Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 24 Nov 2016 20:44:15 +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/24/t1480020286wagrpve2bgsb8qi.htm/, Retrieved Tue, 07 May 2024 19:40:56 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 19:40:56 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
77.34
78.15
78.31
78.71
78.68
78.85
78.97
79.47
80.6
82.24
83.25
84.55
85.91
86.84
87.44
87.79
88.08
88.38
88.53
88.79
88.85
89.26
89.31
89.39
89.76
89.94
89.99
90.08
89.95
90.2
89.7
89.5
89.25
89.13
89.07
89.06
89.15
89.38
89.4
89.51
89.62
89.65
89.68
89.92
90.26
90.89
91.08
91.13
91.83
92.66
93.45
93.95
94.12
94.31
94.25
94.51
94.58
94.85
95.31
95.75
96.06
96.4
96.57
96.47
96.34
96.22
96.2
96.71
97.05
97.82
98.22
98.5
98.94
99.5
99.89
100
100.1
100.16
100.05
100.03
100
100.32
100.53
100.49
100.38
100.22
100.5
100.57
100.6
100.23
100.29
100.01
100.13
100.22
100.2
100.34
100.73
100.29
101.11
101.09
101.01
101.27
101.57
101.69
101
101.43
101.13
101.23




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

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

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.876417920810581
beta0.737925167983047
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.876417920810581 \tabularnewline
beta & 0.737925167983047 \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]0.876417920810581[/C][/ROW]
[ROW][C]beta[/C][C]0.737925167983047[/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
alpha0.876417920810581
beta0.737925167983047
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
378.3178.96-0.650000000000006
478.7178.7799533045388-0.0699533045387568
578.6879.063028968381-0.383028968380984
678.8578.82400286284630.0259971371537375
778.9778.96026771666790.00973228333207032
879.4779.08857192890940.381428071090625
980.679.78931828799660.810681712003444
1082.2481.39056309629490.849436903705097
1183.2583.5751306926063-0.325130692606294
1284.5584.52001415190050.0299858480994715
1385.9185.79552088421810.114479115781847
1486.8487.2191162053971-0.379116205397082
1587.4487.9649295989475-0.52492959894748
1687.7988.2434613600733-0.453461360073334
1788.0888.2913617195577-0.211361719557658
1888.3888.4147483998745-0.034748399874502
1988.5388.6704492967261-0.140449296726061
2088.7988.74267914148030.047320858519754
2188.8589.0100779739333-0.160077973933269
2289.2688.99218139009180.267818609908218
2389.3189.5225075955212-0.212507595521174
2489.3989.494432090614-0.10443209061404
2589.7689.49353644117230.266463558827752
2689.9489.990030587265-0.0500305872650415
2789.9990.1767872680909-0.186787268090939
2890.0890.1228868559882-0.0428868559881863
2989.9590.1673670914045-0.217367091404455
3090.289.91835171974980.281648280250181
3189.790.2888329918489-0.588832991848889
3289.589.5155924210657-0.0155924210657332
3389.2589.23466605985670.0153339401432646
3489.1388.99076104784820.139238952151842
3589.0788.94549873352820.124501266471825
3689.0688.96783885619230.0921611438076866
3789.1589.0214389698750.128561030125013
3889.3889.19008497943050.189915020569529
3989.489.5353266267793-0.135326626779289
4089.5189.50800076259180.00199923740821362
4189.6289.60232271526030.0176772847397473
4289.6589.7218176348075-0.0718176348074451
4389.6889.7164309236529-0.0364309236529294
4489.9289.71849675840440.201503241595631
4590.2690.05941072054230.200589279457731
4690.8990.52925094337060.360749056629388
4791.0891.3727656060469-0.292765606046927
4891.1391.4541877600985-0.324187760098539
4991.8391.29840875235660.531591247643419
5092.6692.23644625814240.423553741857603
5193.4593.35372302560340.0962769743965879
5293.9594.2464338576592-0.296433857659196
5394.1294.6032529606104-0.483252960610358
5494.3194.4838058599427-0.173805859942675
