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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 17:31:32 +0100
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/Dec/16/t148190592099ecgmnm01zmbay.htm/, Retrieved Thu, 02 May 2024 23:40:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300431, Retrieved Thu, 02 May 2024 23:40:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- R  D    [ARIMA Backward Selection] [] [2016-12-16 14:51:40] [683f400e1b95307fc738e729f07c4fce]
- RM D        [Exponential Smoothing] [] [2016-12-16 16:31:32] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Post a new message
Dataseries X:
512
308
396
532
442
818
350
598
446
684
622
794
618
624
672
640
734
1042
760
682
1352
1196
1140
1134
1008
1262
842
890
792
1138
800
1212
1606
1686
1374
1670
1350
1056
1914
928
1296
966
1302
1822
1308
2030
2824
1342
1562
1278
2340
1826
1412
3068
1448
1202
2094
2408
2344
2386
3020
1990
2570
3664
2272
1596
3282
3870
3950
4292
3056
3170
3138
3232
3660
3310
2160
4444
2654
3226
5788
4288
4446
2778
3398
3896
2078
3230
2926
4746
2236
4306
3278
3498
2964
4184
3344
4152
2220
3520
2872
2900
1430
2730
3226
5472
4664
4566




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300431&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300431&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.104488484975097
beta0
gamma0.15019041008877

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.104488484975097 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.15019041008877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300431&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]0.104488484975097[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.15019041008877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300431&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
alpha0.104488484975097
beta0
gamma0.15019041008877







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13618503.1375914647114.8624085353
14624531.90771360253892.0922863974623
15672578.00515001972593.9948499802751
16640542.40088446168297.599115538318
17734627.687350961666106.312649038334
181042905.706401795342136.293598204658
19760510.714812998023249.285187001977
20682920.487125175925-238.487125175925
211352662.795009704185689.204990295815
2211961131.2286185114964.7713814885115
2311401037.28174773282102.718252267184
2411341330.32873660606-196.328736606057
2510081037.28865758618-29.288657586183
2612621034.0176412443227.982358755704
278421101.81108585029-259.811085850289
28890974.043782094816-84.0437820948157
297921075.76390237006-283.763902370063
3011381457.44326570675-319.443265706749
31800812.920172651592-12.9201726515918
3212121249.96234439112-37.9623443911198
3316061065.64118927675540.358810723249
3416861533.45282721609152.547172783909
3513741409.26870738753-35.2687073875277
3616701713.68274820643-43.6827482064264
3713501366.6160051655-16.6160051654986
3810561400.19715902984-344.197159029839
3919141329.06841302592584.931586974081
409281278.78785407703-350.787854077028
4112961341.72249347557-45.7224934755723
429661863.1508818684-897.150881868398
4313021033.48869414322268.511305856777
4418221622.21437080761199.785629192389
4513081493.54552602423-185.54552602423
4620301908.93099914564121.069000854362
4728241712.302679684811111.69732031519
4813422218.00662557128-876.00662557128
4915621696.31468992594-134.31468992594
