Free Statistics

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 17:06:24 +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/t14817316140xywznr2qkpbfsy.htm/, Retrieved Fri, 03 May 2024 20:51:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299591, Retrieved Fri, 03 May 2024 20:51:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2194] [2016-12-14 16:06:24] [94c1b173d9287822f5e2740a4a602bdd] [Current]
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Dataseries X:
1400
1305
1245
1260
1306
1422
1516
1676
1834
2132
2176
2216
2370
2626
2578
2739
3450
3526
4696
4878
4924
5217
5210
5422
5678
5837
5673
5621
5556
5320
5122
4930
4740
4785
4423
4142
4156
3787
3562
3558
3632
3404
3407
3369
3254
3154
3140
3071
3184
3202
3170
3113
3076
3274
3268
3324
3318
3262
3224
3273
3287
3188
3124
3080
3214
3846
3996
4290
4144
3950
3988
3857
4002
3896
3804
4046
3796
3696
3650
3800
4366
4288
3992
3803
3763
3560
3489
3424
3322
3344
3502
3229
2692
2899
2708
3044
3024
2924
2412
2368
2222
1946
1788
2422
2630
2734
2566
2509
2562
2521
2404
2591
2638
2515
2513
2803




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299591&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299591&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999957717861686
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999957717861686 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299591&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]0.999957717861686[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299591&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
alpha0.999957717861686
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
213051400-95
312451305.00401680314-60.0040168031398
412601245.0025370981414.997462901862
513061259.999365875246.0006341248009
614221305.99805499483116.001945005175
715161421.9950951897294.0049048102833
816761515.99602527161160.003974728387
918341675.99323468981158.00676531019
1021321833.99331913609298.006680863905
1121762131.987399640344.0126003596984
1222162175.9981390531440.0018609468557
1323702215.99830863578154.001691364218
1426262369.99348847919256.006511520815
1525782625.98917549727-47.9891754972705
1627392578.00202908496160.997970915044
1734502738.99319266153711.006807338474
1835263449.9699371118376.0300628881701
1946963525.996785286361170.00321471364
2048784695.95052976225182.049470237752
2149244877.9923025591246.0076974408803
2252174923.99805469617293.001945303827
2352105216.98761125122-6.98761125122201
2454225210.00029545114211.999704548855
2556785421.99103619917256.00896380083
2658375677.98917539358159.010824606417
2756735836.99327668232-163.99327668232
2856215673.00693398641-52.0069339864076
2955565621.00219896438-65.0021989643756
3053205556.00274843197-236.002748431967
3151225320.00997870085-198.009978700852
3249305122.00837228531-192.008372285307
3347404930.00811852455-190.008118524554
3447854740.0080339495544.991966050452
3544234784.99809764347-361.998097643469
3641424423.01530605363-281.015306053634
3741564142.0118819280413.9881180719613
3837874155.99940855246-368.999408552458
3935623787.01560208403-225.01560208403
4035583562.00951414081-4.0095141408101
4136323558.0001695308373.9998304691685
4234043631.99687112893-227.996871128933
4334073404.009640195242.99035980475992
4433693406.99987356119-37.999873561193
4532543369.00160671591-115.001606715909
4631543254.00486251384-100.004862513842
4731403154.00422841943-14.0042284194287
4830713140.00059212872-69.0005921287234
4931843071.00291749258112.99708250742
5032023183.9952222417318.0047777582718
5131703201.9992387195-31.9992387194966
5231133170.00135299624-57.0013529962375
5330763113.00241013909-37.0024101390918
5432743076.00156454102197.998435458976
5532683273.99162820277-5.99162820276615
5633243268.0002533388555.9997466611476
5733183323.99763221097-5.99763221096646
5832623318.00025359271-56.0002535927147
5932243262.00236781047-38.0023678104681
