FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 07 Dec 2010 12:46:53 +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/Dec/07/t1291725969aknw6293tl9n1zg.htm/, Retrieved Fri, 09 May 2025 12:04:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106242, Retrieved Fri, 09 May 2025 12:04:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact359

Tree of Dependent Computations

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]
-  M D      [Structural Time Series Models] [] [2010-12-07 12:42:20] [b2f924a86c4fbfa8afa1027f3839f526]
- RMP           [Exponential Smoothing] [] [2010-12-07 12:46:53] [ae555db68faeb138426117ca316fbf2a] [Current]
- RMPD            [Multiple Regression] [] [2010-12-07 12:51:30] [b2f924a86c4fbfa8afa1027f3839f526]
-    D              [Multiple Regression] [] [2010-12-09 16:17:21] [b2f924a86c4fbfa8afa1027f3839f526]
-    D            [Exponential Smoothing] [] [2010-12-09 16:12:25] [b2f924a86c4fbfa8afa1027f3839f526]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106242&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106242&T=0

As an alternative you can also use a QR Code:  
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' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491527
beta0.177842898062282
gamma0.593783465800473

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.118633222491527 \tabularnewline
beta & 0.177842898062282 \tabularnewline
gamma & 0.593783465800473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106242&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]0.118633222491527[/C][/ROW]
[ROW][C]beta[/C][C]0.177842898062282[/C][/ROW]
[ROW][C]gamma[/C][C]0.593783465800473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106242&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491527
beta0.177842898062282
gamma0.593783465800473






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206924271-59.8206924271071
1591339216.54046372288-83.540463722884
1694879563.6837390525-76.6837390525016
1787008755.77257036377-55.7725703637716
1896279656.62380040247-29.6238004024708
1989479350.24380475744-403.243804757440
2092839699.78239553113-416.782395531127
2188299042.42155295763-213.421552957634
2299479575.43327830275371.566721697251
2396289462.01672409177165.983275908229
2493188775.37973766809542.620262331908
2596059309.97278290418295.027217095818
2686408661.11902781597-21.1190278159702
2792148776.5991422721437.400857727909
2895679201.70519948736365.294800512638
2985478479.0693673372667.9306326627375
3091859432.78885628325-247.788856283250
3194708924.90192534264545.098074657359
3291239419.77362094013-296.773620940128
3392788925.52238256696352.477617433044
34101709886.20179988823283.798200111771
3594349707.31587557403-273.315875574028
3696559208.93777542882446.062224571177
3794299643.7278195637-214.727819563708
3887398799.42061989-60.4206198899992
3995529179.84407265357372.155927346434
4096879587.7408618339299.2591381660786
4190198700.57566008587318.424339914131
4296729546.72216589657125.277834103428
4392069533.85368355207-327.853683552074
4490699501.97079455985-432.970794559853
4597889345.86084071642442.139159283584
461031210297.645014354214.3549856457503
47101059805.95946625138299.040533748623
4898639774.7634805105288.2365194894774
4996569836.53709924992-180.537099249921
5092959093.01482721702201.985172782981
5199469752.4631185878193.536881412205
52970110014.0928950343-313.092895034275
5390499201.74857262883-152.748572628829
54101909890.0173758482299.982624151804
5597069663.5188578316242.4811421683844
5697659631.15772152543133.842278474573
57989310022.8300650879-129.830065087885
58999410693.3737308997-699.373730899686
591043310261.4366175686171.563382431439
601007310097.5384434724-24.5384434723783
61101129995.63683516307116.363164836932
6292669484.15430846739-218.154308467389
63982010077.1025414262-257.102541426164
64100979998.387521829998.6124781701055
6591159305.7422417943-190.742241794302
661041110212.5772925215198.422707478492
6796789823.26733998628-145.267339986278
68104089796.4829285558611.517071444208
691015310096.947740159156.0522598409407
701036810485.5143429546-117.514342954579
711058110584.7149952137-3.71499521370242
721059710300.0096105413296.990389458748
731068010319.3899927210360.610007278967
7497389676.3680764103361.6319235896663
75955610302.5795309447-746.5795309447

