Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 09:42:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/29/t1417254224u24dnpcn41olfcy.htm/, Retrieved Sun, 19 May 2024 16:12:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261075, Retrieved Sun, 19 May 2024 16:12:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-29 09:42:39] [11722998b98bb8551244d4a68b29baca] [Current]
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Dataseries X:
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226
33.865
32.810
32.242
32.700
32.819
33.947
34.148
35.261
39.506
41.591
39.148
41.216
40.225
41.126
42.362
40.740
40.256
39.804
41.002
41.702
42.254
43.605
43.271
43.221
41.373
40.435
39.217
39.457
36.710
34.977
32.729
31.584
32.510
32.565
30.988
30.383
28.673




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=261075&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=261075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261075&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
alpha1
beta0.120173063327349
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.120173063327349 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261075&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.120173063327349[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261075&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
alpha1
beta0.120173063327349
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315.92817.117-1.189
416.17116.5541142277038-0.383114227703782
515.93716.7510742173563-0.814074217356326
615.71316.4192444248808-0.706244424880802
715.59416.110372868885-0.516372868885016
815.68315.929318759412-0.246318759411972
916.43815.98871787953840.449282120461556
1017.03216.79770948825250.234290511747485
1117.69617.41986489675770.276135103242257
1217.74518.1170488980066-0.372048898006579
1319.39418.12133864222561.27266135777444
1420.14819.92327825616770.22472174383234
1520.10820.7042837565203-0.596283756520254
1618.58420.5926265108869-2.00862651088688
1718.44118.8272437099931-0.386243709993078
1818.39118.6378276201723-0.24682762017229
1919.17818.55816558894240.619834411057617
2018.07919.4196529888749-1.34065298887488
2118.48318.15954261234280.323457387657179
2219.64418.60241347747341.04158652252655
2319.19519.8885841206059-0.693584120605941
2419.6519.35623399215750.293766007842475
2520.8319.84653675322140.983463246778602
2623.59521.14472254425662.45027745574336
2722.93724.2041798921153-1.26717989211526
2821.81423.393899002693-1.57989900269295
2921.92822.0810376997915-0.153037699791518
3021.77722.176646690603-0.399646690602999
3121.38321.9776199235446-0.594619923544602
3221.46721.5121626258168-0.0451626258167721
3322.05221.59073529472450.461264705275536
3422.6822.23116688736220.448833112637789
3524.3222.91310453743061.40689546256936
3624.97724.7221754749490.254824525051049
3725.20425.4097985187353-0.205798518735271
3825.73925.61206708031060.126932919689377
3926.43426.16232099810680.271679001893219
4027.52526.8899694960060.635030503993992
4130.69528.05728305697732.63771694302273
