Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 02 Aug 2010 14:17:42 +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/02/t12807588609cyavhudg1gbie0.htm/, Retrieved Thu, 02 May 2024 07:30:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78222, Retrieved Thu, 02 May 2024 07:30:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Puyenbroeck Cassandra
Estimated Impact211
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2010-08-02 14:17:42] [0e5311d1fc10a1511b42f76588fb6510] [Current]
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Dataseries X:
408
407
406
404
402
401
402
404
405
405
406
408
405
400
402
404
410
402
400
392
390
397
394
397
400
395
391
392
395
386
385
372
367
364
364
368
370
357
350
353
353
348
337
322
315
316
317
326
329
310
301
299
300
295
274
258
250
247
248
256
253
237
225
214
221
221
207
194
191
185
180
185
189
179
162
148
152
151
134
122
119
115
113
109




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78222&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78222&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.385319959597228
beta0.126395076856841
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.385319959597228 \tabularnewline
beta & 0.126395076856841 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78222&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]0.385319959597228[/C][/ROW]
[ROW][C]beta[/C][C]0.126395076856841[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78222&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
alpha0.385319959597228
beta0.126395076856841
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13405404.6044337606840.395566239316054
14400399.9907163130630.00928368693701032
15402402.770275293822-0.770275293822124
16404405.045273605086-1.04527360508581
17410411.038402092426-1.03840209242622
18402403.10860548517-1.10860548516996
19400397.3060995332562.6939004667438
20392400.349974832255-8.3499748322547
21390397.773426181316-7.77342618131627
22397393.7487809211413.25121907885949
23394394.630494173634-0.630494173633792
24397394.9441324944062.05586750559428
25400392.0528189090847.94718109091576
26395389.879673808155.12032619185021
27391394.166585508922-3.16658550892197
28392395.249640657892-3.24964065789209
29395400.190686981649-5.19068698164949
30386390.208633337376-4.2086333373764
31385384.988823875090.0111761249100937
32372379.519761302911-7.51976130291058
33367376.967156034955-9.96715603495471
34364378.116664632598-14.1166646325984
35364368.31712618489-4.31712618489041
36368367.0788883574480.921111642552262
37370365.5337419058514.46625809414854
38357358.274324945194-1.27432494519417
39350352.684623450914-2.68462345091416
40353351.6069813792911.39301862070857
41353355.074569403655-2.07456940365512
42348344.9793845394343.02061546056621
43337343.573582111179-6.57358211117884
44322329.052069877344-7.05206987734368
45315323.311994559176-8.31199455917624
46316320.765944176461-4.76594417646083
47317319.265703917486-2.26570391748641
48326320.8103680332075.18963196679306
49329322.0695939901966.93040600980396
50310311.331546432876-1.33154643287583
51301303.950633025261-2.95063302526131
52299304.361701015488-5.36170101548828
53300301.850895219406-1.85089521940648
54295293.7404900470291.2595099529708
55274284.439651568884-10.439651568884
56258266.626976107296-8.62697610729606
57250257.921532865865-7.92153286586466
58247256.140563474066-9.1405634740658
59248252.713429684825-4.7134296848252
60256256.000258710118-0.000258710118487215
61253254.179650712091-1.17965071209116
62237232.6931142071094.30688579289065
