Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 08 Aug 2012 10:37:44 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/08/t1344436834atfdvwc5i96pd5d.htm/, Retrieved Fri, 03 May 2024 20:22:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169117, Retrieved Fri, 03 May 2024 20:22:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmatthew lauwers
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 1 - 32] [2012-08-08 14:37:44] [9bda411d6223d16f0472c7feaae49b5f] [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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169117&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169117&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405348713655826
beta0.0645208222842271
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405348713655826 \tabularnewline
beta & 0.0645208222842271 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169117&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]0.405348713655826[/C][/ROW]
[ROW][C]beta[/C][C]0.0645208222842271[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169117&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
alpha0.405348713655826
beta0.0645208222842271
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138374683742.28525641033.71474358973501
148374683558.5370690149187.462930985144
158311582809.8404387609305.15956123911
168146681152.8746227794313.125377220611
178998189753.3687100857227.63128991425
189127991067.2862186113211.713781388709
198931986167.45529425023151.54470574984
208472884508.5380979333219.461902066672
218669285243.63625747971448.36374252028
228374686253.8312137069-2507.83121370686
238507585906.0909062124-831.090906212383
248571086344.9459123975-634.945912397481
258637287008.6193349581-636.619334958101
268472886712.6051094252-1984.60510942523
278507585134.6713720281-59.6713720280532
288276483306.2365345759-542.236534575874
298998191458.478797678-1477.47879767798
309226191976.4794728118284.52052718823
319030188760.95177048561540.0482295144
328669284569.72043604172122.27956395826
339061786721.12725675943895.8727432406
348637286349.107088721722.8929112783371
359030188068.70212312092232.29787687908
368998189990.4876285373-9.48762853734661
379096491047.6044636173-83.6044636172883
388735590329.5456716518-2974.54567165181
399127989624.48782193631654.5121780637
409096488378.25156839142585.74843160862
419685297498.397523737-646.397523737018
429552399678.9087417863-4155.90874178635
439030195571.7850965973-5270.7850965973
448767088949.6143642171-1279.61436421706
459127990671.3646378172607.635362182802
468637286472.0178594742-100.017859474188
478998189261.0307587432719.969241256826
489061789002.5766608081614.42333919203
499194690482.20239023811463.79760976188
508900488521.0813493249482.918650675128
519061791909.4041984153-1292.40419841534
529159989884.55481882321714.44518117681
539520896568.8866021651-1360.88660216509
549226196193.5261191076-3932.5261191076
558833791340.5107844819-3003.5107844819
568409287896.551703628-3804.55170362798
578802189536.8616898582-1515.86168985824
587722183820.1988158143-6599.19881581432
598244884056.6551709324-1608.65517093241
608539082919.55463396872470.44536603133
618833784212.35611234474124.64388765529
628409282371.87312094491720.12687905511
638409284863.7043280109-771.704328010936
648409284509.2705212889-417.270521288898
658637288116.3361022969-1744.33610229692
668311585661.8596067369-2546.85960673689
677883981564.7460054616-2725.74600546159
687526177406.0864410824-2145.0864410824
697785780772.4796435841-2915.47964358405
706772471121.5143041053-3397.51430410532
717393375362.9814273278-1429.9814273278
727754176468.20024735671072.79975264329
