Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Jun 2010 14:36:17 +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/2010/Jun/03/t127557584429418ylkqys8ohc.htm/, Retrieved Sun, 05 May 2024 19:44:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77387, Retrieved Sun, 05 May 2024 19:44:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Jeroen De Laet op...] [2010-06-03 14:36:17] [9646448ed4269a7a4a2c0c7243faa64c] [Current]
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Dataseries X:
15136
16733
20016
17708
18019
19227
22893
23739
21133
22591
26786
29740
15028
17977
20008
21354
19498
22125
25817
28779
20960
22254
27392
29945
16933
17892
20533
23569
22417
22084
26580
27454
24081
23451
28991
31386
16896
20045
23471
21747
25621
23859
25500
30998
24475
23145
29701
34365
17556
22077
25702
22214
26886
23191
27831
35406
23195
25110
30009
36242
18450
21845
26488
22394
28057
25451
24872
33424
24052
28449
33533
37351
19969
21701
26249
24493
24603
26485
30723
34569
26689
26157
32064
38870
21337
19419
23166
28286
24570
24001
33151
24878
26804
28967
33311
40226
20504
23060
23562
27562
23940
24584
34303
25517
23494
29095
32903
34379
16991
21109
23740
25552
21752
20294
29009
25500
24166
26960
31222
38641
14672
17543
25453
32683
22449
22316
27595
25451
25421
25288
32568
35110
16052
22146
21198
19543
22084
23816
29961
26773
26635
26972
30207
38687
16974
21697
24179
23757
25013
24019
30345
24488
25156
25650
30923
37240
17466
19463
24352
26805
25236
24735
29356
31234
22724
28496
32857
37198
13652
22784
23565
26323
23779
27549
29660
23356




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77387&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77387&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77387&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0694442869754801
beta0.095535532556981
gamma0.274990418870521

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0694442869754801 \tabularnewline
beta & 0.095535532556981 \tabularnewline
gamma & 0.274990418870521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77387&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]0.0694442869754801[/C][/ROW]
[ROW][C]beta[/C][C]0.095535532556981[/C][/ROW]
[ROW][C]gamma[/C][C]0.274990418870521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77387&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77387&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
alpha0.0694442869754801
beta0.095535532556981
gamma0.274990418870521







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131502814321.6838979972706.316102002796
141797717069.4177170777907.582282922289
152000819050.8472294842957.152770515797
162135420594.1469296704759.853070329562
171949819004.1326734229493.867326577136
182212521757.4677963716367.532203628394
192581724290.91398071891526.08601928110
202877925468.28637819143310.71362180858
212096023042.1560743632-2082.15607436320
222225424523.2253877757-2269.22538777566
232739228844.4884130028-1452.48841300276
242994531899.8472081405-1954.84720814051
251693316195.4055778487737.594422151315
261789219314.1959907242-1422.19599072425
272053321332.7820221934-799.782022193409
282356922812.3942319425756.60576805746
292241720958.63512177141458.36487822863
302208423985.7996975873-1901.79969758735
312658026864.8500198210-284.850019821031
322745428432.5724659408-978.572465940793
332408123975.6939369364105.306063063606
342345125609.0510861706-2158.05108617062
352899130404.3276855657-1413.32768556568
363138633461.1562610029-2075.15626100286
371689617419.7937823049-523.793782304892
382004519987.122828907957.8771710920773
392347122355.33418635311115.66581364689
402174724450.3158901976-2703.31589019757
412562122387.29066525703233.70933474305
422385924738.7662104173-879.766210417307
432550028245.7602996728-2745.76029967275
443099829465.55622944831532.44377055173
452447525204.5757707592-729.575770759151
462314526197.9615570337-3052.96155703366
472970131277.9213466602-1576.92134666025
483436534202.1819789929162.818021007057
491755618008.2929235411-452.292923541081
502207720811.9988862381265.00111376199
512570223622.38909238312079.61090761694
522221424825.295149348-2611.29514934800
532688624240.36888833812645.63111166187
542319125513.8403421907-2322.84034219074
552783128509.5516194940-678.551619493963
563540631036.42468151164369.57531848839
572319526154.5448188867-2959.54481888669
582511026383.8234382992-1273.82343829916
593000932191.5934576834-2182.59345768342
603624235640.0809205167601.919079483254
611845018627.0347185142-177.034718514227
622184522015.8591144154-170.859114415376
632648825017.01825781411470.98174218589
642239424940.7459548851-2546.74595488509
652805725704.23187220622352.76812779382
662545125647.1201444505-196.120144450495
672487229319.6525240786-4447.65252407861
683342432916.9056485469507.094351453132
692405225720.7714886625-1668.77148866251
702844926433.85219018942015.14780981059
713353332331.3230587461201.67694125399
723735136839.9276251758511.072374824173
731996919112.5594963099856.440503690137
742170122683.4127434211-982.412743421144
752624926141.2090244468107.790975553195
762449324890.2582868928-397.25828689276
772460327118.6027141374-2515.60271413739
782648526022.1738900225462.826109977508
793072328656.214370622066.78562938001
803456934157.3975312452411.602468754798
812668926144.2559703611544.744029638925
822615728046.0543017333-1889.05430173325
833206433630.5321022938-1566.53210229376
843887037851.12460303511018.87539696486
852133719799.21540360431537.78459639566
