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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 01:32:33 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243928004m0x7l2ea7ysxyj8.htm/, Retrieved Fri, 10 May 2024 11:32:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41159, Retrieved Fri, 10 May 2024 11:32:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 - Aanta...] [2009-06-02 07:32:33] [32d3db078a25d9ceaa1d8e026862f0e2] [Current]
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Dataseries X:
2194
2419
2742
2137
2710
2173
2363
2126
1905
2121
1983
1734
2074
2049
2406
2558
2251
2059
2397
1747
1707
2319
1631
1627
1791
2034
1997
2169
2028
2253
2218
1855
2187
1852
1570
1851
1954
1828
2251
2277
2085
2282
2266
1878
2267
2069
1746
2299
2360
2214
2825
2355
2333
3016
2155
2172
2150
2533
2058
2160
2260
2498
2695
2799
2945
2930
2318
2540
2570
2669
2450
2842
3440
2678
2981
2259
2844
2546
2456
2295
2379
2479
2057
2280
2351
2275
2543
2305
2188
2720
2398
2147
1898
2538
2081
2057
2497
2460
2195
2823
2100
2640
2342
2171
2482




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41159&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41159&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.243472330170413
beta0.0205562664353707
gamma0.397243808484191

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.243472330170413 \tabularnewline
beta & 0.0205562664353707 \tabularnewline
gamma & 0.397243808484191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41159&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]0.243472330170413[/C][/ROW]
[ROW][C]beta[/C][C]0.0205562664353707[/C][/ROW]
[ROW][C]gamma[/C][C]0.397243808484191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41159&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
alpha0.243472330170413
beta0.0205562664353707
gamma0.397243808484191







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320742141.93536324786-67.9353632478637
1420492102.77000853926-53.7700085392644
1524062458.45107986328-52.4510798632814
1625582585.14909568857-27.1490956885655
1722512265.28823320274-14.2882332027352
1820592076.19545728523-17.1954572852301
1923972224.14212484319172.857875156807
2017472037.68498672405-290.684986724054
2117071761.91314380543-54.9131438054333
2223191947.31205372759371.687946272413
2316311889.56177944909-258.561779449087
2416271588.3607313078138.6392686921906
2517911907.75529479443-116.755294794434
2620341859.44629684248174.553703157516
2719972270.74258262418-273.742582624177
2821692349.68694120936-180.686941209358
2920281994.061243775833.9387562241989
3022531813.83043889310439.169561106896
3122182130.2830987762087.7169012237955
3218551783.6415007293471.3584992706608
3321871668.53642928732518.463570712676
3418522126.27472463116-274.274724631161
3515701723.14439010108-153.144390101079
3618511538.75414635396312.245853646036
3719541881.2615799350872.7384200649212
3818281970.7806937783-142.780693778301
3922512172.6476809531278.3523190468832
4022772369.6027385011-92.6027385011012
4120852104.68424549635-19.6842454963517
4222822037.67226268747244.327737312528
4322662204.5827045430661.4172954569367
4418781850.0071430339927.9928569660087
4522671861.87875317538405.121246824616
4620692056.3839951004012.616004899603
4717461763.54335798965-17.5433579896455
