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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Dec 2013 12:15:53 -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/2013/Dec/14/t13870413679ycmsodzdwctn36.htm/, Retrieved Fri, 29 Mar 2024 08:55:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232330, Retrieved Fri, 29 Mar 2024 08:55:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-14 17:15:53] [cbeaf4c3f774367e9472b81246022ded] [Current]
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Dataseries X:
86.5
86.6
98.8
84.4
91.4
95.7
78.5
81.7
94.3
98.5
95.4
91.7
92.8
90.6
102.2
91.8
95
102
88.9
89.6
97.9
108.6
100.8
95.1
101
100.9
102.5
105.4
98.4
105.3
96.5
88.1
107.9
107.1
92.5
95.7
85.2
85.5
94.7
86.2
88.8
93.4
83.4
82.9
96.7
96.2
92.8
92.8
90.2
95.9
107.5
98
95
108.5
91.8
91.7
108.3
105.1
104.8
103.2
98.6
102.4
121.2
102.6
108.9
105.5
90.8
99.6
111.6
104.7
103.1
101.7
98.8
101.4
114.2
96.9
98.3
104.8
94.4
94.5
102.4
105.5
101.2
99.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232330&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]4 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=232330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232330&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.433012478246557
beta0.0200180352765457
gamma0.414206205773625

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.433012478246557 \tabularnewline
beta & 0.0200180352765457 \tabularnewline
gamma & 0.414206205773625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232330&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]0.433012478246557[/C][/ROW]
[ROW][C]beta[/C][C]0.0200180352765457[/C][/ROW]
[ROW][C]gamma[/C][C]0.414206205773625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232330&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
alpha0.433012478246557
beta0.0200180352765457
gamma0.414206205773625







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.890.09065170940182.70934829059824
1490.688.85480063563911.7451993643609
15102.2101.2999218704310.900078129568996
1691.891.29523032865010.504769671349848
179594.64874066502940.351259334970621
18102102.017990513546-0.0179905135457545
1988.984.67302796056324.22697203943676
2089.689.894493472681-0.294493472680969
2197.9102.676388644608-4.77638864460819
22108.6104.9344985953443.66550140465627
23100.8103.57149172674-2.77149172674027
2495.198.8429963892033-3.74299638920328
2510198.81433933202952.18566066797047
26100.997.14242362556463.75757637443544
27102.5110.29502488563-7.79502488562959
28105.496.3916096592669.00839034073398
2998.4103.424154391118-5.02415439111802
30105.3108.365382781666-3.06538278166573
3196.590.65769276489755.84230723510248
3288.195.4906583681818-7.39065836818178
33107.9104.0596484956133.84035150438746
34107.1112.018575497805-4.91857549780549
3592.5105.339507978894-12.8395079788937
3695.795.8486861772715-0.148686177271514
3785.298.6253174456046-13.4253174456046
3885.590.28406407354-4.78406407353995
3994.796.6721101163778-1.97211011637776
4086.288.9340480813099-2.73404808130989
4188.887.18232724753191.61767275246808
4293.495.1130348623733-1.71303486237326
