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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 computationSun, 07 Jun 2009 14:09:31 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/07/t12444055084y3e31ez43k253d.htm/, Retrieved Mon, 13 May 2024 06:36:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42255, Retrieved Mon, 13 May 2024 06:36:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [thomas van eester...] [2009-06-07 20:09:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
0.63
0.63
0.63
0.64
0.63
0.63
0.63
0.63
0.63
0.64
0.65
0.65
0.65
0.65
0.65
0.66
0.65
0.66
0.66
0.66
0.66
0.68
0.69
0.7
0.71
0.71
0.7
0.7
0.7
0.7
0.71
0.7
0.7
0.7
0.69
0.7
0.69
0.69
0.69
0.7
0.7
0.71
0.71
0.71
0.72
0.73
0.74
0.74
0.74
0.74
0.75
0.75
0.76
0.76
0.76
0.76
0.76
0.77
0.77
0.78
0.78
0.78
0.78
0.78
0.78
0.78
0.8
0.8
0.8
0.81
0.81
0.81
0.8
0.81
0.81
0.81
0.8
0.82
0.83
0.83




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42255&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42255&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.891917722178237
beta0.0383687115475383
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.891917722178237 \tabularnewline
beta & 0.0383687115475383 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42255&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]0.891917722178237[/C][/ROW]
[ROW][C]beta[/C][C]0.0383687115475383[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42255&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
alpha0.891917722178237
beta0.0383687115475383
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.630.630
40.640.630.01
50.630.639261394559846-0.00926139455984631
60.630.631026268978595-0.00102626897859526
70.630.630101077143826-0.000101077143826012
80.630.6299976212677922.37873220787499e-06
90.630.6299865209253971.34790746032509e-05
100.640.6299857824524090.0100142175475909
110.650.6392475837455420.0107524162544581
120.650.6495357638746540.000464236125345852
130.650.650663620782754-0.00066362078275406
140.650.650762811872663-0.000762811872662805
150.650.650747427926749-0.000747427926749089
160.660.6507201869152840.00927981308471582
170.650.659953991159656-0.00995399115965556
180.660.6516921816977880.00830781830221183
190.660.660002711680453-2.71168045262726e-06
200.660.660900839892478-0.000900839892478467
210.660.660967083332408-0.000967083332407581
220.680.6609411478059160.0190588521940843
230.690.6794289260451420.0105710739548579
240.70.6907080649298140.00929193507018555
250.710.7011643033026380.0088356966973615
260.710.711515987445574-0.00151598744557402
270.70.712582941328218-0.0125829413282177
280.70.703348472843767-0.00334847284376660
290.70.702235799909176-0.00223579990917644
300.70.702039026734599-0.00203902673459910
310.710.7019479800115410.00805201998845906
320.70.711132870780756-0.0111328707807559
330.70.702825431334494-0.0028254313344942
340.70.701830853197259-0.00183085319725873
350.690.70166070195596-0.0116607019559594
360.70.692324084962110.00767591503788945
370.690.700496822473196-0.0104968224731956
380.690.69210175387316-0.00210175387315992
390.690.691122470074824-0.00112247007482424
400.70.690978213979160.00902178602084003
410.70.700190540833197-0.000190540833196695
420.710.7011797094659470.00882029053405331
430.710.710507643921458-0.000507643921457968
440.710.711498455869633-0.00149845586963304
450.720.7115542653239940.0084457346760064
