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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 computationMon, 10 Dec 2012 16:28:15 -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/2012/Dec/10/t1355174945mab2w5zhdft5ey4.htm/, Retrieved Wed, 24 Apr 2024 23:24:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198345, Retrieved Wed, 24 Apr 2024 23:24:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [Exponential Smoothing] [Paper Triple Expo...] [2012-12-10 21:28:15] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
- R P       [Exponential Smoothing] [PAPER SINGLE SMOO...] [2012-12-12 12:54:46] [86dcce9422b96d4554cb918e531c1d5d]
-   P         [Exponential Smoothing] [PAPER Double SMOO...] [2012-12-12 12:58:32] [86dcce9422b96d4554cb918e531c1d5d]
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Dataseries X:
68.897
38.683
44.720
39.525
45.315
50.380
40.600
36.279
42.438
38.064
31.879
11.379
70.249
39.253
47.060
41.697
38.708
49.267
39.018
32.228
40.870
39.383
34.571
12.066
70.938
34.077
45.409
40.809
37.013
44.953
37.848
32.745
43.412
34.931
33.008
8.620
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198345&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]3 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=198345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198345&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.435378644958913
beta0
gamma0.382502042123754

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.435378644958913 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.382502042123754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198345&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]0.435378644958913[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.382502042123754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198345&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
alpha0.435378644958913
beta0
gamma0.382502042123754







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1370.24970.7213266559829-0.472326655982897
1439.25339.6707298598797-0.417729859879742
1547.0647.4463200095497-0.386320009549735
1641.69741.8418353372948-0.144835337294772
1738.70838.53898793442450.169012065575487
1849.26748.94711632187310.319883678126878
1939.01839.9350143208905-0.917014320890452
2032.22835.0510183451432-2.82301834514322
2140.8739.77602225336391.09397774663606
2239.38335.60665261233293.77634738766715
2334.57131.16692109755953.40407890244052
2412.06612.3869868341272-0.320986834127234
2570.93871.0438556667499-0.105855666749918
2634.07740.1646037190586-6.08760371905856
2745.40945.4784354191852-0.0694354191852398
2840.80940.06406869052770.744931309472328
2937.01337.2163879383318-0.203387938331844
3044.95347.4949648810314-2.54196488103145
3137.84836.96974372933170.878256270668274
3232.74532.4557327885040.289267211495989
3343.41239.38170839419494.03029160580512
3434.93137.0700553120875-2.13905531208749
3533.00829.9744853995363.03351460046402
368.6210.2287172959361-1.60871729593615
3768.90668.3713974096740.534602590326045
3839.55636.47911623375163.07688376624843
3950.66947.08270679126273.58629320873729
4036.43243.435844061486-7.00384406148601
4140.89137.00970459799863.88129540200137
4248.42848.5616057325946-0.133605732594653
4336.22239.8235938543359-3.60159385433592
4433.42533.23194856357920.193051436420781
4539.40140.9239785044995-1.5229785044995
4637.96734.86216362444433.10483637555565
4734.80131.16678599643053.63421400356955
4812.65710.67997223397671.97702776602326
