Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 22:19:29 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448835678w14ipexl16iwgup.htm/, Retrieved Thu, 31 Oct 2024 23:58:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284548, Retrieved Thu, 31 Oct 2024 23:58:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Aantal niet-werke...] [2015-11-29 22:19:29] [f442d180d44854b5d66611a6a05f7502] [Current]
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Dataseries X:
64076
63136
60198
59057
57388
56708
70019
72263
74152
67057
61941
58331
59252
56568
53031
51840
48290
45817
59421
61621
60976
57497
53037
53088
53119
51644
47866
47691
42401
43069
55797
57170
58335
55439
54399
56316
58381
58468
59025
58298
54255
55670
67816
70485
71361
66953
64505
66770
66418
65277
62008
59096
55106
54954
67943
69411
69951
63966
60410
59440
59445
57614
55396
53030
50090
48764
61658
63943
64878
60634
57905
57224
60953
60621
57258
54903
53278
53042
63753
69210
71446
68408
65427
64630
66086
65058
62689
60841
57346
56222
68202
70745
73690
68992
65925
65546
67221
65315
62038
58774
55320
53900
65544
67906
70911
66544
63657
61720




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284548&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284548&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284548&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]0.999933893038648[/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=284548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284548&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26313664076-940
36019863136.0621405437-2938.06214054367
45905760198.1942263604-1141.19422636038
55738859057.0754408826-1669.07544088262
65670857388.1103375057-680.110337505663
77001956708.044960027813310.9550399722
87226370018.12005320962244.87994679039
97415272262.85159780811889.14840219189
106705774151.8751141396-7094.87511413959
116194167057.469020635-5116.46902063496
125833161941.3382342198-3610.33823421981
135925258331.2386684901920.761331509886
145656859251.9391312662-2683.93913126625
155303156568.1774270604-3537.17742706042
165184053031.2338320515-1191.23383205147
174829051840.0787488489-3550.0787488489
184581748290.2346849186-2473.23468491864
195942145817.163498029713603.8365019703
206162159420.10069170612200.89930829387
216097661620.8545052345-644.854505234485
225749760976.0426293719-3479.04262937186
235303757497.2299889366-4460.22998893664
245308853037.294852251550.7051477485002
255311953087.996648036831.0033519632416
265164453118.9979504626-1474.99795046261
274786651644.0975076325-3778.0975076325
284769147866.2497585459-175.24975854592
294240147691.011585229-5290.01158522902
304306942401.3497065914667.65029340858
315579743068.955863667912728.0441363321
325717055796.15858767821373.84141232181
335833557169.90917951891165.09082048114
345543958334.9229793862-2895.92297938616
355439955439.1914406685-1040.19144066847
365631654399.06876389541916.93123610463
375838156315.87327750092065.12672249914
385846858380.863480747687.1365192524318
395902558467.9942396695557.00576033051
405829859024.9631780417-726.963178041733
415425558298.0480573267-4043.04805732671
425567054255.26727362171414.73272637833
436781655669.906476318312146.0935236817
447048567815.19705866492669.80294133515
457136170484.8235074401876.176492559855
466695371360.9420786345-4407.94207863446
476450566953.2913956566-2448.29139565663
486677064505.16184910472264.83815089532
496641866769.8502784319-351.850278431899
506527766418.0232597528-1141.02325975276
516200865277.0754295805-3269.07542958054
525909662008.2161086431-2912.21610864308
535510659096.1925177577-3990.19251775774
545495455106.2637795026-152.263779502558
