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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 20 Dec 2010 10:32:02 +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/Dec/20/t12928412109tgpd7ryayfafzl.htm/, Retrieved Fri, 03 May 2024 17:16:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112836, Retrieved Fri, 03 May 2024 17:16:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Prijsevolutie kor...] [2010-12-20 10:32:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
4.23
4.38
4.43
4.44
4.44
4.44
4.44
4.44
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.46
4.46
4.46
4.48
4.58
4.67
4.68
4.68
4.69
4.69
4.69
4.69
4.69
4.69
4.69
4.73
4.78
4.79
4.79
4.8
4.8
4.81
5.16
5.26
5.29
5.29
5.29
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.35
5.44
5.47
5.47
5.48
5.48
5.48
5.48
5.48
5.48
5.48
5.5
5.55
5.57
5.58
5.58
5.58
5.59
5.59
5.59
5.55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112836&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]3 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=112836&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112836&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.500243980146683
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.500243980146683 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112836&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]0.500243980146683[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112836&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112836&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
beta0.500243980146683
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34.434.53-0.0999999999999996
44.444.52997560198533-0.0899756019853308
54.444.49496584873210-0.0549658487320954
64.444.46746951379021-0.0274695137902112
74.444.4537280548791-0.0137280548791017
84.444.44686067806671-0.0068606780667082
94.454.443428665164110.00657133483588712
104.454.45671593585729-0.00671593585729369
114.454.45335632937363-0.00335632937363162
124.454.45167734580908-0.00167734580908263
134.454.45083826366546-0.000838263665464467
144.454.45041892731304-0.000418927313040385
154.454.45020936144657-0.000209361446573020
164.454.45010462964325-0.000104629643249865
174.464.450052289294070.00994771070593092
184.464.46502857169095-0.00502857169095172
194.464.46251305897382-0.00251305897381737
204.484.461255916350410.0187440836495893
214.584.490632531359490.089367468640515
224.674.635338069567850.0346619304321507
234.684.7426774916068-0.062677491606796
244.684.7213234537398-0.0413234537398015
254.694.7006516447676-0.0106516447675951
264.694.70532322359395-0.0153232235939456
274.694.69765787323463-0.00765787323463307
284.694.69382706824828-0.00382706824828105
294.694.69191260039547-0.00191260039546837
304.694.69095583356121-0.000955833561208763
314.694.69047768357619-0.000477683576192156
324.734.690238725242790.0397612747572129
334.784.750129063583040.0298709364169589
344.794.81507181970697-0.0250718197069695
354.794.81252979282723-0.0225297928272346
364.84.80125939959146-0.00125939959145871
374.84.81062939252723-0.0106293925272318
