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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 computationThu, 06 Dec 2018 10:54:57 +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/2018/Dec/06/t1544090189fujbxt5opqgqhxr.htm/, Retrieved Fri, 03 May 2024 02:13:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315784, Retrieved Fri, 03 May 2024 02:13:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2018-12-06 09:54:57] [31e4af57f5325aef593e09d831d2befc] [Current]
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Dataseries X:
2570
2669
2450
2842
3440
2678
2981
2260
2844
2546
2456
2295
2379
2471
2057
2280
2351
2276
2548
2311
2201
2725
2408
2139
1898
2539
2070
2063
2565
2443
2196
2799
2076
2628
2292
2155
2476
2138
1854
2081
1795
1756
2237
1960
1829
2524
2077
2366
2185
2098
1836
1863
2044
2136
2931
3263
3328
3570
2313
1623
1316
1507
1419
1660
1790
1733
2086
1814
2241
1943
1773
2143
2087
1805
1913
2296
2500
2210
2526
2249
2024
2091
2045
1882
1831
1964
1763
1688
2149
1823
2094
2145
1791
1996
2097
1796
1963
2042
1746
2210
2968
3126
3708
3015
1569
1518
1393
1615
1777
1648
1463
1779




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315784&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315784&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 time3 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.84683402486491
beta0.0224388718805353
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.84683402486491 \tabularnewline
beta & 0.0224388718805353 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315784&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]0.84683402486491[/C][/ROW]
[ROW][C]beta[/C][C]0.0224388718805353[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315784&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
alpha0.84683402486491
beta0.0224388718805353
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
324502768-318
428422591.66414403317250.335855966832
534402901.37131043192538.628689568077
626783465.44967990938-787.449679909375
729812891.5966475102489.4033524897559
822603061.99144027349-801.991440273491
928442462.28335143855381.716648561454
1025462872.23292756458-326.232927564584
1124562676.46763658748-220.467636587481
1222952566.07866658764-271.078666587639
1323792407.67951747674-28.6795174767367
1424712454.0072472347616.9927527652358
1520572539.33470571776-482.334705717759
1622802192.6493586392987.3506413607051
1723512330.0527838374120.9472161625899
1822762411.62156821565-135.621568215649
1925482358.02549768592189.974502314076
2023112583.76515357178-272.765153571777
2122012412.45804069975-211.458040699753
2227252289.04975124486435.950248755144
2324082722.17275598877-314.17275598877
2421392514.09616671327-375.096166713266
2518982247.29998289503-349.299982895026
2625391995.71148690509543.288513094905
2720702510.32086795041-440.320867950413
2820632183.60938073466-120.609380734658
2925652125.34863955797439.65136044203
3024432549.89001203952-106.890012039517
3121962509.57043027845-313.570430278452
3227992288.26837270424510.731627295763
3320762774.71826672792-698.718266727924
3426282223.68779448736404.312205512645
3522922614.42379720808-322.42379720808
3621552383.60832867541-228.608328675407
3724762227.89497545037248.105024549629
3821382480.59320156688-342.593201566881
3918542226.5581153-372.558115299996
4020811940.06837115479140.931628845213
4117952091.09719660873-296.097196608734
4217561866.4087038359-110.408703835898
4322371796.86955855793440.130441442067
4419602201.90905225243-241.909052252431
4518292024.77754052841-195.777540528407
4625241882.99159768881641.00840231119
4720772462.00490455569-385.004904555688
4823662164.83936993477201.160630065225
4921852367.8812085643-182.881208564304
5020982242.22824251114-144.228242511144
