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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 01:54:10 +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/2011/May/20/t1305856259n2wxbz3hgkee2id.htm/, Retrieved Mon, 13 May 2024 20:00:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122351, Retrieved Mon, 13 May 2024 20:00:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2011-05-20 01:54:10] [118c7cedabc991c3d34fa0c13010a5e0] [Current]
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Dataseries X:
1394
1657
2411
3595
3336
3249
2920
2113
2040
1853
1832
2093
2164
2368
2072
2521
1819
1947
2226
1754
1787
2072
1846
2137
2467
2154
2289
2628
2074
2798
2194
2442
2565
2063
2069
2539
1898
2139
2408
2725
2201
2311
2548
2276
2351
2280
2057
2479
2379
2295
2456
2546
2844
2260
2981
2678
3440
2842
2450
2669
2570
2540
2318
2930
2947
2799
2695
2498
2260
2160
2058
2533
2150
2172
2155
3016
2333
2355
2825
2214
2360
2299
1746
2069
2267
1878
2266
2282
2085
2277
2251
1828
1954
1851
1570
1852
2187
1855
2218




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122351&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122351&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'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.71784635643899
beta0.0864815573358333
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.71784635643899 \tabularnewline
beta & 0.0864815573358333 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122351&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]0.71784635643899[/C][/ROW]
[ROW][C]beta[/C][C]0.0864815573358333[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122351&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
alpha0.71784635643899
beta0.0864815573358333
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
324111920491
435952565.94407219041029.0559278096
533363662.01390823092-326.013908230917
632493765.11270282839-516.112702828388
729203699.7092507663-779.709250766298
821133396.6792597969-1283.6792597969
920402652.184821244-612.184821244003
1018532351.71549683589-498.715496835888
1118322101.7392206666-269.739220666598
1220931999.3871922353793.6128077646267
1321642163.677620700220.322379299781915
1423682261.01986845966106.980131540341
1520722441.56737198673-369.567371986726
1625212257.08406997945263.915930020547
1718192543.72847337897-724.728473378966
1819472075.68660913111-128.686609131111
1922262027.52230013396198.477699866041
2017542226.53328736477-472.533287364767
2117871914.52639331768-127.526393317683
2220721842.26454256787229.735457432127
2318462040.72389503782-194.723895037816
2421371922.39809679443214.601903205567
2524672111.22791860914355.772081390862
2621542423.48273679387-269.482736793874
2722892270.1710467173318.8289532826734
2826282324.99176316607303.008236833929
2920742602.62043689636-528.620436896363
3027982250.45049166486547.549508335137
3121942704.7973518086-510.797351808599
3224422367.7032344491474.2967655508633
3325652455.22917559679109.770824403205
3420632575.03466510235-512.034665102354
3520692216.69199646037-147.691996460368
3625392110.72259631981428.277403680191
3718982444.79839435797-546.798394357972
3821392044.9740817502994.0259182497055
3924082111.00034034098296.999659659024
4027252341.16843836391383.83156163609
4122012657.49694491057-456.496944910566
4223112342.25914954715-31.2591495471515
4325482330.3361734838217.663826516204
