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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 21 Jan 2010 04:12:44 -0700
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/Jan/21/t1264073808b80cu7nw6nlgkt4.htm/, Retrieved Tue, 07 May 2024 16:32:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72324, Retrieved Tue, 07 May 2024 16:32:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-21 11:12:44] [78f120c3f265da07819051adc047c7c7] [Current]
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Dataseries X:
104.0
99.0
105.4
107.1
110.7
117.1
118.7
126.5
127.5
134.6
131.8
135.9
142.7
141.7
153.4
145.0
137.7
148.3
152.2
169.4
168.6
161.1
174.1
179.0
190.6
190.0
181.6
174.8
180.5
196.8
193.8
197.0
216.3
221.4
217.9
229.7
227.4
204.2
196.6
198.8
207.5
190.7
201.6
210.5
223.5
223.8
231.2
244.0
234.7
250.2
265.7
287.6
283.3
295.4
312.3
333.8
347.7
383.2
407.1
413.6
362.7
321.9
239.4
191.0
159.7
163.4
157.6
166.2
176.7
198.3
226.2
216.2
235.9




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=72324&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=72324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72324&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
alpha0.936888096626754
beta0.828413409801924
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.936888096626754 \tabularnewline
beta & 0.828413409801924 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72324&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]0.936888096626754[/C][/ROW]
[ROW][C]beta[/C][C]0.828413409801924[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72324&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
alpha0.936888096626754
beta0.828413409801924
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3105.49411.4
4107.1108.528413856660-1.42841385666023
5110.7109.9294036791920.770596320807812
6117.1113.9887033945203.11129660547955
7118.7122.655750040687-3.95575004068711
8126.5121.6315859050844.86841409491615
9127.5132.653201568736-5.15320156873645
10134.6130.2861270594234.31387294057691
11131.8140.136771032064-8.33677103206435
12135.9131.6647536259364.23524637406433
13142.7138.2584142533184.44158574668188
14141.7148.492642671913-6.79264267191309
15153.4142.92967795170410.4703220482955
16145161.666517380681-16.6665173806808
17137.7142.043779788519-4.34377978851876
18148.3130.59472767829517.7052723217053
19152.2153.544774772892-1.34477477289232
20169.4157.60333856867611.7966614313244
21168.6183.129708171458-14.5297081714576
22161.1172.714263433619-11.6142634336185
23174.1156.01607819118618.0839218088142
24179181.177255412026-2.17725541202628
25190.6185.6661421851494.93385781485097
26190200.646664629951-10.6466646299511
27181.6192.766778181890-11.1667781818905
28174.8175.732724587261-0.93272458726065
29180.5167.56291783362512.9370821663748
30196.8182.42843408555714.3715659144427
31193.8209.792114063494-15.9921140634945
32197196.2964536137740.703546386225923
33216.3198.98880262772117.3111973722788
34221.4230.676413252619-9.27641325261911
35217.9230.254699199796-12.3546991997960
36229.7217.36011480728912.3398851927106
