Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Nov 2015 15:28:55 +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/2015/Nov/30/t144889734645dmf1jo90zwbph.htm/, Retrieved Tue, 14 May 2024 22:08:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284618, Retrieved Tue, 14 May 2024 22:08:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-30 15:28:55] [07f175c9375843c217f66b4a3796ae0c] [Current]
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Dataseries X:
85.95
86.41
86.42
86.81
86.71
86.7
87.07
86.96
87.04
87.5
88.32
88.56
88.92
89.56
90.21
90.42
91.23
91.73
92.21
91.65
91.8
91.63
91.09
90.89
90.98
91.29
90.77
90.96
90.89
90.72
90.66
90.94
90.7
90.74
90.98
91.13
91.54
91.93
92.27
92.59
92.96
92.95
92.99
93.05
93.34
93.47
93.59
93.96
94.49
95.04
95.52
95.75
96.07
96.37
96.48
96.4
96.66
96.81
97.19
97.23
97.94
98.52
98.73
98.8
98.77
98.54
98.72
99.15
99.32
99.5
99.39
99.4
99.37
99.69
99.83
99.79
99.94
100.11
100.21
100.15
100.21
100.13
100.2
100.36
100.5
100.66
100.72
100.41
100.3
100.38
100.55
100.17
100.09
100.22
100.09
99.98




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=284618&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=284618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284618&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
alpha0.999954352805111
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999954352805111 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284618&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]0.999954352805111[/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=284618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284618&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
alpha0.999954352805111
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
286.4185.950.459999999999994
386.4286.40997900229030.0100209977096597
486.8186.41999954256960.390000457430432
586.7186.8099821975731-0.0999821975731123
686.786.7100045639068-0.0100045639068469
787.0786.70000045668030.369999543319722
886.9687.0699831105587-0.109983110558744
987.0486.96000502042050.0799949795795243
1087.587.03999634845360.460003651546415
1188.3287.49997900212370.820020997876313
1288.5688.31996256834170.240037431658322
1388.9288.55998904296460.360010957035428
1489.5688.91998356650970.640016433490317
1590.2189.55997078504510.650029214954856
1690.4290.20997032798970.210029672010265
1791.2390.41999041273460.81000958726537
1891.7391.22996302533450.500036974665491
1992.2191.72997717471480.480022825285218
2091.6592.2099780883045-0.559978088304533
2191.891.65002556142890.149974438571064
2291.6391.7999931540876-0.169993154087578
2391.0991.6300077597106-0.540007759710633
2490.8991.0900246498394-0.200024649839449
2590.9890.89000913056420.0899908694358231
2691.2990.97999589216930.31000410783075
2790.7791.2899858491821-0.519985849182092
2890.9690.77002373589540.189976264104601
2990.8990.9599913281164-0.0699913281164442
3090.7290.8900031949078-0.170003194907807
3190.6690.720007760169-0.0600077601689719
3290.9490.66000273918590.279997260814085
3390.790.9399872189105-0.239987218910471
3490.7490.70001095474340.0399890452566325
3590.9890.73999817461230.240001825387751
3691.1390.97998904458990.150010955410082
3791.5491.12999315242070.410006847579325
3891.9391.53998128433750.390018715662478
3992.2791.92998219673970.340017803260309
4092.5992.26998447914110.320015520858931
4192.9692.58998539218910.370014607810845
4292.9592.9599831098711-0.00998310987107232
