Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 08 Jul 2010 15:42:46 +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/Jul/08/t1278603776x4yshytbx37ybjy.htm/, Retrieved Wed, 08 May 2024 22:39:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77972, Retrieved Wed, 08 May 2024 22:39:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Kelly Janbroers -...] [2010-07-08 15:42:46] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
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Dataseries X:
268
267
266
264
262
261
262
264
265
265
266
268
260
264
265
262
258
265
273
273
270
263
260
257
248
248
237
228
225
231
243
250
246
240
236
235
225
230
225
221
231
234
249
257
253
252
245
239
229
232
222
218
223
221
230
234
237
226
215
211
203
202
187
179
181
172
182
180
175
163
160
151
145
140
125
122
124
108
115
116
104
98
101
91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77972&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77972&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77972&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0475220280630285
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0475220280630285 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77972&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0475220280630285[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77972&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77972&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
alpha1
beta0.0475220280630285
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32662660
4264265-1
5262262.952477971937-0.952477971936958
6261260.9072142870250.0927857129748304
7262259.9116236522812.08837634771902
8264261.0108675316832.98913246831654
9265263.1529171687271.8470828312731
10265264.2406942908690.759305709130558
11266264.2767780380871.72322196191288
12268265.358669040522.64133095948
13260267.4841904445-7.48419044450014
14264259.1285265361684.87147346383244
15265263.3600288348241.63997116517589
16262264.437963590558-2.43796359055813
17258261.322106616391-3.32210661639101
18265257.1642333725387.83576662746151
19273264.5366048941048.46339510589593
20273272.9388025938350.0611974061650358
21270272.941710818688-2.94171081868814
22263269.801914754609-6.80191475460907
23260262.478673970758-2.47867397075822
24257259.360882356761-2.36088235676078
25248256.248688439149-8.24868843914925
26248246.8566940356611.14330596433916
27237246.911026253783-9.9110262537828
28228235.440034186017-7.44003418601713
29225226.086468672639-1.08646867263931
30231223.0348374778897.96516252211146
31243229.41335815479113.5866418452091
32250242.0590229298417.94097707015874
33246249.436394265017-3.43639426501721
34240245.273089840319-5.27308984031944
35236239.022501916949-3.0225019169489
36235234.8788664960310.121133503968906
37225233.884623005806-8.88462300580608
38230223.4624077019956.53759229800528
39225228.773087346645-3.77308734664518
40221223.593782583874-2.59378258387366
41231219.47052077513311.5294792248666
42234230.0184250104103.98157498959037
43249233.207637528815.7923624712000
44257248.9581226213388.04187737866212
45253257.340288943806-4.34028894380612
46252253.134029610817-1.13402961081690
47245252.080138223827-7.08013822382733
48239244.743675696464-5.74367569646449
49229238.470724578832-9.47072457883218
