Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Jan 2014 15:44:28 -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/2014/Jan/12/t1389559530qxbik1sgt0q1mxt.htm/, Retrieved Sat, 18 May 2024 03:43:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233063, Retrieved Sat, 18 May 2024 03:43:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2014-01-12 20:24:03] [256d78ccaa024c70359216b2e3721f69]
- RMPD    [Exponential Smoothing] [] [2014-01-12 20:44:28] [b4fcddd00e162930a5ba50e371bf31bc] [Current]
Feedback Forum

Post a new message
Dataseries X:
93.61
93.17
91.60
90.30
90.88
91.06
92.05
95.29
96.44
96.49
96.52
96.09
99.16
98.09
99.41
99.87
100.06
99.65
99.92
98.44
102.64
112.33
115.63
118.29
121.43
129.96
147.73
154.10
150.09
144.14
141.54
136.68
129.32
118.99
109.61
106.22
104.97
102.45
101.91
101.77
102.67
103.45
101.41
102.45
102.17
101.40
101.68
100.61
97.93
98.30
99.79
101.62
101.55
102.43
102.09
102.01
102.26
101.24
100.91
100.67
100.33
99.99
99.23
98.17
97.38
96.70
98.65
100.68
101.07
101.12
101.13
99.88
99.20
99.91
103.62
108.05
113.96
117.39
126.04
139.67
145.04
142.37
137.72
132.46




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=233063&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=233063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233063&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
alpha0.99994390474329
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99994390474329 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233063&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]0.99994390474329[/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=233063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233063&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
alpha0.99994390474329
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
293.1793.61-0.439999999999998
391.693.1700246819129-1.57002468191295
490.391.6000880709376-1.30008807093758
590.8890.30007292877410.57992707122591
691.0690.87996746884210.180032531157934
792.0591.0599899010290.990010098971041
895.2992.04994446512943.24005553487065
996.4495.2898182482531.15018175174697
1096.4996.43993548025940.05006451974063
1196.5296.48999719161790.0300028083820933
1296.0996.5199983169848-0.429998316984751
1399.1696.0900241208663.06997587913402
1498.0999.159827788915-1.06982778891496
1599.4198.09006001226451.31993998773554
1699.8799.40992595762760.460074042372455
17100.0699.86997419202850.190025807971509
1899.65100.059989340454-0.409989340453521
1999.9299.65002299845730.269977001542699
2098.4499.9199848555708-1.47998485557079
21102.6498.44008302013044.1999169798696
22112.33102.6397644045799.69023559542114
23115.63112.3294564237473.3005435762533
24118.29115.6298148551612.6601851448392
25121.43118.2898507762313.14014922376859
26129.96121.4298238525238.53017614747681
27147.73129.95952149757917.7704785024208
28154.1147.7290031604476.37099683955344
29150.09154.099642617297-4.00964261729678
30144.14150.090224921932-5.95022492193195
31141.54144.140333779394-2.60033377939448
32136.68141.540145866391-4.86014586639087
