Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 21:08:22 +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/2016/Nov/28/t1480367339dmmt9xhli59lopj.htm/, Retrieved Sat, 04 May 2024 15:24:05 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 15:24:05 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
89,8
101,7
92,7
116,2
134,2
153,3
129,7
137,6
158,8
197,1
171,1
184,4
216,6
219,3
184,2
205,3
216,8
219,4
172,1
165,3
178,9
163
116,2
121,8
124,1
125,7
81,8
94,8
121,5
136,3
109,6
120,7
154,1
154,4
153,3
157,3
192,1
223
220,6
221,7
239,2
251,2
238,3
240,6
250,3
256,7
239,2
189,9
155,9
138,4
124,7
119,4
116
124,9
123,4
124,4
135,5
143,6
130,6
116,6
118,2
116,1
106
94,9
97,1
96,8
93,7
91
105,7
112,9
112,1
112,9
127
136,5
130,9
136,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955271348884
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955271348884 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \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]0.999955271348884[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/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
alpha0.999955271348884
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101.789.811.9
392.7101.699467729052-8.99946772905173
4116.292.700402534052323.4995974659477
5134.2116.19894889470418.0010511052964
6153.3134.19919483726519.1008051627346
7129.7153.29914564675-23.5991456467499
8137.6129.7010555579527.89894444204776
9158.8137.5996466908721.2003533091302
10197.1158.79905173679338.3009482632067
11171.1197.098286850248-25.9982868502477
12184.4171.10116286830213.2988371316979
13216.6184.39940516095432.2005948390463
14219.3216.5985597108282.7014402891723
15184.2219.29987916822-35.0998791682198
16205.3184.20156997024921.0984300297505
17216.8205.29905629568411.5009437043159
18219.4216.7994855783022.60051442169842
19172.1219.399883682498-47.2998836824977
20165.3172.102115659995-6.80211565999502
21178.9165.30030424945813.5996957505418
22163178.899391703954-15.8993917039535
23116.2163.000711158344-46.8007111583445
24121.8116.2020933326815.59790666731861
25124.1121.7997496131862.3002503868143
26125.7124.0998971129031.60010288709704
2781.8125.699928429556-43.8999284295562
2894.881.801963584582712.9980364154173
29121.594.79941861536426.700581384636
30136.3121.49880571901114.8011942809893
31109.6136.299337962545-26.6993379625449
32120.7109.60119422537311.0988057746273
33154.1120.69950356538933.4004964346113
34154.4154.0985060408480.30149395915214
35153.3154.399986514582-1.09998651458187
36157.3153.3000492009133.99995079908695
37192.1157.29982108759634.8001789124038
38223192.09844343493930.9015565650613
39220.6222.998617815057-2.39861781505746
40221.7220.6001072869391.09989271306057
41239.2221.69995080328317.5000491967174
42251.2239.19921724640512.000782753595
43238.3251.199463221175-12.8994632211751
44240.6238.300576975592.29942302440998
45250.3240.599897149919.70010285009025
46256.7250.2995661274846.40043387251615
47239.2256.699713717226-17.4997137172264
48189.9239.200782738589-49.3007827385894
49155.9189.902205157511-34.0022051575108
