Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 21:59:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448834420jqrweqib55puvx5.htm/, Retrieved Wed, 15 May 2024 09:59:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284528, Retrieved Wed, 15 May 2024 09:59:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-29 21:59:54] [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 Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284528&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284528&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284528&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999928670767705
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999928670767705 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284528&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]0.999928670767705[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284528&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284528&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
alpha0.999928670767705
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2173690173019671
3172439173689.952138085-1250.95213808512
4171914172439.089229456-525.089229455654
5171968171914.03745421253.9625457883812
6169500171967.996150893-2467.99615089304
7173898169500.1760402714397.82395972926
8172308173897.686306593-1589.68630659318
9171568172308.113391104-740.113391103834
10164939171568.05279172-6629.05279171999
11161275164939.472845246-3664.47284524649
12160770161275.261384035-505.26138403482
13162466160770.0360399071695.96396009336
14160185162465.879028193-2280.87902819272
15154836160185.16269335-5349.16269335005
16154103154836.381551668-733.381551668339
17150495154103.052311543-3608.05231154306
18142707150495.257359601-7788.25735960147
19149962142707.5555304187254.44446958162
20149967149961.4825460455.51745395475882
21144572149966.999606444-5394.99960644424
22143819144572.38482118-753.384821180167
23141070143819.053738361-2749.05373836093
24144119141070.1960878933048.80391210731
25145330144118.7825311581211.21746884246
26143279145329.913604788-2050.91360478781
27139063143279.146290093-4216.14629009293
28139202139063.300734478138.699265521864
29133632139201.990106688-5569.99010668788
30134476133632.397303118843.602696881804
31141859134475.9398264677383.06017353272
32140693141858.473371986-1165.47337198583
33138047140693.083132321-2646.08313232087
34138346138047.188743078298.811256921588
35140167138345.9786860221821.02131397757
36146796140166.8701079486629.12989205233
37152228146795.5271492545432.47285074598
38155410152227.6125058823182.38749411789
39159032155409.7730027433622.22699725683
40160312159031.7416293291280.25837067093
41157687160311.908680153-2624.90868015328
42160141157687.1872327212453.81276727899
43167421160140.8249714197280.17502858091
44167628167420.480710704207.519289295771
45164403167627.985197808-3224.98519780842
46163405164403.230035718-998.230035718327
47163229163405.071202982-176.071202982101
48171154163229.0125590247924.98744097626
49173323171153.434716732169.56528327012
50172381173322.845246574-941.845246573939
51168983172381.067181098-3398.06718109836
52165380168983.242381523-3603.24238152333
53161641165380.257016513-3739.25701651286
54161933161641.266718332291.733281667664
55172018161932.97919088910085.020809111
56168455172017.280643208-3562.28064320801
57164332168455.254094744-4123.25409474352
58161193164332.294108549-3139.29410854913
59157645161193.223923439-3548.22392343869
60161694157645.2530920884048.74690791153
61163411161693.7112059911717.28879400869
62161834163410.877507109-1576.87750710867
63159511161834.112477462-2323.11247746198
64156359159511.16570583-3152.16570582954