6032733224.0016068213748.9983931786282
6132873272.9979282431614.0020717568377
6231883286.99940796247-98.9994079624653
6331243188.00418590666-64.0041859066605
6430803124.00270623384-44.0027062338413
6532143080.00186052851133.998139471489
6638463213.99433427213632.005665727867
6739963845.97327744903150.026722550973
6842903995.99365654937294.006343450633
6941444289.98756878312-145.987568783122
7039504144.00617266658-194.006172666575
7139883950.0082029958337.9917970041738
7238573987.99839362558-130.998393625584
7340023857.0055388922144.994461107802
7438964001.99386932414-105.993869324141
7538043896.00448164744-92.0044816474428
7640463804.00389014622241.996109853781
7737964045.98976788701-249.989767887012
7836963796.01057010194-100.010570101943
7936503696.00422866076-46.0042286607581
8038003650.00194515716149.998054842841
8143663799.9936577615566.006342238501
8242884365.97606804155-77.9760680415511
8339924288.00329699489-296.003296994894
8438033992.01251565234-189.012515652345
8537633803.00799185333-40.0079918533297
8635603763.00169162345-203.001691623445
8734893560.0085833456-71.0085833456033
8834243489.00300239474-65.0030023947425
8933223424.00274846594-102.002748465938
9033443322.0043128943221.9956871056811
9135023343.99906997532158.000930024684
9232293501.99331938282-272.993319382823
9326923229.01154274129-537.011542741289
9428992692.02270599633206.977294003674
9527082898.99124855743-190.991248557427
9630442708.00807551839335.991924481612
9730243043.98579354298-19.9857935429764
9829243024.00084504209-100.000845042087
9924122924.00422824956-512.004228249561
10023682412.0216486336-44.0216486335962
10122222368.00186132944-146.001861329436
10219462222.00617327089-276.006173270895
10317881946.01167013119-158.011670131194
10424221788.00668107129633.993318928708
10526302421.9731934068208.026806593201
10627342629.99120418179104.008795818209
10725662733.99560228571-167.99560228571
10825092566.00710321329-57.0071032132919
10925622509.0024103822252.9975896177771
11025212561.99775914859-40.9977591485858
11124042521.00173347292-117.001733472923
11225912404.00494708348186.995052916523
11326382590.9920934493147.0079065506911
11425152637.99801240519-122.998012405194
11525132515.00520061897-2.00520061897305
11628032513.00008478417289.99991521583

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1305 & 1400 & -95 \tabularnewline
3 & 1245 & 1305.00401680314 & -60.0040168031398 \tabularnewline
4 & 1260 & 1245.00253709814 & 14.997462901862 \tabularnewline
5 & 1306 & 1259.9993658752 & 46.0006341248009 \tabularnewline
6 & 1422 & 1305.99805499483 & 116.001945005175 \tabularnewline
7 & 1516 & 1421.99509518972 & 94.0049048102833 \tabularnewline
8 & 1676 & 1515.99602527161 & 160.003974728387 \tabularnewline
9 & 1834 & 1675.99323468981 & 158.00676531019 \tabularnewline
10 & 2132 & 1833.99331913609 & 298.006680863905 \tabularnewline
11 & 2176 & 2131.9873996403 & 44.0126003596984 \tabularnewline
12 & 2216 & 2175.99813905314 & 40.0018609468557 \tabularnewline
13 & 2370 & 2215.99830863578 & 154.001691364218 \tabularnewline
14 & 2626 & 2369.99348847919 & 256.006511520815 \tabularnewline
15 & 2578 & 2625.98917549727 & -47.9891754972705 \tabularnewline
16 & 2739 & 2578.00202908496 & 160.997970915044 \tabularnewline
17 & 3450 & 2738.99319266153 & 711.006807338474 \tabularnewline
18 & 3526 & 3449.96993711183 & 76.0300628881701 \tabularnewline
19 & 4696 & 3525.99678528636 & 1170.00321471364 \tabularnewline
20 & 4878 & 4695.95052976225 & 182.049470237752 \tabularnewline
21 & 4924 & 4877.99230255912 & 46.0076974408803 \tabularnewline
22 & 5217 & 4923.99805469617 & 293.001945303827 \tabularnewline
23 & 5210 & 5216.98761125122 & -6.98761125122201 \tabularnewline
24 & 5422 & 5210.00029545114 & 211.999704548855 \tabularnewline
25 & 5678 & 5421.99103619917 & 256.00896380083 \tabularnewline
26 & 5837 & 5677.98917539358 & 159.010824606417 \tabularnewline
