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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 31 May 2008 08:16:17 -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/May/31/t1212243501fq7bhj3nw1axgeg.htm/, Retrieved Wed, 15 May 2024 08:02:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13605, Retrieved Wed, 15 May 2024 08:02:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Plantaardige stof...] [2008-05-31 14:16:17] [506d2bb30770262a8edd99d84e6e5636] [Current]
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Dataseries X:
79,2
81,5
81,5
82
85,8
88,2
88
88,8
89
90,4
90,9
94,6
97,9
101,7
102,3
103,5
103,6
102,3
101,6
104,3
110,8
112,1
111,1
114,4
115
115,3
114,1
114,8
114,5
114,1
112,3
113
112,2
113,7
113,6
115,8
117,9
120,1
118,8
114,7
110,9
112,9
113,3
114,3
116,5
114,3
115,9
120,1
122,6
122,4
123,1
127,9
130,9
135
134,9
130,2
130,8
132,6
138,6
146,2
149,3
149,9
156,8
158,8
156,7
159,9
158,2
157,5
159,1
160,6
161,6
161,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13605&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13605&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13605&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.082827106149464
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.082827106149464 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13605&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.082827106149464[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13605&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13605&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.082827106149464
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
381.583.8-2.30000000000000
48283.6094976558562-1.60949765585623
585.883.97618762266731.82381237733269
688.287.92724872404130.272751275958655
78890.3498399229276-2.34983992292759
888.889.955209482197-1.15520948219701
98990.6595268237902-1.65952682379020
1090.490.7220730193983-0.322073019398246
1190.992.0953966432327-1.19539664323268
1294.692.4963853985732.10361460142705
1397.996.37062170846291.52937829153711
14101.799.79729568655871.90270431344128
15102.3103.754891178699-1.45489117869917
16103.5104.234386752605-0.734386752605133
17103.6105.373559623092-1.77355962309235
18102.3105.326660811928-3.02666081192807
19101.6103.77597125558-2.17597125558009
20104.3102.8957418534161.40425814658403
21110.8105.7120524919845.08794750801566
22112.1112.633472460314-0.533472460313646
23111.1113.889286480215-2.78928648021544
24114.4112.6582579528371.74174204716265
25115116.102521406263-1.10252140626270
26115.3116.611202748714-1.31120274871412
27114.1116.802599619463-2.7025996194629
28114.8115.378751113902-0.578751113902143
29114.5116.030814833957-1.53081483395685
30114.1115.604021871210-1.50402187120955
31112.3115.079448092032-2.77944809203174
32113113.049234449876-0.0492344498761099
33112.2113.74515650287-1.54515650287001
34113.7112.8171756611890.882824338810735
35113.6114.390297446411-0.790297446411273
36115.8114.2248393959281.57516060407229
37117.9116.5553053904841.34469460951635
38120.1118.7666825536451.33331744635531
39118.8121.077117379305-2.27711737930488
40114.7119.588510336414-4.88851033641441
41110.9115.083609171867-4.18360917186746
42112.9110.9370929309011.96290706909868
43113.3113.0996748430750.200325156924890
44114.3113.5162671961120.783732803887872
45116.5114.5811815162531.91881848374744
46114.3116.940111698487-2.64011169848747
47115.9114.5214388865901.37856111340960
48120.1116.2356211142643.86437888573569
49122.6120.7556964344351.84430356556513
50122.4123.408454761632-1.00845476163177
