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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 computationMon, 19 Dec 2016 19:11:45 +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/19/t1482171177s72qsgjtius13h7.htm/, Retrieved Fri, 17 May 2024 16:24:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301436, Retrieved Fri, 17 May 2024 16:24:43 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-19 18:11:45] [9412b5b3b31fe4708efb1e5c8c74b28f] [Current]
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Dataseries X:
40548
40331
39814
39360
38915
38583
38191
37477
37110
36670
36330
36108
35341
34764
34253
33743
33296
32875
32622
32346
31780
31003
28467
28153
27682
27217
26780
26490
26020
25227
25343
24453
23958
23475
23102
22393
21557
20893
20376
19704
19016
18274
18020
17317
16919
16372
16069
15478
15018
14561
14047
13506
13035
12471
11815
11172
10594
9914
9319
8939
8073
7431
7022




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=301436&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=301436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301436&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
alpha0.999948928927805
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999948928927805 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301436&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]0.999948928927805[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301436&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
alpha0.999948928927805
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24033140548-217
33981440331.0110824227-517.011082422665
43936039814.0264043103-454.026404310316
53891539360.0231876153-445.023187615276
63858338915.0227278113-332.022727811345
73819138583.0169567567-392.016956756699
83747738191.0200207263-714.020020726304
93711037477.036465768-367.036465768026
103667037110.0187449458-440.018744945846
113633036670.0224722291-340.022472229088
123610836330.0173653122-222.017365312233
133534136108.0113386649-767.011338664888
143476435341.0391720914-577.039172091449
153425334764.0294700092-511.02947000922
163374334253.026098823-510.026098822957
173329633743.0260475797-447.026047579719
183287533296.0228300995-421.022830099544
193262232875.0215020874-253.021502087351
203234632622.0129220794-276.012922079401
213178032346.0140962759-566.014096275871
223100331780.0289069468-777.028906946773
232846731003.0396836994-2536.0396836994
242815328467.1295182658-314.129518265778
252768228153.0160429313-471.016042931307
262721727682.0240552943-465.024055294332
272678027217.0237492771-437.023749277101
282649026780.0223192715-290.022319271451
292602026490.0148117508-470.014811750803
302522726020.0240041604-793.024004160387
312534325227.0405005862115.959499413832
322445325342.994077824-889.994077824034
332395824453.0454529518-495.045452951803
342347523958.0252825021-483.025282502069
352310223475.0246686191-373.024668619077
362239323102.0190507698-709.019050769781
372155722393.0362103631-836.036210363127
382089321557.0426972657-664.042697265657
392037620893.0339133725-517.033913372532
401970420376.0264054763-672.026405476317
411901619704.0343211091-688.034321109069
421827419016.0351386505-742.035138650484
431802018274.0378965301-254.037896530139
