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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Dec 2016 13:31:12 +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/18/t1482064311e0vh0vfjzjtpgff.htm/, Retrieved Thu, 20 Feb 2025 19:11:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301029, Retrieved Thu, 20 Feb 2025 19:11:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-18 12:31:12] [404ac5ee4f7301873f6a96ef36861981] [Current]
- R       [Exponential Smoothing] [] [2016-12-18 12:33:21] [683f400e1b95307fc738e729f07c4fce]
- RM      [ARIMA Backward Selection] [] [2016-12-18 12:34:55] [683f400e1b95307fc738e729f07c4fce]
- RM      [ARIMA Forecasting] [] [2016-12-18 12:36:26] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 12:38:54] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 12:40:05] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-18 12:41:27] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 12:42:26] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Spectral Analysis] [] [2016-12-18 12:44:19] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 12:56:40] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 12:57:11] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 12:57:56] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-18 13:05:35] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Spectral Analysis] [] [2016-12-18 13:06:51] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Spectral Analysis] [] [2016-12-18 13:08:39] [683f400e1b95307fc738e729f07c4fce]
-    D    [Exponential Smoothing] [] [2016-12-18 13:12:12] [683f400e1b95307fc738e729f07c4fce]
- RM D    [ARIMA Backward Selection] [] [2016-12-18 13:13:41] [683f400e1b95307fc738e729f07c4fce]
- RM D    [ARIMA Forecasting] [] [2016-12-18 13:15:15] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 13:16:55] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 13:20:15] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-18 13:25:37] [683f400e1b95307fc738e729f07c4fce]
- R P       [(Partial) Autocorrelation Function] [] [2016-12-20 22:53:44] [683f400e1b95307fc738e729f07c4fce]
-   P       [(Partial) Autocorrelation Function] [] [2016-12-20 22:57:51] [683f400e1b95307fc738e729f07c4fce]
- RMP       [Spectral Analysis] [] [2016-12-20 23:03:30] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Spectral Analysis] [] [2016-12-18 13:27:55] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-19 18:56:24] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-19 19:02:26] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-19 19:03:22] [683f400e1b95307fc738e729f07c4fce]
- R P       [Spectral Analysis] [] [2016-12-19 19:05:42] [683f400e1b95307fc738e729f07c4fce]
- R  D    [Exponential Smoothing] [] [2016-12-18 13:29:07] [683f400e1b95307fc738e729f07c4fce]
- R P       [Exponential Smoothing] [] [2016-12-20 23:20:29] [683f400e1b95307fc738e729f07c4fce]
- RMP       [ARIMA Backward Selection] [] [2016-12-20 23:27:16] [683f400e1b95307fc738e729f07c4fce]
- RMP       [ARIMA Forecasting] [] [2016-12-20 23:32:48] [683f400e1b95307fc738e729f07c4fce]
- RM D    [ARIMA Backward Selection] [] [2016-12-18 13:30:22] [683f400e1b95307fc738e729f07c4fce]
- R P       [ARIMA Backward Selection] [] [2016-12-19 19:38:16] [683f400e1b95307fc738e729f07c4fce]
- RM D    [ARIMA Forecasting] [] [2016-12-18 13:31:53] [683f400e1b95307fc738e729f07c4fce]
- R P       [ARIMA Forecasting] [] [2016-12-19 19:45:05] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 13:33:45] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 13:34:31] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-18 13:36:05] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Spectral Analysis] [] [2016-12-18 13:38:15] [683f400e1b95307fc738e729f07c4fce]
- R  D    [Exponential Smoothing] [] [2016-12-18 13:40:39] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Univariate Data Series] [] [2016-12-18 13:43:34] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-18 13:44:30] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 13:45:26] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Spectral Analysis] [] [2016-12-18 13:46:28] [683f400e1b95307fc738e729f07c4fce]
-    D    [Exponential Smoothing] [] [2016-12-18 13:47:10] [683f400e1b95307fc738e729f07c4fce]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9290
6160
8320
8310
6750
8710
6300
5710
5740
6710
7310
7240
8650
8330
7810
8260
6680
5580
6340
4490
5000
7030
6100
9740
7940
7740
7820
7820
5380
7070
6970
4080
4930
4820
6220
6360
7630
5130
6960
5350
6290
4630
5130
3620
3980
3120
4310
4250
5730
3630
5680

