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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Dec 2016 17:41:53 +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/2016/Dec/14/t14817337295ztyl2k76ec18ls.htm/, Retrieved Fri, 03 May 2024 15:58:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299615, Retrieved Fri, 03 May 2024 15:58:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-14 16:41:53] [4d72a1efe36cb2a85639504d1000816e] [Current]
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Dataseries X:
4435
4610
4955
5195
5290
5150
5375
5250
5020
5320
5305
5550
5175
5060
4910
4945
4840
4445
4145
4200
4605
4780
4840
5155
4520
4610
4755
4890
4830
4780
4550
4455
4340
4265
3900
3925
3855
3945
4095
4160
3985
3925
3935
3505
3435
3795
3685
3555
3895
3760
4020
4010
4200
3990
4320
4375
4270
4265
4245
3975
3990
4340
4625
4830
4745
4715
4470
4400
4535
4175
4245
4425
4215
4120
4515
4605
4610
4620
4495
4190
4205
4220
3870
4350
3950
3830
4505
4405
4540
4525
4575
4470
4425
4230
4110
4655
4275
4350
4455
4420
4500
4435
4720
4830
4810
4745
4870
4970
4550
4540
4840
4710
4520
4490
4630
4725
4770
4900
4795
4805
4635
4635
4775
4725
4650
4550




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299615&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299615&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299615&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.83352467999034
beta0.0111900025566938
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.83352467999034 \tabularnewline
beta & 0.0111900025566938 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299615&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]0.83352467999034[/C][/ROW]
[ROW][C]beta[/C][C]0.0111900025566938[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299615&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299615&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
alpha0.83352467999034
beta0.0111900025566938
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1351755337.90731837607-162.907318376069
1450605136.70708572443-76.7070857244307
1549104937.68308309482-27.6830830948202
1649454943.013592485881.98640751411585
1748404835.176215383114.82378461689041
1844454433.7071875856411.29281241436
1941454949.61058379256-804.610583792555
2042004050.64197789055149.358022109453
2146053875.93116595242729.068834047583
2247804750.3904191794629.6095808205355
2348404743.9842949975396.0157050024736
2451555072.7831997966982.2168002033059
2545204776.22717680753-256.227176807525
2646104511.0251378644398.9748621355748
2747554467.66865936254287.331340637461
2848904744.51988633452145.480113665479
2948304762.1079772567967.8920227432109
3047804420.22063169197359.779368308029
3145505099.9545937037-549.954593703697
3244554583.62168210975-128.621682109754
3343404282.6841252780957.3158747219077
3442654483.48112510115-218.481125101148
3539004281.72939793068-381.729397930677
3639254205.95193706193-280.951937061934
3738553542.88905779205312.110942207951
3839453808.39003041678136.609969583219
3940953825.95786556938269.042134430621
4041604061.9770910677698.022908932242
4139854024.67651986828-39.676519868277
4239253638.30146282632286.698537173681
4339354101.57214493977-166.572144939772
4435053974.41500952825-469.415009528254
4534353416.668701566418.3312984336039
4637953534.99097015519260.009029844813
4736853705.2920030914-20.2920030914033
4835553951.32588480334-396.325884803342
4938953293.51758959454601.482410405459
5037603776.39053553724-16.3905355372422
5140203692.43859647725327.56140352275
5240103953.2736501686756.7263498313296
5342003862.75169580305337.24830419695
5439903852.52568055001137.474319449985
5543204122.20358318543197.796416814572
5643754257.98696230603117.013037693969
5742704285.35651436789-15.3565143678916
5842654430.63421311414-165.634213114138
5942454210.3195343605334.680465639467
6039754450.91834112528-475.91834112528
6139903903.4802306766486.5197693233572
