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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 computationTue, 20 Dec 2016 14:29:51 +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/20/t1482240774em4qjd3ixq0gqr1.htm/, Retrieved Sat, 27 Apr 2024 22:10:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301660, Retrieved Sat, 27 Apr 2024 22:10:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-20 13:29:51] [361c8dad91b3f1ef2e651cd04783c23b] [Current]
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Dataseries X:
2755
2765
3000
2890
2940
3290
2815
3035
3070
3040
2685
2540
3090
2995
3440
3335
3205
3285
2790
3225
3360
3275
3505
3185
3470
3510
3840
3605
3655
3555
3140
3380
3255
3460
3245
3120
3265
3220
3140
3050
3300
2950
2630
2795
2840
2945
2790
2605
4590
4230
4245
4300
4475
3910
4100
3500
4390
3550
3865
3715
3310
3945
5050
4350
4060
4345
4360
4915
4650
4805
4775
4220
3975
3820
5515
4895
5535
4230
3695
5590
5000
4875
4360
4405
4500
4070
4800
4080
4850
4105
3805
5060
4060
4600
4635
3900
4120
3960
4400
3700
3970
4550
5140
5000
3650
4300
3650
3355
4000
3450
3295
3390
3415
3440
3680
3900
3965
4295
4210
4100
4690
3860
4250
4495
3800
3845




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=301660&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=301660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301660&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
alpha0.435538810584028
beta0
gamma0.0484435412673426

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.435538810584028 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.0484435412673426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301660&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]0.435538810584028[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.0484435412673426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301660&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
alpha0.435538810584028
beta0
gamma0.0484435412673426







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1330902967.00988247863122.990117521366
1429952940.0851561732854.9148438267166
1534403410.3860061327829.6139938672163
1633353317.7923539941617.2076460058415
1732053172.7119225309632.2880774690357
1832853227.1162709170157.8837290829897
1927903084.96018562979-294.960185629788
2032253174.3352147400850.6647852599167
2133603224.86833257982135.13166742018
2232753238.2317224760536.7682775239537
2335052891.04570519852613.954294801477
2431853023.99659937178161.003400628216
2534703670.11623631332-200.116236313323
2635103500.604668718429.39533128157518
2738403950.38816526117-110.388165261174
2836053796.47889389084-191.478893890836
2936553560.9197418980594.0802581019452
3035553642.93688340835-87.9368834083498
3131403427.62192195206-287.621921952064
3233803529.64399134066-149.643991340662
3332553495.24456743853-240.244567438525
3434603342.42734087377117.572659126227
3532453046.21763027726198.782369722737
3631202985.95932277583134.040677224174
3732653610.46101171234-345.461011712337
3832203383.37514235006-163.375142350064
3931403754.63497261101-614.634972611009
4030503378.88926118503-328.889261185029
4133003091.29103318322208.708966816778
4229503218.25625861591-268.256258615911
4326302918.94492363501-288.944923635013
4427953024.16371181926-229.163711819259
4528402952.65293608634-112.652936086344
4629452865.1911496477379.8088503522713
4727902554.75447353865235.245526461346
4826052508.6069568124796.3930431875287
4945903103.599906582521486.40009341748
5042303679.33969096235550.660309037647
5142454349.25019849284-104.250198492839
5243004203.610437824996.3895621750953
5344754115.9379968827359.062003117304
5439104295.34542982012-385.345429820124
5541003944.47149530233155.528504697666
5635004244.91039908093-744.910399080929
5743903951.95785339699438.042146603007
5835504109.60791937941-559.607919379415
5938653524.93076193642340.069238063576
6037153520.6411883031194.358811696896
