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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 computationFri, 15 Jan 2010 08:25:06 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/15/t1263569168phq6ou4ia1q08gh.htm/, Retrieved Fri, 03 May 2024 14:27:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72209, Retrieved Fri, 03 May 2024 14:27:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-15 15:25:06] [3124dd9566c5de02f2943664af57df92] [Current]
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Dataseries X:
-9
-13
-18
-11
-9
-10
-13
-11
-5
-15
-6
-6
-3
-1
-3
-4
-6
0
-4
-2
-2
-6
-7
-6
-6
-3
-2
-5
-11
-11
-11
-10
-14
-8
-9
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72209&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72209&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.70504327667519
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.70504327667519 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72209&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]0.70504327667519[/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=72209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72209&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
alpha0.70504327667519
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2-13-9-4
3-18-11.8201731067008-6.17982689329924
4-11-16.17721850883795.17721850883791
5-9-12.52705540730343.52705540730339
6-10-10.04032870592330.0403287059232618
7-13-10.0118952229551-2.98810477704495
8-11-12.11863840601161.11863840601161
9-5-11.32994991882256.32994991882247
10-15-6.86706128686603-8.13293871313397
11-6-12.60113504617256.6011350461725
12-6-7.947049163443611.94704916344361
13-3-6.574295241401643.57429524140164
14-1-4.054262412599293.05426241259929
15-3-1.90087523339442-1.09912476660558
16-4-2.67580576031687-1.32419423968313
17-6-3.60942000601748-2.39057999398252
180-5.294882358129075.29488235812907
19-4-1.56176115074409-2.43823884925590
20-2-3.280825058340221.28082505834022
21-2-2.377787962360340.377787962360341
22-6-2.11143109948936-3.88856890051064
23-7-4.85304045868262-2.14695954131738
24-6-6.366739848582090.366739848582089
25-6-6.108172384050410.108172384050410
26-3-6.031906171953743.03190617195374
27-2-3.894281109907741.89428110990774
28-5-2.55873094923447-2.44126905076553
29-11-4.27993128003193-6.72006871996807
30-11-9.01787054984067-1.98212945015933
31-11-10.4153575921754-0.584642407824605
32-10-10.82755579107130.827555791071328
33-14-10.2440931445029-3.75590685549713
34-8-12.89217002078944.89217002078938
35-9-9.44297843927990.442978439279903
36-5-9.130659468953544.13065946895354
37-1-6.218365782133145.21836578213314
38-2-2.53919207220830.539192072208301
39-5-2.15903832686127-2.84096167313873
40-4-4.162039253799630.162039253799631
41-6-4.04779456735074-1.95220543264926
42-2-5.424183882328883.42418388232888
43-2-3.009986057993351.00998605799335
44-2-2.297902178269460.297902178269462
45-2-2.087868250373680.0878682503736838
462-2.025917331214514.02591733121451
4710.8125286156084050.187471384391595
48-80.94470405474269-8.94470405474269
49-1-5.361699400902954.36169940090295
501-2.286512563418123.28651256341812
51-10.0306210231283678-1.03062102312837
522-0.6960114000283932.69601140002839
5321.204793311401290.795206688598709