4969.11670.8466994435275-1.73069944352753
5041.51938.51720760673643.00179239326356
5151.32149.1981215408982.12287845910204
5238.52942.6269798164402-4.09797981644024
5341.54739.81684233033641.73015766966364
5452.07349.56509056811242.50790943188758
5538.40141.2281606757658-2.82716067576583
5640.89835.7932121237165.10478787628404
5740.43945.2530982565119-4.81409825651187
5841.88838.75786384340653.13013615659347
5937.89835.18783026213922.71016973786079
608.77113.9408068009522-5.16980680095217
6168.18470.1952013857282-2.01120138572821
6250.5338.765655677378611.7643443226214
6347.22153.0717795905147-5.85077959051474
6441.75641.68556599961990.0704340003800539
6545.63341.94896285613373.68403714386628
6648.13852.7158586231759-4.57785862317593
6739.48640.1417278336604-0.655727833660372
6839.34137.36522834966131.97577165033875
6941.11743.3206374909453-2.20363749094525
7041.62939.67764889123751.95135110876252
7129.72235.5036978206959-5.78169782069586
727.0548.8576673234992-1.8036673234992
7356.67667.2597674412836-10.5837674412836
7434.8735.0729979096539-0.20299790965386
7535.11740.3644790288423-5.24747902884235
7630.16930.5197271390595-0.35072713905954
7730.93631.3801850410275-0.444185041027488
7835.69938.5654291363627-2.86642913636274
7933.22827.5834761614725.64452383852799
8027.73328.1182935552999-0.385293555299906
8133.66632.14312326059481.52287673940519
8235.42931.01992736743524.40907263256484
8327.43826.24591830103141.19208169896859
848.173.495253039042424.67474696095758
8563.4162.82168851587970.588311484120339
8638.0437.74092612840970.299073871590295
8745.38942.16154793785633.22745206214368
8837.35337.06414579656850.288854203431491
8937.02438.1828797638392-1.15887976383923
9050.95744.53383183695466.42316816304544
9137.99439.4344716288755-1.44047162887547
9236.45435.58238074118570.871619258814306
9346.0840.56654873376535.51345126623468
9443.37341.80409209587711.56890790412287
9537.39535.09876621838652.29623378161354
9610.96313.5809723056863-2.61797230568633
9776.05868.84977089677327.20822910322683
9850.17946.5887129657873.59028703421296
9957.45253.07469708846924.37730291153076
10047.56847.8432699359838-0.275269935983808
10150.0548.40373090133661.64626909866343
10250.85657.6134708391524-6.75747083915241
10341.99245.0772408653798-3.08524086537979
10439.28441.0083921200526-1.72439212005261
10544.52145.8648031836572-1.3438031836572
10643.83243.26494601463670.567053985363344
10741.15336.28051404803414.87248595196591
10817.114.82305001788812.27694998211193

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 70.249 & 70.7213266559829 & -0.472326655982897 \tabularnewline
14 & 39.253 & 39.6707298598797 & -0.417729859879742 \tabularnewline
15 & 47.06 & 47.4463200095497 & -0.386320009549735 \tabularnewline
16 & 41.697 & 41.8418353372948 & -0.144835337294772 \tabularnewline
17 & 38.708 & 38.5389879344245 & 0.169012065575487 \tabularnewline
18 & 49.267 & 48.9471163218731 & 0.319883678126878 \tabularnewline
19 & 39.018 & 39.9350143208905 & -0.917014320890452 \tabularnewline
20 & 32.228 & 35.0510183451432 & -2.82301834514322 \tabularnewline
21 & 40.87 & 39.7760222533639 & 1.09397774663606 \tabularnewline
22 & 39.383 & 35.6066526123329 & 3.77634738766715 \tabularnewline
23 & 34.571 & 31.1669210975595 & 3.40407890244052 \tabularnewline
24 & 12.066 & 12.3869868341272 & -0.320986834127234 \tabularnewline
25 & 70.938 & 71.0438556667499 & -0.105855666749918 \tabularnewline
26 & 34.077 & 40.1646037190586 & -6.08760371905856 \tabularnewline
27 & 45.409 & 45.4784354191852 & -0.0694354191852398 \tabularnewline