6133104196.31107865605-886.311078656046
6239453713.05572576509231.94427423491
6350504226.24483091552823.755169084482
6443504490.27381797736-140.273817977358
6540604306.70793621328-246.707936213275
6643454201.92360203866143.076397961338
6743604095.9878085995264.012191400497
6849154419.05351761756495.946482382439
6946504698.88954680294-48.8895468029377
7048054617.1817210486187.818278951404
7147754382.63890208896392.361097911044
7242204397.14008429993-177.140084299933
7339754881.45741070395-906.457410703954
7438204420.00568060831-600.005680608307
7555154587.03106433789927.968935662112
7648954870.088301742724.9116982572996
7755354755.55673561367779.443264386333
7842305108.35953213373-878.359532133729
7936954560.85567728666-865.855677286659
8055904398.162205629631191.83779437037
8150004966.1876409205633.8123590794366
8248754926.97236177374-51.9723617737363
8343604593.5845332563-233.584533256296
8444054319.889375314685.1106246853969
8545004898.48424673833-398.484246738325
8640704666.65431328851-596.654313288513
8748004876.9210478038-76.9210478038012
8840804697.61604938619-617.616049386185
8948504323.87099987887526.129000121126
9041054521.01381625244-416.013816252436
9138054175.22137622433-370.221376224328
9250604284.66247545681775.337524543188
9340604639.62025335084-579.620253350837
9446004330.88552360567269.114476394328
9546354132.37738085057502.622619149425
9639004188.04356981432-288.043569814316
9741204590.89164776024-470.891647760239
9839604322.10661982045-362.106619820453
9944004648.73982349249-248.739823492489
10037004379.81604598682-679.816045986823
10139704010.25561921651-40.2556192165066
10245503934.95352892276615.046471077239
10351404039.480031405691100.51996859431
10450004820.81080076583179.189199234167
10536504879.07220462439-1229.07220462439
10643004310.68417039373-10.6841703937343
10736503996.69802097169-346.69802097169
10833553660.83173777982-305.831737779818
10940004050.93248913706-50.9324891370602
11034503968.03064571725-518.030645717251
11132954229.85284284885-934.85284284885
11233903650.31265366465-260.312653664648
11334153480.95069482349-65.950694823493
11434403412.3763091644827.6236908355218
11536803274.3324221611405.667577838895
11639003727.83467948941172.16532051059
11739653744.52870912149220.471290878506
11842953840.78933510215454.210664897849
11942103720.09479891432489.905201085679
12041003749.71915602482350.28084397518
12146904432.55249307891257.447506921093
12238604471.1895413105-611.189541310497
12342504681.03962973943-431.039629739425
12444954339.37461162628155.625388373721
12538004356.48454326542-556.484543265425
12638454076.82237339271-231.822373392705

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3090 & 2967.00988247863 & 122.990117521366 \tabularnewline
14 & 2995 & 2940.08515617328 & 54.9148438267166 \tabularnewline
15 & 3440 & 3410.38600613278 & 29.6139938672163 \tabularnewline
16 & 3335 & 3317.79235399416 & 17.2076460058415 \tabularnewline
17 & 3205 & 3172.71192253096 & 32.2880774690357 \tabularnewline
18 & 3285 & 3227.11627091701 & 57.8837290829897 \tabularnewline
19 & 2790 & 3084.96018562979 & -294.960185629788 \tabularnewline
20 & 3225 & 3174.33521474008 & 50.6647852599167 \tabularnewline
21 & 3360 & 3224.86833257982 & 135.13166742018 \tabularnewline
22 & 3275 & 3238.23172247605 & 36.7682775239537 \tabularnewline
23 & 3505 & 2891.04570519852 & 613.954294801477 \tabularnewline
24 & 3185 & 3023.99659937178 & 161.003400628216 \tabularnewline
25 & 3470 & 3670.11623631332 & -200.116236313323 \tabularnewline
26 & 3510 & 3500.60466871842 & 9.39533128157518 \tabularnewline
27 & 3840 & 3950.38816526117 & -110.388165261174 \tabularnewline
28 & 3605 & 3796.47889389084 & -191.478893890836 \tabularnewline
29 & 3655 & 3560.91974189805 & 94.0802581019452 \tabularnewline
30 & 3555 & 3642.93688340835 & -87.9368834083498 \tabularnewline
31 & 3140 & 3427.62192195206 & -287.621921952064 \tabularnewline
