Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 18:09:56 -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/2011/Aug/18/t1313705431vqnz5akzx94kxr0.htm/, Retrieved Wed, 15 May 2024 21:02:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124173, Retrieved Wed, 15 May 2024 21:02:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Datareeks-exponen...] [2011-08-18 22:09:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
34671
34355
34035
33373
39924
39577
34671
31409
31724
31724
32075
32706
34671
34035
35017
36631
45813
45813
43853
41888
43502
45466
45813
46795
49742
47777
47777
50724
58893
59555
57911
53982
56928
56928
57244
58893
60191
60853
60853
62817
70355
72315
72630
67724
70355
69373
67408
71653
72630
70986
71333
73613
82133
86372
86372
84412
87355
84412
82764
89004
89981
87670
93559
95870
102741
107301
106670
106319
108950
108630
104706
110594
112559
110594
118763
122692
131839
135448
134470
132505
134150
136114
129559
134785
138079
136750
145265
148207
160652
162932
159990
161634
162616
163598
157358
163247
166509
163247
172749
175692
188451
190416
191047
194340
194340
195638
189749
192696
194656
191047
201527
203491
216567
218878
222140
225087
225402
225749
219860
225749




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124173&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124173&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124173&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.972367396450504
beta0.0390646066580028
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.972367396450504 \tabularnewline
beta & 0.0390646066580028 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124173&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]0.972367396450504[/C][/ROW]
[ROW][C]beta[/C][C]0.0390646066580028[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124173&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124173&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
alpha0.972367396450504
beta0.0390646066580028
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33403534039-4
43337333718.9585898147-345.95858981472
53992433053.26650707476870.7334929253
63957739665.8363572551-88.8363572550661
73467139507.7729294559-4836.77292945594
83140934549.2452338241-3140.24523382405
93172431121.0830707664602.916929233579
103172431355.5516446089368.448355391083
113207531376.0261877534698.973812246611
123270631744.4435338541961.55646614594
133467132404.71255795432266.28744204566
143403534419.7447122918-384.744712291802
153501733842.38504725171174.61495274829
163663134825.91380485561805.08619514442
174581336491.05871261489321.94128738516
184581345819.4437727871-6.44377278706088
194385346076.9665712368-2223.9665712368
204188844093.7647960754-2205.76479607535
214350242044.47552728281457.52447271716
224546643612.61359276571853.38640723433
234581345636.0760573135176.923942686473
244679546036.1215624404758.878437559579
254974247030.86675578312711.13324421689
264777750026.9036752807-2249.90367528066
274777748113.5271133743-336.527113374279
285072448047.87250456162676.12749543841
295889351013.27811810867879.72188189144
305955559337.8016740082217.198325991791
315791160219.7874605812-2308.78746058123
325398258557.8873866865-4575.88738668649
335692854517.71749198282410.28250801716
345692857362.2263712477-434.2263712477
355724457424.3334036124-180.333403612356
365889357726.4676885311166.53231146899
376019159382.5611868704808.438813129585
386085360721.1649120206131.835087979351
396085361406.8690100928-553.869010092785
406281761404.77800223071412.22199776932
417035563368.09325310236986.90674689766
427231571017.44889942071297.55110057928
437263073183.9482814662-553.948281466233
446772473529.068221371-5805.06822137104
457035568547.66395047041807.33604952962
466937371036.9653318998-1663.96533189985
476740870087.680454264-2679.680454264
487165368048.95924390223604.04075609782
497263072257.2236951365372.776304863481
507098673337.671908489-2351.67190848906
517133371679.6268959721-346.626895972135
527361371958.05560745011654.94439254991
538213374245.61029233497887.38970766515
