Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 15:20:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/26/t1480173673djtrsexr24t4w6j.htm/, Retrieved Fri, 03 May 2024 17:25:16 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 17:25:16 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
1336
1756
2279
1944
1642
2679
2690
2263
2002
2620
3694
3194
2089
2420
3108
2160
1713
1191
2897
1287
2891
2662
2440
1899
519
1079
955
684
1090
1802
1360
804
1905
1732
964
1424
661
579
378
629
737
877
746
518
1032
1227
1610
1268
935
1224
1313
1642
1431
1124
1915
1503
2035
2200
2205
2297
1818
3525
3458
3958
1987
2375
1728
1618
1614
1820
1969
1632




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.595326670202751
beta0.126604099841145
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.595326670202751 \tabularnewline
beta & 0.126604099841145 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.595326670202751[/C][/ROW]
[ROW][C]beta[/C][C]0.126604099841145[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.595326670202751
beta0.126604099841145
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
322792176103
419442665.08183914171-721.081839141705
516422609.21726795551-967.217267955515
626792333.92177497057345.078225029434
726902865.87960906065-175.879609060647
822633074.44116412105-811.441164121047
920022843.47700748389-841.477007483887
1026202531.2089193576288.7910806423788
1136942779.44648906304914.55351093696
1231943588.21308396873-394.213083968732
1320893588.12386545421-1499.12386545421
1424202817.26162969731-397.261629697314
1531082672.42544405147435.574555948527
1621603056.22845314912-896.228453149116
1717132579.62415849425-866.624158494255
1811912055.32593630803-864.325936308028
1928971467.250972229671429.74902777033
2012872352.66134171975-1065.66134171975
2128911672.16762028931218.8323797107
2226622443.55830723989218.441692760112
2324402635.85386214974-195.853862149737
2418992566.74656215186-667.74656215186
255192166.38036165683-1647.38036165683
2610791058.6476621471920.3523378528146
27955945.2946893535599.70531064644149
28684826.334754306026-142.334754306026
291090606.133429752695483.866570247305
301802795.1958637565651006.80413624344
3113601371.46060801416-11.4606080141616
328041340.66139752569-536.66139752569
331905956.74755247554948.25244752446
3417321528.31306524667203.686934753333
359641671.970917202-707.970917201999
3614241219.53420336999204.465796630011
376611325.70615024492-664.706150244922
38579864.337423710478-285.337423710478
39378607.310908828945-229.310908828945
40629366.355126491538262.644873508462
41737438.069495434891298.930504565109
42877553.916298725615323.083701274385
43746708.49322031296137.5067796870388
44518695.885499970094-177.885499970094
451032541.641639049843490.358360950157
461227822.17987130947404.82012869053
4716101082.3065284019527.693471598103
4812681455.35564121177-187.355641211769
499351388.59580262448-453.595802624475
5012241129.1482180221694.8517819778417
5113131203.35516216467109.644837835326
5216421294.63282582863347.367174171365
5314311553.61427725213-122.614277252131
5411241523.56170031895-399.561700318952
5519151298.51965230956616.480347690438
5615031724.81914878649-221.81914878649
5720351635.33791131658399.662088683422
5822001945.96387977478254.036120225218
5922052189.0417302327615.9582697672377
6022972291.588274242735.41172575726614
