Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 12:21:29 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/16/t12819612633xjg3ggggkk2809.htm/, Retrieved Thu, 16 May 2024 11:01:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78973, Retrieved Thu, 16 May 2024 11:01:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMagali De Reu
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 1 stap 32] [2010-08-16 12:21:29] [07915b1f88a41fb8d82e27c5eaa7bbed] [Current]
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Dataseries X:
333
332
331
329
349
348
333
323
324
324
325
327
329
333
329
333
355
358
338
326
320
322
322
324
326
330
331
333
364
363
341
327
313
321
312
312
312
314
312
319
356
351
329
313
298
303
278
275
276
276
273
287
320
313
281
266
258
259
237
231
237
236
229
243
271
262
227
208
212
222
200
193
204
203
190
209
240
234
210
195
202
204
180
169
178
181
163
174
194
187
160
143
151
154
141
127
134
138
120
129
151
152
124
99
104
109
96
87
94
89
63
76
100
104
80
55
60
71
62
61




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' @ 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78973&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78973&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' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999950136832542
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999950136832542 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78973&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]0.999950136832542[/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=78973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78973&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
alpha0.999950136832542
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2332333-1
3331332.000049863167-1.00004986316748
4329331.000049865654-2.00004986565381
5349329.00009972882119.9999002711786
6348348.999002741624-0.999002741623599
7333348.000049813441-15.0000498134410
8323333.000747949996-10.0007479499957
9324323.000498668970.999501331030274
10324323.9999501616984.98383022318194e-05
11325323.9999999975151.00000000248508
12327324.9999501368322.00004986316759
13329326.9999002711792.00009972882128
14333328.9999002686924.00009973130773
15329332.999800542357-3.99980054235721
16333329.0001994427243.99980055727576
17355332.99980055727522.0001994427250
18358354.9989030003713.00109699962894
19338357.999850355798-19.9998503557977
20326338.000997255887-12.0009972558875
21320326.000598407736-6.00059840773582
22322320.0002992088431.99970079115678
23322321.9999002885859.97114154301926e-05
24324321.9999999950282.00000000497192
25326323.9999002736652.00009972633512
26330325.9999002686924.00009973130761
27331329.9998005423571.00019945764279
28333330.9999501268872.00004987311303
29364332.99990027117831.0000997288218
30363363.998454236836-0.998454236835983
31341363.000049786091-22.0000497860908
32327341.001096992167-14.0010969921666
33313327.000698139044-14.0006981390439
34321313.0006981191567.99930188084414
35312320.999601129471-8.99960112947082
36312312.000448748618-0.000448748618168793
37312312.000000022376-2.23760707740439e-08
38314312.0000000000011.99999999999886
39312313.999900273665-1.99990027366505
40319312.0000997213626.99990027863777
41356318.999650962837.0003490371998
42351355.9981550454-4.99815504539998
43329351.000249223842-22.000249223842
44313329.001097002111-16.0010970021112
45298313.000797865379-15.0007978653793
46303298.0007479872964.99925201270406
47278302.99975072146-24.9997507214597
48275278.001246566757-3.00124656675661
49276275.000149651660.999850348339862
50276275.9999501442954.98557053560944e-05
51273275.999999997514-2.99999999751401