28 & 40.809 & 40.0640686905277 & 0.744931309472328 \tabularnewline
29 & 37.013 & 37.2163879383318 & -0.203387938331844 \tabularnewline
30 & 44.953 & 47.4949648810314 & -2.54196488103145 \tabularnewline
31 & 37.848 & 36.9697437293317 & 0.878256270668274 \tabularnewline
32 & 32.745 & 32.455732788504 & 0.289267211495989 \tabularnewline
33 & 43.412 & 39.3817083941949 & 4.03029160580512 \tabularnewline
34 & 34.931 & 37.0700553120875 & -2.13905531208749 \tabularnewline
35 & 33.008 & 29.974485399536 & 3.03351460046402 \tabularnewline
36 & 8.62 & 10.2287172959361 & -1.60871729593615 \tabularnewline
37 & 68.906 & 68.371397409674 & 0.534602590326045 \tabularnewline
38 & 39.556 & 36.4791162337516 & 3.07688376624843 \tabularnewline
39 & 50.669 & 47.0827067912627 & 3.58629320873729 \tabularnewline
40 & 36.432 & 43.435844061486 & -7.00384406148601 \tabularnewline
41 & 40.891 & 37.0097045979986 & 3.88129540200137 \tabularnewline
42 & 48.428 & 48.5616057325946 & -0.133605732594653 \tabularnewline
43 & 36.222 & 39.8235938543359 & -3.60159385433592 \tabularnewline
44 & 33.425 & 33.2319485635792 & 0.193051436420781 \tabularnewline
45 & 39.401 & 40.9239785044995 & -1.5229785044995 \tabularnewline
46 & 37.967 & 34.8621636244443 & 3.10483637555565 \tabularnewline
47 & 34.801 & 31.1667859964305 & 3.63421400356955 \tabularnewline
48 & 12.657 & 10.6799722339767 & 1.97702776602326 \tabularnewline
49 & 69.116 & 70.8466994435275 & -1.73069944352753 \tabularnewline
50 & 41.519 & 38.5172076067364 & 3.00179239326356 \tabularnewline
51 & 51.321 & 49.198121540898 & 2.12287845910204 \tabularnewline
52 & 38.529 & 42.6269798164402 & -4.09797981644024 \tabularnewline
53 & 41.547 & 39.8168423303364 & 1.73015766966364 \tabularnewline
54 & 52.073 & 49.5650905681124 & 2.50790943188758 \tabularnewline
55 & 38.401 & 41.2281606757658 & -2.82716067576583 \tabularnewline
56 & 40.898 & 35.793212123716 & 5.10478787628404 \tabularnewline
57 & 40.439 & 45.2530982565119 & -4.81409825651187 \tabularnewline
58 & 41.888 & 38.7578638434065 & 3.13013615659347 \tabularnewline
59 & 37.898 & 35.1878302621392 & 2.71016973786079 \tabularnewline
60 & 8.771 & 13.9408068009522 & -5.16980680095217 \tabularnewline
61 & 68.184 & 70.1952013857282 & -2.01120138572821 \tabularnewline
62 & 50.53 & 38.7656556773786 & 11.7643443226214 \tabularnewline
63 & 47.221 & 53.0717795905147 & -5.85077959051474 \tabularnewline
64 & 41.756 & 41.6855659996199 & 0.0704340003800539 \tabularnewline
65 & 45.633 & 41.9489628561337 & 3.68403714386628 \tabularnewline
66 & 48.138 & 52.7158586231759 & -4.57785862317593 \tabularnewline
67 & 39.486 & 40.1417278336604 & -0.655727833660372 \tabularnewline
68 & 39.341 & 37.3652283496613 & 1.97577165033875 \tabularnewline
69 & 41.117 & 43.3206374909453 & -2.20363749094525 \tabularnewline
70 & 41.629 & 39.6776488912375 & 1.95135110876252 \tabularnewline
71 & 29.722 & 35.5036978206959 & -5.78169782069586 \tabularnewline
72 & 7.054 & 8.8576673234992 & -1.8036673234992 \tabularnewline
73 & 56.676 & 67.2597674412836 & -10.5837674412836 \tabularnewline
74 & 34.87 & 35.0729979096539 & -0.20299790965386 \tabularnewline
75 & 35.117 & 40.3644790288423 & -5.24747902884235 \tabularnewline
76 & 30.169 & 30.5197271390595 & -0.35072713905954 \tabularnewline
77 & 30.936 & 31.3801850410275 & -0.444185041027488 \tabularnewline
78 & 35.699 & 38.5654291363627 & -2.86642913636274 \tabularnewline
79 & 33.228 & 27.583476161472 & 5.64452383852799 \tabularnewline
