Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 09:17:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/19/t1282209525sdow2xutdrlvce6.htm/, Retrieved Fri, 03 May 2024 12:15:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79250, Retrieved Fri, 03 May 2024 12:15:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDeGroodtOlivierREEKSBStap27
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-08-19 09:17:21] [461523bf9c5715e033e9a40193969321] [Current]
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Dataseries X:
80
79
78
76
74
73
74
76
77
77
78
80
90
90
89
82
78
76
74
78
81
82
88
99
117
113
106
100
97
96
100
104
104
111
117
118
140
147
134
126
116
114
120
122
117
119
132
134
154
152
132
130
123
129
124
128
128
129
141
138
155
160
142
133
131
140
134
134
134
136
145
137
152
168
160
157
147
161
159
164
163
158
175
163




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79250&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79250&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.635975324827265
beta0.008138384857576
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.635975324827265 \tabularnewline
beta & 0.008138384857576 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79250&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]0.635975324827265[/C][/ROW]
[ROW][C]beta[/C][C]0.008138384857576[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79250&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
alpha0.635975324827265
beta0.008138384857576
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139087.03659188034192.9634081196581
149089.27967877060.720321229399957
158988.93327932777320.0667206722267792
168282.0465513919437-0.046551391943737
177877.83754427705870.162455722941317
187675.17896803689320.821031963106776
197480.0268128753726-6.0268128753726
207877.73840371821230.261596281787732
218178.40895492391932.59104507608068
228279.78272217865512.21727782134488
238882.22192556186895.77807443813114
249988.080613956831410.9193860431686
25117106.51098670348110.4890132965191
26113112.8683161750760.131683824924238
27106112.051266821771-6.05126682177128
28100101.342386107546-1.34238610754639
299796.48860697053270.511393029467314
309694.39675341795861.60324658204138
3110097.358400724442.64159927555993
32104103.0260077373230.973992262677044
33104105.155273112518-1.15527311251789
34111104.1486947618596.85130523814149
35117110.9935087480066.00649125199371
36118119.032476809319-1.03247680931877
37140129.80668072412010.1933192758804
38147132.30568946904414.6943105309564
39134138.67479505276-4.67479505275992
40126130.738019838492-4.73801983849214
41116124.564502270107-8.56450227010698
42114117.216069249189-3.21606924918862
43120117.5837970920342.41620290796637
44122122.592901352030-0.592901352029642
45117123.034339844768-6.03433984476798
46119121.897918325330-2.89791832532987
47132122.2430042019159.75699579808528
48134130.1323251043023.86767489569758
49154148.1622161848215.83778381517891
50152149.5599851173602.44001488264047
51132141.051704134660-9.05170413465979
52130130.252528762407-0.252528762407167
53123125.506176271455-2.50617627145536
54129123.9564449022165.04355509778377
55124131.668920540651-7.66892054065073
56128129.158092712267-1.15809271226669
57128127.2456860156820.754313984317804
58129131.589972890176-2.58997289017583
59141136.7607565807124.23924341928804
60138138.991657257165-0.991657257165173
61155154.6177425273170.382257472682511
62160151.2502640861738.74973591382664
63142142.545403129008-0.545403129007838
64133140.377031698605-7.37703169860461