4422762510.61432165484-234.614321654843
4523512351.6612815119-0.661281511903326
4622802360.60952614579-80.6095261457858
4720572307.16293732881-250.162937328812
4824792116.47281713804362.527182861963
4923792388.1059255541-9.10592555409949
5022952392.39826101583-97.3982610158287
5124562327.26373526272128.736264737282
5225462432.45106281467113.54893718533
5328442533.78539410243310.214605897574
5422602795.5537279052-535.553727905205
5529812416.94291731162564.057082688378
5626782862.70064987338-184.700649873379
5734402759.49906895291680.500931047085
5828423319.62510868295-477.625108682951
5924503018.74339886711-568.743398867108
6026692617.1448984529651.8551015470407
6125702664.25995949173-94.2599594917256
6225402600.63515367704-60.6351536770353
6323182557.38353331311-239.383533313106
6429302370.95699745038559.043002549622
6529472792.38369405492154.616305945082
6627992933.09281312672-134.092813126716
6726952858.22859802793-163.228598027926
6824982752.31605767688-254.316057676878
6922602565.22865569865-305.22865569865
7021602322.64509207625-162.645092076246
7120582172.31753619355-114.317536193551
7225332049.58485374552483.415146254479
7321502385.94303940445-235.943039404448
7421722191.26511753763-19.2651175376263
7521552150.932664836294.06733516370832
7630162127.60183037539888.398169624607
7723332794.2368399761-461.236839976103
7823552463.40747522134-108.407475221341
7928252379.12539729694445.874602703057
8022142720.41279471815-506.412794718154
8123602346.6658088859813.3341911140242
8222992346.84509596611-47.8450959661054
8317462300.13680864162-554.136808641618
8420691855.58778609156213.412213908442
8522671975.26976348825291.730236511749
8618782169.28279849302-291.282798493017
8722661926.69907728726339.300922712737
8822822157.84154381477124.158456185226
8920852242.25259004805-157.252590048055
9022772114.89142725125162.108572748754
9122512226.846288078524.1537119214959
9218282241.27022851631-413.270228516311
9319541916.0349767242237.965023275776
9418511917.07419284805-66.0741928480511
9515701839.32731974872-269.327319748723
9618521598.95596325081253.044036749194
9721871749.27607466581437.723925334192
9818552059.34207858859-204.342078588593
9922181895.81768855235322.182311447648

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2411 & 1920 & 491 \tabularnewline
4 & 3595 & 2565.9440721904 & 1029.0559278096 \tabularnewline
5 & 3336 & 3662.01390823092 & -326.013908230917 \tabularnewline
6 & 3249 & 3765.11270282839 & -516.112702828388 \tabularnewline
7 & 2920 & 3699.7092507663 & -779.709250766298 \tabularnewline
8 & 2113 & 3396.6792597969 & -1283.6792597969 \tabularnewline
9 & 2040 & 2652.184821244 & -612.184821244003 \tabularnewline
10 & 1853 & 2351.71549683589 & -498.715496835888 \tabularnewline
11 & 1832 & 2101.7392206666 & -269.739220666598 \tabularnewline
12 & 2093 & 1999.38719223537 & 93.6128077646267 \tabularnewline
13 & 2164 & 2163.67762070022 & 0.322379299781915 \tabularnewline
14 & 2368 & 2261.01986845966 & 106.980131540341 \tabularnewline
15 & 2072 & 2441.56737198673 & -369.567371986726 \tabularnewline
16 & 2521 & 2257.08406997945 & 263.915930020547 \tabularnewline
17 & 1819 & 2543.72847337897 & -724.728473378966 \tabularnewline
18 & 1947 & 2075.68660913111 & -128.686609131111 \tabularnewline
19 & 2226 & 2027.52230013396 & 198.477699866041 \tabularnewline
20 & 1754 & 2226.53328736477 & -472.533287364767 \tabularnewline