51123.1123.124927372043-0.0249273720431802
52127.9123.8228627099534.07713729004709
53130.9128.9605601930621.93943980693842
54135132.1211983798212.87880162017862
55134.9136.459641187199-1.55964118719916
56130.2136.230460621032-6.03046062103195
57130.8131.030975019044-0.230975019043541
58132.6131.6118440266230.98815597337662
59138.6133.4936901263225.10630987367753
60146.2139.9166309962626.28336900373839
61149.3148.0370642677101.26293573228952
62149.9151.241669579669-1.34166957966880
63156.8151.7305429709765.06945702902394
64158.8159.050431426439-0.250431426439178
65156.7161.029688916098-4.32968891609835
66159.9158.5710733126501.32892668734951
67158.2161.881144464448-3.68114446444847
68157.5159.87624592114-2.37624592114005
69159.1158.9794283479930.120571652007413
70160.6160.5894149490120.0105850509879986
71161.6162.090291678154-0.490291678153795
72161.3163.049682237283-1.74968223728311

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 81.5 & 83.8 & -2.30000000000000 \tabularnewline
4 & 82 & 83.6094976558562 & -1.60949765585623 \tabularnewline
5 & 85.8 & 83.9761876226673 & 1.82381237733269 \tabularnewline
6 & 88.2 & 87.9272487240413 & 0.272751275958655 \tabularnewline
7 & 88 & 90.3498399229276 & -2.34983992292759 \tabularnewline
8 & 88.8 & 89.955209482197 & -1.15520948219701 \tabularnewline
9 & 89 & 90.6595268237902 & -1.65952682379020 \tabularnewline
10 & 90.4 & 90.7220730193983 & -0.322073019398246 \tabularnewline
11 & 90.9 & 92.0953966432327 & -1.19539664323268 \tabularnewline
12 & 94.6 & 92.496385398573 & 2.10361460142705 \tabularnewline
13 & 97.9 & 96.3706217084629 & 1.52937829153711 \tabularnewline
14 & 101.7 & 99.7972956865587 & 1.90270431344128 \tabularnewline
15 & 102.3 & 103.754891178699 & -1.45489117869917 \tabularnewline
16 & 103.5 & 104.234386752605 & -0.734386752605133 \tabularnewline
17 & 103.6 & 105.373559623092 & -1.77355962309235 \tabularnewline
18 & 102.3 & 105.326660811928 & -3.02666081192807 \tabularnewline
19 & 101.6 & 103.77597125558 & -2.17597125558009 \tabularnewline
20 & 104.3 & 102.895741853416 & 1.40425814658403 \tabularnewline
21 & 110.8 & 105.712052491984 & 5.08794750801566 \tabularnewline
22 & 112.1 & 112.633472460314 & -0.533472460313646 \tabularnewline
23 & 111.1 & 113.889286480215 & -2.78928648021544 \tabularnewline
24 & 114.4 & 112.658257952837 & 1.74174204716265 \tabularnewline
25 & 115 & 116.102521406263 & -1.10252140626270 \tabularnewline
26 & 115.3 & 116.611202748714 & -1.31120274871412 \tabularnewline
27 & 114.1 & 116.802599619463 & -2.7025996194629 \tabularnewline
28 & 114.8 & 115.378751113902 & -0.578751113902143 \tabularnewline
29 & 114.5 & 116.030814833957 & -1.53081483395685 \tabularnewline
30 & 114.1 & 115.604021871210 & -1.50402187120955 \tabularnewline
31 & 112.3 & 115.079448092032 & -2.77944809203174 \tabularnewline
32 & 113 & 113.049234449876 & -0.0492344498761099 \tabularnewline
33 & 112.2 & 113.74515650287 & -1.54515650287001 \tabularnewline
34 & 113.7 & 112.817175661189 & 0.882824338810735 \tabularnewline
35 & 113.6 & 114.390297446411 & -0.790297446411273 \tabularnewline
36 & 115.8 & 114.224839395928 & 1.57516060407229 \tabularnewline
37 & 117.9 & 116.555305390484 & 1.34469460951635 \tabularnewline
38 & 120.1 & 118.766682553645 & 1.33331744635531 \tabularnewline
39 & 118.8 & 121.077117379305 & -2.27711737930488 \tabularnewline
40 & 114.7 & 119.588510336414 & -4.88851033641441 \tabularnewline
41 & 110.9 & 115.083609171867 & -4.18360917186746 \tabularnewline
42 & 112.9 & 110.937092930901 & 1.96290706909868 \tabularnewline
