Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Aug 2016 10:39:16 +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/2016/Aug/07/t1470562792caaqk7k7c8ve72w.htm/, Retrieved Fri, 03 May 2024 02:14:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296070, Retrieved Fri, 03 May 2024 02:14:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-08-07 09:39:16] [e98d32ae432942f69cb1b3451eac7d8c] [Current]
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Dataseries X:
107478
107564
107641
107726
107808
107894
107976
108061
108147
108229
108314
108397
108482
108567
108647
108732
108815
108900
108983
109068
109153
109236
109321
109403
109489
109574
109651
109736
109819
109904
109986
110072
110157
110239
110325
110407
110492
110578
110655
110740
110822
110908
110990
111075
111161
111243
111328
111411
111496
111581
111658
111744
111826
111911
111994
112079
112164
112247
112332
112415
112500
112585
112665
112750
112833
112918
113000
113086
113171
113253
113339
113421
113506
113592
113669
113754
113836
113922
114004
114089
114175
114257
114342
114425
114510
114595
114672
114758
114840
114925
115008
115093
115178
115261
115346
115429
115514
115599
115676
115761
115844
115929
116012
116097
116182
116265
116350
116432




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296070&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296070&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.64035286875736
beta0.126686023109955
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.64035286875736 \tabularnewline
beta & 0.126686023109955 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296070&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]0.64035286875736[/C][/ROW]
[ROW][C]beta[/C][C]0.126686023109955[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296070&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
alpha0.64035286875736
beta0.126686023109955
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3107641107650-9
4107726107729.506710356-3.50671035620326
5107808107812.246586971-4.24658697124687
6107894107894.168182378-0.168182378154597
7107976107978.68775228-2.6877522795985
8108061108061.3758678-0.375867800234118
9108147108145.5139133711.48608662911283
10108229108230.964823734-1.96482373442268
11108314108314.046539861-0.0465398610540433
12108397108398.352859081-1.35285908063815
13108482108481.7129240270.287075972664752
14108567108566.1464147720.853585228163865
15108647108651.011917385-4.01191738503985
16108732108732.436319626-0.436319625543547
17108815108816.114970261-1.11497026099823
18108900108899.2685944370.73140556285216
19108983108983.663885037-0.66388503703638
20109068109067.1118404490.888159550755518
21109153109151.6257029061.37429709357093
22109236109236.562353079-0.56235307904717
23109321109320.2132435630.786756437417353
24109403109404.791864834-1.79186483436206
25109489109487.5738957681.42610423246515
26109574109572.5322533591.46774664068653
27109651109657.63634591-6.63634591043228
28109736109737.012594226-1.0125942259474
29109819109819.907882617-0.90788261652051
30109904109902.7965725371.20342746340611
31109986109987.134872482-1.13487248188176
32110072110069.8837702282.11622977176739
33110157110154.8861971422.11380285808991
34110239110240.058549607-1.05854960667784
35110325110323.1136035471.88639645255171
36110407110408.207493716-1.2074937155121
37110492110491.222246010.777753989517805
38110578110575.5713516952.42864830476174
39110655110661.174633369-6.17463336893707
40110740110740.767869477-0.7678694769711
41110822110823.761049896-1.76104989602754
42110908110905.9753813982.02461860163021
43110990110990.778121253-0.778121253490099
44111075111073.7229944811.27700551851012
45111161111158.0874695212.91253047934151
46111243111243.735533079-0.735533079161542
47111328111326.9878794651.01212053518975