5118362146.56729818243-310.567298182433
5218631904.14338198892-41.1433819889198
5320441889.09499858814154.905001411863
5421362043.0105616368592.9894383631486
5529312146.26090455251784.739095447494
5632632850.22000621506412.77999378494
5733283247.0351302510980.9648697489101
5835703364.39641175883205.603588241168
5923133591.21288032379-1278.21288032379
6016232537.19447526081-914.194475260806
6113161774.06771769142-458.06771769142
6215071388.5004152254118.499584774601
6314191493.44165124435-74.4416512443499
6416601433.57914353202226.42085646798
6517901632.79969331385157.20030668615
6617331776.38904657778-43.3890465777779
6720861749.28803180094336.711968199065
6818142050.46769010583-236.467690105831
6922411861.76595230585379.234047694154
7019432201.66760068893-258.66760068893
7117731996.45722690688-223.45722690688
7221431816.81806140398326.181938596018
7320872108.83015190582-21.8301519058246
7418052105.71894655572-300.718946555722
7519131860.7209592635352.2790407364707
7622961915.6470846611380.352915338899
7725002255.62479591006244.375204089943
7822102485.09557232421-275.095572324205
7925262269.43345423083256.566545769168
8022492508.87618502162-259.876185021619
8120242306.03947216798-282.039472167976
8220912079.0748195527811.9251804472187
8320452101.27603916083-56.2760391608272
8418822064.65278816078-182.652788160781
8518311917.53863784079-86.5386378407873
8619641850.17281307022113.827186929777
8717631954.64653036293-191.646530362935
8816881796.79304274422-108.793042744224
8921491707.03542210108441.964577898921
9018232092.07630506452-269.076305064524
9120941869.87058726511224.129412734892
9221452069.5871596990975.4128403009122
9317912144.79847334026-353.798473340264
9419961849.81616407619146.183835923806
9520971981.01367140518115.986328594822
9617962088.84287429964-292.842874299638
9719631844.89699747217118.103002527833
9820421951.1982647963890.8017352036175
9917462036.10530461793-290.105304617932
10022101792.93472175512417.065278244876
10129682156.54532433972811.454675660282
10231262869.55754960111256.442450398885
10337083117.43945778587590.560542214131
10430153659.4857659769-644.485765976903
10515693143.40631946171-1574.40631946171
10615181809.92163865593-291.921638655933
10713931556.94152689188-163.941526891875
10816151409.22411135081205.775888649189
10917771578.50613634984198.493863650159
11016481745.39327524418-97.3932752441772
11114631659.86245036836-196.862450368358
11217791486.35696325322292.643036746778

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2450 & 2768 & -318 \tabularnewline
4 & 2842 & 2591.66414403317 & 250.335855966832 \tabularnewline
5 & 3440 & 2901.37131043192 & 538.628689568077 \tabularnewline
6 & 2678 & 3465.44967990938 & -787.449679909375 \tabularnewline
7 & 2981 & 2891.59664751024 & 89.4033524897559 \tabularnewline
8 & 2260 & 3061.99144027349 & -801.991440273491 \tabularnewline
9 & 2844 & 2462.28335143855 & 381.716648561454 \tabularnewline
10 & 2546 & 2872.23292756458 & -326.232927564584 \tabularnewline
11 & 2456 & 2676.46763658748 & -220.467636587481 \tabularnewline
12 & 2295 & 2566.07866658764 & -271.078666587639 \tabularnewline
13 & 2379 & 2407.67951747674 & -28.6795174767367 \tabularnewline
14 & 2471 & 2454.00724723476 & 16.9927527652358 \tabularnewline
15 & 2057 & 2539.33470571776 & -482.334705717759 \tabularnewline
16 & 2280 & 2192.64935863929 & 87.3506413607051 \tabularnewline
17 & 2351 & 2330.05278383741 & 20.9472161625899 \tabularnewline
18 & 2276 & 2411.62156821565 & -135.621568215649 \tabularnewline
19 & 2548 & 2358.02549768592 & 189.974502314076 \tabularnewline
20 & 2311 & 2583.76515357178 & -272.765153571777 \tabularnewline
21 & 2201 & 2412.45804069975 & -211.458040699753 \tabularnewline
22 & 2725 & 2289.04975124486 & 435.950248755144 \tabularnewline
