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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 12:02:28 -0400
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/May/26/t1369584168t47ezjv9hq8x7gh.htm/, Retrieved Mon, 29 Apr 2024 13:54:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210629, Retrieved Mon, 29 Apr 2024 13:54:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-26 16:02:28] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210629&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210629&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.401139133991933
beta0.538290779234139
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.401139133991933 \tabularnewline
beta & 0.538290779234139 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210629&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]0.401139133991933[/C][/ROW]
[ROW][C]beta[/C][C]0.538290779234139[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210629&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
alpha0.401139133991933
beta0.538290779234139
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
350.66910.20640.463
436.4325.8244480165478430.6075519834522
540.8914.0985634553689536.7924365446311
648.42812.798250448043935.6297495519561
736.22228.72505208699857.49694791300154
833.42534.9854982317592-1.56049823175924
939.40137.27569067555112.12530932444889
1037.96741.5033217439368-3.5363217439368
1134.80142.6962548531069-7.89525485310694
1212.65740.4358309004769-27.7788309004769
1369.11624.201057487458944.9149425125411
1441.51946.8250623332623-5.30606233326232
1551.32148.15772141624893.1632785837511
1638.52953.5708097336853-15.0418097336853
1741.54748.4331542791861-6.88615427918615
1852.07345.08012756094956.99287243905047
1938.40148.8044890295913-10.4034890295912
2040.89843.3040689707013-2.40606897070128
2140.43940.4921858057704-0.0531858057704397
2241.88838.61265177171563.27534822828435
2337.89838.7755672930359-0.877567293035931
248.77137.0830932144076-28.3120932144076
2568.18418.272141118892249.9118588811078
2650.5341.61732000782068.91267999217943
2747.22150.440634290656-3.21963429065601
2841.75653.7019885157942-11.9459885157942
2945.63350.8833692725574-5.25036927255743
3048.13849.6169153379112-1.47891533791122
3139.48649.5439977234523-10.0579977234524
3239.34143.8578560409806-4.51685604098056
3341.11739.41916068131121.69783931868875
3441.62937.84003642634493.78896357365509
3529.72237.9178929427635-8.19589294276351
367.05431.4184194544255-24.3644194544255
3756.67613.172120405348443.5038795946516
3834.8731.54422290152083.32577709847925
3935.11734.51744953300740.599550466992561
4030.16936.5265406052483-6.35754060524831
4130.93634.3720896445058-3.43608964450581
4235.69932.64759388350923.05140611649085
4333.22834.184375141786-0.956375141786012
4427.73333.9069688935624-6.17396889356239
4533.66630.20343960843883.46256039156115
4635.42931.11316825918134.3158317408187
4727.43833.2970928170336-5.85909281703361
488.1730.134305984353-21.964305984353
