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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 13:19:15 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356113998dpnfq5uc1hpujke.htm/, Retrieved Wed, 24 Apr 2024 14:13:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204066, Retrieved Wed, 24 Apr 2024 14:13:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [oefening 10.2 sin...] [2012-12-21 18:19:15] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
101,81
101,72
101,78
102,04
102,36
102,56
102,69
102,77
102,85
102,9
102,72
102,79
102,9
102,91
103,29
103,35
102,97
103,05
103,18
103,21
103,32
103,31
103,6
103,68
103,77
103,82
103,86
103,9
103,63
103,65
103,7
103,77
103,94
104,03
104,03
104,29
104,35
104,67
104,73
104,86
104,05
104,15
104,27
104,33
104,41
104,4
104,41
104,6
104,61
104,65
104,55
104,51
104,74
104,89
104,91
104,93
104,95
104,97
105,16
105,29
105,35
105,36
105,45
105,3
105,73
105,86
105,85
105,95
105,97
106,15
105,37
105,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204066&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204066&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919133050049
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919133050049 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204066&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]0.999919133050049[/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=204066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204066&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
alpha0.999919133050049
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101.72101.81-0.0900000000000034
3101.78101.7200072780250.0599927219745098
4102.04101.7799951485720.260004851428448
5102.36102.0399789742010.320021025799306
6102.56102.3599741208760.200025879124283
7102.69102.5599838245170.130016175482751
8102.77102.6899894859880.0800105140115477
9102.85102.7699935297940.0800064702062286
10102.9102.8499935301210.0500064698792357
11102.72102.899995956129-0.179995956129304
12102.79102.7200145557240.0699854442760284
13102.9102.7899943404910.110005659509426
14102.91102.8999911041780.0100088958221534
15103.29102.9099991906110.380000809388889
16103.35103.2899692704940.0600307295064226
17102.97103.349995145498-0.379995145498
18103.05102.9700307290480.0799692709515796
19103.18103.0499935331290.130006466871038
20103.21103.1799894867740.0300105132264434
21103.32103.2099975731410.110002426858671
22103.31103.319991104439-0.00999110443923712
23103.6103.310000807950.289999192049848
24103.68103.599976548650.0800234513501579
25103.77103.6799935287480.0900064712524227
26103.82103.7699927214510.0500072785488044
27103.86103.8199959560640.0400040439360936
28103.9103.8599967649950.040003235005031
29103.63103.89999676506-0.269996765060412
30103.65103.6300218338150.0199781661851262
31103.7103.6499983844270.0500016155733647
32103.77103.6999959565220.0700040434781357
33103.94103.7699943389870.170005661013477
34104.03103.9399862521610.0900137478392793
35104.03104.0299927208637.27913723608253e-06
36104.29104.0299999994110.260000000588647
37104.35104.2899789745930.0600210254070248
38104.67104.3499951462830.320004853717265
