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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 09 Jan 2016 12:11:42 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/09/t1452341528hft8v3wdon8hdof.htm/, Retrieved Sun, 05 May 2024 20:16:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287514, Retrieved Sun, 05 May 2024 20:16:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-01-09 12:11:42] [1d0d2a0cfdb7bd945f85de3fbad0315e] [Current]
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Dataseries X:
173019
173690
172439
171914
171968
169500
173898
172308
171568
164939
161275
160770
162466
160185
154836
154103
150495
142707
149962
149967
144572
143819
141070
144119
145330
143279
139063
139202
133632
134476
141859
140693
138047
138346
140167
146796
152228
155410
159032
160312
157687
160141
167421
167628
164403
163405
163229
171154
173323
172381
168983
165380
161641
161933
172018
168455
164332
161193
157645
161694
163411
161834
159511
156359
154223
151497
160607
159672
155601
154668
153960
157307
165218
165616
162212
159787
157454
156485
165887
166836
163541
163973
164805
167521
174347
173374
172198
171055
168385
167281
177670
177280
174846
174476
174595
178392
185345
183293
181081
177795
173552
170734
179293
178659
175894
174815
173506
175376




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287514&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287514&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.829554622591177
beta0.130862329102611
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.829554622591177 \tabularnewline
beta & 0.130862329102611 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287514&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]0.829554622591177[/C][/ROW]
[ROW][C]beta[/C][C]0.130862329102611[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287514&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
alpha0.829554622591177
beta0.130862329102611
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13162466172768.727831197-10302.7278311966
14160185160952.28769443-767.287694430357
15154836154022.221206013813.778793986858
16154103153057.202482451045.7975175498
17150495149240.2267419661254.77325803367
18142707141366.6144449351340.38555506495
19149962152370.781062572-2408.7810625718
20149967147006.818051852960.18194815019
21144572147561.80292911-2989.80292910963
22143819137146.8016316816672.19836831908
23141070138597.5250149762472.47498502399
24144119140366.0040316923752.99596830813
25145330144151.733488181178.26651181976
26143279145148.317856495-1869.31785649509
27139063139117.549925997-54.549925997213
28139202138921.495364885280.50463511463
29133632135871.951828393-2239.95182839292
30134476126101.1534608668374.84653913375
31141859144052.691792287-2193.69179228655
32140693141556.551755491-863.551755490684
33138047139284.578213729-1237.5782137294
34138346133519.3885017824826.61149821768
35140167134072.323139446094.67686055979
36146796140806.1421582715989.85784172913
37152228147993.7148190954234.28518090516
38155410153322.835358272087.16464172985
39159032153629.8586543335402.14134566655
40160312161356.254628992-1044.25462899235
41157687159973.056846547-2286.05684654709
42160141155163.1561973264977.84380267409
43167421171316.467781756-3895.46778175555
44167628170271.718445473-2643.71844547288
45164403168902.388578339-4499.38857833925
46163405163554.008551003-149.008551002538
47163229161744.4362774311484.56372256944
48171154165684.4924097335469.50759026714