4963.4115.768346345431447.6416536545686
5038.0439.6112993874727-1.57129938747273
5145.38943.37372117864252.01527882135748
5237.35349.0100179887432-11.6570179887432
5337.02446.6447274657224-9.62072746572236
5450.95743.01887391704317.93812608295693
5537.99448.1506392471292-10.1566392471292
5636.45443.8307680788931-7.37676807889314
5746.0839.03315020279997.04684979720008
5843.37341.54303264282291.82996735717713
5937.39542.3553633097116-4.96036330971159
6010.96339.372737858874-28.409737858874
6176.05820.84915020245855.208849797542
6250.17947.78946955188122.38953044811883
6357.45254.05786298720453.39413701279554
6447.56861.4621377278673-13.8941377278673
6550.0558.9312547397712-8.88125473977125
6650.85656.493510423477-5.63751042347695
6741.99254.1396541029381-12.1476541029381
6839.28446.5512875442632-7.26728754426318
6944.52139.35140525638175.16959474361833
7043.83238.2567111517965.57528884820395
7141.15338.52862614571132.62437385428868
7217.138.1834933808269-21.0834933808269

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 50.669 & 10.206 & 40.463 \tabularnewline
4 & 36.432 & 5.82444801654784 & 30.6075519834522 \tabularnewline
5 & 40.891 & 4.09856345536895 & 36.7924365446311 \tabularnewline
6 & 48.428 & 12.7982504480439 & 35.6297495519561 \tabularnewline
7 & 36.222 & 28.7250520869985 & 7.49694791300154 \tabularnewline
8 & 33.425 & 34.9854982317592 & -1.56049823175924 \tabularnewline
9 & 39.401 & 37.2756906755511 & 2.12530932444889 \tabularnewline
10 & 37.967 & 41.5033217439368 & -3.5363217439368 \tabularnewline
11 & 34.801 & 42.6962548531069 & -7.89525485310694 \tabularnewline
12 & 12.657 & 40.4358309004769 & -27.7788309004769 \tabularnewline
13 & 69.116 & 24.2010574874589 & 44.9149425125411 \tabularnewline
14 & 41.519 & 46.8250623332623 & -5.30606233326232 \tabularnewline
15 & 51.321 & 48.1577214162489 & 3.1632785837511 \tabularnewline
16 & 38.529 & 53.5708097336853 & -15.0418097336853 \tabularnewline
17 & 41.547 & 48.4331542791861 & -6.88615427918615 \tabularnewline
18 & 52.073 & 45.0801275609495 & 6.99287243905047 \tabularnewline
19 & 38.401 & 48.8044890295913 & -10.4034890295912 \tabularnewline
20 & 40.898 & 43.3040689707013 & -2.40606897070128 \tabularnewline
21 & 40.439 & 40.4921858057704 & -0.0531858057704397 \tabularnewline
22 & 41.888 & 38.6126517717156 & 3.27534822828435 \tabularnewline
23 & 37.898 & 38.7755672930359 & -0.877567293035931 \tabularnewline
24 & 8.771 & 37.0830932144076 & -28.3120932144076 \tabularnewline
25 & 68.184 & 18.2721411188922 & 49.9118588811078 \tabularnewline
26 & 50.53 & 41.6173200078206 & 8.91267999217943 \tabularnewline
27 & 47.221 & 50.440634290656 & -3.21963429065601 \tabularnewline
28 & 41.756 & 53.7019885157942 & -11.9459885157942 \tabularnewline
29 & 45.633 & 50.8833692725574 & -5.25036927255743 \tabularnewline
30 & 48.138 & 49.6169153379112 & -1.47891533791122 \tabularnewline
31 & 39.486 & 49.5439977234523 & -10.0579977234524 \tabularnewline
32 & 39.341 & 43.8578560409806 & -4.51685604098056 \tabularnewline