23 & 2408 & 2722.17275598877 & -314.17275598877 \tabularnewline
24 & 2139 & 2514.09616671327 & -375.096166713266 \tabularnewline
25 & 1898 & 2247.29998289503 & -349.299982895026 \tabularnewline
26 & 2539 & 1995.71148690509 & 543.288513094905 \tabularnewline
27 & 2070 & 2510.32086795041 & -440.320867950413 \tabularnewline
28 & 2063 & 2183.60938073466 & -120.609380734658 \tabularnewline
29 & 2565 & 2125.34863955797 & 439.65136044203 \tabularnewline
30 & 2443 & 2549.89001203952 & -106.890012039517 \tabularnewline
31 & 2196 & 2509.57043027845 & -313.570430278452 \tabularnewline
32 & 2799 & 2288.26837270424 & 510.731627295763 \tabularnewline
33 & 2076 & 2774.71826672792 & -698.718266727924 \tabularnewline
34 & 2628 & 2223.68779448736 & 404.312205512645 \tabularnewline
35 & 2292 & 2614.42379720808 & -322.42379720808 \tabularnewline
36 & 2155 & 2383.60832867541 & -228.608328675407 \tabularnewline
37 & 2476 & 2227.89497545037 & 248.105024549629 \tabularnewline
38 & 2138 & 2480.59320156688 & -342.593201566881 \tabularnewline
39 & 1854 & 2226.5581153 & -372.558115299996 \tabularnewline
40 & 2081 & 1940.06837115479 & 140.931628845213 \tabularnewline
41 & 1795 & 2091.09719660873 & -296.097196608734 \tabularnewline
42 & 1756 & 1866.4087038359 & -110.408703835898 \tabularnewline
43 & 2237 & 1796.86955855793 & 440.130441442067 \tabularnewline
44 & 1960 & 2201.90905225243 & -241.909052252431 \tabularnewline
45 & 1829 & 2024.77754052841 & -195.777540528407 \tabularnewline
46 & 2524 & 1882.99159768881 & 641.00840231119 \tabularnewline
47 & 2077 & 2462.00490455569 & -385.004904555688 \tabularnewline
48 & 2366 & 2164.83936993477 & 201.160630065225 \tabularnewline
49 & 2185 & 2367.8812085643 & -182.881208564304 \tabularnewline
50 & 2098 & 2242.22824251114 & -144.228242511144 \tabularnewline
51 & 1836 & 2146.56729818243 & -310.567298182433 \tabularnewline
52 & 1863 & 1904.14338198892 & -41.1433819889198 \tabularnewline
53 & 2044 & 1889.09499858814 & 154.905001411863 \tabularnewline
54 & 2136 & 2043.01056163685 & 92.9894383631486 \tabularnewline
55 & 2931 & 2146.26090455251 & 784.739095447494 \tabularnewline
56 & 3263 & 2850.22000621506 & 412.77999378494 \tabularnewline
57 & 3328 & 3247.03513025109 & 80.9648697489101 \tabularnewline
58 & 3570 & 3364.39641175883 & 205.603588241168 \tabularnewline
59 & 2313 & 3591.21288032379 & -1278.21288032379 \tabularnewline
60 & 1623 & 2537.19447526081 & -914.194475260806 \tabularnewline
61 & 1316 & 1774.06771769142 & -458.06771769142 \tabularnewline
62 & 1507 & 1388.5004152254 & 118.499584774601 \tabularnewline
63 & 1419 & 1493.44165124435 & -74.4416512443499 \tabularnewline
64 & 1660 & 1433.57914353202 & 226.42085646798 \tabularnewline
65 & 1790 & 1632.79969331385 & 157.20030668615 \tabularnewline
66 & 1733 & 1776.38904657778 & -43.3890465777779 \tabularnewline
67 & 2086 & 1749.28803180094 & 336.711968199065 \tabularnewline
68 & 1814 & 2050.46769010583 & -236.467690105831 \tabularnewline
69 & 2241 & 1861.76595230585 & 379.234047694154 \tabularnewline
70 & 1943 & 2201.66760068893 & -258.66760068893 \tabularnewline
71 & 1773 & 1996.45722690688 & -223.45722690688 \tabularnewline
72 & 2143 & 1816.81806140398 & 326.181938596018 \tabularnewline
73 & 2087 & 2108.83015190582 & -21.8301519058246 \tabularnewline
74 & 1805 & 2105.71894655572 & -300.718946555722 \tabularnewline
75 & 1913 & 1860.72095926353 & 52.2790407364707 \tabularnewline
76 & 2296 & 1915.6470846611 & 380.352915338899 \tabularnewline
77 & 2500 & 2255.62479591006 & 244.375204089943 \tabularnewline
78 & 2210 & 2485.09557232421 & -275.095572324205 \tabularnewline
79 & 2526 & 2269.43345423083 & 256.566545769168 \tabularnewline
80 & 2249 & 2508.87618502162 & -259.876185021619 \tabularnewline
81 & 2024 & 2306.03947216798 & -282.039472167976 \tabularnewline