441731718020.0129739878-703.012973987752
451691917317.0359036264-398.035903626351
461637216919.0203281204-547.020328120372
471606916372.0279369147-303.027936914668
481547816069.0154759616-591.015475961643
491501815478.030183794-460.030183794042
501456115018.0234942347-457.023494234729
511404714561.0233406799-514.023340679869
521350614047.0262517231-541.026251723142
531303513506.0276307908-471.027630790761
541247113035.0240558861-564.024055886137
551181512471.0288053133-656.028805313279
561117211815.0335040945-643.033504094477
571059411172.0328404105-578.032840410511
58991410594.0295207569-680.029520756923
5993199914.03472983675-595.034729836749
6089399319.03038906165-380.030389061645
6180738939.01940855944-866.019408559436
6274318073.04422853974-642.044228539737
6370227431.03278988715-409.032789887148

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 40331 & 40548 & -217 \tabularnewline
3 & 39814 & 40331.0110824227 & -517.011082422665 \tabularnewline
4 & 39360 & 39814.0264043103 & -454.026404310316 \tabularnewline
5 & 38915 & 39360.0231876153 & -445.023187615276 \tabularnewline
6 & 38583 & 38915.0227278113 & -332.022727811345 \tabularnewline
7 & 38191 & 38583.0169567567 & -392.016956756699 \tabularnewline
8 & 37477 & 38191.0200207263 & -714.020020726304 \tabularnewline
9 & 37110 & 37477.036465768 & -367.036465768026 \tabularnewline
10 & 36670 & 37110.0187449458 & -440.018744945846 \tabularnewline
11 & 36330 & 36670.0224722291 & -340.022472229088 \tabularnewline
12 & 36108 & 36330.0173653122 & -222.017365312233 \tabularnewline
13 & 35341 & 36108.0113386649 & -767.011338664888 \tabularnewline
14 & 34764 & 35341.0391720914 & -577.039172091449 \tabularnewline
15 & 34253 & 34764.0294700092 & -511.02947000922 \tabularnewline
16 & 33743 & 34253.026098823 & -510.026098822957 \tabularnewline
17 & 33296 & 33743.0260475797 & -447.026047579719 \tabularnewline
18 & 32875 & 33296.0228300995 & -421.022830099544 \tabularnewline
19 & 32622 & 32875.0215020874 & -253.021502087351 \tabularnewline
20 & 32346 & 32622.0129220794 & -276.012922079401 \tabularnewline
21 & 31780 & 32346.0140962759 & -566.014096275871 \tabularnewline
22 & 31003 & 31780.0289069468 & -777.028906946773 \tabularnewline
23 & 28467 & 31003.0396836994 & -2536.0396836994 \tabularnewline
24 & 28153 & 28467.1295182658 & -314.129518265778 \tabularnewline
25 & 27682 & 28153.0160429313 & -471.016042931307 \tabularnewline
26 & 27217 & 27682.0240552943 & -465.024055294332 \tabularnewline
27 & 26780 & 27217.0237492771 & -437.023749277101 \tabularnewline
28 & 26490 & 26780.0223192715 & -290.022319271451 \tabularnewline
29 & 26020 & 26490.0148117508 & -470.014811750803 \tabularnewline
30 & 25227 & 26020.0240041604 & -793.024004160387 \tabularnewline
31 & 25343 & 25227.0405005862 & 115.959499413832 \tabularnewline
32 & 24453 & 25342.994077824 & -889.994077824034 \tabularnewline
33 & 23958 & 24453.0454529518 & -495.045452951803 \tabularnewline
34 & 23475 & 23958.0252825021 & -483.025282502069 \tabularnewline
35 & 23102 & 23475.0246686191 & -373.024668619077 \tabularnewline
36 & 22393 & 23102.0190507698 & -709.019050769781 \tabularnewline
37 & 21557 & 22393.0362103631 & -836.036210363127 \tabularnewline