5012781663.47259317822-385.472593178222
5123401722.82879602363617.171203976374
5218261491.7772511763334.222748823702
5314121699.09283698858-287.092836988578
5430682168.9461832444899.053816755599
5514481458.81818631279-10.8181863127861
5612022179.28607813684-977.286078136842
5720941819.71894434936274.281055650642
5824082445.68848357102-37.6884835710212
5923442325.3888235113218.6111764886823
6023862459.08268208989-73.0826820898851
6130202041.79986364331978.200136356686
6219902066.85958130645-76.8595813064521
6325702352.73482789778217.26517210222
6436641943.830685430541720.16931456946
6522722233.7114742558638.2885257441376
6615963122.69478988701-1526.69478988701
6732821806.418329436481475.58167056352
6838702738.286478048661131.71352195134
6939502711.995222953011238.00477704699
7042923660.54470281739631.455297182609
7130563542.66184255636-486.661842556362
7231703653.66544703445-483.665447034453
7331383183.75431962108-45.754319621079
7432322862.28890462056369.711095379441
7536603359.98754683086300.012453169139
7633103028.95246471191281.047535288095
7721602899.95142798419-739.951427984191
7844443649.12353048289794.876469517112
7926542683.84764259183-29.8476425918343
8032263573.62859786139-347.628597861386
8157883370.154894291112417.84510570889
8242884502.05951349206-214.059513492059
8344464080.04273357482365.957266425183
8427784305.41948268593-1527.41948268593
8533983718.27786747819-320.277867478194
8638963376.76502029674519.234979703263
8720783948.43736378843-1870.43736378843
8832303350.9248441375-120.924844137505
8929263014.60777629221-88.6077762922073
9047464139.212677835606.787322165002
9122362931.38063445508-695.380634455079
9243063764.10853932111541.891460678886
9332784017.07858815392-739.078588153925
9434984463.98510589215-965.985105892149
9529644047.95923758181-1083.95923758181
9641843865.27219044506318.727809554944
9733443636.12946397469-292.12946397469
9841523411.58782902531740.412170974693
9922203671.34232510779-1451.34232510779
10035203351.85055471381168.149445286188
10128723045.14199572521-173.141995725212
10229004266.59735477302-1366.59735477302
10314302730.14544896005-1300.14544896005
10427303600.75212232576-870.752122325756
10532263532.74864566996-306.748645669958
10654723950.961063280431521.03893671957
10746643785.4133304459878.586669554103
10845663998.09858547447567.901414525534

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 618 & 503.1375914647 & 114.8624085353 \tabularnewline
14 & 624 & 531.907713602538 & 92.0922863974623 \tabularnewline
15 & 672 & 578.005150019725 & 93.9948499802751 \tabularnewline
16 & 640 & 542.400884461682 & 97.599115538318 \tabularnewline
17 & 734 & 627.687350961666 & 106.312649038334 \tabularnewline
18 & 1042 & 905.706401795342 & 136.293598204658 \tabularnewline
19 & 760 & 510.714812998023 & 249.285187001977 \tabularnewline
20 & 682 & 920.487125175925 & -238.487125175925 \tabularnewline
21 & 1352 & 662.795009704185 & 689.204990295815 \tabularnewline
22 & 1196 & 1131.22861851149 & 64.7713814885115 \tabularnewline
23 & 1140 & 1037.28174773282 & 102.718252267184 \tabularnewline
24 & 1134 & 1330.32873660606 & -196.328736606057 \tabularnewline
25 & 1008 & 1037.28865758618 & -29.288657586183 \tabularnewline
26 & 1262 & 1034.0176412443 & 227.982358755704 \tabularnewline
27 & 842 & 1101.81108585029 & -259.811085850289 \tabularnewline
28 & 890 & 974.043782094816 & -84.0437820948157 \tabularnewline
