Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 Jun 2016 09:09:49 +0100
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/Jun/22/t1466583040b5fbbny0stkalyr.htm/, Retrieved Wed, 08 May 2024 22:18:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295774, Retrieved Wed, 08 May 2024 22:18:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [FEDEX23] [2016-06-22 08:09:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295774&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295774&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.127737177175837
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.127737177175837 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295774&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]0.127737177175837[/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=295774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295774&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
alpha0.127737177175837
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2990005179993810012
3429993283461.646358554146531.353641446
4649994302179.147840466347814.852159534
5770004346608.035235156423395.964764844
6589996400691.440601857189304.559398143
7710007424872.670645891285134.329354109
8970001461294.92499351508706.07500649
9710007526275.603027039183731.396972961
10289993549744.933034938-259751.933034938
11699997516564.954343088183432.045656912
12919998539996.046058891380001.953941109
13199997588536.422976631-388539.422976631
1418538905.493864067-538887.493864067
1557470069.526582511-470012.526582511
16559998410031.453199578149966.546800422
1740001429187.756558672-389186.756558672
18279999379474.138881647-99475.1388816475
1925366767.465441732-366742.465441732
20220001319920.818155698-99919.818155698
21880005307157.342640566572847.657359434
22309998380331.285343451-70333.2853434511
23149994371347.110012176-221353.110012176
24979996343072.088580128636923.911419872
25210007424430.951100695-214423.951100695
26910004397041.040868203512962.959131797
27330002462565.481263463-132563.481263463
28770004445632.196370266324371.803629734
29639999487066.534921363152932.465078637
30419998506601.69630905-86603.6963090502
31600006495539.184609539104466.815390461
32110001508883.480716065-398882.480716065
3389996457931.3586045-367935.3586045
34330002410932.334513182-80930.3345131822
35759995400594.522034572359400.477965428
36389999446503.324565522-56504.3245655223
37809998439285.621647295370712.378352705
38490005486639.374402213365.62559778965
39979996487069.289915503492926.710084497
40380005550034.356416268-170029.356416268
41880005528315.28639063351689.71360937
42380005573239.137648869-193234.137648869
43270004548555.954371596-278551.954371596
44860001512974.514023355347026.485976645
45910004557302.697747262352701.302252738
4680002602355.766483268-522353.766483268
47529999535631.770865529-5632.77086552943
48979996534912.256615488445083.743384512
49610001591765.9976022818235.0023977197
50419998594095.28533436-174097.28533436
51839996571856.589551772268139.410448228
5270007606107.960932022-536100.960932022
53270004537627.937501312-267623.937501312
54339996503442.411180212-163446.411180212
55710007482564.227996531227442.772003469
56539993511617.12566130128375.8743386989
57419998515241.779749223-95243.7797492227
58630005503075.6081805126929.3918195
59649994519289.210392168130704.789607832
60190002535985.071260034-345983.071260034
61990005491790.170386651498214.829613349
62570007555430.72634860114576.2736513992
63720001557292.658398573162708.341601427
64669998578076.56265770191921.4373422989