49173323173133.13266791189.867332089867
50172381175294.125024308-2913.12502430764
51168983172028.242783501-3045.24278350075
52165380170741.372744173-5361.37274417302
53161641164189.633825301-2548.63382530131
54161933158995.9084298672937.09157013291
55172018170318.2496785291699.75032147134
56168455173110.15693605-4655.15693605022
57164332168519.344605251-4187.34460525072
58161193162968.604992281-1775.60499228138
59157645158708.818530965-1063.81853096528
60161694159558.1233335712135.87666642893
61163411161323.6095874142087.39041258598
62161834162717.965765356-883.96576535597
63159511159521.298943243-10.2989432431932
64156359159095.208551699-2736.20855169918
65154223154223.487802048-0.487802048010053
66151497151378.108220929118.891779070953
67160607159145.2660927271461.73390727284
68159672159624.2890960147.7109039901698
69155601158492.758239493-2891.75823949269
70154668154046.752974771621.24702522927
71153960151775.7078604242184.29213957608
72157307156096.578715931210.42128406954
73165218157217.3274210278000.67257897329
74165616163783.7935624341832.20643756574
75162212164057.286479244-1845.28647924369
76159787162513.187496083-2726.18749608268
77157454158985.99106861-1531.99106861022
78156485155594.157835138890.84216486162
79165887165018.037180832868.962819168199
80166836165487.4260152131348.57398478687
81163541165798.34710391-2257.34710390971
82163973163410.599983391562.40001660859
83164805162283.9675401152521.03245988549
84167521167681.562434602-160.562434602412
85174347169636.9130416764710.08695832398
86173374172879.595385491494.404614509054
87172198171728.591847747469.40815225293
88171055172517.885236548-1462.88523654794
89168385170942.725417687-2557.72541768744
90167281167702.112251626-421.112251625862
91177670176480.6641005091189.33589949057
92177280177779.085882768-499.08588276786
93174846176223.600834753-1377.60083475269
94174476175422.708400592-946.708400592121
95174595173590.6472181611004.35278183871
96178392177320.9804208521071.01957914772
97185345181309.8450574174035.15494258303
98183293183382.491763821-89.4917638205516
99181081181787.868357271-706.868357271247
100177795181189.346678223-3394.3466782232
101173552177532.970139239-3980.97013923893
102170734173029.016250113-2295.01625011265
103179293179877.272255308-584.272255307646
104178659178573.78356518285.2164348181977
105175894176573.878821801-679.878821800667
106174815175721.579883527-906.579883527302
107173506173556.064458195-50.0644581945962
108175376175609.30676654-233.306766540423

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 162466 & 172768.727831197 & -10302.7278311966 \tabularnewline
14 & 160185 & 160952.28769443 & -767.287694430357 \tabularnewline
15 & 154836 & 154022.221206013 & 813.778793986858 \tabularnewline
16 & 154103 & 153057.20248245 & 1045.7975175498 \tabularnewline
17 & 150495 & 149240.226741966 & 1254.77325803367 \tabularnewline
18 & 142707 & 141366.614444935 & 1340.38555506495 \tabularnewline
19 & 149962 & 152370.781062572 & -2408.7810625718 \tabularnewline
20 & 149967 & 147006.81805185 & 2960.18194815019 \tabularnewline
21 & 144572 & 147561.80292911 & -2989.80292910963 \tabularnewline
22 & 143819 & 137146.801631681 & 6672.19836831908 \tabularnewline
23 & 141070 & 138597.525014976 & 2472.47498502399 \tabularnewline
24 & 144119 & 140366.004031692 & 3752.99596830813 \tabularnewline
25 & 145330 & 144151.73348818 & 1178.26651181976 \tabularnewline
26 & 143279 & 145148.317856495 & -1869.31785649509 \tabularnewline