4232.43631.54426558221080.891734417789237
4330.1633.3924280388709-3.23242803887092
4430.23630.7279772594546-0.491977259454593
4531.29330.74485484509850.548145154901459
4631.07731.8677271275111-0.79072712751109
4732.22631.55670302634210.669296973657946
4833.86532.78613449394221.07886550605775
4932.8134.5547850667234-1.74478506672342
5032.24233.2901089004075-1.04810890040746
5132.732.59615444314480.103845556855177
5232.81933.0666338818251-0.247633881825053
5333.94733.15587495966250.791125040337505
5434.14834.3789468792348-0.230946879234821
5535.26134.55219328529130.708806714708714
5639.50635.75037275950483.75562724049517
5741.59140.44669798971081.14430201028924
5839.14842.6692122676589-3.52121226765886
5941.21639.80305740282851.41294259717154
6040.22542.0408550430363-1.81585504303627
6141.12640.83163817995620.294361820043811
6242.36241.76801254159750.593987458402545
6340.7443.0753938340517-2.33539383405172
6440.25641.1727424029379-0.916742402937928
6539.80440.5785746600948-0.7745746600948
6641.00240.03349165041550.968508349584532
6741.70241.34788026564320.354119734356843
6842.25442.09043591890550.163564081094513
6943.60542.66209191558090.942908084419066
7043.27144.1264040685217-0.855404068521693
7143.22143.6896075412248-0.46860754122477
7241.37343.5832935374975-2.21029353749749
7340.43541.4696757922438-1.03467579224377
7439.21740.4073356327392-1.19033563273919
7539.45739.04628935336520.410710646634776
7636.7139.3356457099125-2.62564570991248
7734.97736.27311382174-1.29611382173999
7832.72934.3843558533606-1.65535585336058
7931.58431.9374266695654-0.353426669565376
8032.5130.74995430402211.76004569597788
8132.56531.88746438690390.677535613096101
8230.98832.023885917043-1.03588591704303
8330.38330.32240033313430.0605996668656879
8428.67329.7246827807382-1.05168278073818

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15.928 & 17.117 & -1.189 \tabularnewline
4 & 16.171 & 16.5541142277038 & -0.383114227703782 \tabularnewline
5 & 15.937 & 16.7510742173563 & -0.814074217356326 \tabularnewline
6 & 15.713 & 16.4192444248808 & -0.706244424880802 \tabularnewline
7 & 15.594 & 16.110372868885 & -0.516372868885016 \tabularnewline
8 & 15.683 & 15.929318759412 & -0.246318759411972 \tabularnewline
9 & 16.438 & 15.9887178795384 & 0.449282120461556 \tabularnewline
10 & 17.032 & 16.7977094882525 & 0.234290511747485 \tabularnewline
11 & 17.696 & 17.4198648967577 & 0.276135103242257 \tabularnewline
12 & 17.745 & 18.1170488980066 & -0.372048898006579 \tabularnewline
13 & 19.394 & 18.1213386422256 & 1.27266135777444 \tabularnewline
14 & 20.148 & 19.9232782561677 & 0.22472174383234 \tabularnewline
15 & 20.108 & 20.7042837565203 & -0.596283756520254 \tabularnewline
16 & 18.584 & 20.5926265108869 & -2.00862651088688 \tabularnewline
17 & 18.441 & 18.8272437099931 & -0.386243709993078 \tabularnewline
18 & 18.391 & 18.6378276201723 & -0.24682762017229 \tabularnewline
19 & 19.178 & 18.5581655889424 & 0.619834411057617 \tabularnewline
20 & 18.079 & 19.4196529888749 & -1.34065298887488 \tabularnewline
