Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Nov 2016 14:29:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/25/t1480084241z1xqrx2n9r50xco.htm/, Retrieved Sun, 19 May 2024 04:00:15 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 04:00:15 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
180
215
264
197
262
191
200
221
211
212
304
191
255
273
248
196
261
230
278
245
244
276
281
215
269
231
290
248
294
250
272
196
204
293
243
228
238
219
185
211
171
129
145
142
169
152
141
146
119
141
150
111
83
107
104
81
106
113
86
131




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.372234347770731
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.372234347770731 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.372234347770731[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.372234347770731
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
221518035
3264193.02820217197670.9717978280244
4197219.446343046606-22.4463430466064
5262211.09104318281550.9089568171852
6191230.041105519348-39.0411055193481
7200215.508665070105-15.5086650701053
8221209.7358072429411.2641927570601
9211213.928726687028-2.92872668702799
10212212.838554018883-0.8385540188834
11304212.52641541059491.4735845894062
12191246.576025508482-55.5760255084822
13255225.88871990164329.1112800983572
14273236.72493826182636.2750617381741
15248250.227762208278-2.22776220827816
16196249.398512595691-53.3985125956914
17261229.52175208770731.4782479122929
18230241.239037168305-11.2390371683048
19278237.0554814983940.9445185016101
20245252.296437637623-7.2964376376234
21244249.580452932533-5.58045293253286
22276247.50321667492628.4967833250737
23281258.11069822949922.889301770501
24215266.630882544969-51.6308825449689
25269247.41209465601521.5879053439849
26231255.44785452147-24.4478545214697
27290246.34752333927743.6524766607233
28248262.596474517658-14.5964745176581
29294257.16316534582636.8368346541745
30250270.87510046726-20.8751004672604
31272263.1046710601818.89532893981868
32196266.415818026301-70.4158180263008
33204240.204631930538-36.2046319305383
34293226.72802437759566.271975622405
35243251.396729998879-8.39672999887873
36228248.271178684339-20.2711786843392
37238240.72554970823-2.72554970823026
38219239.71100649027-20.7110064902705
39185232.001658497689-47.0016584976893
40211214.506026802659-3.50602680265928
41171213.200963202505-42.2009632025047
42129197.492315189524-68.4923151895237
43145171.997122917644-26.997122917644
44142161.947866476709-19.9478664767086
45169154.52258540933314.4774145906667
46152159.911576386897-7.9115763868966
47141156.966615910682-15.9666159106818
48146151.023293051063-5.02329305106343
49119149.15345083854-30.1534508385396
50141137.9293007326193.07069926738097
51150139.07232047161310.9276795283873
52111143.13997813351-32.1399781335095
5383131.176374335617-48.176374335617
54107113.24347305684-6.24347305684005
55104110.919437935703-6.91943793570306
5681108.343785468767-27.3437854687666
5710698.16548931921757.83451068078253
58113101.08176329258111.9182367074186
5986105.518140359945-19.5181403599446
6013198.25281811336332.747181886637

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 215 & 180 & 35 \tabularnewline
3 & 264 & 193.028202171976 & 70.9717978280244 \tabularnewline
4 & 197 & 219.446343046606 & -22.4463430466064 \tabularnewline
5 & 262 & 211.091043182815 & 50.9089568171852 \tabularnewline
6 & 191 & 230.041105519348 & -39.0411055193481 \tabularnewline
