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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 31 May 2009 02:52:16 -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/May/31/t12437599749irha7s02v18yeg.htm/, Retrieved Mon, 06 May 2024 05:52:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40819, Retrieved Mon, 06 May 2024 05:52:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 - Sofie...] [2009-05-31 08:52:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
30,06
30,46
30,46
30,49
30,49
30,5
30,5
30,5
30,51
30,51
30,61
30,88
30,95
31,09
31,28
31,31
31,32
31,34
31,34
31,34
31,34
31,36
31,36
31,36
31,72
32,07
32,13
32,19
32,26
32,27
32,28
32,28
32,28
32,29
32,61
32,68
32,69
32,74
32,86
32,86
32,9
32,95
32,95
32,96
32,99
33
33,06
33,42
33,48
33,5
33,51
33,52
33,55
33,56
33,56
33,56
33,6
33,61
33,62
33,72
33,83
33,96
34,06
34,11
34,11
34,21
34,19
34,17
34,12
34,15
34,15
34,15




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=40819&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=40819&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40819&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
alpha1
beta0.601307369123789
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.601307369123789 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40819&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]0.601307369123789[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40819&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40819&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
beta0.601307369123789
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
330.4630.86-0.400000000000002
430.4930.6194770523505-0.129477052350488
530.4930.5716215466397-0.0816215466397097
630.530.522541909166-0.0225419091659695
730.530.5189872930704-0.0189872930703530
830.530.5075700938274-0.0075700938274359
930.5130.50301814062400.00698185937596207
1030.5130.517216384117-0.00721638411699033
1130.6130.5128771191690.0971228808309803
1230.8830.67127782312320.208722176876783
1330.9531.0667840061788-0.116784006178786
1431.0931.06656092266770.0234390773323163
1531.2831.22065501259310.0593449874069343
1631.3131.4463395908414-0.136339590841416
1731.3231.3943575901651-0.0743575901651461
1831.3431.3596458232486-0.0196458232485597
1931.3431.3678326449567-0.0278326449566961
2031.3431.351096670442-0.0110966704420292
2131.3431.3444241607325-0.00442416073249774
2231.3631.34176388028190.0182361197181393
2331.3631.3727293934526-0.0127293934526023
2431.3631.3650751153651-0.00507511536507721
2531.7231.36202341109690.357976588903096
2632.0731.93727737197810.132722628021870
2732.1332.3670844662572-0.237084466257159
2832.1932.2845238295920-0.0945238295919566
2932.2632.2876859543005-0.0276859543005088
3032.2732.3410381859584-0.0710381859583791
3132.2832.3083224012524-0.0283224012524315
3232.2832.3012919326681-0.0212919326680634
3332.2832.2884889366519-0.00848893665186523
3432.2932.28338447648710.00661552351292016
3532.6132.2973624395260.312637560473995
3632.6832.8053537085039-0.125353708503901
3732.6932.7999775998335-0.109977599833513
3832.7432.7438472586151-0.00384725861506752
