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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Jan 2013 14:34:38 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/12/t1358019302m7479f0fosd2d0j.htm/, Retrieved Sun, 28 Apr 2024 07:57:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205253, Retrieved Sun, 28 Apr 2024 07:57:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-12 19:34:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
98.68
99.21
99.36
100.72
102.27
102.62
102.97
102.88
102.9
103.01
103.02
103.73
104.18
103.73
103.78
103.61
103.84
103.86
104.14
104.05
104.01
104.49
104.83
104.78
104.95
105.28
105.28
105.91
106.81
106.39
107.02
106.92
107.01
106.79
107.41
107.13
107.54
108.48
108.5
108.27
109.42
110.09
109.98
109.99
109.54
108.85
106.76
107.56
106.24
108.85
111.11
111.85
110.68
106.96
106.74
105.73
105.66
104.01
106.86
108.84
110.66
106.93
103.74
101.64
102.17
101.13
100.64
100.43
99.77
99.79
99.47
99.63




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=205253&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=205253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205253&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
alpha1
beta0.0313932057167741
gamma0.088434070466107

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0313932057167741 \tabularnewline
gamma & 0.088434070466107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205253&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0313932057167741[/C][/ROW]
[ROW][C]gamma[/C][C]0.088434070466107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205253&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0313932057167741
gamma0.088434070466107







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.18102.9144577991451.26554220085472
14103.73103.83776992782-0.107769927820215
15103.78103.886886684306-0.106886684306033
16103.61103.700614501971-0.0906145019705775
17103.84103.898603155603-0.0586031556026114
18103.86103.93468008135-0.0746800813498254
19104.14105.216085634193-1.07608563419306
20104.05103.7902205231770.259779476823368
21104.01103.8633758337340.146624166266463
22104.49103.9858955030150.504104496985136
23104.83104.5004709591910.329529040808538
24104.78105.619565932159-0.839565932159218
25104.95105.299875932805-0.349875932804821
26105.28104.5618088723380.718191127662394
27105.28105.416855194152-0.136855194152247
28105.91105.1796422042220.730357795777834
29106.81106.2034038100850.606596189914811
30106.39106.930363475729-0.540363475728881
31107.02107.757149733973-0.737149733973496
32106.92106.6919249073970.228075092602552
33107.01106.7540849156980.255915084301591
34106.79107.010035577253-0.220035577252574
35107.41106.8018779551110.608122044889114
36107.13108.209718855567-1.07971885556699
37107.54107.652489686085-0.112489686084558
38108.48107.1618749408951.31812505910503
39108.5108.645755112036-0.145755112035872
40108.27108.428262725153-0.158262725152795
41109.42108.5641276841980.855872315801903
42110.09109.5489129265420.541087073457959
43109.98111.49964938435-1.5196493843498
44109.99109.6698593852760.320140614723798
45109.54109.844909625453-0.30490962545251
46108.85109.543254201522-0.693254201522336
47106.76108.85024072976-2.09024072975991
48107.56107.4633713725330.0966286274670125
