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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 14 Dec 2010 10:21:18 +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/Dec/14/t1292321955bf89juhfjju8r97.htm/, Retrieved Fri, 03 May 2024 02:32:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109355, Retrieved Fri, 03 May 2024 02:32:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [Paper - ES] [2010-12-14 10:21:18] [5398da98f4f83c6a353e4d3806d4bcaa] [Current]
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Dataseries X:
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109355&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109355&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.931014256544288
beta0.206391957488703
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.931014256544288 \tabularnewline
beta & 0.206391957488703 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109355&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]0.931014256544288[/C][/ROW]
[ROW][C]beta[/C][C]0.206391957488703[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109355&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
alpha0.931014256544288
beta0.206391957488703
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13299.5239.39449786324860.105502136752
14347.4351.546379551372-4.14637955137209
15338.3347.761267230222-9.46126723022172
16327.7334.364066404668-6.66406640466812
17351.6356.944740044102-5.34474004410174
18396.6403.143379598236-6.54337959823573
19438.8386.10623302541252.6937669745876
20395.6440.036691546718-44.4366915467175
21363.5394.211126862163-30.7111268621633
22378.8340.71716383111738.0828361688831
23357415.401624919934-58.4016249199345
24369374.768913175063-5.76891317506329
25464.8445.99674360433918.8032563956606
26479.1503.369179174461-24.2691791744608
27431.3464.722125847542-33.4221258475416
28366.5408.845143482560-42.3451434825595
29326.3371.076136331253-44.7761363312532
30355.1345.68289589469.4171041053998
31331.6315.86057540555415.7394245944456
32261.3289.853347712182-28.5533477121820
33249223.98226688487025.0177331151295
34205.5202.0469809716703.4530190283304
35235.6206.10879475745229.4912052425480
36240.9236.0996722582714.80032774172892
37264.9306.056870999756-41.1568709997564
38253.8280.306744485138-26.506744485138
39232.3214.18766165789118.1123383421087
40193.8190.8195836384262.98041636157421
41177188.936240573508-11.9362405735080
42213.2198.0209103501815.1790896498201
43207.2175.27135635993031.9286436400704
44180.6165.66389925145914.9361007485408
45188.6156.717367634731.8826323652999
46175.4153.74447165936621.6555283406338
47199194.1057557863644.89424421363597
48179.6212.323203513490-32.7232035134896
49225.8249.794787152436-23.9947871524365
50234249.950934783951-15.9509347839508
51200.2207.683360947197-7.48336094719704
52183.6165.46894187736818.131058122632
53178.2185.600786619152-7.40078661915223
54203.2210.588865862496-7.38886586249606
55208.5173.45745029659735.0425497034026
56191.8171.64893628859520.1510637114047
57172.8175.800849222989-3.00084922298859
58148140.0165853412557.98341465874466
59159.4164.236672863252-4.83667286325192
60154.5166.673623033259-12.1736230332594
61213.2223.702169031232-10.5021690312323
62196.4239.39057988577-42.9905798857699
