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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, 07 Dec 2016 11:36:38 +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/07/t1481107032g8uuejzyjke9nq4.htm/, Retrieved Tue, 07 May 2024 10:27:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297984, Retrieved Tue, 07 May 2024 10:27:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [multiplicatief ex...] [2016-12-07 10:36:38] [6b2845a830bced35782aaf33b6e68e42] [Current]
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Dataseries X:
2620
2940
3080
3120
2420
2930
2780
2890
3000
3380
3460
2810
3530
3590
3840
3520
2820
3310
2870
3340
3660
3650
3670
3050
3770
3480
3780
2750
3600
3550
2750
3480
3870
3640
3340
3030
3850
3400
3450
3000
3190
4100
2960
3640
4210
4040
3470
3380
4490
3670
3650
3520
3470
3570
3440
3580
4120
4370
3250
3260
3610
3600
3620
3020
3240
3360
3450
3640
3690
3870
3810
3430
3910
3800
4140
3350
3360
3310
2850
3630
4340
4260
3690
2990
3620
3590
3940
2970
3470
4310
3060
3480
4190
3470
2650
2620
3620
3090
3620
2820
3060
3600
2940
3550
4590
3120
2800
3380
3490
2940
3500
2980
3040
4160
3110
3890




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297984&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297984&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.215910571616562
beta0.0365256457145078
gamma0.508168337144729

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.215910571616562 \tabularnewline
beta & 0.0365256457145078 \tabularnewline
gamma & 0.508168337144729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297984&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]0.215910571616562[/C][/ROW]
[ROW][C]beta[/C][C]0.0365256457145078[/C][/ROW]
[ROW][C]gamma[/C][C]0.508168337144729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297984&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
alpha0.215910571616562
beta0.0365256457145078
gamma0.508168337144729







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1335303279.03437661238250.965623387615
1435903406.82732832801183.17267167199
1538403678.96993312007161.030066879929
1635203405.96473408718114.035265912819
1728202765.4659621878654.5340378121418
1833103281.2722367808928.7277632191062
1928703171.70922939659-301.709229396592
2033403196.86633718438143.133662815617
2136603325.31294698335334.687053016646
2236503814.40481914231-164.404819142307
2336703872.24593149569-202.245931495688
2430503112.32345035062-62.3234503506224
2537704028.96019195197-258.960191951965
2634804019.88722867707-539.887228677074
2737804140.30280628812-360.302806288121
2827503699.10186019336-949.101860193362
2936002787.8398941279812.160105872099
3035503474.6466715770475.3533284229557
3127503216.49305720506-466.49305720506
3234803382.8412827342597.158717265746
3338703568.91269821937301.087301780634
3436403844.70413643461-204.704136434614
3533403866.57733362777-526.577333627766
3630303079.42363746603-49.42363746603
3738503902.69743041838-52.6974304183764
3834003806.18405968274-406.184059682741
3934504013.40762611173-563.407626111726
4030003263.75201626241-263.752016262406
4131903174.1372994862515.8627005137487
4241003373.66531416309726.334685836913
4329603023.9760397105-63.9760397104969
4436403507.5703992634132.429600736598
4542103779.33992177708430.660078222922
4640403874.00097870553165.999021294475
4734703833.35996873512-363.359968735117
4833803239.69207534852140.307924651475
4944904160.79155482009329.208445179907
5036703980.95799075444-310.957990754436
5136504162.85986789513-512.859867895133
5235203489.4785927547530.5214072452513
5334703588.43690822333-118.436908223334