6243403860.05738544805479.942614551945
6346254257.49913186798367.50086813202
6448304517.33813015373312.661869846268
6547454700.0326449702744.9673550297266
6647154423.38757539901291.612424600993
6744704843.48496980592-373.484969805922
6844004496.21378824972-96.2137882497191
6945354328.39947093251206.600529067494
7041754640.31875646137-465.318756461367
7142454207.4143053543437.5856946456624
7244254369.3169304213155.6830695786912
7342154367.45644064813-152.456440648128
7441204196.94991569401-76.949915694011
7545154112.90869705929402.091302940712
7646054394.19244532865210.807554671348
7746104448.21644353869161.783556461307
7846204311.88253809381308.117461906189
7944954637.05059204016-142.050592040162
8041904533.03871160783-343.038711607835
8142054211.79289476247-6.79289476246777
8242204233.88722120763-13.887221207633
8338704265.09554641766-395.095546417663
8443504069.43703575894280.562964241057
8539504222.54347463778-272.54347463778
8638303965.56542502546-135.565425025461
8745053912.92256666212592.077433337885
8844054322.9997418901682.0002581098352
8945404262.57631117261277.423688827386
9045254249.14880338467275.85119661533
9145754474.33581555626100.664184443737
9244704543.2925230149-73.2925230149003
9344254509.49879602846-84.498796028457
9442304471.55288601808-241.552886018082
9541104253.32159290806-143.321592908062
9646554386.13879481668268.861205183319
9742754443.43925508542-168.439255085425
9843504303.0353991541446.9646008458585
9944554532.37017634999-77.3701763499867
10044204301.98672863682118.013271363177
10145004306.90585263801193.094147361993
10244354224.93089712966210.069102870344
10347204367.5141252231352.4858747769
10448304621.15123345367208.848766546326
10548104827.03554437776-17.0355443777589
10647454826.17740683942-81.1774068394243
10748704766.47308184031103.52691815969
10849705184.46222678843-214.462226788432
10945504772.39227074808-222.392270748077
11045404628.66476976158-88.6647697615799
11148404728.77351203923111.226487960768
11247104694.3986933262115.6013066737942
11345204631.78095177132-111.78095177132
11444904300.99429591331189.005704086692
11546304452.0163855572177.983614442804
11647254536.94875854213188.051241457872
11747704688.358913594181.6410864058962
11849004760.4577746667139.542225333301
11947954918.92173428555-123.921734285551
12048055095.71233538261-290.712335382613
12146354619.3775457391115.6224542608898
12246354699.13518858514-64.1351885851436
12347754856.02736199399-81.0273619939935
12447254646.752261390678.2477386094024
12546504616.997456502933.0025434971049
12645504460.1669801765789.8330198234335

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5175 & 5337.90731837607 & -162.907318376069 \tabularnewline
14 & 5060 & 5136.70708572443 & -76.7070857244307 \tabularnewline
15 & 4910 & 4937.68308309482 & -27.6830830948202 \tabularnewline
16 & 4945 & 4943.01359248588 & 1.98640751411585 \tabularnewline
17 & 4840 & 4835.17621538311 & 4.82378461689041 \tabularnewline
18 & 4445 & 4433.70718758564 & 11.29281241436 \tabularnewline
19 & 4145 & 4949.61058379256 & -804.610583792555 \tabularnewline
20 & 4200 & 4050.64197789055 & 149.358022109453 \tabularnewline
21 & 4605 & 3875.93116595242 & 729.068834047583 \tabularnewline
22 & 4780 & 4750.39041917946 & 29.6095808205355 \tabularnewline
23 & 4840 & 4743.98429499753 & 96.0157050024736 \tabularnewline
24 & 5155 & 5072.78319979669 & 82.2168002033059 \tabularnewline
25 & 4520 & 4776.22717680753 & -256.227176807525 \tabularnewline
26 & 4610 & 4511.02513786443 & 98.9748621355748 \tabularnewline
27 & 4755 & 4467.66865936254 & 287.331340637461 \tabularnewline
28 & 4890 & 4744.51988633452 & 145.480113665479 \tabularnewline
29 & 4830 & 4762.10797725679 & 67.8920227432109 \tabularnewline
30 & 4780 & 4420.22063169197 & 359.779368308029 \tabularnewline
31 & 4550 & 5099.9545937037 & -549.954593703697 \tabularnewline
32 & 4455 & 4583.62168210975 & -128.621682109754 \tabularnewline