29 & 792 & 1075.76390237006 & -283.763902370063 \tabularnewline
30 & 1138 & 1457.44326570675 & -319.443265706749 \tabularnewline
31 & 800 & 812.920172651592 & -12.9201726515918 \tabularnewline
32 & 1212 & 1249.96234439112 & -37.9623443911198 \tabularnewline
33 & 1606 & 1065.64118927675 & 540.358810723249 \tabularnewline
34 & 1686 & 1533.45282721609 & 152.547172783909 \tabularnewline
35 & 1374 & 1409.26870738753 & -35.2687073875277 \tabularnewline
36 & 1670 & 1713.68274820643 & -43.6827482064264 \tabularnewline
37 & 1350 & 1366.6160051655 & -16.6160051654986 \tabularnewline
38 & 1056 & 1400.19715902984 & -344.197159029839 \tabularnewline
39 & 1914 & 1329.06841302592 & 584.931586974081 \tabularnewline
40 & 928 & 1278.78785407703 & -350.787854077028 \tabularnewline
41 & 1296 & 1341.72249347557 & -45.7224934755723 \tabularnewline
42 & 966 & 1863.1508818684 & -897.150881868398 \tabularnewline
43 & 1302 & 1033.48869414322 & 268.511305856777 \tabularnewline
44 & 1822 & 1622.21437080761 & 199.785629192389 \tabularnewline
45 & 1308 & 1493.54552602423 & -185.54552602423 \tabularnewline
46 & 2030 & 1908.93099914564 & 121.069000854362 \tabularnewline
47 & 2824 & 1712.30267968481 & 1111.69732031519 \tabularnewline
48 & 1342 & 2218.00662557128 & -876.00662557128 \tabularnewline
49 & 1562 & 1696.31468992594 & -134.31468992594 \tabularnewline
50 & 1278 & 1663.47259317822 & -385.472593178222 \tabularnewline
51 & 2340 & 1722.82879602363 & 617.171203976374 \tabularnewline
52 & 1826 & 1491.7772511763 & 334.222748823702 \tabularnewline
53 & 1412 & 1699.09283698858 & -287.092836988578 \tabularnewline
54 & 3068 & 2168.9461832444 & 899.053816755599 \tabularnewline
55 & 1448 & 1458.81818631279 & -10.8181863127861 \tabularnewline
56 & 1202 & 2179.28607813684 & -977.286078136842 \tabularnewline
57 & 2094 & 1819.71894434936 & 274.281055650642 \tabularnewline
58 & 2408 & 2445.68848357102 & -37.6884835710212 \tabularnewline
59 & 2344 & 2325.38882351132 & 18.6111764886823 \tabularnewline
60 & 2386 & 2459.08268208989 & -73.0826820898851 \tabularnewline
61 & 3020 & 2041.79986364331 & 978.200136356686 \tabularnewline
62 & 1990 & 2066.85958130645 & -76.8595813064521 \tabularnewline
63 & 2570 & 2352.73482789778 & 217.26517210222 \tabularnewline
64 & 3664 & 1943.83068543054 & 1720.16931456946 \tabularnewline
65 & 2272 & 2233.71147425586 & 38.2885257441376 \tabularnewline
66 & 1596 & 3122.69478988701 & -1526.69478988701 \tabularnewline
67 & 3282 & 1806.41832943648 & 1475.58167056352 \tabularnewline
68 & 3870 & 2738.28647804866 & 1131.71352195134 \tabularnewline
69 & 3950 & 2711.99522295301 & 1238.00477704699 \tabularnewline
70 & 4292 & 3660.54470281739 & 631.455297182609 \tabularnewline
71 & 3056 & 3542.66184255636 & -486.661842556362 \tabularnewline
72 & 3170 & 3653.66544703445 & -483.665447034453 \tabularnewline
73 & 3138 & 3183.75431962108 & -45.754319621079 \tabularnewline
74 & 3232 & 2862.28890462056 & 369.711095379441 \tabularnewline
75 & 3660 & 3359.98754683086 & 300.012453169139 \tabularnewline
76 & 3310 & 3028.95246471191 & 281.047535288095 \tabularnewline
77 & 2160 & 2899.95142798419 & -739.951427984191 \tabularnewline
78 & 4444 & 3649.12353048289 & 794.876469517112 \tabularnewline
79 & 2654 & 2683.84764259183 & -29.8476425918343 \tabularnewline
80 & 3226 & 3573.62859786139 & -347.628597861386 \tabularnewline