6118182388.26406540961-570.264065409614
6235252099.243447484651425.75655251535
6334583105.96754565043352.032454349567
6439583500.00801846067457.991981539333
6519873991.64824452541-2004.64824452541
6623752866.12112861936-491.121128619361
6717282604.62087990514-876.620879905139
6816182047.55073333997-429.550733339973
6916141724.25778727007-110.25778727007
7018201582.73823027997237.261769720032
7119691665.98894271021303.011057289792
7216321811.22014452361-179.220144523614

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2279 & 2176 & 103 \tabularnewline
4 & 1944 & 2665.08183914171 & -721.081839141705 \tabularnewline
5 & 1642 & 2609.21726795551 & -967.217267955515 \tabularnewline
6 & 2679 & 2333.92177497057 & 345.078225029434 \tabularnewline
7 & 2690 & 2865.87960906065 & -175.879609060647 \tabularnewline
8 & 2263 & 3074.44116412105 & -811.441164121047 \tabularnewline
9 & 2002 & 2843.47700748389 & -841.477007483887 \tabularnewline
10 & 2620 & 2531.20891935762 & 88.7910806423788 \tabularnewline
11 & 3694 & 2779.44648906304 & 914.55351093696 \tabularnewline
12 & 3194 & 3588.21308396873 & -394.213083968732 \tabularnewline
13 & 2089 & 3588.12386545421 & -1499.12386545421 \tabularnewline
14 & 2420 & 2817.26162969731 & -397.261629697314 \tabularnewline
15 & 3108 & 2672.42544405147 & 435.574555948527 \tabularnewline
16 & 2160 & 3056.22845314912 & -896.228453149116 \tabularnewline
17 & 1713 & 2579.62415849425 & -866.624158494255 \tabularnewline
18 & 1191 & 2055.32593630803 & -864.325936308028 \tabularnewline
19 & 2897 & 1467.25097222967 & 1429.74902777033 \tabularnewline
20 & 1287 & 2352.66134171975 & -1065.66134171975 \tabularnewline
21 & 2891 & 1672.1676202893 & 1218.8323797107 \tabularnewline
22 & 2662 & 2443.55830723989 & 218.441692760112 \tabularnewline
23 & 2440 & 2635.85386214974 & -195.853862149737 \tabularnewline
24 & 1899 & 2566.74656215186 & -667.74656215186 \tabularnewline
25 & 519 & 2166.38036165683 & -1647.38036165683 \tabularnewline
26 & 1079 & 1058.64766214719 & 20.3523378528146 \tabularnewline
27 & 955 & 945.294689353559 & 9.70531064644149 \tabularnewline
28 & 684 & 826.334754306026 & -142.334754306026 \tabularnewline
29 & 1090 & 606.133429752695 & 483.866570247305 \tabularnewline
30 & 1802 & 795.195863756565 & 1006.80413624344 \tabularnewline
31 & 1360 & 1371.46060801416 & -11.4606080141616 \tabularnewline
32 & 804 & 1340.66139752569 & -536.66139752569 \tabularnewline
33 & 1905 & 956.74755247554 & 948.25244752446 \tabularnewline
34 & 1732 & 1528.31306524667 & 203.686934753333 \tabularnewline
35 & 964 & 1671.970917202 & -707.970917201999 \tabularnewline
36 & 1424 & 1219.53420336999 & 204.465796630011 \tabularnewline
37 & 661 & 1325.70615024492 & -664.706150244922 \tabularnewline
38 & 579 & 864.337423710478 & -285.337423710478 \tabularnewline
39 & 378 & 607.310908828945 & -229.310908828945 \tabularnewline
40 & 629 & 366.355126491538 & 262.644873508462 \tabularnewline
41 & 737 & 438.069495434891 & 298.930504565109 \tabularnewline
42 & 877 & 553.916298725615 & 323.083701274385 \tabularnewline
43 & 746 & 708.493220312961 & 37.5067796870388 \tabularnewline
44 & 518 & 695.885499970094 & -177.885499970094 \tabularnewline
45 & 1032 & 541.641639049843 & 490.358360950157 \tabularnewline
46 & 1227 & 822.17987130947 & 404.82012869053 \tabularnewline