33 & 4340 & 4282.68412527809 & 57.3158747219077 \tabularnewline
34 & 4265 & 4483.48112510115 & -218.481125101148 \tabularnewline
35 & 3900 & 4281.72939793068 & -381.729397930677 \tabularnewline
36 & 3925 & 4205.95193706193 & -280.951937061934 \tabularnewline
37 & 3855 & 3542.88905779205 & 312.110942207951 \tabularnewline
38 & 3945 & 3808.39003041678 & 136.609969583219 \tabularnewline
39 & 4095 & 3825.95786556938 & 269.042134430621 \tabularnewline
40 & 4160 & 4061.97709106776 & 98.022908932242 \tabularnewline
41 & 3985 & 4024.67651986828 & -39.676519868277 \tabularnewline
42 & 3925 & 3638.30146282632 & 286.698537173681 \tabularnewline
43 & 3935 & 4101.57214493977 & -166.572144939772 \tabularnewline
44 & 3505 & 3974.41500952825 & -469.415009528254 \tabularnewline
45 & 3435 & 3416.6687015664 & 18.3312984336039 \tabularnewline
46 & 3795 & 3534.99097015519 & 260.009029844813 \tabularnewline
47 & 3685 & 3705.2920030914 & -20.2920030914033 \tabularnewline
48 & 3555 & 3951.32588480334 & -396.325884803342 \tabularnewline
49 & 3895 & 3293.51758959454 & 601.482410405459 \tabularnewline
50 & 3760 & 3776.39053553724 & -16.3905355372422 \tabularnewline
51 & 4020 & 3692.43859647725 & 327.56140352275 \tabularnewline
52 & 4010 & 3953.27365016867 & 56.7263498313296 \tabularnewline
53 & 4200 & 3862.75169580305 & 337.24830419695 \tabularnewline
54 & 3990 & 3852.52568055001 & 137.474319449985 \tabularnewline
55 & 4320 & 4122.20358318543 & 197.796416814572 \tabularnewline
56 & 4375 & 4257.98696230603 & 117.013037693969 \tabularnewline
57 & 4270 & 4285.35651436789 & -15.3565143678916 \tabularnewline
58 & 4265 & 4430.63421311414 & -165.634213114138 \tabularnewline
59 & 4245 & 4210.31953436053 & 34.680465639467 \tabularnewline
60 & 3975 & 4450.91834112528 & -475.91834112528 \tabularnewline
61 & 3990 & 3903.48023067664 & 86.5197693233572 \tabularnewline
62 & 4340 & 3860.05738544805 & 479.942614551945 \tabularnewline
63 & 4625 & 4257.49913186798 & 367.50086813202 \tabularnewline
64 & 4830 & 4517.33813015373 & 312.661869846268 \tabularnewline
65 & 4745 & 4700.03264497027 & 44.9673550297266 \tabularnewline
66 & 4715 & 4423.38757539901 & 291.612424600993 \tabularnewline
67 & 4470 & 4843.48496980592 & -373.484969805922 \tabularnewline
68 & 4400 & 4496.21378824972 & -96.2137882497191 \tabularnewline
69 & 4535 & 4328.39947093251 & 206.600529067494 \tabularnewline
70 & 4175 & 4640.31875646137 & -465.318756461367 \tabularnewline
71 & 4245 & 4207.41430535434 & 37.5856946456624 \tabularnewline
72 & 4425 & 4369.31693042131 & 55.6830695786912 \tabularnewline
73 & 4215 & 4367.45644064813 & -152.456440648128 \tabularnewline
74 & 4120 & 4196.94991569401 & -76.949915694011 \tabularnewline
75 & 4515 & 4112.90869705929 & 402.091302940712 \tabularnewline
76 & 4605 & 4394.19244532865 & 210.807554671348 \tabularnewline
77 & 4610 & 4448.21644353869 & 161.783556461307 \tabularnewline
78 & 4620 & 4311.88253809381 & 308.117461906189 \tabularnewline
79 & 4495 & 4637.05059204016 & -142.050592040162 \tabularnewline
80 & 4190 & 4533.03871160783 & -343.038711607835 \tabularnewline
81 & 4205 & 4211.79289476247 & -6.79289476246777 \tabularnewline
82 & 4220 & 4233.88722120763 & -13.887221207633 \tabularnewline
83 & 3870 & 4265.09554641766 & -395.095546417663 \tabularnewline
84 & 4350 & 4069.43703575894 & 280.562964241057 \tabularnewline
85 & 3950 & 4222.54347463778 & -272.54347463778 \tabularnewline
86 & 3830 & 3965.56542502546 & -135.565425025461 \tabularnewline
87 & 4505 & 3912.92256666212 & 592.077433337885 \tabularnewline
88 & 4405 & 4322.99974189016 & 82.0002581098352 \tabularnewline
89 & 4540 & 4262.57631117261 & 277.423688827386 \tabularnewline
90 & 4525 & 4249.14880338467 & 275.85119661533 \tabularnewline
91 & 4575 & 4474.33581555626 & 100.664184443737 \tabularnewline
92 & 4470 & 4543.2925230149 & -73.2925230149003 \tabularnewline
93 & 4425 & 4509.49879602846 & -84.498796028457 \tabularnewline