81 & 5788 & 3370.15489429111 & 2417.84510570889 \tabularnewline
82 & 4288 & 4502.05951349206 & -214.059513492059 \tabularnewline
83 & 4446 & 4080.04273357482 & 365.957266425183 \tabularnewline
84 & 2778 & 4305.41948268593 & -1527.41948268593 \tabularnewline
85 & 3398 & 3718.27786747819 & -320.277867478194 \tabularnewline
86 & 3896 & 3376.76502029674 & 519.234979703263 \tabularnewline
87 & 2078 & 3948.43736378843 & -1870.43736378843 \tabularnewline
88 & 3230 & 3350.9248441375 & -120.924844137505 \tabularnewline
89 & 2926 & 3014.60777629221 & -88.6077762922073 \tabularnewline
90 & 4746 & 4139.212677835 & 606.787322165002 \tabularnewline
91 & 2236 & 2931.38063445508 & -695.380634455079 \tabularnewline
92 & 4306 & 3764.10853932111 & 541.891460678886 \tabularnewline
93 & 3278 & 4017.07858815392 & -739.078588153925 \tabularnewline
94 & 3498 & 4463.98510589215 & -965.985105892149 \tabularnewline
95 & 2964 & 4047.95923758181 & -1083.95923758181 \tabularnewline
96 & 4184 & 3865.27219044506 & 318.727809554944 \tabularnewline
97 & 3344 & 3636.12946397469 & -292.12946397469 \tabularnewline
98 & 4152 & 3411.58782902531 & 740.412170974693 \tabularnewline
99 & 2220 & 3671.34232510779 & -1451.34232510779 \tabularnewline
100 & 3520 & 3351.85055471381 & 168.149445286188 \tabularnewline
101 & 2872 & 3045.14199572521 & -173.141995725212 \tabularnewline
102 & 2900 & 4266.59735477302 & -1366.59735477302 \tabularnewline
103 & 1430 & 2730.14544896005 & -1300.14544896005 \tabularnewline
104 & 2730 & 3600.75212232576 & -870.752122325756 \tabularnewline
105 & 3226 & 3532.74864566996 & -306.748645669958 \tabularnewline
106 & 5472 & 3950.96106328043 & 1521.03893671957 \tabularnewline
107 & 4664 & 3785.4133304459 & 878.586669554103 \tabularnewline
108 & 4566 & 3998.09858547447 & 567.901414525534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300431&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]618[/C][C]503.1375914647[/C][C]114.8624085353[/C][/ROW]
[ROW][C]14[/C][C]624[/C][C]531.907713602538[/C][C]92.0922863974623[/C][/ROW]
[ROW][C]15[/C][C]672[/C][C]578.005150019725[/C][C]93.9948499802751[/C][/ROW]
[ROW][C]16[/C][C]640[/C][C]542.400884461682[/C][C]97.599115538318[/C][/ROW]
[ROW][C]17[/C][C]734[/C][C]627.687350961666[/C][C]106.312649038334[/C][/ROW]
[ROW][C]18[/C][C]1042[/C][C]905.706401795342[/C][C]136.293598204658[/C][/ROW]
[ROW][C]19[/C][C]760[/C][C]510.714812998023[/C][C]249.285187001977[/C][/ROW]
[ROW][C]20[/C][C]682[/C][C]920.487125175925[/C][C]-238.487125175925[/C][/ROW]
[ROW][C]21[/C][C]1352[/C][C]662.795009704185[/C][C]689.204990295815[/C][/ROW]
[ROW][C]22[/C][C]1196[/C][C]1131.22861851149[/C][C]64.7713814885115[/C][/ROW]
[ROW][C]23[/C][C]1140[/C][C]1037.28174773282[/C][C]102.718252267184[/C][/ROW]
[ROW][C]24[/C][C]1134[/C][C]1330.32873660606[/C][C]-196.328736606057[/C][/ROW]
[ROW][C]25[/C][C]1008[/C][C]1037.28865758618[/C][C]-29.288657586183[/C][/ROW]
[ROW][C]26[/C][C]1262[/C][C]1034.0176412443[/C][C]227.982358755704[/C][/ROW]
[ROW][C]27[/C][C]842[/C][C]1101.81108585029[/C][C]-259.811085850289[/C][/ROW]
[ROW][C]28[/C][C]890[/C][C]974.043782094816[/C][C]-84.0437820948157[/C][/ROW]
[ROW][C]29[/C][C]792[/C][C]1075.76390237006[/C][C]-283.763902370063[/C][/ROW]
[ROW][C]30[/C][C]1138[/C][C]1457.44326570675[/C][C]-319.443265706749[/C][/ROW]
[ROW][C]31[/C][C]800[/C][C]812.920172651592[/C][C]-12.9201726515918[/C][/ROW]
