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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 05 Dec 2012 10:42:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/05/t1354722188tpmjbswfq41gpj9.htm/, Retrieved Sat, 27 Apr 2024 01:42:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196881, Retrieved Sat, 27 Apr 2024 01:42:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
- RM D      [Structural Time Series Models] [Workshop 8 - OLO ...] [2012-11-22 14:39:38] [9f87ad58f325f963ff5b3a15384d509e]
- RMPD          [Exponential Smoothing] [Paper stat - wiss...] [2012-12-05 15:42:49] [3353489d44052879174bf0d9e8b7362f] [Current]
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Dataseries X:
1.0137
0.9834
0.9643
0.9470
0.9060
0.9492
0.9397
0.9041
0.8721
0.8552
0.8564
0.8973
0.9383
0.9217
0.9095
0.8920
0.8742
0.8532
0.8607
0.9005
0.9111
0.9059
0.8883
0.8924
0.8833
0.8700
0.8758
0.8858
0.9170
0.9554
0.9922
0.9778
0.9808
0.9811
1.0014
1.0183
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.2490
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.2020
1.2271
1.2770
1.2650
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.4570
1.4718
1.4748
1.5527
1.5750
1.5557
1.5553
1.5770
1.4975
1.4369
1.3322
1.2732
1.3449
1.3239
1.2785
1.3050
1.3190
1.3650
1.4016
1.4088
1.4268
1.4562
1.4816
1.4914
1.4614
1.4272
1.3686
1.3569
1.3406
1.2565
1.2208
1.2770
1.2894
1.3067
1.3898
1.3661
1.3220
1.3360
1.3649
1.3999
1.4442
1.4349
1.4388
1.4264
1.4343
1.3770
1.3706
1.3556
1.3179
1.2905
1.3224
1.3201
1.3162
1.2789
1.2526
1.2288
1.2400
1.2856
1.2974
1.2828




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=196881&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=196881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196881&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
alpha1
beta0.104796466407934
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.104796466407934 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196881&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.104796466407934[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196881&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
alpha1
beta0.104796466407934
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.96430.95310.0112
40.9470.9351737204237690.0118262795762311
50.9060.91911307273411-0.0131130727341101
60.94920.8767388690478250.0724611309521748
70.93970.9275325395235360.0121674604764642
80.90410.919307646386627-0.0152076463866273
90.87210.882113938782927-0.0100139387829274
100.85520.8490645133836510.00613548661634866
110.85640.8328074907007380.0235925092992623
120.89730.8364799023089970.0608200976910032
130.93830.8837536336335990.0545463663664008
140.92170.930469900084191-0.00876990008419076
150.90950.912950845544617-0.00345084554461683
160.8920.900389209125421-0.0083892091254214
170.87420.88201004965312-0.00781004965312004
180.85320.863391584047003-0.0101915840470026
190.86070.8413235420517770.0193764579482228
200.90050.8508541263762530.0496458736237471
210.91110.8958568385037560.0152431614962436
220.90590.908054267965448-0.00215426796544826
230.88830.902628508294974-0.0143285082949736
240.89240.8835269312567630.00887306874323657
250.88330.888556797507249-0.00525679750724939
260.870.878905903703868-0.00890590370386757
270.87580.8646725964655330.0111274035344671
280.88580.871638709036240.0141612909637597
290.9170.8831227622890170.0338772377109832
300.95540.917872977092790.0375270229072104
310.99220.9602056764882750.0319943235117252
320.97781.00035856853742-0.0225585685374159
330.98080.983594510267473-0.00279451026747346
340.98110.986301655466102-0.00520165546610163
351.00140.9860565403537830.0153434596462175
361.01831.007964480707180.0103355192928209
371.06221.025947606607560.0362523933924426
381.07731.073646729333920.0036532706660839
391.08071.08912957919055-0.00842957919055309
401.08481.09164618907808-0.00684618907807732
411.15821.095028732654330.0631712673456657
421.16631.17504885825067-0.00874885825067095
431.13721.1822320088209-0.0450320088208966
441.11391.14841281342122-0.034512813421216
451.12221.121495992528880.00070400747112398
461.16921.129869770024170.0393302299758251
471.17021.18099143914865-0.0107914391486528
481.22861.180860534458420.0477394655415824
491.26131.244263461755380.0170365382446214
501.26461.27874883076324-0.0141488307632389
511.22621.28056608329545-0.0543660832954473
521.19851.23646870987365-0.0379687098736452
531.20071.20478972324482-0.00408972324481893
541.21381.206561134700180.00723886529982432
551.22661.22041974220440.00618025779559961
561.21761.23386741138287-0.0162674113828691
571.22181.22316264415234-0.00136264415234022
581.2491.22721984386020.0217801561397966
591.29911.256702327261470.0423976727385325
601.34081.311245453548390.0295545464516145
611.31191.3560426655828-0.0441426655828039
621.30141.3225166702119-0.021116670211899
631.32011.309803717791390.0102962822086099
641.29381.32958273178399-0.0357827317839914
651.26941.29953282793461-0.0301328279346063
661.21651.27197501404418-0.0554750140441813
671.20371.21326142859842-0.00956142859842046
681.22921.199459424667490.0297405753325057
691.22561.22807613187128-0.00247613187127982
701.20151.22421664200081-0.0227166420008096
711.17861.19773601819047-0.0191360181904707
721.18561.172830631102990.0127693688970085
731.21031.181168815841660.0291311841583426