21 & 1787 & 1914.52639331768 & -127.526393317683 \tabularnewline
22 & 2072 & 1842.26454256787 & 229.735457432127 \tabularnewline
23 & 1846 & 2040.72389503782 & -194.723895037816 \tabularnewline
24 & 2137 & 1922.39809679443 & 214.601903205567 \tabularnewline
25 & 2467 & 2111.22791860914 & 355.772081390862 \tabularnewline
26 & 2154 & 2423.48273679387 & -269.482736793874 \tabularnewline
27 & 2289 & 2270.17104671733 & 18.8289532826734 \tabularnewline
28 & 2628 & 2324.99176316607 & 303.008236833929 \tabularnewline
29 & 2074 & 2602.62043689636 & -528.620436896363 \tabularnewline
30 & 2798 & 2250.45049166486 & 547.549508335137 \tabularnewline
31 & 2194 & 2704.7973518086 & -510.797351808599 \tabularnewline
32 & 2442 & 2367.70323444914 & 74.2967655508633 \tabularnewline
33 & 2565 & 2455.22917559679 & 109.770824403205 \tabularnewline
34 & 2063 & 2575.03466510235 & -512.034665102354 \tabularnewline
35 & 2069 & 2216.69199646037 & -147.691996460368 \tabularnewline
36 & 2539 & 2110.72259631981 & 428.277403680191 \tabularnewline
37 & 1898 & 2444.79839435797 & -546.798394357972 \tabularnewline
38 & 2139 & 2044.97408175029 & 94.0259182497055 \tabularnewline
39 & 2408 & 2111.00034034098 & 296.999659659024 \tabularnewline
40 & 2725 & 2341.16843836391 & 383.83156163609 \tabularnewline
41 & 2201 & 2657.49694491057 & -456.496944910566 \tabularnewline
42 & 2311 & 2342.25914954715 & -31.2591495471515 \tabularnewline
43 & 2548 & 2330.3361734838 & 217.663826516204 \tabularnewline
44 & 2276 & 2510.61432165484 & -234.614321654843 \tabularnewline
45 & 2351 & 2351.6612815119 & -0.661281511903326 \tabularnewline
46 & 2280 & 2360.60952614579 & -80.6095261457858 \tabularnewline
47 & 2057 & 2307.16293732881 & -250.162937328812 \tabularnewline
48 & 2479 & 2116.47281713804 & 362.527182861963 \tabularnewline
49 & 2379 & 2388.1059255541 & -9.10592555409949 \tabularnewline
50 & 2295 & 2392.39826101583 & -97.3982610158287 \tabularnewline
51 & 2456 & 2327.26373526272 & 128.736264737282 \tabularnewline
52 & 2546 & 2432.45106281467 & 113.54893718533 \tabularnewline
53 & 2844 & 2533.78539410243 & 310.214605897574 \tabularnewline
54 & 2260 & 2795.5537279052 & -535.553727905205 \tabularnewline
55 & 2981 & 2416.94291731162 & 564.057082688378 \tabularnewline
56 & 2678 & 2862.70064987338 & -184.700649873379 \tabularnewline
57 & 3440 & 2759.49906895291 & 680.500931047085 \tabularnewline
58 & 2842 & 3319.62510868295 & -477.625108682951 \tabularnewline
59 & 2450 & 3018.74339886711 & -568.743398867108 \tabularnewline
60 & 2669 & 2617.14489845296 & 51.8551015470407 \tabularnewline
61 & 2570 & 2664.25995949173 & -94.2599594917256 \tabularnewline
62 & 2540 & 2600.63515367704 & -60.6351536770353 \tabularnewline
63 & 2318 & 2557.38353331311 & -239.383533313106 \tabularnewline
64 & 2930 & 2370.95699745038 & 559.043002549622 \tabularnewline
65 & 2947 & 2792.38369405492 & 154.616305945082 \tabularnewline
66 & 2799 & 2933.09281312672 & -134.092813126716 \tabularnewline
67 & 2695 & 2858.22859802793 & -163.228598027926 \tabularnewline
68 & 2498 & 2752.31605767688 & -254.316057676878 \tabularnewline
69 & 2260 & 2565.22865569865 & -305.22865569865 \tabularnewline
70 & 2160 & 2322.64509207625 & -162.645092076246 \tabularnewline
71 & 2058 & 2172.31753619355 & -114.317536193551 \tabularnewline
72 & 2533 & 2049.58485374552 & 483.415146254479 \tabularnewline
73 & 2150 & 2385.94303940445 & -235.943039404448 \tabularnewline