82 & 2091 & 2079.07481955278 & 11.9251804472187 \tabularnewline
83 & 2045 & 2101.27603916083 & -56.2760391608272 \tabularnewline
84 & 1882 & 2064.65278816078 & -182.652788160781 \tabularnewline
85 & 1831 & 1917.53863784079 & -86.5386378407873 \tabularnewline
86 & 1964 & 1850.17281307022 & 113.827186929777 \tabularnewline
87 & 1763 & 1954.64653036293 & -191.646530362935 \tabularnewline
88 & 1688 & 1796.79304274422 & -108.793042744224 \tabularnewline
89 & 2149 & 1707.03542210108 & 441.964577898921 \tabularnewline
90 & 1823 & 2092.07630506452 & -269.076305064524 \tabularnewline
91 & 2094 & 1869.87058726511 & 224.129412734892 \tabularnewline
92 & 2145 & 2069.58715969909 & 75.4128403009122 \tabularnewline
93 & 1791 & 2144.79847334026 & -353.798473340264 \tabularnewline
94 & 1996 & 1849.81616407619 & 146.183835923806 \tabularnewline
95 & 2097 & 1981.01367140518 & 115.986328594822 \tabularnewline
96 & 1796 & 2088.84287429964 & -292.842874299638 \tabularnewline
97 & 1963 & 1844.89699747217 & 118.103002527833 \tabularnewline
98 & 2042 & 1951.19826479638 & 90.8017352036175 \tabularnewline
99 & 1746 & 2036.10530461793 & -290.105304617932 \tabularnewline
100 & 2210 & 1792.93472175512 & 417.065278244876 \tabularnewline
101 & 2968 & 2156.54532433972 & 811.454675660282 \tabularnewline
102 & 3126 & 2869.55754960111 & 256.442450398885 \tabularnewline
103 & 3708 & 3117.43945778587 & 590.560542214131 \tabularnewline
104 & 3015 & 3659.4857659769 & -644.485765976903 \tabularnewline
105 & 1569 & 3143.40631946171 & -1574.40631946171 \tabularnewline
106 & 1518 & 1809.92163865593 & -291.921638655933 \tabularnewline
107 & 1393 & 1556.94152689188 & -163.941526891875 \tabularnewline
108 & 1615 & 1409.22411135081 & 205.775888649189 \tabularnewline
109 & 1777 & 1578.50613634984 & 198.493863650159 \tabularnewline
110 & 1648 & 1745.39327524418 & -97.3932752441772 \tabularnewline
111 & 1463 & 1659.86245036836 & -196.862450368358 \tabularnewline
112 & 1779 & 1486.35696325322 & 292.643036746778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315784&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]3[/C][C]2450[/C][C]2768[/C][C]-318[/C][/ROW]
[ROW][C]4[/C][C]2842[/C][C]2591.66414403317[/C][C]250.335855966832[/C][/ROW]
[ROW][C]5[/C][C]3440[/C][C]2901.37131043192[/C][C]538.628689568077[/C][/ROW]
[ROW][C]6[/C][C]2678[/C][C]3465.44967990938[/C][C]-787.449679909375[/C][/ROW]
[ROW][C]7[/C][C]2981[/C][C]2891.59664751024[/C][C]89.4033524897559[/C][/ROW]
[ROW][C]8[/C][C]2260[/C][C]3061.99144027349[/C][C]-801.991440273491[/C][/ROW]
[ROW][C]9[/C][C]2844[/C][C]2462.28335143855[/C][C]381.716648561454[/C][/ROW]
[ROW][C]10[/C][C]2546[/C][C]2872.23292756458[/C][C]-326.232927564584[/C][/ROW]
[ROW][C]11[/C][C]2456[/C][C]2676.46763658748[/C][C]-220.467636587481[/C][/ROW]
[ROW][C]12[/C][C]2295[/C][C]2566.07866658764[/C][C]-271.078666587639[/C][/ROW]
[ROW][C]13[/C][C]2379[/C][C]2407.67951747674[/C][C]-28.6795174767367[/C][/ROW]
[ROW][C]14[/C][C]2471[/C][C]2454.00724723476[/C][C]16.9927527652358[/C][/ROW]
[ROW][C]15[/C][C]2057[/C][C]2539.33470571776[/C][C]-482.334705717759[/C][/ROW]
[ROW][C]16[/C][C]2280[/C][C]2192.64935863929[/C][C]87.3506413607051[/C][/ROW]
[ROW][C]17[/C][C]2351[/C][C]2330.05278383741[/C][C]20.9472161625899[/C][/ROW]
[ROW][C]18[/C][C]2276[/C][C]2411.62156821565[/C][C]-135.621568215649[/C][/ROW]
[ROW][C]19[/C][C]2548[/C][C]2358.02549768592[/C][C]189.974502314076[/C][/ROW]
[ROW][C]20[/C][C]2311[/C][C]2583.76515357178[/C][C]-272.765153571777[/C][/ROW]
[ROW][C]21[/C][C]2201[/C][C]2412.45804069975[/C][C]-211.458040699753[/C][/ROW]
[ROW][C]22[/C][C]2725[/C][C]2289.04975124486[/C][C]435.950248755144[/C][/ROW]
[ROW][C]23[/C][C]2408[/C][C]2722.17275598877[/C][C]-314.17275598877[/C][/ROW]