5411.76544844076495-0.765448440764952
55-11.22577416396212-2.22577416396212
56-2-0.343492945736715-1.65650705426328
57-2-1.51140210711007-0.488597892889932
58-1-1.855884766489780.855884766489779
59-8-1.25244896626745-6.74755103373255
60-4-6.009764456623312.00976445662331
61-6-4.59279353878028-1.40720646121972
62-3-5.584934993157132.58493499315713
63-3-3.762443955589270.762443955589267
64-7-3.22488797085942-3.77511202914058
65-9-5.88650532570062-3.11349467429938
66-11-8.0816538127794-2.91834618722059
67-13-10.1392141710900-2.86078582891004
68-11-12.15619198577061.15619198577064
69-9-11.34102659965732.34102659965732
70-17-9.69050153505114-7.30949846494886
71-22-14.8440142836310-7.15598571636905
72-25-19.8892939009406-5.11070609905936
73-20-23.49256287514533.49256287514533
74-24-21.0301549016587-2.96984509834125
75-24-23.124024221011-0.875975778988984
76-22-23.74162505451751.74162505451751
77-19-22.51370401934093.51370401934088
78-18-20.0363906242782.03639062427800
79-17-18.60064710594641.60064710594640
80-11-17.47212162556936.47212162556929
81-11-12.90899578763761.90899578763756

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & -13 & -9 & -4 \tabularnewline
3 & -18 & -11.8201731067008 & -6.17982689329924 \tabularnewline
4 & -11 & -16.1772185088379 & 5.17721850883791 \tabularnewline
5 & -9 & -12.5270554073034 & 3.52705540730339 \tabularnewline
6 & -10 & -10.0403287059233 & 0.0403287059232618 \tabularnewline
7 & -13 & -10.0118952229551 & -2.98810477704495 \tabularnewline
8 & -11 & -12.1186384060116 & 1.11863840601161 \tabularnewline
9 & -5 & -11.3299499188225 & 6.32994991882247 \tabularnewline
10 & -15 & -6.86706128686603 & -8.13293871313397 \tabularnewline
11 & -6 & -12.6011350461725 & 6.6011350461725 \tabularnewline
12 & -6 & -7.94704916344361 & 1.94704916344361 \tabularnewline
13 & -3 & -6.57429524140164 & 3.57429524140164 \tabularnewline
14 & -1 & -4.05426241259929 & 3.05426241259929 \tabularnewline
15 & -3 & -1.90087523339442 & -1.09912476660558 \tabularnewline
16 & -4 & -2.67580576031687 & -1.32419423968313 \tabularnewline
17 & -6 & -3.60942000601748 & -2.39057999398252 \tabularnewline
18 & 0 & -5.29488235812907 & 5.29488235812907 \tabularnewline
19 & -4 & -1.56176115074409 & -2.43823884925590 \tabularnewline
20 & -2 & -3.28082505834022 & 1.28082505834022 \tabularnewline
21 & -2 & -2.37778796236034 & 0.377787962360341 \tabularnewline
22 & -6 & -2.11143109948936 & -3.88856890051064 \tabularnewline
23 & -7 & -4.85304045868262 & -2.14695954131738 \tabularnewline
24 & -6 & -6.36673984858209 & 0.366739848582089 \tabularnewline
25 & -6 & -6.10817238405041 & 0.108172384050410 \tabularnewline
26 & -3 & -6.03190617195374 & 3.03190617195374 \tabularnewline
27 & -2 & -3.89428110990774 & 1.89428110990774 \tabularnewline
28 & -5 & -2.55873094923447 & -2.44126905076553 \tabularnewline
29 & -11 & -4.27993128003193 & -6.72006871996807 \tabularnewline
30 & -11 & -9.01787054984067 & -1.98212945015933 \tabularnewline
31 & -11 & -10.4153575921754 & -0.584642407824605 \tabularnewline
32 & -10 & -10.8275557910713 & 0.827555791071328 \tabularnewline
33 & -14 & -10.2440931445029 & -3.75590685549713 \tabularnewline
34 & -8 & -12.8921700207894 & 4.89217002078938 \tabularnewline