48111411111411.441447878-0.441447877688915
49111496111494.9284076771.07159232348204
50111581111579.4711787051.5288212946034
51111658111664.430761347-6.43076134682633
52111744111743.771714880.228285119665088
53111826111827.395327269-1.39532726873585
54111911111909.8660606141.13393938566151
55111994111994.048406543-0.0484065426135203
56112079112077.4697069431.53029305681412
57112164112162.0260752851.97392471473722
58112247112247.026656624-0.0266566236969084
59112332112330.7439974771.25600252262666
60112415112415.38458444-0.38458444015123
61112500112498.94341791.05658210032561
62112585112583.5108203991.4891796012671
63112665112668.476045795-3.4760457946104
64112750112749.9797849650.0202150347759016
65112833112833.724004707-0.724004707459244
66112918112916.932927221.06707278014801
67113000113001.375336294-1.37533629393147
68113086113084.1421692621.85783073838684
69113171113169.1300842251.86991577455774
70113253113254.277432472-1.2774324722559
71113339113337.3057371171.69426288289833
72113421113422.37442038-1.37442038033623
73113506113505.3665653660.633434634131845
74113592113589.6958326682.30416733186576
75113669113675.28188116-6.28188116010278
76113754113754.86021906-0.860219059861265
77113836113837.840549636-1.84054963583185
78113922113920.0438104111.95618958870182
79114004114004.837017493-0.837017492565792
80114089114087.7736844021.22631559848378
81114175114172.1310959052.86890409523039
82114257114257.773079947-0.773079946593498
83114342114341.0201939090.9798060914909
84114425114425.469259026-0.469259026096552
85114510114508.9523430831.0476569172024
86114595114593.4917784821.50822151798639
87114672114678.448490343-6.4484903425182
88114758114757.7869731650.213026834870107
89114840114841.40845916-1.40845916002581
90114925114923.8773624461.12263755407184
91115008115008.058133351-0.0581333514273865
92115093115091.4780782241.52192177571123
93115178115176.0332799451.96672005503206
94115261115261.032857242-0.0328572422586149
95115346115344.7493339781.25066602205334
96115429115429.389177246-0.389177246179315
97115514115512.9473706521.05262934757047
98115599115597.5142222961.48577770401607
99115676115682.478973604-6.47897360357456
100115761115761.817874874-0.817874873551773
101115844115844.715527872-0.715527872031089
102115929115927.6206727561.37932724361599
103116012116011.9791603340.0208396663510939
104116097116095.4694270861.53057291431469
105116182116180.0506216811.94937831866264
106116265116265.058140415-0.0581404147378635
107116350116348.7754221991.22457780083641
108116432116433.413438626-1.4134386263031

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 107641 & 107650 & -9 \tabularnewline
4 & 107726 & 107729.506710356 & -3.50671035620326 \tabularnewline
5 & 107808 & 107812.246586971 & -4.24658697124687 \tabularnewline
6 & 107894 & 107894.168182378 & -0.168182378154597 \tabularnewline
7 & 107976 & 107978.68775228 & -2.6877522795985 \tabularnewline
8 & 108061 & 108061.3758678 & -0.375867800234118 \tabularnewline
9 & 108147 & 108145.513913371 & 1.48608662911283 \tabularnewline
10 & 108229 & 108230.964823734 & -1.96482373442268 \tabularnewline
11 & 108314 & 108314.046539861 & -0.0465398610540433 \tabularnewline
12 & 108397 & 108398.352859081 & -1.35285908063815 \tabularnewline
13 & 108482 & 108481.712924027 & 0.287075972664752 \tabularnewline
14 & 108567 & 108566.146414772 & 0.853585228163865 \tabularnewline
15 & 108647 & 108651.011917385 & -4.01191738503985 \tabularnewline
16 & 108732 & 108732.436319626 & -0.436319625543547 \tabularnewline
17 & 108815 & 108816.114970261 & -1.11497026099823 \tabularnewline
18 & 108900 & 108899.268594437 & 0.73140556285216 \tabularnewline
19 & 108983 & 108983.663885037 & -0.66388503703638 \tabularnewline
20 & 109068 & 109067.111840449 & 0.888159550755518 \tabularnewline