[ROW][C]24[/C][C]2139[/C][C]2514.09616671327[/C][C]-375.096166713266[/C][/ROW]
[ROW][C]25[/C][C]1898[/C][C]2247.29998289503[/C][C]-349.299982895026[/C][/ROW]
[ROW][C]26[/C][C]2539[/C][C]1995.71148690509[/C][C]543.288513094905[/C][/ROW]
[ROW][C]27[/C][C]2070[/C][C]2510.32086795041[/C][C]-440.320867950413[/C][/ROW]
[ROW][C]28[/C][C]2063[/C][C]2183.60938073466[/C][C]-120.609380734658[/C][/ROW]
[ROW][C]29[/C][C]2565[/C][C]2125.34863955797[/C][C]439.65136044203[/C][/ROW]
[ROW][C]30[/C][C]2443[/C][C]2549.89001203952[/C][C]-106.890012039517[/C][/ROW]
[ROW][C]31[/C][C]2196[/C][C]2509.57043027845[/C][C]-313.570430278452[/C][/ROW]
[ROW][C]32[/C][C]2799[/C][C]2288.26837270424[/C][C]510.731627295763[/C][/ROW]
[ROW][C]33[/C][C]2076[/C][C]2774.71826672792[/C][C]-698.718266727924[/C][/ROW]
[ROW][C]34[/C][C]2628[/C][C]2223.68779448736[/C][C]404.312205512645[/C][/ROW]
[ROW][C]35[/C][C]2292[/C][C]2614.42379720808[/C][C]-322.42379720808[/C][/ROW]
[ROW][C]36[/C][C]2155[/C][C]2383.60832867541[/C][C]-228.608328675407[/C][/ROW]
[ROW][C]37[/C][C]2476[/C][C]2227.89497545037[/C][C]248.105024549629[/C][/ROW]
[ROW][C]38[/C][C]2138[/C][C]2480.59320156688[/C][C]-342.593201566881[/C][/ROW]
[ROW][C]39[/C][C]1854[/C][C]2226.5581153[/C][C]-372.558115299996[/C][/ROW]
[ROW][C]40[/C][C]2081[/C][C]1940.06837115479[/C][C]140.931628845213[/C][/ROW]
[ROW][C]41[/C][C]1795[/C][C]2091.09719660873[/C][C]-296.097196608734[/C][/ROW]
[ROW][C]42[/C][C]1756[/C][C]1866.4087038359[/C][C]-110.408703835898[/C][/ROW]
[ROW][C]43[/C][C]2237[/C][C]1796.86955855793[/C][C]440.130441442067[/C][/ROW]
[ROW][C]44[/C][C]1960[/C][C]2201.90905225243[/C][C]-241.909052252431[/C][/ROW]
[ROW][C]45[/C][C]1829[/C][C]2024.77754052841[/C][C]-195.777540528407[/C][/ROW]
[ROW][C]46[/C][C]2524[/C][C]1882.99159768881[/C][C]641.00840231119[/C][/ROW]
[ROW][C]47[/C][C]2077[/C][C]2462.00490455569[/C][C]-385.004904555688[/C][/ROW]
[ROW][C]48[/C][C]2366[/C][C]2164.83936993477[/C][C]201.160630065225[/C][/ROW]
[ROW][C]49[/C][C]2185[/C][C]2367.8812085643[/C][C]-182.881208564304[/C][/ROW]
[ROW][C]50[/C][C]2098[/C][C]2242.22824251114[/C][C]-144.228242511144[/C][/ROW]
[ROW][C]51[/C][C]1836[/C][C]2146.56729818243[/C][C]-310.567298182433[/C][/ROW]
[ROW][C]52[/C][C]1863[/C][C]1904.14338198892[/C][C]-41.1433819889198[/C][/ROW]
[ROW][C]53[/C][C]2044[/C][C]1889.09499858814[/C][C]154.905001411863[/C][/ROW]
[ROW][C]54[/C][C]2136[/C][C]2043.01056163685[/C][C]92.9894383631486[/C][/ROW]
[ROW][C]55[/C][C]2931[/C][C]2146.26090455251[/C][C]784.739095447494[/C][/ROW]
[ROW][C]56[/C][C]3263[/C][C]2850.22000621506[/C][C]412.77999378494[/C][/ROW]
[ROW][C]57[/C][C]3328[/C][C]3247.03513025109[/C][C]80.9648697489101[/C][/ROW]
[ROW][C]58[/C][C]3570[/C][C]3364.39641175883[/C][C]205.603588241168[/C][/ROW]
[ROW][C]59[/C][C]2313[/C][C]3591.21288032379[/C][C]-1278.21288032379[/C][/ROW]
[ROW][C]60[/C][C]1623[/C][C]2537.19447526081[/C][C]-914.194475260806[/C][/ROW]
[ROW][C]61[/C][C]1316[/C][C]1774.06771769142[/C][C]-458.06771769142[/C][/ROW]
[ROW][C]62[/C][C]1507[/C][C]1388.5004152254[/C][C]118.499584774601[/C][/ROW]
[ROW][C]63[/C][C]1419[/C][C]1493.44165124435[/C][C]-74.4416512443499[/C][/ROW]
[ROW][C]64[/C][C]1660[/C][C]1433.57914353202[/C][C]226.42085646798[/C][/ROW]
[ROW][C]65[/C][C]1790[/C][C]1632.79969331385[/C][C]157.20030668615[/C][/ROW]
[ROW][C]66[/C][C]1733[/C][C]1776.38904657778[/C][C]-43.3890465777779[/C][/ROW]
[ROW][C]67[/C][C]2086[/C][C]1749.28803180094[/C][C]336.711968199065[/C][/ROW]
[ROW][C]68[/C][C]1814[/C][C]2050.46769010583[/C][C]-236.467690105831[/C][/ROW]
[ROW][C]69[/C][C]2241[/C][C]1861.76595230585[/C][C]379.234047694154[/C][/ROW]
[ROW][C]70[/C][C]1943[/C][C]2201.66760068893[/C][C]-258.66760068893[/C][/ROW]
[ROW][C]71[/C][C]1773[/C][C]1996.45722690688[/C][C]-223.45722690688[/C][/ROW]
[ROW][C]72[/C][C]2143[/C][C]1816.81806140398[/C][C]326.181938596018[/C][/ROW]