52287273.00014958950213.9998504104978
53320286.99930192311533.0006980768854
54313319.998354480666-6.99835448066557
55281313.000348960121-32.0003489601214
56266281.001595638759-15.0015956387589
57258266.000748027075-8.00074802707547
58259258.0003989426390.999601057361303
59237258.999950156725-21.9999501567251
60231237.001096987199-6.00109698719874
61237231.0002992337045.999700766296
62236236.999700835916-0.999700835916002
63229236.00004984825-7.00004984825017
64243229.00034904465813.9996509553422
65271242.9993019330628.0006980669399
66262270.998603796503-8.99860379650335
67227262.000448698888-35.000448698888
68208227.001745233235-19.0017452332346
69212208.0009474872053.99905251279543
70222211.99980059457510.0001994054251
71200221.999501358382-21.9995013583824
72193200.001096964820-7.00109696482025
73204193.00034909687010.9996509031297
74203203.999451522565-0.99945152256504
75190203.000049835819-13.0000498358186
76209190.00064822366218.9993517763381
77240208.99905263214131.0009473678592
78234239.99845419457-5.99845419457006
79210234.000299101926-24.000299101926
80195210.001196730933-15.0011967309332
81202195.0007480071856.99925199281535
82204201.9996509951262.00034900487418
83180203.999900256263-23.9999002562626
84169180.001196711045-11.0011967110455
85178169.0005485545148.99945144548616
86181177.9995512588463.00044874115446
87163180.999850388122-17.999850388122
88174163.00089752955410.9991024704459
89194173.99945154991220.0005484500884
90187193.999002709303-6.9990027093034
91160187.000348992444-27.0003489924441
92143160.001346322923-17.0013463229232
93151143.0008477409797.99915225902132
94154150.9996011369313.00039886306860
95141153.999850390609-12.9998503906090
96127141.000648213717-14.0006482137169
97134127.0006981166666.9993018833336
98138133.9996509926384.00034900736190
99120137.999800529928-17.9998005299275
100129120.0008975270688.99910247293197
101151128.99955127624622.0004487237536
102152150.9989029879411.00109701205884
103124151.999950082132-27.9999500821320
10499124.001396166200-25.0013961661998
10510499.00124664880374.99875335119629
106109103.9997507463255.00024925367542
10796108.999750671734-12.9997506717341
1088796.0006482087447-9.00064820874466
1099487.00044880082896.99955119917114
1108993.9996509802064-4.99965098020643
1116389.000249298434-26.0002492984341
1127663.001296454784712.9987035452153
11310075.999351843468424.0006481565316
11410499.99880325166194.00119674833812
11580103.999800487657-23.9998004876565
1165580.0011967060707-25.0011967060707
1176055.0012466388584.998753361142
1187159.999750746324111.0002492536759
1196270.9994514927294-8.9994514927294
1206162.0004487411568-1.00044874115681

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 332 & 333 & -1 \tabularnewline
3 & 331 & 332.000049863167 & -1.00004986316748 \tabularnewline
4 & 329 & 331.000049865654 & -2.00004986565381 \tabularnewline
5 & 349 & 329.000099728821 & 19.9999002711786 \tabularnewline
6 & 348 & 348.999002741624 & -0.999002741623599 \tabularnewline
7 & 333 & 348.000049813441 & -15.0000498134410 \tabularnewline
8 & 323 & 333.000747949996 & -10.0007479499957 \tabularnewline
9 & 324 & 323.00049866897 & 0.999501331030274 \tabularnewline
10 & 324 & 323.999950161698 & 4.98383022318194e-05 \tabularnewline
11 & 325 & 323.999999997515 & 1.00000000248508 \tabularnewline
12 & 327 & 324.999950136832 & 2.00004986316759 \tabularnewline
13 & 329 & 326.999900271179 & 2.00009972882128 \tabularnewline
14 & 333 & 328.999900268692 & 4.00009973130773 \tabularnewline
15 & 329 & 332.999800542357 & -3.99980054235721 \tabularnewline
16 & 333 & 329.000199442724 & 3.99980055727576 \tabularnewline
17 & 355 & 332.999800557275 & 22.0001994427250 \tabularnewline