37227.4237.17895585589-9.77895585589027
38204.2228.685170525644-24.4851705256441
39196.6187.4096160977579.19038390224287
40198.8184.81722650944913.9827734905508
41207.5197.5672289368419.93277106315867
42190.7214.231960486689-23.5319604866891
43201.6181.28010730281920.3198926971814
44210.5205.1834251675945.31657483240585
45223.5219.1566698630804.34333013692046
46223.8235.589084885880-11.7890848858802
47231.2227.7573620385253.44263796147504
48244236.8679959005527.13200409944841
49234.7254.970520049637-20.270520049637
50250.2231.66737334592318.5326266540773
51265.7259.1021727077266.59782729227436
52287.6280.4761766807547.12382331924613
53283.3307.871997784259-24.5719977842586
54295.4286.5013004581978.8986995418034
55312.3303.3954546155298.9045453844713
56333.8327.2061763838256.59382361617509
57347.7353.969679125931-6.26967912593091
58383.2363.81542905292319.3845709470772
59407.1412.741300397082-5.64130039708209
60413.6433.842344555343-20.2423445553430
61362.7425.553139948472-62.8531399484724
62321.9328.560139187149-6.66013918714884
63239.4279.044553711655-39.6445537116554
64191167.85690914811123.1430908518893
65159.7133.45632383186626.2436761681338
66163.4122.32916176781641.0708382321836
67157.6156.9697282443270.630271755672595
68166.2154.21118260358211.9888173964179
69176.7171.3992119598665.3007880401336
70198.3186.43541035693511.8645896430654
71226.2216.8296281670949.370371832906
72216.2252.159675901215-35.9596759012148
73235.9217.11113440497118.7888655950291

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 105.4 & 94 & 11.4 \tabularnewline
4 & 107.1 & 108.528413856660 & -1.42841385666023 \tabularnewline
5 & 110.7 & 109.929403679192 & 0.770596320807812 \tabularnewline
6 & 117.1 & 113.988703394520 & 3.11129660547955 \tabularnewline
7 & 118.7 & 122.655750040687 & -3.95575004068711 \tabularnewline
8 & 126.5 & 121.631585905084 & 4.86841409491615 \tabularnewline
9 & 127.5 & 132.653201568736 & -5.15320156873645 \tabularnewline
10 & 134.6 & 130.286127059423 & 4.31387294057691 \tabularnewline
11 & 131.8 & 140.136771032064 & -8.33677103206435 \tabularnewline
12 & 135.9 & 131.664753625936 & 4.23524637406433 \tabularnewline
13 & 142.7 & 138.258414253318 & 4.44158574668188 \tabularnewline
14 & 141.7 & 148.492642671913 & -6.79264267191309 \tabularnewline
15 & 153.4 & 142.929677951704 & 10.4703220482955 \tabularnewline
16 & 145 & 161.666517380681 & -16.6665173806808 \tabularnewline
17 & 137.7 & 142.043779788519 & -4.34377978851876 \tabularnewline
18 & 148.3 & 130.594727678295 & 17.7052723217053 \tabularnewline
19 & 152.2 & 153.544774772892 & -1.34477477289232 \tabularnewline
20 & 169.4 & 157.603338568676 & 11.7966614313244 \tabularnewline
21 & 168.6 & 183.129708171458 & -14.5297081714576 \tabularnewline
22 & 161.1 & 172.714263433619 & -11.6142634336185 \tabularnewline
23 & 174.1 & 156.016078191186 & 18.0839218088142 \tabularnewline
24 & 179 & 181.177255412026 & -2.17725541202628 \tabularnewline
25 & 190.6 & 185.666142185149 & 4.93385781485097 \tabularnewline
26 & 190 & 200.646664629951 & -10.6466646299511 \tabularnewline