[ROW][C]32[/C][C]1212[/C][C]1249.96234439112[/C][C]-37.9623443911198[/C][/ROW]
[ROW][C]33[/C][C]1606[/C][C]1065.64118927675[/C][C]540.358810723249[/C][/ROW]
[ROW][C]34[/C][C]1686[/C][C]1533.45282721609[/C][C]152.547172783909[/C][/ROW]
[ROW][C]35[/C][C]1374[/C][C]1409.26870738753[/C][C]-35.2687073875277[/C][/ROW]
[ROW][C]36[/C][C]1670[/C][C]1713.68274820643[/C][C]-43.6827482064264[/C][/ROW]
[ROW][C]37[/C][C]1350[/C][C]1366.6160051655[/C][C]-16.6160051654986[/C][/ROW]
[ROW][C]38[/C][C]1056[/C][C]1400.19715902984[/C][C]-344.197159029839[/C][/ROW]
[ROW][C]39[/C][C]1914[/C][C]1329.06841302592[/C][C]584.931586974081[/C][/ROW]
[ROW][C]40[/C][C]928[/C][C]1278.78785407703[/C][C]-350.787854077028[/C][/ROW]
[ROW][C]41[/C][C]1296[/C][C]1341.72249347557[/C][C]-45.7224934755723[/C][/ROW]
[ROW][C]42[/C][C]966[/C][C]1863.1508818684[/C][C]-897.150881868398[/C][/ROW]
[ROW][C]43[/C][C]1302[/C][C]1033.48869414322[/C][C]268.511305856777[/C][/ROW]
[ROW][C]44[/C][C]1822[/C][C]1622.21437080761[/C][C]199.785629192389[/C][/ROW]
[ROW][C]45[/C][C]1308[/C][C]1493.54552602423[/C][C]-185.54552602423[/C][/ROW]
[ROW][C]46[/C][C]2030[/C][C]1908.93099914564[/C][C]121.069000854362[/C][/ROW]
[ROW][C]47[/C][C]2824[/C][C]1712.30267968481[/C][C]1111.69732031519[/C][/ROW]
[ROW][C]48[/C][C]1342[/C][C]2218.00662557128[/C][C]-876.00662557128[/C][/ROW]
[ROW][C]49[/C][C]1562[/C][C]1696.31468992594[/C][C]-134.31468992594[/C][/ROW]
[ROW][C]50[/C][C]1278[/C][C]1663.47259317822[/C][C]-385.472593178222[/C][/ROW]
[ROW][C]51[/C][C]2340[/C][C]1722.82879602363[/C][C]617.171203976374[/C][/ROW]
[ROW][C]52[/C][C]1826[/C][C]1491.7772511763[/C][C]334.222748823702[/C][/ROW]
[ROW][C]53[/C][C]1412[/C][C]1699.09283698858[/C][C]-287.092836988578[/C][/ROW]
[ROW][C]54[/C][C]3068[/C][C]2168.9461832444[/C][C]899.053816755599[/C][/ROW]
[ROW][C]55[/C][C]1448[/C][C]1458.81818631279[/C][C]-10.8181863127861[/C][/ROW]
[ROW][C]56[/C][C]1202[/C][C]2179.28607813684[/C][C]-977.286078136842[/C][/ROW]
[ROW][C]57[/C][C]2094[/C][C]1819.71894434936[/C][C]274.281055650642[/C][/ROW]
[ROW][C]58[/C][C]2408[/C][C]2445.68848357102[/C][C]-37.6884835710212[/C][/ROW]
[ROW][C]59[/C][C]2344[/C][C]2325.38882351132[/C][C]18.6111764886823[/C][/ROW]
[ROW][C]60[/C][C]2386[/C][C]2459.08268208989[/C][C]-73.0826820898851[/C][/ROW]
[ROW][C]61[/C][C]3020[/C][C]2041.79986364331[/C][C]978.200136356686[/C][/ROW]
[ROW][C]62[/C][C]1990[/C][C]2066.85958130645[/C][C]-76.8595813064521[/C][/ROW]
[ROW][C]63[/C][C]2570[/C][C]2352.73482789778[/C][C]217.26517210222[/C][/ROW]
[ROW][C]64[/C][C]3664[/C][C]1943.83068543054[/C][C]1720.16931456946[/C][/ROW]
[ROW][C]65[/C][C]2272[/C][C]2233.71147425586[/C][C]38.2885257441376[/C][/ROW]
[ROW][C]66[/C][C]1596[/C][C]3122.69478988701[/C][C]-1526.69478988701[/C][/ROW]
[ROW][C]67[/C][C]3282[/C][C]1806.41832943648[/C][C]1475.58167056352[/C][/ROW]
[ROW][C]68[/C][C]3870[/C][C]2738.28647804866[/C][C]1131.71352195134[/C][/ROW]
[ROW][C]69[/C][C]3950[/C][C]2711.99522295301[/C][C]1238.00477704699[/C][/ROW]
[ROW][C]70[/C][C]4292[/C][C]3660.54470281739[/C][C]631.455297182609[/C][/ROW]
[ROW][C]71[/C][C]3056[/C][C]3542.66184255636[/C][C]-486.661842556362[/C][/ROW]
[ROW][C]72[/C][C]3170[/C][C]3653.66544703445[/C][C]-483.665447034453[/C][/ROW]
[ROW][C]73[/C][C]3138[/C][C]3183.75431962108[/C][C]-45.754319621079[/C][/ROW]
[ROW][C]74[/C][C]3232[/C][C]2862.28890462056[/C][C]369.711095379441[/C][/ROW]
