Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Aug 2015 00:39:19 +0100
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/Aug/17/t1439768509n5fl53fk2k1fklw.htm/, Retrieved Sun, 19 May 2024 16:33:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280232, Retrieved Sun, 19 May 2024 16:33:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [] [2014-11-24 12:14:04] [46d78fa4bef23992fc20db72a2a0da97]
- RMPD  [Central Tendency] [] [2015-08-16 17:50:33] [46d78fa4bef23992fc20db72a2a0da97]
- RMPD    [Standard Deviation-Mean Plot] [] [2015-08-16 20:08:52] [46d78fa4bef23992fc20db72a2a0da97]
- RM D        [Exponential Smoothing] [] [2015-08-16 23:39:19] [fced41568b3cc41e6659ad201d611503] [Current]
Feedback Forum

Post a new message
Dataseries X:
193590
193745
193885
194040
194190
194345
194495
194650
194805
194955
195110
195260
195415
195570
195710
195865
196015
196170
196320
196475
196630
196780
196935
197085
197240
197395
197540
197695
197845
198000
198150
198305
198460
198610
198765
198915
199070
199225
199365
199520
199670
199825
199975
200130
200285
200435
200590
200740
200895
201050
201190
201345
201495
201650
201800
201955
202110
202260
202415
202565
202720
202875
203015
203170
203320
203475
203625
203780
203935
204085
204240
204390
204545
204700
204845
205000
205150
205305
205455
205610
205765
205915
206070
206220
206375
206530
206670
206825
206975
207130
207280
207435
207590
207740
207895
208045
208200
208355
208495
208650
208800
208955
209105
209260
209415
209565
209720
209870




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280232&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280232&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.614406407945639
beta0.09194566143641
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.614406407945639 \tabularnewline
beta & 0.09194566143641 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280232&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]0.614406407945639[/C][/ROW]
[ROW][C]beta[/C][C]0.09194566143641[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280232&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
alpha0.614406407945639
beta0.09194566143641
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3193885193900-15
4194040194044.936523827-4.9365238272585
5194190194195.77723778-5.77723777960637
6194345194345.775043955-0.775043955130968
7194495194498.802446284-3.80244628430228
8194650194649.7549854140.245014586078469
9194805194803.2081518031.79184819691
10194955194957.71292777-2.71292776952032
11195110195109.2966817910.70331820944557
12195260195263.019131087-3.01913108699955
13195415195414.2839269180.716073081683135
14195570195567.8841085292.1158914710395
15195710195722.463878476-12.4638784764975
16195865195867.381634875-2.3816348745022
17196015196018.359443022-3.35944302222924
18196170196168.5466979111.4533020889503
19196320196321.773034183-1.77303418275551
20196475196472.9169265222.08307347842492
21196630196626.5477131123.45228688843781
22196780196781.214779798-1.21477979767951
23196935196932.9457454612.05425453910721
24197085197086.801275723-1.80127572314814
25197240197238.1861858121.81381418829551
26197395197391.8946963053.10530369525077
27197540197546.572131054-6.57213105406845
28197695197694.932415030.0675849700055551
29197845197847.376001088-2.37600108841434
30198000197998.1840071521.81599284781259
31198150198151.670190227-1.67019022686873
32198305198302.9200876892.07991231104825
33198460198456.5915705943.40842940550647
34198610198611.271851922-1.27185192206525
35198765198763.0046889481.99531105230562
36198915198916.85761096-1.85761095967609
37199070199068.2383328331.76166716680746
38199225199221.9422824883.05771751236171
39199365199376.615270368-11.6152703680273
40199520199521.616910576-1.61691057591815
41199670199672.670264591-2.67026459096815