3932.8632.79153387365890.068466126341093
4032.8632.9527030599632-0.0927030599631635
4132.932.8969600268670.00303997313300641
4232.9532.93878798511380.0112120148861976
4332.9532.9955298522876-0.0455298522876006
4432.9632.9681524165920-0.00815241659195465
4532.9932.97325030841900.0167496915809622
463333.0133220213972-0.0133220213972223
4733.0633.01531139175940.0446886082405555
4833.4233.10218298121040.317817018789619
4933.4833.6532886966415-0.173288696641535
5033.533.6090889263651-0.109088926365118
5133.5133.563492951052-0.0534929510519717
5233.5233.5413272453882-0.0213272453882354
5333.5533.53850301557320.0114969844268131
5433.5633.5754162370317-0.0154162370317223
5533.5633.5761463401004-0.0161463401003914
5633.5633.5664374268136-0.00643742681364756
5733.633.56256655463240.03743344536759
5833.6133.6250755611836-0.0150755611836360
5933.6233.6260105151502-0.00601051515023698
6033.7233.63239634809820.08760365190183
6133.8333.78507306954890.0449269304511049
6233.9633.92208796390130.0379120360987457
6334.0634.0748847505859-0.0148847505859209
6434.1134.1659344403710-0.0559344403710398
6534.1134.1823006491881-0.0723006491881151
6634.2134.13882573603890.071174263961133
6734.1934.2816233454507-0.0916233454506639
6834.1734.2065295526474-0.0365295526473943
6934.1234.1645640634497-0.0445640634497266
7034.1534.08776736369930.0622326363006991
7134.1534.1551883065069-0.00518830650691626
7234.1534.152068539571-0.00206853957103448

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 30.46 & 30.86 & -0.400000000000002 \tabularnewline
4 & 30.49 & 30.6194770523505 & -0.129477052350488 \tabularnewline
5 & 30.49 & 30.5716215466397 & -0.0816215466397097 \tabularnewline
6 & 30.5 & 30.522541909166 & -0.0225419091659695 \tabularnewline
7 & 30.5 & 30.5189872930704 & -0.0189872930703530 \tabularnewline
8 & 30.5 & 30.5075700938274 & -0.0075700938274359 \tabularnewline
9 & 30.51 & 30.5030181406240 & 0.00698185937596207 \tabularnewline
10 & 30.51 & 30.517216384117 & -0.00721638411699033 \tabularnewline
11 & 30.61 & 30.512877119169 & 0.0971228808309803 \tabularnewline
12 & 30.88 & 30.6712778231232 & 0.208722176876783 \tabularnewline
13 & 30.95 & 31.0667840061788 & -0.116784006178786 \tabularnewline
14 & 31.09 & 31.0665609226677 & 0.0234390773323163 \tabularnewline
15 & 31.28 & 31.2206550125931 & 0.0593449874069343 \tabularnewline
16 & 31.31 & 31.4463395908414 & -0.136339590841416 \tabularnewline
17 & 31.32 & 31.3943575901651 & -0.0743575901651461 \tabularnewline
18 & 31.34 & 31.3596458232486 & -0.0196458232485597 \tabularnewline
19 & 31.34 & 31.3678326449567 & -0.0278326449566961 \tabularnewline
20 & 31.34 & 31.351096670442 & -0.0110966704420292 \tabularnewline
21 & 31.34 & 31.3444241607325 & -0.00442416073249774 \tabularnewline
22 & 31.36 & 31.3417638802819 & 0.0182361197181393 \tabularnewline
23 & 31.36 & 31.3727293934526 & -0.0127293934526023 \tabularnewline
24 & 31.36 & 31.3650751153651 & -0.00507511536507721 \tabularnewline
25 & 31.72 & 31.3620234110969 & 0.357976588903096 \tabularnewline
26 & 32.07 & 31.9372773719781 & 0.132722628021870 \tabularnewline