47 & 1610 & 1082.3065284019 & 527.693471598103 \tabularnewline
48 & 1268 & 1455.35564121177 & -187.355641211769 \tabularnewline
49 & 935 & 1388.59580262448 & -453.595802624475 \tabularnewline
50 & 1224 & 1129.14821802216 & 94.8517819778417 \tabularnewline
51 & 1313 & 1203.35516216467 & 109.644837835326 \tabularnewline
52 & 1642 & 1294.63282582863 & 347.367174171365 \tabularnewline
53 & 1431 & 1553.61427725213 & -122.614277252131 \tabularnewline
54 & 1124 & 1523.56170031895 & -399.561700318952 \tabularnewline
55 & 1915 & 1298.51965230956 & 616.480347690438 \tabularnewline
56 & 1503 & 1724.81914878649 & -221.81914878649 \tabularnewline
57 & 2035 & 1635.33791131658 & 399.662088683422 \tabularnewline
58 & 2200 & 1945.96387977478 & 254.036120225218 \tabularnewline
59 & 2205 & 2189.04173023276 & 15.9582697672377 \tabularnewline
60 & 2297 & 2291.58827424273 & 5.41172575726614 \tabularnewline
61 & 1818 & 2388.26406540961 & -570.264065409614 \tabularnewline
62 & 3525 & 2099.24344748465 & 1425.75655251535 \tabularnewline
63 & 3458 & 3105.96754565043 & 352.032454349567 \tabularnewline
64 & 3958 & 3500.00801846067 & 457.991981539333 \tabularnewline
65 & 1987 & 3991.64824452541 & -2004.64824452541 \tabularnewline
66 & 2375 & 2866.12112861936 & -491.121128619361 \tabularnewline
67 & 1728 & 2604.62087990514 & -876.620879905139 \tabularnewline
68 & 1618 & 2047.55073333997 & -429.550733339973 \tabularnewline
69 & 1614 & 1724.25778727007 & -110.25778727007 \tabularnewline
70 & 1820 & 1582.73823027997 & 237.261769720032 \tabularnewline
71 & 1969 & 1665.98894271021 & 303.011057289792 \tabularnewline
72 & 1632 & 1811.22014452361 & -179.220144523614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2279[/C][C]2176[/C][C]103[/C][/ROW]
[ROW][C]4[/C][C]1944[/C][C]2665.08183914171[/C][C]-721.081839141705[/C][/ROW]
[ROW][C]5[/C][C]1642[/C][C]2609.21726795551[/C][C]-967.217267955515[/C][/ROW]
[ROW][C]6[/C][C]2679[/C][C]2333.92177497057[/C][C]345.078225029434[/C][/ROW]
[ROW][C]7[/C][C]2690[/C][C]2865.87960906065[/C][C]-175.879609060647[/C][/ROW]
[ROW][C]8[/C][C]2263[/C][C]3074.44116412105[/C][C]-811.441164121047[/C][/ROW]
[ROW][C]9[/C][C]2002[/C][C]2843.47700748389[/C][C]-841.477007483887[/C][/ROW]
[ROW][C]10[/C][C]2620[/C][C]2531.20891935762[/C][C]88.7910806423788[/C][/ROW]
[ROW][C]11[/C][C]3694[/C][C]2779.44648906304[/C][C]914.55351093696[/C][/ROW]
[ROW][C]12[/C][C]3194[/C][C]3588.21308396873[/C][C]-394.213083968732[/C][/ROW]
[ROW][C]13[/C][C]2089[/C][C]3588.12386545421[/C][C]-1499.12386545421[/C][/ROW]
[ROW][C]14[/C][C]2420[/C][C]2817.26162969731[/C][C]-397.261629697314[/C][/ROW]
[ROW][C]15[/C][C]3108[/C][C]2672.42544405147[/C][C]435.574555948527[/C][/ROW]
[ROW][C]16[/C][C]2160[/C][C]3056.22845314912[/C][C]-896.228453149116[/C][/ROW]
[ROW][C]17[/C][C]1713[/C][C]2579.62415849425[/C][C]-866.624158494255[/C][/ROW]
[ROW][C]18[/C][C]1191[/C][C]2055.32593630803[/C][C]-864.325936308028[/C][/ROW]
[ROW][C]19[/C][C]2897[/C][C]1467.25097222967[/C][C]1429.74902777033[/C][/ROW]
[ROW][C]20[/C][C]1287[/C][C]2352.66134171975[/C][C]-1065.66134171975[/C][/ROW]
[ROW][C]21[/C][C]2891[/C][C]1672.1676202893[/C][C]1218.8323797107[/C][/ROW]
[ROW][C]22[/C][C]2662[/C][C]2443.55830723989[/C][C]218.441692760112[/C][/ROW]
[ROW][C]23[/C][C]2440[/C][C]2635.85386214974[/C][C]-195.853862149737[/C][/ROW]
