Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 11 Aug 2016 17:10:01 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/11/t1470931831ju0jbgc5xxg7x60.htm/, Retrieved Sun, 05 May 2024 19:50:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296338, Retrieved Sun, 05 May 2024 19:50:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-11 16:10:01] [b787349f7d799cee4daf21043f8c3664] [Current]
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Dataseries X:
84728
84412
84092
83430
89981
89635
84728
81466
81781
81781
82133
82764
83746
83746
83115
81466
89981
91279
89319
84728
86692
83746
85075
85710
86372
84728
85075
82764
89981
92261
90301
86692
90617
86372
90301
89981
90964
87355
91279
90964
96852
95523
90301
87670
91279
86372
89981
90617
91946
89004
90617
91599
95208
92261
88337
84092
88021
77221
82448
85390
88337
84092
84092
84092
86372
83115
78839
75261
77857
67724
73933
77541
78204
74595
74910
73933
77221
74910
70355
67062
72630
60537
68390
71968
71968
67724
63799
63484
67062
63799
57595
53319
57911
47115
56928
62150
63799
60191
55631
58893
60191
59208
49391
44835
48093
38280
48413
52022
54964
50057
45466
48093
49391
46795
36982
32706
36631
25835
37613
44835




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296338&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296338&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405348713655848
beta0.0645208222842562
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405348713655848 \tabularnewline
beta & 0.0645208222842562 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296338&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]0.405348713655848[/C][/ROW]
[ROW][C]beta[/C][C]0.0645208222842562[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296338&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
alpha0.405348713655848
beta0.0645208222842562
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138374683742.28525641043.7147435896477
148374683558.5370690149187.462930985101
158311582809.8404387609305.159561239096
168146681152.8746227794313.125377220582
178998189753.3687100858227.631289914236
189127991067.2862186113211.713781388709
198931986167.45529425023151.54470574984
208472884508.5380979335219.461902066541
218669285243.63625747981448.36374252016
228374686253.831213707-2507.83121370702
238507585906.0909062125-831.090906212456
248571086344.9459123975-634.945912397525
258637287008.6193349581-636.619334958072
268472886712.6051094252-1984.60510942523
278507585134.671372028-59.6713720279804
288276483306.2365345758-542.236534575815
298998191458.4787976779-1477.47879767792
309226191976.4794728116284.520527188361
319030188760.95177048541540.04822951458
328669284569.72043604172122.27956395835
339061786721.12725675943895.87274324062
348637286349.107088721822.8929112781771
359030188068.70212312112232.2978768789
368998189990.4876285376-9.48762853759399
379096491047.6044636175-83.604463617492
388735590329.5456716521-2974.54567165206
399127989624.48782193641654.5121780636
409096488378.25156839152585.74843160847
419685297498.3975237373-646.39752373728
429552399678.9087417866-4155.90874178655
439030195571.7850965973-5270.78509659728
448767088949.6143642168-1279.6143642168
459127990671.3646378168607.635362183151
468637286472.017859474-100.017859473955
478998189261.030758743719.969241257044
489061789002.57666080781614.42333919216
499194690482.2023902381463.79760976195
508900488521.081349325482.918650675012
519061791909.4041984154-1292.4041984154
529159989884.55481882311714.44518117687
539520896568.8866021651-1360.88660216515
549226196193.5261191077-3932.52611910773
558833791340.5107844819-3003.51078448193
568409287896.5517036278-3804.5517036278
578802189536.8616898578-1515.86168985783
587722183820.1988158138-6599.19881581384
598244884056.6551709317-1608.6551709317