27 & 32.13 & 32.3670844662572 & -0.237084466257159 \tabularnewline
28 & 32.19 & 32.2845238295920 & -0.0945238295919566 \tabularnewline
29 & 32.26 & 32.2876859543005 & -0.0276859543005088 \tabularnewline
30 & 32.27 & 32.3410381859584 & -0.0710381859583791 \tabularnewline
31 & 32.28 & 32.3083224012524 & -0.0283224012524315 \tabularnewline
32 & 32.28 & 32.3012919326681 & -0.0212919326680634 \tabularnewline
33 & 32.28 & 32.2884889366519 & -0.00848893665186523 \tabularnewline
34 & 32.29 & 32.2833844764871 & 0.00661552351292016 \tabularnewline
35 & 32.61 & 32.297362439526 & 0.312637560473995 \tabularnewline
36 & 32.68 & 32.8053537085039 & -0.125353708503901 \tabularnewline
37 & 32.69 & 32.7999775998335 & -0.109977599833513 \tabularnewline
38 & 32.74 & 32.7438472586151 & -0.00384725861506752 \tabularnewline
39 & 32.86 & 32.7915338736589 & 0.068466126341093 \tabularnewline
40 & 32.86 & 32.9527030599632 & -0.0927030599631635 \tabularnewline
41 & 32.9 & 32.896960026867 & 0.00303997313300641 \tabularnewline
42 & 32.95 & 32.9387879851138 & 0.0112120148861976 \tabularnewline
43 & 32.95 & 32.9955298522876 & -0.0455298522876006 \tabularnewline
44 & 32.96 & 32.9681524165920 & -0.00815241659195465 \tabularnewline
45 & 32.99 & 32.9732503084190 & 0.0167496915809622 \tabularnewline
46 & 33 & 33.0133220213972 & -0.0133220213972223 \tabularnewline
47 & 33.06 & 33.0153113917594 & 0.0446886082405555 \tabularnewline
48 & 33.42 & 33.1021829812104 & 0.317817018789619 \tabularnewline
49 & 33.48 & 33.6532886966415 & -0.173288696641535 \tabularnewline
50 & 33.5 & 33.6090889263651 & -0.109088926365118 \tabularnewline
51 & 33.51 & 33.563492951052 & -0.0534929510519717 \tabularnewline
52 & 33.52 & 33.5413272453882 & -0.0213272453882354 \tabularnewline
53 & 33.55 & 33.5385030155732 & 0.0114969844268131 \tabularnewline
54 & 33.56 & 33.5754162370317 & -0.0154162370317223 \tabularnewline
55 & 33.56 & 33.5761463401004 & -0.0161463401003914 \tabularnewline
56 & 33.56 & 33.5664374268136 & -0.00643742681364756 \tabularnewline
57 & 33.6 & 33.5625665546324 & 0.03743344536759 \tabularnewline
58 & 33.61 & 33.6250755611836 & -0.0150755611836360 \tabularnewline
59 & 33.62 & 33.6260105151502 & -0.00601051515023698 \tabularnewline
60 & 33.72 & 33.6323963480982 & 0.08760365190183 \tabularnewline
61 & 33.83 & 33.7850730695489 & 0.0449269304511049 \tabularnewline
62 & 33.96 & 33.9220879639013 & 0.0379120360987457 \tabularnewline
63 & 34.06 & 34.0748847505859 & -0.0148847505859209 \tabularnewline
64 & 34.11 & 34.1659344403710 & -0.0559344403710398 \tabularnewline
65 & 34.11 & 34.1823006491881 & -0.0723006491881151 \tabularnewline
66 & 34.21 & 34.1388257360389 & 0.071174263961133 \tabularnewline
67 & 34.19 & 34.2816233454507 & -0.0916233454506639 \tabularnewline
68 & 34.17 & 34.2065295526474 & -0.0365295526473943 \tabularnewline
69 & 34.12 & 34.1645640634497 & -0.0445640634497266 \tabularnewline
70 & 34.15 & 34.0877673636993 & 0.0622326363006991 \tabularnewline
71 & 34.15 & 34.1551883065069 & -0.00518830650691626 \tabularnewline