63225224.2191221112410.780877888758567
64214222.49725549439-8.49725549438966
65221218.6948458637512.30515413624943
66221212.0587292647298.94127073527062
67207196.861682597610.1383174023995
68194187.4296213467766.57037865322368
69191185.0910905878895.90890941211131
70185188.640977102408-3.64097710240847
71180191.073082575933-11.0730825759331
72185195.515639332241-10.5156393322413
73189189.11530756775-0.115307567749511
74179171.660195414977.33980458502995
75162162.584038865561-0.584038865560757
76148154.96324233736-6.96324233735993
77152158.796737688916-6.79673768891575
78151152.694077120603-1.69407712060283
79134133.5783590257010.421640974299237
80122117.1794404765134.82055952348716
81119112.6451696997336.35483030026651
82115109.4035634451335.59643655486659
83113110.183357086692.81664291330964
84109120.353711739743-11.353711739743

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 405 & 404.604433760684 & 0.395566239316054 \tabularnewline
14 & 400 & 399.990716313063 & 0.00928368693701032 \tabularnewline
15 & 402 & 402.770275293822 & -0.770275293822124 \tabularnewline
16 & 404 & 405.045273605086 & -1.04527360508581 \tabularnewline
17 & 410 & 411.038402092426 & -1.03840209242622 \tabularnewline
18 & 402 & 403.10860548517 & -1.10860548516996 \tabularnewline
19 & 400 & 397.306099533256 & 2.6939004667438 \tabularnewline
20 & 392 & 400.349974832255 & -8.3499748322547 \tabularnewline
21 & 390 & 397.773426181316 & -7.77342618131627 \tabularnewline
22 & 397 & 393.748780921141 & 3.25121907885949 \tabularnewline
23 & 394 & 394.630494173634 & -0.630494173633792 \tabularnewline
24 & 397 & 394.944132494406 & 2.05586750559428 \tabularnewline
25 & 400 & 392.052818909084 & 7.94718109091576 \tabularnewline
26 & 395 & 389.87967380815 & 5.12032619185021 \tabularnewline
27 & 391 & 394.166585508922 & -3.16658550892197 \tabularnewline
28 & 392 & 395.249640657892 & -3.24964065789209 \tabularnewline
29 & 395 & 400.190686981649 & -5.19068698164949 \tabularnewline
30 & 386 & 390.208633337376 & -4.2086333373764 \tabularnewline
31 & 385 & 384.98882387509 & 0.0111761249100937 \tabularnewline
32 & 372 & 379.519761302911 & -7.51976130291058 \tabularnewline
33 & 367 & 376.967156034955 & -9.96715603495471 \tabularnewline
34 & 364 & 378.116664632598 & -14.1166646325984 \tabularnewline
35 & 364 & 368.31712618489 & -4.31712618489041 \tabularnewline
36 & 368 & 367.078888357448 & 0.921111642552262 \tabularnewline
37 & 370 & 365.533741905851 & 4.46625809414854 \tabularnewline
38 & 357 & 358.274324945194 & -1.27432494519417 \tabularnewline
39 & 350 & 352.684623450914 & -2.68462345091416 \tabularnewline
40 & 353 & 351.606981379291 & 1.39301862070857 \tabularnewline
41 & 353 & 355.074569403655 & -2.07456940365512 \tabularnewline
42 & 348 & 344.979384539434 & 3.02061546056621 \tabularnewline
43 & 337 & 343.573582111179 & -6.57358211117884 \tabularnewline
44 & 322 & 329.052069877344 & -7.05206987734368 \tabularnewline
45 & 315 & 323.311994559176 & -8.31199455917624 \tabularnewline
46 & 316 & 320.765944176461 & -4.76594417646083 \tabularnewline
47 & 317 & 319.265703917486 & -2.26570391748641 \tabularnewline
48 & 326 & 320.810368033207 & 5.18963196679306 \tabularnewline
49 & 329 & 322.069593990196 & 6.93040600980396 \tabularnewline
50 & 310 & 311.331546432876 & -1.33154643287583 \tabularnewline
51 & 301 & 303.950633025261 & -2.95063302526131 \tabularnewline
52 & 299 & 304.361701015488 & -5.36170101548828 \tabularnewline
53 & 300 & 301.850895219406 & -1.85089521940648 \tabularnewline