33 & 41.117 & 39.4191606813112 & 1.69783931868875 \tabularnewline
34 & 41.629 & 37.8400364263449 & 3.78896357365509 \tabularnewline
35 & 29.722 & 37.9178929427635 & -8.19589294276351 \tabularnewline
36 & 7.054 & 31.4184194544255 & -24.3644194544255 \tabularnewline
37 & 56.676 & 13.1721204053484 & 43.5038795946516 \tabularnewline
38 & 34.87 & 31.5442229015208 & 3.32577709847925 \tabularnewline
39 & 35.117 & 34.5174495330074 & 0.599550466992561 \tabularnewline
40 & 30.169 & 36.5265406052483 & -6.35754060524831 \tabularnewline
41 & 30.936 & 34.3720896445058 & -3.43608964450581 \tabularnewline
42 & 35.699 & 32.6475938835092 & 3.05140611649085 \tabularnewline
43 & 33.228 & 34.184375141786 & -0.956375141786012 \tabularnewline
44 & 27.733 & 33.9069688935624 & -6.17396889356239 \tabularnewline
45 & 33.666 & 30.2034396084388 & 3.46256039156115 \tabularnewline
46 & 35.429 & 31.1131682591813 & 4.3158317408187 \tabularnewline
47 & 27.438 & 33.2970928170336 & -5.85909281703361 \tabularnewline
48 & 8.17 & 30.134305984353 & -21.964305984353 \tabularnewline
49 & 63.41 & 15.7683463454314 & 47.6416536545686 \tabularnewline
50 & 38.04 & 39.6112993874727 & -1.57129938747273 \tabularnewline
51 & 45.389 & 43.3737211786425 & 2.01527882135748 \tabularnewline
52 & 37.353 & 49.0100179887432 & -11.6570179887432 \tabularnewline
53 & 37.024 & 46.6447274657224 & -9.62072746572236 \tabularnewline
54 & 50.957 & 43.0188739170431 & 7.93812608295693 \tabularnewline
55 & 37.994 & 48.1506392471292 & -10.1566392471292 \tabularnewline
56 & 36.454 & 43.8307680788931 & -7.37676807889314 \tabularnewline
57 & 46.08 & 39.0331502027999 & 7.04684979720008 \tabularnewline
58 & 43.373 & 41.5430326428229 & 1.82996735717713 \tabularnewline
59 & 37.395 & 42.3553633097116 & -4.96036330971159 \tabularnewline
60 & 10.963 & 39.372737858874 & -28.409737858874 \tabularnewline
61 & 76.058 & 20.849150202458 & 55.208849797542 \tabularnewline
62 & 50.179 & 47.7894695518812 & 2.38953044811883 \tabularnewline
63 & 57.452 & 54.0578629872045 & 3.39413701279554 \tabularnewline
64 & 47.568 & 61.4621377278673 & -13.8941377278673 \tabularnewline
65 & 50.05 & 58.9312547397712 & -8.88125473977125 \tabularnewline
66 & 50.856 & 56.493510423477 & -5.63751042347695 \tabularnewline
67 & 41.992 & 54.1396541029381 & -12.1476541029381 \tabularnewline
68 & 39.284 & 46.5512875442632 & -7.26728754426318 \tabularnewline
69 & 44.521 & 39.3514052563817 & 5.16959474361833 \tabularnewline
70 & 43.832 & 38.256711151796 & 5.57528884820395 \tabularnewline
71 & 41.153 & 38.5286261457113 & 2.62437385428868 \tabularnewline
72 & 17.1 & 38.1834933808269 & -21.0834933808269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210629&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]50.669[/C][C]10.206[/C][C]40.463[/C][/ROW]
[ROW][C]4[/C][C]36.432[/C][C]5.82444801654784[/C][C]30.6075519834522[/C][/ROW]
[ROW][C]5[/C][C]40.891[/C][C]4.09856345536895[/C][C]36.7924365446311[/C][/ROW]
[ROW][C]6[/C][C]48.428[/C][C]12.7982504480439[/C][C]35.6297495519561[/C][/ROW]
