Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 13 Jan 2013 17:44:17 -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/13/t1358117076fs38w2qogoaas30.htm/, Retrieved Sat, 04 May 2024 18:57:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205301, Retrieved Sat, 04 May 2024 18:57:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-13 22:44:17] [6f8d6446e5f32bdf63bde1c9ab07ce03] [Current]
- R PD    [Exponential Smoothing] [] [2013-01-14 21:10:01] [74be16979710d4c4e7c6647856088456]
Feedback Forum

Post a new message
Dataseries X:
103,51
104,35
104,51
105,25
105,2
105,87
107,63
107,77
106,58
106,32
106,3
106,38
106,42
107,35
107,58
108,2
108,29
108,76
110,69
110,56
108,81
108,81
108,81
109,74
109,57
110,44
111,2
111,44
111,83
112,87
115,07
115,35
113,81
114,66
114,51
115,11
114,54
115,39
115,65
116,46
116,18
116,63
118,84
118,77
117,83
117,66
117,36
118
117,34
118,04
118,17
118,82
119
118,89
121,4
121,01
120,21
120,39
120,09
120,76
120,33
120,84
121,49
122,29
121,91
122,46
124,94
124,6
123,09
123,25
123,01
123,82




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=205301&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=205301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205301&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
beta0.0575223584008343
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0575223584008343 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205301&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]0.0575223584008343[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205301&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
beta0.0575223584008343
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3104.51105.19-0.679999999999978
4105.25105.310884796287-0.060884796287425
5105.2106.047382559214-0.847382559214211
6105.87105.94863911594-0.0786391159404758
7107.63106.6141156085291.01588439147096
8107.77108.432551674589-0.662551674589039
9106.58108.534440139704-1.95444013970425
10106.32107.232016133515-0.912016133515209
11106.3106.919554814616-0.619554814615796
12106.38106.863916560521-0.483916560520512
13106.42106.91608053869-0.496080538690137
14107.35106.9275448161480.422455183852051
15107.58107.881845434642-0.301845434641763
16108.2108.0944825733690.105517426631366
17108.29108.720552184601-0.43055218460087
18108.76108.785785807528-0.0257858075279955
19110.69109.2543025470661.43569745293428
20110.56111.266887250509-0.706887250508558
21108.81111.096225428736-2.28622542873583
22108.81109.214716350239-0.404716350238985
23108.81109.19143611129-0.381436111289858
24109.74109.1694950065890.570504993410765
25109.57110.13231179929-0.562311799289674
26110.44109.9299662984380.510033701562094
27111.2110.8293046398160.370695360184342
28111.44111.610627911182-0.170627911181725
29111.83111.840812991322-0.0108129913215294
30112.87112.2301910025590.639808997440653
31115.07113.3069943250181.76300567498177
32115.35115.608406569317-0.258406569317216
33113.81115.873542414024-2.06354241402381
34114.66114.2148425877090.445157412290968
35114.51115.090449091924-0.580449091923612
36115.11114.9070602912250.202939708775446