35 & -9 & -9.4429784392799 & 0.442978439279903 \tabularnewline
36 & -5 & -9.13065946895354 & 4.13065946895354 \tabularnewline
37 & -1 & -6.21836578213314 & 5.21836578213314 \tabularnewline
38 & -2 & -2.5391920722083 & 0.539192072208301 \tabularnewline
39 & -5 & -2.15903832686127 & -2.84096167313873 \tabularnewline
40 & -4 & -4.16203925379963 & 0.162039253799631 \tabularnewline
41 & -6 & -4.04779456735074 & -1.95220543264926 \tabularnewline
42 & -2 & -5.42418388232888 & 3.42418388232888 \tabularnewline
43 & -2 & -3.00998605799335 & 1.00998605799335 \tabularnewline
44 & -2 & -2.29790217826946 & 0.297902178269462 \tabularnewline
45 & -2 & -2.08786825037368 & 0.0878682503736838 \tabularnewline
46 & 2 & -2.02591733121451 & 4.02591733121451 \tabularnewline
47 & 1 & 0.812528615608405 & 0.187471384391595 \tabularnewline
48 & -8 & 0.94470405474269 & -8.94470405474269 \tabularnewline
49 & -1 & -5.36169940090295 & 4.36169940090295 \tabularnewline
50 & 1 & -2.28651256341812 & 3.28651256341812 \tabularnewline
51 & -1 & 0.0306210231283678 & -1.03062102312837 \tabularnewline
52 & 2 & -0.696011400028393 & 2.69601140002839 \tabularnewline
53 & 2 & 1.20479331140129 & 0.795206688598709 \tabularnewline
54 & 1 & 1.76544844076495 & -0.765448440764952 \tabularnewline
55 & -1 & 1.22577416396212 & -2.22577416396212 \tabularnewline
56 & -2 & -0.343492945736715 & -1.65650705426328 \tabularnewline
57 & -2 & -1.51140210711007 & -0.488597892889932 \tabularnewline
58 & -1 & -1.85588476648978 & 0.855884766489779 \tabularnewline
59 & -8 & -1.25244896626745 & -6.74755103373255 \tabularnewline
60 & -4 & -6.00976445662331 & 2.00976445662331 \tabularnewline
61 & -6 & -4.59279353878028 & -1.40720646121972 \tabularnewline
62 & -3 & -5.58493499315713 & 2.58493499315713 \tabularnewline
63 & -3 & -3.76244395558927 & 0.762443955589267 \tabularnewline
64 & -7 & -3.22488797085942 & -3.77511202914058 \tabularnewline
65 & -9 & -5.88650532570062 & -3.11349467429938 \tabularnewline
66 & -11 & -8.0816538127794 & -2.91834618722059 \tabularnewline
67 & -13 & -10.1392141710900 & -2.86078582891004 \tabularnewline
68 & -11 & -12.1561919857706 & 1.15619198577064 \tabularnewline
69 & -9 & -11.3410265996573 & 2.34102659965732 \tabularnewline
70 & -17 & -9.69050153505114 & -7.30949846494886 \tabularnewline
71 & -22 & -14.8440142836310 & -7.15598571636905 \tabularnewline
72 & -25 & -19.8892939009406 & -5.11070609905936 \tabularnewline
73 & -20 & -23.4925628751453 & 3.49256287514533 \tabularnewline
74 & -24 & -21.0301549016587 & -2.96984509834125 \tabularnewline
75 & -24 & -23.124024221011 & -0.875975778988984 \tabularnewline
76 & -22 & -23.7416250545175 & 1.74162505451751 \tabularnewline
77 & -19 & -22.5137040193409 & 3.51370401934088 \tabularnewline
78 & -18 & -20.036390624278 & 2.03639062427800 \tabularnewline
79 & -17 & -18.6006471059464 & 1.60064710594640 \tabularnewline
80 & -11 & -17.4721216255693 & 6.47212162556929 \tabularnewline
81 & -11 & -12.9089957876376 & 1.90899578763756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72209&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]-13[/C][C]-9[/C][C]-4[/C][/ROW]
[ROW][C]3[/C][C]-18[/C][C]-11.8201731067008[/C][C]-6.17982689329924[/C][/ROW]
[ROW][C]4[/C][C]-11[/C][C]-16.1772185088379[/C][C]5.17721850883791[/C][/ROW]
