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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 computationSat, 17 Dec 2016 14:22:30 +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/17/t1481981149em5l34kp103fxwe.htm/, Retrieved Fri, 01 Nov 2024 03:38:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300774, Retrieved Fri, 01 Nov 2024 03:38:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2568] [2016-12-17 13:22:30] [563c2945bc7c763925d38f2fb19cdb55] [Current]
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Dataseries X:
5750.5
3881.6
4350.4
6623.4
3375.5
6651.7
4394.8
4968.3
6355.6
4515.7
4620
5804.4
6254.4
4788.6
4446.4
8018
3745.9
6928.2
5201.7
5520.9
6801.9
5225.1
5149.4
6240.4
7045.4
5402.1
4960.6
9459.3
3979.4
7215.1
5797
5577.6
7380.8
5788.6
5116.3
6819.3
7671
5337
4955.7
9143.8
4624.6
7702.4
6297.4
5652.3
7801.3
5901.2
5296.7
7803.5
8177.1
5546.3
5651.5
12289.7
4769.1
8294.5
6422.3
6021.3
9241
6229.5
5691.5
8546.9
8174
6027.9
6566.4
10926.6
5963.5
9914
6063.1
6939
9774.2
6358.2
6432
9365.5
8930.6
6189.7
6820.5
12889.2
7102.5
10824.9
6619.1
7613.6
9923.3
6842.6
7121.3
8913
9952.4
6514.1
6480.5
13960.4
6918.6
11060.1
7232.9
7846.2
10293.9
7698.6
7050.7
10190
10071.3
6765.7
6480.5
14038
6356
10338.9
7859.3
7642.6
10935
7806.5
7309.5
10363.6
10403.1
6274.7
7212.7
13835.1
6218.4
12087.8
7905
7810.1




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=300774&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=300774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300774&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
alpha0.0695116989335066
beta0.0548385371888588
gamma0.698597822344278

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0695116989335066 \tabularnewline
beta & 0.0548385371888588 \tabularnewline
gamma & 0.698597822344278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300774&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]0.0695116989335066[/C][/ROW]
[ROW][C]beta[/C][C]0.0548385371888588[/C][/ROW]
[ROW][C]gamma[/C][C]0.698597822344278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300774&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
alpha0.0695116989335066
beta0.0548385371888588
gamma0.698597822344278







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136254.45967.03253205128287.367467948718
144788.64515.20539435962273.394605640385
154446.44202.07413760418244.325862395822
1680187795.1202804004222.879719599602
173745.93540.36276501084205.537234989163
186928.26750.97490219252177.225097807477
195201.74831.40708249308370.292917506915
205520.95428.1962618866192.7037381133878
216801.96836.83895837119-34.9389583711882
225225.14988.95914298975236.14085701025
235149.45093.589362817755.8106371822969
246240.46312.58476837414-72.1847683741435
257045.46956.6198490222288.7801509777764
265402.15488.99573619254-86.8957361925422
274960.65137.64097172067-177.040971720668
289459.38691.56683253854767.733167461462
293979.44469.5971162783-490.197116278304
307215.17616.97892223132-401.878922231317
3157975783.9856309989513.0143690010473
325577.66175.46237586694-597.862375866945
337380.87450.46364724483-69.6636472448272
345788.65773.5831163685215.016883631477
355116.35741.9795123056-625.679512305604
366819.36824.16204402681-4.86204402681142
3776717571.5270665767799.4729334232261
3853375984.50819831013-647.508198310133
394955.75527.50736727545-571.807367275448
409143.89658.54657544652-514.746575446525
414624.64515.25543647459109.344563525407
427702.47749.5351886035-47.1351886034954
436297.46200.0617064874597.3382935125492
445652.36189.79377576247-537.493775762466
457801.37802.05663494423-0.756634944226789
465901.26174.99059598699-273.790595986989
475296.75695.71331627826-399.013316278261
487803.57186.94847165037616.551528349625