33129.32136.68027263113-7.36027263113004
34118.99129.320412876383-10.3304128763827
35109.61118.990579487162-9.38057948716221
36106.22109.610526206014-3.39052620601441
37104.97106.220190192438-1.25019019243791
38102.45104.97007012974-2.52007012973978
39101.91102.450141363981-0.540141363980865
40101.77101.910030299368-0.140030299368476
41102.67101.7700078550360.899992144964415
42103.45102.669949514710.780050485290403
43101.41103.449956242868-2.03995624286779
44102.45101.4101144318691.03988556813088
45102.17102.449941667352-0.279941667352105
46101.4102.1700157034-0.770015703399693
47101.68101.4000431942290.279956805771448
48100.61101.679984295751-1.06998429575113
4997.93100.610060021044-2.68006002104374
5098.397.93015033865490.369849661345114
5199.7998.29997925318831.49002074681171
52101.6299.78991641690371.8300835830963
53101.55101.619897340992-0.0698973409916164
54102.43101.5500039209090.879996079090716
55102.09102.429950636394-0.33995063639405
56102.01102.090019069618-0.080019069618217
57102.26102.010004488690.249995511309749
58101.24102.259985976438-1.01998597643762
59100.91101.240057216375-0.330057216375181
60100.67100.910018514644-0.240018514644277
61100.33100.6700134639-0.340013463900192
6299.99100.330019073143-0.340019073142543
6399.2399.9900190734572-0.760019073457187
6498.1799.230042633465-1.06004263346503
6597.3898.1700594633636-0.790059463363647
6696.797.3800443185884-0.680044318588401
6798.6596.70003814726061.94996185273938
68100.6898.64989061638932.03010938361071
69101.07100.6798861204930.390113879507012
70101.12101.0699781164620.0500218835382213
71101.13101.119997194010.0100028059903821
7299.88101.12999943889-1.24999943889003
7399.299.8800701190394-0.680070119039399
7499.9199.20003814870790.709961851292093
75103.6299.90996017450773.71003982549232
76108.05103.6197918843644.4302081156364
77113.96108.0497514863385.91024851366151
78117.39113.9596684630923.4303315369076
79126.04117.3898075746728.65019242532817
80139.67126.03951476523513.6304852347647
81145.04139.6692353944325.37076460556833
82142.37145.039698725581-2.6696987255807
83137.72142.370149757435-4.65014975743534
84132.46137.720260851344-5.26026085134438

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 93.17 & 93.61 & -0.439999999999998 \tabularnewline
3 & 91.6 & 93.1700246819129 & -1.57002468191295 \tabularnewline
4 & 90.3 & 91.6000880709376 & -1.30008807093758 \tabularnewline
5 & 90.88 & 90.3000729287741 & 0.57992707122591 \tabularnewline
6 & 91.06 & 90.8799674688421 & 0.180032531157934 \tabularnewline
7 & 92.05 & 91.059989901029 & 0.990010098971041 \tabularnewline
8 & 95.29 & 92.0499444651294 & 3.24005553487065 \tabularnewline
9 & 96.44 & 95.289818248253 & 1.15018175174697 \tabularnewline
10 & 96.49 & 96.4399354802594 & 0.05006451974063 \tabularnewline
11 & 96.52 & 96.4899971916179 & 0.0300028083820933 \tabularnewline
12 & 96.09 & 96.5199983169848 & -0.429998316984751 \tabularnewline
13 & 99.16 & 96.090024120866 & 3.06997587913402 \tabularnewline
14 & 98.09 & 99.159827788915 & -1.06982778891496 \tabularnewline
15 & 99.41 & 98.0900600122645 & 1.31993998773554 \tabularnewline