39104.73104.6699741221840.0600258778164857
40104.86104.729995145890.130004854109657
41104.05104.859989486904-0.809989486903973
42104.15104.0500655013790.099934498620712
43104.27104.1499919186020.120008081398083
44104.33104.2699902953120.0600097046875163
45104.41104.3299951471980.0800048528017783
46104.4104.409993530252-0.00999353025156324
47104.41104.4000008081460.00999919185368014
48104.6104.4099991913960.19000080860414
49104.61104.5999846352140.010015364785886
50104.65104.6099991900880.0400008099120157
51104.55104.649996765257-0.0999967652565203
52104.51104.550008086433-0.0400080864334029
53104.74104.5100032353320.229996764668073
54104.89104.7399814008630.150018599136857
55104.91104.8899878684530.0200121315465509
56104.93104.909998381680.0200016183200518
57104.95104.929998382530.020001617469859
58104.97104.949998382530.0200016174697879
59105.16104.969998382530.19000161746979
60105.29105.1599846351490.130015364851303
61105.35105.2899894860540.060010513945997
62105.36105.3499951471330.0100048528672261
63105.45105.3599991909380.0900008090619338
64105.3105.449992721909-0.149992721909086
65105.73105.3000121294540.429987870546071
66105.86105.7299652281920.130034771807601
67105.85105.859989484485-0.00998948448462045
68105.95105.8500008078190.0999991921808601
69105.97105.949991913370.0200080866296588
70106.15105.9699983820070.180001617992943
71105.37106.149985443818-0.779985443818163
72105.39105.3700630750440.0199369249561414

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101.72 & 101.81 & -0.0900000000000034 \tabularnewline
3 & 101.78 & 101.720007278025 & 0.0599927219745098 \tabularnewline
4 & 102.04 & 101.779995148572 & 0.260004851428448 \tabularnewline
5 & 102.36 & 102.039978974201 & 0.320021025799306 \tabularnewline
6 & 102.56 & 102.359974120876 & 0.200025879124283 \tabularnewline
7 & 102.69 & 102.559983824517 & 0.130016175482751 \tabularnewline
8 & 102.77 & 102.689989485988 & 0.0800105140115477 \tabularnewline
9 & 102.85 & 102.769993529794 & 0.0800064702062286 \tabularnewline
10 & 102.9 & 102.849993530121 & 0.0500064698792357 \tabularnewline
11 & 102.72 & 102.899995956129 & -0.179995956129304 \tabularnewline
12 & 102.79 & 102.720014555724 & 0.0699854442760284 \tabularnewline
13 & 102.9 & 102.789994340491 & 0.110005659509426 \tabularnewline
14 & 102.91 & 102.899991104178 & 0.0100088958221534 \tabularnewline
15 & 103.29 & 102.909999190611 & 0.380000809388889 \tabularnewline
16 & 103.35 & 103.289969270494 & 0.0600307295064226 \tabularnewline
17 & 102.97 & 103.349995145498 & -0.379995145498 \tabularnewline
18 & 103.05 & 102.970030729048 & 0.0799692709515796 \tabularnewline
19 & 103.18 & 103.049993533129 & 0.130006466871038 \tabularnewline
20 & 103.21 & 103.179989486774 & 0.0300105132264434 \tabularnewline
21 & 103.32 & 103.209997573141 & 0.110002426858671 \tabularnewline
22 & 103.31 & 103.319991104439 & -0.00999110443923712 \tabularnewline
23 & 103.6 & 103.31000080795 & 0.289999192049848 \tabularnewline
24 & 103.68 & 103.59997654865 & 0.0800234513501579 \tabularnewline
25 & 103.77 & 103.679993528748 & 0.0900064712524227 \tabularnewline
26 & 103.82 & 103.769992721451 & 0.0500072785488044 \tabularnewline
