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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Dec 2016 21:01:50 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/22/t1482437039zpnu6jx6ttlhftg.htm/, Retrieved Mon, 29 Apr 2024 04:06:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302671, Retrieved Mon, 29 Apr 2024 04:06:51 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-22 20:01:50] [bde5266f17215258f6d7c4cd7e531432] [Current]
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Dataseries X:
1549.5
1746.5
1869.5
1784
1795
1942.5
2100
2072.5
2075
2278
2451
2290.5
2388
2574.5
2939.5
2924
3087.5
3259.5
3474.5
3376
3496
3771.5
3743
3474.5
3405
3684.5
3804
3470.5
3453.5
3842
4156.5
4055
4133.5
4552
4588
4423.5
4462.5
4846
4869.5
4637
4841
5114.5
5374.5
5166.5
5236.5
5740.5
5992
5842
5844.5
6384.5
6487
6372
6583.5
6990
6874
6710
6924
7428.5
7415.5
7228.5
6734
7158.5
7192




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302671&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302671&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302671&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.810719755145697
beta0.0270743628961957
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.810719755145697 \tabularnewline
beta & 0.0270743628961957 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302671&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]0.810719755145697[/C][/ROW]
[ROW][C]beta[/C][C]0.0270743628961957[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302671&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302671&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
alpha0.810719755145697
beta0.0270743628961957
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
517951689.328125105.671875
61942.51917.2866197845725.2133802154292
721002098.319250035621.68074996438372
82072.52019.2479040441553.2520959558497
920752101.53193406296-26.5319340629635
1022782208.2578042862469.7421957137612
1124512423.0907767343527.9092232656494
122290.52377.77473067507-87.2747306750698
1323882330.6747423440557.3252576559544
142574.52525.0941241775349.4058758224719
152939.52716.56154734532222.938452654677
1629242812.87800279208111.121997207916
173087.52963.66733452015123.832665479853
183259.53221.6416744550437.8583255449616
193474.53447.4751648647127.0248351352889
2033763370.377290746325.62270925367966
2134963442.3078205831253.6921794168752
223771.53629.87075123152141.629248768475
2337433942.78666870311-199.786668703113
243474.53677.78263421701-203.282634217008
2534053584.88806836988-179.888068369879
263684.53590.0405986482794.4594013517303
2738043789.369306435914.6306935640951
283470.53691.51995334663-221.019953346633
293453.53582.26819959498-128.768199594983
3038423675.50991842899166.490081571009
314156.53914.42312242984242.07687757016
3240553957.6550501878997.3449498121072
334133.54132.247646454171.25235354582946
3445524397.91827003974154.081729960262
3545884651.93861965224-63.938619652241
364423.54423.82564310166-0.325643101657988
374462.54503.04528719008-40.5452871900779
3848464764.8388300986481.161169901362
394869.54917.95502061655-48.4550206165504
4046374714.25636879839-77.2563687983939
4148414721.62614708736119.373852912643
425114.55137.74828196841-23.2482819684083
435374.55181.03448249647193.465517503534
445166.55172.6747516965-6.17475169649697
455236.55281.11092718716-44.6109271871574
465740.55539.91329801628200.586701983723
