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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 08:43:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/01/t1212331487ymq737xbl7v7w1h.htm/, Retrieved Sat, 18 May 2024 16:46:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13693, Retrieved Sat, 18 May 2024 16:46:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact214
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-06-01 14:43:51] [27c64ea554ef4b85171a9127abe82aee] [Current]
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Dataseries X:
42.3
50.8
54.1
38.2
48.4
61.1
54.1
61.4
64.3
57.4
71.7
55.3
55.1
66.8
59.4
64.9
59.2
77.4
75.8
38.3
54
61.8
61.3
104.3
39.7
62.6
50.2
90.9
56.2
50.2
52.8
45.6
69
81.9
73.9
54.9
55.4
64.6
49.6
55.8
44.6
61.5
40.5
48.3
50.9
65.3
56.5
53.2
56.9
79.5
94
68.4
65.9
85.5
77.5
114.8
87.4
107.5
151.7
94.4
67.5
95.2
96.2
70.6
80.1
83.4
115.4
61.5
80.6
94.3
82.6
107.7
79.1
102.8
125.2
106.4
62.3
107.4
67.9
88
76.5
130.5
100.9
85.6






Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13693&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13693&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 time7 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.176253502446095
beta0
gamma0.418332059342259

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.176253502446095 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.418332059342259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13693&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]0.176253502446095[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.418332059342259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13693&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
alpha0.176253502446095
beta0
gamma0.418332059342259







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1355.149.82911686001515.27088313998491
1466.861.5930616681875.20693833181301
1559.456.83963076297432.56036923702569
1664.962.84600068962192.05399931037810
1759.257.89212042075931.30787957924071
1877.474.045768361153.35423163885002
1975.871.50054225099394.29945774900614
2038.336.98077681934091.31922318065913
215452.93399465506971.06600534493033
2261.860.1253004316471.67469956835297
2361.359.04117624082232.25882375917774
24104.3103.1463683007881.15363169921187
2539.756.6300743549653-16.9300743549653
2662.664.652505069366-2.05250506936604
2750.257.7020879009876-7.50208790098762
2890.961.5906152084529.3093847915500
2956.260.9339263879327-4.73392638793268
3050.277.1517397456751-26.9517397456751
3152.869.7016294630241-16.9016294630241
3245.633.870369008396611.7296309916035
336950.851892903771618.1481070962284
3481.961.336583240439520.5634167595605
3573.963.700855823024310.1991441769757
3654.9112.623356679300-57.7233566792996
3755.449.8400912768515.55990872314898
3864.667.9640419486506-3.36404194865058
3949.658.3359411989728-8.73594119897277
4055.874.8655780331879-19.0655780331879
4144.655.1524772585909-10.5524772585909
4261.561.30133679022960.19866320977043
4340.561.8256271891787-21.3256271891787