27 & 181.6 & 192.766778181890 & -11.1667781818905 \tabularnewline
28 & 174.8 & 175.732724587261 & -0.93272458726065 \tabularnewline
29 & 180.5 & 167.562917833625 & 12.9370821663748 \tabularnewline
30 & 196.8 & 182.428434085557 & 14.3715659144427 \tabularnewline
31 & 193.8 & 209.792114063494 & -15.9921140634945 \tabularnewline
32 & 197 & 196.296453613774 & 0.703546386225923 \tabularnewline
33 & 216.3 & 198.988802627721 & 17.3111973722788 \tabularnewline
34 & 221.4 & 230.676413252619 & -9.27641325261911 \tabularnewline
35 & 217.9 & 230.254699199796 & -12.3546991997960 \tabularnewline
36 & 229.7 & 217.360114807289 & 12.3398851927106 \tabularnewline
37 & 227.4 & 237.17895585589 & -9.77895585589027 \tabularnewline
38 & 204.2 & 228.685170525644 & -24.4851705256441 \tabularnewline
39 & 196.6 & 187.409616097757 & 9.19038390224287 \tabularnewline
40 & 198.8 & 184.817226509449 & 13.9827734905508 \tabularnewline
41 & 207.5 & 197.567228936841 & 9.93277106315867 \tabularnewline
42 & 190.7 & 214.231960486689 & -23.5319604866891 \tabularnewline
43 & 201.6 & 181.280107302819 & 20.3198926971814 \tabularnewline
44 & 210.5 & 205.183425167594 & 5.31657483240585 \tabularnewline
45 & 223.5 & 219.156669863080 & 4.34333013692046 \tabularnewline
46 & 223.8 & 235.589084885880 & -11.7890848858802 \tabularnewline
47 & 231.2 & 227.757362038525 & 3.44263796147504 \tabularnewline
48 & 244 & 236.867995900552 & 7.13200409944841 \tabularnewline
49 & 234.7 & 254.970520049637 & -20.270520049637 \tabularnewline
50 & 250.2 & 231.667373345923 & 18.5326266540773 \tabularnewline
51 & 265.7 & 259.102172707726 & 6.59782729227436 \tabularnewline
52 & 287.6 & 280.476176680754 & 7.12382331924613 \tabularnewline
53 & 283.3 & 307.871997784259 & -24.5719977842586 \tabularnewline
54 & 295.4 & 286.501300458197 & 8.8986995418034 \tabularnewline
55 & 312.3 & 303.395454615529 & 8.9045453844713 \tabularnewline
56 & 333.8 & 327.206176383825 & 6.59382361617509 \tabularnewline
57 & 347.7 & 353.969679125931 & -6.26967912593091 \tabularnewline
58 & 383.2 & 363.815429052923 & 19.3845709470772 \tabularnewline
59 & 407.1 & 412.741300397082 & -5.64130039708209 \tabularnewline
60 & 413.6 & 433.842344555343 & -20.2423445553430 \tabularnewline
61 & 362.7 & 425.553139948472 & -62.8531399484724 \tabularnewline
62 & 321.9 & 328.560139187149 & -6.66013918714884 \tabularnewline
63 & 239.4 & 279.044553711655 & -39.6445537116554 \tabularnewline
64 & 191 & 167.856909148111 & 23.1430908518893 \tabularnewline
65 & 159.7 & 133.456323831866 & 26.2436761681338 \tabularnewline
66 & 163.4 & 122.329161767816 & 41.0708382321836 \tabularnewline
67 & 157.6 & 156.969728244327 & 0.630271755672595 \tabularnewline
68 & 166.2 & 154.211182603582 & 11.9888173964179 \tabularnewline
69 & 176.7 & 171.399211959866 & 5.3007880401336 \tabularnewline
70 & 198.3 & 186.435410356935 & 11.8645896430654 \tabularnewline
71 & 226.2 & 216.829628167094 & 9.370371832906 \tabularnewline
72 & 216.2 & 252.159675901215 & -35.9596759012148 \tabularnewline