737820477885.8377264245318.162273575523
747459572680.69919121581914.30080878416
757491073382.6922472311527.30775276896
767393373844.275935016388.7240649836895
777722176553.8893968349667.1106031651
787491074349.3205763017560.679423698326
797035571236.394197397-881.394197396992
806706268049.7916538721-987.791653872089
817263071336.606162761293.39383723997
826053763124.5648933716-2587.56489337163
836839068905.0280311949-515.028031194903
847196871934.021359961433.9786400385929
857196872519.2764304596-551.276430459591
866772467925.5676026078-201.567602607756
876379967499.1427144404-3700.14271444039
886348464808.9871804091-1324.98718040912
896706267075.1762462102-13.1762462102051
906379964299.456092367-500.456092366971
915759559639.0080311032-2044.00803110317
925331955627.6049069196-2308.60490691957
935791159410.728375037-1499.72837503695
944711547360.8208013324-245.820801332418
955692854986.32754419941941.67245580059
966215059065.24386691273084.75613308731
976379960346.52838048053452.47161951946
986019157495.82362358032695.17637641965
995563156151.0529328366-520.052932836566
1005889356233.39719989012659.6028001099
1016019161070.0806577909-879.080657790895
1025920857806.23521440531401.7647855947
1034939153201.3539353551-3810.3539353551
1044483548472.8050325408-3637.80503254084
1054809352319.558398299-4226.55839829898
1063828039960.0755580889-1680.07555808893
1074841348317.597998888995.4020011110624
1085202252292.1741768708-270.174176870838
1095496452308.76857915852655.23142084153
1105005748540.29046247211516.70953752792
1114546644630.7820768223835.217923177661
1124809347013.60756531411079.39243468585
1134939148924.4817408099466.518259190059
1144679547416.5824213125-621.582421312531
1153698238693.4310353743-1711.43103537433
1163270634774.4624778512-2068.46247785119
1173663138804.4657981421-2173.46579814213
1182583528742.3880323564-2907.38803235636
1193761337577.029854534535.9701454655369
1204483541227.38961439513607.61038560489

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 83746 & 83742.2852564103 & 3.71474358973501 \tabularnewline
14 & 83746 & 83558.5370690149 & 187.462930985144 \tabularnewline
15 & 83115 & 82809.8404387609 & 305.15956123911 \tabularnewline
16 & 81466 & 81152.8746227794 & 313.125377220611 \tabularnewline
17 & 89981 & 89753.3687100857 & 227.63128991425 \tabularnewline
18 & 91279 & 91067.2862186113 & 211.713781388709 \tabularnewline
19 & 89319 & 86167.4552942502 & 3151.54470574984 \tabularnewline
20 & 84728 & 84508.5380979333 & 219.461902066672 \tabularnewline
21 & 86692 & 85243.6362574797 & 1448.36374252028 \tabularnewline
22 & 83746 & 86253.8312137069 & -2507.83121370686 \tabularnewline
23 & 85075 & 85906.0909062124 & -831.090906212383 \tabularnewline
24 & 85710 & 86344.9459123975 & -634.945912397481 \tabularnewline
25 & 86372 & 87008.6193349581 & -636.619334958101 \tabularnewline
26 & 84728 & 86712.6051094252 & -1984.60510942523 \tabularnewline
27 & 85075 & 85134.6713720281 & -59.6713720280532 \tabularnewline
28 & 82764 & 83306.2365345759 & -542.236534575874 \tabularnewline
29 & 89981 & 91458.478797678 & -1477.47879767798 \tabularnewline
30 & 92261 & 91976.4794728118 & 284.52052718823 \tabularnewline
31 & 90301 & 88760.9517704856 & 1540.0482295144 \tabularnewline
32 & 86692 & 84569.7204360417 & 2122.27956395826 \tabularnewline
33 & 90617 & 86721.1272567594 & 3895.8727432406 \tabularnewline
34 & 86372 & 86349.1070887217 & 22.8929112783371 \tabularnewline
35 & 90301 & 88068.7021231209 & 2232.29787687908 \tabularnewline
36 & 89981 & 89990.4876285373 & -9.48762853734661 \tabularnewline
37 & 90964 & 91047.6044636173 & -83.6044636172883 \tabularnewline