63182.8169.75261306159713.0473869384029
64176.4149.58446528071126.8155347192886
65153.6178.873926475988-25.2739264759875
66173.2186.621865566447-13.4218655664472
67171145.04072536644125.9592746335586
68151.2130.24278757188320.9572124281166
69161.9130.19752414363531.7024758563652
70157.2130.79812557626226.4018744237381
71201.7178.1386538043723.5613461956299
72236.4218.82220379632217.577796203678
73356.1321.69568582985234.4043141701481
74398.3403.611023511471-5.31102351147098
75403.7406.818941593635-3.1189415936347
76384.6403.342954976271-18.7429549762708
77365.8408.662580727233-42.8625807272334
78368.1419.512325649181-51.4123256491812
79367.9356.63771984107511.2622801589251
80347336.34697264586810.6530273541316
81343.3334.0050200783999.29497992160105
82292.9315.627954770634-22.7279547706338
83311.5309.8411669362801.65883306372035
84300.9318.320944264907-17.420944264907
85366.9371.646305877894-4.74630587789386
86356.9388.724539548477-31.8245395484767
87329.7336.657017800339-6.95701780033909
88316.2297.05019138995819.1498086100416
89269311.786148591763-42.7861485917631
90289.3297.933467787587-8.633467787587
91266.2263.2465906251952.95340937480455
92253.6217.61790278623435.9820972137661
93233.8226.0708341345447.72916586545617
94228.4191.03281513638837.3671848636118
95253.6241.43127995509512.1687200449046
96260.1258.9526747867561.14732521324379
97306.6334.580689426555-27.9806894265545
98309.2327.835752397094-18.6357523970942
99309.5291.97334398816917.5266560118306
100271283.877458081835-12.8774580818352
101279.9265.28400488888514.6159951111154
102317.9319.020759041934-1.12075904193443
103298.4305.362418845651-6.96241884565143
104246.7264.109866220531-17.4098662205309
105227.3221.9750014270045.32499857299592
106209.1187.35123164087421.7487683591257

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 299.5 & 239.394497863248 & 60.105502136752 \tabularnewline
14 & 347.4 & 351.546379551372 & -4.14637955137209 \tabularnewline
15 & 338.3 & 347.761267230222 & -9.46126723022172 \tabularnewline
16 & 327.7 & 334.364066404668 & -6.66406640466812 \tabularnewline
17 & 351.6 & 356.944740044102 & -5.34474004410174 \tabularnewline
18 & 396.6 & 403.143379598236 & -6.54337959823573 \tabularnewline
19 & 438.8 & 386.106233025412 & 52.6937669745876 \tabularnewline
20 & 395.6 & 440.036691546718 & -44.4366915467175 \tabularnewline
21 & 363.5 & 394.211126862163 & -30.7111268621633 \tabularnewline
22 & 378.8 & 340.717163831117 & 38.0828361688831 \tabularnewline
23 & 357 & 415.401624919934 & -58.4016249199345 \tabularnewline
24 & 369 & 374.768913175063 & -5.76891317506329 \tabularnewline
25 & 464.8 & 445.996743604339 & 18.8032563956606 \tabularnewline
26 & 479.1 & 503.369179174461 & -24.2691791744608 \tabularnewline
27 & 431.3 & 464.722125847542 & -33.4221258475416 \tabularnewline
28 & 366.5 & 408.845143482560 & -42.3451434825595 \tabularnewline
29 & 326.3 & 371.076136331253 & -44.7761363312532 \tabularnewline
30 & 355.1 & 345.6828958946 & 9.4171041053998 \tabularnewline
31 & 331.6 & 315.860575405554 & 15.7394245944456 \tabularnewline
32 & 261.3 & 289.853347712182 & -28.5533477121820 \tabularnewline
33 & 249 & 223.982266884870 & 25.0177331151295 \tabularnewline
34 & 205.5 & 202.046980971670 & 3.4530190283304 \tabularnewline
35 & 235.6 & 206.108794757452 & 29.4912052425480 \tabularnewline