65154223156359.22484156-2136.22484155989
66151497154223.152375278-2726.15237527795
67160607151497.1944543569109.80554564396
68159672160606.350204564-934.350204564049
69155601159672.066646483-4071.0666464828
70154668155601.290386059-933.290386058507
71153960154668.066570887-708.066570886731
72157307153960.0505058453346.94949415509
73165218157306.7612646627911.23873533795
74165616165217.435697415398.564302585495
75162212165615.971570714-3403.97157071426
76159787162212.242802679-2425.2428026789
77157454159787.172990707-2333.17299070724
78156485157454.166423438-969.166423438262
79165887156485.0691298979401.93087010304
80166836165886.329367489949.670632511086
81163541166835.932260723-3294.93226072285
82163973163541.235024989431.764975011378
83164805163972.969202536832.03079746422
84167521164804.9406518822716.05934811805
85174347167520.8062655726826.19373442818
86173374174346.513092841-972.513092841429
87172198173374.069368612-1176.06936861231
88171055172198.083888125-1143.08388812517
89168385171055.081535296-2670.08153529619
90167281168385.190454866-1104.1904548661
91177670167281.07876105710388.9212389425
92177280177669.258966224-389.258966223628
93174846177280.027765543-2434.02776554323
94174476174846.173617332-370.173617331922
95174595174476.0264042118.973595800053
96178392174594.9915137053797.00848629526
97185345178391.72916236953.27083770034
98183293185344.504028529-2051.50402852919
99181081183293.146332207-2212.1463322074
100177795181081.1577907-3286.1577906996
101173552177795.234399112-4243.23439911241
102170734173552.302666652-2818.30266665213
103179293170734.2010273668558.79897263442
104178659179292.38950744-633.38950743989
105175894178659.045179187-2765.04517918732
106174815175894.19722855-1079.19722854989
107173506174815.07697831-1309.07697830981
108175376173506.0933754561869.90662454412

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 173690 & 173019 & 671 \tabularnewline
3 & 172439 & 173689.952138085 & -1250.95213808512 \tabularnewline
4 & 171914 & 172439.089229456 & -525.089229455654 \tabularnewline
5 & 171968 & 171914.037454212 & 53.9625457883812 \tabularnewline
6 & 169500 & 171967.996150893 & -2467.99615089304 \tabularnewline
7 & 173898 & 169500.176040271 & 4397.82395972926 \tabularnewline
8 & 172308 & 173897.686306593 & -1589.68630659318 \tabularnewline
9 & 171568 & 172308.113391104 & -740.113391103834 \tabularnewline
10 & 164939 & 171568.05279172 & -6629.05279171999 \tabularnewline
11 & 161275 & 164939.472845246 & -3664.47284524649 \tabularnewline
12 & 160770 & 161275.261384035 & -505.26138403482 \tabularnewline
13 & 162466 & 160770.036039907 & 1695.96396009336 \tabularnewline
14 & 160185 & 162465.879028193 & -2280.87902819272 \tabularnewline
15 & 154836 & 160185.16269335 & -5349.16269335005 \tabularnewline
16 & 154103 & 154836.381551668 & -733.381551668339 \tabularnewline
17 & 150495 & 154103.052311543 & -3608.05231154306 \tabularnewline
18 & 142707 & 150495.257359601 & -7788.25735960147 \tabularnewline
19 & 149962 & 142707.555530418 & 7254.44446958162 \tabularnewline
20 & 149967 & 149961.482546045 & 5.51745395475882 \tabularnewline
21 & 144572 & 149966.999606444 & -5394.99960644424 \tabularnewline
22 & 143819 & 144572.38482118 & -753.384821180167 \tabularnewline
23 & 141070 & 143819.053738361 & -2749.05373836093 \tabularnewline
24 & 144119 & 141070.196087893 & 3048.80391210731 \tabularnewline
25 & 145330 & 144118.782531158 & 1211.21746884246 \tabularnewline
26 & 143279 & 145329.913604788 & -2050.91360478781 \tabularnewline
27 & 139063 & 143279.146290093 & -4216.14629009293 \tabularnewline
28 & 139202 & 139063.300734478 & 138.699265521864 \tabularnewline
29 & 133632 & 139201.990106688 & -5569.99010668788 \tabularnewline