5435704087.74873381603-517.74873381603
5534403116.04664182097323.953358179033
5635803797.40948293704-217.409482937037
5741204119.020164130960.979835869037743
5843704004.7561611896365.243838810397
5932503779.01103273655-529.011032736551
6032603338.27808119199-78.2780811919947
6136104273.5628187131-663.562818713104
6236003634.64275941057-34.6427594105662
6336203769.77943539581-149.779435395811
6430203391.06418021684-371.064180216839
6532403328.98298395013-88.982983950134
6633603634.85822806035-274.858228060347
6734503064.64219841504385.357801584963
6836403511.25459293497128.745407065029
6936903969.04403166432-279.044031664318
7038703923.26430007917-53.2643000791704
7138103282.07289493178527.927105068221
7234303246.33785507017183.662144929827
7339103990.93671674587-80.9367167458718
7438003721.5191393766478.4808606233569
7541403838.82778305772301.172216942276
7633503442.42326748683-92.4232674868267
7733603569.34887464007-209.348874640073
7833103797.85823562123-487.858235621233
7928503427.84504838556-577.845048385564
8036303559.7840724551570.2159275448503
8143403834.63636944384505.363630556164
8242604053.03980834916206.96019165084
8336903673.5500146679616.4499853320426
8429903382.20042528805-392.200425288053
8536203879.2091252099-259.209125209903
8635903632.7557484068-42.7557484068016
8739403794.5681503914145.431849608603
8829703229.60581256688-259.605812566882
8934703256.80632569155213.193674308447
9043103446.64484887453863.35515112547
9130603314.31260683337-254.312606833367
9234803811.020667944-331.020667943998
9341904185.981978227374.01802177262562
9434704174.85851997149-704.858519971492
9526503534.25224644065-884.252246440649
9626202912.19725763747-292.19725763747
9736203409.37482085608210.625179143919
9830903347.68253098685-257.682530986849
9936203503.39168332485116.608316675151
10028202828.10370243293-8.10370243292755
10130603065.91145721852-5.91145721852399
10236003400.85870993864199.141290061363
10329402767.06177991859172.938220081408
10435503252.33116747379297.668832526212
10545903840.32908942775749.670910572254
10631203707.20401796218-587.204017962179
10728003022.73654286021-222.736542860207
10833802779.5428653409600.457134659096
10934903729.38549527517-239.385495275166
11029403377.70219299694-437.702192996945
11135003660.20243213003-160.202432130028
11229802867.92786604239112.072133957606
11330403142.90488259035-102.904882590352
11441603549.75113351936610.248866480636
11531102968.52438060409141.475619395913
11638903522.8176993864367.182300613596

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3530 & 3279.03437661238 & 250.965623387615 \tabularnewline
14 & 3590 & 3406.82732832801 & 183.17267167199 \tabularnewline
15 & 3840 & 3678.96993312007 & 161.030066879929 \tabularnewline
16 & 3520 & 3405.96473408718 & 114.035265912819 \tabularnewline
17 & 2820 & 2765.46596218786 & 54.5340378121418 \tabularnewline
18 & 3310 & 3281.27223678089 & 28.7277632191062 \tabularnewline
19 & 2870 & 3171.70922939659 & -301.709229396592 \tabularnewline
20 & 3340 & 3196.86633718438 & 143.133662815617 \tabularnewline
21 & 3660 & 3325.31294698335 & 334.687053016646 \tabularnewline
22 & 3650 & 3814.40481914231 & -164.404819142307 \tabularnewline
23 & 3670 & 3872.24593149569 & -202.245931495688 \tabularnewline
24 & 3050 & 3112.32345035062 & -62.3234503506224 \tabularnewline
25 & 3770 & 4028.96019195197 & -258.960191951965 \tabularnewline
26 & 3480 & 4019.88722867707 & -539.887228677074 \tabularnewline
27 & 3780 & 4140.30280628812 & -360.302806288121 \tabularnewline
28 & 2750 & 3699.10186019336 & -949.101860193362 \tabularnewline
29 & 3600 & 2787.8398941279 & 812.160105872099 \tabularnewline