4392.9992.9500004557010.0399995442990217
4493.0592.9899981741330.0600018258669905
4593.3493.0499972610850.290002738915049
4693.4793.33998676218850.130013237811539
4793.5993.46999406526040.120005934739609
4893.9693.58999452206570.370005477934285
4994.4993.95998311028780.530016889712172
5095.0494.48997580621570.550024193784267
5195.5295.03997489293840.480025107061564
5295.7595.51997808820040.230021911799625
5396.0795.7499895001450.32001049985503
5496.3796.06998539241830.300014607581673
5596.4896.36998630517470.110013694825255
5696.496.4799949781834-0.0799949781834357
5796.6696.40000365154640.25999634845364
5896.8196.6599881318960.150011868104002
5997.1996.8099931523790.380006847620962
6097.2397.18998265375340.0400173462466427
6197.9497.22999817332040.710001826679601
6298.5297.93996759040820.580032409591752
6398.7398.51997352314750.210026476852462
6498.898.72999041288050.0700095871195145
6598.7798.7999968042587-0.0299968042587295
6698.5498.77000136927-0.230001369269971
6798.7298.54001049891730.179989501082659
6899.1598.71999178398420.430008216015835
6999.3299.14998037133120.170019628668825
7099.599.31999223908090.180007760919125
7199.3999.4999917831506-0.109991783150647
7299.499.39000502081640.00999497918364511
7399.3799.3999995437572-0.0299995437572278
7499.6999.3700013693950.319998630604971
7599.8399.68998539296010.140014607039859
7699.7999.8299936087259-0.0399936087259363
7799.9499.79000182559610.149998174403947
78100.1199.93999315300410.170006846995904
79100.21100.1099922396640.100007760335671
80100.15100.209995434926-0.0599954349262646
81100.21100.1500027386230.0599972613766795
82100.13100.209997261293-0.0799972612933146
83100.2100.1300036516510.0699963483494344
84100.36100.1999968048630.160003195136952
85100.5100.3599926963030.140007303697033
86100.66100.4999936090590.160006390940666
87100.72100.6599926961570.0600073038429088
88100.41100.719997260835-0.309997260834905
89100.3100.410014150505-0.110014150505378
90100.38100.3000050218370.079994978162631
91100.55100.3799963484540.170003651546367
92100.17100.54999223981-0.379992239810178
93100.09100.17001734558-0.0800173455798188
94100.22100.0900036525670.129996347432638
95100.09100.219994066031-0.129994066031387
9699.98100.090005933864-0.110005933864457

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 86.41 & 85.95 & 0.459999999999994 \tabularnewline
3 & 86.42 & 86.4099790022903 & 0.0100209977096597 \tabularnewline
4 & 86.81 & 86.4199995425696 & 0.390000457430432 \tabularnewline
5 & 86.71 & 86.8099821975731 & -0.0999821975731123 \tabularnewline
6 & 86.7 & 86.7100045639068 & -0.0100045639068469 \tabularnewline
7 & 87.07 & 86.7000004566803 & 0.369999543319722 \tabularnewline
8 & 86.96 & 87.0699831105587 & -0.109983110558744 \tabularnewline
9 & 87.04 & 86.9600050204205 & 0.0799949795795243 \tabularnewline
10 & 87.5 & 87.0399963484536 & 0.460003651546415 \tabularnewline
11 & 88.32 & 87.4999790021237 & 0.820020997876313 \tabularnewline
12 & 88.56 & 88.3199625683417 & 0.240037431658322 \tabularnewline
13 & 88.92 & 88.5599890429646 & 0.360010957035428 \tabularnewline
14 & 89.56 & 88.9199835665097 & 0.640016433490317 \tabularnewline
15 & 90.21 & 89.5599707850451 & 0.650029214954856 \tabularnewline
16 & 90.42 & 90.2099703279897 & 0.210029672010265 \tabularnewline
17 & 91.23 & 90.4199904127346 & 0.81000958726537 \tabularnewline
18 & 91.73 & 91.2299630253345 & 0.500036974665491 \tabularnewline
