Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 16:54:09 +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/2010/Aug/16/t1281977686e8xjhxghrjs0o31.htm/, Retrieved Thu, 31 Oct 2024 23:22:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79033, Retrieved Thu, 31 Oct 2024 23:22:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-08-16 16:54:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
257
256
255
253
251
250
251
253
254
254
255
257
260
251
255
252
245
239
240
247
251
255
259
260
259
266
261
243
232
225
229
238
240
241
239
246
242
251
246
219
203
192
197
203
208
207
208
212
208
215
200
170
162
150
148
152
155
150
146
147
142
146
130
102
98
90
86
104
108
94
88
92
93
95
81
50
49
34
27
45
47
42
32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79033&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79033&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79033&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0285328075927933
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0285328075927933 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79033&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]0.0285328075927933[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79033&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79033&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
beta0.0285328075927933
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32552550
4253254-1
5251251.971467192407-0.971467192407204
6250249.9437485059240.0562514940764629
7251248.9453535189812.05464648101918
8253250.0039783516952.99602164830503
9254252.089463260931.9105367390701
10254253.1439762381050.856023761895244
11255253.1684009993981.83159900060224
12257254.2206616612692.77933833873089
13260256.2999639873233.70003601267661
14251259.40553640296-8.40553640295951
15255250.165702850064.83429714994037
16252254.303638920485-2.30363892048527
17245251.237909634404-6.23790963440379
18239244.059924559024-5.0599245590241
19240237.9155507051472.08444929485256
20247238.9750258958148.02497410418562
21251246.2040009378664.79599906213375
22255250.3408442563214.65915574367867
23259254.4737830507014.52621694929942
24260258.6029287280381.39707127196181
25259259.642791093834-0.64279109383449
26266258.6244504592327.37554954076825
27261265.83489559517-4.8348955951696
28243260.696942449421-17.6969424494214
29232242.191998995531-10.1919989955313
30225230.901192649206-5.90119264920588
31229223.7328150547785.26718494522191
32238227.88310262937610.1168973706243
33240237.1717661154882.8282338845122
34241239.2524635687421.747536431258
35239240.302325689496-1.30232568949648
36246238.2651666811757.73483331882505
37242245.485863192023-3.48586319202329
38251241.386401728279.6135982717295
39246250.660704678032-4.66070467803218
40219245.527721688207-26.527721688207
41203217.770811309402-14.7708113094023
42192201.349358592322-9.34935859232164
43197190.0825951424916.9174048575091
44203195.2799681243327.72003187566835
45208201.500242308456.49975769154966
46207206.6856986440630.314301355936919
47208205.6946665441782.3053334558218
48212206.760444180115.2395558198896
49208210.909943418191-2.90994341819101
50215206.8269145625348.17308543746617
51200214.060115636761-14.0601156367605
52170198.658941062564-28.6589410625644