16 & 99.87 & 99.4099259576276 & 0.460074042372455 \tabularnewline
17 & 100.06 & 99.8699741920285 & 0.190025807971509 \tabularnewline
18 & 99.65 & 100.059989340454 & -0.409989340453521 \tabularnewline
19 & 99.92 & 99.6500229984573 & 0.269977001542699 \tabularnewline
20 & 98.44 & 99.9199848555708 & -1.47998485557079 \tabularnewline
21 & 102.64 & 98.4400830201304 & 4.1999169798696 \tabularnewline
22 & 112.33 & 102.639764404579 & 9.69023559542114 \tabularnewline
23 & 115.63 & 112.329456423747 & 3.3005435762533 \tabularnewline
24 & 118.29 & 115.629814855161 & 2.6601851448392 \tabularnewline
25 & 121.43 & 118.289850776231 & 3.14014922376859 \tabularnewline
26 & 129.96 & 121.429823852523 & 8.53017614747681 \tabularnewline
27 & 147.73 & 129.959521497579 & 17.7704785024208 \tabularnewline
28 & 154.1 & 147.729003160447 & 6.37099683955344 \tabularnewline
29 & 150.09 & 154.099642617297 & -4.00964261729678 \tabularnewline
30 & 144.14 & 150.090224921932 & -5.95022492193195 \tabularnewline
31 & 141.54 & 144.140333779394 & -2.60033377939448 \tabularnewline
32 & 136.68 & 141.540145866391 & -4.86014586639087 \tabularnewline
33 & 129.32 & 136.68027263113 & -7.36027263113004 \tabularnewline
34 & 118.99 & 129.320412876383 & -10.3304128763827 \tabularnewline
35 & 109.61 & 118.990579487162 & -9.38057948716221 \tabularnewline
36 & 106.22 & 109.610526206014 & -3.39052620601441 \tabularnewline
37 & 104.97 & 106.220190192438 & -1.25019019243791 \tabularnewline
38 & 102.45 & 104.97007012974 & -2.52007012973978 \tabularnewline
39 & 101.91 & 102.450141363981 & -0.540141363980865 \tabularnewline
40 & 101.77 & 101.910030299368 & -0.140030299368476 \tabularnewline
41 & 102.67 & 101.770007855036 & 0.899992144964415 \tabularnewline
42 & 103.45 & 102.66994951471 & 0.780050485290403 \tabularnewline
43 & 101.41 & 103.449956242868 & -2.03995624286779 \tabularnewline
44 & 102.45 & 101.410114431869 & 1.03988556813088 \tabularnewline
45 & 102.17 & 102.449941667352 & -0.279941667352105 \tabularnewline
46 & 101.4 & 102.1700157034 & -0.770015703399693 \tabularnewline
47 & 101.68 & 101.400043194229 & 0.279956805771448 \tabularnewline
48 & 100.61 & 101.679984295751 & -1.06998429575113 \tabularnewline
49 & 97.93 & 100.610060021044 & -2.68006002104374 \tabularnewline
50 & 98.3 & 97.9301503386549 & 0.369849661345114 \tabularnewline
51 & 99.79 & 98.2999792531883 & 1.49002074681171 \tabularnewline
52 & 101.62 & 99.7899164169037 & 1.8300835830963 \tabularnewline
53 & 101.55 & 101.619897340992 & -0.0698973409916164 \tabularnewline
54 & 102.43 & 101.550003920909 & 0.879996079090716 \tabularnewline
55 & 102.09 & 102.429950636394 & -0.33995063639405 \tabularnewline
56 & 102.01 & 102.090019069618 & -0.080019069618217 \tabularnewline
57 & 102.26 & 102.01000448869 & 0.249995511309749 \tabularnewline
58 & 101.24 & 102.259985976438 & -1.01998597643762 \tabularnewline
59 & 100.91 & 101.240057216375 & -0.330057216375181 \tabularnewline
60 & 100.67 & 100.910018514644 & -0.240018514644277 \tabularnewline
61 & 100.33 & 100.6700134639 & -0.340013463900192 \tabularnewline
62 & 99.99 & 100.330019073143 & -0.340019073142543 \tabularnewline
