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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Mar 2015 14:08:16 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/30/t1427720921bfif4cnubw2l9t9.htm/, Retrieved Sun, 19 May 2024 16:29:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278458, Retrieved Sun, 19 May 2024 16:29:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-03-30 13:08:16] [3d92bf785db8aeb0f2ab1bed7b74f49c] [Current]
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Dataseries X:
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116
118
116
111
108
102
102
129
136
137
126
119
117
120
116
110
104
98
98
124
130
131
121
114
111




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278458&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278458&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278458&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278458&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101105-4
395101.000264427845-6.00026442784541
49395.0003966592486-2.00039665924864
58493.0001322401447-9.00013224014465
68784.00059497139422.99940502860585
711686.999801718447729.0001982815523
8120115.9980828850134.00191711498699
9117119.99973544542-2.99973544541994
10109117.000198303395-8.00019830339515
11105109.0005288688-4.00052886880005
12107105.0002644628071.99973553719268
13109106.999867803562.00013219643988
14109108.9998677773380.000132222661804349
15108108.999999991259-0.999999991259159
16107108.000066106961-1.00006610696077
1799107.000066111331-8.00006611133148
1810399.00052886006123.99947113993878
19131102.99973560711628.0002643928841
20137130.9981489876046.00185101239609
21135136.999603235867-1.99960323586708
22124135.000132187694-11.0001321876938
23118124.000727185313-6.00072718531339
24121118.000396689842.99960331015988
25121120.999801705340.000198294660094689
26118120.999999986891-2.99999998689134
27113118.000198320883-5.00019832088319
28107113.000330547917-6.00033054791714
29100107.00039666362-7.00039666361963
30102100.0004627749521.9995372250483
31130101.9998678166728.0001321833301
32136129.9981489963446.0018510036561
33133135.999603235868-2.99960323586765
34120133.000198294655-13.0001982946552
35112120.000859403606-8.00085940360623
36109112.000528912503-3.00052891250338
37110109.0001983558490.999801644151148
38106109.999933906151-3.99993390615134
39102106.000264423476-4.00026442347614
4098102.000264445326-4.00026444532564
419298.0002644453271-6.00026444532709
429292.0003966592498-0.00039665924978749
4312092.000000026221927.9999999737781
44127119.9981490050847.00185099491611
45124126.999537128907-2.99953712890689
46114124.000198290285-10.0001982902851
47108114.000661082722-6.00066108272188
48106108.00039668547-2.00039668547029
49111106.0001322401464.99986775985363
50110110.999669473935-0.999669473935228
51104110.000066085111-6.00006608511127
52100104.000396646137-4.00039664613681
5396100.000264454066-4.00026445406648
549896.00026444532771.99973555467233
5512297.99986780355924.000132196441
56134121.99841342418812.0015865758116
57133133.99920661158-0.999206611580064
58125133.000066054513-8.00006605451287
59118125.000528860057-7.00052886005747
60116118.000462783691-2.00046278369079
61118116.0001322445161.99986775548408
62116117.99986779482-1.99986779481958