53162167.841221011413-5.84122101141307
54150159.674554576187-9.67455457618743
55148147.3985123719190.601487628080918
56152145.4156745026816.58432549731944
57155149.6035437952245.39645620477609
58150152.757519841798-2.75751984179772
59146147.678840058718-1.67884005871841
60147143.6309380383443.36906196165609
61142144.727066835064-2.72706683506405
62146139.6492559617666.35074403823353
63130143.83046051948-13.8304605194805
64102127.435838650558-25.4358386505584
659898.7100827603807-0.710082760380686
669094.6898221056038-4.68982210560378
678686.5560083138202-0.556008313820172
6810482.54014383558221.4598561644181
69108101.152453782496.8475462175097
7094105.347833501197-11.3478335011973
718891.0240479513126-3.02404795131255
729284.93776337296647.06223662703363
739389.13926881182033.8607311881797
749590.24942631198014.75057368801987
758192.3849735169758-11.3849735169758
765078.0601282581669-28.0601282581669
774946.25949401754752.74050598245251
783445.3376883474517-11.3376883474517
792730.0141922672868-3.01419226728681
804522.928188899276622.0718111007234
814741.5579596386385.44204036136195
824243.713236329181-1.713236329181
833238.6643528866395-6.6643528866395

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 255 & 255 & 0 \tabularnewline
4 & 253 & 254 & -1 \tabularnewline
5 & 251 & 251.971467192407 & -0.971467192407204 \tabularnewline
6 & 250 & 249.943748505924 & 0.0562514940764629 \tabularnewline
7 & 251 & 248.945353518981 & 2.05464648101918 \tabularnewline
8 & 253 & 250.003978351695 & 2.99602164830503 \tabularnewline
9 & 254 & 252.08946326093 & 1.9105367390701 \tabularnewline
10 & 254 & 253.143976238105 & 0.856023761895244 \tabularnewline
11 & 255 & 253.168400999398 & 1.83159900060224 \tabularnewline
12 & 257 & 254.220661661269 & 2.77933833873089 \tabularnewline
13 & 260 & 256.299963987323 & 3.70003601267661 \tabularnewline
14 & 251 & 259.40553640296 & -8.40553640295951 \tabularnewline
15 & 255 & 250.16570285006 & 4.83429714994037 \tabularnewline
16 & 252 & 254.303638920485 & -2.30363892048527 \tabularnewline
17 & 245 & 251.237909634404 & -6.23790963440379 \tabularnewline
18 & 239 & 244.059924559024 & -5.0599245590241 \tabularnewline
19 & 240 & 237.915550705147 & 2.08444929485256 \tabularnewline
20 & 247 & 238.975025895814 & 8.02497410418562 \tabularnewline
21 & 251 & 246.204000937866 & 4.79599906213375 \tabularnewline
22 & 255 & 250.340844256321 & 4.65915574367867 \tabularnewline
23 & 259 & 254.473783050701 & 4.52621694929942 \tabularnewline
24 & 260 & 258.602928728038 & 1.39707127196181 \tabularnewline
25 & 259 & 259.642791093834 & -0.64279109383449 \tabularnewline
26 & 266 & 258.624450459232 & 7.37554954076825 \tabularnewline
27 & 261 & 265.83489559517 & -4.8348955951696 \tabularnewline
28 & 243 & 260.696942449421 & -17.6969424494214 \tabularnewline
29 & 232 & 242.191998995531 & -10.1919989955313 \tabularnewline
30 & 225 & 230.901192649206 & -5.90119264920588 \tabularnewline
31 & 229 & 223.732815054778 & 5.26718494522191 \tabularnewline
32 & 238 & 227.883102629376 & 10.1168973706243 \tabularnewline
33 & 240 & 237.171766115488 & 2.8282338845122 \tabularnewline
34 & 241 & 239.252463568742 & 1.747536431258 \tabularnewline
35 & 239 & 240.302325689496 & -1.30232568949648 \tabularnewline