63 & 99.23 & 99.9900190734572 & -0.760019073457187 \tabularnewline
64 & 98.17 & 99.230042633465 & -1.06004263346503 \tabularnewline
65 & 97.38 & 98.1700594633636 & -0.790059463363647 \tabularnewline
66 & 96.7 & 97.3800443185884 & -0.680044318588401 \tabularnewline
67 & 98.65 & 96.7000381472606 & 1.94996185273938 \tabularnewline
68 & 100.68 & 98.6498906163893 & 2.03010938361071 \tabularnewline
69 & 101.07 & 100.679886120493 & 0.390113879507012 \tabularnewline
70 & 101.12 & 101.069978116462 & 0.0500218835382213 \tabularnewline
71 & 101.13 & 101.11999719401 & 0.0100028059903821 \tabularnewline
72 & 99.88 & 101.12999943889 & -1.24999943889003 \tabularnewline
73 & 99.2 & 99.8800701190394 & -0.680070119039399 \tabularnewline
74 & 99.91 & 99.2000381487079 & 0.709961851292093 \tabularnewline
75 & 103.62 & 99.9099601745077 & 3.71003982549232 \tabularnewline
76 & 108.05 & 103.619791884364 & 4.4302081156364 \tabularnewline
77 & 113.96 & 108.049751486338 & 5.91024851366151 \tabularnewline
78 & 117.39 & 113.959668463092 & 3.4303315369076 \tabularnewline
79 & 126.04 & 117.389807574672 & 8.65019242532817 \tabularnewline
80 & 139.67 & 126.039514765235 & 13.6304852347647 \tabularnewline
81 & 145.04 & 139.669235394432 & 5.37076460556833 \tabularnewline
82 & 142.37 & 145.039698725581 & -2.6696987255807 \tabularnewline
83 & 137.72 & 142.370149757435 & -4.65014975743534 \tabularnewline
84 & 132.46 & 137.720260851344 & -5.26026085134438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233063&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]93.17[/C][C]93.61[/C][C]-0.439999999999998[/C][/ROW]
[ROW][C]3[/C][C]91.6[/C][C]93.1700246819129[/C][C]-1.57002468191295[/C][/ROW]
[ROW][C]4[/C][C]90.3[/C][C]91.6000880709376[/C][C]-1.30008807093758[/C][/ROW]
[ROW][C]5[/C][C]90.88[/C][C]90.3000729287741[/C][C]0.57992707122591[/C][/ROW]
[ROW][C]6[/C][C]91.06[/C][C]90.8799674688421[/C][C]0.180032531157934[/C][/ROW]
[ROW][C]7[/C][C]92.05[/C][C]91.059989901029[/C][C]0.990010098971041[/C][/ROW]
[ROW][C]8[/C][C]95.29[/C][C]92.0499444651294[/C][C]3.24005553487065[/C][/ROW]
[ROW][C]9[/C][C]96.44[/C][C]95.289818248253[/C][C]1.15018175174697[/C][/ROW]
[ROW][C]10[/C][C]96.49[/C][C]96.4399354802594[/C][C]0.05006451974063[/C][/ROW]
[ROW][C]11[/C][C]96.52[/C][C]96.4899971916179[/C][C]0.0300028083820933[/C][/ROW]
[ROW][C]12[/C][C]96.09[/C][C]96.5199983169848[/C][C]-0.429998316984751[/C][/ROW]
[ROW][C]13[/C][C]99.16[/C][C]96.090024120866[/C][C]3.06997587913402[/C][/ROW]
[ROW][C]14[/C][C]98.09[/C][C]99.159827788915[/C][C]-1.06982778891496[/C][/ROW]
[ROW][C]15[/C][C]99.41[/C][C]98.0900600122645[/C][C]1.31993998773554[/C][/ROW]
[ROW][C]16[/C][C]99.87[/C][C]99.4099259576276[/C][C]0.460074042372455[/C][/ROW]
[ROW][C]17[/C][C]100.06[/C][C]99.8699741920285[/C][C]0.190025807971509[/C][/ROW]
[ROW][C]18[/C][C]99.65[/C][C]100.059989340454[/C][C]-0.409989340453521[/C][/ROW]
[ROW][C]19[/C][C]99.92[/C][C]99.6500229984573[/C][C]0.269977001542699[/C][/ROW]
[ROW][C]20[/C][C]98.44[/C][C]99.9199848555708[/C][C]-1.47998485557079[/C][/ROW]