741.19381.20892166100373-0.0151216610037304
751.2021.190836964364320.0111630356356791
761.22711.200206811053330.0268931889466744
771.2771.228125122225380.0488748777746215
781.2651.28314703671228-0.0181470367122782
791.26841.26924529138906-0.000845291389056424
801.28111.27255670783840.00854329216160177
811.27271.28615201466842-0.0134520146684247
821.26111.27634229106511-0.015242291065106
831.28811.263144952821520.0249550471784781
841.32131.292760153584870.0285398464151303
851.29991.328951028641-0.0290510286410002
861.30741.304506583493910.00289341650609187
871.32421.312309803319590.0118901966804075
881.35161.330355853916590.0212441460834052
891.35111.35998216535799-0.00888216535798958
901.34191.35855134581442-0.0166513458144211
911.37161.347606343612130.0239936563878664
921.36221.37982079401779-0.0176207940177877
931.38961.368574197069420.0210258029305781
941.42271.398177626919940.0245223730800641
951.46841.433847484966660.0345525150333361
961.4571.48316846644766-0.0261684664476642
971.47181.469026103632630.00277389636736536
981.47481.48411679817012-0.0093167981701161
991.55271.486140430643650.0665595693563477
1001.5751.571015638317830.00398436168216887
1011.55571.59373318534301-0.0380331853430136
1021.55531.57044744191283-0.0151474419128279
1031.5771.568460043525240.00853995647475614
1041.49751.59105500078708-0.093555000787076
1051.43691.5017507672898-0.0648507672897989
1061.33221.43435463603398-0.102154636033985
1071.27321.31894919115043-0.0457491911504346
1081.34491.255154837576850.089745162423152
1091.32391.336259813476-0.0123598134760003
1101.27851.31396454869825-0.0354645486982545
1111.3051.264847989311930.0401520106880748
1121.3191.295555778151210.0234442218487909
1131.3651.312012649758650.052987350241354
1141.40161.363565536828260.0380344631717404
1151.40881.404151414170380.00464858582961947
1161.42681.411838569539120.0149614304608814
1171.45621.431406474583830.0247935254161729
1181.48161.463404748437240.0181952515627628
1191.49141.490711546506420.00068845349358182
1201.46141.50058369399983-0.0391836939998318
1211.42721.46647738132784-0.0392773813278398
1221.36861.42816125055493-0.0595612505549252
1231.35691.36331944196193-0.00641944196193145
1241.34061.35094670712801-0.0103467071280101
1251.25651.33356240878204-0.0770624087820371
1261.22081.2413865406488-0.0205865406487955
1271.2771.203529143933240.0734708560667612
1281.28941.2674286300330.021971369966999
1291.30671.282131151967680.0245688480323158
1301.38981.302005880425180.0877941195748158
1311.36611.39430639392802-0.0282063939280204
1321.3221.36765046351425-0.0456504635142538
1331.3361.318766456248080.0172335437519242
1341.36491.334572470736960.0303275292630361
1351.39991.366650688638610.0332493113613865
1361.44421.405135098979780.0390649010202162
1371.43491.45352896256728-0.018628962567278
1381.43881.44227671311738-0.00347671311738162
1391.42641.44581236586797-0.0194123658679661
1401.43431.431378018520390.00292198147961487
1411.3771.43958423185436-0.0625842318543581
1421.37061.37572562550317-0.00512562550316664
1431.35561.3687884780623-0.0131884780623046
1441.31791.35240637216408-0.0345063721640761
1451.29051.31109022629272-0.0205902262927242
1461.32241.281532443334710.0408675566652932
1471.32011.317715218863960.00238478113604446
1481.31621.315665135500170.000534864499830645
1491.27891.31182118740976-0.0329211874097588
1501.25261.27107116329926-0.0184711632992625
1511.22881.24283545065506-0.014035450655056
1521.241.217564585021960.022435414978037
1531.28561.231115737234060.054484262765943
1541.29741.282425495446770.0149745045532308
1551.28281.29579477061016-0.0129947706101574

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.9643 & 0.9531 & 0.0112 \tabularnewline
4 & 0.947 & 0.935173720423769 & 0.0118262795762311 \tabularnewline
5 & 0.906 & 0.91911307273411 & -0.0131130727341101 \tabularnewline
6 & 0.9492 & 0.876738869047825 & 0.0724611309521748 \tabularnewline
7 & 0.9397 & 0.927532539523536 & 0.0121674604764642 \tabularnewline
8 & 0.9041 & 0.919307646386627 & -0.0152076463866273 \tabularnewline
9 & 0.8721 & 0.882113938782927 & -0.0100139387829274 \tabularnewline
10 & 0.8552 & 0.849064513383651 & 0.00613548661634866 \tabularnewline
11 & 0.8564 & 0.832807490700738 & 0.0235925092992623 \tabularnewline
12 & 0.8973 & 0.836479902308997 & 0.0608200976910032 \tabularnewline
13 & 0.9383 & 0.883753633633599 & 0.0545463663664008 \tabularnewline
14 & 0.9217 & 0.930469900084191 & -0.00876990008419076 \tabularnewline
15 & 0.9095 & 0.912950845544617 & -0.00345084554461683 \tabularnewline
16 & 0.892 & 0.900389209125421 & -0.0083892091254214 \tabularnewline
17 & 0.8742 & 0.88201004965312 & -0.00781004965312004 \tabularnewline
18 & 0.8532 & 0.863391584047003 & -0.0101915840470026 \tabularnewline
19 & 0.8607 & 0.841323542051777 & 0.0193764579482228 \tabularnewline
20 & 0.9005 & 0.850854126376253 & 0.0496458736237471 \tabularnewline
21 & 0.9111 & 0.895856838503756 & 0.0152431614962436 \tabularnewline
22 & 0.9059 & 0.908054267965448 & -0.00215426796544826 \tabularnewline
23 & 0.8883 & 0.902628508294974 & -0.0143285082949736 \tabularnewline
24 & 0.8924 & 0.883526931256763 & 0.00887306874323657 \tabularnewline
25 & 0.8833 & 0.888556797507249 & -0.00525679750724939 \tabularnewline
26 & 0.87 & 0.878905903703868 & -0.00890590370386757 \tabularnewline
27 & 0.8758 & 0.864672596465533 & 0.0111274035344671 \tabularnewline