21 & 18.483 & 18.1595426123428 & 0.323457387657179 \tabularnewline
22 & 19.644 & 18.6024134774734 & 1.04158652252655 \tabularnewline
23 & 19.195 & 19.8885841206059 & -0.693584120605941 \tabularnewline
24 & 19.65 & 19.3562339921575 & 0.293766007842475 \tabularnewline
25 & 20.83 & 19.8465367532214 & 0.983463246778602 \tabularnewline
26 & 23.595 & 21.1447225442566 & 2.45027745574336 \tabularnewline
27 & 22.937 & 24.2041798921153 & -1.26717989211526 \tabularnewline
28 & 21.814 & 23.393899002693 & -1.57989900269295 \tabularnewline
29 & 21.928 & 22.0810376997915 & -0.153037699791518 \tabularnewline
30 & 21.777 & 22.176646690603 & -0.399646690602999 \tabularnewline
31 & 21.383 & 21.9776199235446 & -0.594619923544602 \tabularnewline
32 & 21.467 & 21.5121626258168 & -0.0451626258167721 \tabularnewline
33 & 22.052 & 21.5907352947245 & 0.461264705275536 \tabularnewline
34 & 22.68 & 22.2311668873622 & 0.448833112637789 \tabularnewline
35 & 24.32 & 22.9131045374306 & 1.40689546256936 \tabularnewline
36 & 24.977 & 24.722175474949 & 0.254824525051049 \tabularnewline
37 & 25.204 & 25.4097985187353 & -0.205798518735271 \tabularnewline
38 & 25.739 & 25.6120670803106 & 0.126932919689377 \tabularnewline
39 & 26.434 & 26.1623209981068 & 0.271679001893219 \tabularnewline
40 & 27.525 & 26.889969496006 & 0.635030503993992 \tabularnewline
41 & 30.695 & 28.0572830569773 & 2.63771694302273 \tabularnewline
42 & 32.436 & 31.5442655822108 & 0.891734417789237 \tabularnewline
43 & 30.16 & 33.3924280388709 & -3.23242803887092 \tabularnewline
44 & 30.236 & 30.7279772594546 & -0.491977259454593 \tabularnewline
45 & 31.293 & 30.7448548450985 & 0.548145154901459 \tabularnewline
46 & 31.077 & 31.8677271275111 & -0.79072712751109 \tabularnewline
47 & 32.226 & 31.5567030263421 & 0.669296973657946 \tabularnewline
48 & 33.865 & 32.7861344939422 & 1.07886550605775 \tabularnewline
49 & 32.81 & 34.5547850667234 & -1.74478506672342 \tabularnewline
50 & 32.242 & 33.2901089004075 & -1.04810890040746 \tabularnewline
51 & 32.7 & 32.5961544431448 & 0.103845556855177 \tabularnewline
52 & 32.819 & 33.0666338818251 & -0.247633881825053 \tabularnewline
53 & 33.947 & 33.1558749596625 & 0.791125040337505 \tabularnewline
54 & 34.148 & 34.3789468792348 & -0.230946879234821 \tabularnewline
55 & 35.261 & 34.5521932852913 & 0.708806714708714 \tabularnewline
56 & 39.506 & 35.7503727595048 & 3.75562724049517 \tabularnewline
57 & 41.591 & 40.4466979897108 & 1.14430201028924 \tabularnewline
58 & 39.148 & 42.6692122676589 & -3.52121226765886 \tabularnewline
59 & 41.216 & 39.8030574028285 & 1.41294259717154 \tabularnewline
60 & 40.225 & 42.0408550430363 & -1.81585504303627 \tabularnewline
61 & 41.126 & 40.8316381799562 & 0.294361820043811 \tabularnewline
62 & 42.362 & 41.7680125415975 & 0.593987458402545 \tabularnewline
63 & 40.74 & 43.0753938340517 & -2.33539383405172 \tabularnewline
64 & 40.256 & 41.1727424029379 & -0.916742402937928 \tabularnewline
65 & 39.804 & 40.5785746600948 & -0.7745746600948 \tabularnewline
