Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Dec 2013 11:04:41 -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/2013/Dec/14/t1387037096rw235nt5batqzb2.htm/, Retrieved Fri, 19 Apr 2024 23:46:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232318, Retrieved Fri, 19 Apr 2024 23:46:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-14 16:04:41] [6db2c0c963bf82ed406b79886f98dcae] [Current]
Feedback Forum

Post a new message
Dataseries X:
4309
4303
4177
4117
4065
3983
4091
4067
4024
3868
3800
3804
3862
3792
3674
3560
3489
3412
3674
3672
3463
3429
3400
3533
3578
3544
3435
3352
3213
3235
3460
3385
3283
3295
3331
3520
3668
3714
3691
3604
3581
3675
3833
3810
3663
3704
3810
4053
4152
4139
4055
3928
3821
3811
3999
3954
3724
3731
3697
3818
3897
3888
3754
3647
3564
3498
3704
3678
3599
3507
3484
2612
2926
2918
2833
2791
2762
2728
2831
2839
2775
2540
2625
2669




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232318&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232318&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.95684880643864
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.95684880643864 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232318&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]0.95684880643864[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232318&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
alpha0.95684880643864
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
341774297-120
441174176.17814322736-59.1781432273629
540654113.55360751301-48.5536075130058
639834061.0951461159-78.0951461158961
740913980.36989876625110.63010123375
840674080.22617908795-13.2261790879497
940244061.5707254139-37.5707254139015
1038684019.62122164458-151.621221644576
1138003868.54263668319-68.5426366831948
1238043796.957696582727.04230341727725
1338623797.6961162021264.3038837978766
1437923853.22521066349-61.2252106634905
1536743788.64194091618-114.641940916175
1635603672.94693658272-112.946936582724
1734893558.87379512264-69.873795122644
1834123486.0151376582-74.0151376582039
1936743409.19384153156264.80615846844
2036723656.5732981996915.426701800312
2134633665.3343194046-202.334319404602
2234293465.73096738073-36.730967380734
2334003424.58498508314-24.5849850831419
2435333395.06087145003137.939128549974
2535783521.0477619642556.9522380357453
2635443569.54244295277-25.542442952767
2734353539.10218689989-104.102186899885
2833523433.49213361708-81.4921336170778
2932133349.51648283144-136.516482831439
3032353212.8908491749822.1091508250247
3134603228.04596375327231.954036246728
3233853443.99090648458-58.9909064845788
3332833381.54552802408-98.5455280240762
3432953281.2523571543713.7476428456266
3533313288.4067728025642.5932271974439
3635203323.1620514088196.8379485912
3736683505.50620758012162.49379241988
3837143654.9881989107759.0118010892297
3936913705.45357034879-14.4535703487941
4036043685.62368881177-81.6236888117737
4135813601.52215959511-20.5221595951089
4236753575.8855556809999.1144443190142
4338333664.72309342846168.276906571537
4438103819.73865063262-9.73865063262474
4536633804.42023439847-141.420234398475
4637043663.1024519080240.8975480919785
4738103696.2352219861113.764778013902
4840533799.09091404346253.909085956543
4941524036.0435198849115.956480115099
5041394140.99633948186-1.99633948185965
5140554133.0861444314-78.086144431396