73 & 235.9 & 217.111134404971 & 18.7888655950291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72324&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]105.4[/C][C]94[/C][C]11.4[/C][/ROW]
[ROW][C]4[/C][C]107.1[/C][C]108.528413856660[/C][C]-1.42841385666023[/C][/ROW]
[ROW][C]5[/C][C]110.7[/C][C]109.929403679192[/C][C]0.770596320807812[/C][/ROW]
[ROW][C]6[/C][C]117.1[/C][C]113.988703394520[/C][C]3.11129660547955[/C][/ROW]
[ROW][C]7[/C][C]118.7[/C][C]122.655750040687[/C][C]-3.95575004068711[/C][/ROW]
[ROW][C]8[/C][C]126.5[/C][C]121.631585905084[/C][C]4.86841409491615[/C][/ROW]
[ROW][C]9[/C][C]127.5[/C][C]132.653201568736[/C][C]-5.15320156873645[/C][/ROW]
[ROW][C]10[/C][C]134.6[/C][C]130.286127059423[/C][C]4.31387294057691[/C][/ROW]
[ROW][C]11[/C][C]131.8[/C][C]140.136771032064[/C][C]-8.33677103206435[/C][/ROW]
[ROW][C]12[/C][C]135.9[/C][C]131.664753625936[/C][C]4.23524637406433[/C][/ROW]
[ROW][C]13[/C][C]142.7[/C][C]138.258414253318[/C][C]4.44158574668188[/C][/ROW]
[ROW][C]14[/C][C]141.7[/C][C]148.492642671913[/C][C]-6.79264267191309[/C][/ROW]
[ROW][C]15[/C][C]153.4[/C][C]142.929677951704[/C][C]10.4703220482955[/C][/ROW]
[ROW][C]16[/C][C]145[/C][C]161.666517380681[/C][C]-16.6665173806808[/C][/ROW]
[ROW][C]17[/C][C]137.7[/C][C]142.043779788519[/C][C]-4.34377978851876[/C][/ROW]
[ROW][C]18[/C][C]148.3[/C][C]130.594727678295[/C][C]17.7052723217053[/C][/ROW]
[ROW][C]19[/C][C]152.2[/C][C]153.544774772892[/C][C]-1.34477477289232[/C][/ROW]
[ROW][C]20[/C][C]169.4[/C][C]157.603338568676[/C][C]11.7966614313244[/C][/ROW]
[ROW][C]21[/C][C]168.6[/C][C]183.129708171458[/C][C]-14.5297081714576[/C][/ROW]
[ROW][C]22[/C][C]161.1[/C][C]172.714263433619[/C][C]-11.6142634336185[/C][/ROW]
[ROW][C]23[/C][C]174.1[/C][C]156.016078191186[/C][C]18.0839218088142[/C][/ROW]
[ROW][C]24[/C][C]179[/C][C]181.177255412026[/C][C]-2.17725541202628[/C][/ROW]
[ROW][C]25[/C][C]190.6[/C][C]185.666142185149[/C][C]4.93385781485097[/C][/ROW]
[ROW][C]26[/C][C]190[/C][C]200.646664629951[/C][C]-10.6466646299511[/C][/ROW]
[ROW][C]27[/C][C]181.6[/C][C]192.766778181890[/C][C]-11.1667781818905[/C][/ROW]
[ROW][C]28[/C][C]174.8[/C][C]175.732724587261[/C][C]-0.93272458726065[/C][/ROW]
[ROW][C]29[/C][C]180.5[/C][C]167.562917833625[/C][C]12.9370821663748[/C][/ROW]
[ROW][C]30[/C][C]196.8[/C][C]182.428434085557[/C][C]14.3715659144427[/C][/ROW]
[ROW][C]31[/C][C]193.8[/C][C]209.792114063494[/C][C]-15.9921140634945[/C][/ROW]
[ROW][C]32[/C][C]197[/C][C]196.296453613774[/C][C]0.703546386225923[/C][/ROW]
[ROW][C]33[/C][C]216.3[/C][C]198.988802627721[/C][C]17.3111973722788[/C][/ROW]
[ROW][C]34[/C][C]221.4[/C][C]230.676413252619[/C][C]-9.27641325261911[/C][/ROW]
[ROW][C]35[/C][C]217.9[/C][C]230.254699199796[/C][C]-12.3546991997960[/C][/ROW]
[ROW][C]36[/C][C]229.7[/C][C]217.360114807289[/C][C]12.3398851927106[/C][/ROW]
[ROW][C]37[/C][C]227.4[/C][C]237.17895585589[/C][C]-9.77895585589027[/C][/ROW]
[ROW][C]38[/C][C]204.2[/C][C]228.685170525644[/C][C]-24.4851705256441[/C][/ROW]
[ROW][C]39[/C][C]196.6[/C][C]187.409616097757[/C][C]9.19038390224287[/C][/ROW]
[ROW][C]40[/C][C]198.8[/C][C]184.817226509449[/C][C]13.9827734905508[/C][/ROW]