72 & 34.15 & 34.152068539571 & -0.00206853957103448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40819&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]30.46[/C][C]30.86[/C][C]-0.400000000000002[/C][/ROW]
[ROW][C]4[/C][C]30.49[/C][C]30.6194770523505[/C][C]-0.129477052350488[/C][/ROW]
[ROW][C]5[/C][C]30.49[/C][C]30.5716215466397[/C][C]-0.0816215466397097[/C][/ROW]
[ROW][C]6[/C][C]30.5[/C][C]30.522541909166[/C][C]-0.0225419091659695[/C][/ROW]
[ROW][C]7[/C][C]30.5[/C][C]30.5189872930704[/C][C]-0.0189872930703530[/C][/ROW]
[ROW][C]8[/C][C]30.5[/C][C]30.5075700938274[/C][C]-0.0075700938274359[/C][/ROW]
[ROW][C]9[/C][C]30.51[/C][C]30.5030181406240[/C][C]0.00698185937596207[/C][/ROW]
[ROW][C]10[/C][C]30.51[/C][C]30.517216384117[/C][C]-0.00721638411699033[/C][/ROW]
[ROW][C]11[/C][C]30.61[/C][C]30.512877119169[/C][C]0.0971228808309803[/C][/ROW]
[ROW][C]12[/C][C]30.88[/C][C]30.6712778231232[/C][C]0.208722176876783[/C][/ROW]
[ROW][C]13[/C][C]30.95[/C][C]31.0667840061788[/C][C]-0.116784006178786[/C][/ROW]
[ROW][C]14[/C][C]31.09[/C][C]31.0665609226677[/C][C]0.0234390773323163[/C][/ROW]
[ROW][C]15[/C][C]31.28[/C][C]31.2206550125931[/C][C]0.0593449874069343[/C][/ROW]
[ROW][C]16[/C][C]31.31[/C][C]31.4463395908414[/C][C]-0.136339590841416[/C][/ROW]
[ROW][C]17[/C][C]31.32[/C][C]31.3943575901651[/C][C]-0.0743575901651461[/C][/ROW]
[ROW][C]18[/C][C]31.34[/C][C]31.3596458232486[/C][C]-0.0196458232485597[/C][/ROW]
[ROW][C]19[/C][C]31.34[/C][C]31.3678326449567[/C][C]-0.0278326449566961[/C][/ROW]
[ROW][C]20[/C][C]31.34[/C][C]31.351096670442[/C][C]-0.0110966704420292[/C][/ROW]
[ROW][C]21[/C][C]31.34[/C][C]31.3444241607325[/C][C]-0.00442416073249774[/C][/ROW]
[ROW][C]22[/C][C]31.36[/C][C]31.3417638802819[/C][C]0.0182361197181393[/C][/ROW]
[ROW][C]23[/C][C]31.36[/C][C]31.3727293934526[/C][C]-0.0127293934526023[/C][/ROW]
[ROW][C]24[/C][C]31.36[/C][C]31.3650751153651[/C][C]-0.00507511536507721[/C][/ROW]
[ROW][C]25[/C][C]31.72[/C][C]31.3620234110969[/C][C]0.357976588903096[/C][/ROW]
[ROW][C]26[/C][C]32.07[/C][C]31.9372773719781[/C][C]0.132722628021870[/C][/ROW]
[ROW][C]27[/C][C]32.13[/C][C]32.3670844662572[/C][C]-0.237084466257159[/C][/ROW]
[ROW][C]28[/C][C]32.19[/C][C]32.2845238295920[/C][C]-0.0945238295919566[/C][/ROW]
[ROW][C]29[/C][C]32.26[/C][C]32.2876859543005[/C][C]-0.0276859543005088[/C][/ROW]
[ROW][C]30[/C][C]32.27[/C][C]32.3410381859584[/C][C]-0.0710381859583791[/C][/ROW]
[ROW][C]31[/C][C]32.28[/C][C]32.3083224012524[/C][C]-0.0283224012524315[/C][/ROW]
[ROW][C]32[/C][C]32.28[/C][C]32.3012919326681[/C][C]-0.0212919326680634[/C][/ROW]
[ROW][C]33[/C][C]32.28[/C][C]32.2884889366519[/C][C]-0.00848893665186523[/C][/ROW]
[ROW][C]34[/C][C]32.29[/C][C]32.2833844764871[/C][C]0.00661552351292016[/C][/ROW]
[ROW][C]35[/C][C]32.61[/C][C]32.297362439526[/C][C]0.312637560473995[/C][/ROW]
[ROW][C]36[/C][C]32.68[/C][C]32.8053537085039[/C][C]-0.125353708503901[/C][/ROW]
[ROW][C]37[/C][C]32.69[/C][C]32.7999775998335[/C][C]-0.109977599833513[/C][/ROW]
[ROW][C]38[/C][C]32.74[/C][C]32.7438472586151[/C][C]-0.00384725861506752[/C][/ROW]
[ROW][C]39[/C][C]32.86[/C][C]32.7915338736589[/C][C]0.068466126341093[/C][/ROW]
[ROW][C]40[/C][C]32.86[/C][C]32.9527030599632[/C][C]-0.0927030599631635[/C][/ROW]