5239284052.36951033282-124.36951033282
5338213927.3666928135-106.366692813503
5438113819.58984975008-8.58984975007706
5539993805.37066226923193.629337730772
5639543984.64466296842-30.6446629684215
5737243949.32235378337-225.322353783373
5837313727.722928501813.27707149819253
5936973724.85859045347-27.8585904534671
6038183692.202131429125.797868570996
6138973806.5716718236990.4283281763137
6238883887.097909707430.902090292566299
6337543881.96107372718-127.961073727176
6436473753.52167306072-106.521673060721
6535643645.59653733272-81.5965373327231
6634983561.52098797638-63.5209879763811
6737043494.74100644738209.258993552623
6836783688.97022466476-10.9702246647553
6935993672.47337828792-73.4733782879202
7035073596.17046396811-89.1704639681093
7134843504.84781195064-20.847811950644
7226123478.89960796881-866.899607968813
7329262643.40775278173282.592247218271
7429182907.8058072413410.1941927586554
7528332911.56010841507-78.5601084150694
7627912830.38996244442-39.3899624444202
7727622786.69972389381-24.6997238938138
7827282757.06582256665-29.0658225666543
7928312723.25422493559107.745775064406
8028392820.3506412047818.6493587952232
8127752832.19525790883-57.195257908832
8225402771.46804364482-231.468043644816
8326252543.9881223545981.0118776454133
8426692615.5042407869553.4957592130463

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4177 & 4297 & -120 \tabularnewline
4 & 4117 & 4176.17814322736 & -59.1781432273629 \tabularnewline
5 & 4065 & 4113.55360751301 & -48.5536075130058 \tabularnewline
6 & 3983 & 4061.0951461159 & -78.0951461158961 \tabularnewline
7 & 4091 & 3980.36989876625 & 110.63010123375 \tabularnewline
8 & 4067 & 4080.22617908795 & -13.2261790879497 \tabularnewline
9 & 4024 & 4061.5707254139 & -37.5707254139015 \tabularnewline
10 & 3868 & 4019.62122164458 & -151.621221644576 \tabularnewline
11 & 3800 & 3868.54263668319 & -68.5426366831948 \tabularnewline
12 & 3804 & 3796.95769658272 & 7.04230341727725 \tabularnewline
13 & 3862 & 3797.69611620212 & 64.3038837978766 \tabularnewline
14 & 3792 & 3853.22521066349 & -61.2252106634905 \tabularnewline
15 & 3674 & 3788.64194091618 & -114.641940916175 \tabularnewline
16 & 3560 & 3672.94693658272 & -112.946936582724 \tabularnewline
17 & 3489 & 3558.87379512264 & -69.873795122644 \tabularnewline
18 & 3412 & 3486.0151376582 & -74.0151376582039 \tabularnewline
19 & 3674 & 3409.19384153156 & 264.80615846844 \tabularnewline
20 & 3672 & 3656.57329819969 & 15.426701800312 \tabularnewline
21 & 3463 & 3665.3343194046 & -202.334319404602 \tabularnewline
22 & 3429 & 3465.73096738073 & -36.730967380734 \tabularnewline
23 & 3400 & 3424.58498508314 & -24.5849850831419 \tabularnewline
24 & 3533 & 3395.06087145003 & 137.939128549974 \tabularnewline
25 & 3578 & 3521.04776196425 & 56.9522380357453 \tabularnewline
26 & 3544 & 3569.54244295277 & -25.542442952767 \tabularnewline
27 & 3435 & 3539.10218689989 & -104.102186899885 \tabularnewline
28 & 3352 & 3433.49213361708 & -81.4921336170778 \tabularnewline
29 & 3213 & 3349.51648283144 & -136.516482831439 \tabularnewline
30 & 3235 & 3212.89084917498 & 22.1091508250247 \tabularnewline
31 & 3460 & 3228.04596375327 & 231.954036246728 \tabularnewline
32 & 3385 & 3443.99090648458 & -58.9909064845788 \tabularnewline
33 & 3283 & 3381.54552802408 & -98.5455280240762 \tabularnewline