42199825199822.9255825532.07441744743846
43199975199976.21325156-1.21325156005332
44200130200127.4124166512.58758334931917
45200285200281.0930168333.90698316702037
46200435200435.804978025-0.804978024912998
47200590200587.5764052452.42359475491685
48200740200741.468401993-1.46840199324652
49200895200892.8861780292.11382197102648
50201050201046.6243094613.37569053858169
51201190201201.32844055-11.328440549667
52201345201346.35829297-1.35829297010787
53201495201497.43713526-2.43713526026113
54201650201647.715451282.28454871964641
55201800201801.023858928-1.02385892844177
56201955201952.2417198752.75828012480633
57202110202105.9391720634.0608279373555
58202260202260.666322279-0.666322279139422
59202415202412.4514392312.54856076929718
60202565202566.355774232-1.35577423209907
61202720202717.7846703872.21532961289631
62202875202871.5328240363.46717596371309
63203015203026.245987822-11.245987822098
64203170203171.283981113-1.28398111258866
65203320203322.370160496-2.37016049580416
66203475203472.6550891912.34491080939188
67203625203625.969456619-0.969456619059201
68203780203777.1926889142.80731108560576
69203935203930.8949821174.10501788335387
70204085204085.626495376-0.626495376025559
71204240204237.4155445912.58445540946559
72204390204391.323423607-1.32342360744951
73204545204542.7555138642.24448613624554
74204700204696.5065462483.4934537516383
75204845204851.222304541-6.22230454100645
76205000204999.617128230.382871769776102
77205150205152.091843764-2.0918437638029
78205305205302.927905772.07209422966116
79205455205456.439374717-1.43937471695244
80205610205607.712061482.28793852013769
81205765205761.4040836113.59591638893471
82205915205916.102876248-1.10287624777993
83206070206067.852396892.14760311003192
84206220206221.720355281-1.72035528105334
85206375206373.1146289341.88537106569856
86206530206526.8307923493.16920765070245
87206670206681.514788079-11.5147880787845
88206825206826.526349289-1.52634928855696
89206975206977.588644767-2.58864476697636
90207130207127.8520213672.14797863308922
91207280207281.146953352-1.14695335246506
92207435207432.3526643192.64733568052179
93207590207586.0391640793.96083592131617
94207740207740.75644236-0.756442359648645
95207895207892.5326616922.46733830776066
96208045208046.428977409-1.42897740917397
97208200208197.8506459852.14935401463299
98208355208351.5922856333.40771436726209
99208495208506.299578556-11.2995785564999
100208650208651.332280632-1.33228063222487
101208800208802.41369122-2.41369122028118
102208955208952.694321962.30567803958547
103209105209106.004815787-1.00481578730978
104209260209257.2245569362.77544306355412
105209415209410.9237036874.07629631328746
106209565209565.652381155-0.652381155290641
107209720209717.4388745682.56112543249037
108209870209871.344450126-1.34445012628566

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 193885 & 193900 & -15 \tabularnewline
4 & 194040 & 194044.936523827 & -4.9365238272585 \tabularnewline
5 & 194190 & 194195.77723778 & -5.77723777960637 \tabularnewline
6 & 194345 & 194345.775043955 & -0.775043955130968 \tabularnewline
7 & 194495 & 194498.802446284 & -3.80244628430228 \tabularnewline
8 & 194650 & 194649.754985414 & 0.245014586078469 \tabularnewline
9 & 194805 & 194803.208151803 & 1.79184819691 \tabularnewline
10 & 194955 & 194957.71292777 & -2.71292776952032 \tabularnewline
11 & 195110 & 195109.296681791 & 0.70331820944557 \tabularnewline
12 & 195260 & 195263.019131087 & -3.01913108699955 \tabularnewline
13 & 195415 & 195414.283926918 & 0.716073081683135 \tabularnewline
14 & 195570 & 195567.884108529 & 2.1158914710395 \tabularnewline
15 & 195710 & 195722.463878476 & -12.4638784764975 \tabularnewline
16 & 195865 & 195867.381634875 & -2.3816348745022 \tabularnewline
17 & 196015 & 196018.359443022 & -3.35944302222924 \tabularnewline