65800003589818.347585752210184.652414248
66940002616666.741770832323335.258229168
67770004657968.674938446112035.325061554
68279999672279.751105786-392280.751105786
69419998622170.915299116-202172.915299116
7050003596345.917797398-546342.917797398
71110001526557.615707948-416556.615707948
72220001473347.849483495-253346.849483495
73699997440986.038084082259010.961915918
74899994474071.367216819425922.632783181
75130005528477.522023843-398472.522023843
76270004477577.766878381-207573.766878381
77399994451062.879841581-51068.8798415815
78570007444539.485289086125467.514710914
79320007460566.351445526-140559.351445526
80559998442611.696666208117386.303333792
81110001457606.291693173-347605.291693173
82559998413204.172960904146793.827039096
83660004431955.202053716228048.797946284
84110001461085.511761717-351084.511761717
85589996416238.967279118173757.032720882
86789993438434.200153333351558.799846667
8725483341.328857071-483316.328857071
88369995421603.865325881-51608.8653258808
8929999415011.494551905-385012.494551905
90289993365831.085320417-75838.0853204174
9125356143.742379167-356118.742379167
92289993310654.139488243-20661.1394882432
93369995308014.94385277961980.0561472212
94759995315932.101266225444062.898733775
95589996372655.442438997217340.557561003
96690002400417.911747661289584.088252339
97490005437408.56573605452596.4342639465
98110001444127.085778444-334126.085778444
99630005401446.762760295228558.237239705
10039993430642.14680558-390649.14680558
101380005380741.727526486-736.72752648592
102220001380647.620031905-160646.620031905
103399994360127.0742661939866.9257338098
104470001365219.562822106104781.437177894

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 990005 & 179993 & 810012 \tabularnewline
3 & 429993 & 283461.646358554 & 146531.353641446 \tabularnewline
4 & 649994 & 302179.147840466 & 347814.852159534 \tabularnewline
5 & 770004 & 346608.035235156 & 423395.964764844 \tabularnewline
6 & 589996 & 400691.440601857 & 189304.559398143 \tabularnewline
7 & 710007 & 424872.670645891 & 285134.329354109 \tabularnewline
8 & 970001 & 461294.92499351 & 508706.07500649 \tabularnewline
9 & 710007 & 526275.603027039 & 183731.396972961 \tabularnewline
10 & 289993 & 549744.933034938 & -259751.933034938 \tabularnewline
11 & 699997 & 516564.954343088 & 183432.045656912 \tabularnewline
12 & 919998 & 539996.046058891 & 380001.953941109 \tabularnewline
13 & 199997 & 588536.422976631 & -388539.422976631 \tabularnewline
14 & 18 & 538905.493864067 & -538887.493864067 \tabularnewline
15 & 57 & 470069.526582511 & -470012.526582511 \tabularnewline
16 & 559998 & 410031.453199578 & 149966.546800422 \tabularnewline
17 & 40001 & 429187.756558672 & -389186.756558672 \tabularnewline
18 & 279999 & 379474.138881647 & -99475.1388816475 \tabularnewline
19 & 25 & 366767.465441732 & -366742.465441732 \tabularnewline
20 & 220001 & 319920.818155698 & -99919.818155698 \tabularnewline
21 & 880005 & 307157.342640566 & 572847.657359434 \tabularnewline
22 & 309998 & 380331.285343451 & -70333.2853434511 \tabularnewline
23 & 149994 & 371347.110012176 & -221353.110012176 \tabularnewline
24 & 979996 & 343072.088580128 & 636923.911419872 \tabularnewline
25 & 210007 & 424430.951100695 & -214423.951100695 \tabularnewline
26 & 910004 & 397041.040868203 & 512962.959131797 \tabularnewline
27 & 330002 & 462565.481263463 & -132563.481263463 \tabularnewline
28 & 770004 & 445632.196370266 & 324371.803629734 \tabularnewline
29 & 639999 & 487066.534921363 & 152932.465078637 \tabularnewline
30 & 419998 & 506601.69630905 & -86603.6963090502 \tabularnewline