4822991756.74565401575542.254345984248
4923602089.14236508221270.857634917789
5022142168.9872751890245.0127248109839
5128252490.83118453767334.168815462334
5223552707.77259984061-352.772599840605
5323332409.20027051493-76.200270514933
5430162415.26421869386600.73578130614
5521552623.25817848311-468.258178483112
5621722136.3027733782235.6972266217767
5721502270.05199379037-120.051993790372
5825332222.77059727665310.229402723346
5920581998.852955073759.1470449263002
6021602184.87083389630-24.8708338962956
6122602300.69797605381-40.6979760538079
6224982238.32763409113259.672365908869
6326952701.92064729472-6.92064729471576
6427992630.25191113638168.748088863620
6529452545.2621503655399.737849634501
6629302876.5122682477753.487731752226
6723182633.13871952370-315.138719523695
6825402338.81433512761201.185664872394
6925702470.7759826316399.2240173683713
7026692612.0176472939156.982352706093
7124502255.54182604720194.458173952797
7228422454.48911570999387.510884290008
7334402673.26169729084766.738302709157
7426782909.08831638889-231.088316388890
7529813181.9598610077-200.959861007702
7622593123.75310501022-864.753105010216
7728442859.29241091157-15.2924109115679
7825462986.09942425485-440.099424254849
7924562509.96132662118-53.9613266211827
8022952433.89451418500-138.894514185003
8123792450.21110390858-71.2111039085758
8224792534.20598417388-55.2059841738787
8320572188.11313454535-131.113134545352
8422802360.56339693259-80.563396932594
8523512571.75109163386-220.751091633858
8622752254.7468988300620.2531011699407
8725432586.59374778731-43.5937477873131
8823052356.72804265566-51.7280426556558
8921882539.08435742891-351.084357428911
9027202448.37213505697271.627864943031
9123982257.02889800291140.971101997091
9221472199.33817364837-52.3381736483684
9318982253.94272245668-355.942722456683
9425382268.87150259653269.128497403467
9520811976.00453059727104.995469402734
9620572219.38538054769-162.385380547686
9724972366.36530768190130.634692318104
9824602206.94414390802253.055856091976
9921952577.05184215065-382.051842150655
10028232261.40990062501561.590099374991
10121002505.27097288365-405.27097288365
10226402590.3788788900649.621121109943
10323422306.4781778875235.5218221124765
10421712165.252040898195.7479591018132
10524822143.28164944744338.718350552561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2074 & 2141.93536324786 & -67.9353632478637 \tabularnewline
14 & 2049 & 2102.77000853926 & -53.7700085392644 \tabularnewline
15 & 2406 & 2458.45107986328 & -52.4510798632814 \tabularnewline
16 & 2558 & 2585.14909568857 & -27.1490956885655 \tabularnewline
17 & 2251 & 2265.28823320274 & -14.2882332027352 \tabularnewline
18 & 2059 & 2076.19545728523 & -17.1954572852301 \tabularnewline
19 & 2397 & 2224.14212484319 & 172.857875156807 \tabularnewline
20 & 1747 & 2037.68498672405 & -290.684986724054 \tabularnewline
21 & 1707 & 1761.91314380543 & -54.9131438054333 \tabularnewline
22 & 2319 & 1947.31205372759 & 371.687946272413 \tabularnewline
23 & 1631 & 1889.56177944909 & -258.561779449087 \tabularnewline
24 & 1627 & 1588.36073130781 & 38.6392686921906 \tabularnewline
25 & 1791 & 1907.75529479443 & -116.755294794434 \tabularnewline
26 & 2034 & 1859.44629684248 & 174.553703157516 \tabularnewline
27 & 1997 & 2270.74258262418 & -273.742582624177 \tabularnewline
