][C]-30.3400609610708[/C][/ROW]
[ROW][C]103[/C][C]257[/C][C]162.495810805281[/C][C]94.504189194719[/C][/ROW]
[ROW][C]104[/C][C]171[/C][C]195.580373617775[/C][C]-24.5803736177746[/C][/ROW]
[ROW][C]105[/C][C]168[/C][C]176.883625082258[/C][C]-8.88362508225811[/C][/ROW]
[ROW][C]106[/C][C]202[/C][C]191.198210009948[/C][C]10.8017899900515[/C][/ROW]
[ROW][C]107[/C][C]189[/C][C]200.649053050797[/C][C]-11.6490530507971[/C][/ROW]
[ROW][C]108[/C][C]132[/C][C]157.266283828934[/C][C]-25.2662838289338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264703&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264703&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
13141146.903388361255-5.90338836125545
14138143.365146880029-5.36514688002879
15130134.323881587174-4.32388158717421
16145148.220536245983-3.22053624598291
17123125.129299713449-2.12929971344914
18116117.440908338987-1.4409083389868
1990112.480574622663-22.4805746226634
20110112.026435255693-2.02643525569329
21102103.482634269071-1.48263426907097
2210992.08893912149716.911060878503
23111119.119844612986-8.11984461298586
249377.240297660115515.7597023398845
25120118.4790215722521.52097842774789
2681117.333601093189-36.3336010931887
278499.5831425923733-15.5831425923733
2887104.709496826634-17.7094968266344
2911083.28425349178826.715746508212
309086.18192711348693.81807288651315
3110880.552670366506427.4473296334936
3210198.52209843764952.47790156235048
338792.3637118714482-5.3637118714482
3411883.658727729938634.3412722700614
3582111.159038814706-29.1590388147058
368670.551786402805315.4482135971947
37103105.418119472793-2.41811947279336
389396.7381255083114-3.7381255083114
398393.3547819011328-10.3547819011328
409199.81506173173-8.81506173173
416988.9572867809021-19.9572867809021
429574.065403955265620.9345960447344
439677.958259034822718.0417409651773
4410587.993977212725717.0060227872743
4512185.814775262613635.1852247373864
4610197.01526515825133.98473484174875
47111103.3516793189727.64832068102827
4813080.541505563747349.4584944362527
49134130.7738555986393.22614440136121
50161122.78913529832638.2108647016744
51186132.03674588380353.9632541161967
52244169.41803392423274.5819660757682
53145176.554396217859-31.5543962178591
54170166.9580613243463.04193867565434
55164164.258554333691-0.258554333690967
56124174.705567404946-50.7055674049456
57154152.0201422025061.97985779749368
58126145.955044133264-19.9550441332636
59173148.91314093604124.0868590639593
60140129.59617378777110.4038262122291
61142167.018047940787-25.0180479407869
62129155.3758061483-26.3758061483004
63171145.49513419786125.5048658021387
64107174.831845426143-67.831845426143
6598125.643487047998-27.6434870479981
66185120.65721928855564.3427807114453
67142137.3720842438944.62791575610555
68135139.114758692082-4.11475869208175
69126140.225704615371-14.2257046153715
70126125.8726863818040.127313618196254
71134141.343769413788-7.3437694137879
72119113.1574919437555.84250805624545
73134138.251268200597-4.2512682005968
74133132.9859046271170.0140953728829629
75129139.816797799784-10.8167977997838
7696138.648797642096-42.6487976420961
77150106.35180850734243.6481914926583
78113140.532755490021-27.5327554900206
7999118.835634949479-19.8356349494795
80164110.90071785549153.0992821445095
81127128.488551957068-1.48855195706801
82148121.02003707929826.9799629207015
83166144.46843350423521.5315664957649
84115125.89919514483-10.8991951448302
85199145.26852219745953.7314778025415
86141159.546538767806-18.5465387678058
87149159.796186126666-10.796186126666
88131152.190312852669-21.1903128526694
89171140.72329551940230.2767044805978
90178159.75496144717818.2450385528223
91181151.33549221551729.6645077844829
92129177.140981057294-48.1409810572942
93112151.463539238146-39.4635392381456
94186136.43199170545849.5680082945416
95153168.282485828353-15.2824858283531
96116130.593259912624-14.5932599126239
97190160.64974787029729.3502521297026
98169154.43851115881114.5614888411891
99165167.276424634789-2.27642463478878
100160160.158297586883-0.158297586883123
101202164.99928647266237.0007135273385
102155185.340060961071-30.3400609610708
103257162.49581080528194.504189194719
104171195.580373617775-24.5803736177746
105168176.883625082258-8.88362508225811
106202191.19821000994810.8017899900515
107189200.649053050797-11.6490530507971
108132157.266283828934-25.2662838289338







