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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Jan 2012 14:53:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/15/t1326657264q9tdysntplpc7ye.htm/, Retrieved Fri, 03 May 2024 07:00:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161125, Retrieved Fri, 03 May 2024 07:00:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [opgave 7 oef 1] [2011-11-28 10:10:48] [0f3802131247472a006387bf3e5d274d]
- RMPD    [Exponential Smoothing] [opgave 10 oef 2] [2012-01-15 19:53:23] [9bda411d6223d16f0472c7feaae49b5f] [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 time13 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 13 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161125&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]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161125&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 time13 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.717846356438993
beta0.0864815573358173
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.717846356438993 \tabularnewline
beta & 0.0864815573358173 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161125&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]0.717846356438993[/C][/ROW]
[ROW][C]beta[/C][C]0.0864815573358173[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161125&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
alpha0.717846356438993
beta0.0864815573358173
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
324111920491
435952565.944072190391029.05592780961
533363662.0139082309-326.013908230903
632493765.11270282837-516.112702828371
729203699.70925076629-779.709250766286
821133396.6792597969-1283.6792597969
920402652.18482124402-612.184821244016
1018532351.71549683591-498.715496835915
1118322101.73922066663-269.739220666632
1220931999.3871922354193.6128077645888
1321642163.677620700250.32237929974508
1423682261.01986845969106.980131540307
1520722441.56737198676-369.567371986756
1625212257.08406997948263.915930020517
1718192543.72847337899-724.728473378993
1819472075.68660913114-128.686609131141
1922262027.52230013399198.477699866009
2017542226.5332873648-472.533287364796
2117871914.52639331771-127.526393317713
2220721842.2645425679229.735457432096
2318462040.72389503784-194.723895037844
2421371922.39809679446214.601903205541
2524672111.22791860916355.772081390839
2621542423.48273679389-269.482736793891
2722892270.1710467173418.8289532826584
2826282324.99176316609303.008236833914
2920742602.62043689637-528.620436896374
3027982250.45049166487547.549508335125
3121942704.79735180861-510.797351808608
3224422367.7032344491574.2967655508528
3325652455.22917559681109.770824403194
3420632575.03466510236-512.034665102363
3520692216.69199646038-147.69199646038
3625392110.72259631982428.277403680176
3718982444.79839435798-546.798394357984
3821392044.9740817503194.0259182496925
3924082111.00034034099296.99965965901
4027252341.16843836392383.83156163608
4122012657.49694491057-456.496944910571
4223112342.25914954716-31.259149547157
4325482330.3361734838217.663826516197
4422762510.61432165485-234.614321654848
4523512351.66128151191-0.661281511909237