4759925813.22118770052178.77881229948
4858425762.3789314832379.6210685167725
495844.55942.1916945926-97.6916945926014
506384.56212.30182789854172.198172101459
5164876465.7739745255721.2260254744342
5263726272.2809214744399.7190785255725
536583.56439.11584277528144.384157224724
5469906966.1700764739923.8299235260138
5568747077.12807145357-203.128071453571
5667106718.02635776379-8.02635776379066
5769246805.02161370829118.978386291712
587428.57287.16017390164141.339826098359
597415.57451.50623477746-36.0062347774556
607228.57269.5698047172-41.0698047171982
6167347357.8376890354-623.837689035397
627158.57229.71067036541-71.2106703654063
6371927171.2218239421520.7781760578528

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 1795 & 1689.328125 & 105.671875 \tabularnewline
6 & 1942.5 & 1917.28661978457 & 25.2133802154292 \tabularnewline
7 & 2100 & 2098.31925003562 & 1.68074996438372 \tabularnewline
8 & 2072.5 & 2019.24790404415 & 53.2520959558497 \tabularnewline
9 & 2075 & 2101.53193406296 & -26.5319340629635 \tabularnewline
10 & 2278 & 2208.25780428624 & 69.7421957137612 \tabularnewline
11 & 2451 & 2423.09077673435 & 27.9092232656494 \tabularnewline
12 & 2290.5 & 2377.77473067507 & -87.2747306750698 \tabularnewline
13 & 2388 & 2330.67474234405 & 57.3252576559544 \tabularnewline
14 & 2574.5 & 2525.09412417753 & 49.4058758224719 \tabularnewline
15 & 2939.5 & 2716.56154734532 & 222.938452654677 \tabularnewline
16 & 2924 & 2812.87800279208 & 111.121997207916 \tabularnewline
17 & 3087.5 & 2963.66733452015 & 123.832665479853 \tabularnewline
18 & 3259.5 & 3221.64167445504 & 37.8583255449616 \tabularnewline
19 & 3474.5 & 3447.47516486471 & 27.0248351352889 \tabularnewline
20 & 3376 & 3370.37729074632 & 5.62270925367966 \tabularnewline
21 & 3496 & 3442.30782058312 & 53.6921794168752 \tabularnewline
22 & 3771.5 & 3629.87075123152 & 141.629248768475 \tabularnewline
23 & 3743 & 3942.78666870311 & -199.786668703113 \tabularnewline
24 & 3474.5 & 3677.78263421701 & -203.282634217008 \tabularnewline
25 & 3405 & 3584.88806836988 & -179.888068369879 \tabularnewline
26 & 3684.5 & 3590.04059864827 & 94.4594013517303 \tabularnewline
27 & 3804 & 3789.3693064359 & 14.6306935640951 \tabularnewline
28 & 3470.5 & 3691.51995334663 & -221.019953346633 \tabularnewline
29 & 3453.5 & 3582.26819959498 & -128.768199594983 \tabularnewline
30 & 3842 & 3675.50991842899 & 166.490081571009 \tabularnewline
31 & 4156.5 & 3914.42312242984 & 242.07687757016 \tabularnewline
32 & 4055 & 3957.65505018789 & 97.3449498121072 \tabularnewline
33 & 4133.5 & 4132.24764645417 & 1.25235354582946 \tabularnewline
34 & 4552 & 4397.91827003974 & 154.081729960262 \tabularnewline
35 & 4588 & 4651.93861965224 & -63.938619652241 \tabularnewline
36 & 4423.5 & 4423.82564310166 & -0.325643101657988 \tabularnewline
37 & 4462.5 & 4503.04528719008 & -40.5452871900779 \tabularnewline
38 & 4846 & 4764.83883009864 & 81.161169901362 \tabularnewline
39 & 4869.5 & 4917.95502061655 & -48.4550206165504 \tabularnewline
40 & 4637 & 4714.25636879839 & -77.2563687983939 \tabularnewline
41 & 4841 & 4721.62614708736 & 119.373852912643 \tabularnewline
42 & 5114.5 & 5137.74828196841 & -23.2482819684083 \tabularnewline
43 & 5374.5 & 5181.03448249647 & 193.465517503534 \tabularnewline
44 & 5166.5 & 5172.6747516965 & -6.17475169649697 \tabularnewline
45 & 5236.5 & 5281.11092718716 & -44.6109271871574 \tabularnewline