[ROW][C]5[/C][C]-9[/C][C]-12.5270554073034[/C][C]3.52705540730339[/C][/ROW]
[ROW][C]6[/C][C]-10[/C][C]-10.0403287059233[/C][C]0.0403287059232618[/C][/ROW]
[ROW][C]7[/C][C]-13[/C][C]-10.0118952229551[/C][C]-2.98810477704495[/C][/ROW]
[ROW][C]8[/C][C]-11[/C][C]-12.1186384060116[/C][C]1.11863840601161[/C][/ROW]
[ROW][C]9[/C][C]-5[/C][C]-11.3299499188225[/C][C]6.32994991882247[/C][/ROW]
[ROW][C]10[/C][C]-15[/C][C]-6.86706128686603[/C][C]-8.13293871313397[/C][/ROW]
[ROW][C]11[/C][C]-6[/C][C]-12.6011350461725[/C][C]6.6011350461725[/C][/ROW]
[ROW][C]12[/C][C]-6[/C][C]-7.94704916344361[/C][C]1.94704916344361[/C][/ROW]
[ROW][C]13[/C][C]-3[/C][C]-6.57429524140164[/C][C]3.57429524140164[/C][/ROW]
[ROW][C]14[/C][C]-1[/C][C]-4.05426241259929[/C][C]3.05426241259929[/C][/ROW]
[ROW][C]15[/C][C]-3[/C][C]-1.90087523339442[/C][C]-1.09912476660558[/C][/ROW]
[ROW][C]16[/C][C]-4[/C][C]-2.67580576031687[/C][C]-1.32419423968313[/C][/ROW]
[ROW][C]17[/C][C]-6[/C][C]-3.60942000601748[/C][C]-2.39057999398252[/C][/ROW]
[ROW][C]18[/C][C]0[/C][C]-5.29488235812907[/C][C]5.29488235812907[/C][/ROW]
[ROW][C]19[/C][C]-4[/C][C]-1.56176115074409[/C][C]-2.43823884925590[/C][/ROW]
[ROW][C]20[/C][C]-2[/C][C]-3.28082505834022[/C][C]1.28082505834022[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-2.37778796236034[/C][C]0.377787962360341[/C][/ROW]
[ROW][C]22[/C][C]-6[/C][C]-2.11143109948936[/C][C]-3.88856890051064[/C][/ROW]
[ROW][C]23[/C][C]-7[/C][C]-4.85304045868262[/C][C]-2.14695954131738[/C][/ROW]
[ROW][C]24[/C][C]-6[/C][C]-6.36673984858209[/C][C]0.366739848582089[/C][/ROW]
[ROW][C]25[/C][C]-6[/C][C]-6.10817238405041[/C][C]0.108172384050410[/C][/ROW]
[ROW][C]26[/C][C]-3[/C][C]-6.03190617195374[/C][C]3.03190617195374[/C][/ROW]
[ROW][C]27[/C][C]-2[/C][C]-3.89428110990774[/C][C]1.89428110990774[/C][/ROW]
[ROW][C]28[/C][C]-5[/C][C]-2.55873094923447[/C][C]-2.44126905076553[/C][/ROW]
[ROW][C]29[/C][C]-11[/C][C]-4.27993128003193[/C][C]-6.72006871996807[/C][/ROW]
[ROW][C]30[/C][C]-11[/C][C]-9.01787054984067[/C][C]-1.98212945015933[/C][/ROW]
[ROW][C]31[/C][C]-11[/C][C]-10.4153575921754[/C][C]-0.584642407824605[/C][/ROW]
[ROW][C]32[/C][C]-10[/C][C]-10.8275557910713[/C][C]0.827555791071328[/C][/ROW]
[ROW][C]33[/C][C]-14[/C][C]-10.2440931445029[/C][C]-3.75590685549713[/C][/ROW]
[ROW][C]34[/C][C]-8[/C][C]-12.8921700207894[/C][C]4.89217002078938[/C][/ROW]
[ROW][C]35[/C][C]-9[/C][C]-9.4429784392799[/C][C]0.442978439279903[/C][/ROW]
[ROW][C]36[/C][C]-5[/C][C]-9.13065946895354[/C][C]4.13065946895354[/C][/ROW]
[ROW][C]37[/C][C]-1[/C][C]-6.21836578213314[/C][C]5.21836578213314[/C][/ROW]
[ROW][C]38[/C][C]-2[/C][C]-2.5391920722083[/C][C]0.539192072208301[/C][/ROW]
[ROW][C]39[/C][C]-5[/C][C]-2.15903832686127[/C][C]-2.84096167313873[/C][/ROW]
[ROW][C]40[/C][C]-4[/C][C]-4.16203925379963[/C][C]0.162039253799631[/C][/ROW]
[ROW][C]41[/C][C]-6[/C][C]-4.04779456735074[/C][C]-1.95220543264926[/C][/ROW]
[ROW][C]42[/C][C]-2[/C][C]-5.42418388232888[/C][C]3.42418388232888[/C][/ROW]
[ROW][C]43[/C][C]-2[/C][C]-3.00998605799335[/C][C]1.00998605799335[/C][/ROW]
[ROW][C]44[/C][C]-2[/C][C]-2.29790217826946[/C][C]0.297902178269462[/C][/ROW]
[ROW][C]45[/C][C]-2[/C][C]-2.08786825037368[/C][C]0.0878682503736838[/C][/ROW]
[ROW][C]46[/C][C]2[/C][C]-2.02591733121451[/C][C]4.02591733121451[/C][/ROW]