4622802360.60952614579-80.6095261457922
4720572307.16293732882-250.162937328818
4824792116.47281713805362.527182861954
4923792388.10592555411-9.1059255541054
5022952392.39826101583-97.3982610158332
5124562327.26373526272128.736264737277
5225462432.45106281467113.548937185326
5328442533.78539410243310.214605897573
5422602795.5537279052-535.553727905203
5529812416.94291731162564.057082688377
5626782862.70064987338-184.700649873377
5734402759.49906895291680.500931047088
5828423319.62510868294-477.625108682944
5924503018.7433988671-568.743398867102
6026692617.1448984529651.8551015470407
6125702664.25995949173-94.2599594917288
6225402600.63515367704-60.6351536770403
6323182557.38353331311-239.383533313111
6429302370.95699745039559.043002549615
6529472792.38369405492154.616305945078
6627992933.09281312672-134.092813126716
6726952858.22859802792-163.228598027925
6824982752.31605767688-254.316057676878
6922602565.22865569865-305.228655698653
7021602322.64509207625-162.645092076254
7120582172.31753619356-114.317536193561
7225332049.58485374553483.415146254467
7321502385.94303940446-235.943039404456
7421722191.26511753763-19.2651175376332
7521552150.93266483634.0673351637015
7630162127.6018303754888.398169624601
7723332794.2368399761-461.236839976102
7823552463.40747522134-108.407475221339
7928252379.12539729694445.874602703057
8022142720.41279471815-506.412794718151
8123602346.6658088859713.3341911140251
8222992346.84509596611-47.8450959661072
8317462300.13680864162-554.13680864162
8420691855.58778609156213.412213908435
8522671975.26976348826291.730236511742
8618782169.28279849302-291.282798493022
8722661926.69907728727339.300922712732
8822822157.84154381478124.158456185222
8920852242.25259004805-157.252590048054
9022772114.89142725125162.108572748754
9122512226.846288078524.1537119214963
9218282241.27022851631-413.27022851631
9319541916.0349767242337.9650232757745
9418511917.07419284805-66.0741928480543
9515701839.32731974873-269.327319748727
9618521598.95596325081253.044036749187
9721871749.27607466581437.723925334186
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 & 2565.94407219039 & 1029.05592780961 \tabularnewline
5 & 3336 & 3662.0139082309 & -326.013908230903 \tabularnewline
6 & 3249 & 3765.11270282837 & -516.112702828371 \tabularnewline
7 & 2920 & 3699.70925076629 & -779.709250766286 \tabularnewline
8 & 2113 & 3396.6792597969 & -1283.6792597969 \tabularnewline
9 & 2040 & 2652.18482124402 & -612.184821244016 \tabularnewline
10 & 1853 & 2351.71549683591 & -498.715496835915 \tabularnewline
11 & 1832 & 2101.73922066663 & -269.739220666632 \tabularnewline
12 & 2093 & 1999.38719223541 & 93.6128077645888 \tabularnewline
13 & 2164 & 2163.67762070025 & 0.32237929974508 \tabularnewline
14 & 2368 & 2261.01986845969 & 106.980131540307 \tabularnewline
15 & 2072 & 2441.56737198676 & -369.567371986756 \tabularnewline
16 & 2521 & 2257.08406997948 & 263.915930020517 \tabularnewline
17 & 1819 & 2543.72847337899 & -724.728473378993 \tabularnewline
18 & 1947 & 2075.68660913114 & -128.686609131141 \tabularnewline
19 & 2226 & 2027.52230013399 & 198.477699866009 \tabularnewline
20 & 1754 & 2226.5332873648 & -472.533287364796 \tabularnewline
21 & 1787 & 1914.52639331771 & -127.526393317713 \tabularnewline