498177.18037.44167641151139.658323588494
505546.35959.91495991688-413.614959916877
515651.55561.536622560889.9633774391959
5212289.79771.346716827862518.35328317214
534769.15251.81427600648-482.714276006477
548294.58348.20486635645-53.704866356451
556422.36897.14629359618-474.846293596182
566021.36437.21777583266-415.917775832656
5792418410.07141577058830.928584229421
586229.56669.74611385494-440.24611385494
595691.56103.27538809238-411.775388092381
608546.98259.50618334198287.393816658021
6181748781.59400313743-607.59400313743
626027.96294.10108371728-266.201083717282
636566.46235.50100471055330.898995289446
6410926.612043.7075713241-1117.1075713241
655963.55309.90982315138653.590176848616
6699148757.737409599411156.26259040059
676063.17115.21898720791-1052.11898720791
6869396649.45927854907289.540721450931
699774.29480.52637346717293.673626532835
706358.26873.17632163455-514.976321634546
7164326316.3646049952115.6353950048
729365.58962.0995951144403.400404885602
738930.68909.2752025438821.3247974561218
746189.76688.61420938282-498.914209382816
756820.57002.28461447603-181.78461447603
7612889.211831.95093750921057.24906249078
777102.56406.95937273495695.540627265052
7810824.910191.2623654024633.637634597628
796619.17081.69687246564-462.596872465642
807613.67536.1030822663277.4969177336798
819923.310361.3675471568-438.06754715685
826842.67180.9614699063-338.361469906304
837121.37050.4818200217970.8181799782124
8489139884.12283880958-971.122838809579
859952.49486.11352438244466.286475617557
866514.16958.62792014228-444.527920142282
876480.57482.85212970324-1002.35212970324
8813960.413058.3966508939902.003349106073
896918.67384.39738703336-465.79738703336
9011060.111040.21522871919.8847712809893
917232.97165.5347232833567.3652767166495
927846.28000.0217698336-153.821769833598
9310293.910465.3503472219-171.450347221929
947698.67360.58575482288338.014245177123
957050.77537.97819431189-487.278194311893
96101909648.27135915135541.728640848645
9710071.310288.3058657223-217.005865722342
986765.77117.16920601769-351.469206017692
996480.57281.51929057371-801.019290573706
1001403814105.9916161724-67.9916161724432
10163567468.77868846199-1112.77868846199
10210338.911386.202501132-1047.302501132
1037859.37455.0033713273404.296628672703
1047642.68157.21494333045-514.614943330451
1051093510572.7132714926362.28672850745
1067806.57824.96342617396-18.4634261739584
1077309.57428.48981759667-118.989817596674
10810363.610222.063864074141.536135925997
10910403.110328.337139999874.7628600001935
1106274.77078.45026846123-803.750268461228
1117212.76905.78784338741306.912156612586
11213835.114274.6434454677-439.543445467667
1136218.46921.9105285668-703.510528566804
11412087.810901.36288394841186.43711605156
11579058068.56058291303-163.560582913025
1167810.18131.34069807533-321.240698075329

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6254.4 & 5967.03253205128 & 287.367467948718 \tabularnewline
14 & 4788.6 & 4515.20539435962 & 273.394605640385 \tabularnewline
15 & 4446.4 & 4202.07413760418 & 244.325862395822 \tabularnewline
16 & 8018 & 7795.1202804004 & 222.879719599602 \tabularnewline
17 & 3745.9 & 3540.36276501084 & 205.537234989163 \tabularnewline
18 & 6928.2 & 6750.97490219252 & 177.225097807477 \tabularnewline
19 & 5201.7 & 4831.40708249308 & 370.292917506915 \tabularnewline
20 & 5520.9 & 5428.19626188661 & 92.7037381133878 \tabularnewline
21 & 6801.9 & 6836.83895837119 & -34.9389583711882 \tabularnewline
22 & 5225.1 & 4988.95914298975 & 236.14085701025 \tabularnewline
23 & 5149.4 & 5093.5893628177 & 55.8106371822969 \tabularnewline
24 & 6240.4 & 6312.58476837414 & -72.1847683741435 \tabularnewline
25 & 7045.4 & 6956.61984902222 & 88.7801509777764 \tabularnewline
26 & 5402.1 & 5488.99573619254 & -86.8957361925422 \tabularnewline