Tables (Output of Computation)





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=301029&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=301029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301029&T=0

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


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

Summary of computational transaction
Raw 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
alpha0.693931469394444
beta0.433586081757043
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.693931469394444 \tabularnewline
beta & 0.433586081757043 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301029&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]0.693931469394444[/C][/ROW]
[ROW][C]beta[/C][C]0.433586081757043[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301029&T=1

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


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.693931469394444
beta0.433586081757043
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3832030305290
483105162.54752498843147.4524750116
567506755.31633536618-5.31633536618301
687106158.68007868632551.3199213137
763008103.81283134949-1803.81283134949
857106484.05246428261-774.052464282609
957405345.97906969559394.02093030441
1067105137.021196232641572.97880376736
1173106219.455623946161090.54437605384
1272407295.23555092395-55.2355509239524
1386507559.303510763381090.69648923662
1483308946.73747329799-616.737473297992
1578108963.76590654603-1153.76590654603
1682608260.98944686094-0.989446860943644
1766808357.86314591984-1677.86314591984
1855806786.26758451596-1206.26758451596
1963405178.986407080111161.01359291989
2044905563.76077553772-1073.76077553772
2150004074.68278554239925.317214457612
2270304251.236465566852778.76353443315
2361006550.02654186616-450.026541866165
2497406472.854028191843267.14597180816
2579409958.16019940935-2018.16019940935
2677409168.60401626388-1428.60401626388
2778208358.32243545073-538.322435450733
2878208003.86532969085-183.86532969085
2953807840.05594270442-2460.05594270442
3070705356.547021037471713.45297896253
3169706284.7093427303685.290657269702
3240806705.58705980478-2625.58705980478
3349304038.95845829225891.041541707752
3448204080.72482146942739.275178530584
3562204239.608125512821980.39187448718
3663605855.59974199454504.400258005462
3776306599.117785994991030.88221400501
3851308018.14906465047-2888.14906465047
3969605848.6577296151111.342270385
4053506788.91887431135-1438.91887431135
4162905526.53304494947763.466955050531
4246306022.16324477703-1392.16324477703
4351304603.06109030045526.938909699554
4436204674.22918014323-1054.22918014323
4539803330.97952427227649.020475727727
4631203364.94505397036-244.94505397036
4743102704.860940593451605.13905940655
4842503811.56109262475438.438907375247
4957304240.56836558651489.4316344135
5036305847.03130662597-2217.03130662597
5156804214.404750760911465.59524923909

