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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 12:29:46 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t12439675011xpk655z9xsc1ni.htm/, Retrieved Fri, 10 May 2024 14:06:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41360, Retrieved Fri, 10 May 2024 14:06:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Martin Horemans -...] [2009-06-02 18:29:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1746
1271
1363
1664
2179
2305
2098
2231
1407
1966
2293
2045
1532
1333
1583
1712
2641
2267
2126
2231
1517
2010
2628
2115
1829
1636
1787
2122
2620
2555
2337
2524
1801
2417
2389
2267
2135
1760
1905
2176
2344
2674
2766
2783
2000
2588
2736
2704
2466
1976
2171
2397
2942
2707
2861
2765
1814
2611
2606
2518
2267
1730
1901
2124
2448
2489
2521
2466
1827
2278
2373
2356
2075
1606
1699
2311
2093
2064
2180
2136




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41360&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41360&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41360&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.279673175984277
beta0.105814685840969
gamma0.78536497988161

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.279673175984277 \tabularnewline
beta & 0.105814685840969 \tabularnewline
gamma & 0.78536497988161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41360&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]0.279673175984277[/C][/ROW]
[ROW][C]beta[/C][C]0.105814685840969[/C][/ROW]
[ROW][C]gamma[/C][C]0.78536497988161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41360&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41360&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
alpha0.279673175984277
beta0.105814685840969
gamma0.78536497988161







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315321461.3245192307770.6754807692303
1413331292.1496039644840.8503960355224
1515831561.4256532501921.5743467498050
1617121703.115836340118.88416365989133
1726412632.144829378628.8551706213807
1822672257.344436259489.65556374052358
1921262204.84530050069-78.8453005006945
2022312333.67820292190-102.678202921904
2115171477.7237380947039.2762619052953
2220102046.21578582993-36.2157858299286
2326282350.43964656270277.560353437296
2421152179.21560048522-64.2156004852159
2518291703.57144991363125.428550086370
2616361540.2390955603295.7609044396831
2717871822.99452763994-35.9945276399433
2821221948.72871381541173.271286184586
2926202935.90432526461-315.904325264612
3025552473.3077825115681.6922174884371
3123372395.59809608675-58.59809608675
3225242521.919438847282.08056115272302
3318011783.9783523547917.0216476452104
3424172311.28922691044105.710773089564
3523892844.66568156603-455.665681566025
3622672265.280200637061.71979936293701
3721351907.56458843248227.435411567518
3817601751.198784432538.80121556746508
3919051927.74539989475-22.7453998947549
4021762168.610931551927.38906844808389
4123442820.78870880933-476.788708809333
4226742521.49522099752152.504779002478
4327662369.69054082385396.309459176148
4427832656.49233463977126.507665360232
4520001964.4127851035435.5872148964602
4625882550.2486859115837.7513140884166
4727362748.18552767517-12.1855276751658
4827042565.85397137374138.14602862626
4924662392.2947176889473.7052823110639
5019762083.00957052961-107.009570529613
5121712219.65370142218-48.653701422184
5223972479.88753334324-82.8875333432361
5329422839.80347393924102.196526060758