5594.2594.5231581337955-0.273158133795519
5694.5194.29877650465540.211223495344626
5794.5894.6355203646807-0.0555203646806888
5894.8594.70257839334670.147421606653253
5995.3195.04284050229140.267159497708576
6095.7595.66082333150810.0891766684918593
6196.0696.1804921214531-0.120492121453083
6296.496.4384774553617-0.038477455361658
6396.5796.7434573553197-0.173457355319684
6496.4796.8179582306458-0.34795823064583
6596.3496.5144880923483-0.174488092348312
6696.2296.250203461195-0.0302034611950006
6796.296.0928389566090.107161043390988
6896.7196.1251675172870.584832482712969
6997.0596.95436509129120.0956349087088455
7097.8297.41667118960110.403328810398918
7198.2298.4094909184016-0.189490918401603
7298.598.7602031919686-0.260203191968642
7398.9498.88066053247370.0593394675263426
7499.599.31954744998730.180452550012674
7599.8999.9812842729459-0.0912842729458561
76100100.345829719867-0.345829719867112
77100.1100.263628229722-0.163628229722093
78100.16100.235287968047-0.0752879680474479
79100.05100.235679643908-0.185679643908102
80100.03100.0192373243940.0107626756063439
8110099.98192112835830.0180788716417197
82100.3299.96270914150960.35729085849043
83100.53100.4718596364380.0581403635617193
84100.49100.75643044284-0.266430442839848
85100.38100.584232793457-0.204232793456754
86100.22100.334462632264-0.11446263226388
87100.5100.0893421346170.410657865382674
88100.57100.570031758515-3.17585150497735e-05
89100.6100.690765096927-0.0907650969267024
90100.23100.673277524031-0.443277524030847
91100.29100.0601604966060.229839503394302
92100.01100.185619590244-0.175619590244466
93100.1399.84214846269090.287851537309109
94100.22100.0910342040370.128965795963452
95100.2100.284075792046-0.0840757920456952
96100.34100.2360295067110.103970493288571
97100.73100.4200312803950.309968719604825
98100.29100.985039922127-0.695039922127023
99101.11100.2197372260060.890262773994294
100101.09101.4195826156-0.329582615600259
101101.01101.337182402826-0.327182402825642
102101.27101.0452868288570.224713171142497
103101.57101.3824113645860.187588635413846
104101.69101.808318647926-0.118318647925747
105101101.889602987309-0.889602987309289
106101.43100.7195862210890.710413778911317
107101.13101.411299323385-0.28129932338534
108101.23101.0519323424180.178067657582275

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 78.31 & 78.96 & -0.650000000000006 \tabularnewline
4 & 78.71 & 78.7799533045388 & -0.0699533045387568 \tabularnewline
5 & 78.68 & 79.063028968381 & -0.383028968380984 \tabularnewline
6 & 78.85 & 78.8240028628463 & 0.0259971371537375 \tabularnewline
7 & 78.97 & 78.9602677166679 & 0.00973228333207032 \tabularnewline
8 & 79.47 & 79.0885719289094 & 0.381428071090625 \tabularnewline
9 & 80.6 & 79.7893182879966 & 0.810681712003444 \tabularnewline
10 & 82.24 & 81.3905630962949 & 0.849436903705097 \tabularnewline
11 & 83.25 & 83.5751306926063 & -0.325130692606294 \tabularnewline
12 & 84.55 & 84.5200141519005 & 0.0299858480994715 \tabularnewline
13 & 85.91 & 85.7955208842181 & 0.114479115781847 \tabularnewline
14 & 86.84 & 87.2191162053971 & -0.379116205397082 \tabularnewline
15 & 87.44 & 87.9649295989475 & -0.52492959894748 \tabularnewline
16 & 87.79 & 88.2434613600733 & -0.453461360073334 \tabularnewline
17 & 88.08 & 88.2913617195577 & -0.211361719557658 \tabularnewline
18 & 88.38 & 88.4147483998745 & -0.034748399874502 \tabularnewline
19 & 88.53 & 88.6704492967261 & -0.140449296726061 \tabularnewline
20 & 88.79 & 88.7426791414803 & 0.047320858519754 \tabularnewline
21 & 88.85 & 89.0100779739333 & -0.160077973933269 \tabularnewline
22 & 89.26 & 88.9921813900918 & 0.267818609908218 \tabularnewline
23 & 89.31 & 89.5225075955212 & -0.212507595521174 \tabularnewline