37114.54115.518733861886-0.978733861886482
38115.39114.8924347819040.497565218095971
39115.65115.771055906707-0.121055906707127
40116.46116.0240924854550.435907514545008
41116.18116.859166913736-0.679166913736239
42116.63116.540099631110.0899003688896585
43118.84116.995270912351.84472908765004
44118.77119.311384080082-0.541384080082224
45117.83119.210242390995-1.38024239099522
46117.66118.1908475935-0.530847593500368
47117.36117.990311987971-0.630311987970813
48118117.6540549558940.345945044105576
49117.34118.313954530708-0.973954530708454
50118.04117.5979303691270.442069630873078
51118.17118.323359256872-0.153359256872136
52118.82118.4445376707340.375462329265744
53119119.116135149404-0.116135149404272
54118.89119.289454781717-0.399454781717324
55121.4119.1564772005982.24352279940156
56121.01121.795529923146-0.785529923146072
57120.21121.360344389372-1.15034438937229
58120.39120.494173867122-0.104173867122412
59120.09120.668181540602-0.578181540601804
60120.76120.3349231748030.425076825197451
61120.33121.029374596289-0.699374596289459
62120.84120.5591449201050.280855079894749
63121.49121.085300366670.404699633330338
64122.29121.7585796440230.531420355977247
65121.91122.589148196201-0.679148196200799
66122.46122.1700819902520.289918009748348
67124.94122.7367587579152.20324124208476
68124.6125.343494390286-0.743494390285946
69123.09124.960726839499-1.8707268394989
70123.25123.343118219767-0.0931182197671916
71123.01123.497761840156-0.487761840156097
72123.82123.2297046287720.590295371227597

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 104.51 & 105.19 & -0.679999999999978 \tabularnewline
4 & 105.25 & 105.310884796287 & -0.060884796287425 \tabularnewline
5 & 105.2 & 106.047382559214 & -0.847382559214211 \tabularnewline
6 & 105.87 & 105.94863911594 & -0.0786391159404758 \tabularnewline
7 & 107.63 & 106.614115608529 & 1.01588439147096 \tabularnewline
8 & 107.77 & 108.432551674589 & -0.662551674589039 \tabularnewline
9 & 106.58 & 108.534440139704 & -1.95444013970425 \tabularnewline
10 & 106.32 & 107.232016133515 & -0.912016133515209 \tabularnewline
11 & 106.3 & 106.919554814616 & -0.619554814615796 \tabularnewline
12 & 106.38 & 106.863916560521 & -0.483916560520512 \tabularnewline
13 & 106.42 & 106.91608053869 & -0.496080538690137 \tabularnewline
14 & 107.35 & 106.927544816148 & 0.422455183852051 \tabularnewline
15 & 107.58 & 107.881845434642 & -0.301845434641763 \tabularnewline
16 & 108.2 & 108.094482573369 & 0.105517426631366 \tabularnewline
17 & 108.29 & 108.720552184601 & -0.43055218460087 \tabularnewline
18 & 108.76 & 108.785785807528 & -0.0257858075279955 \tabularnewline
19 & 110.69 & 109.254302547066 & 1.43569745293428 \tabularnewline
20 & 110.56 & 111.266887250509 & -0.706887250508558 \tabularnewline
21 & 108.81 & 111.096225428736 & -2.28622542873583 \tabularnewline
22 & 108.81 & 109.214716350239 & -0.404716350238985 \tabularnewline
23 & 108.81 & 109.19143611129 & -0.381436111289858 \tabularnewline
24 & 109.74 & 109.169495006589 & 0.570504993410765 \tabularnewline
25 & 109.57 & 110.13231179929 & -0.562311799289674 \tabularnewline
