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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, 21 Dec 2016 15:18:03 +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/21/t14823304169i39l03qo6l0yiq.htm/, Retrieved Mon, 06 May 2024 16:11:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302319, Retrieved Mon, 06 May 2024 16:11:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-21 14:18:03] [02b5df5aa2382aa6805f6181aa5e25f1] [Current]
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Dataseries X:
3800
4150
4200
3650
3750
4250
2700
3950
4400
4500
4500
4050
4250
4450
4500
3950
4300
4500
2800
4300
4750
4900
5000
4500
4500
4800
4450
4550
4150
4750
2950
4650
4950
5050
5300
4650
4600
4950
4950
4400
4550
4900
3100
4800
5200
5350
5450
4700
4800
5200
5200
4550
4800
5200
3350
5050
5550
5650
5700
5100
5200
5500
5200
5700
5200
5800
3700
5450
5950
6000
6200
5500
5550
6100
6150
5500
5700
6000
3750
5900
6350
6350
6500
5750
5850
6300
6550
5450
5750
6600
3850
6000
6750
6750
6850
6100
6400
6750
5800
6750
5850
6800
3800
6400
6800
7000
7300
6300
6500
6950
7100
6100
6550
6800




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=302319&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=302319&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302319&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0943206896457194
beta0
gamma0.171809937649672

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0943206896457194 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.171809937649672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302319&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]0.0943206896457194[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.171809937649672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302319&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302319&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
alpha0.0943206896457194
beta0
gamma0.171809937649672







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1342504079.33459790119170.665402098808
1444504298.50288434988151.49711565012
1545004360.77081938493139.22918061507
1639503836.94055717216113.059442827838
1743004179.80375623677120.196243763226
1845004374.89409772791125.105902272092
1928002861.30565408386-61.3056540838575
2043004172.4106044225127.589395577498
2147504662.59648858987.4035114110038
2249004778.40180425628121.598195743722
2350004779.09733699629220.902663003705
2445004312.40721389658187.592786103422
2545004585.92341196359-85.9234119635912
2648004796.665479215423.33452078457958
2744504844.7070430679-394.707043067895
2845504213.2580883496336.741911650397
2941504608.27656914426-458.276569144258
3047504762.63152567145-12.631525671447
3129503080.18474803489-130.184748034892
3246504516.97356895317133.026431046826
3349505035.56192546808-85.5619254680787
3450505146.34258435391-96.3425843539108
3553005140.0076343713159.992365628702
3646504627.7581880539522.2418119460472
3746004854.56542518662-254.565425186617
3849505075.12794824886-125.127948248864
3949505046.19683550638-96.1968355063846
4044004525.23161180745-125.231611807448
4145504762.9139171842-212.913917184195
4249005022.942894549-122.942894549004
4331003220.79267857353-120.792678573533
4448004776.9892342424723.0107657575318
4552005273.39988006505-73.3998800650461
4653505387.97719037052-37.9771903705205
4754505427.5688363107822.4311636892226
4847004853.14064439761-153.140644397613
4948005026.92959498145-226.929594981446
5052005280.72445587842-80.7244558784214
5152005258.5484863241-58.5484863241008
5245504711.62105353988-161.621053539885