460.730.7207685022426090.00923149775739096
470.740.7309994930378330.00900050696216748
480.740.741332472002518-0.00133247200251796
490.740.742403684403531-0.00240368440353089
500.740.742437205232051-0.00243720523205115
510.750.7423574228508690.00764257714913075
520.750.751529519251956-0.00152951925195577
530.760.7524685175226940.00753148247730606
540.760.761746924204954-0.00174692420495415
550.760.762689972758608-0.00268997275860772
560.760.762699844062692-0.00269984406269164
570.760.76260851763089-0.00260851763088987
580.770.7625093788661220.00749062113387833
590.770.771674182986876-0.00167418298687572
600.780.7726074424475170.00739255755248303
610.780.781880474614314-0.00188047461431362
620.780.782818371951535-0.00281837195153478
630.780.782823292457412-0.00282329245741186
640.780.78272720631396-0.00272720631395995
650.780.782623491376197-0.00262349137619700
660.780.78252250120596-0.00252250120595987
670.80.7824252615935260.0175747384064736
680.80.800854544177748-0.000854544177748218
690.80.802817179034695-0.00281717903469514
700.810.8029328963295560.00706710367044405
710.810.812106429080742-0.00210642908074243
720.810.81302583974088-0.00302583974088
730.80.813021662257128-0.0130216622571281
740.810.8036564096639060.006343590336094
750.810.811780457712896-0.00178045771289548
760.810.81259759298126-0.00259759298125939
770.80.81259701668681-0.0125970166868107
780.820.8032466854260010.0167533145739991
790.830.8206477622402350.00935223775976457
800.830.83176773727176-0.00176773727176049

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.63 & 0.63 & 0 \tabularnewline
4 & 0.64 & 0.63 & 0.01 \tabularnewline
5 & 0.63 & 0.639261394559846 & -0.00926139455984631 \tabularnewline
6 & 0.63 & 0.631026268978595 & -0.00102626897859526 \tabularnewline
7 & 0.63 & 0.630101077143826 & -0.000101077143826012 \tabularnewline
8 & 0.63 & 0.629997621267792 & 2.37873220787499e-06 \tabularnewline
9 & 0.63 & 0.629986520925397 & 1.34790746032509e-05 \tabularnewline
10 & 0.64 & 0.629985782452409 & 0.0100142175475909 \tabularnewline
11 & 0.65 & 0.639247583745542 & 0.0107524162544581 \tabularnewline
12 & 0.65 & 0.649535763874654 & 0.000464236125345852 \tabularnewline
13 & 0.65 & 0.650663620782754 & -0.00066362078275406 \tabularnewline
14 & 0.65 & 0.650762811872663 & -0.000762811872662805 \tabularnewline
15 & 0.65 & 0.650747427926749 & -0.000747427926749089 \tabularnewline
16 & 0.66 & 0.650720186915284 & 0.00927981308471582 \tabularnewline
17 & 0.65 & 0.659953991159656 & -0.00995399115965556 \tabularnewline
18 & 0.66 & 0.651692181697788 & 0.00830781830221183 \tabularnewline
19 & 0.66 & 0.660002711680453 & -2.71168045262726e-06 \tabularnewline
20 & 0.66 & 0.660900839892478 & -0.000900839892478467 \tabularnewline
21 & 0.66 & 0.660967083332408 & -0.000967083332407581 \tabularnewline
22 & 0.68 & 0.660941147805916 & 0.0190588521940843 \tabularnewline
23 & 0.69 & 0.679428926045142 & 0.0105710739548579 \tabularnewline
24 & 0.7 & 0.690708064929814 & 0.00929193507018555 \tabularnewline
25 & 0.71 & 0.701164303302638 & 0.0088356966973615 \tabularnewline
26 & 0.71 & 0.711515987445574 & -0.00151598744557402 \tabularnewline
27 & 0.7 & 0.712582941328218 & -0.0125829413282177 \tabularnewline
28 & 0.7 & 0.703348472843767 & -0.00334847284376660 \tabularnewline
29 & 0.7 & 0.702235799909176 & -0.00223579990917644 \tabularnewline
30 & 0.7 & 0.702039026734599 & -0.00203902673459910 \tabularnewline