26 & 110.44 & 109.929966298438 & 0.510033701562094 \tabularnewline
27 & 111.2 & 110.829304639816 & 0.370695360184342 \tabularnewline
28 & 111.44 & 111.610627911182 & -0.170627911181725 \tabularnewline
29 & 111.83 & 111.840812991322 & -0.0108129913215294 \tabularnewline
30 & 112.87 & 112.230191002559 & 0.639808997440653 \tabularnewline
31 & 115.07 & 113.306994325018 & 1.76300567498177 \tabularnewline
32 & 115.35 & 115.608406569317 & -0.258406569317216 \tabularnewline
33 & 113.81 & 115.873542414024 & -2.06354241402381 \tabularnewline
34 & 114.66 & 114.214842587709 & 0.445157412290968 \tabularnewline
35 & 114.51 & 115.090449091924 & -0.580449091923612 \tabularnewline
36 & 115.11 & 114.907060291225 & 0.202939708775446 \tabularnewline
37 & 114.54 & 115.518733861886 & -0.978733861886482 \tabularnewline
38 & 115.39 & 114.892434781904 & 0.497565218095971 \tabularnewline
39 & 115.65 & 115.771055906707 & -0.121055906707127 \tabularnewline
40 & 116.46 & 116.024092485455 & 0.435907514545008 \tabularnewline
41 & 116.18 & 116.859166913736 & -0.679166913736239 \tabularnewline
42 & 116.63 & 116.54009963111 & 0.0899003688896585 \tabularnewline
43 & 118.84 & 116.99527091235 & 1.84472908765004 \tabularnewline
44 & 118.77 & 119.311384080082 & -0.541384080082224 \tabularnewline
45 & 117.83 & 119.210242390995 & -1.38024239099522 \tabularnewline
46 & 117.66 & 118.1908475935 & -0.530847593500368 \tabularnewline
47 & 117.36 & 117.990311987971 & -0.630311987970813 \tabularnewline
48 & 118 & 117.654054955894 & 0.345945044105576 \tabularnewline
49 & 117.34 & 118.313954530708 & -0.973954530708454 \tabularnewline
50 & 118.04 & 117.597930369127 & 0.442069630873078 \tabularnewline
51 & 118.17 & 118.323359256872 & -0.153359256872136 \tabularnewline
52 & 118.82 & 118.444537670734 & 0.375462329265744 \tabularnewline
53 & 119 & 119.116135149404 & -0.116135149404272 \tabularnewline
54 & 118.89 & 119.289454781717 & -0.399454781717324 \tabularnewline
55 & 121.4 & 119.156477200598 & 2.24352279940156 \tabularnewline
56 & 121.01 & 121.795529923146 & -0.785529923146072 \tabularnewline
57 & 120.21 & 121.360344389372 & -1.15034438937229 \tabularnewline
58 & 120.39 & 120.494173867122 & -0.104173867122412 \tabularnewline
59 & 120.09 & 120.668181540602 & -0.578181540601804 \tabularnewline
60 & 120.76 & 120.334923174803 & 0.425076825197451 \tabularnewline
61 & 120.33 & 121.029374596289 & -0.699374596289459 \tabularnewline
62 & 120.84 & 120.559144920105 & 0.280855079894749 \tabularnewline
63 & 121.49 & 121.08530036667 & 0.404699633330338 \tabularnewline
64 & 122.29 & 121.758579644023 & 0.531420355977247 \tabularnewline
65 & 121.91 & 122.589148196201 & -0.679148196200799 \tabularnewline
66 & 122.46 & 122.170081990252 & 0.289918009748348 \tabularnewline
67 & 124.94 & 122.736758757915 & 2.20324124208476 \tabularnewline
68 & 124.6 & 125.343494390286 & -0.743494390285946 \tabularnewline
69 & 123.09 & 124.960726839499 & -1.8707268394989 \tabularnewline
70 & 123.25 & 123.343118219767 & -0.0931182197671916 \tabularnewline
71 & 123.01 & 123.497761840156 & -0.487761840156097 \tabularnewline