18 & 196170 & 196168.546697911 & 1.4533020889503 \tabularnewline
19 & 196320 & 196321.773034183 & -1.77303418275551 \tabularnewline
20 & 196475 & 196472.916926522 & 2.08307347842492 \tabularnewline
21 & 196630 & 196626.547713112 & 3.45228688843781 \tabularnewline
22 & 196780 & 196781.214779798 & -1.21477979767951 \tabularnewline
23 & 196935 & 196932.945745461 & 2.05425453910721 \tabularnewline
24 & 197085 & 197086.801275723 & -1.80127572314814 \tabularnewline
25 & 197240 & 197238.186185812 & 1.81381418829551 \tabularnewline
26 & 197395 & 197391.894696305 & 3.10530369525077 \tabularnewline
27 & 197540 & 197546.572131054 & -6.57213105406845 \tabularnewline
28 & 197695 & 197694.93241503 & 0.0675849700055551 \tabularnewline
29 & 197845 & 197847.376001088 & -2.37600108841434 \tabularnewline
30 & 198000 & 197998.184007152 & 1.81599284781259 \tabularnewline
31 & 198150 & 198151.670190227 & -1.67019022686873 \tabularnewline
32 & 198305 & 198302.920087689 & 2.07991231104825 \tabularnewline
33 & 198460 & 198456.591570594 & 3.40842940550647 \tabularnewline
34 & 198610 & 198611.271851922 & -1.27185192206525 \tabularnewline
35 & 198765 & 198763.004688948 & 1.99531105230562 \tabularnewline
36 & 198915 & 198916.85761096 & -1.85761095967609 \tabularnewline
37 & 199070 & 199068.238332833 & 1.76166716680746 \tabularnewline
38 & 199225 & 199221.942282488 & 3.05771751236171 \tabularnewline
39 & 199365 & 199376.615270368 & -11.6152703680273 \tabularnewline
40 & 199520 & 199521.616910576 & -1.61691057591815 \tabularnewline
41 & 199670 & 199672.670264591 & -2.67026459096815 \tabularnewline
42 & 199825 & 199822.925582553 & 2.07441744743846 \tabularnewline
43 & 199975 & 199976.21325156 & -1.21325156005332 \tabularnewline
44 & 200130 & 200127.412416651 & 2.58758334931917 \tabularnewline
45 & 200285 & 200281.093016833 & 3.90698316702037 \tabularnewline
46 & 200435 & 200435.804978025 & -0.804978024912998 \tabularnewline
47 & 200590 & 200587.576405245 & 2.42359475491685 \tabularnewline
48 & 200740 & 200741.468401993 & -1.46840199324652 \tabularnewline
49 & 200895 & 200892.886178029 & 2.11382197102648 \tabularnewline
50 & 201050 & 201046.624309461 & 3.37569053858169 \tabularnewline
51 & 201190 & 201201.32844055 & -11.328440549667 \tabularnewline
52 & 201345 & 201346.35829297 & -1.35829297010787 \tabularnewline
53 & 201495 & 201497.43713526 & -2.43713526026113 \tabularnewline
54 & 201650 & 201647.71545128 & 2.28454871964641 \tabularnewline
55 & 201800 & 201801.023858928 & -1.02385892844177 \tabularnewline
56 & 201955 & 201952.241719875 & 2.75828012480633 \tabularnewline
57 & 202110 & 202105.939172063 & 4.0608279373555 \tabularnewline
58 & 202260 & 202260.666322279 & -0.666322279139422 \tabularnewline
59 & 202415 & 202412.451439231 & 2.54856076929718 \tabularnewline
60 & 202565 & 202566.355774232 & -1.35577423209907 \tabularnewline
61 & 202720 & 202717.784670387 & 2.21532961289631 \tabularnewline
62 & 202875 & 202871.532824036 & 3.46717596371309 \tabularnewline
63 & 203015 & 203026.245987822 & -11.245987822098 \tabularnewline
64 & 203170 & 203171.283981113 & -1.28398111258866 \tabularnewline
65 & 203320 & 203322.370160496 & -2.37016049580416 \tabularnewline
66 & 203475 & 203472.655089191 & 2.34491080939188 \tabularnewline
67 & 203625 & 203625.969456619 & -0.969456619059201 \tabularnewline
68 & 203780 & 203777.192688914 & 2.80731108560576 \tabularnewline
69 & 203935 & 203930.894982117 & 4.10501788335387 \tabularnewline
70 & 204085 & 204085.626495376 & -0.626495376025559 \tabularnewline
71 & 204240 & 204237.415544591 & 2.58445540946559 \tabularnewline
72 & 204390 & 204391.323423607 & -1.32342360744951 \tabularnewline
73 & 204545 & 204542.755513864 & 2.24448613624554 \tabularnewline
74 & 204700 & 204696.506546248 & 3.4934537516383 \tabularnewline