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9737 & 9768.09802350428 & -31.0980235042771 \tabularnewline
14 & 9035 & 9094.8206924271 & -59.8206924271071 \tabularnewline
15 & 9133 & 9216.54046372288 & -83.540463722884 \tabularnewline
16 & 9487 & 9563.6837390525 & -76.6837390525016 \tabularnewline
17 & 8700 & 8755.77257036377 & -55.7725703637716 \tabularnewline
18 & 9627 & 9656.62380040247 & -29.6238004024708 \tabularnewline
19 & 8947 & 9350.24380475744 & -403.243804757440 \tabularnewline
20 & 9283 & 9699.78239553113 & -416.782395531127 \tabularnewline
21 & 8829 & 9042.42155295763 & -213.421552957634 \tabularnewline
22 & 9947 & 9575.43327830275 & 371.566721697251 \tabularnewline
23 & 9628 & 9462.01672409177 & 165.983275908229 \tabularnewline
24 & 9318 & 8775.37973766809 & 542.620262331908 \tabularnewline
25 & 9605 & 9309.97278290418 & 295.027217095818 \tabularnewline
26 & 8640 & 8661.11902781597 & -21.1190278159702 \tabularnewline
27 & 9214 & 8776.5991422721 & 437.400857727909 \tabularnewline
28 & 9567 & 9201.70519948736 & 365.294800512638 \tabularnewline
29 & 8547 & 8479.06936733726 & 67.9306326627375 \tabularnewline
30 & 9185 & 9432.78885628325 & -247.788856283250 \tabularnewline
31 & 9470 & 8924.90192534264 & 545.098074657359 \tabularnewline
32 & 9123 & 9419.77362094013 & -296.773620940128 \tabularnewline
33 & 9278 & 8925.52238256696 & 352.477617433044 \tabularnewline
34 & 10170 & 9886.20179988823 & 283.798200111771 \tabularnewline
35 & 9434 & 9707.31587557403 & -273.315875574028 \tabularnewline
36 & 9655 & 9208.93777542882 & 446.062224571177 \tabularnewline
37 & 9429 & 9643.7278195637 & -214.727819563708 \tabularnewline
38 & 8739 & 8799.42061989 & -60.4206198899992 \tabularnewline
39 & 9552 & 9179.84407265357 & 372.155927346434 \tabularnewline
40 & 9687 & 9587.74086183392 & 99.2591381660786 \tabularnewline
41 & 9019 & 8700.57566008587 & 318.424339914131 \tabularnewline
42 & 9672 & 9546.72216589657 & 125.277834103428 \tabularnewline
43 & 9206 & 9533.85368355207 & -327.853683552074 \tabularnewline
44 & 9069 & 9501.97079455985 & -432.970794559853 \tabularnewline
45 & 9788 & 9345.86084071642 & 442.139159283584 \tabularnewline
46 & 10312 & 10297.6450143542 & 14.3549856457503 \tabularnewline
47 & 10105 & 9805.95946625138 & 299.040533748623 \tabularnewline
48 & 9863 & 9774.76348051052 & 88.2365194894774 \tabularnewline
49 & 9656 & 9836.53709924992 & -180.537099249921 \tabularnewline
50 & 9295 & 9093.01482721702 & 201.985172782981 \tabularnewline
51 & 9946 & 9752.4631185878 & 193.536881412205 \tabularnewline
52 & 9701 & 10014.0928950343 & -313.092895034275 \tabularnewline
53 & 9049 & 9201.74857262883 & -152.748572628829 \tabularnewline
54 & 10190 & 9890.0173758482 & 299.982624151804 \tabularnewline
55 & 9706 & 9663.51885783162 & 42.4811421683844 \tabularnewline
56 & 9765 & 9631.15772152543 & 133.842278474573 \tabularnewline
57 & 9893 & 10022.8300650879 & -129.830065087885 \tabularnewline
58 & 9994 & 10693.3737308997 & -699.373730899686 \tabularnewline
59 & 10433 & 10261.4366175686 & 171.563382431439 \tabularnewline
60 & 10073 & 10097.5384434724 & -24.5384434723783 \tabularnewline
61 & 10112 & 9995.63683516307 & 116.363164836932 \tabularnewline
62 & 9266 & 9484.15430846739 & -218.154308467389 \tabularnewline
63 & 9820 & 10077.1025414262 & -257.102541426164 \tabularnewline
64 & 10097 & 9998.3875218299 & 98.6124781701055 \tabularnewline
65 & 9115 & 9305.7422417943 & -190.742241794302 \tabularnewline
66 & 10411 & 10212.5772925215 & 198.422707478492 \tabularnewline
67 & 9678 & 9823.26733998628 & -145.267339986278 \tabularnewline
68 & 10408 & 9796.4829285558 & 611.517071444208 \tabularnewline
69 & 10153 & 10096.9477401591 & 56.0522598409407 \tabularnewline
70 & 10368 & 10485.5143429546 & -117.514342954579 \tabularnewline
71 & 10581 & 10584.7149952137 & -3.71499521370242 \tabularnewline
72 & 10597 & 10300.0096105413 & 296.990389458748 \tabularnewline
73 & 10680 & 10319.3899927210 & 360.610007278967 \tabularnewline
74 & 9738 & 9676.36807641033 & 61.6319235896663 \tabularnewline
