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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 computationTue, 19 May 2015 20:23:10 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/19/t1432063511njsubhw79xj9u8d.htm/, Retrieved Sat, 04 May 2024 13:21:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279134, Retrieved Sat, 04 May 2024 13:21:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2015-03-12 21:39:53] [0335ebbfcd60b9f5a1dafeadb8874636]
- RMPD    [Exponential Smoothing] [] [2015-05-19 19:23:10] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
-23.5
5.9
8.4
7.8
4.8
3.5
8.7
6.8
6
3.6
8.7
8.9
8.1
7
7.9
8
7.5
6.3
7.6
8.4
6.8
8.8
8.7
8.7
7.4
2.8
4.8
-21.1
8.5
9.4
1.8
4.8
5.8
3.3
-9
-6
-0.9
-17.3
-9.2
-8.1
-20.9
-14.6
-13.9
-20.8
-16.1
-5
-7.2
-9.7
-1.4
0.2
2.6
-4.8
-6.2
-2
-0.8
-3.1
0.6
0.2
0.3
-0.1
4.3
-3.2
-1.3
1.5
2.5
-2.2
1.7
5.7
2.7
-4.8
-3.1
-0.5
-3.4
-4.7
-5.6
-1.7
-1.8
-5.4
-4.8
-2.8
-4.9
-6.8
-7.6
-6.6
-5.6
-1.4
0.1
-3.7
-5.6
-3.1
-3.8
-5.1
-4.1
-0.3
-0.3
-2.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279134&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279134&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.602313513255501
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.602313513255501 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279134&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]0.602313513255501[/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=279134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279134&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
alpha0.602313513255501
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25.9-23.529.4
38.4-5.7919827102882714.1919827102883
47.82.756040256006795.04395974399321
54.85.79408537013066-0.994085370130657
63.55.19533431837137-1.69533431837137
78.74.174211548930494.52578845106951
86.86.90015509114534-0.100155091145338
966.83983032632716-0.839830326327164
103.66.33398917193854-2.73398917193854
118.74.687270548585744.01272945141426
128.97.104191722210881.79580827778912
138.18.18583131513936-0.085831315139357
1478.13413395417043-1.13413395417043
157.97.451029747731680.448970252268316
1687.721450597722620.278549402277378
177.57.88922466682353-0.38922466682353
186.37.65478939030335-1.35478939030335
197.66.838781432908460.761218567091539
208.47.297273662408681.10272633759132
216.87.96146063696268-1.16146063696268
228.87.261897200205721.53810279979428
238.78.188317301297930.511682698702066
248.78.496510705225230.203489294774769
257.48.6190750572709-1.2190750572709
262.87.88480967660391-5.08480967660392
274.84.82216009605304-0.0221600960530424
28-21.14.80881277074525-25.9088127707453
298.5-10.796415273481319.2964152734813
309.40.8260764031263278.57392359687367
311.85.99026644714355-4.19026644714355
324.83.466412341887871.33358765811213
335.84.269650209479561.53034979052044
343.35.19140056831775-1.89140056831775
35-94.05218444704083-13.0521844470408
36-6-3.80932262291514-2.19067737708486
37-0.9-5.128797210316474.22879721031647
38-17.3-2.58173550572569-14.7182644942743
39-9.2-11.44674510229582.24674510229575
40-8.1-10.09350016634241.99350016634241
41-20.9-8.89278807747729-12.0072119225227
42-14.6-16.12489407493531.52489407493528
43-13.9-15.20642976731851.30642976731851
44-20.8-14.4195494643433-6.38045053565667
45-16.1-18.26258104262762.16258104262764