4383.479.74808754546263.65191245453738
4482.980.17103014145322.72896985854683
4596.795.49346689354831.2065331064517
4696.299.9659772181531-3.76597721815313
4792.891.64685228472781.15314771527223
4892.891.03783265905871.76216734094126
4990.291.3828085282299-1.18280852822991
5095.990.33716398684035.56283601315975
51107.5101.9206746129995.57932538700099
529897.39373477833310.606265221666888
539598.2595632087737-3.25956320877374
54108.5103.4030261450675.09697385493261
5591.892.4127588772679-0.612758877267936
5691.790.90123107077870.798768929221339
57108.3105.1425300863513.15746991364861
58105.1109.421145663265-4.32114566326504
59104.8102.1411869717192.65881302828068
60103.2102.4645243621930.735475637806545
6198.6101.801760681976-3.20176068197577
62102.4101.5770548196920.822945180308466
63121.2111.18187766113310.0181223388666
64102.6107.517417678198-4.91741767819809
65108.9105.1440013569093.7559986430911
66105.5115.409099773274-9.90909977327412
6790.896.5712915522401-5.77129155224013
6899.693.10404269735146.49595730264861
69111.6110.3621102883151.23788971168459
70104.7112.03240823284-7.33240823284029
71103.1105.04091057348-1.94091057347967
72101.7102.834078012146-1.13407801214646
7398.8100.334172975238-1.53417297523764
74101.4101.68826698159-0.288266981589686
75114.2112.8732865132081.32671348679169
7696.9101.764272922169-4.86427292216926
7798.3101.277821980003-2.97782198000277
78104.8105.186481318123-0.386481318122804
7994.491.29502578576113.10497421423892
8094.594.48038793730560.0196120626943639
81102.4107.571240864343-5.17124086434283
82105.5104.2699977399271.23000226007302
83101.2102.142966801557-0.94296680155702
8499.5100.457035262709-0.957035262709368

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.8 & 90.0906517094018 & 2.70934829059824 \tabularnewline
14 & 90.6 & 88.8548006356391 & 1.7451993643609 \tabularnewline
15 & 102.2 & 101.299921870431 & 0.900078129568996 \tabularnewline
16 & 91.8 & 91.2952303286501 & 0.504769671349848 \tabularnewline
17 & 95 & 94.6487406650294 & 0.351259334970621 \tabularnewline
18 & 102 & 102.017990513546 & -0.0179905135457545 \tabularnewline
19 & 88.9 & 84.6730279605632 & 4.22697203943676 \tabularnewline
20 & 89.6 & 89.894493472681 & -0.294493472680969 \tabularnewline
21 & 97.9 & 102.676388644608 & -4.77638864460819 \tabularnewline
22 & 108.6 & 104.934498595344 & 3.66550140465627 \tabularnewline
23 & 100.8 & 103.57149172674 & -2.77149172674027 \tabularnewline
24 & 95.1 & 98.8429963892033 & -3.74299638920328 \tabularnewline
25 & 101 & 98.8143393320295 & 2.18566066797047 \tabularnewline
26 & 100.9 & 97.1424236255646 & 3.75757637443544 \tabularnewline
27 & 102.5 & 110.29502488563 & -7.79502488562959 \tabularnewline
28 & 105.4 & 96.391609659266 & 9.00839034073398 \tabularnewline
29 & 98.4 & 103.424154391118 & -5.02415439111802 \tabularnewline
30 & 105.3 & 108.365382781666 & -3.06538278166573 \tabularnewline
31 & 96.5 & 90.6576927648975 & 5.84230723510248 \tabularnewline
32 & 88.1 & 95.4906583681818 & -7.39065836818178 \tabularnewline
33 & 107.9 & 104.059648495613 & 3.84035150438746 \tabularnewline
34 & 107.1 & 112.018575497805 & -4.91857549780549 \tabularnewline