27 & 4960.6 & 5137.64097172067 & -177.040971720668 \tabularnewline
28 & 9459.3 & 8691.56683253854 & 767.733167461462 \tabularnewline
29 & 3979.4 & 4469.5971162783 & -490.197116278304 \tabularnewline
30 & 7215.1 & 7616.97892223132 & -401.878922231317 \tabularnewline
31 & 5797 & 5783.98563099895 & 13.0143690010473 \tabularnewline
32 & 5577.6 & 6175.46237586694 & -597.862375866945 \tabularnewline
33 & 7380.8 & 7450.46364724483 & -69.6636472448272 \tabularnewline
34 & 5788.6 & 5773.58311636852 & 15.016883631477 \tabularnewline
35 & 5116.3 & 5741.9795123056 & -625.679512305604 \tabularnewline
36 & 6819.3 & 6824.16204402681 & -4.86204402681142 \tabularnewline
37 & 7671 & 7571.52706657677 & 99.4729334232261 \tabularnewline
38 & 5337 & 5984.50819831013 & -647.508198310133 \tabularnewline
39 & 4955.7 & 5527.50736727545 & -571.807367275448 \tabularnewline
40 & 9143.8 & 9658.54657544652 & -514.746575446525 \tabularnewline
41 & 4624.6 & 4515.25543647459 & 109.344563525407 \tabularnewline
42 & 7702.4 & 7749.5351886035 & -47.1351886034954 \tabularnewline
43 & 6297.4 & 6200.06170648745 & 97.3382935125492 \tabularnewline
44 & 5652.3 & 6189.79377576247 & -537.493775762466 \tabularnewline
45 & 7801.3 & 7802.05663494423 & -0.756634944226789 \tabularnewline
46 & 5901.2 & 6174.99059598699 & -273.790595986989 \tabularnewline
47 & 5296.7 & 5695.71331627826 & -399.013316278261 \tabularnewline
48 & 7803.5 & 7186.94847165037 & 616.551528349625 \tabularnewline
49 & 8177.1 & 8037.44167641151 & 139.658323588494 \tabularnewline
50 & 5546.3 & 5959.91495991688 & -413.614959916877 \tabularnewline
51 & 5651.5 & 5561.5366225608 & 89.9633774391959 \tabularnewline
52 & 12289.7 & 9771.34671682786 & 2518.35328317214 \tabularnewline
53 & 4769.1 & 5251.81427600648 & -482.714276006477 \tabularnewline
54 & 8294.5 & 8348.20486635645 & -53.704866356451 \tabularnewline
55 & 6422.3 & 6897.14629359618 & -474.846293596182 \tabularnewline
56 & 6021.3 & 6437.21777583266 & -415.917775832656 \tabularnewline
57 & 9241 & 8410.07141577058 & 830.928584229421 \tabularnewline
58 & 6229.5 & 6669.74611385494 & -440.24611385494 \tabularnewline
59 & 5691.5 & 6103.27538809238 & -411.775388092381 \tabularnewline
60 & 8546.9 & 8259.50618334198 & 287.393816658021 \tabularnewline
61 & 8174 & 8781.59400313743 & -607.59400313743 \tabularnewline
62 & 6027.9 & 6294.10108371728 & -266.201083717282 \tabularnewline
63 & 6566.4 & 6235.50100471055 & 330.898995289446 \tabularnewline
64 & 10926.6 & 12043.7075713241 & -1117.1075713241 \tabularnewline
65 & 5963.5 & 5309.90982315138 & 653.590176848616 \tabularnewline
66 & 9914 & 8757.73740959941 & 1156.26259040059 \tabularnewline
67 & 6063.1 & 7115.21898720791 & -1052.11898720791 \tabularnewline
68 & 6939 & 6649.45927854907 & 289.540721450931 \tabularnewline
69 & 9774.2 & 9480.52637346717 & 293.673626532835 \tabularnewline
70 & 6358.2 & 6873.17632163455 & -514.976321634546 \tabularnewline
71 & 6432 & 6316.3646049952 & 115.6353950048 \tabularnewline
72 & 9365.5 & 8962.0995951144 & 403.400404885602 \tabularnewline
73 & 8930.6 & 8909.27520254388 & 21.3247974561218 \tabularnewline
74 & 6189.7 & 6688.61420938282 & -498.914209382816 \tabularnewline
75 & 6820.5 & 7002.28461447603 & -181.78461447603 \tabularnewline
76 & 12889.2 & 11831.9509375092 & 1057.24906249078 \tabularnewline
77 & 7102.5 & 6406.95937273495 & 695.540627265052 \tabularnewline
78 & 10824.9 & 10191.2623654024 & 633.637634597628 \tabularnewline
79 & 6619.1 & 7081.69687246564 & -462.596872465642 \tabularnewline
80 & 7613.6 & 7536.10308226632 & 77.4969177336798 \tabularnewline
81 & 9923.3 & 10361.3675471568 & -438.06754715685 \tabularnewline
82 & 6842.6 & 7180.9614699063 & -338.361469906304 \tabularnewline