28 & 0.8858 & 0.87163870903624 & 0.0141612909637597 \tabularnewline
29 & 0.917 & 0.883122762289017 & 0.0338772377109832 \tabularnewline
30 & 0.9554 & 0.91787297709279 & 0.0375270229072104 \tabularnewline
31 & 0.9922 & 0.960205676488275 & 0.0319943235117252 \tabularnewline
32 & 0.9778 & 1.00035856853742 & -0.0225585685374159 \tabularnewline
33 & 0.9808 & 0.983594510267473 & -0.00279451026747346 \tabularnewline
34 & 0.9811 & 0.986301655466102 & -0.00520165546610163 \tabularnewline
35 & 1.0014 & 0.986056540353783 & 0.0153434596462175 \tabularnewline
36 & 1.0183 & 1.00796448070718 & 0.0103355192928209 \tabularnewline
37 & 1.0622 & 1.02594760660756 & 0.0362523933924426 \tabularnewline
38 & 1.0773 & 1.07364672933392 & 0.0036532706660839 \tabularnewline
39 & 1.0807 & 1.08912957919055 & -0.00842957919055309 \tabularnewline
40 & 1.0848 & 1.09164618907808 & -0.00684618907807732 \tabularnewline
41 & 1.1582 & 1.09502873265433 & 0.0631712673456657 \tabularnewline
42 & 1.1663 & 1.17504885825067 & -0.00874885825067095 \tabularnewline
43 & 1.1372 & 1.1822320088209 & -0.0450320088208966 \tabularnewline
44 & 1.1139 & 1.14841281342122 & -0.034512813421216 \tabularnewline
45 & 1.1222 & 1.12149599252888 & 0.00070400747112398 \tabularnewline
46 & 1.1692 & 1.12986977002417 & 0.0393302299758251 \tabularnewline
47 & 1.1702 & 1.18099143914865 & -0.0107914391486528 \tabularnewline
48 & 1.2286 & 1.18086053445842 & 0.0477394655415824 \tabularnewline
49 & 1.2613 & 1.24426346175538 & 0.0170365382446214 \tabularnewline
50 & 1.2646 & 1.27874883076324 & -0.0141488307632389 \tabularnewline
51 & 1.2262 & 1.28056608329545 & -0.0543660832954473 \tabularnewline
52 & 1.1985 & 1.23646870987365 & -0.0379687098736452 \tabularnewline
53 & 1.2007 & 1.20478972324482 & -0.00408972324481893 \tabularnewline
54 & 1.2138 & 1.20656113470018 & 0.00723886529982432 \tabularnewline
55 & 1.2266 & 1.2204197422044 & 0.00618025779559961 \tabularnewline
56 & 1.2176 & 1.23386741138287 & -0.0162674113828691 \tabularnewline
57 & 1.2218 & 1.22316264415234 & -0.00136264415234022 \tabularnewline
58 & 1.249 & 1.2272198438602 & 0.0217801561397966 \tabularnewline
59 & 1.2991 & 1.25670232726147 & 0.0423976727385325 \tabularnewline
60 & 1.3408 & 1.31124545354839 & 0.0295545464516145 \tabularnewline
61 & 1.3119 & 1.3560426655828 & -0.0441426655828039 \tabularnewline
62 & 1.3014 & 1.3225166702119 & -0.021116670211899 \tabularnewline
63 & 1.3201 & 1.30980371779139 & 0.0102962822086099 \tabularnewline
64 & 1.2938 & 1.32958273178399 & -0.0357827317839914 \tabularnewline
65 & 1.2694 & 1.29953282793461 & -0.0301328279346063 \tabularnewline
66 & 1.2165 & 1.27197501404418 & -0.0554750140441813 \tabularnewline
67 & 1.2037 & 1.21326142859842 & -0.00956142859842046 \tabularnewline
68 & 1.2292 & 1.19945942466749 & 0.0297405753325057 \tabularnewline
69 & 1.2256 & 1.22807613187128 & -0.00247613187127982 \tabularnewline
70 & 1.2015 & 1.22421664200081 & -0.0227166420008096 \tabularnewline
71 & 1.1786 & 1.19773601819047 & -0.0191360181904707 \tabularnewline
72 & 1.1856 & 1.17283063110299 & 0.0127693688970085 \tabularnewline
73 & 1.2103 & 1.18116881584166 & 0.0291311841583426 \tabularnewline
74 & 1.1938 & 1.20892166100373 & -0.0151216610037304 \tabularnewline
75 & 1.202 & 1.19083696436432 & 0.0111630356356791 \tabularnewline
76 & 1.2271 & 1.20020681105333 & 0.0268931889466744 \tabularnewline
77 & 1.277 & 1.22812512222538 & 0.0488748777746215 \tabularnewline
78 & 1.265 & 1.28314703671228 & -0.0181470367122782 \tabularnewline
79 & 1.2684 & 1.26924529138906 & -0.000845291389056424 \tabularnewline
80 & 1.2811 & 1.2725567078384 & 0.00854329216160177 \tabularnewline
81 & 1.2727 & 1.28615201466842 & -0.0134520146684247 \tabularnewline
82 & 1.2611 & 1.27634229106511 & -0.015242291065106 \tabularnewline
83 & 1.2881 & 1.26314495282152 & 0.0249550471784781 \tabularnewline
84 & 1.3213 & 1.29276015358487 & 0.0285398464151303 \tabularnewline
85 & 1.2999 & 1.328951028641 & -0.0290510286410002 \tabularnewline
86 & 1.3074 & 1.30450658349391 & 0.00289341650609187 \tabularnewline
87 & 1.3242 & 1.31230980331959 & 0.0118901966804075 \tabularnewline
88 & 1.3516 & 1.33035585391659 & 0.0212441460834052 \tabularnewline
89 & 1.3511 & 1.35998216535799 & -0.00888216535798958 \tabularnewline
90 & 1.3419 & 1.35855134581442 & -0.0166513458144211 \tabularnewline
91 & 1.3716 & 1.34760634361213 & 0.0239936563878664 \tabularnewline
92 & 1.3622 & 1.37982079401779 & -0.0176207940177877 \tabularnewline
93 & 1.3896 & 1.36857419706942 & 0.0210258029305781 \tabularnewline
94 & 1.4227 & 1.39817762691994 & 0.0245223730800641 \tabularnewline
95 & 1.4684 & 1.43384748496666 & 0.0345525150333361 \tabularnewline
96 & 1.457 & 1.48316846644766 & -0.0261684664476642 \tabularnewline
97 & 1.4718 & 1.46902610363263 & 0.00277389636736536 \tabularnewline
98 & 1.4748 & 1.48411679817012 & -0.0093167981701161 \tabularnewline
99 & 1.5527 & 1.48614043064365 & 0.0665595693563477 \tabularnewline
100 & 1.575 & 1.57101563831783 & 0.00398436168216887 \tabularnewline
101 & 1.5557 & 1.59373318534301 & -0.0380331853430136 \tabularnewline
102 & 1.5553 & 1.57044744191283 & -0.0151474419128279 \tabularnewline
103 & 1.577 & 1.56846004352524 & 0.00853995647475614 \tabularnewline
104 & 1.4975 & 1.59105500078708 & -0.093555000787076 \tabularnewline
105 & 1.4369 & 1.5017507672898 & -0.0648507672897989 \tabularnewline