27 & 5673 & 5836.99327668232 & -163.99327668232 \tabularnewline
28 & 5621 & 5673.00693398641 & -52.0069339864076 \tabularnewline
29 & 5556 & 5621.00219896438 & -65.0021989643756 \tabularnewline
30 & 5320 & 5556.00274843197 & -236.002748431967 \tabularnewline
31 & 5122 & 5320.00997870085 & -198.009978700852 \tabularnewline
32 & 4930 & 5122.00837228531 & -192.008372285307 \tabularnewline
33 & 4740 & 4930.00811852455 & -190.008118524554 \tabularnewline
34 & 4785 & 4740.00803394955 & 44.991966050452 \tabularnewline
35 & 4423 & 4784.99809764347 & -361.998097643469 \tabularnewline
36 & 4142 & 4423.01530605363 & -281.015306053634 \tabularnewline
37 & 4156 & 4142.01188192804 & 13.9881180719613 \tabularnewline
38 & 3787 & 4155.99940855246 & -368.999408552458 \tabularnewline
39 & 3562 & 3787.01560208403 & -225.01560208403 \tabularnewline
40 & 3558 & 3562.00951414081 & -4.0095141408101 \tabularnewline
41 & 3632 & 3558.00016953083 & 73.9998304691685 \tabularnewline
42 & 3404 & 3631.99687112893 & -227.996871128933 \tabularnewline
43 & 3407 & 3404.00964019524 & 2.99035980475992 \tabularnewline
44 & 3369 & 3406.99987356119 & -37.999873561193 \tabularnewline
45 & 3254 & 3369.00160671591 & -115.001606715909 \tabularnewline
46 & 3154 & 3254.00486251384 & -100.004862513842 \tabularnewline
47 & 3140 & 3154.00422841943 & -14.0042284194287 \tabularnewline
48 & 3071 & 3140.00059212872 & -69.0005921287234 \tabularnewline
49 & 3184 & 3071.00291749258 & 112.99708250742 \tabularnewline
50 & 3202 & 3183.99522224173 & 18.0047777582718 \tabularnewline
51 & 3170 & 3201.9992387195 & -31.9992387194966 \tabularnewline
52 & 3113 & 3170.00135299624 & -57.0013529962375 \tabularnewline
53 & 3076 & 3113.00241013909 & -37.0024101390918 \tabularnewline
54 & 3274 & 3076.00156454102 & 197.998435458976 \tabularnewline
55 & 3268 & 3273.99162820277 & -5.99162820276615 \tabularnewline
56 & 3324 & 3268.00025333885 & 55.9997466611476 \tabularnewline
57 & 3318 & 3323.99763221097 & -5.99763221096646 \tabularnewline
58 & 3262 & 3318.00025359271 & -56.0002535927147 \tabularnewline
59 & 3224 & 3262.00236781047 & -38.0023678104681 \tabularnewline
60 & 3273 & 3224.00160682137 & 48.9983931786282 \tabularnewline
61 & 3287 & 3272.99792824316 & 14.0020717568377 \tabularnewline
62 & 3188 & 3286.99940796247 & -98.9994079624653 \tabularnewline
63 & 3124 & 3188.00418590666 & -64.0041859066605 \tabularnewline
64 & 3080 & 3124.00270623384 & -44.0027062338413 \tabularnewline
65 & 3214 & 3080.00186052851 & 133.998139471489 \tabularnewline
66 & 3846 & 3213.99433427213 & 632.005665727867 \tabularnewline
67 & 3996 & 3845.97327744903 & 150.026722550973 \tabularnewline
68 & 4290 & 3995.99365654937 & 294.006343450633 \tabularnewline
69 & 4144 & 4289.98756878312 & -145.987568783122 \tabularnewline
70 & 3950 & 4144.00617266658 & -194.006172666575 \tabularnewline
71 & 3988 & 3950.00820299583 & 37.9917970041738 \tabularnewline
72 & 3857 & 3987.99839362558 & -130.998393625584 \tabularnewline
73 & 4002 & 3857.0055388922 & 144.994461107802 \tabularnewline
74 & 3896 & 4001.99386932414 & -105.993869324141 \tabularnewline
75 & 3804 & 3896.00448164744 & -92.0044816474428 \tabularnewline
76 & 4046 & 3804.00389014622 & 241.996109853781 \tabularnewline
77 & 3796 & 4045.98976788701 & -249.989767887012 \tabularnewline
78 & 3696 & 3796.01057010194 & -100.010570101943 \tabularnewline
79 & 3650 & 3696.00422866076 & -46.0042286607581 \tabularnewline
80 & 3800 & 3650.00194515716 & 149.998054842841 \tabularnewline
81 & 4366 & 3799.9936577615 & 566.006342238501 \tabularnewline
82 & 4288 & 4365.97606804155 & -77.9760680415511 \tabularnewline
83 & 3992 & 4288.00329699489 & -296.003296994894 \tabularnewline
84 & 3803 & 3992.01251565234 & -189.012515652345 \tabularnewline
85 & 3763 & 3803.00799185333 & -40.0079918533297 \tabularnewline
86 & 3560 & 3763.00169162345 & -203.001691623445 \tabularnewline