[ROW][C]41[/C][C]207.5[/C][C]197.567228936841[/C][C]9.93277106315867[/C][/ROW]
[ROW][C]42[/C][C]190.7[/C][C]214.231960486689[/C][C]-23.5319604866891[/C][/ROW]
[ROW][C]43[/C][C]201.6[/C][C]181.280107302819[/C][C]20.3198926971814[/C][/ROW]
[ROW][C]44[/C][C]210.5[/C][C]205.183425167594[/C][C]5.31657483240585[/C][/ROW]
[ROW][C]45[/C][C]223.5[/C][C]219.156669863080[/C][C]4.34333013692046[/C][/ROW]
[ROW][C]46[/C][C]223.8[/C][C]235.589084885880[/C][C]-11.7890848858802[/C][/ROW]
[ROW][C]47[/C][C]231.2[/C][C]227.757362038525[/C][C]3.44263796147504[/C][/ROW]
[ROW][C]48[/C][C]244[/C][C]236.867995900552[/C][C]7.13200409944841[/C][/ROW]
[ROW][C]49[/C][C]234.7[/C][C]254.970520049637[/C][C]-20.270520049637[/C][/ROW]
[ROW][C]50[/C][C]250.2[/C][C]231.667373345923[/C][C]18.5326266540773[/C][/ROW]
[ROW][C]51[/C][C]265.7[/C][C]259.102172707726[/C][C]6.59782729227436[/C][/ROW]
[ROW][C]52[/C][C]287.6[/C][C]280.476176680754[/C][C]7.12382331924613[/C][/ROW]
[ROW][C]53[/C][C]283.3[/C][C]307.871997784259[/C][C]-24.5719977842586[/C][/ROW]
[ROW][C]54[/C][C]295.4[/C][C]286.501300458197[/C][C]8.8986995418034[/C][/ROW]
[ROW][C]55[/C][C]312.3[/C][C]303.395454615529[/C][C]8.9045453844713[/C][/ROW]
[ROW][C]56[/C][C]333.8[/C][C]327.206176383825[/C][C]6.59382361617509[/C][/ROW]
[ROW][C]57[/C][C]347.7[/C][C]353.969679125931[/C][C]-6.26967912593091[/C][/ROW]
[ROW][C]58[/C][C]383.2[/C][C]363.815429052923[/C][C]19.3845709470772[/C][/ROW]
[ROW][C]59[/C][C]407.1[/C][C]412.741300397082[/C][C]-5.64130039708209[/C][/ROW]
[ROW][C]60[/C][C]413.6[/C][C]433.842344555343[/C][C]-20.2423445553430[/C][/ROW]
[ROW][C]61[/C][C]362.7[/C][C]425.553139948472[/C][C]-62.8531399484724[/C][/ROW]
[ROW][C]62[/C][C]321.9[/C][C]328.560139187149[/C][C]-6.66013918714884[/C][/ROW]
[ROW][C]63[/C][C]239.4[/C][C]279.044553711655[/C][C]-39.6445537116554[/C][/ROW]
[ROW][C]64[/C][C]191[/C][C]167.856909148111[/C][C]23.1430908518893[/C][/ROW]
[ROW][C]65[/C][C]159.7[/C][C]133.456323831866[/C][C]26.2436761681338[/C][/ROW]
[ROW][C]66[/C][C]163.4[/C][C]122.329161767816[/C][C]41.0708382321836[/C][/ROW]
[ROW][C]67[/C][C]157.6[/C][C]156.969728244327[/C][C]0.630271755672595[/C][/ROW]
[ROW][C]68[/C][C]166.2[/C][C]154.211182603582[/C][C]11.9888173964179[/C][/ROW]
[ROW][C]69[/C][C]176.7[/C][C]171.399211959866[/C][C]5.3007880401336[/C][/ROW]
[ROW][C]70[/C][C]198.3[/C][C]186.435410356935[/C][C]11.8645896430654[/C][/ROW]
[ROW][C]71[/C][C]226.2[/C][C]216.829628167094[/C][C]9.370371832906[/C][/ROW]
[ROW][C]72[/C][C]216.2[/C][C]252.159675901215[/C][C]-35.9596759012148[/C][/ROW]
[ROW][C]73[/C][C]235.9[/C][C]217.111134404971[/C][C]18.7888655950291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72324&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72324&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
3105.49411.4
4107.1108.528413856660-1.42841385666023
5110.7109.9294036791920.770596320807812
6117.1113.9887033945203.11129660547955
7118.7122.655750040687-3.95575004068711
8126.5121.6315859050844.86841409491615
9127.5132.653201568736-5.15320156873645
10134.6130.2861270594234.31387294057691
11131.8140.136771032064-8.33677103206435