27 & 139063 & 139117.549925997 & -54.549925997213 \tabularnewline
28 & 139202 & 138921.495364885 & 280.50463511463 \tabularnewline
29 & 133632 & 135871.951828393 & -2239.95182839292 \tabularnewline
30 & 134476 & 126101.153460866 & 8374.84653913375 \tabularnewline
31 & 141859 & 144052.691792287 & -2193.69179228655 \tabularnewline
32 & 140693 & 141556.551755491 & -863.551755490684 \tabularnewline
33 & 138047 & 139284.578213729 & -1237.5782137294 \tabularnewline
34 & 138346 & 133519.388501782 & 4826.61149821768 \tabularnewline
35 & 140167 & 134072.32313944 & 6094.67686055979 \tabularnewline
36 & 146796 & 140806.142158271 & 5989.85784172913 \tabularnewline
37 & 152228 & 147993.714819095 & 4234.28518090516 \tabularnewline
38 & 155410 & 153322.83535827 & 2087.16464172985 \tabularnewline
39 & 159032 & 153629.858654333 & 5402.14134566655 \tabularnewline
40 & 160312 & 161356.254628992 & -1044.25462899235 \tabularnewline
41 & 157687 & 159973.056846547 & -2286.05684654709 \tabularnewline
42 & 160141 & 155163.156197326 & 4977.84380267409 \tabularnewline
43 & 167421 & 171316.467781756 & -3895.46778175555 \tabularnewline
44 & 167628 & 170271.718445473 & -2643.71844547288 \tabularnewline
45 & 164403 & 168902.388578339 & -4499.38857833925 \tabularnewline
46 & 163405 & 163554.008551003 & -149.008551002538 \tabularnewline
47 & 163229 & 161744.436277431 & 1484.56372256944 \tabularnewline
48 & 171154 & 165684.492409733 & 5469.50759026714 \tabularnewline
49 & 173323 & 173133.13266791 & 189.867332089867 \tabularnewline
50 & 172381 & 175294.125024308 & -2913.12502430764 \tabularnewline
51 & 168983 & 172028.242783501 & -3045.24278350075 \tabularnewline
52 & 165380 & 170741.372744173 & -5361.37274417302 \tabularnewline
53 & 161641 & 164189.633825301 & -2548.63382530131 \tabularnewline
54 & 161933 & 158995.908429867 & 2937.09157013291 \tabularnewline
55 & 172018 & 170318.249678529 & 1699.75032147134 \tabularnewline
56 & 168455 & 173110.15693605 & -4655.15693605022 \tabularnewline
57 & 164332 & 168519.344605251 & -4187.34460525072 \tabularnewline
58 & 161193 & 162968.604992281 & -1775.60499228138 \tabularnewline
59 & 157645 & 158708.818530965 & -1063.81853096528 \tabularnewline
60 & 161694 & 159558.123333571 & 2135.87666642893 \tabularnewline
61 & 163411 & 161323.609587414 & 2087.39041258598 \tabularnewline
62 & 161834 & 162717.965765356 & -883.96576535597 \tabularnewline
63 & 159511 & 159521.298943243 & -10.2989432431932 \tabularnewline
64 & 156359 & 159095.208551699 & -2736.20855169918 \tabularnewline
65 & 154223 & 154223.487802048 & -0.487802048010053 \tabularnewline
66 & 151497 & 151378.108220929 & 118.891779070953 \tabularnewline
67 & 160607 & 159145.266092727 & 1461.73390727284 \tabularnewline
68 & 159672 & 159624.28909601 & 47.7109039901698 \tabularnewline
69 & 155601 & 158492.758239493 & -2891.75823949269 \tabularnewline
70 & 154668 & 154046.752974771 & 621.24702522927 \tabularnewline
71 & 153960 & 151775.707860424 & 2184.29213957608 \tabularnewline
72 & 157307 & 156096.57871593 & 1210.42128406954 \tabularnewline
73 & 165218 & 157217.327421027 & 8000.67257897329 \tabularnewline
74 & 165616 & 163783.793562434 & 1832.20643756574 \tabularnewline
75 & 162212 & 164057.286479244 & -1845.28647924369 \tabularnewline
76 & 159787 & 162513.187496083 & -2726.18749608268 \tabularnewline
77 & 157454 & 158985.99106861 & -1531.99106861022 \tabularnewline
78 & 156485 & 155594.157835138 & 890.84216486162 \tabularnewline
79 & 165887 & 165018.037180832 & 868.962819168199 \tabularnewline