46 & 5740.5 & 5539.91329801628 & 200.586701983723 \tabularnewline
47 & 5992 & 5813.22118770052 & 178.77881229948 \tabularnewline
48 & 5842 & 5762.37893148323 & 79.6210685167725 \tabularnewline
49 & 5844.5 & 5942.1916945926 & -97.6916945926014 \tabularnewline
50 & 6384.5 & 6212.30182789854 & 172.198172101459 \tabularnewline
51 & 6487 & 6465.77397452557 & 21.2260254744342 \tabularnewline
52 & 6372 & 6272.28092147443 & 99.7190785255725 \tabularnewline
53 & 6583.5 & 6439.11584277528 & 144.384157224724 \tabularnewline
54 & 6990 & 6966.17007647399 & 23.8299235260138 \tabularnewline
55 & 6874 & 7077.12807145357 & -203.128071453571 \tabularnewline
56 & 6710 & 6718.02635776379 & -8.02635776379066 \tabularnewline
57 & 6924 & 6805.02161370829 & 118.978386291712 \tabularnewline
58 & 7428.5 & 7287.16017390164 & 141.339826098359 \tabularnewline
59 & 7415.5 & 7451.50623477746 & -36.0062347774556 \tabularnewline
60 & 7228.5 & 7269.5698047172 & -41.0698047171982 \tabularnewline
61 & 6734 & 7357.8376890354 & -623.837689035397 \tabularnewline
62 & 7158.5 & 7229.71067036541 & -71.2106703654063 \tabularnewline
63 & 7192 & 7171.22182394215 & 20.7781760578528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302671&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]5[/C][C]1795[/C][C]1689.328125[/C][C]105.671875[/C][/ROW]
[ROW][C]6[/C][C]1942.5[/C][C]1917.28661978457[/C][C]25.2133802154292[/C][/ROW]
[ROW][C]7[/C][C]2100[/C][C]2098.31925003562[/C][C]1.68074996438372[/C][/ROW]
[ROW][C]8[/C][C]2072.5[/C][C]2019.24790404415[/C][C]53.2520959558497[/C][/ROW]
[ROW][C]9[/C][C]2075[/C][C]2101.53193406296[/C][C]-26.5319340629635[/C][/ROW]
[ROW][C]10[/C][C]2278[/C][C]2208.25780428624[/C][C]69.7421957137612[/C][/ROW]
[ROW][C]11[/C][C]2451[/C][C]2423.09077673435[/C][C]27.9092232656494[/C][/ROW]
[ROW][C]12[/C][C]2290.5[/C][C]2377.77473067507[/C][C]-87.2747306750698[/C][/ROW]
[ROW][C]13[/C][C]2388[/C][C]2330.67474234405[/C][C]57.3252576559544[/C][/ROW]
[ROW][C]14[/C][C]2574.5[/C][C]2525.09412417753[/C][C]49.4058758224719[/C][/ROW]
[ROW][C]15[/C][C]2939.5[/C][C]2716.56154734532[/C][C]222.938452654677[/C][/ROW]
[ROW][C]16[/C][C]2924[/C][C]2812.87800279208[/C][C]111.121997207916[/C][/ROW]
[ROW][C]17[/C][C]3087.5[/C][C]2963.66733452015[/C][C]123.832665479853[/C][/ROW]
[ROW][C]18[/C][C]3259.5[/C][C]3221.64167445504[/C][C]37.8583255449616[/C][/ROW]
[ROW][C]19[/C][C]3474.5[/C][C]3447.47516486471[/C][C]27.0248351352889[/C][/ROW]
[ROW][C]20[/C][C]3376[/C][C]3370.37729074632[/C][C]5.62270925367966[/C][/ROW]
[ROW][C]21[/C][C]3496[/C][C]3442.30782058312[/C][C]53.6921794168752[/C][/ROW]
[ROW][C]22[/C][C]3771.5[/C][C]3629.87075123152[/C][C]141.629248768475[/C][/ROW]
[ROW][C]23[/C][C]3743[/C][C]3942.78666870311[/C][C]-199.786668703113[/C][/ROW]
[ROW][C]24[/C][C]3474.5[/C][C]3677.78263421701[/C][C]-203.282634217008[/C][/ROW]
[ROW][C]25[/C][C]3405[/C][C]3584.88806836988[/C][C]-179.888068369879[/C][/ROW]
[ROW][C]26[/C][C]3684.5[/C][C]3590.04059864827[/C][C]94.4594013517303[/C][/ROW]
[ROW][C]27[/C][C]3804[/C][C]3789.3693064359[/C][C]14.6306935640951[/C][/ROW]
[ROW][C]28[/C][C]3470.5[/C][C]3691.51995334663[/C][C]-221.019953346633[/C][/ROW]
[ROW][C]29[/C][C]3453.5[/C][C]3582.26819959498[/C][C]-128.768199594983[/C][/ROW]
[ROW][C]30[/C][C]3842[/C][C]3675.50991842899[/C][C]166.490081571009[/C][/ROW]
[ROW][C]31[/C][C]4156.5[/C][C]3914.42312242984[/C][C]242.07687757016[/C][/ROW]
[ROW][C]32[/C][C]4055[/C][C]3957.65505018789[/C][C]97.3449498121072[/C][/ROW]