32 & 3380 & 3529.64399134066 & -149.643991340662 \tabularnewline
33 & 3255 & 3495.24456743853 & -240.244567438525 \tabularnewline
34 & 3460 & 3342.42734087377 & 117.572659126227 \tabularnewline
35 & 3245 & 3046.21763027726 & 198.782369722737 \tabularnewline
36 & 3120 & 2985.95932277583 & 134.040677224174 \tabularnewline
37 & 3265 & 3610.46101171234 & -345.461011712337 \tabularnewline
38 & 3220 & 3383.37514235006 & -163.375142350064 \tabularnewline
39 & 3140 & 3754.63497261101 & -614.634972611009 \tabularnewline
40 & 3050 & 3378.88926118503 & -328.889261185029 \tabularnewline
41 & 3300 & 3091.29103318322 & 208.708966816778 \tabularnewline
42 & 2950 & 3218.25625861591 & -268.256258615911 \tabularnewline
43 & 2630 & 2918.94492363501 & -288.944923635013 \tabularnewline
44 & 2795 & 3024.16371181926 & -229.163711819259 \tabularnewline
45 & 2840 & 2952.65293608634 & -112.652936086344 \tabularnewline
46 & 2945 & 2865.19114964773 & 79.8088503522713 \tabularnewline
47 & 2790 & 2554.75447353865 & 235.245526461346 \tabularnewline
48 & 2605 & 2508.60695681247 & 96.3930431875287 \tabularnewline
49 & 4590 & 3103.59990658252 & 1486.40009341748 \tabularnewline
50 & 4230 & 3679.33969096235 & 550.660309037647 \tabularnewline
51 & 4245 & 4349.25019849284 & -104.250198492839 \tabularnewline
52 & 4300 & 4203.6104378249 & 96.3895621750953 \tabularnewline
53 & 4475 & 4115.9379968827 & 359.062003117304 \tabularnewline
54 & 3910 & 4295.34542982012 & -385.345429820124 \tabularnewline
55 & 4100 & 3944.47149530233 & 155.528504697666 \tabularnewline
56 & 3500 & 4244.91039908093 & -744.910399080929 \tabularnewline
57 & 4390 & 3951.95785339699 & 438.042146603007 \tabularnewline
58 & 3550 & 4109.60791937941 & -559.607919379415 \tabularnewline
59 & 3865 & 3524.93076193642 & 340.069238063576 \tabularnewline
60 & 3715 & 3520.6411883031 & 194.358811696896 \tabularnewline
61 & 3310 & 4196.31107865605 & -886.311078656046 \tabularnewline
62 & 3945 & 3713.05572576509 & 231.94427423491 \tabularnewline
63 & 5050 & 4226.24483091552 & 823.755169084482 \tabularnewline
64 & 4350 & 4490.27381797736 & -140.273817977358 \tabularnewline
65 & 4060 & 4306.70793621328 & -246.707936213275 \tabularnewline
66 & 4345 & 4201.92360203866 & 143.076397961338 \tabularnewline
67 & 4360 & 4095.9878085995 & 264.012191400497 \tabularnewline
68 & 4915 & 4419.05351761756 & 495.946482382439 \tabularnewline
69 & 4650 & 4698.88954680294 & -48.8895468029377 \tabularnewline
70 & 4805 & 4617.1817210486 & 187.818278951404 \tabularnewline
71 & 4775 & 4382.63890208896 & 392.361097911044 \tabularnewline
72 & 4220 & 4397.14008429993 & -177.140084299933 \tabularnewline
73 & 3975 & 4881.45741070395 & -906.457410703954 \tabularnewline
74 & 3820 & 4420.00568060831 & -600.005680608307 \tabularnewline
75 & 5515 & 4587.03106433789 & 927.968935662112 \tabularnewline
76 & 4895 & 4870.0883017427 & 24.9116982572996 \tabularnewline
77 & 5535 & 4755.55673561367 & 779.443264386333 \tabularnewline
78 & 4230 & 5108.35953213373 & -878.359532133729 \tabularnewline
79 & 3695 & 4560.85567728666 & -865.855677286659 \tabularnewline
80 & 5590 & 4398.16220562963 & 1191.83779437037 \tabularnewline
81 & 5000 & 4966.18764092056 & 33.8123590794366 \tabularnewline
82 & 4875 & 4926.97236177374 & -51.9723617737363 \tabularnewline
83 & 4360 & 4593.5845332563 & -233.584533256296 \tabularnewline
84 & 4405 & 4319.8893753146 & 85.1106246853969 \tabularnewline
85 & 4500 & 4898.48424673833 & -398.484246738325 \tabularnewline
86 & 4070 & 4666.65431328851 & -596.654313288513 \tabularnewline
87 & 4800 & 4876.9210478038 & -76.9210478038012 \tabularnewline
88 & 4080 & 4697.61604938619 & -617.616049386185 \tabularnewline
89 & 4850 & 4323.87099987887 & 526.129000121126 \tabularnewline
90 & 4105 & 4521.01381625244 & -416.013816252436 \tabularnewline
91 & 3805 & 4175.22137622433 & -370.221376224328 \tabularnewline
92 & 5060 & 4284.66247545681 & 775.337524543188 \tabularnewline