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8320 & 3030 & 5290 \tabularnewline
4 & 8310 & 5162.5475249884 & 3147.4524750116 \tabularnewline
5 & 6750 & 6755.31633536618 & -5.31633536618301 \tabularnewline
6 & 8710 & 6158.6800786863 & 2551.3199213137 \tabularnewline
7 & 6300 & 8103.81283134949 & -1803.81283134949 \tabularnewline
8 & 5710 & 6484.05246428261 & -774.052464282609 \tabularnewline
9 & 5740 & 5345.97906969559 & 394.02093030441 \tabularnewline
10 & 6710 & 5137.02119623264 & 1572.97880376736 \tabularnewline
11 & 7310 & 6219.45562394616 & 1090.54437605384 \tabularnewline
12 & 7240 & 7295.23555092395 & -55.2355509239524 \tabularnewline
13 & 8650 & 7559.30351076338 & 1090.69648923662 \tabularnewline
14 & 8330 & 8946.73747329799 & -616.737473297992 \tabularnewline
15 & 7810 & 8963.76590654603 & -1153.76590654603 \tabularnewline
16 & 8260 & 8260.98944686094 & -0.989446860943644 \tabularnewline
17 & 6680 & 8357.86314591984 & -1677.86314591984 \tabularnewline
18 & 5580 & 6786.26758451596 & -1206.26758451596 \tabularnewline
19 & 6340 & 5178.98640708011 & 1161.01359291989 \tabularnewline
20 & 4490 & 5563.76077553772 & -1073.76077553772 \tabularnewline
21 & 5000 & 4074.68278554239 & 925.317214457612 \tabularnewline
22 & 7030 & 4251.23646556685 & 2778.76353443315 \tabularnewline
23 & 6100 & 6550.02654186616 & -450.026541866165 \tabularnewline
24 & 9740 & 6472.85402819184 & 3267.14597180816 \tabularnewline
25 & 7940 & 9958.16019940935 & -2018.16019940935 \tabularnewline
26 & 7740 & 9168.60401626388 & -1428.60401626388 \tabularnewline
27 & 7820 & 8358.32243545073 & -538.322435450733 \tabularnewline
28 & 7820 & 8003.86532969085 & -183.86532969085 \tabularnewline
29 & 5380 & 7840.05594270442 & -2460.05594270442 \tabularnewline
30 & 7070 & 5356.54702103747 & 1713.45297896253 \tabularnewline
31 & 6970 & 6284.7093427303 & 685.290657269702 \tabularnewline
32 & 4080 & 6705.58705980478 & -2625.58705980478 \tabularnewline
33 & 4930 & 4038.95845829225 & 891.041541707752 \tabularnewline
34 & 4820 & 4080.72482146942 & 739.275178530584 \tabularnewline
35 & 6220 & 4239.60812551282 & 1980.39187448718 \tabularnewline
36 & 6360 & 5855.59974199454 & 504.400258005462 \tabularnewline
37 & 7630 & 6599.11778599499 & 1030.88221400501 \tabularnewline
38 & 5130 & 8018.14906465047 & -2888.14906465047 \tabularnewline
39 & 6960 & 5848.657729615 & 1111.342270385 \tabularnewline
40 & 5350 & 6788.91887431135 & -1438.91887431135 \tabularnewline
41 & 6290 & 5526.53304494947 & 763.466955050531 \tabularnewline
42 & 4630 & 6022.16324477703 & -1392.16324477703 \tabularnewline
43 & 5130 & 4603.06109030045 & 526.938909699554 \tabularnewline
44 & 3620 & 4674.22918014323 & -1054.22918014323 \tabularnewline
45 & 3980 & 3330.97952427227 & 649.020475727727 \tabularnewline
46 & 3120 & 3364.94505397036 & -244.94505397036 \tabularnewline
47 & 4310 & 2704.86094059345 & 1605.13905940655 \tabularnewline
48 & 4250 & 3811.56109262475 & 438.438907375247 \tabularnewline
49 & 5730 & 4240.5683655865 & 1489.4316344135 \tabularnewline
50 & 3630 & 5847.03130662597 & -2217.03130662597 \tabularnewline
51 & 5680 & 4214.40475076091 & 1465.59524923909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301029&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]8320[/C][C]3030[/C][C]5290[/C][/ROW]
[ROW][C]4[/C][C]8310[/C][C]5162.5475249884[/C][C]3147.4524750116[/C][/ROW]
[ROW][C]5[/C][C]6750[/C][C]6755.31633536618[/C][C]-5.31633536618301[/C][/ROW]
[ROW][C]6[/C][C]8710[/C][C]6158.6800786863[/C][C]2551.3199213137[/C][/ROW]