4448.335.927954033349512.3720459666505
4550.954.0801733459901-3.18017334599011
4665.360.37373823659414.92626176340593
4756.557.0530012679981-0.553001267998113
4853.274.9000841626525-21.7000841626525
4956.944.52572317312212.3742768268779
5079.559.158031499902320.3419685000977
519452.349985709792241.6500142902078
5268.475.4511122681335-7.0511122681335
5365.958.72785537938767.17214462061242
5485.574.143684738461711.3563152615383
5577.566.964313413683110.5356865863169
56114.854.206093242943260.5939067570568
5787.481.11948944240566.2805105575944
58107.597.320849295372310.1791507046277
59151.789.544359569126462.1556404308736
6094.4118.655250946366-24.2552509463664
6167.587.3905255427864-19.8905255427864
6295.2108.235746459935-13.0357464599350
6396.298.6241737833614-2.42417378336138
6470.696.7872624601969-26.1872624601969
6580.178.5199823759641.58001762403606
6683.498.340186507812-14.9401865078121
67115.484.276282125162431.1237178748376
6861.588.7683680484569-27.2683680484569
6980.681.5030701162586-0.903070116258633
7094.397.1270994408894-2.82709944088941
7182.6102.283715607434-19.6837156074336
72107.789.142073826712418.5579261732876
7379.169.9490164178059.15098358219494
74102.896.28812086778236.51187913221773
75125.293.919708829915731.2802911700843
76106.489.168857979649917.2311420203501
7762.387.6758576226446-25.3758576226446
78107.497.57739547188489.8226045281152
7967.9103.462129093953-35.5621290939532
808876.250416540069911.7495834599301
8176.585.2807586458286-8.78075864582861
82130.599.351987096466231.1480129035338
83100.9104.412252298965-3.51225229896471
8485.6107.491704678564-21.8917046785639

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 55.1 & 49.8291168600151 & 5.27088313998491 \tabularnewline
14 & 66.8 & 61.593061668187 & 5.20693833181301 \tabularnewline
15 & 59.4 & 56.8396307629743 & 2.56036923702569 \tabularnewline
16 & 64.9 & 62.8460006896219 & 2.05399931037810 \tabularnewline
17 & 59.2 & 57.8921204207593 & 1.30787957924071 \tabularnewline
18 & 77.4 & 74.04576836115 & 3.35423163885002 \tabularnewline
19 & 75.8 & 71.5005422509939 & 4.29945774900614 \tabularnewline
20 & 38.3 & 36.9807768193409 & 1.31922318065913 \tabularnewline
21 & 54 & 52.9339946550697 & 1.06600534493033 \tabularnewline
22 & 61.8 & 60.125300431647 & 1.67469956835297 \tabularnewline
23 & 61.3 & 59.0411762408223 & 2.25882375917774 \tabularnewline
24 & 104.3 & 103.146368300788 & 1.15363169921187 \tabularnewline
25 & 39.7 & 56.6300743549653 & -16.9300743549653 \tabularnewline
26 & 62.6 & 64.652505069366 & -2.05250506936604 \tabularnewline
27 & 50.2 & 57.7020879009876 & -7.50208790098762 \tabularnewline
28 & 90.9 & 61.59061520845 & 29.3093847915500 \tabularnewline
29 & 56.2 & 60.9339263879327 & -4.73392638793268 \tabularnewline
30 & 50.2 & 77.1517397456751 & -26.9517397456751 \tabularnewline
31 & 52.8 & 69.7016294630241 & -16.9016294630241 \tabularnewline
32 & 45.6 & 33.8703690083966 & 11.7296309916035 \tabularnewline
33 & 69 & 50.8518929037716 & 18.1481070962284 \tabularnewline
34 & 81.9 & 61.3365832404395 & 20.5634167595605 \tabularnewline