[ROW][C]73[/C][C]2087[/C][C]2108.83015190582[/C][C]-21.8301519058246[/C][/ROW]
[ROW][C]74[/C][C]1805[/C][C]2105.71894655572[/C][C]-300.718946555722[/C][/ROW]
[ROW][C]75[/C][C]1913[/C][C]1860.72095926353[/C][C]52.2790407364707[/C][/ROW]
[ROW][C]76[/C][C]2296[/C][C]1915.6470846611[/C][C]380.352915338899[/C][/ROW]
[ROW][C]77[/C][C]2500[/C][C]2255.62479591006[/C][C]244.375204089943[/C][/ROW]
[ROW][C]78[/C][C]2210[/C][C]2485.09557232421[/C][C]-275.095572324205[/C][/ROW]
[ROW][C]79[/C][C]2526[/C][C]2269.43345423083[/C][C]256.566545769168[/C][/ROW]
[ROW][C]80[/C][C]2249[/C][C]2508.87618502162[/C][C]-259.876185021619[/C][/ROW]
[ROW][C]81[/C][C]2024[/C][C]2306.03947216798[/C][C]-282.039472167976[/C][/ROW]
[ROW][C]82[/C][C]2091[/C][C]2079.07481955278[/C][C]11.9251804472187[/C][/ROW]
[ROW][C]83[/C][C]2045[/C][C]2101.27603916083[/C][C]-56.2760391608272[/C][/ROW]
[ROW][C]84[/C][C]1882[/C][C]2064.65278816078[/C][C]-182.652788160781[/C][/ROW]
[ROW][C]85[/C][C]1831[/C][C]1917.53863784079[/C][C]-86.5386378407873[/C][/ROW]
[ROW][C]86[/C][C]1964[/C][C]1850.17281307022[/C][C]113.827186929777[/C][/ROW]
[ROW][C]87[/C][C]1763[/C][C]1954.64653036293[/C][C]-191.646530362935[/C][/ROW]
[ROW][C]88[/C][C]1688[/C][C]1796.79304274422[/C][C]-108.793042744224[/C][/ROW]
[ROW][C]89[/C][C]2149[/C][C]1707.03542210108[/C][C]441.964577898921[/C][/ROW]
[ROW][C]90[/C][C]1823[/C][C]2092.07630506452[/C][C]-269.076305064524[/C][/ROW]
[ROW][C]91[/C][C]2094[/C][C]1869.87058726511[/C][C]224.129412734892[/C][/ROW]
[ROW][C]92[/C][C]2145[/C][C]2069.58715969909[/C][C]75.4128403009122[/C][/ROW]
[ROW][C]93[/C][C]1791[/C][C]2144.79847334026[/C][C]-353.798473340264[/C][/ROW]
[ROW][C]94[/C][C]1996[/C][C]1849.81616407619[/C][C]146.183835923806[/C][/ROW]
[ROW][C]95[/C][C]2097[/C][C]1981.01367140518[/C][C]115.986328594822[/C][/ROW]
[ROW][C]96[/C][C]1796[/C][C]2088.84287429964[/C][C]-292.842874299638[/C][/ROW]
[ROW][C]97[/C][C]1963[/C][C]1844.89699747217[/C][C]118.103002527833[/C][/ROW]
[ROW][C]98[/C][C]2042[/C][C]1951.19826479638[/C][C]90.8017352036175[/C][/ROW]
[ROW][C]99[/C][C]1746[/C][C]2036.10530461793[/C][C]-290.105304617932[/C][/ROW]
[ROW][C]100[/C][C]2210[/C][C]1792.93472175512[/C][C]417.065278244876[/C][/ROW]
[ROW][C]101[/C][C]2968[/C][C]2156.54532433972[/C][C]811.454675660282[/C][/ROW]
[ROW][C]102[/C][C]3126[/C][C]2869.55754960111[/C][C]256.442450398885[/C][/ROW]
[ROW][C]103[/C][C]3708[/C][C]3117.43945778587[/C][C]590.560542214131[/C][/ROW]
[ROW][C]104[/C][C]3015[/C][C]3659.4857659769[/C][C]-644.485765976903[/C][/ROW]
[ROW][C]105[/C][C]1569[/C][C]3143.40631946171[/C][C]-1574.40631946171[/C][/ROW]
[ROW][C]106[/C][C]1518[/C][C]1809.92163865593[/C][C]-291.921638655933[/C][/ROW]
[ROW][C]107[/C][C]1393[/C][C]1556.94152689188[/C][C]-163.941526891875[/C][/ROW]
[ROW][C]108[/C][C]1615[/C][C]1409.22411135081[/C][C]205.775888649189[/C][/ROW]
[ROW][C]109[/C][C]1777[/C][C]1578.50613634984[/C][C]198.493863650159[/C][/ROW]
[ROW][C]110[/C][C]1648[/C][C]1745.39327524418[/C][C]-97.3932752441772[/C][/ROW]
[ROW][C]111[/C][C]1463[/C][C]1659.86245036836[/C][C]-196.862450368358[/C][/ROW]
[ROW][C]112[/C][C]1779[/C][C]1486.35696325322[/C][C]292.643036746778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315784&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
324502768-318
428422591.66414403317250.335855966832
534402901.37131043192538.628689568077
626783465.44967990938-787.449679909375
729812891.5966475102489.4033524897559
822603061.99144027349-801.991440273491
928442462.28335143855381.716648561454
1025462872.23292756458-326.232927564584
1124562676.46763658748-220.467636587481
1222952566.07866658764-271.078666587639
1323792407.67951747674-28.6795174767367
1424712454.0072472347616.9927527652358
1520572539.33470571776-482.334705717759