80 & 166836 & 165487.426015213 & 1348.57398478687 \tabularnewline
81 & 163541 & 165798.34710391 & -2257.34710390971 \tabularnewline
82 & 163973 & 163410.599983391 & 562.40001660859 \tabularnewline
83 & 164805 & 162283.967540115 & 2521.03245988549 \tabularnewline
84 & 167521 & 167681.562434602 & -160.562434602412 \tabularnewline
85 & 174347 & 169636.913041676 & 4710.08695832398 \tabularnewline
86 & 173374 & 172879.595385491 & 494.404614509054 \tabularnewline
87 & 172198 & 171728.591847747 & 469.40815225293 \tabularnewline
88 & 171055 & 172517.885236548 & -1462.88523654794 \tabularnewline
89 & 168385 & 170942.725417687 & -2557.72541768744 \tabularnewline
90 & 167281 & 167702.112251626 & -421.112251625862 \tabularnewline
91 & 177670 & 176480.664100509 & 1189.33589949057 \tabularnewline
92 & 177280 & 177779.085882768 & -499.08588276786 \tabularnewline
93 & 174846 & 176223.600834753 & -1377.60083475269 \tabularnewline
94 & 174476 & 175422.708400592 & -946.708400592121 \tabularnewline
95 & 174595 & 173590.647218161 & 1004.35278183871 \tabularnewline
96 & 178392 & 177320.980420852 & 1071.01957914772 \tabularnewline
97 & 185345 & 181309.845057417 & 4035.15494258303 \tabularnewline
98 & 183293 & 183382.491763821 & -89.4917638205516 \tabularnewline
99 & 181081 & 181787.868357271 & -706.868357271247 \tabularnewline
100 & 177795 & 181189.346678223 & -3394.3466782232 \tabularnewline
101 & 173552 & 177532.970139239 & -3980.97013923893 \tabularnewline
102 & 170734 & 173029.016250113 & -2295.01625011265 \tabularnewline
103 & 179293 & 179877.272255308 & -584.272255307646 \tabularnewline
104 & 178659 & 178573.783565182 & 85.2164348181977 \tabularnewline
105 & 175894 & 176573.878821801 & -679.878821800667 \tabularnewline
106 & 174815 & 175721.579883527 & -906.579883527302 \tabularnewline
107 & 173506 & 173556.064458195 & -50.0644581945962 \tabularnewline
108 & 175376 & 175609.30676654 & -233.306766540423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287514&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]162466[/C][C]172768.727831197[/C][C]-10302.7278311966[/C][/ROW]
[ROW][C]14[/C][C]160185[/C][C]160952.28769443[/C][C]-767.287694430357[/C][/ROW]
[ROW][C]15[/C][C]154836[/C][C]154022.221206013[/C][C]813.778793986858[/C][/ROW]
[ROW][C]16[/C][C]154103[/C][C]153057.20248245[/C][C]1045.7975175498[/C][/ROW]
[ROW][C]17[/C][C]150495[/C][C]149240.226741966[/C][C]1254.77325803367[/C][/ROW]
[ROW][C]18[/C][C]142707[/C][C]141366.614444935[/C][C]1340.38555506495[/C][/ROW]
[ROW][C]19[/C][C]149962[/C][C]152370.781062572[/C][C]-2408.7810625718[/C][/ROW]
[ROW][C]20[/C][C]149967[/C][C]147006.81805185[/C][C]2960.18194815019[/C][/ROW]
[ROW][C]21[/C][C]144572[/C][C]147561.80292911[/C][C]-2989.80292910963[/C][/ROW]
[ROW][C]22[/C][C]143819[/C][C]137146.801631681[/C][C]6672.19836831908[/C][/ROW]
[ROW][C]23[/C][C]141070[/C][C]138597.525014976[/C][C]2472.47498502399[/C][/ROW]
[ROW][C]24[/C][C]144119[/C][C]140366.004031692[/C][C]3752.99596830813[/C][/ROW]
[ROW][C]25[/C][C]145330[/C][C]144151.73348818[/C][C]1178.26651181976[/C][/ROW]
[ROW][C]26[/C][C]143279[/C][C]145148.317856495[/C][C]-1869.31785649509[/C][/ROW]
[ROW][C]27[/C][C]139063[/C][C]139117.549925997[/C][C]-54.549925997213[/C][/ROW]
[ROW][C]28[/C][C]139202[/C][C]138921.495364885[/C][C]280.50463511463[/C][/ROW]
[ROW][C]29[/C][C]133632[/C][C]135871.951828393[/C][C]-2239.95182839292[/C][/ROW]
[ROW][C]30[/C][C]134476[/C][C]126101.153460866[/C][C]8374.84653913375[/C][/ROW]