83 & 7121.3 & 7050.48182002179 & 70.8181799782124 \tabularnewline
84 & 8913 & 9884.12283880958 & -971.122838809579 \tabularnewline
85 & 9952.4 & 9486.11352438244 & 466.286475617557 \tabularnewline
86 & 6514.1 & 6958.62792014228 & -444.527920142282 \tabularnewline
87 & 6480.5 & 7482.85212970324 & -1002.35212970324 \tabularnewline
88 & 13960.4 & 13058.3966508939 & 902.003349106073 \tabularnewline
89 & 6918.6 & 7384.39738703336 & -465.79738703336 \tabularnewline
90 & 11060.1 & 11040.215228719 & 19.8847712809893 \tabularnewline
91 & 7232.9 & 7165.53472328335 & 67.3652767166495 \tabularnewline
92 & 7846.2 & 8000.0217698336 & -153.821769833598 \tabularnewline
93 & 10293.9 & 10465.3503472219 & -171.450347221929 \tabularnewline
94 & 7698.6 & 7360.58575482288 & 338.014245177123 \tabularnewline
95 & 7050.7 & 7537.97819431189 & -487.278194311893 \tabularnewline
96 & 10190 & 9648.27135915135 & 541.728640848645 \tabularnewline
97 & 10071.3 & 10288.3058657223 & -217.005865722342 \tabularnewline
98 & 6765.7 & 7117.16920601769 & -351.469206017692 \tabularnewline
99 & 6480.5 & 7281.51929057371 & -801.019290573706 \tabularnewline
100 & 14038 & 14105.9916161724 & -67.9916161724432 \tabularnewline
101 & 6356 & 7468.77868846199 & -1112.77868846199 \tabularnewline
102 & 10338.9 & 11386.202501132 & -1047.302501132 \tabularnewline
103 & 7859.3 & 7455.0033713273 & 404.296628672703 \tabularnewline
104 & 7642.6 & 8157.21494333045 & -514.614943330451 \tabularnewline
105 & 10935 & 10572.7132714926 & 362.28672850745 \tabularnewline
106 & 7806.5 & 7824.96342617396 & -18.4634261739584 \tabularnewline
107 & 7309.5 & 7428.48981759667 & -118.989817596674 \tabularnewline
108 & 10363.6 & 10222.063864074 & 141.536135925997 \tabularnewline
109 & 10403.1 & 10328.3371399998 & 74.7628600001935 \tabularnewline
110 & 6274.7 & 7078.45026846123 & -803.750268461228 \tabularnewline
111 & 7212.7 & 6905.78784338741 & 306.912156612586 \tabularnewline
112 & 13835.1 & 14274.6434454677 & -439.543445467667 \tabularnewline
113 & 6218.4 & 6921.9105285668 & -703.510528566804 \tabularnewline
114 & 12087.8 & 10901.3628839484 & 1186.43711605156 \tabularnewline
115 & 7905 & 8068.56058291303 & -163.560582913025 \tabularnewline
116 & 7810.1 & 8131.34069807533 & -321.240698075329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300774&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]6254.4[/C][C]5967.03253205128[/C][C]287.367467948718[/C][/ROW]
[ROW][C]14[/C][C]4788.6[/C][C]4515.20539435962[/C][C]273.394605640385[/C][/ROW]
[ROW][C]15[/C][C]4446.4[/C][C]4202.07413760418[/C][C]244.325862395822[/C][/ROW]
[ROW][C]16[/C][C]8018[/C][C]7795.1202804004[/C][C]222.879719599602[/C][/ROW]
[ROW][C]17[/C][C]3745.9[/C][C]3540.36276501084[/C][C]205.537234989163[/C][/ROW]
[ROW][C]18[/C][C]6928.2[/C][C]6750.97490219252[/C][C]177.225097807477[/C][/ROW]
[ROW][C]19[/C][C]5201.7[/C][C]4831.40708249308[/C][C]370.292917506915[/C][/ROW]
[ROW][C]20[/C][C]5520.9[/C][C]5428.19626188661[/C][C]92.7037381133878[/C][/ROW]
[ROW][C]21[/C][C]6801.9[/C][C]6836.83895837119[/C][C]-34.9389583711882[/C][/ROW]
[ROW][C]22[/C][C]5225.1[/C][C]4988.95914298975[/C][C]236.14085701025[/C][/ROW]
[ROW][C]23[/C][C]5149.4[/C][C]5093.5893628177[/C][C]55.8106371822969[/C][/ROW]
[ROW][C]24[/C][C]6240.4[/C][C]6312.58476837414[/C][C]-72.1847683741435[/C][/ROW]
[ROW][C]25[/C][C]7045.4[/C][C]6956.61984902222[/C][C]88.7801509777764[/C][/ROW]
[ROW][C]26[/C][C]5402.1[/C][C]5488.99573619254[/C][C]-86.8957361925422[/C][/ROW]
[ROW][C]27[/C][C]4960.6[/C][C]5137.64097172067[/C][C]-177.040971720668[/C][/ROW]
[ROW][C]28[/C][C]9459.3[/C][C]8691.56683253854[/C][C]767.733167461462[/C][/ROW]
[ROW][C]29[/C][C]3979.4[/C][C]4469.5971162783[/C][C]-490.197116278304[/C][/ROW]
[ROW][C]30[/C][C]7215.1[/C][C]7616.97892223132[/C][C]-401.878922231317[/C][/ROW]