[ROW][C]7[/C][C]36.222[/C][C]28.7250520869985[/C][C]7.49694791300154[/C][/ROW]
[ROW][C]8[/C][C]33.425[/C][C]34.9854982317592[/C][C]-1.56049823175924[/C][/ROW]
[ROW][C]9[/C][C]39.401[/C][C]37.2756906755511[/C][C]2.12530932444889[/C][/ROW]
[ROW][C]10[/C][C]37.967[/C][C]41.5033217439368[/C][C]-3.5363217439368[/C][/ROW]
[ROW][C]11[/C][C]34.801[/C][C]42.6962548531069[/C][C]-7.89525485310694[/C][/ROW]
[ROW][C]12[/C][C]12.657[/C][C]40.4358309004769[/C][C]-27.7788309004769[/C][/ROW]
[ROW][C]13[/C][C]69.116[/C][C]24.2010574874589[/C][C]44.9149425125411[/C][/ROW]
[ROW][C]14[/C][C]41.519[/C][C]46.8250623332623[/C][C]-5.30606233326232[/C][/ROW]
[ROW][C]15[/C][C]51.321[/C][C]48.1577214162489[/C][C]3.1632785837511[/C][/ROW]
[ROW][C]16[/C][C]38.529[/C][C]53.5708097336853[/C][C]-15.0418097336853[/C][/ROW]
[ROW][C]17[/C][C]41.547[/C][C]48.4331542791861[/C][C]-6.88615427918615[/C][/ROW]
[ROW][C]18[/C][C]52.073[/C][C]45.0801275609495[/C][C]6.99287243905047[/C][/ROW]
[ROW][C]19[/C][C]38.401[/C][C]48.8044890295913[/C][C]-10.4034890295912[/C][/ROW]
[ROW][C]20[/C][C]40.898[/C][C]43.3040689707013[/C][C]-2.40606897070128[/C][/ROW]
[ROW][C]21[/C][C]40.439[/C][C]40.4921858057704[/C][C]-0.0531858057704397[/C][/ROW]
[ROW][C]22[/C][C]41.888[/C][C]38.6126517717156[/C][C]3.27534822828435[/C][/ROW]
[ROW][C]23[/C][C]37.898[/C][C]38.7755672930359[/C][C]-0.877567293035931[/C][/ROW]
[ROW][C]24[/C][C]8.771[/C][C]37.0830932144076[/C][C]-28.3120932144076[/C][/ROW]
[ROW][C]25[/C][C]68.184[/C][C]18.2721411188922[/C][C]49.9118588811078[/C][/ROW]
[ROW][C]26[/C][C]50.53[/C][C]41.6173200078206[/C][C]8.91267999217943[/C][/ROW]
[ROW][C]27[/C][C]47.221[/C][C]50.440634290656[/C][C]-3.21963429065601[/C][/ROW]
[ROW][C]28[/C][C]41.756[/C][C]53.7019885157942[/C][C]-11.9459885157942[/C][/ROW]
[ROW][C]29[/C][C]45.633[/C][C]50.8833692725574[/C][C]-5.25036927255743[/C][/ROW]
[ROW][C]30[/C][C]48.138[/C][C]49.6169153379112[/C][C]-1.47891533791122[/C][/ROW]
[ROW][C]31[/C][C]39.486[/C][C]49.5439977234523[/C][C]-10.0579977234524[/C][/ROW]
[ROW][C]32[/C][C]39.341[/C][C]43.8578560409806[/C][C]-4.51685604098056[/C][/ROW]
[ROW][C]33[/C][C]41.117[/C][C]39.4191606813112[/C][C]1.69783931868875[/C][/ROW]
[ROW][C]34[/C][C]41.629[/C][C]37.8400364263449[/C][C]3.78896357365509[/C][/ROW]
[ROW][C]35[/C][C]29.722[/C][C]37.9178929427635[/C][C]-8.19589294276351[/C][/ROW]
[ROW][C]36[/C][C]7.054[/C][C]31.4184194544255[/C][C]-24.3644194544255[/C][/ROW]
[ROW][C]37[/C][C]56.676[/C][C]13.1721204053484[/C][C]43.5038795946516[/C][/ROW]
[ROW][C]38[/C][C]34.87[/C][C]31.5442229015208[/C][C]3.32577709847925[/C][/ROW]
[ROW][C]39[/C][C]35.117[/C][C]34.5174495330074[/C][C]0.599550466992561[/C][/ROW]
[ROW][C]40[/C][C]30.169[/C][C]36.5265406052483[/C][C]-6.35754060524831[/C][/ROW]
[ROW][C]41[/C][C]30.936[/C][C]34.3720896445058[/C][C]-3.43608964450581[/C][/ROW]
[ROW][C]42[/C][C]35.699[/C][C]32.6475938835092[/C][C]3.05140611649085[/C][/ROW]
[ROW][C]43[/C][C]33.228[/C][C]34.184375141786[/C][C]-0.956375141786012[/C][/ROW]