[ROW][C]31[/C][C]141859[/C][C]144052.691792287[/C][C]-2193.69179228655[/C][/ROW]
[ROW][C]32[/C][C]140693[/C][C]141556.551755491[/C][C]-863.551755490684[/C][/ROW]
[ROW][C]33[/C][C]138047[/C][C]139284.578213729[/C][C]-1237.5782137294[/C][/ROW]
[ROW][C]34[/C][C]138346[/C][C]133519.388501782[/C][C]4826.61149821768[/C][/ROW]
[ROW][C]35[/C][C]140167[/C][C]134072.32313944[/C][C]6094.67686055979[/C][/ROW]
[ROW][C]36[/C][C]146796[/C][C]140806.142158271[/C][C]5989.85784172913[/C][/ROW]
[ROW][C]37[/C][C]152228[/C][C]147993.714819095[/C][C]4234.28518090516[/C][/ROW]
[ROW][C]38[/C][C]155410[/C][C]153322.83535827[/C][C]2087.16464172985[/C][/ROW]
[ROW][C]39[/C][C]159032[/C][C]153629.858654333[/C][C]5402.14134566655[/C][/ROW]
[ROW][C]40[/C][C]160312[/C][C]161356.254628992[/C][C]-1044.25462899235[/C][/ROW]
[ROW][C]41[/C][C]157687[/C][C]159973.056846547[/C][C]-2286.05684654709[/C][/ROW]
[ROW][C]42[/C][C]160141[/C][C]155163.156197326[/C][C]4977.84380267409[/C][/ROW]
[ROW][C]43[/C][C]167421[/C][C]171316.467781756[/C][C]-3895.46778175555[/C][/ROW]
[ROW][C]44[/C][C]167628[/C][C]170271.718445473[/C][C]-2643.71844547288[/C][/ROW]
[ROW][C]45[/C][C]164403[/C][C]168902.388578339[/C][C]-4499.38857833925[/C][/ROW]
[ROW][C]46[/C][C]163405[/C][C]163554.008551003[/C][C]-149.008551002538[/C][/ROW]
[ROW][C]47[/C][C]163229[/C][C]161744.436277431[/C][C]1484.56372256944[/C][/ROW]
[ROW][C]48[/C][C]171154[/C][C]165684.492409733[/C][C]5469.50759026714[/C][/ROW]
[ROW][C]49[/C][C]173323[/C][C]173133.13266791[/C][C]189.867332089867[/C][/ROW]
[ROW][C]50[/C][C]172381[/C][C]175294.125024308[/C][C]-2913.12502430764[/C][/ROW]
[ROW][C]51[/C][C]168983[/C][C]172028.242783501[/C][C]-3045.24278350075[/C][/ROW]
[ROW][C]52[/C][C]165380[/C][C]170741.372744173[/C][C]-5361.37274417302[/C][/ROW]
[ROW][C]53[/C][C]161641[/C][C]164189.633825301[/C][C]-2548.63382530131[/C][/ROW]
[ROW][C]54[/C][C]161933[/C][C]158995.908429867[/C][C]2937.09157013291[/C][/ROW]
[ROW][C]55[/C][C]172018[/C][C]170318.249678529[/C][C]1699.75032147134[/C][/ROW]
[ROW][C]56[/C][C]168455[/C][C]173110.15693605[/C][C]-4655.15693605022[/C][/ROW]
[ROW][C]57[/C][C]164332[/C][C]168519.344605251[/C][C]-4187.34460525072[/C][/ROW]
[ROW][C]58[/C][C]161193[/C][C]162968.604992281[/C][C]-1775.60499228138[/C][/ROW]
[ROW][C]59[/C][C]157645[/C][C]158708.818530965[/C][C]-1063.81853096528[/C][/ROW]
[ROW][C]60[/C][C]161694[/C][C]159558.123333571[/C][C]2135.87666642893[/C][/ROW]
[ROW][C]61[/C][C]163411[/C][C]161323.609587414[/C][C]2087.39041258598[/C][/ROW]
[ROW][C]62[/C][C]161834[/C][C]162717.965765356[/C][C]-883.96576535597[/C][/ROW]
[ROW][C]63[/C][C]159511[/C][C]159521.298943243[/C][C]-10.2989432431932[/C][/ROW]
[ROW][C]64[/C][C]156359[/C][C]159095.208551699[/C][C]-2736.20855169918[/C][/ROW]
[ROW][C]65[/C][C]154223[/C][C]154223.487802048[/C][C]-0.487802048010053[/C][/ROW]
[ROW][C]66[/C][C]151497[/C][C]151378.108220929[/C][C]118.891779070953[/C][/ROW]
[ROW][C]67[/C][C]160607[/C][C]159145.266092727[/C][C]1461.73390727284[/C][/ROW]
[ROW][C]68[/C][C]159672[/C][C]159624.28909601[/C][C]47.7109039901698[/C][/ROW]
[ROW][C]69[/C][C]155601[/C][C]158492.758239493[/C][C]-2891.75823949269[/C][/ROW]
[ROW][C]70[/C][C]154668[/C][C]154046.752974771[/C][C]621.24702522927[/C][/ROW]
[ROW][C]71[/C][C]153960[/C][C]151775.707860424[/C][C]2184.29213957608[/C][/ROW]
[ROW][C]72[/C][C]157307[/C][C]156096.57871593[/C][C]1210.42128406954[/C][/ROW]
[ROW][C]73[/C][C]165218[/C][C]157217.327421027[/C][C]8000.67257897329[/C][/ROW]
[ROW][C]74[/C][C]165616[/C][C]163783.793562434[/C][C]1832.20643756574[/C][/ROW]