30 & 3550 & 3474.64667157704 & 75.3533284229557 \tabularnewline
31 & 2750 & 3216.49305720506 & -466.49305720506 \tabularnewline
32 & 3480 & 3382.84128273425 & 97.158717265746 \tabularnewline
33 & 3870 & 3568.91269821937 & 301.087301780634 \tabularnewline
34 & 3640 & 3844.70413643461 & -204.704136434614 \tabularnewline
35 & 3340 & 3866.57733362777 & -526.577333627766 \tabularnewline
36 & 3030 & 3079.42363746603 & -49.42363746603 \tabularnewline
37 & 3850 & 3902.69743041838 & -52.6974304183764 \tabularnewline
38 & 3400 & 3806.18405968274 & -406.184059682741 \tabularnewline
39 & 3450 & 4013.40762611173 & -563.407626111726 \tabularnewline
40 & 3000 & 3263.75201626241 & -263.752016262406 \tabularnewline
41 & 3190 & 3174.13729948625 & 15.8627005137487 \tabularnewline
42 & 4100 & 3373.66531416309 & 726.334685836913 \tabularnewline
43 & 2960 & 3023.9760397105 & -63.9760397104969 \tabularnewline
44 & 3640 & 3507.5703992634 & 132.429600736598 \tabularnewline
45 & 4210 & 3779.33992177708 & 430.660078222922 \tabularnewline
46 & 4040 & 3874.00097870553 & 165.999021294475 \tabularnewline
47 & 3470 & 3833.35996873512 & -363.359968735117 \tabularnewline
48 & 3380 & 3239.69207534852 & 140.307924651475 \tabularnewline
49 & 4490 & 4160.79155482009 & 329.208445179907 \tabularnewline
50 & 3670 & 3980.95799075444 & -310.957990754436 \tabularnewline
51 & 3650 & 4162.85986789513 & -512.859867895133 \tabularnewline
52 & 3520 & 3489.47859275475 & 30.5214072452513 \tabularnewline
53 & 3470 & 3588.43690822333 & -118.436908223334 \tabularnewline
54 & 3570 & 4087.74873381603 & -517.74873381603 \tabularnewline
55 & 3440 & 3116.04664182097 & 323.953358179033 \tabularnewline
56 & 3580 & 3797.40948293704 & -217.409482937037 \tabularnewline
57 & 4120 & 4119.02016413096 & 0.979835869037743 \tabularnewline
58 & 4370 & 4004.7561611896 & 365.243838810397 \tabularnewline
59 & 3250 & 3779.01103273655 & -529.011032736551 \tabularnewline
60 & 3260 & 3338.27808119199 & -78.2780811919947 \tabularnewline
61 & 3610 & 4273.5628187131 & -663.562818713104 \tabularnewline
62 & 3600 & 3634.64275941057 & -34.6427594105662 \tabularnewline
63 & 3620 & 3769.77943539581 & -149.779435395811 \tabularnewline
64 & 3020 & 3391.06418021684 & -371.064180216839 \tabularnewline
65 & 3240 & 3328.98298395013 & -88.982983950134 \tabularnewline
66 & 3360 & 3634.85822806035 & -274.858228060347 \tabularnewline
67 & 3450 & 3064.64219841504 & 385.357801584963 \tabularnewline
68 & 3640 & 3511.25459293497 & 128.745407065029 \tabularnewline
69 & 3690 & 3969.04403166432 & -279.044031664318 \tabularnewline
70 & 3870 & 3923.26430007917 & -53.2643000791704 \tabularnewline
71 & 3810 & 3282.07289493178 & 527.927105068221 \tabularnewline
72 & 3430 & 3246.33785507017 & 183.662144929827 \tabularnewline
73 & 3910 & 3990.93671674587 & -80.9367167458718 \tabularnewline
74 & 3800 & 3721.51913937664 & 78.4808606233569 \tabularnewline
75 & 4140 & 3838.82778305772 & 301.172216942276 \tabularnewline
76 & 3350 & 3442.42326748683 & -92.4232674868267 \tabularnewline
77 & 3360 & 3569.34887464007 & -209.348874640073 \tabularnewline
78 & 3310 & 3797.85823562123 & -487.858235621233 \tabularnewline
79 & 2850 & 3427.84504838556 & -577.845048385564 \tabularnewline
80 & 3630 & 3559.78407245515 & 70.2159275448503 \tabularnewline
81 & 4340 & 3834.63636944384 & 505.363630556164 \tabularnewline
82 & 4260 & 4053.03980834916 & 206.96019165084 \tabularnewline
83 & 3690 & 3673.55001466796 & 16.4499853320426 \tabularnewline
84 & 2990 & 3382.20042528805 & -392.200425288053 \tabularnewline
85 & 3620 & 3879.2091252099 & -259.209125209903 \tabularnewline