43 & 113.3 & 113.099674843075 & 0.200325156924890 \tabularnewline
44 & 114.3 & 113.516267196112 & 0.783732803887872 \tabularnewline
45 & 116.5 & 114.581181516253 & 1.91881848374744 \tabularnewline
46 & 114.3 & 116.940111698487 & -2.64011169848747 \tabularnewline
47 & 115.9 & 114.521438886590 & 1.37856111340960 \tabularnewline
48 & 120.1 & 116.235621114264 & 3.86437888573569 \tabularnewline
49 & 122.6 & 120.755696434435 & 1.84430356556513 \tabularnewline
50 & 122.4 & 123.408454761632 & -1.00845476163177 \tabularnewline
51 & 123.1 & 123.124927372043 & -0.0249273720431802 \tabularnewline
52 & 127.9 & 123.822862709953 & 4.07713729004709 \tabularnewline
53 & 130.9 & 128.960560193062 & 1.93943980693842 \tabularnewline
54 & 135 & 132.121198379821 & 2.87880162017862 \tabularnewline
55 & 134.9 & 136.459641187199 & -1.55964118719916 \tabularnewline
56 & 130.2 & 136.230460621032 & -6.03046062103195 \tabularnewline
57 & 130.8 & 131.030975019044 & -0.230975019043541 \tabularnewline
58 & 132.6 & 131.611844026623 & 0.98815597337662 \tabularnewline
59 & 138.6 & 133.493690126322 & 5.10630987367753 \tabularnewline
60 & 146.2 & 139.916630996262 & 6.28336900373839 \tabularnewline
61 & 149.3 & 148.037064267710 & 1.26293573228952 \tabularnewline
62 & 149.9 & 151.241669579669 & -1.34166957966880 \tabularnewline
63 & 156.8 & 151.730542970976 & 5.06945702902394 \tabularnewline
64 & 158.8 & 159.050431426439 & -0.250431426439178 \tabularnewline
65 & 156.7 & 161.029688916098 & -4.32968891609835 \tabularnewline
66 & 159.9 & 158.571073312650 & 1.32892668734951 \tabularnewline
67 & 158.2 & 161.881144464448 & -3.68114446444847 \tabularnewline
68 & 157.5 & 159.87624592114 & -2.37624592114005 \tabularnewline
69 & 159.1 & 158.979428347993 & 0.120571652007413 \tabularnewline
70 & 160.6 & 160.589414949012 & 0.0105850509879986 \tabularnewline
71 & 161.6 & 162.090291678154 & -0.490291678153795 \tabularnewline
72 & 161.3 & 163.049682237283 & -1.74968223728311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13605&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]81.5[/C][C]83.8[/C][C]-2.30000000000000[/C][/ROW]
[ROW][C]4[/C][C]82[/C][C]83.6094976558562[/C][C]-1.60949765585623[/C][/ROW]
[ROW][C]5[/C][C]85.8[/C][C]83.9761876226673[/C][C]1.82381237733269[/C][/ROW]
[ROW][C]6[/C][C]88.2[/C][C]87.9272487240413[/C][C]0.272751275958655[/C][/ROW]
[ROW][C]7[/C][C]88[/C][C]90.3498399229276[/C][C]-2.34983992292759[/C][/ROW]
[ROW][C]8[/C][C]88.8[/C][C]89.955209482197[/C][C]-1.15520948219701[/C][/ROW]
[ROW][C]9[/C][C]89[/C][C]90.6595268237902[/C][C]-1.65952682379020[/C][/ROW]
[ROW][C]10[/C][C]90.4[/C][C]90.7220730193983[/C][C]-0.322073019398246[/C][/ROW]
[ROW][C]11[/C][C]90.9[/C][C]92.0953966432327[/C][C]-1.19539664323268[/C][/ROW]
[ROW][C]12[/C][C]94.6[/C][C]92.496385398573[/C][C]2.10361460142705[/C][/ROW]
[ROW][C]13[/C][C]97.9[/C][C]96.3706217084629[/C][C]1.52937829153711[/C][/ROW]
[ROW][C]14[/C][C]101.7[/C][C]99.7972956865587[/C][C]1.90270431344128[/C][/ROW]
[ROW][C]15[/C][C]102.3[/C][C]103.754891178699[/C][C]-1.45489117869917[/C][/ROW]
[ROW][C]16[/C][C]103.5[/C][C]104.234386752605[/C][C]-0.734386752605133[/C][/ROW]
[ROW][C]17[/C][C]103.6[/C][C]105.373559623092[/C][C]-1.77355962309235[/C][/ROW]
[ROW][C]18[/C][C]102.3[/C][C]105.326660811928[/C][C]-3.02666081192807[/C][/ROW]
[ROW][C]19[/C][C]101.6[/C][C]103.77597125558[/C][C]-2.17597125558009[/C][/ROW]
[ROW][C]20[/C][C]104.3[/C][C]102.895741853416[/C][C]1.40425814658403[/C][/ROW]
[ROW][C]21[/C][C]110.8[/C][C]105.712052491984[/C][C]5.08794750801566[/C][/ROW]