19 & 92.21 & 91.7299771747148 & 0.480022825285218 \tabularnewline
20 & 91.65 & 92.2099780883045 & -0.559978088304533 \tabularnewline
21 & 91.8 & 91.6500255614289 & 0.149974438571064 \tabularnewline
22 & 91.63 & 91.7999931540876 & -0.169993154087578 \tabularnewline
23 & 91.09 & 91.6300077597106 & -0.540007759710633 \tabularnewline
24 & 90.89 & 91.0900246498394 & -0.200024649839449 \tabularnewline
25 & 90.98 & 90.8900091305642 & 0.0899908694358231 \tabularnewline
26 & 91.29 & 90.9799958921693 & 0.31000410783075 \tabularnewline
27 & 90.77 & 91.2899858491821 & -0.519985849182092 \tabularnewline
28 & 90.96 & 90.7700237358954 & 0.189976264104601 \tabularnewline
29 & 90.89 & 90.9599913281164 & -0.0699913281164442 \tabularnewline
30 & 90.72 & 90.8900031949078 & -0.170003194907807 \tabularnewline
31 & 90.66 & 90.720007760169 & -0.0600077601689719 \tabularnewline
32 & 90.94 & 90.6600027391859 & 0.279997260814085 \tabularnewline
33 & 90.7 & 90.9399872189105 & -0.239987218910471 \tabularnewline
34 & 90.74 & 90.7000109547434 & 0.0399890452566325 \tabularnewline
35 & 90.98 & 90.7399981746123 & 0.240001825387751 \tabularnewline
36 & 91.13 & 90.9799890445899 & 0.150010955410082 \tabularnewline
37 & 91.54 & 91.1299931524207 & 0.410006847579325 \tabularnewline
38 & 91.93 & 91.5399812843375 & 0.390018715662478 \tabularnewline
39 & 92.27 & 91.9299821967397 & 0.340017803260309 \tabularnewline
40 & 92.59 & 92.2699844791411 & 0.320015520858931 \tabularnewline
41 & 92.96 & 92.5899853921891 & 0.370014607810845 \tabularnewline
42 & 92.95 & 92.9599831098711 & -0.00998310987107232 \tabularnewline
43 & 92.99 & 92.950000455701 & 0.0399995442990217 \tabularnewline
44 & 93.05 & 92.989998174133 & 0.0600018258669905 \tabularnewline
45 & 93.34 & 93.049997261085 & 0.290002738915049 \tabularnewline
46 & 93.47 & 93.3399867621885 & 0.130013237811539 \tabularnewline
47 & 93.59 & 93.4699940652604 & 0.120005934739609 \tabularnewline
48 & 93.96 & 93.5899945220657 & 0.370005477934285 \tabularnewline
49 & 94.49 & 93.9599831102878 & 0.530016889712172 \tabularnewline
50 & 95.04 & 94.4899758062157 & 0.550024193784267 \tabularnewline
51 & 95.52 & 95.0399748929384 & 0.480025107061564 \tabularnewline
52 & 95.75 & 95.5199780882004 & 0.230021911799625 \tabularnewline
53 & 96.07 & 95.749989500145 & 0.32001049985503 \tabularnewline
54 & 96.37 & 96.0699853924183 & 0.300014607581673 \tabularnewline
55 & 96.48 & 96.3699863051747 & 0.110013694825255 \tabularnewline
56 & 96.4 & 96.4799949781834 & -0.0799949781834357 \tabularnewline
57 & 96.66 & 96.4000036515464 & 0.25999634845364 \tabularnewline
58 & 96.81 & 96.659988131896 & 0.150011868104002 \tabularnewline
59 & 97.19 & 96.809993152379 & 0.380006847620962 \tabularnewline
60 & 97.23 & 97.1899826537534 & 0.0400173462466427 \tabularnewline
61 & 97.94 & 97.2299981733204 & 0.710001826679601 \tabularnewline
62 & 98.52 & 97.9399675904082 & 0.580032409591752 \tabularnewline
63 & 98.73 & 98.5199735231475 & 0.210026476852462 \tabularnewline
64 & 98.8 & 98.7299904128805 & 0.0700095871195145 \tabularnewline
65 & 98.77 & 98.7999968042587 & -0.0299968042587295 \tabularnewline
66 & 98.54 & 98.77000136927 & -0.230001369269971 \tabularnewline
67 & 98.72 & 98.5400104989173 & 0.179989501082659 \tabularnewline
68 & 99.15 & 98.7199917839842 & 0.430008216015835 \tabularnewline
69 & 99.32 & 99.1499803713312 & 0.170019628668825 \tabularnewline
70 & 99.5 & 99.3199922390809 & 0.180007760919125 \tabularnewline