31 & 0.71 & 0.701947980011541 & 0.00805201998845906 \tabularnewline
32 & 0.7 & 0.711132870780756 & -0.0111328707807559 \tabularnewline
33 & 0.7 & 0.702825431334494 & -0.0028254313344942 \tabularnewline
34 & 0.7 & 0.701830853197259 & -0.00183085319725873 \tabularnewline
35 & 0.69 & 0.70166070195596 & -0.0116607019559594 \tabularnewline
36 & 0.7 & 0.69232408496211 & 0.00767591503788945 \tabularnewline
37 & 0.69 & 0.700496822473196 & -0.0104968224731956 \tabularnewline
38 & 0.69 & 0.69210175387316 & -0.00210175387315992 \tabularnewline
39 & 0.69 & 0.691122470074824 & -0.00112247007482424 \tabularnewline
40 & 0.7 & 0.69097821397916 & 0.00902178602084003 \tabularnewline
41 & 0.7 & 0.700190540833197 & -0.000190540833196695 \tabularnewline
42 & 0.71 & 0.701179709465947 & 0.00882029053405331 \tabularnewline
43 & 0.71 & 0.710507643921458 & -0.000507643921457968 \tabularnewline
44 & 0.71 & 0.711498455869633 & -0.00149845586963304 \tabularnewline
45 & 0.72 & 0.711554265323994 & 0.0084457346760064 \tabularnewline
46 & 0.73 & 0.720768502242609 & 0.00923149775739096 \tabularnewline
47 & 0.74 & 0.730999493037833 & 0.00900050696216748 \tabularnewline
48 & 0.74 & 0.741332472002518 & -0.00133247200251796 \tabularnewline
49 & 0.74 & 0.742403684403531 & -0.00240368440353089 \tabularnewline
50 & 0.74 & 0.742437205232051 & -0.00243720523205115 \tabularnewline
51 & 0.75 & 0.742357422850869 & 0.00764257714913075 \tabularnewline
52 & 0.75 & 0.751529519251956 & -0.00152951925195577 \tabularnewline
53 & 0.76 & 0.752468517522694 & 0.00753148247730606 \tabularnewline
54 & 0.76 & 0.761746924204954 & -0.00174692420495415 \tabularnewline
55 & 0.76 & 0.762689972758608 & -0.00268997275860772 \tabularnewline
56 & 0.76 & 0.762699844062692 & -0.00269984406269164 \tabularnewline
57 & 0.76 & 0.76260851763089 & -0.00260851763088987 \tabularnewline
58 & 0.77 & 0.762509378866122 & 0.00749062113387833 \tabularnewline
59 & 0.77 & 0.771674182986876 & -0.00167418298687572 \tabularnewline
60 & 0.78 & 0.772607442447517 & 0.00739255755248303 \tabularnewline
61 & 0.78 & 0.781880474614314 & -0.00188047461431362 \tabularnewline
62 & 0.78 & 0.782818371951535 & -0.00281837195153478 \tabularnewline
63 & 0.78 & 0.782823292457412 & -0.00282329245741186 \tabularnewline
64 & 0.78 & 0.78272720631396 & -0.00272720631395995 \tabularnewline
65 & 0.78 & 0.782623491376197 & -0.00262349137619700 \tabularnewline
66 & 0.78 & 0.78252250120596 & -0.00252250120595987 \tabularnewline
67 & 0.8 & 0.782425261593526 & 0.0175747384064736 \tabularnewline
68 & 0.8 & 0.800854544177748 & -0.000854544177748218 \tabularnewline
69 & 0.8 & 0.802817179034695 & -0.00281717903469514 \tabularnewline
70 & 0.81 & 0.802932896329556 & 0.00706710367044405 \tabularnewline
71 & 0.81 & 0.812106429080742 & -0.00210642908074243 \tabularnewline
72 & 0.81 & 0.81302583974088 & -0.00302583974088 \tabularnewline
73 & 0.8 & 0.813021662257128 & -0.0130216622571281 \tabularnewline
74 & 0.81 & 0.803656409663906 & 0.006343590336094 \tabularnewline
75 & 0.81 & 0.811780457712896 & -0.00178045771289548 \tabularnewline
76 & 0.81 & 0.81259759298126 & -0.00259759298125939 \tabularnewline
77 & 0.8 & 0.81259701668681 & -0.0125970166868107 \tabularnewline
78 & 0.82 & 0.803246685426001 & 0.0167533145739991 \tabularnewline
79 & 0.83 & 0.820647762240235 & 0.00935223775976457 \tabularnewline