50232228.0206565396203.97934346038031
51222231.209763011216-9.20976301121632
52218220.772096394943-2.77209639494345
53223216.6403607522706.35963924773046
54221221.942583707071-0.942583707070924
55230219.89779021769210.1022097823083
56234229.3778677144654.6221322855348
57237233.5975208146493.40247918535059
58226236.759213525980-10.7592135259795
59215225.247913878862-10.2479138788618
60211213.760912227923-2.76091222792303
61203209.629708079548-6.62970807954812
62202201.3146509061420.685349093857866
63187200.347220085013-13.3472200850134
64179184.71293311757-5.71293311757
65181176.4414429496354.55855705036538
66172178.658074825709-6.65807482570901
67182169.34166960699612.6583303930041
68180179.9432191391630.0567808608366533
69175177.945917480825-2.94591748082547
70163172.805921507630-9.80592150763033
71160160.339924230561-0.339924230560854
72151157.323770341737-6.32377034173683
73145148.023251950093-3.02325195009269
74140141.879580886079-1.87958088607877
75125136.790259390464-11.7902593904638
76122121.2299623528400.770037647160208
77124118.2665561035185.73344389648227
78108120.539020985264-12.5390209852642
79115103.94314127812011.0568587218805
80116111.4685856285904.53141437141032
81104112.683927629513-8.68392762951305
8298100.271249777006-2.27124977700602
8310194.1633153813656.836684618635
849197.4882084996698-6.48820849966984

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 266 & 266 & 0 \tabularnewline
4 & 264 & 265 & -1 \tabularnewline
5 & 262 & 262.952477971937 & -0.952477971936958 \tabularnewline
6 & 261 & 260.907214287025 & 0.0927857129748304 \tabularnewline
7 & 262 & 259.911623652281 & 2.08837634771902 \tabularnewline
8 & 264 & 261.010867531683 & 2.98913246831654 \tabularnewline
9 & 265 & 263.152917168727 & 1.8470828312731 \tabularnewline
10 & 265 & 264.240694290869 & 0.759305709130558 \tabularnewline
11 & 266 & 264.276778038087 & 1.72322196191288 \tabularnewline
12 & 268 & 265.35866904052 & 2.64133095948 \tabularnewline
13 & 260 & 267.4841904445 & -7.48419044450014 \tabularnewline
14 & 264 & 259.128526536168 & 4.87147346383244 \tabularnewline
15 & 265 & 263.360028834824 & 1.63997116517589 \tabularnewline
16 & 262 & 264.437963590558 & -2.43796359055813 \tabularnewline
17 & 258 & 261.322106616391 & -3.32210661639101 \tabularnewline
18 & 265 & 257.164233372538 & 7.83576662746151 \tabularnewline
19 & 273 & 264.536604894104 & 8.46339510589593 \tabularnewline
20 & 273 & 272.938802593835 & 0.0611974061650358 \tabularnewline
21 & 270 & 272.941710818688 & -2.94171081868814 \tabularnewline
22 & 263 & 269.801914754609 & -6.80191475460907 \tabularnewline
23 & 260 & 262.478673970758 & -2.47867397075822 \tabularnewline
24 & 257 & 259.360882356761 & -2.36088235676078 \tabularnewline
25 & 248 & 256.248688439149 & -8.24868843914925 \tabularnewline
26 & 248 & 246.856694035661 & 1.14330596433916 \tabularnewline
27 & 237 & 246.911026253783 & -9.9110262537828 \tabularnewline
28 & 228 & 235.440034186017 & -7.44003418601713 \tabularnewline
29 & 225 & 226.086468672639 & -1.08646867263931 \tabularnewline
30 & 231 & 223.034837477889 & 7.96516252211146 \tabularnewline
31 & 243 & 229.413358154791 & 13.5866418452091 \tabularnewline
32 & 250 & 242.059022929841 & 7.94097707015874 \tabularnewline
33 & 246 & 249.436394265017 & -3.43639426501721 \tabularnewline