22 & 2072 & 1842.2645425679 & 229.735457432096 \tabularnewline
23 & 1846 & 2040.72389503784 & -194.723895037844 \tabularnewline
24 & 2137 & 1922.39809679446 & 214.601903205541 \tabularnewline
25 & 2467 & 2111.22791860916 & 355.772081390839 \tabularnewline
26 & 2154 & 2423.48273679389 & -269.482736793891 \tabularnewline
27 & 2289 & 2270.17104671734 & 18.8289532826584 \tabularnewline
28 & 2628 & 2324.99176316609 & 303.008236833914 \tabularnewline
29 & 2074 & 2602.62043689637 & -528.620436896374 \tabularnewline
30 & 2798 & 2250.45049166487 & 547.549508335125 \tabularnewline
31 & 2194 & 2704.79735180861 & -510.797351808608 \tabularnewline
32 & 2442 & 2367.70323444915 & 74.2967655508528 \tabularnewline
33 & 2565 & 2455.22917559681 & 109.770824403194 \tabularnewline
34 & 2063 & 2575.03466510236 & -512.034665102363 \tabularnewline
35 & 2069 & 2216.69199646038 & -147.69199646038 \tabularnewline
36 & 2539 & 2110.72259631982 & 428.277403680176 \tabularnewline
37 & 1898 & 2444.79839435798 & -546.798394357984 \tabularnewline
38 & 2139 & 2044.97408175031 & 94.0259182496925 \tabularnewline
39 & 2408 & 2111.00034034099 & 296.99965965901 \tabularnewline
40 & 2725 & 2341.16843836392 & 383.83156163608 \tabularnewline
41 & 2201 & 2657.49694491057 & -456.496944910571 \tabularnewline
42 & 2311 & 2342.25914954716 & -31.259149547157 \tabularnewline
43 & 2548 & 2330.3361734838 & 217.663826516197 \tabularnewline
44 & 2276 & 2510.61432165485 & -234.614321654848 \tabularnewline
45 & 2351 & 2351.66128151191 & -0.661281511909237 \tabularnewline
46 & 2280 & 2360.60952614579 & -80.6095261457922 \tabularnewline
47 & 2057 & 2307.16293732882 & -250.162937328818 \tabularnewline
48 & 2479 & 2116.47281713805 & 362.527182861954 \tabularnewline
49 & 2379 & 2388.10592555411 & -9.1059255541054 \tabularnewline
50 & 2295 & 2392.39826101583 & -97.3982610158332 \tabularnewline
51 & 2456 & 2327.26373526272 & 128.736264737277 \tabularnewline
52 & 2546 & 2432.45106281467 & 113.548937185326 \tabularnewline
53 & 2844 & 2533.78539410243 & 310.214605897573 \tabularnewline
54 & 2260 & 2795.5537279052 & -535.553727905203 \tabularnewline
55 & 2981 & 2416.94291731162 & 564.057082688377 \tabularnewline
56 & 2678 & 2862.70064987338 & -184.700649873377 \tabularnewline
57 & 3440 & 2759.49906895291 & 680.500931047088 \tabularnewline
58 & 2842 & 3319.62510868294 & -477.625108682944 \tabularnewline
59 & 2450 & 3018.7433988671 & -568.743398867102 \tabularnewline
60 & 2669 & 2617.14489845296 & 51.8551015470407 \tabularnewline
61 & 2570 & 2664.25995949173 & -94.2599594917288 \tabularnewline
62 & 2540 & 2600.63515367704 & -60.6351536770403 \tabularnewline
63 & 2318 & 2557.38353331311 & -239.383533313111 \tabularnewline
64 & 2930 & 2370.95699745039 & 559.043002549615 \tabularnewline
65 & 2947 & 2792.38369405492 & 154.616305945078 \tabularnewline
66 & 2799 & 2933.09281312672 & -134.092813126716 \tabularnewline
67 & 2695 & 2858.22859802792 & -163.228598027925 \tabularnewline
68 & 2498 & 2752.31605767688 & -254.316057676878 \tabularnewline
69 & 2260 & 2565.22865569865 & -305.228655698653 \tabularnewline
70 & 2160 & 2322.64509207625 & -162.645092076254 \tabularnewline