[ROW][C]47[/C][C]1[/C][C]0.812528615608405[/C][C]0.187471384391595[/C][/ROW]
[ROW][C]48[/C][C]-8[/C][C]0.94470405474269[/C][C]-8.94470405474269[/C][/ROW]
[ROW][C]49[/C][C]-1[/C][C]-5.36169940090295[/C][C]4.36169940090295[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]-2.28651256341812[/C][C]3.28651256341812[/C][/ROW]
[ROW][C]51[/C][C]-1[/C][C]0.0306210231283678[/C][C]-1.03062102312837[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]-0.696011400028393[/C][C]2.69601140002839[/C][/ROW]
[ROW][C]53[/C][C]2[/C][C]1.20479331140129[/C][C]0.795206688598709[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]1.76544844076495[/C][C]-0.765448440764952[/C][/ROW]
[ROW][C]55[/C][C]-1[/C][C]1.22577416396212[/C][C]-2.22577416396212[/C][/ROW]
[ROW][C]56[/C][C]-2[/C][C]-0.343492945736715[/C][C]-1.65650705426328[/C][/ROW]
[ROW][C]57[/C][C]-2[/C][C]-1.51140210711007[/C][C]-0.488597892889932[/C][/ROW]
[ROW][C]58[/C][C]-1[/C][C]-1.85588476648978[/C][C]0.855884766489779[/C][/ROW]
[ROW][C]59[/C][C]-8[/C][C]-1.25244896626745[/C][C]-6.74755103373255[/C][/ROW]
[ROW][C]60[/C][C]-4[/C][C]-6.00976445662331[/C][C]2.00976445662331[/C][/ROW]
[ROW][C]61[/C][C]-6[/C][C]-4.59279353878028[/C][C]-1.40720646121972[/C][/ROW]
[ROW][C]62[/C][C]-3[/C][C]-5.58493499315713[/C][C]2.58493499315713[/C][/ROW]
[ROW][C]63[/C][C]-3[/C][C]-3.76244395558927[/C][C]0.762443955589267[/C][/ROW]
[ROW][C]64[/C][C]-7[/C][C]-3.22488797085942[/C][C]-3.77511202914058[/C][/ROW]
[ROW][C]65[/C][C]-9[/C][C]-5.88650532570062[/C][C]-3.11349467429938[/C][/ROW]
[ROW][C]66[/C][C]-11[/C][C]-8.0816538127794[/C][C]-2.91834618722059[/C][/ROW]
[ROW][C]67[/C][C]-13[/C][C]-10.1392141710900[/C][C]-2.86078582891004[/C][/ROW]
[ROW][C]68[/C][C]-11[/C][C]-12.1561919857706[/C][C]1.15619198577064[/C][/ROW]
[ROW][C]69[/C][C]-9[/C][C]-11.3410265996573[/C][C]2.34102659965732[/C][/ROW]
[ROW][C]70[/C][C]-17[/C][C]-9.69050153505114[/C][C]-7.30949846494886[/C][/ROW]
[ROW][C]71[/C][C]-22[/C][C]-14.8440142836310[/C][C]-7.15598571636905[/C][/ROW]
[ROW][C]72[/C][C]-25[/C][C]-19.8892939009406[/C][C]-5.11070609905936[/C][/ROW]
[ROW][C]73[/C][C]-20[/C][C]-23.4925628751453[/C][C]3.49256287514533[/C][/ROW]
[ROW][C]74[/C][C]-24[/C][C]-21.0301549016587[/C][C]-2.96984509834125[/C][/ROW]
[ROW][C]75[/C][C]-24[/C][C]-23.124024221011[/C][C]-0.875975778988984[/C][/ROW]
[ROW][C]76[/C][C]-22[/C][C]-23.7416250545175[/C][C]1.74162505451751[/C][/ROW]
[ROW][C]77[/C][C]-19[/C][C]-22.5137040193409[/C][C]3.51370401934088[/C][/ROW]
[ROW][C]78[/C][C]-18[/C][C]-20.036390624278[/C][C]2.03639062427800[/C][/ROW]
[ROW][C]79[/C][C]-17[/C][C]-18.6006471059464[/C][C]1.60064710594640[/C][/ROW]
[ROW][C]80[/C][C]-11[/C][C]-17.4721216255693[/C][C]6.47212162556929[/C][/ROW]
[ROW][C]81[/C][C]-11[/C][C]-12.9089957876376[/C][C]1.90899578763756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72209&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72209&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
2-13-9-4
3-18-11.8201731067008-6.17982689329924
4-11-16.17721850883795.17721850883791
5-9-12.52705540730343.52705540730339
6-10-10.04032870592330.0403287059232618
7-13-10.0118952229551-2.98810477704495
8-11-12.11863840601161.11863840601161
9-5-11.32994991882256.32994991882247
10-15-6.86706128686603-8.13293871313397