75 & 204845 & 204851.222304541 & -6.22230454100645 \tabularnewline
76 & 205000 & 204999.61712823 & 0.382871769776102 \tabularnewline
77 & 205150 & 205152.091843764 & -2.0918437638029 \tabularnewline
78 & 205305 & 205302.92790577 & 2.07209422966116 \tabularnewline
79 & 205455 & 205456.439374717 & -1.43937471695244 \tabularnewline
80 & 205610 & 205607.71206148 & 2.28793852013769 \tabularnewline
81 & 205765 & 205761.404083611 & 3.59591638893471 \tabularnewline
82 & 205915 & 205916.102876248 & -1.10287624777993 \tabularnewline
83 & 206070 & 206067.85239689 & 2.14760311003192 \tabularnewline
84 & 206220 & 206221.720355281 & -1.72035528105334 \tabularnewline
85 & 206375 & 206373.114628934 & 1.88537106569856 \tabularnewline
86 & 206530 & 206526.830792349 & 3.16920765070245 \tabularnewline
87 & 206670 & 206681.514788079 & -11.5147880787845 \tabularnewline
88 & 206825 & 206826.526349289 & -1.52634928855696 \tabularnewline
89 & 206975 & 206977.588644767 & -2.58864476697636 \tabularnewline
90 & 207130 & 207127.852021367 & 2.14797863308922 \tabularnewline
91 & 207280 & 207281.146953352 & -1.14695335246506 \tabularnewline
92 & 207435 & 207432.352664319 & 2.64733568052179 \tabularnewline
93 & 207590 & 207586.039164079 & 3.96083592131617 \tabularnewline
94 & 207740 & 207740.75644236 & -0.756442359648645 \tabularnewline
95 & 207895 & 207892.532661692 & 2.46733830776066 \tabularnewline
96 & 208045 & 208046.428977409 & -1.42897740917397 \tabularnewline
97 & 208200 & 208197.850645985 & 2.14935401463299 \tabularnewline
98 & 208355 & 208351.592285633 & 3.40771436726209 \tabularnewline
99 & 208495 & 208506.299578556 & -11.2995785564999 \tabularnewline
100 & 208650 & 208651.332280632 & -1.33228063222487 \tabularnewline
101 & 208800 & 208802.41369122 & -2.41369122028118 \tabularnewline
102 & 208955 & 208952.69432196 & 2.30567803958547 \tabularnewline
103 & 209105 & 209106.004815787 & -1.00481578730978 \tabularnewline
104 & 209260 & 209257.224556936 & 2.77544306355412 \tabularnewline
105 & 209415 & 209410.923703687 & 4.07629631328746 \tabularnewline
106 & 209565 & 209565.652381155 & -0.652381155290641 \tabularnewline
107 & 209720 & 209717.438874568 & 2.56112543249037 \tabularnewline
108 & 209870 & 209871.344450126 & -1.34445012628566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280232&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]193885[/C][C]193900[/C][C]-15[/C][/ROW]
[ROW][C]4[/C][C]194040[/C][C]194044.936523827[/C][C]-4.9365238272585[/C][/ROW]
[ROW][C]5[/C][C]194190[/C][C]194195.77723778[/C][C]-5.77723777960637[/C][/ROW]
[ROW][C]6[/C][C]194345[/C][C]194345.775043955[/C][C]-0.775043955130968[/C][/ROW]
[ROW][C]7[/C][C]194495[/C][C]194498.802446284[/C][C]-3.80244628430228[/C][/ROW]
[ROW][C]8[/C][C]194650[/C][C]194649.754985414[/C][C]0.245014586078469[/C][/ROW]
[ROW][C]9[/C][C]194805[/C][C]194803.208151803[/C][C]1.79184819691[/C][/ROW]
[ROW][C]10[/C][C]194955[/C][C]194957.71292777[/C][C]-2.71292776952032[/C][/ROW]
[ROW][C]11[/C][C]195110[/C][C]195109.296681791[/C][C]0.70331820944557[/C][/ROW]
[ROW][C]12[/C][C]195260[/C][C]195263.019131087[/C][C]-3.01913108699955[/C][/ROW]
[ROW][C]13[/C][C]195415[/C][C]195414.283926918[/C][C]0.716073081683135[/C][/ROW]
[ROW][C]14[/C][C]195570[/C][C]195567.884108529[/C][C]2.1158914710395[/C][/ROW]
[ROW][C]15[/C][C]195710[/C][C]195722.463878476[/C][C]-12.4638784764975[/C][/ROW]
[ROW][C]16[/C][C]195865[/C][C]195867.381634875[/C][C]-2.3816348745022[/C][/ROW]
[ROW][C]17[/C][C]196015[/C][C]196018.359443022[/C][C]-3.35944302222924[/C][/ROW]
[ROW][C]18[/C][C]196170[/C][C]196168.546697911[/C][C]1.4533020889503[/C][/ROW]
[ROW][C]19[/C][C]196320[/C][C]196321.773034183[/C][C]-1.77303418275551[/C][/ROW]
[ROW][C]20[/C][C]196475[/C][C]196472.916926522[/C][C]2.08307347842492[/C][/ROW]
[ROW][C]21[/C][C]196630[/C][C]196626.547713112[/C][C]3.45228688843781[/C][/ROW]