21 & 109153 & 109151.625702906 & 1.37429709357093 \tabularnewline
22 & 109236 & 109236.562353079 & -0.56235307904717 \tabularnewline
23 & 109321 & 109320.213243563 & 0.786756437417353 \tabularnewline
24 & 109403 & 109404.791864834 & -1.79186483436206 \tabularnewline
25 & 109489 & 109487.573895768 & 1.42610423246515 \tabularnewline
26 & 109574 & 109572.532253359 & 1.46774664068653 \tabularnewline
27 & 109651 & 109657.63634591 & -6.63634591043228 \tabularnewline
28 & 109736 & 109737.012594226 & -1.0125942259474 \tabularnewline
29 & 109819 & 109819.907882617 & -0.90788261652051 \tabularnewline
30 & 109904 & 109902.796572537 & 1.20342746340611 \tabularnewline
31 & 109986 & 109987.134872482 & -1.13487248188176 \tabularnewline
32 & 110072 & 110069.883770228 & 2.11622977176739 \tabularnewline
33 & 110157 & 110154.886197142 & 2.11380285808991 \tabularnewline
34 & 110239 & 110240.058549607 & -1.05854960667784 \tabularnewline
35 & 110325 & 110323.113603547 & 1.88639645255171 \tabularnewline
36 & 110407 & 110408.207493716 & -1.2074937155121 \tabularnewline
37 & 110492 & 110491.22224601 & 0.777753989517805 \tabularnewline
38 & 110578 & 110575.571351695 & 2.42864830476174 \tabularnewline
39 & 110655 & 110661.174633369 & -6.17463336893707 \tabularnewline
40 & 110740 & 110740.767869477 & -0.7678694769711 \tabularnewline
41 & 110822 & 110823.761049896 & -1.76104989602754 \tabularnewline
42 & 110908 & 110905.975381398 & 2.02461860163021 \tabularnewline
43 & 110990 & 110990.778121253 & -0.778121253490099 \tabularnewline
44 & 111075 & 111073.722994481 & 1.27700551851012 \tabularnewline
45 & 111161 & 111158.087469521 & 2.91253047934151 \tabularnewline
46 & 111243 & 111243.735533079 & -0.735533079161542 \tabularnewline
47 & 111328 & 111326.987879465 & 1.01212053518975 \tabularnewline
48 & 111411 & 111411.441447878 & -0.441447877688915 \tabularnewline
49 & 111496 & 111494.928407677 & 1.07159232348204 \tabularnewline
50 & 111581 & 111579.471178705 & 1.5288212946034 \tabularnewline
51 & 111658 & 111664.430761347 & -6.43076134682633 \tabularnewline
52 & 111744 & 111743.77171488 & 0.228285119665088 \tabularnewline
53 & 111826 & 111827.395327269 & -1.39532726873585 \tabularnewline
54 & 111911 & 111909.866060614 & 1.13393938566151 \tabularnewline
55 & 111994 & 111994.048406543 & -0.0484065426135203 \tabularnewline
56 & 112079 & 112077.469706943 & 1.53029305681412 \tabularnewline
57 & 112164 & 112162.026075285 & 1.97392471473722 \tabularnewline
58 & 112247 & 112247.026656624 & -0.0266566236969084 \tabularnewline
59 & 112332 & 112330.743997477 & 1.25600252262666 \tabularnewline
60 & 112415 & 112415.38458444 & -0.38458444015123 \tabularnewline
61 & 112500 & 112498.9434179 & 1.05658210032561 \tabularnewline
62 & 112585 & 112583.510820399 & 1.4891796012671 \tabularnewline
63 & 112665 & 112668.476045795 & -3.4760457946104 \tabularnewline
64 & 112750 & 112749.979784965 & 0.0202150347759016 \tabularnewline
65 & 112833 & 112833.724004707 & -0.724004707459244 \tabularnewline
66 & 112918 & 112916.93292722 & 1.06707278014801 \tabularnewline
67 & 113000 & 113001.375336294 & -1.37533629393147 \tabularnewline
68 & 113086 & 113084.142169262 & 1.85783073838684 \tabularnewline
69 & 113171 & 113169.130084225 & 1.86991577455774 \tabularnewline
70 & 113253 & 113254.277432472 & -1.2774324722559 \tabularnewline
71 & 113339 & 113337.305737117 & 1.69426288289833 \tabularnewline
72 & 113421 & 113422.37442038 & -1.37442038033623 \tabularnewline
73 & 113506 & 113505.366565366 & 0.633434634131845 \tabularnewline
74 & 113592 & 113589.695832668 & 2.30416733186576 \tabularnewline
75 & 113669 & 113675.28188116 & -6.28188116010278 \tabularnewline
76 & 113754 & 113754.86021906 & -0.860219059861265 \tabularnewline
77 & 113836 & 113837.840549636 & -1.84054963583185 \tabularnewline