35 & 92.5 & 105.339507978894 & -12.8395079788937 \tabularnewline
36 & 95.7 & 95.8486861772715 & -0.148686177271514 \tabularnewline
37 & 85.2 & 98.6253174456046 & -13.4253174456046 \tabularnewline
38 & 85.5 & 90.28406407354 & -4.78406407353995 \tabularnewline
39 & 94.7 & 96.6721101163778 & -1.97211011637776 \tabularnewline
40 & 86.2 & 88.9340480813099 & -2.73404808130989 \tabularnewline
41 & 88.8 & 87.1823272475319 & 1.61767275246808 \tabularnewline
42 & 93.4 & 95.1130348623733 & -1.71303486237326 \tabularnewline
43 & 83.4 & 79.7480875454626 & 3.65191245453738 \tabularnewline
44 & 82.9 & 80.1710301414532 & 2.72896985854683 \tabularnewline
45 & 96.7 & 95.4934668935483 & 1.2065331064517 \tabularnewline
46 & 96.2 & 99.9659772181531 & -3.76597721815313 \tabularnewline
47 & 92.8 & 91.6468522847278 & 1.15314771527223 \tabularnewline
48 & 92.8 & 91.0378326590587 & 1.76216734094126 \tabularnewline
49 & 90.2 & 91.3828085282299 & -1.18280852822991 \tabularnewline
50 & 95.9 & 90.3371639868403 & 5.56283601315975 \tabularnewline
51 & 107.5 & 101.920674612999 & 5.57932538700099 \tabularnewline
52 & 98 & 97.3937347783331 & 0.606265221666888 \tabularnewline
53 & 95 & 98.2595632087737 & -3.25956320877374 \tabularnewline
54 & 108.5 & 103.403026145067 & 5.09697385493261 \tabularnewline
55 & 91.8 & 92.4127588772679 & -0.612758877267936 \tabularnewline
56 & 91.7 & 90.9012310707787 & 0.798768929221339 \tabularnewline
57 & 108.3 & 105.142530086351 & 3.15746991364861 \tabularnewline
58 & 105.1 & 109.421145663265 & -4.32114566326504 \tabularnewline
59 & 104.8 & 102.141186971719 & 2.65881302828068 \tabularnewline
60 & 103.2 & 102.464524362193 & 0.735475637806545 \tabularnewline
61 & 98.6 & 101.801760681976 & -3.20176068197577 \tabularnewline
62 & 102.4 & 101.577054819692 & 0.822945180308466 \tabularnewline
63 & 121.2 & 111.181877661133 & 10.0181223388666 \tabularnewline
64 & 102.6 & 107.517417678198 & -4.91741767819809 \tabularnewline
65 & 108.9 & 105.144001356909 & 3.7559986430911 \tabularnewline
66 & 105.5 & 115.409099773274 & -9.90909977327412 \tabularnewline
67 & 90.8 & 96.5712915522401 & -5.77129155224013 \tabularnewline
68 & 99.6 & 93.1040426973514 & 6.49595730264861 \tabularnewline
69 & 111.6 & 110.362110288315 & 1.23788971168459 \tabularnewline
70 & 104.7 & 112.03240823284 & -7.33240823284029 \tabularnewline
71 & 103.1 & 105.04091057348 & -1.94091057347967 \tabularnewline
72 & 101.7 & 102.834078012146 & -1.13407801214646 \tabularnewline
73 & 98.8 & 100.334172975238 & -1.53417297523764 \tabularnewline
74 & 101.4 & 101.68826698159 & -0.288266981589686 \tabularnewline
75 & 114.2 & 112.873286513208 & 1.32671348679169 \tabularnewline
76 & 96.9 & 101.764272922169 & -4.86427292216926 \tabularnewline
77 & 98.3 & 101.277821980003 & -2.97782198000277 \tabularnewline
78 & 104.8 & 105.186481318123 & -0.386481318122804 \tabularnewline
79 & 94.4 & 91.2950257857611 & 3.10497421423892 \tabularnewline
80 & 94.5 & 94.4803879373056 & 0.0196120626943639 \tabularnewline
81 & 102.4 & 107.571240864343 & -5.17124086434283 \tabularnewline
82 & 105.5 & 104.269997739927 & 1.23000226007302 \tabularnewline