35 & 73.9 & 63.7008558230243 & 10.1991441769757 \tabularnewline
36 & 54.9 & 112.623356679300 & -57.7233566792996 \tabularnewline
37 & 55.4 & 49.840091276851 & 5.55990872314898 \tabularnewline
38 & 64.6 & 67.9640419486506 & -3.36404194865058 \tabularnewline
39 & 49.6 & 58.3359411989728 & -8.73594119897277 \tabularnewline
40 & 55.8 & 74.8655780331879 & -19.0655780331879 \tabularnewline
41 & 44.6 & 55.1524772585909 & -10.5524772585909 \tabularnewline
42 & 61.5 & 61.3013367902296 & 0.19866320977043 \tabularnewline
43 & 40.5 & 61.8256271891787 & -21.3256271891787 \tabularnewline
44 & 48.3 & 35.9279540333495 & 12.3720459666505 \tabularnewline
45 & 50.9 & 54.0801733459901 & -3.18017334599011 \tabularnewline
46 & 65.3 & 60.3737382365941 & 4.92626176340593 \tabularnewline
47 & 56.5 & 57.0530012679981 & -0.553001267998113 \tabularnewline
48 & 53.2 & 74.9000841626525 & -21.7000841626525 \tabularnewline
49 & 56.9 & 44.525723173122 & 12.3742768268779 \tabularnewline
50 & 79.5 & 59.1580314999023 & 20.3419685000977 \tabularnewline
51 & 94 & 52.3499857097922 & 41.6500142902078 \tabularnewline
52 & 68.4 & 75.4511122681335 & -7.0511122681335 \tabularnewline
53 & 65.9 & 58.7278553793876 & 7.17214462061242 \tabularnewline
54 & 85.5 & 74.1436847384617 & 11.3563152615383 \tabularnewline
55 & 77.5 & 66.9643134136831 & 10.5356865863169 \tabularnewline
56 & 114.8 & 54.2060932429432 & 60.5939067570568 \tabularnewline
57 & 87.4 & 81.1194894424056 & 6.2805105575944 \tabularnewline
58 & 107.5 & 97.3208492953723 & 10.1791507046277 \tabularnewline
59 & 151.7 & 89.5443595691264 & 62.1556404308736 \tabularnewline
60 & 94.4 & 118.655250946366 & -24.2552509463664 \tabularnewline
61 & 67.5 & 87.3905255427864 & -19.8905255427864 \tabularnewline
62 & 95.2 & 108.235746459935 & -13.0357464599350 \tabularnewline
63 & 96.2 & 98.6241737833614 & -2.42417378336138 \tabularnewline
64 & 70.6 & 96.7872624601969 & -26.1872624601969 \tabularnewline
65 & 80.1 & 78.519982375964 & 1.58001762403606 \tabularnewline
66 & 83.4 & 98.340186507812 & -14.9401865078121 \tabularnewline
67 & 115.4 & 84.2762821251624 & 31.1237178748376 \tabularnewline
68 & 61.5 & 88.7683680484569 & -27.2683680484569 \tabularnewline
69 & 80.6 & 81.5030701162586 & -0.903070116258633 \tabularnewline
70 & 94.3 & 97.1270994408894 & -2.82709944088941 \tabularnewline
71 & 82.6 & 102.283715607434 & -19.6837156074336 \tabularnewline
72 & 107.7 & 89.1420738267124 & 18.5579261732876 \tabularnewline
73 & 79.1 & 69.949016417805 & 9.15098358219494 \tabularnewline
74 & 102.8 & 96.2881208677823 & 6.51187913221773 \tabularnewline
75 & 125.2 & 93.9197088299157 & 31.2802911700843 \tabularnewline
76 & 106.4 & 89.1688579796499 & 17.2311420203501 \tabularnewline
77 & 62.3 & 87.6758576226446 & -25.3758576226446 \tabularnewline
78 & 107.4 & 97.5773954718848 & 9.8226045281152 \tabularnewline
79 & 67.9 & 103.462129093953 & -35.5621290939532 \tabularnewline
80 & 88 & 76.2504165400699 & 11.7495834599301 \tabularnewline
81 & 76.5 & 85.2807586458286 & -8.78075864582861 \tabularnewline