5427073082.46931401563-375.469314015630
5528612929.33399331702-68.3339933170246
5627652928.20941041026-163.209410410261
5718142089.74860599598-275.748605995978
5826112566.6032844125244.3967155874766
5926062715.21186676898-109.211866768981
6025182564.98222464364-46.9822246436352
6122672271.90567319405-4.90567319405318
6217301804.78835867401-74.7883586740134
6319011950.79760594561-49.7976059456057
6421242158.65157818861-34.6515781886083
6524482605.49775285329-157.497752853291
6624892466.3582138709222.6417861290806
6725212571.14683632024-50.1468363202389
6824662494.80458474976-28.8045847497588
6918271607.61384605312219.386153946877
7022782396.05591370195-118.055913701951
7123732399.52298152739-26.5229815273888
7223562297.2622709075858.7377290924205
7320752050.3234539717124.6765460282932
7416061545.5881149689960.4118850310088
7516991741.19066886177-42.1906688617651
7623111957.60928603307353.390713966933
7720932452.83633609464-359.836336094642
7820642362.38098007643-298.380980076427
7921802330.07442315643-150.074423156432
8021362228.76584063650-92.7658406365035

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1532 & 1461.32451923077 & 70.6754807692303 \tabularnewline
14 & 1333 & 1292.14960396448 & 40.8503960355224 \tabularnewline
15 & 1583 & 1561.42565325019 & 21.5743467498050 \tabularnewline
16 & 1712 & 1703.11583634011 & 8.88416365989133 \tabularnewline
17 & 2641 & 2632.14482937862 & 8.8551706213807 \tabularnewline
18 & 2267 & 2257.34443625948 & 9.65556374052358 \tabularnewline
19 & 2126 & 2204.84530050069 & -78.8453005006945 \tabularnewline
20 & 2231 & 2333.67820292190 & -102.678202921904 \tabularnewline
21 & 1517 & 1477.72373809470 & 39.2762619052953 \tabularnewline
22 & 2010 & 2046.21578582993 & -36.2157858299286 \tabularnewline
23 & 2628 & 2350.43964656270 & 277.560353437296 \tabularnewline
24 & 2115 & 2179.21560048522 & -64.2156004852159 \tabularnewline
25 & 1829 & 1703.57144991363 & 125.428550086370 \tabularnewline
26 & 1636 & 1540.23909556032 & 95.7609044396831 \tabularnewline
27 & 1787 & 1822.99452763994 & -35.9945276399433 \tabularnewline
28 & 2122 & 1948.72871381541 & 173.271286184586 \tabularnewline
29 & 2620 & 2935.90432526461 & -315.904325264612 \tabularnewline
30 & 2555 & 2473.30778251156 & 81.6922174884371 \tabularnewline
31 & 2337 & 2395.59809608675 & -58.59809608675 \tabularnewline
32 & 2524 & 2521.91943884728 & 2.08056115272302 \tabularnewline
33 & 1801 & 1783.97835235479 & 17.0216476452104 \tabularnewline
34 & 2417 & 2311.28922691044 & 105.710773089564 \tabularnewline
35 & 2389 & 2844.66568156603 & -455.665681566025 \tabularnewline
36 & 2267 & 2265.28020063706 & 1.71979936293701 \tabularnewline
37 & 2135 & 1907.56458843248 & 227.435411567518 \tabularnewline
38 & 1760 & 1751.19878443253 & 8.80121556746508 \tabularnewline
39 & 1905 & 1927.74539989475 & -22.7453998947549 \tabularnewline
40 & 2176 & 2168.61093155192 & 7.38906844808389 \tabularnewline
41 & 2344 & 2820.78870880933 & -476.788708809333 \tabularnewline
42 & 2674 & 2521.49522099752 & 152.504779002478 \tabularnewline
43 & 2766 & 2369.69054082385 & 396.309459176148 \tabularnewline
44 & 2783 & 2656.49233463977 & 126.507665360232 \tabularnewline
45 & 2000 & 1964.41278510354 & 35.5872148964602 \tabularnewline
46 & 2588 & 2550.24868591158 & 37.7513140884166 \tabularnewline
47 & 2736 & 2748.18552767517 & -12.1855276751658 \tabularnewline
48 & 2704 & 2565.85397137374 & 138.14602862626 \tabularnewline
49 & 2466 & 2392.29471768894 & 73.7052823110639 \tabularnewline
