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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 11 Dec 2013 18:28:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/11/t13868045298yptybqtzslbs14.htm/, Retrieved Sat, 20 Apr 2024 04:20:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232203, Retrieved Sat, 20 Apr 2024 04:20:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-11 23:28:36] [c37684f2e387cbe6dfbcb0e59307bb9b] [Current]
- R P     [Exponential Smoothing] [] [2014-01-11 18:54:06] [bbad914f60bdb4cc08661b92002a4d31]
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Dataseries X:
3.875
3.863
3.876
3.878
3.881
3.883
3.884
3.885
3.895
3.903
3.911
3.929
3.946
3.965
3.992
4.010
4.015
4.020
4.037
4.059
4.083
4.102
4.126
4.145
4.162
4.169
4.178
4.174
4.168
4.170
4.159
4.159
4.143
4.159
4.167
4.176
4.185
4.195
4.210
4.226
4.250
4.259
4.270
4.277
4.286
4.303
4.320
4.336
4.352
4.371
4.392
4.415
4.442
4.457
4.472
4.474
4.461
4.453
4.446
4.450
4.459
4.474
4.492
4.509
4.526
4.541
4.550
4.562
4.555
4.554
4.551
4.553




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232203&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232203&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232203&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955362702845
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955362702845 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232203&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]0.999955362702845[/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=232203&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232203&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
alpha0.999955362702845
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23.8633.875-0.012
33.8763.863000535647570.012999464352434
43.8783.875999419739050.00200058026095329
53.8813.87799991069950.00300008930049511
63.8833.880999866084120.00200013391587772
73.8843.882999910719430.00100008928057171
83.8853.883999955358720.00100004464128212
93.8953.884999955360710.0100000446392903
103.9033.894999553625040.00800044637496411
113.9113.90299964288170.00800035711830205
123.9293.910999642885680.0180003571143179
133.9463.928999196512710.0170008034872899
143.9653.945999241130080.0190007588699168
153.9923.964999151857480.0270008481425199
164.013.991998794755120.0180012052448819
174.0154.009999196474850.00500080352514765
184.024.014999776777650.0050002232223525
194.0374.019999776803550.0170002231964501
204.0594.036999241155990.0220007588440145
214.0834.058999017945590.0240009820544103
224.1024.082998928661030.0190010713389679
234.1264.101999151843530.0240008481564677
244.1454.125998928667010.0190010713329904
254.1624.144999151843530.0170008481564681
264.1694.161999241128090.00700075887191076
274.1784.168999687505050.0090003124949547
284.1744.17799959825038-0.00399959825037666
294.1684.17400017853126-0.00600017853125578
304.174.168000267831750.00199973216824745
314.1594.16999991073736-0.0109999107373611
324.1594.15900049100628-4.91006284519813e-07
334.1434.15900000002192-0.0160000000219176
344.1594.143000714196750.0159992858032449
354.1674.158999285835130.0080007141648748