556794354954.010065695812988.9899343042
566941167942.14133734441468.85866265559
576995169410.9028982172540.097101782841
586396669950.9642958218-5984.96429582176
596041063966.3956478034-3556.39564780339
605944060410.2351025096-970.235102509643
615944559440.06413929444.93586070557649
625761459444.9996737052-1830.99967370525
635539657614.1210418247-2218.12104182467
645303055396.146633242-2366.14663324199
655009053030.156418764-2940.15641876403
664876450090.1943648067-1326.19436480674
676165848764.087670679612893.9123293204
686394361657.1476226362285.85237736403
696487863942.8488892452935.151110754763
706063464877.9381800017-4243.93818000166
715790560634.2805538573-2729.28055385725
725722457905.1804244441-681.180424444086
736095357224.0450307683728.95496923201
746062160952.753490118-331.753490117968
755725860621.0219312151-3363.02193121515
765490357258.2223191608-2355.22231916083
775327854903.1556965908-1625.15569659083
785304253278.1074341048-236.107434104822
796375353042.01560834510710.984391655
806921063752.29192936885457.70807063122
817144669209.63920750352236.36079249649
826840871445.8521609835-3037.85216098352
836542768408.2008231754-2981.2008231754
846463065427.1970781276-797.197078127603
856608664630.05270027641455.94729972357
866505866085.9037517481-1027.90375174813
876268965058.0679515936-2369.06795159359
886084162689.1566118835-1848.15661188352
895734660841.1221760177-3495.12217601771
905622257346.2310519066-1124.23105190662
916820256222.074319498711979.9256805013
927074568201.2080435162543.79195648395
937369070744.83183764342945.16816235655
946899273689.8053038821-4697.80530388211
956592568992.3105576337-3067.31055763365
966554665925.2027705805-379.202770580494
976722165546.02506794291674.9749320571
986531567220.8892724969-1905.88927249689
996203865315.1259925485-3277.12599254848
1005877462038.2166408413-3264.21664084134
1015532058774.2157874433-3454.21578744333
1025390055320.2283477096-1420.22834770956
1036554453900.093886980511643.9061130195
1046790665543.23025674862362.7697432514
1057091167905.84380447193005.15619552811
1066654470910.8013382555-4366.80133825552
1076365766544.2886759673-2887.2886759673
1086172063657.1908698809-1937.19086988091

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 63136 & 64076 & -940 \tabularnewline
3 & 60198 & 63136.0621405437 & -2938.06214054367 \tabularnewline
4 & 59057 & 60198.1942263604 & -1141.19422636038 \tabularnewline
5 & 57388 & 59057.0754408826 & -1669.07544088262 \tabularnewline
6 & 56708 & 57388.1103375057 & -680.110337505663 \tabularnewline
7 & 70019 & 56708.0449600278 & 13310.9550399722 \tabularnewline
8 & 72263 & 70018.1200532096 & 2244.87994679039 \tabularnewline
9 & 74152 & 72262.8515978081 & 1889.14840219189 \tabularnewline
10 & 67057 & 74151.8751141396 & -7094.87511413959 \tabularnewline
11 & 61941 & 67057.469020635 & -5116.46902063496 \tabularnewline
12 & 58331 & 61941.3382342198 & -3610.33823421981 \tabularnewline
13 & 59252 & 58331.2386684901 & 920.761331509886 \tabularnewline
14 & 56568 & 59251.9391312662 & -2683.93913126625 \tabularnewline
15 & 53031 & 56568.1774270604 & -3537.17742706042 \tabularnewline
16 & 51840 & 53031.2338320515 & -1191.23383205147 \tabularnewline
17 & 48290 & 51840.0787488489 & -3550.0787488489 \tabularnewline
18 & 45817 & 48290.2346849186 & -2473.23468491864 \tabularnewline
19 & 59421 & 45817.1634980297 & 13603.8365019703 \tabularnewline
20 & 61621 & 59420.1006917061 & 2200.89930829387 \tabularnewline
21 & 60976 & 61620.8545052345 & -644.854505234485 \tabularnewline
22 & 57497 & 60976.0426293719 & -3479.04262937186 \tabularnewline
23 & 53037 & 57497.2299889366 & -4460.22998893664 \tabularnewline
24 & 53088 & 53037.2948522515 & 50.7051477485002 \tabularnewline