[ROW][C]7[/C][C]6300[/C][C]8103.81283134949[/C][C]-1803.81283134949[/C][/ROW]
[ROW][C]8[/C][C]5710[/C][C]6484.05246428261[/C][C]-774.052464282609[/C][/ROW]
[ROW][C]9[/C][C]5740[/C][C]5345.97906969559[/C][C]394.02093030441[/C][/ROW]
[ROW][C]10[/C][C]6710[/C][C]5137.02119623264[/C][C]1572.97880376736[/C][/ROW]
[ROW][C]11[/C][C]7310[/C][C]6219.45562394616[/C][C]1090.54437605384[/C][/ROW]
[ROW][C]12[/C][C]7240[/C][C]7295.23555092395[/C][C]-55.2355509239524[/C][/ROW]
[ROW][C]13[/C][C]8650[/C][C]7559.30351076338[/C][C]1090.69648923662[/C][/ROW]
[ROW][C]14[/C][C]8330[/C][C]8946.73747329799[/C][C]-616.737473297992[/C][/ROW]
[ROW][C]15[/C][C]7810[/C][C]8963.76590654603[/C][C]-1153.76590654603[/C][/ROW]
[ROW][C]16[/C][C]8260[/C][C]8260.98944686094[/C][C]-0.989446860943644[/C][/ROW]
[ROW][C]17[/C][C]6680[/C][C]8357.86314591984[/C][C]-1677.86314591984[/C][/ROW]
[ROW][C]18[/C][C]5580[/C][C]6786.26758451596[/C][C]-1206.26758451596[/C][/ROW]
[ROW][C]19[/C][C]6340[/C][C]5178.98640708011[/C][C]1161.01359291989[/C][/ROW]
[ROW][C]20[/C][C]4490[/C][C]5563.76077553772[/C][C]-1073.76077553772[/C][/ROW]
[ROW][C]21[/C][C]5000[/C][C]4074.68278554239[/C][C]925.317214457612[/C][/ROW]
[ROW][C]22[/C][C]7030[/C][C]4251.23646556685[/C][C]2778.76353443315[/C][/ROW]
[ROW][C]23[/C][C]6100[/C][C]6550.02654186616[/C][C]-450.026541866165[/C][/ROW]
[ROW][C]24[/C][C]9740[/C][C]6472.85402819184[/C][C]3267.14597180816[/C][/ROW]
[ROW][C]25[/C][C]7940[/C][C]9958.16019940935[/C][C]-2018.16019940935[/C][/ROW]
[ROW][C]26[/C][C]7740[/C][C]9168.60401626388[/C][C]-1428.60401626388[/C][/ROW]
[ROW][C]27[/C][C]7820[/C][C]8358.32243545073[/C][C]-538.322435450733[/C][/ROW]
[ROW][C]28[/C][C]7820[/C][C]8003.86532969085[/C][C]-183.86532969085[/C][/ROW]
[ROW][C]29[/C][C]5380[/C][C]7840.05594270442[/C][C]-2460.05594270442[/C][/ROW]
[ROW][C]30[/C][C]7070[/C][C]5356.54702103747[/C][C]1713.45297896253[/C][/ROW]
[ROW][C]31[/C][C]6970[/C][C]6284.7093427303[/C][C]685.290657269702[/C][/ROW]
[ROW][C]32[/C][C]4080[/C][C]6705.58705980478[/C][C]-2625.58705980478[/C][/ROW]
[ROW][C]33[/C][C]4930[/C][C]4038.95845829225[/C][C]891.041541707752[/C][/ROW]
[ROW][C]34[/C][C]4820[/C][C]4080.72482146942[/C][C]739.275178530584[/C][/ROW]
[ROW][C]35[/C][C]6220[/C][C]4239.60812551282[/C][C]1980.39187448718[/C][/ROW]
[ROW][C]36[/C][C]6360[/C][C]5855.59974199454[/C][C]504.400258005462[/C][/ROW]
[ROW][C]37[/C][C]7630[/C][C]6599.11778599499[/C][C]1030.88221400501[/C][/ROW]
[ROW][C]38[/C][C]5130[/C][C]8018.14906465047[/C][C]-2888.14906465047[/C][/ROW]
[ROW][C]39[/C][C]6960[/C][C]5848.657729615[/C][C]1111.342270385[/C][/ROW]
[ROW][C]40[/C][C]5350[/C][C]6788.91887431135[/C][C]-1438.91887431135[/C][/ROW]
[ROW][C]41[/C][C]6290[/C][C]5526.53304494947[/C][C]763.466955050531[/C][/ROW]
[ROW][C]42[/C][C]4630[/C][C]6022.16324477703[/C][C]-1392.16324477703[/C][/ROW]
[ROW][C]43[/C][C]5130[/C][C]4603.06109030045[/C][C]526.938909699554[/C][/ROW]
[ROW][C]44[/C][C]3620[/C][C]4674.22918014323[/C][C]-1054.22918014323[/C][/ROW]
[ROW][C]45[/C][C]3980[/C][C]3330.97952427227[/C][C]649.020475727727[/C][/ROW]
[ROW][C]46[/C][C]3120[/C][C]3364.94505397036[/C][C]-244.94505397036[/C][/ROW]
[ROW][C]47[/C][C]4310[/C][C]2704.86094059345[/C][C]1605.13905940655[/C][/ROW]
[ROW][C]48[/C][C]4250[/C][C]3811.56109262475[/C][C]438.438907375247[/C][/ROW]
[ROW][C]49[/C][C]5730[/C][C]4240.5683655865[/C][C]1489.4316344135[/C][/ROW]
[ROW][C]50[/C][C]3630[/C][C]5847.03130662597[/C][C]-2217.03130662597[/C][/ROW]
[ROW][C]51[/C][C]5680[/C][C]4214.40475076091[/C][C]1465.59524923909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301029&T=2