36 & 246 & 238.265166681175 & 7.73483331882505 \tabularnewline
37 & 242 & 245.485863192023 & -3.48586319202329 \tabularnewline
38 & 251 & 241.38640172827 & 9.6135982717295 \tabularnewline
39 & 246 & 250.660704678032 & -4.66070467803218 \tabularnewline
40 & 219 & 245.527721688207 & -26.527721688207 \tabularnewline
41 & 203 & 217.770811309402 & -14.7708113094023 \tabularnewline
42 & 192 & 201.349358592322 & -9.34935859232164 \tabularnewline
43 & 197 & 190.082595142491 & 6.9174048575091 \tabularnewline
44 & 203 & 195.279968124332 & 7.72003187566835 \tabularnewline
45 & 208 & 201.50024230845 & 6.49975769154966 \tabularnewline
46 & 207 & 206.685698644063 & 0.314301355936919 \tabularnewline
47 & 208 & 205.694666544178 & 2.3053334558218 \tabularnewline
48 & 212 & 206.76044418011 & 5.2395558198896 \tabularnewline
49 & 208 & 210.909943418191 & -2.90994341819101 \tabularnewline
50 & 215 & 206.826914562534 & 8.17308543746617 \tabularnewline
51 & 200 & 214.060115636761 & -14.0601156367605 \tabularnewline
52 & 170 & 198.658941062564 & -28.6589410625644 \tabularnewline
53 & 162 & 167.841221011413 & -5.84122101141307 \tabularnewline
54 & 150 & 159.674554576187 & -9.67455457618743 \tabularnewline
55 & 148 & 147.398512371919 & 0.601487628080918 \tabularnewline
56 & 152 & 145.415674502681 & 6.58432549731944 \tabularnewline
57 & 155 & 149.603543795224 & 5.39645620477609 \tabularnewline
58 & 150 & 152.757519841798 & -2.75751984179772 \tabularnewline
59 & 146 & 147.678840058718 & -1.67884005871841 \tabularnewline
60 & 147 & 143.630938038344 & 3.36906196165609 \tabularnewline
61 & 142 & 144.727066835064 & -2.72706683506405 \tabularnewline
62 & 146 & 139.649255961766 & 6.35074403823353 \tabularnewline
63 & 130 & 143.83046051948 & -13.8304605194805 \tabularnewline
64 & 102 & 127.435838650558 & -25.4358386505584 \tabularnewline
65 & 98 & 98.7100827603807 & -0.710082760380686 \tabularnewline
66 & 90 & 94.6898221056038 & -4.68982210560378 \tabularnewline
67 & 86 & 86.5560083138202 & -0.556008313820172 \tabularnewline
68 & 104 & 82.540143835582 & 21.4598561644181 \tabularnewline
69 & 108 & 101.15245378249 & 6.8475462175097 \tabularnewline
70 & 94 & 105.347833501197 & -11.3478335011973 \tabularnewline
71 & 88 & 91.0240479513126 & -3.02404795131255 \tabularnewline
72 & 92 & 84.9377633729664 & 7.06223662703363 \tabularnewline
73 & 93 & 89.1392688118203 & 3.8607311881797 \tabularnewline
74 & 95 & 90.2494263119801 & 4.75057368801987 \tabularnewline
75 & 81 & 92.3849735169758 & -11.3849735169758 \tabularnewline
76 & 50 & 78.0601282581669 & -28.0601282581669 \tabularnewline
77 & 49 & 46.2594940175475 & 2.74050598245251 \tabularnewline
78 & 34 & 45.3376883474517 & -11.3376883474517 \tabularnewline
79 & 27 & 30.0141922672868 & -3.01419226728681 \tabularnewline
80 & 45 & 22.9281888992766 & 22.0718111007234 \tabularnewline
81 & 47 & 41.557959638638 & 5.44204036136195 \tabularnewline
82 & 42 & 43.713236329181 & -1.713236329181 \tabularnewline
83 & 32 & 38.6643528866395 & -6.6643528866395 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79033&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]255[/C][C]255[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]253[/C][C]254[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]251[/C][C]251.971467192407[/C][C]-0.971467192407204[/C][/ROW]