[ROW][C]24[/C][C]1899[/C][C]2566.74656215186[/C][C]-667.74656215186[/C][/ROW]
[ROW][C]25[/C][C]519[/C][C]2166.38036165683[/C][C]-1647.38036165683[/C][/ROW]
[ROW][C]26[/C][C]1079[/C][C]1058.64766214719[/C][C]20.3523378528146[/C][/ROW]
[ROW][C]27[/C][C]955[/C][C]945.294689353559[/C][C]9.70531064644149[/C][/ROW]
[ROW][C]28[/C][C]684[/C][C]826.334754306026[/C][C]-142.334754306026[/C][/ROW]
[ROW][C]29[/C][C]1090[/C][C]606.133429752695[/C][C]483.866570247305[/C][/ROW]
[ROW][C]30[/C][C]1802[/C][C]795.195863756565[/C][C]1006.80413624344[/C][/ROW]
[ROW][C]31[/C][C]1360[/C][C]1371.46060801416[/C][C]-11.4606080141616[/C][/ROW]
[ROW][C]32[/C][C]804[/C][C]1340.66139752569[/C][C]-536.66139752569[/C][/ROW]
[ROW][C]33[/C][C]1905[/C][C]956.74755247554[/C][C]948.25244752446[/C][/ROW]
[ROW][C]34[/C][C]1732[/C][C]1528.31306524667[/C][C]203.686934753333[/C][/ROW]
[ROW][C]35[/C][C]964[/C][C]1671.970917202[/C][C]-707.970917201999[/C][/ROW]
[ROW][C]36[/C][C]1424[/C][C]1219.53420336999[/C][C]204.465796630011[/C][/ROW]
[ROW][C]37[/C][C]661[/C][C]1325.70615024492[/C][C]-664.706150244922[/C][/ROW]
[ROW][C]38[/C][C]579[/C][C]864.337423710478[/C][C]-285.337423710478[/C][/ROW]
[ROW][C]39[/C][C]378[/C][C]607.310908828945[/C][C]-229.310908828945[/C][/ROW]
[ROW][C]40[/C][C]629[/C][C]366.355126491538[/C][C]262.644873508462[/C][/ROW]
[ROW][C]41[/C][C]737[/C][C]438.069495434891[/C][C]298.930504565109[/C][/ROW]
[ROW][C]42[/C][C]877[/C][C]553.916298725615[/C][C]323.083701274385[/C][/ROW]
[ROW][C]43[/C][C]746[/C][C]708.493220312961[/C][C]37.5067796870388[/C][/ROW]
[ROW][C]44[/C][C]518[/C][C]695.885499970094[/C][C]-177.885499970094[/C][/ROW]
[ROW][C]45[/C][C]1032[/C][C]541.641639049843[/C][C]490.358360950157[/C][/ROW]
[ROW][C]46[/C][C]1227[/C][C]822.17987130947[/C][C]404.82012869053[/C][/ROW]
[ROW][C]47[/C][C]1610[/C][C]1082.3065284019[/C][C]527.693471598103[/C][/ROW]
[ROW][C]48[/C][C]1268[/C][C]1455.35564121177[/C][C]-187.355641211769[/C][/ROW]
[ROW][C]49[/C][C]935[/C][C]1388.59580262448[/C][C]-453.595802624475[/C][/ROW]
[ROW][C]50[/C][C]1224[/C][C]1129.14821802216[/C][C]94.8517819778417[/C][/ROW]
[ROW][C]51[/C][C]1313[/C][C]1203.35516216467[/C][C]109.644837835326[/C][/ROW]
[ROW][C]52[/C][C]1642[/C][C]1294.63282582863[/C][C]347.367174171365[/C][/ROW]
[ROW][C]53[/C][C]1431[/C][C]1553.61427725213[/C][C]-122.614277252131[/C][/ROW]
[ROW][C]54[/C][C]1124[/C][C]1523.56170031895[/C][C]-399.561700318952[/C][/ROW]
[ROW][C]55[/C][C]1915[/C][C]1298.51965230956[/C][C]616.480347690438[/C][/ROW]
[ROW][C]56[/C][C]1503[/C][C]1724.81914878649[/C][C]-221.81914878649[/C][/ROW]
[ROW][C]57[/C][C]2035[/C][C]1635.33791131658[/C][C]399.662088683422[/C][/ROW]
[ROW][C]58[/C][C]2200[/C][C]1945.96387977478[/C][C]254.036120225218[/C][/ROW]
[ROW][C]59[/C][C]2205[/C][C]2189.04173023276[/C][C]15.9582697672377[/C][/ROW]
[ROW][C]60[/C][C]2297[/C][C]2291.58827424273[/C][C]5.41172575726614[/C][/ROW]
[ROW][C]61[/C][C]1818[/C][C]2388.26406540961[/C][C]-570.264065409614[/C][/ROW]
[ROW][C]62[/C][C]3525[/C][C]2099.24344748465[/C][C]1425.75655251535[/C][/ROW]
[ROW][C]63[/C][C]3458[/C][C]3105.96754565043[/C][C]352.032454349567[/C][/ROW]
[ROW][C]64[/C][C]3958[/C][C]3500.00801846067[/C][C]457.991981539333[/C][/ROW]
[ROW][C]65[/C][C]1987[/C][C]3991.64824452541[/C][C]-2004.64824452541[/C][/ROW]
[ROW][C]66[/C][C]2375[/C][C]2866.12112861936[/C][C]-491.121128619361[/C][/ROW]