93 & 4060 & 4639.62025335084 & -579.620253350837 \tabularnewline
94 & 4600 & 4330.88552360567 & 269.114476394328 \tabularnewline
95 & 4635 & 4132.37738085057 & 502.622619149425 \tabularnewline
96 & 3900 & 4188.04356981432 & -288.043569814316 \tabularnewline
97 & 4120 & 4590.89164776024 & -470.891647760239 \tabularnewline
98 & 3960 & 4322.10661982045 & -362.106619820453 \tabularnewline
99 & 4400 & 4648.73982349249 & -248.739823492489 \tabularnewline
100 & 3700 & 4379.81604598682 & -679.816045986823 \tabularnewline
101 & 3970 & 4010.25561921651 & -40.2556192165066 \tabularnewline
102 & 4550 & 3934.95352892276 & 615.046471077239 \tabularnewline
103 & 5140 & 4039.48003140569 & 1100.51996859431 \tabularnewline
104 & 5000 & 4820.81080076583 & 179.189199234167 \tabularnewline
105 & 3650 & 4879.07220462439 & -1229.07220462439 \tabularnewline
106 & 4300 & 4310.68417039373 & -10.6841703937343 \tabularnewline
107 & 3650 & 3996.69802097169 & -346.69802097169 \tabularnewline
108 & 3355 & 3660.83173777982 & -305.831737779818 \tabularnewline
109 & 4000 & 4050.93248913706 & -50.9324891370602 \tabularnewline
110 & 3450 & 3968.03064571725 & -518.030645717251 \tabularnewline
111 & 3295 & 4229.85284284885 & -934.85284284885 \tabularnewline
112 & 3390 & 3650.31265366465 & -260.312653664648 \tabularnewline
113 & 3415 & 3480.95069482349 & -65.950694823493 \tabularnewline
114 & 3440 & 3412.37630916448 & 27.6236908355218 \tabularnewline
115 & 3680 & 3274.3324221611 & 405.667577838895 \tabularnewline
116 & 3900 & 3727.83467948941 & 172.16532051059 \tabularnewline
117 & 3965 & 3744.52870912149 & 220.471290878506 \tabularnewline
118 & 4295 & 3840.78933510215 & 454.210664897849 \tabularnewline
119 & 4210 & 3720.09479891432 & 489.905201085679 \tabularnewline
120 & 4100 & 3749.71915602482 & 350.28084397518 \tabularnewline
121 & 4690 & 4432.55249307891 & 257.447506921093 \tabularnewline
122 & 3860 & 4471.1895413105 & -611.189541310497 \tabularnewline
123 & 4250 & 4681.03962973943 & -431.039629739425 \tabularnewline
124 & 4495 & 4339.37461162628 & 155.625388373721 \tabularnewline
125 & 3800 & 4356.48454326542 & -556.484543265425 \tabularnewline
126 & 3845 & 4076.82237339271 & -231.822373392705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301660&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]3090[/C][C]2967.00988247863[/C][C]122.990117521366[/C][/ROW]
[ROW][C]14[/C][C]2995[/C][C]2940.08515617328[/C][C]54.9148438267166[/C][/ROW]
[ROW][C]15[/C][C]3440[/C][C]3410.38600613278[/C][C]29.6139938672163[/C][/ROW]
[ROW][C]16[/C][C]3335[/C][C]3317.79235399416[/C][C]17.2076460058415[/C][/ROW]
[ROW][C]17[/C][C]3205[/C][C]3172.71192253096[/C][C]32.2880774690357[/C][/ROW]
[ROW][C]18[/C][C]3285[/C][C]3227.11627091701[/C][C]57.8837290829897[/C][/ROW]
[ROW][C]19[/C][C]2790[/C][C]3084.96018562979[/C][C]-294.960185629788[/C][/ROW]
[ROW][C]20[/C][C]3225[/C][C]3174.33521474008[/C][C]50.6647852599167[/C][/ROW]
[ROW][C]21[/C][C]3360[/C][C]3224.86833257982[/C][C]135.13166742018[/C][/ROW]
[ROW][C]22[/C][C]3275[/C][C]3238.23172247605[/C][C]36.7682775239537[/C][/ROW]
[ROW][C]23[/C][C]3505[/C][C]2891.04570519852[/C][C]613.954294801477[/C][/ROW]
[ROW][C]24[/C][C]3185[/C][C]3023.99659937178[/C][C]161.003400628216[/C][/ROW]
[ROW][C]25[/C][C]3470[/C][C]3670.11623631332[/C][C]-200.116236313323[/C][/ROW]
[ROW][C]26[/C][C]3510[/C][C]3500.60466871842[/C][C]9.39533128157518[/C][/ROW]
[ROW][C]27[/C][C]3840[/C][C]3950.38816526117[/C][C]-110.388165261174[/C][/ROW]
[ROW][C]28[/C][C]3605[/C][C]3796.47889389084[/C][C]-191.478893890836[/C][/ROW]
[ROW][C]29[/C][C]3655[/C][C]3560.91974189805[/C][C]94.0802581019452[/C][/ROW]
[ROW][C]30[/C][C]3555[/C][C]3642.93688340835[/C][C]-87.9368834083498[/C][/ROW]
[ROW][C]31[/C][C]3140[/C][C]3427.62192195206[/C][C]-287.621921952064[/C][/ROW]
[ROW][C]32[/C][C]3380[/C][C]3529.64399134066[/C][C]-149.643991340662[/C][/ROW]