36 & 240.9 & 236.099672258271 & 4.80032774172892 \tabularnewline
37 & 264.9 & 306.056870999756 & -41.1568709997564 \tabularnewline
38 & 253.8 & 280.306744485138 & -26.506744485138 \tabularnewline
39 & 232.3 & 214.187661657891 & 18.1123383421087 \tabularnewline
40 & 193.8 & 190.819583638426 & 2.98041636157421 \tabularnewline
41 & 177 & 188.936240573508 & -11.9362405735080 \tabularnewline
42 & 213.2 & 198.02091035018 & 15.1790896498201 \tabularnewline
43 & 207.2 & 175.271356359930 & 31.9286436400704 \tabularnewline
44 & 180.6 & 165.663899251459 & 14.9361007485408 \tabularnewline
45 & 188.6 & 156.7173676347 & 31.8826323652999 \tabularnewline
46 & 175.4 & 153.744471659366 & 21.6555283406338 \tabularnewline
47 & 199 & 194.105755786364 & 4.89424421363597 \tabularnewline
48 & 179.6 & 212.323203513490 & -32.7232035134896 \tabularnewline
49 & 225.8 & 249.794787152436 & -23.9947871524365 \tabularnewline
50 & 234 & 249.950934783951 & -15.9509347839508 \tabularnewline
51 & 200.2 & 207.683360947197 & -7.48336094719704 \tabularnewline
52 & 183.6 & 165.468941877368 & 18.131058122632 \tabularnewline
53 & 178.2 & 185.600786619152 & -7.40078661915223 \tabularnewline
54 & 203.2 & 210.588865862496 & -7.38886586249606 \tabularnewline
55 & 208.5 & 173.457450296597 & 35.0425497034026 \tabularnewline
56 & 191.8 & 171.648936288595 & 20.1510637114047 \tabularnewline
57 & 172.8 & 175.800849222989 & -3.00084922298859 \tabularnewline
58 & 148 & 140.016585341255 & 7.98341465874466 \tabularnewline
59 & 159.4 & 164.236672863252 & -4.83667286325192 \tabularnewline
60 & 154.5 & 166.673623033259 & -12.1736230332594 \tabularnewline
61 & 213.2 & 223.702169031232 & -10.5021690312323 \tabularnewline
62 & 196.4 & 239.39057988577 & -42.9905798857699 \tabularnewline
63 & 182.8 & 169.752613061597 & 13.0473869384029 \tabularnewline
64 & 176.4 & 149.584465280711 & 26.8155347192886 \tabularnewline
65 & 153.6 & 178.873926475988 & -25.2739264759875 \tabularnewline
66 & 173.2 & 186.621865566447 & -13.4218655664472 \tabularnewline
67 & 171 & 145.040725366441 & 25.9592746335586 \tabularnewline
68 & 151.2 & 130.242787571883 & 20.9572124281166 \tabularnewline
69 & 161.9 & 130.197524143635 & 31.7024758563652 \tabularnewline
70 & 157.2 & 130.798125576262 & 26.4018744237381 \tabularnewline
71 & 201.7 & 178.13865380437 & 23.5613461956299 \tabularnewline
72 & 236.4 & 218.822203796322 & 17.577796203678 \tabularnewline
73 & 356.1 & 321.695685829852 & 34.4043141701481 \tabularnewline
74 & 398.3 & 403.611023511471 & -5.31102351147098 \tabularnewline
75 & 403.7 & 406.818941593635 & -3.1189415936347 \tabularnewline
76 & 384.6 & 403.342954976271 & -18.7429549762708 \tabularnewline
77 & 365.8 & 408.662580727233 & -42.8625807272334 \tabularnewline
78 & 368.1 & 419.512325649181 & -51.4123256491812 \tabularnewline
79 & 367.9 & 356.637719841075 & 11.2622801589251 \tabularnewline
80 & 347 & 336.346972645868 & 10.6530273541316 \tabularnewline
81 & 343.3 & 334.005020078399 & 9.29497992160105 \tabularnewline
82 & 292.9 & 315.627954770634 & -22.7279547706338 \tabularnewline
83 & 311.5 & 309.841166936280 & 1.65883306372035 \tabularnewline
84 & 300.9 & 318.320944264907 & -17.420944264907 \tabularnewline
85 & 366.9 & 371.646305877894 & -4.74630587789386 \tabularnewline