608539082919.55463396792470.44536603206
618833784212.35611234414124.64388765591
628409282371.87312094451720.12687905546
638409284863.7043280108-771.704328010761
648409284509.2705212886-417.270521288636
658637288116.3361022967-1744.3361022967
668311585661.8596067367-2546.85960673675
677883981564.7460054615-2725.74600546148
687526177406.0864410822-2145.08644108224
697785780772.4796435837-2915.47964358373
706772471121.514304105-3397.51430410496
717393375362.9814273272-1429.98142732721
727754176468.2002473561072.79975264403
737820477885.8377264237318.162273576323
747459572680.69919121511914.30080878493
757491073382.69224723051527.3077527695
767393373844.275935015988.7240649841115
777722176553.8893968346667.11060316542
787491074349.3205763015560.679423698515
797035571236.3941973969-881.394197396949
806706268049.7916538721-987.791653872104
817263071336.606162761293.39383723997
826053763124.5648933717-2587.56489337173
836839068905.0280311948-515.028031194845
847196871934.021359961233.9786400388111
857196872519.2764304592-551.276430459213
866772467925.5676026072-201.567602607232
876379967499.1427144398-3700.14271443985
886348464808.9871804085-1324.98718040854
896706267075.1762462097-13.1762462096522
906379964299.4560923665-500.456092366527
915759559639.0080311028-2044.00803110284
925331955627.6049069193-2308.6049069193
935791159410.7283750367-1499.72837503666
944711547360.8208013322-245.820801332193
955692854986.32754419921941.6724558008
966215059065.24386691253084.7561330875
976379960346.52838048043452.47161951959
986019157495.82362358022695.1763764198
995563156151.0529328365-520.052932836501
1005889356233.397199892659.60280011003
1016019161070.0806577908-879.080657790822
1025920857806.23521440521401.76478559479
1034939153201.3539353552-3810.35393535515
1044483548472.8050325409-3637.80503254085
1054809352319.5583982989-4226.55839829893
1063828039960.0755580888-1680.07555808879
1074841348317.597998888795.4020011112661
1085202252292.1741768706-270.174176870591
1095496452308.76857915822655.23142084185
1105005748540.29046247181516.70953752819
1114546644630.7820768221835.217923177857
1124809347013.60756531391079.39243468609
1134939148924.4817408098466.518259190234
1144679547416.5824213123-621.582421312341
1153698238693.4310353743-1711.43103537425
1163270634774.4624778512-2068.46247785118
1173663138804.4657981421-2173.46579814215
1182583528742.3880323563-2907.38803235632
1193761337577.029854534335.970145465697
1204483541227.38961439493607.61038560508

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 83746 & 83742.2852564104 & 3.7147435896477 \tabularnewline
14 & 83746 & 83558.5370690149 & 187.462930985101 \tabularnewline
15 & 83115 & 82809.8404387609 & 305.159561239096 \tabularnewline
16 & 81466 & 81152.8746227794 & 313.125377220582 \tabularnewline
17 & 89981 & 89753.3687100858 & 227.631289914236 \tabularnewline
18 & 91279 & 91067.2862186113 & 211.713781388709 \tabularnewline
19 & 89319 & 86167.4552942502 & 3151.54470574984 \tabularnewline
20 & 84728 & 84508.5380979335 & 219.461902066541 \tabularnewline
21 & 86692 & 85243.6362574798 & 1448.36374252016 \tabularnewline
22 & 83746 & 86253.831213707 & -2507.83121370702 \tabularnewline
23 & 85075 & 85906.0909062125 & -831.090906212456 \tabularnewline
24 & 85710 & 86344.9459123975 & -634.945912397525 \tabularnewline
25 & 86372 & 87008.6193349581 & -636.619334958072 \tabularnewline
26 & 84728 & 86712.6051094252 & -1984.60510942523 \tabularnewline
27 & 85075 & 85134.671372028 & -59.6713720279804 \tabularnewline
28 & 82764 & 83306.2365345758 & -542.236534575815 \tabularnewline
29 & 89981 & 91458.4787976779 & -1477.47879767792 \tabularnewline
30 & 92261 & 91976.4794728116 & 284.520527188361 \tabularnewline
31 & 90301 & 88760.9517704854 & 1540.04822951458 \tabularnewline