80 & 0.83 & 0.83176773727176 & -0.00176773727176049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42255&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]0.63[/C][C]0.63[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.64[/C][C]0.63[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]0.63[/C][C]0.639261394559846[/C][C]-0.00926139455984631[/C][/ROW]
[ROW][C]6[/C][C]0.63[/C][C]0.631026268978595[/C][C]-0.00102626897859526[/C][/ROW]
[ROW][C]7[/C][C]0.63[/C][C]0.630101077143826[/C][C]-0.000101077143826012[/C][/ROW]
[ROW][C]8[/C][C]0.63[/C][C]0.629997621267792[/C][C]2.37873220787499e-06[/C][/ROW]
[ROW][C]9[/C][C]0.63[/C][C]0.629986520925397[/C][C]1.34790746032509e-05[/C][/ROW]
[ROW][C]10[/C][C]0.64[/C][C]0.629985782452409[/C][C]0.0100142175475909[/C][/ROW]
[ROW][C]11[/C][C]0.65[/C][C]0.639247583745542[/C][C]0.0107524162544581[/C][/ROW]
[ROW][C]12[/C][C]0.65[/C][C]0.649535763874654[/C][C]0.000464236125345852[/C][/ROW]
[ROW][C]13[/C][C]0.65[/C][C]0.650663620782754[/C][C]-0.00066362078275406[/C][/ROW]
[ROW][C]14[/C][C]0.65[/C][C]0.650762811872663[/C][C]-0.000762811872662805[/C][/ROW]
[ROW][C]15[/C][C]0.65[/C][C]0.650747427926749[/C][C]-0.000747427926749089[/C][/ROW]
[ROW][C]16[/C][C]0.66[/C][C]0.650720186915284[/C][C]0.00927981308471582[/C][/ROW]
[ROW][C]17[/C][C]0.65[/C][C]0.659953991159656[/C][C]-0.00995399115965556[/C][/ROW]
[ROW][C]18[/C][C]0.66[/C][C]0.651692181697788[/C][C]0.00830781830221183[/C][/ROW]
[ROW][C]19[/C][C]0.66[/C][C]0.660002711680453[/C][C]-2.71168045262726e-06[/C][/ROW]
[ROW][C]20[/C][C]0.66[/C][C]0.660900839892478[/C][C]-0.000900839892478467[/C][/ROW]
[ROW][C]21[/C][C]0.66[/C][C]0.660967083332408[/C][C]-0.000967083332407581[/C][/ROW]
[ROW][C]22[/C][C]0.68[/C][C]0.660941147805916[/C][C]0.0190588521940843[/C][/ROW]
[ROW][C]23[/C][C]0.69[/C][C]0.679428926045142[/C][C]0.0105710739548579[/C][/ROW]
[ROW][C]24[/C][C]0.7[/C][C]0.690708064929814[/C][C]0.00929193507018555[/C][/ROW]
[ROW][C]25[/C][C]0.71[/C][C]0.701164303302638[/C][C]0.0088356966973615[/C][/ROW]
[ROW][C]26[/C][C]0.71[/C][C]0.711515987445574[/C][C]-0.00151598744557402[/C][/ROW]
[ROW][C]27[/C][C]0.7[/C][C]0.712582941328218[/C][C]-0.0125829413282177[/C][/ROW]
[ROW][C]28[/C][C]0.7[/C][C]0.703348472843767[/C][C]-0.00334847284376660[/C][/ROW]
[ROW][C]29[/C][C]0.7[/C][C]0.702235799909176[/C][C]-0.00223579990917644[/C][/ROW]
[ROW][C]30[/C][C]0.7[/C][C]0.702039026734599[/C][C]-0.00203902673459910[/C][/ROW]
[ROW][C]31[/C][C]0.71[/C][C]0.701947980011541[/C][C]0.00805201998845906[/C][/ROW]
[ROW][C]32[/C][C]0.7[/C][C]0.711132870780756[/C][C]-0.0111328707807559[/C][/ROW]
[ROW][C]33[/C][C]0.7[/C][C]0.702825431334494[/C][C]-0.0028254313344942[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]0.701830853197259[/C][C]-0.00183085319725873[/C][/ROW]
[ROW][C]35[/C][C]0.69[/C][C]0.70166070195596[/C][C]-0.0116607019559594[/C][/ROW]
[ROW][C]36[/C][C]0.7[/C][C]0.69232408496211[/C][C]0.00767591503788945[/C][/ROW]
[ROW][C]37[/C][C]0.69[/C][C]0.700496822473196[/C][C]-0.0104968224731956[/C][/ROW]
[ROW][C]38[/C][C]0.69[/C][C]0.69210175387316[/C][C]-0.00210175387315992[/C][/ROW]
[ROW][C]39[/C][C]0.69[/C][C]0.691122470074824[/C][C]-0.00112247007482424[/C][/ROW]
[ROW][C]40[/C][C]0.7[/C][C]0.69097821397916[/C][C]0.00902178602084003[/C][/ROW]
[ROW][C]41[/C][C]0.7[/C][C]0.700190540833197[/C][C]-0.000190540833196695[/C][/ROW]
[ROW][C]42[/C][C]0.71[/C][C]0.701179709465947[/C][C]0.00882029053405331[/C][/ROW]
[ROW][C]43[/C][C]0.71[/C][C]0.710507643921458[/C][C]-0.000507643921457968[/C][/ROW]