364.1764.166999642869740.00900035713025638
374.1854.175999598248380.00900040175161543
384.1954.184999598246390.0100004017536079
394.214.19499955360910.0150004463909044
404.2264.209999330420620.0160006695793831
414.254.225999285773360.0240007142266423
424.2594.249998928672990.00900107132701322
434.274.25899959821650.0110004017834946
444.2774.26999950897180.00700049102820355
454.2864.2769996875170.00900031248299804
464.3034.285999598250380.0170004017496233
474.324.302999241148020.0170007588519852
484.3364.319999241132080.016000758867925
494.3524.335999285769370.0160007142306284
504.3714.351999285771360.0190007142286364
514.3924.370999151859470.0210008481405275
524.4154.39199906257890.0230009374210987
534.4424.414998973300320.0270010266996783
544.4574.441998794747150.0150012052528519
554.4724.456999330386740.015000669613257
564.4744.471999330410650.00200066958934642
574.4614.47399991069552-0.012999910695517
584.4534.46100058028088-0.00800058028087669
594.4464.45300035712428-0.00700035712428004
604.454.446000312477020.0039996875229793
614.4594.449999821464760.00900017853524027
624.4744.458999598256360.0150004017436443
634.4924.473999330422610.0180006695773898
644.5094.491999196498760.0170008035012374
654.5264.508999241130080.0170007588699175
664.5414.525999241132070.0150007588679264
674.554.540999330406670.00900066959333046
684.5624.549999598234440.0120004017655635
694.5554.5619994643345-0.00699946433450105
704.5544.55500031243717-0.00100031243716892
714.5514.55400004465124-0.00300004465124371
724.5534.551000133913880.00199986608611535

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.863 & 3.875 & -0.012 \tabularnewline
3 & 3.876 & 3.86300053564757 & 0.012999464352434 \tabularnewline
4 & 3.878 & 3.87599941973905 & 0.00200058026095329 \tabularnewline
5 & 3.881 & 3.8779999106995 & 0.00300008930049511 \tabularnewline
6 & 3.883 & 3.88099986608412 & 0.00200013391587772 \tabularnewline
7 & 3.884 & 3.88299991071943 & 0.00100008928057171 \tabularnewline
8 & 3.885 & 3.88399995535872 & 0.00100004464128212 \tabularnewline
9 & 3.895 & 3.88499995536071 & 0.0100000446392903 \tabularnewline
10 & 3.903 & 3.89499955362504 & 0.00800044637496411 \tabularnewline
11 & 3.911 & 3.9029996428817 & 0.00800035711830205 \tabularnewline
12 & 3.929 & 3.91099964288568 & 0.0180003571143179 \tabularnewline
13 & 3.946 & 3.92899919651271 & 0.0170008034872899 \tabularnewline
14 & 3.965 & 3.94599924113008 & 0.0190007588699168 \tabularnewline
15 & 3.992 & 3.96499915185748 & 0.0270008481425199 \tabularnewline
16 & 4.01 & 3.99199879475512 & 0.0180012052448819 \tabularnewline
17 & 4.015 & 4.00999919647485 & 0.00500080352514765 \tabularnewline
18 & 4.02 & 4.01499977677765 & 0.0050002232223525 \tabularnewline
19 & 4.037 & 4.01999977680355 & 0.0170002231964501 \tabularnewline
20 & 4.059 & 4.03699924115599 & 0.0220007588440145 \tabularnewline
21 & 4.083 & 4.05899901794559 & 0.0240009820544103 \tabularnewline
22 & 4.102 & 4.08299892866103 & 0.0190010713389679 \tabularnewline
23 & 4.126 & 4.10199915184353 & 0.0240008481564677 \tabularnewline
24 & 4.145 & 4.12599892866701 & 0.0190010713329904 \tabularnewline
25 & 4.162 & 4.14499915184353 & 0.0170008481564681 \tabularnewline