72 & 123.82 & 123.229704628772 & 0.590295371227597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205301&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]104.51[/C][C]105.19[/C][C]-0.679999999999978[/C][/ROW]
[ROW][C]4[/C][C]105.25[/C][C]105.310884796287[/C][C]-0.060884796287425[/C][/ROW]
[ROW][C]5[/C][C]105.2[/C][C]106.047382559214[/C][C]-0.847382559214211[/C][/ROW]
[ROW][C]6[/C][C]105.87[/C][C]105.94863911594[/C][C]-0.0786391159404758[/C][/ROW]
[ROW][C]7[/C][C]107.63[/C][C]106.614115608529[/C][C]1.01588439147096[/C][/ROW]
[ROW][C]8[/C][C]107.77[/C][C]108.432551674589[/C][C]-0.662551674589039[/C][/ROW]
[ROW][C]9[/C][C]106.58[/C][C]108.534440139704[/C][C]-1.95444013970425[/C][/ROW]
[ROW][C]10[/C][C]106.32[/C][C]107.232016133515[/C][C]-0.912016133515209[/C][/ROW]
[ROW][C]11[/C][C]106.3[/C][C]106.919554814616[/C][C]-0.619554814615796[/C][/ROW]
[ROW][C]12[/C][C]106.38[/C][C]106.863916560521[/C][C]-0.483916560520512[/C][/ROW]
[ROW][C]13[/C][C]106.42[/C][C]106.91608053869[/C][C]-0.496080538690137[/C][/ROW]
[ROW][C]14[/C][C]107.35[/C][C]106.927544816148[/C][C]0.422455183852051[/C][/ROW]
[ROW][C]15[/C][C]107.58[/C][C]107.881845434642[/C][C]-0.301845434641763[/C][/ROW]
[ROW][C]16[/C][C]108.2[/C][C]108.094482573369[/C][C]0.105517426631366[/C][/ROW]
[ROW][C]17[/C][C]108.29[/C][C]108.720552184601[/C][C]-0.43055218460087[/C][/ROW]
[ROW][C]18[/C][C]108.76[/C][C]108.785785807528[/C][C]-0.0257858075279955[/C][/ROW]
[ROW][C]19[/C][C]110.69[/C][C]109.254302547066[/C][C]1.43569745293428[/C][/ROW]
[ROW][C]20[/C][C]110.56[/C][C]111.266887250509[/C][C]-0.706887250508558[/C][/ROW]
[ROW][C]21[/C][C]108.81[/C][C]111.096225428736[/C][C]-2.28622542873583[/C][/ROW]
[ROW][C]22[/C][C]108.81[/C][C]109.214716350239[/C][C]-0.404716350238985[/C][/ROW]
[ROW][C]23[/C][C]108.81[/C][C]109.19143611129[/C][C]-0.381436111289858[/C][/ROW]
[ROW][C]24[/C][C]109.74[/C][C]109.169495006589[/C][C]0.570504993410765[/C][/ROW]
[ROW][C]25[/C][C]109.57[/C][C]110.13231179929[/C][C]-0.562311799289674[/C][/ROW]
[ROW][C]26[/C][C]110.44[/C][C]109.929966298438[/C][C]0.510033701562094[/C][/ROW]
[ROW][C]27[/C][C]111.2[/C][C]110.829304639816[/C][C]0.370695360184342[/C][/ROW]
[ROW][C]28[/C][C]111.44[/C][C]111.610627911182[/C][C]-0.170627911181725[/C][/ROW]
[ROW][C]29[/C][C]111.83[/C][C]111.840812991322[/C][C]-0.0108129913215294[/C][/ROW]
[ROW][C]30[/C][C]112.87[/C][C]112.230191002559[/C][C]0.639808997440653[/C][/ROW]
[ROW][C]31[/C][C]115.07[/C][C]113.306994325018[/C][C]1.76300567498177[/C][/ROW]
[ROW][C]32[/C][C]115.35[/C][C]115.608406569317[/C][C]-0.258406569317216[/C][/ROW]
[ROW][C]33[/C][C]113.81[/C][C]115.873542414024[/C][C]-2.06354241402381[/C][/ROW]
[ROW][C]34[/C][C]114.66[/C][C]114.214842587709[/C][C]0.445157412290968[/C][/ROW]
[ROW][C]35[/C][C]114.51[/C][C]115.090449091924[/C][C]-0.580449091923612[/C][/ROW]
[ROW][C]36[/C][C]115.11[/C][C]114.907060291225[/C][C]0.202939708775446[/C][/ROW]
[ROW][C]37[/C][C]114.54[/C][C]115.518733861886[/C][C]-0.978733861886482[/C][/ROW]
[ROW][C]38[/C][C]115.39[/C][C]114.892434781904[/C][C]0.497565218095971[/C][/ROW]
[ROW][C]39[/C][C]115.65[/C][C]115.771055906707[/C][C]-0.121055906707127[/C][/ROW]