82 & 130.5 & 99.3519870964662 & 31.1480129035338 \tabularnewline
83 & 100.9 & 104.412252298965 & -3.51225229896471 \tabularnewline
84 & 85.6 & 107.491704678564 & -21.8917046785639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13693&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]55.1[/C][C]49.8291168600151[/C][C]5.27088313998491[/C][/ROW]
[ROW][C]14[/C][C]66.8[/C][C]61.593061668187[/C][C]5.20693833181301[/C][/ROW]
[ROW][C]15[/C][C]59.4[/C][C]56.8396307629743[/C][C]2.56036923702569[/C][/ROW]
[ROW][C]16[/C][C]64.9[/C][C]62.8460006896219[/C][C]2.05399931037810[/C][/ROW]
[ROW][C]17[/C][C]59.2[/C][C]57.8921204207593[/C][C]1.30787957924071[/C][/ROW]
[ROW][C]18[/C][C]77.4[/C][C]74.04576836115[/C][C]3.35423163885002[/C][/ROW]
[ROW][C]19[/C][C]75.8[/C][C]71.5005422509939[/C][C]4.29945774900614[/C][/ROW]
[ROW][C]20[/C][C]38.3[/C][C]36.9807768193409[/C][C]1.31922318065913[/C][/ROW]
[ROW][C]21[/C][C]54[/C][C]52.9339946550697[/C][C]1.06600534493033[/C][/ROW]
[ROW][C]22[/C][C]61.8[/C][C]60.125300431647[/C][C]1.67469956835297[/C][/ROW]
[ROW][C]23[/C][C]61.3[/C][C]59.0411762408223[/C][C]2.25882375917774[/C][/ROW]
[ROW][C]24[/C][C]104.3[/C][C]103.146368300788[/C][C]1.15363169921187[/C][/ROW]
[ROW][C]25[/C][C]39.7[/C][C]56.6300743549653[/C][C]-16.9300743549653[/C][/ROW]
[ROW][C]26[/C][C]62.6[/C][C]64.652505069366[/C][C]-2.05250506936604[/C][/ROW]
[ROW][C]27[/C][C]50.2[/C][C]57.7020879009876[/C][C]-7.50208790098762[/C][/ROW]
[ROW][C]28[/C][C]90.9[/C][C]61.59061520845[/C][C]29.3093847915500[/C][/ROW]
[ROW][C]29[/C][C]56.2[/C][C]60.9339263879327[/C][C]-4.73392638793268[/C][/ROW]
[ROW][C]30[/C][C]50.2[/C][C]77.1517397456751[/C][C]-26.9517397456751[/C][/ROW]
[ROW][C]31[/C][C]52.8[/C][C]69.7016294630241[/C][C]-16.9016294630241[/C][/ROW]
[ROW][C]32[/C][C]45.6[/C][C]33.8703690083966[/C][C]11.7296309916035[/C][/ROW]
[ROW][C]33[/C][C]69[/C][C]50.8518929037716[/C][C]18.1481070962284[/C][/ROW]
[ROW][C]34[/C][C]81.9[/C][C]61.3365832404395[/C][C]20.5634167595605[/C][/ROW]
[ROW][C]35[/C][C]73.9[/C][C]63.7008558230243[/C][C]10.1991441769757[/C][/ROW]
[ROW][C]36[/C][C]54.9[/C][C]112.623356679300[/C][C]-57.7233566792996[/C][/ROW]
[ROW][C]37[/C][C]55.4[/C][C]49.840091276851[/C][C]5.55990872314898[/C][/ROW]
[ROW][C]38[/C][C]64.6[/C][C]67.9640419486506[/C][C]-3.36404194865058[/C][/ROW]
[ROW][C]39[/C][C]49.6[/C][C]58.3359411989728[/C][C]-8.73594119897277[/C][/ROW]
[ROW][C]40[/C][C]55.8[/C][C]74.8655780331879[/C][C]-19.0655780331879[/C][/ROW]
[ROW][C]41[/C][C]44.6[/C][C]55.1524772585909[/C][C]-10.5524772585909[/C][/ROW]
[ROW][C]42[/C][C]61.5[/C][C]61.3013367902296[/C][C]0.19866320977043[/C][/ROW]
[ROW][C]43[/C][C]40.5[/C][C]61.8256271891787[/C][C]-21.3256271891787[/C][/ROW]
[ROW][C]44[/C][C]48.3[/C][C]35.9279540333495[/C][C]12.3720459666505[/C][/ROW]
[ROW][C]45[/C][C]50.9[/C][C]54.0801733459901[/C][C]-3.18017334599011[/C][/ROW]
[ROW][C]46[/C][C]65.3[/C][C]60.3737382365941[/C][C]4.92626176340593[/C][/ROW]
[ROW][C]47[/C][C]56.5[/C][C]57.0530012679981[/C][C]-0.553001267998113[/C][/ROW]
[ROW][C]48[/C][C]53.2[/C][C]74.9000841626525[/C][C]-21.7000841626525[/C][/ROW]
