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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 19:51:19 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t15029061179nbwg0j279r9d7z.htm/, Retrieved Sat, 11 May 2024 19:55:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307479, Retrieved Sat, 11 May 2024 19:55:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2017-08-16 17:51:19] [7f8e680169e3605c7c9c65666ad372ce] [Current]
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Dataseries X:
64800
62400
66000
52800
68400
67200
72000
74400
82800
72000
68400
85200
72000
54000
63600
48000
67200
55200
73200
66000
69600
78000
76800
91200
66000
55200
61200
44400
63600
49200
69600
66000
58800
84000
75600
86400
64800
60000
54000
44400
58800
52800
72000
69600
60000
80400
74400
96000
76800
46800
46800
46800
55200
55200
74400
68400
61200
76800
70800
102000
80400
46800
49200
40800
56400
64800
81600
80400
64800
75600
67200
96000
73200
58800
52800
39600
58800
70800
82800
78000
57600
82800
64800
99600
82800
60000
55200
37200
58800
56400
85200
85200
64800
84000
62400
97200
82800
61200
46800

32400
63600
61200
80400
92400
68400
76800
57600
99600




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=307479&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [ROW]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307479&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.548594506058194
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548594506058194 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307479&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]0.548594506058194[/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=307479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307479&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
alpha0.548594506058194
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26240064800-2400
36600063483.37318546032516.62681453966
45280064863.9808297155-12063.9808297155
56840058245.747225342210154.2527746578
66720063816.31451064573383.68548935435
77200065672.58578033436327.41421966572
87440069143.77045879745256.2295412026
98280072027.309107681910772.6908923181
107200077937.1481466708-5937.14814667078
116840074680.0612917536-6280.06129175361
128520071234.854169388913965.1458306111
137200078896.0564483636-6896.05644836363
145400075112.9177673242-21112.9177673242
156360063530.487073311769.5129266883087
164800063568.6214829929-15568.6214829929
176720055027.761270523412172.2387294766
185520061705.3845639431-6505.38456394305
197320058136.566332368115063.4336676319
206600066400.283284803-400.283284802994
216960066180.69007389313419.30992610686
227800068056.50471386569943.49528613439
237680073511.45159885453288.54840114551
249120075315.531184629415884.4688153706
256600084029.6635083944-18029.6635083944
265520074138.6891616113-18938.6891616113
276120063749.0283356075-2549.02833560748
284440062350.6453949065-17950.6453949065
296360052503.01995106211096.980048938
304920058590.7622397468-9390.76223974677
316960053439.041667322916160.9583326771
326600062304.8546212653695.14537873503
335880064331.9910751253-5531.99107512533
348400061297.171163748622702.8288362514
357560073751.81833529571848.18166470432
368640074765.7206427511634.27935725
376480081148.2223800836-16348.2223800836
386000072179.6773985521-12179.6773985521
395400065497.9732921453-11497.9732921453
404440059190.2483132705-14790.2483132705
415880051076.39934537387723.60065462616
425280055313.5242314892-2513.52423148922
437200053934.618647250118065.3813527499
446960063845.18760721485754.81239278516
456000067002.2460692924-7002.24606929239
468040063160.85234561117239.147654389
477440072618.15403793481781.84596206518
489600073595.664943365822404.3350566342