75 & 9556 & 10302.5795309447 & -746.5795309447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106242&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]9737[/C][C]9768.09802350428[/C][C]-31.0980235042771[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9094.8206924271[/C][C]-59.8206924271071[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9216.54046372288[/C][C]-83.540463722884[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9563.6837390525[/C][C]-76.6837390525016[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]8755.77257036377[/C][C]-55.7725703637716[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9656.62380040247[/C][C]-29.6238004024708[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9350.24380475744[/C][C]-403.243804757440[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9699.78239553113[/C][C]-416.782395531127[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9042.42155295763[/C][C]-213.421552957634[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9575.43327830275[/C][C]371.566721697251[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9462.01672409177[/C][C]165.983275908229[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]8775.37973766809[/C][C]542.620262331908[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9309.97278290418[/C][C]295.027217095818[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]8661.11902781597[/C][C]-21.1190278159702[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]8776.5991422721[/C][C]437.400857727909[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9201.70519948736[/C][C]365.294800512638[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]8479.06936733726[/C][C]67.9306326627375[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]9432.78885628325[/C][C]-247.788856283250[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]8924.90192534264[/C][C]545.098074657359[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9419.77362094013[/C][C]-296.773620940128[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]8925.52238256696[/C][C]352.477617433044[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9886.20179988823[/C][C]283.798200111771[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9707.31587557403[/C][C]-273.315875574028[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9208.93777542882[/C][C]446.062224571177[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9643.7278195637[/C][C]-214.727819563708[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]8799.42061989[/C][C]-60.4206198899992[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9179.84407265357[/C][C]372.155927346434[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9587.74086183392[/C][C]99.2591381660786[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]8700.57566008587[/C][C]318.424339914131[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9546.72216589657[/C][C]125.277834103428[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9533.85368355207[/C][C]-327.853683552074[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9501.97079455985[/C][C]-432.970794559853[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9345.86084071642[/C][C]442.139159283584[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]10297.6450143542[/C][C]14.3549856457503[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9805.95946625138[/C][C]299.040533748623[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9774.76348051052[/C][C]88.2365194894774[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9836.53709924992[/C][C]-180.537099249921[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9093.01482721702[/C][C]201.985172782981[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9752.4631185878[/C][C]193.536881412205[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]10014.0928950343[/C][C]-313.092895034275[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9201.74857262883[/C][C]-152.748572628829[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9890.0173758482[/C][C]299.982624151804[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9663.51885783162[/C][C]42.4811421683844[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9631.15772152543[/C][C]133.842278474573[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]10022.8300650879[/C][C]-129.830065087885[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