[ROW][C]33[/C][C]3255[/C][C]3495.24456743853[/C][C]-240.244567438525[/C][/ROW]
[ROW][C]34[/C][C]3460[/C][C]3342.42734087377[/C][C]117.572659126227[/C][/ROW]
[ROW][C]35[/C][C]3245[/C][C]3046.21763027726[/C][C]198.782369722737[/C][/ROW]
[ROW][C]36[/C][C]3120[/C][C]2985.95932277583[/C][C]134.040677224174[/C][/ROW]
[ROW][C]37[/C][C]3265[/C][C]3610.46101171234[/C][C]-345.461011712337[/C][/ROW]
[ROW][C]38[/C][C]3220[/C][C]3383.37514235006[/C][C]-163.375142350064[/C][/ROW]
[ROW][C]39[/C][C]3140[/C][C]3754.63497261101[/C][C]-614.634972611009[/C][/ROW]
[ROW][C]40[/C][C]3050[/C][C]3378.88926118503[/C][C]-328.889261185029[/C][/ROW]
[ROW][C]41[/C][C]3300[/C][C]3091.29103318322[/C][C]208.708966816778[/C][/ROW]
[ROW][C]42[/C][C]2950[/C][C]3218.25625861591[/C][C]-268.256258615911[/C][/ROW]
[ROW][C]43[/C][C]2630[/C][C]2918.94492363501[/C][C]-288.944923635013[/C][/ROW]
[ROW][C]44[/C][C]2795[/C][C]3024.16371181926[/C][C]-229.163711819259[/C][/ROW]
[ROW][C]45[/C][C]2840[/C][C]2952.65293608634[/C][C]-112.652936086344[/C][/ROW]
[ROW][C]46[/C][C]2945[/C][C]2865.19114964773[/C][C]79.8088503522713[/C][/ROW]
[ROW][C]47[/C][C]2790[/C][C]2554.75447353865[/C][C]235.245526461346[/C][/ROW]
[ROW][C]48[/C][C]2605[/C][C]2508.60695681247[/C][C]96.3930431875287[/C][/ROW]
[ROW][C]49[/C][C]4590[/C][C]3103.59990658252[/C][C]1486.40009341748[/C][/ROW]
[ROW][C]50[/C][C]4230[/C][C]3679.33969096235[/C][C]550.660309037647[/C][/ROW]
[ROW][C]51[/C][C]4245[/C][C]4349.25019849284[/C][C]-104.250198492839[/C][/ROW]
[ROW][C]52[/C][C]4300[/C][C]4203.6104378249[/C][C]96.3895621750953[/C][/ROW]
[ROW][C]53[/C][C]4475[/C][C]4115.9379968827[/C][C]359.062003117304[/C][/ROW]
[ROW][C]54[/C][C]3910[/C][C]4295.34542982012[/C][C]-385.345429820124[/C][/ROW]
[ROW][C]55[/C][C]4100[/C][C]3944.47149530233[/C][C]155.528504697666[/C][/ROW]
[ROW][C]56[/C][C]3500[/C][C]4244.91039908093[/C][C]-744.910399080929[/C][/ROW]
[ROW][C]57[/C][C]4390[/C][C]3951.95785339699[/C][C]438.042146603007[/C][/ROW]
[ROW][C]58[/C][C]3550[/C][C]4109.60791937941[/C][C]-559.607919379415[/C][/ROW]
[ROW][C]59[/C][C]3865[/C][C]3524.93076193642[/C][C]340.069238063576[/C][/ROW]
[ROW][C]60[/C][C]3715[/C][C]3520.6411883031[/C][C]194.358811696896[/C][/ROW]
[ROW][C]61[/C][C]3310[/C][C]4196.31107865605[/C][C]-886.311078656046[/C][/ROW]
[ROW][C]62[/C][C]3945[/C][C]3713.05572576509[/C][C]231.94427423491[/C][/ROW]
[ROW][C]63[/C][C]5050[/C][C]4226.24483091552[/C][C]823.755169084482[/C][/ROW]
[ROW][C]64[/C][C]4350[/C][C]4490.27381797736[/C][C]-140.273817977358[/C][/ROW]
[ROW][C]65[/C][C]4060[/C][C]4306.70793621328[/C][C]-246.707936213275[/C][/ROW]
[ROW][C]66[/C][C]4345[/C][C]4201.92360203866[/C][C]143.076397961338[/C][/ROW]
[ROW][C]67[/C][C]4360[/C][C]4095.9878085995[/C][C]264.012191400497[/C][/ROW]
[ROW][C]68[/C][C]4915[/C][C]4419.05351761756[/C][C]495.946482382439[/C][/ROW]
[ROW][C]69[/C][C]4650[/C][C]4698.88954680294[/C][C]-48.8895468029377[/C][/ROW]
[ROW][C]70[/C][C]4805[/C][C]4617.1817210486[/C][C]187.818278951404[/C][/ROW]
[ROW][C]71[/C][C]4775[/C][C]4382.63890208896[/C][C]392.361097911044[/C][/ROW]
[ROW][C]72[/C][C]4220[/C][C]4397.14008429993[/C][C]-177.140084299933[/C][/ROW]
[ROW][C]73[/C][C]3975[/C][C]4881.45741070395[/C][C]-906.457410703954[/C][/ROW]
[ROW][C]74[/C][C]3820[/C][C]4420.00568060831[/C][C]-600.005680608307[/C][/ROW]
[ROW][C]75[/C][C]5515[/C][C]4587.03106433789[/C][C]927.968935662112[/C][/ROW]
[ROW][C]76[/C][C]4895[/C][C]4870.0883017427[/C][C]24.9116982572996[/C][/ROW]
[ROW][C]77[/C][C]5535[/C][C]4755.55673561367[/C][C]779.443264386333[/C][/ROW]
[ROW][C]78[/C][C]4230[/C][C]5108.35953213373[/C][C]-878.359532133729[/C][/ROW]
[ROW][C]79[/C][C]3695[/C][C]4560.85567728666[/C][C]-865.855677286659[/C][/ROW]
[ROW][C]80[/C][C]5590[/C][C]4398.16220562963[/C][C]1191.83779437037[/C][/ROW]
[ROW][C]81[/C][C]5000[/C][C]4966.18764092056[/C][C]33.8123590794366[/C][/ROW]
[ROW][C]82[/C][C]4875[/C][C]4926.97236177374[/C][C]-51.9723617737363[/C][/ROW]