18 & 358 & 354.998903000371 & 3.00109699962894 \tabularnewline
19 & 338 & 357.999850355798 & -19.9998503557977 \tabularnewline
20 & 326 & 338.000997255887 & -12.0009972558875 \tabularnewline
21 & 320 & 326.000598407736 & -6.00059840773582 \tabularnewline
22 & 322 & 320.000299208843 & 1.99970079115678 \tabularnewline
23 & 322 & 321.999900288585 & 9.97114154301926e-05 \tabularnewline
24 & 324 & 321.999999995028 & 2.00000000497192 \tabularnewline
25 & 326 & 323.999900273665 & 2.00009972633512 \tabularnewline
26 & 330 & 325.999900268692 & 4.00009973130761 \tabularnewline
27 & 331 & 329.999800542357 & 1.00019945764279 \tabularnewline
28 & 333 & 330.999950126887 & 2.00004987311303 \tabularnewline
29 & 364 & 332.999900271178 & 31.0000997288218 \tabularnewline
30 & 363 & 363.998454236836 & -0.998454236835983 \tabularnewline
31 & 341 & 363.000049786091 & -22.0000497860908 \tabularnewline
32 & 327 & 341.001096992167 & -14.0010969921666 \tabularnewline
33 & 313 & 327.000698139044 & -14.0006981390439 \tabularnewline
34 & 321 & 313.000698119156 & 7.99930188084414 \tabularnewline
35 & 312 & 320.999601129471 & -8.99960112947082 \tabularnewline
36 & 312 & 312.000448748618 & -0.000448748618168793 \tabularnewline
37 & 312 & 312.000000022376 & -2.23760707740439e-08 \tabularnewline
38 & 314 & 312.000000000001 & 1.99999999999886 \tabularnewline
39 & 312 & 313.999900273665 & -1.99990027366505 \tabularnewline
40 & 319 & 312.000099721362 & 6.99990027863777 \tabularnewline
41 & 356 & 318.9996509628 & 37.0003490371998 \tabularnewline
42 & 351 & 355.9981550454 & -4.99815504539998 \tabularnewline
43 & 329 & 351.000249223842 & -22.000249223842 \tabularnewline
44 & 313 & 329.001097002111 & -16.0010970021112 \tabularnewline
45 & 298 & 313.000797865379 & -15.0007978653793 \tabularnewline
46 & 303 & 298.000747987296 & 4.99925201270406 \tabularnewline
47 & 278 & 302.99975072146 & -24.9997507214597 \tabularnewline
48 & 275 & 278.001246566757 & -3.00124656675661 \tabularnewline
49 & 276 & 275.00014965166 & 0.999850348339862 \tabularnewline
50 & 276 & 275.999950144295 & 4.98557053560944e-05 \tabularnewline
51 & 273 & 275.999999997514 & -2.99999999751401 \tabularnewline
52 & 287 & 273.000149589502 & 13.9998504104978 \tabularnewline
53 & 320 & 286.999301923115 & 33.0006980768854 \tabularnewline
54 & 313 & 319.998354480666 & -6.99835448066557 \tabularnewline
55 & 281 & 313.000348960121 & -32.0003489601214 \tabularnewline
56 & 266 & 281.001595638759 & -15.0015956387589 \tabularnewline
57 & 258 & 266.000748027075 & -8.00074802707547 \tabularnewline
58 & 259 & 258.000398942639 & 0.999601057361303 \tabularnewline
59 & 237 & 258.999950156725 & -21.9999501567251 \tabularnewline
60 & 231 & 237.001096987199 & -6.00109698719874 \tabularnewline
61 & 237 & 231.000299233704 & 5.999700766296 \tabularnewline
62 & 236 & 236.999700835916 & -0.999700835916002 \tabularnewline
63 & 229 & 236.00004984825 & -7.00004984825017 \tabularnewline
64 & 243 & 229.000349044658 & 13.9996509553422 \tabularnewline
65 & 271 & 242.99930193306 & 28.0006980669399 \tabularnewline
66 & 262 & 270.998603796503 & -8.99860379650335 \tabularnewline
67 & 227 & 262.000448698888 & -35.000448698888 \tabularnewline
68 & 208 & 227.001745233235 & -19.0017452332346 \tabularnewline
69 & 212 & 208.000947487205 & 3.99905251279543 \tabularnewline
70 & 222 & 211.999800594575 & 10.0001994054251 \tabularnewline
71 & 200 & 221.999501358382 & -21.9995013583824 \tabularnewline
72 & 193 & 200.001096964820 & -7.00109696482025 \tabularnewline
73 & 204 & 193.000349096870 & 10.9996509031297 \tabularnewline
74 & 203 & 203.999451522565 & -0.99945152256504 \tabularnewline
75 & 190 & 203.000049835819 & -13.0000498358186 \tabularnewline