50138.4155.901520872772-17.5015208727716
51124.7138.400782819421-13.7007828194211
52119.4124.700612817535-5.30061281753474
53116119.400237089261-3.40023708926142
54124.9116.0001520880188.89984791198154
55123.4124.899601921808-1.49960192180777
56124.4123.4000670751710.999932924828826
57135.5124.39995527434911.1000447256509
58143.6135.4995035099728.10049649002789
59130.6143.599637675719-12.9996376757186
60116.6130.600581456258-14.0005814562582
61118.2116.6006262271231.59937377287663
62116.1118.199928462169-2.09992846216852
63106116.100093926968-10.1000939269675
6494.9106.000451763577-11.1004517635775
6597.194.90049650823422.19950349176582
6696.897.0999016191757-0.299901619175685
6793.796.8000134141949-3.10001341419489
689193.7001386594185-2.70013865941846
69105.791.000120773560114.6998792264399
70112.9105.6993424942317.20065750576936
71112.1112.899677924303-0.799677924302628
72112.9112.1000357685150.79996423148512
73127112.89996421867914.100035781321
74136.5126.9993693244199.50063067558118
75130.9136.499575049605-5.59957504960514
76136.3130.9002504614395.3997495385612

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101.7 & 89.8 & 11.9 \tabularnewline
3 & 92.7 & 101.699467729052 & -8.99946772905173 \tabularnewline
4 & 116.2 & 92.7004025340523 & 23.4995974659477 \tabularnewline
5 & 134.2 & 116.198948894704 & 18.0010511052964 \tabularnewline
6 & 153.3 & 134.199194837265 & 19.1008051627346 \tabularnewline
7 & 129.7 & 153.29914564675 & -23.5991456467499 \tabularnewline
8 & 137.6 & 129.701055557952 & 7.89894444204776 \tabularnewline
9 & 158.8 & 137.59964669087 & 21.2003533091302 \tabularnewline
10 & 197.1 & 158.799051736793 & 38.3009482632067 \tabularnewline
11 & 171.1 & 197.098286850248 & -25.9982868502477 \tabularnewline
12 & 184.4 & 171.101162868302 & 13.2988371316979 \tabularnewline
13 & 216.6 & 184.399405160954 & 32.2005948390463 \tabularnewline
14 & 219.3 & 216.598559710828 & 2.7014402891723 \tabularnewline
15 & 184.2 & 219.29987916822 & -35.0998791682198 \tabularnewline
16 & 205.3 & 184.201569970249 & 21.0984300297505 \tabularnewline
17 & 216.8 & 205.299056295684 & 11.5009437043159 \tabularnewline
18 & 219.4 & 216.799485578302 & 2.60051442169842 \tabularnewline
19 & 172.1 & 219.399883682498 & -47.2998836824977 \tabularnewline
20 & 165.3 & 172.102115659995 & -6.80211565999502 \tabularnewline
21 & 178.9 & 165.300304249458 & 13.5996957505418 \tabularnewline
22 & 163 & 178.899391703954 & -15.8993917039535 \tabularnewline
23 & 116.2 & 163.000711158344 & -46.8007111583445 \tabularnewline
24 & 121.8 & 116.202093332681 & 5.59790666731861 \tabularnewline
25 & 124.1 & 121.799749613186 & 2.3002503868143 \tabularnewline
26 & 125.7 & 124.099897112903 & 1.60010288709704 \tabularnewline
27 & 81.8 & 125.699928429556 & -43.8999284295562 \tabularnewline
28 & 94.8 & 81.8019635845827 & 12.9980364154173 \tabularnewline
29 & 121.5 & 94.799418615364 & 26.700581384636 \tabularnewline
30 & 136.3 & 121.498805719011 & 14.8011942809893 \tabularnewline
31 & 109.6 & 136.299337962545 & -26.6993379625449 \tabularnewline