7 & 200 & 215.508665070105 & -15.5086650701053 \tabularnewline
8 & 221 & 209.73580724294 & 11.2641927570601 \tabularnewline
9 & 211 & 213.928726687028 & -2.92872668702799 \tabularnewline
10 & 212 & 212.838554018883 & -0.8385540188834 \tabularnewline
11 & 304 & 212.526415410594 & 91.4735845894062 \tabularnewline
12 & 191 & 246.576025508482 & -55.5760255084822 \tabularnewline
13 & 255 & 225.888719901643 & 29.1112800983572 \tabularnewline
14 & 273 & 236.724938261826 & 36.2750617381741 \tabularnewline
15 & 248 & 250.227762208278 & -2.22776220827816 \tabularnewline
16 & 196 & 249.398512595691 & -53.3985125956914 \tabularnewline
17 & 261 & 229.521752087707 & 31.4782479122929 \tabularnewline
18 & 230 & 241.239037168305 & -11.2390371683048 \tabularnewline
19 & 278 & 237.05548149839 & 40.9445185016101 \tabularnewline
20 & 245 & 252.296437637623 & -7.2964376376234 \tabularnewline
21 & 244 & 249.580452932533 & -5.58045293253286 \tabularnewline
22 & 276 & 247.503216674926 & 28.4967833250737 \tabularnewline
23 & 281 & 258.110698229499 & 22.889301770501 \tabularnewline
24 & 215 & 266.630882544969 & -51.6308825449689 \tabularnewline
25 & 269 & 247.412094656015 & 21.5879053439849 \tabularnewline
26 & 231 & 255.44785452147 & -24.4478545214697 \tabularnewline
27 & 290 & 246.347523339277 & 43.6524766607233 \tabularnewline
28 & 248 & 262.596474517658 & -14.5964745176581 \tabularnewline
29 & 294 & 257.163165345826 & 36.8368346541745 \tabularnewline
30 & 250 & 270.87510046726 & -20.8751004672604 \tabularnewline
31 & 272 & 263.104671060181 & 8.89532893981868 \tabularnewline
32 & 196 & 266.415818026301 & -70.4158180263008 \tabularnewline
33 & 204 & 240.204631930538 & -36.2046319305383 \tabularnewline
34 & 293 & 226.728024377595 & 66.271975622405 \tabularnewline
35 & 243 & 251.396729998879 & -8.39672999887873 \tabularnewline
36 & 228 & 248.271178684339 & -20.2711786843392 \tabularnewline
37 & 238 & 240.72554970823 & -2.72554970823026 \tabularnewline
38 & 219 & 239.71100649027 & -20.7110064902705 \tabularnewline
39 & 185 & 232.001658497689 & -47.0016584976893 \tabularnewline
40 & 211 & 214.506026802659 & -3.50602680265928 \tabularnewline
41 & 171 & 213.200963202505 & -42.2009632025047 \tabularnewline
42 & 129 & 197.492315189524 & -68.4923151895237 \tabularnewline
43 & 145 & 171.997122917644 & -26.997122917644 \tabularnewline
44 & 142 & 161.947866476709 & -19.9478664767086 \tabularnewline
45 & 169 & 154.522585409333 & 14.4774145906667 \tabularnewline
46 & 152 & 159.911576386897 & -7.9115763868966 \tabularnewline
47 & 141 & 156.966615910682 & -15.9666159106818 \tabularnewline
48 & 146 & 151.023293051063 & -5.02329305106343 \tabularnewline
49 & 119 & 149.15345083854 & -30.1534508385396 \tabularnewline
50 & 141 & 137.929300732619 & 3.07069926738097 \tabularnewline
51 & 150 & 139.072320471613 & 10.9276795283873 \tabularnewline
52 & 111 & 143.13997813351 & -32.1399781335095 \tabularnewline
53 & 83 & 131.176374335617 & -48.176374335617 \tabularnewline
54 & 107 & 113.24347305684 & -6.24347305684005 \tabularnewline
55 & 104 & 110.919437935703 & -6.91943793570306 \tabularnewline
56 & 81 & 108.343785468767 & -27.3437854687666 \tabularnewline
57 & 106 & 98.1654893192175 & 7.83451068078253 \tabularnewline
58 & 113 & 101.081763292581 & 11.9182367074186 \tabularnewline
59 & 86 & 105.518140359945 & -19.5181403599446 \tabularnewline