548637282892.99528192243479.00471807757
558637287385.9609522458-1013.96095224579
568441287471.5978326426-3059.59783264255
578735585451.90482335171903.09517664826
588441288330.0620503889-3918.06205038888
598276485399.0876060612-2635.08760606124
608900483615.54148424185388.45851575825
618998189838.5114194826142.488580517427
628767090965.8836770213-3295.88367702128
639355988624.70021904574934.29978095434
649587094473.70893909191396.29106090809
6510274196935.51165661755805.48834338247
66107301103905.1964009283395.80359907214
67106670108660.772372784-1990.77237278447
68106319108102.997704168-1783.99770416794
69108950107678.5185615661271.48143843352
70108630110273.38513076-1643.3851307603
71104706109971.506252581-5265.50625258141
72110594105947.5838454064646.41615459364
73112559111738.186437103820.813562896597
74110594113840.076523059-3246.07652305915
75118763111864.1525812686898.84741873221
76122692120014.8756730712677.12432692882
77131839124162.223842347676.77615765984
78135448133462.6739382791985.32606172137
79134470137304.356430396-2834.35643039559
80132505136351.873352143-3846.87335214281
81134150134268.727770019-118.727770018828
82136114135806.199509035307.800490964641
83129559137770.105270476-8211.1052704761
84134785131138.6047517653646.39524823497
85138079136175.4600108311903.53998916916
86136750139589.92589102-2839.92589101975
87145265138284.1251925496980.8748074508
88148207146792.920476091414.07952390969
89160652149942.45954584510709.5404541554
90162932162537.405258333394.594741667184
91159990165117.42280424-5127.42280424049
92161634162133.244602217-499.244602217019
93162616163630.392107767-1014.3921077674
94163598164588.095138318-990.095138317905
95157358165531.81483758-8173.81483757967
96163247159179.836134434067.16386557018
97166509164885.0778518451623.92214815502
98163247168276.275907772-5029.27590777184
99172749165007.0832928967741.91670710378
100175692174450.2598569111241.74014308909
101188451177620.0443443410830.9556556598
102190416190525.48482754-109.484827539709
103191047192788.638884486-1741.63888448631
104194340193398.583136428941.416863571998
105194340196653.203181293-2313.20318129309
106195638196655.269437177-1017.26943717728
107189749197878.818281771-8129.81828177097
108192696191877.544158376818.455841624032
109194656194608.36921487847.6307851224556
110191047196591.478380581-5544.47838058116
111201527192926.3950739288600.60492607151
112203491203342.224861826148.775138174475
113216567205545.42216954311021.5778304573
114218878218739.634608962138.365391037776
115222140221356.621933761783.378066239064
116225087224630.555287473456.444712526805
117225402227603.927428036-2201.92742803585
118225749227908.744628128-2159.74462812755
119219860228172.540784162-8312.540784162
120225749222137.8054535813611.19454641934

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 34035 & 34039 & -4 \tabularnewline
4 & 33373 & 33718.9585898147 & -345.95858981472 \tabularnewline
5 & 39924 & 33053.2665070747 & 6870.7334929253 \tabularnewline
6 & 39577 & 39665.8363572551 & -88.8363572550661 \tabularnewline
7 & 34671 & 39507.7729294559 & -4836.77292945594 \tabularnewline
8 & 31409 & 34549.2452338241 & -3140.24523382405 \tabularnewline
9 & 31724 & 31121.0830707664 & 602.916929233579 \tabularnewline
10 & 31724 & 31355.5516446089 & 368.448355391083 \tabularnewline
11 & 32075 & 31376.0261877534 & 698.973812246611 \tabularnewline
12 & 32706 & 31744.4435338541 & 961.55646614594 \tabularnewline
13 & 34671 & 32404.7125579543 & 2266.28744204566 \tabularnewline
14 & 34035 & 34419.7447122918 & -384.744712291802 \tabularnewline
15 & 35017 & 33842.3850472517 & 1174.61495274829 \tabularnewline
16 & 36631 & 34825.9138048556 & 1805.08619514442 \tabularnewline
17 & 45813 & 36491.0587126148 & 9321.94128738516 \tabularnewline
18 & 45813 & 45819.4437727871 & -6.44377278706088 \tabularnewline
19 & 43853 & 46076.9665712368 & -2223.9665712368 \tabularnewline
20 & 41888 & 44093.7647960754 & -2205.76479607535 \tabularnewline
21 & 43502 & 42044.4755272828 & 1457.52447271716 \tabularnewline
22 & 45466 & 43612.6135927657 & 1853.38640723433 \tabularnewline