[ROW][C]49[/C][C]56.9[/C][C]44.525723173122[/C][C]12.3742768268779[/C][/ROW]
[ROW][C]50[/C][C]79.5[/C][C]59.1580314999023[/C][C]20.3419685000977[/C][/ROW]
[ROW][C]51[/C][C]94[/C][C]52.3499857097922[/C][C]41.6500142902078[/C][/ROW]
[ROW][C]52[/C][C]68.4[/C][C]75.4511122681335[/C][C]-7.0511122681335[/C][/ROW]
[ROW][C]53[/C][C]65.9[/C][C]58.7278553793876[/C][C]7.17214462061242[/C][/ROW]
[ROW][C]54[/C][C]85.5[/C][C]74.1436847384617[/C][C]11.3563152615383[/C][/ROW]
[ROW][C]55[/C][C]77.5[/C][C]66.9643134136831[/C][C]10.5356865863169[/C][/ROW]
[ROW][C]56[/C][C]114.8[/C][C]54.2060932429432[/C][C]60.5939067570568[/C][/ROW]
[ROW][C]57[/C][C]87.4[/C][C]81.1194894424056[/C][C]6.2805105575944[/C][/ROW]
[ROW][C]58[/C][C]107.5[/C][C]97.3208492953723[/C][C]10.1791507046277[/C][/ROW]
[ROW][C]59[/C][C]151.7[/C][C]89.5443595691264[/C][C]62.1556404308736[/C][/ROW]
[ROW][C]60[/C][C]94.4[/C][C]118.655250946366[/C][C]-24.2552509463664[/C][/ROW]
[ROW][C]61[/C][C]67.5[/C][C]87.3905255427864[/C][C]-19.8905255427864[/C][/ROW]
[ROW][C]62[/C][C]95.2[/C][C]108.235746459935[/C][C]-13.0357464599350[/C][/ROW]
[ROW][C]63[/C][C]96.2[/C][C]98.6241737833614[/C][C]-2.42417378336138[/C][/ROW]
[ROW][C]64[/C][C]70.6[/C][C]96.7872624601969[/C][C]-26.1872624601969[/C][/ROW]
[ROW][C]65[/C][C]80.1[/C][C]78.519982375964[/C][C]1.58001762403606[/C][/ROW]
[ROW][C]66[/C][C]83.4[/C][C]98.340186507812[/C][C]-14.9401865078121[/C][/ROW]
[ROW][C]67[/C][C]115.4[/C][C]84.2762821251624[/C][C]31.1237178748376[/C][/ROW]
[ROW][C]68[/C][C]61.5[/C][C]88.7683680484569[/C][C]-27.2683680484569[/C][/ROW]
[ROW][C]69[/C][C]80.6[/C][C]81.5030701162586[/C][C]-0.903070116258633[/C][/ROW]
[ROW][C]70[/C][C]94.3[/C][C]97.1270994408894[/C][C]-2.82709944088941[/C][/ROW]
[ROW][C]71[/C][C]82.6[/C][C]102.283715607434[/C][C]-19.6837156074336[/C][/ROW]
[ROW][C]72[/C][C]107.7[/C][C]89.1420738267124[/C][C]18.5579261732876[/C][/ROW]
[ROW][C]73[/C][C]79.1[/C][C]69.949016417805[/C][C]9.15098358219494[/C][/ROW]
[ROW][C]74[/C][C]102.8[/C][C]96.2881208677823[/C][C]6.51187913221773[/C][/ROW]
[ROW][C]75[/C][C]125.2[/C][C]93.9197088299157[/C][C]31.2802911700843[/C][/ROW]
[ROW][C]76[/C][C]106.4[/C][C]89.1688579796499[/C][C]17.2311420203501[/C][/ROW]
[ROW][C]77[/C][C]62.3[/C][C]87.6758576226446[/C][C]-25.3758576226446[/C][/ROW]
[ROW][C]78[/C][C]107.4[/C][C]97.5773954718848[/C][C]9.8226045281152[/C][/ROW]
[ROW][C]79[/C][C]67.9[/C][C]103.462129093953[/C][C]-35.5621290939532[/C][/ROW]
[ROW][C]80[/C][C]88[/C][C]76.2504165400699[/C][C]11.7495834599301[/C][/ROW]
[ROW][C]81[/C][C]76.5[/C][C]85.2807586458286[/C][C]-8.78075864582861[/C][/ROW]
[ROW][C]82[/C][C]130.5[/C][C]99.3519870964662[/C][C]31.1480129035338[/C][/ROW]
[ROW][C]83[/C][C]100.9[/C][C]104.412252298965[/C][C]-3.51225229896471[/C][/ROW]
[ROW][C]84[/C][C]85.6[/C][C]107.491704678564[/C][C]-21.8917046785639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13693&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
1355.149.82911686001515.27088313998491
1466.861.5930616681875.20693833181301
1559.456.83963076297432.56036923702569