27 & 103.86 & 103.819995956064 & 0.0400040439360936 \tabularnewline
28 & 103.9 & 103.859996764995 & 0.040003235005031 \tabularnewline
29 & 103.63 & 103.89999676506 & -0.269996765060412 \tabularnewline
30 & 103.65 & 103.630021833815 & 0.0199781661851262 \tabularnewline
31 & 103.7 & 103.649998384427 & 0.0500016155733647 \tabularnewline
32 & 103.77 & 103.699995956522 & 0.0700040434781357 \tabularnewline
33 & 103.94 & 103.769994338987 & 0.170005661013477 \tabularnewline
34 & 104.03 & 103.939986252161 & 0.0900137478392793 \tabularnewline
35 & 104.03 & 104.029992720863 & 7.27913723608253e-06 \tabularnewline
36 & 104.29 & 104.029999999411 & 0.260000000588647 \tabularnewline
37 & 104.35 & 104.289978974593 & 0.0600210254070248 \tabularnewline
38 & 104.67 & 104.349995146283 & 0.320004853717265 \tabularnewline
39 & 104.73 & 104.669974122184 & 0.0600258778164857 \tabularnewline
40 & 104.86 & 104.72999514589 & 0.130004854109657 \tabularnewline
41 & 104.05 & 104.859989486904 & -0.809989486903973 \tabularnewline
42 & 104.15 & 104.050065501379 & 0.099934498620712 \tabularnewline
43 & 104.27 & 104.149991918602 & 0.120008081398083 \tabularnewline
44 & 104.33 & 104.269990295312 & 0.0600097046875163 \tabularnewline
45 & 104.41 & 104.329995147198 & 0.0800048528017783 \tabularnewline
46 & 104.4 & 104.409993530252 & -0.00999353025156324 \tabularnewline
47 & 104.41 & 104.400000808146 & 0.00999919185368014 \tabularnewline
48 & 104.6 & 104.409999191396 & 0.19000080860414 \tabularnewline
49 & 104.61 & 104.599984635214 & 0.010015364785886 \tabularnewline
50 & 104.65 & 104.609999190088 & 0.0400008099120157 \tabularnewline
51 & 104.55 & 104.649996765257 & -0.0999967652565203 \tabularnewline
52 & 104.51 & 104.550008086433 & -0.0400080864334029 \tabularnewline
53 & 104.74 & 104.510003235332 & 0.229996764668073 \tabularnewline
54 & 104.89 & 104.739981400863 & 0.150018599136857 \tabularnewline
55 & 104.91 & 104.889987868453 & 0.0200121315465509 \tabularnewline
56 & 104.93 & 104.90999838168 & 0.0200016183200518 \tabularnewline
57 & 104.95 & 104.92999838253 & 0.020001617469859 \tabularnewline
58 & 104.97 & 104.94999838253 & 0.0200016174697879 \tabularnewline
59 & 105.16 & 104.96999838253 & 0.19000161746979 \tabularnewline
60 & 105.29 & 105.159984635149 & 0.130015364851303 \tabularnewline
61 & 105.35 & 105.289989486054 & 0.060010513945997 \tabularnewline
62 & 105.36 & 105.349995147133 & 0.0100048528672261 \tabularnewline
63 & 105.45 & 105.359999190938 & 0.0900008090619338 \tabularnewline
64 & 105.3 & 105.449992721909 & -0.149992721909086 \tabularnewline
65 & 105.73 & 105.300012129454 & 0.429987870546071 \tabularnewline
66 & 105.86 & 105.729965228192 & 0.130034771807601 \tabularnewline
67 & 105.85 & 105.859989484485 & -0.00998948448462045 \tabularnewline
68 & 105.95 & 105.850000807819 & 0.0999991921808601 \tabularnewline
69 & 105.97 & 105.94999191337 & 0.0200080866296588 \tabularnewline
70 & 106.15 & 105.969998382007 & 0.180001617992943 \tabularnewline
71 & 105.37 & 106.149985443818 & -0.779985443818163 \tabularnewline