[ROW][C]83[/C][C]4360[/C][C]4593.5845332563[/C][C]-233.584533256296[/C][/ROW]
[ROW][C]84[/C][C]4405[/C][C]4319.8893753146[/C][C]85.1106246853969[/C][/ROW]
[ROW][C]85[/C][C]4500[/C][C]4898.48424673833[/C][C]-398.484246738325[/C][/ROW]
[ROW][C]86[/C][C]4070[/C][C]4666.65431328851[/C][C]-596.654313288513[/C][/ROW]
[ROW][C]87[/C][C]4800[/C][C]4876.9210478038[/C][C]-76.9210478038012[/C][/ROW]
[ROW][C]88[/C][C]4080[/C][C]4697.61604938619[/C][C]-617.616049386185[/C][/ROW]
[ROW][C]89[/C][C]4850[/C][C]4323.87099987887[/C][C]526.129000121126[/C][/ROW]
[ROW][C]90[/C][C]4105[/C][C]4521.01381625244[/C][C]-416.013816252436[/C][/ROW]
[ROW][C]91[/C][C]3805[/C][C]4175.22137622433[/C][C]-370.221376224328[/C][/ROW]
[ROW][C]92[/C][C]5060[/C][C]4284.66247545681[/C][C]775.337524543188[/C][/ROW]
[ROW][C]93[/C][C]4060[/C][C]4639.62025335084[/C][C]-579.620253350837[/C][/ROW]
[ROW][C]94[/C][C]4600[/C][C]4330.88552360567[/C][C]269.114476394328[/C][/ROW]
[ROW][C]95[/C][C]4635[/C][C]4132.37738085057[/C][C]502.622619149425[/C][/ROW]
[ROW][C]96[/C][C]3900[/C][C]4188.04356981432[/C][C]-288.043569814316[/C][/ROW]
[ROW][C]97[/C][C]4120[/C][C]4590.89164776024[/C][C]-470.891647760239[/C][/ROW]
[ROW][C]98[/C][C]3960[/C][C]4322.10661982045[/C][C]-362.106619820453[/C][/ROW]
[ROW][C]99[/C][C]4400[/C][C]4648.73982349249[/C][C]-248.739823492489[/C][/ROW]
[ROW][C]100[/C][C]3700[/C][C]4379.81604598682[/C][C]-679.816045986823[/C][/ROW]
[ROW][C]101[/C][C]3970[/C][C]4010.25561921651[/C][C]-40.2556192165066[/C][/ROW]
[ROW][C]102[/C][C]4550[/C][C]3934.95352892276[/C][C]615.046471077239[/C][/ROW]
[ROW][C]103[/C][C]5140[/C][C]4039.48003140569[/C][C]1100.51996859431[/C][/ROW]
[ROW][C]104[/C][C]5000[/C][C]4820.81080076583[/C][C]179.189199234167[/C][/ROW]
[ROW][C]105[/C][C]3650[/C][C]4879.07220462439[/C][C]-1229.07220462439[/C][/ROW]
[ROW][C]106[/C][C]4300[/C][C]4310.68417039373[/C][C]-10.6841703937343[/C][/ROW]
[ROW][C]107[/C][C]3650[/C][C]3996.69802097169[/C][C]-346.69802097169[/C][/ROW]
[ROW][C]108[/C][C]3355[/C][C]3660.83173777982[/C][C]-305.831737779818[/C][/ROW]
[ROW][C]109[/C][C]4000[/C][C]4050.93248913706[/C][C]-50.9324891370602[/C][/ROW]
[ROW][C]110[/C][C]3450[/C][C]3968.03064571725[/C][C]-518.030645717251[/C][/ROW]
[ROW][C]111[/C][C]3295[/C][C]4229.85284284885[/C][C]-934.85284284885[/C][/ROW]
[ROW][C]112[/C][C]3390[/C][C]3650.31265366465[/C][C]-260.312653664648[/C][/ROW]
[ROW][C]113[/C][C]3415[/C][C]3480.95069482349[/C][C]-65.950694823493[/C][/ROW]
[ROW][C]114[/C][C]3440[/C][C]3412.37630916448[/C][C]27.6236908355218[/C][/ROW]
[ROW][C]115[/C][C]3680[/C][C]3274.3324221611[/C][C]405.667577838895[/C][/ROW]
[ROW][C]116[/C][C]3900[/C][C]3727.83467948941[/C][C]172.16532051059[/C][/ROW]
[ROW][C]117[/C][C]3965[/C][C]3744.52870912149[/C][C]220.471290878506[/C][/ROW]
[ROW][C]118[/C][C]4295[/C][C]3840.78933510215[/C][C]454.210664897849[/C][/ROW]
[ROW][C]119[/C][C]4210[/C][C]3720.09479891432[/C][C]489.905201085679[/C][/ROW]
[ROW][C]120[/C][C]4100[/C][C]3749.71915602482[/C][C]350.28084397518[/C][/ROW]
[ROW][C]121[/C][C]4690[/C][C]4432.55249307891[/C][C]257.447506921093[/C][/ROW]
[ROW][C]122[/C][C]3860[/C][C]4471.1895413105[/C][C]-611.189541310497[/C][/ROW]
[ROW][C]123[/C][C]4250[/C][C]4681.03962973943[/C][C]-431.039629739425[/C][/ROW]
[ROW][C]124[/C][C]4495[/C][C]4339.37461162628[/C][C]155.625388373721[/C][/ROW]
[ROW][C]125[/C][C]3800[/C][C]4356.48454326542[/C][C]-556.484543265425[/C][/ROW]
[ROW][C]126[/C][C]3845[/C][C]4076.82237339271[/C][C]-231.822373392705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301660&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
1330902967.00988247863122.990117521366
1429952940.0851561732854.9148438267166
1534403410.3860061327829.6139938672163
1633353317.7923539941617.2076460058415
1732053172.7119225309632.2880774690357
1832853227.1162709170157.8837290829897
1927903084.96018562979-294.960185629788
2032253174.3352147400850.6647852599167
2133603224.86833257982135.13166742018