106 & 1.3322 & 1.43435463603398 & -0.102154636033985 \tabularnewline
107 & 1.2732 & 1.31894919115043 & -0.0457491911504346 \tabularnewline
108 & 1.3449 & 1.25515483757685 & 0.089745162423152 \tabularnewline
109 & 1.3239 & 1.336259813476 & -0.0123598134760003 \tabularnewline
110 & 1.2785 & 1.31396454869825 & -0.0354645486982545 \tabularnewline
111 & 1.305 & 1.26484798931193 & 0.0401520106880748 \tabularnewline
112 & 1.319 & 1.29555577815121 & 0.0234442218487909 \tabularnewline
113 & 1.365 & 1.31201264975865 & 0.052987350241354 \tabularnewline
114 & 1.4016 & 1.36356553682826 & 0.0380344631717404 \tabularnewline
115 & 1.4088 & 1.40415141417038 & 0.00464858582961947 \tabularnewline
116 & 1.4268 & 1.41183856953912 & 0.0149614304608814 \tabularnewline
117 & 1.4562 & 1.43140647458383 & 0.0247935254161729 \tabularnewline
118 & 1.4816 & 1.46340474843724 & 0.0181952515627628 \tabularnewline
119 & 1.4914 & 1.49071154650642 & 0.00068845349358182 \tabularnewline
120 & 1.4614 & 1.50058369399983 & -0.0391836939998318 \tabularnewline
121 & 1.4272 & 1.46647738132784 & -0.0392773813278398 \tabularnewline
122 & 1.3686 & 1.42816125055493 & -0.0595612505549252 \tabularnewline
123 & 1.3569 & 1.36331944196193 & -0.00641944196193145 \tabularnewline
124 & 1.3406 & 1.35094670712801 & -0.0103467071280101 \tabularnewline
125 & 1.2565 & 1.33356240878204 & -0.0770624087820371 \tabularnewline
126 & 1.2208 & 1.2413865406488 & -0.0205865406487955 \tabularnewline
127 & 1.277 & 1.20352914393324 & 0.0734708560667612 \tabularnewline
128 & 1.2894 & 1.267428630033 & 0.021971369966999 \tabularnewline
129 & 1.3067 & 1.28213115196768 & 0.0245688480323158 \tabularnewline
130 & 1.3898 & 1.30200588042518 & 0.0877941195748158 \tabularnewline
131 & 1.3661 & 1.39430639392802 & -0.0282063939280204 \tabularnewline
132 & 1.322 & 1.36765046351425 & -0.0456504635142538 \tabularnewline
133 & 1.336 & 1.31876645624808 & 0.0172335437519242 \tabularnewline
134 & 1.3649 & 1.33457247073696 & 0.0303275292630361 \tabularnewline
135 & 1.3999 & 1.36665068863861 & 0.0332493113613865 \tabularnewline
136 & 1.4442 & 1.40513509897978 & 0.0390649010202162 \tabularnewline
137 & 1.4349 & 1.45352896256728 & -0.018628962567278 \tabularnewline
138 & 1.4388 & 1.44227671311738 & -0.00347671311738162 \tabularnewline
139 & 1.4264 & 1.44581236586797 & -0.0194123658679661 \tabularnewline
140 & 1.4343 & 1.43137801852039 & 0.00292198147961487 \tabularnewline
141 & 1.377 & 1.43958423185436 & -0.0625842318543581 \tabularnewline
142 & 1.3706 & 1.37572562550317 & -0.00512562550316664 \tabularnewline
143 & 1.3556 & 1.3687884780623 & -0.0131884780623046 \tabularnewline
144 & 1.3179 & 1.35240637216408 & -0.0345063721640761 \tabularnewline
145 & 1.2905 & 1.31109022629272 & -0.0205902262927242 \tabularnewline
146 & 1.3224 & 1.28153244333471 & 0.0408675566652932 \tabularnewline
147 & 1.3201 & 1.31771521886396 & 0.00238478113604446 \tabularnewline
148 & 1.3162 & 1.31566513550017 & 0.000534864499830645 \tabularnewline
149 & 1.2789 & 1.31182118740976 & -0.0329211874097588 \tabularnewline
150 & 1.2526 & 1.27107116329926 & -0.0184711632992625 \tabularnewline
151 & 1.2288 & 1.24283545065506 & -0.014035450655056 \tabularnewline
152 & 1.24 & 1.21756458502196 & 0.022435414978037 \tabularnewline
153 & 1.2856 & 1.23111573723406 & 0.054484262765943 \tabularnewline
154 & 1.2974 & 1.28242549544677 & 0.0149745045532308 \tabularnewline
155 & 1.2828 & 1.29579477061016 & -0.0129947706101574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196881&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]0.9643[/C][C]0.9531[/C][C]0.0112[/C][/ROW]
[ROW][C]4[/C][C]0.947[/C][C]0.935173720423769[/C][C]0.0118262795762311[/C][/ROW]
[ROW][C]5[/C][C]0.906[/C][C]0.91911307273411[/C][C]-0.0131130727341101[/C][/ROW]
[ROW][C]6[/C][C]0.9492[/C][C]0.876738869047825[/C][C]0.0724611309521748[/C][/ROW]
[ROW][C]7[/C][C]0.9397[/C][C]0.927532539523536[/C][C]0.0121674604764642[/C][/ROW]
[ROW][C]8[/C][C]0.9041[/C][C]0.919307646386627[/C][C]-0.0152076463866273[/C][/ROW]
[ROW][C]9[/C][C]0.8721[/C][C]0.882113938782927[/C][C]-0.0100139387829274[/C][/ROW]
[ROW][C]10[/C][C]0.8552[/C][C]0.849064513383651[/C][C]0.00613548661634866[/C][/ROW]
[ROW][C]11[/C][C]0.8564[/C][C]0.832807490700738[/C][C]0.0235925092992623[/C][/ROW]
[ROW][C]12[/C][C]0.8973[/C][C]0.836479902308997[/C][C]0.0608200976910032[/C][/ROW]
[ROW][C]13[/C][C]0.9383[/C][C]0.883753633633599[/C][C]0.0545463663664008[/C][/ROW]
[ROW][C]14[/C][C]0.9217[/C][C]0.930469900084191[/C][C]-0.00876990008419076[/C][/ROW]
[ROW][C]15[/C][C]0.9095[/C][C]0.912950845544617[/C][C]-0.00345084554461683[/C][/ROW]
[ROW][C]16[/C][C]0.892[/C][C]0.900389209125421[/C][C]-0.0083892091254214[/C][/ROW]
[ROW][C]17[/C][C]0.8742[/C][C]0.88201004965312[/C][C]-0.00781004965312004[/C][/ROW]
[ROW][C]18[/C][C]0.8532[/C][C]0.863391584047003[/C][C]-0.0101915840470026[/C][/ROW]
[ROW][C]19[/C][C]0.8607[/C][C]0.841323542051777[/C][C]0.0193764579482228[/C][/ROW]
[ROW][C]20[/C][C]0.9005[/C][C]0.850854126376253[/C][C]0.0496458736237471[/C][/ROW]
[ROW][C]21[/C][C]0.9111[/C][C]0.895856838503756[/C][C]0.0152431614962436[/C][/ROW]
[ROW][C]22[/C][C]0.9059[/C][C]0.908054267965448[/C][C]-0.00215426796544826[/C][/ROW]
[ROW][C]23[/C][C]0.8883[/C][C]0.902628508294974[/C][C]-0.0143285082949736[/C][/ROW]
[ROW][C]24[/C][C]0.8924[/C][C]0.883526931256763[/C][C]0.00887306874323657[/C][/ROW]