71 & 99.39 & 99.4999917831506 & -0.109991783150647 \tabularnewline
72 & 99.4 & 99.3900050208164 & 0.00999497918364511 \tabularnewline
73 & 99.37 & 99.3999995437572 & -0.0299995437572278 \tabularnewline
74 & 99.69 & 99.370001369395 & 0.319998630604971 \tabularnewline
75 & 99.83 & 99.6899853929601 & 0.140014607039859 \tabularnewline
76 & 99.79 & 99.8299936087259 & -0.0399936087259363 \tabularnewline
77 & 99.94 & 99.7900018255961 & 0.149998174403947 \tabularnewline
78 & 100.11 & 99.9399931530041 & 0.170006846995904 \tabularnewline
79 & 100.21 & 100.109992239664 & 0.100007760335671 \tabularnewline
80 & 100.15 & 100.209995434926 & -0.0599954349262646 \tabularnewline
81 & 100.21 & 100.150002738623 & 0.0599972613766795 \tabularnewline
82 & 100.13 & 100.209997261293 & -0.0799972612933146 \tabularnewline
83 & 100.2 & 100.130003651651 & 0.0699963483494344 \tabularnewline
84 & 100.36 & 100.199996804863 & 0.160003195136952 \tabularnewline
85 & 100.5 & 100.359992696303 & 0.140007303697033 \tabularnewline
86 & 100.66 & 100.499993609059 & 0.160006390940666 \tabularnewline
87 & 100.72 & 100.659992696157 & 0.0600073038429088 \tabularnewline
88 & 100.41 & 100.719997260835 & -0.309997260834905 \tabularnewline
89 & 100.3 & 100.410014150505 & -0.110014150505378 \tabularnewline
90 & 100.38 & 100.300005021837 & 0.079994978162631 \tabularnewline
91 & 100.55 & 100.379996348454 & 0.170003651546367 \tabularnewline
92 & 100.17 & 100.54999223981 & -0.379992239810178 \tabularnewline
93 & 100.09 & 100.17001734558 & -0.0800173455798188 \tabularnewline
94 & 100.22 & 100.090003652567 & 0.129996347432638 \tabularnewline
95 & 100.09 & 100.219994066031 & -0.129994066031387 \tabularnewline
96 & 99.98 & 100.090005933864 & -0.110005933864457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284618&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]86.41[/C][C]85.95[/C][C]0.459999999999994[/C][/ROW]
[ROW][C]3[/C][C]86.42[/C][C]86.4099790022903[/C][C]0.0100209977096597[/C][/ROW]
[ROW][C]4[/C][C]86.81[/C][C]86.4199995425696[/C][C]0.390000457430432[/C][/ROW]
[ROW][C]5[/C][C]86.71[/C][C]86.8099821975731[/C][C]-0.0999821975731123[/C][/ROW]
[ROW][C]6[/C][C]86.7[/C][C]86.7100045639068[/C][C]-0.0100045639068469[/C][/ROW]
[ROW][C]7[/C][C]87.07[/C][C]86.7000004566803[/C][C]0.369999543319722[/C][/ROW]
[ROW][C]8[/C][C]86.96[/C][C]87.0699831105587[/C][C]-0.109983110558744[/C][/ROW]
[ROW][C]9[/C][C]87.04[/C][C]86.9600050204205[/C][C]0.0799949795795243[/C][/ROW]
[ROW][C]10[/C][C]87.5[/C][C]87.0399963484536[/C][C]0.460003651546415[/C][/ROW]
[ROW][C]11[/C][C]88.32[/C][C]87.4999790021237[/C][C]0.820020997876313[/C][/ROW]
[ROW][C]12[/C][C]88.56[/C][C]88.3199625683417[/C][C]0.240037431658322[/C][/ROW]
[ROW][C]13[/C][C]88.92[/C][C]88.5599890429646[/C][C]0.360010957035428[/C][/ROW]
[ROW][C]14[/C][C]89.56[/C][C]88.9199835665097[/C][C]0.640016433490317[/C][/ROW]
[ROW][C]15[/C][C]90.21[/C][C]89.5599707850451[/C][C]0.650029214954856[/C][/ROW]
[ROW][C]16[/C][C]90.42[/C][C]90.2099703279897[/C][C]0.210029672010265[/C][/ROW]
[ROW][C]17[/C][C]91.23[/C][C]90.4199904127346[/C][C]0.81000958726537[/C][/ROW]
[ROW][C]18[/C][C]91.73[/C][C]91.2299630253345[/C][C]0.500036974665491[/C][/ROW]
[ROW][C]19[/C][C]92.21[/C][C]91.7299771747148[/C][C]0.480022825285218[/C][/ROW]
[ROW][C]20[/C][C]91.65[/C][C]92.2099780883045[/C][C]-0.559978088304533[/C][/ROW]
[ROW][C]21[/C][C]91.8[/C][C]91.6500255614289[/C][C]0.149974438571064[/C][/ROW]