[ROW][C]67[/C][C]1728[/C][C]2604.62087990514[/C][C]-876.620879905139[/C][/ROW]
[ROW][C]68[/C][C]1618[/C][C]2047.55073333997[/C][C]-429.550733339973[/C][/ROW]
[ROW][C]69[/C][C]1614[/C][C]1724.25778727007[/C][C]-110.25778727007[/C][/ROW]
[ROW][C]70[/C][C]1820[/C][C]1582.73823027997[/C][C]237.261769720032[/C][/ROW]
[ROW][C]71[/C][C]1969[/C][C]1665.98894271021[/C][C]303.011057289792[/C][/ROW]
[ROW][C]72[/C][C]1632[/C][C]1811.22014452361[/C][C]-179.220144523614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
322792176103
419442665.08183914171-721.081839141705
516422609.21726795551-967.217267955515
626792333.92177497057345.078225029434
726902865.87960906065-175.879609060647
822633074.44116412105-811.441164121047
920022843.47700748389-841.477007483887
1026202531.2089193576288.7910806423788
1136942779.44648906304914.55351093696
1231943588.21308396873-394.213083968732
1320893588.12386545421-1499.12386545421
1424202817.26162969731-397.261629697314
1531082672.42544405147435.574555948527
1621603056.22845314912-896.228453149116
1717132579.62415849425-866.624158494255
1811912055.32593630803-864.325936308028
1928971467.250972229671429.74902777033
2012872352.66134171975-1065.66134171975
2128911672.16762028931218.8323797107
2226622443.55830723989218.441692760112
2324402635.85386214974-195.853862149737
2418992566.74656215186-667.74656215186
255192166.38036165683-1647.38036165683
2610791058.6476621471920.3523378528146
27955945.2946893535599.70531064644149
28684826.334754306026-142.334754306026
291090606.133429752695483.866570247305
301802795.1958637565651006.80413624344
3113601371.46060801416-11.4606080141616
328041340.66139752569-536.66139752569
331905956.74755247554948.25244752446
3417321528.31306524667203.686934753333
359641671.970917202-707.970917201999
3614241219.53420336999204.465796630011
376611325.70615024492-664.706150244922
38579864.337423710478-285.337423710478
39378607.310908828945-229.310908828945
40629366.355126491538262.644873508462
41737438.069495434891298.930504565109
42877553.916298725615323.083701274385
43746708.49322031296137.5067796870388
44518695.885499970094-177.885499970094
451032541.641639049843490.358360950157
461227822.17987130947404.82012869053
4716101082.3065284019527.693471598103
4812681455.35564121177-187.355641211769
499351388.59580262448-453.595802624475
5012241129.1482180221694.8517819778417
5113131203.35516216467109.644837835326
5216421294.63282582863347.367174171365
5314311553.61427725213-122.614277252131
5411241523.56170031895-399.561700318952
5519151298.51965230956616.480347690438
5615031724.81914878649-221.81914878649
5720351635.33791131658399.662088683422
5822001945.96387977478254.036120225218
5922052189.0417302327615.9582697672377
6022972291.588274242735.41172575726614
6118182388.26406540961-570.264065409614
6235252099.243447484651425.75655251535
6334583105.96754565043352.032454349567
6439583500.00801846067457.991981539333
6519873991.64824452541-2004.64824452541
6623752866.12112861936-491.121128619361
6717282604.62087990514-876.620879905139
6816182047.55073333997-429.550733339973
6916141724.25778727007-110.25778727007
7018201582.73823027997237.261769720032
7119691665.98894271021303.011057289792
7216321811.22014452361-179.220144523614







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731655.85828552788360.483873247392951.23269780838
