Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 May 2014 02:26:18 -0400
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/May/23/t1400826508yyn3umqv7mp6imv.htm/, Retrieved Tue, 14 May 2024 01:41:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235200, Retrieved Tue, 14 May 2024 01:41:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-23 06:26:18] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
812
100
113
213
149
134
228
138
162
291
182
2081
2752
125
144
274
257
186
327
209
213
375
400
1054
3377
101
120
221
222
167
297
185
189
298
237
1011
3013
110
109
215
176
134
202
139
169
262
214
1238
3748
127
160
138
134
163
172
163
193
226
344
1294
3524
141
186
135
161
131
170
146
160
151
151
1365




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235200&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235200&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0133783187667234
beta0.074757944762844
gamma0.809647756580098

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0133783187667234 \tabularnewline
beta & 0.074757944762844 \tabularnewline
gamma & 0.809647756580098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235200&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]0.0133783187667234[/C][/ROW]
[ROW][C]beta[/C][C]0.074757944762844[/C][/ROW]
[ROW][C]gamma[/C][C]0.809647756580098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235200&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
alpha0.0133783187667234
beta0.074757944762844
gamma0.809647756580098







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1327522486.15254470092265.847455299077
14125113.35237878973911.6476212102609
15144131.51999860378912.4800013962113
16274251.77902359728422.2209764027156
17257234.8240509537122.1759490462901
18186182.808073511813.19192648819029
19327278.53144324186148.4685567581386
20209145.66141849113963.3385815088615
21213173.68003517750539.3199648224949
22375315.14669822226159.8533017777385
23400197.865355217023202.134644782977
2410542299.67317925755-1245.67317925755
2533773286.2263976467690.7736023532407
26101149.085955567504-48.085955567504
27120170.801608918697-50.8016089186969
28221323.194935837434-102.194935837434
29222300.65498497516-78.6549849751604
30167219.205616411551-52.2056164115509
31297372.988933986417-75.9889339864166
32185228.746663600085-43.746663600085
33189236.617175826841-47.6171758268411
34298415.114977397789-117.114977397789
35237404.642097069587-167.642097069587
3610111435.45581377212-424.455813772117
3730133712.78923951941-699.789239519409
38110121.277982995122-11.2779829951221
39109142.59538257731-33.5953825773099
40215263.647938610875-48.6479386108752
41176259.19033804309-83.1903380430904
42134192.610309409615-58.6103094096147
43202337.381291188868-135.381291188868
44139208.03309025297-69.0330902529702
45169211.920294806394-42.9202948063943
46262341.641186987138-79.6411869871376
47214286.269927245539-72.269927245539
4812381159.5130666515978.4869333484148
4937483343.58655344631404.413446553689
50127119.2196741194547.780325880546
51160122.77941351042137.2205864895788
52138239.700519060602-101.700519060602
53134204.166495160531-70.1664951605307
54163154.0562648941698.943735105831
55172242.628224358985-70.6282243589852
56163161.9095906300411.09040936995899
57193188.8865783812984.11342161870218
58226296.075748688013-70.0757486880127
59344243.015942968641100.984057031359
6012941311.45037530459-17.4503753045863
6135243926.79139841071-402.791398410714
62141133.8206521444727.17934785552831
63186162.40894777846723.5910522215327
64135167.848721469996-32.8487214699958
65161157.4264169990113.57358300098872
66131172.385224542274-41.3852245422742
67170197.95394218184-27.9539421818404