86 & 356.9 & 388.724539548477 & -31.8245395484767 \tabularnewline
87 & 329.7 & 336.657017800339 & -6.95701780033909 \tabularnewline
88 & 316.2 & 297.050191389958 & 19.1498086100416 \tabularnewline
89 & 269 & 311.786148591763 & -42.7861485917631 \tabularnewline
90 & 289.3 & 297.933467787587 & -8.633467787587 \tabularnewline
91 & 266.2 & 263.246590625195 & 2.95340937480455 \tabularnewline
92 & 253.6 & 217.617902786234 & 35.9820972137661 \tabularnewline
93 & 233.8 & 226.070834134544 & 7.72916586545617 \tabularnewline
94 & 228.4 & 191.032815136388 & 37.3671848636118 \tabularnewline
95 & 253.6 & 241.431279955095 & 12.1687200449046 \tabularnewline
96 & 260.1 & 258.952674786756 & 1.14732521324379 \tabularnewline
97 & 306.6 & 334.580689426555 & -27.9806894265545 \tabularnewline
98 & 309.2 & 327.835752397094 & -18.6357523970942 \tabularnewline
99 & 309.5 & 291.973343988169 & 17.5266560118306 \tabularnewline
100 & 271 & 283.877458081835 & -12.8774580818352 \tabularnewline
101 & 279.9 & 265.284004888885 & 14.6159951111154 \tabularnewline
102 & 317.9 & 319.020759041934 & -1.12075904193443 \tabularnewline
103 & 298.4 & 305.362418845651 & -6.96241884565143 \tabularnewline
104 & 246.7 & 264.109866220531 & -17.4098662205309 \tabularnewline
105 & 227.3 & 221.975001427004 & 5.32499857299592 \tabularnewline
106 & 209.1 & 187.351231640874 & 21.7487683591257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109355&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]299.5[/C][C]239.394497863248[/C][C]60.105502136752[/C][/ROW]
[ROW][C]14[/C][C]347.4[/C][C]351.546379551372[/C][C]-4.14637955137209[/C][/ROW]
[ROW][C]15[/C][C]338.3[/C][C]347.761267230222[/C][C]-9.46126723022172[/C][/ROW]
[ROW][C]16[/C][C]327.7[/C][C]334.364066404668[/C][C]-6.66406640466812[/C][/ROW]
[ROW][C]17[/C][C]351.6[/C][C]356.944740044102[/C][C]-5.34474004410174[/C][/ROW]
[ROW][C]18[/C][C]396.6[/C][C]403.143379598236[/C][C]-6.54337959823573[/C][/ROW]
[ROW][C]19[/C][C]438.8[/C][C]386.106233025412[/C][C]52.6937669745876[/C][/ROW]
[ROW][C]20[/C][C]395.6[/C][C]440.036691546718[/C][C]-44.4366915467175[/C][/ROW]
[ROW][C]21[/C][C]363.5[/C][C]394.211126862163[/C][C]-30.7111268621633[/C][/ROW]
[ROW][C]22[/C][C]378.8[/C][C]340.717163831117[/C][C]38.0828361688831[/C][/ROW]
[ROW][C]23[/C][C]357[/C][C]415.401624919934[/C][C]-58.4016249199345[/C][/ROW]
[ROW][C]24[/C][C]369[/C][C]374.768913175063[/C][C]-5.76891317506329[/C][/ROW]
[ROW][C]25[/C][C]464.8[/C][C]445.996743604339[/C][C]18.8032563956606[/C][/ROW]
[ROW][C]26[/C][C]479.1[/C][C]503.369179174461[/C][C]-24.2691791744608[/C][/ROW]
[ROW][C]27[/C][C]431.3[/C][C]464.722125847542[/C][C]-33.4221258475416[/C][/ROW]
[ROW][C]28[/C][C]366.5[/C][C]408.845143482560[/C][C]-42.3451434825595[/C][/ROW]
[ROW][C]29[/C][C]326.3[/C][C]371.076136331253[/C][C]-44.7761363312532[/C][/ROW]
[ROW][C]30[/C][C]355.1[/C][C]345.6828958946[/C][C]9.4171041053998[/C][/ROW]
[ROW][C]31[/C][C]331.6[/C][C]315.860575405554[/C][C]15.7394245944456[/C][/ROW]
[ROW][C]32[/C][C]261.3[/C][C]289.853347712182[/C][C]-28.5533477121820[/C][/ROW]
[ROW][C]33[/C][C]249[/C][C]223.982266884870[/C][C]25.0177331151295[/C][/ROW]
[ROW][C]34[/C][C]205.5[/C][C]202.046980971670[/C][C]3.4530190283304[/C][/ROW]
[ROW][C]35[/C][C]235.6[/C][C]206.108794757452[/C][C]29.4912052425480[/C][/ROW]