63111116.000132205183-5.00013220518302
64108111.000330543546-3.00033054354644
65102108.000198342735-6.00019834273529
66102102.00039665488-0.000396654879949665
67129102.00000002622226.9999999737784
68136128.9982151120457.00178488795478
69137135.9995371332771.00046286672298
70126136.99993386244-10.9999338624399
71119126.000727172203-7.00072717220272
72117119.000462796801-2.00046279680062
73120117.0001322445172.99986775548321
74116119.999801687858-3.99980168785822
75110116.000264414736-6.0002644147356
76104110.000396659248-6.00039665924777
7798104.00039666799-6.00039666799006
789898.0003966679906-0.00039666799062843
7912498.000000026222525.9999999737775
80130123.9982812190076.00171878099341
81131129.9996032446081.00039675539151
82121130.99993386681-9.99993386681035
83114121.000661065242-7.00066106524166
84111114.00046279243-3.00046279243047

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101 & 105 & -4 \tabularnewline
3 & 95 & 101.000264427845 & -6.00026442784541 \tabularnewline
4 & 93 & 95.0003966592486 & -2.00039665924864 \tabularnewline
5 & 84 & 93.0001322401447 & -9.00013224014465 \tabularnewline
6 & 87 & 84.0005949713942 & 2.99940502860585 \tabularnewline
7 & 116 & 86.9998017184477 & 29.0001982815523 \tabularnewline
8 & 120 & 115.998082885013 & 4.00191711498699 \tabularnewline
9 & 117 & 119.99973544542 & -2.99973544541994 \tabularnewline
10 & 109 & 117.000198303395 & -8.00019830339515 \tabularnewline
11 & 105 & 109.0005288688 & -4.00052886880005 \tabularnewline
12 & 107 & 105.000264462807 & 1.99973553719268 \tabularnewline
13 & 109 & 106.99986780356 & 2.00013219643988 \tabularnewline
14 & 109 & 108.999867777338 & 0.000132222661804349 \tabularnewline
15 & 108 & 108.999999991259 & -0.999999991259159 \tabularnewline
16 & 107 & 108.000066106961 & -1.00006610696077 \tabularnewline
17 & 99 & 107.000066111331 & -8.00006611133148 \tabularnewline
18 & 103 & 99.0005288600612 & 3.99947113993878 \tabularnewline
19 & 131 & 102.999735607116 & 28.0002643928841 \tabularnewline
20 & 137 & 130.998148987604 & 6.00185101239609 \tabularnewline
21 & 135 & 136.999603235867 & -1.99960323586708 \tabularnewline
22 & 124 & 135.000132187694 & -11.0001321876938 \tabularnewline
23 & 118 & 124.000727185313 & -6.00072718531339 \tabularnewline
24 & 121 & 118.00039668984 & 2.99960331015988 \tabularnewline
25 & 121 & 120.99980170534 & 0.000198294660094689 \tabularnewline
26 & 118 & 120.999999986891 & -2.99999998689134 \tabularnewline
27 & 113 & 118.000198320883 & -5.00019832088319 \tabularnewline
28 & 107 & 113.000330547917 & -6.00033054791714 \tabularnewline
29 & 100 & 107.00039666362 & -7.00039666361963 \tabularnewline
30 & 102 & 100.000462774952 & 1.9995372250483 \tabularnewline
31 & 130 & 101.99986781667 & 28.0001321833301 \tabularnewline
32 & 136 & 129.998148996344 & 6.0018510036561 \tabularnewline
33 & 133 & 135.999603235868 & -2.99960323586765 \tabularnewline
34 & 120 & 133.000198294655 & -13.0001982946552 \tabularnewline
35 & 112 & 120.000859403606 & -8.00085940360623 \tabularnewline
36 & 109 & 112.000528912503 & -3.00052891250338 \tabularnewline
37 & 110 & 109.000198355849 & 0.999801644151148 \tabularnewline
38 & 106 & 109.999933906151 & -3.99993390615134 \tabularnewline
39 & 102 & 106.000264423476 & -4.00026442347614 \tabularnewline