497680085886.5600673223-9086.56006732231
504680080901.7231354215-34101.7231354215
514680062193.7051762116-15393.7051762116
524680053748.8030886623-6948.80308866235
535520049936.7278905425263.27210945803
545520052824.130053682375.86994632003
557440054127.519253339920272.4807466601
566840065248.89081512823151.10918487184
576120066977.5720019384-5777.57200193837
587680063808.027743319312991.9722566807
597080070935.3523461948-135.352346194835
6010200070861.098792690331138.9012073097
618040087943.7289197093-7543.72891970926
624680083805.2806791645-37005.2806791645
634920063504.3870034334-14304.3870034334
644080055657.0788808196-14857.0788808196
655640047506.56703072878893.43296927126
666480052385.455497667812414.5445023322
678160059196.006406862222403.9935931378
688040071486.71420582068913.28579417942
696480076376.493823434-11576.493823434
707560070025.69291248155574.30708751854
716720073083.7271557754-5883.72715577538
729600069855.946762971626144.0532370284
737320084198.4307348983-10998.4307348983
745880078164.7520584715-19364.7520584715
755280067541.3554680149-14741.3554680149
763960059454.328846411-19854.328846411
775880048562.353119797210237.6468802028
787080054178.669953240316621.3300467597
798280063297.040300272719502.9596997273
807800073996.25684341744003.74315658255
815760076192.6883427867-18592.6883427867
828280065992.841665081716807.1583349183
836480075213.1563900681-10413.1563900681
849960069500.556003751930099.4439962481
858280086012.9456154999-3212.94561549994
866000084250.3413025729-24250.3413025729
875520070946.7372939453-15746.7372939453
883720062308.1637261452-25108.1637261452
895880048533.963048772310266.0369512277
905640054165.85451920622234.14548079376
918520055391.494455704429808.5055442956
928520071744.276831110213455.7231688898
936480079126.0126366031-14326.0126366031
948400071266.840810442412733.1591895576
956240078252.1819865981-15852.1819865981
969720069555.762039715727644.2379602843
978280084721.2391088931-1921.23910889306
986120083667.2578889302-22467.2578889302
994680071341.8436448704-24541.8436448704
1003240057878.3230527553-25478.3230527553
1016360043901.055002437919698.9449975621
1026120054707.7880032436492.21199675697
1038040058269.37983682922130.620163171
1049240070410.116474005321989.8835259947
1056840082473.6457652256-14073.6457652256
1067680074752.92101821372047.07898178634
1075760075875.9373010889-18275.9373010889
1089960065849.858504647533750.1414953525

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 62400 & 64800 & -2400 \tabularnewline
3 & 66000 & 63483.3731854603 & 2516.62681453966 \tabularnewline
4 & 52800 & 64863.9808297155 & -12063.9808297155 \tabularnewline
5 & 68400 & 58245.7472253422 & 10154.2527746578 \tabularnewline
6 & 67200 & 63816.3145106457 & 3383.68548935435 \tabularnewline
7 & 72000 & 65672.5857803343 & 6327.41421966572 \tabularnewline
8 & 74400 & 69143.7704587974 & 5256.2295412026 \tabularnewline
9 & 82800 & 72027.3091076819 & 10772.6908923181 \tabularnewline
10 & 72000 & 77937.1481466708 & -5937.14814667078 \tabularnewline
11 & 68400 & 74680.0612917536 & -6280.06129175361 \tabularnewline
12 & 85200 & 71234.8541693889 & 13965.1458306111 \tabularnewline
13 & 72000 & 78896.0564483636 & -6896.05644836363 \tabularnewline
14 & 54000 & 75112.9177673242 & -21112.9177673242 \tabularnewline
15 & 63600 & 63530.4870733117 & 69.5129266883087 \tabularnewline
16 & 48000 & 63568.6214829929 & -15568.6214829929 \tabularnewline
17 & 67200 & 55027.7612705234 & 12172.2387294766 \tabularnewline
18 & 55200 & 61705.3845639431 & -6505.38456394305 \tabularnewline
19 & 73200 & 58136.5663323681 & 15063.4336676319 \tabularnewline
20 & 66000 & 66400.283284803 & -400.283284802994 \tabularnewline
21 & 69600 & 66180.6900738931 & 3419.30992610686 \tabularnewline