[ROW][C]36[/C][C]240.9[/C][C]236.099672258271[/C][C]4.80032774172892[/C][/ROW]
[ROW][C]37[/C][C]264.9[/C][C]306.056870999756[/C][C]-41.1568709997564[/C][/ROW]
[ROW][C]38[/C][C]253.8[/C][C]280.306744485138[/C][C]-26.506744485138[/C][/ROW]
[ROW][C]39[/C][C]232.3[/C][C]214.187661657891[/C][C]18.1123383421087[/C][/ROW]
[ROW][C]40[/C][C]193.8[/C][C]190.819583638426[/C][C]2.98041636157421[/C][/ROW]
[ROW][C]41[/C][C]177[/C][C]188.936240573508[/C][C]-11.9362405735080[/C][/ROW]
[ROW][C]42[/C][C]213.2[/C][C]198.02091035018[/C][C]15.1790896498201[/C][/ROW]
[ROW][C]43[/C][C]207.2[/C][C]175.271356359930[/C][C]31.9286436400704[/C][/ROW]
[ROW][C]44[/C][C]180.6[/C][C]165.663899251459[/C][C]14.9361007485408[/C][/ROW]
[ROW][C]45[/C][C]188.6[/C][C]156.7173676347[/C][C]31.8826323652999[/C][/ROW]
[ROW][C]46[/C][C]175.4[/C][C]153.744471659366[/C][C]21.6555283406338[/C][/ROW]
[ROW][C]47[/C][C]199[/C][C]194.105755786364[/C][C]4.89424421363597[/C][/ROW]
[ROW][C]48[/C][C]179.6[/C][C]212.323203513490[/C][C]-32.7232035134896[/C][/ROW]
[ROW][C]49[/C][C]225.8[/C][C]249.794787152436[/C][C]-23.9947871524365[/C][/ROW]
[ROW][C]50[/C][C]234[/C][C]249.950934783951[/C][C]-15.9509347839508[/C][/ROW]
[ROW][C]51[/C][C]200.2[/C][C]207.683360947197[/C][C]-7.48336094719704[/C][/ROW]
[ROW][C]52[/C][C]183.6[/C][C]165.468941877368[/C][C]18.131058122632[/C][/ROW]
[ROW][C]53[/C][C]178.2[/C][C]185.600786619152[/C][C]-7.40078661915223[/C][/ROW]
[ROW][C]54[/C][C]203.2[/C][C]210.588865862496[/C][C]-7.38886586249606[/C][/ROW]
[ROW][C]55[/C][C]208.5[/C][C]173.457450296597[/C][C]35.0425497034026[/C][/ROW]
[ROW][C]56[/C][C]191.8[/C][C]171.648936288595[/C][C]20.1510637114047[/C][/ROW]
[ROW][C]57[/C][C]172.8[/C][C]175.800849222989[/C][C]-3.00084922298859[/C][/ROW]
[ROW][C]58[/C][C]148[/C][C]140.016585341255[/C][C]7.98341465874466[/C][/ROW]
[ROW][C]59[/C][C]159.4[/C][C]164.236672863252[/C][C]-4.83667286325192[/C][/ROW]
[ROW][C]60[/C][C]154.5[/C][C]166.673623033259[/C][C]-12.1736230332594[/C][/ROW]
[ROW][C]61[/C][C]213.2[/C][C]223.702169031232[/C][C]-10.5021690312323[/C][/ROW]
[ROW][C]62[/C][C]196.4[/C][C]239.39057988577[/C][C]-42.9905798857699[/C][/ROW]
[ROW][C]63[/C][C]182.8[/C][C]169.752613061597[/C][C]13.0473869384029[/C][/ROW]
[ROW][C]64[/C][C]176.4[/C][C]149.584465280711[/C][C]26.8155347192886[/C][/ROW]
[ROW][C]65[/C][C]153.6[/C][C]178.873926475988[/C][C]-25.2739264759875[/C][/ROW]
[ROW][C]66[/C][C]173.2[/C][C]186.621865566447[/C][C]-13.4218655664472[/C][/ROW]
[ROW][C]67[/C][C]171[/C][C]145.040725366441[/C][C]25.9592746335586[/C][/ROW]
[ROW][C]68[/C][C]151.2[/C][C]130.242787571883[/C][C]20.9572124281166[/C][/ROW]
[ROW][C]69[/C][C]161.9[/C][C]130.197524143635[/C][C]31.7024758563652[/C][/ROW]
[ROW][C]70[/C][C]157.2[/C][C]130.798125576262[/C][C]26.4018744237381[/C][/ROW]
[ROW][C]71[/C][C]201.7[/C][C]178.13865380437[/C][C]23.5613461956299[/C][/ROW]
[ROW][C]72[/C][C]236.4[/C][C]218.822203796322[/C][C]17.577796203678[/C][/ROW]
[ROW][C]73[/C][C]356.1[/C][C]321.695685829852[/C][C]34.4043141701481[/C][/ROW]
[ROW][C]74[/C][C]398.3[/C][C]403.611023511471[/C][C]-5.31102351147098[/C][/ROW]
[ROW][C]75[/C][C]403.7[/C][C]406.818941593635[/C][C]-3.1189415936347[/C][/ROW]
[ROW][C]76[/C][C]384.6[/C][C]403.342954976271[/C][C]-18.7429549762708[/C][/ROW]
[ROW][C]77[/C][C]365.8[/C][C]408.662580727233[/C][C]-42.8625807272334[/C][/ROW]
