Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Apr 2017 10:37:47 +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/2017/Apr/28/t1493372376jo9rzo4ux3a7v3g.htm/, Retrieved Fri, 10 May 2024 23:55:37 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 23:55:37 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
88
90
82
75
79
70
71
75
89
92
94
90
102
98
100
98
100
91
93
92
106
109
108
108
118
119
124
118
119
113
114
115
125
125
118
122
132
133
136
128
126
114
108
107
117
119
113
114
124
125
124
118
111
99
94
93
107
107
103
97
103
107
104
101
92
85
83
77
90
87
87
78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.516501181429655
beta0.0906971290783302
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.516501181429655 \tabularnewline
beta & 0.0906971290783302 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.516501181429655[/C][/ROW]
[ROW][C]beta[/C][C]0.0906971290783302[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.516501181429655
beta0.0906971290783302
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310291.337983509200510.6620164907995
149893.52468793186364.47531206813638
1510098.64760687685421.35239312314583
169898.2243656472524-0.224365647252426
17100101.087583225721-1.08758322572066
189192.2667133293056-1.26671332930559
199387.13533601419535.8646639858047
209296.3969981963996-4.39699819639959
21106112.602021601825-6.60202160182452
22109112.700584839738-3.70058483973784
23108112.733907380184-4.7339073801836
24108105.1051363452862.8948636547138
25118126.749226746692-8.74922674669182
26119113.47992274915.52007725089996
27124116.7856268136577.21437318634298
28118117.4115104771710.588489522829335
29119120.006385531876-1.00638553187602
30113108.8325857884424.16741421155791
31114109.1698118598854.83018814011483
32115112.6118930345062.38810696549392
33125134.99265302608-9.99265302608006
34125135.454607732787-10.4546077327871
35118131.143441141696-13.143441141696
36122121.7708769307950.229123069205428
37132137.041123566904-5.04112356690422
38133131.415132430411.5848675695901
39136132.5165946300223.48340536997821
40128126.3867118784251.61328812157521
41126127.81570216861-1.81570216860983
42114117.179602966703-3.17960296670267
43108112.752858381079-4.75285838107909
44107108.5458897475-1.5458897475004
45117119.965703508717-2.96570350871734
46119121.767811382993-2.76781138299322
47113118.531535394352-5.53153539435171
48114118.472836809865-4.47283680986524
49124126.806025134517-2.80602513451682
50125124.3095972885950.690402711404957
51124124.525764876054-0.525764876054481
52118114.8813520381363.11864796186438
53111114.322305772829-3.32230577282871
5499102.182579059382-3.18257905938243
559496.254194430479-2.25419443047902
569393.8885841805808-0.888584180580807
57107102.3856721100814.61432788991932
58107107.037399506307-0.0373995063070964
59103103.475409053646-0.475409053645976
6097105.750768428859-8.75076842885878
61103110.619963440298-7.61996344029814
62107106.210989164260.789010835739745
63104104.979583733327-0.979583733327289
6410197.05839834950323.94160165049681
659293.7499966777882-1.7499966777882
668583.3978644430911.60213555690896
678380.41003321356462.58996678643535
687780.9557841541451-3.95578415414509
699088.18070762298831.81929237701173
708788.4776405402446-1.47764054024459
718783.92555493413343.07444506586663
727883.5907619566722-5.59076195667218

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102 & 91.3379835092005 & 10.6620164907995 \tabularnewline
14 & 98 & 93.5246879318636 & 4.47531206813638 \tabularnewline