94 & 4230 & 4471.55288601808 & -241.552886018082 \tabularnewline
95 & 4110 & 4253.32159290806 & -143.321592908062 \tabularnewline
96 & 4655 & 4386.13879481668 & 268.861205183319 \tabularnewline
97 & 4275 & 4443.43925508542 & -168.439255085425 \tabularnewline
98 & 4350 & 4303.03539915414 & 46.9646008458585 \tabularnewline
99 & 4455 & 4532.37017634999 & -77.3701763499867 \tabularnewline
100 & 4420 & 4301.98672863682 & 118.013271363177 \tabularnewline
101 & 4500 & 4306.90585263801 & 193.094147361993 \tabularnewline
102 & 4435 & 4224.93089712966 & 210.069102870344 \tabularnewline
103 & 4720 & 4367.5141252231 & 352.4858747769 \tabularnewline
104 & 4830 & 4621.15123345367 & 208.848766546326 \tabularnewline
105 & 4810 & 4827.03554437776 & -17.0355443777589 \tabularnewline
106 & 4745 & 4826.17740683942 & -81.1774068394243 \tabularnewline
107 & 4870 & 4766.47308184031 & 103.52691815969 \tabularnewline
108 & 4970 & 5184.46222678843 & -214.462226788432 \tabularnewline
109 & 4550 & 4772.39227074808 & -222.392270748077 \tabularnewline
110 & 4540 & 4628.66476976158 & -88.6647697615799 \tabularnewline
111 & 4840 & 4728.77351203923 & 111.226487960768 \tabularnewline
112 & 4710 & 4694.39869332621 & 15.6013066737942 \tabularnewline
113 & 4520 & 4631.78095177132 & -111.78095177132 \tabularnewline
114 & 4490 & 4300.99429591331 & 189.005704086692 \tabularnewline
115 & 4630 & 4452.0163855572 & 177.983614442804 \tabularnewline
116 & 4725 & 4536.94875854213 & 188.051241457872 \tabularnewline
117 & 4770 & 4688.3589135941 & 81.6410864058962 \tabularnewline
118 & 4900 & 4760.4577746667 & 139.542225333301 \tabularnewline
119 & 4795 & 4918.92173428555 & -123.921734285551 \tabularnewline
120 & 4805 & 5095.71233538261 & -290.712335382613 \tabularnewline
121 & 4635 & 4619.37754573911 & 15.6224542608898 \tabularnewline
122 & 4635 & 4699.13518858514 & -64.1351885851436 \tabularnewline
123 & 4775 & 4856.02736199399 & -81.0273619939935 \tabularnewline
124 & 4725 & 4646.7522613906 & 78.2477386094024 \tabularnewline
125 & 4650 & 4616.9974565029 & 33.0025434971049 \tabularnewline
126 & 4550 & 4460.16698017657 & 89.8330198234335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299615&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]5175[/C][C]5337.90731837607[/C][C]-162.907318376069[/C][/ROW]
[ROW][C]14[/C][C]5060[/C][C]5136.70708572443[/C][C]-76.7070857244307[/C][/ROW]
[ROW][C]15[/C][C]4910[/C][C]4937.68308309482[/C][C]-27.6830830948202[/C][/ROW]
[ROW][C]16[/C][C]4945[/C][C]4943.01359248588[/C][C]1.98640751411585[/C][/ROW]
[ROW][C]17[/C][C]4840[/C][C]4835.17621538311[/C][C]4.82378461689041[/C][/ROW]
[ROW][C]18[/C][C]4445[/C][C]4433.70718758564[/C][C]11.29281241436[/C][/ROW]
[ROW][C]19[/C][C]4145[/C][C]4949.61058379256[/C][C]-804.610583792555[/C][/ROW]
[ROW][C]20[/C][C]4200[/C][C]4050.64197789055[/C][C]149.358022109453[/C][/ROW]
[ROW][C]21[/C][C]4605[/C][C]3875.93116595242[/C][C]729.068834047583[/C][/ROW]
[ROW][C]22[/C][C]4780[/C][C]4750.39041917946[/C][C]29.6095808205355[/C][/ROW]
[ROW][C]23[/C][C]4840[/C][C]4743.98429499753[/C][C]96.0157050024736[/C][/ROW]
[ROW][C]24[/C][C]5155[/C][C]5072.78319979669[/C][C]82.2168002033059[/C][/ROW]
[ROW][C]25[/C][C]4520[/C][C]4776.22717680753[/C][C]-256.227176807525[/C][/ROW]
[ROW][C]26[/C][C]4610[/C][C]4511.02513786443[/C][C]98.9748621355748[/C][/ROW]
[ROW][C]27[/C][C]4755[/C][C]4467.66865936254[/C][C]287.331340637461[/C][/ROW]
[ROW][C]28[/C][C]4890[/C][C]4744.51988633452[/C][C]145.480113665479[/C][/ROW]
[ROW][C]29[/C][C]4830[/C][C]4762.10797725679[/C][C]67.8920227432109[/C][/ROW]
[ROW][C]30[/C][C]4780[/C][C]4420.22063169197[/C][C]359.779368308029[/C][/ROW]
[ROW][C]31[/C][C]4550[/C][C]5099.9545937037[/C][C]-549.954593703697[/C][/ROW]
[ROW][C]32[/C][C]4455[/C][C]4583.62168210975[/C][C]-128.621682109754[/C][/ROW]
[ROW][C]33[/C][C]4340[/C][C]4282.68412527809[/C][C]57.3158747219077[/C][/ROW]