66 & 41.002 & 40.0334916504155 & 0.968508349584532 \tabularnewline
67 & 41.702 & 41.3478802656432 & 0.354119734356843 \tabularnewline
68 & 42.254 & 42.0904359189055 & 0.163564081094513 \tabularnewline
69 & 43.605 & 42.6620919155809 & 0.942908084419066 \tabularnewline
70 & 43.271 & 44.1264040685217 & -0.855404068521693 \tabularnewline
71 & 43.221 & 43.6896075412248 & -0.46860754122477 \tabularnewline
72 & 41.373 & 43.5832935374975 & -2.21029353749749 \tabularnewline
73 & 40.435 & 41.4696757922438 & -1.03467579224377 \tabularnewline
74 & 39.217 & 40.4073356327392 & -1.19033563273919 \tabularnewline
75 & 39.457 & 39.0462893533652 & 0.410710646634776 \tabularnewline
76 & 36.71 & 39.3356457099125 & -2.62564570991248 \tabularnewline
77 & 34.977 & 36.27311382174 & -1.29611382173999 \tabularnewline
78 & 32.729 & 34.3843558533606 & -1.65535585336058 \tabularnewline
79 & 31.584 & 31.9374266695654 & -0.353426669565376 \tabularnewline
80 & 32.51 & 30.7499543040221 & 1.76004569597788 \tabularnewline
81 & 32.565 & 31.8874643869039 & 0.677535613096101 \tabularnewline
82 & 30.988 & 32.023885917043 & -1.03588591704303 \tabularnewline
83 & 30.383 & 30.3224003331343 & 0.0605996668656879 \tabularnewline
84 & 28.673 & 29.7246827807382 & -1.05168278073818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261075&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]15.928[/C][C]17.117[/C][C]-1.189[/C][/ROW]
[ROW][C]4[/C][C]16.171[/C][C]16.5541142277038[/C][C]-0.383114227703782[/C][/ROW]
[ROW][C]5[/C][C]15.937[/C][C]16.7510742173563[/C][C]-0.814074217356326[/C][/ROW]
[ROW][C]6[/C][C]15.713[/C][C]16.4192444248808[/C][C]-0.706244424880802[/C][/ROW]
[ROW][C]7[/C][C]15.594[/C][C]16.110372868885[/C][C]-0.516372868885016[/C][/ROW]
[ROW][C]8[/C][C]15.683[/C][C]15.929318759412[/C][C]-0.246318759411972[/C][/ROW]
[ROW][C]9[/C][C]16.438[/C][C]15.9887178795384[/C][C]0.449282120461556[/C][/ROW]
[ROW][C]10[/C][C]17.032[/C][C]16.7977094882525[/C][C]0.234290511747485[/C][/ROW]
[ROW][C]11[/C][C]17.696[/C][C]17.4198648967577[/C][C]0.276135103242257[/C][/ROW]
[ROW][C]12[/C][C]17.745[/C][C]18.1170488980066[/C][C]-0.372048898006579[/C][/ROW]
[ROW][C]13[/C][C]19.394[/C][C]18.1213386422256[/C][C]1.27266135777444[/C][/ROW]
[ROW][C]14[/C][C]20.148[/C][C]19.9232782561677[/C][C]0.22472174383234[/C][/ROW]
[ROW][C]15[/C][C]20.108[/C][C]20.7042837565203[/C][C]-0.596283756520254[/C][/ROW]
[ROW][C]16[/C][C]18.584[/C][C]20.5926265108869[/C][C]-2.00862651088688[/C][/ROW]
[ROW][C]17[/C][C]18.441[/C][C]18.8272437099931[/C][C]-0.386243709993078[/C][/ROW]
[ROW][C]18[/C][C]18.391[/C][C]18.6378276201723[/C][C]-0.24682762017229[/C][/ROW]
[ROW][C]19[/C][C]19.178[/C][C]18.5581655889424[/C][C]0.619834411057617[/C][/ROW]
[ROW][C]20[/C][C]18.079[/C][C]19.4196529888749[/C][C]-1.34065298887488[/C][/ROW]
[ROW][C]21[/C][C]18.483[/C][C]18.1595426123428[/C][C]0.323457387657179[/C][/ROW]
[ROW][C]22[/C][C]19.644[/C][C]18.6024134774734[/C][C]1.04158652252655[/C][/ROW]
[ROW][C]23[/C][C]19.195[/C][C]19.8885841206059[/C][C]-0.693584120605941[/C][/ROW]