32 & 86692 & 84569.7204360417 & 2122.27956395835 \tabularnewline
33 & 90617 & 86721.1272567594 & 3895.87274324062 \tabularnewline
34 & 86372 & 86349.1070887218 & 22.8929112781771 \tabularnewline
35 & 90301 & 88068.7021231211 & 2232.2978768789 \tabularnewline
36 & 89981 & 89990.4876285376 & -9.48762853759399 \tabularnewline
37 & 90964 & 91047.6044636175 & -83.604463617492 \tabularnewline
38 & 87355 & 90329.5456716521 & -2974.54567165206 \tabularnewline
39 & 91279 & 89624.4878219364 & 1654.5121780636 \tabularnewline
40 & 90964 & 88378.2515683915 & 2585.74843160847 \tabularnewline
41 & 96852 & 97498.3975237373 & -646.39752373728 \tabularnewline
42 & 95523 & 99678.9087417866 & -4155.90874178655 \tabularnewline
43 & 90301 & 95571.7850965973 & -5270.78509659728 \tabularnewline
44 & 87670 & 88949.6143642168 & -1279.6143642168 \tabularnewline
45 & 91279 & 90671.3646378168 & 607.635362183151 \tabularnewline
46 & 86372 & 86472.017859474 & -100.017859473955 \tabularnewline
47 & 89981 & 89261.030758743 & 719.969241257044 \tabularnewline
48 & 90617 & 89002.5766608078 & 1614.42333919216 \tabularnewline
49 & 91946 & 90482.202390238 & 1463.79760976195 \tabularnewline
50 & 89004 & 88521.081349325 & 482.918650675012 \tabularnewline
51 & 90617 & 91909.4041984154 & -1292.4041984154 \tabularnewline
52 & 91599 & 89884.5548188231 & 1714.44518117687 \tabularnewline
53 & 95208 & 96568.8866021651 & -1360.88660216515 \tabularnewline
54 & 92261 & 96193.5261191077 & -3932.52611910773 \tabularnewline
55 & 88337 & 91340.5107844819 & -3003.51078448193 \tabularnewline
56 & 84092 & 87896.5517036278 & -3804.5517036278 \tabularnewline
57 & 88021 & 89536.8616898578 & -1515.86168985783 \tabularnewline
58 & 77221 & 83820.1988158138 & -6599.19881581384 \tabularnewline
59 & 82448 & 84056.6551709317 & -1608.6551709317 \tabularnewline
60 & 85390 & 82919.5546339679 & 2470.44536603206 \tabularnewline
61 & 88337 & 84212.3561123441 & 4124.64388765591 \tabularnewline
62 & 84092 & 82371.8731209445 & 1720.12687905546 \tabularnewline
63 & 84092 & 84863.7043280108 & -771.704328010761 \tabularnewline
64 & 84092 & 84509.2705212886 & -417.270521288636 \tabularnewline
65 & 86372 & 88116.3361022967 & -1744.3361022967 \tabularnewline
66 & 83115 & 85661.8596067367 & -2546.85960673675 \tabularnewline
67 & 78839 & 81564.7460054615 & -2725.74600546148 \tabularnewline
68 & 75261 & 77406.0864410822 & -2145.08644108224 \tabularnewline
69 & 77857 & 80772.4796435837 & -2915.47964358373 \tabularnewline
70 & 67724 & 71121.514304105 & -3397.51430410496 \tabularnewline
71 & 73933 & 75362.9814273272 & -1429.98142732721 \tabularnewline
72 & 77541 & 76468.200247356 & 1072.79975264403 \tabularnewline
73 & 78204 & 77885.8377264237 & 318.162273576323 \tabularnewline
74 & 74595 & 72680.6991912151 & 1914.30080878493 \tabularnewline
75 & 74910 & 73382.6922472305 & 1527.3077527695 \tabularnewline
76 & 73933 & 73844.2759350159 & 88.7240649841115 \tabularnewline
77 & 77221 & 76553.8893968346 & 667.11060316542 \tabularnewline
78 & 74910 & 74349.3205763015 & 560.679423698515 \tabularnewline
79 & 70355 & 71236.3941973969 & -881.394197396949 \tabularnewline
80 & 67062 & 68049.7916538721 & -987.791653872104 \tabularnewline
81 & 72630 & 71336.60616276 & 1293.39383723997 \tabularnewline
82 & 60537 & 63124.5648933717 & -2587.56489337173 \tabularnewline
83 & 68390 & 68905.0280311948 & -515.028031194845 \tabularnewline
84 & 71968 & 71934.0213599612 & 33.9786400388111 \tabularnewline
85 & 71968 & 72519.2764304592 & -551.276430459213 \tabularnewline
86 & 67724 & 67925.5676026072 & -201.567602607232 \tabularnewline
87 & 63799 & 67499.1427144398 & -3700.14271443985 \tabularnewline
88 & 63484 & 64808.9871804085 & -1324.98718040854 \tabularnewline
89 & 67062 & 67075.1762462097 & -13.1762462096522 \tabularnewline