[ROW][C]34[/C][C]4265[/C][C]4483.48112510115[/C][C]-218.481125101148[/C][/ROW]
[ROW][C]35[/C][C]3900[/C][C]4281.72939793068[/C][C]-381.729397930677[/C][/ROW]
[ROW][C]36[/C][C]3925[/C][C]4205.95193706193[/C][C]-280.951937061934[/C][/ROW]
[ROW][C]37[/C][C]3855[/C][C]3542.88905779205[/C][C]312.110942207951[/C][/ROW]
[ROW][C]38[/C][C]3945[/C][C]3808.39003041678[/C][C]136.609969583219[/C][/ROW]
[ROW][C]39[/C][C]4095[/C][C]3825.95786556938[/C][C]269.042134430621[/C][/ROW]
[ROW][C]40[/C][C]4160[/C][C]4061.97709106776[/C][C]98.022908932242[/C][/ROW]
[ROW][C]41[/C][C]3985[/C][C]4024.67651986828[/C][C]-39.676519868277[/C][/ROW]
[ROW][C]42[/C][C]3925[/C][C]3638.30146282632[/C][C]286.698537173681[/C][/ROW]
[ROW][C]43[/C][C]3935[/C][C]4101.57214493977[/C][C]-166.572144939772[/C][/ROW]
[ROW][C]44[/C][C]3505[/C][C]3974.41500952825[/C][C]-469.415009528254[/C][/ROW]
[ROW][C]45[/C][C]3435[/C][C]3416.6687015664[/C][C]18.3312984336039[/C][/ROW]
[ROW][C]46[/C][C]3795[/C][C]3534.99097015519[/C][C]260.009029844813[/C][/ROW]
[ROW][C]47[/C][C]3685[/C][C]3705.2920030914[/C][C]-20.2920030914033[/C][/ROW]
[ROW][C]48[/C][C]3555[/C][C]3951.32588480334[/C][C]-396.325884803342[/C][/ROW]
[ROW][C]49[/C][C]3895[/C][C]3293.51758959454[/C][C]601.482410405459[/C][/ROW]
[ROW][C]50[/C][C]3760[/C][C]3776.39053553724[/C][C]-16.3905355372422[/C][/ROW]
[ROW][C]51[/C][C]4020[/C][C]3692.43859647725[/C][C]327.56140352275[/C][/ROW]
[ROW][C]52[/C][C]4010[/C][C]3953.27365016867[/C][C]56.7263498313296[/C][/ROW]
[ROW][C]53[/C][C]4200[/C][C]3862.75169580305[/C][C]337.24830419695[/C][/ROW]
[ROW][C]54[/C][C]3990[/C][C]3852.52568055001[/C][C]137.474319449985[/C][/ROW]
[ROW][C]55[/C][C]4320[/C][C]4122.20358318543[/C][C]197.796416814572[/C][/ROW]
[ROW][C]56[/C][C]4375[/C][C]4257.98696230603[/C][C]117.013037693969[/C][/ROW]
[ROW][C]57[/C][C]4270[/C][C]4285.35651436789[/C][C]-15.3565143678916[/C][/ROW]
[ROW][C]58[/C][C]4265[/C][C]4430.63421311414[/C][C]-165.634213114138[/C][/ROW]
[ROW][C]59[/C][C]4245[/C][C]4210.31953436053[/C][C]34.680465639467[/C][/ROW]
[ROW][C]60[/C][C]3975[/C][C]4450.91834112528[/C][C]-475.91834112528[/C][/ROW]
[ROW][C]61[/C][C]3990[/C][C]3903.48023067664[/C][C]86.5197693233572[/C][/ROW]
[ROW][C]62[/C][C]4340[/C][C]3860.05738544805[/C][C]479.942614551945[/C][/ROW]
[ROW][C]63[/C][C]4625[/C][C]4257.49913186798[/C][C]367.50086813202[/C][/ROW]
[ROW][C]64[/C][C]4830[/C][C]4517.33813015373[/C][C]312.661869846268[/C][/ROW]
[ROW][C]65[/C][C]4745[/C][C]4700.03264497027[/C][C]44.9673550297266[/C][/ROW]
[ROW][C]66[/C][C]4715[/C][C]4423.38757539901[/C][C]291.612424600993[/C][/ROW]
[ROW][C]67[/C][C]4470[/C][C]4843.48496980592[/C][C]-373.484969805922[/C][/ROW]
[ROW][C]68[/C][C]4400[/C][C]4496.21378824972[/C][C]-96.2137882497191[/C][/ROW]
[ROW][C]69[/C][C]4535[/C][C]4328.39947093251[/C][C]206.600529067494[/C][/ROW]
[ROW][C]70[/C][C]4175[/C][C]4640.31875646137[/C][C]-465.318756461367[/C][/ROW]
[ROW][C]71[/C][C]4245[/C][C]4207.41430535434[/C][C]37.5856946456624[/C][/ROW]
[ROW][C]72[/C][C]4425[/C][C]4369.31693042131[/C][C]55.6830695786912[/C][/ROW]
[ROW][C]73[/C][C]4215[/C][C]4367.45644064813[/C][C]-152.456440648128[/C][/ROW]
[ROW][C]74[/C][C]4120[/C][C]4196.94991569401[/C][C]-76.949915694011[/C][/ROW]
[ROW][C]75[/C][C]4515[/C][C]4112.90869705929[/C][C]402.091302940712[/C][/ROW]
[ROW][C]76[/C][C]4605[/C][C]4394.19244532865[/C][C]210.807554671348[/C][/ROW]
[ROW][C]77[/C][C]4610[/C][C]4448.21644353869[/C][C]161.783556461307[/C][/ROW]
[ROW][C]78[/C][C]4620[/C][C]4311.88253809381[/C][C]308.117461906189[/C][/ROW]
[ROW][C]79[/C][C]4495[/C][C]4637.05059204016[/C][C]-142.050592040162[/C][/ROW]
[ROW][C]80[/C][C]4190[/C][C]4533.03871160783[/C][C]-343.038711607835[/C][/ROW]
[ROW][C]81[/C][C]4205[/C][C]4211.79289476247[/C][C]-6.79289476246777[/C][/ROW]
[ROW][C]82[/C][C]4220[/C][C]4233.88722120763[/C][C]-13.887221207633[/C][/ROW]
[ROW][C]83[/C][C]3870[/C][C]4265.09554641766[/C][C]-395.095546417663[/C][/ROW]