12135.9131.6647536259364.23524637406433
13142.7138.2584142533184.44158574668188
14141.7148.492642671913-6.79264267191309
15153.4142.92967795170410.4703220482955
16145161.666517380681-16.6665173806808
17137.7142.043779788519-4.34377978851876
18148.3130.59472767829517.7052723217053
19152.2153.544774772892-1.34477477289232
20169.4157.60333856867611.7966614313244
21168.6183.129708171458-14.5297081714576
22161.1172.714263433619-11.6142634336185
23174.1156.01607819118618.0839218088142
24179181.177255412026-2.17725541202628
25190.6185.6661421851494.93385781485097
26190200.646664629951-10.6466646299511
27181.6192.766778181890-11.1667781818905
28174.8175.732724587261-0.93272458726065
29180.5167.56291783362512.9370821663748
30196.8182.42843408555714.3715659144427
31193.8209.792114063494-15.9921140634945
32197196.2964536137740.703546386225923
33216.3198.98880262772117.3111973722788
34221.4230.676413252619-9.27641325261911
35217.9230.254699199796-12.3546991997960
36229.7217.36011480728912.3398851927106
37227.4237.17895585589-9.77895585589027
38204.2228.685170525644-24.4851705256441
39196.6187.4096160977579.19038390224287
40198.8184.81722650944913.9827734905508
41207.5197.5672289368419.93277106315867
42190.7214.231960486689-23.5319604866891
43201.6181.28010730281920.3198926971814
44210.5205.1834251675945.31657483240585
45223.5219.1566698630804.34333013692046
46223.8235.589084885880-11.7890848858802
47231.2227.7573620385253.44263796147504
48244236.8679959005527.13200409944841
49234.7254.970520049637-20.270520049637
50250.2231.66737334592318.5326266540773
51265.7259.1021727077266.59782729227436
52287.6280.4761766807547.12382331924613
53283.3307.871997784259-24.5719977842586
54295.4286.5013004581978.8986995418034
55312.3303.3954546155298.9045453844713
56333.8327.2061763838256.59382361617509
57347.7353.969679125931-6.26967912593091
58383.2363.81542905292319.3845709470772
59407.1412.741300397082-5.64130039708209
60413.6433.842344555343-20.2423445553430
61362.7425.553139948472-62.8531399484724
62321.9328.560139187149-6.66013918714884
63239.4279.044553711655-39.6445537116554
64191167.85690914811123.1430908518893
65159.7133.45632383186626.2436761681338
66163.4122.32916176781641.0708382321836
67157.6156.9697282443270.630271755672595
68166.2154.21118260358211.9888173964179
69176.7171.3992119598665.3007880401336
70198.3186.43541035693511.8645896430654
71226.2216.8296281670949.370371832906
72216.2252.159675901215-35.9596759012148
73235.9217.11113440497118.7888655950291







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74247.938464450437215.801375336682280.075553564193
75261.162729970801197.417509287621324.907950653982
76274.386995491165172.100652888896376.673338093434
77287.611261011529141.070531905368434.15199011769
78300.835526531893105.022386029901496.648667033884
79314.05979205225764.4349482905303563.684635813983
80327.28405757262019.6677709464701634.90034419877
81340.508323092984-28.9949950765487710.011641262517
82353.732588613348-81.3209647179877788.786141944684
83366.956854133712-137.115284357096871.02899262452