25 & 53119 & 53087.9966480368 & 31.0033519632416 \tabularnewline
26 & 51644 & 53118.9979504626 & -1474.99795046261 \tabularnewline
27 & 47866 & 51644.0975076325 & -3778.0975076325 \tabularnewline
28 & 47691 & 47866.2497585459 & -175.24975854592 \tabularnewline
29 & 42401 & 47691.011585229 & -5290.01158522902 \tabularnewline
30 & 43069 & 42401.3497065914 & 667.65029340858 \tabularnewline
31 & 55797 & 43068.9558636679 & 12728.0441363321 \tabularnewline
32 & 57170 & 55796.1585876782 & 1373.84141232181 \tabularnewline
33 & 58335 & 57169.9091795189 & 1165.09082048114 \tabularnewline
34 & 55439 & 58334.9229793862 & -2895.92297938616 \tabularnewline
35 & 54399 & 55439.1914406685 & -1040.19144066847 \tabularnewline
36 & 56316 & 54399.0687638954 & 1916.93123610463 \tabularnewline
37 & 58381 & 56315.8732775009 & 2065.12672249914 \tabularnewline
38 & 58468 & 58380.8634807476 & 87.1365192524318 \tabularnewline
39 & 59025 & 58467.9942396695 & 557.00576033051 \tabularnewline
40 & 58298 & 59024.9631780417 & -726.963178041733 \tabularnewline
41 & 54255 & 58298.0480573267 & -4043.04805732671 \tabularnewline
42 & 55670 & 54255.2672736217 & 1414.73272637833 \tabularnewline
43 & 67816 & 55669.9064763183 & 12146.0935236817 \tabularnewline
44 & 70485 & 67815.1970586649 & 2669.80294133515 \tabularnewline
45 & 71361 & 70484.8235074401 & 876.176492559855 \tabularnewline
46 & 66953 & 71360.9420786345 & -4407.94207863446 \tabularnewline
47 & 64505 & 66953.2913956566 & -2448.29139565663 \tabularnewline
48 & 66770 & 64505.1618491047 & 2264.83815089532 \tabularnewline
49 & 66418 & 66769.8502784319 & -351.850278431899 \tabularnewline
50 & 65277 & 66418.0232597528 & -1141.02325975276 \tabularnewline
51 & 62008 & 65277.0754295805 & -3269.07542958054 \tabularnewline
52 & 59096 & 62008.2161086431 & -2912.21610864308 \tabularnewline
53 & 55106 & 59096.1925177577 & -3990.19251775774 \tabularnewline
54 & 54954 & 55106.2637795026 & -152.263779502558 \tabularnewline
55 & 67943 & 54954.0100656958 & 12988.9899343042 \tabularnewline
56 & 69411 & 67942.1413373444 & 1468.85866265559 \tabularnewline
57 & 69951 & 69410.9028982172 & 540.097101782841 \tabularnewline
58 & 63966 & 69950.9642958218 & -5984.96429582176 \tabularnewline
59 & 60410 & 63966.3956478034 & -3556.39564780339 \tabularnewline
60 & 59440 & 60410.2351025096 & -970.235102509643 \tabularnewline
61 & 59445 & 59440.0641392944 & 4.93586070557649 \tabularnewline
62 & 57614 & 59444.9996737052 & -1830.99967370525 \tabularnewline
63 & 55396 & 57614.1210418247 & -2218.12104182467 \tabularnewline
64 & 53030 & 55396.146633242 & -2366.14663324199 \tabularnewline
65 & 50090 & 53030.156418764 & -2940.15641876403 \tabularnewline
66 & 48764 & 50090.1943648067 & -1326.19436480674 \tabularnewline
67 & 61658 & 48764.0876706796 & 12893.9123293204 \tabularnewline
68 & 63943 & 61657.147622636 & 2285.85237736403 \tabularnewline
69 & 64878 & 63942.8488892452 & 935.151110754763 \tabularnewline
70 & 60634 & 64877.9381800017 & -4243.93818000166 \tabularnewline
71 & 57905 & 60634.2805538573 & -2729.28055385725 \tabularnewline
72 & 57224 & 57905.1804244441 & -681.180424444086 \tabularnewline
73 & 60953 & 57224.045030768 & 3728.95496923201 \tabularnewline
74 & 60621 & 60952.753490118 & -331.753490117968 \tabularnewline
75 & 57258 & 60621.0219312151 & -3363.02193121515 \tabularnewline
76 & 54903 & 57258.2223191608 & -2355.22231916083 \tabularnewline
77 & 53278 & 54903.1556965908 & -1625.15569659083 \tabularnewline
78 & 53042 & 53278.1074341048 & -236.107434104822 \tabularnewline
79 & 63753 & 53042.015608345 & 10710.984391655 \tabularnewline
80 & 69210 & 63752.2919293688 & 5457.70807063122 \tabularnewline