[ROW][C]84[/C][C]4350[/C][C]4069.43703575894[/C][C]280.562964241057[/C][/ROW]
[ROW][C]85[/C][C]3950[/C][C]4222.54347463778[/C][C]-272.54347463778[/C][/ROW]
[ROW][C]86[/C][C]3830[/C][C]3965.56542502546[/C][C]-135.565425025461[/C][/ROW]
[ROW][C]87[/C][C]4505[/C][C]3912.92256666212[/C][C]592.077433337885[/C][/ROW]
[ROW][C]88[/C][C]4405[/C][C]4322.99974189016[/C][C]82.0002581098352[/C][/ROW]
[ROW][C]89[/C][C]4540[/C][C]4262.57631117261[/C][C]277.423688827386[/C][/ROW]
[ROW][C]90[/C][C]4525[/C][C]4249.14880338467[/C][C]275.85119661533[/C][/ROW]
[ROW][C]91[/C][C]4575[/C][C]4474.33581555626[/C][C]100.664184443737[/C][/ROW]
[ROW][C]92[/C][C]4470[/C][C]4543.2925230149[/C][C]-73.2925230149003[/C][/ROW]
[ROW][C]93[/C][C]4425[/C][C]4509.49879602846[/C][C]-84.498796028457[/C][/ROW]
[ROW][C]94[/C][C]4230[/C][C]4471.55288601808[/C][C]-241.552886018082[/C][/ROW]
[ROW][C]95[/C][C]4110[/C][C]4253.32159290806[/C][C]-143.321592908062[/C][/ROW]
[ROW][C]96[/C][C]4655[/C][C]4386.13879481668[/C][C]268.861205183319[/C][/ROW]
[ROW][C]97[/C][C]4275[/C][C]4443.43925508542[/C][C]-168.439255085425[/C][/ROW]
[ROW][C]98[/C][C]4350[/C][C]4303.03539915414[/C][C]46.9646008458585[/C][/ROW]
[ROW][C]99[/C][C]4455[/C][C]4532.37017634999[/C][C]-77.3701763499867[/C][/ROW]
[ROW][C]100[/C][C]4420[/C][C]4301.98672863682[/C][C]118.013271363177[/C][/ROW]
[ROW][C]101[/C][C]4500[/C][C]4306.90585263801[/C][C]193.094147361993[/C][/ROW]
[ROW][C]102[/C][C]4435[/C][C]4224.93089712966[/C][C]210.069102870344[/C][/ROW]
[ROW][C]103[/C][C]4720[/C][C]4367.5141252231[/C][C]352.4858747769[/C][/ROW]
[ROW][C]104[/C][C]4830[/C][C]4621.15123345367[/C][C]208.848766546326[/C][/ROW]
[ROW][C]105[/C][C]4810[/C][C]4827.03554437776[/C][C]-17.0355443777589[/C][/ROW]
[ROW][C]106[/C][C]4745[/C][C]4826.17740683942[/C][C]-81.1774068394243[/C][/ROW]
[ROW][C]107[/C][C]4870[/C][C]4766.47308184031[/C][C]103.52691815969[/C][/ROW]
[ROW][C]108[/C][C]4970[/C][C]5184.46222678843[/C][C]-214.462226788432[/C][/ROW]
[ROW][C]109[/C][C]4550[/C][C]4772.39227074808[/C][C]-222.392270748077[/C][/ROW]
[ROW][C]110[/C][C]4540[/C][C]4628.66476976158[/C][C]-88.6647697615799[/C][/ROW]
[ROW][C]111[/C][C]4840[/C][C]4728.77351203923[/C][C]111.226487960768[/C][/ROW]
[ROW][C]112[/C][C]4710[/C][C]4694.39869332621[/C][C]15.6013066737942[/C][/ROW]
[ROW][C]113[/C][C]4520[/C][C]4631.78095177132[/C][C]-111.78095177132[/C][/ROW]
[ROW][C]114[/C][C]4490[/C][C]4300.99429591331[/C][C]189.005704086692[/C][/ROW]
[ROW][C]115[/C][C]4630[/C][C]4452.0163855572[/C][C]177.983614442804[/C][/ROW]
[ROW][C]116[/C][C]4725[/C][C]4536.94875854213[/C][C]188.051241457872[/C][/ROW]
[ROW][C]117[/C][C]4770[/C][C]4688.3589135941[/C][C]81.6410864058962[/C][/ROW]
[ROW][C]118[/C][C]4900[/C][C]4760.4577746667[/C][C]139.542225333301[/C][/ROW]
[ROW][C]119[/C][C]4795[/C][C]4918.92173428555[/C][C]-123.921734285551[/C][/ROW]
[ROW][C]120[/C][C]4805[/C][C]5095.71233538261[/C][C]-290.712335382613[/C][/ROW]
[ROW][C]121[/C][C]4635[/C][C]4619.37754573911[/C][C]15.6224542608898[/C][/ROW]
[ROW][C]122[/C][C]4635[/C][C]4699.13518858514[/C][C]-64.1351885851436[/C][/ROW]
[ROW][C]123[/C][C]4775[/C][C]4856.02736199399[/C][C]-81.0273619939935[/C][/ROW]
[ROW][C]124[/C][C]4725[/C][C]4646.7522613906[/C][C]78.2477386094024[/C][/ROW]
[ROW][C]125[/C][C]4650[/C][C]4616.9974565029[/C][C]33.0025434971049[/C][/ROW]
[ROW][C]126[/C][C]4550[/C][C]4460.16698017657[/C][C]89.8330198234335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299615&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299615&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
1351755337.90731837607-162.907318376069
1450605136.70708572443-76.7070857244307
1549104937.68308309482-27.6830830948202
1649454943.013592485881.98640751411585
1748404835.176215383114.82378461689041
1844454433.7071875856411.29281241436
1941454949.61058379256-804.610583792555
2042004050.64197789055149.358022109453
2146053875.93116595242729.068834047583