90 & 63799 & 64299.4560923665 & -500.456092366527 \tabularnewline
91 & 57595 & 59639.0080311028 & -2044.00803110284 \tabularnewline
92 & 53319 & 55627.6049069193 & -2308.6049069193 \tabularnewline
93 & 57911 & 59410.7283750367 & -1499.72837503666 \tabularnewline
94 & 47115 & 47360.8208013322 & -245.820801332193 \tabularnewline
95 & 56928 & 54986.3275441992 & 1941.6724558008 \tabularnewline
96 & 62150 & 59065.2438669125 & 3084.7561330875 \tabularnewline
97 & 63799 & 60346.5283804804 & 3452.47161951959 \tabularnewline
98 & 60191 & 57495.8236235802 & 2695.1763764198 \tabularnewline
99 & 55631 & 56151.0529328365 & -520.052932836501 \tabularnewline
100 & 58893 & 56233.39719989 & 2659.60280011003 \tabularnewline
101 & 60191 & 61070.0806577908 & -879.080657790822 \tabularnewline
102 & 59208 & 57806.2352144052 & 1401.76478559479 \tabularnewline
103 & 49391 & 53201.3539353552 & -3810.35393535515 \tabularnewline
104 & 44835 & 48472.8050325409 & -3637.80503254085 \tabularnewline
105 & 48093 & 52319.5583982989 & -4226.55839829893 \tabularnewline
106 & 38280 & 39960.0755580888 & -1680.07555808879 \tabularnewline
107 & 48413 & 48317.5979988887 & 95.4020011112661 \tabularnewline
108 & 52022 & 52292.1741768706 & -270.174176870591 \tabularnewline
109 & 54964 & 52308.7685791582 & 2655.23142084185 \tabularnewline
110 & 50057 & 48540.2904624718 & 1516.70953752819 \tabularnewline
111 & 45466 & 44630.7820768221 & 835.217923177857 \tabularnewline
112 & 48093 & 47013.6075653139 & 1079.39243468609 \tabularnewline
113 & 49391 & 48924.4817408098 & 466.518259190234 \tabularnewline
114 & 46795 & 47416.5824213123 & -621.582421312341 \tabularnewline
115 & 36982 & 38693.4310353743 & -1711.43103537425 \tabularnewline
116 & 32706 & 34774.4624778512 & -2068.46247785118 \tabularnewline
117 & 36631 & 38804.4657981421 & -2173.46579814215 \tabularnewline
118 & 25835 & 28742.3880323563 & -2907.38803235632 \tabularnewline
119 & 37613 & 37577.0298545343 & 35.970145465697 \tabularnewline
120 & 44835 & 41227.3896143949 & 3607.61038560508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296338&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]83746[/C][C]83742.2852564104[/C][C]3.7147435896477[/C][/ROW]
[ROW][C]14[/C][C]83746[/C][C]83558.5370690149[/C][C]187.462930985101[/C][/ROW]
[ROW][C]15[/C][C]83115[/C][C]82809.8404387609[/C][C]305.159561239096[/C][/ROW]
[ROW][C]16[/C][C]81466[/C][C]81152.8746227794[/C][C]313.125377220582[/C][/ROW]
[ROW][C]17[/C][C]89981[/C][C]89753.3687100858[/C][C]227.631289914236[/C][/ROW]
[ROW][C]18[/C][C]91279[/C][C]91067.2862186113[/C][C]211.713781388709[/C][/ROW]
[ROW][C]19[/C][C]89319[/C][C]86167.4552942502[/C][C]3151.54470574984[/C][/ROW]
[ROW][C]20[/C][C]84728[/C][C]84508.5380979335[/C][C]219.461902066541[/C][/ROW]
[ROW][C]21[/C][C]86692[/C][C]85243.6362574798[/C][C]1448.36374252016[/C][/ROW]
[ROW][C]22[/C][C]83746[/C][C]86253.831213707[/C][C]-2507.83121370702[/C][/ROW]
[ROW][C]23[/C][C]85075[/C][C]85906.0909062125[/C][C]-831.090906212456[/C][/ROW]
[ROW][C]24[/C][C]85710[/C][C]86344.9459123975[/C][C]-634.945912397525[/C][/ROW]
[ROW][C]25[/C][C]86372[/C][C]87008.6193349581[/C][C]-636.619334958072[/C][/ROW]
[ROW][C]26[/C][C]84728[/C][C]86712.6051094252[/C][C]-1984.60510942523[/C][/ROW]
[ROW][C]27[/C][C]85075[/C][C]85134.671372028[/C][C]-59.6713720279804[/C][/ROW]
[ROW][C]28[/C][C]82764[/C][C]83306.2365345758[/C][C]-542.236534575815[/C][/ROW]
[ROW][C]29[/C][C]89981[/C][C]91458.4787976779[/C][C]-1477.47879767792[/C][/ROW]
[ROW][C]30[/C][C]92261[/C][C]91976.4794728116[/C][C]284.520527188361[/C][/ROW]
[ROW][C]31[/C][C]90301[/C][C]88760.9517704854[/C][C]1540.04822951458[/C][/ROW]
[ROW][C]32[/C][C]86692[/C][C]84569.7204360417[/C][C]2122.27956395835[/C][/ROW]
[ROW][C]33[/C][C]90617[/C][C]86721.1272567594[/C][C]3895.87274324062[/C][/ROW]