46-5-16.960029257142811.9600292571428
47-7.2-9.756342016634562.55634201663456
48-9.7-8.21662267551275-1.48337732448725
49-1.4-9.110080883308217.71008088330821
500.2-4.466194978998764.66619497899876
512.6-1.655682687662844.25568268766284
52-4.80.907572503243979-5.70757250324398
53-6.2-2.5301755433454-3.6698244566546
54-2-4.740560404863992.74056040486399
55-0.8-3.089883839121442.28988383912144
56-3.1-1.71065585903321-1.38934414096679
570.6-2.547476609699863.14747660969986
580.2-0.6517089150220250.851708915022025
590.3-0.1387131261440780.438713126144078
60-0.10.125529718175065-0.225529718175065
614.3-0.01030987872248134.31030987872248
62-3.22.58584800755075-5.78584800755075
63-1.3-0.899046433039484-0.400953566960516
641.5-1.14054618460782.6405461846078
652.50.4498904647567342.05010953524327
66-2.21.68469914148771-3.88469914148771
671.7-0.6551076463623822.35510764636238
685.70.7634055142130384.93659448578696
692.73.73678308246512-1.03678308246512
70-4.83.11231462158168-7.91231462158168
71-3.1-1.65337939612605-1.44662060387395
72-0.5-2.524698534393162.02469853439316
73-3.4-1.30519524685955-2.09480475314045
74-4.7-2.5669244573079-2.1330755426921
75-5.6-3.85170468146616-1.74829531853384
76-1.7-4.904726576980423.20472657698042
77-1.8-2.974476453376071.17447645337607
78-5.4-2.26707341450727-3.13292658549273
79-4.8-4.15407743298696-0.645922567013043
80-2.8-4.543125323615591.74312532361559
81-4.9-3.49321738590405-1.40678261409595
82-6.8-4.34054156458694-2.45945843541306
83-7.6-5.82190661552646-1.77809338447354
84-6.6-6.892876288825080.292876288825083
85-5.6-6.716472942353611.11647294235361
86-1.4-6.04400620198994.6440062019899
870.1-3.246858510889033.34685851088903
88-3.7-1.23100040282638-2.46899959717362
89-5.6-2.71811222442644-2.88188777557356
90-3.1-4.453912175340231.35391217534023
91-3.8-3.63843257637166-0.161567423628341
92-5.1-3.73574681892489-1.36425318107511
93-4.1-4.557454945388230.457454945388231
94-0.3-4.281923650075343.98192365007534
95-0.3-1.883557226883291.58355722688329
96-2.4-0.929759310118079-1.47024068988192

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5.9 & -23.5 & 29.4 \tabularnewline
3 & 8.4 & -5.79198271028827 & 14.1919827102883 \tabularnewline
4 & 7.8 & 2.75604025600679 & 5.04395974399321 \tabularnewline
5 & 4.8 & 5.79408537013066 & -0.994085370130657 \tabularnewline
6 & 3.5 & 5.19533431837137 & -1.69533431837137 \tabularnewline
7 & 8.7 & 4.17421154893049 & 4.52578845106951 \tabularnewline
8 & 6.8 & 6.90015509114534 & -0.100155091145338 \tabularnewline
9 & 6 & 6.83983032632716 & -0.839830326327164 \tabularnewline
10 & 3.6 & 6.33398917193854 & -2.73398917193854 \tabularnewline
11 & 8.7 & 4.68727054858574 & 4.01272945141426 \tabularnewline
12 & 8.9 & 7.10419172221088 & 1.79580827778912 \tabularnewline
13 & 8.1 & 8.18583131513936 & -0.085831315139357 \tabularnewline
14 & 7 & 8.13413395417043 & -1.13413395417043 \tabularnewline
15 & 7.9 & 7.45102974773168 & 0.448970252268316 \tabularnewline
16 & 8 & 7.72145059772262 & 0.278549402277378 \tabularnewline
17 & 7.5 & 7.88922466682353 & -0.38922466682353 \tabularnewline
18 & 6.3 & 7.65478939030335 & -1.35478939030335 \tabularnewline
19 & 7.6 & 6.83878143290846 & 0.761218567091539 \tabularnewline
20 & 8.4 & 7.29727366240868 & 1.10272633759132 \tabularnewline
21 & 6.8 & 7.96146063696268 & -1.16146063696268 \tabularnewline