22 & 78000 & 68056.5047138656 & 9943.49528613439 \tabularnewline
23 & 76800 & 73511.4515988545 & 3288.54840114551 \tabularnewline
24 & 91200 & 75315.5311846294 & 15884.4688153706 \tabularnewline
25 & 66000 & 84029.6635083944 & -18029.6635083944 \tabularnewline
26 & 55200 & 74138.6891616113 & -18938.6891616113 \tabularnewline
27 & 61200 & 63749.0283356075 & -2549.02833560748 \tabularnewline
28 & 44400 & 62350.6453949065 & -17950.6453949065 \tabularnewline
29 & 63600 & 52503.019951062 & 11096.980048938 \tabularnewline
30 & 49200 & 58590.7622397468 & -9390.76223974677 \tabularnewline
31 & 69600 & 53439.0416673229 & 16160.9583326771 \tabularnewline
32 & 66000 & 62304.854621265 & 3695.14537873503 \tabularnewline
33 & 58800 & 64331.9910751253 & -5531.99107512533 \tabularnewline
34 & 84000 & 61297.1711637486 & 22702.8288362514 \tabularnewline
35 & 75600 & 73751.8183352957 & 1848.18166470432 \tabularnewline
36 & 86400 & 74765.72064275 & 11634.27935725 \tabularnewline
37 & 64800 & 81148.2223800836 & -16348.2223800836 \tabularnewline
38 & 60000 & 72179.6773985521 & -12179.6773985521 \tabularnewline
39 & 54000 & 65497.9732921453 & -11497.9732921453 \tabularnewline
40 & 44400 & 59190.2483132705 & -14790.2483132705 \tabularnewline
41 & 58800 & 51076.3993453738 & 7723.60065462616 \tabularnewline
42 & 52800 & 55313.5242314892 & -2513.52423148922 \tabularnewline
43 & 72000 & 53934.6186472501 & 18065.3813527499 \tabularnewline
44 & 69600 & 63845.1876072148 & 5754.81239278516 \tabularnewline
45 & 60000 & 67002.2460692924 & -7002.24606929239 \tabularnewline
46 & 80400 & 63160.852345611 & 17239.147654389 \tabularnewline
47 & 74400 & 72618.1540379348 & 1781.84596206518 \tabularnewline
48 & 96000 & 73595.6649433658 & 22404.3350566342 \tabularnewline
49 & 76800 & 85886.5600673223 & -9086.56006732231 \tabularnewline
50 & 46800 & 80901.7231354215 & -34101.7231354215 \tabularnewline
51 & 46800 & 62193.7051762116 & -15393.7051762116 \tabularnewline
52 & 46800 & 53748.8030886623 & -6948.80308866235 \tabularnewline
53 & 55200 & 49936.727890542 & 5263.27210945803 \tabularnewline
54 & 55200 & 52824.13005368 & 2375.86994632003 \tabularnewline
55 & 74400 & 54127.5192533399 & 20272.4807466601 \tabularnewline
56 & 68400 & 65248.8908151282 & 3151.10918487184 \tabularnewline
57 & 61200 & 66977.5720019384 & -5777.57200193837 \tabularnewline
58 & 76800 & 63808.0277433193 & 12991.9722566807 \tabularnewline
59 & 70800 & 70935.3523461948 & -135.352346194835 \tabularnewline
60 & 102000 & 70861.0987926903 & 31138.9012073097 \tabularnewline
61 & 80400 & 87943.7289197093 & -7543.72891970926 \tabularnewline
62 & 46800 & 83805.2806791645 & -37005.2806791645 \tabularnewline
63 & 49200 & 63504.3870034334 & -14304.3870034334 \tabularnewline
64 & 40800 & 55657.0788808196 & -14857.0788808196 \tabularnewline
65 & 56400 & 47506.5670307287 & 8893.43296927126 \tabularnewline
66 & 64800 & 52385.4554976678 & 12414.5445023322 \tabularnewline
67 & 81600 & 59196.0064068622 & 22403.9935931378 \tabularnewline
68 & 80400 & 71486.7142058206 & 8913.28579417942 \tabularnewline
69 & 64800 & 76376.493823434 & -11576.493823434 \tabularnewline
70 & 75600 & 70025.6929124815 & 5574.30708751854 \tabularnewline
71 & 67200 & 73083.7271557754 & -5883.72715577538 \tabularnewline
72 & 96000 & 69855.9467629716 & 26144.0532370284 \tabularnewline
73 & 73200 & 84198.4307348983 & -10998.4307348983 \tabularnewline
74 & 58800 & 78164.7520584715 & -19364.7520584715 \tabularnewline
75 & 52800 & 67541.3554680149 & -14741.3554680149 \tabularnewline
76 & 39600 & 59454.328846411 & -19854.328846411 \tabularnewline
77 & 58800 & 48562.3531197972 & 10237.6468802028 \tabularnewline
78 & 70800 & 54178.6699532403 & 16621.3300467597 \tabularnewline