15 & 100 & 98.6476068768542 & 1.35239312314583 \tabularnewline
16 & 98 & 98.2243656472524 & -0.224365647252426 \tabularnewline
17 & 100 & 101.087583225721 & -1.08758322572066 \tabularnewline
18 & 91 & 92.2667133293056 & -1.26671332930559 \tabularnewline
19 & 93 & 87.1353360141953 & 5.8646639858047 \tabularnewline
20 & 92 & 96.3969981963996 & -4.39699819639959 \tabularnewline
21 & 106 & 112.602021601825 & -6.60202160182452 \tabularnewline
22 & 109 & 112.700584839738 & -3.70058483973784 \tabularnewline
23 & 108 & 112.733907380184 & -4.7339073801836 \tabularnewline
24 & 108 & 105.105136345286 & 2.8948636547138 \tabularnewline
25 & 118 & 126.749226746692 & -8.74922674669182 \tabularnewline
26 & 119 & 113.4799227491 & 5.52007725089996 \tabularnewline
27 & 124 & 116.785626813657 & 7.21437318634298 \tabularnewline
28 & 118 & 117.411510477171 & 0.588489522829335 \tabularnewline
29 & 119 & 120.006385531876 & -1.00638553187602 \tabularnewline
30 & 113 & 108.832585788442 & 4.16741421155791 \tabularnewline
31 & 114 & 109.169811859885 & 4.83018814011483 \tabularnewline
32 & 115 & 112.611893034506 & 2.38810696549392 \tabularnewline
33 & 125 & 134.99265302608 & -9.99265302608006 \tabularnewline
34 & 125 & 135.454607732787 & -10.4546077327871 \tabularnewline
35 & 118 & 131.143441141696 & -13.143441141696 \tabularnewline
36 & 122 & 121.770876930795 & 0.229123069205428 \tabularnewline
37 & 132 & 137.041123566904 & -5.04112356690422 \tabularnewline
38 & 133 & 131.41513243041 & 1.5848675695901 \tabularnewline
39 & 136 & 132.516594630022 & 3.48340536997821 \tabularnewline
40 & 128 & 126.386711878425 & 1.61328812157521 \tabularnewline
41 & 126 & 127.81570216861 & -1.81570216860983 \tabularnewline
42 & 114 & 117.179602966703 & -3.17960296670267 \tabularnewline
43 & 108 & 112.752858381079 & -4.75285838107909 \tabularnewline
44 & 107 & 108.5458897475 & -1.5458897475004 \tabularnewline
45 & 117 & 119.965703508717 & -2.96570350871734 \tabularnewline
46 & 119 & 121.767811382993 & -2.76781138299322 \tabularnewline
47 & 113 & 118.531535394352 & -5.53153539435171 \tabularnewline
48 & 114 & 118.472836809865 & -4.47283680986524 \tabularnewline
49 & 124 & 126.806025134517 & -2.80602513451682 \tabularnewline
50 & 125 & 124.309597288595 & 0.690402711404957 \tabularnewline
51 & 124 & 124.525764876054 & -0.525764876054481 \tabularnewline
52 & 118 & 114.881352038136 & 3.11864796186438 \tabularnewline
53 & 111 & 114.322305772829 & -3.32230577282871 \tabularnewline
54 & 99 & 102.182579059382 & -3.18257905938243 \tabularnewline
55 & 94 & 96.254194430479 & -2.25419443047902 \tabularnewline
56 & 93 & 93.8885841805808 & -0.888584180580807 \tabularnewline
57 & 107 & 102.385672110081 & 4.61432788991932 \tabularnewline
58 & 107 & 107.037399506307 & -0.0373995063070964 \tabularnewline
59 & 103 & 103.475409053646 & -0.475409053645976 \tabularnewline
60 & 97 & 105.750768428859 & -8.75076842885878 \tabularnewline
61 & 103 & 110.619963440298 & -7.61996344029814 \tabularnewline
62 & 107 & 106.21098916426 & 0.789010835739745 \tabularnewline
63 & 104 & 104.979583733327 & -0.979583733327289 \tabularnewline
64 & 101 & 97.0583983495032 & 3.94160165049681 \tabularnewline
65 & 92 & 93.7499966777882 & -1.7499966777882 \tabularnewline
66 & 85 & 83.397864443091 & 1.60213555690896 \tabularnewline
67 & 83 & 80.4100332135646 & 2.58996678643535 \tabularnewline
68 & 77 & 80.9557841541451 & -3.95578415414509 \tabularnewline
69 & 90 & 88.1807076229883 & 1.81929237701173 \tabularnewline
70 & 87 & 88.4776405402446 & -1.47764054024459 \tabularnewline