[ROW][C]22[/C][C]196780[/C][C]196781.214779798[/C][C]-1.21477979767951[/C][/ROW]
[ROW][C]23[/C][C]196935[/C][C]196932.945745461[/C][C]2.05425453910721[/C][/ROW]
[ROW][C]24[/C][C]197085[/C][C]197086.801275723[/C][C]-1.80127572314814[/C][/ROW]
[ROW][C]25[/C][C]197240[/C][C]197238.186185812[/C][C]1.81381418829551[/C][/ROW]
[ROW][C]26[/C][C]197395[/C][C]197391.894696305[/C][C]3.10530369525077[/C][/ROW]
[ROW][C]27[/C][C]197540[/C][C]197546.572131054[/C][C]-6.57213105406845[/C][/ROW]
[ROW][C]28[/C][C]197695[/C][C]197694.93241503[/C][C]0.0675849700055551[/C][/ROW]
[ROW][C]29[/C][C]197845[/C][C]197847.376001088[/C][C]-2.37600108841434[/C][/ROW]
[ROW][C]30[/C][C]198000[/C][C]197998.184007152[/C][C]1.81599284781259[/C][/ROW]
[ROW][C]31[/C][C]198150[/C][C]198151.670190227[/C][C]-1.67019022686873[/C][/ROW]
[ROW][C]32[/C][C]198305[/C][C]198302.920087689[/C][C]2.07991231104825[/C][/ROW]
[ROW][C]33[/C][C]198460[/C][C]198456.591570594[/C][C]3.40842940550647[/C][/ROW]
[ROW][C]34[/C][C]198610[/C][C]198611.271851922[/C][C]-1.27185192206525[/C][/ROW]
[ROW][C]35[/C][C]198765[/C][C]198763.004688948[/C][C]1.99531105230562[/C][/ROW]
[ROW][C]36[/C][C]198915[/C][C]198916.85761096[/C][C]-1.85761095967609[/C][/ROW]
[ROW][C]37[/C][C]199070[/C][C]199068.238332833[/C][C]1.76166716680746[/C][/ROW]
[ROW][C]38[/C][C]199225[/C][C]199221.942282488[/C][C]3.05771751236171[/C][/ROW]
[ROW][C]39[/C][C]199365[/C][C]199376.615270368[/C][C]-11.6152703680273[/C][/ROW]
[ROW][C]40[/C][C]199520[/C][C]199521.616910576[/C][C]-1.61691057591815[/C][/ROW]
[ROW][C]41[/C][C]199670[/C][C]199672.670264591[/C][C]-2.67026459096815[/C][/ROW]
[ROW][C]42[/C][C]199825[/C][C]199822.925582553[/C][C]2.07441744743846[/C][/ROW]
[ROW][C]43[/C][C]199975[/C][C]199976.21325156[/C][C]-1.21325156005332[/C][/ROW]
[ROW][C]44[/C][C]200130[/C][C]200127.412416651[/C][C]2.58758334931917[/C][/ROW]
[ROW][C]45[/C][C]200285[/C][C]200281.093016833[/C][C]3.90698316702037[/C][/ROW]
[ROW][C]46[/C][C]200435[/C][C]200435.804978025[/C][C]-0.804978024912998[/C][/ROW]
[ROW][C]47[/C][C]200590[/C][C]200587.576405245[/C][C]2.42359475491685[/C][/ROW]
[ROW][C]48[/C][C]200740[/C][C]200741.468401993[/C][C]-1.46840199324652[/C][/ROW]
[ROW][C]49[/C][C]200895[/C][C]200892.886178029[/C][C]2.11382197102648[/C][/ROW]
[ROW][C]50[/C][C]201050[/C][C]201046.624309461[/C][C]3.37569053858169[/C][/ROW]
[ROW][C]51[/C][C]201190[/C][C]201201.32844055[/C][C]-11.328440549667[/C][/ROW]
[ROW][C]52[/C][C]201345[/C][C]201346.35829297[/C][C]-1.35829297010787[/C][/ROW]
[ROW][C]53[/C][C]201495[/C][C]201497.43713526[/C][C]-2.43713526026113[/C][/ROW]
[ROW][C]54[/C][C]201650[/C][C]201647.71545128[/C][C]2.28454871964641[/C][/ROW]
[ROW][C]55[/C][C]201800[/C][C]201801.023858928[/C][C]-1.02385892844177[/C][/ROW]
[ROW][C]56[/C][C]201955[/C][C]201952.241719875[/C][C]2.75828012480633[/C][/ROW]
[ROW][C]57[/C][C]202110[/C][C]202105.939172063[/C][C]4.0608279373555[/C][/ROW]
[ROW][C]58[/C][C]202260[/C][C]202260.666322279[/C][C]-0.666322279139422[/C][/ROW]
[ROW][C]59[/C][C]202415[/C][C]202412.451439231[/C][C]2.54856076929718[/C][/ROW]
[ROW][C]60[/C][C]202565[/C][C]202566.355774232[/C][C]-1.35577423209907[/C][/ROW]
[ROW][C]61[/C][C]202720[/C][C]202717.784670387[/C][C]2.21532961289631[/C][/ROW]
[ROW][C]62[/C][C]202875[/C][C]202871.532824036[/C][C]3.46717596371309[/C][/ROW]
[ROW][C]63[/C][C]203015[/C][C]203026.245987822[/C][C]-11.245987822098[/C][/ROW]
[ROW][C]64[/C][C]203170[/C][C]203171.283981113[/C][C]-1.28398111258866[/C][/ROW]
[ROW][C]65[/C][C]203320[/C][C]203322.370160496[/C][C]-2.37016049580416[/C][/ROW]
[ROW][C]66[/C][C]203475[/C][C]203472.655089191[/C][C]2.34491080939188[/C][/ROW]
[ROW][C]67[/C][C]203625[/C][C]203625.969456619[/C][C]-0.969456619059201[/C][/ROW]
[ROW][C]68[/C][C]203780[/C][C]203777.192688914[/C][C]2.80731108560576[/C][/ROW]