80 & 27.733 & 28.1182935552999 & -0.385293555299906 \tabularnewline
81 & 33.666 & 32.1431232605948 & 1.52287673940519 \tabularnewline
82 & 35.429 & 31.0199273674352 & 4.40907263256484 \tabularnewline
83 & 27.438 & 26.2459183010314 & 1.19208169896859 \tabularnewline
84 & 8.17 & 3.49525303904242 & 4.67474696095758 \tabularnewline
85 & 63.41 & 62.8216885158797 & 0.588311484120339 \tabularnewline
86 & 38.04 & 37.7409261284097 & 0.299073871590295 \tabularnewline
87 & 45.389 & 42.1615479378563 & 3.22745206214368 \tabularnewline
88 & 37.353 & 37.0641457965685 & 0.288854203431491 \tabularnewline
89 & 37.024 & 38.1828797638392 & -1.15887976383923 \tabularnewline
90 & 50.957 & 44.5338318369546 & 6.42316816304544 \tabularnewline
91 & 37.994 & 39.4344716288755 & -1.44047162887547 \tabularnewline
92 & 36.454 & 35.5823807411857 & 0.871619258814306 \tabularnewline
93 & 46.08 & 40.5665487337653 & 5.51345126623468 \tabularnewline
94 & 43.373 & 41.8040920958771 & 1.56890790412287 \tabularnewline
95 & 37.395 & 35.0987662183865 & 2.29623378161354 \tabularnewline
96 & 10.963 & 13.5809723056863 & -2.61797230568633 \tabularnewline
97 & 76.058 & 68.8497708967732 & 7.20822910322683 \tabularnewline
98 & 50.179 & 46.588712965787 & 3.59028703421296 \tabularnewline
99 & 57.452 & 53.0746970884692 & 4.37730291153076 \tabularnewline
100 & 47.568 & 47.8432699359838 & -0.275269935983808 \tabularnewline
101 & 50.05 & 48.4037309013366 & 1.64626909866343 \tabularnewline
102 & 50.856 & 57.6134708391524 & -6.75747083915241 \tabularnewline
103 & 41.992 & 45.0772408653798 & -3.08524086537979 \tabularnewline
104 & 39.284 & 41.0083921200526 & -1.72439212005261 \tabularnewline
105 & 44.521 & 45.8648031836572 & -1.3438031836572 \tabularnewline
106 & 43.832 & 43.2649460146367 & 0.567053985363344 \tabularnewline
107 & 41.153 & 36.2805140480341 & 4.87248595196591 \tabularnewline
108 & 17.1 & 14.8230500178881 & 2.27694998211193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198345&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]70.249[/C][C]70.7213266559829[/C][C]-0.472326655982897[/C][/ROW]
[ROW][C]14[/C][C]39.253[/C][C]39.6707298598797[/C][C]-0.417729859879742[/C][/ROW]
[ROW][C]15[/C][C]47.06[/C][C]47.4463200095497[/C][C]-0.386320009549735[/C][/ROW]
[ROW][C]16[/C][C]41.697[/C][C]41.8418353372948[/C][C]-0.144835337294772[/C][/ROW]
[ROW][C]17[/C][C]38.708[/C][C]38.5389879344245[/C][C]0.169012065575487[/C][/ROW]
[ROW][C]18[/C][C]49.267[/C][C]48.9471163218731[/C][C]0.319883678126878[/C][/ROW]
[ROW][C]19[/C][C]39.018[/C][C]39.9350143208905[/C][C]-0.917014320890452[/C][/ROW]
[ROW][C]20[/C][C]32.228[/C][C]35.0510183451432[/C][C]-2.82301834514322[/C][/ROW]
[ROW][C]21[/C][C]40.87[/C][C]39.7760222533639[/C][C]1.09397774663606[/C][/ROW]
[ROW][C]22[/C][C]39.383[/C][C]35.6066526123329[/C][C]3.77634738766715[/C][/ROW]
[ROW][C]23[/C][C]34.571[/C][C]31.1669210975595[/C][C]3.40407890244052[/C][/ROW]
[ROW][C]24[/C][C]12.066[/C][C]12.3869868341272[/C][C]-0.320986834127234[/C][/ROW]
[ROW][C]25[/C][C]70.938[/C][C]71.0438556667499[/C][C]-0.105855666749918[/C][/ROW]
[ROW][C]26[/C][C]34.077[/C][C]40.1646037190586[/C][C]-6.08760371905856[/C][/ROW]
[ROW][C]27[/C][C]45.409[/C][C]45.4784354191852[/C][C]-0.0694354191852398[/C][/ROW]
[ROW][C]28[/C][C]40.809[/C][C]40.0640686905277[/C][C]0.744931309472328[/C][/ROW]
[ROW][C]29[/C][C]37.013[/C][C]37.2163879383318[/C][C]-0.203387938331844[/C][/ROW]
[ROW][C]30[/C][C]44.953[/C][C]47.4949648810314[/C][C]-2.54196488103145[/C][/ROW]
[ROW][C]31[/C][C]37.848[/C][C]36.9697437293317[/C][C]0.878256270668274[/C][/ROW]