50 & 1976 & 2083.00957052961 & -107.009570529613 \tabularnewline
51 & 2171 & 2219.65370142218 & -48.653701422184 \tabularnewline
52 & 2397 & 2479.88753334324 & -82.8875333432361 \tabularnewline
53 & 2942 & 2839.80347393924 & 102.196526060758 \tabularnewline
54 & 2707 & 3082.46931401563 & -375.469314015630 \tabularnewline
55 & 2861 & 2929.33399331702 & -68.3339933170246 \tabularnewline
56 & 2765 & 2928.20941041026 & -163.209410410261 \tabularnewline
57 & 1814 & 2089.74860599598 & -275.748605995978 \tabularnewline
58 & 2611 & 2566.60328441252 & 44.3967155874766 \tabularnewline
59 & 2606 & 2715.21186676898 & -109.211866768981 \tabularnewline
60 & 2518 & 2564.98222464364 & -46.9822246436352 \tabularnewline
61 & 2267 & 2271.90567319405 & -4.90567319405318 \tabularnewline
62 & 1730 & 1804.78835867401 & -74.7883586740134 \tabularnewline
63 & 1901 & 1950.79760594561 & -49.7976059456057 \tabularnewline
64 & 2124 & 2158.65157818861 & -34.6515781886083 \tabularnewline
65 & 2448 & 2605.49775285329 & -157.497752853291 \tabularnewline
66 & 2489 & 2466.35821387092 & 22.6417861290806 \tabularnewline
67 & 2521 & 2571.14683632024 & -50.1468363202389 \tabularnewline
68 & 2466 & 2494.80458474976 & -28.8045847497588 \tabularnewline
69 & 1827 & 1607.61384605312 & 219.386153946877 \tabularnewline
70 & 2278 & 2396.05591370195 & -118.055913701951 \tabularnewline
71 & 2373 & 2399.52298152739 & -26.5229815273888 \tabularnewline
72 & 2356 & 2297.26227090758 & 58.7377290924205 \tabularnewline
73 & 2075 & 2050.32345397171 & 24.6765460282932 \tabularnewline
74 & 1606 & 1545.58811496899 & 60.4118850310088 \tabularnewline
75 & 1699 & 1741.19066886177 & -42.1906688617651 \tabularnewline
76 & 2311 & 1957.60928603307 & 353.390713966933 \tabularnewline
77 & 2093 & 2452.83633609464 & -359.836336094642 \tabularnewline
78 & 2064 & 2362.38098007643 & -298.380980076427 \tabularnewline
79 & 2180 & 2330.07442315643 & -150.074423156432 \tabularnewline
80 & 2136 & 2228.76584063650 & -92.7658406365035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41360&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1532[/C][C]1461.32451923077[/C][C]70.6754807692303[/C][/ROW]
[ROW][C]14[/C][C]1333[/C][C]1292.14960396448[/C][C]40.8503960355224[/C][/ROW]
[ROW][C]15[/C][C]1583[/C][C]1561.42565325019[/C][C]21.5743467498050[/C][/ROW]
[ROW][C]16[/C][C]1712[/C][C]1703.11583634011[/C][C]8.88416365989133[/C][/ROW]
[ROW][C]17[/C][C]2641[/C][C]2632.14482937862[/C][C]8.8551706213807[/C][/ROW]
[ROW][C]18[/C][C]2267[/C][C]2257.34443625948[/C][C]9.65556374052358[/C][/ROW]
[ROW][C]19[/C][C]2126[/C][C]2204.84530050069[/C][C]-78.8453005006945[/C][/ROW]
[ROW][C]20[/C][C]2231[/C][C]2333.67820292190[/C][C]-102.678202921904[/C][/ROW]
[ROW][C]21[/C][C]1517[/C][C]1477.72373809470[/C][C]39.2762619052953[/C][/ROW]
[ROW][C]22[/C][C]2010[/C][C]2046.21578582993[/C][C]-36.2157858299286[/C][/ROW]
[ROW][C]23[/C][C]2628[/C][C]2350.43964656270[/C][C]277.560353437296[/C][/ROW]
[ROW][C]24[/C][C]2115[/C][C]2179.21560048522[/C][C]-64.2156004852159[/C][/ROW]
[ROW][C]25[/C][C]1829[/C][C]1703.57144991363[/C][C]125.428550086370[/C][/ROW]
[ROW][C]26[/C][C]1636[/C][C]1540.23909556032[/C][C]95.7609044396831[/C][/ROW]
[ROW][C]27[/C][C]1787[/C][C]1822.99452763994[/C][C]-35.9945276399433[/C][/ROW]
[ROW][C]28[/C][C]2122[/C][C]1948.72871381541[/C][C]173.271286184586[/C][/ROW]
[ROW][C]29[/C][C]2620[/C][C]2935.90432526461[/C][C]-315.904325264612[/C][/ROW]
[ROW][C]30[/C][C]2555[/C][C]2473.30778251156[/C][C]81.6922174884371[/C][/ROW]