86 & 3590 & 3632.7557484068 & -42.7557484068016 \tabularnewline
87 & 3940 & 3794.5681503914 & 145.431849608603 \tabularnewline
88 & 2970 & 3229.60581256688 & -259.605812566882 \tabularnewline
89 & 3470 & 3256.80632569155 & 213.193674308447 \tabularnewline
90 & 4310 & 3446.64484887453 & 863.35515112547 \tabularnewline
91 & 3060 & 3314.31260683337 & -254.312606833367 \tabularnewline
92 & 3480 & 3811.020667944 & -331.020667943998 \tabularnewline
93 & 4190 & 4185.98197822737 & 4.01802177262562 \tabularnewline
94 & 3470 & 4174.85851997149 & -704.858519971492 \tabularnewline
95 & 2650 & 3534.25224644065 & -884.252246440649 \tabularnewline
96 & 2620 & 2912.19725763747 & -292.19725763747 \tabularnewline
97 & 3620 & 3409.37482085608 & 210.625179143919 \tabularnewline
98 & 3090 & 3347.68253098685 & -257.682530986849 \tabularnewline
99 & 3620 & 3503.39168332485 & 116.608316675151 \tabularnewline
100 & 2820 & 2828.10370243293 & -8.10370243292755 \tabularnewline
101 & 3060 & 3065.91145721852 & -5.91145721852399 \tabularnewline
102 & 3600 & 3400.85870993864 & 199.141290061363 \tabularnewline
103 & 2940 & 2767.06177991859 & 172.938220081408 \tabularnewline
104 & 3550 & 3252.33116747379 & 297.668832526212 \tabularnewline
105 & 4590 & 3840.32908942775 & 749.670910572254 \tabularnewline
106 & 3120 & 3707.20401796218 & -587.204017962179 \tabularnewline
107 & 2800 & 3022.73654286021 & -222.736542860207 \tabularnewline
108 & 3380 & 2779.5428653409 & 600.457134659096 \tabularnewline
109 & 3490 & 3729.38549527517 & -239.385495275166 \tabularnewline
110 & 2940 & 3377.70219299694 & -437.702192996945 \tabularnewline
111 & 3500 & 3660.20243213003 & -160.202432130028 \tabularnewline
112 & 2980 & 2867.92786604239 & 112.072133957606 \tabularnewline
113 & 3040 & 3142.90488259035 & -102.904882590352 \tabularnewline
114 & 4160 & 3549.75113351936 & 610.248866480636 \tabularnewline
115 & 3110 & 2968.52438060409 & 141.475619395913 \tabularnewline
116 & 3890 & 3522.8176993864 & 367.182300613596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297984&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]3530[/C][C]3279.03437661238[/C][C]250.965623387615[/C][/ROW]
[ROW][C]14[/C][C]3590[/C][C]3406.82732832801[/C][C]183.17267167199[/C][/ROW]
[ROW][C]15[/C][C]3840[/C][C]3678.96993312007[/C][C]161.030066879929[/C][/ROW]
[ROW][C]16[/C][C]3520[/C][C]3405.96473408718[/C][C]114.035265912819[/C][/ROW]
[ROW][C]17[/C][C]2820[/C][C]2765.46596218786[/C][C]54.5340378121418[/C][/ROW]
[ROW][C]18[/C][C]3310[/C][C]3281.27223678089[/C][C]28.7277632191062[/C][/ROW]
[ROW][C]19[/C][C]2870[/C][C]3171.70922939659[/C][C]-301.709229396592[/C][/ROW]
[ROW][C]20[/C][C]3340[/C][C]3196.86633718438[/C][C]143.133662815617[/C][/ROW]
[ROW][C]21[/C][C]3660[/C][C]3325.31294698335[/C][C]334.687053016646[/C][/ROW]
[ROW][C]22[/C][C]3650[/C][C]3814.40481914231[/C][C]-164.404819142307[/C][/ROW]
[ROW][C]23[/C][C]3670[/C][C]3872.24593149569[/C][C]-202.245931495688[/C][/ROW]
[ROW][C]24[/C][C]3050[/C][C]3112.32345035062[/C][C]-62.3234503506224[/C][/ROW]
[ROW][C]25[/C][C]3770[/C][C]4028.96019195197[/C][C]-258.960191951965[/C][/ROW]
[ROW][C]26[/C][C]3480[/C][C]4019.88722867707[/C][C]-539.887228677074[/C][/ROW]
[ROW][C]27[/C][C]3780[/C][C]4140.30280628812[/C][C]-360.302806288121[/C][/ROW]
[ROW][C]28[/C][C]2750[/C][C]3699.10186019336[/C][C]-949.101860193362[/C][/ROW]
[ROW][C]29[/C][C]3600[/C][C]2787.8398941279[/C][C]812.160105872099[/C][/ROW]
[ROW][C]30[/C][C]3550[/C][C]3474.64667157704[/C][C]75.3533284229557[/C][/ROW]
[ROW][C]31[/C][C]2750[/C][C]3216.49305720506[/C][C]-466.49305720506[/C][/ROW]
[ROW][C]32[/C][C]3480[/C][C]3382.84128273425[/C][C]97.158717265746[/C][/ROW]