22 & 8.8 & 7.26189720020572 & 1.53810279979428 \tabularnewline
23 & 8.7 & 8.18831730129793 & 0.511682698702066 \tabularnewline
24 & 8.7 & 8.49651070522523 & 0.203489294774769 \tabularnewline
25 & 7.4 & 8.6190750572709 & -1.2190750572709 \tabularnewline
26 & 2.8 & 7.88480967660391 & -5.08480967660392 \tabularnewline
27 & 4.8 & 4.82216009605304 & -0.0221600960530424 \tabularnewline
28 & -21.1 & 4.80881277074525 & -25.9088127707453 \tabularnewline
29 & 8.5 & -10.7964152734813 & 19.2964152734813 \tabularnewline
30 & 9.4 & 0.826076403126327 & 8.57392359687367 \tabularnewline
31 & 1.8 & 5.99026644714355 & -4.19026644714355 \tabularnewline
32 & 4.8 & 3.46641234188787 & 1.33358765811213 \tabularnewline
33 & 5.8 & 4.26965020947956 & 1.53034979052044 \tabularnewline
34 & 3.3 & 5.19140056831775 & -1.89140056831775 \tabularnewline
35 & -9 & 4.05218444704083 & -13.0521844470408 \tabularnewline
36 & -6 & -3.80932262291514 & -2.19067737708486 \tabularnewline
37 & -0.9 & -5.12879721031647 & 4.22879721031647 \tabularnewline
38 & -17.3 & -2.58173550572569 & -14.7182644942743 \tabularnewline
39 & -9.2 & -11.4467451022958 & 2.24674510229575 \tabularnewline
40 & -8.1 & -10.0935001663424 & 1.99350016634241 \tabularnewline
41 & -20.9 & -8.89278807747729 & -12.0072119225227 \tabularnewline
42 & -14.6 & -16.1248940749353 & 1.52489407493528 \tabularnewline
43 & -13.9 & -15.2064297673185 & 1.30642976731851 \tabularnewline
44 & -20.8 & -14.4195494643433 & -6.38045053565667 \tabularnewline
45 & -16.1 & -18.2625810426276 & 2.16258104262764 \tabularnewline
46 & -5 & -16.9600292571428 & 11.9600292571428 \tabularnewline
47 & -7.2 & -9.75634201663456 & 2.55634201663456 \tabularnewline
48 & -9.7 & -8.21662267551275 & -1.48337732448725 \tabularnewline
49 & -1.4 & -9.11008088330821 & 7.71008088330821 \tabularnewline
50 & 0.2 & -4.46619497899876 & 4.66619497899876 \tabularnewline
51 & 2.6 & -1.65568268766284 & 4.25568268766284 \tabularnewline
52 & -4.8 & 0.907572503243979 & -5.70757250324398 \tabularnewline
53 & -6.2 & -2.5301755433454 & -3.6698244566546 \tabularnewline
54 & -2 & -4.74056040486399 & 2.74056040486399 \tabularnewline
55 & -0.8 & -3.08988383912144 & 2.28988383912144 \tabularnewline
56 & -3.1 & -1.71065585903321 & -1.38934414096679 \tabularnewline
57 & 0.6 & -2.54747660969986 & 3.14747660969986 \tabularnewline
58 & 0.2 & -0.651708915022025 & 0.851708915022025 \tabularnewline
59 & 0.3 & -0.138713126144078 & 0.438713126144078 \tabularnewline
60 & -0.1 & 0.125529718175065 & -0.225529718175065 \tabularnewline
61 & 4.3 & -0.0103098787224813 & 4.31030987872248 \tabularnewline
62 & -3.2 & 2.58584800755075 & -5.78584800755075 \tabularnewline
63 & -1.3 & -0.899046433039484 & -0.400953566960516 \tabularnewline
64 & 1.5 & -1.1405461846078 & 2.6405461846078 \tabularnewline
65 & 2.5 & 0.449890464756734 & 2.05010953524327 \tabularnewline
66 & -2.2 & 1.68469914148771 & -3.88469914148771 \tabularnewline
67 & 1.7 & -0.655107646362382 & 2.35510764636238 \tabularnewline
68 & 5.7 & 0.763405514213038 & 4.93659448578696 \tabularnewline
69 & 2.7 & 3.73678308246512 & -1.03678308246512 \tabularnewline
70 & -4.8 & 3.11231462158168 & -7.91231462158168 \tabularnewline
71 & -3.1 & -1.65337939612605 & -1.44662060387395 \tabularnewline
72 & -0.5 & -2.52469853439316 & 2.02469853439316 \tabularnewline
73 & -3.4 & -1.30519524685955 & -2.09480475314045 \tabularnewline
