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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 23 Nov 2015 19:10:52 +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/2015/Nov/23/t1448305889ca2tqnikbes12tx.htm/, Retrieved Tue, 14 May 2024 20:51:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283963, Retrieved Tue, 14 May 2024 20:51:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-23 19:10:52] [dce38ba7cc70e884f4588278752279c3] [Current]
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Dataseries X:
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594
580523
564478
557560
575093
580112
574761
563250
551531
537034
544686
600991
604378
586111
563668
548604
551174
555654
547970
540324
530577
520579
518654
572273
581302
563280
547612
538712
540735
561649
558685
545732
536352
527676
530455
581744
598714
583775
571477
563278
564872
577537
572399
565430
560619
551227
553397
610893
621668
613148
598778
590623
595902
612186
603453
593362
581940
568075
567467
619423
627325
617144
602280
590816
589812




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283963&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283963&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.874805762117524
beta0.0886485880798259
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.874805762117524 \tabularnewline
beta & 0.0886485880798259 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283963&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]0.874805762117524[/C][/ROW]
[ROW][C]beta[/C][C]0.0886485880798259[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283963&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
alpha0.874805762117524
beta0.0886485880798259
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13528222504024.24091880324197.7590811966
14532638530899.8005204981738.19947950204
15536322537347.614184886-1025.61418488575
16536535538022.924380314-1487.92438031442
17523597525314.247310623-1717.24731062283
18536214537799.784183459-1585.78418345889
19586570581338.9310585045231.06894149608
20596594596040.796269777553.203730222885
21580523584487.339152656-3964.33915265626
22564478571664.515484278-7186.51548427797
23557560562489.430327231-4929.43032723072
24575093572975.3274918672117.67250813323
25580112590461.091958856-10349.0919588562
26574761582549.973106505-7788.973106505
27563250577825.426046113-14575.4260461131
28551531563046.690556741-11515.6905567405
29537034537216.586093097-182.586093096877
30544686546859.75544693-2173.75544693007
31600991586491.0186381414499.9813618604
32604378605187.593205548-809.593205547892
33586111588242.550965087-2131.55096508726
34563668573127.964146588-9459.96414658765
35548604558578.621532838-9974.62153283809
36551174561473.951435834-10299.9514358342
37555654561513.687847587-5859.68784758705
38547970553176.340324064-5206.34032406402
39540324545387.657050541-5063.65705054149
40530577535576.760188012-4999.76018801192
41520579513634.8079080976944.19209190318
42518654526585.064084513-7931.06408451335
43572273560142.59842143912130.4015785608
44581302571541.1609513079760.83904869307
45563280561189.0129381962090.98706180428
46547612546689.631363124922.368636876461
47538712539802.313880171-1090.31388017081
48540735549761.871292883-9026.87129288341
49561649550902.84211873910746.1578812612
50558685557893.608868298791.391131702345
51545732556554.19400263-10822.1940026301
52536352542451.674355905-6099.67435590457
53527676521695.5051620055980.4948379948
54530455532518.362395424-2063.36239542381
55581744574753.5632136266990.43678637419
56598714581993.38089065116720.6191093487
57583775577943.5818443915831.41815560893
58571477568034.2327279923442.767272008
59563278564759.441977483-1481.44197748275