[ROW][C]31[/C][C]2337[/C][C]2395.59809608675[/C][C]-58.59809608675[/C][/ROW]
[ROW][C]32[/C][C]2524[/C][C]2521.91943884728[/C][C]2.08056115272302[/C][/ROW]
[ROW][C]33[/C][C]1801[/C][C]1783.97835235479[/C][C]17.0216476452104[/C][/ROW]
[ROW][C]34[/C][C]2417[/C][C]2311.28922691044[/C][C]105.710773089564[/C][/ROW]
[ROW][C]35[/C][C]2389[/C][C]2844.66568156603[/C][C]-455.665681566025[/C][/ROW]
[ROW][C]36[/C][C]2267[/C][C]2265.28020063706[/C][C]1.71979936293701[/C][/ROW]
[ROW][C]37[/C][C]2135[/C][C]1907.56458843248[/C][C]227.435411567518[/C][/ROW]
[ROW][C]38[/C][C]1760[/C][C]1751.19878443253[/C][C]8.80121556746508[/C][/ROW]
[ROW][C]39[/C][C]1905[/C][C]1927.74539989475[/C][C]-22.7453998947549[/C][/ROW]
[ROW][C]40[/C][C]2176[/C][C]2168.61093155192[/C][C]7.38906844808389[/C][/ROW]
[ROW][C]41[/C][C]2344[/C][C]2820.78870880933[/C][C]-476.788708809333[/C][/ROW]
[ROW][C]42[/C][C]2674[/C][C]2521.49522099752[/C][C]152.504779002478[/C][/ROW]
[ROW][C]43[/C][C]2766[/C][C]2369.69054082385[/C][C]396.309459176148[/C][/ROW]
[ROW][C]44[/C][C]2783[/C][C]2656.49233463977[/C][C]126.507665360232[/C][/ROW]
[ROW][C]45[/C][C]2000[/C][C]1964.41278510354[/C][C]35.5872148964602[/C][/ROW]
[ROW][C]46[/C][C]2588[/C][C]2550.24868591158[/C][C]37.7513140884166[/C][/ROW]
[ROW][C]47[/C][C]2736[/C][C]2748.18552767517[/C][C]-12.1855276751658[/C][/ROW]
[ROW][C]48[/C][C]2704[/C][C]2565.85397137374[/C][C]138.14602862626[/C][/ROW]
[ROW][C]49[/C][C]2466[/C][C]2392.29471768894[/C][C]73.7052823110639[/C][/ROW]
[ROW][C]50[/C][C]1976[/C][C]2083.00957052961[/C][C]-107.009570529613[/C][/ROW]
[ROW][C]51[/C][C]2171[/C][C]2219.65370142218[/C][C]-48.653701422184[/C][/ROW]
[ROW][C]52[/C][C]2397[/C][C]2479.88753334324[/C][C]-82.8875333432361[/C][/ROW]
[ROW][C]53[/C][C]2942[/C][C]2839.80347393924[/C][C]102.196526060758[/C][/ROW]
[ROW][C]54[/C][C]2707[/C][C]3082.46931401563[/C][C]-375.469314015630[/C][/ROW]
[ROW][C]55[/C][C]2861[/C][C]2929.33399331702[/C][C]-68.3339933170246[/C][/ROW]
[ROW][C]56[/C][C]2765[/C][C]2928.20941041026[/C][C]-163.209410410261[/C][/ROW]
[ROW][C]57[/C][C]1814[/C][C]2089.74860599598[/C][C]-275.748605995978[/C][/ROW]
[ROW][C]58[/C][C]2611[/C][C]2566.60328441252[/C][C]44.3967155874766[/C][/ROW]
[ROW][C]59[/C][C]2606[/C][C]2715.21186676898[/C][C]-109.211866768981[/C][/ROW]
[ROW][C]60[/C][C]2518[/C][C]2564.98222464364[/C][C]-46.9822246436352[/C][/ROW]
[ROW][C]61[/C][C]2267[/C][C]2271.90567319405[/C][C]-4.90567319405318[/C][/ROW]
[ROW][C]62[/C][C]1730[/C][C]1804.78835867401[/C][C]-74.7883586740134[/C][/ROW]
[ROW][C]63[/C][C]1901[/C][C]1950.79760594561[/C][C]-49.7976059456057[/C][/ROW]
[ROW][C]64[/C][C]2124[/C][C]2158.65157818861[/C][C]-34.6515781886083[/C][/ROW]
[ROW][C]65[/C][C]2448[/C][C]2605.49775285329[/C][C]-157.497752853291[/C][/ROW]
[ROW][C]66[/C][C]2489[/C][C]2466.35821387092[/C][C]22.6417861290806[/C][/ROW]
[ROW][C]67[/C][C]2521[/C][C]2571.14683632024[/C][C]-50.1468363202389[/C][/ROW]
[ROW][C]68[/C][C]2466[/C][C]2494.80458474976[/C][C]-28.8045847497588[/C][/ROW]
[ROW][C]69[/C][C]1827[/C][C]1607.61384605312[/C][C]219.386153946877[/C][/ROW]
[ROW][C]70[/C][C]2278[/C][C]2396.05591370195[/C][C]-118.055913701951[/C][/ROW]
[ROW][C]71[/C][C]2373[/C][C]2399.52298152739[/C][C]-26.5229815273888[/C][/ROW]
[ROW][C]72[/C][C]2356[/C][C]2297.26227090758[/C][C]58.7377290924205[/C][/ROW]
[ROW][C]73[/C][C]2075[/C][C]2050.32345397171[/C][C]24.6765460282932[/C][/ROW]
[ROW][C]74[/C][C]1606[/C][C]1545.58811496899[/C][C]60.4118850310088[/C][/ROW]