74 & -4.7 & -2.5669244573079 & -2.1330755426921 \tabularnewline
75 & -5.6 & -3.85170468146616 & -1.74829531853384 \tabularnewline
76 & -1.7 & -4.90472657698042 & 3.20472657698042 \tabularnewline
77 & -1.8 & -2.97447645337607 & 1.17447645337607 \tabularnewline
78 & -5.4 & -2.26707341450727 & -3.13292658549273 \tabularnewline
79 & -4.8 & -4.15407743298696 & -0.645922567013043 \tabularnewline
80 & -2.8 & -4.54312532361559 & 1.74312532361559 \tabularnewline
81 & -4.9 & -3.49321738590405 & -1.40678261409595 \tabularnewline
82 & -6.8 & -4.34054156458694 & -2.45945843541306 \tabularnewline
83 & -7.6 & -5.82190661552646 & -1.77809338447354 \tabularnewline
84 & -6.6 & -6.89287628882508 & 0.292876288825083 \tabularnewline
85 & -5.6 & -6.71647294235361 & 1.11647294235361 \tabularnewline
86 & -1.4 & -6.0440062019899 & 4.6440062019899 \tabularnewline
87 & 0.1 & -3.24685851088903 & 3.34685851088903 \tabularnewline
88 & -3.7 & -1.23100040282638 & -2.46899959717362 \tabularnewline
89 & -5.6 & -2.71811222442644 & -2.88188777557356 \tabularnewline
90 & -3.1 & -4.45391217534023 & 1.35391217534023 \tabularnewline
91 & -3.8 & -3.63843257637166 & -0.161567423628341 \tabularnewline
92 & -5.1 & -3.73574681892489 & -1.36425318107511 \tabularnewline
93 & -4.1 & -4.55745494538823 & 0.457454945388231 \tabularnewline
94 & -0.3 & -4.28192365007534 & 3.98192365007534 \tabularnewline
95 & -0.3 & -1.88355722688329 & 1.58355722688329 \tabularnewline
96 & -2.4 & -0.929759310118079 & -1.47024068988192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279134&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]5.9[/C][C]-23.5[/C][C]29.4[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]-5.79198271028827[/C][C]14.1919827102883[/C][/ROW]
[ROW][C]4[/C][C]7.8[/C][C]2.75604025600679[/C][C]5.04395974399321[/C][/ROW]
[ROW][C]5[/C][C]4.8[/C][C]5.79408537013066[/C][C]-0.994085370130657[/C][/ROW]
[ROW][C]6[/C][C]3.5[/C][C]5.19533431837137[/C][C]-1.69533431837137[/C][/ROW]
[ROW][C]7[/C][C]8.7[/C][C]4.17421154893049[/C][C]4.52578845106951[/C][/ROW]
[ROW][C]8[/C][C]6.8[/C][C]6.90015509114534[/C][C]-0.100155091145338[/C][/ROW]
[ROW][C]9[/C][C]6[/C][C]6.83983032632716[/C][C]-0.839830326327164[/C][/ROW]
[ROW][C]10[/C][C]3.6[/C][C]6.33398917193854[/C][C]-2.73398917193854[/C][/ROW]
[ROW][C]11[/C][C]8.7[/C][C]4.68727054858574[/C][C]4.01272945141426[/C][/ROW]
[ROW][C]12[/C][C]8.9[/C][C]7.10419172221088[/C][C]1.79580827778912[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]8.18583131513936[/C][C]-0.085831315139357[/C][/ROW]
[ROW][C]14[/C][C]7[/C][C]8.13413395417043[/C][C]-1.13413395417043[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.45102974773168[/C][C]0.448970252268316[/C][/ROW]
[ROW][C]16[/C][C]8[/C][C]7.72145059772262[/C][C]0.278549402277378[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]7.88922466682353[/C][C]-0.38922466682353[/C][/ROW]
[ROW][C]18[/C][C]6.3[/C][C]7.65478939030335[/C][C]-1.35478939030335[/C][/ROW]
[ROW][C]19[/C][C]7.6[/C][C]6.83878143290846[/C][C]0.761218567091539[/C][/ROW]
[ROW][C]20[/C][C]8.4[/C][C]7.29727366240868[/C][C]1.10272633759132[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]7.96146063696268[/C][C]-1.16146063696268[/C][/ROW]
[ROW][C]22[/C][C]8.8[/C][C]7.26189720020572[/C][C]1.53810279979428[/C][/ROW]
[ROW][C]23[/C][C]8.7[/C][C]8.18831730129793[/C][C]0.511682698702066[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.49651070522523[/C][C]0.203489294774769[/C][/ROW]