[ROW][C]31[/C][C]5797[/C][C]5783.98563099895[/C][C]13.0143690010473[/C][/ROW]
[ROW][C]32[/C][C]5577.6[/C][C]6175.46237586694[/C][C]-597.862375866945[/C][/ROW]
[ROW][C]33[/C][C]7380.8[/C][C]7450.46364724483[/C][C]-69.6636472448272[/C][/ROW]
[ROW][C]34[/C][C]5788.6[/C][C]5773.58311636852[/C][C]15.016883631477[/C][/ROW]
[ROW][C]35[/C][C]5116.3[/C][C]5741.9795123056[/C][C]-625.679512305604[/C][/ROW]
[ROW][C]36[/C][C]6819.3[/C][C]6824.16204402681[/C][C]-4.86204402681142[/C][/ROW]
[ROW][C]37[/C][C]7671[/C][C]7571.52706657677[/C][C]99.4729334232261[/C][/ROW]
[ROW][C]38[/C][C]5337[/C][C]5984.50819831013[/C][C]-647.508198310133[/C][/ROW]
[ROW][C]39[/C][C]4955.7[/C][C]5527.50736727545[/C][C]-571.807367275448[/C][/ROW]
[ROW][C]40[/C][C]9143.8[/C][C]9658.54657544652[/C][C]-514.746575446525[/C][/ROW]
[ROW][C]41[/C][C]4624.6[/C][C]4515.25543647459[/C][C]109.344563525407[/C][/ROW]
[ROW][C]42[/C][C]7702.4[/C][C]7749.5351886035[/C][C]-47.1351886034954[/C][/ROW]
[ROW][C]43[/C][C]6297.4[/C][C]6200.06170648745[/C][C]97.3382935125492[/C][/ROW]
[ROW][C]44[/C][C]5652.3[/C][C]6189.79377576247[/C][C]-537.493775762466[/C][/ROW]
[ROW][C]45[/C][C]7801.3[/C][C]7802.05663494423[/C][C]-0.756634944226789[/C][/ROW]
[ROW][C]46[/C][C]5901.2[/C][C]6174.99059598699[/C][C]-273.790595986989[/C][/ROW]
[ROW][C]47[/C][C]5296.7[/C][C]5695.71331627826[/C][C]-399.013316278261[/C][/ROW]
[ROW][C]48[/C][C]7803.5[/C][C]7186.94847165037[/C][C]616.551528349625[/C][/ROW]
[ROW][C]49[/C][C]8177.1[/C][C]8037.44167641151[/C][C]139.658323588494[/C][/ROW]
[ROW][C]50[/C][C]5546.3[/C][C]5959.91495991688[/C][C]-413.614959916877[/C][/ROW]
[ROW][C]51[/C][C]5651.5[/C][C]5561.5366225608[/C][C]89.9633774391959[/C][/ROW]
[ROW][C]52[/C][C]12289.7[/C][C]9771.34671682786[/C][C]2518.35328317214[/C][/ROW]
[ROW][C]53[/C][C]4769.1[/C][C]5251.81427600648[/C][C]-482.714276006477[/C][/ROW]
[ROW][C]54[/C][C]8294.5[/C][C]8348.20486635645[/C][C]-53.704866356451[/C][/ROW]
[ROW][C]55[/C][C]6422.3[/C][C]6897.14629359618[/C][C]-474.846293596182[/C][/ROW]
[ROW][C]56[/C][C]6021.3[/C][C]6437.21777583266[/C][C]-415.917775832656[/C][/ROW]
[ROW][C]57[/C][C]9241[/C][C]8410.07141577058[/C][C]830.928584229421[/C][/ROW]
[ROW][C]58[/C][C]6229.5[/C][C]6669.74611385494[/C][C]-440.24611385494[/C][/ROW]
[ROW][C]59[/C][C]5691.5[/C][C]6103.27538809238[/C][C]-411.775388092381[/C][/ROW]
[ROW][C]60[/C][C]8546.9[/C][C]8259.50618334198[/C][C]287.393816658021[/C][/ROW]
[ROW][C]61[/C][C]8174[/C][C]8781.59400313743[/C][C]-607.59400313743[/C][/ROW]
[ROW][C]62[/C][C]6027.9[/C][C]6294.10108371728[/C][C]-266.201083717282[/C][/ROW]
[ROW][C]63[/C][C]6566.4[/C][C]6235.50100471055[/C][C]330.898995289446[/C][/ROW]
[ROW][C]64[/C][C]10926.6[/C][C]12043.7075713241[/C][C]-1117.1075713241[/C][/ROW]
[ROW][C]65[/C][C]5963.5[/C][C]5309.90982315138[/C][C]653.590176848616[/C][/ROW]
[ROW][C]66[/C][C]9914[/C][C]8757.73740959941[/C][C]1156.26259040059[/C][/ROW]
[ROW][C]67[/C][C]6063.1[/C][C]7115.21898720791[/C][C]-1052.11898720791[/C][/ROW]
[ROW][C]68[/C][C]6939[/C][C]6649.45927854907[/C][C]289.540721450931[/C][/ROW]
[ROW][C]69[/C][C]9774.2[/C][C]9480.52637346717[/C][C]293.673626532835[/C][/ROW]
[ROW][C]70[/C][C]6358.2[/C][C]6873.17632163455[/C][C]-514.976321634546[/C][/ROW]
[ROW][C]71[/C][C]6432[/C][C]6316.3646049952[/C][C]115.6353950048[/C][/ROW]
[ROW][C]72[/C][C]9365.5[/C][C]8962.0995951144[/C][C]403.400404885602[/C][/ROW]
[ROW][C]73[/C][C]8930.6[/C][C]8909.27520254388[/C][C]21.3247974561218[/C][/ROW]
[ROW][C]74[/C][C]6189.7[/C][C]6688.61420938282[/C][C]-498.914209382816[/C][/ROW]
[ROW][C]75[/C][C]6820.5[/C][C]7002.28461447603[/C][C]-181.78461447603[/C][/ROW]
[ROW][C]76[/C][C]12889.2[/C][C]11831.9509375092[/C][C]1057.24906249078[/C][/ROW]
[ROW][C]77[/C][C]7102.5[/C][C]6406.95937273495[/C][C]695.540627265052[/C][/ROW]