54 & 295 & 293.740490047029 & 1.2595099529708 \tabularnewline
55 & 274 & 284.439651568884 & -10.439651568884 \tabularnewline
56 & 258 & 266.626976107296 & -8.62697610729606 \tabularnewline
57 & 250 & 257.921532865865 & -7.92153286586466 \tabularnewline
58 & 247 & 256.140563474066 & -9.1405634740658 \tabularnewline
59 & 248 & 252.713429684825 & -4.7134296848252 \tabularnewline
60 & 256 & 256.000258710118 & -0.000258710118487215 \tabularnewline
61 & 253 & 254.179650712091 & -1.17965071209116 \tabularnewline
62 & 237 & 232.693114207109 & 4.30688579289065 \tabularnewline
63 & 225 & 224.219122111241 & 0.780877888758567 \tabularnewline
64 & 214 & 222.49725549439 & -8.49725549438966 \tabularnewline
65 & 221 & 218.694845863751 & 2.30515413624943 \tabularnewline
66 & 221 & 212.058729264729 & 8.94127073527062 \tabularnewline
67 & 207 & 196.8616825976 & 10.1383174023995 \tabularnewline
68 & 194 & 187.429621346776 & 6.57037865322368 \tabularnewline
69 & 191 & 185.091090587889 & 5.90890941211131 \tabularnewline
70 & 185 & 188.640977102408 & -3.64097710240847 \tabularnewline
71 & 180 & 191.073082575933 & -11.0730825759331 \tabularnewline
72 & 185 & 195.515639332241 & -10.5156393322413 \tabularnewline
73 & 189 & 189.11530756775 & -0.115307567749511 \tabularnewline
74 & 179 & 171.66019541497 & 7.33980458502995 \tabularnewline
75 & 162 & 162.584038865561 & -0.584038865560757 \tabularnewline
76 & 148 & 154.96324233736 & -6.96324233735993 \tabularnewline
77 & 152 & 158.796737688916 & -6.79673768891575 \tabularnewline
78 & 151 & 152.694077120603 & -1.69407712060283 \tabularnewline
79 & 134 & 133.578359025701 & 0.421640974299237 \tabularnewline
80 & 122 & 117.179440476513 & 4.82055952348716 \tabularnewline
81 & 119 & 112.645169699733 & 6.35483030026651 \tabularnewline
82 & 115 & 109.403563445133 & 5.59643655486659 \tabularnewline
83 & 113 & 110.18335708669 & 2.81664291330964 \tabularnewline
84 & 109 & 120.353711739743 & -11.353711739743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78222&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]405[/C][C]404.604433760684[/C][C]0.395566239316054[/C][/ROW]
[ROW][C]14[/C][C]400[/C][C]399.990716313063[/C][C]0.00928368693701032[/C][/ROW]
[ROW][C]15[/C][C]402[/C][C]402.770275293822[/C][C]-0.770275293822124[/C][/ROW]
[ROW][C]16[/C][C]404[/C][C]405.045273605086[/C][C]-1.04527360508581[/C][/ROW]
[ROW][C]17[/C][C]410[/C][C]411.038402092426[/C][C]-1.03840209242622[/C][/ROW]
[ROW][C]18[/C][C]402[/C][C]403.10860548517[/C][C]-1.10860548516996[/C][/ROW]
[ROW][C]19[/C][C]400[/C][C]397.306099533256[/C][C]2.6939004667438[/C][/ROW]
[ROW][C]20[/C][C]392[/C][C]400.349974832255[/C][C]-8.3499748322547[/C][/ROW]
[ROW][C]21[/C][C]390[/C][C]397.773426181316[/C][C]-7.77342618131627[/C][/ROW]
[ROW][C]22[/C][C]397[/C][C]393.748780921141[/C][C]3.25121907885949[/C][/ROW]
[ROW][C]23[/C][C]394[/C][C]394.630494173634[/C][C]-0.630494173633792[/C][/ROW]
[ROW][C]24[/C][C]397[/C][C]394.944132494406[/C][C]2.05586750559428[/C][/ROW]
[ROW][C]25[/C][C]400[/C][C]392.052818909084[/C][C]7.94718109091576[/C][/ROW]
[ROW][C]26[/C][C]395[/C][C]389.87967380815[/C][C]5.12032619185021[/C][/ROW]
[ROW][C]27[/C][C]391[/C][C]394.166585508922[/C][C]-3.16658550892197[/C][/ROW]
[ROW][C]28[/C][C]392[/C][C]395.249640657892[/C][C]-3.24964065789209[/C][/ROW]
[ROW][C]29[/C][C]395[/C][C]400.190686981649[/C][C]-5.19068698164949[/C][/ROW]
[ROW][C]30[/C][C]386[/C][C]390.208633337376[/C][C]-4.2086333373764[/C][/ROW]
[ROW][C]31[/C][C]385[/C][C]384.98882387509[/C][C]0.0111761249100937[/C][/ROW]
