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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 computationWed, 21 Dec 2011 17:45:33 -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/2011/Dec/21/t13245075519ab7w4yj9m44un6.htm/, Retrieved Tue, 07 May 2024 22:01:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159115, Retrieved Tue, 07 May 2024 22:01:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2011-12-21 22:45:33] [e569a00cc6e8044e6afea1f18dd335a0] [Current]
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Dataseries X:
2582
2624
2566
2645
3167
3051
2503
2574
2988
3086
2632
2604
2377
2258
2266
2601
2843
3018
2493
2647
3015
3101
2496
2342
2271
1969
2196
2294
2706
3001
2691
2554
2961
3226
2960
2749
2379
2254
2592
2780
2833
2911
2494
2643
2902
2880
2657
2609
2394
2492
2414
2621
3055
2940
2582
2430
2781
2904
2474
2254
2244
1972
2408
2523
2634
2798
2418
2551
2741
3011
2558
2167
1944
1836
2292
2576
2653
2900
2438
2439
2717
2872
2157
1541




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159115&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159115&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159115&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.621326496880825
beta0
gamma0.681722555897902

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.621326496880825 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.681722555897902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159115&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]0.621326496880825[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.681722555897902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159115&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159115&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
alpha0.621326496880825
beta0
gamma0.681722555897902







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323772466.81490384615-89.8149038461534
1422582281.37751145122-23.3775114512218
1522662262.677764668263.32223533173601
1626012589.9839446882311.0160553117685
1728432835.862165590697.13783440930729
1830183023.87241175236-5.8724117523634
1924932386.25738057618106.742619423821
2026472539.36305221682107.636947783181
2130153039.98272709737-24.9827270973747
2231013128.78561730025-27.7856173002538
2324962664.84699755224-168.846997552236
2423422538.80487123375-196.804871233747
2522712160.1227023332110.8772976668
2619692116.53152313398-147.531523133975
2721962027.58414599663168.415854003371
2822942459.45352745607-165.453527456068
2927062594.68535692449111.314643075506
3030012844.06481613241156.935183867591
3126912336.67805853205354.321941467946
3225542643.8421941445-89.842194144504
3329612987.52704089893-26.5270408989331
3432263074.64684115924151.353158840756
3529602685.59685647391274.403143526093
3627492827.74045495885-78.7404549588505
3723792601.84307071138-222.843070711378
3822542284.19427764403-30.1942776440333
3925922349.713540408242.286459592
4027802741.2922160269238.7077839730796
4128333074.82265543075-241.822655430746
4229113116.56550888972-205.565508889716
4324942434.9029101941859.0970898058213