[ROW][C]33[/C][C]3870[/C][C]3568.91269821937[/C][C]301.087301780634[/C][/ROW]
[ROW][C]34[/C][C]3640[/C][C]3844.70413643461[/C][C]-204.704136434614[/C][/ROW]
[ROW][C]35[/C][C]3340[/C][C]3866.57733362777[/C][C]-526.577333627766[/C][/ROW]
[ROW][C]36[/C][C]3030[/C][C]3079.42363746603[/C][C]-49.42363746603[/C][/ROW]
[ROW][C]37[/C][C]3850[/C][C]3902.69743041838[/C][C]-52.6974304183764[/C][/ROW]
[ROW][C]38[/C][C]3400[/C][C]3806.18405968274[/C][C]-406.184059682741[/C][/ROW]
[ROW][C]39[/C][C]3450[/C][C]4013.40762611173[/C][C]-563.407626111726[/C][/ROW]
[ROW][C]40[/C][C]3000[/C][C]3263.75201626241[/C][C]-263.752016262406[/C][/ROW]
[ROW][C]41[/C][C]3190[/C][C]3174.13729948625[/C][C]15.8627005137487[/C][/ROW]
[ROW][C]42[/C][C]4100[/C][C]3373.66531416309[/C][C]726.334685836913[/C][/ROW]
[ROW][C]43[/C][C]2960[/C][C]3023.9760397105[/C][C]-63.9760397104969[/C][/ROW]
[ROW][C]44[/C][C]3640[/C][C]3507.5703992634[/C][C]132.429600736598[/C][/ROW]
[ROW][C]45[/C][C]4210[/C][C]3779.33992177708[/C][C]430.660078222922[/C][/ROW]
[ROW][C]46[/C][C]4040[/C][C]3874.00097870553[/C][C]165.999021294475[/C][/ROW]
[ROW][C]47[/C][C]3470[/C][C]3833.35996873512[/C][C]-363.359968735117[/C][/ROW]
[ROW][C]48[/C][C]3380[/C][C]3239.69207534852[/C][C]140.307924651475[/C][/ROW]
[ROW][C]49[/C][C]4490[/C][C]4160.79155482009[/C][C]329.208445179907[/C][/ROW]
[ROW][C]50[/C][C]3670[/C][C]3980.95799075444[/C][C]-310.957990754436[/C][/ROW]
[ROW][C]51[/C][C]3650[/C][C]4162.85986789513[/C][C]-512.859867895133[/C][/ROW]
[ROW][C]52[/C][C]3520[/C][C]3489.47859275475[/C][C]30.5214072452513[/C][/ROW]
[ROW][C]53[/C][C]3470[/C][C]3588.43690822333[/C][C]-118.436908223334[/C][/ROW]
[ROW][C]54[/C][C]3570[/C][C]4087.74873381603[/C][C]-517.74873381603[/C][/ROW]
[ROW][C]55[/C][C]3440[/C][C]3116.04664182097[/C][C]323.953358179033[/C][/ROW]
[ROW][C]56[/C][C]3580[/C][C]3797.40948293704[/C][C]-217.409482937037[/C][/ROW]
[ROW][C]57[/C][C]4120[/C][C]4119.02016413096[/C][C]0.979835869037743[/C][/ROW]
[ROW][C]58[/C][C]4370[/C][C]4004.7561611896[/C][C]365.243838810397[/C][/ROW]
[ROW][C]59[/C][C]3250[/C][C]3779.01103273655[/C][C]-529.011032736551[/C][/ROW]
[ROW][C]60[/C][C]3260[/C][C]3338.27808119199[/C][C]-78.2780811919947[/C][/ROW]
[ROW][C]61[/C][C]3610[/C][C]4273.5628187131[/C][C]-663.562818713104[/C][/ROW]
[ROW][C]62[/C][C]3600[/C][C]3634.64275941057[/C][C]-34.6427594105662[/C][/ROW]
[ROW][C]63[/C][C]3620[/C][C]3769.77943539581[/C][C]-149.779435395811[/C][/ROW]
[ROW][C]64[/C][C]3020[/C][C]3391.06418021684[/C][C]-371.064180216839[/C][/ROW]
[ROW][C]65[/C][C]3240[/C][C]3328.98298395013[/C][C]-88.982983950134[/C][/ROW]
[ROW][C]66[/C][C]3360[/C][C]3634.85822806035[/C][C]-274.858228060347[/C][/ROW]
[ROW][C]67[/C][C]3450[/C][C]3064.64219841504[/C][C]385.357801584963[/C][/ROW]
[ROW][C]68[/C][C]3640[/C][C]3511.25459293497[/C][C]128.745407065029[/C][/ROW]
[ROW][C]69[/C][C]3690[/C][C]3969.04403166432[/C][C]-279.044031664318[/C][/ROW]
[ROW][C]70[/C][C]3870[/C][C]3923.26430007917[/C][C]-53.2643000791704[/C][/ROW]
[ROW][C]71[/C][C]3810[/C][C]3282.07289493178[/C][C]527.927105068221[/C][/ROW]
[ROW][C]72[/C][C]3430[/C][C]3246.33785507017[/C][C]183.662144929827[/C][/ROW]
[ROW][C]73[/C][C]3910[/C][C]3990.93671674587[/C][C]-80.9367167458718[/C][/ROW]
[ROW][C]74[/C][C]3800[/C][C]3721.51913937664[/C][C]78.4808606233569[/C][/ROW]
[ROW][C]75[/C][C]4140[/C][C]3838.82778305772[/C][C]301.172216942276[/C][/ROW]
[ROW][C]76[/C][C]3350[/C][C]3442.42326748683[/C][C]-92.4232674868267[/C][/ROW]
[ROW][C]77[/C][C]3360[/C][C]3569.34887464007[/C][C]-209.348874640073[/C][/ROW]
[ROW][C]78[/C][C]3310[/C][C]3797.85823562123[/C][C]-487.858235621233[/C][/ROW]