[ROW][C]22[/C][C]112.1[/C][C]112.633472460314[/C][C]-0.533472460313646[/C][/ROW]
[ROW][C]23[/C][C]111.1[/C][C]113.889286480215[/C][C]-2.78928648021544[/C][/ROW]
[ROW][C]24[/C][C]114.4[/C][C]112.658257952837[/C][C]1.74174204716265[/C][/ROW]
[ROW][C]25[/C][C]115[/C][C]116.102521406263[/C][C]-1.10252140626270[/C][/ROW]
[ROW][C]26[/C][C]115.3[/C][C]116.611202748714[/C][C]-1.31120274871412[/C][/ROW]
[ROW][C]27[/C][C]114.1[/C][C]116.802599619463[/C][C]-2.7025996194629[/C][/ROW]
[ROW][C]28[/C][C]114.8[/C][C]115.378751113902[/C][C]-0.578751113902143[/C][/ROW]
[ROW][C]29[/C][C]114.5[/C][C]116.030814833957[/C][C]-1.53081483395685[/C][/ROW]
[ROW][C]30[/C][C]114.1[/C][C]115.604021871210[/C][C]-1.50402187120955[/C][/ROW]
[ROW][C]31[/C][C]112.3[/C][C]115.079448092032[/C][C]-2.77944809203174[/C][/ROW]
[ROW][C]32[/C][C]113[/C][C]113.049234449876[/C][C]-0.0492344498761099[/C][/ROW]
[ROW][C]33[/C][C]112.2[/C][C]113.74515650287[/C][C]-1.54515650287001[/C][/ROW]
[ROW][C]34[/C][C]113.7[/C][C]112.817175661189[/C][C]0.882824338810735[/C][/ROW]
[ROW][C]35[/C][C]113.6[/C][C]114.390297446411[/C][C]-0.790297446411273[/C][/ROW]
[ROW][C]36[/C][C]115.8[/C][C]114.224839395928[/C][C]1.57516060407229[/C][/ROW]
[ROW][C]37[/C][C]117.9[/C][C]116.555305390484[/C][C]1.34469460951635[/C][/ROW]
[ROW][C]38[/C][C]120.1[/C][C]118.766682553645[/C][C]1.33331744635531[/C][/ROW]
[ROW][C]39[/C][C]118.8[/C][C]121.077117379305[/C][C]-2.27711737930488[/C][/ROW]
[ROW][C]40[/C][C]114.7[/C][C]119.588510336414[/C][C]-4.88851033641441[/C][/ROW]
[ROW][C]41[/C][C]110.9[/C][C]115.083609171867[/C][C]-4.18360917186746[/C][/ROW]
[ROW][C]42[/C][C]112.9[/C][C]110.937092930901[/C][C]1.96290706909868[/C][/ROW]
[ROW][C]43[/C][C]113.3[/C][C]113.099674843075[/C][C]0.200325156924890[/C][/ROW]
[ROW][C]44[/C][C]114.3[/C][C]113.516267196112[/C][C]0.783732803887872[/C][/ROW]
[ROW][C]45[/C][C]116.5[/C][C]114.581181516253[/C][C]1.91881848374744[/C][/ROW]
[ROW][C]46[/C][C]114.3[/C][C]116.940111698487[/C][C]-2.64011169848747[/C][/ROW]
[ROW][C]47[/C][C]115.9[/C][C]114.521438886590[/C][C]1.37856111340960[/C][/ROW]
[ROW][C]48[/C][C]120.1[/C][C]116.235621114264[/C][C]3.86437888573569[/C][/ROW]
[ROW][C]49[/C][C]122.6[/C][C]120.755696434435[/C][C]1.84430356556513[/C][/ROW]
[ROW][C]50[/C][C]122.4[/C][C]123.408454761632[/C][C]-1.00845476163177[/C][/ROW]
[ROW][C]51[/C][C]123.1[/C][C]123.124927372043[/C][C]-0.0249273720431802[/C][/ROW]
[ROW][C]52[/C][C]127.9[/C][C]123.822862709953[/C][C]4.07713729004709[/C][/ROW]
[ROW][C]53[/C][C]130.9[/C][C]128.960560193062[/C][C]1.93943980693842[/C][/ROW]
[ROW][C]54[/C][C]135[/C][C]132.121198379821[/C][C]2.87880162017862[/C][/ROW]
[ROW][C]55[/C][C]134.9[/C][C]136.459641187199[/C][C]-1.55964118719916[/C][/ROW]
[ROW][C]56[/C][C]130.2[/C][C]136.230460621032[/C][C]-6.03046062103195[/C][/ROW]
[ROW][C]57[/C][C]130.8[/C][C]131.030975019044[/C][C]-0.230975019043541[/C][/ROW]
[ROW][C]58[/C][C]132.6[/C][C]131.611844026623[/C][C]0.98815597337662[/C][/ROW]
[ROW][C]59[/C][C]138.6[/C][C]133.493690126322[/C][C]5.10630987367753[/C][/ROW]
[ROW][C]60[/C][C]146.2[/C][C]139.916630996262[/C][C]6.28336900373839[/C][/ROW]
[ROW][C]61[/C][C]149.3[/C][C]148.037064267710[/C][C]1.26293573228952[/C][/ROW]
[ROW][C]62[/C][C]149.9[/C][C]151.241669579669[/C][C]-1.34166957966880[/C][/ROW]
[ROW][C]63[/C][C]156.8[/C][C]151.730542970976[/C][C]5.06945702902394[/C][/ROW]
[ROW][C]64[/C][C]158.8[/C][C]159.050431426439[/C][C]-0.250431426439178[/C][/ROW]
[ROW][C]65[/C][C]156.7[/C][C]161.029688916098[/C][C]-4.32968891609835[/C][/ROW]
[ROW][C]66[/C][C]159.9[/C][C]158.571073312650[/C][C]1.32892668734951[/C][/ROW]