4426432443.97493211047199.025067889532
4529022983.48548665201-81.485486652015
4628803082.3779696439-202.377969643899
4726572505.31084863228151.689151367716
4826092480.04487751956128.955122480445
4923942345.9941298868248.0058701131752
5024922246.36329804262245.636701957384
5124142553.60463254409-139.604632544091
5226212655.35036394513-34.3503639451274
5330552871.06883200865183.931167991354
5429403186.70360921897-246.703609218971
5525822547.8035396454834.1964603545166
5624302577.52658579326-147.526585793256
5727812829.30154042067-48.3015404206672
5829042917.6036615456-13.603661545596
5924742549.22954240558-75.2295424055792
6022542377.10417855492-123.104178554917
6122442065.54523717849178.454762821509
6219722097.98421114688-125.984211146882
6324082074.87747164237333.122528357627
6425232497.5125315956725.4874684043325
6526342806.75926646938-172.759266469376
6627982789.604342247298.39565775270512
6724182381.7186349313836.2813650686221
6825512365.82523448449185.174765515511
6927412849.93132632275-108.931326322753
7030112909.51982171092101.480178289082
7125582596.74160393876-38.7416039387554
7221672434.92831290272-267.928312902718
7319442111.23382112208-167.233821122079
7418361850.29631537659-14.2963153765945
7522922015.10275292109276.897247078912
7625762323.387482526252.612517473997
7726532722.57558067553-69.5755806755324
7829002816.296606792483.7033932076001
7924382462.40029376275-24.4002937627511
8024392447.24064209719-8.24064209718608
8127172735.24904973537-18.249049735372
8228722905.49863275416-33.4986327541596
8321572472.65621244611-315.656212446109
8415412079.62392733895-538.623927338951

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2377 & 2466.81490384615 & -89.8149038461534 \tabularnewline
14 & 2258 & 2281.37751145122 & -23.3775114512218 \tabularnewline
15 & 2266 & 2262.67776466826 & 3.32223533173601 \tabularnewline
16 & 2601 & 2589.98394468823 & 11.0160553117685 \tabularnewline
17 & 2843 & 2835.86216559069 & 7.13783440930729 \tabularnewline
18 & 3018 & 3023.87241175236 & -5.8724117523634 \tabularnewline
19 & 2493 & 2386.25738057618 & 106.742619423821 \tabularnewline
20 & 2647 & 2539.36305221682 & 107.636947783181 \tabularnewline
21 & 3015 & 3039.98272709737 & -24.9827270973747 \tabularnewline
22 & 3101 & 3128.78561730025 & -27.7856173002538 \tabularnewline
23 & 2496 & 2664.84699755224 & -168.846997552236 \tabularnewline
24 & 2342 & 2538.80487123375 & -196.804871233747 \tabularnewline
25 & 2271 & 2160.1227023332 & 110.8772976668 \tabularnewline
26 & 1969 & 2116.53152313398 & -147.531523133975 \tabularnewline
27 & 2196 & 2027.58414599663 & 168.415854003371 \tabularnewline
28 & 2294 & 2459.45352745607 & -165.453527456068 \tabularnewline
29 & 2706 & 2594.68535692449 & 111.314643075506 \tabularnewline
30 & 3001 & 2844.06481613241 & 156.935183867591 \tabularnewline
31 & 2691 & 2336.67805853205 & 354.321941467946 \tabularnewline
32 & 2554 & 2643.8421941445 & -89.842194144504 \tabularnewline
33 & 2961 & 2987.52704089893 & -26.5270408989331 \tabularnewline
34 & 3226 & 3074.64684115924 & 151.353158840756 \tabularnewline
35 & 2960 & 2685.59685647391 & 274.403143526093 \tabularnewline