34 & 3295 & 3281.25235715437 & 13.7476428456266 \tabularnewline
35 & 3331 & 3288.40677280256 & 42.5932271974439 \tabularnewline
36 & 3520 & 3323.1620514088 & 196.8379485912 \tabularnewline
37 & 3668 & 3505.50620758012 & 162.49379241988 \tabularnewline
38 & 3714 & 3654.98819891077 & 59.0118010892297 \tabularnewline
39 & 3691 & 3705.45357034879 & -14.4535703487941 \tabularnewline
40 & 3604 & 3685.62368881177 & -81.6236888117737 \tabularnewline
41 & 3581 & 3601.52215959511 & -20.5221595951089 \tabularnewline
42 & 3675 & 3575.88555568099 & 99.1144443190142 \tabularnewline
43 & 3833 & 3664.72309342846 & 168.276906571537 \tabularnewline
44 & 3810 & 3819.73865063262 & -9.73865063262474 \tabularnewline
45 & 3663 & 3804.42023439847 & -141.420234398475 \tabularnewline
46 & 3704 & 3663.10245190802 & 40.8975480919785 \tabularnewline
47 & 3810 & 3696.2352219861 & 113.764778013902 \tabularnewline
48 & 4053 & 3799.09091404346 & 253.909085956543 \tabularnewline
49 & 4152 & 4036.0435198849 & 115.956480115099 \tabularnewline
50 & 4139 & 4140.99633948186 & -1.99633948185965 \tabularnewline
51 & 4055 & 4133.0861444314 & -78.086144431396 \tabularnewline
52 & 3928 & 4052.36951033282 & -124.36951033282 \tabularnewline
53 & 3821 & 3927.3666928135 & -106.366692813503 \tabularnewline
54 & 3811 & 3819.58984975008 & -8.58984975007706 \tabularnewline
55 & 3999 & 3805.37066226923 & 193.629337730772 \tabularnewline
56 & 3954 & 3984.64466296842 & -30.6446629684215 \tabularnewline
57 & 3724 & 3949.32235378337 & -225.322353783373 \tabularnewline
58 & 3731 & 3727.72292850181 & 3.27707149819253 \tabularnewline
59 & 3697 & 3724.85859045347 & -27.8585904534671 \tabularnewline
60 & 3818 & 3692.202131429 & 125.797868570996 \tabularnewline
61 & 3897 & 3806.57167182369 & 90.4283281763137 \tabularnewline
62 & 3888 & 3887.09790970743 & 0.902090292566299 \tabularnewline
63 & 3754 & 3881.96107372718 & -127.961073727176 \tabularnewline
64 & 3647 & 3753.52167306072 & -106.521673060721 \tabularnewline
65 & 3564 & 3645.59653733272 & -81.5965373327231 \tabularnewline
66 & 3498 & 3561.52098797638 & -63.5209879763811 \tabularnewline
67 & 3704 & 3494.74100644738 & 209.258993552623 \tabularnewline
68 & 3678 & 3688.97022466476 & -10.9702246647553 \tabularnewline
69 & 3599 & 3672.47337828792 & -73.4733782879202 \tabularnewline
70 & 3507 & 3596.17046396811 & -89.1704639681093 \tabularnewline
71 & 3484 & 3504.84781195064 & -20.847811950644 \tabularnewline
72 & 2612 & 3478.89960796881 & -866.899607968813 \tabularnewline
73 & 2926 & 2643.40775278173 & 282.592247218271 \tabularnewline
74 & 2918 & 2907.80580724134 & 10.1941927586554 \tabularnewline
75 & 2833 & 2911.56010841507 & -78.5601084150694 \tabularnewline
76 & 2791 & 2830.38996244442 & -39.3899624444202 \tabularnewline
77 & 2762 & 2786.69972389381 & -24.6997238938138 \tabularnewline
78 & 2728 & 2757.06582256665 & -29.0658225666543 \tabularnewline
79 & 2831 & 2723.25422493559 & 107.745775064406 \tabularnewline
80 & 2839 & 2820.35064120478 & 18.6493587952232 \tabularnewline
81 & 2775 & 2832.19525790883 & -57.195257908832 \tabularnewline
82 & 2540 & 2771.46804364482 & -231.468043644816 \tabularnewline
83 & 2625 & 2543.98812235459 & 81.0118776454133 \tabularnewline
84 & 2669 & 2615.50424078695 & 53.4957592130463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232318&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]4177[/C][C]4297[/C][C]-120[/C][/ROW]