[ROW][C]40[/C][C]116.46[/C][C]116.024092485455[/C][C]0.435907514545008[/C][/ROW]
[ROW][C]41[/C][C]116.18[/C][C]116.859166913736[/C][C]-0.679166913736239[/C][/ROW]
[ROW][C]42[/C][C]116.63[/C][C]116.54009963111[/C][C]0.0899003688896585[/C][/ROW]
[ROW][C]43[/C][C]118.84[/C][C]116.99527091235[/C][C]1.84472908765004[/C][/ROW]
[ROW][C]44[/C][C]118.77[/C][C]119.311384080082[/C][C]-0.541384080082224[/C][/ROW]
[ROW][C]45[/C][C]117.83[/C][C]119.210242390995[/C][C]-1.38024239099522[/C][/ROW]
[ROW][C]46[/C][C]117.66[/C][C]118.1908475935[/C][C]-0.530847593500368[/C][/ROW]
[ROW][C]47[/C][C]117.36[/C][C]117.990311987971[/C][C]-0.630311987970813[/C][/ROW]
[ROW][C]48[/C][C]118[/C][C]117.654054955894[/C][C]0.345945044105576[/C][/ROW]
[ROW][C]49[/C][C]117.34[/C][C]118.313954530708[/C][C]-0.973954530708454[/C][/ROW]
[ROW][C]50[/C][C]118.04[/C][C]117.597930369127[/C][C]0.442069630873078[/C][/ROW]
[ROW][C]51[/C][C]118.17[/C][C]118.323359256872[/C][C]-0.153359256872136[/C][/ROW]
[ROW][C]52[/C][C]118.82[/C][C]118.444537670734[/C][C]0.375462329265744[/C][/ROW]
[ROW][C]53[/C][C]119[/C][C]119.116135149404[/C][C]-0.116135149404272[/C][/ROW]
[ROW][C]54[/C][C]118.89[/C][C]119.289454781717[/C][C]-0.399454781717324[/C][/ROW]
[ROW][C]55[/C][C]121.4[/C][C]119.156477200598[/C][C]2.24352279940156[/C][/ROW]
[ROW][C]56[/C][C]121.01[/C][C]121.795529923146[/C][C]-0.785529923146072[/C][/ROW]
[ROW][C]57[/C][C]120.21[/C][C]121.360344389372[/C][C]-1.15034438937229[/C][/ROW]
[ROW][C]58[/C][C]120.39[/C][C]120.494173867122[/C][C]-0.104173867122412[/C][/ROW]
[ROW][C]59[/C][C]120.09[/C][C]120.668181540602[/C][C]-0.578181540601804[/C][/ROW]
[ROW][C]60[/C][C]120.76[/C][C]120.334923174803[/C][C]0.425076825197451[/C][/ROW]
[ROW][C]61[/C][C]120.33[/C][C]121.029374596289[/C][C]-0.699374596289459[/C][/ROW]
[ROW][C]62[/C][C]120.84[/C][C]120.559144920105[/C][C]0.280855079894749[/C][/ROW]
[ROW][C]63[/C][C]121.49[/C][C]121.08530036667[/C][C]0.404699633330338[/C][/ROW]
[ROW][C]64[/C][C]122.29[/C][C]121.758579644023[/C][C]0.531420355977247[/C][/ROW]
[ROW][C]65[/C][C]121.91[/C][C]122.589148196201[/C][C]-0.679148196200799[/C][/ROW]
[ROW][C]66[/C][C]122.46[/C][C]122.170081990252[/C][C]0.289918009748348[/C][/ROW]
[ROW][C]67[/C][C]124.94[/C][C]122.736758757915[/C][C]2.20324124208476[/C][/ROW]
[ROW][C]68[/C][C]124.6[/C][C]125.343494390286[/C][C]-0.743494390285946[/C][/ROW]
[ROW][C]69[/C][C]123.09[/C][C]124.960726839499[/C][C]-1.8707268394989[/C][/ROW]
[ROW][C]70[/C][C]123.25[/C][C]123.343118219767[/C][C]-0.0931182197671916[/C][/ROW]
[ROW][C]71[/C][C]123.01[/C][C]123.497761840156[/C][C]-0.487761840156097[/C][/ROW]
[ROW][C]72[/C][C]123.82[/C][C]123.229704628772[/C][C]0.590295371227597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205301&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
3104.51105.19-0.679999999999978
4105.25105.310884796287-0.060884796287425
5105.2106.047382559214-0.847382559214211
6105.87105.94863911594-0.0786391159404758
7107.63106.6141156085291.01588439147096
8107.77108.432551674589-0.662551674589039
9106.58108.534440139704-1.95444013970425