81 & 71446 & 69209.6392075035 & 2236.36079249649 \tabularnewline
82 & 68408 & 71445.8521609835 & -3037.85216098352 \tabularnewline
83 & 65427 & 68408.2008231754 & -2981.2008231754 \tabularnewline
84 & 64630 & 65427.1970781276 & -797.197078127603 \tabularnewline
85 & 66086 & 64630.0527002764 & 1455.94729972357 \tabularnewline
86 & 65058 & 66085.9037517481 & -1027.90375174813 \tabularnewline
87 & 62689 & 65058.0679515936 & -2369.06795159359 \tabularnewline
88 & 60841 & 62689.1566118835 & -1848.15661188352 \tabularnewline
89 & 57346 & 60841.1221760177 & -3495.12217601771 \tabularnewline
90 & 56222 & 57346.2310519066 & -1124.23105190662 \tabularnewline
91 & 68202 & 56222.0743194987 & 11979.9256805013 \tabularnewline
92 & 70745 & 68201.208043516 & 2543.79195648395 \tabularnewline
93 & 73690 & 70744.8318376434 & 2945.16816235655 \tabularnewline
94 & 68992 & 73689.8053038821 & -4697.80530388211 \tabularnewline
95 & 65925 & 68992.3105576337 & -3067.31055763365 \tabularnewline
96 & 65546 & 65925.2027705805 & -379.202770580494 \tabularnewline
97 & 67221 & 65546.0250679429 & 1674.9749320571 \tabularnewline
98 & 65315 & 67220.8892724969 & -1905.88927249689 \tabularnewline
99 & 62038 & 65315.1259925485 & -3277.12599254848 \tabularnewline
100 & 58774 & 62038.2166408413 & -3264.21664084134 \tabularnewline
101 & 55320 & 58774.2157874433 & -3454.21578744333 \tabularnewline
102 & 53900 & 55320.2283477096 & -1420.22834770956 \tabularnewline
103 & 65544 & 53900.0938869805 & 11643.9061130195 \tabularnewline
104 & 67906 & 65543.2302567486 & 2362.7697432514 \tabularnewline
105 & 70911 & 67905.8438044719 & 3005.15619552811 \tabularnewline
106 & 66544 & 70910.8013382555 & -4366.80133825552 \tabularnewline
107 & 63657 & 66544.2886759673 & -2887.2886759673 \tabularnewline
108 & 61720 & 63657.1908698809 & -1937.19086988091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284548&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]63136[/C][C]64076[/C][C]-940[/C][/ROW]
[ROW][C]3[/C][C]60198[/C][C]63136.0621405437[/C][C]-2938.06214054367[/C][/ROW]
[ROW][C]4[/C][C]59057[/C][C]60198.1942263604[/C][C]-1141.19422636038[/C][/ROW]
[ROW][C]5[/C][C]57388[/C][C]59057.0754408826[/C][C]-1669.07544088262[/C][/ROW]
[ROW][C]6[/C][C]56708[/C][C]57388.1103375057[/C][C]-680.110337505663[/C][/ROW]
[ROW][C]7[/C][C]70019[/C][C]56708.0449600278[/C][C]13310.9550399722[/C][/ROW]
[ROW][C]8[/C][C]72263[/C][C]70018.1200532096[/C][C]2244.87994679039[/C][/ROW]
[ROW][C]9[/C][C]74152[/C][C]72262.8515978081[/C][C]1889.14840219189[/C][/ROW]
[ROW][C]10[/C][C]67057[/C][C]74151.8751141396[/C][C]-7094.87511413959[/C][/ROW]
[ROW][C]11[/C][C]61941[/C][C]67057.469020635[/C][C]-5116.46902063496[/C][/ROW]
[ROW][C]12[/C][C]58331[/C][C]61941.3382342198[/C][C]-3610.33823421981[/C][/ROW]
[ROW][C]13[/C][C]59252[/C][C]58331.2386684901[/C][C]920.761331509886[/C][/ROW]
[ROW][C]14[/C][C]56568[/C][C]59251.9391312662[/C][C]-2683.93913126625[/C][/ROW]
[ROW][C]15[/C][C]53031[/C][C]56568.1774270604[/C][C]-3537.17742706042[/C][/ROW]
[ROW][C]16[/C][C]51840[/C][C]53031.2338320515[/C][C]-1191.23383205147[/C][/ROW]
[ROW][C]17[/C][C]48290[/C][C]51840.0787488489[/C][C]-3550.0787488489[/C][/ROW]
[ROW][C]18[/C][C]45817[/C][C]48290.2346849186[/C][C]-2473.23468491864[/C][/ROW]
[ROW][C]19[/C][C]59421[/C][C]45817.1634980297[/C][C]13603.8365019703[/C][/ROW]
[ROW][C]20[/C][C]61621[/C][C]59420.1006917061[/C][C]2200.89930829387[/C][/ROW]
[ROW][C]21[/C][C]60976[/C][C]61620.8545052345[/C][C]-644.854505234485[/C][/ROW]
[ROW][C]22[/C][C]57497[/C][C]60976.0426293719[/C][C]-3479.04262937186[/C][/ROW]
[ROW][C]23[/C][C]53037[/C][C]57497.2299889366[/C][C]-4460.22998893664[/C][/ROW]
[ROW][C]24[/C][C]53088[/C][C]53037.2948522515[/C][C]50.7051477485002[/C][/ROW]