[ROW][C]33[/C][C]4133.5[/C][C]4132.24764645417[/C][C]1.25235354582946[/C][/ROW]
[ROW][C]34[/C][C]4552[/C][C]4397.91827003974[/C][C]154.081729960262[/C][/ROW]
[ROW][C]35[/C][C]4588[/C][C]4651.93861965224[/C][C]-63.938619652241[/C][/ROW]
[ROW][C]36[/C][C]4423.5[/C][C]4423.82564310166[/C][C]-0.325643101657988[/C][/ROW]
[ROW][C]37[/C][C]4462.5[/C][C]4503.04528719008[/C][C]-40.5452871900779[/C][/ROW]
[ROW][C]38[/C][C]4846[/C][C]4764.83883009864[/C][C]81.161169901362[/C][/ROW]
[ROW][C]39[/C][C]4869.5[/C][C]4917.95502061655[/C][C]-48.4550206165504[/C][/ROW]
[ROW][C]40[/C][C]4637[/C][C]4714.25636879839[/C][C]-77.2563687983939[/C][/ROW]
[ROW][C]41[/C][C]4841[/C][C]4721.62614708736[/C][C]119.373852912643[/C][/ROW]
[ROW][C]42[/C][C]5114.5[/C][C]5137.74828196841[/C][C]-23.2482819684083[/C][/ROW]
[ROW][C]43[/C][C]5374.5[/C][C]5181.03448249647[/C][C]193.465517503534[/C][/ROW]
[ROW][C]44[/C][C]5166.5[/C][C]5172.6747516965[/C][C]-6.17475169649697[/C][/ROW]
[ROW][C]45[/C][C]5236.5[/C][C]5281.11092718716[/C][C]-44.6109271871574[/C][/ROW]
[ROW][C]46[/C][C]5740.5[/C][C]5539.91329801628[/C][C]200.586701983723[/C][/ROW]
[ROW][C]47[/C][C]5992[/C][C]5813.22118770052[/C][C]178.77881229948[/C][/ROW]
[ROW][C]48[/C][C]5842[/C][C]5762.37893148323[/C][C]79.6210685167725[/C][/ROW]
[ROW][C]49[/C][C]5844.5[/C][C]5942.1916945926[/C][C]-97.6916945926014[/C][/ROW]
[ROW][C]50[/C][C]6384.5[/C][C]6212.30182789854[/C][C]172.198172101459[/C][/ROW]
[ROW][C]51[/C][C]6487[/C][C]6465.77397452557[/C][C]21.2260254744342[/C][/ROW]
[ROW][C]52[/C][C]6372[/C][C]6272.28092147443[/C][C]99.7190785255725[/C][/ROW]
[ROW][C]53[/C][C]6583.5[/C][C]6439.11584277528[/C][C]144.384157224724[/C][/ROW]
[ROW][C]54[/C][C]6990[/C][C]6966.17007647399[/C][C]23.8299235260138[/C][/ROW]
[ROW][C]55[/C][C]6874[/C][C]7077.12807145357[/C][C]-203.128071453571[/C][/ROW]
[ROW][C]56[/C][C]6710[/C][C]6718.02635776379[/C][C]-8.02635776379066[/C][/ROW]
[ROW][C]57[/C][C]6924[/C][C]6805.02161370829[/C][C]118.978386291712[/C][/ROW]
[ROW][C]58[/C][C]7428.5[/C][C]7287.16017390164[/C][C]141.339826098359[/C][/ROW]
[ROW][C]59[/C][C]7415.5[/C][C]7451.50623477746[/C][C]-36.0062347774556[/C][/ROW]
[ROW][C]60[/C][C]7228.5[/C][C]7269.5698047172[/C][C]-41.0698047171982[/C][/ROW]
[ROW][C]61[/C][C]6734[/C][C]7357.8376890354[/C][C]-623.837689035397[/C][/ROW]
[ROW][C]62[/C][C]7158.5[/C][C]7229.71067036541[/C][C]-71.2106703654063[/C][/ROW]
[ROW][C]63[/C][C]7192[/C][C]7171.22182394215[/C][C]20.7781760578528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302671&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302671&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
517951689.328125105.671875
61942.51917.2866197845725.2133802154292
721002098.319250035621.68074996438372
82072.52019.2479040441553.2520959558497
920752101.53193406296-26.5319340629635
1022782208.2578042862469.7421957137612
1124512423.0907767343527.9092232656494
122290.52377.77473067507-87.2747306750698
1323882330.6747423440557.3252576559544
142574.52525.0941241775349.4058758224719
152939.52716.56154734532222.938452654677
1629242812.87800279208111.121997207916
173087.52963.66733452015123.832665479853
183259.53221.6416744550437.8583255449616
193474.53447.4751648647127.0248351352889
2033763370.377290746325.62270925367966
2134963442.3078205831253.6921794168752
223771.53629.87075123152141.629248768475
2337433942.78666870311-199.786668703113
243474.53677.78263421701-203.282634217008