74 & 2172 & 2191.26511753763 & -19.2651175376263 \tabularnewline
75 & 2155 & 2150.93266483629 & 4.06733516370832 \tabularnewline
76 & 3016 & 2127.60183037539 & 888.398169624607 \tabularnewline
77 & 2333 & 2794.2368399761 & -461.236839976103 \tabularnewline
78 & 2355 & 2463.40747522134 & -108.407475221341 \tabularnewline
79 & 2825 & 2379.12539729694 & 445.874602703057 \tabularnewline
80 & 2214 & 2720.41279471815 & -506.412794718154 \tabularnewline
81 & 2360 & 2346.66580888598 & 13.3341911140242 \tabularnewline
82 & 2299 & 2346.84509596611 & -47.8450959661054 \tabularnewline
83 & 1746 & 2300.13680864162 & -554.136808641618 \tabularnewline
84 & 2069 & 1855.58778609156 & 213.412213908442 \tabularnewline
85 & 2267 & 1975.26976348825 & 291.730236511749 \tabularnewline
86 & 1878 & 2169.28279849302 & -291.282798493017 \tabularnewline
87 & 2266 & 1926.69907728726 & 339.300922712737 \tabularnewline
88 & 2282 & 2157.84154381477 & 124.158456185226 \tabularnewline
89 & 2085 & 2242.25259004805 & -157.252590048055 \tabularnewline
90 & 2277 & 2114.89142725125 & 162.108572748754 \tabularnewline
91 & 2251 & 2226.8462880785 & 24.1537119214959 \tabularnewline
92 & 1828 & 2241.27022851631 & -413.270228516311 \tabularnewline
93 & 1954 & 1916.03497672422 & 37.965023275776 \tabularnewline
94 & 1851 & 1917.07419284805 & -66.0741928480511 \tabularnewline
95 & 1570 & 1839.32731974872 & -269.327319748723 \tabularnewline
96 & 1852 & 1598.95596325081 & 253.044036749194 \tabularnewline
97 & 2187 & 1749.27607466581 & 437.723925334192 \tabularnewline
98 & 1855 & 2059.34207858859 & -204.342078588593 \tabularnewline
99 & 2218 & 1895.81768855235 & 322.182311447648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122351&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]2411[/C][C]1920[/C][C]491[/C][/ROW]
[ROW][C]4[/C][C]3595[/C][C]2565.9440721904[/C][C]1029.0559278096[/C][/ROW]
[ROW][C]5[/C][C]3336[/C][C]3662.01390823092[/C][C]-326.013908230917[/C][/ROW]
[ROW][C]6[/C][C]3249[/C][C]3765.11270282839[/C][C]-516.112702828388[/C][/ROW]
[ROW][C]7[/C][C]2920[/C][C]3699.7092507663[/C][C]-779.709250766298[/C][/ROW]
[ROW][C]8[/C][C]2113[/C][C]3396.6792597969[/C][C]-1283.6792597969[/C][/ROW]
[ROW][C]9[/C][C]2040[/C][C]2652.184821244[/C][C]-612.184821244003[/C][/ROW]
[ROW][C]10[/C][C]1853[/C][C]2351.71549683589[/C][C]-498.715496835888[/C][/ROW]
[ROW][C]11[/C][C]1832[/C][C]2101.7392206666[/C][C]-269.739220666598[/C][/ROW]
[ROW][C]12[/C][C]2093[/C][C]1999.38719223537[/C][C]93.6128077646267[/C][/ROW]
[ROW][C]13[/C][C]2164[/C][C]2163.67762070022[/C][C]0.322379299781915[/C][/ROW]
[ROW][C]14[/C][C]2368[/C][C]2261.01986845966[/C][C]106.980131540341[/C][/ROW]
[ROW][C]15[/C][C]2072[/C][C]2441.56737198673[/C][C]-369.567371986726[/C][/ROW]
[ROW][C]16[/C][C]2521[/C][C]2257.08406997945[/C][C]263.915930020547[/C][/ROW]
[ROW][C]17[/C][C]1819[/C][C]2543.72847337897[/C][C]-724.728473378966[/C][/ROW]
[ROW][C]18[/C][C]1947[/C][C]2075.68660913111[/C][C]-128.686609131111[/C][/ROW]
[ROW][C]19[/C][C]2226[/C][C]2027.52230013396[/C][C]198.477699866041[/C][/ROW]
[ROW][C]20[/C][C]1754[/C][C]2226.53328736477[/C][C]-472.533287364767[/C][/ROW]
[ROW][C]21[/C][C]1787[/C][C]1914.52639331768[/C][C]-127.526393317683[/C][/ROW]
[ROW][C]22[/C][C]2072[/C][C]1842.26454256787[/C][C]229.735457432127[/C][/ROW]
[ROW][C]23[/C][C]1846[/C][C]2040.72389503782[/C][C]-194.723895037816[/C][/ROW]