83 & 101.2 & 102.142966801557 & -0.94296680155702 \tabularnewline
84 & 99.5 & 100.457035262709 & -0.957035262709368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232330&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]92.8[/C][C]90.0906517094018[/C][C]2.70934829059824[/C][/ROW]
[ROW][C]14[/C][C]90.6[/C][C]88.8548006356391[/C][C]1.7451993643609[/C][/ROW]
[ROW][C]15[/C][C]102.2[/C][C]101.299921870431[/C][C]0.900078129568996[/C][/ROW]
[ROW][C]16[/C][C]91.8[/C][C]91.2952303286501[/C][C]0.504769671349848[/C][/ROW]
[ROW][C]17[/C][C]95[/C][C]94.6487406650294[/C][C]0.351259334970621[/C][/ROW]
[ROW][C]18[/C][C]102[/C][C]102.017990513546[/C][C]-0.0179905135457545[/C][/ROW]
[ROW][C]19[/C][C]88.9[/C][C]84.6730279605632[/C][C]4.22697203943676[/C][/ROW]
[ROW][C]20[/C][C]89.6[/C][C]89.894493472681[/C][C]-0.294493472680969[/C][/ROW]
[ROW][C]21[/C][C]97.9[/C][C]102.676388644608[/C][C]-4.77638864460819[/C][/ROW]
[ROW][C]22[/C][C]108.6[/C][C]104.934498595344[/C][C]3.66550140465627[/C][/ROW]
[ROW][C]23[/C][C]100.8[/C][C]103.57149172674[/C][C]-2.77149172674027[/C][/ROW]
[ROW][C]24[/C][C]95.1[/C][C]98.8429963892033[/C][C]-3.74299638920328[/C][/ROW]
[ROW][C]25[/C][C]101[/C][C]98.8143393320295[/C][C]2.18566066797047[/C][/ROW]
[ROW][C]26[/C][C]100.9[/C][C]97.1424236255646[/C][C]3.75757637443544[/C][/ROW]
[ROW][C]27[/C][C]102.5[/C][C]110.29502488563[/C][C]-7.79502488562959[/C][/ROW]
[ROW][C]28[/C][C]105.4[/C][C]96.391609659266[/C][C]9.00839034073398[/C][/ROW]
[ROW][C]29[/C][C]98.4[/C][C]103.424154391118[/C][C]-5.02415439111802[/C][/ROW]
[ROW][C]30[/C][C]105.3[/C][C]108.365382781666[/C][C]-3.06538278166573[/C][/ROW]
[ROW][C]31[/C][C]96.5[/C][C]90.6576927648975[/C][C]5.84230723510248[/C][/ROW]
[ROW][C]32[/C][C]88.1[/C][C]95.4906583681818[/C][C]-7.39065836818178[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]104.059648495613[/C][C]3.84035150438746[/C][/ROW]
[ROW][C]34[/C][C]107.1[/C][C]112.018575497805[/C][C]-4.91857549780549[/C][/ROW]
[ROW][C]35[/C][C]92.5[/C][C]105.339507978894[/C][C]-12.8395079788937[/C][/ROW]
[ROW][C]36[/C][C]95.7[/C][C]95.8486861772715[/C][C]-0.148686177271514[/C][/ROW]
[ROW][C]37[/C][C]85.2[/C][C]98.6253174456046[/C][C]-13.4253174456046[/C][/ROW]
[ROW][C]38[/C][C]85.5[/C][C]90.28406407354[/C][C]-4.78406407353995[/C][/ROW]
[ROW][C]39[/C][C]94.7[/C][C]96.6721101163778[/C][C]-1.97211011637776[/C][/ROW]
[ROW][C]40[/C][C]86.2[/C][C]88.9340480813099[/C][C]-2.73404808130989[/C][/ROW]
[ROW][C]41[/C][C]88.8[/C][C]87.1823272475319[/C][C]1.61767275246808[/C][/ROW]
[ROW][C]42[/C][C]93.4[/C][C]95.1130348623733[/C][C]-1.71303486237326[/C][/ROW]
[ROW][C]43[/C][C]83.4[/C][C]79.7480875454626[/C][C]3.65191245453738[/C][/ROW]
[ROW][C]44[/C][C]82.9[/C][C]80.1710301414532[/C][C]2.72896985854683[/C][/ROW]
[ROW][C]45[/C][C]96.7[/C][C]95.4934668935483[/C][C]1.2065331064517[/C][/ROW]
[ROW][C]46[/C][C]96.2[/C][C]99.9659772181531[/C][C]-3.76597721815313[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]91.6468522847278[/C][C]1.15314771527223[/C][/ROW]
[ROW][C]48[/C][C]92.8[/C][C]91.0378326590587[/C][C]1.76216734094126[/C][/ROW]
[ROW][C]49[/C][C]90.2[/C][C]91.3828085282299[/C][C]-1.18280852822991[/C][/ROW]