31 & 600006 & 495539.184609539 & 104466.815390461 \tabularnewline
32 & 110001 & 508883.480716065 & -398882.480716065 \tabularnewline
33 & 89996 & 457931.3586045 & -367935.3586045 \tabularnewline
34 & 330002 & 410932.334513182 & -80930.3345131822 \tabularnewline
35 & 759995 & 400594.522034572 & 359400.477965428 \tabularnewline
36 & 389999 & 446503.324565522 & -56504.3245655223 \tabularnewline
37 & 809998 & 439285.621647295 & 370712.378352705 \tabularnewline
38 & 490005 & 486639.37440221 & 3365.62559778965 \tabularnewline
39 & 979996 & 487069.289915503 & 492926.710084497 \tabularnewline
40 & 380005 & 550034.356416268 & -170029.356416268 \tabularnewline
41 & 880005 & 528315.28639063 & 351689.71360937 \tabularnewline
42 & 380005 & 573239.137648869 & -193234.137648869 \tabularnewline
43 & 270004 & 548555.954371596 & -278551.954371596 \tabularnewline
44 & 860001 & 512974.514023355 & 347026.485976645 \tabularnewline
45 & 910004 & 557302.697747262 & 352701.302252738 \tabularnewline
46 & 80002 & 602355.766483268 & -522353.766483268 \tabularnewline
47 & 529999 & 535631.770865529 & -5632.77086552943 \tabularnewline
48 & 979996 & 534912.256615488 & 445083.743384512 \tabularnewline
49 & 610001 & 591765.99760228 & 18235.0023977197 \tabularnewline
50 & 419998 & 594095.28533436 & -174097.28533436 \tabularnewline
51 & 839996 & 571856.589551772 & 268139.410448228 \tabularnewline
52 & 70007 & 606107.960932022 & -536100.960932022 \tabularnewline
53 & 270004 & 537627.937501312 & -267623.937501312 \tabularnewline
54 & 339996 & 503442.411180212 & -163446.411180212 \tabularnewline
55 & 710007 & 482564.227996531 & 227442.772003469 \tabularnewline
56 & 539993 & 511617.125661301 & 28375.8743386989 \tabularnewline
57 & 419998 & 515241.779749223 & -95243.7797492227 \tabularnewline
58 & 630005 & 503075.6081805 & 126929.3918195 \tabularnewline
59 & 649994 & 519289.210392168 & 130704.789607832 \tabularnewline
60 & 190002 & 535985.071260034 & -345983.071260034 \tabularnewline
61 & 990005 & 491790.170386651 & 498214.829613349 \tabularnewline
62 & 570007 & 555430.726348601 & 14576.2736513992 \tabularnewline
63 & 720001 & 557292.658398573 & 162708.341601427 \tabularnewline
64 & 669998 & 578076.562657701 & 91921.4373422989 \tabularnewline
65 & 800003 & 589818.347585752 & 210184.652414248 \tabularnewline
66 & 940002 & 616666.741770832 & 323335.258229168 \tabularnewline
67 & 770004 & 657968.674938446 & 112035.325061554 \tabularnewline
68 & 279999 & 672279.751105786 & -392280.751105786 \tabularnewline
69 & 419998 & 622170.915299116 & -202172.915299116 \tabularnewline
70 & 50003 & 596345.917797398 & -546342.917797398 \tabularnewline
71 & 110001 & 526557.615707948 & -416556.615707948 \tabularnewline
72 & 220001 & 473347.849483495 & -253346.849483495 \tabularnewline
73 & 699997 & 440986.038084082 & 259010.961915918 \tabularnewline
74 & 899994 & 474071.367216819 & 425922.632783181 \tabularnewline
75 & 130005 & 528477.522023843 & -398472.522023843 \tabularnewline
76 & 270004 & 477577.766878381 & -207573.766878381 \tabularnewline
77 & 399994 & 451062.879841581 & -51068.8798415815 \tabularnewline
78 & 570007 & 444539.485289086 & 125467.514710914 \tabularnewline
79 & 320007 & 460566.351445526 & -140559.351445526 \tabularnewline
80 & 559998 & 442611.696666208 & 117386.303333792 \tabularnewline
81 & 110001 & 457606.291693173 & -347605.291693173 \tabularnewline
82 & 559998 & 413204.172960904 & 146793.827039096 \tabularnewline
83 & 660004 & 431955.202053716 & 228048.797946284 \tabularnewline
84 & 110001 & 461085.511761717 & -351084.511761717 \tabularnewline