49106.24108.02307152158-1.78307152157987
50108.85105.7500118571623.09998814283814
51111.11108.959830422652.1501695773505
52111.85111.0544144718510.795585528149431
53110.68112.190223785334-1.51022378533436
54106.96110.78072968603-3.82072968602971
55106.74108.204534733008-1.46453473300798
56105.73106.266474959522-0.536474959521939
57105.66105.3946332907560.265366709244205
58104.01105.490880669116-1.48088066911612
59106.86103.8131410776293.04685892237141
60108.84107.5275417465691.31245825343143
61110.66109.305410685181.35458931482009
62106.93110.270852252868-3.34085225286846
63103.74106.938472190825-3.1984721908248
64101.64103.415145228692-1.77514522869218
65102.17101.6302510626840.539748937315977
66101.13101.985112178775-0.855112178775286
67100.64102.182017466236-1.54201746623608
68100.4399.97152526136630.458474738633683
6999.7799.9309182531522-0.160918253152218
7099.7999.42378317999410.366216820005945
7199.4799.4740298999615-0.00402989996148051
7299.6399.922653388483-0.292653388482961

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.18 & 102.914457799145 & 1.26554220085472 \tabularnewline
14 & 103.73 & 103.83776992782 & -0.107769927820215 \tabularnewline
15 & 103.78 & 103.886886684306 & -0.106886684306033 \tabularnewline
16 & 103.61 & 103.700614501971 & -0.0906145019705775 \tabularnewline
17 & 103.84 & 103.898603155603 & -0.0586031556026114 \tabularnewline
18 & 103.86 & 103.93468008135 & -0.0746800813498254 \tabularnewline
19 & 104.14 & 105.216085634193 & -1.07608563419306 \tabularnewline
20 & 104.05 & 103.790220523177 & 0.259779476823368 \tabularnewline
21 & 104.01 & 103.863375833734 & 0.146624166266463 \tabularnewline
22 & 104.49 & 103.985895503015 & 0.504104496985136 \tabularnewline
23 & 104.83 & 104.500470959191 & 0.329529040808538 \tabularnewline
24 & 104.78 & 105.619565932159 & -0.839565932159218 \tabularnewline
25 & 104.95 & 105.299875932805 & -0.349875932804821 \tabularnewline
26 & 105.28 & 104.561808872338 & 0.718191127662394 \tabularnewline
27 & 105.28 & 105.416855194152 & -0.136855194152247 \tabularnewline
28 & 105.91 & 105.179642204222 & 0.730357795777834 \tabularnewline
29 & 106.81 & 106.203403810085 & 0.606596189914811 \tabularnewline
30 & 106.39 & 106.930363475729 & -0.540363475728881 \tabularnewline
31 & 107.02 & 107.757149733973 & -0.737149733973496 \tabularnewline
32 & 106.92 & 106.691924907397 & 0.228075092602552 \tabularnewline
33 & 107.01 & 106.754084915698 & 0.255915084301591 \tabularnewline
34 & 106.79 & 107.010035577253 & -0.220035577252574 \tabularnewline
35 & 107.41 & 106.801877955111 & 0.608122044889114 \tabularnewline
36 & 107.13 & 108.209718855567 & -1.07971885556699 \tabularnewline
37 & 107.54 & 107.652489686085 & -0.112489686084558 \tabularnewline
38 & 108.48 & 107.161874940895 & 1.31812505910503 \tabularnewline
39 & 108.5 & 108.645755112036 & -0.145755112035872 \tabularnewline
40 & 108.27 & 108.428262725153 & -0.158262725152795 \tabularnewline
41 & 109.42 & 108.564127684198 & 0.855872315801903 \tabularnewline
42 & 110.09 & 109.548912926542 & 0.541087073457959 \tabularnewline
43 & 109.98 & 111.49964938435 & -1.5196493843498 \tabularnewline
44 & 109.99 & 109.669859385276 & 0.320140614723798 \tabularnewline
45 & 109.54 & 109.844909625453 & -0.30490962545251 \tabularnewline