79 & 82800 & 63297.0403002727 & 19502.9596997273 \tabularnewline
80 & 78000 & 73996.2568434174 & 4003.74315658255 \tabularnewline
81 & 57600 & 76192.6883427867 & -18592.6883427867 \tabularnewline
82 & 82800 & 65992.8416650817 & 16807.1583349183 \tabularnewline
83 & 64800 & 75213.1563900681 & -10413.1563900681 \tabularnewline
84 & 99600 & 69500.5560037519 & 30099.4439962481 \tabularnewline
85 & 82800 & 86012.9456154999 & -3212.94561549994 \tabularnewline
86 & 60000 & 84250.3413025729 & -24250.3413025729 \tabularnewline
87 & 55200 & 70946.7372939453 & -15746.7372939453 \tabularnewline
88 & 37200 & 62308.1637261452 & -25108.1637261452 \tabularnewline
89 & 58800 & 48533.9630487723 & 10266.0369512277 \tabularnewline
90 & 56400 & 54165.8545192062 & 2234.14548079376 \tabularnewline
91 & 85200 & 55391.4944557044 & 29808.5055442956 \tabularnewline
92 & 85200 & 71744.2768311102 & 13455.7231688898 \tabularnewline
93 & 64800 & 79126.0126366031 & -14326.0126366031 \tabularnewline
94 & 84000 & 71266.8408104424 & 12733.1591895576 \tabularnewline
95 & 62400 & 78252.1819865981 & -15852.1819865981 \tabularnewline
96 & 97200 & 69555.7620397157 & 27644.2379602843 \tabularnewline
97 & 82800 & 84721.2391088931 & -1921.23910889306 \tabularnewline
98 & 61200 & 83667.2578889302 & -22467.2578889302 \tabularnewline
99 & 46800 & 71341.8436448704 & -24541.8436448704 \tabularnewline
100 & 32400 & 57878.3230527553 & -25478.3230527553 \tabularnewline
101 & 63600 & 43901.0550024379 & 19698.9449975621 \tabularnewline
102 & 61200 & 54707.788003243 & 6492.21199675697 \tabularnewline
103 & 80400 & 58269.379836829 & 22130.620163171 \tabularnewline
104 & 92400 & 70410.1164740053 & 21989.8835259947 \tabularnewline
105 & 68400 & 82473.6457652256 & -14073.6457652256 \tabularnewline
106 & 76800 & 74752.9210182137 & 2047.07898178634 \tabularnewline
107 & 57600 & 75875.9373010889 & -18275.9373010889 \tabularnewline
108 & 99600 & 65849.8585046475 & 33750.1414953525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307479&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]62400[/C][C]64800[/C][C]-2400[/C][/ROW]
[ROW][C]3[/C][C]66000[/C][C]63483.3731854603[/C][C]2516.62681453966[/C][/ROW]
[ROW][C]4[/C][C]52800[/C][C]64863.9808297155[/C][C]-12063.9808297155[/C][/ROW]
[ROW][C]5[/C][C]68400[/C][C]58245.7472253422[/C][C]10154.2527746578[/C][/ROW]
[ROW][C]6[/C][C]67200[/C][C]63816.3145106457[/C][C]3383.68548935435[/C][/ROW]
[ROW][C]7[/C][C]72000[/C][C]65672.5857803343[/C][C]6327.41421966572[/C][/ROW]
[ROW][C]8[/C][C]74400[/C][C]69143.7704587974[/C][C]5256.2295412026[/C][/ROW]
[ROW][C]9[/C][C]82800[/C][C]72027.3091076819[/C][C]10772.6908923181[/C][/ROW]
[ROW][C]10[/C][C]72000[/C][C]77937.1481466708[/C][C]-5937.14814667078[/C][/ROW]
[ROW][C]11[/C][C]68400[/C][C]74680.0612917536[/C][C]-6280.06129175361[/C][/ROW]
[ROW][C]12[/C][C]85200[/C][C]71234.8541693889[/C][C]13965.1458306111[/C][/ROW]
[ROW][C]13[/C][C]72000[/C][C]78896.0564483636[/C][C]-6896.05644836363[/C][/ROW]
[ROW][C]14[/C][C]54000[/C][C]75112.9177673242[/C][C]-21112.9177673242[/C][/ROW]
[ROW][C]15[/C][C]63600[/C][C]63530.4870733117[/C][C]69.5129266883087[/C][/ROW]
[ROW][C]16[/C][C]48000[/C][C]63568.6214829929[/C][C]-15568.6214829929[/C][/ROW]
[ROW][C]17[/C][C]67200[/C][C]55027.7612705234[/C][C]12172.2387294766[/C][/ROW]
[ROW][C]18[/C][C]55200[/C][C]61705.3845639431[/C][C]-6505.38456394305[/C][/ROW]
[ROW][C]19[/C][C]73200[/C][C]58136.5663323681[/C][C]15063.4336676319[/C][/ROW]
[ROW][C]20[/C][C]66000[/C][C]66400.283284803[/C][C]-400.283284802994[/C][/ROW]
[ROW][C]21[/C][C]69600[/C][C]66180.6900738931[/C][C]3419.30992610686[/C][/ROW]
[ROW][C]22[/C][C]78000[/C][C]68056.5047138656[/C][C]9943.49528613439[/C][/ROW]