23 & 45813 & 45636.0760573135 & 176.923942686473 \tabularnewline
24 & 46795 & 46036.1215624404 & 758.878437559579 \tabularnewline
25 & 49742 & 47030.8667557831 & 2711.13324421689 \tabularnewline
26 & 47777 & 50026.9036752807 & -2249.90367528066 \tabularnewline
27 & 47777 & 48113.5271133743 & -336.527113374279 \tabularnewline
28 & 50724 & 48047.8725045616 & 2676.12749543841 \tabularnewline
29 & 58893 & 51013.2781181086 & 7879.72188189144 \tabularnewline
30 & 59555 & 59337.8016740082 & 217.198325991791 \tabularnewline
31 & 57911 & 60219.7874605812 & -2308.78746058123 \tabularnewline
32 & 53982 & 58557.8873866865 & -4575.88738668649 \tabularnewline
33 & 56928 & 54517.7174919828 & 2410.28250801716 \tabularnewline
34 & 56928 & 57362.2263712477 & -434.2263712477 \tabularnewline
35 & 57244 & 57424.3334036124 & -180.333403612356 \tabularnewline
36 & 58893 & 57726.467688531 & 1166.53231146899 \tabularnewline
37 & 60191 & 59382.5611868704 & 808.438813129585 \tabularnewline
38 & 60853 & 60721.1649120206 & 131.835087979351 \tabularnewline
39 & 60853 & 61406.8690100928 & -553.869010092785 \tabularnewline
40 & 62817 & 61404.7780022307 & 1412.22199776932 \tabularnewline
41 & 70355 & 63368.0932531023 & 6986.90674689766 \tabularnewline
42 & 72315 & 71017.4488994207 & 1297.55110057928 \tabularnewline
43 & 72630 & 73183.9482814662 & -553.948281466233 \tabularnewline
44 & 67724 & 73529.068221371 & -5805.06822137104 \tabularnewline
45 & 70355 & 68547.6639504704 & 1807.33604952962 \tabularnewline
46 & 69373 & 71036.9653318998 & -1663.96533189985 \tabularnewline
47 & 67408 & 70087.680454264 & -2679.680454264 \tabularnewline
48 & 71653 & 68048.9592439022 & 3604.04075609782 \tabularnewline
49 & 72630 & 72257.2236951365 & 372.776304863481 \tabularnewline
50 & 70986 & 73337.671908489 & -2351.67190848906 \tabularnewline
51 & 71333 & 71679.6268959721 & -346.626895972135 \tabularnewline
52 & 73613 & 71958.0556074501 & 1654.94439254991 \tabularnewline
53 & 82133 & 74245.6102923349 & 7887.38970766515 \tabularnewline
54 & 86372 & 82892.9952819224 & 3479.00471807757 \tabularnewline
55 & 86372 & 87385.9609522458 & -1013.96095224579 \tabularnewline
56 & 84412 & 87471.5978326426 & -3059.59783264255 \tabularnewline
57 & 87355 & 85451.9048233517 & 1903.09517664826 \tabularnewline
58 & 84412 & 88330.0620503889 & -3918.06205038888 \tabularnewline
59 & 82764 & 85399.0876060612 & -2635.08760606124 \tabularnewline
60 & 89004 & 83615.5414842418 & 5388.45851575825 \tabularnewline
61 & 89981 & 89838.5114194826 & 142.488580517427 \tabularnewline
62 & 87670 & 90965.8836770213 & -3295.88367702128 \tabularnewline
63 & 93559 & 88624.7002190457 & 4934.29978095434 \tabularnewline
64 & 95870 & 94473.7089390919 & 1396.29106090809 \tabularnewline
65 & 102741 & 96935.5116566175 & 5805.48834338247 \tabularnewline
66 & 107301 & 103905.196400928 & 3395.80359907214 \tabularnewline
67 & 106670 & 108660.772372784 & -1990.77237278447 \tabularnewline
68 & 106319 & 108102.997704168 & -1783.99770416794 \tabularnewline
69 & 108950 & 107678.518561566 & 1271.48143843352 \tabularnewline
70 & 108630 & 110273.38513076 & -1643.3851307603 \tabularnewline
71 & 104706 & 109971.506252581 & -5265.50625258141 \tabularnewline
72 & 110594 & 105947.583845406 & 4646.41615459364 \tabularnewline
73 & 112559 & 111738.186437103 & 820.813562896597 \tabularnewline
74 & 110594 & 113840.076523059 & -3246.07652305915 \tabularnewline
75 & 118763 & 111864.152581268 & 6898.84741873221 \tabularnewline
76 & 122692 & 120014.875673071 & 2677.12432692882 \tabularnewline
77 & 131839 & 124162.22384234 & 7676.77615765984 \tabularnewline
78 & 135448 & 133462.673938279 & 1985.32606172137 \tabularnewline
79 & 134470 & 137304.356430396 & -2834.35643039559 \tabularnewline
80 & 132505 & 136351.873352143 & -3846.87335214281 \tabularnewline
81 & 134150 & 134268.727770019 & -118.727770018828 \tabularnewline
82 & 136114 & 135806.199509035 & 307.800490964641 \tabularnewline
83 & 129559 & 137770.105270476 & -8211.1052704761 \tabularnewline
84 & 134785 & 131138.604751765 & 3646.39524823497 \tabularnewline
85 & 138079 & 136175.460010831 & 1903.53998916916 \tabularnewline