[ROW][C]75[/C][C]3660[/C][C]3359.98754683086[/C][C]300.012453169139[/C][/ROW]
[ROW][C]76[/C][C]3310[/C][C]3028.95246471191[/C][C]281.047535288095[/C][/ROW]
[ROW][C]77[/C][C]2160[/C][C]2899.95142798419[/C][C]-739.951427984191[/C][/ROW]
[ROW][C]78[/C][C]4444[/C][C]3649.12353048289[/C][C]794.876469517112[/C][/ROW]
[ROW][C]79[/C][C]2654[/C][C]2683.84764259183[/C][C]-29.8476425918343[/C][/ROW]
[ROW][C]80[/C][C]3226[/C][C]3573.62859786139[/C][C]-347.628597861386[/C][/ROW]
[ROW][C]81[/C][C]5788[/C][C]3370.15489429111[/C][C]2417.84510570889[/C][/ROW]
[ROW][C]82[/C][C]4288[/C][C]4502.05951349206[/C][C]-214.059513492059[/C][/ROW]
[ROW][C]83[/C][C]4446[/C][C]4080.04273357482[/C][C]365.957266425183[/C][/ROW]
[ROW][C]84[/C][C]2778[/C][C]4305.41948268593[/C][C]-1527.41948268593[/C][/ROW]
[ROW][C]85[/C][C]3398[/C][C]3718.27786747819[/C][C]-320.277867478194[/C][/ROW]
[ROW][C]86[/C][C]3896[/C][C]3376.76502029674[/C][C]519.234979703263[/C][/ROW]
[ROW][C]87[/C][C]2078[/C][C]3948.43736378843[/C][C]-1870.43736378843[/C][/ROW]
[ROW][C]88[/C][C]3230[/C][C]3350.9248441375[/C][C]-120.924844137505[/C][/ROW]
[ROW][C]89[/C][C]2926[/C][C]3014.60777629221[/C][C]-88.6077762922073[/C][/ROW]
[ROW][C]90[/C][C]4746[/C][C]4139.212677835[/C][C]606.787322165002[/C][/ROW]
[ROW][C]91[/C][C]2236[/C][C]2931.38063445508[/C][C]-695.380634455079[/C][/ROW]
[ROW][C]92[/C][C]4306[/C][C]3764.10853932111[/C][C]541.891460678886[/C][/ROW]
[ROW][C]93[/C][C]3278[/C][C]4017.07858815392[/C][C]-739.078588153925[/C][/ROW]
[ROW][C]94[/C][C]3498[/C][C]4463.98510589215[/C][C]-965.985105892149[/C][/ROW]
[ROW][C]95[/C][C]2964[/C][C]4047.95923758181[/C][C]-1083.95923758181[/C][/ROW]
[ROW][C]96[/C][C]4184[/C][C]3865.27219044506[/C][C]318.727809554944[/C][/ROW]
[ROW][C]97[/C][C]3344[/C][C]3636.12946397469[/C][C]-292.12946397469[/C][/ROW]
[ROW][C]98[/C][C]4152[/C][C]3411.58782902531[/C][C]740.412170974693[/C][/ROW]
[ROW][C]99[/C][C]2220[/C][C]3671.34232510779[/C][C]-1451.34232510779[/C][/ROW]
[ROW][C]100[/C][C]3520[/C][C]3351.85055471381[/C][C]168.149445286188[/C][/ROW]
[ROW][C]101[/C][C]2872[/C][C]3045.14199572521[/C][C]-173.141995725212[/C][/ROW]
[ROW][C]102[/C][C]2900[/C][C]4266.59735477302[/C][C]-1366.59735477302[/C][/ROW]
[ROW][C]103[/C][C]1430[/C][C]2730.14544896005[/C][C]-1300.14544896005[/C][/ROW]
[ROW][C]104[/C][C]2730[/C][C]3600.75212232576[/C][C]-870.752122325756[/C][/ROW]
[ROW][C]105[/C][C]3226[/C][C]3532.74864566996[/C][C]-306.748645669958[/C][/ROW]
[ROW][C]106[/C][C]5472[/C][C]3950.96106328043[/C][C]1521.03893671957[/C][/ROW]
[ROW][C]107[/C][C]4664[/C][C]3785.4133304459[/C][C]878.586669554103[/C][/ROW]
[ROW][C]108[/C][C]4566[/C][C]3998.09858547447[/C][C]567.901414525534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300431&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
13618503.1375914647114.8624085353
14624531.90771360253892.0922863974623
15672578.00515001972593.9948499802751
16640542.40088446168297.599115538318
17734627.687350961666106.312649038334
181042905.706401795342136.293598204658
19760510.714812998023249.285187001977
20682920.487125175925-238.487125175925
211352662.795009704185689.204990295815
2211961131.2286185114964.7713814885115
2311401037.28174773282102.718252267184
2411341330.32873660606-196.328736606057
2510081037.28865758618-29.288657586183
2612621034.0176412443227.982358755704
278421101.81108585029-259.811085850289
28890974.043782094816-84.0437820948157