[ROW][C]34[/C][C]86372[/C][C]86349.1070887218[/C][C]22.8929112781771[/C][/ROW]
[ROW][C]35[/C][C]90301[/C][C]88068.7021231211[/C][C]2232.2978768789[/C][/ROW]
[ROW][C]36[/C][C]89981[/C][C]89990.4876285376[/C][C]-9.48762853759399[/C][/ROW]
[ROW][C]37[/C][C]90964[/C][C]91047.6044636175[/C][C]-83.604463617492[/C][/ROW]
[ROW][C]38[/C][C]87355[/C][C]90329.5456716521[/C][C]-2974.54567165206[/C][/ROW]
[ROW][C]39[/C][C]91279[/C][C]89624.4878219364[/C][C]1654.5121780636[/C][/ROW]
[ROW][C]40[/C][C]90964[/C][C]88378.2515683915[/C][C]2585.74843160847[/C][/ROW]
[ROW][C]41[/C][C]96852[/C][C]97498.3975237373[/C][C]-646.39752373728[/C][/ROW]
[ROW][C]42[/C][C]95523[/C][C]99678.9087417866[/C][C]-4155.90874178655[/C][/ROW]
[ROW][C]43[/C][C]90301[/C][C]95571.7850965973[/C][C]-5270.78509659728[/C][/ROW]
[ROW][C]44[/C][C]87670[/C][C]88949.6143642168[/C][C]-1279.6143642168[/C][/ROW]
[ROW][C]45[/C][C]91279[/C][C]90671.3646378168[/C][C]607.635362183151[/C][/ROW]
[ROW][C]46[/C][C]86372[/C][C]86472.017859474[/C][C]-100.017859473955[/C][/ROW]
[ROW][C]47[/C][C]89981[/C][C]89261.030758743[/C][C]719.969241257044[/C][/ROW]
[ROW][C]48[/C][C]90617[/C][C]89002.5766608078[/C][C]1614.42333919216[/C][/ROW]
[ROW][C]49[/C][C]91946[/C][C]90482.202390238[/C][C]1463.79760976195[/C][/ROW]
[ROW][C]50[/C][C]89004[/C][C]88521.081349325[/C][C]482.918650675012[/C][/ROW]
[ROW][C]51[/C][C]90617[/C][C]91909.4041984154[/C][C]-1292.4041984154[/C][/ROW]
[ROW][C]52[/C][C]91599[/C][C]89884.5548188231[/C][C]1714.44518117687[/C][/ROW]
[ROW][C]53[/C][C]95208[/C][C]96568.8866021651[/C][C]-1360.88660216515[/C][/ROW]
[ROW][C]54[/C][C]92261[/C][C]96193.5261191077[/C][C]-3932.52611910773[/C][/ROW]
[ROW][C]55[/C][C]88337[/C][C]91340.5107844819[/C][C]-3003.51078448193[/C][/ROW]
[ROW][C]56[/C][C]84092[/C][C]87896.5517036278[/C][C]-3804.5517036278[/C][/ROW]
[ROW][C]57[/C][C]88021[/C][C]89536.8616898578[/C][C]-1515.86168985783[/C][/ROW]
[ROW][C]58[/C][C]77221[/C][C]83820.1988158138[/C][C]-6599.19881581384[/C][/ROW]
[ROW][C]59[/C][C]82448[/C][C]84056.6551709317[/C][C]-1608.6551709317[/C][/ROW]
[ROW][C]60[/C][C]85390[/C][C]82919.5546339679[/C][C]2470.44536603206[/C][/ROW]
[ROW][C]61[/C][C]88337[/C][C]84212.3561123441[/C][C]4124.64388765591[/C][/ROW]
[ROW][C]62[/C][C]84092[/C][C]82371.8731209445[/C][C]1720.12687905546[/C][/ROW]
[ROW][C]63[/C][C]84092[/C][C]84863.7043280108[/C][C]-771.704328010761[/C][/ROW]
[ROW][C]64[/C][C]84092[/C][C]84509.2705212886[/C][C]-417.270521288636[/C][/ROW]
[ROW][C]65[/C][C]86372[/C][C]88116.3361022967[/C][C]-1744.3361022967[/C][/ROW]
[ROW][C]66[/C][C]83115[/C][C]85661.8596067367[/C][C]-2546.85960673675[/C][/ROW]
[ROW][C]67[/C][C]78839[/C][C]81564.7460054615[/C][C]-2725.74600546148[/C][/ROW]
[ROW][C]68[/C][C]75261[/C][C]77406.0864410822[/C][C]-2145.08644108224[/C][/ROW]
[ROW][C]69[/C][C]77857[/C][C]80772.4796435837[/C][C]-2915.47964358373[/C][/ROW]
[ROW][C]70[/C][C]67724[/C][C]71121.514304105[/C][C]-3397.51430410496[/C][/ROW]
[ROW][C]71[/C][C]73933[/C][C]75362.9814273272[/C][C]-1429.98142732721[/C][/ROW]
[ROW][C]72[/C][C]77541[/C][C]76468.200247356[/C][C]1072.79975264403[/C][/ROW]
[ROW][C]73[/C][C]78204[/C][C]77885.8377264237[/C][C]318.162273576323[/C][/ROW]
[ROW][C]74[/C][C]74595[/C][C]72680.6991912151[/C][C]1914.30080878493[/C][/ROW]
[ROW][C]75[/C][C]74910[/C][C]73382.6922472305[/C][C]1527.3077527695[/C][/ROW]
[ROW][C]76[/C][C]73933[/C][C]73844.2759350159[/C][C]88.7240649841115[/C][/ROW]
[ROW][C]77[/C][C]77221[/C][C]76553.8893968346[/C][C]667.11060316542[/C][/ROW]
[ROW][C]78[/C][C]74910[/C][C]74349.3205763015[/C][C]560.679423698515[/C][/ROW]
[ROW][C]79[/C][C]70355[/C][C]71236.3941973969[/C][C]-881.394197396949[/C][/ROW]
[ROW][C]80[/C][C]67062[/C][C]68049.7916538721[/C][C]-987.791653872104[/C][/ROW]
[ROW][C]81[/C][C]72630[/C][C]71336.60616276[/C][C]1293.39383723997[/C][/ROW]