[ROW][C]25[/C][C]53119[/C][C]53087.9966480368[/C][C]31.0033519632416[/C][/ROW]
[ROW][C]26[/C][C]51644[/C][C]53118.9979504626[/C][C]-1474.99795046261[/C][/ROW]
[ROW][C]27[/C][C]47866[/C][C]51644.0975076325[/C][C]-3778.0975076325[/C][/ROW]
[ROW][C]28[/C][C]47691[/C][C]47866.2497585459[/C][C]-175.24975854592[/C][/ROW]
[ROW][C]29[/C][C]42401[/C][C]47691.011585229[/C][C]-5290.01158522902[/C][/ROW]
[ROW][C]30[/C][C]43069[/C][C]42401.3497065914[/C][C]667.65029340858[/C][/ROW]
[ROW][C]31[/C][C]55797[/C][C]43068.9558636679[/C][C]12728.0441363321[/C][/ROW]
[ROW][C]32[/C][C]57170[/C][C]55796.1585876782[/C][C]1373.84141232181[/C][/ROW]
[ROW][C]33[/C][C]58335[/C][C]57169.9091795189[/C][C]1165.09082048114[/C][/ROW]
[ROW][C]34[/C][C]55439[/C][C]58334.9229793862[/C][C]-2895.92297938616[/C][/ROW]
[ROW][C]35[/C][C]54399[/C][C]55439.1914406685[/C][C]-1040.19144066847[/C][/ROW]
[ROW][C]36[/C][C]56316[/C][C]54399.0687638954[/C][C]1916.93123610463[/C][/ROW]
[ROW][C]37[/C][C]58381[/C][C]56315.8732775009[/C][C]2065.12672249914[/C][/ROW]
[ROW][C]38[/C][C]58468[/C][C]58380.8634807476[/C][C]87.1365192524318[/C][/ROW]
[ROW][C]39[/C][C]59025[/C][C]58467.9942396695[/C][C]557.00576033051[/C][/ROW]
[ROW][C]40[/C][C]58298[/C][C]59024.9631780417[/C][C]-726.963178041733[/C][/ROW]
[ROW][C]41[/C][C]54255[/C][C]58298.0480573267[/C][C]-4043.04805732671[/C][/ROW]
[ROW][C]42[/C][C]55670[/C][C]54255.2672736217[/C][C]1414.73272637833[/C][/ROW]
[ROW][C]43[/C][C]67816[/C][C]55669.9064763183[/C][C]12146.0935236817[/C][/ROW]
[ROW][C]44[/C][C]70485[/C][C]67815.1970586649[/C][C]2669.80294133515[/C][/ROW]
[ROW][C]45[/C][C]71361[/C][C]70484.8235074401[/C][C]876.176492559855[/C][/ROW]
[ROW][C]46[/C][C]66953[/C][C]71360.9420786345[/C][C]-4407.94207863446[/C][/ROW]
[ROW][C]47[/C][C]64505[/C][C]66953.2913956566[/C][C]-2448.29139565663[/C][/ROW]
[ROW][C]48[/C][C]66770[/C][C]64505.1618491047[/C][C]2264.83815089532[/C][/ROW]
[ROW][C]49[/C][C]66418[/C][C]66769.8502784319[/C][C]-351.850278431899[/C][/ROW]
[ROW][C]50[/C][C]65277[/C][C]66418.0232597528[/C][C]-1141.02325975276[/C][/ROW]
[ROW][C]51[/C][C]62008[/C][C]65277.0754295805[/C][C]-3269.07542958054[/C][/ROW]
[ROW][C]52[/C][C]59096[/C][C]62008.2161086431[/C][C]-2912.21610864308[/C][/ROW]
[ROW][C]53[/C][C]55106[/C][C]59096.1925177577[/C][C]-3990.19251775774[/C][/ROW]
[ROW][C]54[/C][C]54954[/C][C]55106.2637795026[/C][C]-152.263779502558[/C][/ROW]
[ROW][C]55[/C][C]67943[/C][C]54954.0100656958[/C][C]12988.9899343042[/C][/ROW]
[ROW][C]56[/C][C]69411[/C][C]67942.1413373444[/C][C]1468.85866265559[/C][/ROW]
[ROW][C]57[/C][C]69951[/C][C]69410.9028982172[/C][C]540.097101782841[/C][/ROW]
[ROW][C]58[/C][C]63966[/C][C]69950.9642958218[/C][C]-5984.96429582176[/C][/ROW]
[ROW][C]59[/C][C]60410[/C][C]63966.3956478034[/C][C]-3556.39564780339[/C][/ROW]
[ROW][C]60[/C][C]59440[/C][C]60410.2351025096[/C][C]-970.235102509643[/C][/ROW]
[ROW][C]61[/C][C]59445[/C][C]59440.0641392944[/C][C]4.93586070557649[/C][/ROW]
[ROW][C]62[/C][C]57614[/C][C]59444.9996737052[/C][C]-1830.99967370525[/C][/ROW]
[ROW][C]63[/C][C]55396[/C][C]57614.1210418247[/C][C]-2218.12104182467[/C][/ROW]
[ROW][C]64[/C][C]53030[/C][C]55396.146633242[/C][C]-2366.14663324199[/C][/ROW]
[ROW][C]65[/C][C]50090[/C][C]53030.156418764[/C][C]-2940.15641876403[/C][/ROW]
[ROW][C]66[/C][C]48764[/C][C]50090.1943648067[/C][C]-1326.19436480674[/C][/ROW]
[ROW][C]67[/C][C]61658[/C][C]48764.0876706796[/C][C]12893.9123293204[/C][/ROW]
[ROW][C]68[/C][C]63943[/C][C]61657.147622636[/C][C]2285.85237736403[/C][/ROW]
[ROW][C]69[/C][C]64878[/C][C]63942.8488892452[/C][C]935.151110754763[/C][/ROW]
[ROW][C]70[/C][C]60634[/C][C]64877.9381800017[/C][C]-4243.93818000166[/C][/ROW]