68146173.492290205636-27.4922902056365
69160204.206178622247-44.2061786222467
70151253.881566028455-102.881566028455
71151340.884352605141-189.884352605141
7213651347.8892683972317.110731602766

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2752 & 2486.15254470092 & 265.847455299077 \tabularnewline
14 & 125 & 113.352378789739 & 11.6476212102609 \tabularnewline
15 & 144 & 131.519998603789 & 12.4800013962113 \tabularnewline
16 & 274 & 251.779023597284 & 22.2209764027156 \tabularnewline
17 & 257 & 234.82405095371 & 22.1759490462901 \tabularnewline
18 & 186 & 182.80807351181 & 3.19192648819029 \tabularnewline
19 & 327 & 278.531443241861 & 48.4685567581386 \tabularnewline
20 & 209 & 145.661418491139 & 63.3385815088615 \tabularnewline
21 & 213 & 173.680035177505 & 39.3199648224949 \tabularnewline
22 & 375 & 315.146698222261 & 59.8533017777385 \tabularnewline
23 & 400 & 197.865355217023 & 202.134644782977 \tabularnewline
24 & 1054 & 2299.67317925755 & -1245.67317925755 \tabularnewline
25 & 3377 & 3286.22639764676 & 90.7736023532407 \tabularnewline
26 & 101 & 149.085955567504 & -48.085955567504 \tabularnewline
27 & 120 & 170.801608918697 & -50.8016089186969 \tabularnewline
28 & 221 & 323.194935837434 & -102.194935837434 \tabularnewline
29 & 222 & 300.65498497516 & -78.6549849751604 \tabularnewline
30 & 167 & 219.205616411551 & -52.2056164115509 \tabularnewline
31 & 297 & 372.988933986417 & -75.9889339864166 \tabularnewline
32 & 185 & 228.746663600085 & -43.746663600085 \tabularnewline
33 & 189 & 236.617175826841 & -47.6171758268411 \tabularnewline
34 & 298 & 415.114977397789 & -117.114977397789 \tabularnewline
35 & 237 & 404.642097069587 & -167.642097069587 \tabularnewline
36 & 1011 & 1435.45581377212 & -424.455813772117 \tabularnewline
37 & 3013 & 3712.78923951941 & -699.789239519409 \tabularnewline
38 & 110 & 121.277982995122 & -11.2779829951221 \tabularnewline
39 & 109 & 142.59538257731 & -33.5953825773099 \tabularnewline
40 & 215 & 263.647938610875 & -48.6479386108752 \tabularnewline
41 & 176 & 259.19033804309 & -83.1903380430904 \tabularnewline
42 & 134 & 192.610309409615 & -58.6103094096147 \tabularnewline
43 & 202 & 337.381291188868 & -135.381291188868 \tabularnewline
44 & 139 & 208.03309025297 & -69.0330902529702 \tabularnewline
45 & 169 & 211.920294806394 & -42.9202948063943 \tabularnewline
46 & 262 & 341.641186987138 & -79.6411869871376 \tabularnewline
47 & 214 & 286.269927245539 & -72.269927245539 \tabularnewline
48 & 1238 & 1159.51306665159 & 78.4869333484148 \tabularnewline
49 & 3748 & 3343.58655344631 & 404.413446553689 \tabularnewline
50 & 127 & 119.219674119454 & 7.780325880546 \tabularnewline
51 & 160 & 122.779413510421 & 37.2205864895788 \tabularnewline
52 & 138 & 239.700519060602 & -101.700519060602 \tabularnewline
53 & 134 & 204.166495160531 & -70.1664951605307 \tabularnewline
54 & 163 & 154.056264894169 & 8.943735105831 \tabularnewline
55 & 172 & 242.628224358985 & -70.6282243589852 \tabularnewline
56 & 163 & 161.909590630041 & 1.09040936995899 \tabularnewline
57 & 193 & 188.886578381298 & 4.11342161870218 \tabularnewline
58 & 226 & 296.075748688013 & -70.0757486880127 \tabularnewline
59 & 344 & 243.015942968641 & 100.984057031359 \tabularnewline
60 & 1294 & 1311.45037530459 & -17.4503753045863 \tabularnewline
61 & 3524 & 3926.79139841071 & -402.791398410714 \tabularnewline
62 & 141 & 133.820652144472 & 7.17934785552831 \tabularnewline
63 & 186 & 162.408947778467 & 23.5910522215327 \tabularnewline
64 & 135 & 167.848721469996 & -32.8487214699958 \tabularnewline
65 & 161 & 157.426416999011 & 3.57358300098872 \tabularnewline
66 & 131 & 172.385224542274 & -41.3852245422742 \tabularnewline
67 & 170 & 197.95394218184 & -27.9539421818404 \tabularnewline