46 & 108.85 & 109.543254201522 & -0.693254201522336 \tabularnewline
47 & 106.76 & 108.85024072976 & -2.09024072975991 \tabularnewline
48 & 107.56 & 107.463371372533 & 0.0966286274670125 \tabularnewline
49 & 106.24 & 108.02307152158 & -1.78307152157987 \tabularnewline
50 & 108.85 & 105.750011857162 & 3.09998814283814 \tabularnewline
51 & 111.11 & 108.95983042265 & 2.1501695773505 \tabularnewline
52 & 111.85 & 111.054414471851 & 0.795585528149431 \tabularnewline
53 & 110.68 & 112.190223785334 & -1.51022378533436 \tabularnewline
54 & 106.96 & 110.78072968603 & -3.82072968602971 \tabularnewline
55 & 106.74 & 108.204534733008 & -1.46453473300798 \tabularnewline
56 & 105.73 & 106.266474959522 & -0.536474959521939 \tabularnewline
57 & 105.66 & 105.394633290756 & 0.265366709244205 \tabularnewline
58 & 104.01 & 105.490880669116 & -1.48088066911612 \tabularnewline
59 & 106.86 & 103.813141077629 & 3.04685892237141 \tabularnewline
60 & 108.84 & 107.527541746569 & 1.31245825343143 \tabularnewline
61 & 110.66 & 109.30541068518 & 1.35458931482009 \tabularnewline
62 & 106.93 & 110.270852252868 & -3.34085225286846 \tabularnewline
63 & 103.74 & 106.938472190825 & -3.1984721908248 \tabularnewline
64 & 101.64 & 103.415145228692 & -1.77514522869218 \tabularnewline
65 & 102.17 & 101.630251062684 & 0.539748937315977 \tabularnewline
66 & 101.13 & 101.985112178775 & -0.855112178775286 \tabularnewline
67 & 100.64 & 102.182017466236 & -1.54201746623608 \tabularnewline
68 & 100.43 & 99.9715252613663 & 0.458474738633683 \tabularnewline
69 & 99.77 & 99.9309182531522 & -0.160918253152218 \tabularnewline
70 & 99.79 & 99.4237831799941 & 0.366216820005945 \tabularnewline
71 & 99.47 & 99.4740298999615 & -0.00402989996148051 \tabularnewline
72 & 99.63 & 99.922653388483 & -0.292653388482961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205253&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]104.18[/C][C]102.914457799145[/C][C]1.26554220085472[/C][/ROW]
[ROW][C]14[/C][C]103.73[/C][C]103.83776992782[/C][C]-0.107769927820215[/C][/ROW]
[ROW][C]15[/C][C]103.78[/C][C]103.886886684306[/C][C]-0.106886684306033[/C][/ROW]
[ROW][C]16[/C][C]103.61[/C][C]103.700614501971[/C][C]-0.0906145019705775[/C][/ROW]
[ROW][C]17[/C][C]103.84[/C][C]103.898603155603[/C][C]-0.0586031556026114[/C][/ROW]
[ROW][C]18[/C][C]103.86[/C][C]103.93468008135[/C][C]-0.0746800813498254[/C][/ROW]
[ROW][C]19[/C][C]104.14[/C][C]105.216085634193[/C][C]-1.07608563419306[/C][/ROW]
[ROW][C]20[/C][C]104.05[/C][C]103.790220523177[/C][C]0.259779476823368[/C][/ROW]
[ROW][C]21[/C][C]104.01[/C][C]103.863375833734[/C][C]0.146624166266463[/C][/ROW]
[ROW][C]22[/C][C]104.49[/C][C]103.985895503015[/C][C]0.504104496985136[/C][/ROW]
[ROW][C]23[/C][C]104.83[/C][C]104.500470959191[/C][C]0.329529040808538[/C][/ROW]
[ROW][C]24[/C][C]104.78[/C][C]105.619565932159[/C][C]-0.839565932159218[/C][/ROW]
[ROW][C]25[/C][C]104.95[/C][C]105.299875932805[/C][C]-0.349875932804821[/C][/ROW]
[ROW][C]26[/C][C]105.28[/C][C]104.561808872338[/C][C]0.718191127662394[/C][/ROW]
[ROW][C]27[/C][C]105.28[/C][C]105.416855194152[/C][C]-0.136855194152247[/C][/ROW]
[ROW][C]28[/C][C]105.91[/C][C]105.179642204222[/C][C]0.730357795777834[/C][/ROW]