]10693.3737308997[/C][C]-699.373730899686[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]10261.4366175686[/C][C]171.563382431439[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]10097.5384434724[/C][C]-24.5384434723783[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]9995.63683516307[/C][C]116.363164836932[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9484.15430846739[/C][C]-218.154308467389[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]10077.1025414262[/C][C]-257.102541426164[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9998.3875218299[/C][C]98.6124781701055[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9305.7422417943[/C][C]-190.742241794302[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10212.5772925215[/C][C]198.422707478492[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9823.26733998628[/C][C]-145.267339986278[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9796.4829285558[/C][C]611.517071444208[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10096.9477401591[/C][C]56.0522598409407[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10485.5143429546[/C][C]-117.514342954579[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10584.7149952137[/C][C]-3.71499521370242[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10300.0096105413[/C][C]296.990389458748[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10319.3899927210[/C][C]360.610007278967[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9676.36807641033[/C][C]61.6319235896663[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10302.5795309447[/C][C]-746.5795309447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106242&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206924271-59.8206924271071
1591339216.54046372288-83.540463722884
1694879563.6837390525-76.6837390525016
1787008755.77257036377-55.7725703637716
1896279656.62380040247-29.6238004024708
1989479350.24380475744-403.243804757440
2092839699.78239553113-416.782395531127
2188299042.42155295763-213.421552957634
2299479575.43327830275371.566721697251
2396289462.01672409177165.983275908229
2493188775.37973766809542.620262331908
2596059309.97278290418295.027217095818
2686408661.11902781597-21.1190278159702
2792148776.5991422721437.400857727909
2895679201.70519948736365.294800512638
2985478479.0693673372667.9306326627375
3091859432.78885628325-247.788856283250
3194708924.90192534264545.098074657359
3291239419.77362094013-296.773620940128
3392788925.52238256696352.477617433044
34101709886.20179988823283.798200111771
3594349707.31587557403-273.315875574028
3696559208.93777542882446.062224571177
3794299643.7278195637-214.727819563708
3887398799.42061989-60.4206198899992
3995529179.84407265357372.155927346434
4096879587.7408618339299.2591381660786
4190198700.57566008587318.424339914131
4296729546.72216589657125.277834103428
4392069533.85368355207-327.853683552074
4490699501.97079455985-432.970794559853
4597889345.86084071642442.139159283584
461031210297.645014354214.3549856457503
47101059805.95946625138299.040533748623
4898639774.7634805105288.2365194894774
4996569836.53709924992-180.537099249921
5092959093.01482721702201.985172782981
5199469752.4631185878193.536881412205
52970110014.0928950343-313.092895034275
5390499201.74857262883-152.748572628829
54101909890.0173758482299.982624151804
5597069663.5188578316242.4811421683844
5697659631.15772152543133.842278474573
57989310022.8300650879-129.830065087885
58999410693.3737308997-699.373730899686
591043310261.4366175686171.563382431439
601007310097.5384434724-24.5384434723783
61101129995.63683516307116.363164836932
6292669484.15430846739-218.154308467389
63982010077.1025414262-257.102541426164
64100979998.387521829998.6124781701055
6591159305.7422417943-190.742241794302
661041110212.5772925215198.422707478492
6796789823.26733998628-145.267339986278
68104089796.4829285558611.517071444208
691015310096.947740159156.0522598409407
701036810485.5143429546-117.514342954579
711058110584.7149952137-3.71499521370242
721059710300.0096105413296.990389458748
731068010319.3899927210360.610007278967
7497389676.3680764103361.6319235896663
75955610302.5795309447-746.5795309447