[ROW][C]24[/C][C]19.65[/C][C]19.3562339921575[/C][C]0.293766007842475[/C][/ROW]
[ROW][C]25[/C][C]20.83[/C][C]19.8465367532214[/C][C]0.983463246778602[/C][/ROW]
[ROW][C]26[/C][C]23.595[/C][C]21.1447225442566[/C][C]2.45027745574336[/C][/ROW]
[ROW][C]27[/C][C]22.937[/C][C]24.2041798921153[/C][C]-1.26717989211526[/C][/ROW]
[ROW][C]28[/C][C]21.814[/C][C]23.393899002693[/C][C]-1.57989900269295[/C][/ROW]
[ROW][C]29[/C][C]21.928[/C][C]22.0810376997915[/C][C]-0.153037699791518[/C][/ROW]
[ROW][C]30[/C][C]21.777[/C][C]22.176646690603[/C][C]-0.399646690602999[/C][/ROW]
[ROW][C]31[/C][C]21.383[/C][C]21.9776199235446[/C][C]-0.594619923544602[/C][/ROW]
[ROW][C]32[/C][C]21.467[/C][C]21.5121626258168[/C][C]-0.0451626258167721[/C][/ROW]
[ROW][C]33[/C][C]22.052[/C][C]21.5907352947245[/C][C]0.461264705275536[/C][/ROW]
[ROW][C]34[/C][C]22.68[/C][C]22.2311668873622[/C][C]0.448833112637789[/C][/ROW]
[ROW][C]35[/C][C]24.32[/C][C]22.9131045374306[/C][C]1.40689546256936[/C][/ROW]
[ROW][C]36[/C][C]24.977[/C][C]24.722175474949[/C][C]0.254824525051049[/C][/ROW]
[ROW][C]37[/C][C]25.204[/C][C]25.4097985187353[/C][C]-0.205798518735271[/C][/ROW]
[ROW][C]38[/C][C]25.739[/C][C]25.6120670803106[/C][C]0.126932919689377[/C][/ROW]
[ROW][C]39[/C][C]26.434[/C][C]26.1623209981068[/C][C]0.271679001893219[/C][/ROW]
[ROW][C]40[/C][C]27.525[/C][C]26.889969496006[/C][C]0.635030503993992[/C][/ROW]
[ROW][C]41[/C][C]30.695[/C][C]28.0572830569773[/C][C]2.63771694302273[/C][/ROW]
[ROW][C]42[/C][C]32.436[/C][C]31.5442655822108[/C][C]0.891734417789237[/C][/ROW]
[ROW][C]43[/C][C]30.16[/C][C]33.3924280388709[/C][C]-3.23242803887092[/C][/ROW]
[ROW][C]44[/C][C]30.236[/C][C]30.7279772594546[/C][C]-0.491977259454593[/C][/ROW]
[ROW][C]45[/C][C]31.293[/C][C]30.7448548450985[/C][C]0.548145154901459[/C][/ROW]
[ROW][C]46[/C][C]31.077[/C][C]31.8677271275111[/C][C]-0.79072712751109[/C][/ROW]
[ROW][C]47[/C][C]32.226[/C][C]31.5567030263421[/C][C]0.669296973657946[/C][/ROW]
[ROW][C]48[/C][C]33.865[/C][C]32.7861344939422[/C][C]1.07886550605775[/C][/ROW]
[ROW][C]49[/C][C]32.81[/C][C]34.5547850667234[/C][C]-1.74478506672342[/C][/ROW]
[ROW][C]50[/C][C]32.242[/C][C]33.2901089004075[/C][C]-1.04810890040746[/C][/ROW]
[ROW][C]51[/C][C]32.7[/C][C]32.5961544431448[/C][C]0.103845556855177[/C][/ROW]
[ROW][C]52[/C][C]32.819[/C][C]33.0666338818251[/C][C]-0.247633881825053[/C][/ROW]
[ROW][C]53[/C][C]33.947[/C][C]33.1558749596625[/C][C]0.791125040337505[/C][/ROW]
[ROW][C]54[/C][C]34.148[/C][C]34.3789468792348[/C][C]-0.230946879234821[/C][/ROW]
[ROW][C]55[/C][C]35.261[/C][C]34.5521932852913[/C][C]0.708806714708714[/C][/ROW]
[ROW][C]56[/C][C]39.506[/C][C]35.7503727595048[/C][C]3.75562724049517[/C][/ROW]
[ROW][C]57[/C][C]41.591[/C][C]40.4466979897108[/C][C]1.14430201028924[/C][/ROW]
[ROW][C]58[/C][C]39.148[/C][C]42.6692122676589[/C][C]-3.52121226765886[/C][/ROW]
[ROW][C]59[/C][C]41.216[/C][C]39.8030574028285[/C][C]1.41294259717154[/C][/ROW]
[ROW][C]60[/C][C]40.225[/C][C]42.0408550430363[/C][C]-1.81585504303627[/C][/ROW]