32 & 120.7 & 109.601194225373 & 11.0988057746273 \tabularnewline
33 & 154.1 & 120.699503565389 & 33.4004964346113 \tabularnewline
34 & 154.4 & 154.098506040848 & 0.30149395915214 \tabularnewline
35 & 153.3 & 154.399986514582 & -1.09998651458187 \tabularnewline
36 & 157.3 & 153.300049200913 & 3.99995079908695 \tabularnewline
37 & 192.1 & 157.299821087596 & 34.8001789124038 \tabularnewline
38 & 223 & 192.098443434939 & 30.9015565650613 \tabularnewline
39 & 220.6 & 222.998617815057 & -2.39861781505746 \tabularnewline
40 & 221.7 & 220.600107286939 & 1.09989271306057 \tabularnewline
41 & 239.2 & 221.699950803283 & 17.5000491967174 \tabularnewline
42 & 251.2 & 239.199217246405 & 12.000782753595 \tabularnewline
43 & 238.3 & 251.199463221175 & -12.8994632211751 \tabularnewline
44 & 240.6 & 238.30057697559 & 2.29942302440998 \tabularnewline
45 & 250.3 & 240.59989714991 & 9.70010285009025 \tabularnewline
46 & 256.7 & 250.299566127484 & 6.40043387251615 \tabularnewline
47 & 239.2 & 256.699713717226 & -17.4997137172264 \tabularnewline
48 & 189.9 & 239.200782738589 & -49.3007827385894 \tabularnewline
49 & 155.9 & 189.902205157511 & -34.0022051575108 \tabularnewline
50 & 138.4 & 155.901520872772 & -17.5015208727716 \tabularnewline
51 & 124.7 & 138.400782819421 & -13.7007828194211 \tabularnewline
52 & 119.4 & 124.700612817535 & -5.30061281753474 \tabularnewline
53 & 116 & 119.400237089261 & -3.40023708926142 \tabularnewline
54 & 124.9 & 116.000152088018 & 8.89984791198154 \tabularnewline
55 & 123.4 & 124.899601921808 & -1.49960192180777 \tabularnewline
56 & 124.4 & 123.400067075171 & 0.999932924828826 \tabularnewline
57 & 135.5 & 124.399955274349 & 11.1000447256509 \tabularnewline
58 & 143.6 & 135.499503509972 & 8.10049649002789 \tabularnewline
59 & 130.6 & 143.599637675719 & -12.9996376757186 \tabularnewline
60 & 116.6 & 130.600581456258 & -14.0005814562582 \tabularnewline
61 & 118.2 & 116.600626227123 & 1.59937377287663 \tabularnewline
62 & 116.1 & 118.199928462169 & -2.09992846216852 \tabularnewline
63 & 106 & 116.100093926968 & -10.1000939269675 \tabularnewline
64 & 94.9 & 106.000451763577 & -11.1004517635775 \tabularnewline
65 & 97.1 & 94.9004965082342 & 2.19950349176582 \tabularnewline
66 & 96.8 & 97.0999016191757 & -0.299901619175685 \tabularnewline
67 & 93.7 & 96.8000134141949 & -3.10001341419489 \tabularnewline
68 & 91 & 93.7001386594185 & -2.70013865941846 \tabularnewline
69 & 105.7 & 91.0001207735601 & 14.6998792264399 \tabularnewline
70 & 112.9 & 105.699342494231 & 7.20065750576936 \tabularnewline
71 & 112.1 & 112.899677924303 & -0.799677924302628 \tabularnewline
72 & 112.9 & 112.100035768515 & 0.79996423148512 \tabularnewline
73 & 127 & 112.899964218679 & 14.100035781321 \tabularnewline
74 & 136.5 & 126.999369324419 & 9.50063067558118 \tabularnewline
75 & 130.9 & 136.499575049605 & -5.59957504960514 \tabularnewline
76 & 136.3 & 130.900250461439 & 5.3997495385612 \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]2[/C][C]101.7[/C][C]89.8[/C][C]11.9[/C][/ROW]
[ROW][C]3[/C][C]92.7[/C][C]101.699467729052[/C][C]-8.99946772905173[/C][/ROW]