65131130.2603021887070.739697811293041
66140133.5209695393686.47903046063232
67134137.523961410038-3.52396141003754
68134140.046024962477-6.04602496247716
69134135.722575839689-1.72257583968891
70136137.262797692503-1.26279769250345
71145145.759083250348-0.759083250348198
72137142.876572122086-5.87657212208572
73152155.840405078971-3.8404050789712
74168152.75582450560215.2441754943977
75160144.75365933166715.2463406683333
76157150.1793534498876.82064655011268
77147152.157958840575-5.15795884057499
78161153.8378676691927.16213233080845
79159154.7182420934494.28175790655095
80164161.4111405799562.58885942004358
81163164.322482979171-1.32248297917127
82158166.45597137444-8.45597137443994
83175170.6951567000814.30484329991936
84163169.330711862381-6.33071186238058

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 90 & 87.0365918803419 & 2.9634081196581 \tabularnewline
14 & 90 & 89.2796787706 & 0.720321229399957 \tabularnewline
15 & 89 & 88.9332793277732 & 0.0667206722267792 \tabularnewline
16 & 82 & 82.0465513919437 & -0.046551391943737 \tabularnewline
17 & 78 & 77.8375442770587 & 0.162455722941317 \tabularnewline
18 & 76 & 75.1789680368932 & 0.821031963106776 \tabularnewline
19 & 74 & 80.0268128753726 & -6.0268128753726 \tabularnewline
20 & 78 & 77.7384037182123 & 0.261596281787732 \tabularnewline
21 & 81 & 78.4089549239193 & 2.59104507608068 \tabularnewline
22 & 82 & 79.7827221786551 & 2.21727782134488 \tabularnewline
23 & 88 & 82.2219255618689 & 5.77807443813114 \tabularnewline
24 & 99 & 88.0806139568314 & 10.9193860431686 \tabularnewline
25 & 117 & 106.510986703481 & 10.4890132965191 \tabularnewline
26 & 113 & 112.868316175076 & 0.131683824924238 \tabularnewline
27 & 106 & 112.051266821771 & -6.05126682177128 \tabularnewline
28 & 100 & 101.342386107546 & -1.34238610754639 \tabularnewline
29 & 97 & 96.4886069705327 & 0.511393029467314 \tabularnewline
30 & 96 & 94.3967534179586 & 1.60324658204138 \tabularnewline
31 & 100 & 97.35840072444 & 2.64159927555993 \tabularnewline
32 & 104 & 103.026007737323 & 0.973992262677044 \tabularnewline
33 & 104 & 105.155273112518 & -1.15527311251789 \tabularnewline
34 & 111 & 104.148694761859 & 6.85130523814149 \tabularnewline
35 & 117 & 110.993508748006 & 6.00649125199371 \tabularnewline
36 & 118 & 119.032476809319 & -1.03247680931877 \tabularnewline
37 & 140 & 129.806680724120 & 10.1933192758804 \tabularnewline
38 & 147 & 132.305689469044 & 14.6943105309564 \tabularnewline
39 & 134 & 138.67479505276 & -4.67479505275992 \tabularnewline
40 & 126 & 130.738019838492 & -4.73801983849214 \tabularnewline
41 & 116 & 124.564502270107 & -8.56450227010698 \tabularnewline
42 & 114 & 117.216069249189 & -3.21606924918862 \tabularnewline
43 & 120 & 117.583797092034 & 2.41620290796637 \tabularnewline
44 & 122 & 122.592901352030 & -0.592901352029642 \tabularnewline
45 & 117 & 123.034339844768 & -6.03433984476798 \tabularnewline
46 & 119 & 121.897918325330 & -2.89791832532987 \tabularnewline
47 & 132 & 122.243004201915 & 9.75699579808528 \tabularnewline
48 & 134 & 130.132325104302 & 3.86767489569758 \tabularnewline
49 & 154 & 148.162216184821 & 5.83778381517891 \tabularnewline
50 & 152 & 149.559985117360 & 2.44001488264047 \tabularnewline
51 & 132 & 141.051704134660 & -9.05170413465979 \tabularnewline
52 & 130 & 130.252528762407 & -0.252528762407167 \tabularnewline
53 & 123 & 125.506176271455 & -2.50617627145536 \tabularnewline
54 & 129 & 123.956444902216 & 5.04355509778377 \tabularnewline
55 & 124 & 131.668920540651 & -7.66892054065073 \tabularnewline