84380.181119654076-196.211408376065956.573647684216
85393.405385174440-258.4647979036911045.27556825257

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 247.938464450437 & 215.801375336682 & 280.075553564193 \tabularnewline
75 & 261.162729970801 & 197.417509287621 & 324.907950653982 \tabularnewline
76 & 274.386995491165 & 172.100652888896 & 376.673338093434 \tabularnewline
77 & 287.611261011529 & 141.070531905368 & 434.15199011769 \tabularnewline
78 & 300.835526531893 & 105.022386029901 & 496.648667033884 \tabularnewline
79 & 314.059792052257 & 64.4349482905303 & 563.684635813983 \tabularnewline
80 & 327.284057572620 & 19.6677709464701 & 634.90034419877 \tabularnewline
81 & 340.508323092984 & -28.9949950765487 & 710.011641262517 \tabularnewline
82 & 353.732588613348 & -81.3209647179877 & 788.786141944684 \tabularnewline
83 & 366.956854133712 & -137.115284357096 & 871.02899262452 \tabularnewline
84 & 380.181119654076 & -196.211408376065 & 956.573647684216 \tabularnewline
85 & 393.405385174440 & -258.464797903691 & 1045.27556825257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72324&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]74[/C][C]247.938464450437[/C][C]215.801375336682[/C][C]280.075553564193[/C][/ROW]
[ROW][C]75[/C][C]261.162729970801[/C][C]197.417509287621[/C][C]324.907950653982[/C][/ROW]
[ROW][C]76[/C][C]274.386995491165[/C][C]172.100652888896[/C][C]376.673338093434[/C][/ROW]
[ROW][C]77[/C][C]287.611261011529[/C][C]141.070531905368[/C][C]434.15199011769[/C][/ROW]
[ROW][C]78[/C][C]300.835526531893[/C][C]105.022386029901[/C][C]496.648667033884[/C][/ROW]
[ROW][C]79[/C][C]314.059792052257[/C][C]64.4349482905303[/C][C]563.684635813983[/C][/ROW]
[ROW][C]80[/C][C]327.284057572620[/C][C]19.6677709464701[/C][C]634.90034419877[/C][/ROW]
[ROW][C]81[/C][C]340.508323092984[/C][C]-28.9949950765487[/C][C]710.011641262517[/C][/ROW]
[ROW][C]82[/C][C]353.732588613348[/C][C]-81.3209647179877[/C][C]788.786141944684[/C][/ROW]
[ROW][C]83[/C][C]366.956854133712[/C][C]-137.115284357096[/C][C]871.02899262452[/C][/ROW]
[ROW][C]84[/C][C]380.181119654076[/C][C]-196.211408376065[/C][C]956.573647684216[/C][/ROW]
[ROW][C]85[/C][C]393.405385174440[/C][C]-258.464797903691[/C][C]1045.27556825257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72324&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72324&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
74247.938464450437215.801375336682280.075553564193
75261.162729970801197.417509287621324.907950653982
76274.386995491165172.100652888896376.673338093434
77287.611261011529141.070531905368434.15199011769
78300.835526531893105.022386029901496.648667033884
79314.05979205225764.4349482905303563.684635813983
80327.28405757262019.6677709464701634.90034419877
81340.508323092984-28.9949950765487710.011641262517
82353.732588613348-81.3209647179877788.786141944684
83366.956854133712-137.115284357096871.02899262452
84380.181119654076-196.211408376065956.573647684216
85393.405385174440-258.4647979036911045.27556825257



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