60 & 131 & 98.252818113363 & 32.747181886637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]215[/C][C]180[/C][C]35[/C][/ROW]
[ROW][C]3[/C][C]264[/C][C]193.028202171976[/C][C]70.9717978280244[/C][/ROW]
[ROW][C]4[/C][C]197[/C][C]219.446343046606[/C][C]-22.4463430466064[/C][/ROW]
[ROW][C]5[/C][C]262[/C][C]211.091043182815[/C][C]50.9089568171852[/C][/ROW]
[ROW][C]6[/C][C]191[/C][C]230.041105519348[/C][C]-39.0411055193481[/C][/ROW]
[ROW][C]7[/C][C]200[/C][C]215.508665070105[/C][C]-15.5086650701053[/C][/ROW]
[ROW][C]8[/C][C]221[/C][C]209.73580724294[/C][C]11.2641927570601[/C][/ROW]
[ROW][C]9[/C][C]211[/C][C]213.928726687028[/C][C]-2.92872668702799[/C][/ROW]
[ROW][C]10[/C][C]212[/C][C]212.838554018883[/C][C]-0.8385540188834[/C][/ROW]
[ROW][C]11[/C][C]304[/C][C]212.526415410594[/C][C]91.4735845894062[/C][/ROW]
[ROW][C]12[/C][C]191[/C][C]246.576025508482[/C][C]-55.5760255084822[/C][/ROW]
[ROW][C]13[/C][C]255[/C][C]225.888719901643[/C][C]29.1112800983572[/C][/ROW]
[ROW][C]14[/C][C]273[/C][C]236.724938261826[/C][C]36.2750617381741[/C][/ROW]
[ROW][C]15[/C][C]248[/C][C]250.227762208278[/C][C]-2.22776220827816[/C][/ROW]
[ROW][C]16[/C][C]196[/C][C]249.398512595691[/C][C]-53.3985125956914[/C][/ROW]
[ROW][C]17[/C][C]261[/C][C]229.521752087707[/C][C]31.4782479122929[/C][/ROW]
[ROW][C]18[/C][C]230[/C][C]241.239037168305[/C][C]-11.2390371683048[/C][/ROW]
[ROW][C]19[/C][C]278[/C][C]237.05548149839[/C][C]40.9445185016101[/C][/ROW]
[ROW][C]20[/C][C]245[/C][C]252.296437637623[/C][C]-7.2964376376234[/C][/ROW]
[ROW][C]21[/C][C]244[/C][C]249.580452932533[/C][C]-5.58045293253286[/C][/ROW]
[ROW][C]22[/C][C]276[/C][C]247.503216674926[/C][C]28.4967833250737[/C][/ROW]
[ROW][C]23[/C][C]281[/C][C]258.110698229499[/C][C]22.889301770501[/C][/ROW]
[ROW][C]24[/C][C]215[/C][C]266.630882544969[/C][C]-51.6308825449689[/C][/ROW]
[ROW][C]25[/C][C]269[/C][C]247.412094656015[/C][C]21.5879053439849[/C][/ROW]
[ROW][C]26[/C][C]231[/C][C]255.44785452147[/C][C]-24.4478545214697[/C][/ROW]
[ROW][C]27[/C][C]290[/C][C]246.347523339277[/C][C]43.6524766607233[/C][/ROW]
[ROW][C]28[/C][C]248[/C][C]262.596474517658[/C][C]-14.5964745176581[/C][/ROW]
[ROW][C]29[/C][C]294[/C][C]257.163165345826[/C][C]36.8368346541745[/C][/ROW]
[ROW][C]30[/C][C]250[/C][C]270.87510046726[/C][C]-20.8751004672604[/C][/ROW]
[ROW][C]31[/C][C]272[/C][C]263.104671060181[/C][C]8.89532893981868[/C][/ROW]
[ROW][C]32[/C][C]196[/C][C]266.415818026301[/C][C]-70.4158180263008[/C][/ROW]
[ROW][C]33[/C][C]204[/C][C]240.204631930538[/C][C]-36.2046319305383[/C][/ROW]
[ROW][C]34[/C][C]293[/C][C]226.728024377595[/C][C]66.271975622405[/C][/ROW]
[ROW][C]35[/C][C]243[/C][C]251.396729998879[/C][C]-8.39672999887873[/C][/ROW]
[ROW][C]36[/C][C]228[/C][C]248.271178684339[/C][C]-20.2711786843392[/C][/ROW]
[ROW][C]37[/C][C]238[/C][C]240.72554970823[/C][C]-2.72554970823026[/C][/ROW]
[ROW][C]38[/C][C]219[/C][C]239.71100649027[/C][C]-20.7110064902705[/C][/ROW]
[ROW][C]39[/C][C]185[/C][C]232.001658497689[/C][C]-47.0016584976893[/C][/ROW]
[ROW][C]40[/C][C]211[/C][C]214.506026802659[/C][C]-3.50602680265928[/C][/ROW]
[ROW][C]41[/C][C]171[/C][C]213.200963202505[/C][C]-42.2009632025047[/C][/ROW]
[ROW][C]42[/C][C]129[/C][C]197.492315189524[/C][C]-68.4923151895237[/C][/ROW]
[ROW][C]43[/C][C]145[/C][C]171.997122917644[/C][C]-26.997122917644[/C][/ROW]
[ROW][C]44[/C][C]142[/C][C]161.947866476709[/C][C]-19.9478664767086[/C][/ROW]
[ROW][C]45[/C][C]169[/C][C]154.522585409333[/C][C]14.4774145906667[/C][/ROW]