38 & 87355 & 90329.5456716518 & -2974.54567165181 \tabularnewline
39 & 91279 & 89624.4878219363 & 1654.5121780637 \tabularnewline
40 & 90964 & 88378.2515683914 & 2585.74843160862 \tabularnewline
41 & 96852 & 97498.397523737 & -646.397523737018 \tabularnewline
42 & 95523 & 99678.9087417863 & -4155.90874178635 \tabularnewline
43 & 90301 & 95571.7850965973 & -5270.7850965973 \tabularnewline
44 & 87670 & 88949.6143642171 & -1279.61436421706 \tabularnewline
45 & 91279 & 90671.3646378172 & 607.635362182802 \tabularnewline
46 & 86372 & 86472.0178594742 & -100.017859474188 \tabularnewline
47 & 89981 & 89261.0307587432 & 719.969241256826 \tabularnewline
48 & 90617 & 89002.576660808 & 1614.42333919203 \tabularnewline
49 & 91946 & 90482.2023902381 & 1463.79760976188 \tabularnewline
50 & 89004 & 88521.0813493249 & 482.918650675128 \tabularnewline
51 & 90617 & 91909.4041984153 & -1292.40419841534 \tabularnewline
52 & 91599 & 89884.5548188232 & 1714.44518117681 \tabularnewline
53 & 95208 & 96568.8866021651 & -1360.88660216509 \tabularnewline
54 & 92261 & 96193.5261191076 & -3932.5261191076 \tabularnewline
55 & 88337 & 91340.5107844819 & -3003.5107844819 \tabularnewline
56 & 84092 & 87896.551703628 & -3804.55170362798 \tabularnewline
57 & 88021 & 89536.8616898582 & -1515.86168985824 \tabularnewline
58 & 77221 & 83820.1988158143 & -6599.19881581432 \tabularnewline
59 & 82448 & 84056.6551709324 & -1608.65517093241 \tabularnewline
60 & 85390 & 82919.5546339687 & 2470.44536603133 \tabularnewline
61 & 88337 & 84212.3561123447 & 4124.64388765529 \tabularnewline
62 & 84092 & 82371.8731209449 & 1720.12687905511 \tabularnewline
63 & 84092 & 84863.7043280109 & -771.704328010936 \tabularnewline
64 & 84092 & 84509.2705212889 & -417.270521288898 \tabularnewline
65 & 86372 & 88116.3361022969 & -1744.33610229692 \tabularnewline
66 & 83115 & 85661.8596067369 & -2546.85960673689 \tabularnewline
67 & 78839 & 81564.7460054616 & -2725.74600546159 \tabularnewline
68 & 75261 & 77406.0864410824 & -2145.0864410824 \tabularnewline
69 & 77857 & 80772.4796435841 & -2915.47964358405 \tabularnewline
70 & 67724 & 71121.5143041053 & -3397.51430410532 \tabularnewline
71 & 73933 & 75362.9814273278 & -1429.9814273278 \tabularnewline
72 & 77541 & 76468.2002473567 & 1072.79975264329 \tabularnewline
73 & 78204 & 77885.8377264245 & 318.162273575523 \tabularnewline
74 & 74595 & 72680.6991912158 & 1914.30080878416 \tabularnewline
75 & 74910 & 73382.692247231 & 1527.30775276896 \tabularnewline
76 & 73933 & 73844.2759350163 & 88.7240649836895 \tabularnewline
77 & 77221 & 76553.8893968349 & 667.1106031651 \tabularnewline
78 & 74910 & 74349.3205763017 & 560.679423698326 \tabularnewline
79 & 70355 & 71236.394197397 & -881.394197396992 \tabularnewline
80 & 67062 & 68049.7916538721 & -987.791653872089 \tabularnewline
81 & 72630 & 71336.60616276 & 1293.39383723997 \tabularnewline
82 & 60537 & 63124.5648933716 & -2587.56489337163 \tabularnewline
83 & 68390 & 68905.0280311949 & -515.028031194903 \tabularnewline
84 & 71968 & 71934.0213599614 & 33.9786400385929 \tabularnewline
85 & 71968 & 72519.2764304596 & -551.276430459591 \tabularnewline
86 & 67724 & 67925.5676026078 & -201.567602607756 \tabularnewline
87 & 63799 & 67499.1427144404 & -3700.14271444039 \tabularnewline
88 & 63484 & 64808.9871804091 & -1324.98718040912 \tabularnewline
89 & 67062 & 67075.1762462102 & -13.1762462102051 \tabularnewline
90 & 63799 & 64299.456092367 & -500.456092366971 \tabularnewline
91 & 57595 & 59639.0080311032 & -2044.00803110317 \tabularnewline
92 & 53319 & 55627.6049069196 & -2308.60490691957 \tabularnewline
93 & 57911 & 59410.728375037 & -1499.72837503695 \tabularnewline