[ROW][C]22[/C][C]91.63[/C][C]91.7999931540876[/C][C]-0.169993154087578[/C][/ROW]
[ROW][C]23[/C][C]91.09[/C][C]91.6300077597106[/C][C]-0.540007759710633[/C][/ROW]
[ROW][C]24[/C][C]90.89[/C][C]91.0900246498394[/C][C]-0.200024649839449[/C][/ROW]
[ROW][C]25[/C][C]90.98[/C][C]90.8900091305642[/C][C]0.0899908694358231[/C][/ROW]
[ROW][C]26[/C][C]91.29[/C][C]90.9799958921693[/C][C]0.31000410783075[/C][/ROW]
[ROW][C]27[/C][C]90.77[/C][C]91.2899858491821[/C][C]-0.519985849182092[/C][/ROW]
[ROW][C]28[/C][C]90.96[/C][C]90.7700237358954[/C][C]0.189976264104601[/C][/ROW]
[ROW][C]29[/C][C]90.89[/C][C]90.9599913281164[/C][C]-0.0699913281164442[/C][/ROW]
[ROW][C]30[/C][C]90.72[/C][C]90.8900031949078[/C][C]-0.170003194907807[/C][/ROW]
[ROW][C]31[/C][C]90.66[/C][C]90.720007760169[/C][C]-0.0600077601689719[/C][/ROW]
[ROW][C]32[/C][C]90.94[/C][C]90.6600027391859[/C][C]0.279997260814085[/C][/ROW]
[ROW][C]33[/C][C]90.7[/C][C]90.9399872189105[/C][C]-0.239987218910471[/C][/ROW]
[ROW][C]34[/C][C]90.74[/C][C]90.7000109547434[/C][C]0.0399890452566325[/C][/ROW]
[ROW][C]35[/C][C]90.98[/C][C]90.7399981746123[/C][C]0.240001825387751[/C][/ROW]
[ROW][C]36[/C][C]91.13[/C][C]90.9799890445899[/C][C]0.150010955410082[/C][/ROW]
[ROW][C]37[/C][C]91.54[/C][C]91.1299931524207[/C][C]0.410006847579325[/C][/ROW]
[ROW][C]38[/C][C]91.93[/C][C]91.5399812843375[/C][C]0.390018715662478[/C][/ROW]
[ROW][C]39[/C][C]92.27[/C][C]91.9299821967397[/C][C]0.340017803260309[/C][/ROW]
[ROW][C]40[/C][C]92.59[/C][C]92.2699844791411[/C][C]0.320015520858931[/C][/ROW]
[ROW][C]41[/C][C]92.96[/C][C]92.5899853921891[/C][C]0.370014607810845[/C][/ROW]
[ROW][C]42[/C][C]92.95[/C][C]92.9599831098711[/C][C]-0.00998310987107232[/C][/ROW]
[ROW][C]43[/C][C]92.99[/C][C]92.950000455701[/C][C]0.0399995442990217[/C][/ROW]
[ROW][C]44[/C][C]93.05[/C][C]92.989998174133[/C][C]0.0600018258669905[/C][/ROW]
[ROW][C]45[/C][C]93.34[/C][C]93.049997261085[/C][C]0.290002738915049[/C][/ROW]
[ROW][C]46[/C][C]93.47[/C][C]93.3399867621885[/C][C]0.130013237811539[/C][/ROW]
[ROW][C]47[/C][C]93.59[/C][C]93.4699940652604[/C][C]0.120005934739609[/C][/ROW]
[ROW][C]48[/C][C]93.96[/C][C]93.5899945220657[/C][C]0.370005477934285[/C][/ROW]
[ROW][C]49[/C][C]94.49[/C][C]93.9599831102878[/C][C]0.530016889712172[/C][/ROW]
[ROW][C]50[/C][C]95.04[/C][C]94.4899758062157[/C][C]0.550024193784267[/C][/ROW]
[ROW][C]51[/C][C]95.52[/C][C]95.0399748929384[/C][C]0.480025107061564[/C][/ROW]
[ROW][C]52[/C][C]95.75[/C][C]95.5199780882004[/C][C]0.230021911799625[/C][/ROW]
[ROW][C]53[/C][C]96.07[/C][C]95.749989500145[/C][C]0.32001049985503[/C][/ROW]
[ROW][C]54[/C][C]96.37[/C][C]96.0699853924183[/C][C]0.300014607581673[/C][/ROW]
[ROW][C]55[/C][C]96.48[/C][C]96.3699863051747[/C][C]0.110013694825255[/C][/ROW]
[ROW][C]56[/C][C]96.4[/C][C]96.4799949781834[/C][C]-0.0799949781834357[/C][/ROW]
[ROW][C]57[/C][C]96.66[/C][C]96.4000036515464[/C][C]0.25999634845364[/C][/ROW]
[ROW][C]58[/C][C]96.81[/C][C]96.659988131896[/C][C]0.150011868104002[/C][/ROW]
[ROW][C]59[/C][C]97.19[/C][C]96.809993152379[/C][C]0.380006847620962[/C][/ROW]
[ROW][C]60[/C][C]97.23[/C][C]97.1899826537534[/C][C]0.0400173462466427[/C][/ROW]
[ROW][C]61[/C][C]97.94[/C][C]97.2299981733204[/C][C]0.710001826679601[/C][/ROW]
[ROW][C]62[/C][C]98.52[/C][C]97.9399675904082[/C][C]0.580032409591752[/C][/ROW]
[ROW][C]63[/C][C]98.73[/C][C]98.5199735231475[/C][C]0.210026476852462[/C][/ROW]
[ROW][C]64[/C][C]98.8[/C][C]98.7299904128805[/C][C]0.0700095871195145[/C][/ROW]