741607.1909584046547.44231035205033166.93960645726
751558.52363128142-276.3653980434963393.41266060634
761509.85630415819-611.2436804992243630.95628881561
771461.18897703496-957.203586725063879.58154079498
781412.52164991173-1314.116326601244139.1596264247
791363.8543227885-1681.786150883714409.49479646071
801315.18699566527-2059.987203482084690.36119481261
811266.51966854204-2448.482909726154981.52224681022
821217.85234141881-2847.036378230965282.74106106857
831169.18501429557-3255.415970742235593.78599933338
841120.51768717234-3673.398190264555914.43356460924

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1655.85828552788 & 360.48387324739 & 2951.23269780838 \tabularnewline
74 & 1607.19095840465 & 47.4423103520503 & 3166.93960645726 \tabularnewline
75 & 1558.52363128142 & -276.365398043496 & 3393.41266060634 \tabularnewline
76 & 1509.85630415819 & -611.243680499224 & 3630.95628881561 \tabularnewline
77 & 1461.18897703496 & -957.20358672506 & 3879.58154079498 \tabularnewline
78 & 1412.52164991173 & -1314.11632660124 & 4139.1596264247 \tabularnewline
79 & 1363.8543227885 & -1681.78615088371 & 4409.49479646071 \tabularnewline
80 & 1315.18699566527 & -2059.98720348208 & 4690.36119481261 \tabularnewline
81 & 1266.51966854204 & -2448.48290972615 & 4981.52224681022 \tabularnewline
82 & 1217.85234141881 & -2847.03637823096 & 5282.74106106857 \tabularnewline
83 & 1169.18501429557 & -3255.41597074223 & 5593.78599933338 \tabularnewline
84 & 1120.51768717234 & -3673.39819026455 & 5914.43356460924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]1655.85828552788[/C][C]360.48387324739[/C][C]2951.23269780838[/C][/ROW]
[ROW][C]74[/C][C]1607.19095840465[/C][C]47.4423103520503[/C][C]3166.93960645726[/C][/ROW]
[ROW][C]75[/C][C]1558.52363128142[/C][C]-276.365398043496[/C][C]3393.41266060634[/C][/ROW]
[ROW][C]76[/C][C]1509.85630415819[/C][C]-611.243680499224[/C][C]3630.95628881561[/C][/ROW]
[ROW][C]77[/C][C]1461.18897703496[/C][C]-957.20358672506[/C][C]3879.58154079498[/C][/ROW]
[ROW][C]78[/C][C]1412.52164991173[/C][C]-1314.11632660124[/C][C]4139.1596264247[/C][/ROW]
[ROW][C]79[/C][C]1363.8543227885[/C][C]-1681.78615088371[/C][C]4409.49479646071[/C][/ROW]
[ROW][C]80[/C][C]1315.18699566527[/C][C]-2059.98720348208[/C][C]4690.36119481261[/C][/ROW]
[ROW][C]81[/C][C]1266.51966854204[/C][C]-2448.48290972615[/C][C]4981.52224681022[/C][/ROW]
[ROW][C]82[/C][C]1217.85234141881[/C][C]-2847.03637823096[/C][C]5282.74106106857[/C][/ROW]
[ROW][C]83[/C][C]1169.18501429557[/C][C]-3255.41597074223[/C][C]5593.78599933338[/C][/ROW]
[ROW][C]84[/C][C]1120.51768717234[/C][C]-3673.39819026455[/C][C]5914.43356460924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731655.85828552788360.483873247392951.23269780838
741607.1909584046547.44231035205033166.93960645726
751558.52363128142-276.3653980434963393.41266060634
761509.85630415819-611.2436804992243630.95628881561
771461.18897703496-957.203586725063879.58154079498
781412.52164991173-1314.116326601244139.1596264247
791363.8543227885-1681.786150883714409.49479646071
801315.18699566527-2059.987203482084690.36119481261
811266.51966854204-2448.482909726154981.52224681022
821217.85234141881-2847.036378230965282.74106106857
831169.18501429557-3255.415970742235593.78599933338
841120.51768717234-3673.398190264555914.43356460924



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