5348004941.47257120125-141.472571201249
5452005234.49325149094-34.4932514909433
5533503354.35341558129-4.3534155812863
5650505023.8980654921326.1019345078676
5755505528.4635017070521.5364982929532
5856505662.55693225156-12.5569322515566
5957005715.09428822099-15.0942882209856
6051005077.155183420522.8448165795044
6152005264.07255946076-64.0725594607638
6255005571.50476189087-71.5047618908711
6352005551.3037311926-351.303731192601
6457004930.12459410277769.875405897227
6552005266.59009695853-66.59009695853
6658005604.5515040125195.448495987498
6737003607.1211381929292.8788618070776
6854505419.5775565822630.4224434177377
6959505960.57036392617-10.5703639261737
7060006093.72893717772-93.7289371777233
7162006139.9155186015360.0844813984668
7255005464.9549670086935.0450329913065
7355505650.35178550716-100.351785507158
7461005974.36532778391125.63467221609
7561505922.17003506851227.82996493149
7655005489.4959926910510.504007308954
7757005631.8158858144468.1841141855584
7860006049.48610628508-49.4861062850832
7937503870.99873691776-120.998736917764
8059005765.1118363698134.888163630199
8163506341.993799919268.00620008074202
8263506469.80094603719-119.800946037189
8365006540.53648681877-40.5364868187671
8457505808.03879981793-58.0387998179276
8558505971.5602200679-121.560220067904
8663006348.88113686494-48.8811368649413
8765506291.6353631969258.364636803097
8854505799.02753847149-349.027538471493
8957505922.53803203326-172.538032033258
9066006315.7706277232284.229372276804
9138504046.08954053025-196.089540530248
9260006066.17828175524-66.178281755243
9367506627.51281912839122.487180871605
9467506749.765950040170.234049959829463
9568506847.216567198572.78343280142599
9661006079.2422997224420.7577002775579
9764006246.79510742105153.204892578955
9867506681.3004411669968.6995588330128
9958006680.89703615761-880.897036157608
10067505961.75203046799788.247969532006
10158506228.81698183305-378.816981833045
10268006697.55302063068102.446979369315
10338004215.96403206594-415.964032065945
10464006326.8115068872973.1884931127142
10568006957.2288709772-157.228870977203
10670007036.69127367555-36.6912736755476
10773007133.87324328746166.126756712541
10863006349.18950053091-49.1895005309116
10965006537.46583650716-37.4658365071582
11069506955.76769053199-5.76769053199405
11171006791.7576995854308.242300414602
11261006420.42901537371-320.429015373713
11365506400.37749484391149.622505156089
11468007018.95982779098-218.959827790976

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4250 & 4079.33459790119 & 170.665402098808 \tabularnewline
14 & 4450 & 4298.50288434988 & 151.49711565012 \tabularnewline
15 & 4500 & 4360.77081938493 & 139.22918061507 \tabularnewline
16 & 3950 & 3836.94055717216 & 113.059442827838 \tabularnewline
17 & 4300 & 4179.80375623677 & 120.196243763226 \tabularnewline
18 & 4500 & 4374.89409772791 & 125.105902272092 \tabularnewline
19 & 2800 & 2861.30565408386 & -61.3056540838575 \tabularnewline
20 & 4300 & 4172.4106044225 & 127.589395577498 \tabularnewline
21 & 4750 & 4662.596488589 & 87.4035114110038 \tabularnewline
22 & 4900 & 4778.40180425628 & 121.598195743722 \tabularnewline
23 & 5000 & 4779.09733699629 & 220.902663003705 \tabularnewline
24 & 4500 & 4312.40721389658 & 187.592786103422 \tabularnewline
25 & 4500 & 4585.92341196359 & -85.9234119635912 \tabularnewline
26 & 4800 & 4796.66547921542 & 3.33452078457958 \tabularnewline
27 & 4450 & 4844.7070430679 & -394.707043067895 \tabularnewline
28 & 4550 & 4213.2580883496 & 336.741911650397 \tabularnewline
29 & 4150 & 4608.27656914426 & -458.276569144258 \tabularnewline