[ROW][C]21[/C][C]102.64[/C][C]98.4400830201304[/C][C]4.1999169798696[/C][/ROW]
[ROW][C]22[/C][C]112.33[/C][C]102.639764404579[/C][C]9.69023559542114[/C][/ROW]
[ROW][C]23[/C][C]115.63[/C][C]112.329456423747[/C][C]3.3005435762533[/C][/ROW]
[ROW][C]24[/C][C]118.29[/C][C]115.629814855161[/C][C]2.6601851448392[/C][/ROW]
[ROW][C]25[/C][C]121.43[/C][C]118.289850776231[/C][C]3.14014922376859[/C][/ROW]
[ROW][C]26[/C][C]129.96[/C][C]121.429823852523[/C][C]8.53017614747681[/C][/ROW]
[ROW][C]27[/C][C]147.73[/C][C]129.959521497579[/C][C]17.7704785024208[/C][/ROW]
[ROW][C]28[/C][C]154.1[/C][C]147.729003160447[/C][C]6.37099683955344[/C][/ROW]
[ROW][C]29[/C][C]150.09[/C][C]154.099642617297[/C][C]-4.00964261729678[/C][/ROW]
[ROW][C]30[/C][C]144.14[/C][C]150.090224921932[/C][C]-5.95022492193195[/C][/ROW]
[ROW][C]31[/C][C]141.54[/C][C]144.140333779394[/C][C]-2.60033377939448[/C][/ROW]
[ROW][C]32[/C][C]136.68[/C][C]141.540145866391[/C][C]-4.86014586639087[/C][/ROW]
[ROW][C]33[/C][C]129.32[/C][C]136.68027263113[/C][C]-7.36027263113004[/C][/ROW]
[ROW][C]34[/C][C]118.99[/C][C]129.320412876383[/C][C]-10.3304128763827[/C][/ROW]
[ROW][C]35[/C][C]109.61[/C][C]118.990579487162[/C][C]-9.38057948716221[/C][/ROW]
[ROW][C]36[/C][C]106.22[/C][C]109.610526206014[/C][C]-3.39052620601441[/C][/ROW]
[ROW][C]37[/C][C]104.97[/C][C]106.220190192438[/C][C]-1.25019019243791[/C][/ROW]
[ROW][C]38[/C][C]102.45[/C][C]104.97007012974[/C][C]-2.52007012973978[/C][/ROW]
[ROW][C]39[/C][C]101.91[/C][C]102.450141363981[/C][C]-0.540141363980865[/C][/ROW]
[ROW][C]40[/C][C]101.77[/C][C]101.910030299368[/C][C]-0.140030299368476[/C][/ROW]
[ROW][C]41[/C][C]102.67[/C][C]101.770007855036[/C][C]0.899992144964415[/C][/ROW]
[ROW][C]42[/C][C]103.45[/C][C]102.66994951471[/C][C]0.780050485290403[/C][/ROW]
[ROW][C]43[/C][C]101.41[/C][C]103.449956242868[/C][C]-2.03995624286779[/C][/ROW]
[ROW][C]44[/C][C]102.45[/C][C]101.410114431869[/C][C]1.03988556813088[/C][/ROW]
[ROW][C]45[/C][C]102.17[/C][C]102.449941667352[/C][C]-0.279941667352105[/C][/ROW]
[ROW][C]46[/C][C]101.4[/C][C]102.1700157034[/C][C]-0.770015703399693[/C][/ROW]
[ROW][C]47[/C][C]101.68[/C][C]101.400043194229[/C][C]0.279956805771448[/C][/ROW]
[ROW][C]48[/C][C]100.61[/C][C]101.679984295751[/C][C]-1.06998429575113[/C][/ROW]
[ROW][C]49[/C][C]97.93[/C][C]100.610060021044[/C][C]-2.68006002104374[/C][/ROW]
[ROW][C]50[/C][C]98.3[/C][C]97.9301503386549[/C][C]0.369849661345114[/C][/ROW]
[ROW][C]51[/C][C]99.79[/C][C]98.2999792531883[/C][C]1.49002074681171[/C][/ROW]
[ROW][C]52[/C][C]101.62[/C][C]99.7899164169037[/C][C]1.8300835830963[/C][/ROW]
[ROW][C]53[/C][C]101.55[/C][C]101.619897340992[/C][C]-0.0698973409916164[/C][/ROW]
[ROW][C]54[/C][C]102.43[/C][C]101.550003920909[/C][C]0.879996079090716[/C][/ROW]
[ROW][C]55[/C][C]102.09[/C][C]102.429950636394[/C][C]-0.33995063639405[/C][/ROW]
[ROW][C]56[/C][C]102.01[/C][C]102.090019069618[/C][C]-0.080019069618217[/C][/ROW]
[ROW][C]57[/C][C]102.26[/C][C]102.01000448869[/C][C]0.249995511309749[/C][/ROW]
[ROW][C]58[/C][C]101.24[/C][C]102.259985976438[/C][C]-1.01998597643762[/C][/ROW]
[ROW][C]59[/C][C]100.91[/C][C]101.240057216375[/C][C]-0.330057216375181[/C][/ROW]