[ROW][C]32[/C][C]372[/C][C]379.519761302911[/C][C]-7.51976130291058[/C][/ROW]
[ROW][C]33[/C][C]367[/C][C]376.967156034955[/C][C]-9.96715603495471[/C][/ROW]
[ROW][C]34[/C][C]364[/C][C]378.116664632598[/C][C]-14.1166646325984[/C][/ROW]
[ROW][C]35[/C][C]364[/C][C]368.31712618489[/C][C]-4.31712618489041[/C][/ROW]
[ROW][C]36[/C][C]368[/C][C]367.078888357448[/C][C]0.921111642552262[/C][/ROW]
[ROW][C]37[/C][C]370[/C][C]365.533741905851[/C][C]4.46625809414854[/C][/ROW]
[ROW][C]38[/C][C]357[/C][C]358.274324945194[/C][C]-1.27432494519417[/C][/ROW]
[ROW][C]39[/C][C]350[/C][C]352.684623450914[/C][C]-2.68462345091416[/C][/ROW]
[ROW][C]40[/C][C]353[/C][C]351.606981379291[/C][C]1.39301862070857[/C][/ROW]
[ROW][C]41[/C][C]353[/C][C]355.074569403655[/C][C]-2.07456940365512[/C][/ROW]
[ROW][C]42[/C][C]348[/C][C]344.979384539434[/C][C]3.02061546056621[/C][/ROW]
[ROW][C]43[/C][C]337[/C][C]343.573582111179[/C][C]-6.57358211117884[/C][/ROW]
[ROW][C]44[/C][C]322[/C][C]329.052069877344[/C][C]-7.05206987734368[/C][/ROW]
[ROW][C]45[/C][C]315[/C][C]323.311994559176[/C][C]-8.31199455917624[/C][/ROW]
[ROW][C]46[/C][C]316[/C][C]320.765944176461[/C][C]-4.76594417646083[/C][/ROW]
[ROW][C]47[/C][C]317[/C][C]319.265703917486[/C][C]-2.26570391748641[/C][/ROW]
[ROW][C]48[/C][C]326[/C][C]320.810368033207[/C][C]5.18963196679306[/C][/ROW]
[ROW][C]49[/C][C]329[/C][C]322.069593990196[/C][C]6.93040600980396[/C][/ROW]
[ROW][C]50[/C][C]310[/C][C]311.331546432876[/C][C]-1.33154643287583[/C][/ROW]
[ROW][C]51[/C][C]301[/C][C]303.950633025261[/C][C]-2.95063302526131[/C][/ROW]
[ROW][C]52[/C][C]299[/C][C]304.361701015488[/C][C]-5.36170101548828[/C][/ROW]
[ROW][C]53[/C][C]300[/C][C]301.850895219406[/C][C]-1.85089521940648[/C][/ROW]
[ROW][C]54[/C][C]295[/C][C]293.740490047029[/C][C]1.2595099529708[/C][/ROW]
[ROW][C]55[/C][C]274[/C][C]284.439651568884[/C][C]-10.439651568884[/C][/ROW]
[ROW][C]56[/C][C]258[/C][C]266.626976107296[/C][C]-8.62697610729606[/C][/ROW]
[ROW][C]57[/C][C]250[/C][C]257.921532865865[/C][C]-7.92153286586466[/C][/ROW]
[ROW][C]58[/C][C]247[/C][C]256.140563474066[/C][C]-9.1405634740658[/C][/ROW]
[ROW][C]59[/C][C]248[/C][C]252.713429684825[/C][C]-4.7134296848252[/C][/ROW]
[ROW][C]60[/C][C]256[/C][C]256.000258710118[/C][C]-0.000258710118487215[/C][/ROW]
[ROW][C]61[/C][C]253[/C][C]254.179650712091[/C][C]-1.17965071209116[/C][/ROW]
[ROW][C]62[/C][C]237[/C][C]232.693114207109[/C][C]4.30688579289065[/C][/ROW]
[ROW][C]63[/C][C]225[/C][C]224.219122111241[/C][C]0.780877888758567[/C][/ROW]
[ROW][C]64[/C][C]214[/C][C]222.49725549439[/C][C]-8.49725549438966[/C][/ROW]
[ROW][C]65[/C][C]221[/C][C]218.694845863751[/C][C]2.30515413624943[/C][/ROW]
[ROW][C]66[/C][C]221[/C][C]212.058729264729[/C][C]8.94127073527062[/C][/ROW]
[ROW][C]67[/C][C]207[/C][C]196.8616825976[/C][C]10.1383174023995[/C][/ROW]
[ROW][C]68[/C][C]194[/C][C]187.429621346776[/C][C]6.57037865322368[/C][/ROW]
[ROW][C]69[/C][C]191[/C][C]185.091090587889[/C][C]5.90890941211131[/C][/ROW]
[ROW][C]70[/C][C]185[/C][C]188.640977102408[/C][C]-3.64097710240847[/C][/ROW]
[ROW][C]71[/C][C]180[/C][C]191.073082575933[/C][C]-11.0730825759331[/C][/ROW]
[ROW][C]72[/C][C]185[/C][C]195.515639332241[/C][C]-10.5156393322413[/C][/ROW]
[ROW][C]73[/C][C]189[/C][C]189.11530756775[/C][C]-0.115307567749511[/C][/ROW]
[ROW][C]74[/C][C]179[/C][C]171.66019541497[/C][C]7.33980458502995[/C][/ROW]
[ROW][C]75[/C][C]162[/C][C]162.584038865561[/C][C]-0.584038865560757[/C][/ROW]
[ROW][C]76[/C][C]148[/C][C]154.96324233736[/C][C]-6.96324233735993[/C][/ROW]
[ROW][C]77[/C][C]152[/C][C]158.796737688916[/C][C]-6.79673768891575[/C][/ROW]