34 & 240 & 245.273089840319 & -5.27308984031944 \tabularnewline
35 & 236 & 239.022501916949 & -3.0225019169489 \tabularnewline
36 & 235 & 234.878866496031 & 0.121133503968906 \tabularnewline
37 & 225 & 233.884623005806 & -8.88462300580608 \tabularnewline
38 & 230 & 223.462407701995 & 6.53759229800528 \tabularnewline
39 & 225 & 228.773087346645 & -3.77308734664518 \tabularnewline
40 & 221 & 223.593782583874 & -2.59378258387366 \tabularnewline
41 & 231 & 219.470520775133 & 11.5294792248666 \tabularnewline
42 & 234 & 230.018425010410 & 3.98157498959037 \tabularnewline
43 & 249 & 233.2076375288 & 15.7923624712000 \tabularnewline
44 & 257 & 248.958122621338 & 8.04187737866212 \tabularnewline
45 & 253 & 257.340288943806 & -4.34028894380612 \tabularnewline
46 & 252 & 253.134029610817 & -1.13402961081690 \tabularnewline
47 & 245 & 252.080138223827 & -7.08013822382733 \tabularnewline
48 & 239 & 244.743675696464 & -5.74367569646449 \tabularnewline
49 & 229 & 238.470724578832 & -9.47072457883218 \tabularnewline
50 & 232 & 228.020656539620 & 3.97934346038031 \tabularnewline
51 & 222 & 231.209763011216 & -9.20976301121632 \tabularnewline
52 & 218 & 220.772096394943 & -2.77209639494345 \tabularnewline
53 & 223 & 216.640360752270 & 6.35963924773046 \tabularnewline
54 & 221 & 221.942583707071 & -0.942583707070924 \tabularnewline
55 & 230 & 219.897790217692 & 10.1022097823083 \tabularnewline
56 & 234 & 229.377867714465 & 4.6221322855348 \tabularnewline
57 & 237 & 233.597520814649 & 3.40247918535059 \tabularnewline
58 & 226 & 236.759213525980 & -10.7592135259795 \tabularnewline
59 & 215 & 225.247913878862 & -10.2479138788618 \tabularnewline
60 & 211 & 213.760912227923 & -2.76091222792303 \tabularnewline
61 & 203 & 209.629708079548 & -6.62970807954812 \tabularnewline
62 & 202 & 201.314650906142 & 0.685349093857866 \tabularnewline
63 & 187 & 200.347220085013 & -13.3472200850134 \tabularnewline
64 & 179 & 184.71293311757 & -5.71293311757 \tabularnewline
65 & 181 & 176.441442949635 & 4.55855705036538 \tabularnewline
66 & 172 & 178.658074825709 & -6.65807482570901 \tabularnewline
67 & 182 & 169.341669606996 & 12.6583303930041 \tabularnewline
68 & 180 & 179.943219139163 & 0.0567808608366533 \tabularnewline
69 & 175 & 177.945917480825 & -2.94591748082547 \tabularnewline
70 & 163 & 172.805921507630 & -9.80592150763033 \tabularnewline
71 & 160 & 160.339924230561 & -0.339924230560854 \tabularnewline
72 & 151 & 157.323770341737 & -6.32377034173683 \tabularnewline
73 & 145 & 148.023251950093 & -3.02325195009269 \tabularnewline
74 & 140 & 141.879580886079 & -1.87958088607877 \tabularnewline
75 & 125 & 136.790259390464 & -11.7902593904638 \tabularnewline
76 & 122 & 121.229962352840 & 0.770037647160208 \tabularnewline
77 & 124 & 118.266556103518 & 5.73344389648227 \tabularnewline
78 & 108 & 120.539020985264 & -12.5390209852642 \tabularnewline
79 & 115 & 103.943141278120 & 11.0568587218805 \tabularnewline
80 & 116 & 111.468585628590 & 4.53141437141032 \tabularnewline
81 & 104 & 112.683927629513 & -8.68392762951305 \tabularnewline
82 & 98 & 100.271249777006 & -2.27124977700602 \tabularnewline
83 & 101 & 94.163315381365 & 6.836684618635 \tabularnewline