[ROW][C]69[/C][C]203935[/C][C]203930.894982117[/C][C]4.10501788335387[/C][/ROW]
[ROW][C]70[/C][C]204085[/C][C]204085.626495376[/C][C]-0.626495376025559[/C][/ROW]
[ROW][C]71[/C][C]204240[/C][C]204237.415544591[/C][C]2.58445540946559[/C][/ROW]
[ROW][C]72[/C][C]204390[/C][C]204391.323423607[/C][C]-1.32342360744951[/C][/ROW]
[ROW][C]73[/C][C]204545[/C][C]204542.755513864[/C][C]2.24448613624554[/C][/ROW]
[ROW][C]74[/C][C]204700[/C][C]204696.506546248[/C][C]3.4934537516383[/C][/ROW]
[ROW][C]75[/C][C]204845[/C][C]204851.222304541[/C][C]-6.22230454100645[/C][/ROW]
[ROW][C]76[/C][C]205000[/C][C]204999.61712823[/C][C]0.382871769776102[/C][/ROW]
[ROW][C]77[/C][C]205150[/C][C]205152.091843764[/C][C]-2.0918437638029[/C][/ROW]
[ROW][C]78[/C][C]205305[/C][C]205302.92790577[/C][C]2.07209422966116[/C][/ROW]
[ROW][C]79[/C][C]205455[/C][C]205456.439374717[/C][C]-1.43937471695244[/C][/ROW]
[ROW][C]80[/C][C]205610[/C][C]205607.71206148[/C][C]2.28793852013769[/C][/ROW]
[ROW][C]81[/C][C]205765[/C][C]205761.404083611[/C][C]3.59591638893471[/C][/ROW]
[ROW][C]82[/C][C]205915[/C][C]205916.102876248[/C][C]-1.10287624777993[/C][/ROW]
[ROW][C]83[/C][C]206070[/C][C]206067.85239689[/C][C]2.14760311003192[/C][/ROW]
[ROW][C]84[/C][C]206220[/C][C]206221.720355281[/C][C]-1.72035528105334[/C][/ROW]
[ROW][C]85[/C][C]206375[/C][C]206373.114628934[/C][C]1.88537106569856[/C][/ROW]
[ROW][C]86[/C][C]206530[/C][C]206526.830792349[/C][C]3.16920765070245[/C][/ROW]
[ROW][C]87[/C][C]206670[/C][C]206681.514788079[/C][C]-11.5147880787845[/C][/ROW]
[ROW][C]88[/C][C]206825[/C][C]206826.526349289[/C][C]-1.52634928855696[/C][/ROW]
[ROW][C]89[/C][C]206975[/C][C]206977.588644767[/C][C]-2.58864476697636[/C][/ROW]
[ROW][C]90[/C][C]207130[/C][C]207127.852021367[/C][C]2.14797863308922[/C][/ROW]
[ROW][C]91[/C][C]207280[/C][C]207281.146953352[/C][C]-1.14695335246506[/C][/ROW]
[ROW][C]92[/C][C]207435[/C][C]207432.352664319[/C][C]2.64733568052179[/C][/ROW]
[ROW][C]93[/C][C]207590[/C][C]207586.039164079[/C][C]3.96083592131617[/C][/ROW]
[ROW][C]94[/C][C]207740[/C][C]207740.75644236[/C][C]-0.756442359648645[/C][/ROW]
[ROW][C]95[/C][C]207895[/C][C]207892.532661692[/C][C]2.46733830776066[/C][/ROW]
[ROW][C]96[/C][C]208045[/C][C]208046.428977409[/C][C]-1.42897740917397[/C][/ROW]
[ROW][C]97[/C][C]208200[/C][C]208197.850645985[/C][C]2.14935401463299[/C][/ROW]
[ROW][C]98[/C][C]208355[/C][C]208351.592285633[/C][C]3.40771436726209[/C][/ROW]
[ROW][C]99[/C][C]208495[/C][C]208506.299578556[/C][C]-11.2995785564999[/C][/ROW]
[ROW][C]100[/C][C]208650[/C][C]208651.332280632[/C][C]-1.33228063222487[/C][/ROW]
[ROW][C]101[/C][C]208800[/C][C]208802.41369122[/C][C]-2.41369122028118[/C][/ROW]
[ROW][C]102[/C][C]208955[/C][C]208952.69432196[/C][C]2.30567803958547[/C][/ROW]
[ROW][C]103[/C][C]209105[/C][C]209106.004815787[/C][C]-1.00481578730978[/C][/ROW]
[ROW][C]104[/C][C]209260[/C][C]209257.224556936[/C][C]2.77544306355412[/C][/ROW]
[ROW][C]105[/C][C]209415[/C][C]209410.923703687[/C][C]4.07629631328746[/C][/ROW]
[ROW][C]106[/C][C]209565[/C][C]209565.652381155[/C][C]-0.652381155290641[/C][/ROW]
[ROW][C]107[/C][C]209720[/C][C]209717.438874568[/C][C]2.56112543249037[/C][/ROW]
[ROW][C]108[/C][C]209870[/C][C]209871.344450126[/C][C]-1.34445012628566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280232&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280232&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
3193885193900-15
4194040194044.936523827-4.9365238272585
5194190194195.77723778-5.77723777960637
6194345194345.775043955-0.775043955130968
7194495194498.802446284-3.80244628430228
8194650194649.7549854140.245014586078469
9194805194803.2081518031.79184819691
10194955194957.71292777-2.71292776952032
11195110195109.2966817910.70331820944557
12195260195263.019131087-3.01913108699955
13195415195414.2839269180.716073081683135