85 & 589996 & 416238.967279118 & 173757.032720882 \tabularnewline
86 & 789993 & 438434.200153333 & 351558.799846667 \tabularnewline
87 & 25 & 483341.328857071 & -483316.328857071 \tabularnewline
88 & 369995 & 421603.865325881 & -51608.8653258808 \tabularnewline
89 & 29999 & 415011.494551905 & -385012.494551905 \tabularnewline
90 & 289993 & 365831.085320417 & -75838.0853204174 \tabularnewline
91 & 25 & 356143.742379167 & -356118.742379167 \tabularnewline
92 & 289993 & 310654.139488243 & -20661.1394882432 \tabularnewline
93 & 369995 & 308014.943852779 & 61980.0561472212 \tabularnewline
94 & 759995 & 315932.101266225 & 444062.898733775 \tabularnewline
95 & 589996 & 372655.442438997 & 217340.557561003 \tabularnewline
96 & 690002 & 400417.911747661 & 289584.088252339 \tabularnewline
97 & 490005 & 437408.565736054 & 52596.4342639465 \tabularnewline
98 & 110001 & 444127.085778444 & -334126.085778444 \tabularnewline
99 & 630005 & 401446.762760295 & 228558.237239705 \tabularnewline
100 & 39993 & 430642.14680558 & -390649.14680558 \tabularnewline
101 & 380005 & 380741.727526486 & -736.72752648592 \tabularnewline
102 & 220001 & 380647.620031905 & -160646.620031905 \tabularnewline
103 & 399994 & 360127.07426619 & 39866.9257338098 \tabularnewline
104 & 470001 & 365219.562822106 & 104781.437177894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295774&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]990005[/C][C]179993[/C][C]810012[/C][/ROW]
[ROW][C]3[/C][C]429993[/C][C]283461.646358554[/C][C]146531.353641446[/C][/ROW]
[ROW][C]4[/C][C]649994[/C][C]302179.147840466[/C][C]347814.852159534[/C][/ROW]
[ROW][C]5[/C][C]770004[/C][C]346608.035235156[/C][C]423395.964764844[/C][/ROW]
[ROW][C]6[/C][C]589996[/C][C]400691.440601857[/C][C]189304.559398143[/C][/ROW]
[ROW][C]7[/C][C]710007[/C][C]424872.670645891[/C][C]285134.329354109[/C][/ROW]
[ROW][C]8[/C][C]970001[/C][C]461294.92499351[/C][C]508706.07500649[/C][/ROW]
[ROW][C]9[/C][C]710007[/C][C]526275.603027039[/C][C]183731.396972961[/C][/ROW]
[ROW][C]10[/C][C]289993[/C][C]549744.933034938[/C][C]-259751.933034938[/C][/ROW]
[ROW][C]11[/C][C]699997[/C][C]516564.954343088[/C][C]183432.045656912[/C][/ROW]
[ROW][C]12[/C][C]919998[/C][C]539996.046058891[/C][C]380001.953941109[/C][/ROW]
[ROW][C]13[/C][C]199997[/C][C]588536.422976631[/C][C]-388539.422976631[/C][/ROW]
[ROW][C]14[/C][C]18[/C][C]538905.493864067[/C][C]-538887.493864067[/C][/ROW]
[ROW][C]15[/C][C]57[/C][C]470069.526582511[/C][C]-470012.526582511[/C][/ROW]
[ROW][C]16[/C][C]559998[/C][C]410031.453199578[/C][C]149966.546800422[/C][/ROW]
[ROW][C]17[/C][C]40001[/C][C]429187.756558672[/C][C]-389186.756558672[/C][/ROW]
[ROW][C]18[/C][C]279999[/C][C]379474.138881647[/C][C]-99475.1388816475[/C][/ROW]
[ROW][C]19[/C][C]25[/C][C]366767.465441732[/C][C]-366742.465441732[/C][/ROW]
[ROW][C]20[/C][C]220001[/C][C]319920.818155698[/C][C]-99919.818155698[/C][/ROW]
[ROW][C]21[/C][C]880005[/C][C]307157.342640566[/C][C]572847.657359434[/C][/ROW]
[ROW][C]22[/C][C]309998[/C][C]380331.285343451[/C][C]-70333.2853434511[/C][/ROW]
[ROW][C]23[/C][C]149994[/C][C]371347.110012176[/C][C]-221353.110012176[/C][/ROW]
[ROW][C]24[/C][C]979996[/C][C]343072.088580128[/C][C]636923.911419872[/C][/ROW]
[ROW][C]25[/C][C]210007[/C][C]424430.951100695[/C][C]-214423.951100695[/C][/ROW]
[ROW][C]26[/C][C]910004[/C][C]397041.040868203[/C][C]512962.959131797[/C][/ROW]
[ROW][C]27[/C][C]330002[/C][C]462565.481263463[/C][C]-132563.481263463[/C][/ROW]
[ROW][C]28[/C][C]770004[/C][C]445632.196370266[/C][C]324371.803629734[/C][/ROW]