861941923019.9361331425-3600.9361331425
872316626616.3705380594-3450.37053805939
882828624930.67319841363355.32680158635
892457026876.3198706050-2306.31987060505
902400126530.5278871889-2529.52788718886
913315129337.85798924993813.14201075008
922487834540.1322844895-9662.1322844895
932680425877.6112577099926.388742290103
942896727079.90012626971887.09987373032
953331132890.1509824285420.849017571491
964022637812.61760145252413.38239854750
972050420053.1465526189450.853447381141
982306021813.6247031471246.37529685299
992356225774.3546544131-2212.35465441307
1002756225905.03428658011656.96571341987
1012394026263.7162865795-2323.71628657951
1022458425838.5724347560-1254.57243475605
1033430330346.0850946413956.91490535902
1042551732052.206096688-6535.20609668801
1052349426286.2819356077-2792.28193560765
1062909527447.76175379161647.23824620836
1073290332813.097975117289.902024882802
1083437938150.9633006975-3771.96330069753
1091699119758.4482116896-2767.44821168961
1102110921370.7489611716-261.748961171554
1112374024135.6278026146-395.627802614552
1122555225253.8253045917298.174695408266
1132175224445.4966791872-2693.49667918718
1142029424178.5442988199-3884.54429881989
1152900929342.9118730520-333.911873051951
1162550027983.9735771297-2483.97357712966
1172416623648.7828814765517.217118523466
1182696025908.41073991931051.58926008070
1193122230365.3107838664856.689216133629
1203864134310.56011648174330.43988351834
1211467217809.4104846895-3137.41048468947
1221754319821.1911947822-2278.19119478216
1232545322127.78608874353325.21391125649
1243268323538.74876861839144.25123138172
1252244922655.6270874520-206.627087451965
1262231622283.851540677032.1484593230489
1272759528516.3079870321-921.307987032145
1282545126667.2264563353-1216.22645633532
1292542123316.93670938952104.06329061055
1302528825861.0196273971-573.019627397141
1313256830156.98825051982411.01174948024
1323511035137.565415337-27.5654153369687
1331605216751.0817364431-699.081736443146
1342214619190.16851277352955.83148722647
1352119823460.9607131809-2262.96071318091
1361954326002.1155805422-6459.11558054222
1372208421756.9543994932327.045600506794
1382381621470.47683168772345.52316831228
1392996127431.68310557872529.31689442132
1402677325798.4071066050974.592893394962
1412663523508.61244249213126.38755750789
1422697225452.67944518331519.32055481666
1433020730688.9002941465-481.900294146508
1443868734849.25693747383837.74306252616
1451697416598.5140631523375.485936847686
1462169720108.95484638081588.04515361924
1472417922998.36840244611180.63159755394
1482375724772.5065126522-1015.50651265220
1492501322670.94844822632342.05155177366
1502401923159.0838924448859.916107555211
1513034529448.8769675645896.123032435542
1522448827314.5303480323-2826.53034803232
1532515625311.9440749653-155.944074965279
1542565026713.8051059842-1063.80510598416
1553092331428.1408246841-505.140824684077
1563724036888.4072085374351.592791462594
1571746617085.1710804427380.828919557305
1581946321009.6016535166-1546.60165351658
1592435223607.114860479744.885139521
1602680524793.45424181152011.54575818852
1612523623744.55094642391491.44905357606
1622473523797.6777859469937.322214053132
1632935630221.0387410972-865.038741097182
1643123426957.45950804914276.54049195087
1652272426134.8563180714-3410.85631807141
1662849627126.781692631369.21830736998
1673285732354.7011662801502.29883371988
1683719838367.4788094046-1169.47880940462
1691365217800.4807464634-4148.48074646339
1702278420965.77567454081818.22432545915
1712356524491.7794077116-926.77940771158
1722632325922.4817383618400.518261638212
1732377924594.0012185227-815.001218522746
1742754924320.09513478513228.90486521490
1752966030540.0813835425-880.081383542452
1762335628536.6528561344-5180.6528561344

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15028 & 14321.6838979972 & 706.316102002796 \tabularnewline
14 & 17977 & 17069.4177170777 & 907.582282922289 \tabularnewline
15 & 20008 & 19050.8472294842 & 957.152770515797 \tabularnewline
16 & 21354 & 20594.1469296704 & 759.853070329562 \tabularnewline
17 & 19498 & 19004.1326734229 & 493.867326577136 \tabularnewline
18 & 22125 & 21757.4677963716 & 367.532203628394 \tabularnewline
19 & 25817 & 24290.9139807189 & 1526.08601928110 \tabularnewline
20 & 28779 & 25468.2863781914 & 3310.71362180858 \tabularnewline
21 & 20960 & 23042.1560743632 & -2082.15607436320 \tabularnewline
22 & 22254 & 24523.2253877757 & -2269.22538777566 \tabularnewline
23 & 27392 & 28844.4884130028 & -1452.48841300276 \tabularnewline
24 & 29945 & 31899.8472081405 & -1954.84720814051 \tabularnewline
25 & 16933 & 16195.4055778487 & 737.594422151315 \tabularnewline
26 & 17892 & 19314.1959907242 & -1422.19599072425 \tabularnewline
27 & 20533 & 21332.7820221934 & -799.782022193409 \tabularnewline
28 & 23569 & 22812.3942319425 & 756.60576805746 \tabularnewline
29 & 22417 & 20958.6351217714 & 1458.36487822863 \tabularnewline
30 & 22084 & 23985.7996975873 & -1901.79969758735 \tabularnewline
31 & 26580 & 26864.8500198210 & -284.850019821031 \tabularnewline
32 & 27454 & 28432.5724659408 & -978.572465940793 \tabularnewline
33 & 24081 & 23975.6939369364 & 105.306063063606 \tabularnewline
34 & 23451 & 25609.0510861706 & -2158.05108617062 \tabularnewline
35 & 28991 & 30404.3276855657 & -1413.32768556568 \tabularnewline
36 & 31386 & 33461.1562610029 & -2075.15626100286 \tabularnewline
37 & 16896 & 17419.7937823049 & -523.793782304892 \tabularnewline