36 & 2749 & 2827.74045495885 & -78.7404549588505 \tabularnewline
37 & 2379 & 2601.84307071138 & -222.843070711378 \tabularnewline
38 & 2254 & 2284.19427764403 & -30.1942776440333 \tabularnewline
39 & 2592 & 2349.713540408 & 242.286459592 \tabularnewline
40 & 2780 & 2741.29221602692 & 38.7077839730796 \tabularnewline
41 & 2833 & 3074.82265543075 & -241.822655430746 \tabularnewline
42 & 2911 & 3116.56550888972 & -205.565508889716 \tabularnewline
43 & 2494 & 2434.90291019418 & 59.0970898058213 \tabularnewline
44 & 2643 & 2443.97493211047 & 199.025067889532 \tabularnewline
45 & 2902 & 2983.48548665201 & -81.485486652015 \tabularnewline
46 & 2880 & 3082.3779696439 & -202.377969643899 \tabularnewline
47 & 2657 & 2505.31084863228 & 151.689151367716 \tabularnewline
48 & 2609 & 2480.04487751956 & 128.955122480445 \tabularnewline
49 & 2394 & 2345.99412988682 & 48.0058701131752 \tabularnewline
50 & 2492 & 2246.36329804262 & 245.636701957384 \tabularnewline
51 & 2414 & 2553.60463254409 & -139.604632544091 \tabularnewline
52 & 2621 & 2655.35036394513 & -34.3503639451274 \tabularnewline
53 & 3055 & 2871.06883200865 & 183.931167991354 \tabularnewline
54 & 2940 & 3186.70360921897 & -246.703609218971 \tabularnewline
55 & 2582 & 2547.80353964548 & 34.1964603545166 \tabularnewline
56 & 2430 & 2577.52658579326 & -147.526585793256 \tabularnewline
57 & 2781 & 2829.30154042067 & -48.3015404206672 \tabularnewline
58 & 2904 & 2917.6036615456 & -13.603661545596 \tabularnewline
59 & 2474 & 2549.22954240558 & -75.2295424055792 \tabularnewline
60 & 2254 & 2377.10417855492 & -123.104178554917 \tabularnewline
61 & 2244 & 2065.54523717849 & 178.454762821509 \tabularnewline
62 & 1972 & 2097.98421114688 & -125.984211146882 \tabularnewline
63 & 2408 & 2074.87747164237 & 333.122528357627 \tabularnewline
64 & 2523 & 2497.51253159567 & 25.4874684043325 \tabularnewline
65 & 2634 & 2806.75926646938 & -172.759266469376 \tabularnewline
66 & 2798 & 2789.60434224729 & 8.39565775270512 \tabularnewline
67 & 2418 & 2381.71863493138 & 36.2813650686221 \tabularnewline
68 & 2551 & 2365.82523448449 & 185.174765515511 \tabularnewline
69 & 2741 & 2849.93132632275 & -108.931326322753 \tabularnewline
70 & 3011 & 2909.51982171092 & 101.480178289082 \tabularnewline
71 & 2558 & 2596.74160393876 & -38.7416039387554 \tabularnewline
72 & 2167 & 2434.92831290272 & -267.928312902718 \tabularnewline
73 & 1944 & 2111.23382112208 & -167.233821122079 \tabularnewline
74 & 1836 & 1850.29631537659 & -14.2963153765945 \tabularnewline
75 & 2292 & 2015.10275292109 & 276.897247078912 \tabularnewline
76 & 2576 & 2323.387482526 & 252.612517473997 \tabularnewline
77 & 2653 & 2722.57558067553 & -69.5755806755324 \tabularnewline
78 & 2900 & 2816.2966067924 & 83.7033932076001 \tabularnewline
79 & 2438 & 2462.40029376275 & -24.4002937627511 \tabularnewline
80 & 2439 & 2447.24064209719 & -8.24064209718608 \tabularnewline
81 & 2717 & 2735.24904973537 & -18.249049735372 \tabularnewline
82 & 2872 & 2905.49863275416 & -33.4986327541596 \tabularnewline
83 & 2157 & 2472.65621244611 & -315.656212446109 \tabularnewline