24 & 89.39 & 89.494432090614 & -0.10443209061404 \tabularnewline
25 & 89.76 & 89.4935364411723 & 0.266463558827752 \tabularnewline
26 & 89.94 & 89.990030587265 & -0.0500305872650415 \tabularnewline
27 & 89.99 & 90.1767872680909 & -0.186787268090939 \tabularnewline
28 & 90.08 & 90.1228868559882 & -0.0428868559881863 \tabularnewline
29 & 89.95 & 90.1673670914045 & -0.217367091404455 \tabularnewline
30 & 90.2 & 89.9183517197498 & 0.281648280250181 \tabularnewline
31 & 89.7 & 90.2888329918489 & -0.588832991848889 \tabularnewline
32 & 89.5 & 89.5155924210657 & -0.0155924210657332 \tabularnewline
33 & 89.25 & 89.2346660598567 & 0.0153339401432646 \tabularnewline
34 & 89.13 & 88.9907610478482 & 0.139238952151842 \tabularnewline
35 & 89.07 & 88.9454987335282 & 0.124501266471825 \tabularnewline
36 & 89.06 & 88.9678388561923 & 0.0921611438076866 \tabularnewline
37 & 89.15 & 89.021438969875 & 0.128561030125013 \tabularnewline
38 & 89.38 & 89.1900849794305 & 0.189915020569529 \tabularnewline
39 & 89.4 & 89.5353266267793 & -0.135326626779289 \tabularnewline
40 & 89.51 & 89.5080007625918 & 0.00199923740821362 \tabularnewline
41 & 89.62 & 89.6023227152603 & 0.0176772847397473 \tabularnewline
42 & 89.65 & 89.7218176348075 & -0.0718176348074451 \tabularnewline
43 & 89.68 & 89.7164309236529 & -0.0364309236529294 \tabularnewline
44 & 89.92 & 89.7184967584044 & 0.201503241595631 \tabularnewline
45 & 90.26 & 90.0594107205423 & 0.200589279457731 \tabularnewline
46 & 90.89 & 90.5292509433706 & 0.360749056629388 \tabularnewline
47 & 91.08 & 91.3727656060469 & -0.292765606046927 \tabularnewline
48 & 91.13 & 91.4541877600985 & -0.324187760098539 \tabularnewline
49 & 91.83 & 91.2984087523566 & 0.531591247643419 \tabularnewline
50 & 92.66 & 92.2364462581424 & 0.423553741857603 \tabularnewline
51 & 93.45 & 93.3537230256034 & 0.0962769743965879 \tabularnewline
52 & 93.95 & 94.2464338576592 & -0.296433857659196 \tabularnewline
53 & 94.12 & 94.6032529606104 & -0.483252960610358 \tabularnewline
54 & 94.31 & 94.4838058599427 & -0.173805859942675 \tabularnewline
55 & 94.25 & 94.5231581337955 & -0.273158133795519 \tabularnewline
56 & 94.51 & 94.2987765046554 & 0.211223495344626 \tabularnewline
57 & 94.58 & 94.6355203646807 & -0.0555203646806888 \tabularnewline
58 & 94.85 & 94.7025783933467 & 0.147421606653253 \tabularnewline
59 & 95.31 & 95.0428405022914 & 0.267159497708576 \tabularnewline
60 & 95.75 & 95.6608233315081 & 0.0891766684918593 \tabularnewline
61 & 96.06 & 96.1804921214531 & -0.120492121453083 \tabularnewline
62 & 96.4 & 96.4384774553617 & -0.038477455361658 \tabularnewline
63 & 96.57 & 96.7434573553197 & -0.173457355319684 \tabularnewline
64 & 96.47 & 96.8179582306458 & -0.34795823064583 \tabularnewline
65 & 96.34 & 96.5144880923483 & -0.174488092348312 \tabularnewline
66 & 96.22 & 96.250203461195 & -0.0302034611950006 \tabularnewline
67 & 96.2 & 96.092838956609 & 0.107161043390988 \tabularnewline
68 & 96.71 & 96.125167517287 & 0.584832482712969 \tabularnewline
69 & 97.05 & 96.9543650912912 & 0.0956349087088455 \tabularnewline
70 & 97.82 & 97.4166711896011 & 0.403328810398918 \tabularnewline
71 & 98.22 & 98.4094909184016 & -0.189490918401603 \tabularnewline
72 & 98.5 & 98.7602031919686 & -0.260203191968642 \tabularnewline
73 & 98.94 & 98.8806605324737 & 0.0593394675263426 \tabularnewline
74 & 99.5 & 99.3195474499873 & 0.180452550012674 \tabularnewline
75 & 99.89 & 99.9812842729459 & -0.0912842729458561 \tabularnewline
76 & 100 & 100.345829719867 & -0.345829719867112 \tabularnewline
77 & 100.1 & 100.263628229722 & -0.163628229722093 \tabularnewline
78 & 100.16 & 100.235287968047 & -0.0752879680474479 \tabularnewline