71 & 2058 & 2172.31753619356 & -114.317536193561 \tabularnewline
72 & 2533 & 2049.58485374553 & 483.415146254467 \tabularnewline
73 & 2150 & 2385.94303940446 & -235.943039404456 \tabularnewline
74 & 2172 & 2191.26511753763 & -19.2651175376332 \tabularnewline
75 & 2155 & 2150.9326648363 & 4.0673351637015 \tabularnewline
76 & 3016 & 2127.6018303754 & 888.398169624601 \tabularnewline
77 & 2333 & 2794.2368399761 & -461.236839976102 \tabularnewline
78 & 2355 & 2463.40747522134 & -108.407475221339 \tabularnewline
79 & 2825 & 2379.12539729694 & 445.874602703057 \tabularnewline
80 & 2214 & 2720.41279471815 & -506.412794718151 \tabularnewline
81 & 2360 & 2346.66580888597 & 13.3341911140251 \tabularnewline
82 & 2299 & 2346.84509596611 & -47.8450959661072 \tabularnewline
83 & 1746 & 2300.13680864162 & -554.13680864162 \tabularnewline
84 & 2069 & 1855.58778609156 & 213.412213908435 \tabularnewline
85 & 2267 & 1975.26976348826 & 291.730236511742 \tabularnewline
86 & 1878 & 2169.28279849302 & -291.282798493022 \tabularnewline
87 & 2266 & 1926.69907728727 & 339.300922712732 \tabularnewline
88 & 2282 & 2157.84154381478 & 124.158456185222 \tabularnewline
89 & 2085 & 2242.25259004805 & -157.252590048054 \tabularnewline
90 & 2277 & 2114.89142725125 & 162.108572748754 \tabularnewline
91 & 2251 & 2226.8462880785 & 24.1537119214963 \tabularnewline
92 & 1828 & 2241.27022851631 & -413.27022851631 \tabularnewline
93 & 1954 & 1916.03497672423 & 37.9650232757745 \tabularnewline
94 & 1851 & 1917.07419284805 & -66.0741928480543 \tabularnewline
95 & 1570 & 1839.32731974873 & -269.327319748727 \tabularnewline
96 & 1852 & 1598.95596325081 & 253.044036749187 \tabularnewline
97 & 2187 & 1749.27607466581 & 437.723925334186 \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=161125&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]2565.94407219039[/C][C]1029.05592780961[/C][/ROW]
[ROW][C]5[/C][C]3336[/C][C]3662.0139082309[/C][C]-326.013908230903[/C][/ROW]
[ROW][C]6[/C][C]3249[/C][C]3765.11270282837[/C][C]-516.112702828371[/C][/ROW]
[ROW][C]7[/C][C]2920[/C][C]3699.70925076629[/C][C]-779.709250766286[/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]2652.18482124402[/C][C]-612.184821244016[/C][/ROW]
[ROW][C]10[/C][C]1853[/C][C]2351.71549683591[/C][C]-498.715496835915[/C][/ROW]
[ROW][C]11[/C][C]1832[/C][C]2101.73922066663[/C][C]-269.739220666632[/C][/ROW]
[ROW][C]12[/C][C]2093[/C][C]1999.38719223541[/C][C]93.6128077645888[/C][/ROW]
[ROW][C]13[/C][C]2164[/C][C]2163.67762070025[/C][C]0.32237929974508[/C][/ROW]
[ROW][C]14[/C][C]2368[/C][C]2261.01986845969[/C][C]106.980131540307[/C][/ROW]
[ROW][C]15[/C][C]2072[/C][C]2441.56737198676[/C][C]-369.567371986756[/C][/ROW]
[ROW][C]16[/C][C]2521[/C][C]2257.08406997948[/C][C]263.915930020517[/C][/ROW]
[ROW][C]17[/C][C]1819[/C][C]2543.72847337899[/C][C]-724.728473378993[/C][/ROW]
[ROW][C]18[/C][C]1947[/C][C]2075.68660913114[/C][C]-128.686609131141[/C][/ROW]
[ROW][C]19[/C][C]2226[/C][C]2027.52230013399[/C][C]198.477699866009[/C][/ROW]
[ROW][C]20[/C][C]1754[/C][C]2226.5332873648[/C][C]-472.533287364796[/C][/ROW]
[ROW][C]21[/C][C]1787[/C][C]1914.52639331771[/C][C]-127.526393317713[/C][/ROW]
[ROW][C]22[/C][C]2072[/C][C]1842.2645425679[/C][C]229.735457432096[/C][/ROW]