[ROW][C]24[/C][C]2137[/C][C]1922.39809679443[/C][C]214.601903205567[/C][/ROW]
[ROW][C]25[/C][C]2467[/C][C]2111.22791860914[/C][C]355.772081390862[/C][/ROW]
[ROW][C]26[/C][C]2154[/C][C]2423.48273679387[/C][C]-269.482736793874[/C][/ROW]
[ROW][C]27[/C][C]2289[/C][C]2270.17104671733[/C][C]18.8289532826734[/C][/ROW]
[ROW][C]28[/C][C]2628[/C][C]2324.99176316607[/C][C]303.008236833929[/C][/ROW]
[ROW][C]29[/C][C]2074[/C][C]2602.62043689636[/C][C]-528.620436896363[/C][/ROW]
[ROW][C]30[/C][C]2798[/C][C]2250.45049166486[/C][C]547.549508335137[/C][/ROW]
[ROW][C]31[/C][C]2194[/C][C]2704.7973518086[/C][C]-510.797351808599[/C][/ROW]
[ROW][C]32[/C][C]2442[/C][C]2367.70323444914[/C][C]74.2967655508633[/C][/ROW]
[ROW][C]33[/C][C]2565[/C][C]2455.22917559679[/C][C]109.770824403205[/C][/ROW]
[ROW][C]34[/C][C]2063[/C][C]2575.03466510235[/C][C]-512.034665102354[/C][/ROW]
[ROW][C]35[/C][C]2069[/C][C]2216.69199646037[/C][C]-147.691996460368[/C][/ROW]
[ROW][C]36[/C][C]2539[/C][C]2110.72259631981[/C][C]428.277403680191[/C][/ROW]
[ROW][C]37[/C][C]1898[/C][C]2444.79839435797[/C][C]-546.798394357972[/C][/ROW]
[ROW][C]38[/C][C]2139[/C][C]2044.97408175029[/C][C]94.0259182497055[/C][/ROW]
[ROW][C]39[/C][C]2408[/C][C]2111.00034034098[/C][C]296.999659659024[/C][/ROW]
[ROW][C]40[/C][C]2725[/C][C]2341.16843836391[/C][C]383.83156163609[/C][/ROW]
[ROW][C]41[/C][C]2201[/C][C]2657.49694491057[/C][C]-456.496944910566[/C][/ROW]
[ROW][C]42[/C][C]2311[/C][C]2342.25914954715[/C][C]-31.2591495471515[/C][/ROW]
[ROW][C]43[/C][C]2548[/C][C]2330.3361734838[/C][C]217.663826516204[/C][/ROW]
[ROW][C]44[/C][C]2276[/C][C]2510.61432165484[/C][C]-234.614321654843[/C][/ROW]
[ROW][C]45[/C][C]2351[/C][C]2351.6612815119[/C][C]-0.661281511903326[/C][/ROW]
[ROW][C]46[/C][C]2280[/C][C]2360.60952614579[/C][C]-80.6095261457858[/C][/ROW]
[ROW][C]47[/C][C]2057[/C][C]2307.16293732881[/C][C]-250.162937328812[/C][/ROW]
[ROW][C]48[/C][C]2479[/C][C]2116.47281713804[/C][C]362.527182861963[/C][/ROW]
[ROW][C]49[/C][C]2379[/C][C]2388.1059255541[/C][C]-9.10592555409949[/C][/ROW]
[ROW][C]50[/C][C]2295[/C][C]2392.39826101583[/C][C]-97.3982610158287[/C][/ROW]
[ROW][C]51[/C][C]2456[/C][C]2327.26373526272[/C][C]128.736264737282[/C][/ROW]
[ROW][C]52[/C][C]2546[/C][C]2432.45106281467[/C][C]113.54893718533[/C][/ROW]
[ROW][C]53[/C][C]2844[/C][C]2533.78539410243[/C][C]310.214605897574[/C][/ROW]
[ROW][C]54[/C][C]2260[/C][C]2795.5537279052[/C][C]-535.553727905205[/C][/ROW]
[ROW][C]55[/C][C]2981[/C][C]2416.94291731162[/C][C]564.057082688378[/C][/ROW]
[ROW][C]56[/C][C]2678[/C][C]2862.70064987338[/C][C]-184.700649873379[/C][/ROW]
[ROW][C]57[/C][C]3440[/C][C]2759.49906895291[/C][C]680.500931047085[/C][/ROW]
[ROW][C]58[/C][C]2842[/C][C]3319.62510868295[/C][C]-477.625108682951[/C][/ROW]
[ROW][C]59[/C][C]2450[/C][C]3018.74339886711[/C][C]-568.743398867108[/C][/ROW]
[ROW][C]60[/C][C]2669[/C][C]2617.14489845296[/C][C]51.8551015470407[/C][/ROW]
[ROW][C]61[/C][C]2570[/C][C]2664.25995949173[/C][C]-94.2599594917256[/C][/ROW]
[ROW][C]62[/C][C]2540[/C][C]2600.63515367704[/C][C]-60.6351536770353[/C][/ROW]
[ROW][C]63[/C][C]2318[/C][C]2557.38353331311[/C][C]-239.383533313106[/C][/ROW]
[ROW][C]64[/C][C]2930[/C][C]2370.95699745038[/C][C]559.043002549622[/C][/ROW]
[ROW][C]65[/C][C]2947[/C][C]2792.38369405492[/C][C]154.616305945082[/C][/ROW]
[ROW][C]66[/C][C]2799[/C][C]2933.09281312672[/C][C]-134.092813126716[/C][/ROW]
[ROW][C]67[/C][C]2695[/C][C]2858.22859802793[/C][C]-163.228598027926[/C][/ROW]