87 & 3489 & 3560.0085833456 & -71.0085833456033 \tabularnewline
88 & 3424 & 3489.00300239474 & -65.0030023947425 \tabularnewline
89 & 3322 & 3424.00274846594 & -102.002748465938 \tabularnewline
90 & 3344 & 3322.00431289432 & 21.9956871056811 \tabularnewline
91 & 3502 & 3343.99906997532 & 158.000930024684 \tabularnewline
92 & 3229 & 3501.99331938282 & -272.993319382823 \tabularnewline
93 & 2692 & 3229.01154274129 & -537.011542741289 \tabularnewline
94 & 2899 & 2692.02270599633 & 206.977294003674 \tabularnewline
95 & 2708 & 2898.99124855743 & -190.991248557427 \tabularnewline
96 & 3044 & 2708.00807551839 & 335.991924481612 \tabularnewline
97 & 3024 & 3043.98579354298 & -19.9857935429764 \tabularnewline
98 & 2924 & 3024.00084504209 & -100.000845042087 \tabularnewline
99 & 2412 & 2924.00422824956 & -512.004228249561 \tabularnewline
100 & 2368 & 2412.0216486336 & -44.0216486335962 \tabularnewline
101 & 2222 & 2368.00186132944 & -146.001861329436 \tabularnewline
102 & 1946 & 2222.00617327089 & -276.006173270895 \tabularnewline
103 & 1788 & 1946.01167013119 & -158.011670131194 \tabularnewline
104 & 2422 & 1788.00668107129 & 633.993318928708 \tabularnewline
105 & 2630 & 2421.9731934068 & 208.026806593201 \tabularnewline
106 & 2734 & 2629.99120418179 & 104.008795818209 \tabularnewline
107 & 2566 & 2733.99560228571 & -167.99560228571 \tabularnewline
108 & 2509 & 2566.00710321329 & -57.0071032132919 \tabularnewline
109 & 2562 & 2509.00241038222 & 52.9975896177771 \tabularnewline
110 & 2521 & 2561.99775914859 & -40.9977591485858 \tabularnewline
111 & 2404 & 2521.00173347292 & -117.001733472923 \tabularnewline
112 & 2591 & 2404.00494708348 & 186.995052916523 \tabularnewline
113 & 2638 & 2590.99209344931 & 47.0079065506911 \tabularnewline
114 & 2515 & 2637.99801240519 & -122.998012405194 \tabularnewline
115 & 2513 & 2515.00520061897 & -2.00520061897305 \tabularnewline
116 & 2803 & 2513.00008478417 & 289.99991521583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299591&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]2[/C][C]1305[/C][C]1400[/C][C]-95[/C][/ROW]
[ROW][C]3[/C][C]1245[/C][C]1305.00401680314[/C][C]-60.0040168031398[/C][/ROW]
[ROW][C]4[/C][C]1260[/C][C]1245.00253709814[/C][C]14.997462901862[/C][/ROW]
[ROW][C]5[/C][C]1306[/C][C]1259.9993658752[/C][C]46.0006341248009[/C][/ROW]
[ROW][C]6[/C][C]1422[/C][C]1305.99805499483[/C][C]116.001945005175[/C][/ROW]
[ROW][C]7[/C][C]1516[/C][C]1421.99509518972[/C][C]94.0049048102833[/C][/ROW]
[ROW][C]8[/C][C]1676[/C][C]1515.99602527161[/C][C]160.003974728387[/C][/ROW]
[ROW][C]9[/C][C]1834[/C][C]1675.99323468981[/C][C]158.00676531019[/C][/ROW]
[ROW][C]10[/C][C]2132[/C][C]1833.99331913609[/C][C]298.006680863905[/C][/ROW]
[ROW][C]11[/C][C]2176[/C][C]2131.9873996403[/C][C]44.0126003596984[/C][/ROW]
[ROW][C]12[/C][C]2216[/C][C]2175.99813905314[/C][C]40.0018609468557[/C][/ROW]
[ROW][C]13[/C][C]2370[/C][C]2215.99830863578[/C][C]154.001691364218[/C][/ROW]
[ROW][C]14[/C][C]2626[/C][C]2369.99348847919[/C][C]256.006511520815[/C][/ROW]
[ROW][C]15[/C][C]2578[/C][C]2625.98917549727[/C][C]-47.9891754972705[/C][/ROW]
[ROW][C]16[/C][C]2739[/C][C]2578.00202908496[/C][C]160.997970915044[/C][/ROW]
[ROW][C]17[/C][C]3450[/C][C]2738.99319266153[/C][C]711.006807338474[/C][/ROW]
[ROW][C]18[/C][C]3526[/C][C]3449.96993711183[/C][C]76.0300628881701[/C][/ROW]
[ROW][C]19[/C][C]4696[/C][C]3525.99678528636[/C][C]1170.00321471364[/C][/ROW]
[ROW][C]20[/C][C]4878[/C][C]4695.95052976225[/C][C]182.049470237752[/C][/ROW]
[ROW][C]21[/C][C]4924[/C][C]4877.99230255912[/C][C]46.0076974408803[/C][/ROW]
[ROW][C]22[/C][C]5217[/C][C]4923.99805469617[/C][C]293.001945303827[/C][/ROW]
[ROW][C]23[/C][C]5210[/C][C]5216.98761125122[/C][C]-6.98761125122201[/C][/ROW]
[ROW][C]24[/C][C]5422[/C][C]5210.00029545114[/C][C]211.999704548855[/C][/ROW]
[ROW][C]25[/C][C]5678[/C][C]5421.99103619917[/C][C]256.00896380083[/C][/ROW]