40 & 98 & 102.000264445326 & -4.00026444532564 \tabularnewline
41 & 92 & 98.0002644453271 & -6.00026444532709 \tabularnewline
42 & 92 & 92.0003966592498 & -0.00039665924978749 \tabularnewline
43 & 120 & 92.0000000262219 & 27.9999999737781 \tabularnewline
44 & 127 & 119.998149005084 & 7.00185099491611 \tabularnewline
45 & 124 & 126.999537128907 & -2.99953712890689 \tabularnewline
46 & 114 & 124.000198290285 & -10.0001982902851 \tabularnewline
47 & 108 & 114.000661082722 & -6.00066108272188 \tabularnewline
48 & 106 & 108.00039668547 & -2.00039668547029 \tabularnewline
49 & 111 & 106.000132240146 & 4.99986775985363 \tabularnewline
50 & 110 & 110.999669473935 & -0.999669473935228 \tabularnewline
51 & 104 & 110.000066085111 & -6.00006608511127 \tabularnewline
52 & 100 & 104.000396646137 & -4.00039664613681 \tabularnewline
53 & 96 & 100.000264454066 & -4.00026445406648 \tabularnewline
54 & 98 & 96.0002644453277 & 1.99973555467233 \tabularnewline
55 & 122 & 97.999867803559 & 24.000132196441 \tabularnewline
56 & 134 & 121.998413424188 & 12.0015865758116 \tabularnewline
57 & 133 & 133.99920661158 & -0.999206611580064 \tabularnewline
58 & 125 & 133.000066054513 & -8.00006605451287 \tabularnewline
59 & 118 & 125.000528860057 & -7.00052886005747 \tabularnewline
60 & 116 & 118.000462783691 & -2.00046278369079 \tabularnewline
61 & 118 & 116.000132244516 & 1.99986775548408 \tabularnewline
62 & 116 & 117.99986779482 & -1.99986779481958 \tabularnewline
63 & 111 & 116.000132205183 & -5.00013220518302 \tabularnewline
64 & 108 & 111.000330543546 & -3.00033054354644 \tabularnewline
65 & 102 & 108.000198342735 & -6.00019834273529 \tabularnewline
66 & 102 & 102.00039665488 & -0.000396654879949665 \tabularnewline
67 & 129 & 102.000000026222 & 26.9999999737784 \tabularnewline
68 & 136 & 128.998215112045 & 7.00178488795478 \tabularnewline
69 & 137 & 135.999537133277 & 1.00046286672298 \tabularnewline
70 & 126 & 136.99993386244 & -10.9999338624399 \tabularnewline
71 & 119 & 126.000727172203 & -7.00072717220272 \tabularnewline
72 & 117 & 119.000462796801 & -2.00046279680062 \tabularnewline
73 & 120 & 117.000132244517 & 2.99986775548321 \tabularnewline
74 & 116 & 119.999801687858 & -3.99980168785822 \tabularnewline
75 & 110 & 116.000264414736 & -6.0002644147356 \tabularnewline
76 & 104 & 110.000396659248 & -6.00039665924777 \tabularnewline
77 & 98 & 104.00039666799 & -6.00039666799006 \tabularnewline
78 & 98 & 98.0003966679906 & -0.00039666799062843 \tabularnewline
79 & 124 & 98.0000000262225 & 25.9999999737775 \tabularnewline
80 & 130 & 123.998281219007 & 6.00171878099341 \tabularnewline
81 & 131 & 129.999603244608 & 1.00039675539151 \tabularnewline
82 & 121 & 130.99993386681 & -9.99993386681035 \tabularnewline
83 & 114 & 121.000661065242 & -7.00066106524166 \tabularnewline
84 & 111 & 114.00046279243 & -3.00046279243047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278458&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]2[/C][C]101[/C][C]105[/C][C]-4[/C][/ROW]
[ROW][C]3[/C][C]95[/C][C]101.000264427845[/C][C]-6.00026442784541[/C][/ROW]
[ROW][C]4[/C][C]93[/C][C]95.0003966592486[/C][C]-2.00039665924864[/C][/ROW]
[ROW][C]5[/C][C]84[/C][C]93.0001322401447[/C][C]-9.00013224014465[/C][/ROW]