[ROW][C]46[/C][C]152[/C][C]159.911576386897[/C][C]-7.9115763868966[/C][/ROW]
[ROW][C]47[/C][C]141[/C][C]156.966615910682[/C][C]-15.9666159106818[/C][/ROW]
[ROW][C]48[/C][C]146[/C][C]151.023293051063[/C][C]-5.02329305106343[/C][/ROW]
[ROW][C]49[/C][C]119[/C][C]149.15345083854[/C][C]-30.1534508385396[/C][/ROW]
[ROW][C]50[/C][C]141[/C][C]137.929300732619[/C][C]3.07069926738097[/C][/ROW]
[ROW][C]51[/C][C]150[/C][C]139.072320471613[/C][C]10.9276795283873[/C][/ROW]
[ROW][C]52[/C][C]111[/C][C]143.13997813351[/C][C]-32.1399781335095[/C][/ROW]
[ROW][C]53[/C][C]83[/C][C]131.176374335617[/C][C]-48.176374335617[/C][/ROW]
[ROW][C]54[/C][C]107[/C][C]113.24347305684[/C][C]-6.24347305684005[/C][/ROW]
[ROW][C]55[/C][C]104[/C][C]110.919437935703[/C][C]-6.91943793570306[/C][/ROW]
[ROW][C]56[/C][C]81[/C][C]108.343785468767[/C][C]-27.3437854687666[/C][/ROW]
[ROW][C]57[/C][C]106[/C][C]98.1654893192175[/C][C]7.83451068078253[/C][/ROW]
[ROW][C]58[/C][C]113[/C][C]101.081763292581[/C][C]11.9182367074186[/C][/ROW]
[ROW][C]59[/C][C]86[/C][C]105.518140359945[/C][C]-19.5181403599446[/C][/ROW]
[ROW][C]60[/C][C]131[/C][C]98.252818113363[/C][C]32.747181886637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
221518035
3264193.02820217197670.9717978280244
4197219.446343046606-22.4463430466064
5262211.09104318281550.9089568171852
6191230.041105519348-39.0411055193481
7200215.508665070105-15.5086650701053
8221209.7358072429411.2641927570601
9211213.928726687028-2.92872668702799
10212212.838554018883-0.8385540188834
11304212.52641541059491.4735845894062
12191246.576025508482-55.5760255084822
13255225.88871990164329.1112800983572
14273236.72493826182636.2750617381741
15248250.227762208278-2.22776220827816
16196249.398512595691-53.3985125956914
17261229.52175208770731.4782479122929
18230241.239037168305-11.2390371683048
19278237.0554814983940.9445185016101
20245252.296437637623-7.2964376376234
21244249.580452932533-5.58045293253286
22276247.50321667492628.4967833250737
23281258.11069822949922.889301770501
24215266.630882544969-51.6308825449689
25269247.41209465601521.5879053439849
26231255.44785452147-24.4478545214697
27290246.34752333927743.6524766607233
28248262.596474517658-14.5964745176581
29294257.16316534582636.8368346541745
30250270.87510046726-20.8751004672604
31272263.1046710601818.89532893981868
32196266.415818026301-70.4158180263008
33204240.204631930538-36.2046319305383
34293226.72802437759566.271975622405
35243251.396729998879-8.39672999887873
36228248.271178684339-20.2711786843392
37238240.72554970823-2.72554970823026
38219239.71100649027-20.7110064902705
39185232.001658497689-47.0016584976893
40211214.506026802659-3.50602680265928
41171213.200963202505-42.2009632025047
42129197.492315189524-68.4923151895237
43145171.997122917644-26.997122917644
44142161.947866476709-19.9478664767086
45169154.52258540933314.4774145906667
46152159.911576386897-7.9115763868966
47141156.966615910682-15.9666159106818
48146151.023293051063-5.02329305106343
49119149.15345083854-30.1534508385396
50141137.9293007326193.07069926738097
51150139.07232047161310.9276795283873
52111143.13997813351-32.1399781335095
5383131.176374335617-48.176374335617
54107113.24347305684-6.24347305684005
55104110.919437935703-6.91943793570306
5681108.343785468767-27.3437854687666
5710698.16548931921757.83451068078253
58113101.08176329258111.9182367074186
5986105.518140359945-19.5181403599446
6013198.25281811336332.747181886637