[ROW][C]67[/C][C]158.2[/C][C]161.881144464448[/C][C]-3.68114446444847[/C][/ROW]
[ROW][C]68[/C][C]157.5[/C][C]159.87624592114[/C][C]-2.37624592114005[/C][/ROW]
[ROW][C]69[/C][C]159.1[/C][C]158.979428347993[/C][C]0.120571652007413[/C][/ROW]
[ROW][C]70[/C][C]160.6[/C][C]160.589414949012[/C][C]0.0105850509879986[/C][/ROW]
[ROW][C]71[/C][C]161.6[/C][C]162.090291678154[/C][C]-0.490291678153795[/C][/ROW]
[ROW][C]72[/C][C]161.3[/C][C]163.049682237283[/C][C]-1.74968223728311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13605&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13605&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
381.583.8-2.30000000000000
48283.6094976558562-1.60949765585623
585.883.97618762266731.82381237733269
688.287.92724872404130.272751275958655
78890.3498399229276-2.34983992292759
888.889.955209482197-1.15520948219701
98990.6595268237902-1.65952682379020
1090.490.7220730193983-0.322073019398246
1190.992.0953966432327-1.19539664323268
1294.692.4963853985732.10361460142705
1397.996.37062170846291.52937829153711
14101.799.79729568655871.90270431344128
15102.3103.754891178699-1.45489117869917
16103.5104.234386752605-0.734386752605133
17103.6105.373559623092-1.77355962309235
18102.3105.326660811928-3.02666081192807
19101.6103.77597125558-2.17597125558009
20104.3102.8957418534161.40425814658403
21110.8105.7120524919845.08794750801566
22112.1112.633472460314-0.533472460313646
23111.1113.889286480215-2.78928648021544
24114.4112.6582579528371.74174204716265
25115116.102521406263-1.10252140626270
26115.3116.611202748714-1.31120274871412
27114.1116.802599619463-2.7025996194629
28114.8115.378751113902-0.578751113902143
29114.5116.030814833957-1.53081483395685
30114.1115.604021871210-1.50402187120955
31112.3115.079448092032-2.77944809203174
32113113.049234449876-0.0492344498761099
33112.2113.74515650287-1.54515650287001
34113.7112.8171756611890.882824338810735
35113.6114.390297446411-0.790297446411273
36115.8114.2248393959281.57516060407229
37117.9116.5553053904841.34469460951635
38120.1118.7666825536451.33331744635531
39118.8121.077117379305-2.27711737930488
40114.7119.588510336414-4.88851033641441
41110.9115.083609171867-4.18360917186746
42112.9110.9370929309011.96290706909868
43113.3113.0996748430750.200325156924890
44114.3113.5162671961120.783732803887872
45116.5114.5811815162531.91881848374744
46114.3116.940111698487-2.64011169848747
47115.9114.5214388865901.37856111340960
48120.1116.2356211142643.86437888573569
49122.6120.7556964344351.84430356556513
50122.4123.408454761632-1.00845476163177
51123.1123.124927372043-0.0249273720431802
52127.9123.8228627099534.07713729004709
53130.9128.9605601930621.93943980693842
54135132.1211983798212.87880162017862
55134.9136.459641187199-1.55964118719916
56130.2136.230460621032-6.03046062103195
57130.8131.030975019044-0.230975019043541
58132.6131.6118440266230.98815597337662
59138.6133.4936901263225.10630987367753
60146.2139.9166309962626.28336900373839
61149.3148.0370642677101.26293573228952
62149.9151.241669579669-1.34166957966880
63156.8151.7305429709765.06945702902394
64158.8159.050431426439-0.250431426439178
65156.7161.029688916098-4.32968891609835
66159.9158.5710733126501.32892668734951
67158.2161.881144464448-3.68114446444847
68157.5159.87624592114-2.37624592114005
69159.1158.9794283479930.120571652007413
70160.6160.5894149490120.0105850509879986
71161.6162.090291678154-0.490291678153795
72161.3163.049682237283-1.74968223728311







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73162.604761120888157.818930998132167.390591243644