[ROW][C]6[/C][C]250[/C][C]249.943748505924[/C][C]0.0562514940764629[/C][/ROW]
[ROW][C]7[/C][C]251[/C][C]248.945353518981[/C][C]2.05464648101918[/C][/ROW]
[ROW][C]8[/C][C]253[/C][C]250.003978351695[/C][C]2.99602164830503[/C][/ROW]
[ROW][C]9[/C][C]254[/C][C]252.08946326093[/C][C]1.9105367390701[/C][/ROW]
[ROW][C]10[/C][C]254[/C][C]253.143976238105[/C][C]0.856023761895244[/C][/ROW]
[ROW][C]11[/C][C]255[/C][C]253.168400999398[/C][C]1.83159900060224[/C][/ROW]
[ROW][C]12[/C][C]257[/C][C]254.220661661269[/C][C]2.77933833873089[/C][/ROW]
[ROW][C]13[/C][C]260[/C][C]256.299963987323[/C][C]3.70003601267661[/C][/ROW]
[ROW][C]14[/C][C]251[/C][C]259.40553640296[/C][C]-8.40553640295951[/C][/ROW]
[ROW][C]15[/C][C]255[/C][C]250.16570285006[/C][C]4.83429714994037[/C][/ROW]
[ROW][C]16[/C][C]252[/C][C]254.303638920485[/C][C]-2.30363892048527[/C][/ROW]
[ROW][C]17[/C][C]245[/C][C]251.237909634404[/C][C]-6.23790963440379[/C][/ROW]
[ROW][C]18[/C][C]239[/C][C]244.059924559024[/C][C]-5.0599245590241[/C][/ROW]
[ROW][C]19[/C][C]240[/C][C]237.915550705147[/C][C]2.08444929485256[/C][/ROW]
[ROW][C]20[/C][C]247[/C][C]238.975025895814[/C][C]8.02497410418562[/C][/ROW]
[ROW][C]21[/C][C]251[/C][C]246.204000937866[/C][C]4.79599906213375[/C][/ROW]
[ROW][C]22[/C][C]255[/C][C]250.340844256321[/C][C]4.65915574367867[/C][/ROW]
[ROW][C]23[/C][C]259[/C][C]254.473783050701[/C][C]4.52621694929942[/C][/ROW]
[ROW][C]24[/C][C]260[/C][C]258.602928728038[/C][C]1.39707127196181[/C][/ROW]
[ROW][C]25[/C][C]259[/C][C]259.642791093834[/C][C]-0.64279109383449[/C][/ROW]
[ROW][C]26[/C][C]266[/C][C]258.624450459232[/C][C]7.37554954076825[/C][/ROW]
[ROW][C]27[/C][C]261[/C][C]265.83489559517[/C][C]-4.8348955951696[/C][/ROW]
[ROW][C]28[/C][C]243[/C][C]260.696942449421[/C][C]-17.6969424494214[/C][/ROW]
[ROW][C]29[/C][C]232[/C][C]242.191998995531[/C][C]-10.1919989955313[/C][/ROW]
[ROW][C]30[/C][C]225[/C][C]230.901192649206[/C][C]-5.90119264920588[/C][/ROW]
[ROW][C]31[/C][C]229[/C][C]223.732815054778[/C][C]5.26718494522191[/C][/ROW]
[ROW][C]32[/C][C]238[/C][C]227.883102629376[/C][C]10.1168973706243[/C][/ROW]
[ROW][C]33[/C][C]240[/C][C]237.171766115488[/C][C]2.8282338845122[/C][/ROW]
[ROW][C]34[/C][C]241[/C][C]239.252463568742[/C][C]1.747536431258[/C][/ROW]
[ROW][C]35[/C][C]239[/C][C]240.302325689496[/C][C]-1.30232568949648[/C][/ROW]
[ROW][C]36[/C][C]246[/C][C]238.265166681175[/C][C]7.73483331882505[/C][/ROW]
[ROW][C]37[/C][C]242[/C][C]245.485863192023[/C][C]-3.48586319202329[/C][/ROW]
[ROW][C]38[/C][C]251[/C][C]241.38640172827[/C][C]9.6135982717295[/C][/ROW]
[ROW][C]39[/C][C]246[/C][C]250.660704678032[/C][C]-4.66070467803218[/C][/ROW]
[ROW][C]40[/C][C]219[/C][C]245.527721688207[/C][C]-26.527721688207[/C][/ROW]
[ROW][C]41[/C][C]203[/C][C]217.770811309402[/C][C]-14.7708113094023[/C][/ROW]
[ROW][C]42[/C][C]192[/C][C]201.349358592322[/C][C]-9.34935859232164[/C][/ROW]
[ROW][C]43[/C][C]197[/C][C]190.082595142491[/C][C]6.9174048575091[/C][/ROW]
[ROW][C]44[/C][C]203[/C][C]195.279968124332[/C][C]7.72003187566835[/C][/ROW]
[ROW][C]45[/C][C]208[/C][C]201.50024230845[/C][C]6.49975769154966[/C][/ROW]
[ROW][C]46[/C][C]207[/C][C]206.685698644063[/C][C]0.314301355936919[/C][/ROW]
[ROW][C]47[/C][C]208[/C][C]205.694666544178[/C][C]2.3053334558218[/C][/ROW]