[ROW][C]6[/C][C]87[/C][C]84.0005949713942[/C][C]2.99940502860585[/C][/ROW]
[ROW][C]7[/C][C]116[/C][C]86.9998017184477[/C][C]29.0001982815523[/C][/ROW]
[ROW][C]8[/C][C]120[/C][C]115.998082885013[/C][C]4.00191711498699[/C][/ROW]
[ROW][C]9[/C][C]117[/C][C]119.99973544542[/C][C]-2.99973544541994[/C][/ROW]
[ROW][C]10[/C][C]109[/C][C]117.000198303395[/C][C]-8.00019830339515[/C][/ROW]
[ROW][C]11[/C][C]105[/C][C]109.0005288688[/C][C]-4.00052886880005[/C][/ROW]
[ROW][C]12[/C][C]107[/C][C]105.000264462807[/C][C]1.99973553719268[/C][/ROW]
[ROW][C]13[/C][C]109[/C][C]106.99986780356[/C][C]2.00013219643988[/C][/ROW]
[ROW][C]14[/C][C]109[/C][C]108.999867777338[/C][C]0.000132222661804349[/C][/ROW]
[ROW][C]15[/C][C]108[/C][C]108.999999991259[/C][C]-0.999999991259159[/C][/ROW]
[ROW][C]16[/C][C]107[/C][C]108.000066106961[/C][C]-1.00006610696077[/C][/ROW]
[ROW][C]17[/C][C]99[/C][C]107.000066111331[/C][C]-8.00006611133148[/C][/ROW]
[ROW][C]18[/C][C]103[/C][C]99.0005288600612[/C][C]3.99947113993878[/C][/ROW]
[ROW][C]19[/C][C]131[/C][C]102.999735607116[/C][C]28.0002643928841[/C][/ROW]
[ROW][C]20[/C][C]137[/C][C]130.998148987604[/C][C]6.00185101239609[/C][/ROW]
[ROW][C]21[/C][C]135[/C][C]136.999603235867[/C][C]-1.99960323586708[/C][/ROW]
[ROW][C]22[/C][C]124[/C][C]135.000132187694[/C][C]-11.0001321876938[/C][/ROW]
[ROW][C]23[/C][C]118[/C][C]124.000727185313[/C][C]-6.00072718531339[/C][/ROW]
[ROW][C]24[/C][C]121[/C][C]118.00039668984[/C][C]2.99960331015988[/C][/ROW]
[ROW][C]25[/C][C]121[/C][C]120.99980170534[/C][C]0.000198294660094689[/C][/ROW]
[ROW][C]26[/C][C]118[/C][C]120.999999986891[/C][C]-2.99999998689134[/C][/ROW]
[ROW][C]27[/C][C]113[/C][C]118.000198320883[/C][C]-5.00019832088319[/C][/ROW]
[ROW][C]28[/C][C]107[/C][C]113.000330547917[/C][C]-6.00033054791714[/C][/ROW]
[ROW][C]29[/C][C]100[/C][C]107.00039666362[/C][C]-7.00039666361963[/C][/ROW]
[ROW][C]30[/C][C]102[/C][C]100.000462774952[/C][C]1.9995372250483[/C][/ROW]
[ROW][C]31[/C][C]130[/C][C]101.99986781667[/C][C]28.0001321833301[/C][/ROW]
[ROW][C]32[/C][C]136[/C][C]129.998148996344[/C][C]6.0018510036561[/C][/ROW]
[ROW][C]33[/C][C]133[/C][C]135.999603235868[/C][C]-2.99960323586765[/C][/ROW]
[ROW][C]34[/C][C]120[/C][C]133.000198294655[/C][C]-13.0001982946552[/C][/ROW]
[ROW][C]35[/C][C]112[/C][C]120.000859403606[/C][C]-8.00085940360623[/C][/ROW]
[ROW][C]36[/C][C]109[/C][C]112.000528912503[/C][C]-3.00052891250338[/C][/ROW]
[ROW][C]37[/C][C]110[/C][C]109.000198355849[/C][C]0.999801644151148[/C][/ROW]
[ROW][C]38[/C][C]106[/C][C]109.999933906151[/C][C]-3.99993390615134[/C][/ROW]
[ROW][C]39[/C][C]102[/C][C]106.000264423476[/C][C]-4.00026442347614[/C][/ROW]
[ROW][C]40[/C][C]98[/C][C]102.000264445326[/C][C]-4.00026444532564[/C][/ROW]
[ROW][C]41[/C][C]92[/C][C]98.0002644453271[/C][C]-6.00026444532709[/C][/ROW]
[ROW][C]42[/C][C]92[/C][C]92.0003966592498[/C][C]-0.00039665924978749[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]92.0000000262219[/C][C]27.9999999737781[/C][/ROW]
[ROW][C]44[/C][C]127[/C][C]119.998149005084[/C][C]7.00185099491611[/C][/ROW]
[ROW][C]45[/C][C]124[/C][C]126.999537128907[/C][C]-2.99953712890689[/C][/ROW]
[ROW][C]46[/C][C]114[/C][C]124.000198290285[/C][C]-10.0001982902851[/C][/ROW]
[ROW][C]47[/C][C]108[/C][C]114.000661082722[/C][C]-6.00066108272188[/C][/ROW]