[ROW][C]50[/C][C]95.9[/C][C]90.3371639868403[/C][C]5.56283601315975[/C][/ROW]
[ROW][C]51[/C][C]107.5[/C][C]101.920674612999[/C][C]5.57932538700099[/C][/ROW]
[ROW][C]52[/C][C]98[/C][C]97.3937347783331[/C][C]0.606265221666888[/C][/ROW]
[ROW][C]53[/C][C]95[/C][C]98.2595632087737[/C][C]-3.25956320877374[/C][/ROW]
[ROW][C]54[/C][C]108.5[/C][C]103.403026145067[/C][C]5.09697385493261[/C][/ROW]
[ROW][C]55[/C][C]91.8[/C][C]92.4127588772679[/C][C]-0.612758877267936[/C][/ROW]
[ROW][C]56[/C][C]91.7[/C][C]90.9012310707787[/C][C]0.798768929221339[/C][/ROW]
[ROW][C]57[/C][C]108.3[/C][C]105.142530086351[/C][C]3.15746991364861[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]109.421145663265[/C][C]-4.32114566326504[/C][/ROW]
[ROW][C]59[/C][C]104.8[/C][C]102.141186971719[/C][C]2.65881302828068[/C][/ROW]
[ROW][C]60[/C][C]103.2[/C][C]102.464524362193[/C][C]0.735475637806545[/C][/ROW]
[ROW][C]61[/C][C]98.6[/C][C]101.801760681976[/C][C]-3.20176068197577[/C][/ROW]
[ROW][C]62[/C][C]102.4[/C][C]101.577054819692[/C][C]0.822945180308466[/C][/ROW]
[ROW][C]63[/C][C]121.2[/C][C]111.181877661133[/C][C]10.0181223388666[/C][/ROW]
[ROW][C]64[/C][C]102.6[/C][C]107.517417678198[/C][C]-4.91741767819809[/C][/ROW]
[ROW][C]65[/C][C]108.9[/C][C]105.144001356909[/C][C]3.7559986430911[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]115.409099773274[/C][C]-9.90909977327412[/C][/ROW]
[ROW][C]67[/C][C]90.8[/C][C]96.5712915522401[/C][C]-5.77129155224013[/C][/ROW]
[ROW][C]68[/C][C]99.6[/C][C]93.1040426973514[/C][C]6.49595730264861[/C][/ROW]
[ROW][C]69[/C][C]111.6[/C][C]110.362110288315[/C][C]1.23788971168459[/C][/ROW]
[ROW][C]70[/C][C]104.7[/C][C]112.03240823284[/C][C]-7.33240823284029[/C][/ROW]
[ROW][C]71[/C][C]103.1[/C][C]105.04091057348[/C][C]-1.94091057347967[/C][/ROW]
[ROW][C]72[/C][C]101.7[/C][C]102.834078012146[/C][C]-1.13407801214646[/C][/ROW]
[ROW][C]73[/C][C]98.8[/C][C]100.334172975238[/C][C]-1.53417297523764[/C][/ROW]
[ROW][C]74[/C][C]101.4[/C][C]101.68826698159[/C][C]-0.288266981589686[/C][/ROW]
[ROW][C]75[/C][C]114.2[/C][C]112.873286513208[/C][C]1.32671348679169[/C][/ROW]
[ROW][C]76[/C][C]96.9[/C][C]101.764272922169[/C][C]-4.86427292216926[/C][/ROW]
[ROW][C]77[/C][C]98.3[/C][C]101.277821980003[/C][C]-2.97782198000277[/C][/ROW]
[ROW][C]78[/C][C]104.8[/C][C]105.186481318123[/C][C]-0.386481318122804[/C][/ROW]
[ROW][C]79[/C][C]94.4[/C][C]91.2950257857611[/C][C]3.10497421423892[/C][/ROW]
[ROW][C]80[/C][C]94.5[/C][C]94.4803879373056[/C][C]0.0196120626943639[/C][/ROW]
[ROW][C]81[/C][C]102.4[/C][C]107.571240864343[/C][C]-5.17124086434283[/C][/ROW]
[ROW][C]82[/C][C]105.5[/C][C]104.269997739927[/C][C]1.23000226007302[/C][/ROW]
[ROW][C]83[/C][C]101.2[/C][C]102.142966801557[/C][C]-0.94296680155702[/C][/ROW]
[ROW][C]84[/C][C]99.5[/C][C]100.457035262709[/C][C]-0.957035262709368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232330&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232330&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
1392.890.09065170940182.70934829059824
1490.688.85480063563911.7451993643609
15102.2101.2999218704310.900078129568996
1691.891.29523032865010.504769671349848
179594.64874066502940.351259334970621