94 & 47115 & 47360.8208013324 & -245.820801332418 \tabularnewline
95 & 56928 & 54986.3275441994 & 1941.67245580059 \tabularnewline
96 & 62150 & 59065.2438669127 & 3084.75613308731 \tabularnewline
97 & 63799 & 60346.5283804805 & 3452.47161951946 \tabularnewline
98 & 60191 & 57495.8236235803 & 2695.17637641965 \tabularnewline
99 & 55631 & 56151.0529328366 & -520.052932836566 \tabularnewline
100 & 58893 & 56233.3971998901 & 2659.6028001099 \tabularnewline
101 & 60191 & 61070.0806577909 & -879.080657790895 \tabularnewline
102 & 59208 & 57806.2352144053 & 1401.7647855947 \tabularnewline
103 & 49391 & 53201.3539353551 & -3810.3539353551 \tabularnewline
104 & 44835 & 48472.8050325408 & -3637.80503254084 \tabularnewline
105 & 48093 & 52319.558398299 & -4226.55839829898 \tabularnewline
106 & 38280 & 39960.0755580889 & -1680.07555808893 \tabularnewline
107 & 48413 & 48317.5979988889 & 95.4020011110624 \tabularnewline
108 & 52022 & 52292.1741768708 & -270.174176870838 \tabularnewline
109 & 54964 & 52308.7685791585 & 2655.23142084153 \tabularnewline
110 & 50057 & 48540.2904624721 & 1516.70953752792 \tabularnewline
111 & 45466 & 44630.7820768223 & 835.217923177661 \tabularnewline
112 & 48093 & 47013.6075653141 & 1079.39243468585 \tabularnewline
113 & 49391 & 48924.4817408099 & 466.518259190059 \tabularnewline
114 & 46795 & 47416.5824213125 & -621.582421312531 \tabularnewline
115 & 36982 & 38693.4310353743 & -1711.43103537433 \tabularnewline
116 & 32706 & 34774.4624778512 & -2068.46247785119 \tabularnewline
117 & 36631 & 38804.4657981421 & -2173.46579814213 \tabularnewline
118 & 25835 & 28742.3880323564 & -2907.38803235636 \tabularnewline
119 & 37613 & 37577.0298545345 & 35.9701454655369 \tabularnewline
120 & 44835 & 41227.3896143951 & 3607.61038560489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169117&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]83742.2852564103[/C][C]3.71474358973501[/C][/ROW]
[ROW][C]14[/C][C]83746[/C][C]83558.5370690149[/C][C]187.462930985144[/C][/ROW]
[ROW][C]15[/C][C]83115[/C][C]82809.8404387609[/C][C]305.15956123911[/C][/ROW]
[ROW][C]16[/C][C]81466[/C][C]81152.8746227794[/C][C]313.125377220611[/C][/ROW]
[ROW][C]17[/C][C]89981[/C][C]89753.3687100857[/C][C]227.63128991425[/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]84508.5380979333[/C][C]219.461902066672[/C][/ROW]
[ROW][C]21[/C][C]86692[/C][C]85243.6362574797[/C][C]1448.36374252028[/C][/ROW]
[ROW][C]22[/C][C]83746[/C][C]86253.8312137069[/C][C]-2507.83121370686[/C][/ROW]
[ROW][C]23[/C][C]85075[/C][C]85906.0909062124[/C][C]-831.090906212383[/C][/ROW]
[ROW][C]24[/C][C]85710[/C][C]86344.9459123975[/C][C]-634.945912397481[/C][/ROW]
[ROW][C]25[/C][C]86372[/C][C]87008.6193349581[/C][C]-636.619334958101[/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]85134.6713720281[/C][C]-59.6713720280532[/C][/ROW]
[ROW][C]28[/C][C]82764[/C][C]83306.2365345759[/C][C]-542.236534575874[/C][/ROW]
[ROW][C]29[/C][C]89981[/C][C]91458.478797678[/C][C]-1477.47879767798[/C][/ROW]
[ROW][C]30[/C][C]92261[/C][C]91976.4794728118[/C][C]284.52052718823[/C][/ROW]
[ROW][C]31[/C][C]90301[/C][C]88760.9517704856[/C][C]1540.0482295144[/C][/ROW]
[ROW][C]32[/C][C]86692[/C][C]84569.7204360417[/C][C]2122.27956395826[/C][/ROW]
[ROW][C]33[/C][C]90617[/C][C]86721.1272567594[/C][C]3895.8727432406[/C][/ROW]
[ROW][C]34[/C][C]86372[/C][C]86349.1070887217[/C][C]22.8929112783371[/C][/ROW]
[ROW][C]35[/C][C]90301[/C][C]88068.7021231209[/C][C]2232.29787687908[/C][/ROW]
[ROW][C]36[/C][C]89981[/C][C]89990.4876285373[/C][C]-9.48762853734661[/C][/ROW]
[ROW][C]37[/C][C]90964[/C][C]91047.6044636173[/C][C]-83.6044636172883[/C][/ROW]
[ROW][C]38[/C][C]87355[/C][C]90329.5456716518[/C][C]-2974.54567165181[/C][/ROW]