[ROW][C]68[/C][C]2498[/C][C]2752.31605767688[/C][C]-254.316057676878[/C][/ROW]
[ROW][C]69[/C][C]2260[/C][C]2565.22865569865[/C][C]-305.22865569865[/C][/ROW]
[ROW][C]70[/C][C]2160[/C][C]2322.64509207625[/C][C]-162.645092076246[/C][/ROW]
[ROW][C]71[/C][C]2058[/C][C]2172.31753619355[/C][C]-114.317536193551[/C][/ROW]
[ROW][C]72[/C][C]2533[/C][C]2049.58485374552[/C][C]483.415146254479[/C][/ROW]
[ROW][C]73[/C][C]2150[/C][C]2385.94303940445[/C][C]-235.943039404448[/C][/ROW]
[ROW][C]74[/C][C]2172[/C][C]2191.26511753763[/C][C]-19.2651175376263[/C][/ROW]
[ROW][C]75[/C][C]2155[/C][C]2150.93266483629[/C][C]4.06733516370832[/C][/ROW]
[ROW][C]76[/C][C]3016[/C][C]2127.60183037539[/C][C]888.398169624607[/C][/ROW]
[ROW][C]77[/C][C]2333[/C][C]2794.2368399761[/C][C]-461.236839976103[/C][/ROW]
[ROW][C]78[/C][C]2355[/C][C]2463.40747522134[/C][C]-108.407475221341[/C][/ROW]
[ROW][C]79[/C][C]2825[/C][C]2379.12539729694[/C][C]445.874602703057[/C][/ROW]
[ROW][C]80[/C][C]2214[/C][C]2720.41279471815[/C][C]-506.412794718154[/C][/ROW]
[ROW][C]81[/C][C]2360[/C][C]2346.66580888598[/C][C]13.3341911140242[/C][/ROW]
[ROW][C]82[/C][C]2299[/C][C]2346.84509596611[/C][C]-47.8450959661054[/C][/ROW]
[ROW][C]83[/C][C]1746[/C][C]2300.13680864162[/C][C]-554.136808641618[/C][/ROW]
[ROW][C]84[/C][C]2069[/C][C]1855.58778609156[/C][C]213.412213908442[/C][/ROW]
[ROW][C]85[/C][C]2267[/C][C]1975.26976348825[/C][C]291.730236511749[/C][/ROW]
[ROW][C]86[/C][C]1878[/C][C]2169.28279849302[/C][C]-291.282798493017[/C][/ROW]
[ROW][C]87[/C][C]2266[/C][C]1926.69907728726[/C][C]339.300922712737[/C][/ROW]
[ROW][C]88[/C][C]2282[/C][C]2157.84154381477[/C][C]124.158456185226[/C][/ROW]
[ROW][C]89[/C][C]2085[/C][C]2242.25259004805[/C][C]-157.252590048055[/C][/ROW]
[ROW][C]90[/C][C]2277[/C][C]2114.89142725125[/C][C]162.108572748754[/C][/ROW]
[ROW][C]91[/C][C]2251[/C][C]2226.8462880785[/C][C]24.1537119214959[/C][/ROW]
[ROW][C]92[/C][C]1828[/C][C]2241.27022851631[/C][C]-413.270228516311[/C][/ROW]
[ROW][C]93[/C][C]1954[/C][C]1916.03497672422[/C][C]37.965023275776[/C][/ROW]
[ROW][C]94[/C][C]1851[/C][C]1917.07419284805[/C][C]-66.0741928480511[/C][/ROW]
[ROW][C]95[/C][C]1570[/C][C]1839.32731974872[/C][C]-269.327319748723[/C][/ROW]
[ROW][C]96[/C][C]1852[/C][C]1598.95596325081[/C][C]253.044036749194[/C][/ROW]
[ROW][C]97[/C][C]2187[/C][C]1749.27607466581[/C][C]437.723925334192[/C][/ROW]
[ROW][C]98[/C][C]1855[/C][C]2059.34207858859[/C][C]-204.342078588593[/C][/ROW]
[ROW][C]99[/C][C]2218[/C][C]1895.81768855235[/C][C]322.182311447648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122351&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122351&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
324111920491
435952565.94407219041029.0559278096
533363662.01390823092-326.013908230917
632493765.11270282839-516.112702828388
729203699.7092507663-779.709250766298
821133396.6792597969-1283.6792597969
920402652.184821244-612.184821244003
1018532351.71549683589-498.715496835888
1118322101.7392206666-269.739220666598
1220931999.3871922353793.6128077646267
1321642163.677620700220.322379299781915
1423682261.01986845966106.980131540341
1520722441.56737198673-369.567371986726
1625212257.08406997945263.915930020547
1718192543.72847337897-724.728473378966
1819472075.68660913111-128.686609131111
1922262027.52230013396198.477699866041
2017542226.53328736477-472.533287364767