[ROW][C]23[/C][C]76800[/C][C]73511.4515988545[/C][C]3288.54840114551[/C][/ROW]
[ROW][C]24[/C][C]91200[/C][C]75315.5311846294[/C][C]15884.4688153706[/C][/ROW]
[ROW][C]25[/C][C]66000[/C][C]84029.6635083944[/C][C]-18029.6635083944[/C][/ROW]
[ROW][C]26[/C][C]55200[/C][C]74138.6891616113[/C][C]-18938.6891616113[/C][/ROW]
[ROW][C]27[/C][C]61200[/C][C]63749.0283356075[/C][C]-2549.02833560748[/C][/ROW]
[ROW][C]28[/C][C]44400[/C][C]62350.6453949065[/C][C]-17950.6453949065[/C][/ROW]
[ROW][C]29[/C][C]63600[/C][C]52503.019951062[/C][C]11096.980048938[/C][/ROW]
[ROW][C]30[/C][C]49200[/C][C]58590.7622397468[/C][C]-9390.76223974677[/C][/ROW]
[ROW][C]31[/C][C]69600[/C][C]53439.0416673229[/C][C]16160.9583326771[/C][/ROW]
[ROW][C]32[/C][C]66000[/C][C]62304.854621265[/C][C]3695.14537873503[/C][/ROW]
[ROW][C]33[/C][C]58800[/C][C]64331.9910751253[/C][C]-5531.99107512533[/C][/ROW]
[ROW][C]34[/C][C]84000[/C][C]61297.1711637486[/C][C]22702.8288362514[/C][/ROW]
[ROW][C]35[/C][C]75600[/C][C]73751.8183352957[/C][C]1848.18166470432[/C][/ROW]
[ROW][C]36[/C][C]86400[/C][C]74765.72064275[/C][C]11634.27935725[/C][/ROW]
[ROW][C]37[/C][C]64800[/C][C]81148.2223800836[/C][C]-16348.2223800836[/C][/ROW]
[ROW][C]38[/C][C]60000[/C][C]72179.6773985521[/C][C]-12179.6773985521[/C][/ROW]
[ROW][C]39[/C][C]54000[/C][C]65497.9732921453[/C][C]-11497.9732921453[/C][/ROW]
[ROW][C]40[/C][C]44400[/C][C]59190.2483132705[/C][C]-14790.2483132705[/C][/ROW]
[ROW][C]41[/C][C]58800[/C][C]51076.3993453738[/C][C]7723.60065462616[/C][/ROW]
[ROW][C]42[/C][C]52800[/C][C]55313.5242314892[/C][C]-2513.52423148922[/C][/ROW]
[ROW][C]43[/C][C]72000[/C][C]53934.6186472501[/C][C]18065.3813527499[/C][/ROW]
[ROW][C]44[/C][C]69600[/C][C]63845.1876072148[/C][C]5754.81239278516[/C][/ROW]
[ROW][C]45[/C][C]60000[/C][C]67002.2460692924[/C][C]-7002.24606929239[/C][/ROW]
[ROW][C]46[/C][C]80400[/C][C]63160.852345611[/C][C]17239.147654389[/C][/ROW]
[ROW][C]47[/C][C]74400[/C][C]72618.1540379348[/C][C]1781.84596206518[/C][/ROW]
[ROW][C]48[/C][C]96000[/C][C]73595.6649433658[/C][C]22404.3350566342[/C][/ROW]
[ROW][C]49[/C][C]76800[/C][C]85886.5600673223[/C][C]-9086.56006732231[/C][/ROW]
[ROW][C]50[/C][C]46800[/C][C]80901.7231354215[/C][C]-34101.7231354215[/C][/ROW]
[ROW][C]51[/C][C]46800[/C][C]62193.7051762116[/C][C]-15393.7051762116[/C][/ROW]
[ROW][C]52[/C][C]46800[/C][C]53748.8030886623[/C][C]-6948.80308866235[/C][/ROW]
[ROW][C]53[/C][C]55200[/C][C]49936.727890542[/C][C]5263.27210945803[/C][/ROW]
[ROW][C]54[/C][C]55200[/C][C]52824.13005368[/C][C]2375.86994632003[/C][/ROW]
[ROW][C]55[/C][C]74400[/C][C]54127.5192533399[/C][C]20272.4807466601[/C][/ROW]
[ROW][C]56[/C][C]68400[/C][C]65248.8908151282[/C][C]3151.10918487184[/C][/ROW]
[ROW][C]57[/C][C]61200[/C][C]66977.5720019384[/C][C]-5777.57200193837[/C][/ROW]
[ROW][C]58[/C][C]76800[/C][C]63808.0277433193[/C][C]12991.9722566807[/C][/ROW]
[ROW][C]59[/C][C]70800[/C][C]70935.3523461948[/C][C]-135.352346194835[/C][/ROW]
[ROW][C]60[/C][C]102000[/C][C]70861.0987926903[/C][C]31138.9012073097[/C][/ROW]
[ROW][C]61[/C][C]80400[/C][C]87943.7289197093[/C][C]-7543.72891970926[/C][/ROW]
[ROW][C]62[/C][C]46800[/C][C]83805.2806791645[/C][C]-37005.2806791645[/C][/ROW]
[ROW][C]63[/C][C]49200[/C][C]63504.3870034334[/C][C]-14304.3870034334[/C][/ROW]
[ROW][C]64[/C][C]40800[/C][C]55657.0788808196[/C][C]-14857.0788808196[/C][/ROW]
[ROW][C]65[/C][C]56400[/C][C]47506.5670307287[/C][C]8893.43296927126[/C][/ROW]
[ROW][C]66[/C][C]64800[/C][C]52385.4554976678[/C][C]12414.5445023322[/C][/ROW]
[ROW][C]67[/C][C]81600[/C][C]59196.0064068622[/C][C]22403.9935931378[/C][/ROW]
[ROW][C]68[/C][C]80400[/C][C]71486.7142058206[/C][C]8913.28579417942[/C][/ROW]
[ROW][C]69[/C][C]64800[/C][C]76376.493823434[/C][C]-11576.493823434[/C][/ROW]