10106.32107.232016133515-0.912016133515209
11106.3106.919554814616-0.619554814615796
12106.38106.863916560521-0.483916560520512
13106.42106.91608053869-0.496080538690137
14107.35106.9275448161480.422455183852051
15107.58107.881845434642-0.301845434641763
16108.2108.0944825733690.105517426631366
17108.29108.720552184601-0.43055218460087
18108.76108.785785807528-0.0257858075279955
19110.69109.2543025470661.43569745293428
20110.56111.266887250509-0.706887250508558
21108.81111.096225428736-2.28622542873583
22108.81109.214716350239-0.404716350238985
23108.81109.19143611129-0.381436111289858
24109.74109.1694950065890.570504993410765
25109.57110.13231179929-0.562311799289674
26110.44109.9299662984380.510033701562094
27111.2110.8293046398160.370695360184342
28111.44111.610627911182-0.170627911181725
29111.83111.840812991322-0.0108129913215294
30112.87112.2301910025590.639808997440653
31115.07113.3069943250181.76300567498177
32115.35115.608406569317-0.258406569317216
33113.81115.873542414024-2.06354241402381
34114.66114.2148425877090.445157412290968
35114.51115.090449091924-0.580449091923612
36115.11114.9070602912250.202939708775446
37114.54115.518733861886-0.978733861886482
38115.39114.8924347819040.497565218095971
39115.65115.771055906707-0.121055906707127
40116.46116.0240924854550.435907514545008
41116.18116.859166913736-0.679166913736239
42116.63116.540099631110.0899003688896585
43118.84116.995270912351.84472908765004
44118.77119.311384080082-0.541384080082224
45117.83119.210242390995-1.38024239099522
46117.66118.1908475935-0.530847593500368
47117.36117.990311987971-0.630311987970813
48118117.6540549558940.345945044105576
49117.34118.313954530708-0.973954530708454
50118.04117.5979303691270.442069630873078
51118.17118.323359256872-0.153359256872136
52118.82118.4445376707340.375462329265744
53119119.116135149404-0.116135149404272
54118.89119.289454781717-0.399454781717324
55121.4119.1564772005982.24352279940156
56121.01121.795529923146-0.785529923146072
57120.21121.360344389372-1.15034438937229
58120.39120.494173867122-0.104173867122412
59120.09120.668181540602-0.578181540601804
60120.76120.3349231748030.425076825197451
61120.33121.029374596289-0.699374596289459
62120.84120.5591449201050.280855079894749
63121.49121.085300366670.404699633330338
64122.29121.7585796440230.531420355977247
65121.91122.589148196201-0.679148196200799
66122.46122.1700819902520.289918009748348
67124.94122.7367587579152.20324124208476
68124.6125.343494390286-0.743494390285946
69123.09124.960726839499-1.8707268394989
70123.25123.343118219767-0.0931182197671916
71123.01123.497761840156-0.487761840156097
72123.82123.2297046287720.590295371227597







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73124.073659810678122.354841256341125.792478365016
74124.327319621357121.825654034242126.828985208472
75124.580979432035121.429546232461127.73241263161
76124.834639242714121.093851962218128.57542652321
77125.088299053392120.79135173469129.385246372095
78125.341958864071120.508545752506130.175371975636
79125.595618674749120.237688256177130.953549093322
80125.849278485428119.973913373397131.724643597459