2117871914.52639331768-127.526393317683
2220721842.26454256787229.735457432127
2318462040.72389503782-194.723895037816
2421371922.39809679443214.601903205567
2524672111.22791860914355.772081390862
2621542423.48273679387-269.482736793874
2722892270.1710467173318.8289532826734
2826282324.99176316607303.008236833929
2920742602.62043689636-528.620436896363
3027982250.45049166486547.549508335137
3121942704.7973518086-510.797351808599
3224422367.7032344491474.2967655508633
3325652455.22917559679109.770824403205
3420632575.03466510235-512.034665102354
3520692216.69199646037-147.691996460368
3625392110.72259631981428.277403680191
3718982444.79839435797-546.798394357972
3821392044.9740817502994.0259182497055
3924082111.00034034098296.999659659024
4027252341.16843836391383.83156163609
4122012657.49694491057-456.496944910566
4223112342.25914954715-31.2591495471515
4325482330.3361734838217.663826516204
4422762510.61432165484-234.614321654843
4523512351.6612815119-0.661281511903326
4622802360.60952614579-80.6095261457858
4720572307.16293732881-250.162937328812
4824792116.47281713804362.527182861963
4923792388.1059255541-9.10592555409949
5022952392.39826101583-97.3982610158287
5124562327.26373526272128.736264737282
5225462432.45106281467113.54893718533
5328442533.78539410243310.214605897574
5422602795.5537279052-535.553727905205
5529812416.94291731162564.057082688378
5626782862.70064987338-184.700649873379
5734402759.49906895291680.500931047085
5828423319.62510868295-477.625108682951
5924503018.74339886711-568.743398867108
6026692617.1448984529651.8551015470407
6125702664.25995949173-94.2599594917256
6225402600.63515367704-60.6351536770353
6323182557.38353331311-239.383533313106
6429302370.95699745038559.043002549622
6529472792.38369405492154.616305945082
6627992933.09281312672-134.092813126716
6726952858.22859802793-163.228598027926
6824982752.31605767688-254.316057676878
6922602565.22865569865-305.22865569865
7021602322.64509207625-162.645092076246
7120582172.31753619355-114.317536193551
7225332049.58485374552483.415146254479
7321502385.94303940445-235.943039404448
7421722191.26511753763-19.2651175376263
7521552150.932664836294.06733516370832
7630162127.60183037539888.398169624607
7723332794.2368399761-461.236839976103
7823552463.40747522134-108.407475221341
7928252379.12539729694445.874602703057
8022142720.41279471815-506.412794718154
8123602346.6658088859813.3341911140242
8222992346.84509596611-47.8450959661054
8317462300.13680864162-554.136808641618
8420691855.58778609156213.412213908442
8522671975.26976348825291.730236511749
8618782169.28279849302-291.282798493017
8722661926.69907728726339.300922712737
8822822157.84154381477124.158456185226
8920852242.25259004805-157.252590048055
9022772114.89142725125162.108572748754
9122512226.846288078524.1537119214959
9218282241.27022851631-413.270228516311
9319541916.0349767242237.965023275776
9418511917.07419284805-66.0741928480511
9515701839.32731974872-269.327319748723
9618521598.95596325081253.044036749194
9721871749.27607466581437.723925334192
9818552059.34207858859-204.342078588593
9922181895.81768855235322.182311447648







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1002130.258143068521385.631211309672874.88507482738
1012133.421199202911189.098648137123077.7437502687
1022136.58425533731003.071730185133270.09678048947
1032139.74731147169821.392354527163458.10226841621
1042142.91036760607641.0294281688943644.79130704326