297921075.76390237006-283.763902370063
3011381457.44326570675-319.443265706749
31800812.920172651592-12.9201726515918
3212121249.96234439112-37.9623443911198
3316061065.64118927675540.358810723249
3416861533.45282721609152.547172783909
3513741409.26870738753-35.2687073875277
3616701713.68274820643-43.6827482064264
3713501366.6160051655-16.6160051654986
3810561400.19715902984-344.197159029839
3919141329.06841302592584.931586974081
409281278.78785407703-350.787854077028
4112961341.72249347557-45.7224934755723
429661863.1508818684-897.150881868398
4313021033.48869414322268.511305856777
4418221622.21437080761199.785629192389
4513081493.54552602423-185.54552602423
4620301908.93099914564121.069000854362
4728241712.302679684811111.69732031519
4813422218.00662557128-876.00662557128
4915621696.31468992594-134.31468992594
5012781663.47259317822-385.472593178222
5123401722.82879602363617.171203976374
5218261491.7772511763334.222748823702
5314121699.09283698858-287.092836988578
5430682168.9461832444899.053816755599
5514481458.81818631279-10.8181863127861
5612022179.28607813684-977.286078136842
5720941819.71894434936274.281055650642
5824082445.68848357102-37.6884835710212
5923442325.3888235113218.6111764886823
6023862459.08268208989-73.0826820898851
6130202041.79986364331978.200136356686
6219902066.85958130645-76.8595813064521
6325702352.73482789778217.26517210222
6436641943.830685430541720.16931456946
6522722233.7114742558638.2885257441376
6615963122.69478988701-1526.69478988701
6732821806.418329436481475.58167056352
6838702738.286478048661131.71352195134
6939502711.995222953011238.00477704699
7042923660.54470281739631.455297182609
7130563542.66184255636-486.661842556362
7231703653.66544703445-483.665447034453
7331383183.75431962108-45.754319621079
7432322862.28890462056369.711095379441
7536603359.98754683086300.012453169139
7633103028.95246471191281.047535288095
7721602899.95142798419-739.951427984191
7844443649.12353048289794.876469517112
7926542683.84764259183-29.8476425918343
8032263573.62859786139-347.628597861386
8157883370.154894291112417.84510570889
8242884502.05951349206-214.059513492059
8344464080.04273357482365.957266425183
8427784305.41948268593-1527.41948268593
8533983718.27786747819-320.277867478194
8638963376.76502029674519.234979703263
8720783948.43736378843-1870.43736378843
8832303350.9248441375-120.924844137505
8929263014.60777629221-88.6077762922073
9047464139.212677835606.787322165002
9122362931.38063445508-695.380634455079
9243063764.10853932111541.891460678886
9332784017.07858815392-739.078588153925
9434984463.98510589215-965.985105892149
9529644047.95923758181-1083.95923758181
9641843865.27219044506318.727809554944
9733443636.12946397469-292.12946397469
9841523411.58782902531740.412170974693
9922203671.34232510779-1451.34232510779
10035203351.85055471381168.149445286188
10128723045.14199572521-173.141995725212
10229004266.59735477302-1366.59735477302
10314302730.14544896005-1300.14544896005
10427303600.75212232576-870.752122325756
10532263532.74864566996-306.748645669958
10654723950.961063280431521.03893671957
10746643785.4133304459878.586669554103
10845663998.09858547447567.901414525534







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093701.488721338523368.531003254364034.44643942268
1103640.881848913773278.881279683064002.88241814448
1113517.915266839423132.052104638883903.77842903996