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429899787.7649000435210936.4031085544
779514.35574484688934.4570012126810094.2544884809
7810659.556369008210072.347474149911246.7652638665
7910074.72467916189478.2925554021510671.1568029215
8010472.17987525389864.4569336373411079.9028168702
8110407.44884061229786.243868411311028.6538128131
8210695.396580954210058.426994430611332.3661674777
8310867.438852322910212.362728107711522.5149765380
8410739.968678644510064.415064700911415.5222925882
8510750.567990175810052.164260742911448.9717196088
869893.847174685399170.2425691304410617.4517802403
8710074.02543693939322.91033408310825.1405397956

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 10362.0840042989 & 9787.76490004352 & 10936.4031085544 \tabularnewline
77 & 9514.3557448468 & 8934.45700121268 & 10094.2544884809 \tabularnewline
78 & 10659.5563690082 & 10072.3474741499 & 11246.7652638665 \tabularnewline
79 & 10074.7246791618 & 9478.29255540215 & 10671.1568029215 \tabularnewline
80 & 10472.1798752538 & 9864.45693363734 & 11079.9028168702 \tabularnewline
81 & 10407.4488406122 & 9786.2438684113 & 11028.6538128131 \tabularnewline
82 & 10695.3965809542 & 10058.4269944306 & 11332.3661674777 \tabularnewline
83 & 10867.4388523229 & 10212.3627281077 & 11522.5149765380 \tabularnewline
84 & 10739.9686786445 & 10064.4150647009 & 11415.5222925882 \tabularnewline
85 & 10750.5679901758 & 10052.1642607429 & 11448.9717196088 \tabularnewline
86 & 9893.84717468539 & 9170.24256913044 & 10617.4517802403 \tabularnewline
87 & 10074.0254369393 & 9322.910334083 & 10825.1405397956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106242&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]76[/C][C]10362.0840042989[/C][C]9787.76490004352[/C][C]10936.4031085544[/C][/ROW]
[ROW][C]77[/C][C]9514.3557448468[/C][C]8934.45700121268[/C][C]10094.2544884809[/C][/ROW]
[ROW][C]78[/C][C]10659.5563690082[/C][C]10072.3474741499[/C][C]11246.7652638665[/C][/ROW]
[ROW][C]79[/C][C]10074.7246791618[/C][C]9478.29255540215[/C][C]10671.1568029215[/C][/ROW]
[ROW][C]80[/C][C]10472.1798752538[/C][C]9864.45693363734[/C][C]11079.9028168702[/C][/ROW]
[ROW][C]81[/C][C]10407.4488406122[/C][C]9786.2438684113[/C][C]11028.6538128131[/C][/ROW]
[ROW][C]82[/C][C]10695.3965809542[/C][C]10058.4269944306[/C][C]11332.3661674777[/C][/ROW]
[ROW][C]83[/C][C]10867.4388523229[/C][C]10212.3627281077[/C][C]11522.5149765380[/C][/ROW]
[ROW][C]84[/C][C]10739.9686786445[/C][C]10064.4150647009[/C][C]11415.5222925882[/C][/ROW]
[ROW][C]85[/C][C]10750.5679901758[/C][C]10052.1642607429[/C][C]11448.9717196088[/C][/ROW]
[ROW][C]86[/C][C]9893.84717468539[/C][C]9170.24256913044[/C][C]10617.4517802403[/C][/ROW]
[ROW][C]87[/C][C]10074.0254369393[/C][C]9322.910334083[/C][C]10825.1405397956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106242&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106242&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429899787.7649000435210936.4031085544
779514.35574484688934.4570012126810094.2544884809
7810659.556369008210072.347474149911246.7652638665
7910074.72467916189478.2925554021510671.1568029215
8010472.17987525389864.4569336373411079.9028168702
8110407.44884061229786.243868411311028.6538128131
8210695.396580954210058.426994430611332.3661674777
8310867.438852322910212.362728107711522.5149765380
8410739.968678644510064.415064700911415.5222925882
8510750.567990175810052.164260742911448.9717196088
869893.847174685399170.2425691304410617.4517802403
8710074.02543693939322.91033408310825.1405397956


Figures (Output of Computation)

Input Parameters & R Code

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')