38 & 20045 & 19987.1228289079 & 57.8771710920773 \tabularnewline
39 & 23471 & 22355.3341863531 & 1115.66581364689 \tabularnewline
40 & 21747 & 24450.3158901976 & -2703.31589019757 \tabularnewline
41 & 25621 & 22387.2906652570 & 3233.70933474305 \tabularnewline
42 & 23859 & 24738.7662104173 & -879.766210417307 \tabularnewline
43 & 25500 & 28245.7602996728 & -2745.76029967275 \tabularnewline
44 & 30998 & 29465.5562294483 & 1532.44377055173 \tabularnewline
45 & 24475 & 25204.5757707592 & -729.575770759151 \tabularnewline
46 & 23145 & 26197.9615570337 & -3052.96155703366 \tabularnewline
47 & 29701 & 31277.9213466602 & -1576.92134666025 \tabularnewline
48 & 34365 & 34202.1819789929 & 162.818021007057 \tabularnewline
49 & 17556 & 18008.2929235411 & -452.292923541081 \tabularnewline
50 & 22077 & 20811.998886238 & 1265.00111376199 \tabularnewline
51 & 25702 & 23622.3890923831 & 2079.61090761694 \tabularnewline
52 & 22214 & 24825.295149348 & -2611.29514934800 \tabularnewline
53 & 26886 & 24240.3688883381 & 2645.63111166187 \tabularnewline
54 & 23191 & 25513.8403421907 & -2322.84034219074 \tabularnewline
55 & 27831 & 28509.5516194940 & -678.551619493963 \tabularnewline
56 & 35406 & 31036.4246815116 & 4369.57531848839 \tabularnewline
57 & 23195 & 26154.5448188867 & -2959.54481888669 \tabularnewline
58 & 25110 & 26383.8234382992 & -1273.82343829916 \tabularnewline
59 & 30009 & 32191.5934576834 & -2182.59345768342 \tabularnewline
60 & 36242 & 35640.0809205167 & 601.919079483254 \tabularnewline
61 & 18450 & 18627.0347185142 & -177.034718514227 \tabularnewline
62 & 21845 & 22015.8591144154 & -170.859114415376 \tabularnewline
63 & 26488 & 25017.0182578141 & 1470.98174218589 \tabularnewline
64 & 22394 & 24940.7459548851 & -2546.74595488509 \tabularnewline
65 & 28057 & 25704.2318722062 & 2352.76812779382 \tabularnewline
66 & 25451 & 25647.1201444505 & -196.120144450495 \tabularnewline
67 & 24872 & 29319.6525240786 & -4447.65252407861 \tabularnewline
68 & 33424 & 32916.9056485469 & 507.094351453132 \tabularnewline
69 & 24052 & 25720.7714886625 & -1668.77148866251 \tabularnewline
70 & 28449 & 26433.8521901894 & 2015.14780981059 \tabularnewline
71 & 33533 & 32331.323058746 & 1201.67694125399 \tabularnewline
72 & 37351 & 36839.9276251758 & 511.072374824173 \tabularnewline
73 & 19969 & 19112.5594963099 & 856.440503690137 \tabularnewline
74 & 21701 & 22683.4127434211 & -982.412743421144 \tabularnewline
75 & 26249 & 26141.2090244468 & 107.790975553195 \tabularnewline
76 & 24493 & 24890.2582868928 & -397.25828689276 \tabularnewline
77 & 24603 & 27118.6027141374 & -2515.60271413739 \tabularnewline
78 & 26485 & 26022.1738900225 & 462.826109977508 \tabularnewline
79 & 30723 & 28656.21437062 & 2066.78562938001 \tabularnewline
80 & 34569 & 34157.3975312452 & 411.602468754798 \tabularnewline
81 & 26689 & 26144.2559703611 & 544.744029638925 \tabularnewline
82 & 26157 & 28046.0543017333 & -1889.05430173325 \tabularnewline
83 & 32064 & 33630.5321022938 & -1566.53210229376 \tabularnewline
84 & 38870 & 37851.1246030351 & 1018.87539696486 \tabularnewline
85 & 21337 & 19799.2154036043 & 1537.78459639566 \tabularnewline
86 & 19419 & 23019.9361331425 & -3600.9361331425 \tabularnewline
87 & 23166 & 26616.3705380594 & -3450.37053805939 \tabularnewline
88 & 28286 & 24930.6731984136 & 3355.32680158635 \tabularnewline
89 & 24570 & 26876.3198706050 & -2306.31987060505 \tabularnewline
90 & 24001 & 26530.5278871889 & -2529.52788718886 \tabularnewline
91 & 33151 & 29337.8579892499 & 3813.14201075008 \tabularnewline
92 & 24878 & 34540.1322844895 & -9662.1322844895 \tabularnewline
93 & 26804 & 25877.6112577099 & 926.388742290103 \tabularnewline
94 & 28967 & 27079.9001262697 & 1887.09987373032 \tabularnewline
95 & 33311 & 32890.1509824285 & 420.849017571491 \tabularnewline
96 & 40226 & 37812.6176014525 & 2413.38239854750 \tabularnewline
97 & 20504 & 20053.1465526189 & 450.853447381141 \tabularnewline
98 & 23060 & 21813.624703147 & 1246.37529685299 \tabularnewline
99 & 23562 & 25774.3546544131 & -2212.35465441307 \tabularnewline
100 & 27562 & 25905.0342865801 & 1656.96571341987 \tabularnewline
101 & 23940 & 26263.7162865795 & -2323.71628657951 \tabularnewline
102 & 24584 & 25838.5724347560 & -1254.57243475605 \tabularnewline
103 & 34303 & 30346.085094641 & 3956.91490535902 \tabularnewline
104 & 25517 & 32052.206096688 & -6535.20609668801 \tabularnewline
105 & 23494 & 26286.2819356077 & -2792.28193560765 \tabularnewline
106 & 29095 & 27447.7617537916 & 1647.23824620836 \tabularnewline
107 & 32903 & 32813.0979751172 & 89.902024882802 \tabularnewline
108 & 34379 & 38150.9633006975 & -3771.96330069753 \tabularnewline
109 & 16991 & 19758.4482116896 & -2767.44821168961 \tabularnewline
110 & 21109 & 21370.7489611716 & -261.748961171554 \tabularnewline
111 & 23740 & 24135.6278026146 & -395.627802614552 \tabularnewline
112 & 25552 & 25253.8253045917 & 298.174695408266 \tabularnewline
113 & 21752 & 24445.4966791872 & -2693.49667918718 \tabularnewline
114 & 20294 & 24178.5442988199 & -3884.54429881989 \tabularnewline
115 & 29009 & 29342.9118730520 & -333.911873051951 \tabularnewline
116 & 25500 & 27983.9735771297 & -2483.97357712966 \tabularnewline
117 & 24166 & 23648.7828814765 & 517.217118523466 \tabularnewline
118 & 26960 & 25908.4107399193 & 1051.58926008070 \tabularnewline
119 & 31222 & 30365.3107838664 & 856.689216133629 \tabularnewline
120 & 38641 & 34310.5601164817 & 4330.43988351834 \tabularnewline
121 & 14672 & 17809.4104846895 & -3137.41048468947 \tabularnewline