[ROW][C]78[/C][C]368.1[/C][C]419.512325649181[/C][C]-51.4123256491812[/C][/ROW]
[ROW][C]79[/C][C]367.9[/C][C]356.637719841075[/C][C]11.2622801589251[/C][/ROW]
[ROW][C]80[/C][C]347[/C][C]336.346972645868[/C][C]10.6530273541316[/C][/ROW]
[ROW][C]81[/C][C]343.3[/C][C]334.005020078399[/C][C]9.29497992160105[/C][/ROW]
[ROW][C]82[/C][C]292.9[/C][C]315.627954770634[/C][C]-22.7279547706338[/C][/ROW]
[ROW][C]83[/C][C]311.5[/C][C]309.841166936280[/C][C]1.65883306372035[/C][/ROW]
[ROW][C]84[/C][C]300.9[/C][C]318.320944264907[/C][C]-17.420944264907[/C][/ROW]
[ROW][C]85[/C][C]366.9[/C][C]371.646305877894[/C][C]-4.74630587789386[/C][/ROW]
[ROW][C]86[/C][C]356.9[/C][C]388.724539548477[/C][C]-31.8245395484767[/C][/ROW]
[ROW][C]87[/C][C]329.7[/C][C]336.657017800339[/C][C]-6.95701780033909[/C][/ROW]
[ROW][C]88[/C][C]316.2[/C][C]297.050191389958[/C][C]19.1498086100416[/C][/ROW]
[ROW][C]89[/C][C]269[/C][C]311.786148591763[/C][C]-42.7861485917631[/C][/ROW]
[ROW][C]90[/C][C]289.3[/C][C]297.933467787587[/C][C]-8.633467787587[/C][/ROW]
[ROW][C]91[/C][C]266.2[/C][C]263.246590625195[/C][C]2.95340937480455[/C][/ROW]
[ROW][C]92[/C][C]253.6[/C][C]217.617902786234[/C][C]35.9820972137661[/C][/ROW]
[ROW][C]93[/C][C]233.8[/C][C]226.070834134544[/C][C]7.72916586545617[/C][/ROW]
[ROW][C]94[/C][C]228.4[/C][C]191.032815136388[/C][C]37.3671848636118[/C][/ROW]
[ROW][C]95[/C][C]253.6[/C][C]241.431279955095[/C][C]12.1687200449046[/C][/ROW]
[ROW][C]96[/C][C]260.1[/C][C]258.952674786756[/C][C]1.14732521324379[/C][/ROW]
[ROW][C]97[/C][C]306.6[/C][C]334.580689426555[/C][C]-27.9806894265545[/C][/ROW]
[ROW][C]98[/C][C]309.2[/C][C]327.835752397094[/C][C]-18.6357523970942[/C][/ROW]
[ROW][C]99[/C][C]309.5[/C][C]291.973343988169[/C][C]17.5266560118306[/C][/ROW]
[ROW][C]100[/C][C]271[/C][C]283.877458081835[/C][C]-12.8774580818352[/C][/ROW]
[ROW][C]101[/C][C]279.9[/C][C]265.284004888885[/C][C]14.6159951111154[/C][/ROW]
[ROW][C]102[/C][C]317.9[/C][C]319.020759041934[/C][C]-1.12075904193443[/C][/ROW]
[ROW][C]103[/C][C]298.4[/C][C]305.362418845651[/C][C]-6.96241884565143[/C][/ROW]
[ROW][C]104[/C][C]246.7[/C][C]264.109866220531[/C][C]-17.4098662205309[/C][/ROW]
[ROW][C]105[/C][C]227.3[/C][C]221.975001427004[/C][C]5.32499857299592[/C][/ROW]
[ROW][C]106[/C][C]209.1[/C][C]187.351231640874[/C][C]21.7487683591257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109355&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
13299.5239.39449786324860.105502136752
14347.4351.546379551372-4.14637955137209
15338.3347.761267230222-9.46126723022172
16327.7334.364066404668-6.66406640466812
17351.6356.944740044102-5.34474004410174
18396.6403.143379598236-6.54337959823573
19438.8386.10623302541252.6937669745876
20395.6440.036691546718-44.4366915467175
21363.5394.211126862163-30.7111268621633
22378.8340.71716383111738.0828361688831
23357415.401624919934-58.4016249199345
24369374.768913175063-5.76891317506329
25464.8445.99674360433918.8032563956606
26479.1503.369179174461-24.2691791744608
27431.3464.722125847542-33.4221258475416
28366.5408.845143482560-42.3451434825595
29326.3371.076136331253-44.7761363312532
30355.1345.68289589469.4171041053998
31331.6315.86057540555415.7394245944456
32261.3289.853347712182-28.5533477121820
33249223.98226688487025.0177331151295