71 & 87 & 83.9255549341334 & 3.07444506586663 \tabularnewline
72 & 78 & 83.5907619566722 & -5.59076195667218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]13[/C][C]102[/C][C]91.3379835092005[/C][C]10.6620164907995[/C][/ROW]
[ROW][C]14[/C][C]98[/C][C]93.5246879318636[/C][C]4.47531206813638[/C][/ROW]
[ROW][C]15[/C][C]100[/C][C]98.6476068768542[/C][C]1.35239312314583[/C][/ROW]
[ROW][C]16[/C][C]98[/C][C]98.2243656472524[/C][C]-0.224365647252426[/C][/ROW]
[ROW][C]17[/C][C]100[/C][C]101.087583225721[/C][C]-1.08758322572066[/C][/ROW]
[ROW][C]18[/C][C]91[/C][C]92.2667133293056[/C][C]-1.26671332930559[/C][/ROW]
[ROW][C]19[/C][C]93[/C][C]87.1353360141953[/C][C]5.8646639858047[/C][/ROW]
[ROW][C]20[/C][C]92[/C][C]96.3969981963996[/C][C]-4.39699819639959[/C][/ROW]
[ROW][C]21[/C][C]106[/C][C]112.602021601825[/C][C]-6.60202160182452[/C][/ROW]
[ROW][C]22[/C][C]109[/C][C]112.700584839738[/C][C]-3.70058483973784[/C][/ROW]
[ROW][C]23[/C][C]108[/C][C]112.733907380184[/C][C]-4.7339073801836[/C][/ROW]
[ROW][C]24[/C][C]108[/C][C]105.105136345286[/C][C]2.8948636547138[/C][/ROW]
[ROW][C]25[/C][C]118[/C][C]126.749226746692[/C][C]-8.74922674669182[/C][/ROW]
[ROW][C]26[/C][C]119[/C][C]113.4799227491[/C][C]5.52007725089996[/C][/ROW]
[ROW][C]27[/C][C]124[/C][C]116.785626813657[/C][C]7.21437318634298[/C][/ROW]
[ROW][C]28[/C][C]118[/C][C]117.411510477171[/C][C]0.588489522829335[/C][/ROW]
[ROW][C]29[/C][C]119[/C][C]120.006385531876[/C][C]-1.00638553187602[/C][/ROW]
[ROW][C]30[/C][C]113[/C][C]108.832585788442[/C][C]4.16741421155791[/C][/ROW]
[ROW][C]31[/C][C]114[/C][C]109.169811859885[/C][C]4.83018814011483[/C][/ROW]
[ROW][C]32[/C][C]115[/C][C]112.611893034506[/C][C]2.38810696549392[/C][/ROW]
[ROW][C]33[/C][C]125[/C][C]134.99265302608[/C][C]-9.99265302608006[/C][/ROW]
[ROW][C]34[/C][C]125[/C][C]135.454607732787[/C][C]-10.4546077327871[/C][/ROW]
[ROW][C]35[/C][C]118[/C][C]131.143441141696[/C][C]-13.143441141696[/C][/ROW]
[ROW][C]36[/C][C]122[/C][C]121.770876930795[/C][C]0.229123069205428[/C][/ROW]
[ROW][C]37[/C][C]132[/C][C]137.041123566904[/C][C]-5.04112356690422[/C][/ROW]
[ROW][C]38[/C][C]133[/C][C]131.41513243041[/C][C]1.5848675695901[/C][/ROW]
[ROW][C]39[/C][C]136[/C][C]132.516594630022[/C][C]3.48340536997821[/C][/ROW]
[ROW][C]40[/C][C]128[/C][C]126.386711878425[/C][C]1.61328812157521[/C][/ROW]
[ROW][C]41[/C][C]126[/C][C]127.81570216861[/C][C]-1.81570216860983[/C][/ROW]
[ROW][C]42[/C][C]114[/C][C]117.179602966703[/C][C]-3.17960296670267[/C][/ROW]
[ROW][C]43[/C][C]108[/C][C]112.752858381079[/C][C]-4.75285838107909[/C][/ROW]
[ROW][C]44[/C][C]107[/C][C]108.5458897475[/C][C]-1.5458897475004[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]119.965703508717[/C][C]-2.96570350871734[/C][/ROW]
[ROW][C]46[/C][C]119[/C][C]121.767811382993[/C][C]-2.76781138299322[/C][/ROW]
[ROW][C]47[/C][C]113[/C][C]118.531535394352[/C][C]-5.53153539435171[/C][/ROW]
[ROW][C]48[/C][C]114[/C][C]118.472836809865[/C][C]-4.47283680986524[/C][/ROW]
[ROW][C]49[/C][C]124[/C][C]126.806025134517[/C][C]-2.80602513451682[/C][/ROW]
[ROW][C]50[/C][C]125[/C][C]124.309597288595[/C][C]0.690402711404957[/C][/ROW]
[ROW][C]51[/C][C]124[/C][C]124.525764876054[/C][C]-0.525764876054481[/C][/ROW]
[ROW][C]52[/C][C]118[/C][C]114.881352038136[/C][C]3.11864796186438[/C][/ROW]
[ROW][C]53[/C][C]111[/C][C]114.322305772829[/C][C]-3.32230577282871[/C][/ROW]
[ROW][C]54[/C][C]99[/C][C]102.182579059382[/C][C]-3.18257905938243[/C][/ROW]
[ROW][C]55[/C][C]94[/C][C]96.254194430479[/C][C]-2.25419443047902[/C][/ROW]
[ROW][C]56[/C][C]93[/C][C]93.8885841805808[/C][C]-0.888584180580807[/C][/ROW]