[ROW][C]25[/C][C]7.4[/C][C]8.6190750572709[/C][C]-1.2190750572709[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]7.88480967660391[/C][C]-5.08480967660392[/C][/ROW]
[ROW][C]27[/C][C]4.8[/C][C]4.82216009605304[/C][C]-0.0221600960530424[/C][/ROW]
[ROW][C]28[/C][C]-21.1[/C][C]4.80881277074525[/C][C]-25.9088127707453[/C][/ROW]
[ROW][C]29[/C][C]8.5[/C][C]-10.7964152734813[/C][C]19.2964152734813[/C][/ROW]
[ROW][C]30[/C][C]9.4[/C][C]0.826076403126327[/C][C]8.57392359687367[/C][/ROW]
[ROW][C]31[/C][C]1.8[/C][C]5.99026644714355[/C][C]-4.19026644714355[/C][/ROW]
[ROW][C]32[/C][C]4.8[/C][C]3.46641234188787[/C][C]1.33358765811213[/C][/ROW]
[ROW][C]33[/C][C]5.8[/C][C]4.26965020947956[/C][C]1.53034979052044[/C][/ROW]
[ROW][C]34[/C][C]3.3[/C][C]5.19140056831775[/C][C]-1.89140056831775[/C][/ROW]
[ROW][C]35[/C][C]-9[/C][C]4.05218444704083[/C][C]-13.0521844470408[/C][/ROW]
[ROW][C]36[/C][C]-6[/C][C]-3.80932262291514[/C][C]-2.19067737708486[/C][/ROW]
[ROW][C]37[/C][C]-0.9[/C][C]-5.12879721031647[/C][C]4.22879721031647[/C][/ROW]
[ROW][C]38[/C][C]-17.3[/C][C]-2.58173550572569[/C][C]-14.7182644942743[/C][/ROW]
[ROW][C]39[/C][C]-9.2[/C][C]-11.4467451022958[/C][C]2.24674510229575[/C][/ROW]
[ROW][C]40[/C][C]-8.1[/C][C]-10.0935001663424[/C][C]1.99350016634241[/C][/ROW]
[ROW][C]41[/C][C]-20.9[/C][C]-8.89278807747729[/C][C]-12.0072119225227[/C][/ROW]
[ROW][C]42[/C][C]-14.6[/C][C]-16.1248940749353[/C][C]1.52489407493528[/C][/ROW]
[ROW][C]43[/C][C]-13.9[/C][C]-15.2064297673185[/C][C]1.30642976731851[/C][/ROW]
[ROW][C]44[/C][C]-20.8[/C][C]-14.4195494643433[/C][C]-6.38045053565667[/C][/ROW]
[ROW][C]45[/C][C]-16.1[/C][C]-18.2625810426276[/C][C]2.16258104262764[/C][/ROW]
[ROW][C]46[/C][C]-5[/C][C]-16.9600292571428[/C][C]11.9600292571428[/C][/ROW]
[ROW][C]47[/C][C]-7.2[/C][C]-9.75634201663456[/C][C]2.55634201663456[/C][/ROW]
[ROW][C]48[/C][C]-9.7[/C][C]-8.21662267551275[/C][C]-1.48337732448725[/C][/ROW]
[ROW][C]49[/C][C]-1.4[/C][C]-9.11008088330821[/C][C]7.71008088330821[/C][/ROW]
[ROW][C]50[/C][C]0.2[/C][C]-4.46619497899876[/C][C]4.66619497899876[/C][/ROW]
[ROW][C]51[/C][C]2.6[/C][C]-1.65568268766284[/C][C]4.25568268766284[/C][/ROW]
[ROW][C]52[/C][C]-4.8[/C][C]0.907572503243979[/C][C]-5.70757250324398[/C][/ROW]
[ROW][C]53[/C][C]-6.2[/C][C]-2.5301755433454[/C][C]-3.6698244566546[/C][/ROW]
[ROW][C]54[/C][C]-2[/C][C]-4.74056040486399[/C][C]2.74056040486399[/C][/ROW]
[ROW][C]55[/C][C]-0.8[/C][C]-3.08988383912144[/C][C]2.28988383912144[/C][/ROW]
[ROW][C]56[/C][C]-3.1[/C][C]-1.71065585903321[/C][C]-1.38934414096679[/C][/ROW]
[ROW][C]57[/C][C]0.6[/C][C]-2.54747660969986[/C][C]3.14747660969986[/C][/ROW]
[ROW][C]58[/C][C]0.2[/C][C]-0.651708915022025[/C][C]0.851708915022025[/C][/ROW]
[ROW][C]59[/C][C]0.3[/C][C]-0.138713126144078[/C][C]0.438713126144078[/C][/ROW]
[ROW][C]60[/C][C]-0.1[/C][C]0.125529718175065[/C][C]-0.225529718175065[/C][/ROW]
[ROW][C]61[/C][C]4.3[/C][C]-0.0103098787224813[/C][C]4.31030987872248[/C][/ROW]
[ROW][C]62[/C][C]-3.2[/C][C]2.58584800755075[/C][C]-5.78584800755075[/C][/ROW]
[ROW][C]63[/C][C]-1.3[/C][C]-0.899046433039484[/C][C]-0.400953566960516[/C][/ROW]
[ROW][C]64[/C][C]1.5[/C][C]-1.1405461846078[/C][C]2.6405461846078[/C][/ROW]
[ROW][C]65[/C][C]2.5[/C][C]0.449890464756734[/C][C]2.05010953524327[/C][/ROW]
[ROW][C]66[/C][C]-2.2[/C][C]1.68469914148771[/C][C]-3.88469914148771[/C][/ROW]