14195570195567.8841085292.1158914710395
15195710195722.463878476-12.4638784764975
16195865195867.381634875-2.3816348745022
17196015196018.359443022-3.35944302222924
18196170196168.5466979111.4533020889503
19196320196321.773034183-1.77303418275551
20196475196472.9169265222.08307347842492
21196630196626.5477131123.45228688843781
22196780196781.214779798-1.21477979767951
23196935196932.9457454612.05425453910721
24197085197086.801275723-1.80127572314814
25197240197238.1861858121.81381418829551
26197395197391.8946963053.10530369525077
27197540197546.572131054-6.57213105406845
28197695197694.932415030.0675849700055551
29197845197847.376001088-2.37600108841434
30198000197998.1840071521.81599284781259
31198150198151.670190227-1.67019022686873
32198305198302.9200876892.07991231104825
33198460198456.5915705943.40842940550647
34198610198611.271851922-1.27185192206525
35198765198763.0046889481.99531105230562
36198915198916.85761096-1.85761095967609
37199070199068.2383328331.76166716680746
38199225199221.9422824883.05771751236171
39199365199376.615270368-11.6152703680273
40199520199521.616910576-1.61691057591815
41199670199672.670264591-2.67026459096815
42199825199822.9255825532.07441744743846
43199975199976.21325156-1.21325156005332
44200130200127.4124166512.58758334931917
45200285200281.0930168333.90698316702037
46200435200435.804978025-0.804978024912998
47200590200587.5764052452.42359475491685
48200740200741.468401993-1.46840199324652
49200895200892.8861780292.11382197102648
50201050201046.6243094613.37569053858169
51201190201201.32844055-11.328440549667
52201345201346.35829297-1.35829297010787
53201495201497.43713526-2.43713526026113
54201650201647.715451282.28454871964641
55201800201801.023858928-1.02385892844177
56201955201952.2417198752.75828012480633
57202110202105.9391720634.0608279373555
58202260202260.666322279-0.666322279139422
59202415202412.4514392312.54856076929718
60202565202566.355774232-1.35577423209907
61202720202717.7846703872.21532961289631
62202875202871.5328240363.46717596371309
63203015203026.245987822-11.245987822098
64203170203171.283981113-1.28398111258866
65203320203322.370160496-2.37016049580416
66203475203472.6550891912.34491080939188
67203625203625.969456619-0.969456619059201
68203780203777.1926889142.80731108560576
69203935203930.8949821174.10501788335387
70204085204085.626495376-0.626495376025559
71204240204237.4155445912.58445540946559
72204390204391.323423607-1.32342360744951
73204545204542.7555138642.24448613624554
74204700204696.5065462483.4934537516383
75204845204851.222304541-6.22230454100645
76205000204999.617128230.382871769776102
77205150205152.091843764-2.0918437638029
78205305205302.927905772.07209422966116
79205455205456.439374717-1.43937471695244
80205610205607.712061482.28793852013769
81205765205761.4040836113.59591638893471
82205915205916.102876248-1.10287624777993
83206070206067.852396892.14760311003192
84206220206221.720355281-1.72035528105334
85206375206373.1146289341.88537106569856
86206530206526.8307923493.16920765070245
87206670206681.514788079-11.5147880787845
88206825206826.526349289-1.52634928855696
89206975206977.588644767-2.58864476697636
90207130207127.8520213672.14797863308922
91207280207281.146953352-1.14695335246506
92207435207432.3526643192.64733568052179
93207590207586.0391640793.96083592131617
94207740207740.75644236-0.756442359648645
95207895207892.5326616922.46733830776066
96208045208046.428977409-1.42897740917397
97208200208197.8506459852.14935401463299
98208355208351.5922856333.40771436726209
99208495208506.299578556-11.2995785564999
100208650208651.332280632-1.33228063222487
101208800208802.41369122-2.41369122028118
102208955208952.694321962.30567803958547
103209105209106.004815787-1.00481578730978
104209260209257.2245569362.77544306355412
105209415209410.9237036874.07629631328746