[ROW][C]57[/C][C]107[/C][C]102.385672110081[/C][C]4.61432788991932[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]107.037399506307[/C][C]-0.0373995063070964[/C][/ROW]
[ROW][C]59[/C][C]103[/C][C]103.475409053646[/C][C]-0.475409053645976[/C][/ROW]
[ROW][C]60[/C][C]97[/C][C]105.750768428859[/C][C]-8.75076842885878[/C][/ROW]
[ROW][C]61[/C][C]103[/C][C]110.619963440298[/C][C]-7.61996344029814[/C][/ROW]
[ROW][C]62[/C][C]107[/C][C]106.21098916426[/C][C]0.789010835739745[/C][/ROW]
[ROW][C]63[/C][C]104[/C][C]104.979583733327[/C][C]-0.979583733327289[/C][/ROW]
[ROW][C]64[/C][C]101[/C][C]97.0583983495032[/C][C]3.94160165049681[/C][/ROW]
[ROW][C]65[/C][C]92[/C][C]93.7499966777882[/C][C]-1.7499966777882[/C][/ROW]
[ROW][C]66[/C][C]85[/C][C]83.397864443091[/C][C]1.60213555690896[/C][/ROW]
[ROW][C]67[/C][C]83[/C][C]80.4100332135646[/C][C]2.58996678643535[/C][/ROW]
[ROW][C]68[/C][C]77[/C][C]80.9557841541451[/C][C]-3.95578415414509[/C][/ROW]
[ROW][C]69[/C][C]90[/C][C]88.1807076229883[/C][C]1.81929237701173[/C][/ROW]
[ROW][C]70[/C][C]87[/C][C]88.4776405402446[/C][C]-1.47764054024459[/C][/ROW]
[ROW][C]71[/C][C]87[/C][C]83.9255549341334[/C][C]3.07444506586663[/C][/ROW]
[ROW][C]72[/C][C]78[/C][C]83.5907619566722[/C][C]-5.59076195667218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1310291.337983509200510.6620164907995
149893.52468793186364.47531206813638
1510098.64760687685421.35239312314583
169898.2243656472524-0.224365647252426
17100101.087583225721-1.08758322572066
189192.2667133293056-1.26671332930559
199387.13533601419535.8646639858047
209296.3969981963996-4.39699819639959
21106112.602021601825-6.60202160182452
22109112.700584839738-3.70058483973784
23108112.733907380184-4.7339073801836
24108105.1051363452862.8948636547138
25118126.749226746692-8.74922674669182
26119113.47992274915.52007725089996
27124116.7856268136577.21437318634298
28118117.4115104771710.588489522829335
29119120.006385531876-1.00638553187602
30113108.8325857884424.16741421155791
31114109.1698118598854.83018814011483
32115112.6118930345062.38810696549392
33125134.99265302608-9.99265302608006
34125135.454607732787-10.4546077327871
35118131.143441141696-13.143441141696
36122121.7708769307950.229123069205428
37132137.041123566904-5.04112356690422
38133131.415132430411.5848675695901
39136132.5165946300223.48340536997821
40128126.3867118784251.61328812157521
41126127.81570216861-1.81570216860983
42114117.179602966703-3.17960296670267
43108112.752858381079-4.75285838107909
44107108.5458897475-1.5458897475004
45117119.965703508717-2.96570350871734
46119121.767811382993-2.76781138299322
47113118.531535394352-5.53153539435171
48114118.472836809865-4.47283680986524
49124126.806025134517-2.80602513451682
50125124.3095972885950.690402711404957
51124124.525764876054-0.525764876054481
52118114.8813520381363.11864796186438
53111114.322305772829-3.32230577282871
5499102.182579059382-3.18257905938243
559496.254194430479-2.25419443047902
569393.8885841805808-0.888584180580807
57107102.3856721100814.61432788991932
58107107.037399506307-0.0373995063070964
59103103.475409053646-0.475409053645976
6097105.750768428859-8.75076842885878
61103110.619963440298-7.61996344029814
62107106.210989164260.789010835739745
63104104.979583733327-0.979583733327289
6410197.05839834950323.94160165049681
659293.7499966777882-1.7499966777882
668583.3978644430911.60213555690896
678380.41003321356462.58996678643535
687780.9557841541451-3.95578415414509
699088.18070762298831.81929237701173
708788.4776405402446-1.47764054024459