26 & 4.169 & 4.16199924112809 & 0.00700075887191076 \tabularnewline
27 & 4.178 & 4.16899968750505 & 0.0090003124949547 \tabularnewline
28 & 4.174 & 4.17799959825038 & -0.00399959825037666 \tabularnewline
29 & 4.168 & 4.17400017853126 & -0.00600017853125578 \tabularnewline
30 & 4.17 & 4.16800026783175 & 0.00199973216824745 \tabularnewline
31 & 4.159 & 4.16999991073736 & -0.0109999107373611 \tabularnewline
32 & 4.159 & 4.15900049100628 & -4.91006284519813e-07 \tabularnewline
33 & 4.143 & 4.15900000002192 & -0.0160000000219176 \tabularnewline
34 & 4.159 & 4.14300071419675 & 0.0159992858032449 \tabularnewline
35 & 4.167 & 4.15899928583513 & 0.0080007141648748 \tabularnewline
36 & 4.176 & 4.16699964286974 & 0.00900035713025638 \tabularnewline
37 & 4.185 & 4.17599959824838 & 0.00900040175161543 \tabularnewline
38 & 4.195 & 4.18499959824639 & 0.0100004017536079 \tabularnewline
39 & 4.21 & 4.1949995536091 & 0.0150004463909044 \tabularnewline
40 & 4.226 & 4.20999933042062 & 0.0160006695793831 \tabularnewline
41 & 4.25 & 4.22599928577336 & 0.0240007142266423 \tabularnewline
42 & 4.259 & 4.24999892867299 & 0.00900107132701322 \tabularnewline
43 & 4.27 & 4.2589995982165 & 0.0110004017834946 \tabularnewline
44 & 4.277 & 4.2699995089718 & 0.00700049102820355 \tabularnewline
45 & 4.286 & 4.276999687517 & 0.00900031248299804 \tabularnewline
46 & 4.303 & 4.28599959825038 & 0.0170004017496233 \tabularnewline
47 & 4.32 & 4.30299924114802 & 0.0170007588519852 \tabularnewline
48 & 4.336 & 4.31999924113208 & 0.016000758867925 \tabularnewline
49 & 4.352 & 4.33599928576937 & 0.0160007142306284 \tabularnewline
50 & 4.371 & 4.35199928577136 & 0.0190007142286364 \tabularnewline
51 & 4.392 & 4.37099915185947 & 0.0210008481405275 \tabularnewline
52 & 4.415 & 4.3919990625789 & 0.0230009374210987 \tabularnewline
53 & 4.442 & 4.41499897330032 & 0.0270010266996783 \tabularnewline
54 & 4.457 & 4.44199879474715 & 0.0150012052528519 \tabularnewline
55 & 4.472 & 4.45699933038674 & 0.015000669613257 \tabularnewline
56 & 4.474 & 4.47199933041065 & 0.00200066958934642 \tabularnewline
57 & 4.461 & 4.47399991069552 & -0.012999910695517 \tabularnewline
58 & 4.453 & 4.46100058028088 & -0.00800058028087669 \tabularnewline
59 & 4.446 & 4.45300035712428 & -0.00700035712428004 \tabularnewline
60 & 4.45 & 4.44600031247702 & 0.0039996875229793 \tabularnewline
61 & 4.459 & 4.44999982146476 & 0.00900017853524027 \tabularnewline
62 & 4.474 & 4.45899959825636 & 0.0150004017436443 \tabularnewline
63 & 4.492 & 4.47399933042261 & 0.0180006695773898 \tabularnewline
64 & 4.509 & 4.49199919649876 & 0.0170008035012374 \tabularnewline
65 & 4.526 & 4.50899924113008 & 0.0170007588699175 \tabularnewline
66 & 4.541 & 4.52599924113207 & 0.0150007588679264 \tabularnewline
67 & 4.55 & 4.54099933040667 & 0.00900066959333046 \tabularnewline
68 & 4.562 & 4.54999959823444 & 0.0120004017655635 \tabularnewline
69 & 4.555 & 4.5619994643345 & -0.00699946433450105 \tabularnewline
70 & 4.554 & 4.55500031243717 & -0.00100031243716892 \tabularnewline
71 & 4.551 & 4.55400004465124 & -0.00300004465124371 \tabularnewline