[ROW][C]65[/C][C]98.77[/C][C]98.7999968042587[/C][C]-0.0299968042587295[/C][/ROW]
[ROW][C]66[/C][C]98.54[/C][C]98.77000136927[/C][C]-0.230001369269971[/C][/ROW]
[ROW][C]67[/C][C]98.72[/C][C]98.5400104989173[/C][C]0.179989501082659[/C][/ROW]
[ROW][C]68[/C][C]99.15[/C][C]98.7199917839842[/C][C]0.430008216015835[/C][/ROW]
[ROW][C]69[/C][C]99.32[/C][C]99.1499803713312[/C][C]0.170019628668825[/C][/ROW]
[ROW][C]70[/C][C]99.5[/C][C]99.3199922390809[/C][C]0.180007760919125[/C][/ROW]
[ROW][C]71[/C][C]99.39[/C][C]99.4999917831506[/C][C]-0.109991783150647[/C][/ROW]
[ROW][C]72[/C][C]99.4[/C][C]99.3900050208164[/C][C]0.00999497918364511[/C][/ROW]
[ROW][C]73[/C][C]99.37[/C][C]99.3999995437572[/C][C]-0.0299995437572278[/C][/ROW]
[ROW][C]74[/C][C]99.69[/C][C]99.370001369395[/C][C]0.319998630604971[/C][/ROW]
[ROW][C]75[/C][C]99.83[/C][C]99.6899853929601[/C][C]0.140014607039859[/C][/ROW]
[ROW][C]76[/C][C]99.79[/C][C]99.8299936087259[/C][C]-0.0399936087259363[/C][/ROW]
[ROW][C]77[/C][C]99.94[/C][C]99.7900018255961[/C][C]0.149998174403947[/C][/ROW]
[ROW][C]78[/C][C]100.11[/C][C]99.9399931530041[/C][C]0.170006846995904[/C][/ROW]
[ROW][C]79[/C][C]100.21[/C][C]100.109992239664[/C][C]0.100007760335671[/C][/ROW]
[ROW][C]80[/C][C]100.15[/C][C]100.209995434926[/C][C]-0.0599954349262646[/C][/ROW]
[ROW][C]81[/C][C]100.21[/C][C]100.150002738623[/C][C]0.0599972613766795[/C][/ROW]
[ROW][C]82[/C][C]100.13[/C][C]100.209997261293[/C][C]-0.0799972612933146[/C][/ROW]
[ROW][C]83[/C][C]100.2[/C][C]100.130003651651[/C][C]0.0699963483494344[/C][/ROW]
[ROW][C]84[/C][C]100.36[/C][C]100.199996804863[/C][C]0.160003195136952[/C][/ROW]
[ROW][C]85[/C][C]100.5[/C][C]100.359992696303[/C][C]0.140007303697033[/C][/ROW]
[ROW][C]86[/C][C]100.66[/C][C]100.499993609059[/C][C]0.160006390940666[/C][/ROW]
[ROW][C]87[/C][C]100.72[/C][C]100.659992696157[/C][C]0.0600073038429088[/C][/ROW]
[ROW][C]88[/C][C]100.41[/C][C]100.719997260835[/C][C]-0.309997260834905[/C][/ROW]
[ROW][C]89[/C][C]100.3[/C][C]100.410014150505[/C][C]-0.110014150505378[/C][/ROW]
[ROW][C]90[/C][C]100.38[/C][C]100.300005021837[/C][C]0.079994978162631[/C][/ROW]
[ROW][C]91[/C][C]100.55[/C][C]100.379996348454[/C][C]0.170003651546367[/C][/ROW]
[ROW][C]92[/C][C]100.17[/C][C]100.54999223981[/C][C]-0.379992239810178[/C][/ROW]
[ROW][C]93[/C][C]100.09[/C][C]100.17001734558[/C][C]-0.0800173455798188[/C][/ROW]
[ROW][C]94[/C][C]100.22[/C][C]100.090003652567[/C][C]0.129996347432638[/C][/ROW]
[ROW][C]95[/C][C]100.09[/C][C]100.219994066031[/C][C]-0.129994066031387[/C][/ROW]
[ROW][C]96[/C][C]99.98[/C][C]100.090005933864[/C][C]-0.110005933864457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284618&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284618&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
286.4185.950.459999999999994
386.4286.40997900229030.0100209977096597
486.8186.41999954256960.390000457430432
586.7186.8099821975731-0.0999821975731123
686.786.7100045639068-0.0100045639068469
787.0786.70000045668030.369999543319722
886.9687.0699831105587-0.109983110558744
987.0486.96000502042050.0799949795795243
1087.587.03999634845360.460003651546415
1188.3287.49997900212370.820020997876313
1288.5688.31996256834170.240037431658322
1388.9288.55998904296460.360010957035428
1489.5688.91998356650970.640016433490317
1590.2189.55997078504510.650029214954856
1690.4290.20997032798970.210029672010265
1791.2390.41999041273460.81000958726537
1891.7391.22996302533450.500036974665491
1992.2191.72997717471480.480022825285218