[ROW][C]61[/C][C]41.126[/C][C]40.8316381799562[/C][C]0.294361820043811[/C][/ROW]
[ROW][C]62[/C][C]42.362[/C][C]41.7680125415975[/C][C]0.593987458402545[/C][/ROW]
[ROW][C]63[/C][C]40.74[/C][C]43.0753938340517[/C][C]-2.33539383405172[/C][/ROW]
[ROW][C]64[/C][C]40.256[/C][C]41.1727424029379[/C][C]-0.916742402937928[/C][/ROW]
[ROW][C]65[/C][C]39.804[/C][C]40.5785746600948[/C][C]-0.7745746600948[/C][/ROW]
[ROW][C]66[/C][C]41.002[/C][C]40.0334916504155[/C][C]0.968508349584532[/C][/ROW]
[ROW][C]67[/C][C]41.702[/C][C]41.3478802656432[/C][C]0.354119734356843[/C][/ROW]
[ROW][C]68[/C][C]42.254[/C][C]42.0904359189055[/C][C]0.163564081094513[/C][/ROW]
[ROW][C]69[/C][C]43.605[/C][C]42.6620919155809[/C][C]0.942908084419066[/C][/ROW]
[ROW][C]70[/C][C]43.271[/C][C]44.1264040685217[/C][C]-0.855404068521693[/C][/ROW]
[ROW][C]71[/C][C]43.221[/C][C]43.6896075412248[/C][C]-0.46860754122477[/C][/ROW]
[ROW][C]72[/C][C]41.373[/C][C]43.5832935374975[/C][C]-2.21029353749749[/C][/ROW]
[ROW][C]73[/C][C]40.435[/C][C]41.4696757922438[/C][C]-1.03467579224377[/C][/ROW]
[ROW][C]74[/C][C]39.217[/C][C]40.4073356327392[/C][C]-1.19033563273919[/C][/ROW]
[ROW][C]75[/C][C]39.457[/C][C]39.0462893533652[/C][C]0.410710646634776[/C][/ROW]
[ROW][C]76[/C][C]36.71[/C][C]39.3356457099125[/C][C]-2.62564570991248[/C][/ROW]
[ROW][C]77[/C][C]34.977[/C][C]36.27311382174[/C][C]-1.29611382173999[/C][/ROW]
[ROW][C]78[/C][C]32.729[/C][C]34.3843558533606[/C][C]-1.65535585336058[/C][/ROW]
[ROW][C]79[/C][C]31.584[/C][C]31.9374266695654[/C][C]-0.353426669565376[/C][/ROW]
[ROW][C]80[/C][C]32.51[/C][C]30.7499543040221[/C][C]1.76004569597788[/C][/ROW]
[ROW][C]81[/C][C]32.565[/C][C]31.8874643869039[/C][C]0.677535613096101[/C][/ROW]
[ROW][C]82[/C][C]30.988[/C][C]32.023885917043[/C][C]-1.03588591704303[/C][/ROW]
[ROW][C]83[/C][C]30.383[/C][C]30.3224003331343[/C][C]0.0605996668656879[/C][/ROW]
[ROW][C]84[/C][C]28.673[/C][C]29.7246827807382[/C][C]-1.05168278073818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261075&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261075&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
315.92817.117-1.189
416.17116.5541142277038-0.383114227703782
515.93716.7510742173563-0.814074217356326
615.71316.4192444248808-0.706244424880802
715.59416.110372868885-0.516372868885016
815.68315.929318759412-0.246318759411972
916.43815.98871787953840.449282120461556
1017.03216.79770948825250.234290511747485
1117.69617.41986489675770.276135103242257
1217.74518.1170488980066-0.372048898006579
1319.39418.12133864222561.27266135777444
1420.14819.92327825616770.22472174383234
1520.10820.7042837565203-0.596283756520254
1618.58420.5926265108869-2.00862651088688
1718.44118.8272437099931-0.386243709993078
1818.39118.6378276201723-0.24682762017229
1919.17818.55816558894240.619834411057617
2018.07919.4196529888749-1.34065298887488
2118.48318.15954261234280.323457387657179
2219.64418.60241347747341.04158652252655
2319.19519.8885841206059-0.693584120605941
2419.6519.35623399215750.293766007842475
2520.8319.84653675322140.983463246778602