[ROW][C]71[/C][C]57905[/C][C]60634.2805538573[/C][C]-2729.28055385725[/C][/ROW]
[ROW][C]72[/C][C]57224[/C][C]57905.1804244441[/C][C]-681.180424444086[/C][/ROW]
[ROW][C]73[/C][C]60953[/C][C]57224.045030768[/C][C]3728.95496923201[/C][/ROW]
[ROW][C]74[/C][C]60621[/C][C]60952.753490118[/C][C]-331.753490117968[/C][/ROW]
[ROW][C]75[/C][C]57258[/C][C]60621.0219312151[/C][C]-3363.02193121515[/C][/ROW]
[ROW][C]76[/C][C]54903[/C][C]57258.2223191608[/C][C]-2355.22231916083[/C][/ROW]
[ROW][C]77[/C][C]53278[/C][C]54903.1556965908[/C][C]-1625.15569659083[/C][/ROW]
[ROW][C]78[/C][C]53042[/C][C]53278.1074341048[/C][C]-236.107434104822[/C][/ROW]
[ROW][C]79[/C][C]63753[/C][C]53042.015608345[/C][C]10710.984391655[/C][/ROW]
[ROW][C]80[/C][C]69210[/C][C]63752.2919293688[/C][C]5457.70807063122[/C][/ROW]
[ROW][C]81[/C][C]71446[/C][C]69209.6392075035[/C][C]2236.36079249649[/C][/ROW]
[ROW][C]82[/C][C]68408[/C][C]71445.8521609835[/C][C]-3037.85216098352[/C][/ROW]
[ROW][C]83[/C][C]65427[/C][C]68408.2008231754[/C][C]-2981.2008231754[/C][/ROW]
[ROW][C]84[/C][C]64630[/C][C]65427.1970781276[/C][C]-797.197078127603[/C][/ROW]
[ROW][C]85[/C][C]66086[/C][C]64630.0527002764[/C][C]1455.94729972357[/C][/ROW]
[ROW][C]86[/C][C]65058[/C][C]66085.9037517481[/C][C]-1027.90375174813[/C][/ROW]
[ROW][C]87[/C][C]62689[/C][C]65058.0679515936[/C][C]-2369.06795159359[/C][/ROW]
[ROW][C]88[/C][C]60841[/C][C]62689.1566118835[/C][C]-1848.15661188352[/C][/ROW]
[ROW][C]89[/C][C]57346[/C][C]60841.1221760177[/C][C]-3495.12217601771[/C][/ROW]
[ROW][C]90[/C][C]56222[/C][C]57346.2310519066[/C][C]-1124.23105190662[/C][/ROW]
[ROW][C]91[/C][C]68202[/C][C]56222.0743194987[/C][C]11979.9256805013[/C][/ROW]
[ROW][C]92[/C][C]70745[/C][C]68201.208043516[/C][C]2543.79195648395[/C][/ROW]
[ROW][C]93[/C][C]73690[/C][C]70744.8318376434[/C][C]2945.16816235655[/C][/ROW]
[ROW][C]94[/C][C]68992[/C][C]73689.8053038821[/C][C]-4697.80530388211[/C][/ROW]
[ROW][C]95[/C][C]65925[/C][C]68992.3105576337[/C][C]-3067.31055763365[/C][/ROW]
[ROW][C]96[/C][C]65546[/C][C]65925.2027705805[/C][C]-379.202770580494[/C][/ROW]
[ROW][C]97[/C][C]67221[/C][C]65546.0250679429[/C][C]1674.9749320571[/C][/ROW]
[ROW][C]98[/C][C]65315[/C][C]67220.8892724969[/C][C]-1905.88927249689[/C][/ROW]
[ROW][C]99[/C][C]62038[/C][C]65315.1259925485[/C][C]-3277.12599254848[/C][/ROW]
[ROW][C]100[/C][C]58774[/C][C]62038.2166408413[/C][C]-3264.21664084134[/C][/ROW]
[ROW][C]101[/C][C]55320[/C][C]58774.2157874433[/C][C]-3454.21578744333[/C][/ROW]
[ROW][C]102[/C][C]53900[/C][C]55320.2283477096[/C][C]-1420.22834770956[/C][/ROW]
[ROW][C]103[/C][C]65544[/C][C]53900.0938869805[/C][C]11643.9061130195[/C][/ROW]
[ROW][C]104[/C][C]67906[/C][C]65543.2302567486[/C][C]2362.7697432514[/C][/ROW]
[ROW][C]105[/C][C]70911[/C][C]67905.8438044719[/C][C]3005.15619552811[/C][/ROW]
[ROW][C]106[/C][C]66544[/C][C]70910.8013382555[/C][C]-4366.80133825552[/C][/ROW]
[ROW][C]107[/C][C]63657[/C][C]66544.2886759673[/C][C]-2887.2886759673[/C][/ROW]
[ROW][C]108[/C][C]61720[/C][C]63657.1908698809[/C][C]-1937.19086988091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284548&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284548&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
26313664076-940
36019863136.0621405437-2938.06214054367
45905760198.1942263604-1141.19422636038
55738859057.0754408826-1669.07544088262
65670857388.1103375057-680.110337505663
77001956708.044960027813310.9550399722
87226370018.12005320962244.87994679039
97415272262.85159780811889.14840219189
106705774151.8751141396-7094.87511413959
116194167057.469020635-5116.46902063496
125833161941.3382342198-3610.33823421981
135925258331.2386684901920.761331509886
145656859251.9391312662-2683.93913126625
155303156568.1774270604-3537.17742706042