122 & 17543 & 19821.1911947822 & -2278.19119478216 \tabularnewline
123 & 25453 & 22127.7860887435 & 3325.21391125649 \tabularnewline
124 & 32683 & 23538.7487686183 & 9144.25123138172 \tabularnewline
125 & 22449 & 22655.6270874520 & -206.627087451965 \tabularnewline
126 & 22316 & 22283.8515406770 & 32.1484593230489 \tabularnewline
127 & 27595 & 28516.3079870321 & -921.307987032145 \tabularnewline
128 & 25451 & 26667.2264563353 & -1216.22645633532 \tabularnewline
129 & 25421 & 23316.9367093895 & 2104.06329061055 \tabularnewline
130 & 25288 & 25861.0196273971 & -573.019627397141 \tabularnewline
131 & 32568 & 30156.9882505198 & 2411.01174948024 \tabularnewline
132 & 35110 & 35137.565415337 & -27.5654153369687 \tabularnewline
133 & 16052 & 16751.0817364431 & -699.081736443146 \tabularnewline
134 & 22146 & 19190.1685127735 & 2955.83148722647 \tabularnewline
135 & 21198 & 23460.9607131809 & -2262.96071318091 \tabularnewline
136 & 19543 & 26002.1155805422 & -6459.11558054222 \tabularnewline
137 & 22084 & 21756.9543994932 & 327.045600506794 \tabularnewline
138 & 23816 & 21470.4768316877 & 2345.52316831228 \tabularnewline
139 & 29961 & 27431.6831055787 & 2529.31689442132 \tabularnewline
140 & 26773 & 25798.4071066050 & 974.592893394962 \tabularnewline
141 & 26635 & 23508.6124424921 & 3126.38755750789 \tabularnewline
142 & 26972 & 25452.6794451833 & 1519.32055481666 \tabularnewline
143 & 30207 & 30688.9002941465 & -481.900294146508 \tabularnewline
144 & 38687 & 34849.2569374738 & 3837.74306252616 \tabularnewline
145 & 16974 & 16598.5140631523 & 375.485936847686 \tabularnewline
146 & 21697 & 20108.9548463808 & 1588.04515361924 \tabularnewline
147 & 24179 & 22998.3684024461 & 1180.63159755394 \tabularnewline
148 & 23757 & 24772.5065126522 & -1015.50651265220 \tabularnewline
149 & 25013 & 22670.9484482263 & 2342.05155177366 \tabularnewline
150 & 24019 & 23159.0838924448 & 859.916107555211 \tabularnewline
151 & 30345 & 29448.8769675645 & 896.123032435542 \tabularnewline
152 & 24488 & 27314.5303480323 & -2826.53034803232 \tabularnewline
153 & 25156 & 25311.9440749653 & -155.944074965279 \tabularnewline
154 & 25650 & 26713.8051059842 & -1063.80510598416 \tabularnewline
155 & 30923 & 31428.1408246841 & -505.140824684077 \tabularnewline
156 & 37240 & 36888.4072085374 & 351.592791462594 \tabularnewline
157 & 17466 & 17085.1710804427 & 380.828919557305 \tabularnewline
158 & 19463 & 21009.6016535166 & -1546.60165351658 \tabularnewline
159 & 24352 & 23607.114860479 & 744.885139521 \tabularnewline
160 & 26805 & 24793.4542418115 & 2011.54575818852 \tabularnewline
161 & 25236 & 23744.5509464239 & 1491.44905357606 \tabularnewline
162 & 24735 & 23797.6777859469 & 937.322214053132 \tabularnewline
163 & 29356 & 30221.0387410972 & -865.038741097182 \tabularnewline
164 & 31234 & 26957.4595080491 & 4276.54049195087 \tabularnewline
165 & 22724 & 26134.8563180714 & -3410.85631807141 \tabularnewline
166 & 28496 & 27126.78169263 & 1369.21830736998 \tabularnewline
167 & 32857 & 32354.7011662801 & 502.29883371988 \tabularnewline
168 & 37198 & 38367.4788094046 & -1169.47880940462 \tabularnewline
169 & 13652 & 17800.4807464634 & -4148.48074646339 \tabularnewline
170 & 22784 & 20965.7756745408 & 1818.22432545915 \tabularnewline
171 & 23565 & 24491.7794077116 & -926.77940771158 \tabularnewline
172 & 26323 & 25922.4817383618 & 400.518261638212 \tabularnewline
173 & 23779 & 24594.0012185227 & -815.001218522746 \tabularnewline
174 & 27549 & 24320.0951347851 & 3228.90486521490 \tabularnewline
175 & 29660 & 30540.0813835425 & -880.081383542452 \tabularnewline
176 & 23356 & 28536.6528561344 & -5180.6528561344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77387&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]15028[/C][C]14321.6838979972[/C][C]706.316102002796[/C][/ROW]
[ROW][C]14[/C][C]17977[/C][C]17069.4177170777[/C][C]907.582282922289[/C][/ROW]
[ROW][C]15[/C][C]20008[/C][C]19050.8472294842[/C][C]957.152770515797[/C][/ROW]
[ROW][C]16[/C][C]21354[/C][C]20594.1469296704[/C][C]759.853070329562[/C][/ROW]
[ROW][C]17[/C][C]19498[/C][C]19004.1326734229[/C][C]493.867326577136[/C][/ROW]
[ROW][C]18[/C][C]22125[/C][C]21757.4677963716[/C][C]367.532203628394[/C][/ROW]
[ROW][C]19[/C][C]25817[/C][C]24290.9139807189[/C][C]1526.08601928110[/C][/ROW]
[ROW][C]20[/C][C]28779[/C][C]25468.2863781914[/C][C]3310.71362180858[/C][/ROW]
[ROW][C]21[/C][C]20960[/C][C]23042.1560743632[/C][C]-2082.15607436320[/C][/ROW]
[ROW][C]22[/C][C]22254[/C][C]24523.2253877757[/C][C]-2269.22538777566[/C][/ROW]
[ROW][C]23[/C][C]27392[/C][C]28844.4884130028[/C][C]-1452.48841300276[/C][/ROW]
[ROW][C]24[/C][C]29945[/C][C]31899.8472081405[/C][C]-1954.84720814051[/C][/ROW]
[ROW][C]25[/C][C]16933[/C][C]16195.4055778487[/C][C]737.594422151315[/C][/ROW]
[ROW][C]26[/C][C]17892[/C][C]19314.1959907242[/C][C]-1422.19599072425[/C][/ROW]
[ROW][C]27[/C][C]20533[/C][C]21332.7820221934[/C][C]-799.782022193409[/C][/ROW]
[ROW][C]28[/C][C]23569[/C][C]22812.3942319425[/C][C]756.60576805746[/C][/ROW]
[ROW][C]29[/C][C]22417[/C][C]20958.6351217714[/C][C]1458.36487822863[/C][/ROW]
[ROW][C]30[/C][C]22084[/C][C]23985.7996975873[/C][C]-1901.79969758735[/C][/ROW]
[ROW][C]31[/C][C]26580[/C][C]26864.8500198210[/C][C]-284.850019821031[/C][/ROW]
[ROW][C]32[/C][C]27454[/C][C]28432.5724659408[/C][C]-978.572465940793[/C][/ROW]
[ROW][C]33[/C][C]24081[/C][C]23975.6939369364[/C][C]105.306063063606[/C][/ROW]
[ROW][C]34[/C][C]23451[/C][C]25609.0510861706[/C][C]-2158.05108617062[/C][/ROW]