[ROW][C]4[/C][C]116.2[/C][C]92.7004025340523[/C][C]23.4995974659477[/C][/ROW]
[ROW][C]5[/C][C]134.2[/C][C]116.198948894704[/C][C]18.0010511052964[/C][/ROW]
[ROW][C]6[/C][C]153.3[/C][C]134.199194837265[/C][C]19.1008051627346[/C][/ROW]
[ROW][C]7[/C][C]129.7[/C][C]153.29914564675[/C][C]-23.5991456467499[/C][/ROW]
[ROW][C]8[/C][C]137.6[/C][C]129.701055557952[/C][C]7.89894444204776[/C][/ROW]
[ROW][C]9[/C][C]158.8[/C][C]137.59964669087[/C][C]21.2003533091302[/C][/ROW]
[ROW][C]10[/C][C]197.1[/C][C]158.799051736793[/C][C]38.3009482632067[/C][/ROW]
[ROW][C]11[/C][C]171.1[/C][C]197.098286850248[/C][C]-25.9982868502477[/C][/ROW]
[ROW][C]12[/C][C]184.4[/C][C]171.101162868302[/C][C]13.2988371316979[/C][/ROW]
[ROW][C]13[/C][C]216.6[/C][C]184.399405160954[/C][C]32.2005948390463[/C][/ROW]
[ROW][C]14[/C][C]219.3[/C][C]216.598559710828[/C][C]2.7014402891723[/C][/ROW]
[ROW][C]15[/C][C]184.2[/C][C]219.29987916822[/C][C]-35.0998791682198[/C][/ROW]
[ROW][C]16[/C][C]205.3[/C][C]184.201569970249[/C][C]21.0984300297505[/C][/ROW]
[ROW][C]17[/C][C]216.8[/C][C]205.299056295684[/C][C]11.5009437043159[/C][/ROW]
[ROW][C]18[/C][C]219.4[/C][C]216.799485578302[/C][C]2.60051442169842[/C][/ROW]
[ROW][C]19[/C][C]172.1[/C][C]219.399883682498[/C][C]-47.2998836824977[/C][/ROW]
[ROW][C]20[/C][C]165.3[/C][C]172.102115659995[/C][C]-6.80211565999502[/C][/ROW]
[ROW][C]21[/C][C]178.9[/C][C]165.300304249458[/C][C]13.5996957505418[/C][/ROW]
[ROW][C]22[/C][C]163[/C][C]178.899391703954[/C][C]-15.8993917039535[/C][/ROW]
[ROW][C]23[/C][C]116.2[/C][C]163.000711158344[/C][C]-46.8007111583445[/C][/ROW]
[ROW][C]24[/C][C]121.8[/C][C]116.202093332681[/C][C]5.59790666731861[/C][/ROW]
[ROW][C]25[/C][C]124.1[/C][C]121.799749613186[/C][C]2.3002503868143[/C][/ROW]
[ROW][C]26[/C][C]125.7[/C][C]124.099897112903[/C][C]1.60010288709704[/C][/ROW]
[ROW][C]27[/C][C]81.8[/C][C]125.699928429556[/C][C]-43.8999284295562[/C][/ROW]
[ROW][C]28[/C][C]94.8[/C][C]81.8019635845827[/C][C]12.9980364154173[/C][/ROW]
[ROW][C]29[/C][C]121.5[/C][C]94.799418615364[/C][C]26.700581384636[/C][/ROW]
[ROW][C]30[/C][C]136.3[/C][C]121.498805719011[/C][C]14.8011942809893[/C][/ROW]
[ROW][C]31[/C][C]109.6[/C][C]136.299337962545[/C][C]-26.6993379625449[/C][/ROW]
[ROW][C]32[/C][C]120.7[/C][C]109.601194225373[/C][C]11.0988057746273[/C][/ROW]
[ROW][C]33[/C][C]154.1[/C][C]120.699503565389[/C][C]33.4004964346113[/C][/ROW]
[ROW][C]34[/C][C]154.4[/C][C]154.098506040848[/C][C]0.30149395915214[/C][/ROW]
[ROW][C]35[/C][C]153.3[/C][C]154.399986514582[/C][C]-1.09998651458187[/C][/ROW]
[ROW][C]36[/C][C]157.3[/C][C]153.300049200913[/C][C]3.99995079908695[/C][/ROW]
[ROW][C]37[/C][C]192.1[/C][C]157.299821087596[/C][C]34.8001789124038[/C][/ROW]
[ROW][C]38[/C][C]223[/C][C]192.098443434939[/C][C]30.9015565650613[/C][/ROW]
[ROW][C]39[/C][C]220.6[/C][C]222.998617815057[/C][C]-2.39861781505746[/C][/ROW]
[ROW][C]40[/C][C]221.7[/C][C]220.600107286939[/C][C]1.09989271306057[/C][/ROW]
[ROW][C]41[/C][C]239.2[/C][C]221.699950803283[/C][C]17.5000491967174[/C][/ROW]