[ROW][C]25[/C][C]0.8833[/C][C]0.888556797507249[/C][C]-0.00525679750724939[/C][/ROW]
[ROW][C]26[/C][C]0.87[/C][C]0.878905903703868[/C][C]-0.00890590370386757[/C][/ROW]
[ROW][C]27[/C][C]0.8758[/C][C]0.864672596465533[/C][C]0.0111274035344671[/C][/ROW]
[ROW][C]28[/C][C]0.8858[/C][C]0.87163870903624[/C][C]0.0141612909637597[/C][/ROW]
[ROW][C]29[/C][C]0.917[/C][C]0.883122762289017[/C][C]0.0338772377109832[/C][/ROW]
[ROW][C]30[/C][C]0.9554[/C][C]0.91787297709279[/C][C]0.0375270229072104[/C][/ROW]
[ROW][C]31[/C][C]0.9922[/C][C]0.960205676488275[/C][C]0.0319943235117252[/C][/ROW]
[ROW][C]32[/C][C]0.9778[/C][C]1.00035856853742[/C][C]-0.0225585685374159[/C][/ROW]
[ROW][C]33[/C][C]0.9808[/C][C]0.983594510267473[/C][C]-0.00279451026747346[/C][/ROW]
[ROW][C]34[/C][C]0.9811[/C][C]0.986301655466102[/C][C]-0.00520165546610163[/C][/ROW]
[ROW][C]35[/C][C]1.0014[/C][C]0.986056540353783[/C][C]0.0153434596462175[/C][/ROW]
[ROW][C]36[/C][C]1.0183[/C][C]1.00796448070718[/C][C]0.0103355192928209[/C][/ROW]
[ROW][C]37[/C][C]1.0622[/C][C]1.02594760660756[/C][C]0.0362523933924426[/C][/ROW]
[ROW][C]38[/C][C]1.0773[/C][C]1.07364672933392[/C][C]0.0036532706660839[/C][/ROW]
[ROW][C]39[/C][C]1.0807[/C][C]1.08912957919055[/C][C]-0.00842957919055309[/C][/ROW]
[ROW][C]40[/C][C]1.0848[/C][C]1.09164618907808[/C][C]-0.00684618907807732[/C][/ROW]
[ROW][C]41[/C][C]1.1582[/C][C]1.09502873265433[/C][C]0.0631712673456657[/C][/ROW]
[ROW][C]42[/C][C]1.1663[/C][C]1.17504885825067[/C][C]-0.00874885825067095[/C][/ROW]
[ROW][C]43[/C][C]1.1372[/C][C]1.1822320088209[/C][C]-0.0450320088208966[/C][/ROW]
[ROW][C]44[/C][C]1.1139[/C][C]1.14841281342122[/C][C]-0.034512813421216[/C][/ROW]
[ROW][C]45[/C][C]1.1222[/C][C]1.12149599252888[/C][C]0.00070400747112398[/C][/ROW]
[ROW][C]46[/C][C]1.1692[/C][C]1.12986977002417[/C][C]0.0393302299758251[/C][/ROW]
[ROW][C]47[/C][C]1.1702[/C][C]1.18099143914865[/C][C]-0.0107914391486528[/C][/ROW]
[ROW][C]48[/C][C]1.2286[/C][C]1.18086053445842[/C][C]0.0477394655415824[/C][/ROW]
[ROW][C]49[/C][C]1.2613[/C][C]1.24426346175538[/C][C]0.0170365382446214[/C][/ROW]
[ROW][C]50[/C][C]1.2646[/C][C]1.27874883076324[/C][C]-0.0141488307632389[/C][/ROW]
[ROW][C]51[/C][C]1.2262[/C][C]1.28056608329545[/C][C]-0.0543660832954473[/C][/ROW]
[ROW][C]52[/C][C]1.1985[/C][C]1.23646870987365[/C][C]-0.0379687098736452[/C][/ROW]
[ROW][C]53[/C][C]1.2007[/C][C]1.20478972324482[/C][C]-0.00408972324481893[/C][/ROW]
[ROW][C]54[/C][C]1.2138[/C][C]1.20656113470018[/C][C]0.00723886529982432[/C][/ROW]
[ROW][C]55[/C][C]1.2266[/C][C]1.2204197422044[/C][C]0.00618025779559961[/C][/ROW]
[ROW][C]56[/C][C]1.2176[/C][C]1.23386741138287[/C][C]-0.0162674113828691[/C][/ROW]
[ROW][C]57[/C][C]1.2218[/C][C]1.22316264415234[/C][C]-0.00136264415234022[/C][/ROW]
[ROW][C]58[/C][C]1.249[/C][C]1.2272198438602[/C][C]0.0217801561397966[/C][/ROW]
[ROW][C]59[/C][C]1.2991[/C][C]1.25670232726147[/C][C]0.0423976727385325[/C][/ROW]
[ROW][C]60[/C][C]1.3408[/C][C]1.31124545354839[/C][C]0.0295545464516145[/C][/ROW]
[ROW][C]61[/C][C]1.3119[/C][C]1.3560426655828[/C][C]-0.0441426655828039[/C][/ROW]
[ROW][C]62[/C][C]1.3014[/C][C]1.3225166702119[/C][C]-0.021116670211899[/C][/ROW]
[ROW][C]63[/C][C]1.3201[/C][C]1.30980371779139[/C][C]0.0102962822086099[/C][/ROW]
[ROW][C]64[/C][C]1.2938[/C][C]1.32958273178399[/C][C]-0.0357827317839914[/C][/ROW]
[ROW][C]65[/C][C]1.2694[/C][C]1.29953282793461[/C][C]-0.0301328279346063[/C][/ROW]
[ROW][C]66[/C][C]1.2165[/C][C]1.27197501404418[/C][C]-0.0554750140441813[/C][/ROW]
[ROW][C]67[/C][C]1.2037[/C][C]1.21326142859842[/C][C]-0.00956142859842046[/C][/ROW]
[ROW][C]68[/C][C]1.2292[/C][C]1.19945942466749[/C][C]0.0297405753325057[/C][/ROW]
[ROW][C]69[/C][C]1.2256[/C][C]1.22807613187128[/C][C]-0.00247613187127982[/C][/ROW]
[ROW][C]70[/C][C]1.2015[/C][C]1.22421664200081[/C][C]-0.0227166420008096[/C][/ROW]
[ROW][C]71[/C][C]1.1786[/C][C]1.19773601819047[/C][C]-0.0191360181904707[/C][/ROW]
[ROW][C]72[/C][C]1.1856[/C][C]1.17283063110299[/C][C]0.0127693688970085[/C][/ROW]
[ROW][C]73[/C][C]1.2103[/C][C]1.18116881584166[/C][C]0.0291311841583426[/C][/ROW]
[ROW][C]74[/C][C]1.1938[/C][C]1.20892166100373[/C][C]-0.0151216610037304[/C][/ROW]
[ROW][C]75[/C][C]1.202[/C][C]1.19083696436432[/C][C]0.0111630356356791[/C][/ROW]
[ROW][C]76[/C][C]1.2271[/C][C]1.20020681105333[/C][C]0.0268931889466744[/C][/ROW]
[ROW][C]77[/C][C]1.277[/C][C]1.22812512222538[/C][C]0.0488748777746215[/C][/ROW]
[ROW][C]78[/C][C]1.265[/C][C]1.28314703671228[/C][C]-0.0181470367122782[/C][/ROW]
[ROW][C]79[/C][C]1.2684[/C][C]1.26924529138906[/C][C]-0.000845291389056424[/C][/ROW]
[ROW][C]80[/C][C]1.2811[/C][C]1.2725567078384[/C][C]0.00854329216160177[/C][/ROW]
[ROW][C]81[/C][C]1.2727[/C][C]1.28615201466842[/C][C]-0.0134520146684247[/C][/ROW]
[ROW][C]82[/C][C]1.2611[/C][C]1.27634229106511[/C][C]-0.015242291065106[/C][/ROW]
[ROW][C]83[/C][C]1.2881[/C][C]1.26314495282152[/C][C]0.0249550471784781[/C][/ROW]
[ROW][C]84[/C][C]1.3213[/C][C]1.29276015358487[/C][C]0.0285398464151303[/C][/ROW]
[ROW][C]85[/C][C]1.2999[/C][C]1.328951028641[/C][C]-0.0290510286410002[/C][/ROW]
[ROW][C]86[/C][C]1.3074[/C][C]1.30450658349391[/C][C]0.00289341650609187[/C][/ROW]
[ROW][C]87[/C][C]1.3242[/C][C]1.31230980331959[/C][C]0.0118901966804075[/C][/ROW]
[ROW][C]88[/C][C]1.3516[/C][C]1.33035585391659[/C][C]0.0212441460834052[/C][/ROW]