[ROW][C]23[/C][C]1846[/C][C]2040.72389503784[/C][C]-194.723895037844[/C][/ROW]
[ROW][C]24[/C][C]2137[/C][C]1922.39809679446[/C][C]214.601903205541[/C][/ROW]
[ROW][C]25[/C][C]2467[/C][C]2111.22791860916[/C][C]355.772081390839[/C][/ROW]
[ROW][C]26[/C][C]2154[/C][C]2423.48273679389[/C][C]-269.482736793891[/C][/ROW]
[ROW][C]27[/C][C]2289[/C][C]2270.17104671734[/C][C]18.8289532826584[/C][/ROW]
[ROW][C]28[/C][C]2628[/C][C]2324.99176316609[/C][C]303.008236833914[/C][/ROW]
[ROW][C]29[/C][C]2074[/C][C]2602.62043689637[/C][C]-528.620436896374[/C][/ROW]
[ROW][C]30[/C][C]2798[/C][C]2250.45049166487[/C][C]547.549508335125[/C][/ROW]
[ROW][C]31[/C][C]2194[/C][C]2704.79735180861[/C][C]-510.797351808608[/C][/ROW]
[ROW][C]32[/C][C]2442[/C][C]2367.70323444915[/C][C]74.2967655508528[/C][/ROW]
[ROW][C]33[/C][C]2565[/C][C]2455.22917559681[/C][C]109.770824403194[/C][/ROW]
[ROW][C]34[/C][C]2063[/C][C]2575.03466510236[/C][C]-512.034665102363[/C][/ROW]
[ROW][C]35[/C][C]2069[/C][C]2216.69199646038[/C][C]-147.69199646038[/C][/ROW]
[ROW][C]36[/C][C]2539[/C][C]2110.72259631982[/C][C]428.277403680176[/C][/ROW]
[ROW][C]37[/C][C]1898[/C][C]2444.79839435798[/C][C]-546.798394357984[/C][/ROW]
[ROW][C]38[/C][C]2139[/C][C]2044.97408175031[/C][C]94.0259182496925[/C][/ROW]
[ROW][C]39[/C][C]2408[/C][C]2111.00034034099[/C][C]296.99965965901[/C][/ROW]
[ROW][C]40[/C][C]2725[/C][C]2341.16843836392[/C][C]383.83156163608[/C][/ROW]
[ROW][C]41[/C][C]2201[/C][C]2657.49694491057[/C][C]-456.496944910571[/C][/ROW]
[ROW][C]42[/C][C]2311[/C][C]2342.25914954716[/C][C]-31.259149547157[/C][/ROW]
[ROW][C]43[/C][C]2548[/C][C]2330.3361734838[/C][C]217.663826516197[/C][/ROW]
[ROW][C]44[/C][C]2276[/C][C]2510.61432165485[/C][C]-234.614321654848[/C][/ROW]
[ROW][C]45[/C][C]2351[/C][C]2351.66128151191[/C][C]-0.661281511909237[/C][/ROW]
[ROW][C]46[/C][C]2280[/C][C]2360.60952614579[/C][C]-80.6095261457922[/C][/ROW]
[ROW][C]47[/C][C]2057[/C][C]2307.16293732882[/C][C]-250.162937328818[/C][/ROW]
[ROW][C]48[/C][C]2479[/C][C]2116.47281713805[/C][C]362.527182861954[/C][/ROW]
[ROW][C]49[/C][C]2379[/C][C]2388.10592555411[/C][C]-9.1059255541054[/C][/ROW]
[ROW][C]50[/C][C]2295[/C][C]2392.39826101583[/C][C]-97.3982610158332[/C][/ROW]
[ROW][C]51[/C][C]2456[/C][C]2327.26373526272[/C][C]128.736264737277[/C][/ROW]
[ROW][C]52[/C][C]2546[/C][C]2432.45106281467[/C][C]113.548937185326[/C][/ROW]
[ROW][C]53[/C][C]2844[/C][C]2533.78539410243[/C][C]310.214605897573[/C][/ROW]
[ROW][C]54[/C][C]2260[/C][C]2795.5537279052[/C][C]-535.553727905203[/C][/ROW]
[ROW][C]55[/C][C]2981[/C][C]2416.94291731162[/C][C]564.057082688377[/C][/ROW]
[ROW][C]56[/C][C]2678[/C][C]2862.70064987338[/C][C]-184.700649873377[/C][/ROW]
[ROW][C]57[/C][C]3440[/C][C]2759.49906895291[/C][C]680.500931047088[/C][/ROW]
[ROW][C]58[/C][C]2842[/C][C]3319.62510868294[/C][C]-477.625108682944[/C][/ROW]
[ROW][C]59[/C][C]2450[/C][C]3018.7433988671[/C][C]-568.743398867102[/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]-94.2599594917288[/C][/ROW]
[ROW][C]62[/C][C]2540[/C][C]2600.63515367704[/C][C]-60.6351536770403[/C][/ROW]
[ROW][C]63[/C][C]2318[/C][C]2557.38353331311[/C][C]-239.383533313111[/C][/ROW]
[ROW][C]64[/C][C]2930[/C][C]2370.95699745039[/C][C]559.043002549615[/C][/ROW]