[ROW][C]32[/C][C]32.745[/C][C]32.455732788504[/C][C]0.289267211495989[/C][/ROW]
[ROW][C]33[/C][C]43.412[/C][C]39.3817083941949[/C][C]4.03029160580512[/C][/ROW]
[ROW][C]34[/C][C]34.931[/C][C]37.0700553120875[/C][C]-2.13905531208749[/C][/ROW]
[ROW][C]35[/C][C]33.008[/C][C]29.974485399536[/C][C]3.03351460046402[/C][/ROW]
[ROW][C]36[/C][C]8.62[/C][C]10.2287172959361[/C][C]-1.60871729593615[/C][/ROW]
[ROW][C]37[/C][C]68.906[/C][C]68.371397409674[/C][C]0.534602590326045[/C][/ROW]
[ROW][C]38[/C][C]39.556[/C][C]36.4791162337516[/C][C]3.07688376624843[/C][/ROW]
[ROW][C]39[/C][C]50.669[/C][C]47.0827067912627[/C][C]3.58629320873729[/C][/ROW]
[ROW][C]40[/C][C]36.432[/C][C]43.435844061486[/C][C]-7.00384406148601[/C][/ROW]
[ROW][C]41[/C][C]40.891[/C][C]37.0097045979986[/C][C]3.88129540200137[/C][/ROW]
[ROW][C]42[/C][C]48.428[/C][C]48.5616057325946[/C][C]-0.133605732594653[/C][/ROW]
[ROW][C]43[/C][C]36.222[/C][C]39.8235938543359[/C][C]-3.60159385433592[/C][/ROW]
[ROW][C]44[/C][C]33.425[/C][C]33.2319485635792[/C][C]0.193051436420781[/C][/ROW]
[ROW][C]45[/C][C]39.401[/C][C]40.9239785044995[/C][C]-1.5229785044995[/C][/ROW]
[ROW][C]46[/C][C]37.967[/C][C]34.8621636244443[/C][C]3.10483637555565[/C][/ROW]
[ROW][C]47[/C][C]34.801[/C][C]31.1667859964305[/C][C]3.63421400356955[/C][/ROW]
[ROW][C]48[/C][C]12.657[/C][C]10.6799722339767[/C][C]1.97702776602326[/C][/ROW]
[ROW][C]49[/C][C]69.116[/C][C]70.8466994435275[/C][C]-1.73069944352753[/C][/ROW]
[ROW][C]50[/C][C]41.519[/C][C]38.5172076067364[/C][C]3.00179239326356[/C][/ROW]
[ROW][C]51[/C][C]51.321[/C][C]49.198121540898[/C][C]2.12287845910204[/C][/ROW]
[ROW][C]52[/C][C]38.529[/C][C]42.6269798164402[/C][C]-4.09797981644024[/C][/ROW]
[ROW][C]53[/C][C]41.547[/C][C]39.8168423303364[/C][C]1.73015766966364[/C][/ROW]
[ROW][C]54[/C][C]52.073[/C][C]49.5650905681124[/C][C]2.50790943188758[/C][/ROW]
[ROW][C]55[/C][C]38.401[/C][C]41.2281606757658[/C][C]-2.82716067576583[/C][/ROW]
[ROW][C]56[/C][C]40.898[/C][C]35.793212123716[/C][C]5.10478787628404[/C][/ROW]
[ROW][C]57[/C][C]40.439[/C][C]45.2530982565119[/C][C]-4.81409825651187[/C][/ROW]
[ROW][C]58[/C][C]41.888[/C][C]38.7578638434065[/C][C]3.13013615659347[/C][/ROW]
[ROW][C]59[/C][C]37.898[/C][C]35.1878302621392[/C][C]2.71016973786079[/C][/ROW]
[ROW][C]60[/C][C]8.771[/C][C]13.9408068009522[/C][C]-5.16980680095217[/C][/ROW]
[ROW][C]61[/C][C]68.184[/C][C]70.1952013857282[/C][C]-2.01120138572821[/C][/ROW]
[ROW][C]62[/C][C]50.53[/C][C]38.7656556773786[/C][C]11.7643443226214[/C][/ROW]
[ROW][C]63[/C][C]47.221[/C][C]53.0717795905147[/C][C]-5.85077959051474[/C][/ROW]
[ROW][C]64[/C][C]41.756[/C][C]41.6855659996199[/C][C]0.0704340003800539[/C][/ROW]
[ROW][C]65[/C][C]45.633[/C][C]41.9489628561337[/C][C]3.68403714386628[/C][/ROW]
[ROW][C]66[/C][C]48.138[/C][C]52.7158586231759[/C][C]-4.57785862317593[/C][/ROW]
[ROW][C]67[/C][C]39.486[/C][C]40.1417278336604[/C][C]-0.655727833660372[/C][/ROW]
[ROW][C]68[/C][C]39.341[/C][C]37.3652283496613[/C][C]1.97577165033875[/C][/ROW]
[ROW][C]69[/C][C]41.117[/C][C]43.3206374909453[/C][C]-2.20363749094525[/C][/ROW]
[ROW][C]70[/C][C]41.629[/C][C]39.6776488912375[/C][C]1.95135110876252[/C][/ROW]
[ROW][C]71[/C][C]29.722[/C][C]35.5036978206959[/C][C]-5.78169782069586[/C][/ROW]
[ROW][C]72[/C][C]7.054[/C][C]8.8576673234992[/C][C]-1.8036673234992[/C][/ROW]
[ROW][C]73[/C][C]56.676[/C][C]67.2597674412836[/C][C]-10.5837674412836[/C][/ROW]
[ROW][C]74[/C][C]34.87[/C][C]35.0729979096539[/C][C]-0.20299790965386[/C][/ROW]