72 & 4.553 & 4.55100013391388 & 0.00199986608611535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232203&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]3.863[/C][C]3.875[/C][C]-0.012[/C][/ROW]
[ROW][C]3[/C][C]3.876[/C][C]3.86300053564757[/C][C]0.012999464352434[/C][/ROW]
[ROW][C]4[/C][C]3.878[/C][C]3.87599941973905[/C][C]0.00200058026095329[/C][/ROW]
[ROW][C]5[/C][C]3.881[/C][C]3.8779999106995[/C][C]0.00300008930049511[/C][/ROW]
[ROW][C]6[/C][C]3.883[/C][C]3.88099986608412[/C][C]0.00200013391587772[/C][/ROW]
[ROW][C]7[/C][C]3.884[/C][C]3.88299991071943[/C][C]0.00100008928057171[/C][/ROW]
[ROW][C]8[/C][C]3.885[/C][C]3.88399995535872[/C][C]0.00100004464128212[/C][/ROW]
[ROW][C]9[/C][C]3.895[/C][C]3.88499995536071[/C][C]0.0100000446392903[/C][/ROW]
[ROW][C]10[/C][C]3.903[/C][C]3.89499955362504[/C][C]0.00800044637496411[/C][/ROW]
[ROW][C]11[/C][C]3.911[/C][C]3.9029996428817[/C][C]0.00800035711830205[/C][/ROW]
[ROW][C]12[/C][C]3.929[/C][C]3.91099964288568[/C][C]0.0180003571143179[/C][/ROW]
[ROW][C]13[/C][C]3.946[/C][C]3.92899919651271[/C][C]0.0170008034872899[/C][/ROW]
[ROW][C]14[/C][C]3.965[/C][C]3.94599924113008[/C][C]0.0190007588699168[/C][/ROW]
[ROW][C]15[/C][C]3.992[/C][C]3.96499915185748[/C][C]0.0270008481425199[/C][/ROW]
[ROW][C]16[/C][C]4.01[/C][C]3.99199879475512[/C][C]0.0180012052448819[/C][/ROW]
[ROW][C]17[/C][C]4.015[/C][C]4.00999919647485[/C][C]0.00500080352514765[/C][/ROW]
[ROW][C]18[/C][C]4.02[/C][C]4.01499977677765[/C][C]0.0050002232223525[/C][/ROW]
[ROW][C]19[/C][C]4.037[/C][C]4.01999977680355[/C][C]0.0170002231964501[/C][/ROW]
[ROW][C]20[/C][C]4.059[/C][C]4.03699924115599[/C][C]0.0220007588440145[/C][/ROW]
[ROW][C]21[/C][C]4.083[/C][C]4.05899901794559[/C][C]0.0240009820544103[/C][/ROW]
[ROW][C]22[/C][C]4.102[/C][C]4.08299892866103[/C][C]0.0190010713389679[/C][/ROW]
[ROW][C]23[/C][C]4.126[/C][C]4.10199915184353[/C][C]0.0240008481564677[/C][/ROW]
[ROW][C]24[/C][C]4.145[/C][C]4.12599892866701[/C][C]0.0190010713329904[/C][/ROW]
[ROW][C]25[/C][C]4.162[/C][C]4.14499915184353[/C][C]0.0170008481564681[/C][/ROW]
[ROW][C]26[/C][C]4.169[/C][C]4.16199924112809[/C][C]0.00700075887191076[/C][/ROW]
[ROW][C]27[/C][C]4.178[/C][C]4.16899968750505[/C][C]0.0090003124949547[/C][/ROW]
[ROW][C]28[/C][C]4.174[/C][C]4.17799959825038[/C][C]-0.00399959825037666[/C][/ROW]
[ROW][C]29[/C][C]4.168[/C][C]4.17400017853126[/C][C]-0.00600017853125578[/C][/ROW]
[ROW][C]30[/C][C]4.17[/C][C]4.16800026783175[/C][C]0.00199973216824745[/C][/ROW]
[ROW][C]31[/C][C]4.159[/C][C]4.16999991073736[/C][C]-0.0109999107373611[/C][/ROW]
[ROW][C]32[/C][C]4.159[/C][C]4.15900049100628[/C][C]-4.91006284519813e-07[/C][/ROW]
[ROW][C]33[/C][C]4.143[/C][C]4.15900000002192[/C][C]-0.0160000000219176[/C][/ROW]
[ROW][C]34[/C][C]4.159[/C][C]4.14300071419675[/C][C]0.0159992858032449[/C][/ROW]
[ROW][C]35[/C][C]4.167[/C][C]4.15899928583513[/C][C]0.0080007141648748[/C][/ROW]
[ROW][C]36[/C][C]4.176[/C][C]4.16699964286974[/C][C]0.00900035713025638[/C][/ROW]
[ROW][C]37[/C][C]4.185[/C][C]4.17599959824838[/C][C]0.00900040175161543[/C][/ROW]
[ROW][C]38[/C][C]4.195[/C][C]4.18499959824639[/C][C]0.0100004017536079[/C][/ROW]
[ROW][C]39[/C][C]4.21[/C][C]4.1949995536091[/C][C]0.0150004463909044[/C][/ROW]