38 & 20893 & 21557.0426972657 & -664.042697265657 \tabularnewline
39 & 20376 & 20893.0339133725 & -517.033913372532 \tabularnewline
40 & 19704 & 20376.0264054763 & -672.026405476317 \tabularnewline
41 & 19016 & 19704.0343211091 & -688.034321109069 \tabularnewline
42 & 18274 & 19016.0351386505 & -742.035138650484 \tabularnewline
43 & 18020 & 18274.0378965301 & -254.037896530139 \tabularnewline
44 & 17317 & 18020.0129739878 & -703.012973987752 \tabularnewline
45 & 16919 & 17317.0359036264 & -398.035903626351 \tabularnewline
46 & 16372 & 16919.0203281204 & -547.020328120372 \tabularnewline
47 & 16069 & 16372.0279369147 & -303.027936914668 \tabularnewline
48 & 15478 & 16069.0154759616 & -591.015475961643 \tabularnewline
49 & 15018 & 15478.030183794 & -460.030183794042 \tabularnewline
50 & 14561 & 15018.0234942347 & -457.023494234729 \tabularnewline
51 & 14047 & 14561.0233406799 & -514.023340679869 \tabularnewline
52 & 13506 & 14047.0262517231 & -541.026251723142 \tabularnewline
53 & 13035 & 13506.0276307908 & -471.027630790761 \tabularnewline
54 & 12471 & 13035.0240558861 & -564.024055886137 \tabularnewline
55 & 11815 & 12471.0288053133 & -656.028805313279 \tabularnewline
56 & 11172 & 11815.0335040945 & -643.033504094477 \tabularnewline
57 & 10594 & 11172.0328404105 & -578.032840410511 \tabularnewline
58 & 9914 & 10594.0295207569 & -680.029520756923 \tabularnewline
59 & 9319 & 9914.03472983675 & -595.034729836749 \tabularnewline
60 & 8939 & 9319.03038906165 & -380.030389061645 \tabularnewline
61 & 8073 & 8939.01940855944 & -866.019408559436 \tabularnewline
62 & 7431 & 8073.04422853974 & -642.044228539737 \tabularnewline
63 & 7022 & 7431.03278988715 & -409.032789887148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301436&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]40331[/C][C]40548[/C][C]-217[/C][/ROW]
[ROW][C]3[/C][C]39814[/C][C]40331.0110824227[/C][C]-517.011082422665[/C][/ROW]
[ROW][C]4[/C][C]39360[/C][C]39814.0264043103[/C][C]-454.026404310316[/C][/ROW]
[ROW][C]5[/C][C]38915[/C][C]39360.0231876153[/C][C]-445.023187615276[/C][/ROW]
[ROW][C]6[/C][C]38583[/C][C]38915.0227278113[/C][C]-332.022727811345[/C][/ROW]
[ROW][C]7[/C][C]38191[/C][C]38583.0169567567[/C][C]-392.016956756699[/C][/ROW]
[ROW][C]8[/C][C]37477[/C][C]38191.0200207263[/C][C]-714.020020726304[/C][/ROW]
[ROW][C]9[/C][C]37110[/C][C]37477.036465768[/C][C]-367.036465768026[/C][/ROW]
[ROW][C]10[/C][C]36670[/C][C]37110.0187449458[/C][C]-440.018744945846[/C][/ROW]
[ROW][C]11[/C][C]36330[/C][C]36670.0224722291[/C][C]-340.022472229088[/C][/ROW]
[ROW][C]12[/C][C]36108[/C][C]36330.0173653122[/C][C]-222.017365312233[/C][/ROW]
[ROW][C]13[/C][C]35341[/C][C]36108.0113386649[/C][C]-767.011338664888[/C][/ROW]
[ROW][C]14[/C][C]34764[/C][C]35341.0391720914[/C][C]-577.039172091449[/C][/ROW]
[ROW][C]15[/C][C]34253[/C][C]34764.0294700092[/C][C]-511.02947000922[/C][/ROW]
[ROW][C]16[/C][C]33743[/C][C]34253.026098823[/C][C]-510.026098822957[/C][/ROW]
[ROW][C]17[/C][C]33296[/C][C]33743.0260475797[/C][C]-447.026047579719[/C][/ROW]
[ROW][C]18[/C][C]32875[/C][C]33296.0228300995[/C][C]-421.022830099544[/C][/ROW]
[ROW][C]19[/C][C]32622[/C][C]32875.0215020874[/C][C]-253.021502087351[/C][/ROW]
[ROW][C]20[/C][C]32346[/C][C]32622.0129220794[/C][C]-276.012922079401[/C][/ROW]