[ROW][C]35[/C][C]28991[/C][C]30404.3276855657[/C][C]-1413.32768556568[/C][/ROW]
[ROW][C]36[/C][C]31386[/C][C]33461.1562610029[/C][C]-2075.15626100286[/C][/ROW]
[ROW][C]37[/C][C]16896[/C][C]17419.7937823049[/C][C]-523.793782304892[/C][/ROW]
[ROW][C]38[/C][C]20045[/C][C]19987.1228289079[/C][C]57.8771710920773[/C][/ROW]
[ROW][C]39[/C][C]23471[/C][C]22355.3341863531[/C][C]1115.66581364689[/C][/ROW]
[ROW][C]40[/C][C]21747[/C][C]24450.3158901976[/C][C]-2703.31589019757[/C][/ROW]
[ROW][C]41[/C][C]25621[/C][C]22387.2906652570[/C][C]3233.70933474305[/C][/ROW]
[ROW][C]42[/C][C]23859[/C][C]24738.7662104173[/C][C]-879.766210417307[/C][/ROW]
[ROW][C]43[/C][C]25500[/C][C]28245.7602996728[/C][C]-2745.76029967275[/C][/ROW]
[ROW][C]44[/C][C]30998[/C][C]29465.5562294483[/C][C]1532.44377055173[/C][/ROW]
[ROW][C]45[/C][C]24475[/C][C]25204.5757707592[/C][C]-729.575770759151[/C][/ROW]
[ROW][C]46[/C][C]23145[/C][C]26197.9615570337[/C][C]-3052.96155703366[/C][/ROW]
[ROW][C]47[/C][C]29701[/C][C]31277.9213466602[/C][C]-1576.92134666025[/C][/ROW]
[ROW][C]48[/C][C]34365[/C][C]34202.1819789929[/C][C]162.818021007057[/C][/ROW]
[ROW][C]49[/C][C]17556[/C][C]18008.2929235411[/C][C]-452.292923541081[/C][/ROW]
[ROW][C]50[/C][C]22077[/C][C]20811.998886238[/C][C]1265.00111376199[/C][/ROW]
[ROW][C]51[/C][C]25702[/C][C]23622.3890923831[/C][C]2079.61090761694[/C][/ROW]
[ROW][C]52[/C][C]22214[/C][C]24825.295149348[/C][C]-2611.29514934800[/C][/ROW]
[ROW][C]53[/C][C]26886[/C][C]24240.3688883381[/C][C]2645.63111166187[/C][/ROW]
[ROW][C]54[/C][C]23191[/C][C]25513.8403421907[/C][C]-2322.84034219074[/C][/ROW]
[ROW][C]55[/C][C]27831[/C][C]28509.5516194940[/C][C]-678.551619493963[/C][/ROW]
[ROW][C]56[/C][C]35406[/C][C]31036.4246815116[/C][C]4369.57531848839[/C][/ROW]
[ROW][C]57[/C][C]23195[/C][C]26154.5448188867[/C][C]-2959.54481888669[/C][/ROW]
[ROW][C]58[/C][C]25110[/C][C]26383.8234382992[/C][C]-1273.82343829916[/C][/ROW]
[ROW][C]59[/C][C]30009[/C][C]32191.5934576834[/C][C]-2182.59345768342[/C][/ROW]
[ROW][C]60[/C][C]36242[/C][C]35640.0809205167[/C][C]601.919079483254[/C][/ROW]
[ROW][C]61[/C][C]18450[/C][C]18627.0347185142[/C][C]-177.034718514227[/C][/ROW]
[ROW][C]62[/C][C]21845[/C][C]22015.8591144154[/C][C]-170.859114415376[/C][/ROW]
[ROW][C]63[/C][C]26488[/C][C]25017.0182578141[/C][C]1470.98174218589[/C][/ROW]
[ROW][C]64[/C][C]22394[/C][C]24940.7459548851[/C][C]-2546.74595488509[/C][/ROW]
[ROW][C]65[/C][C]28057[/C][C]25704.2318722062[/C][C]2352.76812779382[/C][/ROW]
[ROW][C]66[/C][C]25451[/C][C]25647.1201444505[/C][C]-196.120144450495[/C][/ROW]
[ROW][C]67[/C][C]24872[/C][C]29319.6525240786[/C][C]-4447.65252407861[/C][/ROW]
[ROW][C]68[/C][C]33424[/C][C]32916.9056485469[/C][C]507.094351453132[/C][/ROW]
[ROW][C]69[/C][C]24052[/C][C]25720.7714886625[/C][C]-1668.77148866251[/C][/ROW]
[ROW][C]70[/C][C]28449[/C][C]26433.8521901894[/C][C]2015.14780981059[/C][/ROW]
[ROW][C]71[/C][C]33533[/C][C]32331.323058746[/C][C]1201.67694125399[/C][/ROW]
[ROW][C]72[/C][C]37351[/C][C]36839.9276251758[/C][C]511.072374824173[/C][/ROW]
[ROW][C]73[/C][C]19969[/C][C]19112.5594963099[/C][C]856.440503690137[/C][/ROW]
[ROW][C]74[/C][C]21701[/C][C]22683.4127434211[/C][C]-982.412743421144[/C][/ROW]
[ROW][C]75[/C][C]26249[/C][C]26141.2090244468[/C][C]107.790975553195[/C][/ROW]
[ROW][C]76[/C][C]24493[/C][C]24890.2582868928[/C][C]-397.25828689276[/C][/ROW]
[ROW][C]77[/C][C]24603[/C][C]27118.6027141374[/C][C]-2515.60271413739[/C][/ROW]
[ROW][C]78[/C][C]26485[/C][C]26022.1738900225[/C][C]462.826109977508[/C][/ROW]
[ROW][C]79[/C][C]30723[/C][C]28656.21437062[/C][C]2066.78562938001[/C][/ROW]
[ROW][C]80[/C][C]34569[/C][C]34157.3975312452[/C][C]411.602468754798[/C][/ROW]
[ROW][C]81[/C][C]26689[/C][C]26144.2559703611[/C][C]544.744029638925[/C][/ROW]
[ROW][C]82[/C][C]26157[/C][C]28046.0543017333[/C][C]-1889.05430173325[/C][/ROW]
[ROW][C]83[/C][C]32064[/C][C]33630.5321022938[/C][C]-1566.53210229376[/C][/ROW]
[ROW][C]84[/C][C]38870[/C][C]37851.1246030351[/C][C]1018.87539696486[/C][/ROW]
[ROW][C]85[/C][C]21337[/C][C]19799.2154036043[/C][C]1537.78459639566[/C][/ROW]
[ROW][C]86[/C][C]19419[/C][C]23019.9361331425[/C][C]-3600.9361331425[/C][/ROW]
[ROW][C]87[/C][C]23166[/C][C]26616.3705380594[/C][C]-3450.37053805939[/C][/ROW]
[ROW][C]88[/C][C]28286[/C][C]24930.6731984136[/C][C]3355.32680158635[/C][/ROW]
[ROW][C]89[/C][C]24570[/C][C]26876.3198706050[/C][C]-2306.31987060505[/C][/ROW]
[ROW][C]90[/C][C]24001[/C][C]26530.5278871889[/C][C]-2529.52788718886[/C][/ROW]
[ROW][C]91[/C][C]33151[/C][C]29337.8579892499[/C][C]3813.14201075008[/C][/ROW]
[ROW][C]92[/C][C]24878[/C][C]34540.1322844895[/C][C]-9662.1322844895[/C][/ROW]
[ROW][C]93[/C][C]26804[/C][C]25877.6112577099[/C][C]926.388742290103[/C][/ROW]
[ROW][C]94[/C][C]28967[/C][C]27079.9001262697[/C][C]1887.09987373032[/C][/ROW]
[ROW][C]95[/C][C]33311[/C][C]32890.1509824285[/C][C]420.849017571491[/C][/ROW]
[ROW][C]96[/C][C]40226[/C][C]37812.6176014525[/C][C]2413.38239854750[/C][/ROW]
[ROW][C]97[/C][C]20504[/C][C]20053.1465526189[/C][C]450.853447381141[/C][/ROW]
[ROW][C]98[/C][C]23060[/C][C]21813.624703147[/C][C]1246.37529685299[/C][/ROW]
[ROW][C]99[/C][C]23562[/C][C]25774.3546544131[/C][C]-2212.35465441307[/C][/ROW]
[ROW][C]100[/C][C]27562[/C][C]25905.0342865801[/C][C]1656.96571341987[/C][/ROW]
[ROW][C]101[/C][C]23940[/C][C]26263.7162865795[/C][C]-2323.71628657951[/C][/ROW]
[ROW][C]102[/C][C]24584[/C][C]25838.5724347560[/C][C]-1254.57243475605[/C][/ROW]
[ROW][C]103[/C][C]34303[/C][C]30346.085094641[/C][C]3956.91490535902[/C][/ROW]