[ROW][C]29[/C][C]639999[/C][C]487066.534921363[/C][C]152932.465078637[/C][/ROW]
[ROW][C]30[/C][C]419998[/C][C]506601.69630905[/C][C]-86603.6963090502[/C][/ROW]
[ROW][C]31[/C][C]600006[/C][C]495539.184609539[/C][C]104466.815390461[/C][/ROW]
[ROW][C]32[/C][C]110001[/C][C]508883.480716065[/C][C]-398882.480716065[/C][/ROW]
[ROW][C]33[/C][C]89996[/C][C]457931.3586045[/C][C]-367935.3586045[/C][/ROW]
[ROW][C]34[/C][C]330002[/C][C]410932.334513182[/C][C]-80930.3345131822[/C][/ROW]
[ROW][C]35[/C][C]759995[/C][C]400594.522034572[/C][C]359400.477965428[/C][/ROW]
[ROW][C]36[/C][C]389999[/C][C]446503.324565522[/C][C]-56504.3245655223[/C][/ROW]
[ROW][C]37[/C][C]809998[/C][C]439285.621647295[/C][C]370712.378352705[/C][/ROW]
[ROW][C]38[/C][C]490005[/C][C]486639.37440221[/C][C]3365.62559778965[/C][/ROW]
[ROW][C]39[/C][C]979996[/C][C]487069.289915503[/C][C]492926.710084497[/C][/ROW]
[ROW][C]40[/C][C]380005[/C][C]550034.356416268[/C][C]-170029.356416268[/C][/ROW]
[ROW][C]41[/C][C]880005[/C][C]528315.28639063[/C][C]351689.71360937[/C][/ROW]
[ROW][C]42[/C][C]380005[/C][C]573239.137648869[/C][C]-193234.137648869[/C][/ROW]
[ROW][C]43[/C][C]270004[/C][C]548555.954371596[/C][C]-278551.954371596[/C][/ROW]
[ROW][C]44[/C][C]860001[/C][C]512974.514023355[/C][C]347026.485976645[/C][/ROW]
[ROW][C]45[/C][C]910004[/C][C]557302.697747262[/C][C]352701.302252738[/C][/ROW]
[ROW][C]46[/C][C]80002[/C][C]602355.766483268[/C][C]-522353.766483268[/C][/ROW]
[ROW][C]47[/C][C]529999[/C][C]535631.770865529[/C][C]-5632.77086552943[/C][/ROW]
[ROW][C]48[/C][C]979996[/C][C]534912.256615488[/C][C]445083.743384512[/C][/ROW]
[ROW][C]49[/C][C]610001[/C][C]591765.99760228[/C][C]18235.0023977197[/C][/ROW]
[ROW][C]50[/C][C]419998[/C][C]594095.28533436[/C][C]-174097.28533436[/C][/ROW]
[ROW][C]51[/C][C]839996[/C][C]571856.589551772[/C][C]268139.410448228[/C][/ROW]
[ROW][C]52[/C][C]70007[/C][C]606107.960932022[/C][C]-536100.960932022[/C][/ROW]
[ROW][C]53[/C][C]270004[/C][C]537627.937501312[/C][C]-267623.937501312[/C][/ROW]
[ROW][C]54[/C][C]339996[/C][C]503442.411180212[/C][C]-163446.411180212[/C][/ROW]
[ROW][C]55[/C][C]710007[/C][C]482564.227996531[/C][C]227442.772003469[/C][/ROW]
[ROW][C]56[/C][C]539993[/C][C]511617.125661301[/C][C]28375.8743386989[/C][/ROW]
[ROW][C]57[/C][C]419998[/C][C]515241.779749223[/C][C]-95243.7797492227[/C][/ROW]
[ROW][C]58[/C][C]630005[/C][C]503075.6081805[/C][C]126929.3918195[/C][/ROW]
[ROW][C]59[/C][C]649994[/C][C]519289.210392168[/C][C]130704.789607832[/C][/ROW]
[ROW][C]60[/C][C]190002[/C][C]535985.071260034[/C][C]-345983.071260034[/C][/ROW]
[ROW][C]61[/C][C]990005[/C][C]491790.170386651[/C][C]498214.829613349[/C][/ROW]
[ROW][C]62[/C][C]570007[/C][C]555430.726348601[/C][C]14576.2736513992[/C][/ROW]
[ROW][C]63[/C][C]720001[/C][C]557292.658398573[/C][C]162708.341601427[/C][/ROW]
[ROW][C]64[/C][C]669998[/C][C]578076.562657701[/C][C]91921.4373422989[/C][/ROW]
[ROW][C]65[/C][C]800003[/C][C]589818.347585752[/C][C]210184.652414248[/C][/ROW]
[ROW][C]66[/C][C]940002[/C][C]616666.741770832[/C][C]323335.258229168[/C][/ROW]
[ROW][C]67[/C][C]770004[/C][C]657968.674938446[/C][C]112035.325061554[/C][/ROW]
[ROW][C]68[/C][C]279999[/C][C]672279.751105786[/C][C]-392280.751105786[/C][/ROW]
[ROW][C]69[/C][C]419998[/C][C]622170.915299116[/C][C]-202172.915299116[/C][/ROW]
[ROW][C]70[/C][C]50003[/C][C]596345.917797398[/C][C]-546342.917797398[/C][/ROW]
[ROW][C]71[/C][C]110001[/C][C]526557.615707948[/C][C]-416556.615707948[/C][/ROW]
[ROW][C]72[/C][C]220001[/C][C]473347.849483495[/C][C]-253346.849483495[/C][/ROW]
[ROW][C]73[/C][C]699997[/C][C]440986.038084082[/C][C]259010.961915918[/C][/ROW]