[ROW][C]44[/C][C]27.733[/C][C]33.9069688935624[/C][C]-6.17396889356239[/C][/ROW]
[ROW][C]45[/C][C]33.666[/C][C]30.2034396084388[/C][C]3.46256039156115[/C][/ROW]
[ROW][C]46[/C][C]35.429[/C][C]31.1131682591813[/C][C]4.3158317408187[/C][/ROW]
[ROW][C]47[/C][C]27.438[/C][C]33.2970928170336[/C][C]-5.85909281703361[/C][/ROW]
[ROW][C]48[/C][C]8.17[/C][C]30.134305984353[/C][C]-21.964305984353[/C][/ROW]
[ROW][C]49[/C][C]63.41[/C][C]15.7683463454314[/C][C]47.6416536545686[/C][/ROW]
[ROW][C]50[/C][C]38.04[/C][C]39.6112993874727[/C][C]-1.57129938747273[/C][/ROW]
[ROW][C]51[/C][C]45.389[/C][C]43.3737211786425[/C][C]2.01527882135748[/C][/ROW]
[ROW][C]52[/C][C]37.353[/C][C]49.0100179887432[/C][C]-11.6570179887432[/C][/ROW]
[ROW][C]53[/C][C]37.024[/C][C]46.6447274657224[/C][C]-9.62072746572236[/C][/ROW]
[ROW][C]54[/C][C]50.957[/C][C]43.0188739170431[/C][C]7.93812608295693[/C][/ROW]
[ROW][C]55[/C][C]37.994[/C][C]48.1506392471292[/C][C]-10.1566392471292[/C][/ROW]
[ROW][C]56[/C][C]36.454[/C][C]43.8307680788931[/C][C]-7.37676807889314[/C][/ROW]
[ROW][C]57[/C][C]46.08[/C][C]39.0331502027999[/C][C]7.04684979720008[/C][/ROW]
[ROW][C]58[/C][C]43.373[/C][C]41.5430326428229[/C][C]1.82996735717713[/C][/ROW]
[ROW][C]59[/C][C]37.395[/C][C]42.3553633097116[/C][C]-4.96036330971159[/C][/ROW]
[ROW][C]60[/C][C]10.963[/C][C]39.372737858874[/C][C]-28.409737858874[/C][/ROW]
[ROW][C]61[/C][C]76.058[/C][C]20.849150202458[/C][C]55.208849797542[/C][/ROW]
[ROW][C]62[/C][C]50.179[/C][C]47.7894695518812[/C][C]2.38953044811883[/C][/ROW]
[ROW][C]63[/C][C]57.452[/C][C]54.0578629872045[/C][C]3.39413701279554[/C][/ROW]
[ROW][C]64[/C][C]47.568[/C][C]61.4621377278673[/C][C]-13.8941377278673[/C][/ROW]
[ROW][C]65[/C][C]50.05[/C][C]58.9312547397712[/C][C]-8.88125473977125[/C][/ROW]
[ROW][C]66[/C][C]50.856[/C][C]56.493510423477[/C][C]-5.63751042347695[/C][/ROW]
[ROW][C]67[/C][C]41.992[/C][C]54.1396541029381[/C][C]-12.1476541029381[/C][/ROW]
[ROW][C]68[/C][C]39.284[/C][C]46.5512875442632[/C][C]-7.26728754426318[/C][/ROW]
[ROW][C]69[/C][C]44.521[/C][C]39.3514052563817[/C][C]5.16959474361833[/C][/ROW]
[ROW][C]70[/C][C]43.832[/C][C]38.256711151796[/C][C]5.57528884820395[/C][/ROW]
[ROW][C]71[/C][C]41.153[/C][C]38.5286261457113[/C][C]2.62437385428868[/C][/ROW]
[ROW][C]72[/C][C]17.1[/C][C]38.1834933808269[/C][C]-21.0834933808269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210629&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
350.66910.20640.463
436.4325.8244480165478430.6075519834522
540.8914.0985634553689536.7924365446311
648.42812.798250448043935.6297495519561
736.22228.72505208699857.49694791300154
833.42534.9854982317592-1.56049823175924
939.40137.27569067555112.12530932444889
1037.96741.5033217439368-3.5363217439368
1134.80142.6962548531069-7.89525485310694
1212.65740.4358309004769-27.7788309004769
1369.11624.201057487458944.9149425125411
1441.51946.8250623332623-5.30606233326232
1551.32148.15772141624893.1632785837511
1638.52953.5708097336853-15.0418097336853