18102102.017990513546-0.0179905135457545
1988.984.67302796056324.22697203943676
2089.689.894493472681-0.294493472680969
2197.9102.676388644608-4.77638864460819
22108.6104.9344985953443.66550140465627
23100.8103.57149172674-2.77149172674027
2495.198.8429963892033-3.74299638920328
2510198.81433933202952.18566066797047
26100.997.14242362556463.75757637443544
27102.5110.29502488563-7.79502488562959
28105.496.3916096592669.00839034073398
2998.4103.424154391118-5.02415439111802
30105.3108.365382781666-3.06538278166573
3196.590.65769276489755.84230723510248
3288.195.4906583681818-7.39065836818178
33107.9104.0596484956133.84035150438746
34107.1112.018575497805-4.91857549780549
3592.5105.339507978894-12.8395079788937
3695.795.8486861772715-0.148686177271514
3785.298.6253174456046-13.4253174456046
3885.590.28406407354-4.78406407353995
3994.796.6721101163778-1.97211011637776
4086.288.9340480813099-2.73404808130989
4188.887.18232724753191.61767275246808
4293.495.1130348623733-1.71303486237326
4383.479.74808754546263.65191245453738
4482.980.17103014145322.72896985854683
4596.795.49346689354831.2065331064517
4696.299.9659772181531-3.76597721815313
4792.891.64685228472781.15314771527223
4892.891.03783265905871.76216734094126
4990.291.3828085282299-1.18280852822991
5095.990.33716398684035.56283601315975
51107.5101.9206746129995.57932538700099
529897.39373477833310.606265221666888
539598.2595632087737-3.25956320877374
54108.5103.4030261450675.09697385493261
5591.892.4127588772679-0.612758877267936
5691.790.90123107077870.798768929221339
57108.3105.1425300863513.15746991364861
58105.1109.421145663265-4.32114566326504
59104.8102.1411869717192.65881302828068
60103.2102.4645243621930.735475637806545
6198.6101.801760681976-3.20176068197577
62102.4101.5770548196920.822945180308466
63121.2111.18187766113310.0181223388666
64102.6107.517417678198-4.91741767819809
65108.9105.1440013569093.7559986430911
66105.5115.409099773274-9.90909977327412
6790.896.5712915522401-5.77129155224013
6899.693.10404269735146.49595730264861
69111.6110.3621102883151.23788971168459
70104.7112.03240823284-7.33240823284029
71103.1105.04091057348-1.94091057347967
72101.7102.834078012146-1.13407801214646
7398.8100.334172975238-1.53417297523764
74101.4101.68826698159-0.288266981589686
75114.2112.8732865132081.32671348679169
7696.9101.764272922169-4.86427292216926
7798.3101.277821980003-2.97782198000277
78104.8105.186481318123-0.386481318122804
7994.491.29502578576113.10497421423892
8094.594.48038793730560.0196120626943639
81102.4107.571240864343-5.17124086434283
82105.5104.2699977399271.23000226007302
83101.2102.142966801557-0.94296680155702
8499.5100.457035262709-0.957035262709368







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8597.840658851645989.0959224572587106.585395246033
86100.06579702155190.506069365271109.62552467783
87111.671543638135101.332411532812122.010675743458
8898.439221035778887.3482478890389109.530194182519
89100.4493833984488.6283858914394112.27038090544
90106.22915435516393.6956778185094118.762630891817
9193.301469394716280.0697902612172106.533148528215
9294.367280215974980.4491133431901108.28544708876