[ROW][C]44[/C][C]0.71[/C][C]0.711498455869633[/C][C]-0.00149845586963304[/C][/ROW]
[ROW][C]45[/C][C]0.72[/C][C]0.711554265323994[/C][C]0.0084457346760064[/C][/ROW]
[ROW][C]46[/C][C]0.73[/C][C]0.720768502242609[/C][C]0.00923149775739096[/C][/ROW]
[ROW][C]47[/C][C]0.74[/C][C]0.730999493037833[/C][C]0.00900050696216748[/C][/ROW]
[ROW][C]48[/C][C]0.74[/C][C]0.741332472002518[/C][C]-0.00133247200251796[/C][/ROW]
[ROW][C]49[/C][C]0.74[/C][C]0.742403684403531[/C][C]-0.00240368440353089[/C][/ROW]
[ROW][C]50[/C][C]0.74[/C][C]0.742437205232051[/C][C]-0.00243720523205115[/C][/ROW]
[ROW][C]51[/C][C]0.75[/C][C]0.742357422850869[/C][C]0.00764257714913075[/C][/ROW]
[ROW][C]52[/C][C]0.75[/C][C]0.751529519251956[/C][C]-0.00152951925195577[/C][/ROW]
[ROW][C]53[/C][C]0.76[/C][C]0.752468517522694[/C][C]0.00753148247730606[/C][/ROW]
[ROW][C]54[/C][C]0.76[/C][C]0.761746924204954[/C][C]-0.00174692420495415[/C][/ROW]
[ROW][C]55[/C][C]0.76[/C][C]0.762689972758608[/C][C]-0.00268997275860772[/C][/ROW]
[ROW][C]56[/C][C]0.76[/C][C]0.762699844062692[/C][C]-0.00269984406269164[/C][/ROW]
[ROW][C]57[/C][C]0.76[/C][C]0.76260851763089[/C][C]-0.00260851763088987[/C][/ROW]
[ROW][C]58[/C][C]0.77[/C][C]0.762509378866122[/C][C]0.00749062113387833[/C][/ROW]
[ROW][C]59[/C][C]0.77[/C][C]0.771674182986876[/C][C]-0.00167418298687572[/C][/ROW]
[ROW][C]60[/C][C]0.78[/C][C]0.772607442447517[/C][C]0.00739255755248303[/C][/ROW]
[ROW][C]61[/C][C]0.78[/C][C]0.781880474614314[/C][C]-0.00188047461431362[/C][/ROW]
[ROW][C]62[/C][C]0.78[/C][C]0.782818371951535[/C][C]-0.00281837195153478[/C][/ROW]
[ROW][C]63[/C][C]0.78[/C][C]0.782823292457412[/C][C]-0.00282329245741186[/C][/ROW]
[ROW][C]64[/C][C]0.78[/C][C]0.78272720631396[/C][C]-0.00272720631395995[/C][/ROW]
[ROW][C]65[/C][C]0.78[/C][C]0.782623491376197[/C][C]-0.00262349137619700[/C][/ROW]
[ROW][C]66[/C][C]0.78[/C][C]0.78252250120596[/C][C]-0.00252250120595987[/C][/ROW]
[ROW][C]67[/C][C]0.8[/C][C]0.782425261593526[/C][C]0.0175747384064736[/C][/ROW]
[ROW][C]68[/C][C]0.8[/C][C]0.800854544177748[/C][C]-0.000854544177748218[/C][/ROW]
[ROW][C]69[/C][C]0.8[/C][C]0.802817179034695[/C][C]-0.00281717903469514[/C][/ROW]
[ROW][C]70[/C][C]0.81[/C][C]0.802932896329556[/C][C]0.00706710367044405[/C][/ROW]
[ROW][C]71[/C][C]0.81[/C][C]0.812106429080742[/C][C]-0.00210642908074243[/C][/ROW]
[ROW][C]72[/C][C]0.81[/C][C]0.81302583974088[/C][C]-0.00302583974088[/C][/ROW]
[ROW][C]73[/C][C]0.8[/C][C]0.813021662257128[/C][C]-0.0130216622571281[/C][/ROW]
[ROW][C]74[/C][C]0.81[/C][C]0.803656409663906[/C][C]0.006343590336094[/C][/ROW]
[ROW][C]75[/C][C]0.81[/C][C]0.811780457712896[/C][C]-0.00178045771289548[/C][/ROW]
[ROW][C]76[/C][C]0.81[/C][C]0.81259759298126[/C][C]-0.00259759298125939[/C][/ROW]
[ROW][C]77[/C][C]0.8[/C][C]0.81259701668681[/C][C]-0.0125970166868107[/C][/ROW]
[ROW][C]78[/C][C]0.82[/C][C]0.803246685426001[/C][C]0.0167533145739991[/C][/ROW]
[ROW][C]79[/C][C]0.83[/C][C]0.820647762240235[/C][C]0.00935223775976457[/C][/ROW]
[ROW][C]80[/C][C]0.83[/C][C]0.83176773727176[/C][C]-0.00176773727176049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42255&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42255&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
30.630.630
40.640.630.01
50.630.639261394559846-0.00926139455984631
60.630.631026268978595-0.00102626897859526
70.630.630101077143826-0.000101077143826012
80.630.6299976212677922.37873220787499e-06
90.630.6299865209253971.34790746032509e-05