1664.962.84600068962192.05399931037810
1759.257.89212042075931.30787957924071
1877.474.045768361153.35423163885002
1975.871.50054225099394.29945774900614
2038.336.98077681934091.31922318065913
215452.93399465506971.06600534493033
2261.860.1253004316471.67469956835297
2361.359.04117624082232.25882375917774
24104.3103.1463683007881.15363169921187
2539.756.6300743549653-16.9300743549653
2662.664.652505069366-2.05250506936604
2750.257.7020879009876-7.50208790098762
2890.961.5906152084529.3093847915500
2956.260.9339263879327-4.73392638793268
3050.277.1517397456751-26.9517397456751
3152.869.7016294630241-16.9016294630241
3245.633.870369008396611.7296309916035
336950.851892903771618.1481070962284
3481.961.336583240439520.5634167595605
3573.963.700855823024310.1991441769757
3654.9112.623356679300-57.7233566792996
3755.449.8400912768515.55990872314898
3864.667.9640419486506-3.36404194865058
3949.658.3359411989728-8.73594119897277
4055.874.8655780331879-19.0655780331879
4144.655.1524772585909-10.5524772585909
4261.561.30133679022960.19866320977043
4340.561.8256271891787-21.3256271891787
4448.335.927954033349512.3720459666505
4550.954.0801733459901-3.18017334599011
4665.360.37373823659414.92626176340593
4756.557.0530012679981-0.553001267998113
4853.274.9000841626525-21.7000841626525
4956.944.52572317312212.3742768268779
5079.559.158031499902320.3419685000977
519452.349985709792241.6500142902078
5268.475.4511122681335-7.0511122681335
5365.958.72785537938767.17214462061242
5485.574.143684738461711.3563152615383
5577.566.964313413683110.5356865863169
56114.854.206093242943260.5939067570568
5787.481.11948944240566.2805105575944
58107.597.320849295372310.1791507046277
59151.789.544359569126462.1556404308736
6094.4118.655250946366-24.2552509463664
6167.587.3905255427864-19.8905255427864
6295.2108.235746459935-13.0357464599350
6396.298.6241737833614-2.42417378336138
6470.696.7872624601969-26.1872624601969
6580.178.5199823759641.58001762403606
6683.498.340186507812-14.9401865078121
67115.484.276282125162431.1237178748376
6861.588.7683680484569-27.2683680484569
6980.681.5030701162586-0.903070116258633
7094.397.1270994408894-2.82709944088941
7182.6102.283715607434-19.6837156074336
72107.789.142073826712418.5579261732876
7379.169.9490164178059.15098358219494
74102.896.28812086778236.51187913221773
75125.293.919708829915731.2802911700843
76106.489.168857979649917.2311420203501
7762.387.6758576226446-25.3758576226446
78107.497.57739547188489.8226045281152
7967.9103.462129093953-35.5621290939532
808876.250416540069911.7495834599301
8176.585.2807586458286-8.78075864582861
82130.599.351987096466231.1480129035338
83100.9104.412252298965-3.51225229896471
8485.6107.491704678564-21.8917046785639







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8576.597779945331156.245142973455596.9504169172067
86100.98751966604779.4013045443748122.573734787718
87105.46687951898783.3812703818284127.552488656145
8890.824654953911368.6537323092663112.995577598556
8972.610016442212447.245998980374697.9740339040501
9098.397909757325673.3259679701948123.469851544456