[ROW][C]60[/C][C]100.67[/C][C]100.910018514644[/C][C]-0.240018514644277[/C][/ROW]
[ROW][C]61[/C][C]100.33[/C][C]100.6700134639[/C][C]-0.340013463900192[/C][/ROW]
[ROW][C]62[/C][C]99.99[/C][C]100.330019073143[/C][C]-0.340019073142543[/C][/ROW]
[ROW][C]63[/C][C]99.23[/C][C]99.9900190734572[/C][C]-0.760019073457187[/C][/ROW]
[ROW][C]64[/C][C]98.17[/C][C]99.230042633465[/C][C]-1.06004263346503[/C][/ROW]
[ROW][C]65[/C][C]97.38[/C][C]98.1700594633636[/C][C]-0.790059463363647[/C][/ROW]
[ROW][C]66[/C][C]96.7[/C][C]97.3800443185884[/C][C]-0.680044318588401[/C][/ROW]
[ROW][C]67[/C][C]98.65[/C][C]96.7000381472606[/C][C]1.94996185273938[/C][/ROW]
[ROW][C]68[/C][C]100.68[/C][C]98.6498906163893[/C][C]2.03010938361071[/C][/ROW]
[ROW][C]69[/C][C]101.07[/C][C]100.679886120493[/C][C]0.390113879507012[/C][/ROW]
[ROW][C]70[/C][C]101.12[/C][C]101.069978116462[/C][C]0.0500218835382213[/C][/ROW]
[ROW][C]71[/C][C]101.13[/C][C]101.11999719401[/C][C]0.0100028059903821[/C][/ROW]
[ROW][C]72[/C][C]99.88[/C][C]101.12999943889[/C][C]-1.24999943889003[/C][/ROW]
[ROW][C]73[/C][C]99.2[/C][C]99.8800701190394[/C][C]-0.680070119039399[/C][/ROW]
[ROW][C]74[/C][C]99.91[/C][C]99.2000381487079[/C][C]0.709961851292093[/C][/ROW]
[ROW][C]75[/C][C]103.62[/C][C]99.9099601745077[/C][C]3.71003982549232[/C][/ROW]
[ROW][C]76[/C][C]108.05[/C][C]103.619791884364[/C][C]4.4302081156364[/C][/ROW]
[ROW][C]77[/C][C]113.96[/C][C]108.049751486338[/C][C]5.91024851366151[/C][/ROW]
[ROW][C]78[/C][C]117.39[/C][C]113.959668463092[/C][C]3.4303315369076[/C][/ROW]
[ROW][C]79[/C][C]126.04[/C][C]117.389807574672[/C][C]8.65019242532817[/C][/ROW]
[ROW][C]80[/C][C]139.67[/C][C]126.039514765235[/C][C]13.6304852347647[/C][/ROW]
[ROW][C]81[/C][C]145.04[/C][C]139.669235394432[/C][C]5.37076460556833[/C][/ROW]
[ROW][C]82[/C][C]142.37[/C][C]145.039698725581[/C][C]-2.6696987255807[/C][/ROW]
[ROW][C]83[/C][C]137.72[/C][C]142.370149757435[/C][C]-4.65014975743534[/C][/ROW]
[ROW][C]84[/C][C]132.46[/C][C]137.720260851344[/C][C]-5.26026085134438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233063&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233063&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
293.1793.61-0.439999999999998
391.693.1700246819129-1.57002468191295
490.391.6000880709376-1.30008807093758
590.8890.30007292877410.57992707122591
691.0690.87996746884210.180032531157934
792.0591.0599899010290.990010098971041
895.2992.04994446512943.24005553487065
996.4495.2898182482531.15018175174697
1096.4996.43993548025940.05006451974063
1196.5296.48999719161790.0300028083820933
1296.0996.5199983169848-0.429998316984751
1399.1696.0900241208663.06997587913402
1498.0999.159827788915-1.06982778891496
1599.4198.09006001226451.31993998773554
1699.8799.40992595762760.460074042372455
17100.0699.86997419202850.190025807971509
1899.65100.059989340454-0.409989340453521
1999.9299.65002299845730.269977001542699
2098.4499.9199848555708-1.47998485557079
21102.6498.44008302013044.1999169798696
22112.33102.6397644045799.69023559542114
23115.63112.3294564237473.3005435762533
24118.29115.6298148551612.6601851448392