[ROW][C]75[/C][C]1699[/C][C]1741.19066886177[/C][C]-42.1906688617651[/C][/ROW]
[ROW][C]76[/C][C]2311[/C][C]1957.60928603307[/C][C]353.390713966933[/C][/ROW]
[ROW][C]77[/C][C]2093[/C][C]2452.83633609464[/C][C]-359.836336094642[/C][/ROW]
[ROW][C]78[/C][C]2064[/C][C]2362.38098007643[/C][C]-298.380980076427[/C][/ROW]
[ROW][C]79[/C][C]2180[/C][C]2330.07442315643[/C][C]-150.074423156432[/C][/ROW]
[ROW][C]80[/C][C]2136[/C][C]2228.76584063650[/C][C]-92.7658406365035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41360&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41360&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
1315321461.3245192307770.6754807692303
1413331292.1496039644840.8503960355224
1515831561.4256532501921.5743467498050
1617121703.115836340118.88416365989133
1726412632.144829378628.8551706213807
1822672257.344436259489.65556374052358
1921262204.84530050069-78.8453005006945
2022312333.67820292190-102.678202921904
2115171477.7237380947039.2762619052953
2220102046.21578582993-36.2157858299286
2326282350.43964656270277.560353437296
2421152179.21560048522-64.2156004852159
2518291703.57144991363125.428550086370
2616361540.2390955603295.7609044396831
2717871822.99452763994-35.9945276399433
2821221948.72871381541173.271286184586
2926202935.90432526461-315.904325264612
3025552473.3077825115681.6922174884371
3123372395.59809608675-58.59809608675
3225242521.919438847282.08056115272302
3318011783.9783523547917.0216476452104
3424172311.28922691044105.710773089564
3523892844.66568156603-455.665681566025
3622672265.280200637061.71979936293701
3721351907.56458843248227.435411567518
3817601751.198784432538.80121556746508
3919051927.74539989475-22.7453998947549
4021762168.610931551927.38906844808389
4123442820.78870880933-476.788708809333
4226742521.49522099752152.504779002478
4327662369.69054082385396.309459176148
4427832656.49233463977126.507665360232
4520001964.4127851035435.5872148964602
4625882550.2486859115837.7513140884166
4727362748.18552767517-12.1855276751658
4827042565.85397137374138.14602862626
4924662392.2947176889473.7052823110639
5019762083.00957052961-107.009570529613
5121712219.65370142218-48.653701422184
5223972479.88753334324-82.8875333432361
5329422839.80347393924102.196526060758
5427073082.46931401563-375.469314015630
5528612929.33399331702-68.3339933170246
5627652928.20941041026-163.209410410261
5718142089.74860599598-275.748605995978
5826112566.6032844125244.3967155874766
5926062715.21186676898-109.211866768981
6025182564.98222464364-46.9822246436352
6122672271.90567319405-4.90567319405318
6217301804.78835867401-74.7883586740134
6319011950.79760594561-49.7976059456057
6421242158.65157818861-34.6515781886083
6524482605.49775285329-157.497752853291
6624892466.3582138709222.6417861290806
6725212571.14683632024-50.1468363202389
6824662494.80458474976-28.8045847497588
6918271607.61384605312219.386153946877
7022782396.05591370195-118.055913701951
7123732399.52298152739-26.5229815273888
7223562297.2622709075858.7377290924205
7320752050.3234539717124.6765460282932
7416061545.5881149689960.4118850310088
7516991741.19066886177-42.1906688617651
7623111957.60928603307353.390713966933
7720932452.83633609464-359.836336094642
7820642362.38098007643-298.380980076427
7921802330.07442315643-150.074423156432
8021362228.76584063650-92.7658406365035







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
811453.107353711711135.996583624811770.2181237986
821971.817211768821639.887521833332303.74690170431