93106.17993814326191.5849515189981120.774924767524
94106.61542959138891.3516286122679121.879230570508
95103.42900175490687.5030224239784119.354981085833
96102.13978699493485.5571238262404118.722450163628

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 97.8406588516459 & 89.0959224572587 & 106.585395246033 \tabularnewline
86 & 100.065797021551 & 90.506069365271 & 109.62552467783 \tabularnewline
87 & 111.671543638135 & 101.332411532812 & 122.010675743458 \tabularnewline
88 & 98.4392210357788 & 87.3482478890389 & 109.530194182519 \tabularnewline
89 & 100.44938339844 & 88.6283858914394 & 112.27038090544 \tabularnewline
90 & 106.229154355163 & 93.6956778185094 & 118.762630891817 \tabularnewline
91 & 93.3014693947162 & 80.0697902612172 & 106.533148528215 \tabularnewline
92 & 94.3672802159749 & 80.4491133431901 & 108.28544708876 \tabularnewline
93 & 106.179938143261 & 91.5849515189981 & 120.774924767524 \tabularnewline
94 & 106.615429591388 & 91.3516286122679 & 121.879230570508 \tabularnewline
95 & 103.429001754906 & 87.5030224239784 & 119.354981085833 \tabularnewline
96 & 102.139786994934 & 85.5571238262404 & 118.722450163628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232330&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]97.8406588516459[/C][C]89.0959224572587[/C][C]106.585395246033[/C][/ROW]
[ROW][C]86[/C][C]100.065797021551[/C][C]90.506069365271[/C][C]109.62552467783[/C][/ROW]
[ROW][C]87[/C][C]111.671543638135[/C][C]101.332411532812[/C][C]122.010675743458[/C][/ROW]
[ROW][C]88[/C][C]98.4392210357788[/C][C]87.3482478890389[/C][C]109.530194182519[/C][/ROW]
[ROW][C]89[/C][C]100.44938339844[/C][C]88.6283858914394[/C][C]112.27038090544[/C][/ROW]
[ROW][C]90[/C][C]106.229154355163[/C][C]93.6956778185094[/C][C]118.762630891817[/C][/ROW]
[ROW][C]91[/C][C]93.3014693947162[/C][C]80.0697902612172[/C][C]106.533148528215[/C][/ROW]
[ROW][C]92[/C][C]94.3672802159749[/C][C]80.4491133431901[/C][C]108.28544708876[/C][/ROW]
[ROW][C]93[/C][C]106.179938143261[/C][C]91.5849515189981[/C][C]120.774924767524[/C][/ROW]
[ROW][C]94[/C][C]106.615429591388[/C][C]91.3516286122679[/C][C]121.879230570508[/C][/ROW]
[ROW][C]95[/C][C]103.429001754906[/C][C]87.5030224239784[/C][C]119.354981085833[/C][/ROW]
[ROW][C]96[/C][C]102.139786994934[/C][C]85.5571238262404[/C][C]118.722450163628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232330&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232330&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
8597.840658851645989.0959224572587106.585395246033
86100.06579702155190.506069365271109.62552467783
87111.671543638135101.332411532812122.010675743458
8898.439221035778887.3482478890389109.530194182519
89100.4493833984488.6283858914394112.27038090544
90106.22915435516393.6956778185094118.762630891817
9193.301469394716280.0697902612172106.533148528215
9294.367280215974980.4491133431901108.28544708876
93106.17993814326191.5849515189981120.774924767524
94106.61542959138891.3516286122679121.879230570508
95103.42900175490687.5030224239784119.354981085833
96102.13978699493485.5571238262404118.722450163628



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')