[ROW][C]48[/C][C]212[/C][C]206.76044418011[/C][C]5.2395558198896[/C][/ROW]
[ROW][C]49[/C][C]208[/C][C]210.909943418191[/C][C]-2.90994341819101[/C][/ROW]
[ROW][C]50[/C][C]215[/C][C]206.826914562534[/C][C]8.17308543746617[/C][/ROW]
[ROW][C]51[/C][C]200[/C][C]214.060115636761[/C][C]-14.0601156367605[/C][/ROW]
[ROW][C]52[/C][C]170[/C][C]198.658941062564[/C][C]-28.6589410625644[/C][/ROW]
[ROW][C]53[/C][C]162[/C][C]167.841221011413[/C][C]-5.84122101141307[/C][/ROW]
[ROW][C]54[/C][C]150[/C][C]159.674554576187[/C][C]-9.67455457618743[/C][/ROW]
[ROW][C]55[/C][C]148[/C][C]147.398512371919[/C][C]0.601487628080918[/C][/ROW]
[ROW][C]56[/C][C]152[/C][C]145.415674502681[/C][C]6.58432549731944[/C][/ROW]
[ROW][C]57[/C][C]155[/C][C]149.603543795224[/C][C]5.39645620477609[/C][/ROW]
[ROW][C]58[/C][C]150[/C][C]152.757519841798[/C][C]-2.75751984179772[/C][/ROW]
[ROW][C]59[/C][C]146[/C][C]147.678840058718[/C][C]-1.67884005871841[/C][/ROW]
[ROW][C]60[/C][C]147[/C][C]143.630938038344[/C][C]3.36906196165609[/C][/ROW]
[ROW][C]61[/C][C]142[/C][C]144.727066835064[/C][C]-2.72706683506405[/C][/ROW]
[ROW][C]62[/C][C]146[/C][C]139.649255961766[/C][C]6.35074403823353[/C][/ROW]
[ROW][C]63[/C][C]130[/C][C]143.83046051948[/C][C]-13.8304605194805[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]127.435838650558[/C][C]-25.4358386505584[/C][/ROW]
[ROW][C]65[/C][C]98[/C][C]98.7100827603807[/C][C]-0.710082760380686[/C][/ROW]
[ROW][C]66[/C][C]90[/C][C]94.6898221056038[/C][C]-4.68982210560378[/C][/ROW]
[ROW][C]67[/C][C]86[/C][C]86.5560083138202[/C][C]-0.556008313820172[/C][/ROW]
[ROW][C]68[/C][C]104[/C][C]82.540143835582[/C][C]21.4598561644181[/C][/ROW]
[ROW][C]69[/C][C]108[/C][C]101.15245378249[/C][C]6.8475462175097[/C][/ROW]
[ROW][C]70[/C][C]94[/C][C]105.347833501197[/C][C]-11.3478335011973[/C][/ROW]
[ROW][C]71[/C][C]88[/C][C]91.0240479513126[/C][C]-3.02404795131255[/C][/ROW]
[ROW][C]72[/C][C]92[/C][C]84.9377633729664[/C][C]7.06223662703363[/C][/ROW]
[ROW][C]73[/C][C]93[/C][C]89.1392688118203[/C][C]3.8607311881797[/C][/ROW]
[ROW][C]74[/C][C]95[/C][C]90.2494263119801[/C][C]4.75057368801987[/C][/ROW]
[ROW][C]75[/C][C]81[/C][C]92.3849735169758[/C][C]-11.3849735169758[/C][/ROW]
[ROW][C]76[/C][C]50[/C][C]78.0601282581669[/C][C]-28.0601282581669[/C][/ROW]
[ROW][C]77[/C][C]49[/C][C]46.2594940175475[/C][C]2.74050598245251[/C][/ROW]
[ROW][C]78[/C][C]34[/C][C]45.3376883474517[/C][C]-11.3376883474517[/C][/ROW]
[ROW][C]79[/C][C]27[/C][C]30.0141922672868[/C][C]-3.01419226728681[/C][/ROW]
[ROW][C]80[/C][C]45[/C][C]22.9281888992766[/C][C]22.0718111007234[/C][/ROW]
[ROW][C]81[/C][C]47[/C][C]41.557959638638[/C][C]5.44204036136195[/C][/ROW]
[ROW][C]82[/C][C]42[/C][C]43.713236329181[/C][C]-1.713236329181[/C][/ROW]
[ROW][C]83[/C][C]32[/C][C]38.6643528866395[/C][C]-6.6643528866395[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79033&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79033&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
32552550
4253254-1
5251251.971467192407-0.971467192407204
6250249.9437485059240.0562514940764629
7251248.9453535189812.05464648101918
8253250.0039783516952.99602164830503
9254252.089463260931.9105367390701
10254253.1439762381050.856023761895244
11255253.1684009993981.83159900060224