2623.59521.14472254425662.45027745574336
2722.93724.2041798921153-1.26717989211526
2821.81423.393899002693-1.57989900269295
2921.92822.0810376997915-0.153037699791518
3021.77722.176646690603-0.399646690602999
3121.38321.9776199235446-0.594619923544602
3221.46721.5121626258168-0.0451626258167721
3322.05221.59073529472450.461264705275536
3422.6822.23116688736220.448833112637789
3524.3222.91310453743061.40689546256936
3624.97724.7221754749490.254824525051049
3725.20425.4097985187353-0.205798518735271
3825.73925.61206708031060.126932919689377
3926.43426.16232099810680.271679001893219
4027.52526.8899694960060.635030503993992
4130.69528.05728305697732.63771694302273
4232.43631.54426558221080.891734417789237
4330.1633.3924280388709-3.23242803887092
4430.23630.7279772594546-0.491977259454593
4531.29330.74485484509850.548145154901459
4631.07731.8677271275111-0.79072712751109
4732.22631.55670302634210.669296973657946
4833.86532.78613449394221.07886550605775
4932.8134.5547850667234-1.74478506672342
5032.24233.2901089004075-1.04810890040746
5132.732.59615444314480.103845556855177
5232.81933.0666338818251-0.247633881825053
5333.94733.15587495966250.791125040337505
5434.14834.3789468792348-0.230946879234821
5535.26134.55219328529130.708806714708714
5639.50635.75037275950483.75562724049517
5741.59140.44669798971081.14430201028924
5839.14842.6692122676589-3.52121226765886
5941.21639.80305740282851.41294259717154
6040.22542.0408550430363-1.81585504303627
6141.12640.83163817995620.294361820043811
6242.36241.76801254159750.593987458402545
6340.7443.0753938340517-2.33539383405172
6440.25641.1727424029379-0.916742402937928
6539.80440.5785746600948-0.7745746600948
6641.00240.03349165041550.968508349584532
6741.70241.34788026564320.354119734356843
6842.25442.09043591890550.163564081094513
6943.60542.66209191558090.942908084419066
7043.27144.1264040685217-0.855404068521693
7143.22143.6896075412248-0.46860754122477
7241.37343.5832935374975-2.21029353749749
7340.43541.4696757922438-1.03467579224377
7439.21740.4073356327392-1.19033563273919
7539.45739.04628935336520.410710646634776
7636.7139.3356457099125-2.62564570991248
7734.97736.27311382174-1.29611382173999
7832.72934.3843558533606-1.65535585336058
7931.58431.9374266695654-0.353426669565376
8032.5130.74995430402211.76004569597788
8132.56531.88746438690390.677535613096101
8230.98832.023885917043-1.03588591704303
8330.38330.32240033313430.0605996668656879
8428.67329.7246827807382-1.05168278073818







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8527.888298839328225.495107191935930.2814904867206
8627.103597678656523.509992949127630.6972024081854
8726.318896517984721.657854752582730.9799382833867
8825.53419535731319.848534737180331.2198559774457
8924.749494196641218.049964491982831.4490239012997
9023.964793035969516.247175571127731.6824105008113
9123.180091875297714.432182172779631.9280015778158
9222.39539071462612.600390101102432.1903913281496
9321.610689553954210.749042249508432.4723368584
9420.82598839328258.8764535123282532.7755232742367