72 & 105.39 & 105.370063075044 & 0.0199369249561414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204066&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]101.72[/C][C]101.81[/C][C]-0.0900000000000034[/C][/ROW]
[ROW][C]3[/C][C]101.78[/C][C]101.720007278025[/C][C]0.0599927219745098[/C][/ROW]
[ROW][C]4[/C][C]102.04[/C][C]101.779995148572[/C][C]0.260004851428448[/C][/ROW]
[ROW][C]5[/C][C]102.36[/C][C]102.039978974201[/C][C]0.320021025799306[/C][/ROW]
[ROW][C]6[/C][C]102.56[/C][C]102.359974120876[/C][C]0.200025879124283[/C][/ROW]
[ROW][C]7[/C][C]102.69[/C][C]102.559983824517[/C][C]0.130016175482751[/C][/ROW]
[ROW][C]8[/C][C]102.77[/C][C]102.689989485988[/C][C]0.0800105140115477[/C][/ROW]
[ROW][C]9[/C][C]102.85[/C][C]102.769993529794[/C][C]0.0800064702062286[/C][/ROW]
[ROW][C]10[/C][C]102.9[/C][C]102.849993530121[/C][C]0.0500064698792357[/C][/ROW]
[ROW][C]11[/C][C]102.72[/C][C]102.899995956129[/C][C]-0.179995956129304[/C][/ROW]
[ROW][C]12[/C][C]102.79[/C][C]102.720014555724[/C][C]0.0699854442760284[/C][/ROW]
[ROW][C]13[/C][C]102.9[/C][C]102.789994340491[/C][C]0.110005659509426[/C][/ROW]
[ROW][C]14[/C][C]102.91[/C][C]102.899991104178[/C][C]0.0100088958221534[/C][/ROW]
[ROW][C]15[/C][C]103.29[/C][C]102.909999190611[/C][C]0.380000809388889[/C][/ROW]
[ROW][C]16[/C][C]103.35[/C][C]103.289969270494[/C][C]0.0600307295064226[/C][/ROW]
[ROW][C]17[/C][C]102.97[/C][C]103.349995145498[/C][C]-0.379995145498[/C][/ROW]
[ROW][C]18[/C][C]103.05[/C][C]102.970030729048[/C][C]0.0799692709515796[/C][/ROW]
[ROW][C]19[/C][C]103.18[/C][C]103.049993533129[/C][C]0.130006466871038[/C][/ROW]
[ROW][C]20[/C][C]103.21[/C][C]103.179989486774[/C][C]0.0300105132264434[/C][/ROW]
[ROW][C]21[/C][C]103.32[/C][C]103.209997573141[/C][C]0.110002426858671[/C][/ROW]
[ROW][C]22[/C][C]103.31[/C][C]103.319991104439[/C][C]-0.00999110443923712[/C][/ROW]
[ROW][C]23[/C][C]103.6[/C][C]103.31000080795[/C][C]0.289999192049848[/C][/ROW]
[ROW][C]24[/C][C]103.68[/C][C]103.59997654865[/C][C]0.0800234513501579[/C][/ROW]
[ROW][C]25[/C][C]103.77[/C][C]103.679993528748[/C][C]0.0900064712524227[/C][/ROW]
[ROW][C]26[/C][C]103.82[/C][C]103.769992721451[/C][C]0.0500072785488044[/C][/ROW]
[ROW][C]27[/C][C]103.86[/C][C]103.819995956064[/C][C]0.0400040439360936[/C][/ROW]
[ROW][C]28[/C][C]103.9[/C][C]103.859996764995[/C][C]0.040003235005031[/C][/ROW]
[ROW][C]29[/C][C]103.63[/C][C]103.89999676506[/C][C]-0.269996765060412[/C][/ROW]
[ROW][C]30[/C][C]103.65[/C][C]103.630021833815[/C][C]0.0199781661851262[/C][/ROW]
[ROW][C]31[/C][C]103.7[/C][C]103.649998384427[/C][C]0.0500016155733647[/C][/ROW]
[ROW][C]32[/C][C]103.77[/C][C]103.699995956522[/C][C]0.0700040434781357[/C][/ROW]
[ROW][C]33[/C][C]103.94[/C][C]103.769994338987[/C][C]0.170005661013477[/C][/ROW]
[ROW][C]34[/C][C]104.03[/C][C]103.939986252161[/C][C]0.0900137478392793[/C][/ROW]
[ROW][C]35[/C][C]104.03[/C][C]104.029992720863[/C][C]7.27913723608253e-06[/C][/ROW]
[ROW][C]36[/C][C]104.29[/C][C]104.029999999411[/C][C]0.260000000588647[/C][/ROW]
[ROW][C]37[/C][C]104.35[/C][C]104.289978974593[/C][C]0.0600210254070248[/C][/ROW]
[ROW][C]38[/C][C]104.67[/C][C]104.349995146283[/C][C]0.320004853717265[/C][/ROW]
[ROW][C]39[/C][C]104.73[/C][C]104.669974122184[/C][C]0.0600258778164857[/C][/ROW]