2534053584.88806836988-179.888068369879
263684.53590.0405986482794.4594013517303
2738043789.369306435914.6306935640951
283470.53691.51995334663-221.019953346633
293453.53582.26819959498-128.768199594983
3038423675.50991842899166.490081571009
314156.53914.42312242984242.07687757016
3240553957.6550501878997.3449498121072
334133.54132.247646454171.25235354582946
3445524397.91827003974154.081729960262
3545884651.93861965224-63.938619652241
364423.54423.82564310166-0.325643101657988
374462.54503.04528719008-40.5452871900779
3848464764.8388300986481.161169901362
394869.54917.95502061655-48.4550206165504
4046374714.25636879839-77.2563687983939
4148414721.62614708736119.373852912643
425114.55137.74828196841-23.2482819684083
435374.55181.03448249647193.465517503534
445166.55172.6747516965-6.17475169649697
455236.55281.11092718716-44.6109271871574
465740.55539.91329801628200.586701983723
4759925813.22118770052178.77881229948
4858425762.3789314832379.6210685167725
495844.55942.1916945926-97.6916945926014
506384.56212.30182789854172.198172101459
5164876465.7739745255721.2260254744342
5263726272.2809214744399.7190785255725
536583.56439.11584277528144.384157224724
5469906966.1700764739923.8299235260138
5568747077.12807145357-203.128071453571
5667106718.02635776379-8.02635776379066
5769246805.02161370829118.978386291712
587428.57287.16017390164141.339826098359
597415.57451.50623477746-36.0062347774556
607228.57269.5698047172-41.0698047171982
6167347357.8376890354-623.837689035397
627158.57229.71067036541-71.2106703654063
6371927171.2218239421520.7781760578528







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
647018.661690715926745.876801198537291.4465802333
657015.119186914156660.148741647577370.08963218073
667496.244104984337071.565038061537920.92317190714
677513.354902342747025.986277870248000.72352681525
687340.016593058666769.420505932057910.61268018527
697336.474089256896713.075330592077959.87284792172
707817.599007327087143.273560661888491.92445399227
717834.709804685497110.888014910898558.53159446008
727661.37149540146869.691604633318453.05138616949
737657.828991599646819.733478725798495.92450447348
748138.953909669827254.996550825249022.9112685144
758156.064707028237226.678715269489085.45069878698
767982.726397744156991.498895938068973.95389955023
777979.183893942386943.844748455929014.52303942884
788460.308812012567380.985587686879539.63203633826
798477.419609370977354.192966579999600.64625216195
808304.081300086897121.92499599889486.23760417499
818300.538796285127075.065791801779526.01180076848

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 7018.66169071592 & 6745.87680119853 & 7291.4465802333 \tabularnewline
65 & 7015.11918691415 & 6660.14874164757 & 7370.08963218073 \tabularnewline
66 & 7496.24410498433 & 7071.56503806153 & 7920.92317190714 \tabularnewline
67 & 7513.35490234274 & 7025.98627787024 & 8000.72352681525 \tabularnewline
68 & 7340.01659305866 & 6769.42050593205 & 7910.61268018527 \tabularnewline
69 & 7336.47408925689 & 6713.07533059207 & 7959.87284792172 \tabularnewline
70 & 7817.59900732708 & 7143.27356066188 & 8491.92445399227 \tabularnewline
71 & 7834.70980468549 & 7110.88801491089 & 8558.53159446008 \tabularnewline
72 & 7661.3714954014 & 6869.69160463331 & 8453.05138616949 \tabularnewline
73 & 7657.82899159964 & 6819.73347872579 & 8495.92450447348 \tabularnewline
74 & 8138.95390966982 & 7254.99655082524 & 9022.9112685144 \tabularnewline