30 & 134476 & 133632.397303118 & 843.602696881804 \tabularnewline
31 & 141859 & 134475.939826467 & 7383.06017353272 \tabularnewline
32 & 140693 & 141858.473371986 & -1165.47337198583 \tabularnewline
33 & 138047 & 140693.083132321 & -2646.08313232087 \tabularnewline
34 & 138346 & 138047.188743078 & 298.811256921588 \tabularnewline
35 & 140167 & 138345.978686022 & 1821.02131397757 \tabularnewline
36 & 146796 & 140166.870107948 & 6629.12989205233 \tabularnewline
37 & 152228 & 146795.527149254 & 5432.47285074598 \tabularnewline
38 & 155410 & 152227.612505882 & 3182.38749411789 \tabularnewline
39 & 159032 & 155409.773002743 & 3622.22699725683 \tabularnewline
40 & 160312 & 159031.741629329 & 1280.25837067093 \tabularnewline
41 & 157687 & 160311.908680153 & -2624.90868015328 \tabularnewline
42 & 160141 & 157687.187232721 & 2453.81276727899 \tabularnewline
43 & 167421 & 160140.824971419 & 7280.17502858091 \tabularnewline
44 & 167628 & 167420.480710704 & 207.519289295771 \tabularnewline
45 & 164403 & 167627.985197808 & -3224.98519780842 \tabularnewline
46 & 163405 & 164403.230035718 & -998.230035718327 \tabularnewline
47 & 163229 & 163405.071202982 & -176.071202982101 \tabularnewline
48 & 171154 & 163229.012559024 & 7924.98744097626 \tabularnewline
49 & 173323 & 171153.43471673 & 2169.56528327012 \tabularnewline
50 & 172381 & 173322.845246574 & -941.845246573939 \tabularnewline
51 & 168983 & 172381.067181098 & -3398.06718109836 \tabularnewline
52 & 165380 & 168983.242381523 & -3603.24238152333 \tabularnewline
53 & 161641 & 165380.257016513 & -3739.25701651286 \tabularnewline
54 & 161933 & 161641.266718332 & 291.733281667664 \tabularnewline
55 & 172018 & 161932.979190889 & 10085.020809111 \tabularnewline
56 & 168455 & 172017.280643208 & -3562.28064320801 \tabularnewline
57 & 164332 & 168455.254094744 & -4123.25409474352 \tabularnewline
58 & 161193 & 164332.294108549 & -3139.29410854913 \tabularnewline
59 & 157645 & 161193.223923439 & -3548.22392343869 \tabularnewline
60 & 161694 & 157645.253092088 & 4048.74690791153 \tabularnewline
61 & 163411 & 161693.711205991 & 1717.28879400869 \tabularnewline
62 & 161834 & 163410.877507109 & -1576.87750710867 \tabularnewline
63 & 159511 & 161834.112477462 & -2323.11247746198 \tabularnewline
64 & 156359 & 159511.16570583 & -3152.16570582954 \tabularnewline
65 & 154223 & 156359.22484156 & -2136.22484155989 \tabularnewline
66 & 151497 & 154223.152375278 & -2726.15237527795 \tabularnewline
67 & 160607 & 151497.194454356 & 9109.80554564396 \tabularnewline
68 & 159672 & 160606.350204564 & -934.350204564049 \tabularnewline
69 & 155601 & 159672.066646483 & -4071.0666464828 \tabularnewline
70 & 154668 & 155601.290386059 & -933.290386058507 \tabularnewline
71 & 153960 & 154668.066570887 & -708.066570886731 \tabularnewline
72 & 157307 & 153960.050505845 & 3346.94949415509 \tabularnewline
73 & 165218 & 157306.761264662 & 7911.23873533795 \tabularnewline
74 & 165616 & 165217.435697415 & 398.564302585495 \tabularnewline
75 & 162212 & 165615.971570714 & -3403.97157071426 \tabularnewline
76 & 159787 & 162212.242802679 & -2425.2428026789 \tabularnewline
77 & 157454 & 159787.172990707 & -2333.17299070724 \tabularnewline
78 & 156485 & 157454.166423438 & -969.166423438262 \tabularnewline
79 & 165887 & 156485.069129897 & 9401.93087010304 \tabularnewline
80 & 166836 & 165886.329367489 & 949.670632511086 \tabularnewline
81 & 163541 & 166835.932260723 & -3294.93226072285 \tabularnewline
82 & 163973 & 163541.235024989 & 431.764975011378 \tabularnewline
83 & 164805 & 163972.969202536 & 832.03079746422 \tabularnewline
84 & 167521 & 164804.940651882 & 2716.05934811805 \tabularnewline
85 & 174347 & 167520.806265572 & 6826.19373442818 \tabularnewline