[ROW][C]89[/C][C]1.3511[/C][C]1.35998216535799[/C][C]-0.00888216535798958[/C][/ROW]
[ROW][C]90[/C][C]1.3419[/C][C]1.35855134581442[/C][C]-0.0166513458144211[/C][/ROW]
[ROW][C]91[/C][C]1.3716[/C][C]1.34760634361213[/C][C]0.0239936563878664[/C][/ROW]
[ROW][C]92[/C][C]1.3622[/C][C]1.37982079401779[/C][C]-0.0176207940177877[/C][/ROW]
[ROW][C]93[/C][C]1.3896[/C][C]1.36857419706942[/C][C]0.0210258029305781[/C][/ROW]
[ROW][C]94[/C][C]1.4227[/C][C]1.39817762691994[/C][C]0.0245223730800641[/C][/ROW]
[ROW][C]95[/C][C]1.4684[/C][C]1.43384748496666[/C][C]0.0345525150333361[/C][/ROW]
[ROW][C]96[/C][C]1.457[/C][C]1.48316846644766[/C][C]-0.0261684664476642[/C][/ROW]
[ROW][C]97[/C][C]1.4718[/C][C]1.46902610363263[/C][C]0.00277389636736536[/C][/ROW]
[ROW][C]98[/C][C]1.4748[/C][C]1.48411679817012[/C][C]-0.0093167981701161[/C][/ROW]
[ROW][C]99[/C][C]1.5527[/C][C]1.48614043064365[/C][C]0.0665595693563477[/C][/ROW]
[ROW][C]100[/C][C]1.575[/C][C]1.57101563831783[/C][C]0.00398436168216887[/C][/ROW]
[ROW][C]101[/C][C]1.5557[/C][C]1.59373318534301[/C][C]-0.0380331853430136[/C][/ROW]
[ROW][C]102[/C][C]1.5553[/C][C]1.57044744191283[/C][C]-0.0151474419128279[/C][/ROW]
[ROW][C]103[/C][C]1.577[/C][C]1.56846004352524[/C][C]0.00853995647475614[/C][/ROW]
[ROW][C]104[/C][C]1.4975[/C][C]1.59105500078708[/C][C]-0.093555000787076[/C][/ROW]
[ROW][C]105[/C][C]1.4369[/C][C]1.5017507672898[/C][C]-0.0648507672897989[/C][/ROW]
[ROW][C]106[/C][C]1.3322[/C][C]1.43435463603398[/C][C]-0.102154636033985[/C][/ROW]
[ROW][C]107[/C][C]1.2732[/C][C]1.31894919115043[/C][C]-0.0457491911504346[/C][/ROW]
[ROW][C]108[/C][C]1.3449[/C][C]1.25515483757685[/C][C]0.089745162423152[/C][/ROW]
[ROW][C]109[/C][C]1.3239[/C][C]1.336259813476[/C][C]-0.0123598134760003[/C][/ROW]
[ROW][C]110[/C][C]1.2785[/C][C]1.31396454869825[/C][C]-0.0354645486982545[/C][/ROW]
[ROW][C]111[/C][C]1.305[/C][C]1.26484798931193[/C][C]0.0401520106880748[/C][/ROW]
[ROW][C]112[/C][C]1.319[/C][C]1.29555577815121[/C][C]0.0234442218487909[/C][/ROW]
[ROW][C]113[/C][C]1.365[/C][C]1.31201264975865[/C][C]0.052987350241354[/C][/ROW]
[ROW][C]114[/C][C]1.4016[/C][C]1.36356553682826[/C][C]0.0380344631717404[/C][/ROW]
[ROW][C]115[/C][C]1.4088[/C][C]1.40415141417038[/C][C]0.00464858582961947[/C][/ROW]
[ROW][C]116[/C][C]1.4268[/C][C]1.41183856953912[/C][C]0.0149614304608814[/C][/ROW]
[ROW][C]117[/C][C]1.4562[/C][C]1.43140647458383[/C][C]0.0247935254161729[/C][/ROW]
[ROW][C]118[/C][C]1.4816[/C][C]1.46340474843724[/C][C]0.0181952515627628[/C][/ROW]
[ROW][C]119[/C][C]1.4914[/C][C]1.49071154650642[/C][C]0.00068845349358182[/C][/ROW]
[ROW][C]120[/C][C]1.4614[/C][C]1.50058369399983[/C][C]-0.0391836939998318[/C][/ROW]
[ROW][C]121[/C][C]1.4272[/C][C]1.46647738132784[/C][C]-0.0392773813278398[/C][/ROW]
[ROW][C]122[/C][C]1.3686[/C][C]1.42816125055493[/C][C]-0.0595612505549252[/C][/ROW]
[ROW][C]123[/C][C]1.3569[/C][C]1.36331944196193[/C][C]-0.00641944196193145[/C][/ROW]
[ROW][C]124[/C][C]1.3406[/C][C]1.35094670712801[/C][C]-0.0103467071280101[/C][/ROW]
[ROW][C]125[/C][C]1.2565[/C][C]1.33356240878204[/C][C]-0.0770624087820371[/C][/ROW]
[ROW][C]126[/C][C]1.2208[/C][C]1.2413865406488[/C][C]-0.0205865406487955[/C][/ROW]
[ROW][C]127[/C][C]1.277[/C][C]1.20352914393324[/C][C]0.0734708560667612[/C][/ROW]
[ROW][C]128[/C][C]1.2894[/C][C]1.267428630033[/C][C]0.021971369966999[/C][/ROW]
[ROW][C]129[/C][C]1.3067[/C][C]1.28213115196768[/C][C]0.0245688480323158[/C][/ROW]
[ROW][C]130[/C][C]1.3898[/C][C]1.30200588042518[/C][C]0.0877941195748158[/C][/ROW]
[ROW][C]131[/C][C]1.3661[/C][C]1.39430639392802[/C][C]-0.0282063939280204[/C][/ROW]
[ROW][C]132[/C][C]1.322[/C][C]1.36765046351425[/C][C]-0.0456504635142538[/C][/ROW]
[ROW][C]133[/C][C]1.336[/C][C]1.31876645624808[/C][C]0.0172335437519242[/C][/ROW]
[ROW][C]134[/C][C]1.3649[/C][C]1.33457247073696[/C][C]0.0303275292630361[/C][/ROW]
[ROW][C]135[/C][C]1.3999[/C][C]1.36665068863861[/C][C]0.0332493113613865[/C][/ROW]
[ROW][C]136[/C][C]1.4442[/C][C]1.40513509897978[/C][C]0.0390649010202162[/C][/ROW]
[ROW][C]137[/C][C]1.4349[/C][C]1.45352896256728[/C][C]-0.018628962567278[/C][/ROW]
[ROW][C]138[/C][C]1.4388[/C][C]1.44227671311738[/C][C]-0.00347671311738162[/C][/ROW]
[ROW][C]139[/C][C]1.4264[/C][C]1.44581236586797[/C][C]-0.0194123658679661[/C][/ROW]
[ROW][C]140[/C][C]1.4343[/C][C]1.43137801852039[/C][C]0.00292198147961487[/C][/ROW]
[ROW][C]141[/C][C]1.377[/C][C]1.43958423185436[/C][C]-0.0625842318543581[/C][/ROW]
[ROW][C]142[/C][C]1.3706[/C][C]1.37572562550317[/C][C]-0.00512562550316664[/C][/ROW]
[ROW][C]143[/C][C]1.3556[/C][C]1.3687884780623[/C][C]-0.0131884780623046[/C][/ROW]
[ROW][C]144[/C][C]1.3179[/C][C]1.35240637216408[/C][C]-0.0345063721640761[/C][/ROW]
[ROW][C]145[/C][C]1.2905[/C][C]1.31109022629272[/C][C]-0.0205902262927242[/C][/ROW]
[ROW][C]146[/C][C]1.3224[/C][C]1.28153244333471[/C][C]0.0408675566652932[/C][/ROW]
[ROW][C]147[/C][C]1.3201[/C][C]1.31771521886396[/C][C]0.00238478113604446[/C][/ROW]
[ROW][C]148[/C][C]1.3162[/C][C]1.31566513550017[/C][C]0.000534864499830645[/C][/ROW]
[ROW][C]149[/C][C]1.2789[/C][C]1.31182118740976[/C][C]-0.0329211874097588[/C][/ROW]
[ROW][C]150[/C][C]1.2526[/C][C]1.27107116329926[/C][C]-0.0184711632992625[/C][/ROW]
[ROW][C]151[/C][C]1.2288[/C][C]1.24283545065506[/C][C]-0.014035450655056[/C][/ROW]
[ROW][C]152[/C][C]1.24[/C][C]1.21756458502196[/C][C]0.022435414978037[/C][/ROW]
[ROW][C]153[/C][C]1.2856[/C][C]1.23111573723406[/C][C]0.054484262765943[/C][/ROW]