84 & 1541 & 2079.62392733895 & -538.623927338951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159115&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]2377[/C][C]2466.81490384615[/C][C]-89.8149038461534[/C][/ROW]
[ROW][C]14[/C][C]2258[/C][C]2281.37751145122[/C][C]-23.3775114512218[/C][/ROW]
[ROW][C]15[/C][C]2266[/C][C]2262.67776466826[/C][C]3.32223533173601[/C][/ROW]
[ROW][C]16[/C][C]2601[/C][C]2589.98394468823[/C][C]11.0160553117685[/C][/ROW]
[ROW][C]17[/C][C]2843[/C][C]2835.86216559069[/C][C]7.13783440930729[/C][/ROW]
[ROW][C]18[/C][C]3018[/C][C]3023.87241175236[/C][C]-5.8724117523634[/C][/ROW]
[ROW][C]19[/C][C]2493[/C][C]2386.25738057618[/C][C]106.742619423821[/C][/ROW]
[ROW][C]20[/C][C]2647[/C][C]2539.36305221682[/C][C]107.636947783181[/C][/ROW]
[ROW][C]21[/C][C]3015[/C][C]3039.98272709737[/C][C]-24.9827270973747[/C][/ROW]
[ROW][C]22[/C][C]3101[/C][C]3128.78561730025[/C][C]-27.7856173002538[/C][/ROW]
[ROW][C]23[/C][C]2496[/C][C]2664.84699755224[/C][C]-168.846997552236[/C][/ROW]
[ROW][C]24[/C][C]2342[/C][C]2538.80487123375[/C][C]-196.804871233747[/C][/ROW]
[ROW][C]25[/C][C]2271[/C][C]2160.1227023332[/C][C]110.8772976668[/C][/ROW]
[ROW][C]26[/C][C]1969[/C][C]2116.53152313398[/C][C]-147.531523133975[/C][/ROW]
[ROW][C]27[/C][C]2196[/C][C]2027.58414599663[/C][C]168.415854003371[/C][/ROW]
[ROW][C]28[/C][C]2294[/C][C]2459.45352745607[/C][C]-165.453527456068[/C][/ROW]
[ROW][C]29[/C][C]2706[/C][C]2594.68535692449[/C][C]111.314643075506[/C][/ROW]
[ROW][C]30[/C][C]3001[/C][C]2844.06481613241[/C][C]156.935183867591[/C][/ROW]
[ROW][C]31[/C][C]2691[/C][C]2336.67805853205[/C][C]354.321941467946[/C][/ROW]
[ROW][C]32[/C][C]2554[/C][C]2643.8421941445[/C][C]-89.842194144504[/C][/ROW]
[ROW][C]33[/C][C]2961[/C][C]2987.52704089893[/C][C]-26.5270408989331[/C][/ROW]
[ROW][C]34[/C][C]3226[/C][C]3074.64684115924[/C][C]151.353158840756[/C][/ROW]
[ROW][C]35[/C][C]2960[/C][C]2685.59685647391[/C][C]274.403143526093[/C][/ROW]
[ROW][C]36[/C][C]2749[/C][C]2827.74045495885[/C][C]-78.7404549588505[/C][/ROW]
[ROW][C]37[/C][C]2379[/C][C]2601.84307071138[/C][C]-222.843070711378[/C][/ROW]
[ROW][C]38[/C][C]2254[/C][C]2284.19427764403[/C][C]-30.1942776440333[/C][/ROW]
[ROW][C]39[/C][C]2592[/C][C]2349.713540408[/C][C]242.286459592[/C][/ROW]
[ROW][C]40[/C][C]2780[/C][C]2741.29221602692[/C][C]38.7077839730796[/C][/ROW]
[ROW][C]41[/C][C]2833[/C][C]3074.82265543075[/C][C]-241.822655430746[/C][/ROW]
[ROW][C]42[/C][C]2911[/C][C]3116.56550888972[/C][C]-205.565508889716[/C][/ROW]
[ROW][C]43[/C][C]2494[/C][C]2434.90291019418[/C][C]59.0970898058213[/C][/ROW]
[ROW][C]44[/C][C]2643[/C][C]2443.97493211047[/C][C]199.025067889532[/C][/ROW]
[ROW][C]45[/C][C]2902[/C][C]2983.48548665201[/C][C]-81.485486652015[/C][/ROW]
[ROW][C]46[/C][C]2880[/C][C]3082.3779696439[/C][C]-202.377969643899[/C][/ROW]
[ROW][C]47[/C][C]2657[/C][C]2505.31084863228[/C][C]151.689151367716[/C][/ROW]
[ROW][C]48[/C][C]2609[/C][C]2480.04487751956[/C][C]128.955122480445[/C][/ROW]
[ROW][C]49[/C][C]2394[/C][C]2345.99412988682[/C][C]48.0058701131752[/C][/ROW]
[ROW][C]50[/C][C]2492[/C][C]2246.36329804262[/C][C]245.636701957384[/C][/ROW]