384.814.805312102902870.00468789709713135
395.164.817657195205260.342342804794745
405.265.33891212245036-0.0789121224503582
415.295.39943680823397-0.109436808233968
425.295.37469170370846-0.0846917037084589
435.295.33232518875994-0.0423251887599356
445.35.3111522678742-0.0111522678742064
455.35.31557341300515-0.0155734130051508
465.35.30778290689899-0.00778290689898586
475.35.30388955457473-0.00388955457472662
485.35.30194382831327-0.00194382831326756
495.35.30097143990112-0.000971439901117144
505.35.30048548293851-0.00048548293850903
515.35.30024262302106-0.000242623021056154
525.355.300121252315330.049878747684672
535.445.375072795581840.0649272044181606
545.475.49755223873978-0.0275522387397791
555.475.51376939717064-0.0437693971706397
565.485.49187401972138-0.0118740197213771
575.485.49593411283562-0.0159341128356161
585.485.48796316881062-0.00796316881062076
595.485.48397964155022-0.0039796415502158
605.485.48198884982158-0.00198884982157921
615.485.48099393967092-0.00099393967091821
625.485.48049672733391-0.000496727333912261
635.55.480248242475350.0197517575246513
645.555.510128940274370.0398710597256278
655.575.58007419788419-0.0100741978841858
665.585.59503464103782-0.0150346410378157
675.585.59751365236498-0.0175136523649817
685.585.58875255319902-0.00875255319901846
695.595.58437414115030.00562585884970446
705.595.59718844317301-0.00718844317301492
715.595.59359246774909-0.00359246774908772
725.555.59179535738374-0.0417953573837355

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.43 & 4.53 & -0.0999999999999996 \tabularnewline
4 & 4.44 & 4.52997560198533 & -0.0899756019853308 \tabularnewline
5 & 4.44 & 4.49496584873210 & -0.0549658487320954 \tabularnewline
6 & 4.44 & 4.46746951379021 & -0.0274695137902112 \tabularnewline
7 & 4.44 & 4.4537280548791 & -0.0137280548791017 \tabularnewline
8 & 4.44 & 4.44686067806671 & -0.0068606780667082 \tabularnewline
9 & 4.45 & 4.44342866516411 & 0.00657133483588712 \tabularnewline
10 & 4.45 & 4.45671593585729 & -0.00671593585729369 \tabularnewline
11 & 4.45 & 4.45335632937363 & -0.00335632937363162 \tabularnewline
12 & 4.45 & 4.45167734580908 & -0.00167734580908263 \tabularnewline
13 & 4.45 & 4.45083826366546 & -0.000838263665464467 \tabularnewline
14 & 4.45 & 4.45041892731304 & -0.000418927313040385 \tabularnewline
15 & 4.45 & 4.45020936144657 & -0.000209361446573020 \tabularnewline
16 & 4.45 & 4.45010462964325 & -0.000104629643249865 \tabularnewline
17 & 4.46 & 4.45005228929407 & 0.00994771070593092 \tabularnewline
18 & 4.46 & 4.46502857169095 & -0.00502857169095172 \tabularnewline
19 & 4.46 & 4.46251305897382 & -0.00251305897381737 \tabularnewline
20 & 4.48 & 4.46125591635041 & 0.0187440836495893 \tabularnewline
21 & 4.58 & 4.49063253135949 & 0.089367468640515 \tabularnewline
22 & 4.67 & 4.63533806956785 & 0.0346619304321507 \tabularnewline
23 & 4.68 & 4.7426774916068 & -0.062677491606796 \tabularnewline
24 & 4.68 & 4.7213234537398 & -0.0413234537398015 \tabularnewline
25 & 4.69 & 4.7006516447676 & -0.0106516447675951 \tabularnewline
26 & 4.69 & 4.70532322359395 & -0.0153232235939456 \tabularnewline