30 & 4750 & 4762.63152567145 & -12.631525671447 \tabularnewline
31 & 2950 & 3080.18474803489 & -130.184748034892 \tabularnewline
32 & 4650 & 4516.97356895317 & 133.026431046826 \tabularnewline
33 & 4950 & 5035.56192546808 & -85.5619254680787 \tabularnewline
34 & 5050 & 5146.34258435391 & -96.3425843539108 \tabularnewline
35 & 5300 & 5140.0076343713 & 159.992365628702 \tabularnewline
36 & 4650 & 4627.75818805395 & 22.2418119460472 \tabularnewline
37 & 4600 & 4854.56542518662 & -254.565425186617 \tabularnewline
38 & 4950 & 5075.12794824886 & -125.127948248864 \tabularnewline
39 & 4950 & 5046.19683550638 & -96.1968355063846 \tabularnewline
40 & 4400 & 4525.23161180745 & -125.231611807448 \tabularnewline
41 & 4550 & 4762.9139171842 & -212.913917184195 \tabularnewline
42 & 4900 & 5022.942894549 & -122.942894549004 \tabularnewline
43 & 3100 & 3220.79267857353 & -120.792678573533 \tabularnewline
44 & 4800 & 4776.98923424247 & 23.0107657575318 \tabularnewline
45 & 5200 & 5273.39988006505 & -73.3998800650461 \tabularnewline
46 & 5350 & 5387.97719037052 & -37.9771903705205 \tabularnewline
47 & 5450 & 5427.56883631078 & 22.4311636892226 \tabularnewline
48 & 4700 & 4853.14064439761 & -153.140644397613 \tabularnewline
49 & 4800 & 5026.92959498145 & -226.929594981446 \tabularnewline
50 & 5200 & 5280.72445587842 & -80.7244558784214 \tabularnewline
51 & 5200 & 5258.5484863241 & -58.5484863241008 \tabularnewline
52 & 4550 & 4711.62105353988 & -161.621053539885 \tabularnewline
53 & 4800 & 4941.47257120125 & -141.472571201249 \tabularnewline
54 & 5200 & 5234.49325149094 & -34.4932514909433 \tabularnewline
55 & 3350 & 3354.35341558129 & -4.3534155812863 \tabularnewline
56 & 5050 & 5023.89806549213 & 26.1019345078676 \tabularnewline
57 & 5550 & 5528.46350170705 & 21.5364982929532 \tabularnewline
58 & 5650 & 5662.55693225156 & -12.5569322515566 \tabularnewline
59 & 5700 & 5715.09428822099 & -15.0942882209856 \tabularnewline
60 & 5100 & 5077.1551834205 & 22.8448165795044 \tabularnewline
61 & 5200 & 5264.07255946076 & -64.0725594607638 \tabularnewline
62 & 5500 & 5571.50476189087 & -71.5047618908711 \tabularnewline
63 & 5200 & 5551.3037311926 & -351.303731192601 \tabularnewline
64 & 5700 & 4930.12459410277 & 769.875405897227 \tabularnewline
65 & 5200 & 5266.59009695853 & -66.59009695853 \tabularnewline
66 & 5800 & 5604.5515040125 & 195.448495987498 \tabularnewline
67 & 3700 & 3607.12113819292 & 92.8788618070776 \tabularnewline
68 & 5450 & 5419.57755658226 & 30.4224434177377 \tabularnewline
69 & 5950 & 5960.57036392617 & -10.5703639261737 \tabularnewline
70 & 6000 & 6093.72893717772 & -93.7289371777233 \tabularnewline
71 & 6200 & 6139.91551860153 & 60.0844813984668 \tabularnewline
72 & 5500 & 5464.95496700869 & 35.0450329913065 \tabularnewline
73 & 5550 & 5650.35178550716 & -100.351785507158 \tabularnewline
74 & 6100 & 5974.36532778391 & 125.63467221609 \tabularnewline
75 & 6150 & 5922.17003506851 & 227.82996493149 \tabularnewline
76 & 5500 & 5489.49599269105 & 10.504007308954 \tabularnewline
77 & 5700 & 5631.81588581444 & 68.1841141855584 \tabularnewline
78 & 6000 & 6049.48610628508 & -49.4861062850832 \tabularnewline
79 & 3750 & 3870.99873691776 & -120.998736917764 \tabularnewline
80 & 5900 & 5765.1118363698 & 134.888163630199 \tabularnewline
81 & 6350 & 6341.99379991926 & 8.00620008074202 \tabularnewline
82 & 6350 & 6469.80094603719 & -119.800946037189 \tabularnewline
83 & 6500 & 6540.53648681877 & -40.5364868187671 \tabularnewline
84 & 5750 & 5808.03879981793 & -58.0387998179276 \tabularnewline
85 & 5850 & 5971.5602200679 & -121.560220067904 \tabularnewline