[ROW][C]4[/C][C]4117[/C][C]4176.17814322736[/C][C]-59.1781432273629[/C][/ROW]
[ROW][C]5[/C][C]4065[/C][C]4113.55360751301[/C][C]-48.5536075130058[/C][/ROW]
[ROW][C]6[/C][C]3983[/C][C]4061.0951461159[/C][C]-78.0951461158961[/C][/ROW]
[ROW][C]7[/C][C]4091[/C][C]3980.36989876625[/C][C]110.63010123375[/C][/ROW]
[ROW][C]8[/C][C]4067[/C][C]4080.22617908795[/C][C]-13.2261790879497[/C][/ROW]
[ROW][C]9[/C][C]4024[/C][C]4061.5707254139[/C][C]-37.5707254139015[/C][/ROW]
[ROW][C]10[/C][C]3868[/C][C]4019.62122164458[/C][C]-151.621221644576[/C][/ROW]
[ROW][C]11[/C][C]3800[/C][C]3868.54263668319[/C][C]-68.5426366831948[/C][/ROW]
[ROW][C]12[/C][C]3804[/C][C]3796.95769658272[/C][C]7.04230341727725[/C][/ROW]
[ROW][C]13[/C][C]3862[/C][C]3797.69611620212[/C][C]64.3038837978766[/C][/ROW]
[ROW][C]14[/C][C]3792[/C][C]3853.22521066349[/C][C]-61.2252106634905[/C][/ROW]
[ROW][C]15[/C][C]3674[/C][C]3788.64194091618[/C][C]-114.641940916175[/C][/ROW]
[ROW][C]16[/C][C]3560[/C][C]3672.94693658272[/C][C]-112.946936582724[/C][/ROW]
[ROW][C]17[/C][C]3489[/C][C]3558.87379512264[/C][C]-69.873795122644[/C][/ROW]
[ROW][C]18[/C][C]3412[/C][C]3486.0151376582[/C][C]-74.0151376582039[/C][/ROW]
[ROW][C]19[/C][C]3674[/C][C]3409.19384153156[/C][C]264.80615846844[/C][/ROW]
[ROW][C]20[/C][C]3672[/C][C]3656.57329819969[/C][C]15.426701800312[/C][/ROW]
[ROW][C]21[/C][C]3463[/C][C]3665.3343194046[/C][C]-202.334319404602[/C][/ROW]
[ROW][C]22[/C][C]3429[/C][C]3465.73096738073[/C][C]-36.730967380734[/C][/ROW]
[ROW][C]23[/C][C]3400[/C][C]3424.58498508314[/C][C]-24.5849850831419[/C][/ROW]
[ROW][C]24[/C][C]3533[/C][C]3395.06087145003[/C][C]137.939128549974[/C][/ROW]
[ROW][C]25[/C][C]3578[/C][C]3521.04776196425[/C][C]56.9522380357453[/C][/ROW]
[ROW][C]26[/C][C]3544[/C][C]3569.54244295277[/C][C]-25.542442952767[/C][/ROW]
[ROW][C]27[/C][C]3435[/C][C]3539.10218689989[/C][C]-104.102186899885[/C][/ROW]
[ROW][C]28[/C][C]3352[/C][C]3433.49213361708[/C][C]-81.4921336170778[/C][/ROW]
[ROW][C]29[/C][C]3213[/C][C]3349.51648283144[/C][C]-136.516482831439[/C][/ROW]
[ROW][C]30[/C][C]3235[/C][C]3212.89084917498[/C][C]22.1091508250247[/C][/ROW]
[ROW][C]31[/C][C]3460[/C][C]3228.04596375327[/C][C]231.954036246728[/C][/ROW]
[ROW][C]32[/C][C]3385[/C][C]3443.99090648458[/C][C]-58.9909064845788[/C][/ROW]
[ROW][C]33[/C][C]3283[/C][C]3381.54552802408[/C][C]-98.5455280240762[/C][/ROW]
[ROW][C]34[/C][C]3295[/C][C]3281.25235715437[/C][C]13.7476428456266[/C][/ROW]
[ROW][C]35[/C][C]3331[/C][C]3288.40677280256[/C][C]42.5932271974439[/C][/ROW]
[ROW][C]36[/C][C]3520[/C][C]3323.1620514088[/C][C]196.8379485912[/C][/ROW]
[ROW][C]37[/C][C]3668[/C][C]3505.50620758012[/C][C]162.49379241988[/C][/ROW]
[ROW][C]38[/C][C]3714[/C][C]3654.98819891077[/C][C]59.0118010892297[/C][/ROW]
[ROW][C]39[/C][C]3691[/C][C]3705.45357034879[/C][C]-14.4535703487941[/C][/ROW]
[ROW][C]40[/C][C]3604[/C][C]3685.62368881177[/C][C]-81.6236888117737[/C][/ROW]
[ROW][C]41[/C][C]3581[/C][C]3601.52215959511[/C][C]-20.5221595951089[/C][/ROW]
[ROW][C]42[/C][C]3675[/C][C]3575.88555568099[/C][C]99.1144443190142[/C][/ROW]
[ROW][C]43[/C][C]3833[/C][C]3664.72309342846[/C][C]168.276906571537[/C][/ROW]
[ROW][C]44[/C][C]3810[/C][C]3819.73865063262[/C][C]-9.73865063262474[/C][/ROW]
[ROW][C]45[/C][C]3663[/C][C]3804.42023439847[/C][C]-141.420234398475[/C][/ROW]