60564872575012.538658078-10140.5386580783
61577537579197.682578263-1660.68257826346
62572399574669.386626257-2270.38662625733
63565430569540.907483874-4110.90748387401
64560619562764.504945042-2145.50494504184
65551227548150.2932607683076.70673923171
66553397556371.125480759-2974.12548075896
67610893599817.70916926411075.2908307364
68621668613040.5652777118627.43472228874
69613148601111.32965482812036.6703451721
70598778597376.337697841401.66230215982
71590623592586.21775611-1963.21775610966
72595902602183.147167416-6281.14716741606
73612186611954.797039898231.20296010212
74603453610300.577226078-6847.57722607802
75593362601877.935483876-8515.93548387592
76581940592092.847634853-10152.8476348527
77568075571105.386938663-3030.38693866273
78567467572730.391871291-5263.3918712911
79619423615259.9075929144163.09240708558
80627325620920.1216748916404.87832510925
81617144606091.6841223611052.3158776396
82602280598706.0810560713573.91894392879
83590816594105.408869388-3289.40886938758
84589812600609.16098081-10797.1609808102

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 528222 & 504024.240918803 & 24197.7590811966 \tabularnewline
14 & 532638 & 530899.800520498 & 1738.19947950204 \tabularnewline
15 & 536322 & 537347.614184886 & -1025.61418488575 \tabularnewline
16 & 536535 & 538022.924380314 & -1487.92438031442 \tabularnewline
17 & 523597 & 525314.247310623 & -1717.24731062283 \tabularnewline
18 & 536214 & 537799.784183459 & -1585.78418345889 \tabularnewline
19 & 586570 & 581338.931058504 & 5231.06894149608 \tabularnewline
20 & 596594 & 596040.796269777 & 553.203730222885 \tabularnewline
21 & 580523 & 584487.339152656 & -3964.33915265626 \tabularnewline
22 & 564478 & 571664.515484278 & -7186.51548427797 \tabularnewline
23 & 557560 & 562489.430327231 & -4929.43032723072 \tabularnewline
24 & 575093 & 572975.327491867 & 2117.67250813323 \tabularnewline
25 & 580112 & 590461.091958856 & -10349.0919588562 \tabularnewline
26 & 574761 & 582549.973106505 & -7788.973106505 \tabularnewline
27 & 563250 & 577825.426046113 & -14575.4260461131 \tabularnewline
28 & 551531 & 563046.690556741 & -11515.6905567405 \tabularnewline
29 & 537034 & 537216.586093097 & -182.586093096877 \tabularnewline
30 & 544686 & 546859.75544693 & -2173.75544693007 \tabularnewline
31 & 600991 & 586491.01863814 & 14499.9813618604 \tabularnewline
32 & 604378 & 605187.593205548 & -809.593205547892 \tabularnewline
33 & 586111 & 588242.550965087 & -2131.55096508726 \tabularnewline
34 & 563668 & 573127.964146588 & -9459.96414658765 \tabularnewline
35 & 548604 & 558578.621532838 & -9974.62153283809 \tabularnewline
36 & 551174 & 561473.951435834 & -10299.9514358342 \tabularnewline
37 & 555654 & 561513.687847587 & -5859.68784758705 \tabularnewline
38 & 547970 & 553176.340324064 & -5206.34032406402 \tabularnewline
39 & 540324 & 545387.657050541 & -5063.65705054149 \tabularnewline
40 & 530577 & 535576.760188012 & -4999.76018801192 \tabularnewline
41 & 520579 & 513634.807908097 & 6944.19209190318 \tabularnewline
42 & 518654 & 526585.064084513 & -7931.06408451335 \tabularnewline
43 & 572273 & 560142.598421439 & 12130.4015785608 \tabularnewline
44 & 581302 & 571541.160951307 & 9760.83904869307 \tabularnewline
45 & 563280 & 561189.012938196 & 2090.98706180428 \tabularnewline
46 & 547612 & 546689.631363124 & 922.368636876461 \tabularnewline
47 & 538712 & 539802.313880171 & -1090.31388017081 \tabularnewline
48 & 540735 & 549761.871292883 & -9026.87129288341 \tabularnewline
49 & 561649 & 550902.842118739 & 10746.1578812612 \tabularnewline
50 & 558685 & 557893.608868298 & 791.391131702345 \tabularnewline
51 & 545732 & 556554.19400263 & -10822.1940026301 \tabularnewline