86 & 136750 & 139589.92589102 & -2839.92589101975 \tabularnewline
87 & 145265 & 138284.125192549 & 6980.8748074508 \tabularnewline
88 & 148207 & 146792.92047609 & 1414.07952390969 \tabularnewline
89 & 160652 & 149942.459545845 & 10709.5404541554 \tabularnewline
90 & 162932 & 162537.405258333 & 394.594741667184 \tabularnewline
91 & 159990 & 165117.42280424 & -5127.42280424049 \tabularnewline
92 & 161634 & 162133.244602217 & -499.244602217019 \tabularnewline
93 & 162616 & 163630.392107767 & -1014.3921077674 \tabularnewline
94 & 163598 & 164588.095138318 & -990.095138317905 \tabularnewline
95 & 157358 & 165531.81483758 & -8173.81483757967 \tabularnewline
96 & 163247 & 159179.83613443 & 4067.16386557018 \tabularnewline
97 & 166509 & 164885.077851845 & 1623.92214815502 \tabularnewline
98 & 163247 & 168276.275907772 & -5029.27590777184 \tabularnewline
99 & 172749 & 165007.083292896 & 7741.91670710378 \tabularnewline
100 & 175692 & 174450.259856911 & 1241.74014308909 \tabularnewline
101 & 188451 & 177620.04434434 & 10830.9556556598 \tabularnewline
102 & 190416 & 190525.48482754 & -109.484827539709 \tabularnewline
103 & 191047 & 192788.638884486 & -1741.63888448631 \tabularnewline
104 & 194340 & 193398.583136428 & 941.416863571998 \tabularnewline
105 & 194340 & 196653.203181293 & -2313.20318129309 \tabularnewline
106 & 195638 & 196655.269437177 & -1017.26943717728 \tabularnewline
107 & 189749 & 197878.818281771 & -8129.81828177097 \tabularnewline
108 & 192696 & 191877.544158376 & 818.455841624032 \tabularnewline
109 & 194656 & 194608.369214878 & 47.6307851224556 \tabularnewline
110 & 191047 & 196591.478380581 & -5544.47838058116 \tabularnewline
111 & 201527 & 192926.395073928 & 8600.60492607151 \tabularnewline
112 & 203491 & 203342.224861826 & 148.775138174475 \tabularnewline
113 & 216567 & 205545.422169543 & 11021.5778304573 \tabularnewline
114 & 218878 & 218739.634608962 & 138.365391037776 \tabularnewline
115 & 222140 & 221356.621933761 & 783.378066239064 \tabularnewline
116 & 225087 & 224630.555287473 & 456.444712526805 \tabularnewline
117 & 225402 & 227603.927428036 & -2201.92742803585 \tabularnewline
118 & 225749 & 227908.744628128 & -2159.74462812755 \tabularnewline
119 & 219860 & 228172.540784162 & -8312.540784162 \tabularnewline
120 & 225749 & 222137.805453581 & 3611.19454641934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124173&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]34035[/C][C]34039[/C][C]-4[/C][/ROW]
[ROW][C]4[/C][C]33373[/C][C]33718.9585898147[/C][C]-345.95858981472[/C][/ROW]
[ROW][C]5[/C][C]39924[/C][C]33053.2665070747[/C][C]6870.7334929253[/C][/ROW]
[ROW][C]6[/C][C]39577[/C][C]39665.8363572551[/C][C]-88.8363572550661[/C][/ROW]
[ROW][C]7[/C][C]34671[/C][C]39507.7729294559[/C][C]-4836.77292945594[/C][/ROW]
[ROW][C]8[/C][C]31409[/C][C]34549.2452338241[/C][C]-3140.24523382405[/C][/ROW]
[ROW][C]9[/C][C]31724[/C][C]31121.0830707664[/C][C]602.916929233579[/C][/ROW]
[ROW][C]10[/C][C]31724[/C][C]31355.5516446089[/C][C]368.448355391083[/C][/ROW]
[ROW][C]11[/C][C]32075[/C][C]31376.0261877534[/C][C]698.973812246611[/C][/ROW]
[ROW][C]12[/C][C]32706[/C][C]31744.4435338541[/C][C]961.55646614594[/C][/ROW]
[ROW][C]13[/C][C]34671[/C][C]32404.7125579543[/C][C]2266.28744204566[/C][/ROW]
[ROW][C]14[/C][C]34035[/C][C]34419.7447122918[/C][C]-384.744712291802[/C][/ROW]
[ROW][C]15[/C][C]35017[/C][C]33842.3850472517[/C][C]1174.61495274829[/C][/ROW]
[ROW][C]16[/C][C]36631[/C][C]34825.9138048556[/C][C]1805.08619514442[/C][/ROW]
[ROW][C]17[/C][C]45813[/C][C]36491.0587126148[/C][C]9321.94128738516[/C][/ROW]
[ROW][C]18[/C][C]45813[/C][C]45819.4437727871[/C][C]-6.44377278706088[/C][/ROW]
[ROW][C]19[/C][C]43853[/C][C]46076.9665712368[/C][C]-2223.9665712368[/C][/ROW]
[ROW][C]20[/C][C]41888[/C][C]44093.7647960754[/C][C]-2205.76479607535[/C][/ROW]
[ROW][C]21[/C][C]43502[/C][C]42044.4755272828[/C][C]1457.52447271716[/C][/ROW]
[ROW][C]22[/C][C]45466[/C][C]43612.6135927657[/C][C]1853.38640723433[/C][/ROW]
[ROW][C]23[/C][C]45813[/C][C]45636.0760573135[/C][C]176.923942686473[/C][/ROW]