11-6-12.60113504617256.6011350461725
12-6-7.947049163443611.94704916344361
13-3-6.574295241401643.57429524140164
14-1-4.054262412599293.05426241259929
15-3-1.90087523339442-1.09912476660558
16-4-2.67580576031687-1.32419423968313
17-6-3.60942000601748-2.39057999398252
180-5.294882358129075.29488235812907
19-4-1.56176115074409-2.43823884925590
20-2-3.280825058340221.28082505834022
21-2-2.377787962360340.377787962360341
22-6-2.11143109948936-3.88856890051064
23-7-4.85304045868262-2.14695954131738
24-6-6.366739848582090.366739848582089
25-6-6.108172384050410.108172384050410
26-3-6.031906171953743.03190617195374
27-2-3.894281109907741.89428110990774
28-5-2.55873094923447-2.44126905076553
29-11-4.27993128003193-6.72006871996807
30-11-9.01787054984067-1.98212945015933
31-11-10.4153575921754-0.584642407824605
32-10-10.82755579107130.827555791071328
33-14-10.2440931445029-3.75590685549713
34-8-12.89217002078944.89217002078938
35-9-9.44297843927990.442978439279903
36-5-9.130659468953544.13065946895354
37-1-6.218365782133145.21836578213314
38-2-2.53919207220830.539192072208301
39-5-2.15903832686127-2.84096167313873
40-4-4.162039253799630.162039253799631
41-6-4.04779456735074-1.95220543264926
42-2-5.424183882328883.42418388232888
43-2-3.009986057993351.00998605799335
44-2-2.297902178269460.297902178269462
45-2-2.087868250373680.0878682503736838
462-2.025917331214514.02591733121451
4710.8125286156084050.187471384391595
48-80.94470405474269-8.94470405474269
49-1-5.361699400902954.36169940090295
501-2.286512563418123.28651256341812
51-10.0306210231283678-1.03062102312837
522-0.6960114000283932.69601140002839
5321.204793311401290.795206688598709
5411.76544844076495-0.765448440764952
55-11.22577416396212-2.22577416396212
56-2-0.343492945736715-1.65650705426328
57-2-1.51140210711007-0.488597892889932
58-1-1.855884766489780.855884766489779
59-8-1.25244896626745-6.74755103373255
60-4-6.009764456623312.00976445662331
61-6-4.59279353878028-1.40720646121972
62-3-5.584934993157132.58493499315713
63-3-3.762443955589270.762443955589267
64-7-3.22488797085942-3.77511202914058
65-9-5.88650532570062-3.11349467429938
66-11-8.0816538127794-2.91834618722059
67-13-10.1392141710900-2.86078582891004
68-11-12.15619198577061.15619198577064
69-9-11.34102659965732.34102659965732
70-17-9.69050153505114-7.30949846494886
71-22-14.8440142836310-7.15598571636905
72-25-19.8892939009406-5.11070609905936
73-20-23.49256287514533.49256287514533
74-24-21.0301549016587-2.96984509834125
75-24-23.124024221011-0.875975778988984
76-22-23.74162505451751.74162505451751
77-19-22.51370401934093.51370401934088
78-18-20.0363906242782.03639062427800
79-17-18.60064710594641.60064710594640
80-11-17.47212162556936.47212162556929
81-11-12.90899578763761.90899578763756







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
82-11.5630711423624-18.5034914750874-4.62265080963752
83-11.5630711423624-20.0550548281408-3.07108745658413
84-11.5630711423624-21.3639965805111-1.76214570421382
85-11.5630711423624-22.5176360341677-0.608506250557186
86-11.5630711423624-23.56085612515810.434713840433171
87-11.5630711423624-24.52035469324681.39421240852196
88-11.5630711423624-25.4135422369732.28739995224814
89-11.5630711423624-26.25251980687223.12637752214729