[ROW][C]79[/C][C]2850[/C][C]3427.84504838556[/C][C]-577.845048385564[/C][/ROW]
[ROW][C]80[/C][C]3630[/C][C]3559.78407245515[/C][C]70.2159275448503[/C][/ROW]
[ROW][C]81[/C][C]4340[/C][C]3834.63636944384[/C][C]505.363630556164[/C][/ROW]
[ROW][C]82[/C][C]4260[/C][C]4053.03980834916[/C][C]206.96019165084[/C][/ROW]
[ROW][C]83[/C][C]3690[/C][C]3673.55001466796[/C][C]16.4499853320426[/C][/ROW]
[ROW][C]84[/C][C]2990[/C][C]3382.20042528805[/C][C]-392.200425288053[/C][/ROW]
[ROW][C]85[/C][C]3620[/C][C]3879.2091252099[/C][C]-259.209125209903[/C][/ROW]
[ROW][C]86[/C][C]3590[/C][C]3632.7557484068[/C][C]-42.7557484068016[/C][/ROW]
[ROW][C]87[/C][C]3940[/C][C]3794.5681503914[/C][C]145.431849608603[/C][/ROW]
[ROW][C]88[/C][C]2970[/C][C]3229.60581256688[/C][C]-259.605812566882[/C][/ROW]
[ROW][C]89[/C][C]3470[/C][C]3256.80632569155[/C][C]213.193674308447[/C][/ROW]
[ROW][C]90[/C][C]4310[/C][C]3446.64484887453[/C][C]863.35515112547[/C][/ROW]
[ROW][C]91[/C][C]3060[/C][C]3314.31260683337[/C][C]-254.312606833367[/C][/ROW]
[ROW][C]92[/C][C]3480[/C][C]3811.020667944[/C][C]-331.020667943998[/C][/ROW]
[ROW][C]93[/C][C]4190[/C][C]4185.98197822737[/C][C]4.01802177262562[/C][/ROW]
[ROW][C]94[/C][C]3470[/C][C]4174.85851997149[/C][C]-704.858519971492[/C][/ROW]
[ROW][C]95[/C][C]2650[/C][C]3534.25224644065[/C][C]-884.252246440649[/C][/ROW]
[ROW][C]96[/C][C]2620[/C][C]2912.19725763747[/C][C]-292.19725763747[/C][/ROW]
[ROW][C]97[/C][C]3620[/C][C]3409.37482085608[/C][C]210.625179143919[/C][/ROW]
[ROW][C]98[/C][C]3090[/C][C]3347.68253098685[/C][C]-257.682530986849[/C][/ROW]
[ROW][C]99[/C][C]3620[/C][C]3503.39168332485[/C][C]116.608316675151[/C][/ROW]
[ROW][C]100[/C][C]2820[/C][C]2828.10370243293[/C][C]-8.10370243292755[/C][/ROW]
[ROW][C]101[/C][C]3060[/C][C]3065.91145721852[/C][C]-5.91145721852399[/C][/ROW]
[ROW][C]102[/C][C]3600[/C][C]3400.85870993864[/C][C]199.141290061363[/C][/ROW]
[ROW][C]103[/C][C]2940[/C][C]2767.06177991859[/C][C]172.938220081408[/C][/ROW]
[ROW][C]104[/C][C]3550[/C][C]3252.33116747379[/C][C]297.668832526212[/C][/ROW]
[ROW][C]105[/C][C]4590[/C][C]3840.32908942775[/C][C]749.670910572254[/C][/ROW]
[ROW][C]106[/C][C]3120[/C][C]3707.20401796218[/C][C]-587.204017962179[/C][/ROW]
[ROW][C]107[/C][C]2800[/C][C]3022.73654286021[/C][C]-222.736542860207[/C][/ROW]
[ROW][C]108[/C][C]3380[/C][C]2779.5428653409[/C][C]600.457134659096[/C][/ROW]
[ROW][C]109[/C][C]3490[/C][C]3729.38549527517[/C][C]-239.385495275166[/C][/ROW]
[ROW][C]110[/C][C]2940[/C][C]3377.70219299694[/C][C]-437.702192996945[/C][/ROW]
[ROW][C]111[/C][C]3500[/C][C]3660.20243213003[/C][C]-160.202432130028[/C][/ROW]
[ROW][C]112[/C][C]2980[/C][C]2867.92786604239[/C][C]112.072133957606[/C][/ROW]
[ROW][C]113[/C][C]3040[/C][C]3142.90488259035[/C][C]-102.904882590352[/C][/ROW]
[ROW][C]114[/C][C]4160[/C][C]3549.75113351936[/C][C]610.248866480636[/C][/ROW]
[ROW][C]115[/C][C]3110[/C][C]2968.52438060409[/C][C]141.475619395913[/C][/ROW]
[ROW][C]116[/C][C]3890[/C][C]3522.8176993864[/C][C]367.182300613596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297984&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
1335303279.03437661238250.965623387615
1435903406.82732832801183.17267167199
1538403678.96993312007161.030066879929
1635203405.96473408718114.035265912819
1728202765.4659621878654.5340378121418
1833103281.2722367808928.7277632191062
1928703171.70922939659-301.709229396592
2033403196.86633718438143.133662815617
2136603325.31294698335334.687053016646
2236503814.40481914231-164.404819142307
2336703872.24593149569-202.245931495688
2430503112.32345035062-62.3234503506224
2537704028.96019195197-258.960191951965
2634804019.88722867707-539.887228677074