[ROW][C]78[/C][C]10824.9[/C][C]10191.2623654024[/C][C]633.637634597628[/C][/ROW]
[ROW][C]79[/C][C]6619.1[/C][C]7081.69687246564[/C][C]-462.596872465642[/C][/ROW]
[ROW][C]80[/C][C]7613.6[/C][C]7536.10308226632[/C][C]77.4969177336798[/C][/ROW]
[ROW][C]81[/C][C]9923.3[/C][C]10361.3675471568[/C][C]-438.06754715685[/C][/ROW]
[ROW][C]82[/C][C]6842.6[/C][C]7180.9614699063[/C][C]-338.361469906304[/C][/ROW]
[ROW][C]83[/C][C]7121.3[/C][C]7050.48182002179[/C][C]70.8181799782124[/C][/ROW]
[ROW][C]84[/C][C]8913[/C][C]9884.12283880958[/C][C]-971.122838809579[/C][/ROW]
[ROW][C]85[/C][C]9952.4[/C][C]9486.11352438244[/C][C]466.286475617557[/C][/ROW]
[ROW][C]86[/C][C]6514.1[/C][C]6958.62792014228[/C][C]-444.527920142282[/C][/ROW]
[ROW][C]87[/C][C]6480.5[/C][C]7482.85212970324[/C][C]-1002.35212970324[/C][/ROW]
[ROW][C]88[/C][C]13960.4[/C][C]13058.3966508939[/C][C]902.003349106073[/C][/ROW]
[ROW][C]89[/C][C]6918.6[/C][C]7384.39738703336[/C][C]-465.79738703336[/C][/ROW]
[ROW][C]90[/C][C]11060.1[/C][C]11040.215228719[/C][C]19.8847712809893[/C][/ROW]
[ROW][C]91[/C][C]7232.9[/C][C]7165.53472328335[/C][C]67.3652767166495[/C][/ROW]
[ROW][C]92[/C][C]7846.2[/C][C]8000.0217698336[/C][C]-153.821769833598[/C][/ROW]
[ROW][C]93[/C][C]10293.9[/C][C]10465.3503472219[/C][C]-171.450347221929[/C][/ROW]
[ROW][C]94[/C][C]7698.6[/C][C]7360.58575482288[/C][C]338.014245177123[/C][/ROW]
[ROW][C]95[/C][C]7050.7[/C][C]7537.97819431189[/C][C]-487.278194311893[/C][/ROW]
[ROW][C]96[/C][C]10190[/C][C]9648.27135915135[/C][C]541.728640848645[/C][/ROW]
[ROW][C]97[/C][C]10071.3[/C][C]10288.3058657223[/C][C]-217.005865722342[/C][/ROW]
[ROW][C]98[/C][C]6765.7[/C][C]7117.16920601769[/C][C]-351.469206017692[/C][/ROW]
[ROW][C]99[/C][C]6480.5[/C][C]7281.51929057371[/C][C]-801.019290573706[/C][/ROW]
[ROW][C]100[/C][C]14038[/C][C]14105.9916161724[/C][C]-67.9916161724432[/C][/ROW]
[ROW][C]101[/C][C]6356[/C][C]7468.77868846199[/C][C]-1112.77868846199[/C][/ROW]
[ROW][C]102[/C][C]10338.9[/C][C]11386.202501132[/C][C]-1047.302501132[/C][/ROW]
[ROW][C]103[/C][C]7859.3[/C][C]7455.0033713273[/C][C]404.296628672703[/C][/ROW]
[ROW][C]104[/C][C]7642.6[/C][C]8157.21494333045[/C][C]-514.614943330451[/C][/ROW]
[ROW][C]105[/C][C]10935[/C][C]10572.7132714926[/C][C]362.28672850745[/C][/ROW]
[ROW][C]106[/C][C]7806.5[/C][C]7824.96342617396[/C][C]-18.4634261739584[/C][/ROW]
[ROW][C]107[/C][C]7309.5[/C][C]7428.48981759667[/C][C]-118.989817596674[/C][/ROW]
[ROW][C]108[/C][C]10363.6[/C][C]10222.063864074[/C][C]141.536135925997[/C][/ROW]
[ROW][C]109[/C][C]10403.1[/C][C]10328.3371399998[/C][C]74.7628600001935[/C][/ROW]
[ROW][C]110[/C][C]6274.7[/C][C]7078.45026846123[/C][C]-803.750268461228[/C][/ROW]
[ROW][C]111[/C][C]7212.7[/C][C]6905.78784338741[/C][C]306.912156612586[/C][/ROW]
[ROW][C]112[/C][C]13835.1[/C][C]14274.6434454677[/C][C]-439.543445467667[/C][/ROW]
[ROW][C]113[/C][C]6218.4[/C][C]6921.9105285668[/C][C]-703.510528566804[/C][/ROW]
[ROW][C]114[/C][C]12087.8[/C][C]10901.3628839484[/C][C]1186.43711605156[/C][/ROW]
[ROW][C]115[/C][C]7905[/C][C]8068.56058291303[/C][C]-163.560582913025[/C][/ROW]
[ROW][C]116[/C][C]7810.1[/C][C]8131.34069807533[/C][C]-321.240698075329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300774&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300774&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
136254.45967.03253205128287.367467948718
144788.64515.20539435962273.394605640385
154446.44202.07413760418244.325862395822
1680187795.1202804004222.879719599602
173745.93540.36276501084205.537234989163
186928.26750.97490219252177.225097807477
195201.74831.40708249308370.292917506915
205520.95428.1962618866192.7037381133878
216801.96836.83895837119-34.9389583711882
225225.14988.95914298975236.14085701025
235149.45093.589362817755.8106371822969