28 & 2169 & 2349.68694120936 & -180.686941209358 \tabularnewline
29 & 2028 & 1994.0612437758 & 33.9387562241989 \tabularnewline
30 & 2253 & 1813.83043889310 & 439.169561106896 \tabularnewline
31 & 2218 & 2130.28309877620 & 87.7169012237955 \tabularnewline
32 & 1855 & 1783.64150072934 & 71.3584992706608 \tabularnewline
33 & 2187 & 1668.53642928732 & 518.463570712676 \tabularnewline
34 & 1852 & 2126.27472463116 & -274.274724631161 \tabularnewline
35 & 1570 & 1723.14439010108 & -153.144390101079 \tabularnewline
36 & 1851 & 1538.75414635396 & 312.245853646036 \tabularnewline
37 & 1954 & 1881.26157993508 & 72.7384200649212 \tabularnewline
38 & 1828 & 1970.7806937783 & -142.780693778301 \tabularnewline
39 & 2251 & 2172.64768095312 & 78.3523190468832 \tabularnewline
40 & 2277 & 2369.6027385011 & -92.6027385011012 \tabularnewline
41 & 2085 & 2104.68424549635 & -19.6842454963517 \tabularnewline
42 & 2282 & 2037.67226268747 & 244.327737312528 \tabularnewline
43 & 2266 & 2204.58270454306 & 61.4172954569367 \tabularnewline
44 & 1878 & 1850.00714303399 & 27.9928569660087 \tabularnewline
45 & 2267 & 1861.87875317538 & 405.121246824616 \tabularnewline
46 & 2069 & 2056.38399510040 & 12.616004899603 \tabularnewline
47 & 1746 & 1763.54335798965 & -17.5433579896455 \tabularnewline
48 & 2299 & 1756.74565401575 & 542.254345984248 \tabularnewline
49 & 2360 & 2089.14236508221 & 270.857634917789 \tabularnewline
50 & 2214 & 2168.98727518902 & 45.0127248109839 \tabularnewline
51 & 2825 & 2490.83118453767 & 334.168815462334 \tabularnewline
52 & 2355 & 2707.77259984061 & -352.772599840605 \tabularnewline
53 & 2333 & 2409.20027051493 & -76.200270514933 \tabularnewline
54 & 3016 & 2415.26421869386 & 600.73578130614 \tabularnewline
55 & 2155 & 2623.25817848311 & -468.258178483112 \tabularnewline
56 & 2172 & 2136.30277337822 & 35.6972266217767 \tabularnewline
57 & 2150 & 2270.05199379037 & -120.051993790372 \tabularnewline
58 & 2533 & 2222.77059727665 & 310.229402723346 \tabularnewline
59 & 2058 & 1998.8529550737 & 59.1470449263002 \tabularnewline
60 & 2160 & 2184.87083389630 & -24.8708338962956 \tabularnewline
61 & 2260 & 2300.69797605381 & -40.6979760538079 \tabularnewline
62 & 2498 & 2238.32763409113 & 259.672365908869 \tabularnewline
63 & 2695 & 2701.92064729472 & -6.92064729471576 \tabularnewline
64 & 2799 & 2630.25191113638 & 168.748088863620 \tabularnewline
65 & 2945 & 2545.2621503655 & 399.737849634501 \tabularnewline
66 & 2930 & 2876.51226824777 & 53.487731752226 \tabularnewline
67 & 2318 & 2633.13871952370 & -315.138719523695 \tabularnewline
68 & 2540 & 2338.81433512761 & 201.185664872394 \tabularnewline
69 & 2570 & 2470.77598263163 & 99.2240173683713 \tabularnewline
70 & 2669 & 2612.01764729391 & 56.982352706093 \tabularnewline
71 & 2450 & 2255.54182604720 & 194.458173952797 \tabularnewline
72 & 2842 & 2454.48911570999 & 387.510884290008 \tabularnewline
73 & 3440 & 2673.26169729084 & 766.738302709157 \tabularnewline
74 & 2678 & 2909.08831638889 & -231.088316388890 \tabularnewline
75 & 2981 & 3181.9598610077 & -200.959861007702 \tabularnewline
76 & 2259 & 3123.75310501022 & -864.753105010216 \tabularnewline
77 & 2844 & 2859.29241091157 & -15.2924109115679 \tabularnewline
78 & 2546 & 2986.09942425485 & -440.099424254849 \tabularnewline
79 & 2456 & 2509.96132662118 & -53.9613266211827 \tabularnewline