52 & 536352 & 542451.674355905 & -6099.67435590457 \tabularnewline
53 & 527676 & 521695.505162005 & 5980.4948379948 \tabularnewline
54 & 530455 & 532518.362395424 & -2063.36239542381 \tabularnewline
55 & 581744 & 574753.563213626 & 6990.43678637419 \tabularnewline
56 & 598714 & 581993.380890651 & 16720.6191093487 \tabularnewline
57 & 583775 & 577943.581844391 & 5831.41815560893 \tabularnewline
58 & 571477 & 568034.232727992 & 3442.767272008 \tabularnewline
59 & 563278 & 564759.441977483 & -1481.44197748275 \tabularnewline
60 & 564872 & 575012.538658078 & -10140.5386580783 \tabularnewline
61 & 577537 & 579197.682578263 & -1660.68257826346 \tabularnewline
62 & 572399 & 574669.386626257 & -2270.38662625733 \tabularnewline
63 & 565430 & 569540.907483874 & -4110.90748387401 \tabularnewline
64 & 560619 & 562764.504945042 & -2145.50494504184 \tabularnewline
65 & 551227 & 548150.293260768 & 3076.70673923171 \tabularnewline
66 & 553397 & 556371.125480759 & -2974.12548075896 \tabularnewline
67 & 610893 & 599817.709169264 & 11075.2908307364 \tabularnewline
68 & 621668 & 613040.565277711 & 8627.43472228874 \tabularnewline
69 & 613148 & 601111.329654828 & 12036.6703451721 \tabularnewline
70 & 598778 & 597376.33769784 & 1401.66230215982 \tabularnewline
71 & 590623 & 592586.21775611 & -1963.21775610966 \tabularnewline
72 & 595902 & 602183.147167416 & -6281.14716741606 \tabularnewline
73 & 612186 & 611954.797039898 & 231.20296010212 \tabularnewline
74 & 603453 & 610300.577226078 & -6847.57722607802 \tabularnewline
75 & 593362 & 601877.935483876 & -8515.93548387592 \tabularnewline
76 & 581940 & 592092.847634853 & -10152.8476348527 \tabularnewline
77 & 568075 & 571105.386938663 & -3030.38693866273 \tabularnewline
78 & 567467 & 572730.391871291 & -5263.3918712911 \tabularnewline
79 & 619423 & 615259.907592914 & 4163.09240708558 \tabularnewline
80 & 627325 & 620920.121674891 & 6404.87832510925 \tabularnewline
81 & 617144 & 606091.68412236 & 11052.3158776396 \tabularnewline
82 & 602280 & 598706.081056071 & 3573.91894392879 \tabularnewline
83 & 590816 & 594105.408869388 & -3289.40886938758 \tabularnewline
84 & 589812 & 600609.16098081 & -10797.1609808102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283963&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]528222[/C][C]504024.240918803[/C][C]24197.7590811966[/C][/ROW]
[ROW][C]14[/C][C]532638[/C][C]530899.800520498[/C][C]1738.19947950204[/C][/ROW]
[ROW][C]15[/C][C]536322[/C][C]537347.614184886[/C][C]-1025.61418488575[/C][/ROW]
[ROW][C]16[/C][C]536535[/C][C]538022.924380314[/C][C]-1487.92438031442[/C][/ROW]
[ROW][C]17[/C][C]523597[/C][C]525314.247310623[/C][C]-1717.24731062283[/C][/ROW]
[ROW][C]18[/C][C]536214[/C][C]537799.784183459[/C][C]-1585.78418345889[/C][/ROW]
[ROW][C]19[/C][C]586570[/C][C]581338.931058504[/C][C]5231.06894149608[/C][/ROW]
[ROW][C]20[/C][C]596594[/C][C]596040.796269777[/C][C]553.203730222885[/C][/ROW]
[ROW][C]21[/C][C]580523[/C][C]584487.339152656[/C][C]-3964.33915265626[/C][/ROW]
[ROW][C]22[/C][C]564478[/C][C]571664.515484278[/C][C]-7186.51548427797[/C][/ROW]
[ROW][C]23[/C][C]557560[/C][C]562489.430327231[/C][C]-4929.43032723072[/C][/ROW]
[ROW][C]24[/C][C]575093[/C][C]572975.327491867[/C][C]2117.67250813323[/C][/ROW]
[ROW][C]25[/C][C]580112[/C][C]590461.091958856[/C][C]-10349.0919588562[/C][/ROW]
[ROW][C]26[/C][C]574761[/C][C]582549.973106505[/C][C]-7788.973106505[/C][/ROW]
[ROW][C]27[/C][C]563250[/C][C]577825.426046113[/C][C]-14575.4260461131[/C][/ROW]
[ROW][C]28[/C][C]551531[/C][C]563046.690556741[/C][C]-11515.6905567405[/C][/ROW]
[ROW][C]29[/C][C]537034[/C][C]537216.586093097[/C][C]-182.586093096877[/C][/ROW]
[ROW][C]30[/C][C]544686[/C][C]546859.75544693[/C][C]-2173.75544693007[/C][/ROW]