[ROW][C]82[/C][C]60537[/C][C]63124.5648933717[/C][C]-2587.56489337173[/C][/ROW]
[ROW][C]83[/C][C]68390[/C][C]68905.0280311948[/C][C]-515.028031194845[/C][/ROW]
[ROW][C]84[/C][C]71968[/C][C]71934.0213599612[/C][C]33.9786400388111[/C][/ROW]
[ROW][C]85[/C][C]71968[/C][C]72519.2764304592[/C][C]-551.276430459213[/C][/ROW]
[ROW][C]86[/C][C]67724[/C][C]67925.5676026072[/C][C]-201.567602607232[/C][/ROW]
[ROW][C]87[/C][C]63799[/C][C]67499.1427144398[/C][C]-3700.14271443985[/C][/ROW]
[ROW][C]88[/C][C]63484[/C][C]64808.9871804085[/C][C]-1324.98718040854[/C][/ROW]
[ROW][C]89[/C][C]67062[/C][C]67075.1762462097[/C][C]-13.1762462096522[/C][/ROW]
[ROW][C]90[/C][C]63799[/C][C]64299.4560923665[/C][C]-500.456092366527[/C][/ROW]
[ROW][C]91[/C][C]57595[/C][C]59639.0080311028[/C][C]-2044.00803110284[/C][/ROW]
[ROW][C]92[/C][C]53319[/C][C]55627.6049069193[/C][C]-2308.6049069193[/C][/ROW]
[ROW][C]93[/C][C]57911[/C][C]59410.7283750367[/C][C]-1499.72837503666[/C][/ROW]
[ROW][C]94[/C][C]47115[/C][C]47360.8208013322[/C][C]-245.820801332193[/C][/ROW]
[ROW][C]95[/C][C]56928[/C][C]54986.3275441992[/C][C]1941.6724558008[/C][/ROW]
[ROW][C]96[/C][C]62150[/C][C]59065.2438669125[/C][C]3084.7561330875[/C][/ROW]
[ROW][C]97[/C][C]63799[/C][C]60346.5283804804[/C][C]3452.47161951959[/C][/ROW]
[ROW][C]98[/C][C]60191[/C][C]57495.8236235802[/C][C]2695.1763764198[/C][/ROW]
[ROW][C]99[/C][C]55631[/C][C]56151.0529328365[/C][C]-520.052932836501[/C][/ROW]
[ROW][C]100[/C][C]58893[/C][C]56233.39719989[/C][C]2659.60280011003[/C][/ROW]
[ROW][C]101[/C][C]60191[/C][C]61070.0806577908[/C][C]-879.080657790822[/C][/ROW]
[ROW][C]102[/C][C]59208[/C][C]57806.2352144052[/C][C]1401.76478559479[/C][/ROW]
[ROW][C]103[/C][C]49391[/C][C]53201.3539353552[/C][C]-3810.35393535515[/C][/ROW]
[ROW][C]104[/C][C]44835[/C][C]48472.8050325409[/C][C]-3637.80503254085[/C][/ROW]
[ROW][C]105[/C][C]48093[/C][C]52319.5583982989[/C][C]-4226.55839829893[/C][/ROW]
[ROW][C]106[/C][C]38280[/C][C]39960.0755580888[/C][C]-1680.07555808879[/C][/ROW]
[ROW][C]107[/C][C]48413[/C][C]48317.5979988887[/C][C]95.4020011112661[/C][/ROW]
[ROW][C]108[/C][C]52022[/C][C]52292.1741768706[/C][C]-270.174176870591[/C][/ROW]
[ROW][C]109[/C][C]54964[/C][C]52308.7685791582[/C][C]2655.23142084185[/C][/ROW]
[ROW][C]110[/C][C]50057[/C][C]48540.2904624718[/C][C]1516.70953752819[/C][/ROW]
[ROW][C]111[/C][C]45466[/C][C]44630.7820768221[/C][C]835.217923177857[/C][/ROW]
[ROW][C]112[/C][C]48093[/C][C]47013.6075653139[/C][C]1079.39243468609[/C][/ROW]
[ROW][C]113[/C][C]49391[/C][C]48924.4817408098[/C][C]466.518259190234[/C][/ROW]
[ROW][C]114[/C][C]46795[/C][C]47416.5824213123[/C][C]-621.582421312341[/C][/ROW]
[ROW][C]115[/C][C]36982[/C][C]38693.4310353743[/C][C]-1711.43103537425[/C][/ROW]
[ROW][C]116[/C][C]32706[/C][C]34774.4624778512[/C][C]-2068.46247785118[/C][/ROW]
[ROW][C]117[/C][C]36631[/C][C]38804.4657981421[/C][C]-2173.46579814215[/C][/ROW]
[ROW][C]118[/C][C]25835[/C][C]28742.3880323563[/C][C]-2907.38803235632[/C][/ROW]
[ROW][C]119[/C][C]37613[/C][C]37577.0298545343[/C][C]35.970145465697[/C][/ROW]
[ROW][C]120[/C][C]44835[/C][C]41227.3896143949[/C][C]3607.61038560508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296338&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296338&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
138374683742.28525641043.7147435896477
148374683558.5370690149187.462930985101
158311582809.8404387609305.159561239096
168146681152.8746227794313.125377220582
178998189753.3687100858227.631289914236
189127991067.2862186113211.713781388709
198931986167.45529425023151.54470574984
208472884508.5380979335219.461902066541
218669285243.63625747981448.36374252016
228374686253.831213707-2507.83121370702
238507585906.0909062125-831.090906212456
248571086344.9459123975-634.945912397525
258637287008.6193349581-636.619334958072