[ROW][C]41[/C][C]32.9[/C][C]32.896960026867[/C][C]0.00303997313300641[/C][/ROW]
[ROW][C]42[/C][C]32.95[/C][C]32.9387879851138[/C][C]0.0112120148861976[/C][/ROW]
[ROW][C]43[/C][C]32.95[/C][C]32.9955298522876[/C][C]-0.0455298522876006[/C][/ROW]
[ROW][C]44[/C][C]32.96[/C][C]32.9681524165920[/C][C]-0.00815241659195465[/C][/ROW]
[ROW][C]45[/C][C]32.99[/C][C]32.9732503084190[/C][C]0.0167496915809622[/C][/ROW]
[ROW][C]46[/C][C]33[/C][C]33.0133220213972[/C][C]-0.0133220213972223[/C][/ROW]
[ROW][C]47[/C][C]33.06[/C][C]33.0153113917594[/C][C]0.0446886082405555[/C][/ROW]
[ROW][C]48[/C][C]33.42[/C][C]33.1021829812104[/C][C]0.317817018789619[/C][/ROW]
[ROW][C]49[/C][C]33.48[/C][C]33.6532886966415[/C][C]-0.173288696641535[/C][/ROW]
[ROW][C]50[/C][C]33.5[/C][C]33.6090889263651[/C][C]-0.109088926365118[/C][/ROW]
[ROW][C]51[/C][C]33.51[/C][C]33.563492951052[/C][C]-0.0534929510519717[/C][/ROW]
[ROW][C]52[/C][C]33.52[/C][C]33.5413272453882[/C][C]-0.0213272453882354[/C][/ROW]
[ROW][C]53[/C][C]33.55[/C][C]33.5385030155732[/C][C]0.0114969844268131[/C][/ROW]
[ROW][C]54[/C][C]33.56[/C][C]33.5754162370317[/C][C]-0.0154162370317223[/C][/ROW]
[ROW][C]55[/C][C]33.56[/C][C]33.5761463401004[/C][C]-0.0161463401003914[/C][/ROW]
[ROW][C]56[/C][C]33.56[/C][C]33.5664374268136[/C][C]-0.00643742681364756[/C][/ROW]
[ROW][C]57[/C][C]33.6[/C][C]33.5625665546324[/C][C]0.03743344536759[/C][/ROW]
[ROW][C]58[/C][C]33.61[/C][C]33.6250755611836[/C][C]-0.0150755611836360[/C][/ROW]
[ROW][C]59[/C][C]33.62[/C][C]33.6260105151502[/C][C]-0.00601051515023698[/C][/ROW]
[ROW][C]60[/C][C]33.72[/C][C]33.6323963480982[/C][C]0.08760365190183[/C][/ROW]
[ROW][C]61[/C][C]33.83[/C][C]33.7850730695489[/C][C]0.0449269304511049[/C][/ROW]
[ROW][C]62[/C][C]33.96[/C][C]33.9220879639013[/C][C]0.0379120360987457[/C][/ROW]
[ROW][C]63[/C][C]34.06[/C][C]34.0748847505859[/C][C]-0.0148847505859209[/C][/ROW]
[ROW][C]64[/C][C]34.11[/C][C]34.1659344403710[/C][C]-0.0559344403710398[/C][/ROW]
[ROW][C]65[/C][C]34.11[/C][C]34.1823006491881[/C][C]-0.0723006491881151[/C][/ROW]
[ROW][C]66[/C][C]34.21[/C][C]34.1388257360389[/C][C]0.071174263961133[/C][/ROW]
[ROW][C]67[/C][C]34.19[/C][C]34.2816233454507[/C][C]-0.0916233454506639[/C][/ROW]
[ROW][C]68[/C][C]34.17[/C][C]34.2065295526474[/C][C]-0.0365295526473943[/C][/ROW]
[ROW][C]69[/C][C]34.12[/C][C]34.1645640634497[/C][C]-0.0445640634497266[/C][/ROW]
[ROW][C]70[/C][C]34.15[/C][C]34.0877673636993[/C][C]0.0622326363006991[/C][/ROW]
[ROW][C]71[/C][C]34.15[/C][C]34.1551883065069[/C][C]-0.00518830650691626[/C][/ROW]
[ROW][C]72[/C][C]34.15[/C][C]34.152068539571[/C][C]-0.00206853957103448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40819&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40819&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
330.4630.86-0.400000000000002
430.4930.6194770523505-0.129477052350488
530.4930.5716215466397-0.0816215466397097
630.530.522541909166-0.0225419091659695
730.530.5189872930704-0.0189872930703530
830.530.5075700938274-0.0075700938274359
930.5130.50301814062400.00698185937596207
1030.5130.517216384117-0.00721638411699033