79 & 100.05 & 100.235679643908 & -0.185679643908102 \tabularnewline
80 & 100.03 & 100.019237324394 & 0.0107626756063439 \tabularnewline
81 & 100 & 99.9819211283583 & 0.0180788716417197 \tabularnewline
82 & 100.32 & 99.9627091415096 & 0.35729085849043 \tabularnewline
83 & 100.53 & 100.471859636438 & 0.0581403635617193 \tabularnewline
84 & 100.49 & 100.75643044284 & -0.266430442839848 \tabularnewline
85 & 100.38 & 100.584232793457 & -0.204232793456754 \tabularnewline
86 & 100.22 & 100.334462632264 & -0.11446263226388 \tabularnewline
87 & 100.5 & 100.089342134617 & 0.410657865382674 \tabularnewline
88 & 100.57 & 100.570031758515 & -3.17585150497735e-05 \tabularnewline
89 & 100.6 & 100.690765096927 & -0.0907650969267024 \tabularnewline
90 & 100.23 & 100.673277524031 & -0.443277524030847 \tabularnewline
91 & 100.29 & 100.060160496606 & 0.229839503394302 \tabularnewline
92 & 100.01 & 100.185619590244 & -0.175619590244466 \tabularnewline
93 & 100.13 & 99.8421484626909 & 0.287851537309109 \tabularnewline
94 & 100.22 & 100.091034204037 & 0.128965795963452 \tabularnewline
95 & 100.2 & 100.284075792046 & -0.0840757920456952 \tabularnewline
96 & 100.34 & 100.236029506711 & 0.103970493288571 \tabularnewline
97 & 100.73 & 100.420031280395 & 0.309968719604825 \tabularnewline
98 & 100.29 & 100.985039922127 & -0.695039922127023 \tabularnewline
99 & 101.11 & 100.219737226006 & 0.890262773994294 \tabularnewline
100 & 101.09 & 101.4195826156 & -0.329582615600259 \tabularnewline
101 & 101.01 & 101.337182402826 & -0.327182402825642 \tabularnewline
102 & 101.27 & 101.045286828857 & 0.224713171142497 \tabularnewline
103 & 101.57 & 101.382411364586 & 0.187588635413846 \tabularnewline
104 & 101.69 & 101.808318647926 & -0.118318647925747 \tabularnewline
105 & 101 & 101.889602987309 & -0.889602987309289 \tabularnewline
106 & 101.43 & 100.719586221089 & 0.710413778911317 \tabularnewline
107 & 101.13 & 101.411299323385 & -0.28129932338534 \tabularnewline
108 & 101.23 & 101.051932342418 & 0.178067657582275 \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]3[/C][C]78.31[/C][C]78.96[/C][C]-0.650000000000006[/C][/ROW]
[ROW][C]4[/C][C]78.71[/C][C]78.7799533045388[/C][C]-0.0699533045387568[/C][/ROW]
[ROW][C]5[/C][C]78.68[/C][C]79.063028968381[/C][C]-0.383028968380984[/C][/ROW]
[ROW][C]6[/C][C]78.85[/C][C]78.8240028628463[/C][C]0.0259971371537375[/C][/ROW]
[ROW][C]7[/C][C]78.97[/C][C]78.9602677166679[/C][C]0.00973228333207032[/C][/ROW]
[ROW][C]8[/C][C]79.47[/C][C]79.0885719289094[/C][C]0.381428071090625[/C][/ROW]
[ROW][C]9[/C][C]80.6[/C][C]79.7893182879966[/C][C]0.810681712003444[/C][/ROW]
[ROW][C]10[/C][C]82.24[/C][C]81.3905630962949[/C][C]0.849436903705097[/C][/ROW]
[ROW][C]11[/C][C]83.25[/C][C]83.5751306926063[/C][C]-0.325130692606294[/C][/ROW]
[ROW][C]12[/C][C]84.55[/C][C]84.5200141519005[/C][C]0.0299858480994715[/C][/ROW]
[ROW][C]13[/C][C]85.91[/C][C]85.7955208842181[/C][C]0.114479115781847[/C][/ROW]
[ROW][C]14[/C][C]86.84[/C][C]87.2191162053971[/C][C]-0.379116205397082[/C][/ROW]
[ROW][C]15[/C][C]87.44[/C][C]87.9649295989475[/C][C]-0.52492959894748[/C][/ROW]
[ROW][C]16[/C][C]87.79[/C][C]88.2434613600733[/C][C]-0.453461360073334[/C][/ROW]
[ROW][C]17[/C][C]88.08[/C][C]88.2913617195577[/C][C]-0.211361719557658[/C][/ROW]
[ROW][C]18[/C][C]88.38[/C][C]88.4147483998745[/C][C]-0.034748399874502[/C][/ROW]
[ROW][C]19[/C][C]88.53[/C][C]88.6704492967261[/C][C]-0.140449296726061[/C][/ROW]
[ROW][C]20[/C][C]88.79[/C][C]88.7426791414803[/C][C]0.047320858519754[/C][/ROW]
[ROW][C]21[/C][C]88.85[/C][C]89.0100779739333[/C][C]-0.160077973933269[/C][/ROW]
[ROW][C]22[/C][C]89.26[/C][C]88.9921813900918[/C][C]0.267818609908218[/C][/ROW]
[ROW][C]23[/C][C]89.31[/C][C]89.5225075955212[/C][C]-0.212507595521174[/C][/ROW]