[ROW][C]40[/C][C]104.86[/C][C]104.72999514589[/C][C]0.130004854109657[/C][/ROW]
[ROW][C]41[/C][C]104.05[/C][C]104.859989486904[/C][C]-0.809989486903973[/C][/ROW]
[ROW][C]42[/C][C]104.15[/C][C]104.050065501379[/C][C]0.099934498620712[/C][/ROW]
[ROW][C]43[/C][C]104.27[/C][C]104.149991918602[/C][C]0.120008081398083[/C][/ROW]
[ROW][C]44[/C][C]104.33[/C][C]104.269990295312[/C][C]0.0600097046875163[/C][/ROW]
[ROW][C]45[/C][C]104.41[/C][C]104.329995147198[/C][C]0.0800048528017783[/C][/ROW]
[ROW][C]46[/C][C]104.4[/C][C]104.409993530252[/C][C]-0.00999353025156324[/C][/ROW]
[ROW][C]47[/C][C]104.41[/C][C]104.400000808146[/C][C]0.00999919185368014[/C][/ROW]
[ROW][C]48[/C][C]104.6[/C][C]104.409999191396[/C][C]0.19000080860414[/C][/ROW]
[ROW][C]49[/C][C]104.61[/C][C]104.599984635214[/C][C]0.010015364785886[/C][/ROW]
[ROW][C]50[/C][C]104.65[/C][C]104.609999190088[/C][C]0.0400008099120157[/C][/ROW]
[ROW][C]51[/C][C]104.55[/C][C]104.649996765257[/C][C]-0.0999967652565203[/C][/ROW]
[ROW][C]52[/C][C]104.51[/C][C]104.550008086433[/C][C]-0.0400080864334029[/C][/ROW]
[ROW][C]53[/C][C]104.74[/C][C]104.510003235332[/C][C]0.229996764668073[/C][/ROW]
[ROW][C]54[/C][C]104.89[/C][C]104.739981400863[/C][C]0.150018599136857[/C][/ROW]
[ROW][C]55[/C][C]104.91[/C][C]104.889987868453[/C][C]0.0200121315465509[/C][/ROW]
[ROW][C]56[/C][C]104.93[/C][C]104.90999838168[/C][C]0.0200016183200518[/C][/ROW]
[ROW][C]57[/C][C]104.95[/C][C]104.92999838253[/C][C]0.020001617469859[/C][/ROW]
[ROW][C]58[/C][C]104.97[/C][C]104.94999838253[/C][C]0.0200016174697879[/C][/ROW]
[ROW][C]59[/C][C]105.16[/C][C]104.96999838253[/C][C]0.19000161746979[/C][/ROW]
[ROW][C]60[/C][C]105.29[/C][C]105.159984635149[/C][C]0.130015364851303[/C][/ROW]
[ROW][C]61[/C][C]105.35[/C][C]105.289989486054[/C][C]0.060010513945997[/C][/ROW]
[ROW][C]62[/C][C]105.36[/C][C]105.349995147133[/C][C]0.0100048528672261[/C][/ROW]
[ROW][C]63[/C][C]105.45[/C][C]105.359999190938[/C][C]0.0900008090619338[/C][/ROW]
[ROW][C]64[/C][C]105.3[/C][C]105.449992721909[/C][C]-0.149992721909086[/C][/ROW]
[ROW][C]65[/C][C]105.73[/C][C]105.300012129454[/C][C]0.429987870546071[/C][/ROW]
[ROW][C]66[/C][C]105.86[/C][C]105.729965228192[/C][C]0.130034771807601[/C][/ROW]
[ROW][C]67[/C][C]105.85[/C][C]105.859989484485[/C][C]-0.00998948448462045[/C][/ROW]
[ROW][C]68[/C][C]105.95[/C][C]105.850000807819[/C][C]0.0999991921808601[/C][/ROW]
[ROW][C]69[/C][C]105.97[/C][C]105.94999191337[/C][C]0.0200080866296588[/C][/ROW]
[ROW][C]70[/C][C]106.15[/C][C]105.969998382007[/C][C]0.180001617992943[/C][/ROW]
[ROW][C]71[/C][C]105.37[/C][C]106.149985443818[/C][C]-0.779985443818163[/C][/ROW]
[ROW][C]72[/C][C]105.39[/C][C]105.370063075044[/C][C]0.0199369249561414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204066&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204066&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
2101.72101.81-0.0900000000000034
3101.78101.7200072780250.0599927219745098
4102.04101.7799951485720.260004851428448
5102.36102.0399789742010.320021025799306
6102.56102.3599741208760.200025879124283
7102.69102.5599838245170.130016175482751
8102.77102.6899894859880.0800105140115477