90-11.5630711423624-27.04610232465653.91996003993162
91-11.5630711423624-27.80094683829374.67480455356879
92-11.5630711423624-28.52222677114125.3960844864163
93-11.5630711423624-29.21405729514616.08791501042124

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & -11.5630711423624 & -18.5034914750874 & -4.62265080963752 \tabularnewline
83 & -11.5630711423624 & -20.0550548281408 & -3.07108745658413 \tabularnewline
84 & -11.5630711423624 & -21.3639965805111 & -1.76214570421382 \tabularnewline
85 & -11.5630711423624 & -22.5176360341677 & -0.608506250557186 \tabularnewline
86 & -11.5630711423624 & -23.5608561251581 & 0.434713840433171 \tabularnewline
87 & -11.5630711423624 & -24.5203546932468 & 1.39421240852196 \tabularnewline
88 & -11.5630711423624 & -25.413542236973 & 2.28739995224814 \tabularnewline
89 & -11.5630711423624 & -26.2525198068722 & 3.12637752214729 \tabularnewline
90 & -11.5630711423624 & -27.0461023246565 & 3.91996003993162 \tabularnewline
91 & -11.5630711423624 & -27.8009468382937 & 4.67480455356879 \tabularnewline
92 & -11.5630711423624 & -28.5222267711412 & 5.3960844864163 \tabularnewline
93 & -11.5630711423624 & -29.2140572951461 & 6.08791501042124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72209&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]82[/C][C]-11.5630711423624[/C][C]-18.5034914750874[/C][C]-4.62265080963752[/C][/ROW]
[ROW][C]83[/C][C]-11.5630711423624[/C][C]-20.0550548281408[/C][C]-3.07108745658413[/C][/ROW]
[ROW][C]84[/C][C]-11.5630711423624[/C][C]-21.3639965805111[/C][C]-1.76214570421382[/C][/ROW]
[ROW][C]85[/C][C]-11.5630711423624[/C][C]-22.5176360341677[/C][C]-0.608506250557186[/C][/ROW]
[ROW][C]86[/C][C]-11.5630711423624[/C][C]-23.5608561251581[/C][C]0.434713840433171[/C][/ROW]
[ROW][C]87[/C][C]-11.5630711423624[/C][C]-24.5203546932468[/C][C]1.39421240852196[/C][/ROW]
[ROW][C]88[/C][C]-11.5630711423624[/C][C]-25.413542236973[/C][C]2.28739995224814[/C][/ROW]
[ROW][C]89[/C][C]-11.5630711423624[/C][C]-26.2525198068722[/C][C]3.12637752214729[/C][/ROW]
[ROW][C]90[/C][C]-11.5630711423624[/C][C]-27.0461023246565[/C][C]3.91996003993162[/C][/ROW]
[ROW][C]91[/C][C]-11.5630711423624[/C][C]-27.8009468382937[/C][C]4.67480455356879[/C][/ROW]
[ROW][C]92[/C][C]-11.5630711423624[/C][C]-28.5222267711412[/C][C]5.3960844864163[/C][/ROW]
[ROW][C]93[/C][C]-11.5630711423624[/C][C]-29.2140572951461[/C][C]6.08791501042124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72209&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72209&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
82-11.5630711423624-18.5034914750874-4.62265080963752
83-11.5630711423624-20.0550548281408-3.07108745658413
84-11.5630711423624-21.3639965805111-1.76214570421382
85-11.5630711423624-22.5176360341677-0.608506250557186
86-11.5630711423624-23.56085612515810.434713840433171
87-11.5630711423624-24.52035469324681.39421240852196
88-11.5630711423624-25.4135422369732.28739995224814
89-11.5630711423624-26.25251980687223.12637752214729
90-11.5630711423624-27.04610232465653.91996003993162
91-11.5630711423624-27.80094683829374.67480455356879
92-11.5630711423624-28.52222677114125.3960844864163
93-11.5630711423624-29.21405729514616.08791501042124



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')