1130.6130.5128771191690.0971228808309803
1230.8830.67127782312320.208722176876783
1330.9531.0667840061788-0.116784006178786
1431.0931.06656092266770.0234390773323163
1531.2831.22065501259310.0593449874069343
1631.3131.4463395908414-0.136339590841416
1731.3231.3943575901651-0.0743575901651461
1831.3431.3596458232486-0.0196458232485597
1931.3431.3678326449567-0.0278326449566961
2031.3431.351096670442-0.0110966704420292
2131.3431.3444241607325-0.00442416073249774
2231.3631.34176388028190.0182361197181393
2331.3631.3727293934526-0.0127293934526023
2431.3631.3650751153651-0.00507511536507721
2531.7231.36202341109690.357976588903096
2632.0731.93727737197810.132722628021870
2732.1332.3670844662572-0.237084466257159
2832.1932.2845238295920-0.0945238295919566
2932.2632.2876859543005-0.0276859543005088
3032.2732.3410381859584-0.0710381859583791
3132.2832.3083224012524-0.0283224012524315
3232.2832.3012919326681-0.0212919326680634
3332.2832.2884889366519-0.00848893665186523
3432.2932.28338447648710.00661552351292016
3532.6132.2973624395260.312637560473995
3632.6832.8053537085039-0.125353708503901
3732.6932.7999775998335-0.109977599833513
3832.7432.7438472586151-0.00384725861506752
3932.8632.79153387365890.068466126341093
4032.8632.9527030599632-0.0927030599631635
4132.932.8969600268670.00303997313300641
4232.9532.93878798511380.0112120148861976
4332.9532.9955298522876-0.0455298522876006
4432.9632.9681524165920-0.00815241659195465
4532.9932.97325030841900.0167496915809622
463333.0133220213972-0.0133220213972223
4733.0633.01531139175940.0446886082405555
4833.4233.10218298121040.317817018789619
4933.4833.6532886966415-0.173288696641535
5033.533.6090889263651-0.109088926365118
5133.5133.563492951052-0.0534929510519717
5233.5233.5413272453882-0.0213272453882354
5333.5533.53850301557320.0114969844268131
5433.5633.5754162370317-0.0154162370317223
5533.5633.5761463401004-0.0161463401003914
5633.5633.5664374268136-0.00643742681364756
5733.633.56256655463240.03743344536759
5833.6133.6250755611836-0.0150755611836360
5933.6233.6260105151502-0.00601051515023698
6033.7233.63239634809820.08760365190183
6133.8333.78507306954890.0449269304511049
6233.9633.92208796390130.0379120360987457
6334.0634.0748847505859-0.0148847505859209
6434.1134.1659344403710-0.0559344403710398
6534.1134.1823006491881-0.0723006491881151
6634.2134.13882573603890.071174263961133
6734.1934.2816233454507-0.0916233454506639
6834.1734.2065295526474-0.0365295526473943
6934.1234.1645640634497-0.0445640634497266
7034.1534.08776736369930.0622326363006991
7134.1534.1551883065069-0.00518830650691626
7234.1534.152068539571-0.00206853957103448







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7334.150824711483633.936451452789434.3651979701779
7434.151649422967333.746933075933634.556365770001
7534.152474134450933.530581154503434.7743671143985
7634.153298845934633.288397024415535.0182006674537
7734.154123557418233.022337020741835.2859100940946
7834.154948268901932.734159654898635.5757368829052
7934.155772980385532.425343461429735.8862024993414
8034.156597691869232.097128958494436.2160664252439
8134.157422403352831.750567959753736.5642768469519