[ROW][C]42[/C][C]251.2[/C][C]239.199217246405[/C][C]12.000782753595[/C][/ROW]
[ROW][C]43[/C][C]238.3[/C][C]251.199463221175[/C][C]-12.8994632211751[/C][/ROW]
[ROW][C]44[/C][C]240.6[/C][C]238.30057697559[/C][C]2.29942302440998[/C][/ROW]
[ROW][C]45[/C][C]250.3[/C][C]240.59989714991[/C][C]9.70010285009025[/C][/ROW]
[ROW][C]46[/C][C]256.7[/C][C]250.299566127484[/C][C]6.40043387251615[/C][/ROW]
[ROW][C]47[/C][C]239.2[/C][C]256.699713717226[/C][C]-17.4997137172264[/C][/ROW]
[ROW][C]48[/C][C]189.9[/C][C]239.200782738589[/C][C]-49.3007827385894[/C][/ROW]
[ROW][C]49[/C][C]155.9[/C][C]189.902205157511[/C][C]-34.0022051575108[/C][/ROW]
[ROW][C]50[/C][C]138.4[/C][C]155.901520872772[/C][C]-17.5015208727716[/C][/ROW]
[ROW][C]51[/C][C]124.7[/C][C]138.400782819421[/C][C]-13.7007828194211[/C][/ROW]
[ROW][C]52[/C][C]119.4[/C][C]124.700612817535[/C][C]-5.30061281753474[/C][/ROW]
[ROW][C]53[/C][C]116[/C][C]119.400237089261[/C][C]-3.40023708926142[/C][/ROW]
[ROW][C]54[/C][C]124.9[/C][C]116.000152088018[/C][C]8.89984791198154[/C][/ROW]
[ROW][C]55[/C][C]123.4[/C][C]124.899601921808[/C][C]-1.49960192180777[/C][/ROW]
[ROW][C]56[/C][C]124.4[/C][C]123.400067075171[/C][C]0.999932924828826[/C][/ROW]
[ROW][C]57[/C][C]135.5[/C][C]124.399955274349[/C][C]11.1000447256509[/C][/ROW]
[ROW][C]58[/C][C]143.6[/C][C]135.499503509972[/C][C]8.10049649002789[/C][/ROW]
[ROW][C]59[/C][C]130.6[/C][C]143.599637675719[/C][C]-12.9996376757186[/C][/ROW]
[ROW][C]60[/C][C]116.6[/C][C]130.600581456258[/C][C]-14.0005814562582[/C][/ROW]
[ROW][C]61[/C][C]118.2[/C][C]116.600626227123[/C][C]1.59937377287663[/C][/ROW]
[ROW][C]62[/C][C]116.1[/C][C]118.199928462169[/C][C]-2.09992846216852[/C][/ROW]
[ROW][C]63[/C][C]106[/C][C]116.100093926968[/C][C]-10.1000939269675[/C][/ROW]
[ROW][C]64[/C][C]94.9[/C][C]106.000451763577[/C][C]-11.1004517635775[/C][/ROW]
[ROW][C]65[/C][C]97.1[/C][C]94.9004965082342[/C][C]2.19950349176582[/C][/ROW]
[ROW][C]66[/C][C]96.8[/C][C]97.0999016191757[/C][C]-0.299901619175685[/C][/ROW]
[ROW][C]67[/C][C]93.7[/C][C]96.8000134141949[/C][C]-3.10001341419489[/C][/ROW]
[ROW][C]68[/C][C]91[/C][C]93.7001386594185[/C][C]-2.70013865941846[/C][/ROW]
[ROW][C]69[/C][C]105.7[/C][C]91.0001207735601[/C][C]14.6998792264399[/C][/ROW]
[ROW][C]70[/C][C]112.9[/C][C]105.699342494231[/C][C]7.20065750576936[/C][/ROW]
[ROW][C]71[/C][C]112.1[/C][C]112.899677924303[/C][C]-0.799677924302628[/C][/ROW]
[ROW][C]72[/C][C]112.9[/C][C]112.100035768515[/C][C]0.79996423148512[/C][/ROW]
[ROW][C]73[/C][C]127[/C][C]112.899964218679[/C][C]14.100035781321[/C][/ROW]
[ROW][C]74[/C][C]136.5[/C][C]126.999369324419[/C][C]9.50063067558118[/C][/ROW]
[ROW][C]75[/C][C]130.9[/C][C]136.499575049605[/C][C]-5.59957504960514[/C][/ROW]
[ROW][C]76[/C][C]136.3[/C][C]130.900250461439[/C][C]5.3997495385612[/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
2101.789.811.9
392.7101.699467729052-8.99946772905173
4116.292.700402534052323.4995974659477
5134.2116.19894889470418.0010511052964
6153.3134.19919483726519.1008051627346
7129.7153.29914564675-23.5991456467499
8137.6129.7010555579527.89894444204776
9158.8137.5996466908721.2003533091302