246240.46312.58476837414-72.1847683741435
257045.46956.6198490222288.7801509777764
265402.15488.99573619254-86.8957361925422
274960.65137.64097172067-177.040971720668
289459.38691.56683253854767.733167461462
293979.44469.5971162783-490.197116278304
307215.17616.97892223132-401.878922231317
3157975783.9856309989513.0143690010473
325577.66175.46237586694-597.862375866945
337380.87450.46364724483-69.6636472448272
345788.65773.5831163685215.016883631477
355116.35741.9795123056-625.679512305604
366819.36824.16204402681-4.86204402681142
3776717571.5270665767799.4729334232261
3853375984.50819831013-647.508198310133
394955.75527.50736727545-571.807367275448
409143.89658.54657544652-514.746575446525
414624.64515.25543647459109.344563525407
427702.47749.5351886035-47.1351886034954
436297.46200.0617064874597.3382935125492
445652.36189.79377576247-537.493775762466
457801.37802.05663494423-0.756634944226789
465901.26174.99059598699-273.790595986989
475296.75695.71331627826-399.013316278261
487803.57186.94847165037616.551528349625
498177.18037.44167641151139.658323588494
505546.35959.91495991688-413.614959916877
515651.55561.536622560889.9633774391959
5212289.79771.346716827862518.35328317214
534769.15251.81427600648-482.714276006477
548294.58348.20486635645-53.704866356451
556422.36897.14629359618-474.846293596182
566021.36437.21777583266-415.917775832656
5792418410.07141577058830.928584229421
586229.56669.74611385494-440.24611385494
595691.56103.27538809238-411.775388092381
608546.98259.50618334198287.393816658021
6181748781.59400313743-607.59400313743
626027.96294.10108371728-266.201083717282
636566.46235.50100471055330.898995289446
6410926.612043.7075713241-1117.1075713241
655963.55309.90982315138653.590176848616
6699148757.737409599411156.26259040059
676063.17115.21898720791-1052.11898720791
6869396649.45927854907289.540721450931
699774.29480.52637346717293.673626532835
706358.26873.17632163455-514.976321634546
7164326316.3646049952115.6353950048
729365.58962.0995951144403.400404885602
738930.68909.2752025438821.3247974561218
746189.76688.61420938282-498.914209382816
756820.57002.28461447603-181.78461447603
7612889.211831.95093750921057.24906249078
777102.56406.95937273495695.540627265052
7810824.910191.2623654024633.637634597628
796619.17081.69687246564-462.596872465642
807613.67536.1030822663277.4969177336798
819923.310361.3675471568-438.06754715685
826842.67180.9614699063-338.361469906304
837121.37050.4818200217970.8181799782124
8489139884.12283880958-971.122838809579
859952.49486.11352438244466.286475617557
866514.16958.62792014228-444.527920142282
876480.57482.85212970324-1002.35212970324
8813960.413058.3966508939902.003349106073
896918.67384.39738703336-465.79738703336
9011060.111040.21522871919.8847712809893
917232.97165.5347232833567.3652767166495
927846.28000.0217698336-153.821769833598
9310293.910465.3503472219-171.450347221929
947698.67360.58575482288338.014245177123
957050.77537.97819431189-487.278194311893
96101909648.27135915135541.728640848645
9710071.310288.3058657223-217.005865722342
986765.77117.16920601769-351.469206017692
996480.57281.51929057371-801.019290573706
1001403814105.9916161724-67.9916161724432
10163567468.77868846199-1112.77868846199
10210338.911386.202501132-1047.302501132
1037859.37455.0033713273404.296628672703
1047642.68157.21494333045-514.614943330451
1051093510572.7132714926362.28672850745
1067806.57824.96342617396-18.4634261739584
1077309.57428.48981759667-118.989817596674
10810363.610222.063864074141.536135925997
10910403.110328.337139999874.7628600001935
1106274.77078.45026846123-803.750268461228
1117212.76905.78784338741306.912156612586
11213835.114274.6434454677-439.543445467667
1136218.46921.9105285668-703.510528566804
11412087.810901.36288394841186.43711605156