80 & 2295 & 2433.89451418500 & -138.894514185003 \tabularnewline
81 & 2379 & 2450.21110390858 & -71.2111039085758 \tabularnewline
82 & 2479 & 2534.20598417388 & -55.2059841738787 \tabularnewline
83 & 2057 & 2188.11313454535 & -131.113134545352 \tabularnewline
84 & 2280 & 2360.56339693259 & -80.563396932594 \tabularnewline
85 & 2351 & 2571.75109163386 & -220.751091633858 \tabularnewline
86 & 2275 & 2254.74689883006 & 20.2531011699407 \tabularnewline
87 & 2543 & 2586.59374778731 & -43.5937477873131 \tabularnewline
88 & 2305 & 2356.72804265566 & -51.7280426556558 \tabularnewline
89 & 2188 & 2539.08435742891 & -351.084357428911 \tabularnewline
90 & 2720 & 2448.37213505697 & 271.627864943031 \tabularnewline
91 & 2398 & 2257.02889800291 & 140.971101997091 \tabularnewline
92 & 2147 & 2199.33817364837 & -52.3381736483684 \tabularnewline
93 & 1898 & 2253.94272245668 & -355.942722456683 \tabularnewline
94 & 2538 & 2268.87150259653 & 269.128497403467 \tabularnewline
95 & 2081 & 1976.00453059727 & 104.995469402734 \tabularnewline
96 & 2057 & 2219.38538054769 & -162.385380547686 \tabularnewline
97 & 2497 & 2366.36530768190 & 130.634692318104 \tabularnewline
98 & 2460 & 2206.94414390802 & 253.055856091976 \tabularnewline
99 & 2195 & 2577.05184215065 & -382.051842150655 \tabularnewline
100 & 2823 & 2261.40990062501 & 561.590099374991 \tabularnewline
101 & 2100 & 2505.27097288365 & -405.27097288365 \tabularnewline
102 & 2640 & 2590.37887889006 & 49.621121109943 \tabularnewline
103 & 2342 & 2306.47817788752 & 35.5218221124765 \tabularnewline
104 & 2171 & 2165.25204089819 & 5.7479591018132 \tabularnewline
105 & 2482 & 2143.28164944744 & 338.718350552561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41159&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]2074[/C][C]2141.93536324786[/C][C]-67.9353632478637[/C][/ROW]
[ROW][C]14[/C][C]2049[/C][C]2102.77000853926[/C][C]-53.7700085392644[/C][/ROW]
[ROW][C]15[/C][C]2406[/C][C]2458.45107986328[/C][C]-52.4510798632814[/C][/ROW]
[ROW][C]16[/C][C]2558[/C][C]2585.14909568857[/C][C]-27.1490956885655[/C][/ROW]
[ROW][C]17[/C][C]2251[/C][C]2265.28823320274[/C][C]-14.2882332027352[/C][/ROW]
[ROW][C]18[/C][C]2059[/C][C]2076.19545728523[/C][C]-17.1954572852301[/C][/ROW]
[ROW][C]19[/C][C]2397[/C][C]2224.14212484319[/C][C]172.857875156807[/C][/ROW]
[ROW][C]20[/C][C]1747[/C][C]2037.68498672405[/C][C]-290.684986724054[/C][/ROW]
[ROW][C]21[/C][C]1707[/C][C]1761.91314380543[/C][C]-54.9131438054333[/C][/ROW]
[ROW][C]22[/C][C]2319[/C][C]1947.31205372759[/C][C]371.687946272413[/C][/ROW]
[ROW][C]23[/C][C]1631[/C][C]1889.56177944909[/C][C]-258.561779449087[/C][/ROW]
[ROW][C]24[/C][C]1627[/C][C]1588.36073130781[/C][C]38.6392686921906[/C][/ROW]
[ROW][C]25[/C][C]1791[/C][C]1907.75529479443[/C][C]-116.755294794434[/C][/ROW]
[ROW][C]26[/C][C]2034[/C][C]1859.44629684248[/C][C]174.553703157516[/C][/ROW]
[ROW][C]27[/C][C]1997[/C][C]2270.74258262418[/C][C]-273.742582624177[/C][/ROW]
[ROW][C]28[/C][C]2169[/C][C]2349.68694120936[/C][C]-180.686941209358[/C][/ROW]
[ROW][C]29[/C][C]2028[/C][C]1994.0612437758[/C][C]33.9387562241989[/C][/ROW]
[ROW][C]30[/C][C]2253[/C][C]1813.83043889310[/C][C]439.169561106896[/C][/ROW]
[ROW][C]31[/C][C]2218[/C][C]2130.28309877620[/C][C]87.7169012237955[/C][/ROW]