[ROW][C]70[/C][C]75600[/C][C]70025.6929124815[/C][C]5574.30708751854[/C][/ROW]
[ROW][C]71[/C][C]67200[/C][C]73083.7271557754[/C][C]-5883.72715577538[/C][/ROW]
[ROW][C]72[/C][C]96000[/C][C]69855.9467629716[/C][C]26144.0532370284[/C][/ROW]
[ROW][C]73[/C][C]73200[/C][C]84198.4307348983[/C][C]-10998.4307348983[/C][/ROW]
[ROW][C]74[/C][C]58800[/C][C]78164.7520584715[/C][C]-19364.7520584715[/C][/ROW]
[ROW][C]75[/C][C]52800[/C][C]67541.3554680149[/C][C]-14741.3554680149[/C][/ROW]
[ROW][C]76[/C][C]39600[/C][C]59454.328846411[/C][C]-19854.328846411[/C][/ROW]
[ROW][C]77[/C][C]58800[/C][C]48562.3531197972[/C][C]10237.6468802028[/C][/ROW]
[ROW][C]78[/C][C]70800[/C][C]54178.6699532403[/C][C]16621.3300467597[/C][/ROW]
[ROW][C]79[/C][C]82800[/C][C]63297.0403002727[/C][C]19502.9596997273[/C][/ROW]
[ROW][C]80[/C][C]78000[/C][C]73996.2568434174[/C][C]4003.74315658255[/C][/ROW]
[ROW][C]81[/C][C]57600[/C][C]76192.6883427867[/C][C]-18592.6883427867[/C][/ROW]
[ROW][C]82[/C][C]82800[/C][C]65992.8416650817[/C][C]16807.1583349183[/C][/ROW]
[ROW][C]83[/C][C]64800[/C][C]75213.1563900681[/C][C]-10413.1563900681[/C][/ROW]
[ROW][C]84[/C][C]99600[/C][C]69500.5560037519[/C][C]30099.4439962481[/C][/ROW]
[ROW][C]85[/C][C]82800[/C][C]86012.9456154999[/C][C]-3212.94561549994[/C][/ROW]
[ROW][C]86[/C][C]60000[/C][C]84250.3413025729[/C][C]-24250.3413025729[/C][/ROW]
[ROW][C]87[/C][C]55200[/C][C]70946.7372939453[/C][C]-15746.7372939453[/C][/ROW]
[ROW][C]88[/C][C]37200[/C][C]62308.1637261452[/C][C]-25108.1637261452[/C][/ROW]
[ROW][C]89[/C][C]58800[/C][C]48533.9630487723[/C][C]10266.0369512277[/C][/ROW]
[ROW][C]90[/C][C]56400[/C][C]54165.8545192062[/C][C]2234.14548079376[/C][/ROW]
[ROW][C]91[/C][C]85200[/C][C]55391.4944557044[/C][C]29808.5055442956[/C][/ROW]
[ROW][C]92[/C][C]85200[/C][C]71744.2768311102[/C][C]13455.7231688898[/C][/ROW]
[ROW][C]93[/C][C]64800[/C][C]79126.0126366031[/C][C]-14326.0126366031[/C][/ROW]
[ROW][C]94[/C][C]84000[/C][C]71266.8408104424[/C][C]12733.1591895576[/C][/ROW]
[ROW][C]95[/C][C]62400[/C][C]78252.1819865981[/C][C]-15852.1819865981[/C][/ROW]
[ROW][C]96[/C][C]97200[/C][C]69555.7620397157[/C][C]27644.2379602843[/C][/ROW]
[ROW][C]97[/C][C]82800[/C][C]84721.2391088931[/C][C]-1921.23910889306[/C][/ROW]
[ROW][C]98[/C][C]61200[/C][C]83667.2578889302[/C][C]-22467.2578889302[/C][/ROW]
[ROW][C]99[/C][C]46800[/C][C]71341.8436448704[/C][C]-24541.8436448704[/C][/ROW]
[ROW][C]100[/C][C]32400[/C][C]57878.3230527553[/C][C]-25478.3230527553[/C][/ROW]
[ROW][C]101[/C][C]63600[/C][C]43901.0550024379[/C][C]19698.9449975621[/C][/ROW]
[ROW][C]102[/C][C]61200[/C][C]54707.788003243[/C][C]6492.21199675697[/C][/ROW]
[ROW][C]103[/C][C]80400[/C][C]58269.379836829[/C][C]22130.620163171[/C][/ROW]
[ROW][C]104[/C][C]92400[/C][C]70410.1164740053[/C][C]21989.8835259947[/C][/ROW]
[ROW][C]105[/C][C]68400[/C][C]82473.6457652256[/C][C]-14073.6457652256[/C][/ROW]
[ROW][C]106[/C][C]76800[/C][C]74752.9210182137[/C][C]2047.07898178634[/C][/ROW]
[ROW][C]107[/C][C]57600[/C][C]75875.9373010889[/C][C]-18275.9373010889[/C][/ROW]
[ROW][C]108[/C][C]99600[/C][C]65849.8585046475[/C][C]33750.1414953525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307479&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
26240064800-2400
36600063483.37318546032516.62681453966
45280064863.9808297155-12063.9808297155
56840058245.747225342210154.2527746578
66720063816.31451064573383.68548935435
77200065672.58578033436327.41421966572
87440069143.77045879745256.2295412026
98280072027.309107681910772.6908923181
107200077937.1481466708-5937.14814667078
116840074680.0612917536-6280.06129175361
128520071234.854169388913965.1458306111
137200078896.0564483636-6896.05644836363
145400075112.9177673242-21112.9177673242
156360063530.487073311769.5129266883087