25121.43118.2898507762313.14014922376859
26129.96121.4298238525238.53017614747681
27147.73129.95952149757917.7704785024208
28154.1147.7290031604476.37099683955344
29150.09154.099642617297-4.00964261729678
30144.14150.090224921932-5.95022492193195
31141.54144.140333779394-2.60033377939448
32136.68141.540145866391-4.86014586639087
33129.32136.68027263113-7.36027263113004
34118.99129.320412876383-10.3304128763827
35109.61118.990579487162-9.38057948716221
36106.22109.610526206014-3.39052620601441
37104.97106.220190192438-1.25019019243791
38102.45104.97007012974-2.52007012973978
39101.91102.450141363981-0.540141363980865
40101.77101.910030299368-0.140030299368476
41102.67101.7700078550360.899992144964415
42103.45102.669949514710.780050485290403
43101.41103.449956242868-2.03995624286779
44102.45101.4101144318691.03988556813088
45102.17102.449941667352-0.279941667352105
46101.4102.1700157034-0.770015703399693
47101.68101.4000431942290.279956805771448
48100.61101.679984295751-1.06998429575113
4997.93100.610060021044-2.68006002104374
5098.397.93015033865490.369849661345114
5199.7998.29997925318831.49002074681171
52101.6299.78991641690371.8300835830963
53101.55101.619897340992-0.0698973409916164
54102.43101.5500039209090.879996079090716
55102.09102.429950636394-0.33995063639405
56102.01102.090019069618-0.080019069618217
57102.26102.010004488690.249995511309749
58101.24102.259985976438-1.01998597643762
59100.91101.240057216375-0.330057216375181
60100.67100.910018514644-0.240018514644277
61100.33100.6700134639-0.340013463900192
6299.99100.330019073143-0.340019073142543
6399.2399.9900190734572-0.760019073457187
6498.1799.230042633465-1.06004263346503
6597.3898.1700594633636-0.790059463363647
6696.797.3800443185884-0.680044318588401
6798.6596.70003814726061.94996185273938
68100.6898.64989061638932.03010938361071
69101.07100.6798861204930.390113879507012
70101.12101.0699781164620.0500218835382213
71101.13101.119997194010.0100028059903821
7299.88101.12999943889-1.24999943889003
7399.299.8800701190394-0.680070119039399
7499.9199.20003814870790.709961851292093
75103.6299.90996017450773.71003982549232
76108.05103.6197918843644.4302081156364
77113.96108.0497514863385.91024851366151
78117.39113.9596684630923.4303315369076
79126.04117.3898075746728.65019242532817
80139.67126.03951476523513.6304852347647
81145.04139.6692353944325.37076460556833
82142.37145.039698725581-2.6696987255807
83137.72142.370149757435-4.65014975743534
84132.46137.720260851344-5.26026085134438







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85132.460295075683124.371302783761140.549287367605
86132.460295075683121.021053318616143.89953683275
87132.460295075683118.450273389244146.470316762121
88132.460295075683116.282991118214148.637599033151
89132.460295075683114.373570136928150.547020014438
90132.460295075683112.647317644514152.273272506852
91132.460295075683111.059862127589153.860728023777
92132.460295075683109.582292845512155.338297305854
93132.460295075683108.194528207076156.726061944289
94132.460295075683106.881946860847158.038643290519