165184053031.2338320515-1191.23383205147
174829051840.0787488489-3550.0787488489
184581748290.2346849186-2473.23468491864
195942145817.163498029713603.8365019703
206162159420.10069170612200.89930829387
216097661620.8545052345-644.854505234485
225749760976.0426293719-3479.04262937186
235303757497.2299889366-4460.22998893664
245308853037.294852251550.7051477485002
255311953087.996648036831.0033519632416
265164453118.9979504626-1474.99795046261
274786651644.0975076325-3778.0975076325
284769147866.2497585459-175.24975854592
294240147691.011585229-5290.01158522902
304306942401.3497065914667.65029340858
315579743068.955863667912728.0441363321
325717055796.15858767821373.84141232181
335833557169.90917951891165.09082048114
345543958334.9229793862-2895.92297938616
355439955439.1914406685-1040.19144066847
365631654399.06876389541916.93123610463
375838156315.87327750092065.12672249914
385846858380.863480747687.1365192524318
395902558467.9942396695557.00576033051
405829859024.9631780417-726.963178041733
415425558298.0480573267-4043.04805732671
425567054255.26727362171414.73272637833
436781655669.906476318312146.0935236817
447048567815.19705866492669.80294133515
457136170484.8235074401876.176492559855
466695371360.9420786345-4407.94207863446
476450566953.2913956566-2448.29139565663
486677064505.16184910472264.83815089532
496641866769.8502784319-351.850278431899
506527766418.0232597528-1141.02325975276
516200865277.0754295805-3269.07542958054
525909662008.2161086431-2912.21610864308
535510659096.1925177577-3990.19251775774
545495455106.2637795026-152.263779502558
556794354954.010065695812988.9899343042
566941167942.14133734441468.85866265559
576995169410.9028982172540.097101782841
586396669950.9642958218-5984.96429582176
596041063966.3956478034-3556.39564780339
605944060410.2351025096-970.235102509643
615944559440.06413929444.93586070557649
625761459444.9996737052-1830.99967370525
635539657614.1210418247-2218.12104182467
645303055396.146633242-2366.14663324199
655009053030.156418764-2940.15641876403
664876450090.1943648067-1326.19436480674
676165848764.087670679612893.9123293204
686394361657.1476226362285.85237736403
696487863942.8488892452935.151110754763
706063464877.9381800017-4243.93818000166
715790560634.2805538573-2729.28055385725
725722457905.1804244441-681.180424444086
736095357224.0450307683728.95496923201
746062160952.753490118-331.753490117968
755725860621.0219312151-3363.02193121515
765490357258.2223191608-2355.22231916083
775327854903.1556965908-1625.15569659083
785304253278.1074341048-236.107434104822
796375353042.01560834510710.984391655
806921063752.29192936885457.70807063122
817144669209.63920750352236.36079249649
826840871445.8521609835-3037.85216098352
836542768408.2008231754-2981.2008231754
846463065427.1970781276-797.197078127603
856608664630.05270027641455.94729972357
866505866085.9037517481-1027.90375174813
876268965058.0679515936-2369.06795159359
886084162689.1566118835-1848.15661188352
895734660841.1221760177-3495.12217601771
905622257346.2310519066-1124.23105190662
916820256222.074319498711979.9256805013
927074568201.2080435162543.79195648395
937369070744.83183764342945.16816235655
946899273689.8053038821-4697.80530388211
956592568992.3105576337-3067.31055763365
966554665925.2027705805-379.202770580494
976722165546.02506794291674.9749320571
986531567220.8892724969-1905.88927249689
996203865315.1259925485-3277.12599254848
1005877462038.2166408413-3264.21664084134
1015532058774.2157874433-3454.21578744333
1025390055320.2283477096-1420.22834770956
1036554453900.093886980511643.9061130195
1046790665543.23025674862362.7697432514
1057091167905.84380447193005.15619552811
1066654470910.8013382555-4366.80133825552