[ROW][C]32[/C][C]1855[/C][C]1783.64150072934[/C][C]71.3584992706608[/C][/ROW]
[ROW][C]33[/C][C]2187[/C][C]1668.53642928732[/C][C]518.463570712676[/C][/ROW]
[ROW][C]34[/C][C]1852[/C][C]2126.27472463116[/C][C]-274.274724631161[/C][/ROW]
[ROW][C]35[/C][C]1570[/C][C]1723.14439010108[/C][C]-153.144390101079[/C][/ROW]
[ROW][C]36[/C][C]1851[/C][C]1538.75414635396[/C][C]312.245853646036[/C][/ROW]
[ROW][C]37[/C][C]1954[/C][C]1881.26157993508[/C][C]72.7384200649212[/C][/ROW]
[ROW][C]38[/C][C]1828[/C][C]1970.7806937783[/C][C]-142.780693778301[/C][/ROW]
[ROW][C]39[/C][C]2251[/C][C]2172.64768095312[/C][C]78.3523190468832[/C][/ROW]
[ROW][C]40[/C][C]2277[/C][C]2369.6027385011[/C][C]-92.6027385011012[/C][/ROW]
[ROW][C]41[/C][C]2085[/C][C]2104.68424549635[/C][C]-19.6842454963517[/C][/ROW]
[ROW][C]42[/C][C]2282[/C][C]2037.67226268747[/C][C]244.327737312528[/C][/ROW]
[ROW][C]43[/C][C]2266[/C][C]2204.58270454306[/C][C]61.4172954569367[/C][/ROW]
[ROW][C]44[/C][C]1878[/C][C]1850.00714303399[/C][C]27.9928569660087[/C][/ROW]
[ROW][C]45[/C][C]2267[/C][C]1861.87875317538[/C][C]405.121246824616[/C][/ROW]
[ROW][C]46[/C][C]2069[/C][C]2056.38399510040[/C][C]12.616004899603[/C][/ROW]
[ROW][C]47[/C][C]1746[/C][C]1763.54335798965[/C][C]-17.5433579896455[/C][/ROW]
[ROW][C]48[/C][C]2299[/C][C]1756.74565401575[/C][C]542.254345984248[/C][/ROW]
[ROW][C]49[/C][C]2360[/C][C]2089.14236508221[/C][C]270.857634917789[/C][/ROW]
[ROW][C]50[/C][C]2214[/C][C]2168.98727518902[/C][C]45.0127248109839[/C][/ROW]
[ROW][C]51[/C][C]2825[/C][C]2490.83118453767[/C][C]334.168815462334[/C][/ROW]
[ROW][C]52[/C][C]2355[/C][C]2707.77259984061[/C][C]-352.772599840605[/C][/ROW]
[ROW][C]53[/C][C]2333[/C][C]2409.20027051493[/C][C]-76.200270514933[/C][/ROW]
[ROW][C]54[/C][C]3016[/C][C]2415.26421869386[/C][C]600.73578130614[/C][/ROW]
[ROW][C]55[/C][C]2155[/C][C]2623.25817848311[/C][C]-468.258178483112[/C][/ROW]
[ROW][C]56[/C][C]2172[/C][C]2136.30277337822[/C][C]35.6972266217767[/C][/ROW]
[ROW][C]57[/C][C]2150[/C][C]2270.05199379037[/C][C]-120.051993790372[/C][/ROW]
[ROW][C]58[/C][C]2533[/C][C]2222.77059727665[/C][C]310.229402723346[/C][/ROW]
[ROW][C]59[/C][C]2058[/C][C]1998.8529550737[/C][C]59.1470449263002[/C][/ROW]
[ROW][C]60[/C][C]2160[/C][C]2184.87083389630[/C][C]-24.8708338962956[/C][/ROW]
[ROW][C]61[/C][C]2260[/C][C]2300.69797605381[/C][C]-40.6979760538079[/C][/ROW]
[ROW][C]62[/C][C]2498[/C][C]2238.32763409113[/C][C]259.672365908869[/C][/ROW]
[ROW][C]63[/C][C]2695[/C][C]2701.92064729472[/C][C]-6.92064729471576[/C][/ROW]
[ROW][C]64[/C][C]2799[/C][C]2630.25191113638[/C][C]168.748088863620[/C][/ROW]
[ROW][C]65[/C][C]2945[/C][C]2545.2621503655[/C][C]399.737849634501[/C][/ROW]
[ROW][C]66[/C][C]2930[/C][C]2876.51226824777[/C][C]53.487731752226[/C][/ROW]
[ROW][C]67[/C][C]2318[/C][C]2633.13871952370[/C][C]-315.138719523695[/C][/ROW]
[ROW][C]68[/C][C]2540[/C][C]2338.81433512761[/C][C]201.185664872394[/C][/ROW]
[ROW][C]69[/C][C]2570[/C][C]2470.77598263163[/C][C]99.2240173683713[/C][/ROW]
[ROW][C]70[/C][C]2669[/C][C]2612.01764729391[/C][C]56.982352706093[/C][/ROW]
[ROW][C]71[/C][C]2450[/C][C]2255.54182604720[/C][C]194.458173952797[/C][/ROW]
[ROW][C]72[/C][C]2842[/C][C]2454.48911570999[/C][C]387.510884290008[/C][/ROW]
[ROW][C]73[/C][C]3440[/C][C]2673.26169729084[/C][C]766.738302709157[/C][/ROW]
[ROW][C]74[/C][C]2678[/C][C]2909.08831638889[/C][C]-231.088316388890[/C][/ROW]