164800063568.6214829929-15568.6214829929
176720055027.761270523412172.2387294766
185520061705.3845639431-6505.38456394305
197320058136.566332368115063.4336676319
206600066400.283284803-400.283284802994
216960066180.69007389313419.30992610686
227800068056.50471386569943.49528613439
237680073511.45159885453288.54840114551
249120075315.531184629415884.4688153706
256600084029.6635083944-18029.6635083944
265520074138.6891616113-18938.6891616113
276120063749.0283356075-2549.02833560748
284440062350.6453949065-17950.6453949065
296360052503.01995106211096.980048938
304920058590.7622397468-9390.76223974677
316960053439.041667322916160.9583326771
326600062304.8546212653695.14537873503
335880064331.9910751253-5531.99107512533
348400061297.171163748622702.8288362514
357560073751.81833529571848.18166470432
368640074765.7206427511634.27935725
376480081148.2223800836-16348.2223800836
386000072179.6773985521-12179.6773985521
395400065497.9732921453-11497.9732921453
404440059190.2483132705-14790.2483132705
415880051076.39934537387723.60065462616
425280055313.5242314892-2513.52423148922
437200053934.618647250118065.3813527499
446960063845.18760721485754.81239278516
456000067002.2460692924-7002.24606929239
468040063160.85234561117239.147654389
477440072618.15403793481781.84596206518
489600073595.664943365822404.3350566342
497680085886.5600673223-9086.56006732231
504680080901.7231354215-34101.7231354215
514680062193.7051762116-15393.7051762116
524680053748.8030886623-6948.80308866235
535520049936.7278905425263.27210945803
545520052824.130053682375.86994632003
557440054127.519253339920272.4807466601
566840065248.89081512823151.10918487184
576120066977.5720019384-5777.57200193837
587680063808.027743319312991.9722566807
597080070935.3523461948-135.352346194835
6010200070861.098792690331138.9012073097
618040087943.7289197093-7543.72891970926
624680083805.2806791645-37005.2806791645
634920063504.3870034334-14304.3870034334
644080055657.0788808196-14857.0788808196
655640047506.56703072878893.43296927126
666480052385.455497667812414.5445023322
678160059196.006406862222403.9935931378
688040071486.71420582068913.28579417942
696480076376.493823434-11576.493823434
707560070025.69291248155574.30708751854
716720073083.7271557754-5883.72715577538
729600069855.946762971626144.0532370284
737320084198.4307348983-10998.4307348983
745880078164.7520584715-19364.7520584715
755280067541.3554680149-14741.3554680149
763960059454.328846411-19854.328846411
775880048562.353119797210237.6468802028
787080054178.669953240316621.3300467597
798280063297.040300272719502.9596997273
807800073996.25684341744003.74315658255
815760076192.6883427867-18592.6883427867
828280065992.841665081716807.1583349183
836480075213.1563900681-10413.1563900681
849960069500.556003751930099.4439962481
858280086012.9456154999-3212.94561549994
866000084250.3413025729-24250.3413025729
875520070946.7372939453-15746.7372939453
883720062308.1637261452-25108.1637261452
895880048533.963048772310266.0369512277
905640054165.85451920622234.14548079376
918520055391.494455704429808.5055442956
928520071744.276831110213455.7231688898
936480079126.0126366031-14326.0126366031
948400071266.840810442412733.1591895576
956240078252.1819865981-15852.1819865981
969720069555.762039715727644.2379602843
978280084721.2391088931-1921.23910889306
986120083667.2578889302-22467.2578889302
994680071341.8436448704-24541.8436448704
1003240057878.3230527553-25478.3230527553
1016360043901.055002437919698.9449975621
1026120054707.7880032436492.21199675697
1038040058269.37983682922130.620163171
1049240070410.116474005321989.8835259947
1056840082473.6457652256-14073.6457652256
1067680074752.92101821372047.07898178634
1075760075875.9373010889-18275.9373010889
1089960065849.858504647533750.1414953525