[ROW][C]21[/C][C]31780[/C][C]32346.0140962759[/C][C]-566.014096275871[/C][/ROW]
[ROW][C]22[/C][C]31003[/C][C]31780.0289069468[/C][C]-777.028906946773[/C][/ROW]
[ROW][C]23[/C][C]28467[/C][C]31003.0396836994[/C][C]-2536.0396836994[/C][/ROW]
[ROW][C]24[/C][C]28153[/C][C]28467.1295182658[/C][C]-314.129518265778[/C][/ROW]
[ROW][C]25[/C][C]27682[/C][C]28153.0160429313[/C][C]-471.016042931307[/C][/ROW]
[ROW][C]26[/C][C]27217[/C][C]27682.0240552943[/C][C]-465.024055294332[/C][/ROW]
[ROW][C]27[/C][C]26780[/C][C]27217.0237492771[/C][C]-437.023749277101[/C][/ROW]
[ROW][C]28[/C][C]26490[/C][C]26780.0223192715[/C][C]-290.022319271451[/C][/ROW]
[ROW][C]29[/C][C]26020[/C][C]26490.0148117508[/C][C]-470.014811750803[/C][/ROW]
[ROW][C]30[/C][C]25227[/C][C]26020.0240041604[/C][C]-793.024004160387[/C][/ROW]
[ROW][C]31[/C][C]25343[/C][C]25227.0405005862[/C][C]115.959499413832[/C][/ROW]
[ROW][C]32[/C][C]24453[/C][C]25342.994077824[/C][C]-889.994077824034[/C][/ROW]
[ROW][C]33[/C][C]23958[/C][C]24453.0454529518[/C][C]-495.045452951803[/C][/ROW]
[ROW][C]34[/C][C]23475[/C][C]23958.0252825021[/C][C]-483.025282502069[/C][/ROW]
[ROW][C]35[/C][C]23102[/C][C]23475.0246686191[/C][C]-373.024668619077[/C][/ROW]
[ROW][C]36[/C][C]22393[/C][C]23102.0190507698[/C][C]-709.019050769781[/C][/ROW]
[ROW][C]37[/C][C]21557[/C][C]22393.0362103631[/C][C]-836.036210363127[/C][/ROW]
[ROW][C]38[/C][C]20893[/C][C]21557.0426972657[/C][C]-664.042697265657[/C][/ROW]
[ROW][C]39[/C][C]20376[/C][C]20893.0339133725[/C][C]-517.033913372532[/C][/ROW]
[ROW][C]40[/C][C]19704[/C][C]20376.0264054763[/C][C]-672.026405476317[/C][/ROW]
[ROW][C]41[/C][C]19016[/C][C]19704.0343211091[/C][C]-688.034321109069[/C][/ROW]
[ROW][C]42[/C][C]18274[/C][C]19016.0351386505[/C][C]-742.035138650484[/C][/ROW]
[ROW][C]43[/C][C]18020[/C][C]18274.0378965301[/C][C]-254.037896530139[/C][/ROW]
[ROW][C]44[/C][C]17317[/C][C]18020.0129739878[/C][C]-703.012973987752[/C][/ROW]
[ROW][C]45[/C][C]16919[/C][C]17317.0359036264[/C][C]-398.035903626351[/C][/ROW]
[ROW][C]46[/C][C]16372[/C][C]16919.0203281204[/C][C]-547.020328120372[/C][/ROW]
[ROW][C]47[/C][C]16069[/C][C]16372.0279369147[/C][C]-303.027936914668[/C][/ROW]
[ROW][C]48[/C][C]15478[/C][C]16069.0154759616[/C][C]-591.015475961643[/C][/ROW]
[ROW][C]49[/C][C]15018[/C][C]15478.030183794[/C][C]-460.030183794042[/C][/ROW]
[ROW][C]50[/C][C]14561[/C][C]15018.0234942347[/C][C]-457.023494234729[/C][/ROW]
[ROW][C]51[/C][C]14047[/C][C]14561.0233406799[/C][C]-514.023340679869[/C][/ROW]
[ROW][C]52[/C][C]13506[/C][C]14047.0262517231[/C][C]-541.026251723142[/C][/ROW]
[ROW][C]53[/C][C]13035[/C][C]13506.0276307908[/C][C]-471.027630790761[/C][/ROW]
[ROW][C]54[/C][C]12471[/C][C]13035.0240558861[/C][C]-564.024055886137[/C][/ROW]
[ROW][C]55[/C][C]11815[/C][C]12471.0288053133[/C][C]-656.028805313279[/C][/ROW]
[ROW][C]56[/C][C]11172[/C][C]11815.0335040945[/C][C]-643.033504094477[/C][/ROW]
[ROW][C]57[/C][C]10594[/C][C]11172.0328404105[/C][C]-578.032840410511[/C][/ROW]
[ROW][C]58[/C][C]9914[/C][C]10594.0295207569[/C][C]-680.029520756923[/C][/ROW]
[ROW][C]59[/C][C]9319[/C][C]9914.03472983675[/C][C]-595.034729836749[/C][/ROW]
[ROW][C]60[/C][C]8939[/C][C]9319.03038906165[/C][C]-380.030389061645[/C][/ROW]