1123569.069846665683155.693295629523982.44639770185
1133178.152288237762760.690830380733595.6137460948
1144311.191725225563797.200120562464825.18332988867
1152784.017680412372356.766228017843211.2691328069
1164000.589007305283453.066943671134548.11107093944
1174111.218483690723537.224579538084685.21238784336
1184922.223501463064251.738118574955592.70888435116
1194445.681061174613813.106927916635078.2551944326
1204528.740307294793965.092021076285092.38859351329

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3701.48872133852 & 3368.53100325436 & 4034.44643942268 \tabularnewline
110 & 3640.88184891377 & 3278.88127968306 & 4002.88241814448 \tabularnewline
111 & 3517.91526683942 & 3132.05210463888 & 3903.77842903996 \tabularnewline
112 & 3569.06984666568 & 3155.69329562952 & 3982.44639770185 \tabularnewline
113 & 3178.15228823776 & 2760.69083038073 & 3595.6137460948 \tabularnewline
114 & 4311.19172522556 & 3797.20012056246 & 4825.18332988867 \tabularnewline
115 & 2784.01768041237 & 2356.76622801784 & 3211.2691328069 \tabularnewline
116 & 4000.58900730528 & 3453.06694367113 & 4548.11107093944 \tabularnewline
117 & 4111.21848369072 & 3537.22457953808 & 4685.21238784336 \tabularnewline
118 & 4922.22350146306 & 4251.73811857495 & 5592.70888435116 \tabularnewline
119 & 4445.68106117461 & 3813.10692791663 & 5078.2551944326 \tabularnewline
120 & 4528.74030729479 & 3965.09202107628 & 5092.38859351329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300431&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]3701.48872133852[/C][C]3368.53100325436[/C][C]4034.44643942268[/C][/ROW]
[ROW][C]110[/C][C]3640.88184891377[/C][C]3278.88127968306[/C][C]4002.88241814448[/C][/ROW]
[ROW][C]111[/C][C]3517.91526683942[/C][C]3132.05210463888[/C][C]3903.77842903996[/C][/ROW]
[ROW][C]112[/C][C]3569.06984666568[/C][C]3155.69329562952[/C][C]3982.44639770185[/C][/ROW]
[ROW][C]113[/C][C]3178.15228823776[/C][C]2760.69083038073[/C][C]3595.6137460948[/C][/ROW]
[ROW][C]114[/C][C]4311.19172522556[/C][C]3797.20012056246[/C][C]4825.18332988867[/C][/ROW]
[ROW][C]115[/C][C]2784.01768041237[/C][C]2356.76622801784[/C][C]3211.2691328069[/C][/ROW]
[ROW][C]116[/C][C]4000.58900730528[/C][C]3453.06694367113[/C][C]4548.11107093944[/C][/ROW]
[ROW][C]117[/C][C]4111.21848369072[/C][C]3537.22457953808[/C][C]4685.21238784336[/C][/ROW]
[ROW][C]118[/C][C]4922.22350146306[/C][C]4251.73811857495[/C][C]5592.70888435116[/C][/ROW]
[ROW][C]119[/C][C]4445.68106117461[/C][C]3813.10692791663[/C][C]5078.2551944326[/C][/ROW]
[ROW][C]120[/C][C]4528.74030729479[/C][C]3965.09202107628[/C][C]5092.38859351329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300431&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
1093701.488721338523368.531003254364034.44643942268
1103640.881848913773278.881279683064002.88241814448
1113517.915266839423132.052104638883903.77842903996
1123569.069846665683155.693295629523982.44639770185
1133178.152288237762760.690830380733595.6137460948
1144311.191725225563797.200120562464825.18332988867
1152784.017680412372356.766228017843211.2691328069
1164000.589007305283453.066943671134548.11107093944
1174111.218483690723537.224579538084685.21238784336
1184922.223501463064251.738118574955592.70888435116
1194445.681061174613813.106927916635078.2551944326
1204528.740307294793965.092021076285092.38859351329



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')