11579058068.56058291303-163.560582913025
1167810.18131.34069807533-321.240698075329







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
11711128.404423054210049.571415076112207.2374310323
1188104.693681070847022.964467050139186.42289509155
1197640.951989706966556.026620886328725.8773585276
12010609.39671286579520.9623448323611697.831080899
12110659.13489719759566.8662171736611751.4035772213
1226829.408447504915732.968131060857925.84876394898
1237434.075125890026333.114321826648535.03592995339
12414294.690256474913188.849098297415400.5314146524
1256800.91520762675689.823349718787912.00706553462
12612060.480442310410943.757618628513177.2032659924
1278265.810267638087143.066870477849388.55366479832
1288236.237288071197107.07496422579365.39961191668

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 11128.4044230542 & 10049.5714150761 & 12207.2374310323 \tabularnewline
118 & 8104.69368107084 & 7022.96446705013 & 9186.42289509155 \tabularnewline
119 & 7640.95198970696 & 6556.02662088632 & 8725.8773585276 \tabularnewline
120 & 10609.3967128657 & 9520.96234483236 & 11697.831080899 \tabularnewline
121 & 10659.1348971975 & 9566.86621717366 & 11751.4035772213 \tabularnewline
122 & 6829.40844750491 & 5732.96813106085 & 7925.84876394898 \tabularnewline
123 & 7434.07512589002 & 6333.11432182664 & 8535.03592995339 \tabularnewline
124 & 14294.6902564749 & 13188.8490982974 & 15400.5314146524 \tabularnewline
125 & 6800.9152076267 & 5689.82334971878 & 7912.00706553462 \tabularnewline
126 & 12060.4804423104 & 10943.7576186285 & 13177.2032659924 \tabularnewline
127 & 8265.81026763808 & 7143.06687047784 & 9388.55366479832 \tabularnewline
128 & 8236.23728807119 & 7107.0749642257 & 9365.39961191668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300774&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]117[/C][C]11128.4044230542[/C][C]10049.5714150761[/C][C]12207.2374310323[/C][/ROW]
[ROW][C]118[/C][C]8104.69368107084[/C][C]7022.96446705013[/C][C]9186.42289509155[/C][/ROW]
[ROW][C]119[/C][C]7640.95198970696[/C][C]6556.02662088632[/C][C]8725.8773585276[/C][/ROW]
[ROW][C]120[/C][C]10609.3967128657[/C][C]9520.96234483236[/C][C]11697.831080899[/C][/ROW]
[ROW][C]121[/C][C]10659.1348971975[/C][C]9566.86621717366[/C][C]11751.4035772213[/C][/ROW]
[ROW][C]122[/C][C]6829.40844750491[/C][C]5732.96813106085[/C][C]7925.84876394898[/C][/ROW]
[ROW][C]123[/C][C]7434.07512589002[/C][C]6333.11432182664[/C][C]8535.03592995339[/C][/ROW]
[ROW][C]124[/C][C]14294.6902564749[/C][C]13188.8490982974[/C][C]15400.5314146524[/C][/ROW]
[ROW][C]125[/C][C]6800.9152076267[/C][C]5689.82334971878[/C][C]7912.00706553462[/C][/ROW]
[ROW][C]126[/C][C]12060.4804423104[/C][C]10943.7576186285[/C][C]13177.2032659924[/C][/ROW]
[ROW][C]127[/C][C]8265.81026763808[/C][C]7143.06687047784[/C][C]9388.55366479832[/C][/ROW]
[ROW][C]128[/C][C]8236.23728807119[/C][C]7107.0749642257[/C][C]9365.39961191668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300774&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300774&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
11711128.404423054210049.571415076112207.2374310323
1188104.693681070847022.964467050139186.42289509155
1197640.951989706966556.026620886328725.8773585276
12010609.39671286579520.9623448323611697.831080899
12110659.13489719759566.8662171736611751.4035772213
1226829.408447504915732.968131060857925.84876394898
1237434.075125890026333.114321826648535.03592995339
12414294.690256474913188.849098297415400.5314146524
1256800.91520762675689.823349718787912.00706553462
12612060.480442310410943.757618628513177.2032659924
1278265.810267638087143.066870477849388.55366479832
1288236.237288071197107.07496422579365.39961191668



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')