1076365766544.2886759673-2887.2886759673
1086172063657.1908698809-1937.19086988091







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10961720.12806180252984.479621718270455.7765018858
11061720.12806180249366.463900059974073.7922235441
11161720.12806180246590.207943920276850.0481796837
11261720.12806180244249.697405236779190.5587183672
11361720.12806180242187.657355866581252.5987677374
11461720.12806180240323.425595519983116.830528084
11561720.12806180238609.084360078584831.1717635254
11661720.12806180237013.412263555186426.8438600489
11761720.12806180235514.722701691387925.5334219126
11861720.12806180234097.225704517289343.0304190867
11961720.12806180232749.001069700790691.2550539033
12061720.12806180231460.787954244691979.4681693594

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 61720.128061802 & 52984.4796217182 & 70455.7765018858 \tabularnewline
110 & 61720.128061802 & 49366.4639000599 & 74073.7922235441 \tabularnewline
111 & 61720.128061802 & 46590.2079439202 & 76850.0481796837 \tabularnewline
112 & 61720.128061802 & 44249.6974052367 & 79190.5587183672 \tabularnewline
113 & 61720.128061802 & 42187.6573558665 & 81252.5987677374 \tabularnewline
114 & 61720.128061802 & 40323.4255955199 & 83116.830528084 \tabularnewline
115 & 61720.128061802 & 38609.0843600785 & 84831.1717635254 \tabularnewline
116 & 61720.128061802 & 37013.4122635551 & 86426.8438600489 \tabularnewline
117 & 61720.128061802 & 35514.7227016913 & 87925.5334219126 \tabularnewline
118 & 61720.128061802 & 34097.2257045172 & 89343.0304190867 \tabularnewline
119 & 61720.128061802 & 32749.0010697007 & 90691.2550539033 \tabularnewline
120 & 61720.128061802 & 31460.7879542446 & 91979.4681693594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284548&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]61720.128061802[/C][C]52984.4796217182[/C][C]70455.7765018858[/C][/ROW]
[ROW][C]110[/C][C]61720.128061802[/C][C]49366.4639000599[/C][C]74073.7922235441[/C][/ROW]
[ROW][C]111[/C][C]61720.128061802[/C][C]46590.2079439202[/C][C]76850.0481796837[/C][/ROW]
[ROW][C]112[/C][C]61720.128061802[/C][C]44249.6974052367[/C][C]79190.5587183672[/C][/ROW]
[ROW][C]113[/C][C]61720.128061802[/C][C]42187.6573558665[/C][C]81252.5987677374[/C][/ROW]
[ROW][C]114[/C][C]61720.128061802[/C][C]40323.4255955199[/C][C]83116.830528084[/C][/ROW]
[ROW][C]115[/C][C]61720.128061802[/C][C]38609.0843600785[/C][C]84831.1717635254[/C][/ROW]
[ROW][C]116[/C][C]61720.128061802[/C][C]37013.4122635551[/C][C]86426.8438600489[/C][/ROW]
[ROW][C]117[/C][C]61720.128061802[/C][C]35514.7227016913[/C][C]87925.5334219126[/C][/ROW]
[ROW][C]118[/C][C]61720.128061802[/C][C]34097.2257045172[/C][C]89343.0304190867[/C][/ROW]
[ROW][C]119[/C][C]61720.128061802[/C][C]32749.0010697007[/C][C]90691.2550539033[/C][/ROW]
[ROW][C]120[/C][C]61720.128061802[/C][C]31460.7879542446[/C][C]91979.4681693594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284548&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284548&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
10961720.12806180252984.479621718270455.7765018858
11061720.12806180249366.463900059974073.7922235441
11161720.12806180246590.207943920276850.0481796837
11261720.12806180244249.697405236779190.5587183672
11361720.12806180242187.657355866581252.5987677374
11461720.12806180240323.425595519983116.830528084
11561720.12806180238609.084360078584831.1717635254
11661720.12806180237013.412263555186426.8438600489
11761720.12806180235514.722701691387925.5334219126
11861720.12806180234097.225704517289343.0304190867
11961720.12806180232749.001069700790691.2550539033
12061720.12806180231460.787954244691979.4681693594



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