[ROW][C]75[/C][C]35.117[/C][C]40.3644790288423[/C][C]-5.24747902884235[/C][/ROW]
[ROW][C]76[/C][C]30.169[/C][C]30.5197271390595[/C][C]-0.35072713905954[/C][/ROW]
[ROW][C]77[/C][C]30.936[/C][C]31.3801850410275[/C][C]-0.444185041027488[/C][/ROW]
[ROW][C]78[/C][C]35.699[/C][C]38.5654291363627[/C][C]-2.86642913636274[/C][/ROW]
[ROW][C]79[/C][C]33.228[/C][C]27.583476161472[/C][C]5.64452383852799[/C][/ROW]
[ROW][C]80[/C][C]27.733[/C][C]28.1182935552999[/C][C]-0.385293555299906[/C][/ROW]
[ROW][C]81[/C][C]33.666[/C][C]32.1431232605948[/C][C]1.52287673940519[/C][/ROW]
[ROW][C]82[/C][C]35.429[/C][C]31.0199273674352[/C][C]4.40907263256484[/C][/ROW]
[ROW][C]83[/C][C]27.438[/C][C]26.2459183010314[/C][C]1.19208169896859[/C][/ROW]
[ROW][C]84[/C][C]8.17[/C][C]3.49525303904242[/C][C]4.67474696095758[/C][/ROW]
[ROW][C]85[/C][C]63.41[/C][C]62.8216885158797[/C][C]0.588311484120339[/C][/ROW]
[ROW][C]86[/C][C]38.04[/C][C]37.7409261284097[/C][C]0.299073871590295[/C][/ROW]
[ROW][C]87[/C][C]45.389[/C][C]42.1615479378563[/C][C]3.22745206214368[/C][/ROW]
[ROW][C]88[/C][C]37.353[/C][C]37.0641457965685[/C][C]0.288854203431491[/C][/ROW]
[ROW][C]89[/C][C]37.024[/C][C]38.1828797638392[/C][C]-1.15887976383923[/C][/ROW]
[ROW][C]90[/C][C]50.957[/C][C]44.5338318369546[/C][C]6.42316816304544[/C][/ROW]
[ROW][C]91[/C][C]37.994[/C][C]39.4344716288755[/C][C]-1.44047162887547[/C][/ROW]
[ROW][C]92[/C][C]36.454[/C][C]35.5823807411857[/C][C]0.871619258814306[/C][/ROW]
[ROW][C]93[/C][C]46.08[/C][C]40.5665487337653[/C][C]5.51345126623468[/C][/ROW]
[ROW][C]94[/C][C]43.373[/C][C]41.8040920958771[/C][C]1.56890790412287[/C][/ROW]
[ROW][C]95[/C][C]37.395[/C][C]35.0987662183865[/C][C]2.29623378161354[/C][/ROW]
[ROW][C]96[/C][C]10.963[/C][C]13.5809723056863[/C][C]-2.61797230568633[/C][/ROW]
[ROW][C]97[/C][C]76.058[/C][C]68.8497708967732[/C][C]7.20822910322683[/C][/ROW]
[ROW][C]98[/C][C]50.179[/C][C]46.588712965787[/C][C]3.59028703421296[/C][/ROW]
[ROW][C]99[/C][C]57.452[/C][C]53.0746970884692[/C][C]4.37730291153076[/C][/ROW]
[ROW][C]100[/C][C]47.568[/C][C]47.8432699359838[/C][C]-0.275269935983808[/C][/ROW]
[ROW][C]101[/C][C]50.05[/C][C]48.4037309013366[/C][C]1.64626909866343[/C][/ROW]
[ROW][C]102[/C][C]50.856[/C][C]57.6134708391524[/C][C]-6.75747083915241[/C][/ROW]
[ROW][C]103[/C][C]41.992[/C][C]45.0772408653798[/C][C]-3.08524086537979[/C][/ROW]
[ROW][C]104[/C][C]39.284[/C][C]41.0083921200526[/C][C]-1.72439212005261[/C][/ROW]
[ROW][C]105[/C][C]44.521[/C][C]45.8648031836572[/C][C]-1.3438031836572[/C][/ROW]
[ROW][C]106[/C][C]43.832[/C][C]43.2649460146367[/C][C]0.567053985363344[/C][/ROW]
[ROW][C]107[/C][C]41.153[/C][C]36.2805140480341[/C][C]4.87248595196591[/C][/ROW]
[ROW][C]108[/C][C]17.1[/C][C]14.8230500178881[/C][C]2.27694998211193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198345&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198345&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
1370.24970.7213266559829-0.472326655982897
1439.25339.6707298598797-0.417729859879742
1547.0647.4463200095497-0.386320009549735
1641.69741.8418353372948-0.144835337294772
1738.70838.53898793442450.169012065575487
1849.26748.94711632187310.319883678126878
1939.01839.9350143208905-0.917014320890452
2032.22835.0510183451432-2.82301834514322
2140.8739.77602225336391.09397774663606
2239.38335.60665261233293.77634738766715
2334.57131.16692109755953.40407890244052
2412.06612.3869868341272-0.320986834127234
2570.93871.0438556667499-0.105855666749918
2634.07740.1646037190586-6.08760371905856
2745.40945.4784354191852-0.0694354191852398