9102.85102.7699935297940.0800064702062286
10102.9102.8499935301210.0500064698792357
11102.72102.899995956129-0.179995956129304
12102.79102.7200145557240.0699854442760284
13102.9102.7899943404910.110005659509426
14102.91102.8999911041780.0100088958221534
15103.29102.9099991906110.380000809388889
16103.35103.2899692704940.0600307295064226
17102.97103.349995145498-0.379995145498
18103.05102.9700307290480.0799692709515796
19103.18103.0499935331290.130006466871038
20103.21103.1799894867740.0300105132264434
21103.32103.2099975731410.110002426858671
22103.31103.319991104439-0.00999110443923712
23103.6103.310000807950.289999192049848
24103.68103.599976548650.0800234513501579
25103.77103.6799935287480.0900064712524227
26103.82103.7699927214510.0500072785488044
27103.86103.8199959560640.0400040439360936
28103.9103.8599967649950.040003235005031
29103.63103.89999676506-0.269996765060412
30103.65103.6300218338150.0199781661851262
31103.7103.6499983844270.0500016155733647
32103.77103.6999959565220.0700040434781357
33103.94103.7699943389870.170005661013477
34104.03103.9399862521610.0900137478392793
35104.03104.0299927208637.27913723608253e-06
36104.29104.0299999994110.260000000588647
37104.35104.2899789745930.0600210254070248
38104.67104.3499951462830.320004853717265
39104.73104.6699741221840.0600258778164857
40104.86104.729995145890.130004854109657
41104.05104.859989486904-0.809989486903973
42104.15104.0500655013790.099934498620712
43104.27104.1499919186020.120008081398083
44104.33104.2699902953120.0600097046875163
45104.41104.3299951471980.0800048528017783
46104.4104.409993530252-0.00999353025156324
47104.41104.4000008081460.00999919185368014
48104.6104.4099991913960.19000080860414
49104.61104.5999846352140.010015364785886
50104.65104.6099991900880.0400008099120157
51104.55104.649996765257-0.0999967652565203
52104.51104.550008086433-0.0400080864334029
53104.74104.5100032353320.229996764668073
54104.89104.7399814008630.150018599136857
55104.91104.8899878684530.0200121315465509
56104.93104.909998381680.0200016183200518
57104.95104.929998382530.020001617469859
58104.97104.949998382530.0200016174697879
59105.16104.969998382530.19000161746979
60105.29105.1599846351490.130015364851303
61105.35105.2899894860540.060010513945997
62105.36105.3499951471330.0100048528672261
63105.45105.3599991909380.0900008090619338
64105.3105.449992721909-0.149992721909086
65105.73105.3000121294540.429987870546071
66105.86105.7299652281920.130034771807601
67105.85105.859989484485-0.00998948448462045
68105.95105.8500008078190.0999991921808601
69105.97105.949991913370.0200080866296588
70106.15105.9699983820070.180001617992943
71105.37106.149985443818-0.779985443818163
72105.39105.3700630750440.0199369249561414







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73105.389998387762105.010405081416105.769591694107
74105.389998387762104.853194091044105.92680268448
75105.389998387762104.732558939807106.047437835717
76105.389998387762104.630857819435106.149138956089
77105.389998387762104.541256862188106.238739913335
78105.389998387762104.460251136093106.31974563943
79105.389998387762104.385758512663106.39423826286
80105.389998387762104.31642235343106.463574422093