[ROW][C]78[/C][C]151[/C][C]152.694077120603[/C][C]-1.69407712060283[/C][/ROW]
[ROW][C]79[/C][C]134[/C][C]133.578359025701[/C][C]0.421640974299237[/C][/ROW]
[ROW][C]80[/C][C]122[/C][C]117.179440476513[/C][C]4.82055952348716[/C][/ROW]
[ROW][C]81[/C][C]119[/C][C]112.645169699733[/C][C]6.35483030026651[/C][/ROW]
[ROW][C]82[/C][C]115[/C][C]109.403563445133[/C][C]5.59643655486659[/C][/ROW]
[ROW][C]83[/C][C]113[/C][C]110.18335708669[/C][C]2.81664291330964[/C][/ROW]
[ROW][C]84[/C][C]109[/C][C]120.353711739743[/C][C]-11.353711739743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78222&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78222&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
13405404.6044337606840.395566239316054
14400399.9907163130630.00928368693701032
15402402.770275293822-0.770275293822124
16404405.045273605086-1.04527360508581
17410411.038402092426-1.03840209242622
18402403.10860548517-1.10860548516996
19400397.3060995332562.6939004667438
20392400.349974832255-8.3499748322547
21390397.773426181316-7.77342618131627
22397393.7487809211413.25121907885949
23394394.630494173634-0.630494173633792
24397394.9441324944062.05586750559428
25400392.0528189090847.94718109091576
26395389.879673808155.12032619185021
27391394.166585508922-3.16658550892197
28392395.249640657892-3.24964065789209
29395400.190686981649-5.19068698164949
30386390.208633337376-4.2086333373764
31385384.988823875090.0111761249100937
32372379.519761302911-7.51976130291058
33367376.967156034955-9.96715603495471
34364378.116664632598-14.1166646325984
35364368.31712618489-4.31712618489041
36368367.0788883574480.921111642552262
37370365.5337419058514.46625809414854
38357358.274324945194-1.27432494519417
39350352.684623450914-2.68462345091416
40353351.6069813792911.39301862070857
41353355.074569403655-2.07456940365512
42348344.9793845394343.02061546056621
43337343.573582111179-6.57358211117884
44322329.052069877344-7.05206987734368
45315323.311994559176-8.31199455917624
46316320.765944176461-4.76594417646083
47317319.265703917486-2.26570391748641
48326320.8103680332075.18963196679306
49329322.0695939901966.93040600980396
50310311.331546432876-1.33154643287583
51301303.950633025261-2.95063302526131
52299304.361701015488-5.36170101548828
53300301.850895219406-1.85089521940648
54295293.7404900470291.2595099529708
55274284.439651568884-10.439651568884
56258266.626976107296-8.62697610729606
57250257.921532865865-7.92153286586466
58247256.140563474066-9.1405634740658
59248252.713429684825-4.7134296848252
60256256.000258710118-0.000258710118487215
61253254.179650712091-1.17965071209116
62237232.6931142071094.30688579289065
63225224.2191221112410.780877888758567
64214222.49725549439-8.49725549438966
65221218.6948458637512.30515413624943
66221212.0587292647298.94127073527062
67207196.861682597610.1383174023995
68194187.4296213467766.57037865322368
69191185.0910905878895.90890941211131
70185188.640977102408-3.64097710240847
71180191.073082575933-11.0730825759331
72185195.515639332241-10.5156393322413
73189189.11530756775-0.115307567749511
74179171.660195414977.33980458502995
75162162.584038865561-0.584038865560757
76148154.96324233736-6.96324233735993
77152158.796737688916-6.79673768891575
78151152.694077120603-1.69407712060283
79134133.5783590257010.421640974299237
80122117.1794404765134.82055952348716
81119112.6451696997336.35483030026651
82115109.4035634451335.59643655486659
83113110.183357086692.81664291330964
84109120.353711739743-11.353711739743







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85120.015674235211109.084749489666130.946598980755