27 & 4.69 & 4.69765787323463 & -0.00765787323463307 \tabularnewline
28 & 4.69 & 4.69382706824828 & -0.00382706824828105 \tabularnewline
29 & 4.69 & 4.69191260039547 & -0.00191260039546837 \tabularnewline
30 & 4.69 & 4.69095583356121 & -0.000955833561208763 \tabularnewline
31 & 4.69 & 4.69047768357619 & -0.000477683576192156 \tabularnewline
32 & 4.73 & 4.69023872524279 & 0.0397612747572129 \tabularnewline
33 & 4.78 & 4.75012906358304 & 0.0298709364169589 \tabularnewline
34 & 4.79 & 4.81507181970697 & -0.0250718197069695 \tabularnewline
35 & 4.79 & 4.81252979282723 & -0.0225297928272346 \tabularnewline
36 & 4.8 & 4.80125939959146 & -0.00125939959145871 \tabularnewline
37 & 4.8 & 4.81062939252723 & -0.0106293925272318 \tabularnewline
38 & 4.81 & 4.80531210290287 & 0.00468789709713135 \tabularnewline
39 & 5.16 & 4.81765719520526 & 0.342342804794745 \tabularnewline
40 & 5.26 & 5.33891212245036 & -0.0789121224503582 \tabularnewline
41 & 5.29 & 5.39943680823397 & -0.109436808233968 \tabularnewline
42 & 5.29 & 5.37469170370846 & -0.0846917037084589 \tabularnewline
43 & 5.29 & 5.33232518875994 & -0.0423251887599356 \tabularnewline
44 & 5.3 & 5.3111522678742 & -0.0111522678742064 \tabularnewline
45 & 5.3 & 5.31557341300515 & -0.0155734130051508 \tabularnewline
46 & 5.3 & 5.30778290689899 & -0.00778290689898586 \tabularnewline
47 & 5.3 & 5.30388955457473 & -0.00388955457472662 \tabularnewline
48 & 5.3 & 5.30194382831327 & -0.00194382831326756 \tabularnewline
49 & 5.3 & 5.30097143990112 & -0.000971439901117144 \tabularnewline
50 & 5.3 & 5.30048548293851 & -0.00048548293850903 \tabularnewline
51 & 5.3 & 5.30024262302106 & -0.000242623021056154 \tabularnewline
52 & 5.35 & 5.30012125231533 & 0.049878747684672 \tabularnewline
53 & 5.44 & 5.37507279558184 & 0.0649272044181606 \tabularnewline
54 & 5.47 & 5.49755223873978 & -0.0275522387397791 \tabularnewline
55 & 5.47 & 5.51376939717064 & -0.0437693971706397 \tabularnewline
56 & 5.48 & 5.49187401972138 & -0.0118740197213771 \tabularnewline
57 & 5.48 & 5.49593411283562 & -0.0159341128356161 \tabularnewline
58 & 5.48 & 5.48796316881062 & -0.00796316881062076 \tabularnewline
59 & 5.48 & 5.48397964155022 & -0.0039796415502158 \tabularnewline
60 & 5.48 & 5.48198884982158 & -0.00198884982157921 \tabularnewline
61 & 5.48 & 5.48099393967092 & -0.00099393967091821 \tabularnewline
62 & 5.48 & 5.48049672733391 & -0.000496727333912261 \tabularnewline
63 & 5.5 & 5.48024824247535 & 0.0197517575246513 \tabularnewline
64 & 5.55 & 5.51012894027437 & 0.0398710597256278 \tabularnewline
65 & 5.57 & 5.58007419788419 & -0.0100741978841858 \tabularnewline
66 & 5.58 & 5.59503464103782 & -0.0150346410378157 \tabularnewline
67 & 5.58 & 5.59751365236498 & -0.0175136523649817 \tabularnewline
68 & 5.58 & 5.58875255319902 & -0.00875255319901846 \tabularnewline
69 & 5.59 & 5.5843741411503 & 0.00562585884970446 \tabularnewline
70 & 5.59 & 5.59718844317301 & -0.00718844317301492 \tabularnewline
71 & 5.59 & 5.59359246774909 & -0.00359246774908772 \tabularnewline