2247804750.3904191794629.6095808205355
2348404743.9842949975396.0157050024736
2451555072.7831997966982.2168002033059
2545204776.22717680753-256.227176807525
2646104511.0251378644398.9748621355748
2747554467.66865936254287.331340637461
2848904744.51988633452145.480113665479
2948304762.1079772567967.8920227432109
3047804420.22063169197359.779368308029
3145505099.9545937037-549.954593703697
3244554583.62168210975-128.621682109754
3343404282.6841252780957.3158747219077
3442654483.48112510115-218.481125101148
3539004281.72939793068-381.729397930677
3639254205.95193706193-280.951937061934
3738553542.88905779205312.110942207951
3839453808.39003041678136.609969583219
3940953825.95786556938269.042134430621
4041604061.9770910677698.022908932242
4139854024.67651986828-39.676519868277
4239253638.30146282632286.698537173681
4339354101.57214493977-166.572144939772
4435053974.41500952825-469.415009528254
4534353416.668701566418.3312984336039
4637953534.99097015519260.009029844813
4736853705.2920030914-20.2920030914033
4835553951.32588480334-396.325884803342
4938953293.51758959454601.482410405459
5037603776.39053553724-16.3905355372422
5140203692.43859647725327.56140352275
5240103953.2736501686756.7263498313296
5342003862.75169580305337.24830419695
5439903852.52568055001137.474319449985
5543204122.20358318543197.796416814572
5643754257.98696230603117.013037693969
5742704285.35651436789-15.3565143678916
5842654430.63421311414-165.634213114138
5942454210.3195343605334.680465639467
6039754450.91834112528-475.91834112528
6139903903.4802306766486.5197693233572
6243403860.05738544805479.942614551945
6346254257.49913186798367.50086813202
6448304517.33813015373312.661869846268
6547454700.0326449702744.9673550297266
6647154423.38757539901291.612424600993
6744704843.48496980592-373.484969805922
6844004496.21378824972-96.2137882497191
6945354328.39947093251206.600529067494
7041754640.31875646137-465.318756461367
7142454207.4143053543437.5856946456624
7244254369.3169304213155.6830695786912
7342154367.45644064813-152.456440648128
7441204196.94991569401-76.949915694011
7545154112.90869705929402.091302940712
7646054394.19244532865210.807554671348
7746104448.21644353869161.783556461307
7846204311.88253809381308.117461906189
7944954637.05059204016-142.050592040162
8041904533.03871160783-343.038711607835
8142054211.79289476247-6.79289476246777
8242204233.88722120763-13.887221207633
8338704265.09554641766-395.095546417663
8443504069.43703575894280.562964241057
8539504222.54347463778-272.54347463778
8638303965.56542502546-135.565425025461
8745053912.92256666212592.077433337885
8844054322.9997418901682.0002581098352
8945404262.57631117261277.423688827386
9045254249.14880338467275.85119661533
9145754474.33581555626100.664184443737
9244704543.2925230149-73.2925230149003
9344254509.49879602846-84.498796028457
9442304471.55288601808-241.552886018082
9541104253.32159290806-143.321592908062
9646554386.13879481668268.861205183319
9742754443.43925508542-168.439255085425
9843504303.0353991541446.9646008458585
9944554532.37017634999-77.3701763499867
10044204301.98672863682118.013271363177
10145004306.90585263801193.094147361993
10244354224.93089712966210.069102870344
10347204367.5141252231352.4858747769
10448304621.15123345367208.848766546326
10548104827.03554437776-17.0355443777589
10647454826.17740683942-81.1774068394243
10748704766.47308184031103.52691815969
10849705184.46222678843-214.462226788432
10945504772.39227074808-222.392270748077
11045404628.66476976158-88.6647697615799
11148404728.77351203923111.226487960768
11247104694.3986933262115.6013066737942
11345204631.78095177132-111.78095177132
11444904300.99429591331189.005704086692
11546304452.0163855572177.983614442804
11647254536.94875854213188.051241457872
11747704688.358913594181.6410864058962
11849004760.4577746667139.542225333301
11947954918.92173428555-123.921734285551
12048055095.71233538261-290.712335382613