[ROW][C]39[/C][C]91279[/C][C]89624.4878219363[/C][C]1654.5121780637[/C][/ROW]
[ROW][C]40[/C][C]90964[/C][C]88378.2515683914[/C][C]2585.74843160862[/C][/ROW]
[ROW][C]41[/C][C]96852[/C][C]97498.397523737[/C][C]-646.397523737018[/C][/ROW]
[ROW][C]42[/C][C]95523[/C][C]99678.9087417863[/C][C]-4155.90874178635[/C][/ROW]
[ROW][C]43[/C][C]90301[/C][C]95571.7850965973[/C][C]-5270.7850965973[/C][/ROW]
[ROW][C]44[/C][C]87670[/C][C]88949.6143642171[/C][C]-1279.61436421706[/C][/ROW]
[ROW][C]45[/C][C]91279[/C][C]90671.3646378172[/C][C]607.635362182802[/C][/ROW]
[ROW][C]46[/C][C]86372[/C][C]86472.0178594742[/C][C]-100.017859474188[/C][/ROW]
[ROW][C]47[/C][C]89981[/C][C]89261.0307587432[/C][C]719.969241256826[/C][/ROW]
[ROW][C]48[/C][C]90617[/C][C]89002.576660808[/C][C]1614.42333919203[/C][/ROW]
[ROW][C]49[/C][C]91946[/C][C]90482.2023902381[/C][C]1463.79760976188[/C][/ROW]
[ROW][C]50[/C][C]89004[/C][C]88521.0813493249[/C][C]482.918650675128[/C][/ROW]
[ROW][C]51[/C][C]90617[/C][C]91909.4041984153[/C][C]-1292.40419841534[/C][/ROW]
[ROW][C]52[/C][C]91599[/C][C]89884.5548188232[/C][C]1714.44518117681[/C][/ROW]
[ROW][C]53[/C][C]95208[/C][C]96568.8866021651[/C][C]-1360.88660216509[/C][/ROW]
[ROW][C]54[/C][C]92261[/C][C]96193.5261191076[/C][C]-3932.5261191076[/C][/ROW]
[ROW][C]55[/C][C]88337[/C][C]91340.5107844819[/C][C]-3003.5107844819[/C][/ROW]
[ROW][C]56[/C][C]84092[/C][C]87896.551703628[/C][C]-3804.55170362798[/C][/ROW]
[ROW][C]57[/C][C]88021[/C][C]89536.8616898582[/C][C]-1515.86168985824[/C][/ROW]
[ROW][C]58[/C][C]77221[/C][C]83820.1988158143[/C][C]-6599.19881581432[/C][/ROW]
[ROW][C]59[/C][C]82448[/C][C]84056.6551709324[/C][C]-1608.65517093241[/C][/ROW]
[ROW][C]60[/C][C]85390[/C][C]82919.5546339687[/C][C]2470.44536603133[/C][/ROW]
[ROW][C]61[/C][C]88337[/C][C]84212.3561123447[/C][C]4124.64388765529[/C][/ROW]
[ROW][C]62[/C][C]84092[/C][C]82371.8731209449[/C][C]1720.12687905511[/C][/ROW]
[ROW][C]63[/C][C]84092[/C][C]84863.7043280109[/C][C]-771.704328010936[/C][/ROW]
[ROW][C]64[/C][C]84092[/C][C]84509.2705212889[/C][C]-417.270521288898[/C][/ROW]
[ROW][C]65[/C][C]86372[/C][C]88116.3361022969[/C][C]-1744.33610229692[/C][/ROW]
[ROW][C]66[/C][C]83115[/C][C]85661.8596067369[/C][C]-2546.85960673689[/C][/ROW]
[ROW][C]67[/C][C]78839[/C][C]81564.7460054616[/C][C]-2725.74600546159[/C][/ROW]
[ROW][C]68[/C][C]75261[/C][C]77406.0864410824[/C][C]-2145.0864410824[/C][/ROW]
[ROW][C]69[/C][C]77857[/C][C]80772.4796435841[/C][C]-2915.47964358405[/C][/ROW]
[ROW][C]70[/C][C]67724[/C][C]71121.5143041053[/C][C]-3397.51430410532[/C][/ROW]
[ROW][C]71[/C][C]73933[/C][C]75362.9814273278[/C][C]-1429.9814273278[/C][/ROW]
[ROW][C]72[/C][C]77541[/C][C]76468.2002473567[/C][C]1072.79975264329[/C][/ROW]
[ROW][C]73[/C][C]78204[/C][C]77885.8377264245[/C][C]318.162273575523[/C][/ROW]
[ROW][C]74[/C][C]74595[/C][C]72680.6991912158[/C][C]1914.30080878416[/C][/ROW]
[ROW][C]75[/C][C]74910[/C][C]73382.692247231[/C][C]1527.30775276896[/C][/ROW]
[ROW][C]76[/C][C]73933[/C][C]73844.2759350163[/C][C]88.7240649836895[/C][/ROW]
[ROW][C]77[/C][C]77221[/C][C]76553.8893968349[/C][C]667.1106031651[/C][/ROW]
[ROW][C]78[/C][C]74910[/C][C]74349.3205763017[/C][C]560.679423698326[/C][/ROW]
[ROW][C]79[/C][C]70355[/C][C]71236.394197397[/C][C]-881.394197396992[/C][/ROW]
[ROW][C]80[/C][C]67062[/C][C]68049.7916538721[/C][C]-987.791653872089[/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]63124.5648933716[/C][C]-2587.56489337163[/C][/ROW]
[ROW][C]83[/C][C]68390[/C][C]68905.0280311949[/C][C]-515.028031194903[/C][/ROW]
[ROW][C]84[/C][C]71968[/C][C]71934.0213599614[/C][C]33.9786400385929[/C][/ROW]
[ROW][C]85[/C][C]71968[/C][C]72519.2764304596[/C][C]-551.276430459591[/C][/ROW]