2232753238.2317224760536.7682775239537
2335052891.04570519852613.954294801477
2431853023.99659937178161.003400628216
2534703670.11623631332-200.116236313323
2635103500.604668718429.39533128157518
2738403950.38816526117-110.388165261174
2836053796.47889389084-191.478893890836
2936553560.9197418980594.0802581019452
3035553642.93688340835-87.9368834083498
3131403427.62192195206-287.621921952064
3233803529.64399134066-149.643991340662
3332553495.24456743853-240.244567438525
3434603342.42734087377117.572659126227
3532453046.21763027726198.782369722737
3631202985.95932277583134.040677224174
3732653610.46101171234-345.461011712337
3832203383.37514235006-163.375142350064
3931403754.63497261101-614.634972611009
4030503378.88926118503-328.889261185029
4133003091.29103318322208.708966816778
4229503218.25625861591-268.256258615911
4326302918.94492363501-288.944923635013
4427953024.16371181926-229.163711819259
4528402952.65293608634-112.652936086344
4629452865.1911496477379.8088503522713
4727902554.75447353865235.245526461346
4826052508.6069568124796.3930431875287
4945903103.599906582521486.40009341748
5042303679.33969096235550.660309037647
5142454349.25019849284-104.250198492839
5243004203.610437824996.3895621750953
5344754115.9379968827359.062003117304
5439104295.34542982012-385.345429820124
5541003944.47149530233155.528504697666
5635004244.91039908093-744.910399080929
5743903951.95785339699438.042146603007
5835504109.60791937941-559.607919379415
5938653524.93076193642340.069238063576
6037153520.6411883031194.358811696896
6133104196.31107865605-886.311078656046
6239453713.05572576509231.94427423491
6350504226.24483091552823.755169084482
6443504490.27381797736-140.273817977358
6540604306.70793621328-246.707936213275
6643454201.92360203866143.076397961338
6743604095.9878085995264.012191400497
6849154419.05351761756495.946482382439
6946504698.88954680294-48.8895468029377
7048054617.1817210486187.818278951404
7147754382.63890208896392.361097911044
7242204397.14008429993-177.140084299933
7339754881.45741070395-906.457410703954
7438204420.00568060831-600.005680608307
7555154587.03106433789927.968935662112
7648954870.088301742724.9116982572996
7755354755.55673561367779.443264386333
7842305108.35953213373-878.359532133729
7936954560.85567728666-865.855677286659
8055904398.162205629631191.83779437037
8150004966.1876409205633.8123590794366
8248754926.97236177374-51.9723617737363
8343604593.5845332563-233.584533256296
8444054319.889375314685.1106246853969
8545004898.48424673833-398.484246738325
8640704666.65431328851-596.654313288513
8748004876.9210478038-76.9210478038012
8840804697.61604938619-617.616049386185
8948504323.87099987887526.129000121126
9041054521.01381625244-416.013816252436
9138054175.22137622433-370.221376224328
9250604284.66247545681775.337524543188
9340604639.62025335084-579.620253350837
9446004330.88552360567269.114476394328
9546354132.37738085057502.622619149425
9639004188.04356981432-288.043569814316
9741204590.89164776024-470.891647760239
9839604322.10661982045-362.106619820453
9944004648.73982349249-248.739823492489
10037004379.81604598682-679.816045986823
10139704010.25561921651-40.2556192165066
10245503934.95352892276615.046471077239
10351404039.480031405691100.51996859431
10450004820.81080076583179.189199234167
10536504879.07220462439-1229.07220462439
10643004310.68417039373-10.6841703937343
10736503996.69802097169-346.69802097169
10833553660.83173777982-305.831737779818
10940004050.93248913706-50.9324891370602
11034503968.03064571725-518.030645717251
11132954229.85284284885-934.85284284885
11233903650.31265366465-260.312653664648
11334153480.95069482349-65.950694823493
11434403412.3763091644827.6236908355218
11536803274.3324221611405.667577838895
11639003727.83467948941172.16532051059
11739653744.52870912149220.471290878506
11842953840.78933510215454.210664897849
11942103720.09479891432489.905201085679
12041003749.71915602482350.28084397518