68 & 146 & 173.492290205636 & -27.4922902056365 \tabularnewline
69 & 160 & 204.206178622247 & -44.2061786222467 \tabularnewline
70 & 151 & 253.881566028455 & -102.881566028455 \tabularnewline
71 & 151 & 340.884352605141 & -189.884352605141 \tabularnewline
72 & 1365 & 1347.88926839723 & 17.110731602766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235200&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]2752[/C][C]2486.15254470092[/C][C]265.847455299077[/C][/ROW]
[ROW][C]14[/C][C]125[/C][C]113.352378789739[/C][C]11.6476212102609[/C][/ROW]
[ROW][C]15[/C][C]144[/C][C]131.519998603789[/C][C]12.4800013962113[/C][/ROW]
[ROW][C]16[/C][C]274[/C][C]251.779023597284[/C][C]22.2209764027156[/C][/ROW]
[ROW][C]17[/C][C]257[/C][C]234.82405095371[/C][C]22.1759490462901[/C][/ROW]
[ROW][C]18[/C][C]186[/C][C]182.80807351181[/C][C]3.19192648819029[/C][/ROW]
[ROW][C]19[/C][C]327[/C][C]278.531443241861[/C][C]48.4685567581386[/C][/ROW]
[ROW][C]20[/C][C]209[/C][C]145.661418491139[/C][C]63.3385815088615[/C][/ROW]
[ROW][C]21[/C][C]213[/C][C]173.680035177505[/C][C]39.3199648224949[/C][/ROW]
[ROW][C]22[/C][C]375[/C][C]315.146698222261[/C][C]59.8533017777385[/C][/ROW]
[ROW][C]23[/C][C]400[/C][C]197.865355217023[/C][C]202.134644782977[/C][/ROW]
[ROW][C]24[/C][C]1054[/C][C]2299.67317925755[/C][C]-1245.67317925755[/C][/ROW]
[ROW][C]25[/C][C]3377[/C][C]3286.22639764676[/C][C]90.7736023532407[/C][/ROW]
[ROW][C]26[/C][C]101[/C][C]149.085955567504[/C][C]-48.085955567504[/C][/ROW]
[ROW][C]27[/C][C]120[/C][C]170.801608918697[/C][C]-50.8016089186969[/C][/ROW]
[ROW][C]28[/C][C]221[/C][C]323.194935837434[/C][C]-102.194935837434[/C][/ROW]
[ROW][C]29[/C][C]222[/C][C]300.65498497516[/C][C]-78.6549849751604[/C][/ROW]
[ROW][C]30[/C][C]167[/C][C]219.205616411551[/C][C]-52.2056164115509[/C][/ROW]
[ROW][C]31[/C][C]297[/C][C]372.988933986417[/C][C]-75.9889339864166[/C][/ROW]
[ROW][C]32[/C][C]185[/C][C]228.746663600085[/C][C]-43.746663600085[/C][/ROW]
[ROW][C]33[/C][C]189[/C][C]236.617175826841[/C][C]-47.6171758268411[/C][/ROW]
[ROW][C]34[/C][C]298[/C][C]415.114977397789[/C][C]-117.114977397789[/C][/ROW]
[ROW][C]35[/C][C]237[/C][C]404.642097069587[/C][C]-167.642097069587[/C][/ROW]
[ROW][C]36[/C][C]1011[/C][C]1435.45581377212[/C][C]-424.455813772117[/C][/ROW]
[ROW][C]37[/C][C]3013[/C][C]3712.78923951941[/C][C]-699.789239519409[/C][/ROW]
[ROW][C]38[/C][C]110[/C][C]121.277982995122[/C][C]-11.2779829951221[/C][/ROW]
[ROW][C]39[/C][C]109[/C][C]142.59538257731[/C][C]-33.5953825773099[/C][/ROW]
[ROW][C]40[/C][C]215[/C][C]263.647938610875[/C][C]-48.6479386108752[/C][/ROW]
[ROW][C]41[/C][C]176[/C][C]259.19033804309[/C][C]-83.1903380430904[/C][/ROW]
[ROW][C]42[/C][C]134[/C][C]192.610309409615[/C][C]-58.6103094096147[/C][/ROW]
[ROW][C]43[/C][C]202[/C][C]337.381291188868[/C][C]-135.381291188868[/C][/ROW]
[ROW][C]44[/C][C]139[/C][C]208.03309025297[/C][C]-69.0330902529702[/C][/ROW]
[ROW][C]45[/C][C]169[/C][C]211.920294806394[/C][C]-42.9202948063943[/C][/ROW]
[ROW][C]46[/C][C]262[/C][C]341.641186987138[/C][C]-79.6411869871376[/C][/ROW]
[ROW][C]47[/C][C]214[/C][C]286.269927245539[/C][C]-72.269927245539[/C][/ROW]
[ROW][C]48[/C][C]1238[/C][C]1159.51306665159[/C][C]78.4869333484148[/C][/ROW]
[ROW][C]49[/C][C]3748[/C][C]3343.58655344631[/C][C]404.413446553689[/C][/ROW]
[ROW][C]50[/C][C]127[/C][C]119.219674119454[/C][C]7.780325880546[/C][/ROW]
[ROW][C]51[/C][C]160[/C][C]122.779413510421[/C][C]37.2205864895788[/C][/ROW]
[ROW][C]52[/C][C]138[/C][C]239.700519060602[/C][C]-101.700519060602[/C][/ROW]
[ROW][C]53[/C][C]134[/C][C]204.166495160531[/C][C]-70.1664951605307[/C][/ROW]
[ROW][C]54[/C][C]163[/C][C]154.056264894169[/C][C]8.943735105831[/C][/ROW]
[ROW][C]55[/C][C]172[/C][C]242.628224358985[/C][C]-70.6282243589852[/C][/ROW]