[ROW][C]26[/C][C]5837[/C][C]5677.98917539358[/C][C]159.010824606417[/C][/ROW]
[ROW][C]27[/C][C]5673[/C][C]5836.99327668232[/C][C]-163.99327668232[/C][/ROW]
[ROW][C]28[/C][C]5621[/C][C]5673.00693398641[/C][C]-52.0069339864076[/C][/ROW]
[ROW][C]29[/C][C]5556[/C][C]5621.00219896438[/C][C]-65.0021989643756[/C][/ROW]
[ROW][C]30[/C][C]5320[/C][C]5556.00274843197[/C][C]-236.002748431967[/C][/ROW]
[ROW][C]31[/C][C]5122[/C][C]5320.00997870085[/C][C]-198.009978700852[/C][/ROW]
[ROW][C]32[/C][C]4930[/C][C]5122.00837228531[/C][C]-192.008372285307[/C][/ROW]
[ROW][C]33[/C][C]4740[/C][C]4930.00811852455[/C][C]-190.008118524554[/C][/ROW]
[ROW][C]34[/C][C]4785[/C][C]4740.00803394955[/C][C]44.991966050452[/C][/ROW]
[ROW][C]35[/C][C]4423[/C][C]4784.99809764347[/C][C]-361.998097643469[/C][/ROW]
[ROW][C]36[/C][C]4142[/C][C]4423.01530605363[/C][C]-281.015306053634[/C][/ROW]
[ROW][C]37[/C][C]4156[/C][C]4142.01188192804[/C][C]13.9881180719613[/C][/ROW]
[ROW][C]38[/C][C]3787[/C][C]4155.99940855246[/C][C]-368.999408552458[/C][/ROW]
[ROW][C]39[/C][C]3562[/C][C]3787.01560208403[/C][C]-225.01560208403[/C][/ROW]
[ROW][C]40[/C][C]3558[/C][C]3562.00951414081[/C][C]-4.0095141408101[/C][/ROW]
[ROW][C]41[/C][C]3632[/C][C]3558.00016953083[/C][C]73.9998304691685[/C][/ROW]
[ROW][C]42[/C][C]3404[/C][C]3631.99687112893[/C][C]-227.996871128933[/C][/ROW]
[ROW][C]43[/C][C]3407[/C][C]3404.00964019524[/C][C]2.99035980475992[/C][/ROW]
[ROW][C]44[/C][C]3369[/C][C]3406.99987356119[/C][C]-37.999873561193[/C][/ROW]
[ROW][C]45[/C][C]3254[/C][C]3369.00160671591[/C][C]-115.001606715909[/C][/ROW]
[ROW][C]46[/C][C]3154[/C][C]3254.00486251384[/C][C]-100.004862513842[/C][/ROW]
[ROW][C]47[/C][C]3140[/C][C]3154.00422841943[/C][C]-14.0042284194287[/C][/ROW]
[ROW][C]48[/C][C]3071[/C][C]3140.00059212872[/C][C]-69.0005921287234[/C][/ROW]
[ROW][C]49[/C][C]3184[/C][C]3071.00291749258[/C][C]112.99708250742[/C][/ROW]
[ROW][C]50[/C][C]3202[/C][C]3183.99522224173[/C][C]18.0047777582718[/C][/ROW]
[ROW][C]51[/C][C]3170[/C][C]3201.9992387195[/C][C]-31.9992387194966[/C][/ROW]
[ROW][C]52[/C][C]3113[/C][C]3170.00135299624[/C][C]-57.0013529962375[/C][/ROW]
[ROW][C]53[/C][C]3076[/C][C]3113.00241013909[/C][C]-37.0024101390918[/C][/ROW]
[ROW][C]54[/C][C]3274[/C][C]3076.00156454102[/C][C]197.998435458976[/C][/ROW]
[ROW][C]55[/C][C]3268[/C][C]3273.99162820277[/C][C]-5.99162820276615[/C][/ROW]
[ROW][C]56[/C][C]3324[/C][C]3268.00025333885[/C][C]55.9997466611476[/C][/ROW]
[ROW][C]57[/C][C]3318[/C][C]3323.99763221097[/C][C]-5.99763221096646[/C][/ROW]
[ROW][C]58[/C][C]3262[/C][C]3318.00025359271[/C][C]-56.0002535927147[/C][/ROW]
[ROW][C]59[/C][C]3224[/C][C]3262.00236781047[/C][C]-38.0023678104681[/C][/ROW]
[ROW][C]60[/C][C]3273[/C][C]3224.00160682137[/C][C]48.9983931786282[/C][/ROW]
[ROW][C]61[/C][C]3287[/C][C]3272.99792824316[/C][C]14.0020717568377[/C][/ROW]
[ROW][C]62[/C][C]3188[/C][C]3286.99940796247[/C][C]-98.9994079624653[/C][/ROW]
[ROW][C]63[/C][C]3124[/C][C]3188.00418590666[/C][C]-64.0041859066605[/C][/ROW]
[ROW][C]64[/C][C]3080[/C][C]3124.00270623384[/C][C]-44.0027062338413[/C][/ROW]
[ROW][C]65[/C][C]3214[/C][C]3080.00186052851[/C][C]133.998139471489[/C][/ROW]
[ROW][C]66[/C][C]3846[/C][C]3213.99433427213[/C][C]632.005665727867[/C][/ROW]
[ROW][C]67[/C][C]3996[/C][C]3845.97327744903[/C][C]150.026722550973[/C][/ROW]
[ROW][C]68[/C][C]4290[/C][C]3995.99365654937[/C][C]294.006343450633[/C][/ROW]
[ROW][C]69[/C][C]4144[/C][C]4289.98756878312[/C][C]-145.987568783122[/C][/ROW]
[ROW][C]70[/C][C]3950[/C][C]4144.00617266658[/C][C]-194.006172666575[/C][/ROW]
[ROW][C]71[/C][C]3988[/C][C]3950.00820299583[/C][C]37.9917970041738[/C][/ROW]
[ROW][C]72[/C][C]3857[/C][C]3987.99839362558[/C][C]-130.998393625584[/C][/ROW]
[ROW][C]73[/C][C]4002[/C][C]3857.0055388922[/C][C]144.994461107802[/C][/ROW]
[ROW][C]74[/C][C]3896[/C][C]4001.99386932414[/C][C]-105.993869324141[/C][/ROW]
[ROW][C]75[/C][C]3804[/C][C]3896.00448164744[/C][C]-92.0044816474428[/C][/ROW]