10197.1158.79905173679338.3009482632067
11171.1197.098286850248-25.9982868502477
12184.4171.10116286830213.2988371316979
13216.6184.39940516095432.2005948390463
14219.3216.5985597108282.7014402891723
15184.2219.29987916822-35.0998791682198
16205.3184.20156997024921.0984300297505
17216.8205.29905629568411.5009437043159
18219.4216.7994855783022.60051442169842
19172.1219.399883682498-47.2998836824977
20165.3172.102115659995-6.80211565999502
21178.9165.30030424945813.5996957505418
22163178.899391703954-15.8993917039535
23116.2163.000711158344-46.8007111583445
24121.8116.2020933326815.59790666731861
25124.1121.7997496131862.3002503868143
26125.7124.0998971129031.60010288709704
2781.8125.699928429556-43.8999284295562
2894.881.801963584582712.9980364154173
29121.594.79941861536426.700581384636
30136.3121.49880571901114.8011942809893
31109.6136.299337962545-26.6993379625449
32120.7109.60119422537311.0988057746273
33154.1120.69950356538933.4004964346113
34154.4154.0985060408480.30149395915214
35153.3154.399986514582-1.09998651458187
36157.3153.3000492009133.99995079908695
37192.1157.29982108759634.8001789124038
38223192.09844343493930.9015565650613
39220.6222.998617815057-2.39861781505746
40221.7220.6001072869391.09989271306057
41239.2221.69995080328317.5000491967174
42251.2239.19921724640512.000782753595
43238.3251.199463221175-12.8994632211751
44240.6238.300576975592.29942302440998
45250.3240.599897149919.70010285009025
46256.7250.2995661274846.40043387251615
47239.2256.699713717226-17.4997137172264
48189.9239.200782738589-49.3007827385894
49155.9189.902205157511-34.0022051575108
50138.4155.901520872772-17.5015208727716
51124.7138.400782819421-13.7007828194211
52119.4124.700612817535-5.30061281753474
53116119.400237089261-3.40023708926142
54124.9116.0001520880188.89984791198154
55123.4124.899601921808-1.49960192180777
56124.4123.4000670751710.999932924828826
57135.5124.39995527434911.1000447256509
58143.6135.4995035099728.10049649002789
59130.6143.599637675719-12.9996376757186
60116.6130.600581456258-14.0005814562582
61118.2116.6006262271231.59937377287663
62116.1118.199928462169-2.09992846216852
63106116.100093926968-10.1000939269675
6494.9106.000451763577-11.1004517635775
6597.194.90049650823422.19950349176582
6696.897.0999016191757-0.299901619175685
6793.796.8000134141949-3.10001341419489
689193.7001386594185-2.70013865941846
69105.791.000120773560114.6998792264399
70112.9105.6993424942317.20065750576936
71112.1112.899677924303-0.799677924302628
72112.9112.1000357685150.79996423148512
73127112.89996421867914.100035781321
74136.5126.9993693244199.50063067558118
75130.9136.499575049605-5.59957504960514
76136.3130.9002504614395.3997495385612







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
77136.29975847648799.2118014535741173.3877154994
78136.29975847648783.850639656258188.748877296716
79136.29975847648772.0634480757209200.536068877253
80136.29975847648762.1263327581838210.47318419479
81136.29975847648753.3715329337099219.227984019264
82136.29975847648745.4565743592469227.142942593727