[ROW][C]51[/C][C]2414[/C][C]2553.60463254409[/C][C]-139.604632544091[/C][/ROW]
[ROW][C]52[/C][C]2621[/C][C]2655.35036394513[/C][C]-34.3503639451274[/C][/ROW]
[ROW][C]53[/C][C]3055[/C][C]2871.06883200865[/C][C]183.931167991354[/C][/ROW]
[ROW][C]54[/C][C]2940[/C][C]3186.70360921897[/C][C]-246.703609218971[/C][/ROW]
[ROW][C]55[/C][C]2582[/C][C]2547.80353964548[/C][C]34.1964603545166[/C][/ROW]
[ROW][C]56[/C][C]2430[/C][C]2577.52658579326[/C][C]-147.526585793256[/C][/ROW]
[ROW][C]57[/C][C]2781[/C][C]2829.30154042067[/C][C]-48.3015404206672[/C][/ROW]
[ROW][C]58[/C][C]2904[/C][C]2917.6036615456[/C][C]-13.603661545596[/C][/ROW]
[ROW][C]59[/C][C]2474[/C][C]2549.22954240558[/C][C]-75.2295424055792[/C][/ROW]
[ROW][C]60[/C][C]2254[/C][C]2377.10417855492[/C][C]-123.104178554917[/C][/ROW]
[ROW][C]61[/C][C]2244[/C][C]2065.54523717849[/C][C]178.454762821509[/C][/ROW]
[ROW][C]62[/C][C]1972[/C][C]2097.98421114688[/C][C]-125.984211146882[/C][/ROW]
[ROW][C]63[/C][C]2408[/C][C]2074.87747164237[/C][C]333.122528357627[/C][/ROW]
[ROW][C]64[/C][C]2523[/C][C]2497.51253159567[/C][C]25.4874684043325[/C][/ROW]
[ROW][C]65[/C][C]2634[/C][C]2806.75926646938[/C][C]-172.759266469376[/C][/ROW]
[ROW][C]66[/C][C]2798[/C][C]2789.60434224729[/C][C]8.39565775270512[/C][/ROW]
[ROW][C]67[/C][C]2418[/C][C]2381.71863493138[/C][C]36.2813650686221[/C][/ROW]
[ROW][C]68[/C][C]2551[/C][C]2365.82523448449[/C][C]185.174765515511[/C][/ROW]
[ROW][C]69[/C][C]2741[/C][C]2849.93132632275[/C][C]-108.931326322753[/C][/ROW]
[ROW][C]70[/C][C]3011[/C][C]2909.51982171092[/C][C]101.480178289082[/C][/ROW]
[ROW][C]71[/C][C]2558[/C][C]2596.74160393876[/C][C]-38.7416039387554[/C][/ROW]
[ROW][C]72[/C][C]2167[/C][C]2434.92831290272[/C][C]-267.928312902718[/C][/ROW]
[ROW][C]73[/C][C]1944[/C][C]2111.23382112208[/C][C]-167.233821122079[/C][/ROW]
[ROW][C]74[/C][C]1836[/C][C]1850.29631537659[/C][C]-14.2963153765945[/C][/ROW]
[ROW][C]75[/C][C]2292[/C][C]2015.10275292109[/C][C]276.897247078912[/C][/ROW]
[ROW][C]76[/C][C]2576[/C][C]2323.387482526[/C][C]252.612517473997[/C][/ROW]
[ROW][C]77[/C][C]2653[/C][C]2722.57558067553[/C][C]-69.5755806755324[/C][/ROW]
[ROW][C]78[/C][C]2900[/C][C]2816.2966067924[/C][C]83.7033932076001[/C][/ROW]
[ROW][C]79[/C][C]2438[/C][C]2462.40029376275[/C][C]-24.4002937627511[/C][/ROW]
[ROW][C]80[/C][C]2439[/C][C]2447.24064209719[/C][C]-8.24064209718608[/C][/ROW]
[ROW][C]81[/C][C]2717[/C][C]2735.24904973537[/C][C]-18.249049735372[/C][/ROW]
[ROW][C]82[/C][C]2872[/C][C]2905.49863275416[/C][C]-33.4986327541596[/C][/ROW]
[ROW][C]83[/C][C]2157[/C][C]2472.65621244611[/C][C]-315.656212446109[/C][/ROW]
[ROW][C]84[/C][C]1541[/C][C]2079.62392733895[/C][C]-538.623927338951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159115&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159115&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
1323772466.81490384615-89.8149038461534
1422582281.37751145122-23.3775114512218
1522662262.677764668263.32223533173601
1626012589.9839446882311.0160553117685
1728432835.862165590697.13783440930729
1830183023.87241175236-5.8724117523634
1924932386.25738057618106.742619423821