12146354619.3775457391115.6224542608898
12246354699.13518858514-64.1351885851436
12347754856.02736199399-81.0273619939935
12447254646.752261390678.2477386094024
12546504616.997456502933.0025434971049
12645504460.1669801765789.8330198234335







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1274528.96829434954044.304700088235013.63188861077
1284467.839875158563833.986013462725101.6937368544
1294443.652965528183687.110608315875200.1953227405
1304455.442549490183591.326509402855319.55858957751
1314450.534315750363488.852369496165412.21626200457
1324700.806000189053648.758418742955752.85358163515
1334518.451592731483381.502497702515655.40068776044
1344572.431436134333354.884546171535789.97832609713
1354781.089521066653486.428740142046075.75030199127
1364667.743632554653298.849027323516036.6382377858
1374566.380902948813125.67308826786007.08871762981
1384392.340749296892881.881511467115902.79998712668

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 4528.9682943495 & 4044.30470008823 & 5013.63188861077 \tabularnewline
128 & 4467.83987515856 & 3833.98601346272 & 5101.6937368544 \tabularnewline
129 & 4443.65296552818 & 3687.11060831587 & 5200.1953227405 \tabularnewline
130 & 4455.44254949018 & 3591.32650940285 & 5319.55858957751 \tabularnewline
131 & 4450.53431575036 & 3488.85236949616 & 5412.21626200457 \tabularnewline
132 & 4700.80600018905 & 3648.75841874295 & 5752.85358163515 \tabularnewline
133 & 4518.45159273148 & 3381.50249770251 & 5655.40068776044 \tabularnewline
134 & 4572.43143613433 & 3354.88454617153 & 5789.97832609713 \tabularnewline
135 & 4781.08952106665 & 3486.42874014204 & 6075.75030199127 \tabularnewline
136 & 4667.74363255465 & 3298.84902732351 & 6036.6382377858 \tabularnewline
137 & 4566.38090294881 & 3125.6730882678 & 6007.08871762981 \tabularnewline
138 & 4392.34074929689 & 2881.88151146711 & 5902.79998712668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299615&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]127[/C][C]4528.9682943495[/C][C]4044.30470008823[/C][C]5013.63188861077[/C][/ROW]
[ROW][C]128[/C][C]4467.83987515856[/C][C]3833.98601346272[/C][C]5101.6937368544[/C][/ROW]
[ROW][C]129[/C][C]4443.65296552818[/C][C]3687.11060831587[/C][C]5200.1953227405[/C][/ROW]
[ROW][C]130[/C][C]4455.44254949018[/C][C]3591.32650940285[/C][C]5319.55858957751[/C][/ROW]
[ROW][C]131[/C][C]4450.53431575036[/C][C]3488.85236949616[/C][C]5412.21626200457[/C][/ROW]
[ROW][C]132[/C][C]4700.80600018905[/C][C]3648.75841874295[/C][C]5752.85358163515[/C][/ROW]
[ROW][C]133[/C][C]4518.45159273148[/C][C]3381.50249770251[/C][C]5655.40068776044[/C][/ROW]
[ROW][C]134[/C][C]4572.43143613433[/C][C]3354.88454617153[/C][C]5789.97832609713[/C][/ROW]
[ROW][C]135[/C][C]4781.08952106665[/C][C]3486.42874014204[/C][C]6075.75030199127[/C][/ROW]
[ROW][C]136[/C][C]4667.74363255465[/C][C]3298.84902732351[/C][C]6036.6382377858[/C][/ROW]
[ROW][C]137[/C][C]4566.38090294881[/C][C]3125.6730882678[/C][C]6007.08871762981[/C][/ROW]
[ROW][C]138[/C][C]4392.34074929689[/C][C]2881.88151146711[/C][C]5902.79998712668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299615&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299615&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
1274528.96829434954044.304700088235013.63188861077
1284467.839875158563833.986013462725101.6937368544
1294443.652965528183687.110608315875200.1953227405
1304455.442549490183591.326509402855319.55858957751
1314450.534315750363488.852369496165412.21626200457
1324700.806000189053648.758418742955752.85358163515
1334518.451592731483381.502497702515655.40068776044
1344572.431436134333354.884546171535789.97832609713
1354781.089521066653486.428740142046075.75030199127
1364667.743632554653298.849027323516036.6382377858
1374566.380902948813125.67308826786007.08871762981
1384392.340749296892881.881511467115902.79998712668



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')