[ROW][C]86[/C][C]67724[/C][C]67925.5676026078[/C][C]-201.567602607756[/C][/ROW]
[ROW][C]87[/C][C]63799[/C][C]67499.1427144404[/C][C]-3700.14271444039[/C][/ROW]
[ROW][C]88[/C][C]63484[/C][C]64808.9871804091[/C][C]-1324.98718040912[/C][/ROW]
[ROW][C]89[/C][C]67062[/C][C]67075.1762462102[/C][C]-13.1762462102051[/C][/ROW]
[ROW][C]90[/C][C]63799[/C][C]64299.456092367[/C][C]-500.456092366971[/C][/ROW]
[ROW][C]91[/C][C]57595[/C][C]59639.0080311032[/C][C]-2044.00803110317[/C][/ROW]
[ROW][C]92[/C][C]53319[/C][C]55627.6049069196[/C][C]-2308.60490691957[/C][/ROW]
[ROW][C]93[/C][C]57911[/C][C]59410.728375037[/C][C]-1499.72837503695[/C][/ROW]
[ROW][C]94[/C][C]47115[/C][C]47360.8208013324[/C][C]-245.820801332418[/C][/ROW]
[ROW][C]95[/C][C]56928[/C][C]54986.3275441994[/C][C]1941.67245580059[/C][/ROW]
[ROW][C]96[/C][C]62150[/C][C]59065.2438669127[/C][C]3084.75613308731[/C][/ROW]
[ROW][C]97[/C][C]63799[/C][C]60346.5283804805[/C][C]3452.47161951946[/C][/ROW]
[ROW][C]98[/C][C]60191[/C][C]57495.8236235803[/C][C]2695.17637641965[/C][/ROW]
[ROW][C]99[/C][C]55631[/C][C]56151.0529328366[/C][C]-520.052932836566[/C][/ROW]
[ROW][C]100[/C][C]58893[/C][C]56233.3971998901[/C][C]2659.6028001099[/C][/ROW]
[ROW][C]101[/C][C]60191[/C][C]61070.0806577909[/C][C]-879.080657790895[/C][/ROW]
[ROW][C]102[/C][C]59208[/C][C]57806.2352144053[/C][C]1401.7647855947[/C][/ROW]
[ROW][C]103[/C][C]49391[/C][C]53201.3539353551[/C][C]-3810.3539353551[/C][/ROW]
[ROW][C]104[/C][C]44835[/C][C]48472.8050325408[/C][C]-3637.80503254084[/C][/ROW]
[ROW][C]105[/C][C]48093[/C][C]52319.558398299[/C][C]-4226.55839829898[/C][/ROW]
[ROW][C]106[/C][C]38280[/C][C]39960.0755580889[/C][C]-1680.07555808893[/C][/ROW]
[ROW][C]107[/C][C]48413[/C][C]48317.5979988889[/C][C]95.4020011110624[/C][/ROW]
[ROW][C]108[/C][C]52022[/C][C]52292.1741768708[/C][C]-270.174176870838[/C][/ROW]
[ROW][C]109[/C][C]54964[/C][C]52308.7685791585[/C][C]2655.23142084153[/C][/ROW]
[ROW][C]110[/C][C]50057[/C][C]48540.2904624721[/C][C]1516.70953752792[/C][/ROW]
[ROW][C]111[/C][C]45466[/C][C]44630.7820768223[/C][C]835.217923177661[/C][/ROW]
[ROW][C]112[/C][C]48093[/C][C]47013.6075653141[/C][C]1079.39243468585[/C][/ROW]
[ROW][C]113[/C][C]49391[/C][C]48924.4817408099[/C][C]466.518259190059[/C][/ROW]
[ROW][C]114[/C][C]46795[/C][C]47416.5824213125[/C][C]-621.582421312531[/C][/ROW]
[ROW][C]115[/C][C]36982[/C][C]38693.4310353743[/C][C]-1711.43103537433[/C][/ROW]
[ROW][C]116[/C][C]32706[/C][C]34774.4624778512[/C][C]-2068.46247785119[/C][/ROW]
[ROW][C]117[/C][C]36631[/C][C]38804.4657981421[/C][C]-2173.46579814213[/C][/ROW]
[ROW][C]118[/C][C]25835[/C][C]28742.3880323564[/C][C]-2907.38803235636[/C][/ROW]
[ROW][C]119[/C][C]37613[/C][C]37577.0298545345[/C][C]35.9701454655369[/C][/ROW]
[ROW][C]120[/C][C]44835[/C][C]41227.3896143951[/C][C]3607.61038560489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169117&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169117&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
138374683742.28525641033.71474358973501
148374683558.5370690149187.462930985144
158311582809.8404387609305.15956123911
168146681152.8746227794313.125377220611
178998189753.3687100857227.63128991425
189127991067.2862186113211.713781388709
198931986167.45529425023151.54470574984
208472884508.5380979333219.461902066672
218669285243.63625747971448.36374252028
228374686253.8312137069-2507.83121370686
238507585906.0909062124-831.090906212383
248571086344.9459123975-634.945912397481
258637287008.6193349581-636.619334958101
268472886712.6051094252-1984.60510942523
278507585134.6713720281-59.6713720280532
288276483306.2365345759-542.236534575874
298998191458.478797678-1477.47879767798