[ROW][C]40[/C][C]4.226[/C][C]4.20999933042062[/C][C]0.0160006695793831[/C][/ROW]
[ROW][C]41[/C][C]4.25[/C][C]4.22599928577336[/C][C]0.0240007142266423[/C][/ROW]
[ROW][C]42[/C][C]4.259[/C][C]4.24999892867299[/C][C]0.00900107132701322[/C][/ROW]
[ROW][C]43[/C][C]4.27[/C][C]4.2589995982165[/C][C]0.0110004017834946[/C][/ROW]
[ROW][C]44[/C][C]4.277[/C][C]4.2699995089718[/C][C]0.00700049102820355[/C][/ROW]
[ROW][C]45[/C][C]4.286[/C][C]4.276999687517[/C][C]0.00900031248299804[/C][/ROW]
[ROW][C]46[/C][C]4.303[/C][C]4.28599959825038[/C][C]0.0170004017496233[/C][/ROW]
[ROW][C]47[/C][C]4.32[/C][C]4.30299924114802[/C][C]0.0170007588519852[/C][/ROW]
[ROW][C]48[/C][C]4.336[/C][C]4.31999924113208[/C][C]0.016000758867925[/C][/ROW]
[ROW][C]49[/C][C]4.352[/C][C]4.33599928576937[/C][C]0.0160007142306284[/C][/ROW]
[ROW][C]50[/C][C]4.371[/C][C]4.35199928577136[/C][C]0.0190007142286364[/C][/ROW]
[ROW][C]51[/C][C]4.392[/C][C]4.37099915185947[/C][C]0.0210008481405275[/C][/ROW]
[ROW][C]52[/C][C]4.415[/C][C]4.3919990625789[/C][C]0.0230009374210987[/C][/ROW]
[ROW][C]53[/C][C]4.442[/C][C]4.41499897330032[/C][C]0.0270010266996783[/C][/ROW]
[ROW][C]54[/C][C]4.457[/C][C]4.44199879474715[/C][C]0.0150012052528519[/C][/ROW]
[ROW][C]55[/C][C]4.472[/C][C]4.45699933038674[/C][C]0.015000669613257[/C][/ROW]
[ROW][C]56[/C][C]4.474[/C][C]4.47199933041065[/C][C]0.00200066958934642[/C][/ROW]
[ROW][C]57[/C][C]4.461[/C][C]4.47399991069552[/C][C]-0.012999910695517[/C][/ROW]
[ROW][C]58[/C][C]4.453[/C][C]4.46100058028088[/C][C]-0.00800058028087669[/C][/ROW]
[ROW][C]59[/C][C]4.446[/C][C]4.45300035712428[/C][C]-0.00700035712428004[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.44600031247702[/C][C]0.0039996875229793[/C][/ROW]
[ROW][C]61[/C][C]4.459[/C][C]4.44999982146476[/C][C]0.00900017853524027[/C][/ROW]
[ROW][C]62[/C][C]4.474[/C][C]4.45899959825636[/C][C]0.0150004017436443[/C][/ROW]
[ROW][C]63[/C][C]4.492[/C][C]4.47399933042261[/C][C]0.0180006695773898[/C][/ROW]
[ROW][C]64[/C][C]4.509[/C][C]4.49199919649876[/C][C]0.0170008035012374[/C][/ROW]
[ROW][C]65[/C][C]4.526[/C][C]4.50899924113008[/C][C]0.0170007588699175[/C][/ROW]
[ROW][C]66[/C][C]4.541[/C][C]4.52599924113207[/C][C]0.0150007588679264[/C][/ROW]
[ROW][C]67[/C][C]4.55[/C][C]4.54099933040667[/C][C]0.00900066959333046[/C][/ROW]
[ROW][C]68[/C][C]4.562[/C][C]4.54999959823444[/C][C]0.0120004017655635[/C][/ROW]
[ROW][C]69[/C][C]4.555[/C][C]4.5619994643345[/C][C]-0.00699946433450105[/C][/ROW]
[ROW][C]70[/C][C]4.554[/C][C]4.55500031243717[/C][C]-0.00100031243716892[/C][/ROW]
[ROW][C]71[/C][C]4.551[/C][C]4.55400004465124[/C][C]-0.00300004465124371[/C][/ROW]
[ROW][C]72[/C][C]4.553[/C][C]4.55100013391388[/C][C]0.00199986608611535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232203&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232203&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
23.8633.875-0.012
33.8763.863000535647570.012999464352434
43.8783.875999419739050.00200058026095329
53.8813.87799991069950.00300008930049511
63.8833.880999866084120.00200013391587772
73.8843.882999910719430.00100008928057171
83.8853.883999955358720.00100004464128212