81105.389998387762104.251300325832106.528696449692
82105.389998387762104.189706318724106.5902904568
83105.389998387762104.131122370932106.648874404591
84105.389998387762104.075146076473106.70485069905

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 105.389998387762 & 105.010405081416 & 105.769591694107 \tabularnewline
74 & 105.389998387762 & 104.853194091044 & 105.92680268448 \tabularnewline
75 & 105.389998387762 & 104.732558939807 & 106.047437835717 \tabularnewline
76 & 105.389998387762 & 104.630857819435 & 106.149138956089 \tabularnewline
77 & 105.389998387762 & 104.541256862188 & 106.238739913335 \tabularnewline
78 & 105.389998387762 & 104.460251136093 & 106.31974563943 \tabularnewline
79 & 105.389998387762 & 104.385758512663 & 106.39423826286 \tabularnewline
80 & 105.389998387762 & 104.31642235343 & 106.463574422093 \tabularnewline
81 & 105.389998387762 & 104.251300325832 & 106.528696449692 \tabularnewline
82 & 105.389998387762 & 104.189706318724 & 106.5902904568 \tabularnewline
83 & 105.389998387762 & 104.131122370932 & 106.648874404591 \tabularnewline
84 & 105.389998387762 & 104.075146076473 & 106.70485069905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204066&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]105.389998387762[/C][C]105.010405081416[/C][C]105.769591694107[/C][/ROW]
[ROW][C]74[/C][C]105.389998387762[/C][C]104.853194091044[/C][C]105.92680268448[/C][/ROW]
[ROW][C]75[/C][C]105.389998387762[/C][C]104.732558939807[/C][C]106.047437835717[/C][/ROW]
[ROW][C]76[/C][C]105.389998387762[/C][C]104.630857819435[/C][C]106.149138956089[/C][/ROW]
[ROW][C]77[/C][C]105.389998387762[/C][C]104.541256862188[/C][C]106.238739913335[/C][/ROW]
[ROW][C]78[/C][C]105.389998387762[/C][C]104.460251136093[/C][C]106.31974563943[/C][/ROW]
[ROW][C]79[/C][C]105.389998387762[/C][C]104.385758512663[/C][C]106.39423826286[/C][/ROW]
[ROW][C]80[/C][C]105.389998387762[/C][C]104.31642235343[/C][C]106.463574422093[/C][/ROW]
[ROW][C]81[/C][C]105.389998387762[/C][C]104.251300325832[/C][C]106.528696449692[/C][/ROW]
[ROW][C]82[/C][C]105.389998387762[/C][C]104.189706318724[/C][C]106.5902904568[/C][/ROW]
[ROW][C]83[/C][C]105.389998387762[/C][C]104.131122370932[/C][C]106.648874404591[/C][/ROW]
[ROW][C]84[/C][C]105.389998387762[/C][C]104.075146076473[/C][C]106.70485069905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204066&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204066&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
73105.389998387762105.010405081416105.769591694107
74105.389998387762104.853194091044105.92680268448
75105.389998387762104.732558939807106.047437835717
76105.389998387762104.630857819435106.149138956089
77105.389998387762104.541256862188106.238739913335
78105.389998387762104.460251136093106.31974563943
79105.389998387762104.385758512663106.39423826286
80105.389998387762104.31642235343106.463574422093
81105.389998387762104.251300325832106.528696449692
82105.389998387762104.189706318724106.5902904568
83105.389998387762104.131122370932106.648874404591
84105.389998387762104.075146076473106.70485069905



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')