56 & 128 & 129.158092712267 & -1.15809271226669 \tabularnewline
57 & 128 & 127.245686015682 & 0.754313984317804 \tabularnewline
58 & 129 & 131.589972890176 & -2.58997289017583 \tabularnewline
59 & 141 & 136.760756580712 & 4.23924341928804 \tabularnewline
60 & 138 & 138.991657257165 & -0.991657257165173 \tabularnewline
61 & 155 & 154.617742527317 & 0.382257472682511 \tabularnewline
62 & 160 & 151.250264086173 & 8.74973591382664 \tabularnewline
63 & 142 & 142.545403129008 & -0.545403129007838 \tabularnewline
64 & 133 & 140.377031698605 & -7.37703169860461 \tabularnewline
65 & 131 & 130.260302188707 & 0.739697811293041 \tabularnewline
66 & 140 & 133.520969539368 & 6.47903046063232 \tabularnewline
67 & 134 & 137.523961410038 & -3.52396141003754 \tabularnewline
68 & 134 & 140.046024962477 & -6.04602496247716 \tabularnewline
69 & 134 & 135.722575839689 & -1.72257583968891 \tabularnewline
70 & 136 & 137.262797692503 & -1.26279769250345 \tabularnewline
71 & 145 & 145.759083250348 & -0.759083250348198 \tabularnewline
72 & 137 & 142.876572122086 & -5.87657212208572 \tabularnewline
73 & 152 & 155.840405078971 & -3.8404050789712 \tabularnewline
74 & 168 & 152.755824505602 & 15.2441754943977 \tabularnewline
75 & 160 & 144.753659331667 & 15.2463406683333 \tabularnewline
76 & 157 & 150.179353449887 & 6.82064655011268 \tabularnewline
77 & 147 & 152.157958840575 & -5.15795884057499 \tabularnewline
78 & 161 & 153.837867669192 & 7.16213233080845 \tabularnewline
79 & 159 & 154.718242093449 & 4.28175790655095 \tabularnewline
80 & 164 & 161.411140579956 & 2.58885942004358 \tabularnewline
81 & 163 & 164.322482979171 & -1.32248297917127 \tabularnewline
82 & 158 & 166.45597137444 & -8.45597137443994 \tabularnewline
83 & 175 & 170.695156700081 & 4.30484329991936 \tabularnewline
84 & 163 & 169.330711862381 & -6.33071186238058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79250&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]90[/C][C]87.0365918803419[/C][C]2.9634081196581[/C][/ROW]
[ROW][C]14[/C][C]90[/C][C]89.2796787706[/C][C]0.720321229399957[/C][/ROW]
[ROW][C]15[/C][C]89[/C][C]88.9332793277732[/C][C]0.0667206722267792[/C][/ROW]
[ROW][C]16[/C][C]82[/C][C]82.0465513919437[/C][C]-0.046551391943737[/C][/ROW]
[ROW][C]17[/C][C]78[/C][C]77.8375442770587[/C][C]0.162455722941317[/C][/ROW]
[ROW][C]18[/C][C]76[/C][C]75.1789680368932[/C][C]0.821031963106776[/C][/ROW]
[ROW][C]19[/C][C]74[/C][C]80.0268128753726[/C][C]-6.0268128753726[/C][/ROW]
[ROW][C]20[/C][C]78[/C][C]77.7384037182123[/C][C]0.261596281787732[/C][/ROW]
[ROW][C]21[/C][C]81[/C][C]78.4089549239193[/C][C]2.59104507608068[/C][/ROW]
[ROW][C]22[/C][C]82[/C][C]79.7827221786551[/C][C]2.21727782134488[/C][/ROW]
[ROW][C]23[/C][C]88[/C][C]82.2219255618689[/C][C]5.77807443813114[/C][/ROW]
[ROW][C]24[/C][C]99[/C][C]88.0806139568314[/C][C]10.9193860431686[/C][/ROW]
[ROW][C]25[/C][C]117[/C][C]106.510986703481[/C][C]10.4890132965191[/C][/ROW]
[ROW][C]26[/C][C]113[/C][C]112.868316175076[/C][C]0.131683824924238[/C][/ROW]
[ROW][C]27[/C][C]106[/C][C]112.051266821771[/C][C]-6.05126682177128[/C][/ROW]
[ROW][C]28[/C][C]100[/C][C]101.342386107546[/C][C]-1.34238610754639[/C][/ROW]
[ROW][C]29[/C][C]97[/C][C]96.4886069705327[/C][C]0.511393029467314[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]94.3967534179586[/C][C]1.60324658204138[/C][/ROW]
[ROW][C]31[/C][C]100[/C][C]97.35840072444[/C][C]2.64159927555993[/C][/ROW]
[ROW][C]32[/C][C]104[/C][C]103.026007737323[/C][C]0.973992262677044[/C][/ROW]
[ROW][C]33[/C][C]104[/C][C]105.155273112518[/C][C]-1.15527311251789[/C][/ROW]