78 & 113922 & 113920.043810411 & 1.95618958870182 \tabularnewline
79 & 114004 & 114004.837017493 & -0.837017492565792 \tabularnewline
80 & 114089 & 114087.773684402 & 1.22631559848378 \tabularnewline
81 & 114175 & 114172.131095905 & 2.86890409523039 \tabularnewline
82 & 114257 & 114257.773079947 & -0.773079946593498 \tabularnewline
83 & 114342 & 114341.020193909 & 0.9798060914909 \tabularnewline
84 & 114425 & 114425.469259026 & -0.469259026096552 \tabularnewline
85 & 114510 & 114508.952343083 & 1.0476569172024 \tabularnewline
86 & 114595 & 114593.491778482 & 1.50822151798639 \tabularnewline
87 & 114672 & 114678.448490343 & -6.4484903425182 \tabularnewline
88 & 114758 & 114757.786973165 & 0.213026834870107 \tabularnewline
89 & 114840 & 114841.40845916 & -1.40845916002581 \tabularnewline
90 & 114925 & 114923.877362446 & 1.12263755407184 \tabularnewline
91 & 115008 & 115008.058133351 & -0.0581333514273865 \tabularnewline
92 & 115093 & 115091.478078224 & 1.52192177571123 \tabularnewline
93 & 115178 & 115176.033279945 & 1.96672005503206 \tabularnewline
94 & 115261 & 115261.032857242 & -0.0328572422586149 \tabularnewline
95 & 115346 & 115344.749333978 & 1.25066602205334 \tabularnewline
96 & 115429 & 115429.389177246 & -0.389177246179315 \tabularnewline
97 & 115514 & 115512.947370652 & 1.05262934757047 \tabularnewline
98 & 115599 & 115597.514222296 & 1.48577770401607 \tabularnewline
99 & 115676 & 115682.478973604 & -6.47897360357456 \tabularnewline
100 & 115761 & 115761.817874874 & -0.817874873551773 \tabularnewline
101 & 115844 & 115844.715527872 & -0.715527872031089 \tabularnewline
102 & 115929 & 115927.620672756 & 1.37932724361599 \tabularnewline
103 & 116012 & 116011.979160334 & 0.0208396663510939 \tabularnewline
104 & 116097 & 116095.469427086 & 1.53057291431469 \tabularnewline
105 & 116182 & 116180.050621681 & 1.94937831866264 \tabularnewline
106 & 116265 & 116265.058140415 & -0.0581404147378635 \tabularnewline
107 & 116350 & 116348.775422199 & 1.22457780083641 \tabularnewline
108 & 116432 & 116433.413438626 & -1.4134386263031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296070&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]107641[/C][C]107650[/C][C]-9[/C][/ROW]
[ROW][C]4[/C][C]107726[/C][C]107729.506710356[/C][C]-3.50671035620326[/C][/ROW]
[ROW][C]5[/C][C]107808[/C][C]107812.246586971[/C][C]-4.24658697124687[/C][/ROW]
[ROW][C]6[/C][C]107894[/C][C]107894.168182378[/C][C]-0.168182378154597[/C][/ROW]
[ROW][C]7[/C][C]107976[/C][C]107978.68775228[/C][C]-2.6877522795985[/C][/ROW]
[ROW][C]8[/C][C]108061[/C][C]108061.3758678[/C][C]-0.375867800234118[/C][/ROW]
[ROW][C]9[/C][C]108147[/C][C]108145.513913371[/C][C]1.48608662911283[/C][/ROW]
[ROW][C]10[/C][C]108229[/C][C]108230.964823734[/C][C]-1.96482373442268[/C][/ROW]
[ROW][C]11[/C][C]108314[/C][C]108314.046539861[/C][C]-0.0465398610540433[/C][/ROW]
[ROW][C]12[/C][C]108397[/C][C]108398.352859081[/C][C]-1.35285908063815[/C][/ROW]
[ROW][C]13[/C][C]108482[/C][C]108481.712924027[/C][C]0.287075972664752[/C][/ROW]
[ROW][C]14[/C][C]108567[/C][C]108566.146414772[/C][C]0.853585228163865[/C][/ROW]
[ROW][C]15[/C][C]108647[/C][C]108651.011917385[/C][C]-4.01191738503985[/C][/ROW]
[ROW][C]16[/C][C]108732[/C][C]108732.436319626[/C][C]-0.436319625543547[/C][/ROW]
[ROW][C]17[/C][C]108815[/C][C]108816.114970261[/C][C]-1.11497026099823[/C][/ROW]
[ROW][C]18[/C][C]108900[/C][C]108899.268594437[/C][C]0.73140556285216[/C][/ROW]
[ROW][C]19[/C][C]108983[/C][C]108983.663885037[/C][C]-0.66388503703638[/C][/ROW]
[ROW][C]20[/C][C]109068[/C][C]109067.111840449[/C][C]0.888159550755518[/C][/ROW]
[ROW][C]21[/C][C]109153[/C][C]109151.625702906[/C][C]1.37429709357093[/C][/ROW]
[ROW][C]22[/C][C]109236[/C][C]109236.562353079[/C][C]-0.56235307904717[/C][/ROW]