[ROW][C]24[/C][C]89.39[/C][C]89.494432090614[/C][C]-0.10443209061404[/C][/ROW]
[ROW][C]25[/C][C]89.76[/C][C]89.4935364411723[/C][C]0.266463558827752[/C][/ROW]
[ROW][C]26[/C][C]89.94[/C][C]89.990030587265[/C][C]-0.0500305872650415[/C][/ROW]
[ROW][C]27[/C][C]89.99[/C][C]90.1767872680909[/C][C]-0.186787268090939[/C][/ROW]
[ROW][C]28[/C][C]90.08[/C][C]90.1228868559882[/C][C]-0.0428868559881863[/C][/ROW]
[ROW][C]29[/C][C]89.95[/C][C]90.1673670914045[/C][C]-0.217367091404455[/C][/ROW]
[ROW][C]30[/C][C]90.2[/C][C]89.9183517197498[/C][C]0.281648280250181[/C][/ROW]
[ROW][C]31[/C][C]89.7[/C][C]90.2888329918489[/C][C]-0.588832991848889[/C][/ROW]
[ROW][C]32[/C][C]89.5[/C][C]89.5155924210657[/C][C]-0.0155924210657332[/C][/ROW]
[ROW][C]33[/C][C]89.25[/C][C]89.2346660598567[/C][C]0.0153339401432646[/C][/ROW]
[ROW][C]34[/C][C]89.13[/C][C]88.9907610478482[/C][C]0.139238952151842[/C][/ROW]
[ROW][C]35[/C][C]89.07[/C][C]88.9454987335282[/C][C]0.124501266471825[/C][/ROW]
[ROW][C]36[/C][C]89.06[/C][C]88.9678388561923[/C][C]0.0921611438076866[/C][/ROW]
[ROW][C]37[/C][C]89.15[/C][C]89.021438969875[/C][C]0.128561030125013[/C][/ROW]
[ROW][C]38[/C][C]89.38[/C][C]89.1900849794305[/C][C]0.189915020569529[/C][/ROW]
[ROW][C]39[/C][C]89.4[/C][C]89.5353266267793[/C][C]-0.135326626779289[/C][/ROW]
[ROW][C]40[/C][C]89.51[/C][C]89.5080007625918[/C][C]0.00199923740821362[/C][/ROW]
[ROW][C]41[/C][C]89.62[/C][C]89.6023227152603[/C][C]0.0176772847397473[/C][/ROW]
[ROW][C]42[/C][C]89.65[/C][C]89.7218176348075[/C][C]-0.0718176348074451[/C][/ROW]
[ROW][C]43[/C][C]89.68[/C][C]89.7164309236529[/C][C]-0.0364309236529294[/C][/ROW]
[ROW][C]44[/C][C]89.92[/C][C]89.7184967584044[/C][C]0.201503241595631[/C][/ROW]
[ROW][C]45[/C][C]90.26[/C][C]90.0594107205423[/C][C]0.200589279457731[/C][/ROW]
[ROW][C]46[/C][C]90.89[/C][C]90.5292509433706[/C][C]0.360749056629388[/C][/ROW]
[ROW][C]47[/C][C]91.08[/C][C]91.3727656060469[/C][C]-0.292765606046927[/C][/ROW]
[ROW][C]48[/C][C]91.13[/C][C]91.4541877600985[/C][C]-0.324187760098539[/C][/ROW]
[ROW][C]49[/C][C]91.83[/C][C]91.2984087523566[/C][C]0.531591247643419[/C][/ROW]
[ROW][C]50[/C][C]92.66[/C][C]92.2364462581424[/C][C]0.423553741857603[/C][/ROW]
[ROW][C]51[/C][C]93.45[/C][C]93.3537230256034[/C][C]0.0962769743965879[/C][/ROW]
[ROW][C]52[/C][C]93.95[/C][C]94.2464338576592[/C][C]-0.296433857659196[/C][/ROW]
[ROW][C]53[/C][C]94.12[/C][C]94.6032529606104[/C][C]-0.483252960610358[/C][/ROW]
[ROW][C]54[/C][C]94.31[/C][C]94.4838058599427[/C][C]-0.173805859942675[/C][/ROW]
[ROW][C]55[/C][C]94.25[/C][C]94.5231581337955[/C][C]-0.273158133795519[/C][/ROW]
[ROW][C]56[/C][C]94.51[/C][C]94.2987765046554[/C][C]0.211223495344626[/C][/ROW]
[ROW][C]57[/C][C]94.58[/C][C]94.6355203646807[/C][C]-0.0555203646806888[/C][/ROW]
[ROW][C]58[/C][C]94.85[/C][C]94.7025783933467[/C][C]0.147421606653253[/C][/ROW]
[ROW][C]59[/C][C]95.31[/C][C]95.0428405022914[/C][C]0.267159497708576[/C][/ROW]
[ROW][C]60[/C][C]95.75[/C][C]95.6608233315081[/C][C]0.0891766684918593[/C][/ROW]
[ROW][C]61[/C][C]96.06[/C][C]96.1804921214531[/C][C]-0.120492121453083[/C][/ROW]
[ROW][C]62[/C][C]96.4[/C][C]96.4384774553617[/C][C]-0.038477455361658[/C][/ROW]
[ROW][C]63[/C][C]96.57[/C][C]96.7434573553197[/C][C]-0.173457355319684[/C][/ROW]
[ROW][C]64[/C][C]96.47[/C][C]96.8179582306458[/C][C]-0.34795823064583[/C][/ROW]
[ROW][C]65[/C][C]96.34[/C][C]96.5144880923483[/C][C]-0.174488092348312[/C][/ROW]
[ROW][C]66[/C][C]96.22[/C][C]96.250203461195[/C][C]-0.0302034611950006[/C][/ROW]
[ROW][C]67[/C][C]96.2[/C][C]96.092838956609[/C][C]0.107161043390988[/C][/ROW]
[ROW][C]68[/C][C]96.71[/C][C]96.125167517287[/C][C]0.584832482712969[/C][/ROW]
[ROW][C]69[/C][C]97.05[/C][C]96.9543650912912[/C][C]0.0956349087088455[/C][/ROW]