93.8953.884999955360710.0100000446392903
103.9033.894999553625040.00800044637496411
113.9113.90299964288170.00800035711830205
123.9293.910999642885680.0180003571143179
133.9463.928999196512710.0170008034872899
143.9653.945999241130080.0190007588699168
153.9923.964999151857480.0270008481425199
164.013.991998794755120.0180012052448819
174.0154.009999196474850.00500080352514765
184.024.014999776777650.0050002232223525
194.0374.019999776803550.0170002231964501
204.0594.036999241155990.0220007588440145
214.0834.058999017945590.0240009820544103
224.1024.082998928661030.0190010713389679
234.1264.101999151843530.0240008481564677
244.1454.125998928667010.0190010713329904
254.1624.144999151843530.0170008481564681
264.1694.161999241128090.00700075887191076
274.1784.168999687505050.0090003124949547
284.1744.17799959825038-0.00399959825037666
294.1684.17400017853126-0.00600017853125578
304.174.168000267831750.00199973216824745
314.1594.16999991073736-0.0109999107373611
324.1594.15900049100628-4.91006284519813e-07
334.1434.15900000002192-0.0160000000219176
344.1594.143000714196750.0159992858032449
354.1674.158999285835130.0080007141648748
364.1764.166999642869740.00900035713025638
374.1854.175999598248380.00900040175161543
384.1954.184999598246390.0100004017536079
394.214.19499955360910.0150004463909044
404.2264.209999330420620.0160006695793831
414.254.225999285773360.0240007142266423
424.2594.249998928672990.00900107132701322
434.274.25899959821650.0110004017834946
444.2774.26999950897180.00700049102820355
454.2864.2769996875170.00900031248299804
464.3034.285999598250380.0170004017496233
474.324.302999241148020.0170007588519852
484.3364.319999241132080.016000758867925
494.3524.335999285769370.0160007142306284
504.3714.351999285771360.0190007142286364
514.3924.370999151859470.0210008481405275
524.4154.39199906257890.0230009374210987
534.4424.414998973300320.0270010266996783
544.4574.441998794747150.0150012052528519
554.4724.456999330386740.015000669613257
564.4744.471999330410650.00200066958934642
574.4614.47399991069552-0.012999910695517
584.4534.46100058028088-0.00800058028087669
594.4464.45300035712428-0.00700035712428004
604.454.446000312477020.0039996875229793
614.4594.449999821464760.00900017853524027
624.4744.458999598256360.0150004017436443
634.4924.473999330422610.0180006695773898
644.5094.491999196498760.0170008035012374
654.5264.508999241130080.0170007588699175
664.5414.525999241132070.0150007588679264
674.554.540999330406670.00900066959333046
684.5624.549999598234440.0120004017655635
694.5554.5619994643345-0.00699946433450105
704.5544.55500031243717-0.00100031243716892
714.5514.55400004465124-0.00300004465124371
724.5534.551000133913880.00199986608611535







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734.552999910731384.533045108761224.57295471270155
744.552999910731384.524780188983784.58121963247898
754.552999910731384.518438208381024.58756161308175
764.552999910731384.513091642876234.59290817858654
774.552999910731384.508381210424874.59761861103789
784.552999910731384.504122646171214.60187717529156
794.552999910731384.500206487232534.60579333423023
804.552999910731384.496561412004254.60943840945851