309226191976.4794728118284.52052718823
319030188760.95177048561540.0482295144
328669284569.72043604172122.27956395826
339061786721.12725675943895.8727432406
348637286349.107088721722.8929112783371
359030188068.70212312092232.29787687908
368998189990.4876285373-9.48762853734661
379096491047.6044636173-83.6044636172883
388735590329.5456716518-2974.54567165181
399127989624.48782193631654.5121780637
409096488378.25156839142585.74843160862
419685297498.397523737-646.397523737018
429552399678.9087417863-4155.90874178635
439030195571.7850965973-5270.7850965973
448767088949.6143642171-1279.61436421706
459127990671.3646378172607.635362182802
468637286472.0178594742-100.017859474188
478998189261.0307587432719.969241256826
489061789002.5766608081614.42333919203
499194690482.20239023811463.79760976188
508900488521.0813493249482.918650675128
519061791909.4041984153-1292.40419841534
529159989884.55481882321714.44518117681
539520896568.8866021651-1360.88660216509
549226196193.5261191076-3932.5261191076
558833791340.5107844819-3003.5107844819
568409287896.551703628-3804.55170362798
578802189536.8616898582-1515.86168985824
587722183820.1988158143-6599.19881581432
598244884056.6551709324-1608.65517093241
608539082919.55463396872470.44536603133
618833784212.35611234474124.64388765529
628409282371.87312094491720.12687905511
638409284863.7043280109-771.704328010936
648409284509.2705212889-417.270521288898
658637288116.3361022969-1744.33610229692
668311585661.8596067369-2546.85960673689
677883981564.7460054616-2725.74600546159
687526177406.0864410824-2145.0864410824
697785780772.4796435841-2915.47964358405
706772471121.5143041053-3397.51430410532
717393375362.9814273278-1429.9814273278
727754176468.20024735671072.79975264329
737820477885.8377264245318.162273575523
747459572680.69919121581914.30080878416
757491073382.6922472311527.30775276896
767393373844.275935016388.7240649836895
777722176553.8893968349667.1106031651
787491074349.3205763017560.679423698326
797035571236.394197397-881.394197396992
806706268049.7916538721-987.791653872089
817263071336.606162761293.39383723997
826053763124.5648933716-2587.56489337163
836839068905.0280311949-515.028031194903
847196871934.021359961433.9786400385929
857196872519.2764304596-551.276430459591
866772467925.5676026078-201.567602607756
876379967499.1427144404-3700.14271444039
886348464808.9871804091-1324.98718040912
896706267075.1762462102-13.1762462102051
906379964299.456092367-500.456092366971
915759559639.0080311032-2044.00803110317
925331955627.6049069196-2308.60490691957
935791159410.728375037-1499.72837503695
944711547360.8208013324-245.820801332418
955692854986.32754419941941.67245580059
966215059065.24386691273084.75613308731
976379960346.52838048053452.47161951946
986019157495.82362358032695.17637641965
995563156151.0529328366-520.052932836566
1005889356233.39719989012659.6028001099
1016019161070.0806577909-879.080657790895
1025920857806.23521440531401.7647855947
1034939153201.3539353551-3810.3539353551
1044483548472.8050325408-3637.80503254084
1054809352319.558398299-4226.55839829898
1063828039960.0755580889-1680.07555808893
1074841348317.597998888995.4020011110624
1085202252292.1741768708-270.174176870838
1095496452308.76857915852655.23142084153
1105005748540.29046247211516.70953752792
1114546644630.7820768223835.217923177661
1124809347013.60756531411079.39243468585
1134939148924.4817408099466.518259190059
1144679547416.5824213125-621.582421312531
1153698238693.4310353743-1711.43103537433
1163270634774.4624778512-2068.46247785119
1173663138804.4657981421-2173.46579814213
1182583528742.3880323564-2907.38803235636
1193761337577.029854534535.9701454655369