[ROW][C]76[/C][C]4046[/C][C]3804.00389014622[/C][C]241.996109853781[/C][/ROW]
[ROW][C]77[/C][C]3796[/C][C]4045.98976788701[/C][C]-249.989767887012[/C][/ROW]
[ROW][C]78[/C][C]3696[/C][C]3796.01057010194[/C][C]-100.010570101943[/C][/ROW]
[ROW][C]79[/C][C]3650[/C][C]3696.00422866076[/C][C]-46.0042286607581[/C][/ROW]
[ROW][C]80[/C][C]3800[/C][C]3650.00194515716[/C][C]149.998054842841[/C][/ROW]
[ROW][C]81[/C][C]4366[/C][C]3799.9936577615[/C][C]566.006342238501[/C][/ROW]
[ROW][C]82[/C][C]4288[/C][C]4365.97606804155[/C][C]-77.9760680415511[/C][/ROW]
[ROW][C]83[/C][C]3992[/C][C]4288.00329699489[/C][C]-296.003296994894[/C][/ROW]
[ROW][C]84[/C][C]3803[/C][C]3992.01251565234[/C][C]-189.012515652345[/C][/ROW]
[ROW][C]85[/C][C]3763[/C][C]3803.00799185333[/C][C]-40.0079918533297[/C][/ROW]
[ROW][C]86[/C][C]3560[/C][C]3763.00169162345[/C][C]-203.001691623445[/C][/ROW]
[ROW][C]87[/C][C]3489[/C][C]3560.0085833456[/C][C]-71.0085833456033[/C][/ROW]
[ROW][C]88[/C][C]3424[/C][C]3489.00300239474[/C][C]-65.0030023947425[/C][/ROW]
[ROW][C]89[/C][C]3322[/C][C]3424.00274846594[/C][C]-102.002748465938[/C][/ROW]
[ROW][C]90[/C][C]3344[/C][C]3322.00431289432[/C][C]21.9956871056811[/C][/ROW]
[ROW][C]91[/C][C]3502[/C][C]3343.99906997532[/C][C]158.000930024684[/C][/ROW]
[ROW][C]92[/C][C]3229[/C][C]3501.99331938282[/C][C]-272.993319382823[/C][/ROW]
[ROW][C]93[/C][C]2692[/C][C]3229.01154274129[/C][C]-537.011542741289[/C][/ROW]
[ROW][C]94[/C][C]2899[/C][C]2692.02270599633[/C][C]206.977294003674[/C][/ROW]
[ROW][C]95[/C][C]2708[/C][C]2898.99124855743[/C][C]-190.991248557427[/C][/ROW]
[ROW][C]96[/C][C]3044[/C][C]2708.00807551839[/C][C]335.991924481612[/C][/ROW]
[ROW][C]97[/C][C]3024[/C][C]3043.98579354298[/C][C]-19.9857935429764[/C][/ROW]
[ROW][C]98[/C][C]2924[/C][C]3024.00084504209[/C][C]-100.000845042087[/C][/ROW]
[ROW][C]99[/C][C]2412[/C][C]2924.00422824956[/C][C]-512.004228249561[/C][/ROW]
[ROW][C]100[/C][C]2368[/C][C]2412.0216486336[/C][C]-44.0216486335962[/C][/ROW]
[ROW][C]101[/C][C]2222[/C][C]2368.00186132944[/C][C]-146.001861329436[/C][/ROW]
[ROW][C]102[/C][C]1946[/C][C]2222.00617327089[/C][C]-276.006173270895[/C][/ROW]
[ROW][C]103[/C][C]1788[/C][C]1946.01167013119[/C][C]-158.011670131194[/C][/ROW]
[ROW][C]104[/C][C]2422[/C][C]1788.00668107129[/C][C]633.993318928708[/C][/ROW]
[ROW][C]105[/C][C]2630[/C][C]2421.9731934068[/C][C]208.026806593201[/C][/ROW]
[ROW][C]106[/C][C]2734[/C][C]2629.99120418179[/C][C]104.008795818209[/C][/ROW]
[ROW][C]107[/C][C]2566[/C][C]2733.99560228571[/C][C]-167.99560228571[/C][/ROW]
[ROW][C]108[/C][C]2509[/C][C]2566.00710321329[/C][C]-57.0071032132919[/C][/ROW]
[ROW][C]109[/C][C]2562[/C][C]2509.00241038222[/C][C]52.9975896177771[/C][/ROW]
[ROW][C]110[/C][C]2521[/C][C]2561.99775914859[/C][C]-40.9977591485858[/C][/ROW]
[ROW][C]111[/C][C]2404[/C][C]2521.00173347292[/C][C]-117.001733472923[/C][/ROW]
[ROW][C]112[/C][C]2591[/C][C]2404.00494708348[/C][C]186.995052916523[/C][/ROW]
[ROW][C]113[/C][C]2638[/C][C]2590.99209344931[/C][C]47.0079065506911[/C][/ROW]
[ROW][C]114[/C][C]2515[/C][C]2637.99801240519[/C][C]-122.998012405194[/C][/ROW]
[ROW][C]115[/C][C]2513[/C][C]2515.00520061897[/C][C]-2.00520061897305[/C][/ROW]
[ROW][C]116[/C][C]2803[/C][C]2513.00008478417[/C][C]289.99991521583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299591&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299591&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
213051400-95
312451305.00401680314-60.0040168031398
412601245.0025370981414.997462901862
513061259.999365875246.0006341248009
614221305.99805499483116.001945005175
715161421.9950951897294.0049048102833
816761515.99602527161160.003974728387
918341675.99323468981158.00676531019
1021321833.99331913609298.006680863905
1121762131.987399640344.0126003596984
1222162175.9981390531440.0018609468557
1323702215.99830863578154.001691364218
1426262369.99348847919256.006511520815