2840.80940.06406869052770.744931309472328
2937.01337.2163879383318-0.203387938331844
3044.95347.4949648810314-2.54196488103145
3137.84836.96974372933170.878256270668274
3232.74532.4557327885040.289267211495989
3343.41239.38170839419494.03029160580512
3434.93137.0700553120875-2.13905531208749
3533.00829.9744853995363.03351460046402
368.6210.2287172959361-1.60871729593615
3768.90668.3713974096740.534602590326045
3839.55636.47911623375163.07688376624843
3950.66947.08270679126273.58629320873729
4036.43243.435844061486-7.00384406148601
4140.89137.00970459799863.88129540200137
4248.42848.5616057325946-0.133605732594653
4336.22239.8235938543359-3.60159385433592
4433.42533.23194856357920.193051436420781
4539.40140.9239785044995-1.5229785044995
4637.96734.86216362444433.10483637555565
4734.80131.16678599643053.63421400356955
4812.65710.67997223397671.97702776602326
4969.11670.8466994435275-1.73069944352753
5041.51938.51720760673643.00179239326356
5151.32149.1981215408982.12287845910204
5238.52942.6269798164402-4.09797981644024
5341.54739.81684233033641.73015766966364
5452.07349.56509056811242.50790943188758
5538.40141.2281606757658-2.82716067576583
5640.89835.7932121237165.10478787628404
5740.43945.2530982565119-4.81409825651187
5841.88838.75786384340653.13013615659347
5937.89835.18783026213922.71016973786079
608.77113.9408068009522-5.16980680095217
6168.18470.1952013857282-2.01120138572821
6250.5338.765655677378611.7643443226214
6347.22153.0717795905147-5.85077959051474
6441.75641.68556599961990.0704340003800539
6545.63341.94896285613373.68403714386628
6648.13852.7158586231759-4.57785862317593
6739.48640.1417278336604-0.655727833660372
6839.34137.36522834966131.97577165033875
6941.11743.3206374909453-2.20363749094525
7041.62939.67764889123751.95135110876252
7129.72235.5036978206959-5.78169782069586
727.0548.8576673234992-1.8036673234992
7356.67667.2597674412836-10.5837674412836
7434.8735.0729979096539-0.20299790965386
7535.11740.3644790288423-5.24747902884235
7630.16930.5197271390595-0.35072713905954
7730.93631.3801850410275-0.444185041027488
7835.69938.5654291363627-2.86642913636274
7933.22827.5834761614725.64452383852799
8027.73328.1182935552999-0.385293555299906
8133.66632.14312326059481.52287673940519
8235.42931.01992736743524.40907263256484
8327.43826.24591830103141.19208169896859
848.173.495253039042424.67474696095758
8563.4162.82168851587970.588311484120339
8638.0437.74092612840970.299073871590295
8745.38942.16154793785633.22745206214368
8837.35337.06414579656850.288854203431491
8937.02438.1828797638392-1.15887976383923
9050.95744.53383183695466.42316816304544
9137.99439.4344716288755-1.44047162887547
9236.45435.58238074118570.871619258814306
9346.0840.56654873376535.51345126623468
9443.37341.80409209587711.56890790412287
9537.39535.09876621838652.29623378161354
9610.96313.5809723056863-2.61797230568633
9776.05868.84977089677327.20822910322683
9850.17946.5887129657873.59028703421296
9957.45253.07469708846924.37730291153076
10047.56847.8432699359838-0.275269935983808
10150.0548.40373090133661.64626909866343
10250.85657.6134708391524-6.75747083915241
10341.99245.0772408653798-3.08524086537979
10439.28441.0083921200526-1.72439212005261
10544.52145.8648031836572-1.3438031836572
10643.83243.26494601463670.567053985363344
10741.15336.28051404803414.87248595196591
10817.114.82305001788812.27694998211193







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10974.345146378248967.553242446412981.1370503100848
11048.164416743461740.756711072273155.5721224146502