[ROW][C]46[/C][C]3704[/C][C]3663.10245190802[/C][C]40.8975480919785[/C][/ROW]
[ROW][C]47[/C][C]3810[/C][C]3696.2352219861[/C][C]113.764778013902[/C][/ROW]
[ROW][C]48[/C][C]4053[/C][C]3799.09091404346[/C][C]253.909085956543[/C][/ROW]
[ROW][C]49[/C][C]4152[/C][C]4036.0435198849[/C][C]115.956480115099[/C][/ROW]
[ROW][C]50[/C][C]4139[/C][C]4140.99633948186[/C][C]-1.99633948185965[/C][/ROW]
[ROW][C]51[/C][C]4055[/C][C]4133.0861444314[/C][C]-78.086144431396[/C][/ROW]
[ROW][C]52[/C][C]3928[/C][C]4052.36951033282[/C][C]-124.36951033282[/C][/ROW]
[ROW][C]53[/C][C]3821[/C][C]3927.3666928135[/C][C]-106.366692813503[/C][/ROW]
[ROW][C]54[/C][C]3811[/C][C]3819.58984975008[/C][C]-8.58984975007706[/C][/ROW]
[ROW][C]55[/C][C]3999[/C][C]3805.37066226923[/C][C]193.629337730772[/C][/ROW]
[ROW][C]56[/C][C]3954[/C][C]3984.64466296842[/C][C]-30.6446629684215[/C][/ROW]
[ROW][C]57[/C][C]3724[/C][C]3949.32235378337[/C][C]-225.322353783373[/C][/ROW]
[ROW][C]58[/C][C]3731[/C][C]3727.72292850181[/C][C]3.27707149819253[/C][/ROW]
[ROW][C]59[/C][C]3697[/C][C]3724.85859045347[/C][C]-27.8585904534671[/C][/ROW]
[ROW][C]60[/C][C]3818[/C][C]3692.202131429[/C][C]125.797868570996[/C][/ROW]
[ROW][C]61[/C][C]3897[/C][C]3806.57167182369[/C][C]90.4283281763137[/C][/ROW]
[ROW][C]62[/C][C]3888[/C][C]3887.09790970743[/C][C]0.902090292566299[/C][/ROW]
[ROW][C]63[/C][C]3754[/C][C]3881.96107372718[/C][C]-127.961073727176[/C][/ROW]
[ROW][C]64[/C][C]3647[/C][C]3753.52167306072[/C][C]-106.521673060721[/C][/ROW]
[ROW][C]65[/C][C]3564[/C][C]3645.59653733272[/C][C]-81.5965373327231[/C][/ROW]
[ROW][C]66[/C][C]3498[/C][C]3561.52098797638[/C][C]-63.5209879763811[/C][/ROW]
[ROW][C]67[/C][C]3704[/C][C]3494.74100644738[/C][C]209.258993552623[/C][/ROW]
[ROW][C]68[/C][C]3678[/C][C]3688.97022466476[/C][C]-10.9702246647553[/C][/ROW]
[ROW][C]69[/C][C]3599[/C][C]3672.47337828792[/C][C]-73.4733782879202[/C][/ROW]
[ROW][C]70[/C][C]3507[/C][C]3596.17046396811[/C][C]-89.1704639681093[/C][/ROW]
[ROW][C]71[/C][C]3484[/C][C]3504.84781195064[/C][C]-20.847811950644[/C][/ROW]
[ROW][C]72[/C][C]2612[/C][C]3478.89960796881[/C][C]-866.899607968813[/C][/ROW]
[ROW][C]73[/C][C]2926[/C][C]2643.40775278173[/C][C]282.592247218271[/C][/ROW]
[ROW][C]74[/C][C]2918[/C][C]2907.80580724134[/C][C]10.1941927586554[/C][/ROW]
[ROW][C]75[/C][C]2833[/C][C]2911.56010841507[/C][C]-78.5601084150694[/C][/ROW]
[ROW][C]76[/C][C]2791[/C][C]2830.38996244442[/C][C]-39.3899624444202[/C][/ROW]
[ROW][C]77[/C][C]2762[/C][C]2786.69972389381[/C][C]-24.6997238938138[/C][/ROW]
[ROW][C]78[/C][C]2728[/C][C]2757.06582256665[/C][C]-29.0658225666543[/C][/ROW]
[ROW][C]79[/C][C]2831[/C][C]2723.25422493559[/C][C]107.745775064406[/C][/ROW]
[ROW][C]80[/C][C]2839[/C][C]2820.35064120478[/C][C]18.6493587952232[/C][/ROW]
[ROW][C]81[/C][C]2775[/C][C]2832.19525790883[/C][C]-57.195257908832[/C][/ROW]
[ROW][C]82[/C][C]2540[/C][C]2771.46804364482[/C][C]-231.468043644816[/C][/ROW]
[ROW][C]83[/C][C]2625[/C][C]2543.98812235459[/C][C]81.0118776454133[/C][/ROW]
[ROW][C]84[/C][C]2669[/C][C]2615.50424078695[/C][C]53.4957592130463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232318&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232318&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
341774297-120
441174176.17814322736-59.1781432273629
540654113.55360751301-48.5536075130058
639834061.0951461159-78.0951461158961