[ROW][C]23[/C][C]109321[/C][C]109320.213243563[/C][C]0.786756437417353[/C][/ROW]
[ROW][C]24[/C][C]109403[/C][C]109404.791864834[/C][C]-1.79186483436206[/C][/ROW]
[ROW][C]25[/C][C]109489[/C][C]109487.573895768[/C][C]1.42610423246515[/C][/ROW]
[ROW][C]26[/C][C]109574[/C][C]109572.532253359[/C][C]1.46774664068653[/C][/ROW]
[ROW][C]27[/C][C]109651[/C][C]109657.63634591[/C][C]-6.63634591043228[/C][/ROW]
[ROW][C]28[/C][C]109736[/C][C]109737.012594226[/C][C]-1.0125942259474[/C][/ROW]
[ROW][C]29[/C][C]109819[/C][C]109819.907882617[/C][C]-0.90788261652051[/C][/ROW]
[ROW][C]30[/C][C]109904[/C][C]109902.796572537[/C][C]1.20342746340611[/C][/ROW]
[ROW][C]31[/C][C]109986[/C][C]109987.134872482[/C][C]-1.13487248188176[/C][/ROW]
[ROW][C]32[/C][C]110072[/C][C]110069.883770228[/C][C]2.11622977176739[/C][/ROW]
[ROW][C]33[/C][C]110157[/C][C]110154.886197142[/C][C]2.11380285808991[/C][/ROW]
[ROW][C]34[/C][C]110239[/C][C]110240.058549607[/C][C]-1.05854960667784[/C][/ROW]
[ROW][C]35[/C][C]110325[/C][C]110323.113603547[/C][C]1.88639645255171[/C][/ROW]
[ROW][C]36[/C][C]110407[/C][C]110408.207493716[/C][C]-1.2074937155121[/C][/ROW]
[ROW][C]37[/C][C]110492[/C][C]110491.22224601[/C][C]0.777753989517805[/C][/ROW]
[ROW][C]38[/C][C]110578[/C][C]110575.571351695[/C][C]2.42864830476174[/C][/ROW]
[ROW][C]39[/C][C]110655[/C][C]110661.174633369[/C][C]-6.17463336893707[/C][/ROW]
[ROW][C]40[/C][C]110740[/C][C]110740.767869477[/C][C]-0.7678694769711[/C][/ROW]
[ROW][C]41[/C][C]110822[/C][C]110823.761049896[/C][C]-1.76104989602754[/C][/ROW]
[ROW][C]42[/C][C]110908[/C][C]110905.975381398[/C][C]2.02461860163021[/C][/ROW]
[ROW][C]43[/C][C]110990[/C][C]110990.778121253[/C][C]-0.778121253490099[/C][/ROW]
[ROW][C]44[/C][C]111075[/C][C]111073.722994481[/C][C]1.27700551851012[/C][/ROW]
[ROW][C]45[/C][C]111161[/C][C]111158.087469521[/C][C]2.91253047934151[/C][/ROW]
[ROW][C]46[/C][C]111243[/C][C]111243.735533079[/C][C]-0.735533079161542[/C][/ROW]
[ROW][C]47[/C][C]111328[/C][C]111326.987879465[/C][C]1.01212053518975[/C][/ROW]
[ROW][C]48[/C][C]111411[/C][C]111411.441447878[/C][C]-0.441447877688915[/C][/ROW]
[ROW][C]49[/C][C]111496[/C][C]111494.928407677[/C][C]1.07159232348204[/C][/ROW]
[ROW][C]50[/C][C]111581[/C][C]111579.471178705[/C][C]1.5288212946034[/C][/ROW]
[ROW][C]51[/C][C]111658[/C][C]111664.430761347[/C][C]-6.43076134682633[/C][/ROW]
[ROW][C]52[/C][C]111744[/C][C]111743.77171488[/C][C]0.228285119665088[/C][/ROW]
[ROW][C]53[/C][C]111826[/C][C]111827.395327269[/C][C]-1.39532726873585[/C][/ROW]
[ROW][C]54[/C][C]111911[/C][C]111909.866060614[/C][C]1.13393938566151[/C][/ROW]
[ROW][C]55[/C][C]111994[/C][C]111994.048406543[/C][C]-0.0484065426135203[/C][/ROW]
[ROW][C]56[/C][C]112079[/C][C]112077.469706943[/C][C]1.53029305681412[/C][/ROW]
[ROW][C]57[/C][C]112164[/C][C]112162.026075285[/C][C]1.97392471473722[/C][/ROW]
[ROW][C]58[/C][C]112247[/C][C]112247.026656624[/C][C]-0.0266566236969084[/C][/ROW]
[ROW][C]59[/C][C]112332[/C][C]112330.743997477[/C][C]1.25600252262666[/C][/ROW]
[ROW][C]60[/C][C]112415[/C][C]112415.38458444[/C][C]-0.38458444015123[/C][/ROW]
[ROW][C]61[/C][C]112500[/C][C]112498.9434179[/C][C]1.05658210032561[/C][/ROW]
[ROW][C]62[/C][C]112585[/C][C]112583.510820399[/C][C]1.4891796012671[/C][/ROW]
[ROW][C]63[/C][C]112665[/C][C]112668.476045795[/C][C]-3.4760457946104[/C][/ROW]
[ROW][C]64[/C][C]112750[/C][C]112749.979784965[/C][C]0.0202150347759016[/C][/ROW]
[ROW][C]65[/C][C]112833[/C][C]112833.724004707[/C][C]-0.724004707459244[/C][/ROW]
[ROW][C]66[/C][C]112918[/C][C]112916.93292722[/C][C]1.06707278014801[/C][/ROW]
[ROW][C]67[/C][C]113000[/C][C]113001.375336294[/C][C]-1.37533629393147[/C][/ROW]
[ROW][C]68[/C][C]113086[/C][C]113084.142169262[/C][C]1.85783073838684[/C][/ROW]
[ROW][C]69[/C][C]113171[/C][C]113169.130084225[/C][C]1.86991577455774[/C][/ROW]