[ROW][C]67[/C][C]1.7[/C][C]-0.655107646362382[/C][C]2.35510764636238[/C][/ROW]
[ROW][C]68[/C][C]5.7[/C][C]0.763405514213038[/C][C]4.93659448578696[/C][/ROW]
[ROW][C]69[/C][C]2.7[/C][C]3.73678308246512[/C][C]-1.03678308246512[/C][/ROW]
[ROW][C]70[/C][C]-4.8[/C][C]3.11231462158168[/C][C]-7.91231462158168[/C][/ROW]
[ROW][C]71[/C][C]-3.1[/C][C]-1.65337939612605[/C][C]-1.44662060387395[/C][/ROW]
[ROW][C]72[/C][C]-0.5[/C][C]-2.52469853439316[/C][C]2.02469853439316[/C][/ROW]
[ROW][C]73[/C][C]-3.4[/C][C]-1.30519524685955[/C][C]-2.09480475314045[/C][/ROW]
[ROW][C]74[/C][C]-4.7[/C][C]-2.5669244573079[/C][C]-2.1330755426921[/C][/ROW]
[ROW][C]75[/C][C]-5.6[/C][C]-3.85170468146616[/C][C]-1.74829531853384[/C][/ROW]
[ROW][C]76[/C][C]-1.7[/C][C]-4.90472657698042[/C][C]3.20472657698042[/C][/ROW]
[ROW][C]77[/C][C]-1.8[/C][C]-2.97447645337607[/C][C]1.17447645337607[/C][/ROW]
[ROW][C]78[/C][C]-5.4[/C][C]-2.26707341450727[/C][C]-3.13292658549273[/C][/ROW]
[ROW][C]79[/C][C]-4.8[/C][C]-4.15407743298696[/C][C]-0.645922567013043[/C][/ROW]
[ROW][C]80[/C][C]-2.8[/C][C]-4.54312532361559[/C][C]1.74312532361559[/C][/ROW]
[ROW][C]81[/C][C]-4.9[/C][C]-3.49321738590405[/C][C]-1.40678261409595[/C][/ROW]
[ROW][C]82[/C][C]-6.8[/C][C]-4.34054156458694[/C][C]-2.45945843541306[/C][/ROW]
[ROW][C]83[/C][C]-7.6[/C][C]-5.82190661552646[/C][C]-1.77809338447354[/C][/ROW]
[ROW][C]84[/C][C]-6.6[/C][C]-6.89287628882508[/C][C]0.292876288825083[/C][/ROW]
[ROW][C]85[/C][C]-5.6[/C][C]-6.71647294235361[/C][C]1.11647294235361[/C][/ROW]
[ROW][C]86[/C][C]-1.4[/C][C]-6.0440062019899[/C][C]4.6440062019899[/C][/ROW]
[ROW][C]87[/C][C]0.1[/C][C]-3.24685851088903[/C][C]3.34685851088903[/C][/ROW]
[ROW][C]88[/C][C]-3.7[/C][C]-1.23100040282638[/C][C]-2.46899959717362[/C][/ROW]
[ROW][C]89[/C][C]-5.6[/C][C]-2.71811222442644[/C][C]-2.88188777557356[/C][/ROW]
[ROW][C]90[/C][C]-3.1[/C][C]-4.45391217534023[/C][C]1.35391217534023[/C][/ROW]
[ROW][C]91[/C][C]-3.8[/C][C]-3.63843257637166[/C][C]-0.161567423628341[/C][/ROW]
[ROW][C]92[/C][C]-5.1[/C][C]-3.73574681892489[/C][C]-1.36425318107511[/C][/ROW]
[ROW][C]93[/C][C]-4.1[/C][C]-4.55745494538823[/C][C]0.457454945388231[/C][/ROW]
[ROW][C]94[/C][C]-0.3[/C][C]-4.28192365007534[/C][C]3.98192365007534[/C][/ROW]
[ROW][C]95[/C][C]-0.3[/C][C]-1.88355722688329[/C][C]1.58355722688329[/C][/ROW]
[ROW][C]96[/C][C]-2.4[/C][C]-0.929759310118079[/C][C]-1.47024068988192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279134&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279134&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
25.9-23.529.4
38.4-5.7919827102882714.1919827102883
47.82.756040256006795.04395974399321
54.85.79408537013066-0.994085370130657
63.55.19533431837137-1.69533431837137
78.74.174211548930494.52578845106951
86.86.90015509114534-0.100155091145338
966.83983032632716-0.839830326327164
103.66.33398917193854-2.73398917193854
118.74.687270548585744.01272945141426
128.97.104191722210881.79580827778912
138.18.18583131513936-0.085831315139357
1478.13413395417043-1.13413395417043
157.97.451029747731680.448970252268316
1687.721450597722620.278549402277378
177.57.88922466682353-0.38922466682353
186.37.65478939030335-1.35478939030335
197.66.838781432908460.761218567091539
208.47.297273662408681.10272633759132
216.87.96146063696268-1.16146063696268
228.87.261897200205721.53810279979428