[ROW][C]104[/C][C]25517[/C][C]32052.206096688[/C][C]-6535.20609668801[/C][/ROW]
[ROW][C]105[/C][C]23494[/C][C]26286.2819356077[/C][C]-2792.28193560765[/C][/ROW]
[ROW][C]106[/C][C]29095[/C][C]27447.7617537916[/C][C]1647.23824620836[/C][/ROW]
[ROW][C]107[/C][C]32903[/C][C]32813.0979751172[/C][C]89.902024882802[/C][/ROW]
[ROW][C]108[/C][C]34379[/C][C]38150.9633006975[/C][C]-3771.96330069753[/C][/ROW]
[ROW][C]109[/C][C]16991[/C][C]19758.4482116896[/C][C]-2767.44821168961[/C][/ROW]
[ROW][C]110[/C][C]21109[/C][C]21370.7489611716[/C][C]-261.748961171554[/C][/ROW]
[ROW][C]111[/C][C]23740[/C][C]24135.6278026146[/C][C]-395.627802614552[/C][/ROW]
[ROW][C]112[/C][C]25552[/C][C]25253.8253045917[/C][C]298.174695408266[/C][/ROW]
[ROW][C]113[/C][C]21752[/C][C]24445.4966791872[/C][C]-2693.49667918718[/C][/ROW]
[ROW][C]114[/C][C]20294[/C][C]24178.5442988199[/C][C]-3884.54429881989[/C][/ROW]
[ROW][C]115[/C][C]29009[/C][C]29342.9118730520[/C][C]-333.911873051951[/C][/ROW]
[ROW][C]116[/C][C]25500[/C][C]27983.9735771297[/C][C]-2483.97357712966[/C][/ROW]
[ROW][C]117[/C][C]24166[/C][C]23648.7828814765[/C][C]517.217118523466[/C][/ROW]
[ROW][C]118[/C][C]26960[/C][C]25908.4107399193[/C][C]1051.58926008070[/C][/ROW]
[ROW][C]119[/C][C]31222[/C][C]30365.3107838664[/C][C]856.689216133629[/C][/ROW]
[ROW][C]120[/C][C]38641[/C][C]34310.5601164817[/C][C]4330.43988351834[/C][/ROW]
[ROW][C]121[/C][C]14672[/C][C]17809.4104846895[/C][C]-3137.41048468947[/C][/ROW]
[ROW][C]122[/C][C]17543[/C][C]19821.1911947822[/C][C]-2278.19119478216[/C][/ROW]
[ROW][C]123[/C][C]25453[/C][C]22127.7860887435[/C][C]3325.21391125649[/C][/ROW]
[ROW][C]124[/C][C]32683[/C][C]23538.7487686183[/C][C]9144.25123138172[/C][/ROW]
[ROW][C]125[/C][C]22449[/C][C]22655.6270874520[/C][C]-206.627087451965[/C][/ROW]
[ROW][C]126[/C][C]22316[/C][C]22283.8515406770[/C][C]32.1484593230489[/C][/ROW]
[ROW][C]127[/C][C]27595[/C][C]28516.3079870321[/C][C]-921.307987032145[/C][/ROW]
[ROW][C]128[/C][C]25451[/C][C]26667.2264563353[/C][C]-1216.22645633532[/C][/ROW]
[ROW][C]129[/C][C]25421[/C][C]23316.9367093895[/C][C]2104.06329061055[/C][/ROW]
[ROW][C]130[/C][C]25288[/C][C]25861.0196273971[/C][C]-573.019627397141[/C][/ROW]
[ROW][C]131[/C][C]32568[/C][C]30156.9882505198[/C][C]2411.01174948024[/C][/ROW]
[ROW][C]132[/C][C]35110[/C][C]35137.565415337[/C][C]-27.5654153369687[/C][/ROW]
[ROW][C]133[/C][C]16052[/C][C]16751.0817364431[/C][C]-699.081736443146[/C][/ROW]
[ROW][C]134[/C][C]22146[/C][C]19190.1685127735[/C][C]2955.83148722647[/C][/ROW]
[ROW][C]135[/C][C]21198[/C][C]23460.9607131809[/C][C]-2262.96071318091[/C][/ROW]
[ROW][C]136[/C][C]19543[/C][C]26002.1155805422[/C][C]-6459.11558054222[/C][/ROW]
[ROW][C]137[/C][C]22084[/C][C]21756.9543994932[/C][C]327.045600506794[/C][/ROW]
[ROW][C]138[/C][C]23816[/C][C]21470.4768316877[/C][C]2345.52316831228[/C][/ROW]
[ROW][C]139[/C][C]29961[/C][C]27431.6831055787[/C][C]2529.31689442132[/C][/ROW]
[ROW][C]140[/C][C]26773[/C][C]25798.4071066050[/C][C]974.592893394962[/C][/ROW]
[ROW][C]141[/C][C]26635[/C][C]23508.6124424921[/C][C]3126.38755750789[/C][/ROW]
[ROW][C]142[/C][C]26972[/C][C]25452.6794451833[/C][C]1519.32055481666[/C][/ROW]
[ROW][C]143[/C][C]30207[/C][C]30688.9002941465[/C][C]-481.900294146508[/C][/ROW]
[ROW][C]144[/C][C]38687[/C][C]34849.2569374738[/C][C]3837.74306252616[/C][/ROW]
[ROW][C]145[/C][C]16974[/C][C]16598.5140631523[/C][C]375.485936847686[/C][/ROW]
[ROW][C]146[/C][C]21697[/C][C]20108.9548463808[/C][C]1588.04515361924[/C][/ROW]
[ROW][C]147[/C][C]24179[/C][C]22998.3684024461[/C][C]1180.63159755394[/C][/ROW]
[ROW][C]148[/C][C]23757[/C][C]24772.5065126522[/C][C]-1015.50651265220[/C][/ROW]
[ROW][C]149[/C][C]25013[/C][C]22670.9484482263[/C][C]2342.05155177366[/C][/ROW]
[ROW][C]150[/C][C]24019[/C][C]23159.0838924448[/C][C]859.916107555211[/C][/ROW]
[ROW][C]151[/C][C]30345[/C][C]29448.8769675645[/C][C]896.123032435542[/C][/ROW]
[ROW][C]152[/C][C]24488[/C][C]27314.5303480323[/C][C]-2826.53034803232[/C][/ROW]
[ROW][C]153[/C][C]25156[/C][C]25311.9440749653[/C][C]-155.944074965279[/C][/ROW]
[ROW][C]154[/C][C]25650[/C][C]26713.8051059842[/C][C]-1063.80510598416[/C][/ROW]
[ROW][C]155[/C][C]30923[/C][C]31428.1408246841[/C][C]-505.140824684077[/C][/ROW]
[ROW][C]156[/C][C]37240[/C][C]36888.4072085374[/C][C]351.592791462594[/C][/ROW]
[ROW][C]157[/C][C]17466[/C][C]17085.1710804427[/C][C]380.828919557305[/C][/ROW]
[ROW][C]158[/C][C]19463[/C][C]21009.6016535166[/C][C]-1546.60165351658[/C][/ROW]
[ROW][C]159[/C][C]24352[/C][C]23607.114860479[/C][C]744.885139521[/C][/ROW]
[ROW][C]160[/C][C]26805[/C][C]24793.4542418115[/C][C]2011.54575818852[/C][/ROW]
[ROW][C]161[/C][C]25236[/C][C]23744.5509464239[/C][C]1491.44905357606[/C][/ROW]
[ROW][C]162[/C][C]24735[/C][C]23797.6777859469[/C][C]937.322214053132[/C][/ROW]
[ROW][C]163[/C][C]29356[/C][C]30221.0387410972[/C][C]-865.038741097182[/C][/ROW]
[ROW][C]164[/C][C]31234[/C][C]26957.4595080491[/C][C]4276.54049195087[/C][/ROW]
[ROW][C]165[/C][C]22724[/C][C]26134.8563180714[/C][C]-3410.85631807141[/C][/ROW]
[ROW][C]166[/C][C]28496[/C][C]27126.78169263[/C][C]1369.21830736998[/C][/ROW]
[ROW][C]167[/C][C]32857[/C][C]32354.7011662801[/C][C]502.29883371988[/C][/ROW]
[ROW][C]168[/C][C]37198[/C][C]38367.4788094046[/C][C]-1169.47880940462[/C][/ROW]
[ROW][C]169[/C][C]13652[/C][C]17800.4807464634[/C][C]-4148.48074646339[/C][/ROW]
[ROW][C]170[/C][C]22784[/C][C]20965.7756745408[/C][C]1818.22432545915[/C][/ROW]
[ROW][C]171[/C][C]23565[/C][C]24491.7794077116[/C][C]-926.77940771158[/C][/ROW]