[ROW][C]70[/C][C]97.82[/C][C]97.4166711896011[/C][C]0.403328810398918[/C][/ROW]
[ROW][C]71[/C][C]98.22[/C][C]98.4094909184016[/C][C]-0.189490918401603[/C][/ROW]
[ROW][C]72[/C][C]98.5[/C][C]98.7602031919686[/C][C]-0.260203191968642[/C][/ROW]
[ROW][C]73[/C][C]98.94[/C][C]98.8806605324737[/C][C]0.0593394675263426[/C][/ROW]
[ROW][C]74[/C][C]99.5[/C][C]99.3195474499873[/C][C]0.180452550012674[/C][/ROW]
[ROW][C]75[/C][C]99.89[/C][C]99.9812842729459[/C][C]-0.0912842729458561[/C][/ROW]
[ROW][C]76[/C][C]100[/C][C]100.345829719867[/C][C]-0.345829719867112[/C][/ROW]
[ROW][C]77[/C][C]100.1[/C][C]100.263628229722[/C][C]-0.163628229722093[/C][/ROW]
[ROW][C]78[/C][C]100.16[/C][C]100.235287968047[/C][C]-0.0752879680474479[/C][/ROW]
[ROW][C]79[/C][C]100.05[/C][C]100.235679643908[/C][C]-0.185679643908102[/C][/ROW]
[ROW][C]80[/C][C]100.03[/C][C]100.019237324394[/C][C]0.0107626756063439[/C][/ROW]
[ROW][C]81[/C][C]100[/C][C]99.9819211283583[/C][C]0.0180788716417197[/C][/ROW]
[ROW][C]82[/C][C]100.32[/C][C]99.9627091415096[/C][C]0.35729085849043[/C][/ROW]
[ROW][C]83[/C][C]100.53[/C][C]100.471859636438[/C][C]0.0581403635617193[/C][/ROW]
[ROW][C]84[/C][C]100.49[/C][C]100.75643044284[/C][C]-0.266430442839848[/C][/ROW]
[ROW][C]85[/C][C]100.38[/C][C]100.584232793457[/C][C]-0.204232793456754[/C][/ROW]
[ROW][C]86[/C][C]100.22[/C][C]100.334462632264[/C][C]-0.11446263226388[/C][/ROW]
[ROW][C]87[/C][C]100.5[/C][C]100.089342134617[/C][C]0.410657865382674[/C][/ROW]
[ROW][C]88[/C][C]100.57[/C][C]100.570031758515[/C][C]-3.17585150497735e-05[/C][/ROW]
[ROW][C]89[/C][C]100.6[/C][C]100.690765096927[/C][C]-0.0907650969267024[/C][/ROW]
[ROW][C]90[/C][C]100.23[/C][C]100.673277524031[/C][C]-0.443277524030847[/C][/ROW]
[ROW][C]91[/C][C]100.29[/C][C]100.060160496606[/C][C]0.229839503394302[/C][/ROW]
[ROW][C]92[/C][C]100.01[/C][C]100.185619590244[/C][C]-0.175619590244466[/C][/ROW]
[ROW][C]93[/C][C]100.13[/C][C]99.8421484626909[/C][C]0.287851537309109[/C][/ROW]
[ROW][C]94[/C][C]100.22[/C][C]100.091034204037[/C][C]0.128965795963452[/C][/ROW]
[ROW][C]95[/C][C]100.2[/C][C]100.284075792046[/C][C]-0.0840757920456952[/C][/ROW]
[ROW][C]96[/C][C]100.34[/C][C]100.236029506711[/C][C]0.103970493288571[/C][/ROW]
[ROW][C]97[/C][C]100.73[/C][C]100.420031280395[/C][C]0.309968719604825[/C][/ROW]
[ROW][C]98[/C][C]100.29[/C][C]100.985039922127[/C][C]-0.695039922127023[/C][/ROW]
[ROW][C]99[/C][C]101.11[/C][C]100.219737226006[/C][C]0.890262773994294[/C][/ROW]
[ROW][C]100[/C][C]101.09[/C][C]101.4195826156[/C][C]-0.329582615600259[/C][/ROW]
[ROW][C]101[/C][C]101.01[/C][C]101.337182402826[/C][C]-0.327182402825642[/C][/ROW]
[ROW][C]102[/C][C]101.27[/C][C]101.045286828857[/C][C]0.224713171142497[/C][/ROW]
[ROW][C]103[/C][C]101.57[/C][C]101.382411364586[/C][C]0.187588635413846[/C][/ROW]
[ROW][C]104[/C][C]101.69[/C][C]101.808318647926[/C][C]-0.118318647925747[/C][/ROW]
[ROW][C]105[/C][C]101[/C][C]101.889602987309[/C][C]-0.889602987309289[/C][/ROW]
[ROW][C]106[/C][C]101.43[/C][C]100.719586221089[/C][C]0.710413778911317[/C][/ROW]
[ROW][C]107[/C][C]101.13[/C][C]101.411299323385[/C][C]-0.28129932338534[/C][/ROW]
[ROW][C]108[/C][C]101.23[/C][C]101.051932342418[/C][C]0.178067657582275[/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
378.3178.96-0.650000000000006
478.7178.7799533045388-0.0699533045387568
578.6879.063028968381-0.383028968380984
678.8578.82400286284630.0259971371537375
778.9778.96026771666790.00973228333207032
879.4779.08857192890940.381428071090625
980.679.78931828799660.810681712003444
1082.2481.39056309629490.849436903705097
1183.2583.5751306926063-0.325130692606294
1284.5584.52001415190050.0299858480994715
1385.9185.79552088421810.114479115781847
1486.8487.2191162053971-0.379116205397082