[ROW][C]24[/C][C]46795[/C][C]46036.1215624404[/C][C]758.878437559579[/C][/ROW]
[ROW][C]25[/C][C]49742[/C][C]47030.8667557831[/C][C]2711.13324421689[/C][/ROW]
[ROW][C]26[/C][C]47777[/C][C]50026.9036752807[/C][C]-2249.90367528066[/C][/ROW]
[ROW][C]27[/C][C]47777[/C][C]48113.5271133743[/C][C]-336.527113374279[/C][/ROW]
[ROW][C]28[/C][C]50724[/C][C]48047.8725045616[/C][C]2676.12749543841[/C][/ROW]
[ROW][C]29[/C][C]58893[/C][C]51013.2781181086[/C][C]7879.72188189144[/C][/ROW]
[ROW][C]30[/C][C]59555[/C][C]59337.8016740082[/C][C]217.198325991791[/C][/ROW]
[ROW][C]31[/C][C]57911[/C][C]60219.7874605812[/C][C]-2308.78746058123[/C][/ROW]
[ROW][C]32[/C][C]53982[/C][C]58557.8873866865[/C][C]-4575.88738668649[/C][/ROW]
[ROW][C]33[/C][C]56928[/C][C]54517.7174919828[/C][C]2410.28250801716[/C][/ROW]
[ROW][C]34[/C][C]56928[/C][C]57362.2263712477[/C][C]-434.2263712477[/C][/ROW]
[ROW][C]35[/C][C]57244[/C][C]57424.3334036124[/C][C]-180.333403612356[/C][/ROW]
[ROW][C]36[/C][C]58893[/C][C]57726.467688531[/C][C]1166.53231146899[/C][/ROW]
[ROW][C]37[/C][C]60191[/C][C]59382.5611868704[/C][C]808.438813129585[/C][/ROW]
[ROW][C]38[/C][C]60853[/C][C]60721.1649120206[/C][C]131.835087979351[/C][/ROW]
[ROW][C]39[/C][C]60853[/C][C]61406.8690100928[/C][C]-553.869010092785[/C][/ROW]
[ROW][C]40[/C][C]62817[/C][C]61404.7780022307[/C][C]1412.22199776932[/C][/ROW]
[ROW][C]41[/C][C]70355[/C][C]63368.0932531023[/C][C]6986.90674689766[/C][/ROW]
[ROW][C]42[/C][C]72315[/C][C]71017.4488994207[/C][C]1297.55110057928[/C][/ROW]
[ROW][C]43[/C][C]72630[/C][C]73183.9482814662[/C][C]-553.948281466233[/C][/ROW]
[ROW][C]44[/C][C]67724[/C][C]73529.068221371[/C][C]-5805.06822137104[/C][/ROW]
[ROW][C]45[/C][C]70355[/C][C]68547.6639504704[/C][C]1807.33604952962[/C][/ROW]
[ROW][C]46[/C][C]69373[/C][C]71036.9653318998[/C][C]-1663.96533189985[/C][/ROW]
[ROW][C]47[/C][C]67408[/C][C]70087.680454264[/C][C]-2679.680454264[/C][/ROW]
[ROW][C]48[/C][C]71653[/C][C]68048.9592439022[/C][C]3604.04075609782[/C][/ROW]
[ROW][C]49[/C][C]72630[/C][C]72257.2236951365[/C][C]372.776304863481[/C][/ROW]
[ROW][C]50[/C][C]70986[/C][C]73337.671908489[/C][C]-2351.67190848906[/C][/ROW]
[ROW][C]51[/C][C]71333[/C][C]71679.6268959721[/C][C]-346.626895972135[/C][/ROW]
[ROW][C]52[/C][C]73613[/C][C]71958.0556074501[/C][C]1654.94439254991[/C][/ROW]
[ROW][C]53[/C][C]82133[/C][C]74245.6102923349[/C][C]7887.38970766515[/C][/ROW]
[ROW][C]54[/C][C]86372[/C][C]82892.9952819224[/C][C]3479.00471807757[/C][/ROW]
[ROW][C]55[/C][C]86372[/C][C]87385.9609522458[/C][C]-1013.96095224579[/C][/ROW]
[ROW][C]56[/C][C]84412[/C][C]87471.5978326426[/C][C]-3059.59783264255[/C][/ROW]
[ROW][C]57[/C][C]87355[/C][C]85451.9048233517[/C][C]1903.09517664826[/C][/ROW]
[ROW][C]58[/C][C]84412[/C][C]88330.0620503889[/C][C]-3918.06205038888[/C][/ROW]
[ROW][C]59[/C][C]82764[/C][C]85399.0876060612[/C][C]-2635.08760606124[/C][/ROW]
[ROW][C]60[/C][C]89004[/C][C]83615.5414842418[/C][C]5388.45851575825[/C][/ROW]
[ROW][C]61[/C][C]89981[/C][C]89838.5114194826[/C][C]142.488580517427[/C][/ROW]
[ROW][C]62[/C][C]87670[/C][C]90965.8836770213[/C][C]-3295.88367702128[/C][/ROW]
[ROW][C]63[/C][C]93559[/C][C]88624.7002190457[/C][C]4934.29978095434[/C][/ROW]
[ROW][C]64[/C][C]95870[/C][C]94473.7089390919[/C][C]1396.29106090809[/C][/ROW]
[ROW][C]65[/C][C]102741[/C][C]96935.5116566175[/C][C]5805.48834338247[/C][/ROW]
[ROW][C]66[/C][C]107301[/C][C]103905.196400928[/C][C]3395.80359907214[/C][/ROW]
[ROW][C]67[/C][C]106670[/C][C]108660.772372784[/C][C]-1990.77237278447[/C][/ROW]
[ROW][C]68[/C][C]106319[/C][C]108102.997704168[/C][C]-1783.99770416794[/C][/ROW]
[ROW][C]69[/C][C]108950[/C][C]107678.518561566[/C][C]1271.48143843352[/C][/ROW]
[ROW][C]70[/C][C]108630[/C][C]110273.38513076[/C][C]-1643.3851307603[/C][/ROW]
[ROW][C]71[/C][C]104706[/C][C]109971.506252581[/C][C]-5265.50625258141[/C][/ROW]
[ROW][C]72[/C][C]110594[/C][C]105947.583845406[/C][C]4646.41615459364[/C][/ROW]
[ROW][C]73[/C][C]112559[/C][C]111738.186437103[/C][C]820.813562896597[/C][/ROW]
[ROW][C]74[/C][C]110594[/C][C]113840.076523059[/C][C]-3246.07652305915[/C][/ROW]
[ROW][C]75[/C][C]118763[/C][C]111864.152581268[/C][C]6898.84741873221[/C][/ROW]