[ROW][C]65[/C][C]2947[/C][C]2792.38369405492[/C][C]154.616305945078[/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]2858.22859802792[/C][C]-163.228598027925[/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]-305.228655698653[/C][/ROW]
[ROW][C]70[/C][C]2160[/C][C]2322.64509207625[/C][C]-162.645092076254[/C][/ROW]
[ROW][C]71[/C][C]2058[/C][C]2172.31753619356[/C][C]-114.317536193561[/C][/ROW]
[ROW][C]72[/C][C]2533[/C][C]2049.58485374553[/C][C]483.415146254467[/C][/ROW]
[ROW][C]73[/C][C]2150[/C][C]2385.94303940446[/C][C]-235.943039404456[/C][/ROW]
[ROW][C]74[/C][C]2172[/C][C]2191.26511753763[/C][C]-19.2651175376332[/C][/ROW]
[ROW][C]75[/C][C]2155[/C][C]2150.9326648363[/C][C]4.0673351637015[/C][/ROW]
[ROW][C]76[/C][C]3016[/C][C]2127.6018303754[/C][C]888.398169624601[/C][/ROW]
[ROW][C]77[/C][C]2333[/C][C]2794.2368399761[/C][C]-461.236839976102[/C][/ROW]
[ROW][C]78[/C][C]2355[/C][C]2463.40747522134[/C][C]-108.407475221339[/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]-506.412794718151[/C][/ROW]
[ROW][C]81[/C][C]2360[/C][C]2346.66580888597[/C][C]13.3341911140251[/C][/ROW]
[ROW][C]82[/C][C]2299[/C][C]2346.84509596611[/C][C]-47.8450959661072[/C][/ROW]
[ROW][C]83[/C][C]1746[/C][C]2300.13680864162[/C][C]-554.13680864162[/C][/ROW]
[ROW][C]84[/C][C]2069[/C][C]1855.58778609156[/C][C]213.412213908435[/C][/ROW]
[ROW][C]85[/C][C]2267[/C][C]1975.26976348826[/C][C]291.730236511742[/C][/ROW]
[ROW][C]86[/C][C]1878[/C][C]2169.28279849302[/C][C]-291.282798493022[/C][/ROW]
[ROW][C]87[/C][C]2266[/C][C]1926.69907728727[/C][C]339.300922712732[/C][/ROW]
[ROW][C]88[/C][C]2282[/C][C]2157.84154381478[/C][C]124.158456185222[/C][/ROW]
[ROW][C]89[/C][C]2085[/C][C]2242.25259004805[/C][C]-157.252590048054[/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]24.1537119214963[/C][/ROW]
[ROW][C]92[/C][C]1828[/C][C]2241.27022851631[/C][C]-413.27022851631[/C][/ROW]
[ROW][C]93[/C][C]1954[/C][C]1916.03497672423[/C][C]37.9650232757745[/C][/ROW]
[ROW][C]94[/C][C]1851[/C][C]1917.07419284805[/C][C]-66.0741928480543[/C][/ROW]
[ROW][C]95[/C][C]1570[/C][C]1839.32731974873[/C][C]-269.327319748727[/C][/ROW]
[ROW][C]96[/C][C]1852[/C][C]1598.95596325081[/C][C]253.044036749187[/C][/ROW]
[ROW][C]97[/C][C]2187[/C][C]1749.27607466581[/C][C]437.723925334186[/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=161125&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161125&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
435952565.944072190391029.05592780961
533363662.0139082309-326.013908230903
632493765.11270282837-516.112702828371
729203699.70925076629-779.709250766286
821133396.6792597969-1283.6792597969
920402652.18482124402-612.184821244016
1018532351.71549683591-498.715496835915
1118322101.73922066663-269.739220666632
1220931999.3871922354193.6128077645888
1321642163.677620700250.32237929974508
1423682261.01986845969106.980131540307
1520722441.56737198676-369.567371986756
1625212257.08406997948263.915930020517
1718192543.72847337899-724.728473378993
1819472075.68660913114-128.686609131141
1922262027.52230013399198.477699866009
2017542226.5332873648-472.533287364796
2117871914.52639331771-127.526393317713
2220721842.2645425679229.735457432096