[ROW][C]74[/C][C]899994[/C][C]474071.367216819[/C][C]425922.632783181[/C][/ROW]
[ROW][C]75[/C][C]130005[/C][C]528477.522023843[/C][C]-398472.522023843[/C][/ROW]
[ROW][C]76[/C][C]270004[/C][C]477577.766878381[/C][C]-207573.766878381[/C][/ROW]
[ROW][C]77[/C][C]399994[/C][C]451062.879841581[/C][C]-51068.8798415815[/C][/ROW]
[ROW][C]78[/C][C]570007[/C][C]444539.485289086[/C][C]125467.514710914[/C][/ROW]
[ROW][C]79[/C][C]320007[/C][C]460566.351445526[/C][C]-140559.351445526[/C][/ROW]
[ROW][C]80[/C][C]559998[/C][C]442611.696666208[/C][C]117386.303333792[/C][/ROW]
[ROW][C]81[/C][C]110001[/C][C]457606.291693173[/C][C]-347605.291693173[/C][/ROW]
[ROW][C]82[/C][C]559998[/C][C]413204.172960904[/C][C]146793.827039096[/C][/ROW]
[ROW][C]83[/C][C]660004[/C][C]431955.202053716[/C][C]228048.797946284[/C][/ROW]
[ROW][C]84[/C][C]110001[/C][C]461085.511761717[/C][C]-351084.511761717[/C][/ROW]
[ROW][C]85[/C][C]589996[/C][C]416238.967279118[/C][C]173757.032720882[/C][/ROW]
[ROW][C]86[/C][C]789993[/C][C]438434.200153333[/C][C]351558.799846667[/C][/ROW]
[ROW][C]87[/C][C]25[/C][C]483341.328857071[/C][C]-483316.328857071[/C][/ROW]
[ROW][C]88[/C][C]369995[/C][C]421603.865325881[/C][C]-51608.8653258808[/C][/ROW]
[ROW][C]89[/C][C]29999[/C][C]415011.494551905[/C][C]-385012.494551905[/C][/ROW]
[ROW][C]90[/C][C]289993[/C][C]365831.085320417[/C][C]-75838.0853204174[/C][/ROW]
[ROW][C]91[/C][C]25[/C][C]356143.742379167[/C][C]-356118.742379167[/C][/ROW]
[ROW][C]92[/C][C]289993[/C][C]310654.139488243[/C][C]-20661.1394882432[/C][/ROW]
[ROW][C]93[/C][C]369995[/C][C]308014.943852779[/C][C]61980.0561472212[/C][/ROW]
[ROW][C]94[/C][C]759995[/C][C]315932.101266225[/C][C]444062.898733775[/C][/ROW]
[ROW][C]95[/C][C]589996[/C][C]372655.442438997[/C][C]217340.557561003[/C][/ROW]
[ROW][C]96[/C][C]690002[/C][C]400417.911747661[/C][C]289584.088252339[/C][/ROW]
[ROW][C]97[/C][C]490005[/C][C]437408.565736054[/C][C]52596.4342639465[/C][/ROW]
[ROW][C]98[/C][C]110001[/C][C]444127.085778444[/C][C]-334126.085778444[/C][/ROW]
[ROW][C]99[/C][C]630005[/C][C]401446.762760295[/C][C]228558.237239705[/C][/ROW]
[ROW][C]100[/C][C]39993[/C][C]430642.14680558[/C][C]-390649.14680558[/C][/ROW]
[ROW][C]101[/C][C]380005[/C][C]380741.727526486[/C][C]-736.72752648592[/C][/ROW]
[ROW][C]102[/C][C]220001[/C][C]380647.620031905[/C][C]-160646.620031905[/C][/ROW]
[ROW][C]103[/C][C]399994[/C][C]360127.07426619[/C][C]39866.9257338098[/C][/ROW]
[ROW][C]104[/C][C]470001[/C][C]365219.562822106[/C][C]104781.437177894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295774&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295774&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
2990005179993810012
3429993283461.646358554146531.353641446
4649994302179.147840466347814.852159534
5770004346608.035235156423395.964764844
6589996400691.440601857189304.559398143
7710007424872.670645891285134.329354109
8970001461294.92499351508706.07500649
9710007526275.603027039183731.396972961
10289993549744.933034938-259751.933034938
11699997516564.954343088183432.045656912
12919998539996.046058891380001.953941109
13199997588536.422976631-388539.422976631
1418538905.493864067-538887.493864067
1557470069.526582511-470012.526582511
16559998410031.453199578149966.546800422
1740001429187.756558672-389186.756558672
18279999379474.138881647-99475.1388816475
1925366767.465441732-366742.465441732
20220001319920.818155698-99919.818155698
21880005307157.342640566572847.657359434
22309998380331.285343451-70333.2853434511
23149994371347.110012176-221353.110012176
24979996343072.088580128636923.911419872
25210007424430.951100695-214423.951100695