2026472539.36305221682107.636947783181
2130153039.98272709737-24.9827270973747
2231013128.78561730025-27.7856173002538
2324962664.84699755224-168.846997552236
2423422538.80487123375-196.804871233747
2522712160.1227023332110.8772976668
2619692116.53152313398-147.531523133975
2721962027.58414599663168.415854003371
2822942459.45352745607-165.453527456068
2927062594.68535692449111.314643075506
3030012844.06481613241156.935183867591
3126912336.67805853205354.321941467946
3225542643.8421941445-89.842194144504
3329612987.52704089893-26.5270408989331
3432263074.64684115924151.353158840756
3529602685.59685647391274.403143526093
3627492827.74045495885-78.7404549588505
3723792601.84307071138-222.843070711378
3822542284.19427764403-30.1942776440333
3925922349.713540408242.286459592
4027802741.2922160269238.7077839730796
4128333074.82265543075-241.822655430746
4229113116.56550888972-205.565508889716
4324942434.9029101941859.0970898058213
4426432443.97493211047199.025067889532
4529022983.48548665201-81.485486652015
4628803082.3779696439-202.377969643899
4726572505.31084863228151.689151367716
4826092480.04487751956128.955122480445
4923942345.9941298868248.0058701131752
5024922246.36329804262245.636701957384
5124142553.60463254409-139.604632544091
5226212655.35036394513-34.3503639451274
5330552871.06883200865183.931167991354
5429403186.70360921897-246.703609218971
5525822547.8035396454834.1964603545166
5624302577.52658579326-147.526585793256
5727812829.30154042067-48.3015404206672
5829042917.6036615456-13.603661545596
5924742549.22954240558-75.2295424055792
6022542377.10417855492-123.104178554917
6122442065.54523717849178.454762821509
6219722097.98421114688-125.984211146882
6324082074.87747164237333.122528357627
6425232497.5125315956725.4874684043325
6526342806.75926646938-172.759266469376
6627982789.604342247298.39565775270512
6724182381.7186349313836.2813650686221
6825512365.82523448449185.174765515511
6927412849.93132632275-108.931326322753
7030112909.51982171092101.480178289082
7125582596.74160393876-38.7416039387554
7221672434.92831290272-267.928312902718
7319442111.23382112208-167.233821122079
7418361850.29631537659-14.2963153765945
7522922015.10275292109276.897247078912
7625762323.387482526252.612517473997
7726532722.57558067553-69.5755806755324
7829002816.296606792483.7033932076001
7924382462.40029376275-24.4002937627511
8024392447.24064209719-8.24064209718608
8127172735.24904973537-18.249049735372
8228722905.49863275416-33.4986327541596
8321572472.65621244611-315.656212446109
8415412079.62392733895-538.623927338951







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851613.733387798941291.197645283871936.26913031401
861496.183544447431116.460663376951875.9064255179
871745.044357846591315.684802674982174.40391301821
881875.016381462561401.191742143462348.84102078167
892034.076685050041519.615850744262548.53751935581
902210.595871224061658.481651842512762.71009060562
911776.785426309571189.426700783162364.14415183599
921780.957942105151160.353048746482401.56283546382
932071.50280591161419.34439350752723.6612183157
942249.154323124631566.900150489422931.40849575983