[ROW][C]48[/C][C]106[/C][C]108.00039668547[/C][C]-2.00039668547029[/C][/ROW]
[ROW][C]49[/C][C]111[/C][C]106.000132240146[/C][C]4.99986775985363[/C][/ROW]
[ROW][C]50[/C][C]110[/C][C]110.999669473935[/C][C]-0.999669473935228[/C][/ROW]
[ROW][C]51[/C][C]104[/C][C]110.000066085111[/C][C]-6.00006608511127[/C][/ROW]
[ROW][C]52[/C][C]100[/C][C]104.000396646137[/C][C]-4.00039664613681[/C][/ROW]
[ROW][C]53[/C][C]96[/C][C]100.000264454066[/C][C]-4.00026445406648[/C][/ROW]
[ROW][C]54[/C][C]98[/C][C]96.0002644453277[/C][C]1.99973555467233[/C][/ROW]
[ROW][C]55[/C][C]122[/C][C]97.999867803559[/C][C]24.000132196441[/C][/ROW]
[ROW][C]56[/C][C]134[/C][C]121.998413424188[/C][C]12.0015865758116[/C][/ROW]
[ROW][C]57[/C][C]133[/C][C]133.99920661158[/C][C]-0.999206611580064[/C][/ROW]
[ROW][C]58[/C][C]125[/C][C]133.000066054513[/C][C]-8.00006605451287[/C][/ROW]
[ROW][C]59[/C][C]118[/C][C]125.000528860057[/C][C]-7.00052886005747[/C][/ROW]
[ROW][C]60[/C][C]116[/C][C]118.000462783691[/C][C]-2.00046278369079[/C][/ROW]
[ROW][C]61[/C][C]118[/C][C]116.000132244516[/C][C]1.99986775548408[/C][/ROW]
[ROW][C]62[/C][C]116[/C][C]117.99986779482[/C][C]-1.99986779481958[/C][/ROW]
[ROW][C]63[/C][C]111[/C][C]116.000132205183[/C][C]-5.00013220518302[/C][/ROW]
[ROW][C]64[/C][C]108[/C][C]111.000330543546[/C][C]-3.00033054354644[/C][/ROW]
[ROW][C]65[/C][C]102[/C][C]108.000198342735[/C][C]-6.00019834273529[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]102.00039665488[/C][C]-0.000396654879949665[/C][/ROW]
[ROW][C]67[/C][C]129[/C][C]102.000000026222[/C][C]26.9999999737784[/C][/ROW]
[ROW][C]68[/C][C]136[/C][C]128.998215112045[/C][C]7.00178488795478[/C][/ROW]
[ROW][C]69[/C][C]137[/C][C]135.999537133277[/C][C]1.00046286672298[/C][/ROW]
[ROW][C]70[/C][C]126[/C][C]136.99993386244[/C][C]-10.9999338624399[/C][/ROW]
[ROW][C]71[/C][C]119[/C][C]126.000727172203[/C][C]-7.00072717220272[/C][/ROW]
[ROW][C]72[/C][C]117[/C][C]119.000462796801[/C][C]-2.00046279680062[/C][/ROW]
[ROW][C]73[/C][C]120[/C][C]117.000132244517[/C][C]2.99986775548321[/C][/ROW]
[ROW][C]74[/C][C]116[/C][C]119.999801687858[/C][C]-3.99980168785822[/C][/ROW]
[ROW][C]75[/C][C]110[/C][C]116.000264414736[/C][C]-6.0002644147356[/C][/ROW]
[ROW][C]76[/C][C]104[/C][C]110.000396659248[/C][C]-6.00039665924777[/C][/ROW]
[ROW][C]77[/C][C]98[/C][C]104.00039666799[/C][C]-6.00039666799006[/C][/ROW]
[ROW][C]78[/C][C]98[/C][C]98.0003966679906[/C][C]-0.00039666799062843[/C][/ROW]
[ROW][C]79[/C][C]124[/C][C]98.0000000262225[/C][C]25.9999999737775[/C][/ROW]
[ROW][C]80[/C][C]130[/C][C]123.998281219007[/C][C]6.00171878099341[/C][/ROW]
[ROW][C]81[/C][C]131[/C][C]129.999603244608[/C][C]1.00039675539151[/C][/ROW]
[ROW][C]82[/C][C]121[/C][C]130.99993386681[/C][C]-9.99993386681035[/C][/ROW]
[ROW][C]83[/C][C]114[/C][C]121.000661065242[/C][C]-7.00066106524166[/C][/ROW]
[ROW][C]84[/C][C]111[/C][C]114.00046279243[/C][C]-3.00046279243047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278458&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278458&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
2101105-4
395101.000264427845-6.00026442784541
49395.0003966592486-2.00039665924864
58493.0001322401447-9.00013224014465
68784.00059497139422.99940502860585
711686.999801718447729.0001982815523
8120115.9980828850134.00191711498699