86 & 173374 & 174346.513092841 & -972.513092841429 \tabularnewline
87 & 172198 & 173374.069368612 & -1176.06936861231 \tabularnewline
88 & 171055 & 172198.083888125 & -1143.08388812517 \tabularnewline
89 & 168385 & 171055.081535296 & -2670.08153529619 \tabularnewline
90 & 167281 & 168385.190454866 & -1104.1904548661 \tabularnewline
91 & 177670 & 167281.078761057 & 10388.9212389425 \tabularnewline
92 & 177280 & 177669.258966224 & -389.258966223628 \tabularnewline
93 & 174846 & 177280.027765543 & -2434.02776554323 \tabularnewline
94 & 174476 & 174846.173617332 & -370.173617331922 \tabularnewline
95 & 174595 & 174476.0264042 & 118.973595800053 \tabularnewline
96 & 178392 & 174594.991513705 & 3797.00848629526 \tabularnewline
97 & 185345 & 178391.7291623 & 6953.27083770034 \tabularnewline
98 & 183293 & 185344.504028529 & -2051.50402852919 \tabularnewline
99 & 181081 & 183293.146332207 & -2212.1463322074 \tabularnewline
100 & 177795 & 181081.1577907 & -3286.1577906996 \tabularnewline
101 & 173552 & 177795.234399112 & -4243.23439911241 \tabularnewline
102 & 170734 & 173552.302666652 & -2818.30266665213 \tabularnewline
103 & 179293 & 170734.201027366 & 8558.79897263442 \tabularnewline
104 & 178659 & 179292.38950744 & -633.38950743989 \tabularnewline
105 & 175894 & 178659.045179187 & -2765.04517918732 \tabularnewline
106 & 174815 & 175894.19722855 & -1079.19722854989 \tabularnewline
107 & 173506 & 174815.07697831 & -1309.07697830981 \tabularnewline
108 & 175376 & 173506.093375456 & 1869.90662454412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284528&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]173690[/C][C]173019[/C][C]671[/C][/ROW]
[ROW][C]3[/C][C]172439[/C][C]173689.952138085[/C][C]-1250.95213808512[/C][/ROW]
[ROW][C]4[/C][C]171914[/C][C]172439.089229456[/C][C]-525.089229455654[/C][/ROW]
[ROW][C]5[/C][C]171968[/C][C]171914.037454212[/C][C]53.9625457883812[/C][/ROW]
[ROW][C]6[/C][C]169500[/C][C]171967.996150893[/C][C]-2467.99615089304[/C][/ROW]
[ROW][C]7[/C][C]173898[/C][C]169500.176040271[/C][C]4397.82395972926[/C][/ROW]
[ROW][C]8[/C][C]172308[/C][C]173897.686306593[/C][C]-1589.68630659318[/C][/ROW]
[ROW][C]9[/C][C]171568[/C][C]172308.113391104[/C][C]-740.113391103834[/C][/ROW]
[ROW][C]10[/C][C]164939[/C][C]171568.05279172[/C][C]-6629.05279171999[/C][/ROW]
[ROW][C]11[/C][C]161275[/C][C]164939.472845246[/C][C]-3664.47284524649[/C][/ROW]
[ROW][C]12[/C][C]160770[/C][C]161275.261384035[/C][C]-505.26138403482[/C][/ROW]
[ROW][C]13[/C][C]162466[/C][C]160770.036039907[/C][C]1695.96396009336[/C][/ROW]
[ROW][C]14[/C][C]160185[/C][C]162465.879028193[/C][C]-2280.87902819272[/C][/ROW]
[ROW][C]15[/C][C]154836[/C][C]160185.16269335[/C][C]-5349.16269335005[/C][/ROW]
[ROW][C]16[/C][C]154103[/C][C]154836.381551668[/C][C]-733.381551668339[/C][/ROW]
[ROW][C]17[/C][C]150495[/C][C]154103.052311543[/C][C]-3608.05231154306[/C][/ROW]
[ROW][C]18[/C][C]142707[/C][C]150495.257359601[/C][C]-7788.25735960147[/C][/ROW]
[ROW][C]19[/C][C]149962[/C][C]142707.555530418[/C][C]7254.44446958162[/C][/ROW]
[ROW][C]20[/C][C]149967[/C][C]149961.482546045[/C][C]5.51745395475882[/C][/ROW]
[ROW][C]21[/C][C]144572[/C][C]149966.999606444[/C][C]-5394.99960644424[/C][/ROW]
[ROW][C]22[/C][C]143819[/C][C]144572.38482118[/C][C]-753.384821180167[/C][/ROW]
[ROW][C]23[/C][C]141070[/C][C]143819.053738361[/C][C]-2749.05373836093[/C][/ROW]
[ROW][C]24[/C][C]144119[/C][C]141070.196087893[/C][C]3048.80391210731[/C][/ROW]
[ROW][C]25[/C][C]145330[/C][C]144118.782531158[/C][C]1211.21746884246[/C][/ROW]
[ROW][C]26[/C][C]143279[/C][C]145329.913604788[/C][C]-2050.91360478781[/C][/ROW]
[ROW][C]27[/C][C]139063[/C][C]143279.146290093[/C][C]-4216.14629009293[/C][/ROW]