[ROW][C]76[/C][C]122692[/C][C]120014.875673071[/C][C]2677.12432692882[/C][/ROW]
[ROW][C]77[/C][C]131839[/C][C]124162.22384234[/C][C]7676.77615765984[/C][/ROW]
[ROW][C]78[/C][C]135448[/C][C]133462.673938279[/C][C]1985.32606172137[/C][/ROW]
[ROW][C]79[/C][C]134470[/C][C]137304.356430396[/C][C]-2834.35643039559[/C][/ROW]
[ROW][C]80[/C][C]132505[/C][C]136351.873352143[/C][C]-3846.87335214281[/C][/ROW]
[ROW][C]81[/C][C]134150[/C][C]134268.727770019[/C][C]-118.727770018828[/C][/ROW]
[ROW][C]82[/C][C]136114[/C][C]135806.199509035[/C][C]307.800490964641[/C][/ROW]
[ROW][C]83[/C][C]129559[/C][C]137770.105270476[/C][C]-8211.1052704761[/C][/ROW]
[ROW][C]84[/C][C]134785[/C][C]131138.604751765[/C][C]3646.39524823497[/C][/ROW]
[ROW][C]85[/C][C]138079[/C][C]136175.460010831[/C][C]1903.53998916916[/C][/ROW]
[ROW][C]86[/C][C]136750[/C][C]139589.92589102[/C][C]-2839.92589101975[/C][/ROW]
[ROW][C]87[/C][C]145265[/C][C]138284.125192549[/C][C]6980.8748074508[/C][/ROW]
[ROW][C]88[/C][C]148207[/C][C]146792.92047609[/C][C]1414.07952390969[/C][/ROW]
[ROW][C]89[/C][C]160652[/C][C]149942.459545845[/C][C]10709.5404541554[/C][/ROW]
[ROW][C]90[/C][C]162932[/C][C]162537.405258333[/C][C]394.594741667184[/C][/ROW]
[ROW][C]91[/C][C]159990[/C][C]165117.42280424[/C][C]-5127.42280424049[/C][/ROW]
[ROW][C]92[/C][C]161634[/C][C]162133.244602217[/C][C]-499.244602217019[/C][/ROW]
[ROW][C]93[/C][C]162616[/C][C]163630.392107767[/C][C]-1014.3921077674[/C][/ROW]
[ROW][C]94[/C][C]163598[/C][C]164588.095138318[/C][C]-990.095138317905[/C][/ROW]
[ROW][C]95[/C][C]157358[/C][C]165531.81483758[/C][C]-8173.81483757967[/C][/ROW]
[ROW][C]96[/C][C]163247[/C][C]159179.83613443[/C][C]4067.16386557018[/C][/ROW]
[ROW][C]97[/C][C]166509[/C][C]164885.077851845[/C][C]1623.92214815502[/C][/ROW]
[ROW][C]98[/C][C]163247[/C][C]168276.275907772[/C][C]-5029.27590777184[/C][/ROW]
[ROW][C]99[/C][C]172749[/C][C]165007.083292896[/C][C]7741.91670710378[/C][/ROW]
[ROW][C]100[/C][C]175692[/C][C]174450.259856911[/C][C]1241.74014308909[/C][/ROW]
[ROW][C]101[/C][C]188451[/C][C]177620.04434434[/C][C]10830.9556556598[/C][/ROW]
[ROW][C]102[/C][C]190416[/C][C]190525.48482754[/C][C]-109.484827539709[/C][/ROW]
[ROW][C]103[/C][C]191047[/C][C]192788.638884486[/C][C]-1741.63888448631[/C][/ROW]
[ROW][C]104[/C][C]194340[/C][C]193398.583136428[/C][C]941.416863571998[/C][/ROW]
[ROW][C]105[/C][C]194340[/C][C]196653.203181293[/C][C]-2313.20318129309[/C][/ROW]
[ROW][C]106[/C][C]195638[/C][C]196655.269437177[/C][C]-1017.26943717728[/C][/ROW]
[ROW][C]107[/C][C]189749[/C][C]197878.818281771[/C][C]-8129.81828177097[/C][/ROW]
[ROW][C]108[/C][C]192696[/C][C]191877.544158376[/C][C]818.455841624032[/C][/ROW]
[ROW][C]109[/C][C]194656[/C][C]194608.369214878[/C][C]47.6307851224556[/C][/ROW]
[ROW][C]110[/C][C]191047[/C][C]196591.478380581[/C][C]-5544.47838058116[/C][/ROW]
[ROW][C]111[/C][C]201527[/C][C]192926.395073928[/C][C]8600.60492607151[/C][/ROW]
[ROW][C]112[/C][C]203491[/C][C]203342.224861826[/C][C]148.775138174475[/C][/ROW]
[ROW][C]113[/C][C]216567[/C][C]205545.422169543[/C][C]11021.5778304573[/C][/ROW]
[ROW][C]114[/C][C]218878[/C][C]218739.634608962[/C][C]138.365391037776[/C][/ROW]
[ROW][C]115[/C][C]222140[/C][C]221356.621933761[/C][C]783.378066239064[/C][/ROW]
[ROW][C]116[/C][C]225087[/C][C]224630.555287473[/C][C]456.444712526805[/C][/ROW]
[ROW][C]117[/C][C]225402[/C][C]227603.927428036[/C][C]-2201.92742803585[/C][/ROW]
[ROW][C]118[/C][C]225749[/C][C]227908.744628128[/C][C]-2159.74462812755[/C][/ROW]
[ROW][C]119[/C][C]219860[/C][C]228172.540784162[/C][C]-8312.540784162[/C][/ROW]
[ROW][C]120[/C][C]225749[/C][C]222137.805453581[/C][C]3611.19454641934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124173&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124173&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
33403534039-4
43337333718.9585898147-345.95858981472
53992433053.26650707476870.7334929253
63957739665.8363572551-88.8363572550661
73467139507.7729294559-4836.77292945594
83140934549.2452338241-3140.24523382405
93172431121.0830707664602.916929233579
103172431355.5516446089368.448355391083