1741.54748.4331542791861-6.88615427918615
1852.07345.08012756094956.99287243905047
1938.40148.8044890295913-10.4034890295912
2040.89843.3040689707013-2.40606897070128
2140.43940.4921858057704-0.0531858057704397
2241.88838.61265177171563.27534822828435
2337.89838.7755672930359-0.877567293035931
248.77137.0830932144076-28.3120932144076
2568.18418.272141118892249.9118588811078
2650.5341.61732000782068.91267999217943
2747.22150.440634290656-3.21963429065601
2841.75653.7019885157942-11.9459885157942
2945.63350.8833692725574-5.25036927255743
3048.13849.6169153379112-1.47891533791122
3139.48649.5439977234523-10.0579977234524
3239.34143.8578560409806-4.51685604098056
3341.11739.41916068131121.69783931868875
3441.62937.84003642634493.78896357365509
3529.72237.9178929427635-8.19589294276351
367.05431.4184194544255-24.3644194544255
3756.67613.172120405348443.5038795946516
3834.8731.54422290152083.32577709847925
3935.11734.51744953300740.599550466992561
4030.16936.5265406052483-6.35754060524831
4130.93634.3720896445058-3.43608964450581
4235.69932.64759388350923.05140611649085
4333.22834.184375141786-0.956375141786012
4427.73333.9069688935624-6.17396889356239
4533.66630.20343960843883.46256039156115
4635.42931.11316825918134.3158317408187
4727.43833.2970928170336-5.85909281703361
488.1730.134305984353-21.964305984353
4963.4115.768346345431447.6416536545686
5038.0439.6112993874727-1.57129938747273
5145.38943.37372117864252.01527882135748
5237.35349.0100179887432-11.6570179887432
5337.02446.6447274657224-9.62072746572236
5450.95743.01887391704317.93812608295693
5537.99448.1506392471292-10.1566392471292
5636.45443.8307680788931-7.37676807889314
5746.0839.03315020279997.04684979720008
5843.37341.54303264282291.82996735717713
5937.39542.3553633097116-4.96036330971159
6010.96339.372737858874-28.409737858874
6176.05820.84915020245855.208849797542
6250.17947.78946955188122.38953044811883
6357.45254.05786298720453.39413701279554
6447.56861.4621377278673-13.8941377278673
6550.0558.9312547397712-8.88125473977125
6650.85656.493510423477-5.63751042347695
6741.99254.1396541029381-12.1476541029381
6839.28446.5512875442632-7.26728754426318
6944.52139.35140525638175.16959474361833
7043.83238.2567111517965.57528884820395
7141.15338.52862614571132.62437385428868
7217.138.1834933808269-21.0834933808269







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7323.7756591633519-12.037685137583459.5890034642871
7417.8252392221864-24.257706346445959.9081847908187
7511.8748192810209-39.7095708657663.4592094278019
765.92439933985547-57.888797372697869.7375960524087
77-0.0260206013099911-78.282662867131278.2306216645112
78-5.97644054247546-100.50943322948288.5565521445307
79-11.9268604836409-124.305156720088100.451435752806
80-17.8772804248064-149.486131882698113.731571033085
81-23.8277003659719-175.920156145167128.264755413224
82-29.7781203071373-203.508258397969143.952017783694
83-35.7285402483028-232.173521242507160.716440745901
84-41.6789601894682-261.854180372433178.496259993497