83136.29975847648738.1780095650258234.421507387948
84136.29975847648731.4032803738886241.196236579085
85136.29975847648725.040311114863247.559205838111
86136.29975847648719.0220618070049253.577455145969
87136.29975847648713.297922534969259.301594418005
88136.2997584764877.82857433829525264.770942614678

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 136.299758476487 & 99.2118014535741 & 173.3877154994 \tabularnewline
78 & 136.299758476487 & 83.850639656258 & 188.748877296716 \tabularnewline
79 & 136.299758476487 & 72.0634480757209 & 200.536068877253 \tabularnewline
80 & 136.299758476487 & 62.1263327581838 & 210.47318419479 \tabularnewline
81 & 136.299758476487 & 53.3715329337099 & 219.227984019264 \tabularnewline
82 & 136.299758476487 & 45.4565743592469 & 227.142942593727 \tabularnewline
83 & 136.299758476487 & 38.1780095650258 & 234.421507387948 \tabularnewline
84 & 136.299758476487 & 31.4032803738886 & 241.196236579085 \tabularnewline
85 & 136.299758476487 & 25.040311114863 & 247.559205838111 \tabularnewline
86 & 136.299758476487 & 19.0220618070049 & 253.577455145969 \tabularnewline
87 & 136.299758476487 & 13.297922534969 & 259.301594418005 \tabularnewline
88 & 136.299758476487 & 7.82857433829525 & 264.770942614678 \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]77[/C][C]136.299758476487[/C][C]99.2118014535741[/C][C]173.3877154994[/C][/ROW]
[ROW][C]78[/C][C]136.299758476487[/C][C]83.850639656258[/C][C]188.748877296716[/C][/ROW]
[ROW][C]79[/C][C]136.299758476487[/C][C]72.0634480757209[/C][C]200.536068877253[/C][/ROW]
[ROW][C]80[/C][C]136.299758476487[/C][C]62.1263327581838[/C][C]210.47318419479[/C][/ROW]
[ROW][C]81[/C][C]136.299758476487[/C][C]53.3715329337099[/C][C]219.227984019264[/C][/ROW]
[ROW][C]82[/C][C]136.299758476487[/C][C]45.4565743592469[/C][C]227.142942593727[/C][/ROW]
[ROW][C]83[/C][C]136.299758476487[/C][C]38.1780095650258[/C][C]234.421507387948[/C][/ROW]
[ROW][C]84[/C][C]136.299758476487[/C][C]31.4032803738886[/C][C]241.196236579085[/C][/ROW]
[ROW][C]85[/C][C]136.299758476487[/C][C]25.040311114863[/C][C]247.559205838111[/C][/ROW]
[ROW][C]86[/C][C]136.299758476487[/C][C]19.0220618070049[/C][C]253.577455145969[/C][/ROW]
[ROW][C]87[/C][C]136.299758476487[/C][C]13.297922534969[/C][C]259.301594418005[/C][/ROW]
[ROW][C]88[/C][C]136.299758476487[/C][C]7.82857433829525[/C][C]264.770942614678[/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
77136.29975847648799.2118014535741173.3877154994
78136.29975847648783.850639656258188.748877296716
79136.29975847648772.0634480757209200.536068877253
80136.29975847648762.1263327581838210.47318419479
81136.29975847648753.3715329337099219.227984019264
82136.29975847648745.4565743592469227.142942593727
83136.29975847648738.1780095650258234.421507387948
84136.29975847648731.4032803738886241.196236579085
85136.29975847648725.040311114863247.559205838111
86136.29975847648719.0220618070049253.577455145969
87136.29975847648713.297922534969259.301594418005
88136.2997584764877.82857433829525264.770942614678



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