72 & 5.55 & 5.59179535738374 & -0.0417953573837355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112836&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]4.43[/C][C]4.53[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]4.44[/C][C]4.52997560198533[/C][C]-0.0899756019853308[/C][/ROW]
[ROW][C]5[/C][C]4.44[/C][C]4.49496584873210[/C][C]-0.0549658487320954[/C][/ROW]
[ROW][C]6[/C][C]4.44[/C][C]4.46746951379021[/C][C]-0.0274695137902112[/C][/ROW]
[ROW][C]7[/C][C]4.44[/C][C]4.4537280548791[/C][C]-0.0137280548791017[/C][/ROW]
[ROW][C]8[/C][C]4.44[/C][C]4.44686067806671[/C][C]-0.0068606780667082[/C][/ROW]
[ROW][C]9[/C][C]4.45[/C][C]4.44342866516411[/C][C]0.00657133483588712[/C][/ROW]
[ROW][C]10[/C][C]4.45[/C][C]4.45671593585729[/C][C]-0.00671593585729369[/C][/ROW]
[ROW][C]11[/C][C]4.45[/C][C]4.45335632937363[/C][C]-0.00335632937363162[/C][/ROW]
[ROW][C]12[/C][C]4.45[/C][C]4.45167734580908[/C][C]-0.00167734580908263[/C][/ROW]
[ROW][C]13[/C][C]4.45[/C][C]4.45083826366546[/C][C]-0.000838263665464467[/C][/ROW]
[ROW][C]14[/C][C]4.45[/C][C]4.45041892731304[/C][C]-0.000418927313040385[/C][/ROW]
[ROW][C]15[/C][C]4.45[/C][C]4.45020936144657[/C][C]-0.000209361446573020[/C][/ROW]
[ROW][C]16[/C][C]4.45[/C][C]4.45010462964325[/C][C]-0.000104629643249865[/C][/ROW]
[ROW][C]17[/C][C]4.46[/C][C]4.45005228929407[/C][C]0.00994771070593092[/C][/ROW]
[ROW][C]18[/C][C]4.46[/C][C]4.46502857169095[/C][C]-0.00502857169095172[/C][/ROW]
[ROW][C]19[/C][C]4.46[/C][C]4.46251305897382[/C][C]-0.00251305897381737[/C][/ROW]
[ROW][C]20[/C][C]4.48[/C][C]4.46125591635041[/C][C]0.0187440836495893[/C][/ROW]
[ROW][C]21[/C][C]4.58[/C][C]4.49063253135949[/C][C]0.089367468640515[/C][/ROW]
[ROW][C]22[/C][C]4.67[/C][C]4.63533806956785[/C][C]0.0346619304321507[/C][/ROW]
[ROW][C]23[/C][C]4.68[/C][C]4.7426774916068[/C][C]-0.062677491606796[/C][/ROW]
[ROW][C]24[/C][C]4.68[/C][C]4.7213234537398[/C][C]-0.0413234537398015[/C][/ROW]
[ROW][C]25[/C][C]4.69[/C][C]4.7006516447676[/C][C]-0.0106516447675951[/C][/ROW]
[ROW][C]26[/C][C]4.69[/C][C]4.70532322359395[/C][C]-0.0153232235939456[/C][/ROW]
[ROW][C]27[/C][C]4.69[/C][C]4.69765787323463[/C][C]-0.00765787323463307[/C][/ROW]
[ROW][C]28[/C][C]4.69[/C][C]4.69382706824828[/C][C]-0.00382706824828105[/C][/ROW]
[ROW][C]29[/C][C]4.69[/C][C]4.69191260039547[/C][C]-0.00191260039546837[/C][/ROW]
[ROW][C]30[/C][C]4.69[/C][C]4.69095583356121[/C][C]-0.000955833561208763[/C][/ROW]
[ROW][C]31[/C][C]4.69[/C][C]4.69047768357619[/C][C]-0.000477683576192156[/C][/ROW]
[ROW][C]32[/C][C]4.73[/C][C]4.69023872524279[/C][C]0.0397612747572129[/C][/ROW]
[ROW][C]33[/C][C]4.78[/C][C]4.75012906358304[/C][C]0.0298709364169589[/C][/ROW]
[ROW][C]34[/C][C]4.79[/C][C]4.81507181970697[/C][C]-0.0250718197069695[/C][/ROW]
[ROW][C]35[/C][C]4.79[/C][C]4.81252979282723[/C][C]-0.0225297928272346[/C][/ROW]
[ROW][C]36[/C][C]4.8[/C][C]4.80125939959146[/C][C]-0.00125939959145871[/C][/ROW]
[ROW][C]37[/C][C]4.8[/C][C]4.81062939252723[/C][C]-0.0106293925272318[/C][/ROW]
[ROW][C]38[/C][C]4.81[/C][C]4.80531210290287[/C][C]0.00468789709713135[/C][/ROW]
[ROW][C]39[/C][C]5.16[/C][C]4.81765719520526[/C][C]0.342342804794745[/C][/ROW]
[ROW][C]40[/C][C]5.26[/C][C]5.33891212245036[/C][C]-0.0789121224503582[/C][/ROW]