95132.460295075683105.633510827897159.287079323469
96132.460295075683104.440644671813160.479945479553

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 132.460295075683 & 124.371302783761 & 140.549287367605 \tabularnewline
86 & 132.460295075683 & 121.021053318616 & 143.89953683275 \tabularnewline
87 & 132.460295075683 & 118.450273389244 & 146.470316762121 \tabularnewline
88 & 132.460295075683 & 116.282991118214 & 148.637599033151 \tabularnewline
89 & 132.460295075683 & 114.373570136928 & 150.547020014438 \tabularnewline
90 & 132.460295075683 & 112.647317644514 & 152.273272506852 \tabularnewline
91 & 132.460295075683 & 111.059862127589 & 153.860728023777 \tabularnewline
92 & 132.460295075683 & 109.582292845512 & 155.338297305854 \tabularnewline
93 & 132.460295075683 & 108.194528207076 & 156.726061944289 \tabularnewline
94 & 132.460295075683 & 106.881946860847 & 158.038643290519 \tabularnewline
95 & 132.460295075683 & 105.633510827897 & 159.287079323469 \tabularnewline
96 & 132.460295075683 & 104.440644671813 & 160.479945479553 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233063&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]132.460295075683[/C][C]124.371302783761[/C][C]140.549287367605[/C][/ROW]
[ROW][C]86[/C][C]132.460295075683[/C][C]121.021053318616[/C][C]143.89953683275[/C][/ROW]
[ROW][C]87[/C][C]132.460295075683[/C][C]118.450273389244[/C][C]146.470316762121[/C][/ROW]
[ROW][C]88[/C][C]132.460295075683[/C][C]116.282991118214[/C][C]148.637599033151[/C][/ROW]
[ROW][C]89[/C][C]132.460295075683[/C][C]114.373570136928[/C][C]150.547020014438[/C][/ROW]
[ROW][C]90[/C][C]132.460295075683[/C][C]112.647317644514[/C][C]152.273272506852[/C][/ROW]
[ROW][C]91[/C][C]132.460295075683[/C][C]111.059862127589[/C][C]153.860728023777[/C][/ROW]
[ROW][C]92[/C][C]132.460295075683[/C][C]109.582292845512[/C][C]155.338297305854[/C][/ROW]
[ROW][C]93[/C][C]132.460295075683[/C][C]108.194528207076[/C][C]156.726061944289[/C][/ROW]
[ROW][C]94[/C][C]132.460295075683[/C][C]106.881946860847[/C][C]158.038643290519[/C][/ROW]
[ROW][C]95[/C][C]132.460295075683[/C][C]105.633510827897[/C][C]159.287079323469[/C][/ROW]
[ROW][C]96[/C][C]132.460295075683[/C][C]104.440644671813[/C][C]160.479945479553[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233063&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233063&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
85132.460295075683124.371302783761140.549287367605
86132.460295075683121.021053318616143.89953683275
87132.460295075683118.450273389244146.470316762121
88132.460295075683116.282991118214148.637599033151
89132.460295075683114.373570136928150.547020014438
90132.460295075683112.647317644514152.273272506852
91132.460295075683111.059862127589153.860728023777
92132.460295075683109.582292845512155.338297305854
93132.460295075683108.194528207076156.726061944289
94132.460295075683106.881946860847158.038643290519
95132.460295075683105.633510827897159.287079323469
96132.460295075683104.440644671813160.479945479553



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):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')