106209565209565.652381155-0.652381155290641
107209720209717.4388745682.56112543249037
108209870209871.344450126-1.34445012628566







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109210022.774464354210015.00726591210030.541662798
110210175.030517354210165.677234288210184.38380042
111210327.286570354210316.359357417210338.213783291
112210479.542623354210467.033639747210492.051606962
113210631.798676354210617.68906853210645.908284178
114210784.054729355210768.319160328210799.790298381
115210936.310782355210918.91995047210953.701614239
116211088.566835355211069.48897384211107.64469687
117211240.822888355211220.024703447211261.621073263
118211393.078941355211370.526221254211415.631661456
119211545.334994356211520.993015609211569.676973102
120211697.591047356211671.424851696211723.757243016

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 210022.774464354 & 210015.00726591 & 210030.541662798 \tabularnewline
110 & 210175.030517354 & 210165.677234288 & 210184.38380042 \tabularnewline
111 & 210327.286570354 & 210316.359357417 & 210338.213783291 \tabularnewline
112 & 210479.542623354 & 210467.033639747 & 210492.051606962 \tabularnewline
113 & 210631.798676354 & 210617.68906853 & 210645.908284178 \tabularnewline
114 & 210784.054729355 & 210768.319160328 & 210799.790298381 \tabularnewline
115 & 210936.310782355 & 210918.91995047 & 210953.701614239 \tabularnewline
116 & 211088.566835355 & 211069.48897384 & 211107.64469687 \tabularnewline
117 & 211240.822888355 & 211220.024703447 & 211261.621073263 \tabularnewline
118 & 211393.078941355 & 211370.526221254 & 211415.631661456 \tabularnewline
119 & 211545.334994356 & 211520.993015609 & 211569.676973102 \tabularnewline
120 & 211697.591047356 & 211671.424851696 & 211723.757243016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280232&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]109[/C][C]210022.774464354[/C][C]210015.00726591[/C][C]210030.541662798[/C][/ROW]
[ROW][C]110[/C][C]210175.030517354[/C][C]210165.677234288[/C][C]210184.38380042[/C][/ROW]
[ROW][C]111[/C][C]210327.286570354[/C][C]210316.359357417[/C][C]210338.213783291[/C][/ROW]
[ROW][C]112[/C][C]210479.542623354[/C][C]210467.033639747[/C][C]210492.051606962[/C][/ROW]
[ROW][C]113[/C][C]210631.798676354[/C][C]210617.68906853[/C][C]210645.908284178[/C][/ROW]
[ROW][C]114[/C][C]210784.054729355[/C][C]210768.319160328[/C][C]210799.790298381[/C][/ROW]
[ROW][C]115[/C][C]210936.310782355[/C][C]210918.91995047[/C][C]210953.701614239[/C][/ROW]
[ROW][C]116[/C][C]211088.566835355[/C][C]211069.48897384[/C][C]211107.64469687[/C][/ROW]
[ROW][C]117[/C][C]211240.822888355[/C][C]211220.024703447[/C][C]211261.621073263[/C][/ROW]
[ROW][C]118[/C][C]211393.078941355[/C][C]211370.526221254[/C][C]211415.631661456[/C][/ROW]
[ROW][C]119[/C][C]211545.334994356[/C][C]211520.993015609[/C][C]211569.676973102[/C][/ROW]
[ROW][C]120[/C][C]211697.591047356[/C][C]211671.424851696[/C][C]211723.757243016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280232&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280232&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
109210022.774464354210015.00726591210030.541662798
110210175.030517354210165.677234288210184.38380042
111210327.286570354210316.359357417210338.213783291
112210479.542623354210467.033639747210492.051606962
113210631.798676354210617.68906853210645.908284178
114210784.054729355210768.319160328210799.790298381
115210936.310782355210918.91995047210953.701614239
116211088.566835355211069.48897384211107.64469687
117211240.822888355211220.024703447211261.621073263
118211393.078941355211370.526221254211415.631661456
119211545.334994356211520.993015609211569.676973102
120211697.591047356211671.424851696211723.757243016



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')