268472886712.6051094252-1984.60510942523
278507585134.671372028-59.6713720279804
288276483306.2365345758-542.236534575815
298998191458.4787976779-1477.47879767792
309226191976.4794728116284.520527188361
319030188760.95177048541540.04822951458
328669284569.72043604172122.27956395835
339061786721.12725675943895.87274324062
348637286349.107088721822.8929112781771
359030188068.70212312112232.2978768789
368998189990.4876285376-9.48762853759399
379096491047.6044636175-83.604463617492
388735590329.5456716521-2974.54567165206
399127989624.48782193641654.5121780636
409096488378.25156839152585.74843160847
419685297498.3975237373-646.39752373728
429552399678.9087417866-4155.90874178655
439030195571.7850965973-5270.78509659728
448767088949.6143642168-1279.6143642168
459127990671.3646378168607.635362183151
468637286472.017859474-100.017859473955
478998189261.030758743719.969241257044
489061789002.57666080781614.42333919216
499194690482.2023902381463.79760976195
508900488521.081349325482.918650675012
519061791909.4041984154-1292.4041984154
529159989884.55481882311714.44518117687
539520896568.8866021651-1360.88660216515
549226196193.5261191077-3932.52611910773
558833791340.5107844819-3003.51078448193
568409287896.5517036278-3804.5517036278
578802189536.8616898578-1515.86168985783
587722183820.1988158138-6599.19881581384
598244884056.6551709317-1608.6551709317
608539082919.55463396792470.44536603206
618833784212.35611234414124.64388765591
628409282371.87312094451720.12687905546
638409284863.7043280108-771.704328010761
648409284509.2705212886-417.270521288636
658637288116.3361022967-1744.3361022967
668311585661.8596067367-2546.85960673675
677883981564.7460054615-2725.74600546148
687526177406.0864410822-2145.08644108224
697785780772.4796435837-2915.47964358373
706772471121.514304105-3397.51430410496
717393375362.9814273272-1429.98142732721
727754176468.2002473561072.79975264403
737820477885.8377264237318.162273576323
747459572680.69919121511914.30080878493
757491073382.69224723051527.3077527695
767393373844.275935015988.7240649841115
777722176553.8893968346667.11060316542
787491074349.3205763015560.679423698515
797035571236.3941973969-881.394197396949
806706268049.7916538721-987.791653872104
817263071336.606162761293.39383723997
826053763124.5648933717-2587.56489337173
836839068905.0280311948-515.028031194845
847196871934.021359961233.9786400388111
857196872519.2764304592-551.276430459213
866772467925.5676026072-201.567602607232
876379967499.1427144398-3700.14271443985
886348464808.9871804085-1324.98718040854
896706267075.1762462097-13.1762462096522
906379964299.4560923665-500.456092366527
915759559639.0080311028-2044.00803110284
925331955627.6049069193-2308.6049069193
935791159410.7283750367-1499.72837503666
944711547360.8208013322-245.820801332193
955692854986.32754419921941.6724558008
966215059065.24386691253084.7561330875
976379960346.52838048043452.47161951959
986019157495.82362358022695.1763764198
995563156151.0529328365-520.052932836501
1005889356233.397199892659.60280011003
1016019161070.0806577908-879.080657790822
1025920857806.23521440521401.76478559479
1034939153201.3539353552-3810.35393535515
1044483548472.8050325409-3637.80503254085
1054809352319.5583982989-4226.55839829893
1063828039960.0755580888-1680.07555808879
1074841348317.597998888795.4020011112661
1085202252292.1741768706-270.174176870591
1095496452308.76857915822655.23142084185
1105005748540.29046247181516.70953752819
1114546644630.7820768221835.217923177857
1124809347013.60756531391079.39243468609
1134939148924.4817408098466.518259190234
1144679547416.5824213123-621.582421312341
1153698238693.4310353743-1711.43103537425
1163270634774.4624778512-2068.46247785118
1173663138804.4657981421-2173.46579814215
1182583528742.3880323563-2907.38803235632