[ROW][C]172[/C][C]26323[/C][C]25922.4817383618[/C][C]400.518261638212[/C][/ROW]
[ROW][C]173[/C][C]23779[/C][C]24594.0012185227[/C][C]-815.001218522746[/C][/ROW]
[ROW][C]174[/C][C]27549[/C][C]24320.0951347851[/C][C]3228.90486521490[/C][/ROW]
[ROW][C]175[/C][C]29660[/C][C]30540.0813835425[/C][C]-880.081383542452[/C][/ROW]
[ROW][C]176[/C][C]23356[/C][C]28536.6528561344[/C][C]-5180.6528561344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77387&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77387&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
131502814321.6838979972706.316102002796
141797717069.4177170777907.582282922289
152000819050.8472294842957.152770515797
162135420594.1469296704759.853070329562
171949819004.1326734229493.867326577136
182212521757.4677963716367.532203628394
192581724290.91398071891526.08601928110
202877925468.28637819143310.71362180858
212096023042.1560743632-2082.15607436320
222225424523.2253877757-2269.22538777566
232739228844.4884130028-1452.48841300276
242994531899.8472081405-1954.84720814051
251693316195.4055778487737.594422151315
261789219314.1959907242-1422.19599072425
272053321332.7820221934-799.782022193409
282356922812.3942319425756.60576805746
292241720958.63512177141458.36487822863
302208423985.7996975873-1901.79969758735
312658026864.8500198210-284.850019821031
322745428432.5724659408-978.572465940793
332408123975.6939369364105.306063063606
342345125609.0510861706-2158.05108617062
352899130404.3276855657-1413.32768556568
363138633461.1562610029-2075.15626100286
371689617419.7937823049-523.793782304892
382004519987.122828907957.8771710920773
392347122355.33418635311115.66581364689
402174724450.3158901976-2703.31589019757
412562122387.29066525703233.70933474305
422385924738.7662104173-879.766210417307
432550028245.7602996728-2745.76029967275
443099829465.55622944831532.44377055173
452447525204.5757707592-729.575770759151
462314526197.9615570337-3052.96155703366
472970131277.9213466602-1576.92134666025
483436534202.1819789929162.818021007057
491755618008.2929235411-452.292923541081
502207720811.9988862381265.00111376199
512570223622.38909238312079.61090761694
522221424825.295149348-2611.29514934800
532688624240.36888833812645.63111166187
542319125513.8403421907-2322.84034219074
552783128509.5516194940-678.551619493963
563540631036.42468151164369.57531848839
572319526154.5448188867-2959.54481888669
582511026383.8234382992-1273.82343829916
593000932191.5934576834-2182.59345768342
603624235640.0809205167601.919079483254
611845018627.0347185142-177.034718514227
622184522015.8591144154-170.859114415376
632648825017.01825781411470.98174218589
642239424940.7459548851-2546.74595488509
652805725704.23187220622352.76812779382
662545125647.1201444505-196.120144450495
672487229319.6525240786-4447.65252407861
683342432916.9056485469507.094351453132
692405225720.7714886625-1668.77148866251
702844926433.85219018942015.14780981059
713353332331.3230587461201.67694125399
723735136839.9276251758511.072374824173
731996919112.5594963099856.440503690137
742170122683.4127434211-982.412743421144
752624926141.2090244468107.790975553195
762449324890.2582868928-397.25828689276
772460327118.6027141374-2515.60271413739
782648526022.1738900225462.826109977508
793072328656.214370622066.78562938001
803456934157.3975312452411.602468754798
812668926144.2559703611544.744029638925
822615728046.0543017333-1889.05430173325
833206433630.5321022938-1566.53210229376
843887037851.12460303511018.87539696486
852133719799.21540360431537.78459639566
861941923019.9361331425-3600.9361331425
872316626616.3705380594-3450.37053805939
882828624930.67319841363355.32680158635
892457026876.3198706050-2306.31987060505
902400126530.5278871889-2529.52788718886
913315129337.85798924993813.14201075008
922487834540.1322844895-9662.1322844895
932680425877.6112577099926.388742290103
942896727079.90012626971887.09987373032
953331132890.1509824285420.849017571491
964022637812.61760145252413.38239854750
972050420053.1465526189450.853447381141
982306021813.6247031471246.37529685299
992356225774.3546544131-2212.35465441307
1002756225905.03428658011656.96571341987
1012394026263.7162865795-2323.71628657951
1022458425838.5724347560-1254.57243475605
1033430330346.0850946413956.91490535902
1042551732052.206096688-6535.20609668801
1052349426286.2819356077-2792.28193560765
1062909527447.76175379161647.23824620836
1073290332813.097975117289.902024882802
1083437938150.9633006975-3771.96330069753
1091699119758.4482116896-2767.44821168961
1102110921370.7489611716-261.748961171554
1112374024135.6278026146-395.627802614552
1122555225253.8253045917298.174695408266
1132175224445.4966791872-2693.49667918718
1142029424178.5442988199-3884.54429881989
1152900929342.9118730520-333.911873051951
1162550027983.9735771297-2483.97357712966
1172416623648.7828814765517.217118523466
1182696025908.41073991931051.58926008070
1193122230365.3107838664856.689216133629
1203864134310.56011648174330.43988351834
1211467217809.4104846895-3137.41048468947
1221754319821.1911947822-2278.19119478216
1232545322127.78608874353325.21391125649
1243268323538.74876861839144.25123138172
1252244922655.6270874520-206.627087451965
1262231622283.851540677032.1484593230489
1272759528516.3079870321-921.307987032145
1282545126667.2264563353-1216.22645633532
1292542123316.93670938952104.06329061055
1302528825861.0196273971-573.019627397141
1313256830156.98825051982411.01174948024
1323511035137.565415337-27.5654153369687
1331605216751.0817364431-699.081736443146