9186.635038196564861.1872628011026112.082813592027
9281.793050002628855.4518909698628108.134209035395
9381.623012990580349.7398467184914113.506179262669
94110.76622580059180.233922491469141.298529109713
9598.900600783925268.1115197089342129.689681858916
9696.089343064161NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 76.5977799453311 & 56.2451429734555 & 96.9504169172067 \tabularnewline
86 & 100.987519666047 & 79.4013045443748 & 122.573734787718 \tabularnewline
87 & 105.466879518987 & 83.3812703818284 & 127.552488656145 \tabularnewline
88 & 90.8246549539113 & 68.6537323092663 & 112.995577598556 \tabularnewline
89 & 72.6100164422124 & 47.2459989803746 & 97.9740339040501 \tabularnewline
90 & 98.3979097573256 & 73.3259679701948 & 123.469851544456 \tabularnewline
91 & 86.6350381965648 & 61.1872628011026 & 112.082813592027 \tabularnewline
92 & 81.7930500026288 & 55.4518909698628 & 108.134209035395 \tabularnewline
93 & 81.6230129905803 & 49.7398467184914 & 113.506179262669 \tabularnewline
94 & 110.766225800591 & 80.233922491469 & 141.298529109713 \tabularnewline
95 & 98.9006007839252 & 68.1115197089342 & 129.689681858916 \tabularnewline
96 & 96.089343064161 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13693&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]76.5977799453311[/C][C]56.2451429734555[/C][C]96.9504169172067[/C][/ROW]
[ROW][C]86[/C][C]100.987519666047[/C][C]79.4013045443748[/C][C]122.573734787718[/C][/ROW]
[ROW][C]87[/C][C]105.466879518987[/C][C]83.3812703818284[/C][C]127.552488656145[/C][/ROW]
[ROW][C]88[/C][C]90.8246549539113[/C][C]68.6537323092663[/C][C]112.995577598556[/C][/ROW]
[ROW][C]89[/C][C]72.6100164422124[/C][C]47.2459989803746[/C][C]97.9740339040501[/C][/ROW]
[ROW][C]90[/C][C]98.3979097573256[/C][C]73.3259679701948[/C][C]123.469851544456[/C][/ROW]
[ROW][C]91[/C][C]86.6350381965648[/C][C]61.1872628011026[/C][C]112.082813592027[/C][/ROW]
[ROW][C]92[/C][C]81.7930500026288[/C][C]55.4518909698628[/C][C]108.134209035395[/C][/ROW]
[ROW][C]93[/C][C]81.6230129905803[/C][C]49.7398467184914[/C][C]113.506179262669[/C][/ROW]
[ROW][C]94[/C][C]110.766225800591[/C][C]80.233922491469[/C][C]141.298529109713[/C][/ROW]
[ROW][C]95[/C][C]98.9006007839252[/C][C]68.1115197089342[/C][C]129.689681858916[/C][/ROW]
[ROW][C]96[/C][C]96.089343064161[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13693&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
8576.597779945331156.245142973455596.9504169172067
86100.98751966604779.4013045443748122.573734787718
87105.46687951898783.3812703818284127.552488656145
8890.824654953911368.6537323092663112.995577598556
8972.610016442212447.245998980374697.9740339040501
9098.397909757325673.3259679701948123.469851544456
9186.635038196564861.1872628011026112.082813592027
9281.793050002628855.4518909698628108.134209035395
9381.623012990580349.7398467184914113.506179262669
94110.76622580059180.233922491469141.298529109713
9598.900600783925268.1115197089342129.689681858916
9696.089343064161NANA



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')