84 & 91 & 97.4882084996698 & -6.48820849966984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77972&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]266[/C][C]266[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]264[/C][C]265[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]262[/C][C]262.952477971937[/C][C]-0.952477971936958[/C][/ROW]
[ROW][C]6[/C][C]261[/C][C]260.907214287025[/C][C]0.0927857129748304[/C][/ROW]
[ROW][C]7[/C][C]262[/C][C]259.911623652281[/C][C]2.08837634771902[/C][/ROW]
[ROW][C]8[/C][C]264[/C][C]261.010867531683[/C][C]2.98913246831654[/C][/ROW]
[ROW][C]9[/C][C]265[/C][C]263.152917168727[/C][C]1.8470828312731[/C][/ROW]
[ROW][C]10[/C][C]265[/C][C]264.240694290869[/C][C]0.759305709130558[/C][/ROW]
[ROW][C]11[/C][C]266[/C][C]264.276778038087[/C][C]1.72322196191288[/C][/ROW]
[ROW][C]12[/C][C]268[/C][C]265.35866904052[/C][C]2.64133095948[/C][/ROW]
[ROW][C]13[/C][C]260[/C][C]267.4841904445[/C][C]-7.48419044450014[/C][/ROW]
[ROW][C]14[/C][C]264[/C][C]259.128526536168[/C][C]4.87147346383244[/C][/ROW]
[ROW][C]15[/C][C]265[/C][C]263.360028834824[/C][C]1.63997116517589[/C][/ROW]
[ROW][C]16[/C][C]262[/C][C]264.437963590558[/C][C]-2.43796359055813[/C][/ROW]
[ROW][C]17[/C][C]258[/C][C]261.322106616391[/C][C]-3.32210661639101[/C][/ROW]
[ROW][C]18[/C][C]265[/C][C]257.164233372538[/C][C]7.83576662746151[/C][/ROW]
[ROW][C]19[/C][C]273[/C][C]264.536604894104[/C][C]8.46339510589593[/C][/ROW]
[ROW][C]20[/C][C]273[/C][C]272.938802593835[/C][C]0.0611974061650358[/C][/ROW]
[ROW][C]21[/C][C]270[/C][C]272.941710818688[/C][C]-2.94171081868814[/C][/ROW]
[ROW][C]22[/C][C]263[/C][C]269.801914754609[/C][C]-6.80191475460907[/C][/ROW]
[ROW][C]23[/C][C]260[/C][C]262.478673970758[/C][C]-2.47867397075822[/C][/ROW]
[ROW][C]24[/C][C]257[/C][C]259.360882356761[/C][C]-2.36088235676078[/C][/ROW]
[ROW][C]25[/C][C]248[/C][C]256.248688439149[/C][C]-8.24868843914925[/C][/ROW]
[ROW][C]26[/C][C]248[/C][C]246.856694035661[/C][C]1.14330596433916[/C][/ROW]
[ROW][C]27[/C][C]237[/C][C]246.911026253783[/C][C]-9.9110262537828[/C][/ROW]
[ROW][C]28[/C][C]228[/C][C]235.440034186017[/C][C]-7.44003418601713[/C][/ROW]
[ROW][C]29[/C][C]225[/C][C]226.086468672639[/C][C]-1.08646867263931[/C][/ROW]
[ROW][C]30[/C][C]231[/C][C]223.034837477889[/C][C]7.96516252211146[/C][/ROW]
[ROW][C]31[/C][C]243[/C][C]229.413358154791[/C][C]13.5866418452091[/C][/ROW]
[ROW][C]32[/C][C]250[/C][C]242.059022929841[/C][C]7.94097707015874[/C][/ROW]
[ROW][C]33[/C][C]246[/C][C]249.436394265017[/C][C]-3.43639426501721[/C][/ROW]
[ROW][C]34[/C][C]240[/C][C]245.273089840319[/C][C]-5.27308984031944[/C][/ROW]
[ROW][C]35[/C][C]236[/C][C]239.022501916949[/C][C]-3.0225019169489[/C][/ROW]
[ROW][C]36[/C][C]235[/C][C]234.878866496031[/C][C]0.121133503968906[/C][/ROW]
[ROW][C]37[/C][C]225[/C][C]233.884623005806[/C][C]-8.88462300580608[/C][/ROW]
[ROW][C]38[/C][C]230[/C][C]223.462407701995[/C][C]6.53759229800528[/C][/ROW]
[ROW][C]39[/C][C]225[/C][C]228.773087346645[/C][C]-3.77308734664518[/C][/ROW]
[ROW][C]40[/C][C]221[/C][C]223.593782583874[/C][C]-2.59378258387366[/C][/ROW]
[ROW][C]41[/C][C]231[/C][C]219.470520775133[/C][C]11.5294792248666[/C][/ROW]
[ROW][C]42[/C][C]234[/C][C]230.018425010410[/C][C]3.98157498959037[/C][/ROW]
[ROW][C]43[/C][C]249[/C][C]233.2076375288[/C][C]15.7923624712000[/C][/ROW]
[ROW][C]44[/C][C]257[/C][C]248.958122621338[/C][C]8.04187737866212[/C][/ROW]
[ROW][C]45[/C][C]253[/C][C]257.340288943806[/C][C]-4.34028894380612[/C][/ROW]