718783.92555493413343.07444506586663
727883.5907619566722-5.59076195667218







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7388.332848345022679.325916400107297.339780289938
7491.199966978990580.7392930546912101.66064090329
7588.823426956145377.0414552900473100.605398622243
7684.288995098028671.344772987054997.2332172090024
7777.168911635188763.381787774414390.9560354959631
7870.333820048137855.808206536334884.8594335599409
7967.226679902971451.537973366316282.9153864396266
8063.553762551915446.844674228025480.2628508758054
8173.188528567749952.553031410809593.8240257246902
8270.973696625553648.910704853723193.0366883973841
8369.325568430980945.679003768714692.9721330932473
8463.938121106518640.753487573547387.1227546394899

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 88.3328483450226 & 79.3259164001072 & 97.339780289938 \tabularnewline
74 & 91.1999669789905 & 80.7392930546912 & 101.66064090329 \tabularnewline
75 & 88.8234269561453 & 77.0414552900473 & 100.605398622243 \tabularnewline
76 & 84.2889950980286 & 71.3447729870549 & 97.2332172090024 \tabularnewline
77 & 77.1689116351887 & 63.3817877744143 & 90.9560354959631 \tabularnewline
78 & 70.3338200481378 & 55.8082065363348 & 84.8594335599409 \tabularnewline
79 & 67.2266799029714 & 51.5379733663162 & 82.9153864396266 \tabularnewline
80 & 63.5537625519154 & 46.8446742280254 & 80.2628508758054 \tabularnewline
81 & 73.1885285677499 & 52.5530314108095 & 93.8240257246902 \tabularnewline
82 & 70.9736966255536 & 48.9107048537231 & 93.0366883973841 \tabularnewline
83 & 69.3255684309809 & 45.6790037687146 & 92.9721330932473 \tabularnewline
84 & 63.9381211065186 & 40.7534875735473 & 87.1227546394899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]88.3328483450226[/C][C]79.3259164001072[/C][C]97.339780289938[/C][/ROW]
[ROW][C]74[/C][C]91.1999669789905[/C][C]80.7392930546912[/C][C]101.66064090329[/C][/ROW]
[ROW][C]75[/C][C]88.8234269561453[/C][C]77.0414552900473[/C][C]100.605398622243[/C][/ROW]
[ROW][C]76[/C][C]84.2889950980286[/C][C]71.3447729870549[/C][C]97.2332172090024[/C][/ROW]
[ROW][C]77[/C][C]77.1689116351887[/C][C]63.3817877744143[/C][C]90.9560354959631[/C][/ROW]
[ROW][C]78[/C][C]70.3338200481378[/C][C]55.8082065363348[/C][C]84.8594335599409[/C][/ROW]
[ROW][C]79[/C][C]67.2266799029714[/C][C]51.5379733663162[/C][C]82.9153864396266[/C][/ROW]
[ROW][C]80[/C][C]63.5537625519154[/C][C]46.8446742280254[/C][C]80.2628508758054[/C][/ROW]
[ROW][C]81[/C][C]73.1885285677499[/C][C]52.5530314108095[/C][C]93.8240257246902[/C][/ROW]
[ROW][C]82[/C][C]70.9736966255536[/C][C]48.9107048537231[/C][C]93.0366883973841[/C][/ROW]
[ROW][C]83[/C][C]69.3255684309809[/C][C]45.6790037687146[/C][C]92.9721330932473[/C][/ROW]
[ROW][C]84[/C][C]63.9381211065186[/C][C]40.7534875735473[/C][C]87.1227546394899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7388.332848345022679.325916400107297.339780289938
7491.199966978990580.7392930546912101.66064090329
7588.823426956145377.0414552900473100.605398622243
7684.288995098028671.344772987054997.2332172090024
7777.168911635188763.381787774414390.9560354959631
7870.333820048137855.808206536334884.8594335599409
7967.226679902971451.537973366316282.9153864396266
8063.553762551915446.844674228025480.2628508758054
8173.188528567749952.553031410809593.8240257246902
8270.973696625553648.910704853723193.0366883973841
8369.325568430980945.679003768714692.9721330932473
8463.938121106518640.753487573547387.1227546394899



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')