[ROW][C]154[/C][C]1.2974[/C][C]1.28242549544677[/C][C]0.0149745045532308[/C][/ROW]
[ROW][C]155[/C][C]1.2828[/C][C]1.29579477061016[/C][C]-0.0129947706101574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196881&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
30.96430.95310.0112
40.9470.9351737204237690.0118262795762311
50.9060.91911307273411-0.0131130727341101
60.94920.8767388690478250.0724611309521748
70.93970.9275325395235360.0121674604764642
80.90410.919307646386627-0.0152076463866273
90.87210.882113938782927-0.0100139387829274
100.85520.8490645133836510.00613548661634866
110.85640.8328074907007380.0235925092992623
120.89730.8364799023089970.0608200976910032
130.93830.8837536336335990.0545463663664008
140.92170.930469900084191-0.00876990008419076
150.90950.912950845544617-0.00345084554461683
160.8920.900389209125421-0.0083892091254214
170.87420.88201004965312-0.00781004965312004
180.85320.863391584047003-0.0101915840470026
190.86070.8413235420517770.0193764579482228
200.90050.8508541263762530.0496458736237471
210.91110.8958568385037560.0152431614962436
220.90590.908054267965448-0.00215426796544826
230.88830.902628508294974-0.0143285082949736
240.89240.8835269312567630.00887306874323657
250.88330.888556797507249-0.00525679750724939
260.870.878905903703868-0.00890590370386757
270.87580.8646725964655330.0111274035344671
280.88580.871638709036240.0141612909637597
290.9170.8831227622890170.0338772377109832
300.95540.917872977092790.0375270229072104
310.99220.9602056764882750.0319943235117252
320.97781.00035856853742-0.0225585685374159
330.98080.983594510267473-0.00279451026747346
340.98110.986301655466102-0.00520165546610163
351.00140.9860565403537830.0153434596462175
361.01831.007964480707180.0103355192928209
371.06221.025947606607560.0362523933924426
381.07731.073646729333920.0036532706660839
391.08071.08912957919055-0.00842957919055309
401.08481.09164618907808-0.00684618907807732
411.15821.095028732654330.0631712673456657
421.16631.17504885825067-0.00874885825067095
431.13721.1822320088209-0.0450320088208966
441.11391.14841281342122-0.034512813421216
451.12221.121495992528880.00070400747112398
461.16921.129869770024170.0393302299758251
471.17021.18099143914865-0.0107914391486528
481.22861.180860534458420.0477394655415824
491.26131.244263461755380.0170365382446214
501.26461.27874883076324-0.0141488307632389
511.22621.28056608329545-0.0543660832954473
521.19851.23646870987365-0.0379687098736452
531.20071.20478972324482-0.00408972324481893
541.21381.206561134700180.00723886529982432
551.22661.22041974220440.00618025779559961
561.21761.23386741138287-0.0162674113828691
571.22181.22316264415234-0.00136264415234022
581.2491.22721984386020.0217801561397966
591.29911.256702327261470.0423976727385325
601.34081.311245453548390.0295545464516145
611.31191.3560426655828-0.0441426655828039
621.30141.3225166702119-0.021116670211899
631.32011.309803717791390.0102962822086099
641.29381.32958273178399-0.0357827317839914
651.26941.29953282793461-0.0301328279346063
661.21651.27197501404418-0.0554750140441813
671.20371.21326142859842-0.00956142859842046
681.22921.199459424667490.0297405753325057
691.22561.22807613187128-0.00247613187127982
701.20151.22421664200081-0.0227166420008096
711.17861.19773601819047-0.0191360181904707
721.18561.172830631102990.0127693688970085
731.21031.181168815841660.0291311841583426
741.19381.20892166100373-0.0151216610037304
751.2021.190836964364320.0111630356356791
761.22711.200206811053330.0268931889466744
771.2771.228125122225380.0488748777746215
781.2651.28314703671228-0.0181470367122782
791.26841.26924529138906-0.000845291389056424
801.28111.27255670783840.00854329216160177
811.27271.28615201466842-0.0134520146684247
821.26111.27634229106511-0.015242291065106
831.28811.263144952821520.0249550471784781
841.32131.292760153584870.0285398464151303
851.29991.328951028641-0.0290510286410002
861.30741.304506583493910.00289341650609187
871.32421.312309803319590.0118901966804075
881.35161.330355853916590.0212441460834052
891.35111.35998216535799-0.00888216535798958
901.34191.35855134581442-0.0166513458144211
911.37161.347606343612130.0239936563878664
921.36221.37982079401779-0.0176207940177877
931.38961.368574197069420.0210258029305781
941.42271.398177626919940.0245223730800641
951.46841.433847484966660.0345525150333361
961.4571.48316846644766-0.0261684664476642
971.47181.469026103632630.00277389636736536
981.47481.48411679817012-0.0093167981701161
991.55271.486140430643650.0665595693563477
1001.5751.571015638317830.00398436168216887
1011.55571.59373318534301-0.0380331853430136
1021.55531.57044744191283-0.0151474419128279
1031.5771.568460043525240.00853995647475614
1041.49751.59105500078708-0.093555000787076
1051.43691.5017507672898-0.0648507672897989
1061.33221.43435463603398-0.102154636033985
1071.27321.31894919115043-0.0457491911504346
1081.34491.255154837576850.089745162423152
1091.32391.336259813476-0.0123598134760003
1101.27851.31396454869825-0.0354645486982545
1111.3051.264847989311930.0401520106880748
1121.3191.295555778151210.0234442218487909
1131.3651.312012649758650.052987350241354
1141.40161.363565536828260.0380344631717404
1151.40881.404151414170380.00464858582961947
1161.42681.411838569539120.0149614304608814
1171.45621.431406474583830.0247935254161729
1181.48161.463404748437240.0181952515627628