[ROW][C]46[/C][C]252[/C][C]253.134029610817[/C][C]-1.13402961081690[/C][/ROW]
[ROW][C]47[/C][C]245[/C][C]252.080138223827[/C][C]-7.08013822382733[/C][/ROW]
[ROW][C]48[/C][C]239[/C][C]244.743675696464[/C][C]-5.74367569646449[/C][/ROW]
[ROW][C]49[/C][C]229[/C][C]238.470724578832[/C][C]-9.47072457883218[/C][/ROW]
[ROW][C]50[/C][C]232[/C][C]228.020656539620[/C][C]3.97934346038031[/C][/ROW]
[ROW][C]51[/C][C]222[/C][C]231.209763011216[/C][C]-9.20976301121632[/C][/ROW]
[ROW][C]52[/C][C]218[/C][C]220.772096394943[/C][C]-2.77209639494345[/C][/ROW]
[ROW][C]53[/C][C]223[/C][C]216.640360752270[/C][C]6.35963924773046[/C][/ROW]
[ROW][C]54[/C][C]221[/C][C]221.942583707071[/C][C]-0.942583707070924[/C][/ROW]
[ROW][C]55[/C][C]230[/C][C]219.897790217692[/C][C]10.1022097823083[/C][/ROW]
[ROW][C]56[/C][C]234[/C][C]229.377867714465[/C][C]4.6221322855348[/C][/ROW]
[ROW][C]57[/C][C]237[/C][C]233.597520814649[/C][C]3.40247918535059[/C][/ROW]
[ROW][C]58[/C][C]226[/C][C]236.759213525980[/C][C]-10.7592135259795[/C][/ROW]
[ROW][C]59[/C][C]215[/C][C]225.247913878862[/C][C]-10.2479138788618[/C][/ROW]
[ROW][C]60[/C][C]211[/C][C]213.760912227923[/C][C]-2.76091222792303[/C][/ROW]
[ROW][C]61[/C][C]203[/C][C]209.629708079548[/C][C]-6.62970807954812[/C][/ROW]
[ROW][C]62[/C][C]202[/C][C]201.314650906142[/C][C]0.685349093857866[/C][/ROW]
[ROW][C]63[/C][C]187[/C][C]200.347220085013[/C][C]-13.3472200850134[/C][/ROW]
[ROW][C]64[/C][C]179[/C][C]184.71293311757[/C][C]-5.71293311757[/C][/ROW]
[ROW][C]65[/C][C]181[/C][C]176.441442949635[/C][C]4.55855705036538[/C][/ROW]
[ROW][C]66[/C][C]172[/C][C]178.658074825709[/C][C]-6.65807482570901[/C][/ROW]
[ROW][C]67[/C][C]182[/C][C]169.341669606996[/C][C]12.6583303930041[/C][/ROW]
[ROW][C]68[/C][C]180[/C][C]179.943219139163[/C][C]0.0567808608366533[/C][/ROW]
[ROW][C]69[/C][C]175[/C][C]177.945917480825[/C][C]-2.94591748082547[/C][/ROW]
[ROW][C]70[/C][C]163[/C][C]172.805921507630[/C][C]-9.80592150763033[/C][/ROW]
[ROW][C]71[/C][C]160[/C][C]160.339924230561[/C][C]-0.339924230560854[/C][/ROW]
[ROW][C]72[/C][C]151[/C][C]157.323770341737[/C][C]-6.32377034173683[/C][/ROW]
[ROW][C]73[/C][C]145[/C][C]148.023251950093[/C][C]-3.02325195009269[/C][/ROW]
[ROW][C]74[/C][C]140[/C][C]141.879580886079[/C][C]-1.87958088607877[/C][/ROW]
[ROW][C]75[/C][C]125[/C][C]136.790259390464[/C][C]-11.7902593904638[/C][/ROW]
[ROW][C]76[/C][C]122[/C][C]121.229962352840[/C][C]0.770037647160208[/C][/ROW]
[ROW][C]77[/C][C]124[/C][C]118.266556103518[/C][C]5.73344389648227[/C][/ROW]
[ROW][C]78[/C][C]108[/C][C]120.539020985264[/C][C]-12.5390209852642[/C][/ROW]
[ROW][C]79[/C][C]115[/C][C]103.943141278120[/C][C]11.0568587218805[/C][/ROW]
[ROW][C]80[/C][C]116[/C][C]111.468585628590[/C][C]4.53141437141032[/C][/ROW]
[ROW][C]81[/C][C]104[/C][C]112.683927629513[/C][C]-8.68392762951305[/C][/ROW]
[ROW][C]82[/C][C]98[/C][C]100.271249777006[/C][C]-2.27124977700602[/C][/ROW]
[ROW][C]83[/C][C]101[/C][C]94.163315381365[/C][C]6.836684618635[/C][/ROW]
[ROW][C]84[/C][C]91[/C][C]97.4882084996698[/C][C]-6.48820849966984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77972&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77972&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
32662660
4264265-1
5262262.952477971937-0.952477971936958
6261260.9072142870250.0927857129748304