[ROW][C]28[/C][C]139202[/C][C]139063.300734478[/C][C]138.699265521864[/C][/ROW]
[ROW][C]29[/C][C]133632[/C][C]139201.990106688[/C][C]-5569.99010668788[/C][/ROW]
[ROW][C]30[/C][C]134476[/C][C]133632.397303118[/C][C]843.602696881804[/C][/ROW]
[ROW][C]31[/C][C]141859[/C][C]134475.939826467[/C][C]7383.06017353272[/C][/ROW]
[ROW][C]32[/C][C]140693[/C][C]141858.473371986[/C][C]-1165.47337198583[/C][/ROW]
[ROW][C]33[/C][C]138047[/C][C]140693.083132321[/C][C]-2646.08313232087[/C][/ROW]
[ROW][C]34[/C][C]138346[/C][C]138047.188743078[/C][C]298.811256921588[/C][/ROW]
[ROW][C]35[/C][C]140167[/C][C]138345.978686022[/C][C]1821.02131397757[/C][/ROW]
[ROW][C]36[/C][C]146796[/C][C]140166.870107948[/C][C]6629.12989205233[/C][/ROW]
[ROW][C]37[/C][C]152228[/C][C]146795.527149254[/C][C]5432.47285074598[/C][/ROW]
[ROW][C]38[/C][C]155410[/C][C]152227.612505882[/C][C]3182.38749411789[/C][/ROW]
[ROW][C]39[/C][C]159032[/C][C]155409.773002743[/C][C]3622.22699725683[/C][/ROW]
[ROW][C]40[/C][C]160312[/C][C]159031.741629329[/C][C]1280.25837067093[/C][/ROW]
[ROW][C]41[/C][C]157687[/C][C]160311.908680153[/C][C]-2624.90868015328[/C][/ROW]
[ROW][C]42[/C][C]160141[/C][C]157687.187232721[/C][C]2453.81276727899[/C][/ROW]
[ROW][C]43[/C][C]167421[/C][C]160140.824971419[/C][C]7280.17502858091[/C][/ROW]
[ROW][C]44[/C][C]167628[/C][C]167420.480710704[/C][C]207.519289295771[/C][/ROW]
[ROW][C]45[/C][C]164403[/C][C]167627.985197808[/C][C]-3224.98519780842[/C][/ROW]
[ROW][C]46[/C][C]163405[/C][C]164403.230035718[/C][C]-998.230035718327[/C][/ROW]
[ROW][C]47[/C][C]163229[/C][C]163405.071202982[/C][C]-176.071202982101[/C][/ROW]
[ROW][C]48[/C][C]171154[/C][C]163229.012559024[/C][C]7924.98744097626[/C][/ROW]
[ROW][C]49[/C][C]173323[/C][C]171153.43471673[/C][C]2169.56528327012[/C][/ROW]
[ROW][C]50[/C][C]172381[/C][C]173322.845246574[/C][C]-941.845246573939[/C][/ROW]
[ROW][C]51[/C][C]168983[/C][C]172381.067181098[/C][C]-3398.06718109836[/C][/ROW]
[ROW][C]52[/C][C]165380[/C][C]168983.242381523[/C][C]-3603.24238152333[/C][/ROW]
[ROW][C]53[/C][C]161641[/C][C]165380.257016513[/C][C]-3739.25701651286[/C][/ROW]
[ROW][C]54[/C][C]161933[/C][C]161641.266718332[/C][C]291.733281667664[/C][/ROW]
[ROW][C]55[/C][C]172018[/C][C]161932.979190889[/C][C]10085.020809111[/C][/ROW]
[ROW][C]56[/C][C]168455[/C][C]172017.280643208[/C][C]-3562.28064320801[/C][/ROW]
[ROW][C]57[/C][C]164332[/C][C]168455.254094744[/C][C]-4123.25409474352[/C][/ROW]
[ROW][C]58[/C][C]161193[/C][C]164332.294108549[/C][C]-3139.29410854913[/C][/ROW]
[ROW][C]59[/C][C]157645[/C][C]161193.223923439[/C][C]-3548.22392343869[/C][/ROW]
[ROW][C]60[/C][C]161694[/C][C]157645.253092088[/C][C]4048.74690791153[/C][/ROW]
[ROW][C]61[/C][C]163411[/C][C]161693.711205991[/C][C]1717.28879400869[/C][/ROW]
[ROW][C]62[/C][C]161834[/C][C]163410.877507109[/C][C]-1576.87750710867[/C][/ROW]
[ROW][C]63[/C][C]159511[/C][C]161834.112477462[/C][C]-2323.11247746198[/C][/ROW]
[ROW][C]64[/C][C]156359[/C][C]159511.16570583[/C][C]-3152.16570582954[/C][/ROW]
[ROW][C]65[/C][C]154223[/C][C]156359.22484156[/C][C]-2136.22484155989[/C][/ROW]
[ROW][C]66[/C][C]151497[/C][C]154223.152375278[/C][C]-2726.15237527795[/C][/ROW]
[ROW][C]67[/C][C]160607[/C][C]151497.194454356[/C][C]9109.80554564396[/C][/ROW]
[ROW][C]68[/C][C]159672[/C][C]160606.350204564[/C][C]-934.350204564049[/C][/ROW]
[ROW][C]69[/C][C]155601[/C][C]159672.066646483[/C][C]-4071.0666464828[/C][/ROW]
[ROW][C]70[/C][C]154668[/C][C]155601.290386059[/C][C]-933.290386058507[/C][/ROW]
[ROW][C]71[/C][C]153960[/C][C]154668.066570887[/C][C]-708.066570886731[/C][/ROW]
[ROW][C]72[/C][C]157307[/C][C]153960.050505845[/C][C]3346.94949415509[/C][/ROW]
[ROW][C]73[/C][C]165218[/C][C]157306.761264662[/C][C]7911.23873533795[/C][/ROW]