[ROW][C]75[/C][C]2981[/C][C]3181.9598610077[/C][C]-200.959861007702[/C][/ROW]
[ROW][C]76[/C][C]2259[/C][C]3123.75310501022[/C][C]-864.753105010216[/C][/ROW]
[ROW][C]77[/C][C]2844[/C][C]2859.29241091157[/C][C]-15.2924109115679[/C][/ROW]
[ROW][C]78[/C][C]2546[/C][C]2986.09942425485[/C][C]-440.099424254849[/C][/ROW]
[ROW][C]79[/C][C]2456[/C][C]2509.96132662118[/C][C]-53.9613266211827[/C][/ROW]
[ROW][C]80[/C][C]2295[/C][C]2433.89451418500[/C][C]-138.894514185003[/C][/ROW]
[ROW][C]81[/C][C]2379[/C][C]2450.21110390858[/C][C]-71.2111039085758[/C][/ROW]
[ROW][C]82[/C][C]2479[/C][C]2534.20598417388[/C][C]-55.2059841738787[/C][/ROW]
[ROW][C]83[/C][C]2057[/C][C]2188.11313454535[/C][C]-131.113134545352[/C][/ROW]
[ROW][C]84[/C][C]2280[/C][C]2360.56339693259[/C][C]-80.563396932594[/C][/ROW]
[ROW][C]85[/C][C]2351[/C][C]2571.75109163386[/C][C]-220.751091633858[/C][/ROW]
[ROW][C]86[/C][C]2275[/C][C]2254.74689883006[/C][C]20.2531011699407[/C][/ROW]
[ROW][C]87[/C][C]2543[/C][C]2586.59374778731[/C][C]-43.5937477873131[/C][/ROW]
[ROW][C]88[/C][C]2305[/C][C]2356.72804265566[/C][C]-51.7280426556558[/C][/ROW]
[ROW][C]89[/C][C]2188[/C][C]2539.08435742891[/C][C]-351.084357428911[/C][/ROW]
[ROW][C]90[/C][C]2720[/C][C]2448.37213505697[/C][C]271.627864943031[/C][/ROW]
[ROW][C]91[/C][C]2398[/C][C]2257.02889800291[/C][C]140.971101997091[/C][/ROW]
[ROW][C]92[/C][C]2147[/C][C]2199.33817364837[/C][C]-52.3381736483684[/C][/ROW]
[ROW][C]93[/C][C]1898[/C][C]2253.94272245668[/C][C]-355.942722456683[/C][/ROW]
[ROW][C]94[/C][C]2538[/C][C]2268.87150259653[/C][C]269.128497403467[/C][/ROW]
[ROW][C]95[/C][C]2081[/C][C]1976.00453059727[/C][C]104.995469402734[/C][/ROW]
[ROW][C]96[/C][C]2057[/C][C]2219.38538054769[/C][C]-162.385380547686[/C][/ROW]
[ROW][C]97[/C][C]2497[/C][C]2366.36530768190[/C][C]130.634692318104[/C][/ROW]
[ROW][C]98[/C][C]2460[/C][C]2206.94414390802[/C][C]253.055856091976[/C][/ROW]
[ROW][C]99[/C][C]2195[/C][C]2577.05184215065[/C][C]-382.051842150655[/C][/ROW]
[ROW][C]100[/C][C]2823[/C][C]2261.40990062501[/C][C]561.590099374991[/C][/ROW]
[ROW][C]101[/C][C]2100[/C][C]2505.27097288365[/C][C]-405.27097288365[/C][/ROW]
[ROW][C]102[/C][C]2640[/C][C]2590.37887889006[/C][C]49.621121109943[/C][/ROW]
[ROW][C]103[/C][C]2342[/C][C]2306.47817788752[/C][C]35.5218221124765[/C][/ROW]
[ROW][C]104[/C][C]2171[/C][C]2165.25204089819[/C][C]5.7479591018132[/C][/ROW]
[ROW][C]105[/C][C]2482[/C][C]2143.28164944744[/C][C]338.718350552561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41159&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
1320742141.93536324786-67.9353632478637
1420492102.77000853926-53.7700085392644
1524062458.45107986328-52.4510798632814
1625582585.14909568857-27.1490956885655
1722512265.28823320274-14.2882332027352
1820592076.19545728523-17.1954572852301
1923972224.14212484319172.857875156807
2017472037.68498672405-290.684986724054
2117071761.91314380543-54.9131438054333
2223191947.31205372759371.687946272413
2316311889.56177944909-258.561779449087
2416271588.3607313078138.6392686921906
2517911907.75529479443-116.755294794434
2620341859.44629684248174.553703157516
2719972270.74258262418-273.742582624177
2821692349.68694120936-180.686941209358
2920281994.061243775833.9387562241989
3022531813.83043889310439.169561106896
3122182130.2830987762087.7169012237955