76 & 209 & 190.000648223662 & 18.9993517763381 \tabularnewline
77 & 240 & 208.999052632141 & 31.0009473678592 \tabularnewline
78 & 234 & 239.99845419457 & -5.99845419457006 \tabularnewline
79 & 210 & 234.000299101926 & -24.000299101926 \tabularnewline
80 & 195 & 210.001196730933 & -15.0011967309332 \tabularnewline
81 & 202 & 195.000748007185 & 6.99925199281535 \tabularnewline
82 & 204 & 201.999650995126 & 2.00034900487418 \tabularnewline
83 & 180 & 203.999900256263 & -23.9999002562626 \tabularnewline
84 & 169 & 180.001196711045 & -11.0011967110455 \tabularnewline
85 & 178 & 169.000548554514 & 8.99945144548616 \tabularnewline
86 & 181 & 177.999551258846 & 3.00044874115446 \tabularnewline
87 & 163 & 180.999850388122 & -17.999850388122 \tabularnewline
88 & 174 & 163.000897529554 & 10.9991024704459 \tabularnewline
89 & 194 & 173.999451549912 & 20.0005484500884 \tabularnewline
90 & 187 & 193.999002709303 & -6.9990027093034 \tabularnewline
91 & 160 & 187.000348992444 & -27.0003489924441 \tabularnewline
92 & 143 & 160.001346322923 & -17.0013463229232 \tabularnewline
93 & 151 & 143.000847740979 & 7.99915225902132 \tabularnewline
94 & 154 & 150.999601136931 & 3.00039886306860 \tabularnewline
95 & 141 & 153.999850390609 & -12.9998503906090 \tabularnewline
96 & 127 & 141.000648213717 & -14.0006482137169 \tabularnewline
97 & 134 & 127.000698116666 & 6.9993018833336 \tabularnewline
98 & 138 & 133.999650992638 & 4.00034900736190 \tabularnewline
99 & 120 & 137.999800529928 & -17.9998005299275 \tabularnewline
100 & 129 & 120.000897527068 & 8.99910247293197 \tabularnewline
101 & 151 & 128.999551276246 & 22.0004487237536 \tabularnewline
102 & 152 & 150.998902987941 & 1.00109701205884 \tabularnewline
103 & 124 & 151.999950082132 & -27.9999500821320 \tabularnewline
104 & 99 & 124.001396166200 & -25.0013961661998 \tabularnewline
105 & 104 & 99.0012466488037 & 4.99875335119629 \tabularnewline
106 & 109 & 103.999750746325 & 5.00024925367542 \tabularnewline
107 & 96 & 108.999750671734 & -12.9997506717341 \tabularnewline
108 & 87 & 96.0006482087447 & -9.00064820874466 \tabularnewline
109 & 94 & 87.0004488008289 & 6.99955119917114 \tabularnewline
110 & 89 & 93.9996509802064 & -4.99965098020643 \tabularnewline
111 & 63 & 89.000249298434 & -26.0002492984341 \tabularnewline
112 & 76 & 63.0012964547847 & 12.9987035452153 \tabularnewline
113 & 100 & 75.9993518434684 & 24.0006481565316 \tabularnewline
114 & 104 & 99.9988032516619 & 4.00119674833812 \tabularnewline
115 & 80 & 103.999800487657 & -23.9998004876565 \tabularnewline
116 & 55 & 80.0011967060707 & -25.0011967060707 \tabularnewline
117 & 60 & 55.001246638858 & 4.998753361142 \tabularnewline
118 & 71 & 59.9997507463241 & 11.0002492536759 \tabularnewline
119 & 62 & 70.9994514927294 & -8.9994514927294 \tabularnewline
120 & 61 & 62.0004487411568 & -1.00044874115681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78973&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]332[/C][C]333[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]331[/C][C]332.000049863167[/C][C]-1.00004986316748[/C][/ROW]
[ROW][C]4[/C][C]329[/C][C]331.000049865654[/C][C]-2.00004986565381[/C][/ROW]
[ROW][C]5[/C][C]349[/C][C]329.000099728821[/C][C]19.9999002711786[/C][/ROW]
[ROW][C]6[/C][C]348[/C][C]348.999002741624[/C][C]-0.999002741623599[/C][/ROW]
[ROW][C]7[/C][C]333[/C][C]348.000049813441[/C][C]-15.0000498134410[/C][/ROW]
[ROW][C]8[/C][C]323[/C][C]333.000747949996[/C][C]-10.0007479499957[/C][/ROW]
[ROW][C]9[/C][C]324[/C][C]323.00049866897[/C][C]0.999501331030274[/C][/ROW]
[ROW][C]10[/C][C]324[/C][C]323.999950161698[/C][C]4.98383022318194e-05[/C][/ROW]
[ROW][C]11[/C][C]325[/C][C]323.999999997515[/C][C]1.00000000248508[/C][/ROW]