951764.286436028231053.209142559472475.36372949699
961509.82054417538771.0437994848312248.59728886593

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1613.73338779894 & 1291.19764528387 & 1936.26913031401 \tabularnewline
86 & 1496.18354444743 & 1116.46066337695 & 1875.9064255179 \tabularnewline
87 & 1745.04435784659 & 1315.68480267498 & 2174.40391301821 \tabularnewline
88 & 1875.01638146256 & 1401.19174214346 & 2348.84102078167 \tabularnewline
89 & 2034.07668505004 & 1519.61585074426 & 2548.53751935581 \tabularnewline
90 & 2210.59587122406 & 1658.48165184251 & 2762.71009060562 \tabularnewline
91 & 1776.78542630957 & 1189.42670078316 & 2364.14415183599 \tabularnewline
92 & 1780.95794210515 & 1160.35304874648 & 2401.56283546382 \tabularnewline
93 & 2071.5028059116 & 1419.3443935075 & 2723.6612183157 \tabularnewline
94 & 2249.15432312463 & 1566.90015048942 & 2931.40849575983 \tabularnewline
95 & 1764.28643602823 & 1053.20914255947 & 2475.36372949699 \tabularnewline
96 & 1509.82054417538 & 771.043799484831 & 2248.59728886593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159115&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]85[/C][C]1613.73338779894[/C][C]1291.19764528387[/C][C]1936.26913031401[/C][/ROW]
[ROW][C]86[/C][C]1496.18354444743[/C][C]1116.46066337695[/C][C]1875.9064255179[/C][/ROW]
[ROW][C]87[/C][C]1745.04435784659[/C][C]1315.68480267498[/C][C]2174.40391301821[/C][/ROW]
[ROW][C]88[/C][C]1875.01638146256[/C][C]1401.19174214346[/C][C]2348.84102078167[/C][/ROW]
[ROW][C]89[/C][C]2034.07668505004[/C][C]1519.61585074426[/C][C]2548.53751935581[/C][/ROW]
[ROW][C]90[/C][C]2210.59587122406[/C][C]1658.48165184251[/C][C]2762.71009060562[/C][/ROW]
[ROW][C]91[/C][C]1776.78542630957[/C][C]1189.42670078316[/C][C]2364.14415183599[/C][/ROW]
[ROW][C]92[/C][C]1780.95794210515[/C][C]1160.35304874648[/C][C]2401.56283546382[/C][/ROW]
[ROW][C]93[/C][C]2071.5028059116[/C][C]1419.3443935075[/C][C]2723.6612183157[/C][/ROW]
[ROW][C]94[/C][C]2249.15432312463[/C][C]1566.90015048942[/C][C]2931.40849575983[/C][/ROW]
[ROW][C]95[/C][C]1764.28643602823[/C][C]1053.20914255947[/C][C]2475.36372949699[/C][/ROW]
[ROW][C]96[/C][C]1509.82054417538[/C][C]771.043799484831[/C][C]2248.59728886593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159115&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159115&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
851613.733387798941291.197645283871936.26913031401
861496.183544447431116.460663376951875.9064255179
871745.044357846591315.684802674982174.40391301821
881875.016381462561401.191742143462348.84102078167
892034.076685050041519.615850744262548.53751935581
902210.595871224061658.481651842512762.71009060562
911776.785426309571189.426700783162364.14415183599
921780.957942105151160.353048746482401.56283546382
932071.50280591161419.34439350752723.6612183157
942249.154323124631566.900150489422931.40849575983
951764.286436028231053.209142559472475.36372949699
961509.82054417538771.0437994848312248.59728886593



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=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')