34205.5202.0469809716703.4530190283304
35235.6206.10879475745229.4912052425480
36240.9236.0996722582714.80032774172892
37264.9306.056870999756-41.1568709997564
38253.8280.306744485138-26.506744485138
39232.3214.18766165789118.1123383421087
40193.8190.8195836384262.98041636157421
41177188.936240573508-11.9362405735080
42213.2198.0209103501815.1790896498201
43207.2175.27135635993031.9286436400704
44180.6165.66389925145914.9361007485408
45188.6156.717367634731.8826323652999
46175.4153.74447165936621.6555283406338
47199194.1057557863644.89424421363597
48179.6212.323203513490-32.7232035134896
49225.8249.794787152436-23.9947871524365
50234249.950934783951-15.9509347839508
51200.2207.683360947197-7.48336094719704
52183.6165.46894187736818.131058122632
53178.2185.600786619152-7.40078661915223
54203.2210.588865862496-7.38886586249606
55208.5173.45745029659735.0425497034026
56191.8171.64893628859520.1510637114047
57172.8175.800849222989-3.00084922298859
58148140.0165853412557.98341465874466
59159.4164.236672863252-4.83667286325192
60154.5166.673623033259-12.1736230332594
61213.2223.702169031232-10.5021690312323
62196.4239.39057988577-42.9905798857699
63182.8169.75261306159713.0473869384029
64176.4149.58446528071126.8155347192886
65153.6178.873926475988-25.2739264759875
66173.2186.621865566447-13.4218655664472
67171145.04072536644125.9592746335586
68151.2130.24278757188320.9572124281166
69161.9130.19752414363531.7024758563652
70157.2130.79812557626226.4018744237381
71201.7178.1386538043723.5613461956299
72236.4218.82220379632217.577796203678
73356.1321.69568582985234.4043141701481
74398.3403.611023511471-5.31102351147098
75403.7406.818941593635-3.1189415936347
76384.6403.342954976271-18.7429549762708
77365.8408.662580727233-42.8625807272334
78368.1419.512325649181-51.4123256491812
79367.9356.63771984107511.2622801589251
80347336.34697264586810.6530273541316
81343.3334.0050200783999.29497992160105
82292.9315.627954770634-22.7279547706338
83311.5309.8411669362801.65883306372035
84300.9318.320944264907-17.420944264907
85366.9371.646305877894-4.74630587789386
86356.9388.724539548477-31.8245395484767
87329.7336.657017800339-6.95701780033909
88316.2297.05019138995819.1498086100416
89269311.786148591763-42.7861485917631
90289.3297.933467787587-8.633467787587
91266.2263.2465906251952.95340937480455
92253.6217.61790278623435.9820972137661
93233.8226.0708341345447.72916586545617
94228.4191.03281513638837.3671848636118
95253.6241.43127995509512.1687200449046
96260.1258.9526747867561.14732521324379
97306.6334.580689426555-27.9806894265545
98309.2327.835752397094-18.6357523970942
99309.5291.97334398816917.5266560118306
100271283.877458081835-12.8774580818352
101279.9265.28400488888514.6159951111154
102317.9319.020759041934-1.12075904193443
103298.4305.362418845651-6.96241884565143
104246.7264.109866220531-17.4098662205309
105227.3221.9750014270045.32499857299592
106209.1187.35123164087421.7487683591257







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
107219.077216722963170.752129011988267.402304433938
108219.777597650389147.104849866391292.450345434387
109287.376112509797190.827733352295383.924491667299
110307.750955103168186.80240432511428.699505881226
111295.739011578135149.53822630925441.93979684702