[ROW][C]31[/C][C]600991[/C][C]586491.01863814[/C][C]14499.9813618604[/C][/ROW]
[ROW][C]32[/C][C]604378[/C][C]605187.593205548[/C][C]-809.593205547892[/C][/ROW]
[ROW][C]33[/C][C]586111[/C][C]588242.550965087[/C][C]-2131.55096508726[/C][/ROW]
[ROW][C]34[/C][C]563668[/C][C]573127.964146588[/C][C]-9459.96414658765[/C][/ROW]
[ROW][C]35[/C][C]548604[/C][C]558578.621532838[/C][C]-9974.62153283809[/C][/ROW]
[ROW][C]36[/C][C]551174[/C][C]561473.951435834[/C][C]-10299.9514358342[/C][/ROW]
[ROW][C]37[/C][C]555654[/C][C]561513.687847587[/C][C]-5859.68784758705[/C][/ROW]
[ROW][C]38[/C][C]547970[/C][C]553176.340324064[/C][C]-5206.34032406402[/C][/ROW]
[ROW][C]39[/C][C]540324[/C][C]545387.657050541[/C][C]-5063.65705054149[/C][/ROW]
[ROW][C]40[/C][C]530577[/C][C]535576.760188012[/C][C]-4999.76018801192[/C][/ROW]
[ROW][C]41[/C][C]520579[/C][C]513634.807908097[/C][C]6944.19209190318[/C][/ROW]
[ROW][C]42[/C][C]518654[/C][C]526585.064084513[/C][C]-7931.06408451335[/C][/ROW]
[ROW][C]43[/C][C]572273[/C][C]560142.598421439[/C][C]12130.4015785608[/C][/ROW]
[ROW][C]44[/C][C]581302[/C][C]571541.160951307[/C][C]9760.83904869307[/C][/ROW]
[ROW][C]45[/C][C]563280[/C][C]561189.012938196[/C][C]2090.98706180428[/C][/ROW]
[ROW][C]46[/C][C]547612[/C][C]546689.631363124[/C][C]922.368636876461[/C][/ROW]
[ROW][C]47[/C][C]538712[/C][C]539802.313880171[/C][C]-1090.31388017081[/C][/ROW]
[ROW][C]48[/C][C]540735[/C][C]549761.871292883[/C][C]-9026.87129288341[/C][/ROW]
[ROW][C]49[/C][C]561649[/C][C]550902.842118739[/C][C]10746.1578812612[/C][/ROW]
[ROW][C]50[/C][C]558685[/C][C]557893.608868298[/C][C]791.391131702345[/C][/ROW]
[ROW][C]51[/C][C]545732[/C][C]556554.19400263[/C][C]-10822.1940026301[/C][/ROW]
[ROW][C]52[/C][C]536352[/C][C]542451.674355905[/C][C]-6099.67435590457[/C][/ROW]
[ROW][C]53[/C][C]527676[/C][C]521695.505162005[/C][C]5980.4948379948[/C][/ROW]
[ROW][C]54[/C][C]530455[/C][C]532518.362395424[/C][C]-2063.36239542381[/C][/ROW]
[ROW][C]55[/C][C]581744[/C][C]574753.563213626[/C][C]6990.43678637419[/C][/ROW]
[ROW][C]56[/C][C]598714[/C][C]581993.380890651[/C][C]16720.6191093487[/C][/ROW]
[ROW][C]57[/C][C]583775[/C][C]577943.581844391[/C][C]5831.41815560893[/C][/ROW]
[ROW][C]58[/C][C]571477[/C][C]568034.232727992[/C][C]3442.767272008[/C][/ROW]
[ROW][C]59[/C][C]563278[/C][C]564759.441977483[/C][C]-1481.44197748275[/C][/ROW]
[ROW][C]60[/C][C]564872[/C][C]575012.538658078[/C][C]-10140.5386580783[/C][/ROW]
[ROW][C]61[/C][C]577537[/C][C]579197.682578263[/C][C]-1660.68257826346[/C][/ROW]
[ROW][C]62[/C][C]572399[/C][C]574669.386626257[/C][C]-2270.38662625733[/C][/ROW]
[ROW][C]63[/C][C]565430[/C][C]569540.907483874[/C][C]-4110.90748387401[/C][/ROW]
[ROW][C]64[/C][C]560619[/C][C]562764.504945042[/C][C]-2145.50494504184[/C][/ROW]
[ROW][C]65[/C][C]551227[/C][C]548150.293260768[/C][C]3076.70673923171[/C][/ROW]
[ROW][C]66[/C][C]553397[/C][C]556371.125480759[/C][C]-2974.12548075896[/C][/ROW]
[ROW][C]67[/C][C]610893[/C][C]599817.709169264[/C][C]11075.2908307364[/C][/ROW]
[ROW][C]68[/C][C]621668[/C][C]613040.565277711[/C][C]8627.43472228874[/C][/ROW]
[ROW][C]69[/C][C]613148[/C][C]601111.329654828[/C][C]12036.6703451721[/C][/ROW]
[ROW][C]70[/C][C]598778[/C][C]597376.33769784[/C][C]1401.66230215982[/C][/ROW]
[ROW][C]71[/C][C]590623[/C][C]592586.21775611[/C][C]-1963.21775610966[/C][/ROW]
[ROW][C]72[/C][C]595902[/C][C]602183.147167416[/C][C]-6281.14716741606[/C][/ROW]
[ROW][C]73[/C][C]612186[/C][C]611954.797039898[/C][C]231.20296010212[/C][/ROW]
[ROW][C]74[/C][C]603453[/C][C]610300.577226078[/C][C]-6847.57722607802[/C][/ROW]
[ROW][C]75[/C][C]593362[/C][C]601877.935483876[/C][C]-8515.93548387592[/C][/ROW]
[ROW][C]76[/C][C]581940[/C][C]592092.847634853[/C][C]-10152.8476348527[/C][/ROW]