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 23.7756591633519 & -12.0376851375834 & 59.5890034642871 \tabularnewline
74 & 17.8252392221864 & -24.2577063464459 & 59.9081847908187 \tabularnewline
75 & 11.8748192810209 & -39.70957086576 & 63.4592094278019 \tabularnewline
76 & 5.92439933985547 & -57.8887973726978 & 69.7375960524087 \tabularnewline
77 & -0.0260206013099911 & -78.2826628671312 & 78.2306216645112 \tabularnewline
78 & -5.97644054247546 & -100.509433229482 & 88.5565521445307 \tabularnewline
79 & -11.9268604836409 & -124.305156720088 & 100.451435752806 \tabularnewline
80 & -17.8772804248064 & -149.486131882698 & 113.731571033085 \tabularnewline
81 & -23.8277003659719 & -175.920156145167 & 128.264755413224 \tabularnewline
82 & -29.7781203071373 & -203.508258397969 & 143.952017783694 \tabularnewline
83 & -35.7285402483028 & -232.173521242507 & 160.716440745901 \tabularnewline
84 & -41.6789601894682 & -261.854180372433 & 178.496259993497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210629&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]23.7756591633519[/C][C]-12.0376851375834[/C][C]59.5890034642871[/C][/ROW]
[ROW][C]74[/C][C]17.8252392221864[/C][C]-24.2577063464459[/C][C]59.9081847908187[/C][/ROW]
[ROW][C]75[/C][C]11.8748192810209[/C][C]-39.70957086576[/C][C]63.4592094278019[/C][/ROW]
[ROW][C]76[/C][C]5.92439933985547[/C][C]-57.8887973726978[/C][C]69.7375960524087[/C][/ROW]
[ROW][C]77[/C][C]-0.0260206013099911[/C][C]-78.2826628671312[/C][C]78.2306216645112[/C][/ROW]
[ROW][C]78[/C][C]-5.97644054247546[/C][C]-100.509433229482[/C][C]88.5565521445307[/C][/ROW]
[ROW][C]79[/C][C]-11.9268604836409[/C][C]-124.305156720088[/C][C]100.451435752806[/C][/ROW]
[ROW][C]80[/C][C]-17.8772804248064[/C][C]-149.486131882698[/C][C]113.731571033085[/C][/ROW]
[ROW][C]81[/C][C]-23.8277003659719[/C][C]-175.920156145167[/C][C]128.264755413224[/C][/ROW]
[ROW][C]82[/C][C]-29.7781203071373[/C][C]-203.508258397969[/C][C]143.952017783694[/C][/ROW]
[ROW][C]83[/C][C]-35.7285402483028[/C][C]-232.173521242507[/C][C]160.716440745901[/C][/ROW]
[ROW][C]84[/C][C]-41.6789601894682[/C][C]-261.854180372433[/C][C]178.496259993497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210629&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210629&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
7323.7756591633519-12.037685137583459.5890034642871
7417.8252392221864-24.257706346445959.9081847908187
7511.8748192810209-39.7095708657663.4592094278019
765.92439933985547-57.888797372697869.7375960524087
77-0.0260206013099911-78.282662867131278.2306216645112
78-5.97644054247546-100.50943322948288.5565521445307
79-11.9268604836409-124.305156720088100.451435752806
80-17.8772804248064-149.486131882698113.731571033085
81-23.8277003659719-175.920156145167128.264755413224
82-29.7781203071373-203.508258397969143.952017783694
83-35.7285402483028-232.173521242507160.716440745901
84-41.6789601894682-261.854180372433178.496259993497



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')