238.78.188317301297930.511682698702066
248.78.496510705225230.203489294774769
257.48.6190750572709-1.2190750572709
262.87.88480967660391-5.08480967660392
274.84.82216009605304-0.0221600960530424
28-21.14.80881277074525-25.9088127707453
298.5-10.796415273481319.2964152734813
309.40.8260764031263278.57392359687367
311.85.99026644714355-4.19026644714355
324.83.466412341887871.33358765811213
335.84.269650209479561.53034979052044
343.35.19140056831775-1.89140056831775
35-94.05218444704083-13.0521844470408
36-6-3.80932262291514-2.19067737708486
37-0.9-5.128797210316474.22879721031647
38-17.3-2.58173550572569-14.7182644942743
39-9.2-11.44674510229582.24674510229575
40-8.1-10.09350016634241.99350016634241
41-20.9-8.89278807747729-12.0072119225227
42-14.6-16.12489407493531.52489407493528
43-13.9-15.20642976731851.30642976731851
44-20.8-14.4195494643433-6.38045053565667
45-16.1-18.26258104262762.16258104262764
46-5-16.960029257142811.9600292571428
47-7.2-9.756342016634562.55634201663456
48-9.7-8.21662267551275-1.48337732448725
49-1.4-9.110080883308217.71008088330821
500.2-4.466194978998764.66619497899876
512.6-1.655682687662844.25568268766284
52-4.80.907572503243979-5.70757250324398
53-6.2-2.5301755433454-3.6698244566546
54-2-4.740560404863992.74056040486399
55-0.8-3.089883839121442.28988383912144
56-3.1-1.71065585903321-1.38934414096679
570.6-2.547476609699863.14747660969986
580.2-0.6517089150220250.851708915022025
590.3-0.1387131261440780.438713126144078
60-0.10.125529718175065-0.225529718175065
614.3-0.01030987872248134.31030987872248
62-3.22.58584800755075-5.78584800755075
63-1.3-0.899046433039484-0.400953566960516
641.5-1.14054618460782.6405461846078
652.50.4498904647567342.05010953524327
66-2.21.68469914148771-3.88469914148771
671.7-0.6551076463623822.35510764636238
685.70.7634055142130384.93659448578696
692.73.73678308246512-1.03678308246512
70-4.83.11231462158168-7.91231462158168
71-3.1-1.65337939612605-1.44662060387395
72-0.5-2.524698534393162.02469853439316
73-3.4-1.30519524685955-2.09480475314045
74-4.7-2.5669244573079-2.1330755426921
75-5.6-3.85170468146616-1.74829531853384
76-1.7-4.904726576980423.20472657698042
77-1.8-2.974476453376071.17447645337607
78-5.4-2.26707341450727-3.13292658549273
79-4.8-4.15407743298696-0.645922567013043
80-2.8-4.543125323615591.74312532361559
81-4.9-3.49321738590405-1.40678261409595
82-6.8-4.34054156458694-2.45945843541306
83-7.6-5.82190661552646-1.77809338447354
84-6.6-6.892876288825080.292876288825083
85-5.6-6.716472942353611.11647294235361
86-1.4-6.04400620198994.6440062019899
870.1-3.246858510889033.34685851088903
88-3.7-1.23100040282638-2.46899959717362
89-5.6-2.71811222442644-2.88188777557356
90-3.1-4.453912175340231.35391217534023
91-3.8-3.63843257637166-0.161567423628341
92-5.1-3.73574681892489-1.36425318107511
93-4.1-4.557454945388230.457454945388231
94-0.3-4.281923650075343.98192365007534
95-0.3-1.883557226883291.58355722688329
96-2.4-0.929759310118079-1.47024068988192







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97-1.81530514537205-13.847949808909310.2173395181652
98-1.81530514537205-15.862002237837512.2313919470934
99-1.81530514537205-17.621470424022113.990860133278
100-1.81530514537205-19.203807738307615.5731974475635
101-1.81530514537205-20.653701680986517.0230913902424
102-1.81530514537205-21.999713624234618.3691033334905