[ROW][C]75[/C][C]162212[/C][C]164057.286479244[/C][C]-1845.28647924369[/C][/ROW]
[ROW][C]76[/C][C]159787[/C][C]162513.187496083[/C][C]-2726.18749608268[/C][/ROW]
[ROW][C]77[/C][C]157454[/C][C]158985.99106861[/C][C]-1531.99106861022[/C][/ROW]
[ROW][C]78[/C][C]156485[/C][C]155594.157835138[/C][C]890.84216486162[/C][/ROW]
[ROW][C]79[/C][C]165887[/C][C]165018.037180832[/C][C]868.962819168199[/C][/ROW]
[ROW][C]80[/C][C]166836[/C][C]165487.426015213[/C][C]1348.57398478687[/C][/ROW]
[ROW][C]81[/C][C]163541[/C][C]165798.34710391[/C][C]-2257.34710390971[/C][/ROW]
[ROW][C]82[/C][C]163973[/C][C]163410.599983391[/C][C]562.40001660859[/C][/ROW]
[ROW][C]83[/C][C]164805[/C][C]162283.967540115[/C][C]2521.03245988549[/C][/ROW]
[ROW][C]84[/C][C]167521[/C][C]167681.562434602[/C][C]-160.562434602412[/C][/ROW]
[ROW][C]85[/C][C]174347[/C][C]169636.913041676[/C][C]4710.08695832398[/C][/ROW]
[ROW][C]86[/C][C]173374[/C][C]172879.595385491[/C][C]494.404614509054[/C][/ROW]
[ROW][C]87[/C][C]172198[/C][C]171728.591847747[/C][C]469.40815225293[/C][/ROW]
[ROW][C]88[/C][C]171055[/C][C]172517.885236548[/C][C]-1462.88523654794[/C][/ROW]
[ROW][C]89[/C][C]168385[/C][C]170942.725417687[/C][C]-2557.72541768744[/C][/ROW]
[ROW][C]90[/C][C]167281[/C][C]167702.112251626[/C][C]-421.112251625862[/C][/ROW]
[ROW][C]91[/C][C]177670[/C][C]176480.664100509[/C][C]1189.33589949057[/C][/ROW]
[ROW][C]92[/C][C]177280[/C][C]177779.085882768[/C][C]-499.08588276786[/C][/ROW]
[ROW][C]93[/C][C]174846[/C][C]176223.600834753[/C][C]-1377.60083475269[/C][/ROW]
[ROW][C]94[/C][C]174476[/C][C]175422.708400592[/C][C]-946.708400592121[/C][/ROW]
[ROW][C]95[/C][C]174595[/C][C]173590.647218161[/C][C]1004.35278183871[/C][/ROW]
[ROW][C]96[/C][C]178392[/C][C]177320.980420852[/C][C]1071.01957914772[/C][/ROW]
[ROW][C]97[/C][C]185345[/C][C]181309.845057417[/C][C]4035.15494258303[/C][/ROW]
[ROW][C]98[/C][C]183293[/C][C]183382.491763821[/C][C]-89.4917638205516[/C][/ROW]
[ROW][C]99[/C][C]181081[/C][C]181787.868357271[/C][C]-706.868357271247[/C][/ROW]
[ROW][C]100[/C][C]177795[/C][C]181189.346678223[/C][C]-3394.3466782232[/C][/ROW]
[ROW][C]101[/C][C]173552[/C][C]177532.970139239[/C][C]-3980.97013923893[/C][/ROW]
[ROW][C]102[/C][C]170734[/C][C]173029.016250113[/C][C]-2295.01625011265[/C][/ROW]
[ROW][C]103[/C][C]179293[/C][C]179877.272255308[/C][C]-584.272255307646[/C][/ROW]
[ROW][C]104[/C][C]178659[/C][C]178573.783565182[/C][C]85.2164348181977[/C][/ROW]
[ROW][C]105[/C][C]175894[/C][C]176573.878821801[/C][C]-679.878821800667[/C][/ROW]
[ROW][C]106[/C][C]174815[/C][C]175721.579883527[/C][C]-906.579883527302[/C][/ROW]
[ROW][C]107[/C][C]173506[/C][C]173556.064458195[/C][C]-50.0644581945962[/C][/ROW]
[ROW][C]108[/C][C]175376[/C][C]175609.30676654[/C][C]-233.306766540423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287514&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
13162466172768.727831197-10302.7278311966
14160185160952.28769443-767.287694430357
15154836154022.221206013813.778793986858
16154103153057.202482451045.7975175498
17150495149240.2267419661254.77325803367
18142707141366.6144449351340.38555506495
19149962152370.781062572-2408.7810625718
20149967147006.818051852960.18194815019
21144572147561.80292911-2989.80292910963
22143819137146.8016316816672.19836831908
23141070138597.5250149762472.47498502399
24144119140366.0040316923752.99596830813
25145330144151.733488181178.26651181976
26143279145148.317856495-1869.31785649509
27139063139117.549925997-54.549925997213