[ROW][C]34[/C][C]111[/C][C]104.148694761859[/C][C]6.85130523814149[/C][/ROW]
[ROW][C]35[/C][C]117[/C][C]110.993508748006[/C][C]6.00649125199371[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]119.032476809319[/C][C]-1.03247680931877[/C][/ROW]
[ROW][C]37[/C][C]140[/C][C]129.806680724120[/C][C]10.1933192758804[/C][/ROW]
[ROW][C]38[/C][C]147[/C][C]132.305689469044[/C][C]14.6943105309564[/C][/ROW]
[ROW][C]39[/C][C]134[/C][C]138.67479505276[/C][C]-4.67479505275992[/C][/ROW]
[ROW][C]40[/C][C]126[/C][C]130.738019838492[/C][C]-4.73801983849214[/C][/ROW]
[ROW][C]41[/C][C]116[/C][C]124.564502270107[/C][C]-8.56450227010698[/C][/ROW]
[ROW][C]42[/C][C]114[/C][C]117.216069249189[/C][C]-3.21606924918862[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]117.583797092034[/C][C]2.41620290796637[/C][/ROW]
[ROW][C]44[/C][C]122[/C][C]122.592901352030[/C][C]-0.592901352029642[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]123.034339844768[/C][C]-6.03433984476798[/C][/ROW]
[ROW][C]46[/C][C]119[/C][C]121.897918325330[/C][C]-2.89791832532987[/C][/ROW]
[ROW][C]47[/C][C]132[/C][C]122.243004201915[/C][C]9.75699579808528[/C][/ROW]
[ROW][C]48[/C][C]134[/C][C]130.132325104302[/C][C]3.86767489569758[/C][/ROW]
[ROW][C]49[/C][C]154[/C][C]148.162216184821[/C][C]5.83778381517891[/C][/ROW]
[ROW][C]50[/C][C]152[/C][C]149.559985117360[/C][C]2.44001488264047[/C][/ROW]
[ROW][C]51[/C][C]132[/C][C]141.051704134660[/C][C]-9.05170413465979[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]130.252528762407[/C][C]-0.252528762407167[/C][/ROW]
[ROW][C]53[/C][C]123[/C][C]125.506176271455[/C][C]-2.50617627145536[/C][/ROW]
[ROW][C]54[/C][C]129[/C][C]123.956444902216[/C][C]5.04355509778377[/C][/ROW]
[ROW][C]55[/C][C]124[/C][C]131.668920540651[/C][C]-7.66892054065073[/C][/ROW]
[ROW][C]56[/C][C]128[/C][C]129.158092712267[/C][C]-1.15809271226669[/C][/ROW]
[ROW][C]57[/C][C]128[/C][C]127.245686015682[/C][C]0.754313984317804[/C][/ROW]
[ROW][C]58[/C][C]129[/C][C]131.589972890176[/C][C]-2.58997289017583[/C][/ROW]
[ROW][C]59[/C][C]141[/C][C]136.760756580712[/C][C]4.23924341928804[/C][/ROW]
[ROW][C]60[/C][C]138[/C][C]138.991657257165[/C][C]-0.991657257165173[/C][/ROW]
[ROW][C]61[/C][C]155[/C][C]154.617742527317[/C][C]0.382257472682511[/C][/ROW]
[ROW][C]62[/C][C]160[/C][C]151.250264086173[/C][C]8.74973591382664[/C][/ROW]
[ROW][C]63[/C][C]142[/C][C]142.545403129008[/C][C]-0.545403129007838[/C][/ROW]
[ROW][C]64[/C][C]133[/C][C]140.377031698605[/C][C]-7.37703169860461[/C][/ROW]
[ROW][C]65[/C][C]131[/C][C]130.260302188707[/C][C]0.739697811293041[/C][/ROW]
[ROW][C]66[/C][C]140[/C][C]133.520969539368[/C][C]6.47903046063232[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]137.523961410038[/C][C]-3.52396141003754[/C][/ROW]
[ROW][C]68[/C][C]134[/C][C]140.046024962477[/C][C]-6.04602496247716[/C][/ROW]
[ROW][C]69[/C][C]134[/C][C]135.722575839689[/C][C]-1.72257583968891[/C][/ROW]
[ROW][C]70[/C][C]136[/C][C]137.262797692503[/C][C]-1.26279769250345[/C][/ROW]
[ROW][C]71[/C][C]145[/C][C]145.759083250348[/C][C]-0.759083250348198[/C][/ROW]
[ROW][C]72[/C][C]137[/C][C]142.876572122086[/C][C]-5.87657212208572[/C][/ROW]
[ROW][C]73[/C][C]152[/C][C]155.840405078971[/C][C]-3.8404050789712[/C][/ROW]
[ROW][C]74[/C][C]168[/C][C]152.755824505602[/C][C]15.2441754943977[/C][/ROW]
[ROW][C]75[/C][C]160[/C][C]144.753659331667[/C][C]15.2463406683333[/C][/ROW]
[ROW][C]76[/C][C]157[/C][C]150.179353449887[/C][C]6.82064655011268[/C][/ROW]
[ROW][C]77[/C][C]147[/C][C]152.157958840575[/C][C]-5.15795884057499[/C][/ROW]