1052146.07342374046460.2845377189643831.86230976196
1062149.23647987485278.1279686467764020.34499110292
1072152.3995360092493.90278686496054210.89628515351
1082155.56259214362-92.82425555387544403.94943984112
1092158.72564827801-282.3447204532994599.79601700932
1102161.8887044124-474.8566536298894798.63406245469
1112165.05176054679-670.4943708714555000.59789196503

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
100 & 2130.25814306852 & 1385.63121130967 & 2874.88507482738 \tabularnewline
101 & 2133.42119920291 & 1189.09864813712 & 3077.7437502687 \tabularnewline
102 & 2136.5842553373 & 1003.07173018513 & 3270.09678048947 \tabularnewline
103 & 2139.74731147169 & 821.39235452716 & 3458.10226841621 \tabularnewline
104 & 2142.91036760607 & 641.029428168894 & 3644.79130704326 \tabularnewline
105 & 2146.07342374046 & 460.284537718964 & 3831.86230976196 \tabularnewline
106 & 2149.23647987485 & 278.127968646776 & 4020.34499110292 \tabularnewline
107 & 2152.39953600924 & 93.9027868649605 & 4210.89628515351 \tabularnewline
108 & 2155.56259214362 & -92.8242555538754 & 4403.94943984112 \tabularnewline
109 & 2158.72564827801 & -282.344720453299 & 4599.79601700932 \tabularnewline
110 & 2161.8887044124 & -474.856653629889 & 4798.63406245469 \tabularnewline
111 & 2165.05176054679 & -670.494370871455 & 5000.59789196503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122351&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]100[/C][C]2130.25814306852[/C][C]1385.63121130967[/C][C]2874.88507482738[/C][/ROW]
[ROW][C]101[/C][C]2133.42119920291[/C][C]1189.09864813712[/C][C]3077.7437502687[/C][/ROW]
[ROW][C]102[/C][C]2136.5842553373[/C][C]1003.07173018513[/C][C]3270.09678048947[/C][/ROW]
[ROW][C]103[/C][C]2139.74731147169[/C][C]821.39235452716[/C][C]3458.10226841621[/C][/ROW]
[ROW][C]104[/C][C]2142.91036760607[/C][C]641.029428168894[/C][C]3644.79130704326[/C][/ROW]
[ROW][C]105[/C][C]2146.07342374046[/C][C]460.284537718964[/C][C]3831.86230976196[/C][/ROW]
[ROW][C]106[/C][C]2149.23647987485[/C][C]278.127968646776[/C][C]4020.34499110292[/C][/ROW]
[ROW][C]107[/C][C]2152.39953600924[/C][C]93.9027868649605[/C][C]4210.89628515351[/C][/ROW]
[ROW][C]108[/C][C]2155.56259214362[/C][C]-92.8242555538754[/C][C]4403.94943984112[/C][/ROW]
[ROW][C]109[/C][C]2158.72564827801[/C][C]-282.344720453299[/C][C]4599.79601700932[/C][/ROW]
[ROW][C]110[/C][C]2161.8887044124[/C][C]-474.856653629889[/C][C]4798.63406245469[/C][/ROW]
[ROW][C]111[/C][C]2165.05176054679[/C][C]-670.494370871455[/C][C]5000.59789196503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122351&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122351&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
1002130.258143068521385.631211309672874.88507482738
1012133.421199202911189.098648137123077.7437502687
1022136.58425533731003.071730185133270.09678048947
1032139.74731147169821.392354527163458.10226841621
1042142.91036760607641.0294281688943644.79130704326
1052146.07342374046460.2845377189643831.86230976196
1062149.23647987485278.1279686467764020.34499110292
1072152.3995360092493.90278686496054210.89628515351
1082155.56259214362-92.82425555387544403.94943984112
1092158.72564827801-282.3447204532994599.79601700932
1102161.8887044124-474.8566536298894798.63406245469
1112165.05176054679-670.4943708714555000.59789196503



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