[ROW][C]41[/C][C]5.29[/C][C]5.39943680823397[/C][C]-0.109436808233968[/C][/ROW]
[ROW][C]42[/C][C]5.29[/C][C]5.37469170370846[/C][C]-0.0846917037084589[/C][/ROW]
[ROW][C]43[/C][C]5.29[/C][C]5.33232518875994[/C][C]-0.0423251887599356[/C][/ROW]
[ROW][C]44[/C][C]5.3[/C][C]5.3111522678742[/C][C]-0.0111522678742064[/C][/ROW]
[ROW][C]45[/C][C]5.3[/C][C]5.31557341300515[/C][C]-0.0155734130051508[/C][/ROW]
[ROW][C]46[/C][C]5.3[/C][C]5.30778290689899[/C][C]-0.00778290689898586[/C][/ROW]
[ROW][C]47[/C][C]5.3[/C][C]5.30388955457473[/C][C]-0.00388955457472662[/C][/ROW]
[ROW][C]48[/C][C]5.3[/C][C]5.30194382831327[/C][C]-0.00194382831326756[/C][/ROW]
[ROW][C]49[/C][C]5.3[/C][C]5.30097143990112[/C][C]-0.000971439901117144[/C][/ROW]
[ROW][C]50[/C][C]5.3[/C][C]5.30048548293851[/C][C]-0.00048548293850903[/C][/ROW]
[ROW][C]51[/C][C]5.3[/C][C]5.30024262302106[/C][C]-0.000242623021056154[/C][/ROW]
[ROW][C]52[/C][C]5.35[/C][C]5.30012125231533[/C][C]0.049878747684672[/C][/ROW]
[ROW][C]53[/C][C]5.44[/C][C]5.37507279558184[/C][C]0.0649272044181606[/C][/ROW]
[ROW][C]54[/C][C]5.47[/C][C]5.49755223873978[/C][C]-0.0275522387397791[/C][/ROW]
[ROW][C]55[/C][C]5.47[/C][C]5.51376939717064[/C][C]-0.0437693971706397[/C][/ROW]
[ROW][C]56[/C][C]5.48[/C][C]5.49187401972138[/C][C]-0.0118740197213771[/C][/ROW]
[ROW][C]57[/C][C]5.48[/C][C]5.49593411283562[/C][C]-0.0159341128356161[/C][/ROW]
[ROW][C]58[/C][C]5.48[/C][C]5.48796316881062[/C][C]-0.00796316881062076[/C][/ROW]
[ROW][C]59[/C][C]5.48[/C][C]5.48397964155022[/C][C]-0.0039796415502158[/C][/ROW]
[ROW][C]60[/C][C]5.48[/C][C]5.48198884982158[/C][C]-0.00198884982157921[/C][/ROW]
[ROW][C]61[/C][C]5.48[/C][C]5.48099393967092[/C][C]-0.00099393967091821[/C][/ROW]
[ROW][C]62[/C][C]5.48[/C][C]5.48049672733391[/C][C]-0.000496727333912261[/C][/ROW]
[ROW][C]63[/C][C]5.5[/C][C]5.48024824247535[/C][C]0.0197517575246513[/C][/ROW]
[ROW][C]64[/C][C]5.55[/C][C]5.51012894027437[/C][C]0.0398710597256278[/C][/ROW]
[ROW][C]65[/C][C]5.57[/C][C]5.58007419788419[/C][C]-0.0100741978841858[/C][/ROW]
[ROW][C]66[/C][C]5.58[/C][C]5.59503464103782[/C][C]-0.0150346410378157[/C][/ROW]
[ROW][C]67[/C][C]5.58[/C][C]5.59751365236498[/C][C]-0.0175136523649817[/C][/ROW]
[ROW][C]68[/C][C]5.58[/C][C]5.58875255319902[/C][C]-0.00875255319901846[/C][/ROW]
[ROW][C]69[/C][C]5.59[/C][C]5.5843741411503[/C][C]0.00562585884970446[/C][/ROW]
[ROW][C]70[/C][C]5.59[/C][C]5.59718844317301[/C][C]-0.00718844317301492[/C][/ROW]
[ROW][C]71[/C][C]5.59[/C][C]5.59359246774909[/C][C]-0.00359246774908772[/C][/ROW]
[ROW][C]72[/C][C]5.55[/C][C]5.59179535738374[/C][C]-0.0417953573837355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112836&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112836&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
34.434.53-0.0999999999999996
44.444.52997560198533-0.0899756019853308
54.444.49496584873210-0.0549658487320954
64.444.46746951379021-0.0274695137902112
74.444.4537280548791-0.0137280548791017
84.444.44686067806671-0.0068606780667082
94.454.443428665164110.00657133483588712
104.454.45671593585729-0.00671593585729369
114.454.45335632937363-0.00335632937363162