2318462040.72389503784-194.723895037844
2421371922.39809679446214.601903205541
2524672111.22791860916355.772081390839
2621542423.48273679389-269.482736793891
2722892270.1710467173418.8289532826584
2826282324.99176316609303.008236833914
2920742602.62043689637-528.620436896374
3027982250.45049166487547.549508335125
3121942704.79735180861-510.797351808608
3224422367.7032344491574.2967655508528
3325652455.22917559681109.770824403194
3420632575.03466510236-512.034665102363
3520692216.69199646038-147.69199646038
3625392110.72259631982428.277403680176
3718982444.79839435798-546.798394357984
3821392044.9740817503194.0259182496925
3924082111.00034034099296.99965965901
4027252341.16843836392383.83156163608
4122012657.49694491057-456.496944910571
4223112342.25914954716-31.259149547157
4325482330.3361734838217.663826516197
4422762510.61432165485-234.614321654848
4523512351.66128151191-0.661281511909237
4622802360.60952614579-80.6095261457922
4720572307.16293732882-250.162937328818
4824792116.47281713805362.527182861954
4923792388.10592555411-9.1059255541054
5022952392.39826101583-97.3982610158332
5124562327.26373526272128.736264737277
5225462432.45106281467113.548937185326
5328442533.78539410243310.214605897573
5422602795.5537279052-535.553727905203
5529812416.94291731162564.057082688377
5626782862.70064987338-184.700649873377
5734402759.49906895291680.500931047088
5828423319.62510868294-477.625108682944
5924503018.7433988671-568.743398867102
6026692617.1448984529651.8551015470407
6125702664.25995949173-94.2599594917288
6225402600.63515367704-60.6351536770403
6323182557.38353331311-239.383533313111
6429302370.95699745039559.043002549615
6529472792.38369405492154.616305945078
6627992933.09281312672-134.092813126716
6726952858.22859802792-163.228598027925
6824982752.31605767688-254.316057676878
6922602565.22865569865-305.228655698653
7021602322.64509207625-162.645092076254
7120582172.31753619356-114.317536193561
7225332049.58485374553483.415146254467
7321502385.94303940446-235.943039404456
7421722191.26511753763-19.2651175376332
7521552150.93266483634.0673351637015
7630162127.6018303754888.398169624601
7723332794.2368399761-461.236839976102
7823552463.40747522134-108.407475221339
7928252379.12539729694445.874602703057
8022142720.41279471815-506.412794718151
8123602346.6658088859713.3341911140251
8222992346.84509596611-47.8450959661072
8317462300.13680864162-554.13680864162
8420691855.58778609156213.412213908435
8522671975.26976348826291.730236511742
8618782169.28279849302-291.282798493022
8722661926.69907728727339.300922712732
8822822157.84154381478124.158456185222
8920852242.25259004805-157.252590048054
9022772114.89142725125162.108572748754
9122512226.846288078524.1537119214963
9218282241.27022851631-413.27022851631
9319541916.0349767242337.9650232757745
9418511917.07419284805-66.0741928480543
9515701839.32731974873-269.327319748727
9618521598.95596325081253.044036749187
9721871749.27607466581437.723925334186
9818552059.34207858859-204.342078588593
9922181895.81768855235322.182311447648







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1002130.258143068521385.631211309672874.88507482738
1012133.421199202911189.098648137123077.74375026869