26910004397041.040868203512962.959131797
27330002462565.481263463-132563.481263463
28770004445632.196370266324371.803629734
29639999487066.534921363152932.465078637
30419998506601.69630905-86603.6963090502
31600006495539.184609539104466.815390461
32110001508883.480716065-398882.480716065
3389996457931.3586045-367935.3586045
34330002410932.334513182-80930.3345131822
35759995400594.522034572359400.477965428
36389999446503.324565522-56504.3245655223
37809998439285.621647295370712.378352705
38490005486639.374402213365.62559778965
39979996487069.289915503492926.710084497
40380005550034.356416268-170029.356416268
41880005528315.28639063351689.71360937
42380005573239.137648869-193234.137648869
43270004548555.954371596-278551.954371596
44860001512974.514023355347026.485976645
45910004557302.697747262352701.302252738
4680002602355.766483268-522353.766483268
47529999535631.770865529-5632.77086552943
48979996534912.256615488445083.743384512
49610001591765.9976022818235.0023977197
50419998594095.28533436-174097.28533436
51839996571856.589551772268139.410448228
5270007606107.960932022-536100.960932022
53270004537627.937501312-267623.937501312
54339996503442.411180212-163446.411180212
55710007482564.227996531227442.772003469
56539993511617.12566130128375.8743386989
57419998515241.779749223-95243.7797492227
58630005503075.6081805126929.3918195
59649994519289.210392168130704.789607832
60190002535985.071260034-345983.071260034
61990005491790.170386651498214.829613349
62570007555430.72634860114576.2736513992
63720001557292.658398573162708.341601427
64669998578076.56265770191921.4373422989
65800003589818.347585752210184.652414248
66940002616666.741770832323335.258229168
67770004657968.674938446112035.325061554
68279999672279.751105786-392280.751105786
69419998622170.915299116-202172.915299116
7050003596345.917797398-546342.917797398
71110001526557.615707948-416556.615707948
72220001473347.849483495-253346.849483495
73699997440986.038084082259010.961915918
74899994474071.367216819425922.632783181
75130005528477.522023843-398472.522023843
76270004477577.766878381-207573.766878381
77399994451062.879841581-51068.8798415815
78570007444539.485289086125467.514710914
79320007460566.351445526-140559.351445526
80559998442611.696666208117386.303333792
81110001457606.291693173-347605.291693173
82559998413204.172960904146793.827039096
83660004431955.202053716228048.797946284
84110001461085.511761717-351084.511761717
85589996416238.967279118173757.032720882
86789993438434.200153333351558.799846667
8725483341.328857071-483316.328857071
88369995421603.865325881-51608.8653258808
8929999415011.494551905-385012.494551905
90289993365831.085320417-75838.0853204174
9125356143.742379167-356118.742379167
92289993310654.139488243-20661.1394882432
93369995308014.94385277961980.0561472212
94759995315932.101266225444062.898733775
95589996372655.442438997217340.557561003
96690002400417.911747661289584.088252339
97490005437408.56573605452596.4342639465
98110001444127.085778444-334126.085778444
99630005401446.762760295228558.237239705
10039993430642.14680558-390649.14680558
101380005380741.727526486-736.72752648592
102220001380647.620031905-160646.620031905
103399994360127.0742661939866.9257338098
104470001365219.562822106104781.437177894







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
105378604.047827637-226372.212311171983580.307966445
106378604.047827637-231287.875705821988495.971361096
107378604.047827637-236164.234902649993372.330557924
108378604.047827637-241002.217885476998210.313540751
109378604.047827637-245802.7166862921003010.81234157