2091.6592.2099780883045-0.559978088304533
2191.891.65002556142890.149974438571064
2291.6391.7999931540876-0.169993154087578
2391.0991.6300077597106-0.540007759710633
2490.8991.0900246498394-0.200024649839449
2590.9890.89000913056420.0899908694358231
2691.2990.97999589216930.31000410783075
2790.7791.2899858491821-0.519985849182092
2890.9690.77002373589540.189976264104601
2990.8990.9599913281164-0.0699913281164442
3090.7290.8900031949078-0.170003194907807
3190.6690.720007760169-0.0600077601689719
3290.9490.66000273918590.279997260814085
3390.790.9399872189105-0.239987218910471
3490.7490.70001095474340.0399890452566325
3590.9890.73999817461230.240001825387751
3691.1390.97998904458990.150010955410082
3791.5491.12999315242070.410006847579325
3891.9391.53998128433750.390018715662478
3992.2791.92998219673970.340017803260309
4092.5992.26998447914110.320015520858931
4192.9692.58998539218910.370014607810845
4292.9592.9599831098711-0.00998310987107232
4392.9992.9500004557010.0399995442990217
4493.0592.9899981741330.0600018258669905
4593.3493.0499972610850.290002738915049
4693.4793.33998676218850.130013237811539
4793.5993.46999406526040.120005934739609
4893.9693.58999452206570.370005477934285
4994.4993.95998311028780.530016889712172
5095.0494.48997580621570.550024193784267
5195.5295.03997489293840.480025107061564
5295.7595.51997808820040.230021911799625
5396.0795.7499895001450.32001049985503
5496.3796.06998539241830.300014607581673
5596.4896.36998630517470.110013694825255
5696.496.4799949781834-0.0799949781834357
5796.6696.40000365154640.25999634845364
5896.8196.6599881318960.150011868104002
5997.1996.8099931523790.380006847620962
6097.2397.18998265375340.0400173462466427
6197.9497.22999817332040.710001826679601
6298.5297.93996759040820.580032409591752
6398.7398.51997352314750.210026476852462
6498.898.72999041288050.0700095871195145
6598.7798.7999968042587-0.0299968042587295
6698.5498.77000136927-0.230001369269971
6798.7298.54001049891730.179989501082659
6899.1598.71999178398420.430008216015835
6999.3299.14998037133120.170019628668825
7099.599.31999223908090.180007760919125
7199.3999.4999917831506-0.109991783150647
7299.499.39000502081640.00999497918364511
7399.3799.3999995437572-0.0299995437572278
7499.6999.3700013693950.319998630604971
7599.8399.68998539296010.140014607039859
7699.7999.8299936087259-0.0399936087259363
7799.9499.79000182559610.149998174403947
78100.1199.93999315300410.170006846995904
79100.21100.1099922396640.100007760335671
80100.15100.209995434926-0.0599954349262646
81100.21100.1500027386230.0599972613766795
82100.13100.209997261293-0.0799972612933146
83100.2100.1300036516510.0699963483494344
84100.36100.1999968048630.160003195136952
85100.5100.3599926963030.140007303697033
86100.66100.4999936090590.160006390940666
87100.72100.6599926961570.0600073038429088
88100.41100.719997260835-0.309997260834905
89100.3100.410014150505-0.110014150505378
90100.38100.3000050218370.079994978162631
91100.55100.3799963484540.170003651546367
92100.17100.54999223981-0.379992239810178
93100.09100.17001734558-0.0800173455798188
94100.22100.0900036525670.129996347432638
95100.09100.219994066031-0.129994066031387
9699.98100.090005933864-0.110005933864457







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9799.980005021462399.4450275484984100.514982494426
9899.980005021462399.2234498911394100.736560151785
9999.980005021462399.0534250552117100.906584987713