[ROW][C]70[/C][C]113253[/C][C]113254.277432472[/C][C]-1.2774324722559[/C][/ROW]
[ROW][C]71[/C][C]113339[/C][C]113337.305737117[/C][C]1.69426288289833[/C][/ROW]
[ROW][C]72[/C][C]113421[/C][C]113422.37442038[/C][C]-1.37442038033623[/C][/ROW]
[ROW][C]73[/C][C]113506[/C][C]113505.366565366[/C][C]0.633434634131845[/C][/ROW]
[ROW][C]74[/C][C]113592[/C][C]113589.695832668[/C][C]2.30416733186576[/C][/ROW]
[ROW][C]75[/C][C]113669[/C][C]113675.28188116[/C][C]-6.28188116010278[/C][/ROW]
[ROW][C]76[/C][C]113754[/C][C]113754.86021906[/C][C]-0.860219059861265[/C][/ROW]
[ROW][C]77[/C][C]113836[/C][C]113837.840549636[/C][C]-1.84054963583185[/C][/ROW]
[ROW][C]78[/C][C]113922[/C][C]113920.043810411[/C][C]1.95618958870182[/C][/ROW]
[ROW][C]79[/C][C]114004[/C][C]114004.837017493[/C][C]-0.837017492565792[/C][/ROW]
[ROW][C]80[/C][C]114089[/C][C]114087.773684402[/C][C]1.22631559848378[/C][/ROW]
[ROW][C]81[/C][C]114175[/C][C]114172.131095905[/C][C]2.86890409523039[/C][/ROW]
[ROW][C]82[/C][C]114257[/C][C]114257.773079947[/C][C]-0.773079946593498[/C][/ROW]
[ROW][C]83[/C][C]114342[/C][C]114341.020193909[/C][C]0.9798060914909[/C][/ROW]
[ROW][C]84[/C][C]114425[/C][C]114425.469259026[/C][C]-0.469259026096552[/C][/ROW]
[ROW][C]85[/C][C]114510[/C][C]114508.952343083[/C][C]1.0476569172024[/C][/ROW]
[ROW][C]86[/C][C]114595[/C][C]114593.491778482[/C][C]1.50822151798639[/C][/ROW]
[ROW][C]87[/C][C]114672[/C][C]114678.448490343[/C][C]-6.4484903425182[/C][/ROW]
[ROW][C]88[/C][C]114758[/C][C]114757.786973165[/C][C]0.213026834870107[/C][/ROW]
[ROW][C]89[/C][C]114840[/C][C]114841.40845916[/C][C]-1.40845916002581[/C][/ROW]
[ROW][C]90[/C][C]114925[/C][C]114923.877362446[/C][C]1.12263755407184[/C][/ROW]
[ROW][C]91[/C][C]115008[/C][C]115008.058133351[/C][C]-0.0581333514273865[/C][/ROW]
[ROW][C]92[/C][C]115093[/C][C]115091.478078224[/C][C]1.52192177571123[/C][/ROW]
[ROW][C]93[/C][C]115178[/C][C]115176.033279945[/C][C]1.96672005503206[/C][/ROW]
[ROW][C]94[/C][C]115261[/C][C]115261.032857242[/C][C]-0.0328572422586149[/C][/ROW]
[ROW][C]95[/C][C]115346[/C][C]115344.749333978[/C][C]1.25066602205334[/C][/ROW]
[ROW][C]96[/C][C]115429[/C][C]115429.389177246[/C][C]-0.389177246179315[/C][/ROW]
[ROW][C]97[/C][C]115514[/C][C]115512.947370652[/C][C]1.05262934757047[/C][/ROW]
[ROW][C]98[/C][C]115599[/C][C]115597.514222296[/C][C]1.48577770401607[/C][/ROW]
[ROW][C]99[/C][C]115676[/C][C]115682.478973604[/C][C]-6.47897360357456[/C][/ROW]
[ROW][C]100[/C][C]115761[/C][C]115761.817874874[/C][C]-0.817874873551773[/C][/ROW]
[ROW][C]101[/C][C]115844[/C][C]115844.715527872[/C][C]-0.715527872031089[/C][/ROW]
[ROW][C]102[/C][C]115929[/C][C]115927.620672756[/C][C]1.37932724361599[/C][/ROW]
[ROW][C]103[/C][C]116012[/C][C]116011.979160334[/C][C]0.0208396663510939[/C][/ROW]
[ROW][C]104[/C][C]116097[/C][C]116095.469427086[/C][C]1.53057291431469[/C][/ROW]
[ROW][C]105[/C][C]116182[/C][C]116180.050621681[/C][C]1.94937831866264[/C][/ROW]
[ROW][C]106[/C][C]116265[/C][C]116265.058140415[/C][C]-0.0581404147378635[/C][/ROW]
[ROW][C]107[/C][C]116350[/C][C]116348.775422199[/C][C]1.22457780083641[/C][/ROW]
[ROW][C]108[/C][C]116432[/C][C]116433.413438626[/C][C]-1.4134386263031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296070&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296070&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
3107641107650-9
4107726107729.506710356-3.50671035620326
5107808107812.246586971-4.24658697124687
6107894107894.168182378-0.168182378154597
7107976107978.68775228-2.6877522795985
8108061108061.3758678-0.375867800234118
9108147108145.5139133711.48608662911283
10108229108230.964823734-1.96482373442268
11108314108314.046539861-0.0465398610540433
12108397108398.352859081-1.35285908063815
13108482108481.7129240270.287075972664752
14108567108566.1464147720.853585228163865