1191.49141.490711546506420.00068845349358182
1201.46141.50058369399983-0.0391836939998318
1211.42721.46647738132784-0.0392773813278398
1221.36861.42816125055493-0.0595612505549252
1231.35691.36331944196193-0.00641944196193145
1241.34061.35094670712801-0.0103467071280101
1251.25651.33356240878204-0.0770624087820371
1261.22081.2413865406488-0.0205865406487955
1271.2771.203529143933240.0734708560667612
1281.28941.2674286300330.021971369966999
1291.30671.282131151967680.0245688480323158
1301.38981.302005880425180.0877941195748158
1311.36611.39430639392802-0.0282063939280204
1321.3221.36765046351425-0.0456504635142538
1331.3361.318766456248080.0172335437519242
1341.36491.334572470736960.0303275292630361
1351.39991.366650688638610.0332493113613865
1361.44421.405135098979780.0390649010202162
1371.43491.45352896256728-0.018628962567278
1381.43881.44227671311738-0.00347671311738162
1391.42641.44581236586797-0.0194123658679661
1401.43431.431378018520390.00292198147961487
1411.3771.43958423185436-0.0625842318543581
1421.37061.37572562550317-0.00512562550316664
1431.35561.3687884780623-0.0131884780623046
1441.31791.35240637216408-0.0345063721640761
1451.29051.31109022629272-0.0205902262927242
1461.32241.281532443334710.0408675566652932
1471.32011.317715218863960.00238478113604446
1481.31621.315665135500170.000534864499830645
1491.27891.31182118740976-0.0329211874097588
1501.25261.27107116329926-0.0184711632992625
1511.22881.24283545065506-0.014035450655056
1521.241.217564585021960.022435414978037
1531.28561.231115737234060.054484262765943
1541.29741.282425495446770.0149745045532308
1551.28281.29579477061016-0.0129947706101574







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1561.279832964568431.216011249514661.3436546796222
1571.276865929136861.181761396354291.37197046191944
1581.273898893705291.15140624501881.39639154239179
1591.270931858273721.122468366991171.41939534955628
1601.267964822842161.094053303981051.44187634170326
1611.264997787410591.065735799363131.46425977545804
1621.262030751979021.037283682676611.48677782128142
1631.259063716547451.008559427796071.50956800529883
1641.256096681115880.9794773273078961.53271603492386
1651.253129645684310.9499822949338481.55627699643478
1661.250162610252740.9200383711660881.5802868493394
1671.247195574821170.8896220519622021.60476909768015

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
156 & 1.27983296456843 & 1.21601124951466 & 1.3436546796222 \tabularnewline
157 & 1.27686592913686 & 1.18176139635429 & 1.37197046191944 \tabularnewline
158 & 1.27389889370529 & 1.1514062450188 & 1.39639154239179 \tabularnewline
159 & 1.27093185827372 & 1.12246836699117 & 1.41939534955628 \tabularnewline
160 & 1.26796482284216 & 1.09405330398105 & 1.44187634170326 \tabularnewline
161 & 1.26499778741059 & 1.06573579936313 & 1.46425977545804 \tabularnewline
162 & 1.26203075197902 & 1.03728368267661 & 1.48677782128142 \tabularnewline
163 & 1.25906371654745 & 1.00855942779607 & 1.50956800529883 \tabularnewline
164 & 1.25609668111588 & 0.979477327307896 & 1.53271603492386 \tabularnewline
165 & 1.25312964568431 & 0.949982294933848 & 1.55627699643478 \tabularnewline
166 & 1.25016261025274 & 0.920038371166088 & 1.5802868493394 \tabularnewline
167 & 1.24719557482117 & 0.889622051962202 & 1.60476909768015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196881&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]156[/C][C]1.27983296456843[/C][C]1.21601124951466[/C][C]1.3436546796222[/C][/ROW]
[ROW][C]157[/C][C]1.27686592913686[/C][C]1.18176139635429[/C][C]1.37197046191944[/C][/ROW]
[ROW][C]158[/C][C]1.27389889370529[/C][C]1.1514062450188[/C][C]1.39639154239179[/C][/ROW]
[ROW][C]159[/C][C]1.27093185827372[/C][C]1.12246836699117[/C][C]1.41939534955628[/C][/ROW]
[ROW][C]160[/C][C]1.26796482284216[/C][C]1.09405330398105[/C][C]1.44187634170326[/C][/ROW]
[ROW][C]161[/C][C]1.26499778741059[/C][C]1.06573579936313[/C][C]1.46425977545804[/C][/ROW]
[ROW][C]162[/C][C]1.26203075197902[/C][C]1.03728368267661[/C][C]1.48677782128142[/C][/ROW]
[ROW][C]163[/C][C]1.25906371654745[/C][C]1.00855942779607[/C][C]1.50956800529883[/C][/ROW]
[ROW][C]164[/C][C]1.25609668111588[/C][C]0.979477327307896[/C][C]1.53271603492386[/C][/ROW]
[ROW][C]165[/C][C]1.25312964568431[/C][C]0.949982294933848[/C][C]1.55627699643478[/C][/ROW]
[ROW][C]166[/C][C]1.25016261025274[/C][C]0.920038371166088[/C][C]1.5802868493394[/C][/ROW]
[ROW][C]167[/C][C]1.24719557482117[/C][C]0.889622051962202[/C][C]1.60476909768015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196881&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196881&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
1561.279832964568431.216011249514661.3436546796222
1571.276865929136861.181761396354291.37197046191944
1581.273898893705291.15140624501881.39639154239179
1591.270931858273721.122468366991171.41939534955628
1601.267964822842161.094053303981051.44187634170326
1611.264997787410591.065735799363131.46425977545804
1621.262030751979021.037283682676611.48677782128142
1631.259063716547451.008559427796071.50956800529883
1641.256096681115880.9794773273078961.53271603492386
1651.253129645684310.9499822949338481.55627699643478
1661.250162610252740.9200383711660881.5802868493394
1671.247195574821170.8896220519622021.60476909768015



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