11153.257237453566945.281132664722361.2333422424115
11245.115215416855336.608606698082653.621824135628
11346.210515554386837.204598822261755.2164322865118
11452.888559273655743.409599389911162.3675191574003
11544.087474976270634.157982301953954.0169676505874
11641.655775117820931.295322952930652.0162272827113
11747.345145030036436.570957666125858.119332393947
11845.743036640731134.570424697039556.9156485844228
11939.441560545505727.884251086293750.9988700047177
12015.30216533988273.3725573736643627.2317733061011

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 74.3451463782489 & 67.5532424464129 & 81.1370503100848 \tabularnewline
110 & 48.1644167434617 & 40.7567110722731 & 55.5721224146502 \tabularnewline
111 & 53.2572374535669 & 45.2811326647223 & 61.2333422424115 \tabularnewline
112 & 45.1152154168553 & 36.6086066980826 & 53.621824135628 \tabularnewline
113 & 46.2105155543868 & 37.2045988222617 & 55.2164322865118 \tabularnewline
114 & 52.8885592736557 & 43.4095993899111 & 62.3675191574003 \tabularnewline
115 & 44.0874749762706 & 34.1579823019539 & 54.0169676505874 \tabularnewline
116 & 41.6557751178209 & 31.2953229529306 & 52.0162272827113 \tabularnewline
117 & 47.3451450300364 & 36.5709576661258 & 58.119332393947 \tabularnewline
118 & 45.7430366407311 & 34.5704246970395 & 56.9156485844228 \tabularnewline
119 & 39.4415605455057 & 27.8842510862937 & 50.9988700047177 \tabularnewline
120 & 15.3021653398827 & 3.37255737366436 & 27.2317733061011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198345&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]109[/C][C]74.3451463782489[/C][C]67.5532424464129[/C][C]81.1370503100848[/C][/ROW]
[ROW][C]110[/C][C]48.1644167434617[/C][C]40.7567110722731[/C][C]55.5721224146502[/C][/ROW]
[ROW][C]111[/C][C]53.2572374535669[/C][C]45.2811326647223[/C][C]61.2333422424115[/C][/ROW]
[ROW][C]112[/C][C]45.1152154168553[/C][C]36.6086066980826[/C][C]53.621824135628[/C][/ROW]
[ROW][C]113[/C][C]46.2105155543868[/C][C]37.2045988222617[/C][C]55.2164322865118[/C][/ROW]
[ROW][C]114[/C][C]52.8885592736557[/C][C]43.4095993899111[/C][C]62.3675191574003[/C][/ROW]
[ROW][C]115[/C][C]44.0874749762706[/C][C]34.1579823019539[/C][C]54.0169676505874[/C][/ROW]
[ROW][C]116[/C][C]41.6557751178209[/C][C]31.2953229529306[/C][C]52.0162272827113[/C][/ROW]
[ROW][C]117[/C][C]47.3451450300364[/C][C]36.5709576661258[/C][C]58.119332393947[/C][/ROW]
[ROW][C]118[/C][C]45.7430366407311[/C][C]34.5704246970395[/C][C]56.9156485844228[/C][/ROW]
[ROW][C]119[/C][C]39.4415605455057[/C][C]27.8842510862937[/C][C]50.9988700047177[/C][/ROW]
[ROW][C]120[/C][C]15.3021653398827[/C][C]3.37255737366436[/C][C]27.2317733061011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198345&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198345&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
10974.345146378248967.553242446412981.1370503100848
11048.164416743461740.756711072273155.5721224146502
11153.257237453566945.281132664722361.2333422424115
11245.115215416855336.608606698082653.621824135628
11346.210515554386837.204598822261755.2164322865118
11452.888559273655743.409599389911162.3675191574003
11544.087474976270634.157982301953954.0169676505874
11641.655775117820931.295322952930652.0162272827113
11747.345145030036436.570957666125858.119332393947
11845.743036640731134.570424697039556.9156485844228
11939.441560545505727.884251086293750.9988700047177
12015.30216533988273.3725573736643627.2317733061011



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