12257254.2206616612692.77933833873089
13260256.2999639873233.70003601267661
14251259.40553640296-8.40553640295951
15255250.165702850064.83429714994037
16252254.303638920485-2.30363892048527
17245251.237909634404-6.23790963440379
18239244.059924559024-5.0599245590241
19240237.9155507051472.08444929485256
20247238.9750258958148.02497410418562
21251246.2040009378664.79599906213375
22255250.3408442563214.65915574367867
23259254.4737830507014.52621694929942
24260258.6029287280381.39707127196181
25259259.642791093834-0.64279109383449
26266258.6244504592327.37554954076825
27261265.83489559517-4.8348955951696
28243260.696942449421-17.6969424494214
29232242.191998995531-10.1919989955313
30225230.901192649206-5.90119264920588
31229223.7328150547785.26718494522191
32238227.88310262937610.1168973706243
33240237.1717661154882.8282338845122
34241239.2524635687421.747536431258
35239240.302325689496-1.30232568949648
36246238.2651666811757.73483331882505
37242245.485863192023-3.48586319202329
38251241.386401728279.6135982717295
39246250.660704678032-4.66070467803218
40219245.527721688207-26.527721688207
41203217.770811309402-14.7708113094023
42192201.349358592322-9.34935859232164
43197190.0825951424916.9174048575091
44203195.2799681243327.72003187566835
45208201.500242308456.49975769154966
46207206.6856986440630.314301355936919
47208205.6946665441782.3053334558218
48212206.760444180115.2395558198896
49208210.909943418191-2.90994341819101
50215206.8269145625348.17308543746617
51200214.060115636761-14.0601156367605
52170198.658941062564-28.6589410625644
53162167.841221011413-5.84122101141307
54150159.674554576187-9.67455457618743
55148147.3985123719190.601487628080918
56152145.4156745026816.58432549731944
57155149.6035437952245.39645620477609
58150152.757519841798-2.75751984179772
59146147.678840058718-1.67884005871841
60147143.6309380383443.36906196165609
61142144.727066835064-2.72706683506405
62146139.6492559617666.35074403823353
63130143.83046051948-13.8304605194805
64102127.435838650558-25.4358386505584
659898.7100827603807-0.710082760380686
669094.6898221056038-4.68982210560378
678686.5560083138202-0.556008313820172
6810482.54014383558221.4598561644181
69108101.152453782496.8475462175097
7094105.347833501197-11.3478335011973
718891.0240479513126-3.02404795131255
729284.93776337296647.06223662703363
739389.13926881182033.8607311881797
749590.24942631198014.75057368801987
758192.3849735169758-11.3849735169758
765078.0601282581669-28.0601282581669
774946.25949401754752.74050598245251
783445.3376883474517-11.3376883474517
792730.0141922672868-3.01419226728681
804522.928188899276622.0718111007234
814741.5579596386385.44204036136195
824243.713236329181-1.713236329181
833238.6643528866395-6.6643528866395







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8428.474200187994510.294819733754246.6535806422349
8524.9484003759891-1.1304879081740851.0272886601522
8621.4226005639836-10.9717467651253.8169478930872
8717.8968007519781-20.035823273882555.8294247778388
8814.3710009399727-28.630361963184557.3723638431299
8910.8452011279672-36.910757605669758.6011598616041
907.31940131596176-44.967932065764559.606734697688
913.7936015039563-52.860226627097360.4474296350099
920.267801691950837-60.627540833790961.1631442176926