[ROW][C]78[/C][C]161[/C][C]153.837867669192[/C][C]7.16213233080845[/C][/ROW]
[ROW][C]79[/C][C]159[/C][C]154.718242093449[/C][C]4.28175790655095[/C][/ROW]
[ROW][C]80[/C][C]164[/C][C]161.411140579956[/C][C]2.58885942004358[/C][/ROW]
[ROW][C]81[/C][C]163[/C][C]164.322482979171[/C][C]-1.32248297917127[/C][/ROW]
[ROW][C]82[/C][C]158[/C][C]166.45597137444[/C][C]-8.45597137443994[/C][/ROW]
[ROW][C]83[/C][C]175[/C][C]170.695156700081[/C][C]4.30484329991936[/C][/ROW]
[ROW][C]84[/C][C]163[/C][C]169.330711862381[/C][C]-6.33071186238058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79250&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79250&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
139087.03659188034192.9634081196581
149089.27967877060.720321229399957
158988.93327932777320.0667206722267792
168282.0465513919437-0.046551391943737
177877.83754427705870.162455722941317
187675.17896803689320.821031963106776
197480.0268128753726-6.0268128753726
207877.73840371821230.261596281787732
218178.40895492391932.59104507608068
228279.78272217865512.21727782134488
238882.22192556186895.77807443813114
249988.080613956831410.9193860431686
25117106.51098670348110.4890132965191
26113112.8683161750760.131683824924238
27106112.051266821771-6.05126682177128
28100101.342386107546-1.34238610754639
299796.48860697053270.511393029467314
309694.39675341795861.60324658204138
3110097.358400724442.64159927555993
32104103.0260077373230.973992262677044
33104105.155273112518-1.15527311251789
34111104.1486947618596.85130523814149
35117110.9935087480066.00649125199371
36118119.032476809319-1.03247680931877
37140129.80668072412010.1933192758804
38147132.30568946904414.6943105309564
39134138.67479505276-4.67479505275992
40126130.738019838492-4.73801983849214
41116124.564502270107-8.56450227010698
42114117.216069249189-3.21606924918862
43120117.5837970920342.41620290796637
44122122.592901352030-0.592901352029642
45117123.034339844768-6.03433984476798
46119121.897918325330-2.89791832532987
47132122.2430042019159.75699579808528
48134130.1323251043023.86767489569758
49154148.1622161848215.83778381517891
50152149.5599851173602.44001488264047
51132141.051704134660-9.05170413465979
52130130.252528762407-0.252528762407167
53123125.506176271455-2.50617627145536
54129123.9564449022165.04355509778377
55124131.668920540651-7.66892054065073
56128129.158092712267-1.15809271226669
57128127.2456860156820.754313984317804
58129131.589972890176-2.58997289017583
59141136.7607565807124.23924341928804
60138138.991657257165-0.991657257165173
61155154.6177425273170.382257472682511
62160151.2502640861738.74973591382664
63142142.545403129008-0.545403129007838
64133140.377031698605-7.37703169860461
65131130.2603021887070.739697811293041
66140133.5209695393686.47903046063232
67134137.523961410038-3.52396141003754
68134140.046024962477-6.04602496247716
69134135.722575839689-1.72257583968891
70136137.262797692503-1.26279769250345
71145145.759083250348-0.759083250348198
72137142.876572122086-5.87657212208572
73152155.840405078971-3.8404050789712
74168152.75582450560215.2441754943977
75160144.75365933166715.2463406683333
76157150.1793534498876.82064655011268
77147152.157958840575-5.15795884057499
78161153.8378676691927.16213233080845
79159154.7182420934494.28175790655095
80164161.4111405799562.58885942004358
81163164.322482979171-1.32248297917127
82158166.45597137444-8.45597137443994
83175170.6951567000814.30484329991936
84163169.330711862381-6.33071186238058







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85182.905013837075171.820819075086193.989208599064