86 & 6300 & 6348.88113686494 & -48.8811368649413 \tabularnewline
87 & 6550 & 6291.6353631969 & 258.364636803097 \tabularnewline
88 & 5450 & 5799.02753847149 & -349.027538471493 \tabularnewline
89 & 5750 & 5922.53803203326 & -172.538032033258 \tabularnewline
90 & 6600 & 6315.7706277232 & 284.229372276804 \tabularnewline
91 & 3850 & 4046.08954053025 & -196.089540530248 \tabularnewline
92 & 6000 & 6066.17828175524 & -66.178281755243 \tabularnewline
93 & 6750 & 6627.51281912839 & 122.487180871605 \tabularnewline
94 & 6750 & 6749.76595004017 & 0.234049959829463 \tabularnewline
95 & 6850 & 6847.21656719857 & 2.78343280142599 \tabularnewline
96 & 6100 & 6079.24229972244 & 20.7577002775579 \tabularnewline
97 & 6400 & 6246.79510742105 & 153.204892578955 \tabularnewline
98 & 6750 & 6681.30044116699 & 68.6995588330128 \tabularnewline
99 & 5800 & 6680.89703615761 & -880.897036157608 \tabularnewline
100 & 6750 & 5961.75203046799 & 788.247969532006 \tabularnewline
101 & 5850 & 6228.81698183305 & -378.816981833045 \tabularnewline
102 & 6800 & 6697.55302063068 & 102.446979369315 \tabularnewline
103 & 3800 & 4215.96403206594 & -415.964032065945 \tabularnewline
104 & 6400 & 6326.81150688729 & 73.1884931127142 \tabularnewline
105 & 6800 & 6957.2288709772 & -157.228870977203 \tabularnewline
106 & 7000 & 7036.69127367555 & -36.6912736755476 \tabularnewline
107 & 7300 & 7133.87324328746 & 166.126756712541 \tabularnewline
108 & 6300 & 6349.18950053091 & -49.1895005309116 \tabularnewline
109 & 6500 & 6537.46583650716 & -37.4658365071582 \tabularnewline
110 & 6950 & 6955.76769053199 & -5.76769053199405 \tabularnewline
111 & 7100 & 6791.7576995854 & 308.242300414602 \tabularnewline
112 & 6100 & 6420.42901537371 & -320.429015373713 \tabularnewline
113 & 6550 & 6400.37749484391 & 149.622505156089 \tabularnewline
114 & 6800 & 7018.95982779098 & -218.959827790976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302319&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]4250[/C][C]4079.33459790119[/C][C]170.665402098808[/C][/ROW]
[ROW][C]14[/C][C]4450[/C][C]4298.50288434988[/C][C]151.49711565012[/C][/ROW]
[ROW][C]15[/C][C]4500[/C][C]4360.77081938493[/C][C]139.22918061507[/C][/ROW]
[ROW][C]16[/C][C]3950[/C][C]3836.94055717216[/C][C]113.059442827838[/C][/ROW]
[ROW][C]17[/C][C]4300[/C][C]4179.80375623677[/C][C]120.196243763226[/C][/ROW]
[ROW][C]18[/C][C]4500[/C][C]4374.89409772791[/C][C]125.105902272092[/C][/ROW]
[ROW][C]19[/C][C]2800[/C][C]2861.30565408386[/C][C]-61.3056540838575[/C][/ROW]
[ROW][C]20[/C][C]4300[/C][C]4172.4106044225[/C][C]127.589395577498[/C][/ROW]
[ROW][C]21[/C][C]4750[/C][C]4662.596488589[/C][C]87.4035114110038[/C][/ROW]
[ROW][C]22[/C][C]4900[/C][C]4778.40180425628[/C][C]121.598195743722[/C][/ROW]
[ROW][C]23[/C][C]5000[/C][C]4779.09733699629[/C][C]220.902663003705[/C][/ROW]
[ROW][C]24[/C][C]4500[/C][C]4312.40721389658[/C][C]187.592786103422[/C][/ROW]
[ROW][C]25[/C][C]4500[/C][C]4585.92341196359[/C][C]-85.9234119635912[/C][/ROW]
[ROW][C]26[/C][C]4800[/C][C]4796.66547921542[/C][C]3.33452078457958[/C][/ROW]
[ROW][C]27[/C][C]4450[/C][C]4844.7070430679[/C][C]-394.707043067895[/C][/ROW]
[ROW][C]28[/C][C]4550[/C][C]4213.2580883496[/C][C]336.741911650397[/C][/ROW]
[ROW][C]29[/C][C]4150[/C][C]4608.27656914426[/C][C]-458.276569144258[/C][/ROW]
[ROW][C]30[/C][C]4750[/C][C]4762.63152567145[/C][C]-12.631525671447[/C][/ROW]
[ROW][C]31[/C][C]2950[/C][C]3080.18474803489[/C][C]-130.184748034892[/C][/ROW]
[ROW][C]32[/C][C]4650[/C][C]4516.97356895317[/C][C]133.026431046826[/C][/ROW]
[ROW][C]33[/C][C]4950[/C][C]5035.56192546808[/C][C]-85.5619254680787[/C][/ROW]