15108647108651.011917385-4.01191738503985
16108732108732.436319626-0.436319625543547
17108815108816.114970261-1.11497026099823
18108900108899.2685944370.73140556285216
19108983108983.663885037-0.66388503703638
20109068109067.1118404490.888159550755518
21109153109151.6257029061.37429709357093
22109236109236.562353079-0.56235307904717
23109321109320.2132435630.786756437417353
24109403109404.791864834-1.79186483436206
25109489109487.5738957681.42610423246515
26109574109572.5322533591.46774664068653
27109651109657.63634591-6.63634591043228
28109736109737.012594226-1.0125942259474
29109819109819.907882617-0.90788261652051
30109904109902.7965725371.20342746340611
31109986109987.134872482-1.13487248188176
32110072110069.8837702282.11622977176739
33110157110154.8861971422.11380285808991
34110239110240.058549607-1.05854960667784
35110325110323.1136035471.88639645255171
36110407110408.207493716-1.2074937155121
37110492110491.222246010.777753989517805
38110578110575.5713516952.42864830476174
39110655110661.174633369-6.17463336893707
40110740110740.767869477-0.7678694769711
41110822110823.761049896-1.76104989602754
42110908110905.9753813982.02461860163021
43110990110990.778121253-0.778121253490099
44111075111073.7229944811.27700551851012
45111161111158.0874695212.91253047934151
46111243111243.735533079-0.735533079161542
47111328111326.9878794651.01212053518975
48111411111411.441447878-0.441447877688915
49111496111494.9284076771.07159232348204
50111581111579.4711787051.5288212946034
51111658111664.430761347-6.43076134682633
52111744111743.771714880.228285119665088
53111826111827.395327269-1.39532726873585
54111911111909.8660606141.13393938566151
55111994111994.048406543-0.0484065426135203
56112079112077.4697069431.53029305681412
57112164112162.0260752851.97392471473722
58112247112247.026656624-0.0266566236969084
59112332112330.7439974771.25600252262666
60112415112415.38458444-0.38458444015123
61112500112498.94341791.05658210032561
62112585112583.5108203991.4891796012671
63112665112668.476045795-3.4760457946104
64112750112749.9797849650.0202150347759016
65112833112833.724004707-0.724004707459244
66112918112916.932927221.06707278014801
67113000113001.375336294-1.37533629393147
68113086113084.1421692621.85783073838684
69113171113169.1300842251.86991577455774
70113253113254.277432472-1.2774324722559
71113339113337.3057371171.69426288289833
72113421113422.37442038-1.37442038033623
73113506113505.3665653660.633434634131845
74113592113589.6958326682.30416733186576
75113669113675.28188116-6.28188116010278
76113754113754.86021906-0.860219059861265
77113836113837.840549636-1.84054963583185
78113922113920.0438104111.95618958870182
79114004114004.837017493-0.837017492565792
80114089114087.7736844021.22631559848378
81114175114172.1310959052.86890409523039
82114257114257.773079947-0.773079946593498
83114342114341.0201939090.9798060914909
84114425114425.469259026-0.469259026096552
85114510114508.9523430831.0476569172024
86114595114593.4917784821.50822151798639
87114672114678.448490343-6.4484903425182
88114758114757.7869731650.213026834870107
89114840114841.40845916-1.40845916002581
90114925114923.8773624461.12263755407184
91115008115008.058133351-0.0581333514273865
92115093115091.4780782241.52192177571123
93115178115176.0332799451.96672005503206
94115261115261.032857242-0.0328572422586149
95115346115344.7493339781.25066602205334
96115429115429.389177246-0.389177246179315
97115514115512.9473706521.05262934757047
98115599115597.5142222961.48577770401607
99115676115682.478973604-6.47897360357456
100115761115761.817874874-0.817874873551773
101115844115844.715527872-0.715527872031089
102115929115927.6206727561.37932724361599
103116012116011.9791603340.0208396663510939
104116097116095.4694270861.53057291431469
105116182116180.0506216811.94937831866264