[ROW][C]74[/C][C]165616[/C][C]165217.435697415[/C][C]398.564302585495[/C][/ROW]
[ROW][C]75[/C][C]162212[/C][C]165615.971570714[/C][C]-3403.97157071426[/C][/ROW]
[ROW][C]76[/C][C]159787[/C][C]162212.242802679[/C][C]-2425.2428026789[/C][/ROW]
[ROW][C]77[/C][C]157454[/C][C]159787.172990707[/C][C]-2333.17299070724[/C][/ROW]
[ROW][C]78[/C][C]156485[/C][C]157454.166423438[/C][C]-969.166423438262[/C][/ROW]
[ROW][C]79[/C][C]165887[/C][C]156485.069129897[/C][C]9401.93087010304[/C][/ROW]
[ROW][C]80[/C][C]166836[/C][C]165886.329367489[/C][C]949.670632511086[/C][/ROW]
[ROW][C]81[/C][C]163541[/C][C]166835.932260723[/C][C]-3294.93226072285[/C][/ROW]
[ROW][C]82[/C][C]163973[/C][C]163541.235024989[/C][C]431.764975011378[/C][/ROW]
[ROW][C]83[/C][C]164805[/C][C]163972.969202536[/C][C]832.03079746422[/C][/ROW]
[ROW][C]84[/C][C]167521[/C][C]164804.940651882[/C][C]2716.05934811805[/C][/ROW]
[ROW][C]85[/C][C]174347[/C][C]167520.806265572[/C][C]6826.19373442818[/C][/ROW]
[ROW][C]86[/C][C]173374[/C][C]174346.513092841[/C][C]-972.513092841429[/C][/ROW]
[ROW][C]87[/C][C]172198[/C][C]173374.069368612[/C][C]-1176.06936861231[/C][/ROW]
[ROW][C]88[/C][C]171055[/C][C]172198.083888125[/C][C]-1143.08388812517[/C][/ROW]
[ROW][C]89[/C][C]168385[/C][C]171055.081535296[/C][C]-2670.08153529619[/C][/ROW]
[ROW][C]90[/C][C]167281[/C][C]168385.190454866[/C][C]-1104.1904548661[/C][/ROW]
[ROW][C]91[/C][C]177670[/C][C]167281.078761057[/C][C]10388.9212389425[/C][/ROW]
[ROW][C]92[/C][C]177280[/C][C]177669.258966224[/C][C]-389.258966223628[/C][/ROW]
[ROW][C]93[/C][C]174846[/C][C]177280.027765543[/C][C]-2434.02776554323[/C][/ROW]
[ROW][C]94[/C][C]174476[/C][C]174846.173617332[/C][C]-370.173617331922[/C][/ROW]
[ROW][C]95[/C][C]174595[/C][C]174476.0264042[/C][C]118.973595800053[/C][/ROW]
[ROW][C]96[/C][C]178392[/C][C]174594.991513705[/C][C]3797.00848629526[/C][/ROW]
[ROW][C]97[/C][C]185345[/C][C]178391.7291623[/C][C]6953.27083770034[/C][/ROW]
[ROW][C]98[/C][C]183293[/C][C]185344.504028529[/C][C]-2051.50402852919[/C][/ROW]
[ROW][C]99[/C][C]181081[/C][C]183293.146332207[/C][C]-2212.1463322074[/C][/ROW]
[ROW][C]100[/C][C]177795[/C][C]181081.1577907[/C][C]-3286.1577906996[/C][/ROW]
[ROW][C]101[/C][C]173552[/C][C]177795.234399112[/C][C]-4243.23439911241[/C][/ROW]
[ROW][C]102[/C][C]170734[/C][C]173552.302666652[/C][C]-2818.30266665213[/C][/ROW]
[ROW][C]103[/C][C]179293[/C][C]170734.201027366[/C][C]8558.79897263442[/C][/ROW]
[ROW][C]104[/C][C]178659[/C][C]179292.38950744[/C][C]-633.38950743989[/C][/ROW]
[ROW][C]105[/C][C]175894[/C][C]178659.045179187[/C][C]-2765.04517918732[/C][/ROW]
[ROW][C]106[/C][C]174815[/C][C]175894.19722855[/C][C]-1079.19722854989[/C][/ROW]
[ROW][C]107[/C][C]173506[/C][C]174815.07697831[/C][C]-1309.07697830981[/C][/ROW]
[ROW][C]108[/C][C]175376[/C][C]173506.093375456[/C][C]1869.90662454412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284528&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284528&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
2173690173019671
3172439173689.952138085-1250.95213808512
4171914172439.089229456-525.089229455654
5171968171914.03745421253.9625457883812
6169500171967.996150893-2467.99615089304
7173898169500.1760402714397.82395972926
8172308173897.686306593-1589.68630659318
9171568172308.113391104-740.113391103834
10164939171568.05279172-6629.05279171999
11161275164939.472845246-3664.47284524649
12160770161275.261384035-505.26138403482
13162466160770.0360399071695.96396009336
14160185162465.879028193-2280.87902819272
15154836160185.16269335-5349.16269335005
16154103154836.381551668-733.381551668339
17150495154103.052311543-3608.05231154306
18142707150495.257359601-7788.25735960147