9520.04128723261076.9815986298981933.1009758353232
9619.2565860719395.0638747728883733.4492973709895

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 27.8882988393282 & 25.4951071919359 & 30.2814904867206 \tabularnewline
86 & 27.1035976786565 & 23.5099929491276 & 30.6972024081854 \tabularnewline
87 & 26.3188965179847 & 21.6578547525827 & 30.9799382833867 \tabularnewline
88 & 25.534195357313 & 19.8485347371803 & 31.2198559774457 \tabularnewline
89 & 24.7494941966412 & 18.0499644919828 & 31.4490239012997 \tabularnewline
90 & 23.9647930359695 & 16.2471755711277 & 31.6824105008113 \tabularnewline
91 & 23.1800918752977 & 14.4321821727796 & 31.9280015778158 \tabularnewline
92 & 22.395390714626 & 12.6003901011024 & 32.1903913281496 \tabularnewline
93 & 21.6106895539542 & 10.7490422495084 & 32.4723368584 \tabularnewline
94 & 20.8259883932825 & 8.87645351232825 & 32.7755232742367 \tabularnewline
95 & 20.0412872326107 & 6.98159862989819 & 33.1009758353232 \tabularnewline
96 & 19.256586071939 & 5.06387477288837 & 33.4492973709895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261075&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]27.8882988393282[/C][C]25.4951071919359[/C][C]30.2814904867206[/C][/ROW]
[ROW][C]86[/C][C]27.1035976786565[/C][C]23.5099929491276[/C][C]30.6972024081854[/C][/ROW]
[ROW][C]87[/C][C]26.3188965179847[/C][C]21.6578547525827[/C][C]30.9799382833867[/C][/ROW]
[ROW][C]88[/C][C]25.534195357313[/C][C]19.8485347371803[/C][C]31.2198559774457[/C][/ROW]
[ROW][C]89[/C][C]24.7494941966412[/C][C]18.0499644919828[/C][C]31.4490239012997[/C][/ROW]
[ROW][C]90[/C][C]23.9647930359695[/C][C]16.2471755711277[/C][C]31.6824105008113[/C][/ROW]
[ROW][C]91[/C][C]23.1800918752977[/C][C]14.4321821727796[/C][C]31.9280015778158[/C][/ROW]
[ROW][C]92[/C][C]22.395390714626[/C][C]12.6003901011024[/C][C]32.1903913281496[/C][/ROW]
[ROW][C]93[/C][C]21.6106895539542[/C][C]10.7490422495084[/C][C]32.4723368584[/C][/ROW]
[ROW][C]94[/C][C]20.8259883932825[/C][C]8.87645351232825[/C][C]32.7755232742367[/C][/ROW]
[ROW][C]95[/C][C]20.0412872326107[/C][C]6.98159862989819[/C][C]33.1009758353232[/C][/ROW]
[ROW][C]96[/C][C]19.256586071939[/C][C]5.06387477288837[/C][C]33.4492973709895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261075&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261075&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
8527.888298839328225.495107191935930.2814904867206
8627.103597678656523.509992949127630.6972024081854
8726.318896517984721.657854752582730.9799382833867
8825.53419535731319.848534737180331.2198559774457
8924.749494196641218.049964491982831.4490239012997
9023.964793035969516.247175571127731.6824105008113
9123.180091875297714.432182172779631.9280015778158
9222.39539071462612.600390101102432.1903913281496
9321.610689553954210.749042249508432.4723368584
9420.82598839328258.8764535123282532.7755232742367
9520.04128723261076.9815986298981933.1009758353232
9619.2565860719395.0638747728883733.4492973709895



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')