1587.4487.9649295989475-0.52492959894748
1687.7988.2434613600733-0.453461360073334
1788.0888.2913617195577-0.211361719557658
1888.3888.4147483998745-0.034748399874502
1988.5388.6704492967261-0.140449296726061
2088.7988.74267914148030.047320858519754
2188.8589.0100779739333-0.160077973933269
2289.2688.99218139009180.267818609908218
2389.3189.5225075955212-0.212507595521174
2489.3989.494432090614-0.10443209061404
2589.7689.49353644117230.266463558827752
2689.9489.990030587265-0.0500305872650415
2789.9990.1767872680909-0.186787268090939
2890.0890.1228868559882-0.0428868559881863
2989.9590.1673670914045-0.217367091404455
3090.289.91835171974980.281648280250181
3189.790.2888329918489-0.588832991848889
3289.589.5155924210657-0.0155924210657332
3389.2589.23466605985670.0153339401432646
3489.1388.99076104784820.139238952151842
3589.0788.94549873352820.124501266471825
3689.0688.96783885619230.0921611438076866
3789.1589.0214389698750.128561030125013
3889.3889.19008497943050.189915020569529
3989.489.5353266267793-0.135326626779289
4089.5189.50800076259180.00199923740821362
4189.6289.60232271526030.0176772847397473
4289.6589.7218176348075-0.0718176348074451
4389.6889.7164309236529-0.0364309236529294
4489.9289.71849675840440.201503241595631
4590.2690.05941072054230.200589279457731
4690.8990.52925094337060.360749056629388
4791.0891.3727656060469-0.292765606046927
4891.1391.4541877600985-0.324187760098539
4991.8391.29840875235660.531591247643419
5092.6692.23644625814240.423553741857603
5193.4593.35372302560340.0962769743965879
5293.9594.2464338576592-0.296433857659196
5394.1294.6032529606104-0.483252960610358
5494.3194.4838058599427-0.173805859942675
5594.2594.5231581337955-0.273158133795519
5694.5194.29877650465540.211223495344626
5794.5894.6355203646807-0.0555203646806888
5894.8594.70257839334670.147421606653253
5995.3195.04284050229140.267159497708576
6095.7595.66082333150810.0891766684918593
6196.0696.1804921214531-0.120492121453083
6296.496.4384774553617-0.038477455361658
6396.5796.7434573553197-0.173457355319684
6496.4796.8179582306458-0.34795823064583
6596.3496.5144880923483-0.174488092348312
6696.2296.250203461195-0.0302034611950006
6796.296.0928389566090.107161043390988
6896.7196.1251675172870.584832482712969
6997.0596.95436509129120.0956349087088455
7097.8297.41667118960110.403328810398918
7198.2298.4094909184016-0.189490918401603
7298.598.7602031919686-0.260203191968642
7398.9498.88066053247370.0593394675263426
7499.599.31954744998730.180452550012674
7599.8999.9812842729459-0.0912842729458561
76100100.345829719867-0.345829719867112
77100.1100.263628229722-0.163628229722093
78100.16100.235287968047-0.0752879680474479
79100.05100.235679643908-0.185679643908102
80100.03100.0192373243940.0107626756063439
8110099.98192112835830.0180788716417197
82100.3299.96270914150960.35729085849043
83100.53100.4718596364380.0581403635617193
84100.49100.75643044284-0.266430442839848
85100.38100.584232793457-0.204232793456754
86100.22100.334462632264-0.11446263226388
87100.5100.0893421346170.410657865382674
88100.57100.570031758515-3.17585150497735e-05
89100.6100.690765096927-0.0907650969267024
90100.23100.673277524031-0.443277524030847
91100.29100.0601604966060.229839503394302
92100.01100.185619590244-0.175619590244466
93100.1399.84214846269090.287851537309109
94100.22100.0910342040370.128965795963452
95100.2100.284075792046-0.0840757920456952
96100.34100.2360295067110.103970493288571
97100.73100.4200312803950.309968719604825
98100.29100.985039922127-0.695039922127023
99101.11100.2197372260060.890262773994294
100101.09101.4195826156-0.329582615600259
101101.01101.337182402826-0.327182402825642
102101.27101.0452868288570.224713171142497
103101.57101.3824113645860.187588635413846