124.454.45167734580908-0.00167734580908263
134.454.45083826366546-0.000838263665464467
144.454.45041892731304-0.000418927313040385
154.454.45020936144657-0.000209361446573020
164.454.45010462964325-0.000104629643249865
174.464.450052289294070.00994771070593092
184.464.46502857169095-0.00502857169095172
194.464.46251305897382-0.00251305897381737
204.484.461255916350410.0187440836495893
214.584.490632531359490.089367468640515
224.674.635338069567850.0346619304321507
234.684.7426774916068-0.062677491606796
244.684.7213234537398-0.0413234537398015
254.694.7006516447676-0.0106516447675951
264.694.70532322359395-0.0153232235939456
274.694.69765787323463-0.00765787323463307
284.694.69382706824828-0.00382706824828105
294.694.69191260039547-0.00191260039546837
304.694.69095583356121-0.000955833561208763
314.694.69047768357619-0.000477683576192156
324.734.690238725242790.0397612747572129
334.784.750129063583040.0298709364169589
344.794.81507181970697-0.0250718197069695
354.794.81252979282723-0.0225297928272346
364.84.80125939959146-0.00125939959145871
374.84.81062939252723-0.0106293925272318
384.814.805312102902870.00468789709713135
395.164.817657195205260.342342804794745
405.265.33891212245036-0.0789121224503582
415.295.39943680823397-0.109436808233968
425.295.37469170370846-0.0846917037084589
435.295.33232518875994-0.0423251887599356
445.35.3111522678742-0.0111522678742064
455.35.31557341300515-0.0155734130051508
465.35.30778290689899-0.00778290689898586
475.35.30388955457473-0.00388955457472662
485.35.30194382831327-0.00194382831326756
495.35.30097143990112-0.000971439901117144
505.35.30048548293851-0.00048548293850903
515.35.30024262302106-0.000242623021056154
525.355.300121252315330.049878747684672
535.445.375072795581840.0649272044181606
545.475.49755223873978-0.0275522387397791
555.475.51376939717064-0.0437693971706397
565.485.49187401972138-0.0118740197213771
575.485.49593411283562-0.0159341128356161
585.485.48796316881062-0.00796316881062076
595.485.48397964155022-0.0039796415502158
605.485.48198884982158-0.00198884982157921
615.485.48099393967092-0.00099393967091821
625.485.48049672733391-0.000496727333912261
635.55.480248242475350.0197517575246513
645.555.510128940274370.0398710597256278
655.575.58007419788419-0.0100741978841858
665.585.59503464103782-0.0150346410378157
675.585.59751365236498-0.0175136523649817
685.585.58875255319902-0.00875255319901846
695.595.58437414115030.00562585884970446
705.595.59718844317301-0.00718844317301492
715.595.59359246774909-0.00359246774908772
725.555.59179535738374-0.0417953573837355







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.530887481454445.42556164278445.63621332012448
745.511774962908895.321874724855345.70167520096243
755.492662444363335.209011452767145.77631343595951
765.473549925817775.086467160994255.86063269064129
775.454437407272214.954697648545425.95417716599901
785.435324888726664.814252956829916.0563968206234
795.41621237018114.665641386258806.16678335410339
805.397099851635544.50930968550936.28489001776179
815.377987333089984.345647148483736.41032751769623
825.358874814544434.174994070709546.54275555837931