2737804140.30280628812-360.302806288121
2827503699.10186019336-949.101860193362
2936002787.8398941279812.160105872099
3035503474.6466715770475.3533284229557
3127503216.49305720506-466.49305720506
3234803382.8412827342597.158717265746
3338703568.91269821937301.087301780634
3436403844.70413643461-204.704136434614
3533403866.57733362777-526.577333627766
3630303079.42363746603-49.42363746603
3738503902.69743041838-52.6974304183764
3834003806.18405968274-406.184059682741
3934504013.40762611173-563.407626111726
4030003263.75201626241-263.752016262406
4131903174.1372994862515.8627005137487
4241003373.66531416309726.334685836913
4329603023.9760397105-63.9760397104969
4436403507.5703992634132.429600736598
4542103779.33992177708430.660078222922
4640403874.00097870553165.999021294475
4734703833.35996873512-363.359968735117
4833803239.69207534852140.307924651475
4944904160.79155482009329.208445179907
5036703980.95799075444-310.957990754436
5136504162.85986789513-512.859867895133
5235203489.4785927547530.5214072452513
5334703588.43690822333-118.436908223334
5435704087.74873381603-517.74873381603
5534403116.04664182097323.953358179033
5635803797.40948293704-217.409482937037
5741204119.020164130960.979835869037743
5843704004.7561611896365.243838810397
5932503779.01103273655-529.011032736551
6032603338.27808119199-78.2780811919947
6136104273.5628187131-663.562818713104
6236003634.64275941057-34.6427594105662
6336203769.77943539581-149.779435395811
6430203391.06418021684-371.064180216839
6532403328.98298395013-88.982983950134
6633603634.85822806035-274.858228060347
6734503064.64219841504385.357801584963
6836403511.25459293497128.745407065029
6936903969.04403166432-279.044031664318
7038703923.26430007917-53.2643000791704
7138103282.07289493178527.927105068221
7234303246.33785507017183.662144929827
7339103990.93671674587-80.9367167458718
7438003721.5191393766478.4808606233569
7541403838.82778305772301.172216942276
7633503442.42326748683-92.4232674868267
7733603569.34887464007-209.348874640073
7833103797.85823562123-487.858235621233
7928503427.84504838556-577.845048385564
8036303559.7840724551570.2159275448503
8143403834.63636944384505.363630556164
8242604053.03980834916206.96019165084
8336903673.5500146679616.4499853320426
8429903382.20042528805-392.200425288053
8536203879.2091252099-259.209125209903
8635903632.7557484068-42.7557484068016
8739403794.5681503914145.431849608603
8829703229.60581256688-259.605812566882
8934703256.80632569155213.193674308447
9043103446.64484887453863.35515112547
9130603314.31260683337-254.312606833367
9234803811.020667944-331.020667943998
9341904185.981978227374.01802177262562
9434704174.85851997149-704.858519971492
9526503534.25224644065-884.252246440649
9626202912.19725763747-292.19725763747
9736203409.37482085608210.625179143919
9830903347.68253098685-257.682530986849
9936203503.39168332485116.608316675151
10028202828.10370243293-8.10370243292755
10130603065.91145721852-5.91145721852399
10236003400.85870993864199.141290061363
10329402767.06177991859172.938220081408
10435503252.33116747379297.668832526212
10545903840.32908942775749.670910572254
10631203707.20401796218-587.204017962179
10728003022.73654286021-222.736542860207
10833802779.5428653409600.457134659096
10934903729.38549527517-239.385495275166
11029403377.70219299694-437.702192996945
11135003660.20243213003-160.202432130028
11229802867.92786604239112.072133957606
11330403142.90488259035-102.904882590352
11441603549.75113351936610.248866480636
11531102968.52438060409141.475619395913
11638903522.8176993864367.182300613596







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174335.998488791683907.097320179884764.89965740348