1525782625.98917549727-47.9891754972705
1627392578.00202908496160.997970915044
1734502738.99319266153711.006807338474
1835263449.9699371118376.0300628881701
1946963525.996785286361170.00321471364
2048784695.95052976225182.049470237752
2149244877.9923025591246.0076974408803
2252174923.99805469617293.001945303827
2352105216.98761125122-6.98761125122201
2454225210.00029545114211.999704548855
2556785421.99103619917256.00896380083
2658375677.98917539358159.010824606417
2756735836.99327668232-163.99327668232
2856215673.00693398641-52.0069339864076
2955565621.00219896438-65.0021989643756
3053205556.00274843197-236.002748431967
3151225320.00997870085-198.009978700852
3249305122.00837228531-192.008372285307
3347404930.00811852455-190.008118524554
3447854740.0080339495544.991966050452
3544234784.99809764347-361.998097643469
3641424423.01530605363-281.015306053634
3741564142.0118819280413.9881180719613
3837874155.99940855246-368.999408552458
3935623787.01560208403-225.01560208403
4035583562.00951414081-4.0095141408101
4136323558.0001695308373.9998304691685
4234043631.99687112893-227.996871128933
4334073404.009640195242.99035980475992
4433693406.99987356119-37.999873561193
4532543369.00160671591-115.001606715909
4631543254.00486251384-100.004862513842
4731403154.00422841943-14.0042284194287
4830713140.00059212872-69.0005921287234
4931843071.00291749258112.99708250742
5032023183.9952222417318.0047777582718
5131703201.9992387195-31.9992387194966
5231133170.00135299624-57.0013529962375
5330763113.00241013909-37.0024101390918
5432743076.00156454102197.998435458976
5532683273.99162820277-5.99162820276615
5633243268.0002533388555.9997466611476
5733183323.99763221097-5.99763221096646
5832623318.00025359271-56.0002535927147
5932243262.00236781047-38.0023678104681
6032733224.0016068213748.9983931786282
6132873272.9979282431614.0020717568377
6231883286.99940796247-98.9994079624653
6331243188.00418590666-64.0041859066605
6430803124.00270623384-44.0027062338413
6532143080.00186052851133.998139471489
6638463213.99433427213632.005665727867
6739963845.97327744903150.026722550973
6842903995.99365654937294.006343450633
6941444289.98756878312-145.987568783122
7039504144.00617266658-194.006172666575
7139883950.0082029958337.9917970041738
7238573987.99839362558-130.998393625584
7340023857.0055388922144.994461107802
7438964001.99386932414-105.993869324141
7538043896.00448164744-92.0044816474428
7640463804.00389014622241.996109853781
7737964045.98976788701-249.989767887012
7836963796.01057010194-100.010570101943
7936503696.00422866076-46.0042286607581
8038003650.00194515716149.998054842841
8143663799.9936577615566.006342238501
8242884365.97606804155-77.9760680415511
8339924288.00329699489-296.003296994894
8438033992.01251565234-189.012515652345
8537633803.00799185333-40.0079918533297
8635603763.00169162345-203.001691623445
8734893560.0085833456-71.0085833456033
8834243489.00300239474-65.0030023947425
8933223424.00274846594-102.002748465938
9033443322.0043128943221.9956871056811
9135023343.99906997532158.000930024684
9232293501.99331938282-272.993319382823
9326923229.01154274129-537.011542741289
9428992692.02270599633206.977294003674
9527082898.99124855743-190.991248557427
9630442708.00807551839335.991924481612
9730243043.98579354298-19.9857935429764
9829243024.00084504209-100.000845042087
9924122924.00422824956-512.004228249561
10023682412.0216486336-44.0216486335962
10122222368.00186132944-146.001861329436
10219462222.00617327089-276.006173270895
10317881946.01167013119-158.011670131194
10424221788.00668107129633.993318928708
10526302421.9731934068208.026806593201
10627342629.99120418179104.008795818209
10725662733.99560228571-167.99560228571
10825092566.00710321329-57.0071032132919
10925622509.0024103822252.9975896177771
11025212561.99775914859-40.9977591485858
11124042521.00173347292-117.001733472923
11225912404.00494708348186.995052916523