[ROW][C]29[/C][C]106.81[/C][C]106.203403810085[/C][C]0.606596189914811[/C][/ROW]
[ROW][C]30[/C][C]106.39[/C][C]106.930363475729[/C][C]-0.540363475728881[/C][/ROW]
[ROW][C]31[/C][C]107.02[/C][C]107.757149733973[/C][C]-0.737149733973496[/C][/ROW]
[ROW][C]32[/C][C]106.92[/C][C]106.691924907397[/C][C]0.228075092602552[/C][/ROW]
[ROW][C]33[/C][C]107.01[/C][C]106.754084915698[/C][C]0.255915084301591[/C][/ROW]
[ROW][C]34[/C][C]106.79[/C][C]107.010035577253[/C][C]-0.220035577252574[/C][/ROW]
[ROW][C]35[/C][C]107.41[/C][C]106.801877955111[/C][C]0.608122044889114[/C][/ROW]
[ROW][C]36[/C][C]107.13[/C][C]108.209718855567[/C][C]-1.07971885556699[/C][/ROW]
[ROW][C]37[/C][C]107.54[/C][C]107.652489686085[/C][C]-0.112489686084558[/C][/ROW]
[ROW][C]38[/C][C]108.48[/C][C]107.161874940895[/C][C]1.31812505910503[/C][/ROW]
[ROW][C]39[/C][C]108.5[/C][C]108.645755112036[/C][C]-0.145755112035872[/C][/ROW]
[ROW][C]40[/C][C]108.27[/C][C]108.428262725153[/C][C]-0.158262725152795[/C][/ROW]
[ROW][C]41[/C][C]109.42[/C][C]108.564127684198[/C][C]0.855872315801903[/C][/ROW]
[ROW][C]42[/C][C]110.09[/C][C]109.548912926542[/C][C]0.541087073457959[/C][/ROW]
[ROW][C]43[/C][C]109.98[/C][C]111.49964938435[/C][C]-1.5196493843498[/C][/ROW]
[ROW][C]44[/C][C]109.99[/C][C]109.669859385276[/C][C]0.320140614723798[/C][/ROW]
[ROW][C]45[/C][C]109.54[/C][C]109.844909625453[/C][C]-0.30490962545251[/C][/ROW]
[ROW][C]46[/C][C]108.85[/C][C]109.543254201522[/C][C]-0.693254201522336[/C][/ROW]
[ROW][C]47[/C][C]106.76[/C][C]108.85024072976[/C][C]-2.09024072975991[/C][/ROW]
[ROW][C]48[/C][C]107.56[/C][C]107.463371372533[/C][C]0.0966286274670125[/C][/ROW]
[ROW][C]49[/C][C]106.24[/C][C]108.02307152158[/C][C]-1.78307152157987[/C][/ROW]
[ROW][C]50[/C][C]108.85[/C][C]105.750011857162[/C][C]3.09998814283814[/C][/ROW]
[ROW][C]51[/C][C]111.11[/C][C]108.95983042265[/C][C]2.1501695773505[/C][/ROW]
[ROW][C]52[/C][C]111.85[/C][C]111.054414471851[/C][C]0.795585528149431[/C][/ROW]
[ROW][C]53[/C][C]110.68[/C][C]112.190223785334[/C][C]-1.51022378533436[/C][/ROW]
[ROW][C]54[/C][C]106.96[/C][C]110.78072968603[/C][C]-3.82072968602971[/C][/ROW]
[ROW][C]55[/C][C]106.74[/C][C]108.204534733008[/C][C]-1.46453473300798[/C][/ROW]
[ROW][C]56[/C][C]105.73[/C][C]106.266474959522[/C][C]-0.536474959521939[/C][/ROW]
[ROW][C]57[/C][C]105.66[/C][C]105.394633290756[/C][C]0.265366709244205[/C][/ROW]
[ROW][C]58[/C][C]104.01[/C][C]105.490880669116[/C][C]-1.48088066911612[/C][/ROW]
[ROW][C]59[/C][C]106.86[/C][C]103.813141077629[/C][C]3.04685892237141[/C][/ROW]
[ROW][C]60[/C][C]108.84[/C][C]107.527541746569[/C][C]1.31245825343143[/C][/ROW]
[ROW][C]61[/C][C]110.66[/C][C]109.30541068518[/C][C]1.35458931482009[/C][/ROW]
[ROW][C]62[/C][C]106.93[/C][C]110.270852252868[/C][C]-3.34085225286846[/C][/ROW]
[ROW][C]63[/C][C]103.74[/C][C]106.938472190825[/C][C]-3.1984721908248[/C][/ROW]
[ROW][C]64[/C][C]101.64[/C][C]103.415145228692[/C][C]-1.77514522869218[/C][/ROW]
[ROW][C]65[/C][C]102.17[/C][C]101.630251062684[/C][C]0.539748937315977[/C][/ROW]
[ROW][C]66[/C][C]101.13[/C][C]101.985112178775[/C][C]-0.855112178775286[/C][/ROW]
[ROW][C]67[/C][C]100.64[/C][C]102.182017466236[/C][C]-1.54201746623608[/C][/ROW]
[ROW][C]68[/C][C]100.43[/C][C]99.9715252613663[/C][C]0.458474738633683[/C][/ROW]
[ROW][C]69[/C][C]99.77[/C][C]99.9309182531522[/C][C]-0.160918253152218[/C][/ROW]