1622802192.6493586392987.3506413607051
1723512330.0527838374120.9472161625899
1822762411.62156821565-135.621568215649
1925482358.02549768592189.974502314076
2023112583.76515357178-272.765153571777
2122012412.45804069975-211.458040699753
2227252289.04975124486435.950248755144
2324082722.17275598877-314.17275598877
2421392514.09616671327-375.096166713266
2518982247.29998289503-349.299982895026
2625391995.71148690509543.288513094905
2720702510.32086795041-440.320867950413
2820632183.60938073466-120.609380734658
2925652125.34863955797439.65136044203
3024432549.89001203952-106.890012039517
3121962509.57043027845-313.570430278452
3227992288.26837270424510.731627295763
3320762774.71826672792-698.718266727924
3426282223.68779448736404.312205512645
3522922614.42379720808-322.42379720808
3621552383.60832867541-228.608328675407
3724762227.89497545037248.105024549629
3821382480.59320156688-342.593201566881
3918542226.5581153-372.558115299996
4020811940.06837115479140.931628845213
4117952091.09719660873-296.097196608734
4217561866.4087038359-110.408703835898
4322371796.86955855793440.130441442067
4419602201.90905225243-241.909052252431
4518292024.77754052841-195.777540528407
4625241882.99159768881641.00840231119
4720772462.00490455569-385.004904555688
4823662164.83936993477201.160630065225
4921852367.8812085643-182.881208564304
5020982242.22824251114-144.228242511144
5118362146.56729818243-310.567298182433
5218631904.14338198892-41.1433819889198
5320441889.09499858814154.905001411863
5421362043.0105616368592.9894383631486
5529312146.26090455251784.739095447494
5632632850.22000621506412.77999378494
5733283247.0351302510980.9648697489101
5835703364.39641175883205.603588241168
5923133591.21288032379-1278.21288032379
6016232537.19447526081-914.194475260806
6113161774.06771769142-458.06771769142
6215071388.5004152254118.499584774601
6314191493.44165124435-74.4416512443499
6416601433.57914353202226.42085646798
6517901632.79969331385157.20030668615
6617331776.38904657778-43.3890465777779
6720861749.28803180094336.711968199065
6818142050.46769010583-236.467690105831
6922411861.76595230585379.234047694154
7019432201.66760068893-258.66760068893
7117731996.45722690688-223.45722690688
7221431816.81806140398326.181938596018
7320872108.83015190582-21.8301519058246
7418052105.71894655572-300.718946555722
7519131860.7209592635352.2790407364707
7622961915.6470846611380.352915338899
7725002255.62479591006244.375204089943
7822102485.09557232421-275.095572324205
7925262269.43345423083256.566545769168
8022492508.87618502162-259.876185021619
8120242306.03947216798-282.039472167976
8220912079.0748195527811.9251804472187
8320452101.27603916083-56.2760391608272
8418822064.65278816078-182.652788160781
8518311917.53863784079-86.5386378407873
8619641850.17281307022113.827186929777
8717631954.64653036293-191.646530362935
8816881796.79304274422-108.793042744224
8921491707.03542210108441.964577898921
9018232092.07630506452-269.076305064524
9120941869.87058726511224.129412734892
9221452069.5871596990975.4128403009122
9317912144.79847334026-353.798473340264
9419961849.81616407619146.183835923806
9520971981.01367140518115.986328594822
9617962088.84287429964-292.842874299638
9719631844.89699747217118.103002527833
9820421951.1982647963890.8017352036175
9917462036.10530461793-290.105304617932
10022101792.93472175512417.065278244876
10129682156.54532433972811.454675660282
10231262869.55754960111256.442450398885
10337083117.43945778587590.560542214131
10430153659.4857659769-644.485765976903
10515693143.40631946171-1574.40631946171
10615181809.92163865593-291.921638655933
10713931556.94152689188-163.941526891875
10816151409.22411135081205.775888649189
10917771578.50613634984198.493863650159
11016481745.39327524418-97.3932752441772