11326382590.9920934493147.0079065506911
11425152637.99801240519-122.998012405194
11525132515.00520061897-2.00520061897305
11628032513.00008478417289.99991521583







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1172802.987738183472348.798651068413257.17682529854
1182802.987738183472160.680950499243445.29452586771
1192802.987738183472016.331337868793589.64413849816
1202802.987738183471894.638369929793711.33710643716
1212802.987738183471787.424417923393818.55105844356
1222802.987738183471690.495428048923915.48004831802
1232802.987738183471601.359916119044004.61556024791
1242802.987738183471518.394531985444087.58094438151
1252802.987738183471440.471687613444165.50378875351
1262802.987738183471366.770390178034239.20508618891
1272802.987738183471296.670854734784309.30462163217
1282802.987738183471229.691568985374376.28390738157

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 2802.98773818347 & 2348.79865106841 & 3257.17682529854 \tabularnewline
118 & 2802.98773818347 & 2160.68095049924 & 3445.29452586771 \tabularnewline
119 & 2802.98773818347 & 2016.33133786879 & 3589.64413849816 \tabularnewline
120 & 2802.98773818347 & 1894.63836992979 & 3711.33710643716 \tabularnewline
121 & 2802.98773818347 & 1787.42441792339 & 3818.55105844356 \tabularnewline
122 & 2802.98773818347 & 1690.49542804892 & 3915.48004831802 \tabularnewline
123 & 2802.98773818347 & 1601.35991611904 & 4004.61556024791 \tabularnewline
124 & 2802.98773818347 & 1518.39453198544 & 4087.58094438151 \tabularnewline
125 & 2802.98773818347 & 1440.47168761344 & 4165.50378875351 \tabularnewline
126 & 2802.98773818347 & 1366.77039017803 & 4239.20508618891 \tabularnewline
127 & 2802.98773818347 & 1296.67085473478 & 4309.30462163217 \tabularnewline
128 & 2802.98773818347 & 1229.69156898537 & 4376.28390738157 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299591&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]117[/C][C]2802.98773818347[/C][C]2348.79865106841[/C][C]3257.17682529854[/C][/ROW]
[ROW][C]118[/C][C]2802.98773818347[/C][C]2160.68095049924[/C][C]3445.29452586771[/C][/ROW]
[ROW][C]119[/C][C]2802.98773818347[/C][C]2016.33133786879[/C][C]3589.64413849816[/C][/ROW]
[ROW][C]120[/C][C]2802.98773818347[/C][C]1894.63836992979[/C][C]3711.33710643716[/C][/ROW]
[ROW][C]121[/C][C]2802.98773818347[/C][C]1787.42441792339[/C][C]3818.55105844356[/C][/ROW]
[ROW][C]122[/C][C]2802.98773818347[/C][C]1690.49542804892[/C][C]3915.48004831802[/C][/ROW]
[ROW][C]123[/C][C]2802.98773818347[/C][C]1601.35991611904[/C][C]4004.61556024791[/C][/ROW]
[ROW][C]124[/C][C]2802.98773818347[/C][C]1518.39453198544[/C][C]4087.58094438151[/C][/ROW]
[ROW][C]125[/C][C]2802.98773818347[/C][C]1440.47168761344[/C][C]4165.50378875351[/C][/ROW]
[ROW][C]126[/C][C]2802.98773818347[/C][C]1366.77039017803[/C][C]4239.20508618891[/C][/ROW]
[ROW][C]127[/C][C]2802.98773818347[/C][C]1296.67085473478[/C][C]4309.30462163217[/C][/ROW]
[ROW][C]128[/C][C]2802.98773818347[/C][C]1229.69156898537[/C][C]4376.28390738157[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299591&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299591&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
1172802.987738183472348.798651068413257.17682529854
1182802.987738183472160.680950499243445.29452586771
1192802.987738183472016.331337868793589.64413849816
1202802.987738183471894.638369929793711.33710643716
1212802.987738183471787.424417923393818.55105844356
1222802.987738183471690.495428048923915.48004831802
1232802.987738183471601.359916119044004.61556024791
1242802.987738183471518.394531985444087.58094438151
1252802.987738183471440.471687613444165.50378875351
1262802.987738183471366.770390178034239.20508618891
1272802.987738183471296.670854734784309.30462163217
1282802.987738183471229.691568985374376.28390738157



Parameters (Session):
par1 = 8 ; par2 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')