[ROW][C]70[/C][C]99.79[/C][C]99.4237831799941[/C][C]0.366216820005945[/C][/ROW]
[ROW][C]71[/C][C]99.47[/C][C]99.4740298999615[/C][C]-0.00402989996148051[/C][/ROW]
[ROW][C]72[/C][C]99.63[/C][C]99.922653388483[/C][C]-0.292653388482961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205253&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
13104.18102.9144577991451.26554220085472
14103.73103.83776992782-0.107769927820215
15103.78103.886886684306-0.106886684306033
16103.61103.700614501971-0.0906145019705775
17103.84103.898603155603-0.0586031556026114
18103.86103.93468008135-0.0746800813498254
19104.14105.216085634193-1.07608563419306
20104.05103.7902205231770.259779476823368
21104.01103.8633758337340.146624166266463
22104.49103.9858955030150.504104496985136
23104.83104.5004709591910.329529040808538
24104.78105.619565932159-0.839565932159218
25104.95105.299875932805-0.349875932804821
26105.28104.5618088723380.718191127662394
27105.28105.416855194152-0.136855194152247
28105.91105.1796422042220.730357795777834
29106.81106.2034038100850.606596189914811
30106.39106.930363475729-0.540363475728881
31107.02107.757149733973-0.737149733973496
32106.92106.6919249073970.228075092602552
33107.01106.7540849156980.255915084301591
34106.79107.010035577253-0.220035577252574
35107.41106.8018779551110.608122044889114
36107.13108.209718855567-1.07971885556699
37107.54107.652489686085-0.112489686084558
38108.48107.1618749408951.31812505910503
39108.5108.645755112036-0.145755112035872
40108.27108.428262725153-0.158262725152795
41109.42108.5641276841980.855872315801903
42110.09109.5489129265420.541087073457959
43109.98111.49964938435-1.5196493843498
44109.99109.6698593852760.320140614723798
45109.54109.844909625453-0.30490962545251
46108.85109.543254201522-0.693254201522336
47106.76108.85024072976-2.09024072975991
48107.56107.4633713725330.0966286274670125
49106.24108.02307152158-1.78307152157987
50108.85105.7500118571623.09998814283814
51111.11108.959830422652.1501695773505
52111.85111.0544144718510.795585528149431
53110.68112.190223785334-1.51022378533436
54106.96110.78072968603-3.82072968602971
55106.74108.204534733008-1.46453473300798
56105.73106.266474959522-0.536474959521939
57105.66105.3946332907560.265366709244205
58104.01105.490880669116-1.48088066911612
59106.86103.8131410776293.04685892237141
60108.84107.5275417465691.31245825343143
61110.66109.305410685181.35458931482009
62106.93110.270852252868-3.34085225286846
63103.74106.938472190825-3.1984721908248
64101.64103.415145228692-1.77514522869218
65102.17101.6302510626840.539748937315977
66101.13101.985112178775-0.855112178775286
67100.64102.182017466236-1.54201746623608
68100.4399.97152526136630.458474738633683
6999.7799.9309182531522-0.160918253152218
7099.7999.42378317999410.366216820005945
7199.4799.4740298999615-0.00402989996148051
7299.6399.922653388483-0.292653388482961







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7399.830132727121397.3116184402726102.34864701397
7499.133182120909295.5151262339472102.751238007871
7598.938731514697194.4382043376282103.439258691766
7698.511364241818493.2341807192082103.788547764429
7798.45483030227392.4644551981851104.445205406361
7898.206213029394291.5447544017499104.867671657039