[ROW][C]34[/C][C]5050[/C][C]5146.34258435391[/C][C]-96.3425843539108[/C][/ROW]
[ROW][C]35[/C][C]5300[/C][C]5140.0076343713[/C][C]159.992365628702[/C][/ROW]
[ROW][C]36[/C][C]4650[/C][C]4627.75818805395[/C][C]22.2418119460472[/C][/ROW]
[ROW][C]37[/C][C]4600[/C][C]4854.56542518662[/C][C]-254.565425186617[/C][/ROW]
[ROW][C]38[/C][C]4950[/C][C]5075.12794824886[/C][C]-125.127948248864[/C][/ROW]
[ROW][C]39[/C][C]4950[/C][C]5046.19683550638[/C][C]-96.1968355063846[/C][/ROW]
[ROW][C]40[/C][C]4400[/C][C]4525.23161180745[/C][C]-125.231611807448[/C][/ROW]
[ROW][C]41[/C][C]4550[/C][C]4762.9139171842[/C][C]-212.913917184195[/C][/ROW]
[ROW][C]42[/C][C]4900[/C][C]5022.942894549[/C][C]-122.942894549004[/C][/ROW]
[ROW][C]43[/C][C]3100[/C][C]3220.79267857353[/C][C]-120.792678573533[/C][/ROW]
[ROW][C]44[/C][C]4800[/C][C]4776.98923424247[/C][C]23.0107657575318[/C][/ROW]
[ROW][C]45[/C][C]5200[/C][C]5273.39988006505[/C][C]-73.3998800650461[/C][/ROW]
[ROW][C]46[/C][C]5350[/C][C]5387.97719037052[/C][C]-37.9771903705205[/C][/ROW]
[ROW][C]47[/C][C]5450[/C][C]5427.56883631078[/C][C]22.4311636892226[/C][/ROW]
[ROW][C]48[/C][C]4700[/C][C]4853.14064439761[/C][C]-153.140644397613[/C][/ROW]
[ROW][C]49[/C][C]4800[/C][C]5026.92959498145[/C][C]-226.929594981446[/C][/ROW]
[ROW][C]50[/C][C]5200[/C][C]5280.72445587842[/C][C]-80.7244558784214[/C][/ROW]
[ROW][C]51[/C][C]5200[/C][C]5258.5484863241[/C][C]-58.5484863241008[/C][/ROW]
[ROW][C]52[/C][C]4550[/C][C]4711.62105353988[/C][C]-161.621053539885[/C][/ROW]
[ROW][C]53[/C][C]4800[/C][C]4941.47257120125[/C][C]-141.472571201249[/C][/ROW]
[ROW][C]54[/C][C]5200[/C][C]5234.49325149094[/C][C]-34.4932514909433[/C][/ROW]
[ROW][C]55[/C][C]3350[/C][C]3354.35341558129[/C][C]-4.3534155812863[/C][/ROW]
[ROW][C]56[/C][C]5050[/C][C]5023.89806549213[/C][C]26.1019345078676[/C][/ROW]
[ROW][C]57[/C][C]5550[/C][C]5528.46350170705[/C][C]21.5364982929532[/C][/ROW]
[ROW][C]58[/C][C]5650[/C][C]5662.55693225156[/C][C]-12.5569322515566[/C][/ROW]
[ROW][C]59[/C][C]5700[/C][C]5715.09428822099[/C][C]-15.0942882209856[/C][/ROW]
[ROW][C]60[/C][C]5100[/C][C]5077.1551834205[/C][C]22.8448165795044[/C][/ROW]
[ROW][C]61[/C][C]5200[/C][C]5264.07255946076[/C][C]-64.0725594607638[/C][/ROW]
[ROW][C]62[/C][C]5500[/C][C]5571.50476189087[/C][C]-71.5047618908711[/C][/ROW]
[ROW][C]63[/C][C]5200[/C][C]5551.3037311926[/C][C]-351.303731192601[/C][/ROW]
[ROW][C]64[/C][C]5700[/C][C]4930.12459410277[/C][C]769.875405897227[/C][/ROW]
[ROW][C]65[/C][C]5200[/C][C]5266.59009695853[/C][C]-66.59009695853[/C][/ROW]
[ROW][C]66[/C][C]5800[/C][C]5604.5515040125[/C][C]195.448495987498[/C][/ROW]
[ROW][C]67[/C][C]3700[/C][C]3607.12113819292[/C][C]92.8788618070776[/C][/ROW]
[ROW][C]68[/C][C]5450[/C][C]5419.57755658226[/C][C]30.4224434177377[/C][/ROW]
[ROW][C]69[/C][C]5950[/C][C]5960.57036392617[/C][C]-10.5703639261737[/C][/ROW]
[ROW][C]70[/C][C]6000[/C][C]6093.72893717772[/C][C]-93.7289371777233[/C][/ROW]
[ROW][C]71[/C][C]6200[/C][C]6139.91551860153[/C][C]60.0844813984668[/C][/ROW]
[ROW][C]72[/C][C]5500[/C][C]5464.95496700869[/C][C]35.0450329913065[/C][/ROW]
[ROW][C]73[/C][C]5550[/C][C]5650.35178550716[/C][C]-100.351785507158[/C][/ROW]
[ROW][C]74[/C][C]6100[/C][C]5974.36532778391[/C][C]125.63467221609[/C][/ROW]
[ROW][C]75[/C][C]6150[/C][C]5922.17003506851[/C][C]227.82996493149[/C][/ROW]
[ROW][C]76[/C][C]5500[/C][C]5489.49599269105[/C][C]10.504007308954[/C][/ROW]
[ROW][C]77[/C][C]5700[/C][C]5631.81588581444[/C][C]68.1841141855584[/C][/ROW]
[ROW][C]78[/C][C]6000[/C][C]6049.48610628508[/C][C]-49.4861062850832[/C][/ROW]