28139202138921.495364885280.50463511463
29133632135871.951828393-2239.95182839292
30134476126101.1534608668374.84653913375
31141859144052.691792287-2193.69179228655
32140693141556.551755491-863.551755490684
33138047139284.578213729-1237.5782137294
34138346133519.3885017824826.61149821768
35140167134072.323139446094.67686055979
36146796140806.1421582715989.85784172913
37152228147993.7148190954234.28518090516
38155410153322.835358272087.16464172985
39159032153629.8586543335402.14134566655
40160312161356.254628992-1044.25462899235
41157687159973.056846547-2286.05684654709
42160141155163.1561973264977.84380267409
43167421171316.467781756-3895.46778175555
44167628170271.718445473-2643.71844547288
45164403168902.388578339-4499.38857833925
46163405163554.008551003-149.008551002538
47163229161744.4362774311484.56372256944
48171154165684.4924097335469.50759026714
49173323173133.13266791189.867332089867
50172381175294.125024308-2913.12502430764
51168983172028.242783501-3045.24278350075
52165380170741.372744173-5361.37274417302
53161641164189.633825301-2548.63382530131
54161933158995.9084298672937.09157013291
55172018170318.2496785291699.75032147134
56168455173110.15693605-4655.15693605022
57164332168519.344605251-4187.34460525072
58161193162968.604992281-1775.60499228138
59157645158708.818530965-1063.81853096528
60161694159558.1233335712135.87666642893
61163411161323.6095874142087.39041258598
62161834162717.965765356-883.96576535597
63159511159521.298943243-10.2989432431932
64156359159095.208551699-2736.20855169918
65154223154223.487802048-0.487802048010053
66151497151378.108220929118.891779070953
67160607159145.2660927271461.73390727284
68159672159624.2890960147.7109039901698
69155601158492.758239493-2891.75823949269
70154668154046.752974771621.24702522927
71153960151775.7078604242184.29213957608
72157307156096.578715931210.42128406954
73165218157217.3274210278000.67257897329
74165616163783.7935624341832.20643756574
75162212164057.286479244-1845.28647924369
76159787162513.187496083-2726.18749608268
77157454158985.99106861-1531.99106861022
78156485155594.157835138890.84216486162
79165887165018.037180832868.962819168199
80166836165487.4260152131348.57398478687
81163541165798.34710391-2257.34710390971
82163973163410.599983391562.40001660859
83164805162283.9675401152521.03245988549
84167521167681.562434602-160.562434602412
85174347169636.9130416764710.08695832398
86173374172879.595385491494.404614509054
87172198171728.591847747469.40815225293
88171055172517.885236548-1462.88523654794
89168385170942.725417687-2557.72541768744
90167281167702.112251626-421.112251625862
91177670176480.6641005091189.33589949057
92177280177779.085882768-499.08588276786
93174846176223.600834753-1377.60083475269
94174476175422.708400592-946.708400592121
95174595173590.6472181611004.35278183871
96178392177320.9804208521071.01957914772
97185345181309.8450574174035.15494258303
98183293183382.491763821-89.4917638205516
99181081181787.868357271-706.868357271247
100177795181189.346678223-3394.3466782232
101173552177532.970139239-3980.97013923893
102170734173029.016250113-2295.01625011265
103179293179877.272255308-584.272255307646
104178659178573.78356518285.2164348181977
105175894176573.878821801-679.878821800667
106174815175721.579883527-906.579883527302
107173506173556.064458195-50.0644581945962
108175376175609.30676654-233.306766540423







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109178066.033036125172148.703398845183983.362673405