86107.18546073812595.2693712604991119.101550215751
8790.050995109519477.0188799564509103.083110262588
8878.403008084591664.134846004884992.6711701642983
8985.029991124854869.4161100469001100.643872202809
9085.021835630414767.9619016480715102.081769612758
9168.280957593865349.68279996476586.8791152229656
9254.824553450763934.603018790178675.0460881113492
9349.542190632448927.618113444412871.466267820485
9443.242555647035419.541872548907566.9432387451634
9539.74146992704214.194475134896665.2884647191874
9639.5633270086512.104054004965167.0226000123348

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 120.015674235211 & 109.084749489666 & 130.946598980755 \tabularnewline
86 & 107.185460738125 & 95.2693712604991 & 119.101550215751 \tabularnewline
87 & 90.0509951095194 & 77.0188799564509 & 103.083110262588 \tabularnewline
88 & 78.4030080845916 & 64.1348460048849 & 92.6711701642983 \tabularnewline
89 & 85.0299911248548 & 69.4161100469001 & 100.643872202809 \tabularnewline
90 & 85.0218356304147 & 67.9619016480715 & 102.081769612758 \tabularnewline
91 & 68.2809575938653 & 49.682799964765 & 86.8791152229656 \tabularnewline
92 & 54.8245534507639 & 34.6030187901786 & 75.0460881113492 \tabularnewline
93 & 49.5421906324489 & 27.6181134444128 & 71.466267820485 \tabularnewline
94 & 43.2425556470354 & 19.5418725489075 & 66.9432387451634 \tabularnewline
95 & 39.741469927042 & 14.1944751348966 & 65.2884647191874 \tabularnewline
96 & 39.56332700865 & 12.1040540049651 & 67.0226000123348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78222&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]85[/C][C]120.015674235211[/C][C]109.084749489666[/C][C]130.946598980755[/C][/ROW]
[ROW][C]86[/C][C]107.185460738125[/C][C]95.2693712604991[/C][C]119.101550215751[/C][/ROW]
[ROW][C]87[/C][C]90.0509951095194[/C][C]77.0188799564509[/C][C]103.083110262588[/C][/ROW]
[ROW][C]88[/C][C]78.4030080845916[/C][C]64.1348460048849[/C][C]92.6711701642983[/C][/ROW]
[ROW][C]89[/C][C]85.0299911248548[/C][C]69.4161100469001[/C][C]100.643872202809[/C][/ROW]
[ROW][C]90[/C][C]85.0218356304147[/C][C]67.9619016480715[/C][C]102.081769612758[/C][/ROW]
[ROW][C]91[/C][C]68.2809575938653[/C][C]49.682799964765[/C][C]86.8791152229656[/C][/ROW]
[ROW][C]92[/C][C]54.8245534507639[/C][C]34.6030187901786[/C][C]75.0460881113492[/C][/ROW]
[ROW][C]93[/C][C]49.5421906324489[/C][C]27.6181134444128[/C][C]71.466267820485[/C][/ROW]
[ROW][C]94[/C][C]43.2425556470354[/C][C]19.5418725489075[/C][C]66.9432387451634[/C][/ROW]
[ROW][C]95[/C][C]39.741469927042[/C][C]14.1944751348966[/C][C]65.2884647191874[/C][/ROW]
[ROW][C]96[/C][C]39.56332700865[/C][C]12.1040540049651[/C][C]67.0226000123348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78222&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78222&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
85120.015674235211109.084749489666130.946598980755
86107.18546073812595.2693712604991119.101550215751
8790.050995109519477.0188799564509103.083110262588
8878.403008084591664.134846004884992.6711701642983
8985.029991124854869.4161100469001100.643872202809
9085.021835630414767.9619016480715102.081769612758
9168.280957593865349.68279996476586.8791152229656
9254.824553450763934.603018790178675.0460881113492
9349.542190632448927.618113444412871.466267820485
9443.242555647035419.541872548907566.9432387451634
9539.74146992704214.194475134896665.2884647191874
9639.5633270086512.104054004965167.0226000123348



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