1183494.831142772483047.863102516563941.79918302841
1193067.885451174032603.377763879423532.39313846864
1203205.294151139782707.653720419063702.9345818605
1213700.65372280773146.534687817324254.77275779807
1223307.743583258392752.52016671263862.96699980418
1233834.324578388333206.177540372654462.47161640401
1243143.106246082772550.767570177483735.44492198806
1253326.991615958822686.735755035463967.24747688219
1264098.392998157523333.598622277064863.18737403799
1273161.8581880162489.90279106343833.8135849686
1283796.558099238833121.197914524474471.91828395319

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4335.99848879168 & 3907.09732017988 & 4764.89965740348 \tabularnewline
118 & 3494.83114277248 & 3047.86310251656 & 3941.79918302841 \tabularnewline
119 & 3067.88545117403 & 2603.37776387942 & 3532.39313846864 \tabularnewline
120 & 3205.29415113978 & 2707.65372041906 & 3702.9345818605 \tabularnewline
121 & 3700.6537228077 & 3146.53468781732 & 4254.77275779807 \tabularnewline
122 & 3307.74358325839 & 2752.5201667126 & 3862.96699980418 \tabularnewline
123 & 3834.32457838833 & 3206.17754037265 & 4462.47161640401 \tabularnewline
124 & 3143.10624608277 & 2550.76757017748 & 3735.44492198806 \tabularnewline
125 & 3326.99161595882 & 2686.73575503546 & 3967.24747688219 \tabularnewline
126 & 4098.39299815752 & 3333.59862227706 & 4863.18737403799 \tabularnewline
127 & 3161.858188016 & 2489.9027910634 & 3833.8135849686 \tabularnewline
128 & 3796.55809923883 & 3121.19791452447 & 4471.91828395319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297984&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]117[/C][C]4335.99848879168[/C][C]3907.09732017988[/C][C]4764.89965740348[/C][/ROW]
[ROW][C]118[/C][C]3494.83114277248[/C][C]3047.86310251656[/C][C]3941.79918302841[/C][/ROW]
[ROW][C]119[/C][C]3067.88545117403[/C][C]2603.37776387942[/C][C]3532.39313846864[/C][/ROW]
[ROW][C]120[/C][C]3205.29415113978[/C][C]2707.65372041906[/C][C]3702.9345818605[/C][/ROW]
[ROW][C]121[/C][C]3700.6537228077[/C][C]3146.53468781732[/C][C]4254.77275779807[/C][/ROW]
[ROW][C]122[/C][C]3307.74358325839[/C][C]2752.5201667126[/C][C]3862.96699980418[/C][/ROW]
[ROW][C]123[/C][C]3834.32457838833[/C][C]3206.17754037265[/C][C]4462.47161640401[/C][/ROW]
[ROW][C]124[/C][C]3143.10624608277[/C][C]2550.76757017748[/C][C]3735.44492198806[/C][/ROW]
[ROW][C]125[/C][C]3326.99161595882[/C][C]2686.73575503546[/C][C]3967.24747688219[/C][/ROW]
[ROW][C]126[/C][C]4098.39299815752[/C][C]3333.59862227706[/C][C]4863.18737403799[/C][/ROW]
[ROW][C]127[/C][C]3161.858188016[/C][C]2489.9027910634[/C][C]3833.8135849686[/C][/ROW]
[ROW][C]128[/C][C]3796.55809923883[/C][C]3121.19791452447[/C][C]4471.91828395319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297984&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297984&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
1174335.998488791683907.097320179884764.89965740348
1183494.831142772483047.863102516563941.79918302841
1193067.885451174032603.377763879423532.39313846864
1203205.294151139782707.653720419063702.9345818605
1213700.65372280773146.534687817324254.77275779807
1223307.743583258392752.52016671263862.96699980418
1233834.324578388333206.177540372654462.47161640401
1243143.106246082772550.767570177483735.44492198806
1253326.991615958822686.735755035463967.24747688219
1264098.392998157523333.598622277064863.18737403799
1273161.8581880162489.90279106343833.8135849686
1283796.558099238833121.197914524474471.91828395319



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
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')