10099.980005021462398.9100867056569101.049923337268
10199.980005021462398.7838027095037101.176207333421
10299.980005021462398.6696330361947101.29037700673
10399.980005021462398.564643050653101.395366992272
10499.980005021462398.4669206625939101.493089380331
10599.980005021462398.3751377229946101.58487231993
10699.980005021462398.2883272110238101.671682831901
10799.980005021462398.2057591019322101.754250940992
10899.980005021462398.1268662377744101.83314380515

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 99.9800050214623 & 99.4450275484984 & 100.514982494426 \tabularnewline
98 & 99.9800050214623 & 99.2234498911394 & 100.736560151785 \tabularnewline
99 & 99.9800050214623 & 99.0534250552117 & 100.906584987713 \tabularnewline
100 & 99.9800050214623 & 98.9100867056569 & 101.049923337268 \tabularnewline
101 & 99.9800050214623 & 98.7838027095037 & 101.176207333421 \tabularnewline
102 & 99.9800050214623 & 98.6696330361947 & 101.29037700673 \tabularnewline
103 & 99.9800050214623 & 98.564643050653 & 101.395366992272 \tabularnewline
104 & 99.9800050214623 & 98.4669206625939 & 101.493089380331 \tabularnewline
105 & 99.9800050214623 & 98.3751377229946 & 101.58487231993 \tabularnewline
106 & 99.9800050214623 & 98.2883272110238 & 101.671682831901 \tabularnewline
107 & 99.9800050214623 & 98.2057591019322 & 101.754250940992 \tabularnewline
108 & 99.9800050214623 & 98.1268662377744 & 101.83314380515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284618&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]97[/C][C]99.9800050214623[/C][C]99.4450275484984[/C][C]100.514982494426[/C][/ROW]
[ROW][C]98[/C][C]99.9800050214623[/C][C]99.2234498911394[/C][C]100.736560151785[/C][/ROW]
[ROW][C]99[/C][C]99.9800050214623[/C][C]99.0534250552117[/C][C]100.906584987713[/C][/ROW]
[ROW][C]100[/C][C]99.9800050214623[/C][C]98.9100867056569[/C][C]101.049923337268[/C][/ROW]
[ROW][C]101[/C][C]99.9800050214623[/C][C]98.7838027095037[/C][C]101.176207333421[/C][/ROW]
[ROW][C]102[/C][C]99.9800050214623[/C][C]98.6696330361947[/C][C]101.29037700673[/C][/ROW]
[ROW][C]103[/C][C]99.9800050214623[/C][C]98.564643050653[/C][C]101.395366992272[/C][/ROW]
[ROW][C]104[/C][C]99.9800050214623[/C][C]98.4669206625939[/C][C]101.493089380331[/C][/ROW]
[ROW][C]105[/C][C]99.9800050214623[/C][C]98.3751377229946[/C][C]101.58487231993[/C][/ROW]
[ROW][C]106[/C][C]99.9800050214623[/C][C]98.2883272110238[/C][C]101.671682831901[/C][/ROW]
[ROW][C]107[/C][C]99.9800050214623[/C][C]98.2057591019322[/C][C]101.754250940992[/C][/ROW]
[ROW][C]108[/C][C]99.9800050214623[/C][C]98.1268662377744[/C][C]101.83314380515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284618&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284618&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
9799.980005021462399.4450275484984100.514982494426
9899.980005021462399.2234498911394100.736560151785
9999.980005021462399.0534250552117100.906584987713
10099.980005021462398.9100867056569101.049923337268
10199.980005021462398.7838027095037101.176207333421
10299.980005021462398.6696330361947101.29037700673
10399.980005021462398.564643050653101.395366992272
10499.980005021462398.4669206625939101.493089380331
10599.980005021462398.3751377229946101.58487231993
10699.980005021462398.2883272110238101.671682831901
10799.980005021462398.2057591019322101.754250940992
10899.980005021462398.1268662377744101.83314380515



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')