110378604.047827637-250566.5893055311007774.68496081
111378604.047827637-255294.6615024581012502.75715773
112378604.047827637-259987.7284662361017195.82412151
113378604.047827637-264646.5563772621021854.65203254
114378604.047827637-269271.8838674451026479.97952272
115378604.047827637-273864.4233873141031072.51904259
116378604.047827637-278424.8624871061035632.95814238

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
105 & 378604.047827637 & -226372.212311171 & 983580.307966445 \tabularnewline
106 & 378604.047827637 & -231287.875705821 & 988495.971361096 \tabularnewline
107 & 378604.047827637 & -236164.234902649 & 993372.330557924 \tabularnewline
108 & 378604.047827637 & -241002.217885476 & 998210.313540751 \tabularnewline
109 & 378604.047827637 & -245802.716686292 & 1003010.81234157 \tabularnewline
110 & 378604.047827637 & -250566.589305531 & 1007774.68496081 \tabularnewline
111 & 378604.047827637 & -255294.661502458 & 1012502.75715773 \tabularnewline
112 & 378604.047827637 & -259987.728466236 & 1017195.82412151 \tabularnewline
113 & 378604.047827637 & -264646.556377262 & 1021854.65203254 \tabularnewline
114 & 378604.047827637 & -269271.883867445 & 1026479.97952272 \tabularnewline
115 & 378604.047827637 & -273864.423387314 & 1031072.51904259 \tabularnewline
116 & 378604.047827637 & -278424.862487106 & 1035632.95814238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295774&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]105[/C][C]378604.047827637[/C][C]-226372.212311171[/C][C]983580.307966445[/C][/ROW]
[ROW][C]106[/C][C]378604.047827637[/C][C]-231287.875705821[/C][C]988495.971361096[/C][/ROW]
[ROW][C]107[/C][C]378604.047827637[/C][C]-236164.234902649[/C][C]993372.330557924[/C][/ROW]
[ROW][C]108[/C][C]378604.047827637[/C][C]-241002.217885476[/C][C]998210.313540751[/C][/ROW]
[ROW][C]109[/C][C]378604.047827637[/C][C]-245802.716686292[/C][C]1003010.81234157[/C][/ROW]
[ROW][C]110[/C][C]378604.047827637[/C][C]-250566.589305531[/C][C]1007774.68496081[/C][/ROW]
[ROW][C]111[/C][C]378604.047827637[/C][C]-255294.661502458[/C][C]1012502.75715773[/C][/ROW]
[ROW][C]112[/C][C]378604.047827637[/C][C]-259987.728466236[/C][C]1017195.82412151[/C][/ROW]
[ROW][C]113[/C][C]378604.047827637[/C][C]-264646.556377262[/C][C]1021854.65203254[/C][/ROW]
[ROW][C]114[/C][C]378604.047827637[/C][C]-269271.883867445[/C][C]1026479.97952272[/C][/ROW]
[ROW][C]115[/C][C]378604.047827637[/C][C]-273864.423387314[/C][C]1031072.51904259[/C][/ROW]
[ROW][C]116[/C][C]378604.047827637[/C][C]-278424.862487106[/C][C]1035632.95814238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295774&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295774&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
105378604.047827637-226372.212311171983580.307966445
106378604.047827637-231287.875705821988495.971361096
107378604.047827637-236164.234902649993372.330557924
108378604.047827637-241002.217885476998210.313540751
109378604.047827637-245802.7166862921003010.81234157
110378604.047827637-250566.5893055311007774.68496081
111378604.047827637-255294.6615024581012502.75715773
112378604.047827637-259987.7284662361017195.82412151
113378604.047827637-264646.5563772621021854.65203254
114378604.047827637-269271.8838674451026479.97952272
115378604.047827637-273864.4233873141031072.51904259
116378604.047827637-278424.8624871061035632.95814238



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):
x <- as.matrix(read.csv(file='https://automated.biganalytics.eu/uploads/temp/fedex1.csv'));
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')