104101.69101.808318647926-0.118318647925747
105101101.889602987309-0.889602987309289
106101.43100.7195862210890.710413778911317
107101.13101.411299323385-0.28129932338534
108101.23101.0519323424180.178067657582275







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109101.21032466182100.599822047951101.820827275688
110101.212655295100.100269582353102.325041007647
111101.2149859281899.4851658352965102.944806021064
112101.2173165613698.7782341494351103.656398973286
113101.21964719454197.9916879042996104.447606484782
114101.22197782772197.1334750594561105.310480595985
115101.22430846090196.2093999908867106.239216930915
116101.22663909408195.2239846612915107.229293526871
117101.22896972726194.1808992432775108.277040211245
118101.23130036044293.0832084539727109.37939226691
119101.23363099362291.9335258556592110.533736131584
120101.23596162680290.7341169335881111.737806320016

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.21032466182 & 100.599822047951 & 101.820827275688 \tabularnewline
110 & 101.212655295 & 100.100269582353 & 102.325041007647 \tabularnewline
111 & 101.21498592818 & 99.4851658352965 & 102.944806021064 \tabularnewline
112 & 101.21731656136 & 98.7782341494351 & 103.656398973286 \tabularnewline
113 & 101.219647194541 & 97.9916879042996 & 104.447606484782 \tabularnewline
114 & 101.221977827721 & 97.1334750594561 & 105.310480595985 \tabularnewline
115 & 101.224308460901 & 96.2093999908867 & 106.239216930915 \tabularnewline
116 & 101.226639094081 & 95.2239846612915 & 107.229293526871 \tabularnewline
117 & 101.228969727261 & 94.1808992432775 & 108.277040211245 \tabularnewline
118 & 101.231300360442 & 93.0832084539727 & 109.37939226691 \tabularnewline
119 & 101.233630993622 & 91.9335258556592 & 110.533736131584 \tabularnewline
120 & 101.235961626802 & 90.7341169335881 & 111.737806320016 \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]109[/C][C]101.21032466182[/C][C]100.599822047951[/C][C]101.820827275688[/C][/ROW]
[ROW][C]110[/C][C]101.212655295[/C][C]100.100269582353[/C][C]102.325041007647[/C][/ROW]
[ROW][C]111[/C][C]101.21498592818[/C][C]99.4851658352965[/C][C]102.944806021064[/C][/ROW]
[ROW][C]112[/C][C]101.21731656136[/C][C]98.7782341494351[/C][C]103.656398973286[/C][/ROW]
[ROW][C]113[/C][C]101.219647194541[/C][C]97.9916879042996[/C][C]104.447606484782[/C][/ROW]
[ROW][C]114[/C][C]101.221977827721[/C][C]97.1334750594561[/C][C]105.310480595985[/C][/ROW]
[ROW][C]115[/C][C]101.224308460901[/C][C]96.2093999908867[/C][C]106.239216930915[/C][/ROW]
[ROW][C]116[/C][C]101.226639094081[/C][C]95.2239846612915[/C][C]107.229293526871[/C][/ROW]
[ROW][C]117[/C][C]101.228969727261[/C][C]94.1808992432775[/C][C]108.277040211245[/C][/ROW]
[ROW][C]118[/C][C]101.231300360442[/C][C]93.0832084539727[/C][C]109.37939226691[/C][/ROW]
[ROW][C]119[/C][C]101.233630993622[/C][C]91.9335258556592[/C][C]110.533736131584[/C][/ROW]
[ROW][C]120[/C][C]101.235961626802[/C][C]90.7341169335881[/C][C]111.737806320016[/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
109101.21032466182100.599822047951101.820827275688
110101.212655295100.100269582353102.325041007647
111101.2149859281899.4851658352965102.944806021064
112101.2173165613698.7782341494351103.656398973286
113101.21964719454197.9916879042996104.447606484782
114101.22197782772197.1334750594561105.310480595985
115101.22430846090196.2093999908867106.239216930915
116101.22663909408195.2239846612915107.229293526871
117101.22896972726194.1808992432775108.277040211245
118101.23130036044293.0832084539727109.37939226691
119101.23363099362291.9335258556592110.533736131584
120101.23596162680290.7341169335881111.737806320016



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