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10984365.000707684653918.1412435452114811.860171824
11084365.000707684649637.4786770418119092.522738327
11184365.000707684645829.4285496317122900.572865737
11284365.000707684642365.2405094617126364.760905907
11384365.000707684639165.7817778408129564.219637528
11484365.000707684636178.2916788697132551.709736499
11584365.000707684633365.5059828602135364.495432509
11684365.000707684630699.9469264098138030.054488959
11784365.000707684628160.6633972346140569.338018135
11884365.000707684625731.2470527585142998.754362611
11984365.000707684623398.5623762035145331.439039166
12084365.000707684621151.8997080816147578.101707288

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 84365.0007076846 & 53918.1412435452 & 114811.860171824 \tabularnewline
110 & 84365.0007076846 & 49637.4786770418 & 119092.522738327 \tabularnewline
111 & 84365.0007076846 & 45829.4285496317 & 122900.572865737 \tabularnewline
112 & 84365.0007076846 & 42365.2405094617 & 126364.760905907 \tabularnewline
113 & 84365.0007076846 & 39165.7817778408 & 129564.219637528 \tabularnewline
114 & 84365.0007076846 & 36178.2916788697 & 132551.709736499 \tabularnewline
115 & 84365.0007076846 & 33365.5059828602 & 135364.495432509 \tabularnewline
116 & 84365.0007076846 & 30699.9469264098 & 138030.054488959 \tabularnewline
117 & 84365.0007076846 & 28160.6633972346 & 140569.338018135 \tabularnewline
118 & 84365.0007076846 & 25731.2470527585 & 142998.754362611 \tabularnewline
119 & 84365.0007076846 & 23398.5623762035 & 145331.439039166 \tabularnewline
120 & 84365.0007076846 & 21151.8997080816 & 147578.101707288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307479&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]109[/C][C]84365.0007076846[/C][C]53918.1412435452[/C][C]114811.860171824[/C][/ROW]
[ROW][C]110[/C][C]84365.0007076846[/C][C]49637.4786770418[/C][C]119092.522738327[/C][/ROW]
[ROW][C]111[/C][C]84365.0007076846[/C][C]45829.4285496317[/C][C]122900.572865737[/C][/ROW]
[ROW][C]112[/C][C]84365.0007076846[/C][C]42365.2405094617[/C][C]126364.760905907[/C][/ROW]
[ROW][C]113[/C][C]84365.0007076846[/C][C]39165.7817778408[/C][C]129564.219637528[/C][/ROW]
[ROW][C]114[/C][C]84365.0007076846[/C][C]36178.2916788697[/C][C]132551.709736499[/C][/ROW]
[ROW][C]115[/C][C]84365.0007076846[/C][C]33365.5059828602[/C][C]135364.495432509[/C][/ROW]
[ROW][C]116[/C][C]84365.0007076846[/C][C]30699.9469264098[/C][C]138030.054488959[/C][/ROW]
[ROW][C]117[/C][C]84365.0007076846[/C][C]28160.6633972346[/C][C]140569.338018135[/C][/ROW]
[ROW][C]118[/C][C]84365.0007076846[/C][C]25731.2470527585[/C][C]142998.754362611[/C][/ROW]
[ROW][C]119[/C][C]84365.0007076846[/C][C]23398.5623762035[/C][C]145331.439039166[/C][/ROW]
[ROW][C]120[/C][C]84365.0007076846[/C][C]21151.8997080816[/C][C]147578.101707288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307479&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
10984365.000707684653918.1412435452114811.860171824
11084365.000707684649637.4786770418119092.522738327
11184365.000707684645829.4285496317122900.572865737
11284365.000707684642365.2405094617126364.760905907
11384365.000707684639165.7817778408129564.219637528
11484365.000707684636178.2916788697132551.709736499
11584365.000707684633365.5059828602135364.495432509
11684365.000707684630699.9469264098138030.054488959
11784365.000707684628160.6633972346140569.338018135
11884365.000707684625731.2470527585142998.754362611
11984365.000707684623398.5623762035145331.439039166
12084365.000707684621151.8997080816147578.101707288



Parameters (Session):
par1 = 126012additive12 ; par2 = 112Single ; par3 = 0additive ; par4 = 012 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')