7999.221345756515591.9184367663315106.5242547467
8098.564395150303490.6416783051716106.487111995435
8198.062444544091489.5361076505203106.588781437662
8297.71841060454688.6007399661814106.836081242911
8397.393126665000687.6935165874569107.092736742544
8497.836592725455287.5622325755516108.110952875359

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 99.8301327271213 & 97.3116184402726 & 102.34864701397 \tabularnewline
74 & 99.1331821209092 & 95.5151262339472 & 102.751238007871 \tabularnewline
75 & 98.9387315146971 & 94.4382043376282 & 103.439258691766 \tabularnewline
76 & 98.5113642418184 & 93.2341807192082 & 103.788547764429 \tabularnewline
77 & 98.454830302273 & 92.4644551981851 & 104.445205406361 \tabularnewline
78 & 98.2062130293942 & 91.5447544017499 & 104.867671657039 \tabularnewline
79 & 99.2213457565155 & 91.9184367663315 & 106.5242547467 \tabularnewline
80 & 98.5643951503034 & 90.6416783051716 & 106.487111995435 \tabularnewline
81 & 98.0624445440914 & 89.5361076505203 & 106.588781437662 \tabularnewline
82 & 97.718410604546 & 88.6007399661814 & 106.836081242911 \tabularnewline
83 & 97.3931266650006 & 87.6935165874569 & 107.092736742544 \tabularnewline
84 & 97.8365927254552 & 87.5622325755516 & 108.110952875359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205253&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]99.8301327271213[/C][C]97.3116184402726[/C][C]102.34864701397[/C][/ROW]
[ROW][C]74[/C][C]99.1331821209092[/C][C]95.5151262339472[/C][C]102.751238007871[/C][/ROW]
[ROW][C]75[/C][C]98.9387315146971[/C][C]94.4382043376282[/C][C]103.439258691766[/C][/ROW]
[ROW][C]76[/C][C]98.5113642418184[/C][C]93.2341807192082[/C][C]103.788547764429[/C][/ROW]
[ROW][C]77[/C][C]98.454830302273[/C][C]92.4644551981851[/C][C]104.445205406361[/C][/ROW]
[ROW][C]78[/C][C]98.2062130293942[/C][C]91.5447544017499[/C][C]104.867671657039[/C][/ROW]
[ROW][C]79[/C][C]99.2213457565155[/C][C]91.9184367663315[/C][C]106.5242547467[/C][/ROW]
[ROW][C]80[/C][C]98.5643951503034[/C][C]90.6416783051716[/C][C]106.487111995435[/C][/ROW]
[ROW][C]81[/C][C]98.0624445440914[/C][C]89.5361076505203[/C][C]106.588781437662[/C][/ROW]
[ROW][C]82[/C][C]97.718410604546[/C][C]88.6007399661814[/C][C]106.836081242911[/C][/ROW]
[ROW][C]83[/C][C]97.3931266650006[/C][C]87.6935165874569[/C][C]107.092736742544[/C][/ROW]
[ROW][C]84[/C][C]97.8365927254552[/C][C]87.5622325755516[/C][C]108.110952875359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205253&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205253&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
7399.830132727121397.3116184402726102.34864701397
7499.133182120909295.5151262339472102.751238007871
7598.938731514697194.4382043376282103.439258691766
7698.511364241818493.2341807192082103.788547764429
7798.45483030227392.4644551981851104.445205406361
7898.206213029394291.5447544017499104.867671657039
7999.221345756515591.9184367663315106.5242547467
8098.564395150303490.6416783051716106.487111995435
8198.062444544091489.5361076505203106.588781437662
8297.71841060454688.6007399661814106.836081242911
8397.393126665000687.6935165874569107.092736742544
8497.836592725455287.5622325755516108.110952875359



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