113207531376.0261877534698.973812246611
123270631744.4435338541961.55646614594
133467132404.71255795432266.28744204566
143403534419.7447122918-384.744712291802
153501733842.38504725171174.61495274829
163663134825.91380485561805.08619514442
174581336491.05871261489321.94128738516
184581345819.4437727871-6.44377278706088
194385346076.9665712368-2223.9665712368
204188844093.7647960754-2205.76479607535
214350242044.47552728281457.52447271716
224546643612.61359276571853.38640723433
234581345636.0760573135176.923942686473
244679546036.1215624404758.878437559579
254974247030.86675578312711.13324421689
264777750026.9036752807-2249.90367528066
274777748113.5271133743-336.527113374279
285072448047.87250456162676.12749543841
295889351013.27811810867879.72188189144
305955559337.8016740082217.198325991791
315791160219.7874605812-2308.78746058123
325398258557.8873866865-4575.88738668649
335692854517.71749198282410.28250801716
345692857362.2263712477-434.2263712477
355724457424.3334036124-180.333403612356
365889357726.4676885311166.53231146899
376019159382.5611868704808.438813129585
386085360721.1649120206131.835087979351
396085361406.8690100928-553.869010092785
406281761404.77800223071412.22199776932
417035563368.09325310236986.90674689766
427231571017.44889942071297.55110057928
437263073183.9482814662-553.948281466233
446772473529.068221371-5805.06822137104
457035568547.66395047041807.33604952962
466937371036.9653318998-1663.96533189985
476740870087.680454264-2679.680454264
487165368048.95924390223604.04075609782
497263072257.2236951365372.776304863481
507098673337.671908489-2351.67190848906
517133371679.6268959721-346.626895972135
527361371958.05560745011654.94439254991
538213374245.61029233497887.38970766515
548637282892.99528192243479.00471807757
558637287385.9609522458-1013.96095224579
568441287471.5978326426-3059.59783264255
578735585451.90482335171903.09517664826
588441288330.0620503889-3918.06205038888
598276485399.0876060612-2635.08760606124
608900483615.54148424185388.45851575825
618998189838.5114194826142.488580517427
628767090965.8836770213-3295.88367702128
639355988624.70021904574934.29978095434
649587094473.70893909191396.29106090809
6510274196935.51165661755805.48834338247
66107301103905.1964009283395.80359907214
67106670108660.772372784-1990.77237278447
68106319108102.997704168-1783.99770416794
69108950107678.5185615661271.48143843352
70108630110273.38513076-1643.3851307603
71104706109971.506252581-5265.50625258141
72110594105947.5838454064646.41615459364
73112559111738.186437103820.813562896597
74110594113840.076523059-3246.07652305915
75118763111864.1525812686898.84741873221
76122692120014.8756730712677.12432692882
77131839124162.223842347676.77615765984
78135448133462.6739382791985.32606172137
79134470137304.356430396-2834.35643039559
80132505136351.873352143-3846.87335214281
81134150134268.727770019-118.727770018828
82136114135806.199509035307.800490964641
83129559137770.105270476-8211.1052704761
84134785131138.6047517653646.39524823497
85138079136175.4600108311903.53998916916
86136750139589.92589102-2839.92589101975
87145265138284.1251925496980.8748074508
88148207146792.920476091414.07952390969
89160652149942.45954584510709.5404541554
90162932162537.405258333394.594741667184
91159990165117.42280424-5127.42280424049
92161634162133.244602217-499.244602217019
93162616163630.392107767-1014.3921077674
94163598164588.095138318-990.095138317905
95157358165531.81483758-8173.81483757967
96163247159179.836134434067.16386557018
97166509164885.0778518451623.92214815502
98163247168276.275907772-5029.27590777184
99172749165007.0832928967741.91670710378
100175692174450.2598569111241.74014308909
101188451177620.0443443410830.9556556598
102190416190525.48482754-109.484827539709
103191047192788.638884486-1741.63888448631
104194340193398.583136428941.416863571998
105194340196653.203181293-2313.20318129309
106195638196655.269437177-1017.26943717728
107189749197878.818281771-8129.81828177097
108192696191877.544158376818.455841624032
109194656194608.36921487847.6307851224556
110191047196591.478380581-5544.47838058116