[ROW][C]79[/C][C]3750[/C][C]3870.99873691776[/C][C]-120.998736917764[/C][/ROW]
[ROW][C]80[/C][C]5900[/C][C]5765.1118363698[/C][C]134.888163630199[/C][/ROW]
[ROW][C]81[/C][C]6350[/C][C]6341.99379991926[/C][C]8.00620008074202[/C][/ROW]
[ROW][C]82[/C][C]6350[/C][C]6469.80094603719[/C][C]-119.800946037189[/C][/ROW]
[ROW][C]83[/C][C]6500[/C][C]6540.53648681877[/C][C]-40.5364868187671[/C][/ROW]
[ROW][C]84[/C][C]5750[/C][C]5808.03879981793[/C][C]-58.0387998179276[/C][/ROW]
[ROW][C]85[/C][C]5850[/C][C]5971.5602200679[/C][C]-121.560220067904[/C][/ROW]
[ROW][C]86[/C][C]6300[/C][C]6348.88113686494[/C][C]-48.8811368649413[/C][/ROW]
[ROW][C]87[/C][C]6550[/C][C]6291.6353631969[/C][C]258.364636803097[/C][/ROW]
[ROW][C]88[/C][C]5450[/C][C]5799.02753847149[/C][C]-349.027538471493[/C][/ROW]
[ROW][C]89[/C][C]5750[/C][C]5922.53803203326[/C][C]-172.538032033258[/C][/ROW]
[ROW][C]90[/C][C]6600[/C][C]6315.7706277232[/C][C]284.229372276804[/C][/ROW]
[ROW][C]91[/C][C]3850[/C][C]4046.08954053025[/C][C]-196.089540530248[/C][/ROW]
[ROW][C]92[/C][C]6000[/C][C]6066.17828175524[/C][C]-66.178281755243[/C][/ROW]
[ROW][C]93[/C][C]6750[/C][C]6627.51281912839[/C][C]122.487180871605[/C][/ROW]
[ROW][C]94[/C][C]6750[/C][C]6749.76595004017[/C][C]0.234049959829463[/C][/ROW]
[ROW][C]95[/C][C]6850[/C][C]6847.21656719857[/C][C]2.78343280142599[/C][/ROW]
[ROW][C]96[/C][C]6100[/C][C]6079.24229972244[/C][C]20.7577002775579[/C][/ROW]
[ROW][C]97[/C][C]6400[/C][C]6246.79510742105[/C][C]153.204892578955[/C][/ROW]
[ROW][C]98[/C][C]6750[/C][C]6681.30044116699[/C][C]68.6995588330128[/C][/ROW]
[ROW][C]99[/C][C]5800[/C][C]6680.89703615761[/C][C]-880.897036157608[/C][/ROW]
[ROW][C]100[/C][C]6750[/C][C]5961.75203046799[/C][C]788.247969532006[/C][/ROW]
[ROW][C]101[/C][C]5850[/C][C]6228.81698183305[/C][C]-378.816981833045[/C][/ROW]
[ROW][C]102[/C][C]6800[/C][C]6697.55302063068[/C][C]102.446979369315[/C][/ROW]
[ROW][C]103[/C][C]3800[/C][C]4215.96403206594[/C][C]-415.964032065945[/C][/ROW]
[ROW][C]104[/C][C]6400[/C][C]6326.81150688729[/C][C]73.1884931127142[/C][/ROW]
[ROW][C]105[/C][C]6800[/C][C]6957.2288709772[/C][C]-157.228870977203[/C][/ROW]
[ROW][C]106[/C][C]7000[/C][C]7036.69127367555[/C][C]-36.6912736755476[/C][/ROW]
[ROW][C]107[/C][C]7300[/C][C]7133.87324328746[/C][C]166.126756712541[/C][/ROW]
[ROW][C]108[/C][C]6300[/C][C]6349.18950053091[/C][C]-49.1895005309116[/C][/ROW]
[ROW][C]109[/C][C]6500[/C][C]6537.46583650716[/C][C]-37.4658365071582[/C][/ROW]
[ROW][C]110[/C][C]6950[/C][C]6955.76769053199[/C][C]-5.76769053199405[/C][/ROW]
[ROW][C]111[/C][C]7100[/C][C]6791.7576995854[/C][C]308.242300414602[/C][/ROW]
[ROW][C]112[/C][C]6100[/C][C]6420.42901537371[/C][C]-320.429015373713[/C][/ROW]
[ROW][C]113[/C][C]6550[/C][C]6400.37749484391[/C][C]149.622505156089[/C][/ROW]
[ROW][C]114[/C][C]6800[/C][C]7018.95982779098[/C][C]-218.959827790976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302319&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302319&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
1342504079.33459790119170.665402098808
1444504298.50288434988151.49711565012
1545004360.77081938493139.22918061507
1639503836.94055717216113.059442827838
1743004179.80375623677120.196243763226
1845004374.89409772791125.105902272092
1928002861.30565408386-61.3056540838575
2043004172.4106044225127.589395577498
2147504662.59648858987.4035114110038
2249004778.40180425628121.598195743722
2350004779.09733699629220.902663003705
2445004312.40721389658187.592786103422
2545004585.92341196359-85.9234119635912
2648004796.665479215423.33452078457958
2744504844.7070430679-394.707043067895
2845504213.2580883496336.741911650397