835.339762295998873.997649917563026.68187467443472
845.320649777453313.813880219887946.82741933501868

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.53088748145444 & 5.4255616427844 & 5.63621332012448 \tabularnewline
74 & 5.51177496290889 & 5.32187472485534 & 5.70167520096243 \tabularnewline
75 & 5.49266244436333 & 5.20901145276714 & 5.77631343595951 \tabularnewline
76 & 5.47354992581777 & 5.08646716099425 & 5.86063269064129 \tabularnewline
77 & 5.45443740727221 & 4.95469764854542 & 5.95417716599901 \tabularnewline
78 & 5.43532488872666 & 4.81425295682991 & 6.0563968206234 \tabularnewline
79 & 5.4162123701811 & 4.66564138625880 & 6.16678335410339 \tabularnewline
80 & 5.39709985163554 & 4.5093096855093 & 6.28489001776179 \tabularnewline
81 & 5.37798733308998 & 4.34564714848373 & 6.41032751769623 \tabularnewline
82 & 5.35887481454443 & 4.17499407070954 & 6.54275555837931 \tabularnewline
83 & 5.33976229599887 & 3.99764991756302 & 6.68187467443472 \tabularnewline
84 & 5.32064977745331 & 3.81388021988794 & 6.82741933501868 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112836&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]5.53088748145444[/C][C]5.4255616427844[/C][C]5.63621332012448[/C][/ROW]
[ROW][C]74[/C][C]5.51177496290889[/C][C]5.32187472485534[/C][C]5.70167520096243[/C][/ROW]
[ROW][C]75[/C][C]5.49266244436333[/C][C]5.20901145276714[/C][C]5.77631343595951[/C][/ROW]
[ROW][C]76[/C][C]5.47354992581777[/C][C]5.08646716099425[/C][C]5.86063269064129[/C][/ROW]
[ROW][C]77[/C][C]5.45443740727221[/C][C]4.95469764854542[/C][C]5.95417716599901[/C][/ROW]
[ROW][C]78[/C][C]5.43532488872666[/C][C]4.81425295682991[/C][C]6.0563968206234[/C][/ROW]
[ROW][C]79[/C][C]5.4162123701811[/C][C]4.66564138625880[/C][C]6.16678335410339[/C][/ROW]
[ROW][C]80[/C][C]5.39709985163554[/C][C]4.5093096855093[/C][C]6.28489001776179[/C][/ROW]
[ROW][C]81[/C][C]5.37798733308998[/C][C]4.34564714848373[/C][C]6.41032751769623[/C][/ROW]
[ROW][C]82[/C][C]5.35887481454443[/C][C]4.17499407070954[/C][C]6.54275555837931[/C][/ROW]
[ROW][C]83[/C][C]5.33976229599887[/C][C]3.99764991756302[/C][C]6.68187467443472[/C][/ROW]
[ROW][C]84[/C][C]5.32064977745331[/C][C]3.81388021988794[/C][C]6.82741933501868[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112836&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112836&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
735.530887481454445.42556164278445.63621332012448
745.511774962908895.321874724855345.70167520096243
755.492662444363335.209011452767145.77631343595951
765.473549925817775.086467160994255.86063269064129
775.454437407272214.954697648545425.95417716599901
785.435324888726664.814252956829916.0563968206234
795.41621237018114.665641386258806.16678335410339
805.397099851635544.50930968550936.28489001776179
815.377987333089984.345647148483736.41032751769623
825.358874814544434.174994070709546.54275555837931
835.339762295998873.997649917563026.68187467443472
845.320649777453313.813880219887946.82741933501868



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
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')