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


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3832030305290
483105162.54752498843147.4524750116
567506755.31633536618-5.31633536618301
687106158.68007868632551.3199213137
763008103.81283134949-1803.81283134949
857106484.05246428261-774.052464282609
957405345.97906969559394.02093030441
1067105137.021196232641572.97880376736
1173106219.455623946161090.54437605384
1272407295.23555092395-55.2355509239524
1386507559.303510763381090.69648923662
1483308946.73747329799-616.737473297992
1578108963.76590654603-1153.76590654603
1682608260.98944686094-0.989446860943644
1766808357.86314591984-1677.86314591984
1855806786.26758451596-1206.26758451596
1963405178.986407080111161.01359291989
2044905563.76077553772-1073.76077553772
2150004074.68278554239925.317214457612
2270304251.236465566852778.76353443315
2361006550.02654186616-450.026541866165
2497406472.854028191843267.14597180816
2579409958.16019940935-2018.16019940935
2677409168.60401626388-1428.60401626388
2778208358.32243545073-538.322435450733
2878208003.86532969085-183.86532969085
2953807840.05594270442-2460.05594270442
3070705356.547021037471713.45297896253
3169706284.7093427303685.290657269702
3240806705.58705980478-2625.58705980478
3349304038.95845829225891.041541707752
3448204080.72482146942739.275178530584
3562204239.608125512821980.39187448718
3663605855.59974199454504.400258005462
3776306599.117785994991030.88221400501
3851308018.14906465047-2888.14906465047
3969605848.6577296151111.342270385
4053506788.91887431135-1438.91887431135
4162905526.53304494947763.466955050531
4246306022.16324477703-1392.16324477703
4351304603.06109030045526.938909699554
4436204674.22918014323-1054.22918014323
4539803330.97952427227649.020475727727
4631203364.94505397036-244.94505397036
4743102704.860940593451605.13905940655
4842503811.56109262475438.438907375247
4957304240.56836558651489.4316344135
5036305847.03130662597-2217.03130662597
5156804214.404750760911465.59524923909