1193761337577.029854534335.970145465697
1204483541227.38961439493607.61038560508







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12144574.117131377540516.64050860648631.5937541491
12239001.559384803134582.458600131143420.660169475
12333981.576227238629188.181926380738774.9705280964
12436058.773430102930878.988715506141238.5581446997
12537027.168574653431449.391629192242604.9455201146
12634530.422876657428543.484725586540517.3610277283
12725274.702426236118867.816317222831681.5885352495
12821745.464007506414908.183785759928582.7442292529
12926513.885943000719236.071457510633791.7004284908
13016915.64590270219187.4339628386924643.8578425656
13128774.357587318320586.137344346836962.5778302898
13234628.368752187625970.760642836743285.9768615386

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 44574.1171313775 & 40516.640508606 & 48631.5937541491 \tabularnewline
122 & 39001.5593848031 & 34582.4586001311 & 43420.660169475 \tabularnewline
123 & 33981.5762272386 & 29188.1819263807 & 38774.9705280964 \tabularnewline
124 & 36058.7734301029 & 30878.9887155061 & 41238.5581446997 \tabularnewline
125 & 37027.1685746534 & 31449.3916291922 & 42604.9455201146 \tabularnewline
126 & 34530.4228766574 & 28543.4847255865 & 40517.3610277283 \tabularnewline
127 & 25274.7024262361 & 18867.8163172228 & 31681.5885352495 \tabularnewline
128 & 21745.4640075064 & 14908.1837857599 & 28582.7442292529 \tabularnewline
129 & 26513.8859430007 & 19236.0714575106 & 33791.7004284908 \tabularnewline
130 & 16915.6459027021 & 9187.43396283869 & 24643.8578425656 \tabularnewline
131 & 28774.3575873183 & 20586.1373443468 & 36962.5778302898 \tabularnewline
132 & 34628.3687521876 & 25970.7606428367 & 43285.9768615386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296338&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]121[/C][C]44574.1171313775[/C][C]40516.640508606[/C][C]48631.5937541491[/C][/ROW]
[ROW][C]122[/C][C]39001.5593848031[/C][C]34582.4586001311[/C][C]43420.660169475[/C][/ROW]
[ROW][C]123[/C][C]33981.5762272386[/C][C]29188.1819263807[/C][C]38774.9705280964[/C][/ROW]
[ROW][C]124[/C][C]36058.7734301029[/C][C]30878.9887155061[/C][C]41238.5581446997[/C][/ROW]
[ROW][C]125[/C][C]37027.1685746534[/C][C]31449.3916291922[/C][C]42604.9455201146[/C][/ROW]
[ROW][C]126[/C][C]34530.4228766574[/C][C]28543.4847255865[/C][C]40517.3610277283[/C][/ROW]
[ROW][C]127[/C][C]25274.7024262361[/C][C]18867.8163172228[/C][C]31681.5885352495[/C][/ROW]
[ROW][C]128[/C][C]21745.4640075064[/C][C]14908.1837857599[/C][C]28582.7442292529[/C][/ROW]
[ROW][C]129[/C][C]26513.8859430007[/C][C]19236.0714575106[/C][C]33791.7004284908[/C][/ROW]
[ROW][C]130[/C][C]16915.6459027021[/C][C]9187.43396283869[/C][C]24643.8578425656[/C][/ROW]
[ROW][C]131[/C][C]28774.3575873183[/C][C]20586.1373443468[/C][C]36962.5778302898[/C][/ROW]
[ROW][C]132[/C][C]34628.3687521876[/C][C]25970.7606428367[/C][C]43285.9768615386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296338&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296338&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
12144574.117131377540516.64050860648631.5937541491
12239001.559384803134582.458600131143420.660169475
12333981.576227238629188.181926380738774.9705280964
12436058.773430102930878.988715506141238.5581446997
12537027.168574653431449.391629192242604.9455201146
12634530.422876657428543.484725586540517.3610277283
12725274.702426236118867.816317222831681.5885352495
12821745.464007506414908.183785759928582.7442292529
12926513.885943000719236.071457510633791.7004284908
13016915.64590270219187.4339628386924643.8578425656
13128774.357587318320586.137344346836962.5778302898
13234628.368752187625970.760642836743285.9768615386



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=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')