814.552999910731384.493137880090794.61286194137198
824.552999910731384.489899821299924.61610000016285
834.552999910731384.486820005472294.61917981599047
844.552999910731384.483877277434144.62212254402863

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.55299991073138 & 4.53304510876122 & 4.57295471270155 \tabularnewline
74 & 4.55299991073138 & 4.52478018898378 & 4.58121963247898 \tabularnewline
75 & 4.55299991073138 & 4.51843820838102 & 4.58756161308175 \tabularnewline
76 & 4.55299991073138 & 4.51309164287623 & 4.59290817858654 \tabularnewline
77 & 4.55299991073138 & 4.50838121042487 & 4.59761861103789 \tabularnewline
78 & 4.55299991073138 & 4.50412264617121 & 4.60187717529156 \tabularnewline
79 & 4.55299991073138 & 4.50020648723253 & 4.60579333423023 \tabularnewline
80 & 4.55299991073138 & 4.49656141200425 & 4.60943840945851 \tabularnewline
81 & 4.55299991073138 & 4.49313788009079 & 4.61286194137198 \tabularnewline
82 & 4.55299991073138 & 4.48989982129992 & 4.61610000016285 \tabularnewline
83 & 4.55299991073138 & 4.48682000547229 & 4.61917981599047 \tabularnewline
84 & 4.55299991073138 & 4.48387727743414 & 4.62212254402863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232203&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]73[/C][C]4.55299991073138[/C][C]4.53304510876122[/C][C]4.57295471270155[/C][/ROW]
[ROW][C]74[/C][C]4.55299991073138[/C][C]4.52478018898378[/C][C]4.58121963247898[/C][/ROW]
[ROW][C]75[/C][C]4.55299991073138[/C][C]4.51843820838102[/C][C]4.58756161308175[/C][/ROW]
[ROW][C]76[/C][C]4.55299991073138[/C][C]4.51309164287623[/C][C]4.59290817858654[/C][/ROW]
[ROW][C]77[/C][C]4.55299991073138[/C][C]4.50838121042487[/C][C]4.59761861103789[/C][/ROW]
[ROW][C]78[/C][C]4.55299991073138[/C][C]4.50412264617121[/C][C]4.60187717529156[/C][/ROW]
[ROW][C]79[/C][C]4.55299991073138[/C][C]4.50020648723253[/C][C]4.60579333423023[/C][/ROW]
[ROW][C]80[/C][C]4.55299991073138[/C][C]4.49656141200425[/C][C]4.60943840945851[/C][/ROW]
[ROW][C]81[/C][C]4.55299991073138[/C][C]4.49313788009079[/C][C]4.61286194137198[/C][/ROW]
[ROW][C]82[/C][C]4.55299991073138[/C][C]4.48989982129992[/C][C]4.61610000016285[/C][/ROW]
[ROW][C]83[/C][C]4.55299991073138[/C][C]4.48682000547229[/C][C]4.61917981599047[/C][/ROW]
[ROW][C]84[/C][C]4.55299991073138[/C][C]4.48387727743414[/C][C]4.62212254402863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232203&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232203&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
734.552999910731384.533045108761224.57295471270155
744.552999910731384.524780188983784.58121963247898
754.552999910731384.518438208381024.58756161308175
764.552999910731384.513091642876234.59290817858654
774.552999910731384.508381210424874.59761861103789
784.552999910731384.504122646171214.60187717529156
794.552999910731384.500206487232534.60579333423023
804.552999910731384.496561412004254.60943840945851
814.552999910731384.493137880090794.61286194137198
824.552999910731384.489899821299924.61610000016285
834.552999910731384.486820005472294.61917981599047
844.552999910731384.483877277434144.62212254402863



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')