[ROW][C]61[/C][C]8073[/C][C]8939.01940855944[/C][C]-866.019408559436[/C][/ROW]
[ROW][C]62[/C][C]7431[/C][C]8073.04422853974[/C][C]-642.044228539737[/C][/ROW]
[ROW][C]63[/C][C]7022[/C][C]7431.03278988715[/C][C]-409.032789887148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301436&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301436&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
24033140548-217
33981440331.0110824227-517.011082422665
43936039814.0264043103-454.026404310316
53891539360.0231876153-445.023187615276
63858338915.0227278113-332.022727811345
73819138583.0169567567-392.016956756699
83747738191.0200207263-714.020020726304
93711037477.036465768-367.036465768026
103667037110.0187449458-440.018744945846
113633036670.0224722291-340.022472229088
123610836330.0173653122-222.017365312233
133534136108.0113386649-767.011338664888
143476435341.0391720914-577.039172091449
153425334764.0294700092-511.02947000922
163374334253.026098823-510.026098822957
173329633743.0260475797-447.026047579719
183287533296.0228300995-421.022830099544
193262232875.0215020874-253.021502087351
203234632622.0129220794-276.012922079401
213178032346.0140962759-566.014096275871
223100331780.0289069468-777.028906946773
232846731003.0396836994-2536.0396836994
242815328467.1295182658-314.129518265778
252768228153.0160429313-471.016042931307
262721727682.0240552943-465.024055294332
272678027217.0237492771-437.023749277101
282649026780.0223192715-290.022319271451
292602026490.0148117508-470.014811750803
302522726020.0240041604-793.024004160387
312534325227.0405005862115.959499413832
322445325342.994077824-889.994077824034
332395824453.0454529518-495.045452951803
342347523958.0252825021-483.025282502069
352310223475.0246686191-373.024668619077
362239323102.0190507698-709.019050769781
372155722393.0362103631-836.036210363127
382089321557.0426972657-664.042697265657
392037620893.0339133725-517.033913372532
401970420376.0264054763-672.026405476317
411901619704.0343211091-688.034321109069
421827419016.0351386505-742.035138650484
431802018274.0378965301-254.037896530139
441731718020.0129739878-703.012973987752
451691917317.0359036264-398.035903626351
461637216919.0203281204-547.020328120372
471606916372.0279369147-303.027936914668
481547816069.0154759616-591.015475961643
491501815478.030183794-460.030183794042
501456115018.0234942347-457.023494234729
511404714561.0233406799-514.023340679869
521350614047.0262517231-541.026251723142
531303513506.0276307908-471.027630790761
541247113035.0240558861-564.024055886137
551181512471.0288053133-656.028805313279
561117211815.0335040945-643.033504094477
571059411172.0328404105-578.032840410511
58991410594.0295207569-680.029520756923
5993199914.03472983675-595.034729836749
6089399319.03038906165-380.030389061645
6180738939.01940855944-866.019408559436
6274318073.04422853974-642.044228539737
6370227431.03278988715-409.032789887148







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
647022.020889743146403.0375307757641.00424871129
657022.020889743146146.668581482997897.37319800329
667022.020889743145949.946765219448094.09501426684
677022.020889743145784.101589719868259.94018976643
687022.020889743145637.988571382398406.05320810389
697022.020889743145505.892028740918538.14975074537