2941504608.27656914426-458.276569144258
3047504762.63152567145-12.631525671447
3129503080.18474803489-130.184748034892
3246504516.97356895317133.026431046826
3349505035.56192546808-85.5619254680787
3450505146.34258435391-96.3425843539108
3553005140.0076343713159.992365628702
3646504627.7581880539522.2418119460472
3746004854.56542518662-254.565425186617
3849505075.12794824886-125.127948248864
3949505046.19683550638-96.1968355063846
4044004525.23161180745-125.231611807448
4145504762.9139171842-212.913917184195
4249005022.942894549-122.942894549004
4331003220.79267857353-120.792678573533
4448004776.9892342424723.0107657575318
4552005273.39988006505-73.3998800650461
4653505387.97719037052-37.9771903705205
4754505427.5688363107822.4311636892226
4847004853.14064439761-153.140644397613
4948005026.92959498145-226.929594981446
5052005280.72445587842-80.7244558784214
5152005258.5484863241-58.5484863241008
5245504711.62105353988-161.621053539885
5348004941.47257120125-141.472571201249
5452005234.49325149094-34.4932514909433
5533503354.35341558129-4.3534155812863
5650505023.8980654921326.1019345078676
5755505528.4635017070521.5364982929532
5856505662.55693225156-12.5569322515566
5957005715.09428822099-15.0942882209856
6051005077.155183420522.8448165795044
6152005264.07255946076-64.0725594607638
6255005571.50476189087-71.5047618908711
6352005551.3037311926-351.303731192601
6457004930.12459410277769.875405897227
6552005266.59009695853-66.59009695853
6658005604.5515040125195.448495987498
6737003607.1211381929292.8788618070776
6854505419.5775565822630.4224434177377
6959505960.57036392617-10.5703639261737
7060006093.72893717772-93.7289371777233
7162006139.9155186015360.0844813984668
7255005464.9549670086935.0450329913065
7355505650.35178550716-100.351785507158
7461005974.36532778391125.63467221609
7561505922.17003506851227.82996493149
7655005489.4959926910510.504007308954
7757005631.8158858144468.1841141855584
7860006049.48610628508-49.4861062850832
7937503870.99873691776-120.998736917764
8059005765.1118363698134.888163630199
8163506341.993799919268.00620008074202
8263506469.80094603719-119.800946037189
8365006540.53648681877-40.5364868187671
8457505808.03879981793-58.0387998179276
8558505971.5602200679-121.560220067904
8663006348.88113686494-48.8811368649413
8765506291.6353631969258.364636803097
8854505799.02753847149-349.027538471493
8957505922.53803203326-172.538032033258
9066006315.7706277232284.229372276804
9138504046.08954053025-196.089540530248
9260006066.17828175524-66.178281755243
9367506627.51281912839122.487180871605
9467506749.765950040170.234049959829463
9568506847.216567198572.78343280142599
9661006079.2422997224420.7577002775579
9764006246.79510742105153.204892578955
9867506681.3004411669968.6995588330128
9958006680.89703615761-880.897036157608
10067505961.75203046799788.247969532006
10158506228.81698183305-378.816981833045
10268006697.55302063068102.446979369315
10338004215.96403206594-415.964032065945
10464006326.8115068872973.1884931127142
10568006957.2288709772-157.228870977203
10670007036.69127367555-36.6912736755476
10773007133.87324328746166.126756712541
10863006349.18950053091-49.1895005309116
10965006537.46583650716-37.4658365071582
11069506955.76769053199-5.76769053199405
11171006791.7576995854308.242300414602
11261006420.42901537371-320.429015373713
11365506400.37749484391149.622505156089
11468007018.95982779098-218.959827790976







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1154319.761456030344216.423174729624423.09973733106
1166657.027065739086537.607737819066776.44639365909