3218551783.6415007293471.3584992706608
3321871668.53642928732518.463570712676
3418522126.27472463116-274.274724631161
3515701723.14439010108-153.144390101079
3618511538.75414635396312.245853646036
3719541881.2615799350872.7384200649212
3818281970.7806937783-142.780693778301
3922512172.6476809531278.3523190468832
4022772369.6027385011-92.6027385011012
4120852104.68424549635-19.6842454963517
4222822037.67226268747244.327737312528
4322662204.5827045430661.4172954569367
4418781850.0071430339927.9928569660087
4522671861.87875317538405.121246824616
4620692056.3839951004012.616004899603
4717461763.54335798965-17.5433579896455
4822991756.74565401575542.254345984248
4923602089.14236508221270.857634917789
5022142168.9872751890245.0127248109839
5128252490.83118453767334.168815462334
5223552707.77259984061-352.772599840605
5323332409.20027051493-76.200270514933
5430162415.26421869386600.73578130614
5521552623.25817848311-468.258178483112
5621722136.3027733782235.6972266217767
5721502270.05199379037-120.051993790372
5825332222.77059727665310.229402723346
5920581998.852955073759.1470449263002
6021602184.87083389630-24.8708338962956
6122602300.69797605381-40.6979760538079
6224982238.32763409113259.672365908869
6326952701.92064729472-6.92064729471576
6427992630.25191113638168.748088863620
6529452545.2621503655399.737849634501
6629302876.5122682477753.487731752226
6723182633.13871952370-315.138719523695
6825402338.81433512761201.185664872394
6925702470.7759826316399.2240173683713
7026692612.0176472939156.982352706093
7124502255.54182604720194.458173952797
7228422454.48911570999387.510884290008
7334402673.26169729084766.738302709157
7426782909.08831638889-231.088316388890
7529813181.9598610077-200.959861007702
7622593123.75310501022-864.753105010216
7728442859.29241091157-15.2924109115679
7825462986.09942425485-440.099424254849
7924562509.96132662118-53.9613266211827
8022952433.89451418500-138.894514185003
8123792450.21110390858-71.2111039085758
8224792534.20598417388-55.2059841738787
8320572188.11313454535-131.113134545352
8422802360.56339693259-80.563396932594
8523512571.75109163386-220.751091633858
8622752254.7468988300620.2531011699407
8725432586.59374778731-43.5937477873131
8823052356.72804265566-51.7280426556558
8921882539.08435742891-351.084357428911
9027202448.37213505697271.627864943031
9123982257.02889800291140.971101997091
9221472199.33817364837-52.3381736483684
9318982253.94272245668-355.942722456683
9425382268.87150259653269.128497403467
9520811976.00453059727104.995469402734
9620572219.38538054769-162.385380547686
9724972366.36530768190130.634692318104
9824602206.94414390802253.055856091976
9921952577.05184215065-382.051842150655
10028232261.40990062501561.590099374991
10121002505.27097288365-405.27097288365
10226402590.3788788900649.621121109943
10323422306.4781778875235.5218221124765
10421712165.252040898195.7479591018132
10524822143.28164944744338.718350552561







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1062519.191721758732006.536268111793031.84717540566
1072114.126650284701585.882300310742642.37100025866
1082253.717113601801709.723703549222797.71052365438
1092531.234222429521971.333346101733091.13509875732
1102379.084752902841803.119699162232955.04980664345
1112497.734396794471905.550090949563089.91870263938