9117119.99973544542-2.99973544541994
10109117.000198303395-8.00019830339515
11105109.0005288688-4.00052886880005
12107105.0002644628071.99973553719268
13109106.999867803562.00013219643988
14109108.9998677773380.000132222661804349
15108108.999999991259-0.999999991259159
16107108.000066106961-1.00006610696077
1799107.000066111331-8.00006611133148
1810399.00052886006123.99947113993878
19131102.99973560711628.0002643928841
20137130.9981489876046.00185101239609
21135136.999603235867-1.99960323586708
22124135.000132187694-11.0001321876938
23118124.000727185313-6.00072718531339
24121118.000396689842.99960331015988
25121120.999801705340.000198294660094689
26118120.999999986891-2.99999998689134
27113118.000198320883-5.00019832088319
28107113.000330547917-6.00033054791714
29100107.00039666362-7.00039666361963
30102100.0004627749521.9995372250483
31130101.9998678166728.0001321833301
32136129.9981489963446.0018510036561
33133135.999603235868-2.99960323586765
34120133.000198294655-13.0001982946552
35112120.000859403606-8.00085940360623
36109112.000528912503-3.00052891250338
37110109.0001983558490.999801644151148
38106109.999933906151-3.99993390615134
39102106.000264423476-4.00026442347614
4098102.000264445326-4.00026444532564
419298.0002644453271-6.00026444532709
429292.0003966592498-0.00039665924978749
4312092.000000026221927.9999999737781
44127119.9981490050847.00185099491611
45124126.999537128907-2.99953712890689
46114124.000198290285-10.0001982902851
47108114.000661082722-6.00066108272188
48106108.00039668547-2.00039668547029
49111106.0001322401464.99986775985363
50110110.999669473935-0.999669473935228
51104110.000066085111-6.00006608511127
52100104.000396646137-4.00039664613681
5396100.000264454066-4.00026445406648
549896.00026444532771.99973555467233
5512297.99986780355924.000132196441
56134121.99841342418812.0015865758116
57133133.99920661158-0.999206611580064
58125133.000066054513-8.00006605451287
59118125.000528860057-7.00052886005747
60116118.000462783691-2.00046278369079
61118116.0001322445161.99986775548408
62116117.99986779482-1.99986779481958
63111116.000132205183-5.00013220518302
64108111.000330543546-3.00033054354644
65102108.000198342735-6.00019834273529
66102102.00039665488-0.000396654879949665
67129102.00000002622226.9999999737784
68136128.9982151120457.00178488795478
69137135.9995371332771.00046286672298
70126136.99993386244-10.9999338624399
71119126.000727172203-7.00072717220272
72117119.000462796801-2.00046279680062
73120117.0001322445172.99986775548321
74116119.999801687858-3.99980168785822
75110116.000264414736-6.0002644147356
76104110.000396659248-6.00039665924777
7798104.00039666799-6.00039666799006
789898.0003966679906-0.00039666799062843
7912498.000000026222525.9999999737775
80130123.9982812190076.00171878099341
81131129.9996032446081.00039675539151
82121130.99993386681-9.99993386681035
83114121.000661065242-7.00066106524166
84111114.00046279243-3.00046279243047







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85111.00019835147892.3762822011556129.6241145018
86111.00019835147884.6628741018176137.337522601138
87111.00019835147878.7440509607982143.256345742157
88111.00019835147873.7542127913298148.246183911626
89111.00019835147869.3580582022941152.642338500662
90111.00019835147865.3836198732342156.616776829722