[ROW][C]56[/C][C]163[/C][C]161.909590630041[/C][C]1.09040936995899[/C][/ROW]
[ROW][C]57[/C][C]193[/C][C]188.886578381298[/C][C]4.11342161870218[/C][/ROW]
[ROW][C]58[/C][C]226[/C][C]296.075748688013[/C][C]-70.0757486880127[/C][/ROW]
[ROW][C]59[/C][C]344[/C][C]243.015942968641[/C][C]100.984057031359[/C][/ROW]
[ROW][C]60[/C][C]1294[/C][C]1311.45037530459[/C][C]-17.4503753045863[/C][/ROW]
[ROW][C]61[/C][C]3524[/C][C]3926.79139841071[/C][C]-402.791398410714[/C][/ROW]
[ROW][C]62[/C][C]141[/C][C]133.820652144472[/C][C]7.17934785552831[/C][/ROW]
[ROW][C]63[/C][C]186[/C][C]162.408947778467[/C][C]23.5910522215327[/C][/ROW]
[ROW][C]64[/C][C]135[/C][C]167.848721469996[/C][C]-32.8487214699958[/C][/ROW]
[ROW][C]65[/C][C]161[/C][C]157.426416999011[/C][C]3.57358300098872[/C][/ROW]
[ROW][C]66[/C][C]131[/C][C]172.385224542274[/C][C]-41.3852245422742[/C][/ROW]
[ROW][C]67[/C][C]170[/C][C]197.95394218184[/C][C]-27.9539421818404[/C][/ROW]
[ROW][C]68[/C][C]146[/C][C]173.492290205636[/C][C]-27.4922902056365[/C][/ROW]
[ROW][C]69[/C][C]160[/C][C]204.206178622247[/C][C]-44.2061786222467[/C][/ROW]
[ROW][C]70[/C][C]151[/C][C]253.881566028455[/C][C]-102.881566028455[/C][/ROW]
[ROW][C]71[/C][C]151[/C][C]340.884352605141[/C][C]-189.884352605141[/C][/ROW]
[ROW][C]72[/C][C]1365[/C][C]1347.88926839723[/C][C]17.110731602766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235200&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
1327522486.15254470092265.847455299077
14125113.35237878973911.6476212102609
15144131.51999860378912.4800013962113
16274251.77902359728422.2209764027156
17257234.8240509537122.1759490462901
18186182.808073511813.19192648819029
19327278.53144324186148.4685567581386
20209145.66141849113963.3385815088615
21213173.68003517750539.3199648224949
22375315.14669822226159.8533017777385
23400197.865355217023202.134644782977
2410542299.67317925755-1245.67317925755
2533773286.2263976467690.7736023532407
26101149.085955567504-48.085955567504
27120170.801608918697-50.8016089186969
28221323.194935837434-102.194935837434
29222300.65498497516-78.6549849751604
30167219.205616411551-52.2056164115509
31297372.988933986417-75.9889339864166
32185228.746663600085-43.746663600085
33189236.617175826841-47.6171758268411
34298415.114977397789-117.114977397789
35237404.642097069587-167.642097069587
3610111435.45581377212-424.455813772117
3730133712.78923951941-699.789239519409
38110121.277982995122-11.2779829951221
39109142.59538257731-33.5953825773099
40215263.647938610875-48.6479386108752
41176259.19033804309-83.1903380430904
42134192.610309409615-58.6103094096147
43202337.381291188868-135.381291188868
44139208.03309025297-69.0330902529702
45169211.920294806394-42.9202948063943
46262341.641186987138-79.6411869871376
47214286.269927245539-72.269927245539
4812381159.5130666515978.4869333484148
4937483343.58655344631404.413446553689
50127119.2196741194547.780325880546
51160122.77941351042137.2205864895788
52138239.700519060602-101.700519060602
53134204.166495160531-70.1664951605307
54163154.0562648941698.943735105831
55172242.628224358985-70.6282243589852
56163161.9095906300411.09040936995899
57193188.8865783812984.11342161870218
58226296.075748688013-70.0757486880127
59344243.015942968641100.984057031359
6012941311.45037530459-17.4503753045863
6135243926.79139841071-402.791398410714
62141133.8206521444727.17934785552831
63186162.40894777846723.5910522215327
64135167.848721469996-32.8487214699958
65161157.4264169990113.57358300098872
66131172.385224542274-41.3852245422742
67170197.95394218184-27.9539421818404
68146173.492290205636-27.4922902056365
69160204.206178622247-44.2061786222467
70151253.881566028455-102.881566028455
71151340.884352605141-189.884352605141