1342214619190.16851277352955.83148722647
1352119823460.9607131809-2262.96071318091
1361954326002.1155805422-6459.11558054222
1372208421756.9543994932327.045600506794
1382381621470.47683168772345.52316831228
1392996127431.68310557872529.31689442132
1402677325798.4071066050974.592893394962
1412663523508.61244249213126.38755750789
1422697225452.67944518331519.32055481666
1433020730688.9002941465-481.900294146508
1443868734849.25693747383837.74306252616
1451697416598.5140631523375.485936847686
1462169720108.95484638081588.04515361924
1472417922998.36840244611180.63159755394
1482375724772.5065126522-1015.50651265220
1492501322670.94844822632342.05155177366
1502401923159.0838924448859.916107555211
1513034529448.8769675645896.123032435542
1522448827314.5303480323-2826.53034803232
1532515625311.9440749653-155.944074965279
1542565026713.8051059842-1063.80510598416
1553092331428.1408246841-505.140824684077
1563724036888.4072085374351.592791462594
1571746617085.1710804427380.828919557305
1581946321009.6016535166-1546.60165351658
1592435223607.114860479744.885139521
1602680524793.45424181152011.54575818852
1612523623744.55094642391491.44905357606
1622473523797.6777859469937.322214053132
1632935630221.0387410972-865.038741097182
1643123426957.45950804914276.54049195087
1652272426134.8563180714-3410.85631807141
1662849627126.781692631369.21830736998
1673285732354.7011662801502.29883371988
1683719838367.4788094046-1169.47880940462
1691365217800.4807464634-4148.48074646339
1702278420965.77567454081818.22432545915
1712356524491.7794077116-926.77940771158
1722632325922.4817383618400.518261638212
1732377924594.0012185227-815.001218522746
1742754924320.09513478513228.90486521490
1752966030540.0813835425-880.081383542452
1762335628536.6528561344-5180.6528561344







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
17725038.034165733823551.120136616926524.9481948507
17827444.588807620525909.641103523028979.5365117179
17932268.847281007230651.767928416833885.9266335975
18037697.584011415535959.139498196539436.0285246345
18116563.061023164815008.586370048318117.5356762813
18221567.308833343519888.655490560123245.9621761269
18324243.452159244922440.645627179726046.2586913101
18426065.166968155124133.309447477927997.0244888323
18524378.284603824822419.171952602626337.3972550471
18625176.524297255223099.742864834127253.3057296764
18730040.666836056627638.719607283832442.6140648294
18826970.036255244025139.68672539628800.3857850921

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
177 & 25038.0341657338 & 23551.1201366169 & 26524.9481948507 \tabularnewline
178 & 27444.5888076205 & 25909.6411035230 & 28979.5365117179 \tabularnewline
179 & 32268.8472810072 & 30651.7679284168 & 33885.9266335975 \tabularnewline
180 & 37697.5840114155 & 35959.1394981965 & 39436.0285246345 \tabularnewline
181 & 16563.0610231648 & 15008.5863700483 & 18117.5356762813 \tabularnewline
182 & 21567.3088333435 & 19888.6554905601 & 23245.9621761269 \tabularnewline
183 & 24243.4521592449 & 22440.6456271797 & 26046.2586913101 \tabularnewline
184 & 26065.1669681551 & 24133.3094474779 & 27997.0244888323 \tabularnewline
185 & 24378.2846038248 & 22419.1719526026 & 26337.3972550471 \tabularnewline
186 & 25176.5242972552 & 23099.7428648341 & 27253.3057296764 \tabularnewline
187 & 30040.6668360566 & 27638.7196072838 & 32442.6140648294 \tabularnewline
188 & 26970.0362552440 & 25139.686725396 & 28800.3857850921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77387&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]177[/C][C]25038.0341657338[/C][C]23551.1201366169[/C][C]26524.9481948507[/C][/ROW]
[ROW][C]178[/C][C]27444.5888076205[/C][C]25909.6411035230[/C][C]28979.5365117179[/C][/ROW]
[ROW][C]179[/C][C]32268.8472810072[/C][C]30651.7679284168[/C][C]33885.9266335975[/C][/ROW]
[ROW][C]180[/C][C]37697.5840114155[/C][C]35959.1394981965[/C][C]39436.0285246345[/C][/ROW]
[ROW][C]181[/C][C]16563.0610231648[/C][C]15008.5863700483[/C][C]18117.5356762813[/C][/ROW]
[ROW][C]182[/C][C]21567.3088333435[/C][C]19888.6554905601[/C][C]23245.9621761269[/C][/ROW]
[ROW][C]183[/C][C]24243.4521592449[/C][C]22440.6456271797[/C][C]26046.2586913101[/C][/ROW]
[ROW][C]184[/C][C]26065.1669681551[/C][C]24133.3094474779[/C][C]27997.0244888323[/C][/ROW]
[ROW][C]185[/C][C]24378.2846038248[/C][C]22419.1719526026[/C][C]26337.3972550471[/C][/ROW]
[ROW][C]186[/C][C]25176.5242972552[/C][C]23099.7428648341[/C][C]27253.3057296764[/C][/ROW]
[ROW][C]187[/C][C]30040.6668360566[/C][C]27638.7196072838[/C][C]32442.6140648294[/C][/ROW]
[ROW][C]188[/C][C]26970.0362552440[/C][C]25139.686725396[/C][C]28800.3857850921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77387&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77387&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
17725038.034165733823551.120136616926524.9481948507
17827444.588807620525909.641103523028979.5365117179
17932268.847281007230651.767928416833885.9266335975
18037697.584011415535959.139498196539436.0285246345
18116563.061023164815008.586370048318117.5356762813
18221567.308833343519888.655490560123245.9621761269
18324243.452159244922440.645627179726046.2586913101
18426065.166968155124133.309447477927997.0244888323
18524378.284603824822419.171952602626337.3972550471
18625176.524297255223099.742864834127253.3057296764
18730040.666836056627638.719607283832442.6140648294
18826970.036255244025139.68672539628800.3857850921



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