100.640.6299857824524090.0100142175475909
110.650.6392475837455420.0107524162544581
120.650.6495357638746540.000464236125345852
130.650.650663620782754-0.00066362078275406
140.650.650762811872663-0.000762811872662805
150.650.650747427926749-0.000747427926749089
160.660.6507201869152840.00927981308471582
170.650.659953991159656-0.00995399115965556
180.660.6516921816977880.00830781830221183
190.660.660002711680453-2.71168045262726e-06
200.660.660900839892478-0.000900839892478467
210.660.660967083332408-0.000967083332407581
220.680.6609411478059160.0190588521940843
230.690.6794289260451420.0105710739548579
240.70.6907080649298140.00929193507018555
250.710.7011643033026380.0088356966973615
260.710.711515987445574-0.00151598744557402
270.70.712582941328218-0.0125829413282177
280.70.703348472843767-0.00334847284376660
290.70.702235799909176-0.00223579990917644
300.70.702039026734599-0.00203902673459910
310.710.7019479800115410.00805201998845906
320.70.711132870780756-0.0111328707807559
330.70.702825431334494-0.0028254313344942
340.70.701830853197259-0.00183085319725873
350.690.70166070195596-0.0116607019559594
360.70.692324084962110.00767591503788945
370.690.700496822473196-0.0104968224731956
380.690.69210175387316-0.00210175387315992
390.690.691122470074824-0.00112247007482424
400.70.690978213979160.00902178602084003
410.70.700190540833197-0.000190540833196695
420.710.7011797094659470.00882029053405331
430.710.710507643921458-0.000507643921457968
440.710.711498455869633-0.00149845586963304
450.720.7115542653239940.0084457346760064
460.730.7207685022426090.00923149775739096
470.740.7309994930378330.00900050696216748
480.740.741332472002518-0.00133247200251796
490.740.742403684403531-0.00240368440353089
500.740.742437205232051-0.00243720523205115
510.750.7423574228508690.00764257714913075
520.750.751529519251956-0.00152951925195577
530.760.7524685175226940.00753148247730606
540.760.761746924204954-0.00174692420495415
550.760.762689972758608-0.00268997275860772
560.760.762699844062692-0.00269984406269164
570.760.76260851763089-0.00260851763088987
580.770.7625093788661220.00749062113387833
590.770.771674182986876-0.00167418298687572
600.780.7726074424475170.00739255755248303
610.780.781880474614314-0.00188047461431362
620.780.782818371951535-0.00281837195153478
630.780.782823292457412-0.00282329245741186
640.780.78272720631396-0.00272720631395995
650.780.782623491376197-0.00262349137619700
660.780.78252250120596-0.00252250120595987
670.80.7824252615935260.0175747384064736
680.80.800854544177748-0.000854544177748218
690.80.802817179034695-0.00281717903469514
700.810.8029328963295560.00706710367044405
710.810.812106429080742-0.00210642908074243
720.810.81302583974088-0.00302583974088
730.80.813021662257128-0.0130216622571281
740.810.8036564096639060.006343590336094
750.810.811780457712896-0.00178045771289548
760.810.81259759298126-0.00259759298125939
770.80.81259701668681-0.0125970166868107
780.820.8032466854260010.0167533145739991
790.830.8206477622402350.00935223775976457
800.830.83176773727176-0.00176773727176049







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
810.8329091144681350.8192313310497990.84658689788647
820.8356271678653480.8169845232157010.854269812514994
830.838345221262560.8155396844011930.861150758123928
840.8410632746597730.8145085596684820.867617989651064
850.8437813280569860.8137285823794850.873834073734487