1177272.045087057897142.746196390037401.34397772575
1187389.321548345387253.597976616377525.04512007438
1197526.68297821867384.518114464877668.84784197232
1206650.667890983516511.965391150336789.37039081669
1216853.668473113186707.732552237276999.6043939891
1227300.246701055417144.232184693127456.2612174177
1237178.287810325277019.415722425597337.15989822496
1246656.161957447716499.969748076436812.35416681899
1256742.229162976566580.399598156566904.05872779655
1267313.737577290267172.683019722347454.79213485819

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 4319.76145603034 & 4216.42317472962 & 4423.09973733106 \tabularnewline
116 & 6657.02706573908 & 6537.60773781906 & 6776.44639365909 \tabularnewline
117 & 7272.04508705789 & 7142.74619639003 & 7401.34397772575 \tabularnewline
118 & 7389.32154834538 & 7253.59797661637 & 7525.04512007438 \tabularnewline
119 & 7526.6829782186 & 7384.51811446487 & 7668.84784197232 \tabularnewline
120 & 6650.66789098351 & 6511.96539115033 & 6789.37039081669 \tabularnewline
121 & 6853.66847311318 & 6707.73255223727 & 6999.6043939891 \tabularnewline
122 & 7300.24670105541 & 7144.23218469312 & 7456.2612174177 \tabularnewline
123 & 7178.28781032527 & 7019.41572242559 & 7337.15989822496 \tabularnewline
124 & 6656.16195744771 & 6499.96974807643 & 6812.35416681899 \tabularnewline
125 & 6742.22916297656 & 6580.39959815656 & 6904.05872779655 \tabularnewline
126 & 7313.73757729026 & 7172.68301972234 & 7454.79213485819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302319&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]115[/C][C]4319.76145603034[/C][C]4216.42317472962[/C][C]4423.09973733106[/C][/ROW]
[ROW][C]116[/C][C]6657.02706573908[/C][C]6537.60773781906[/C][C]6776.44639365909[/C][/ROW]
[ROW][C]117[/C][C]7272.04508705789[/C][C]7142.74619639003[/C][C]7401.34397772575[/C][/ROW]
[ROW][C]118[/C][C]7389.32154834538[/C][C]7253.59797661637[/C][C]7525.04512007438[/C][/ROW]
[ROW][C]119[/C][C]7526.6829782186[/C][C]7384.51811446487[/C][C]7668.84784197232[/C][/ROW]
[ROW][C]120[/C][C]6650.66789098351[/C][C]6511.96539115033[/C][C]6789.37039081669[/C][/ROW]
[ROW][C]121[/C][C]6853.66847311318[/C][C]6707.73255223727[/C][C]6999.6043939891[/C][/ROW]
[ROW][C]122[/C][C]7300.24670105541[/C][C]7144.23218469312[/C][C]7456.2612174177[/C][/ROW]
[ROW][C]123[/C][C]7178.28781032527[/C][C]7019.41572242559[/C][C]7337.15989822496[/C][/ROW]
[ROW][C]124[/C][C]6656.16195744771[/C][C]6499.96974807643[/C][C]6812.35416681899[/C][/ROW]
[ROW][C]125[/C][C]6742.22916297656[/C][C]6580.39959815656[/C][C]6904.05872779655[/C][/ROW]
[ROW][C]126[/C][C]7313.73757729026[/C][C]7172.68301972234[/C][C]7454.79213485819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302319&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302319&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
1154319.761456030344216.423174729624423.09973733106
1166657.027065739086537.607737819066776.44639365909
1177272.045087057897142.746196390037401.34397772575
1187389.321548345387253.597976616377525.04512007438
1197526.68297821867384.518114464877668.84784197232
1206650.667890983516511.965391150336789.37039081669
1216853.668473113186707.732552237276999.6043939891
1227300.246701055417144.232184693127456.2612174177
1237178.287810325277019.415722425597337.15989822496
1246656.161957447716499.969748076436812.35416681899
1256742.229162976566580.399598156566904.05872779655
1267313.737577290267172.683019722347454.79213485819



Parameters (Session):
par4 = 4 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '4'
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')