[ROW][C]77[/C][C]568075[/C][C]571105.386938663[/C][C]-3030.38693866273[/C][/ROW]
[ROW][C]78[/C][C]567467[/C][C]572730.391871291[/C][C]-5263.3918712911[/C][/ROW]
[ROW][C]79[/C][C]619423[/C][C]615259.907592914[/C][C]4163.09240708558[/C][/ROW]
[ROW][C]80[/C][C]627325[/C][C]620920.121674891[/C][C]6404.87832510925[/C][/ROW]
[ROW][C]81[/C][C]617144[/C][C]606091.68412236[/C][C]11052.3158776396[/C][/ROW]
[ROW][C]82[/C][C]602280[/C][C]598706.081056071[/C][C]3573.91894392879[/C][/ROW]
[ROW][C]83[/C][C]590816[/C][C]594105.408869388[/C][C]-3289.40886938758[/C][/ROW]
[ROW][C]84[/C][C]589812[/C][C]600609.16098081[/C][C]-10797.1609808102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283963&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
13528222504024.24091880324197.7590811966
14532638530899.8005204981738.19947950204
15536322537347.614184886-1025.61418488575
16536535538022.924380314-1487.92438031442
17523597525314.247310623-1717.24731062283
18536214537799.784183459-1585.78418345889
19586570581338.9310585045231.06894149608
20596594596040.796269777553.203730222885
21580523584487.339152656-3964.33915265626
22564478571664.515484278-7186.51548427797
23557560562489.430327231-4929.43032723072
24575093572975.3274918672117.67250813323
25580112590461.091958856-10349.0919588562
26574761582549.973106505-7788.973106505
27563250577825.426046113-14575.4260461131
28551531563046.690556741-11515.6905567405
29537034537216.586093097-182.586093096877
30544686546859.75544693-2173.75544693007
31600991586491.0186381414499.9813618604
32604378605187.593205548-809.593205547892
33586111588242.550965087-2131.55096508726
34563668573127.964146588-9459.96414658765
35548604558578.621532838-9974.62153283809
36551174561473.951435834-10299.9514358342
37555654561513.687847587-5859.68784758705
38547970553176.340324064-5206.34032406402
39540324545387.657050541-5063.65705054149
40530577535576.760188012-4999.76018801192
41520579513634.8079080976944.19209190318
42518654526585.064084513-7931.06408451335
43572273560142.59842143912130.4015785608
44581302571541.1609513079760.83904869307
45563280561189.0129381962090.98706180428
46547612546689.631363124922.368636876461
47538712539802.313880171-1090.31388017081
48540735549761.871292883-9026.87129288341
49561649550902.84211873910746.1578812612
50558685557893.608868298791.391131702345
51545732556554.19400263-10822.1940026301
52536352542451.674355905-6099.67435590457
53527676521695.5051620055980.4948379948
54530455532518.362395424-2063.36239542381
55581744574753.5632136266990.43678637419
56598714581993.38089065116720.6191093487
57583775577943.5818443915831.41815560893
58571477568034.2327279923442.767272008
59563278564759.441977483-1481.44197748275
60564872575012.538658078-10140.5386580783
61577537579197.682578263-1660.68257826346
62572399574669.386626257-2270.38662625733
63565430569540.907483874-4110.90748387401
64560619562764.504945042-2145.50494504184
65551227548150.2932607683076.70673923171
66553397556371.125480759-2974.12548075896
67610893599817.70916926411075.2908307364
68621668613040.5652777118627.43472228874
69613148601111.32965482812036.6703451721
70598778597376.337697841401.66230215982
71590623592586.21775611-1963.21775610966
72595902602183.147167416-6281.14716741606
73612186611954.797039898231.20296010212
74603453610300.577226078-6847.57722607802
75593362601877.935483876-8515.93548387592
76581940592092.847634853-10152.8476348527
77568075571105.386938663-3030.38693866273
78567467572730.391871291-5263.3918712911
79619423615259.9075929144163.09240708558
80627325620920.1216748916404.87832510925
81617144606091.6841223611052.3158776396
82602280598706.0810560713573.91894392879