7213651347.8892683972317.110731602766







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733738.398345487033397.545774439054079.25091653501
74144.658395374858-196.194255046018485.511045795734
75187.355639993816-153.585993718766528.297273706399
76145.754482798438-195.191367207106486.700332803981
77165.183992159908-175.871903077176506.239887396991
78143.172870444804-197.891421762258484.237162651866
79180.860929244113-160.454652713445522.176511201671
80156.10821036799-185.169181483759497.385602219738
81174.088230062594-167.417606485388515.594066610576
82176.947134949416-164.708130053479518.602399952311
83195.24424230411-146.751668150033537.240152758253
841423.940957173651140.332798521451707.54911582585

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3738.39834548703 & 3397.54577443905 & 4079.25091653501 \tabularnewline
74 & 144.658395374858 & -196.194255046018 & 485.511045795734 \tabularnewline
75 & 187.355639993816 & -153.585993718766 & 528.297273706399 \tabularnewline
76 & 145.754482798438 & -195.191367207106 & 486.700332803981 \tabularnewline
77 & 165.183992159908 & -175.871903077176 & 506.239887396991 \tabularnewline
78 & 143.172870444804 & -197.891421762258 & 484.237162651866 \tabularnewline
79 & 180.860929244113 & -160.454652713445 & 522.176511201671 \tabularnewline
80 & 156.10821036799 & -185.169181483759 & 497.385602219738 \tabularnewline
81 & 174.088230062594 & -167.417606485388 & 515.594066610576 \tabularnewline
82 & 176.947134949416 & -164.708130053479 & 518.602399952311 \tabularnewline
83 & 195.24424230411 & -146.751668150033 & 537.240152758253 \tabularnewline
84 & 1423.94095717365 & 1140.33279852145 & 1707.54911582585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235200&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]3738.39834548703[/C][C]3397.54577443905[/C][C]4079.25091653501[/C][/ROW]
[ROW][C]74[/C][C]144.658395374858[/C][C]-196.194255046018[/C][C]485.511045795734[/C][/ROW]
[ROW][C]75[/C][C]187.355639993816[/C][C]-153.585993718766[/C][C]528.297273706399[/C][/ROW]
[ROW][C]76[/C][C]145.754482798438[/C][C]-195.191367207106[/C][C]486.700332803981[/C][/ROW]
[ROW][C]77[/C][C]165.183992159908[/C][C]-175.871903077176[/C][C]506.239887396991[/C][/ROW]
[ROW][C]78[/C][C]143.172870444804[/C][C]-197.891421762258[/C][C]484.237162651866[/C][/ROW]
[ROW][C]79[/C][C]180.860929244113[/C][C]-160.454652713445[/C][C]522.176511201671[/C][/ROW]
[ROW][C]80[/C][C]156.10821036799[/C][C]-185.169181483759[/C][C]497.385602219738[/C][/ROW]
[ROW][C]81[/C][C]174.088230062594[/C][C]-167.417606485388[/C][C]515.594066610576[/C][/ROW]
[ROW][C]82[/C][C]176.947134949416[/C][C]-164.708130053479[/C][C]518.602399952311[/C][/ROW]
[ROW][C]83[/C][C]195.24424230411[/C][C]-146.751668150033[/C][C]537.240152758253[/C][/ROW]
[ROW][C]84[/C][C]1423.94095717365[/C][C]1140.33279852145[/C][C]1707.54911582585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235200&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
733738.398345487033397.545774439054079.25091653501
74144.658395374858-196.194255046018485.511045795734
75187.355639993816-153.585993718766528.297273706399
76145.754482798438-195.191367207106486.700332803981
77165.183992159908-175.871903077176506.239887396991
78143.172870444804-197.891421762258484.237162651866
79180.860929244113-160.454652713445522.176511201671
80156.10821036799-185.169181483759497.385602219738
81174.088230062594-167.417606485388515.594066610576
82176.947134949416-164.708130053479518.602399952311
83195.24424230411-146.751668150033537.240152758253
841423.940957173651140.332798521451707.54911582585



Parameters (Session):
par1 = 750 ; par2 = 5 ; par3 = 0 ; par4 = P1 P5 Q1 Q3 P95 P99 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')