12146904432.55249307891257.447506921093
12238604471.1895413105-611.189541310497
12342504681.03962973943-431.039629739425
12444954339.37461162628155.625388373721
12538004356.48454326542-556.484543265425
12638454076.82237339271-231.822373392705







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1273836.117076825782938.230103084534734.00405056703
1284106.550357585533127.19722504665085.90349012446
1294049.580610853332995.036112591925104.12510911473
1304056.208919098042931.488669696895180.92916849918
1313738.664059372372547.896584164654929.43153458009
1323551.097729820412297.758701220354804.43675842048
1334078.831683634062765.89975043585391.76361683233
1343981.587906083322611.652943462355351.52286870429
1354462.5608694393037.901842720375887.21989615764
1364324.672399933272847.315001396795802.02979846976
1374254.529145764482726.289497145835782.76879438314
1384226.11531632852648.633790538215803.59684211878

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 3836.11707682578 & 2938.23010308453 & 4734.00405056703 \tabularnewline
128 & 4106.55035758553 & 3127.1972250466 & 5085.90349012446 \tabularnewline
129 & 4049.58061085333 & 2995.03611259192 & 5104.12510911473 \tabularnewline
130 & 4056.20891909804 & 2931.48866969689 & 5180.92916849918 \tabularnewline
131 & 3738.66405937237 & 2547.89658416465 & 4929.43153458009 \tabularnewline
132 & 3551.09772982041 & 2297.75870122035 & 4804.43675842048 \tabularnewline
133 & 4078.83168363406 & 2765.8997504358 & 5391.76361683233 \tabularnewline
134 & 3981.58790608332 & 2611.65294346235 & 5351.52286870429 \tabularnewline
135 & 4462.560869439 & 3037.90184272037 & 5887.21989615764 \tabularnewline
136 & 4324.67239993327 & 2847.31500139679 & 5802.02979846976 \tabularnewline
137 & 4254.52914576448 & 2726.28949714583 & 5782.76879438314 \tabularnewline
138 & 4226.1153163285 & 2648.63379053821 & 5803.59684211878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301660&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]3836.11707682578[/C][C]2938.23010308453[/C][C]4734.00405056703[/C][/ROW]
[ROW][C]128[/C][C]4106.55035758553[/C][C]3127.1972250466[/C][C]5085.90349012446[/C][/ROW]
[ROW][C]129[/C][C]4049.58061085333[/C][C]2995.03611259192[/C][C]5104.12510911473[/C][/ROW]
[ROW][C]130[/C][C]4056.20891909804[/C][C]2931.48866969689[/C][C]5180.92916849918[/C][/ROW]
[ROW][C]131[/C][C]3738.66405937237[/C][C]2547.89658416465[/C][C]4929.43153458009[/C][/ROW]
[ROW][C]132[/C][C]3551.09772982041[/C][C]2297.75870122035[/C][C]4804.43675842048[/C][/ROW]
[ROW][C]133[/C][C]4078.83168363406[/C][C]2765.8997504358[/C][C]5391.76361683233[/C][/ROW]
[ROW][C]134[/C][C]3981.58790608332[/C][C]2611.65294346235[/C][C]5351.52286870429[/C][/ROW]
[ROW][C]135[/C][C]4462.560869439[/C][C]3037.90184272037[/C][C]5887.21989615764[/C][/ROW]
[ROW][C]136[/C][C]4324.67239993327[/C][C]2847.31500139679[/C][C]5802.02979846976[/C][/ROW]
[ROW][C]137[/C][C]4254.52914576448[/C][C]2726.28949714583[/C][C]5782.76879438314[/C][/ROW]
[ROW][C]138[/C][C]4226.1153163285[/C][C]2648.63379053821[/C][C]5803.59684211878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301660&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
1273836.117076825782938.230103084534734.00405056703
1284106.550357585533127.19722504665085.90349012446
1294049.580610853332995.036112591925104.12510911473
1304056.208919098042931.488669696895180.92916849918
1313738.664059372372547.896584164654929.43153458009
1323551.097729820412297.758701220354804.43675842048
1334078.831683634062765.89975043585391.76361683233
1343981.587906083322611.652943462355351.52286870429
1354462.5608694393037.901842720375887.21989615764
1364324.672399933272847.315001396795802.02979846976
1374254.529145764482726.289497145835782.76879438314
1384226.11531632852648.633790538215803.59684211878



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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')