1022136.584255337291003.071730185133270.09678048945
1032139.74731147167821.392354527173458.10226841618
1042142.91036760606641.0294281689133644.7913070432
1052146.07342374044460.2845377189943831.86230976189
1062149.23647987482278.1279686468194020.34499110283
1072152.3995360092193.90278686501784210.8962851534
1082155.56259214359-92.82425555380224403.94943984099
1092158.72564827798-282.3447204532094599.79601700916
1102161.88870441236-474.856653629784798.6340624545
1112165.05176054674-670.4943708713275000.59789196481

\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 & 3077.74375026869 \tabularnewline
102 & 2136.58425533729 & 1003.07173018513 & 3270.09678048945 \tabularnewline
103 & 2139.74731147167 & 821.39235452717 & 3458.10226841618 \tabularnewline
104 & 2142.91036760606 & 641.029428168913 & 3644.7913070432 \tabularnewline
105 & 2146.07342374044 & 460.284537718994 & 3831.86230976189 \tabularnewline
106 & 2149.23647987482 & 278.127968646819 & 4020.34499110283 \tabularnewline
107 & 2152.39953600921 & 93.9027868650178 & 4210.8962851534 \tabularnewline
108 & 2155.56259214359 & -92.8242555538022 & 4403.94943984099 \tabularnewline
109 & 2158.72564827798 & -282.344720453209 & 4599.79601700916 \tabularnewline
110 & 2161.88870441236 & -474.85665362978 & 4798.6340624545 \tabularnewline
111 & 2165.05176054674 & -670.494370871327 & 5000.59789196481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161125&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]3077.74375026869[/C][/ROW]
[ROW][C]102[/C][C]2136.58425533729[/C][C]1003.07173018513[/C][C]3270.09678048945[/C][/ROW]
[ROW][C]103[/C][C]2139.74731147167[/C][C]821.39235452717[/C][C]3458.10226841618[/C][/ROW]
[ROW][C]104[/C][C]2142.91036760606[/C][C]641.029428168913[/C][C]3644.7913070432[/C][/ROW]
[ROW][C]105[/C][C]2146.07342374044[/C][C]460.284537718994[/C][C]3831.86230976189[/C][/ROW]
[ROW][C]106[/C][C]2149.23647987482[/C][C]278.127968646819[/C][C]4020.34499110283[/C][/ROW]
[ROW][C]107[/C][C]2152.39953600921[/C][C]93.9027868650178[/C][C]4210.8962851534[/C][/ROW]
[ROW][C]108[/C][C]2155.56259214359[/C][C]-92.8242555538022[/C][C]4403.94943984099[/C][/ROW]
[ROW][C]109[/C][C]2158.72564827798[/C][C]-282.344720453209[/C][C]4599.79601700916[/C][/ROW]
[ROW][C]110[/C][C]2161.88870441236[/C][C]-474.85665362978[/C][C]4798.6340624545[/C][/ROW]
[ROW][C]111[/C][C]2165.05176054674[/C][C]-670.494370871327[/C][C]5000.59789196481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161125&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161125&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
1012133.421199202911189.098648137123077.74375026869
1022136.584255337291003.071730185133270.09678048945
1032139.74731147167821.392354527173458.10226841618
1042142.91036760606641.0294281689133644.7913070432
1052146.07342374044460.2845377189943831.86230976189
1062149.23647987482278.1279686468194020.34499110283
1072152.3995360092193.90278686501784210.8962851534
1082155.56259214359-92.82425555380224403.94943984099
1092158.72564827798-282.3447204532094599.79601700916
1102161.88870441236-474.856653629784798.6340624545
1112165.05176054674-670.4943708713275000.59789196481



Parameters (Session):
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')