19149962142707.5555304187254.44446958162
20149967149961.4825460455.51745395475882
21144572149966.999606444-5394.99960644424
22143819144572.38482118-753.384821180167
23141070143819.053738361-2749.05373836093
24144119141070.1960878933048.80391210731
25145330144118.7825311581211.21746884246
26143279145329.913604788-2050.91360478781
27139063143279.146290093-4216.14629009293
28139202139063.300734478138.699265521864
29133632139201.990106688-5569.99010668788
30134476133632.397303118843.602696881804
31141859134475.9398264677383.06017353272
32140693141858.473371986-1165.47337198583
33138047140693.083132321-2646.08313232087
34138346138047.188743078298.811256921588
35140167138345.9786860221821.02131397757
36146796140166.8701079486629.12989205233
37152228146795.5271492545432.47285074598
38155410152227.6125058823182.38749411789
39159032155409.7730027433622.22699725683
40160312159031.7416293291280.25837067093
41157687160311.908680153-2624.90868015328
42160141157687.1872327212453.81276727899
43167421160140.8249714197280.17502858091
44167628167420.480710704207.519289295771
45164403167627.985197808-3224.98519780842
46163405164403.230035718-998.230035718327
47163229163405.071202982-176.071202982101
48171154163229.0125590247924.98744097626
49173323171153.434716732169.56528327012
50172381173322.845246574-941.845246573939
51168983172381.067181098-3398.06718109836
52165380168983.242381523-3603.24238152333
53161641165380.257016513-3739.25701651286
54161933161641.266718332291.733281667664
55172018161932.97919088910085.020809111
56168455172017.280643208-3562.28064320801
57164332168455.254094744-4123.25409474352
58161193164332.294108549-3139.29410854913
59157645161193.223923439-3548.22392343869
60161694157645.2530920884048.74690791153
61163411161693.7112059911717.28879400869
62161834163410.877507109-1576.87750710867
63159511161834.112477462-2323.11247746198
64156359159511.16570583-3152.16570582954
65154223156359.22484156-2136.22484155989
66151497154223.152375278-2726.15237527795
67160607151497.1944543569109.80554564396
68159672160606.350204564-934.350204564049
69155601159672.066646483-4071.0666464828
70154668155601.290386059-933.290386058507
71153960154668.066570887-708.066570886731
72157307153960.0505058453346.94949415509
73165218157306.7612646627911.23873533795
74165616165217.435697415398.564302585495
75162212165615.971570714-3403.97157071426
76159787162212.242802679-2425.2428026789
77157454159787.172990707-2333.17299070724
78156485157454.166423438-969.166423438262
79165887156485.0691298979401.93087010304
80166836165886.329367489949.670632511086
81163541166835.932260723-3294.93226072285
82163973163541.235024989431.764975011378
83164805163972.969202536832.03079746422
84167521164804.9406518822716.05934811805
85174347167520.8062655726826.19373442818
86173374174346.513092841-972.513092841429
87172198173374.069368612-1176.06936861231
88171055172198.083888125-1143.08388812517
89168385171055.081535296-2670.08153529619
90167281168385.190454866-1104.1904548661
91177670167281.07876105710388.9212389425
92177280177669.258966224-389.258966223628
93174846177280.027765543-2434.02776554323
94174476174846.173617332-370.173617331922
95174595174476.0264042118.973595800053
96178392174594.9915137053797.00848629526
97185345178391.72916236953.27083770034
98183293185344.504028529-2051.50402852919
99181081183293.146332207-2212.1463322074
100177795181081.1577907-3286.1577906996
101173552177795.234399112-4243.23439911241
102170734173552.302666652-2818.30266665213
103179293170734.2010273668558.79897263442
104178659179292.38950744-633.38950743989
105175894178659.045179187-2765.04517918732
106174815175894.19722855-1079.19722854989
107173506174815.07697831-1309.07697830981