111201527192926.3950739288600.60492607151
112203491203342.224861826148.775138174475
113216567205545.42216954311021.5778304573
114218878218739.634608962138.365391037776
115222140221356.621933761783.378066239064
116225087224630.555287473456.444712526805
117225402227603.927428036-2201.92742803585
118225749227908.744628128-2159.74462812755
119219860228172.540784162-8312.540784162
120225749222137.8054535813611.19454641934







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121227834.493368415220139.872358932235529.114377897
122230019.773444071219081.463661112240958.08322703
123232205.053519727218614.025909437245796.081130018
124234390.333595383218434.573474943250346.093715824
125236575.61367104218425.455924772254725.771417307
126238760.893746696218526.943963273258994.843530119
127240946.173822352218704.082404357263188.265240347
128243131.453898008218934.495341325267328.412454692
129245316.733973664219202.942620538271430.525326791
130247502.014049321219498.561160023275505.466938618
131249687.294124977219813.334146199279561.254103755
132251872.574200633220141.181403269283603.966997997

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 227834.493368415 & 220139.872358932 & 235529.114377897 \tabularnewline
122 & 230019.773444071 & 219081.463661112 & 240958.08322703 \tabularnewline
123 & 232205.053519727 & 218614.025909437 & 245796.081130018 \tabularnewline
124 & 234390.333595383 & 218434.573474943 & 250346.093715824 \tabularnewline
125 & 236575.61367104 & 218425.455924772 & 254725.771417307 \tabularnewline
126 & 238760.893746696 & 218526.943963273 & 258994.843530119 \tabularnewline
127 & 240946.173822352 & 218704.082404357 & 263188.265240347 \tabularnewline
128 & 243131.453898008 & 218934.495341325 & 267328.412454692 \tabularnewline
129 & 245316.733973664 & 219202.942620538 & 271430.525326791 \tabularnewline
130 & 247502.014049321 & 219498.561160023 & 275505.466938618 \tabularnewline
131 & 249687.294124977 & 219813.334146199 & 279561.254103755 \tabularnewline
132 & 251872.574200633 & 220141.181403269 & 283603.966997997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124173&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]227834.493368415[/C][C]220139.872358932[/C][C]235529.114377897[/C][/ROW]
[ROW][C]122[/C][C]230019.773444071[/C][C]219081.463661112[/C][C]240958.08322703[/C][/ROW]
[ROW][C]123[/C][C]232205.053519727[/C][C]218614.025909437[/C][C]245796.081130018[/C][/ROW]
[ROW][C]124[/C][C]234390.333595383[/C][C]218434.573474943[/C][C]250346.093715824[/C][/ROW]
[ROW][C]125[/C][C]236575.61367104[/C][C]218425.455924772[/C][C]254725.771417307[/C][/ROW]
[ROW][C]126[/C][C]238760.893746696[/C][C]218526.943963273[/C][C]258994.843530119[/C][/ROW]
[ROW][C]127[/C][C]240946.173822352[/C][C]218704.082404357[/C][C]263188.265240347[/C][/ROW]
[ROW][C]128[/C][C]243131.453898008[/C][C]218934.495341325[/C][C]267328.412454692[/C][/ROW]
[ROW][C]129[/C][C]245316.733973664[/C][C]219202.942620538[/C][C]271430.525326791[/C][/ROW]
[ROW][C]130[/C][C]247502.014049321[/C][C]219498.561160023[/C][C]275505.466938618[/C][/ROW]
[ROW][C]131[/C][C]249687.294124977[/C][C]219813.334146199[/C][C]279561.254103755[/C][/ROW]
[ROW][C]132[/C][C]251872.574200633[/C][C]220141.181403269[/C][C]283603.966997997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124173&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124173&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
121227834.493368415220139.872358932235529.114377897
122230019.773444071219081.463661112240958.08322703
123232205.053519727218614.025909437245796.081130018
124234390.333595383218434.573474943250346.093715824
125236575.61367104218425.455924772254725.771417307
126238760.893746696218526.943963273258994.843530119
127240946.173822352218704.082404357263188.265240347
128243131.453898008218934.495341325267328.412454692
129245316.733973664219202.942620538271430.525326791
130247502.014049321219498.561160023275505.466938618
131249687.294124977219813.334146199279561.254103755
132251872.574200633220141.181403269283603.966997997



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