110174694.873623184166581.322908574182808.424337794
111171685.576814899161478.275209007181892.878420791
112169908.425897246157623.55830938182193.293485111
113168029.392803304153647.394300953182411.391305656
114166608.932834125150092.698006712183125.167661537
115175395.458387874156698.516218121194092.400557627
116174497.033610117153567.72256589195426.344654344
117172093.046260346148876.833504496195309.259016196
118171636.925735501146077.771850726197196.079620276
119170338.694880654142379.889871892198297.499889417
120172376.908399669141961.598038735202792.218760603

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 178066.033036125 & 172148.703398845 & 183983.362673405 \tabularnewline
110 & 174694.873623184 & 166581.322908574 & 182808.424337794 \tabularnewline
111 & 171685.576814899 & 161478.275209007 & 181892.878420791 \tabularnewline
112 & 169908.425897246 & 157623.55830938 & 182193.293485111 \tabularnewline
113 & 168029.392803304 & 153647.394300953 & 182411.391305656 \tabularnewline
114 & 166608.932834125 & 150092.698006712 & 183125.167661537 \tabularnewline
115 & 175395.458387874 & 156698.516218121 & 194092.400557627 \tabularnewline
116 & 174497.033610117 & 153567.72256589 & 195426.344654344 \tabularnewline
117 & 172093.046260346 & 148876.833504496 & 195309.259016196 \tabularnewline
118 & 171636.925735501 & 146077.771850726 & 197196.079620276 \tabularnewline
119 & 170338.694880654 & 142379.889871892 & 198297.499889417 \tabularnewline
120 & 172376.908399669 & 141961.598038735 & 202792.218760603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287514&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]178066.033036125[/C][C]172148.703398845[/C][C]183983.362673405[/C][/ROW]
[ROW][C]110[/C][C]174694.873623184[/C][C]166581.322908574[/C][C]182808.424337794[/C][/ROW]
[ROW][C]111[/C][C]171685.576814899[/C][C]161478.275209007[/C][C]181892.878420791[/C][/ROW]
[ROW][C]112[/C][C]169908.425897246[/C][C]157623.55830938[/C][C]182193.293485111[/C][/ROW]
[ROW][C]113[/C][C]168029.392803304[/C][C]153647.394300953[/C][C]182411.391305656[/C][/ROW]
[ROW][C]114[/C][C]166608.932834125[/C][C]150092.698006712[/C][C]183125.167661537[/C][/ROW]
[ROW][C]115[/C][C]175395.458387874[/C][C]156698.516218121[/C][C]194092.400557627[/C][/ROW]
[ROW][C]116[/C][C]174497.033610117[/C][C]153567.72256589[/C][C]195426.344654344[/C][/ROW]
[ROW][C]117[/C][C]172093.046260346[/C][C]148876.833504496[/C][C]195309.259016196[/C][/ROW]
[ROW][C]118[/C][C]171636.925735501[/C][C]146077.771850726[/C][C]197196.079620276[/C][/ROW]
[ROW][C]119[/C][C]170338.694880654[/C][C]142379.889871892[/C][C]198297.499889417[/C][/ROW]
[ROW][C]120[/C][C]172376.908399669[/C][C]141961.598038735[/C][C]202792.218760603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287514&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
109178066.033036125172148.703398845183983.362673405
110174694.873623184166581.322908574182808.424337794
111171685.576814899161478.275209007181892.878420791
112169908.425897246157623.55830938182193.293485111
113168029.392803304153647.394300953182411.391305656
114166608.932834125150092.698006712183125.167661537
115175395.458387874156698.516218121194092.400557627
116174497.033610117153567.72256589195426.344654344
117172093.046260346148876.833504496195309.259016196
118171636.925735501146077.771850726197196.079620276
119170338.694880654142379.889871892198297.499889417
120172376.908399669141961.598038735202792.218760603



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')