11114631659.86245036836-196.862450368358
11217791486.35696325322292.643036746778







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1131732.94218102454977.6588140666192488.22554798246
1141731.7073181389732.6549712406832730.75966503711
1151730.47245525325528.5011229592062932.4437875473
1161729.23759236761346.9375548913543111.53762984386
1171728.00272948196179.9160150324543276.08944393147
1181726.7678665963223.06475778796223430.47097540467
1191725.53300371067-126.2933299106163577.35933733196
1201724.29814082503-269.9320088836183718.52829053367
1211723.06327793938-409.0942202455493855.22077612431
1221721.82841505374-544.6882614419183988.34509154939
1231720.59355216809-677.3998980041324118.58700234031
1241719.35868928245-807.7605753222174246.47795388711

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
113 & 1732.94218102454 & 977.658814066619 & 2488.22554798246 \tabularnewline
114 & 1731.7073181389 & 732.654971240683 & 2730.75966503711 \tabularnewline
115 & 1730.47245525325 & 528.501122959206 & 2932.4437875473 \tabularnewline
116 & 1729.23759236761 & 346.937554891354 & 3111.53762984386 \tabularnewline
117 & 1728.00272948196 & 179.916015032454 & 3276.08944393147 \tabularnewline
118 & 1726.76786659632 & 23.0647577879622 & 3430.47097540467 \tabularnewline
119 & 1725.53300371067 & -126.293329910616 & 3577.35933733196 \tabularnewline
120 & 1724.29814082503 & -269.932008883618 & 3718.52829053367 \tabularnewline
121 & 1723.06327793938 & -409.094220245549 & 3855.22077612431 \tabularnewline
122 & 1721.82841505374 & -544.688261441918 & 3988.34509154939 \tabularnewline
123 & 1720.59355216809 & -677.399898004132 & 4118.58700234031 \tabularnewline
124 & 1719.35868928245 & -807.760575322217 & 4246.47795388711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315784&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]113[/C][C]1732.94218102454[/C][C]977.658814066619[/C][C]2488.22554798246[/C][/ROW]
[ROW][C]114[/C][C]1731.7073181389[/C][C]732.654971240683[/C][C]2730.75966503711[/C][/ROW]
[ROW][C]115[/C][C]1730.47245525325[/C][C]528.501122959206[/C][C]2932.4437875473[/C][/ROW]
[ROW][C]116[/C][C]1729.23759236761[/C][C]346.937554891354[/C][C]3111.53762984386[/C][/ROW]
[ROW][C]117[/C][C]1728.00272948196[/C][C]179.916015032454[/C][C]3276.08944393147[/C][/ROW]
[ROW][C]118[/C][C]1726.76786659632[/C][C]23.0647577879622[/C][C]3430.47097540467[/C][/ROW]
[ROW][C]119[/C][C]1725.53300371067[/C][C]-126.293329910616[/C][C]3577.35933733196[/C][/ROW]
[ROW][C]120[/C][C]1724.29814082503[/C][C]-269.932008883618[/C][C]3718.52829053367[/C][/ROW]
[ROW][C]121[/C][C]1723.06327793938[/C][C]-409.094220245549[/C][C]3855.22077612431[/C][/ROW]
[ROW][C]122[/C][C]1721.82841505374[/C][C]-544.688261441918[/C][C]3988.34509154939[/C][/ROW]
[ROW][C]123[/C][C]1720.59355216809[/C][C]-677.399898004132[/C][C]4118.58700234031[/C][/ROW]
[ROW][C]124[/C][C]1719.35868928245[/C][C]-807.760575322217[/C][C]4246.47795388711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315784&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315784&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
1131732.94218102454977.6588140666192488.22554798246
1141731.7073181389732.6549712406832730.75966503711
1151730.47245525325528.5011229592062932.4437875473
1161729.23759236761346.9375548913543111.53762984386
1171728.00272948196179.9160150324543276.08944393147
1181726.7678665963223.06475778796223430.47097540467
1191725.53300371067-126.2933299106163577.35933733196
1201724.29814082503-269.9320088836183718.52829053367
1211723.06327793938-409.0942202455493855.22077612431
1221721.82841505374-544.6882614419183988.34509154939
1231720.59355216809-677.3998980041324118.58700234031
1241719.35868928245-807.7605753222174246.47795388711



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')