112269.86591721645997.4350712451952442.296763187724
113268.27047918171268.5852591143745467.955699249049
114307.61766381199879.6428952150977535.592432408898
115295.11887517170237.8257063089802552.412044034423
116261.484664602242-26.1409255037481549.110254708233
117242.329343696241-76.6237331483823561.282420540865
118208.060039970237-143.194830840926559.3149107814

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
107 & 219.077216722963 & 170.752129011988 & 267.402304433938 \tabularnewline
108 & 219.777597650389 & 147.104849866391 & 292.450345434387 \tabularnewline
109 & 287.376112509797 & 190.827733352295 & 383.924491667299 \tabularnewline
110 & 307.750955103168 & 186.80240432511 & 428.699505881226 \tabularnewline
111 & 295.739011578135 & 149.53822630925 & 441.93979684702 \tabularnewline
112 & 269.865917216459 & 97.4350712451952 & 442.296763187724 \tabularnewline
113 & 268.270479181712 & 68.5852591143745 & 467.955699249049 \tabularnewline
114 & 307.617663811998 & 79.6428952150977 & 535.592432408898 \tabularnewline
115 & 295.118875171702 & 37.8257063089802 & 552.412044034423 \tabularnewline
116 & 261.484664602242 & -26.1409255037481 & 549.110254708233 \tabularnewline
117 & 242.329343696241 & -76.6237331483823 & 561.282420540865 \tabularnewline
118 & 208.060039970237 & -143.194830840926 & 559.3149107814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109355&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]107[/C][C]219.077216722963[/C][C]170.752129011988[/C][C]267.402304433938[/C][/ROW]
[ROW][C]108[/C][C]219.777597650389[/C][C]147.104849866391[/C][C]292.450345434387[/C][/ROW]
[ROW][C]109[/C][C]287.376112509797[/C][C]190.827733352295[/C][C]383.924491667299[/C][/ROW]
[ROW][C]110[/C][C]307.750955103168[/C][C]186.80240432511[/C][C]428.699505881226[/C][/ROW]
[ROW][C]111[/C][C]295.739011578135[/C][C]149.53822630925[/C][C]441.93979684702[/C][/ROW]
[ROW][C]112[/C][C]269.865917216459[/C][C]97.4350712451952[/C][C]442.296763187724[/C][/ROW]
[ROW][C]113[/C][C]268.270479181712[/C][C]68.5852591143745[/C][C]467.955699249049[/C][/ROW]
[ROW][C]114[/C][C]307.617663811998[/C][C]79.6428952150977[/C][C]535.592432408898[/C][/ROW]
[ROW][C]115[/C][C]295.118875171702[/C][C]37.8257063089802[/C][C]552.412044034423[/C][/ROW]
[ROW][C]116[/C][C]261.484664602242[/C][C]-26.1409255037481[/C][C]549.110254708233[/C][/ROW]
[ROW][C]117[/C][C]242.329343696241[/C][C]-76.6237331483823[/C][C]561.282420540865[/C][/ROW]
[ROW][C]118[/C][C]208.060039970237[/C][C]-143.194830840926[/C][C]559.3149107814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109355&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
107219.077216722963170.752129011988267.402304433938
108219.777597650389147.104849866391292.450345434387
109287.376112509797190.827733352295383.924491667299
110307.750955103168186.80240432511428.699505881226
111295.739011578135149.53822630925441.93979684702
112269.86591721645997.4350712451952442.296763187724
113268.27047918171268.5852591143745467.955699249049
114307.61766381199879.6428952150977535.592432408898
115295.11887517170237.8257063089802552.412044034423
116261.484664602242-26.1409255037481549.110254708233
117242.329343696241-76.6237331483823561.282420540865
118208.060039970237-143.194830840926559.3149107814



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')