740913980.36989876625110.63010123375
840674080.22617908795-13.2261790879497
940244061.5707254139-37.5707254139015
1038684019.62122164458-151.621221644576
1138003868.54263668319-68.5426366831948
1238043796.957696582727.04230341727725
1338623797.6961162021264.3038837978766
1437923853.22521066349-61.2252106634905
1536743788.64194091618-114.641940916175
1635603672.94693658272-112.946936582724
1734893558.87379512264-69.873795122644
1834123486.0151376582-74.0151376582039
1936743409.19384153156264.80615846844
2036723656.5732981996915.426701800312
2134633665.3343194046-202.334319404602
2234293465.73096738073-36.730967380734
2334003424.58498508314-24.5849850831419
2435333395.06087145003137.939128549974
2535783521.0477619642556.9522380357453
2635443569.54244295277-25.542442952767
2734353539.10218689989-104.102186899885
2833523433.49213361708-81.4921336170778
2932133349.51648283144-136.516482831439
3032353212.8908491749822.1091508250247
3134603228.04596375327231.954036246728
3233853443.99090648458-58.9909064845788
3332833381.54552802408-98.5455280240762
3432953281.2523571543713.7476428456266
3533313288.4067728025642.5932271974439
3635203323.1620514088196.8379485912
3736683505.50620758012162.49379241988
3837143654.9881989107759.0118010892297
3936913705.45357034879-14.4535703487941
4036043685.62368881177-81.6236888117737
4135813601.52215959511-20.5221595951089
4236753575.8855556809999.1144443190142
4338333664.72309342846168.276906571537
4438103819.73865063262-9.73865063262474
4536633804.42023439847-141.420234398475
4637043663.1024519080240.8975480919785
4738103696.2352219861113.764778013902
4840533799.09091404346253.909085956543
4941524036.0435198849115.956480115099
5041394140.99633948186-1.99633948185965
5140554133.0861444314-78.086144431396
5239284052.36951033282-124.36951033282
5338213927.3666928135-106.366692813503
5438113819.58984975008-8.58984975007706
5539993805.37066226923193.629337730772
5639543984.64466296842-30.6446629684215
5737243949.32235378337-225.322353783373
5837313727.722928501813.27707149819253
5936973724.85859045347-27.8585904534671
6038183692.202131429125.797868570996
6138973806.5716718236990.4283281763137
6238883887.097909707430.902090292566299
6337543881.96107372718-127.961073727176
6436473753.52167306072-106.521673060721
6535643645.59653733272-81.5965373327231
6634983561.52098797638-63.5209879763811
6737043494.74100644738209.258993552623
6836783688.97022466476-10.9702246647553
6935993672.47337828792-73.4733782879202
7035073596.17046396811-89.1704639681093
7134843504.84781195064-20.847811950644
7226123478.89960796881-866.899607968813
7329262643.40775278173282.592247218271
7429182907.8058072413410.1941927586554
7528332911.56010841507-78.5601084150694
7627912830.38996244442-39.3899624444202
7727622786.69972389381-24.6997238938138
7827282757.06582256665-29.0658225666543
7928312723.25422493559107.745775064406
8028392820.3506412047818.6493587952232
8127752832.19525790883-57.195257908832
8225402771.46804364482-231.468043644816
8326252543.9881223545981.0118776454133
8426692615.5042407869553.4957592130463







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852660.691594139492374.666453402432946.71673487655
862654.691594139492258.82209026183050.56109801717
872648.691594139492167.427688296683129.95549998229
882642.691594139492089.051611810013196.33157646896