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109200.647034909901173.498207232047227.795862587756
110179.96708952085148.411006182624211.523172859077
111185.97300417935149.008216678787222.937791679913
112179.46367414315138.932158307484219.995189978816
113191.964391623177145.309554845215238.619228401139
114188.148793118365138.393441729169237.90414450756
115195.091211552243140.188462252052249.993960852435
116177.636810205448123.287229512062231.986390898835
117169.609149650357113.778876618249225.439422682465
118189.649767184859124.760062135964254.539472233754
119191.333663217727122.683188460152259.984137975302
120149.70502592876581.5898560672636217.820195790267

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 200.647034909901 & 173.498207232047 & 227.795862587756 \tabularnewline
110 & 179.96708952085 & 148.411006182624 & 211.523172859077 \tabularnewline
111 & 185.97300417935 & 149.008216678787 & 222.937791679913 \tabularnewline
112 & 179.46367414315 & 138.932158307484 & 219.995189978816 \tabularnewline
113 & 191.964391623177 & 145.309554845215 & 238.619228401139 \tabularnewline
114 & 188.148793118365 & 138.393441729169 & 237.90414450756 \tabularnewline
115 & 195.091211552243 & 140.188462252052 & 249.993960852435 \tabularnewline
116 & 177.636810205448 & 123.287229512062 & 231.986390898835 \tabularnewline
117 & 169.609149650357 & 113.778876618249 & 225.439422682465 \tabularnewline
118 & 189.649767184859 & 124.760062135964 & 254.539472233754 \tabularnewline
119 & 191.333663217727 & 122.683188460152 & 259.984137975302 \tabularnewline
120 & 149.705025928765 & 81.5898560672636 & 217.820195790267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264703&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]200.647034909901[/C][C]173.498207232047[/C][C]227.795862587756[/C][/ROW]
[ROW][C]110[/C][C]179.96708952085[/C][C]148.411006182624[/C][C]211.523172859077[/C][/ROW]
[ROW][C]111[/C][C]185.97300417935[/C][C]149.008216678787[/C][C]222.937791679913[/C][/ROW]
[ROW][C]112[/C][C]179.46367414315[/C][C]138.932158307484[/C][C]219.995189978816[/C][/ROW]
[ROW][C]113[/C][C]191.964391623177[/C][C]145.309554845215[/C][C]238.619228401139[/C][/ROW]
[ROW][C]114[/C][C]188.148793118365[/C][C]138.393441729169[/C][C]237.90414450756[/C][/ROW]
[ROW][C]115[/C][C]195.091211552243[/C][C]140.188462252052[/C][C]249.993960852435[/C][/ROW]
[ROW][C]116[/C][C]177.636810205448[/C][C]123.287229512062[/C][C]231.986390898835[/C][/ROW]
[ROW][C]117[/C][C]169.609149650357[/C][C]113.778876618249[/C][C]225.439422682465[/C][/ROW]
[ROW][C]118[/C][C]189.649767184859[/C][C]124.760062135964[/C][C]254.539472233754[/C][/ROW]
[ROW][C]119[/C][C]191.333663217727[/C][C]122.683188460152[/C][C]259.984137975302[/C][/ROW]
[ROW][C]120[/C][C]149.705025928765[/C][C]81.5898560672636[/C][C]217.820195790267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264703&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264703&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
109200.647034909901173.498207232047227.795862587756
110179.96708952085148.411006182624211.523172859077
111185.97300417935149.008216678787222.937791679913
112179.46367414315138.932158307484219.995189978816
113191.964391623177145.309554845215238.619228401139
114188.148793118365138.393441729169237.90414450756
115195.091211552243140.188462252052249.993960852435
116177.636810205448123.287229512062231.986390898835
117169.609149650357113.778876618249225.439422682465
118189.649767184859124.760062135964254.539472233754
119191.333663217727122.683188460152259.984137975302
120149.70502592876581.5898560672636217.820195790267



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')