83590816594105.408869388-3289.40886938758
84589812600609.16098081-10797.1609808102







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85605502.828661716590653.02953883620352.627784602
86600999.542820867580492.932315376621506.153326357
87597128.778035623571547.055517459622710.500553788
88594019.406746695563607.578687452624431.234805938
89583023.622136116547887.63281822618159.611454012
90587473.290510481547648.018389366627298.562631597
91636648.793717384592128.288973801681169.298460967
92639486.320638753590239.399223783688733.242053724
93619678.542202336565657.652979692673699.431424979
94600872.798130939542019.426541203659726.169720674
95591193.97430718527442.109328397654945.839285963
96598798.069921398530076.518069136667519.62177366

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 605502.828661716 & 590653.02953883 & 620352.627784602 \tabularnewline
86 & 600999.542820867 & 580492.932315376 & 621506.153326357 \tabularnewline
87 & 597128.778035623 & 571547.055517459 & 622710.500553788 \tabularnewline
88 & 594019.406746695 & 563607.578687452 & 624431.234805938 \tabularnewline
89 & 583023.622136116 & 547887.63281822 & 618159.611454012 \tabularnewline
90 & 587473.290510481 & 547648.018389366 & 627298.562631597 \tabularnewline
91 & 636648.793717384 & 592128.288973801 & 681169.298460967 \tabularnewline
92 & 639486.320638753 & 590239.399223783 & 688733.242053724 \tabularnewline
93 & 619678.542202336 & 565657.652979692 & 673699.431424979 \tabularnewline
94 & 600872.798130939 & 542019.426541203 & 659726.169720674 \tabularnewline
95 & 591193.97430718 & 527442.109328397 & 654945.839285963 \tabularnewline
96 & 598798.069921398 & 530076.518069136 & 667519.62177366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283963&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]85[/C][C]605502.828661716[/C][C]590653.02953883[/C][C]620352.627784602[/C][/ROW]
[ROW][C]86[/C][C]600999.542820867[/C][C]580492.932315376[/C][C]621506.153326357[/C][/ROW]
[ROW][C]87[/C][C]597128.778035623[/C][C]571547.055517459[/C][C]622710.500553788[/C][/ROW]
[ROW][C]88[/C][C]594019.406746695[/C][C]563607.578687452[/C][C]624431.234805938[/C][/ROW]
[ROW][C]89[/C][C]583023.622136116[/C][C]547887.63281822[/C][C]618159.611454012[/C][/ROW]
[ROW][C]90[/C][C]587473.290510481[/C][C]547648.018389366[/C][C]627298.562631597[/C][/ROW]
[ROW][C]91[/C][C]636648.793717384[/C][C]592128.288973801[/C][C]681169.298460967[/C][/ROW]
[ROW][C]92[/C][C]639486.320638753[/C][C]590239.399223783[/C][C]688733.242053724[/C][/ROW]
[ROW][C]93[/C][C]619678.542202336[/C][C]565657.652979692[/C][C]673699.431424979[/C][/ROW]
[ROW][C]94[/C][C]600872.798130939[/C][C]542019.426541203[/C][C]659726.169720674[/C][/ROW]
[ROW][C]95[/C][C]591193.97430718[/C][C]527442.109328397[/C][C]654945.839285963[/C][/ROW]
[ROW][C]96[/C][C]598798.069921398[/C][C]530076.518069136[/C][C]667519.62177366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283963&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283963&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
85605502.828661716590653.02953883620352.627784602
86600999.542820867580492.932315376621506.153326357
87597128.778035623571547.055517459622710.500553788
88594019.406746695563607.578687452624431.234805938
89583023.622136116547887.63281822618159.611454012
90587473.290510481547648.018389366627298.562631597
91636648.793717384592128.288973801681169.298460967
92639486.320638753590239.399223783688733.242053724
93619678.542202336565657.652979692673699.431424979
94600872.798130939542019.426541203659726.169720674
95591193.97430718527442.109328397654945.839285963
96598798.069921398530076.518069136667519.62177366



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