81126.102938296106119.713969400769132.491907191444
82126.356598106785119.455584111847133.257612101723
83126.610257917463119.197115683011134.023400151916
84126.863917728142118.937346894195134.790488562089

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 124.073659810678 & 122.354841256341 & 125.792478365016 \tabularnewline
74 & 124.327319621357 & 121.825654034242 & 126.828985208472 \tabularnewline
75 & 124.580979432035 & 121.429546232461 & 127.73241263161 \tabularnewline
76 & 124.834639242714 & 121.093851962218 & 128.57542652321 \tabularnewline
77 & 125.088299053392 & 120.79135173469 & 129.385246372095 \tabularnewline
78 & 125.341958864071 & 120.508545752506 & 130.175371975636 \tabularnewline
79 & 125.595618674749 & 120.237688256177 & 130.953549093322 \tabularnewline
80 & 125.849278485428 & 119.973913373397 & 131.724643597459 \tabularnewline
81 & 126.102938296106 & 119.713969400769 & 132.491907191444 \tabularnewline
82 & 126.356598106785 & 119.455584111847 & 133.257612101723 \tabularnewline
83 & 126.610257917463 & 119.197115683011 & 134.023400151916 \tabularnewline
84 & 126.863917728142 & 118.937346894195 & 134.790488562089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205301&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]124.073659810678[/C][C]122.354841256341[/C][C]125.792478365016[/C][/ROW]
[ROW][C]74[/C][C]124.327319621357[/C][C]121.825654034242[/C][C]126.828985208472[/C][/ROW]
[ROW][C]75[/C][C]124.580979432035[/C][C]121.429546232461[/C][C]127.73241263161[/C][/ROW]
[ROW][C]76[/C][C]124.834639242714[/C][C]121.093851962218[/C][C]128.57542652321[/C][/ROW]
[ROW][C]77[/C][C]125.088299053392[/C][C]120.79135173469[/C][C]129.385246372095[/C][/ROW]
[ROW][C]78[/C][C]125.341958864071[/C][C]120.508545752506[/C][C]130.175371975636[/C][/ROW]
[ROW][C]79[/C][C]125.595618674749[/C][C]120.237688256177[/C][C]130.953549093322[/C][/ROW]
[ROW][C]80[/C][C]125.849278485428[/C][C]119.973913373397[/C][C]131.724643597459[/C][/ROW]
[ROW][C]81[/C][C]126.102938296106[/C][C]119.713969400769[/C][C]132.491907191444[/C][/ROW]
[ROW][C]82[/C][C]126.356598106785[/C][C]119.455584111847[/C][C]133.257612101723[/C][/ROW]
[ROW][C]83[/C][C]126.610257917463[/C][C]119.197115683011[/C][C]134.023400151916[/C][/ROW]
[ROW][C]84[/C][C]126.863917728142[/C][C]118.937346894195[/C][C]134.790488562089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205301&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
73124.073659810678122.354841256341125.792478365016
74124.327319621357121.825654034242126.828985208472
75124.580979432035121.429546232461127.73241263161
76124.834639242714121.093851962218128.57542652321
77125.088299053392120.79135173469129.385246372095
78125.341958864071120.508545752506130.175371975636
79125.595618674749120.237688256177130.953549093322
80125.849278485428119.973913373397131.724643597459
81126.102938296106119.713969400769132.491907191444
82126.356598106785119.455584111847133.257612101723
83126.610257917463119.197115683011134.023400151916
84126.863917728142118.937346894195134.790488562089



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