832046.09876187041697.208864613942394.98865912686
841986.289818506761618.35517827752354.22445873603
851688.716660938991299.732508029942077.70081384805
861181.62796535169769.6830533264271593.57287737696
871284.8347077243848.1175768458651721.55183860273
881720.633614765361257.433299861972183.83392966875
891686.874864839451195.577822867992178.17190681090
901715.805923979741194.890630954802236.72121700469
911843.661928500331291.692233831002395.63162316966
921814.000448371011229.618447995552398.38244874647

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 1453.10735371171 & 1135.99658362481 & 1770.2181237986 \tabularnewline
82 & 1971.81721176882 & 1639.88752183333 & 2303.74690170431 \tabularnewline
83 & 2046.0987618704 & 1697.20886461394 & 2394.98865912686 \tabularnewline
84 & 1986.28981850676 & 1618.3551782775 & 2354.22445873603 \tabularnewline
85 & 1688.71666093899 & 1299.73250802994 & 2077.70081384805 \tabularnewline
86 & 1181.62796535169 & 769.683053326427 & 1593.57287737696 \tabularnewline
87 & 1284.8347077243 & 848.117576845865 & 1721.55183860273 \tabularnewline
88 & 1720.63361476536 & 1257.43329986197 & 2183.83392966875 \tabularnewline
89 & 1686.87486483945 & 1195.57782286799 & 2178.17190681090 \tabularnewline
90 & 1715.80592397974 & 1194.89063095480 & 2236.72121700469 \tabularnewline
91 & 1843.66192850033 & 1291.69223383100 & 2395.63162316966 \tabularnewline
92 & 1814.00044837101 & 1229.61844799555 & 2398.38244874647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41360&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]81[/C][C]1453.10735371171[/C][C]1135.99658362481[/C][C]1770.2181237986[/C][/ROW]
[ROW][C]82[/C][C]1971.81721176882[/C][C]1639.88752183333[/C][C]2303.74690170431[/C][/ROW]
[ROW][C]83[/C][C]2046.0987618704[/C][C]1697.20886461394[/C][C]2394.98865912686[/C][/ROW]
[ROW][C]84[/C][C]1986.28981850676[/C][C]1618.3551782775[/C][C]2354.22445873603[/C][/ROW]
[ROW][C]85[/C][C]1688.71666093899[/C][C]1299.73250802994[/C][C]2077.70081384805[/C][/ROW]
[ROW][C]86[/C][C]1181.62796535169[/C][C]769.683053326427[/C][C]1593.57287737696[/C][/ROW]
[ROW][C]87[/C][C]1284.8347077243[/C][C]848.117576845865[/C][C]1721.55183860273[/C][/ROW]
[ROW][C]88[/C][C]1720.63361476536[/C][C]1257.43329986197[/C][C]2183.83392966875[/C][/ROW]
[ROW][C]89[/C][C]1686.87486483945[/C][C]1195.57782286799[/C][C]2178.17190681090[/C][/ROW]
[ROW][C]90[/C][C]1715.80592397974[/C][C]1194.89063095480[/C][C]2236.72121700469[/C][/ROW]
[ROW][C]91[/C][C]1843.66192850033[/C][C]1291.69223383100[/C][C]2395.63162316966[/C][/ROW]
[ROW][C]92[/C][C]1814.00044837101[/C][C]1229.61844799555[/C][C]2398.38244874647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41360&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41360&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
811453.107353711711135.996583624811770.2181237986
821971.817211768821639.887521833332303.74690170431
832046.09876187041697.208864613942394.98865912686
841986.289818506761618.35517827752354.22445873603
851688.716660938991299.732508029942077.70081384805
861181.62796535169769.6830533264271593.57287737696
871284.8347077243848.1175768458651721.55183860273
881720.633614765361257.433299861972183.83392966875
891686.874864839451195.577822867992178.17190681090
901715.805923979741194.890630954802236.72121700469
911843.661928500331291.692233831002395.63162316966
921814.000448371011229.618447995552398.38244874647



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')