108175376173506.0933754561869.90662454412







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109175375.866620996167802.441601165182949.291640827
110175375.866620996164665.808221269186085.925020723
111175375.866620996162258.933468763188492.799773229
112175375.866620996160229.826883998190521.906357994
113175375.866620996158442.139798194192309.593443798
114175375.866620996156825.942402718193925.790839274
115175375.866620996155339.692512688195412.040729304
116175375.866620996153956.322804822196795.41043717
117175375.866620996152657.032106709198094.701135283
118175375.866620996151428.131319257199323.601922735
119175375.866620996150259.286231207200492.447010785
120175375.866620996149142.468158896201609.265083096

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 175375.866620996 & 167802.441601165 & 182949.291640827 \tabularnewline
110 & 175375.866620996 & 164665.808221269 & 186085.925020723 \tabularnewline
111 & 175375.866620996 & 162258.933468763 & 188492.799773229 \tabularnewline
112 & 175375.866620996 & 160229.826883998 & 190521.906357994 \tabularnewline
113 & 175375.866620996 & 158442.139798194 & 192309.593443798 \tabularnewline
114 & 175375.866620996 & 156825.942402718 & 193925.790839274 \tabularnewline
115 & 175375.866620996 & 155339.692512688 & 195412.040729304 \tabularnewline
116 & 175375.866620996 & 153956.322804822 & 196795.41043717 \tabularnewline
117 & 175375.866620996 & 152657.032106709 & 198094.701135283 \tabularnewline
118 & 175375.866620996 & 151428.131319257 & 199323.601922735 \tabularnewline
119 & 175375.866620996 & 150259.286231207 & 200492.447010785 \tabularnewline
120 & 175375.866620996 & 149142.468158896 & 201609.265083096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284528&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]175375.866620996[/C][C]167802.441601165[/C][C]182949.291640827[/C][/ROW]
[ROW][C]110[/C][C]175375.866620996[/C][C]164665.808221269[/C][C]186085.925020723[/C][/ROW]
[ROW][C]111[/C][C]175375.866620996[/C][C]162258.933468763[/C][C]188492.799773229[/C][/ROW]
[ROW][C]112[/C][C]175375.866620996[/C][C]160229.826883998[/C][C]190521.906357994[/C][/ROW]
[ROW][C]113[/C][C]175375.866620996[/C][C]158442.139798194[/C][C]192309.593443798[/C][/ROW]
[ROW][C]114[/C][C]175375.866620996[/C][C]156825.942402718[/C][C]193925.790839274[/C][/ROW]
[ROW][C]115[/C][C]175375.866620996[/C][C]155339.692512688[/C][C]195412.040729304[/C][/ROW]
[ROW][C]116[/C][C]175375.866620996[/C][C]153956.322804822[/C][C]196795.41043717[/C][/ROW]
[ROW][C]117[/C][C]175375.866620996[/C][C]152657.032106709[/C][C]198094.701135283[/C][/ROW]
[ROW][C]118[/C][C]175375.866620996[/C][C]151428.131319257[/C][C]199323.601922735[/C][/ROW]
[ROW][C]119[/C][C]175375.866620996[/C][C]150259.286231207[/C][C]200492.447010785[/C][/ROW]
[ROW][C]120[/C][C]175375.866620996[/C][C]149142.468158896[/C][C]201609.265083096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284528&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284528&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
109175375.866620996167802.441601165182949.291640827
110175375.866620996164665.808221269186085.925020723
111175375.866620996162258.933468763188492.799773229
112175375.866620996160229.826883998190521.906357994
113175375.866620996158442.139798194192309.593443798
114175375.866620996156825.942402718193925.790839274
115175375.866620996155339.692512688195412.040729304
116175375.866620996153956.322804822196795.41043717
117175375.866620996152657.032106709198094.701135283
118175375.866620996151428.131319257199323.601922735
119175375.866620996150259.286231207200492.447010785
120175375.866620996149142.468158896201609.265083096



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')