103-1.81530514537205-23.261412187213119.630801896469
104-1.81530514537205-24.452899294455720.8222890037116
105-1.81530514537205-25.584735733149121.954125442405
106-1.81530514537205-26.665073596520223.0344633057761
107-1.81530514537205-27.700361716378524.0697514256344
108-1.81530514537205-28.695805797196425.0651955064523

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & -1.81530514537205 & -13.8479498089093 & 10.2173395181652 \tabularnewline
98 & -1.81530514537205 & -15.8620022378375 & 12.2313919470934 \tabularnewline
99 & -1.81530514537205 & -17.6214704240221 & 13.990860133278 \tabularnewline
100 & -1.81530514537205 & -19.2038077383076 & 15.5731974475635 \tabularnewline
101 & -1.81530514537205 & -20.6537016809865 & 17.0230913902424 \tabularnewline
102 & -1.81530514537205 & -21.9997136242346 & 18.3691033334905 \tabularnewline
103 & -1.81530514537205 & -23.2614121872131 & 19.630801896469 \tabularnewline
104 & -1.81530514537205 & -24.4528992944557 & 20.8222890037116 \tabularnewline
105 & -1.81530514537205 & -25.5847357331491 & 21.954125442405 \tabularnewline
106 & -1.81530514537205 & -26.6650735965202 & 23.0344633057761 \tabularnewline
107 & -1.81530514537205 & -27.7003617163785 & 24.0697514256344 \tabularnewline
108 & -1.81530514537205 & -28.6958057971964 & 25.0651955064523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279134&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]97[/C][C]-1.81530514537205[/C][C]-13.8479498089093[/C][C]10.2173395181652[/C][/ROW]
[ROW][C]98[/C][C]-1.81530514537205[/C][C]-15.8620022378375[/C][C]12.2313919470934[/C][/ROW]
[ROW][C]99[/C][C]-1.81530514537205[/C][C]-17.6214704240221[/C][C]13.990860133278[/C][/ROW]
[ROW][C]100[/C][C]-1.81530514537205[/C][C]-19.2038077383076[/C][C]15.5731974475635[/C][/ROW]
[ROW][C]101[/C][C]-1.81530514537205[/C][C]-20.6537016809865[/C][C]17.0230913902424[/C][/ROW]
[ROW][C]102[/C][C]-1.81530514537205[/C][C]-21.9997136242346[/C][C]18.3691033334905[/C][/ROW]
[ROW][C]103[/C][C]-1.81530514537205[/C][C]-23.2614121872131[/C][C]19.630801896469[/C][/ROW]
[ROW][C]104[/C][C]-1.81530514537205[/C][C]-24.4528992944557[/C][C]20.8222890037116[/C][/ROW]
[ROW][C]105[/C][C]-1.81530514537205[/C][C]-25.5847357331491[/C][C]21.954125442405[/C][/ROW]
[ROW][C]106[/C][C]-1.81530514537205[/C][C]-26.6650735965202[/C][C]23.0344633057761[/C][/ROW]
[ROW][C]107[/C][C]-1.81530514537205[/C][C]-27.7003617163785[/C][C]24.0697514256344[/C][/ROW]
[ROW][C]108[/C][C]-1.81530514537205[/C][C]-28.6958057971964[/C][C]25.0651955064523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279134&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279134&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
97-1.81530514537205-13.847949808909310.2173395181652
98-1.81530514537205-15.862002237837512.2313919470934
99-1.81530514537205-17.621470424022113.990860133278
100-1.81530514537205-19.203807738307615.5731974475635
101-1.81530514537205-20.653701680986517.0230913902424
102-1.81530514537205-21.999713624234618.3691033334905
103-1.81530514537205-23.261412187213119.630801896469
104-1.81530514537205-24.452899294455720.8222890037116
105-1.81530514537205-25.584735733149121.954125442405
106-1.81530514537205-26.665073596520223.0344633057761
107-1.81530514537205-27.700361716378524.0697514256344
108-1.81530514537205-28.695805797196425.0651955064523



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')