1122561.632884667981953.075833403723170.18993593224
1132378.317291437011753.235530985853003.39905188818
1142700.954480081412059.197527364993342.71143279784
1152402.636999908291744.055806408283061.2181934083
1162245.538477426711569.985385568022921.09156928539
1172323.93009986661631.258801718143016.60139801507

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
106 & 2519.19172175873 & 2006.53626811179 & 3031.84717540566 \tabularnewline
107 & 2114.12665028470 & 1585.88230031074 & 2642.37100025866 \tabularnewline
108 & 2253.71711360180 & 1709.72370354922 & 2797.71052365438 \tabularnewline
109 & 2531.23422242952 & 1971.33334610173 & 3091.13509875732 \tabularnewline
110 & 2379.08475290284 & 1803.11969916223 & 2955.04980664345 \tabularnewline
111 & 2497.73439679447 & 1905.55009094956 & 3089.91870263938 \tabularnewline
112 & 2561.63288466798 & 1953.07583340372 & 3170.18993593224 \tabularnewline
113 & 2378.31729143701 & 1753.23553098585 & 3003.39905188818 \tabularnewline
114 & 2700.95448008141 & 2059.19752736499 & 3342.71143279784 \tabularnewline
115 & 2402.63699990829 & 1744.05580640828 & 3061.2181934083 \tabularnewline
116 & 2245.53847742671 & 1569.98538556802 & 2921.09156928539 \tabularnewline
117 & 2323.9300998666 & 1631.25880171814 & 3016.60139801507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41159&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]106[/C][C]2519.19172175873[/C][C]2006.53626811179[/C][C]3031.84717540566[/C][/ROW]
[ROW][C]107[/C][C]2114.12665028470[/C][C]1585.88230031074[/C][C]2642.37100025866[/C][/ROW]
[ROW][C]108[/C][C]2253.71711360180[/C][C]1709.72370354922[/C][C]2797.71052365438[/C][/ROW]
[ROW][C]109[/C][C]2531.23422242952[/C][C]1971.33334610173[/C][C]3091.13509875732[/C][/ROW]
[ROW][C]110[/C][C]2379.08475290284[/C][C]1803.11969916223[/C][C]2955.04980664345[/C][/ROW]
[ROW][C]111[/C][C]2497.73439679447[/C][C]1905.55009094956[/C][C]3089.91870263938[/C][/ROW]
[ROW][C]112[/C][C]2561.63288466798[/C][C]1953.07583340372[/C][C]3170.18993593224[/C][/ROW]
[ROW][C]113[/C][C]2378.31729143701[/C][C]1753.23553098585[/C][C]3003.39905188818[/C][/ROW]
[ROW][C]114[/C][C]2700.95448008141[/C][C]2059.19752736499[/C][C]3342.71143279784[/C][/ROW]
[ROW][C]115[/C][C]2402.63699990829[/C][C]1744.05580640828[/C][C]3061.2181934083[/C][/ROW]
[ROW][C]116[/C][C]2245.53847742671[/C][C]1569.98538556802[/C][C]2921.09156928539[/C][/ROW]
[ROW][C]117[/C][C]2323.9300998666[/C][C]1631.25880171814[/C][C]3016.60139801507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41159&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41159&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
1062519.191721758732006.536268111793031.84717540566
1072114.126650284701585.882300310742642.37100025866
1082253.717113601801709.723703549222797.71052365438
1092531.234222429521971.333346101733091.13509875732
1102379.084752902841803.119699162232955.04980664345
1112497.734396794471905.550090949563089.91870263938
1122561.632884667981953.075833403723170.18993593224
1132378.317291437011753.235530985853003.39905188818
1142700.954480081412059.197527364993342.71143279784
1152402.636999908291744.055806408283061.2181934083
1162245.538477426711569.985385568022921.09156928539
1172323.93009986661631.258801718143016.60139801507



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')