7262259.9116236522812.08837634771902
8264261.0108675316832.98913246831654
9265263.1529171687271.8470828312731
10265264.2406942908690.759305709130558
11266264.2767780380871.72322196191288
12268265.358669040522.64133095948
13260267.4841904445-7.48419044450014
14264259.1285265361684.87147346383244
15265263.3600288348241.63997116517589
16262264.437963590558-2.43796359055813
17258261.322106616391-3.32210661639101
18265257.1642333725387.83576662746151
19273264.5366048941048.46339510589593
20273272.9388025938350.0611974061650358
21270272.941710818688-2.94171081868814
22263269.801914754609-6.80191475460907
23260262.478673970758-2.47867397075822
24257259.360882356761-2.36088235676078
25248256.248688439149-8.24868843914925
26248246.8566940356611.14330596433916
27237246.911026253783-9.9110262537828
28228235.440034186017-7.44003418601713
29225226.086468672639-1.08646867263931
30231223.0348374778897.96516252211146
31243229.41335815479113.5866418452091
32250242.0590229298417.94097707015874
33246249.436394265017-3.43639426501721
34240245.273089840319-5.27308984031944
35236239.022501916949-3.0225019169489
36235234.8788664960310.121133503968906
37225233.884623005806-8.88462300580608
38230223.4624077019956.53759229800528
39225228.773087346645-3.77308734664518
40221223.593782583874-2.59378258387366
41231219.47052077513311.5294792248666
42234230.0184250104103.98157498959037
43249233.207637528815.7923624712000
44257248.9581226213388.04187737866212
45253257.340288943806-4.34028894380612
46252253.134029610817-1.13402961081690
47245252.080138223827-7.08013822382733
48239244.743675696464-5.74367569646449
49229238.470724578832-9.47072457883218
50232228.0206565396203.97934346038031
51222231.209763011216-9.20976301121632
52218220.772096394943-2.77209639494345
53223216.6403607522706.35963924773046
54221221.942583707071-0.942583707070924
55230219.89779021769210.1022097823083
56234229.3778677144654.6221322855348
57237233.5975208146493.40247918535059
58226236.759213525980-10.7592135259795
59215225.247913878862-10.2479138788618
60211213.760912227923-2.76091222792303
61203209.629708079548-6.62970807954812
62202201.3146509061420.685349093857866
63187200.347220085013-13.3472200850134
64179184.71293311757-5.71293311757
65181176.4414429496354.55855705036538
66172178.658074825709-6.65807482570901
67182169.34166960699612.6583303930041
68180179.9432191391630.0567808608366533
69175177.945917480825-2.94591748082547
70163172.805921507630-9.80592150763033
71160160.339924230561-0.339924230560854
72151157.323770341737-6.32377034173683
73145148.023251950093-3.02325195009269
74140141.879580886079-1.87958088607877
75125136.790259390464-11.7902593904638
76122121.2299623528400.770037647160208
77124118.2665561035185.73344389648227
78108120.539020985264-12.5390209852642
79115103.94314127812011.0568587218805
80116111.4685856285904.53141437141032
81104112.683927629513-8.68392762951305
8298100.271249777006-2.27124977700602
8310194.1633153813656.836684618635
849197.4882084996698-6.48820849966984







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8587.179875673269774.368511501546999.9912398449926
8683.359751346539564.8062490078778101.913253685201
8779.539627019809256.2792418178234102.800012221795
8875.71950269307948.2365699427932103.202435443365
8971.899378366348740.470538172337103.328218560360