106116265116265.058140415-0.0581404147378635
107116350116348.7754221991.22457780083641
108116432116433.413438626-1.4134386263031







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109116516.247530213116511.777523688116520.717536738
110116599.986721279116594.474769077116605.49867348
111116683.725912345116677.149233956116690.302590733
112116767.46510341116759.793259113116775.136947708
113116851.204294476116842.403266245116860.005322707
114116934.943485542116924.977623836116944.909347248
115117018.682676608117007.515712305117029.849640911
116117102.421867674117090.017466582117114.826268765
117117186.16105874117172.483134351117199.838983128
118117269.900249805117254.913140975117284.887358635
119117353.639440871117337.3080109117369.970870843
120117437.378631937117419.668320562117455.088943312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 116516.247530213 & 116511.777523688 & 116520.717536738 \tabularnewline
110 & 116599.986721279 & 116594.474769077 & 116605.49867348 \tabularnewline
111 & 116683.725912345 & 116677.149233956 & 116690.302590733 \tabularnewline
112 & 116767.46510341 & 116759.793259113 & 116775.136947708 \tabularnewline
113 & 116851.204294476 & 116842.403266245 & 116860.005322707 \tabularnewline
114 & 116934.943485542 & 116924.977623836 & 116944.909347248 \tabularnewline
115 & 117018.682676608 & 117007.515712305 & 117029.849640911 \tabularnewline
116 & 117102.421867674 & 117090.017466582 & 117114.826268765 \tabularnewline
117 & 117186.16105874 & 117172.483134351 & 117199.838983128 \tabularnewline
118 & 117269.900249805 & 117254.913140975 & 117284.887358635 \tabularnewline
119 & 117353.639440871 & 117337.3080109 & 117369.970870843 \tabularnewline
120 & 117437.378631937 & 117419.668320562 & 117455.088943312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296070&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]109[/C][C]116516.247530213[/C][C]116511.777523688[/C][C]116520.717536738[/C][/ROW]
[ROW][C]110[/C][C]116599.986721279[/C][C]116594.474769077[/C][C]116605.49867348[/C][/ROW]
[ROW][C]111[/C][C]116683.725912345[/C][C]116677.149233956[/C][C]116690.302590733[/C][/ROW]
[ROW][C]112[/C][C]116767.46510341[/C][C]116759.793259113[/C][C]116775.136947708[/C][/ROW]
[ROW][C]113[/C][C]116851.204294476[/C][C]116842.403266245[/C][C]116860.005322707[/C][/ROW]
[ROW][C]114[/C][C]116934.943485542[/C][C]116924.977623836[/C][C]116944.909347248[/C][/ROW]
[ROW][C]115[/C][C]117018.682676608[/C][C]117007.515712305[/C][C]117029.849640911[/C][/ROW]
[ROW][C]116[/C][C]117102.421867674[/C][C]117090.017466582[/C][C]117114.826268765[/C][/ROW]
[ROW][C]117[/C][C]117186.16105874[/C][C]117172.483134351[/C][C]117199.838983128[/C][/ROW]
[ROW][C]118[/C][C]117269.900249805[/C][C]117254.913140975[/C][C]117284.887358635[/C][/ROW]
[ROW][C]119[/C][C]117353.639440871[/C][C]117337.3080109[/C][C]117369.970870843[/C][/ROW]
[ROW][C]120[/C][C]117437.378631937[/C][C]117419.668320562[/C][C]117455.088943312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296070&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296070&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
109116516.247530213116511.777523688116520.717536738
110116599.986721279116594.474769077116605.49867348
111116683.725912345116677.149233956116690.302590733
112116767.46510341116759.793259113116775.136947708
113116851.204294476116842.403266245116860.005322707
114116934.943485542116924.977623836116944.909347248
115117018.682676608117007.515712305117029.849640911
116117102.421867674117090.017466582117114.826268765
117117186.16105874117172.483134351117199.838983128
118117269.900249805117254.913140975117284.887358635
119117353.639440871117337.3080109117369.970870843
120117437.378631937117419.668320562117455.088943312



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')