892636.691594139492019.099890017353254.28329826162
902630.691594139491955.17564616553306.20754211347
912624.691594139491895.840389205383353.5427990736
922618.691594139491840.150418670513397.23276960846
932612.691594139491787.446997145773437.9361911332
942606.691594139491737.248710544463476.13447773451
952600.691594139491689.19106709593512.19212118307
962594.691594139491642.990226184473546.3929620945

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2660.69159413949 & 2374.66645340243 & 2946.71673487655 \tabularnewline
86 & 2654.69159413949 & 2258.8220902618 & 3050.56109801717 \tabularnewline
87 & 2648.69159413949 & 2167.42768829668 & 3129.95549998229 \tabularnewline
88 & 2642.69159413949 & 2089.05161181001 & 3196.33157646896 \tabularnewline
89 & 2636.69159413949 & 2019.09989001735 & 3254.28329826162 \tabularnewline
90 & 2630.69159413949 & 1955.1756461655 & 3306.20754211347 \tabularnewline
91 & 2624.69159413949 & 1895.84038920538 & 3353.5427990736 \tabularnewline
92 & 2618.69159413949 & 1840.15041867051 & 3397.23276960846 \tabularnewline
93 & 2612.69159413949 & 1787.44699714577 & 3437.9361911332 \tabularnewline
94 & 2606.69159413949 & 1737.24871054446 & 3476.13447773451 \tabularnewline
95 & 2600.69159413949 & 1689.1910670959 & 3512.19212118307 \tabularnewline
96 & 2594.69159413949 & 1642.99022618447 & 3546.3929620945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232318&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]2660.69159413949[/C][C]2374.66645340243[/C][C]2946.71673487655[/C][/ROW]
[ROW][C]86[/C][C]2654.69159413949[/C][C]2258.8220902618[/C][C]3050.56109801717[/C][/ROW]
[ROW][C]87[/C][C]2648.69159413949[/C][C]2167.42768829668[/C][C]3129.95549998229[/C][/ROW]
[ROW][C]88[/C][C]2642.69159413949[/C][C]2089.05161181001[/C][C]3196.33157646896[/C][/ROW]
[ROW][C]89[/C][C]2636.69159413949[/C][C]2019.09989001735[/C][C]3254.28329826162[/C][/ROW]
[ROW][C]90[/C][C]2630.69159413949[/C][C]1955.1756461655[/C][C]3306.20754211347[/C][/ROW]
[ROW][C]91[/C][C]2624.69159413949[/C][C]1895.84038920538[/C][C]3353.5427990736[/C][/ROW]
[ROW][C]92[/C][C]2618.69159413949[/C][C]1840.15041867051[/C][C]3397.23276960846[/C][/ROW]
[ROW][C]93[/C][C]2612.69159413949[/C][C]1787.44699714577[/C][C]3437.9361911332[/C][/ROW]
[ROW][C]94[/C][C]2606.69159413949[/C][C]1737.24871054446[/C][C]3476.13447773451[/C][/ROW]
[ROW][C]95[/C][C]2600.69159413949[/C][C]1689.1910670959[/C][C]3512.19212118307[/C][/ROW]
[ROW][C]96[/C][C]2594.69159413949[/C][C]1642.99022618447[/C][C]3546.3929620945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232318&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232318&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
852660.691594139492374.666453402432946.71673487655
862654.691594139492258.82209026183050.56109801717
872648.691594139492167.427688296683129.95549998229
882642.691594139492089.051611810013196.33157646896
892636.691594139492019.099890017353254.28329826162
902630.691594139491955.17564616553306.20754211347
912624.691594139491895.840389205383353.5427990736
922618.691594139491840.150418670513397.23276960846
932612.691594139491787.446997145773437.9361911332
942606.691594139491737.248710544463476.13447773451
952600.691594139491689.19106709593512.19212118307
962594.691594139491642.990226184473546.3929620945



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')