93-3.25799812005462-68.298468967137361.782472727028
94-6.78379793206009-75.894250683553562.3266548194333
95-10.3095977440655-83.431115462252162.811919974121

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
84 & 28.4742001879945 & 10.2948197337542 & 46.6535806422349 \tabularnewline
85 & 24.9484003759891 & -1.13048790817408 & 51.0272886601522 \tabularnewline
86 & 21.4226005639836 & -10.97174676512 & 53.8169478930872 \tabularnewline
87 & 17.8968007519781 & -20.0358232738825 & 55.8294247778388 \tabularnewline
88 & 14.3710009399727 & -28.6303619631845 & 57.3723638431299 \tabularnewline
89 & 10.8452011279672 & -36.9107576056697 & 58.6011598616041 \tabularnewline
90 & 7.31940131596176 & -44.9679320657645 & 59.606734697688 \tabularnewline
91 & 3.7936015039563 & -52.8602266270973 & 60.4474296350099 \tabularnewline
92 & 0.267801691950837 & -60.6275408337909 & 61.1631442176926 \tabularnewline
93 & -3.25799812005462 & -68.2984689671373 & 61.782472727028 \tabularnewline
94 & -6.78379793206009 & -75.8942506835535 & 62.3266548194333 \tabularnewline
95 & -10.3095977440655 & -83.4311154622521 & 62.811919974121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79033&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]84[/C][C]28.4742001879945[/C][C]10.2948197337542[/C][C]46.6535806422349[/C][/ROW]
[ROW][C]85[/C][C]24.9484003759891[/C][C]-1.13048790817408[/C][C]51.0272886601522[/C][/ROW]
[ROW][C]86[/C][C]21.4226005639836[/C][C]-10.97174676512[/C][C]53.8169478930872[/C][/ROW]
[ROW][C]87[/C][C]17.8968007519781[/C][C]-20.0358232738825[/C][C]55.8294247778388[/C][/ROW]
[ROW][C]88[/C][C]14.3710009399727[/C][C]-28.6303619631845[/C][C]57.3723638431299[/C][/ROW]
[ROW][C]89[/C][C]10.8452011279672[/C][C]-36.9107576056697[/C][C]58.6011598616041[/C][/ROW]
[ROW][C]90[/C][C]7.31940131596176[/C][C]-44.9679320657645[/C][C]59.606734697688[/C][/ROW]
[ROW][C]91[/C][C]3.7936015039563[/C][C]-52.8602266270973[/C][C]60.4474296350099[/C][/ROW]
[ROW][C]92[/C][C]0.267801691950837[/C][C]-60.6275408337909[/C][C]61.1631442176926[/C][/ROW]
[ROW][C]93[/C][C]-3.25799812005462[/C][C]-68.2984689671373[/C][C]61.782472727028[/C][/ROW]
[ROW][C]94[/C][C]-6.78379793206009[/C][C]-75.8942506835535[/C][C]62.3266548194333[/C][/ROW]
[ROW][C]95[/C][C]-10.3095977440655[/C][C]-83.4311154622521[/C][C]62.811919974121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79033&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79033&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
8428.474200187994510.294819733754246.6535806422349
8524.9484003759891-1.1304879081740851.0272886601522
8621.4226005639836-10.9717467651253.8169478930872
8717.8968007519781-20.035823273882555.8294247778388
8814.3710009399727-28.630361963184557.3723638431299
8910.8452011279672-36.910757605669758.6011598616041
907.31940131596176-44.967932065764559.606734697688
913.7936015039563-52.860226627097360.4474296350099
920.267801691950837-60.627540833790961.1631442176926
93-3.25799812005462-68.298468967137361.782472727028
94-6.78379793206009-75.894250683553562.3266548194333
95-10.3095977440655-83.431115462252162.811919974121



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
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=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')