8234.158247114836531.386563607865236.9299306218077
8334.159071826320131.005900801756537.3122428508838
8434.159896537803830.609269121327137.7105239542804

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 34.1508247114836 & 33.9364514527894 & 34.3651979701779 \tabularnewline
74 & 34.1516494229673 & 33.7469330759336 & 34.556365770001 \tabularnewline
75 & 34.1524741344509 & 33.5305811545034 & 34.7743671143985 \tabularnewline
76 & 34.1532988459346 & 33.2883970244155 & 35.0182006674537 \tabularnewline
77 & 34.1541235574182 & 33.0223370207418 & 35.2859100940946 \tabularnewline
78 & 34.1549482689019 & 32.7341596548986 & 35.5757368829052 \tabularnewline
79 & 34.1557729803855 & 32.4253434614297 & 35.8862024993414 \tabularnewline
80 & 34.1565976918692 & 32.0971289584944 & 36.2160664252439 \tabularnewline
81 & 34.1574224033528 & 31.7505679597537 & 36.5642768469519 \tabularnewline
82 & 34.1582471148365 & 31.3865636078652 & 36.9299306218077 \tabularnewline
83 & 34.1590718263201 & 31.0059008017565 & 37.3122428508838 \tabularnewline
84 & 34.1598965378038 & 30.6092691213271 & 37.7105239542804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40819&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]34.1508247114836[/C][C]33.9364514527894[/C][C]34.3651979701779[/C][/ROW]
[ROW][C]74[/C][C]34.1516494229673[/C][C]33.7469330759336[/C][C]34.556365770001[/C][/ROW]
[ROW][C]75[/C][C]34.1524741344509[/C][C]33.5305811545034[/C][C]34.7743671143985[/C][/ROW]
[ROW][C]76[/C][C]34.1532988459346[/C][C]33.2883970244155[/C][C]35.0182006674537[/C][/ROW]
[ROW][C]77[/C][C]34.1541235574182[/C][C]33.0223370207418[/C][C]35.2859100940946[/C][/ROW]
[ROW][C]78[/C][C]34.1549482689019[/C][C]32.7341596548986[/C][C]35.5757368829052[/C][/ROW]
[ROW][C]79[/C][C]34.1557729803855[/C][C]32.4253434614297[/C][C]35.8862024993414[/C][/ROW]
[ROW][C]80[/C][C]34.1565976918692[/C][C]32.0971289584944[/C][C]36.2160664252439[/C][/ROW]
[ROW][C]81[/C][C]34.1574224033528[/C][C]31.7505679597537[/C][C]36.5642768469519[/C][/ROW]
[ROW][C]82[/C][C]34.1582471148365[/C][C]31.3865636078652[/C][C]36.9299306218077[/C][/ROW]
[ROW][C]83[/C][C]34.1590718263201[/C][C]31.0059008017565[/C][C]37.3122428508838[/C][/ROW]
[ROW][C]84[/C][C]34.1598965378038[/C][C]30.6092691213271[/C][C]37.7105239542804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40819&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40819&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
7334.150824711483633.936451452789434.3651979701779
7434.151649422967333.746933075933634.556365770001
7534.152474134450933.530581154503434.7743671143985
7634.153298845934633.288397024415535.0182006674537
7734.154123557418233.022337020741835.2859100940946
7834.154948268901932.734159654898635.5757368829052
7934.155772980385532.425343461429735.8862024993414
8034.156597691869232.097128958494436.2160664252439
8134.157422403352831.750567959753736.5642768469519
8234.158247114836531.386563607865236.9299306218077
8334.159071826320131.005900801756537.3122428508838
8434.159896537803830.609269121327137.7105239542804



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')