707022.020889743145384.416545568158659.62523391814
717022.020889743145271.349803285818772.69197620047
727022.020889743145165.15511164978878.88666783659
737022.020889743145064.7136111718979.32816831528
747022.020889743144969.180650550549074.86112893575
757022.020889743144877.900018023169166.14176146312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 7022.02088974314 & 6403.037530775 & 7641.00424871129 \tabularnewline
65 & 7022.02088974314 & 6146.66858148299 & 7897.37319800329 \tabularnewline
66 & 7022.02088974314 & 5949.94676521944 & 8094.09501426684 \tabularnewline
67 & 7022.02088974314 & 5784.10158971986 & 8259.94018976643 \tabularnewline
68 & 7022.02088974314 & 5637.98857138239 & 8406.05320810389 \tabularnewline
69 & 7022.02088974314 & 5505.89202874091 & 8538.14975074537 \tabularnewline
70 & 7022.02088974314 & 5384.41654556815 & 8659.62523391814 \tabularnewline
71 & 7022.02088974314 & 5271.34980328581 & 8772.69197620047 \tabularnewline
72 & 7022.02088974314 & 5165.1551116497 & 8878.88666783659 \tabularnewline
73 & 7022.02088974314 & 5064.713611171 & 8979.32816831528 \tabularnewline
74 & 7022.02088974314 & 4969.18065055054 & 9074.86112893575 \tabularnewline
75 & 7022.02088974314 & 4877.90001802316 & 9166.14176146312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301436&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]64[/C][C]7022.02088974314[/C][C]6403.037530775[/C][C]7641.00424871129[/C][/ROW]
[ROW][C]65[/C][C]7022.02088974314[/C][C]6146.66858148299[/C][C]7897.37319800329[/C][/ROW]
[ROW][C]66[/C][C]7022.02088974314[/C][C]5949.94676521944[/C][C]8094.09501426684[/C][/ROW]
[ROW][C]67[/C][C]7022.02088974314[/C][C]5784.10158971986[/C][C]8259.94018976643[/C][/ROW]
[ROW][C]68[/C][C]7022.02088974314[/C][C]5637.98857138239[/C][C]8406.05320810389[/C][/ROW]
[ROW][C]69[/C][C]7022.02088974314[/C][C]5505.89202874091[/C][C]8538.14975074537[/C][/ROW]
[ROW][C]70[/C][C]7022.02088974314[/C][C]5384.41654556815[/C][C]8659.62523391814[/C][/ROW]
[ROW][C]71[/C][C]7022.02088974314[/C][C]5271.34980328581[/C][C]8772.69197620047[/C][/ROW]
[ROW][C]72[/C][C]7022.02088974314[/C][C]5165.1551116497[/C][C]8878.88666783659[/C][/ROW]
[ROW][C]73[/C][C]7022.02088974314[/C][C]5064.713611171[/C][C]8979.32816831528[/C][/ROW]
[ROW][C]74[/C][C]7022.02088974314[/C][C]4969.18065055054[/C][C]9074.86112893575[/C][/ROW]
[ROW][C]75[/C][C]7022.02088974314[/C][C]4877.90001802316[/C][C]9166.14176146312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301436&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301436&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
647022.020889743146403.0375307757641.00424871129
657022.020889743146146.668581482997897.37319800329
667022.020889743145949.946765219448094.09501426684
677022.020889743145784.101589719868259.94018976643
687022.020889743145637.988571382398406.05320810389
697022.020889743145505.892028740918538.14975074537
707022.020889743145384.416545568158659.62523391814
717022.020889743145271.349803285818772.69197620047
727022.020889743145165.15511164978878.88666783659
737022.020889743145064.7136111718979.32816831528
747022.020889743144969.180650550549074.86112893575
757022.020889743144877.900018023169166.14176146312



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