91111.00019835147861.7287397986882160.271656904268
92111.00019835147858.3268557218632163.673540981092
93111.00019835147855.1317330097998166.868663693156
94111.00019835147852.109708325568169.890688377388
95111.00019835147849.2353684614077172.765028241548
96111.00019835147846.4889698156113175.511426887344

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 111.000198351478 & 92.3762822011556 & 129.6241145018 \tabularnewline
86 & 111.000198351478 & 84.6628741018176 & 137.337522601138 \tabularnewline
87 & 111.000198351478 & 78.7440509607982 & 143.256345742157 \tabularnewline
88 & 111.000198351478 & 73.7542127913298 & 148.246183911626 \tabularnewline
89 & 111.000198351478 & 69.3580582022941 & 152.642338500662 \tabularnewline
90 & 111.000198351478 & 65.3836198732342 & 156.616776829722 \tabularnewline
91 & 111.000198351478 & 61.7287397986882 & 160.271656904268 \tabularnewline
92 & 111.000198351478 & 58.3268557218632 & 163.673540981092 \tabularnewline
93 & 111.000198351478 & 55.1317330097998 & 166.868663693156 \tabularnewline
94 & 111.000198351478 & 52.109708325568 & 169.890688377388 \tabularnewline
95 & 111.000198351478 & 49.2353684614077 & 172.765028241548 \tabularnewline
96 & 111.000198351478 & 46.4889698156113 & 175.511426887344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278458&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]111.000198351478[/C][C]92.3762822011556[/C][C]129.6241145018[/C][/ROW]
[ROW][C]86[/C][C]111.000198351478[/C][C]84.6628741018176[/C][C]137.337522601138[/C][/ROW]
[ROW][C]87[/C][C]111.000198351478[/C][C]78.7440509607982[/C][C]143.256345742157[/C][/ROW]
[ROW][C]88[/C][C]111.000198351478[/C][C]73.7542127913298[/C][C]148.246183911626[/C][/ROW]
[ROW][C]89[/C][C]111.000198351478[/C][C]69.3580582022941[/C][C]152.642338500662[/C][/ROW]
[ROW][C]90[/C][C]111.000198351478[/C][C]65.3836198732342[/C][C]156.616776829722[/C][/ROW]
[ROW][C]91[/C][C]111.000198351478[/C][C]61.7287397986882[/C][C]160.271656904268[/C][/ROW]
[ROW][C]92[/C][C]111.000198351478[/C][C]58.3268557218632[/C][C]163.673540981092[/C][/ROW]
[ROW][C]93[/C][C]111.000198351478[/C][C]55.1317330097998[/C][C]166.868663693156[/C][/ROW]
[ROW][C]94[/C][C]111.000198351478[/C][C]52.109708325568[/C][C]169.890688377388[/C][/ROW]
[ROW][C]95[/C][C]111.000198351478[/C][C]49.2353684614077[/C][C]172.765028241548[/C][/ROW]
[ROW][C]96[/C][C]111.000198351478[/C][C]46.4889698156113[/C][C]175.511426887344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278458&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278458&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
85111.00019835147892.3762822011556129.6241145018
86111.00019835147884.6628741018176137.337522601138
87111.00019835147878.7440509607982143.256345742157
88111.00019835147873.7542127913298148.246183911626
89111.00019835147869.3580582022941152.642338500662
90111.00019835147865.3836198732342156.616776829722
91111.00019835147861.7287397986882160.271656904268
92111.00019835147858.3268557218632163.673540981092
93111.00019835147855.1317330097998166.868663693156
94111.00019835147852.109708325568169.890688377388
95111.00019835147849.2353684614077172.765028241548
96111.00019835147846.4889698156113175.511426887344



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')