1204483541227.38961439513607.61038560489







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12144574.117131377740516.640508606248631.5937541492
12239001.559384803434582.458600131543420.6601694752
12333981.57622723929188.181926381338774.9705280967
12436058.773430103530878.98871550741238.5581447
12537027.168574654131449.391629193342604.945520115
12634530.422876658228543.484725587840517.3610277286
12725274.70242623718867.816317224331681.5885352497
12821745.464007507214908.183785761528582.744229253
12926513.885943001519236.071457512333791.7004284908
13016915.64590270299187.4339628404824643.8578425653
13128774.35758731920586.137344348736962.5778302893
13234628.368752188525970.760642838943285.976861538

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 44574.1171313777 & 40516.6405086062 & 48631.5937541492 \tabularnewline
122 & 39001.5593848034 & 34582.4586001315 & 43420.6601694752 \tabularnewline
123 & 33981.576227239 & 29188.1819263813 & 38774.9705280967 \tabularnewline
124 & 36058.7734301035 & 30878.988715507 & 41238.5581447 \tabularnewline
125 & 37027.1685746541 & 31449.3916291933 & 42604.945520115 \tabularnewline
126 & 34530.4228766582 & 28543.4847255878 & 40517.3610277286 \tabularnewline
127 & 25274.702426237 & 18867.8163172243 & 31681.5885352497 \tabularnewline
128 & 21745.4640075072 & 14908.1837857615 & 28582.744229253 \tabularnewline
129 & 26513.8859430015 & 19236.0714575123 & 33791.7004284908 \tabularnewline
130 & 16915.6459027029 & 9187.43396284048 & 24643.8578425653 \tabularnewline
131 & 28774.357587319 & 20586.1373443487 & 36962.5778302893 \tabularnewline
132 & 34628.3687521885 & 25970.7606428389 & 43285.976861538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169117&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]44574.1171313777[/C][C]40516.6405086062[/C][C]48631.5937541492[/C][/ROW]
[ROW][C]122[/C][C]39001.5593848034[/C][C]34582.4586001315[/C][C]43420.6601694752[/C][/ROW]
[ROW][C]123[/C][C]33981.576227239[/C][C]29188.1819263813[/C][C]38774.9705280967[/C][/ROW]
[ROW][C]124[/C][C]36058.7734301035[/C][C]30878.988715507[/C][C]41238.5581447[/C][/ROW]
[ROW][C]125[/C][C]37027.1685746541[/C][C]31449.3916291933[/C][C]42604.945520115[/C][/ROW]
[ROW][C]126[/C][C]34530.4228766582[/C][C]28543.4847255878[/C][C]40517.3610277286[/C][/ROW]
[ROW][C]127[/C][C]25274.702426237[/C][C]18867.8163172243[/C][C]31681.5885352497[/C][/ROW]
[ROW][C]128[/C][C]21745.4640075072[/C][C]14908.1837857615[/C][C]28582.744229253[/C][/ROW]
[ROW][C]129[/C][C]26513.8859430015[/C][C]19236.0714575123[/C][C]33791.7004284908[/C][/ROW]
[ROW][C]130[/C][C]16915.6459027029[/C][C]9187.43396284048[/C][C]24643.8578425653[/C][/ROW]
[ROW][C]131[/C][C]28774.357587319[/C][C]20586.1373443487[/C][C]36962.5778302893[/C][/ROW]
[ROW][C]132[/C][C]34628.3687521885[/C][C]25970.7606428389[/C][C]43285.976861538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169117&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169117&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
12144574.117131377740516.640508606248631.5937541492
12239001.559384803434582.458600131543420.6601694752
12333981.57622723929188.181926381338774.9705280967
12436058.773430103530878.98871550741238.5581447
12537027.168574654131449.391629193342604.945520115
12634530.422876658228543.484725587840517.3610277286
12725274.70242623718867.816317224331681.5885352497
12821745.464007507214908.183785761528582.744229253
12926513.885943001519236.071457512333791.7004284908
13016915.64590270299187.4339628404824643.8578425653
13128774.35758731920586.137344348736962.5778302893
13234628.368752188525970.760642838943285.976861538



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')