75 & 8156.06470702823 & 7226.67871526948 & 9085.45069878698 \tabularnewline
76 & 7982.72639774415 & 6991.49889593806 & 8973.95389955023 \tabularnewline
77 & 7979.18389394238 & 6943.84474845592 & 9014.52303942884 \tabularnewline
78 & 8460.30881201256 & 7380.98558768687 & 9539.63203633826 \tabularnewline
79 & 8477.41960937097 & 7354.19296657999 & 9600.64625216195 \tabularnewline
80 & 8304.08130008689 & 7121.9249959988 & 9486.23760417499 \tabularnewline
81 & 8300.53879628512 & 7075.06579180177 & 9526.01180076848 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302671&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]64[/C][C]7018.66169071592[/C][C]6745.87680119853[/C][C]7291.4465802333[/C][/ROW]
[ROW][C]65[/C][C]7015.11918691415[/C][C]6660.14874164757[/C][C]7370.08963218073[/C][/ROW]
[ROW][C]66[/C][C]7496.24410498433[/C][C]7071.56503806153[/C][C]7920.92317190714[/C][/ROW]
[ROW][C]67[/C][C]7513.35490234274[/C][C]7025.98627787024[/C][C]8000.72352681525[/C][/ROW]
[ROW][C]68[/C][C]7340.01659305866[/C][C]6769.42050593205[/C][C]7910.61268018527[/C][/ROW]
[ROW][C]69[/C][C]7336.47408925689[/C][C]6713.07533059207[/C][C]7959.87284792172[/C][/ROW]
[ROW][C]70[/C][C]7817.59900732708[/C][C]7143.27356066188[/C][C]8491.92445399227[/C][/ROW]
[ROW][C]71[/C][C]7834.70980468549[/C][C]7110.88801491089[/C][C]8558.53159446008[/C][/ROW]
[ROW][C]72[/C][C]7661.3714954014[/C][C]6869.69160463331[/C][C]8453.05138616949[/C][/ROW]
[ROW][C]73[/C][C]7657.82899159964[/C][C]6819.73347872579[/C][C]8495.92450447348[/C][/ROW]
[ROW][C]74[/C][C]8138.95390966982[/C][C]7254.99655082524[/C][C]9022.9112685144[/C][/ROW]
[ROW][C]75[/C][C]8156.06470702823[/C][C]7226.67871526948[/C][C]9085.45069878698[/C][/ROW]
[ROW][C]76[/C][C]7982.72639774415[/C][C]6991.49889593806[/C][C]8973.95389955023[/C][/ROW]
[ROW][C]77[/C][C]7979.18389394238[/C][C]6943.84474845592[/C][C]9014.52303942884[/C][/ROW]
[ROW][C]78[/C][C]8460.30881201256[/C][C]7380.98558768687[/C][C]9539.63203633826[/C][/ROW]
[ROW][C]79[/C][C]8477.41960937097[/C][C]7354.19296657999[/C][C]9600.64625216195[/C][/ROW]
[ROW][C]80[/C][C]8304.08130008689[/C][C]7121.9249959988[/C][C]9486.23760417499[/C][/ROW]
[ROW][C]81[/C][C]8300.53879628512[/C][C]7075.06579180177[/C][C]9526.01180076848[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302671&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302671&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
647018.661690715926745.876801198537291.4465802333
657015.119186914156660.148741647577370.08963218073
667496.244104984337071.565038061537920.92317190714
677513.354902342747025.986277870248000.72352681525
687340.016593058666769.420505932057910.61268018527
697336.474089256896713.075330592077959.87284792172
707817.599007327087143.273560661888491.92445399227
717834.709804685497110.888014910898558.53159446008
727661.37149540146869.691604633318453.05138616949
737657.828991599646819.733478725798495.92450447348
748138.953909669827254.996550825249022.9112685144
758156.064707028237226.678715269489085.45069878698
767982.726397744156991.498895938068973.95389955023
777979.183893942386943.844748455929014.52303942884
788460.308812012567380.985587686879539.63203633826
798477.419609370977354.192966579999600.64625216195
808304.081300086897121.92499599889486.23760417499
818300.538796285127075.065791801779526.01180076848



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '3'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')