9068.079254039618532.8774350756663103.281073003571
9164.259129712888225.3973090102854103.120950415491
9260.43900538615817.9921860204390102.885824751877
9356.618881059427710.6364552352157102.601306883640
9452.79875673269753.31203661472124102.285476850674
9548.9786324059672-3.99428286974069101.951547681675
9645.158508079237-11.2924234230024101.609439581476

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 87.1798756732697 & 74.3685115015469 & 99.9912398449926 \tabularnewline
86 & 83.3597513465395 & 64.8062490078778 & 101.913253685201 \tabularnewline
87 & 79.5396270198092 & 56.2792418178234 & 102.800012221795 \tabularnewline
88 & 75.719502693079 & 48.2365699427932 & 103.202435443365 \tabularnewline
89 & 71.8993783663487 & 40.470538172337 & 103.328218560360 \tabularnewline
90 & 68.0792540396185 & 32.8774350756663 & 103.281073003571 \tabularnewline
91 & 64.2591297128882 & 25.3973090102854 & 103.120950415491 \tabularnewline
92 & 60.439005386158 & 17.9921860204390 & 102.885824751877 \tabularnewline
93 & 56.6188810594277 & 10.6364552352157 & 102.601306883640 \tabularnewline
94 & 52.7987567326975 & 3.31203661472124 & 102.285476850674 \tabularnewline
95 & 48.9786324059672 & -3.99428286974069 & 101.951547681675 \tabularnewline
96 & 45.158508079237 & -11.2924234230024 & 101.609439581476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77972&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]87.1798756732697[/C][C]74.3685115015469[/C][C]99.9912398449926[/C][/ROW]
[ROW][C]86[/C][C]83.3597513465395[/C][C]64.8062490078778[/C][C]101.913253685201[/C][/ROW]
[ROW][C]87[/C][C]79.5396270198092[/C][C]56.2792418178234[/C][C]102.800012221795[/C][/ROW]
[ROW][C]88[/C][C]75.719502693079[/C][C]48.2365699427932[/C][C]103.202435443365[/C][/ROW]
[ROW][C]89[/C][C]71.8993783663487[/C][C]40.470538172337[/C][C]103.328218560360[/C][/ROW]
[ROW][C]90[/C][C]68.0792540396185[/C][C]32.8774350756663[/C][C]103.281073003571[/C][/ROW]
[ROW][C]91[/C][C]64.2591297128882[/C][C]25.3973090102854[/C][C]103.120950415491[/C][/ROW]
[ROW][C]92[/C][C]60.439005386158[/C][C]17.9921860204390[/C][C]102.885824751877[/C][/ROW]
[ROW][C]93[/C][C]56.6188810594277[/C][C]10.6364552352157[/C][C]102.601306883640[/C][/ROW]
[ROW][C]94[/C][C]52.7987567326975[/C][C]3.31203661472124[/C][C]102.285476850674[/C][/ROW]
[ROW][C]95[/C][C]48.9786324059672[/C][C]-3.99428286974069[/C][C]101.951547681675[/C][/ROW]
[ROW][C]96[/C][C]45.158508079237[/C][C]-11.2924234230024[/C][C]101.609439581476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77972&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77972&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
8587.179875673269774.368511501546999.9912398449926
8683.359751346539564.8062490078778101.913253685201
8779.539627019809256.2792418178234102.800012221795
8875.71950269307948.2365699427932103.202435443365
8971.899378366348740.470538172337103.328218560360
9068.079254039618532.8774350756663103.281073003571
9164.259129712888225.3973090102854103.120950415491
9260.43900538615817.9921860204390102.885824751877
9356.618881059427710.6364552352157102.601306883640
9452.79875673269753.31203661472124102.285476850674
9548.9786324059672-3.99428286974069101.951547681675
9645.158508079237-11.2924234230024101.609439581476



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