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61110.44244400426543.3760199130432177.508868095486
62110.44244400426538.8803881555549182.004499852975
63110.44244400426534.6509508523011186.233937156229
64110.44244400426530.6453699281156190.239518080414
65110.44244400426526.8314660885345194.053421919995
66110.44244400426523.1841021398045197.700785868725
67110.44244400426519.6831975230092201.20169048552
68110.44244400426516.3124093779268204.572478630603
69110.44244400426513.0582254898367207.826662518693
70110.4424440042659.9093220365463210.975565971983
71110.4424440042656.85609736781636214.028790640713
72110.4424440042653.89032621021653216.994561798313

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 110.442444004265 & 43.3760199130432 & 177.508868095486 \tabularnewline
62 & 110.442444004265 & 38.8803881555549 & 182.004499852975 \tabularnewline
63 & 110.442444004265 & 34.6509508523011 & 186.233937156229 \tabularnewline
64 & 110.442444004265 & 30.6453699281156 & 190.239518080414 \tabularnewline
65 & 110.442444004265 & 26.8314660885345 & 194.053421919995 \tabularnewline
66 & 110.442444004265 & 23.1841021398045 & 197.700785868725 \tabularnewline
67 & 110.442444004265 & 19.6831975230092 & 201.20169048552 \tabularnewline
68 & 110.442444004265 & 16.3124093779268 & 204.572478630603 \tabularnewline
69 & 110.442444004265 & 13.0582254898367 & 207.826662518693 \tabularnewline
70 & 110.442444004265 & 9.9093220365463 & 210.975565971983 \tabularnewline
71 & 110.442444004265 & 6.85609736781636 & 214.028790640713 \tabularnewline
72 & 110.442444004265 & 3.89032621021653 & 216.994561798313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]110.442444004265[/C][C]43.3760199130432[/C][C]177.508868095486[/C][/ROW]
[ROW][C]62[/C][C]110.442444004265[/C][C]38.8803881555549[/C][C]182.004499852975[/C][/ROW]
[ROW][C]63[/C][C]110.442444004265[/C][C]34.6509508523011[/C][C]186.233937156229[/C][/ROW]
[ROW][C]64[/C][C]110.442444004265[/C][C]30.6453699281156[/C][C]190.239518080414[/C][/ROW]
[ROW][C]65[/C][C]110.442444004265[/C][C]26.8314660885345[/C][C]194.053421919995[/C][/ROW]
[ROW][C]66[/C][C]110.442444004265[/C][C]23.1841021398045[/C][C]197.700785868725[/C][/ROW]
[ROW][C]67[/C][C]110.442444004265[/C][C]19.6831975230092[/C][C]201.20169048552[/C][/ROW]
[ROW][C]68[/C][C]110.442444004265[/C][C]16.3124093779268[/C][C]204.572478630603[/C][/ROW]
[ROW][C]69[/C][C]110.442444004265[/C][C]13.0582254898367[/C][C]207.826662518693[/C][/ROW]
[ROW][C]70[/C][C]110.442444004265[/C][C]9.9093220365463[/C][C]210.975565971983[/C][/ROW]
[ROW][C]71[/C][C]110.442444004265[/C][C]6.85609736781636[/C][C]214.028790640713[/C][/ROW]
[ROW][C]72[/C][C]110.442444004265[/C][C]3.89032621021653[/C][C]216.994561798313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61110.44244400426543.3760199130432177.508868095486
62110.44244400426538.8803881555549182.004499852975
63110.44244400426534.6509508523011186.233937156229
64110.44244400426530.6453699281156190.239518080414
65110.44244400426526.8314660885345194.053421919995
66110.44244400426523.1841021398045197.700785868725
67110.44244400426519.6831975230092201.20169048552
68110.44244400426516.3124093779268204.572478630603
69110.44244400426513.0582254898367207.826662518693
70110.4424440042659.9093220365463210.975565971983
71110.4424440042656.85609736781636214.028790640713
72110.4424440042653.89032621021653216.994561798313



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')