860.8464993814541980.8131141360900870.87988462681831
870.8492174348514110.812613987785760.885820881917062
880.8519354882486240.8121948427710080.89167613372624
890.8546535416458370.8118337740295340.89747330926214
900.857371595043050.8115143020863050.903228887999794
910.8600896484402620.8112241846460820.908955112234442
920.8628077018374750.8109540867731790.91466131690177

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 0.832909114468135 & 0.819231331049799 & 0.84658689788647 \tabularnewline
82 & 0.835627167865348 & 0.816984523215701 & 0.854269812514994 \tabularnewline
83 & 0.83834522126256 & 0.815539684401193 & 0.861150758123928 \tabularnewline
84 & 0.841063274659773 & 0.814508559668482 & 0.867617989651064 \tabularnewline
85 & 0.843781328056986 & 0.813728582379485 & 0.873834073734487 \tabularnewline
86 & 0.846499381454198 & 0.813114136090087 & 0.87988462681831 \tabularnewline
87 & 0.849217434851411 & 0.81261398778576 & 0.885820881917062 \tabularnewline
88 & 0.851935488248624 & 0.812194842771008 & 0.89167613372624 \tabularnewline
89 & 0.854653541645837 & 0.811833774029534 & 0.89747330926214 \tabularnewline
90 & 0.85737159504305 & 0.811514302086305 & 0.903228887999794 \tabularnewline
91 & 0.860089648440262 & 0.811224184646082 & 0.908955112234442 \tabularnewline
92 & 0.862807701837475 & 0.810954086773179 & 0.91466131690177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42255&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]81[/C][C]0.832909114468135[/C][C]0.819231331049799[/C][C]0.84658689788647[/C][/ROW]
[ROW][C]82[/C][C]0.835627167865348[/C][C]0.816984523215701[/C][C]0.854269812514994[/C][/ROW]
[ROW][C]83[/C][C]0.83834522126256[/C][C]0.815539684401193[/C][C]0.861150758123928[/C][/ROW]
[ROW][C]84[/C][C]0.841063274659773[/C][C]0.814508559668482[/C][C]0.867617989651064[/C][/ROW]
[ROW][C]85[/C][C]0.843781328056986[/C][C]0.813728582379485[/C][C]0.873834073734487[/C][/ROW]
[ROW][C]86[/C][C]0.846499381454198[/C][C]0.813114136090087[/C][C]0.87988462681831[/C][/ROW]
[ROW][C]87[/C][C]0.849217434851411[/C][C]0.81261398778576[/C][C]0.885820881917062[/C][/ROW]
[ROW][C]88[/C][C]0.851935488248624[/C][C]0.812194842771008[/C][C]0.89167613372624[/C][/ROW]
[ROW][C]89[/C][C]0.854653541645837[/C][C]0.811833774029534[/C][C]0.89747330926214[/C][/ROW]
[ROW][C]90[/C][C]0.85737159504305[/C][C]0.811514302086305[/C][C]0.903228887999794[/C][/ROW]
[ROW][C]91[/C][C]0.860089648440262[/C][C]0.811224184646082[/C][C]0.908955112234442[/C][/ROW]
[ROW][C]92[/C][C]0.862807701837475[/C][C]0.810954086773179[/C][C]0.91466131690177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42255&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42255&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
810.8329091144681350.8192313310497990.84658689788647
820.8356271678653480.8169845232157010.854269812514994
830.838345221262560.8155396844011930.861150758123928
840.8410632746597730.8145085596684820.867617989651064
850.8437813280569860.8137285823794850.873834073734487
860.8464993814541980.8131141360900870.87988462681831
870.8492174348514110.812613987785760.885820881917062
880.8519354882486240.8121948427710080.89167613372624
890.8546535416458370.8118337740295340.89747330926214
900.857371595043050.8115143020863050.903228887999794
910.8600896484402620.8112241846460820.908955112234442
920.8628077018374750.8109540867731790.91466131690177



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')