86189.388047230008176.221279840589202.554814619426
87171.79080264156.801244376908186.780360903092
88164.473179411447147.834813013414181.111545809480
89157.738351253270139.577528461572175.899174044969
90167.194945735493147.608364009266186.781527461721
91162.446317427679141.510751595773183.381883259585
92165.752169210966143.530259617282187.974078804650
93165.532138797572142.076077445583188.988200149562
94165.855675906723141.209679401325190.501672412121
95180.107416276005154.309454392476205.905378159534
96172.100826234940145.183871029814199.017781440066

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 182.905013837075 & 171.820819075086 & 193.989208599064 \tabularnewline
86 & 189.388047230008 & 176.221279840589 & 202.554814619426 \tabularnewline
87 & 171.79080264 & 156.801244376908 & 186.780360903092 \tabularnewline
88 & 164.473179411447 & 147.834813013414 & 181.111545809480 \tabularnewline
89 & 157.738351253270 & 139.577528461572 & 175.899174044969 \tabularnewline
90 & 167.194945735493 & 147.608364009266 & 186.781527461721 \tabularnewline
91 & 162.446317427679 & 141.510751595773 & 183.381883259585 \tabularnewline
92 & 165.752169210966 & 143.530259617282 & 187.974078804650 \tabularnewline
93 & 165.532138797572 & 142.076077445583 & 188.988200149562 \tabularnewline
94 & 165.855675906723 & 141.209679401325 & 190.501672412121 \tabularnewline
95 & 180.107416276005 & 154.309454392476 & 205.905378159534 \tabularnewline
96 & 172.100826234940 & 145.183871029814 & 199.017781440066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79250&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]85[/C][C]182.905013837075[/C][C]171.820819075086[/C][C]193.989208599064[/C][/ROW]
[ROW][C]86[/C][C]189.388047230008[/C][C]176.221279840589[/C][C]202.554814619426[/C][/ROW]
[ROW][C]87[/C][C]171.79080264[/C][C]156.801244376908[/C][C]186.780360903092[/C][/ROW]
[ROW][C]88[/C][C]164.473179411447[/C][C]147.834813013414[/C][C]181.111545809480[/C][/ROW]
[ROW][C]89[/C][C]157.738351253270[/C][C]139.577528461572[/C][C]175.899174044969[/C][/ROW]
[ROW][C]90[/C][C]167.194945735493[/C][C]147.608364009266[/C][C]186.781527461721[/C][/ROW]
[ROW][C]91[/C][C]162.446317427679[/C][C]141.510751595773[/C][C]183.381883259585[/C][/ROW]
[ROW][C]92[/C][C]165.752169210966[/C][C]143.530259617282[/C][C]187.974078804650[/C][/ROW]
[ROW][C]93[/C][C]165.532138797572[/C][C]142.076077445583[/C][C]188.988200149562[/C][/ROW]
[ROW][C]94[/C][C]165.855675906723[/C][C]141.209679401325[/C][C]190.501672412121[/C][/ROW]
[ROW][C]95[/C][C]180.107416276005[/C][C]154.309454392476[/C][C]205.905378159534[/C][/ROW]
[ROW][C]96[/C][C]172.100826234940[/C][C]145.183871029814[/C][C]199.017781440066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79250&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79250&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
85182.905013837075171.820819075086193.989208599064
86189.388047230008176.221279840589202.554814619426
87171.79080264156.801244376908186.780360903092
88164.473179411447147.834813013414181.111545809480
89157.738351253270139.577528461572175.899174044969
90167.194945735493147.608364009266186.781527461721
91162.446317427679141.510751595773183.381883259585
92165.752169210966143.530259617282187.974078804650
93165.532138797572142.076077445583188.988200149562
94165.855675906723141.209679401325190.501672412121
95180.107416276005154.309454392476205.905378159534
96172.100826234940145.183871029814199.017781440066



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')