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
525578.235524345242279.935982107828876.53506658266
535925.043633087571272.6311644926410577.4561016825
546271.85174182991-45.454708774721412589.1581924345
556618.65985057224-1605.6157640150214842.9354651595
566965.46795931457-3369.2144274402517300.1503460694
577312.2760680569-5312.2589815082619936.8111176221
587659.08417679924-7418.3180334000622736.4863869985
598005.89228554157-9675.2515994564325687.0361705396
608352.7003942839-12073.580048199228778.980836767
618699.50850302623-14605.597821182132004.6148272345
629046.31661176857-17264.853369072135357.4865926092
639393.1247205109-20045.823292702938832.0727337247

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
52 & 5578.23552434524 & 2279.93598210782 & 8876.53506658266 \tabularnewline
53 & 5925.04363308757 & 1272.63116449264 & 10577.4561016825 \tabularnewline
54 & 6271.85174182991 & -45.4547087747214 & 12589.1581924345 \tabularnewline
55 & 6618.65985057224 & -1605.61576401502 & 14842.9354651595 \tabularnewline
56 & 6965.46795931457 & -3369.21442744025 & 17300.1503460694 \tabularnewline
57 & 7312.2760680569 & -5312.25898150826 & 19936.8111176221 \tabularnewline
58 & 7659.08417679924 & -7418.31803340006 & 22736.4863869985 \tabularnewline
59 & 8005.89228554157 & -9675.25159945643 & 25687.0361705396 \tabularnewline
60 & 8352.7003942839 & -12073.5800481992 & 28778.980836767 \tabularnewline
61 & 8699.50850302623 & -14605.5978211821 & 32004.6148272345 \tabularnewline
62 & 9046.31661176857 & -17264.8533690721 & 35357.4865926092 \tabularnewline
63 & 9393.1247205109 & -20045.8232927029 & 38832.0727337247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301029&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]52[/C][C]5578.23552434524[/C][C]2279.93598210782[/C][C]8876.53506658266[/C][/ROW]
[ROW][C]53[/C][C]5925.04363308757[/C][C]1272.63116449264[/C][C]10577.4561016825[/C][/ROW]
[ROW][C]54[/C][C]6271.85174182991[/C][C]-45.4547087747214[/C][C]12589.1581924345[/C][/ROW]
[ROW][C]55[/C][C]6618.65985057224[/C][C]-1605.61576401502[/C][C]14842.9354651595[/C][/ROW]
[ROW][C]56[/C][C]6965.46795931457[/C][C]-3369.21442744025[/C][C]17300.1503460694[/C][/ROW]
[ROW][C]57[/C][C]7312.2760680569[/C][C]-5312.25898150826[/C][C]19936.8111176221[/C][/ROW]
[ROW][C]58[/C][C]7659.08417679924[/C][C]-7418.31803340006[/C][C]22736.4863869985[/C][/ROW]
[ROW][C]59[/C][C]8005.89228554157[/C][C]-9675.25159945643[/C][C]25687.0361705396[/C][/ROW]
[ROW][C]60[/C][C]8352.7003942839[/C][C]-12073.5800481992[/C][C]28778.980836767[/C][/ROW]
[ROW][C]61[/C][C]8699.50850302623[/C][C]-14605.5978211821[/C][C]32004.6148272345[/C][/ROW]
[ROW][C]62[/C][C]9046.31661176857[/C][C]-17264.8533690721[/C][C]35357.4865926092[/C][/ROW]
[ROW][C]63[/C][C]9393.1247205109[/C][C]-20045.8232927029[/C][C]38832.0727337247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301029&T=3

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


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
525578.235524345242279.935982107828876.53506658266
535925.043633087571272.6311644926410577.4561016825
546271.85174182991-45.454708774721412589.1581924345
556618.65985057224-1605.6157640150214842.9354651595
566965.46795931457-3369.2144274402517300.1503460694
577312.2760680569-5312.2589815082619936.8111176221
587659.08417679924-7418.3180334000622736.4863869985
598005.89228554157-9675.2515994564325687.0361705396
608352.7003942839-12073.580048199228778.980836767
618699.50850302623-14605.597821182132004.6148272345
629046.31661176857-17264.853369072135357.4865926092
639393.1247205109-20045.823292702938832.0727337247


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')