74163.909522241776156.855470759495170.963573724056
75165.214283362664156.220914841431174.207651883896
76166.519044483551155.721751517148177.316337449955
77167.823805604439155.286801307082180.360809901797
78169.128566725327154.881470118865183.375663331790
79170.433327846215154.486364166741186.380291525689
80171.738088967103154.089621506724189.386556427482
81173.042850087991153.683555644829192.402144531153
82174.347611208879153.262983068650195.432239349107
83175.652372329766152.824309524734198.480435134799
84176.957133450654152.36499518454201.549271716769

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 162.604761120888 & 157.818930998132 & 167.390591243644 \tabularnewline
74 & 163.909522241776 & 156.855470759495 & 170.963573724056 \tabularnewline
75 & 165.214283362664 & 156.220914841431 & 174.207651883896 \tabularnewline
76 & 166.519044483551 & 155.721751517148 & 177.316337449955 \tabularnewline
77 & 167.823805604439 & 155.286801307082 & 180.360809901797 \tabularnewline
78 & 169.128566725327 & 154.881470118865 & 183.375663331790 \tabularnewline
79 & 170.433327846215 & 154.486364166741 & 186.380291525689 \tabularnewline
80 & 171.738088967103 & 154.089621506724 & 189.386556427482 \tabularnewline
81 & 173.042850087991 & 153.683555644829 & 192.402144531153 \tabularnewline
82 & 174.347611208879 & 153.262983068650 & 195.432239349107 \tabularnewline
83 & 175.652372329766 & 152.824309524734 & 198.480435134799 \tabularnewline
84 & 176.957133450654 & 152.36499518454 & 201.549271716769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13605&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]73[/C][C]162.604761120888[/C][C]157.818930998132[/C][C]167.390591243644[/C][/ROW]
[ROW][C]74[/C][C]163.909522241776[/C][C]156.855470759495[/C][C]170.963573724056[/C][/ROW]
[ROW][C]75[/C][C]165.214283362664[/C][C]156.220914841431[/C][C]174.207651883896[/C][/ROW]
[ROW][C]76[/C][C]166.519044483551[/C][C]155.721751517148[/C][C]177.316337449955[/C][/ROW]
[ROW][C]77[/C][C]167.823805604439[/C][C]155.286801307082[/C][C]180.360809901797[/C][/ROW]
[ROW][C]78[/C][C]169.128566725327[/C][C]154.881470118865[/C][C]183.375663331790[/C][/ROW]
[ROW][C]79[/C][C]170.433327846215[/C][C]154.486364166741[/C][C]186.380291525689[/C][/ROW]
[ROW][C]80[/C][C]171.738088967103[/C][C]154.089621506724[/C][C]189.386556427482[/C][/ROW]
[ROW][C]81[/C][C]173.042850087991[/C][C]153.683555644829[/C][C]192.402144531153[/C][/ROW]
[ROW][C]82[/C][C]174.347611208879[/C][C]153.262983068650[/C][C]195.432239349107[/C][/ROW]
[ROW][C]83[/C][C]175.652372329766[/C][C]152.824309524734[/C][C]198.480435134799[/C][/ROW]
[ROW][C]84[/C][C]176.957133450654[/C][C]152.36499518454[/C][C]201.549271716769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13605&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13605&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
73162.604761120888157.818930998132167.390591243644
74163.909522241776156.855470759495170.963573724056
75165.214283362664156.220914841431174.207651883896
76166.519044483551155.721751517148177.316337449955
77167.823805604439155.286801307082180.360809901797
78169.128566725327154.881470118865183.375663331790
79170.433327846215154.486364166741186.380291525689
80171.738088967103154.089621506724189.386556427482
81173.042850087991153.683555644829192.402144531153
82174.347611208879153.262983068650195.432239349107
83175.652372329766152.824309524734198.480435134799
84176.957133450654152.36499518454201.549271716769



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