[ROW][C]12[/C][C]327[/C][C]324.999950136832[/C][C]2.00004986316759[/C][/ROW]
[ROW][C]13[/C][C]329[/C][C]326.999900271179[/C][C]2.00009972882128[/C][/ROW]
[ROW][C]14[/C][C]333[/C][C]328.999900268692[/C][C]4.00009973130773[/C][/ROW]
[ROW][C]15[/C][C]329[/C][C]332.999800542357[/C][C]-3.99980054235721[/C][/ROW]
[ROW][C]16[/C][C]333[/C][C]329.000199442724[/C][C]3.99980055727576[/C][/ROW]
[ROW][C]17[/C][C]355[/C][C]332.999800557275[/C][C]22.0001994427250[/C][/ROW]
[ROW][C]18[/C][C]358[/C][C]354.998903000371[/C][C]3.00109699962894[/C][/ROW]
[ROW][C]19[/C][C]338[/C][C]357.999850355798[/C][C]-19.9998503557977[/C][/ROW]
[ROW][C]20[/C][C]326[/C][C]338.000997255887[/C][C]-12.0009972558875[/C][/ROW]
[ROW][C]21[/C][C]320[/C][C]326.000598407736[/C][C]-6.00059840773582[/C][/ROW]
[ROW][C]22[/C][C]322[/C][C]320.000299208843[/C][C]1.99970079115678[/C][/ROW]
[ROW][C]23[/C][C]322[/C][C]321.999900288585[/C][C]9.97114154301926e-05[/C][/ROW]
[ROW][C]24[/C][C]324[/C][C]321.999999995028[/C][C]2.00000000497192[/C][/ROW]
[ROW][C]25[/C][C]326[/C][C]323.999900273665[/C][C]2.00009972633512[/C][/ROW]
[ROW][C]26[/C][C]330[/C][C]325.999900268692[/C][C]4.00009973130761[/C][/ROW]
[ROW][C]27[/C][C]331[/C][C]329.999800542357[/C][C]1.00019945764279[/C][/ROW]
[ROW][C]28[/C][C]333[/C][C]330.999950126887[/C][C]2.00004987311303[/C][/ROW]
[ROW][C]29[/C][C]364[/C][C]332.999900271178[/C][C]31.0000997288218[/C][/ROW]
[ROW][C]30[/C][C]363[/C][C]363.998454236836[/C][C]-0.998454236835983[/C][/ROW]
[ROW][C]31[/C][C]341[/C][C]363.000049786091[/C][C]-22.0000497860908[/C][/ROW]
[ROW][C]32[/C][C]327[/C][C]341.001096992167[/C][C]-14.0010969921666[/C][/ROW]
[ROW][C]33[/C][C]313[/C][C]327.000698139044[/C][C]-14.0006981390439[/C][/ROW]
[ROW][C]34[/C][C]321[/C][C]313.000698119156[/C][C]7.99930188084414[/C][/ROW]
[ROW][C]35[/C][C]312[/C][C]320.999601129471[/C][C]-8.99960112947082[/C][/ROW]
[ROW][C]36[/C][C]312[/C][C]312.000448748618[/C][C]-0.000448748618168793[/C][/ROW]
[ROW][C]37[/C][C]312[/C][C]312.000000022376[/C][C]-2.23760707740439e-08[/C][/ROW]
[ROW][C]38[/C][C]314[/C][C]312.000000000001[/C][C]1.99999999999886[/C][/ROW]
[ROW][C]39[/C][C]312[/C][C]313.999900273665[/C][C]-1.99990027366505[/C][/ROW]
[ROW][C]40[/C][C]319[/C][C]312.000099721362[/C][C]6.99990027863777[/C][/ROW]
[ROW][C]41[/C][C]356[/C][C]318.9996509628[/C][C]37.0003490371998[/C][/ROW]
[ROW][C]42[/C][C]351[/C][C]355.9981550454[/C][C]-4.99815504539998[/C][/ROW]
[ROW][C]43[/C][C]329[/C][C]351.000249223842[/C][C]-22.000249223842[/C][/ROW]
[ROW][C]44[/C][C]313[/C][C]329.001097002111[/C][C]-16.0010970021112[/C][/ROW]
[ROW][C]45[/C][C]298[/C][C]313.000797865379[/C][C]-15.0007978653793[/C][/ROW]
[ROW][C]46[/C][C]303[/C][C]298.000747987296[/C][C]4.99925201270406[/C][/ROW]
[ROW][C]47[/C][C]278[/C][C]302.99975072146[/C][C]-24.9997507214597[/C][/ROW]
[ROW][C]48[/C][C]275[/C][C]278.001246566757[/C][C]-3.00124656675661[/C][/ROW]
[ROW][C]49[/C][C]276[/C][C]275.00014965166[/C][C]0.999850348339862[/C][/ROW]
[ROW][C]50[/C][C]276[/C][C]275.999950144295[/C][C]4.98557053560944e-05[/C][/ROW]
[ROW][C]51[/C][C]273[/C][C]275.999999997514[/C][C]-2.99999999751401[/C][/ROW]
[ROW][C]52[/C][C]287[/C][C]273.000149589502[/C][C]13.9998504104978[/C][/ROW]
[ROW][C]53[/C][C]320[/C][C]286.999301923115[/C][C]33.0006980768854[/C][/ROW]
[ROW][C]54[/C][C]313[/C][C]319.998354480666[/C][C]-6.99835448066557[/C][/ROW]
[ROW][C]55[/C][C]281[/C][C]313.000348960121[/C][C]-32.0003489601214[/C][/ROW]
[ROW][C]56[/C][C]266[/C][C]281.001595638759[/C][C]-15.0015956387589[/C][/ROW]
[ROW][C]57[/C][C]258[/C][C]266.000748027075[/C][C]-8.00074802707547[/C][/ROW]
[ROW][C]58[/C][C]259[/C][C]258.000398942639[/C][C]0.999601057361303[/C][/ROW]
[ROW][C]59[/C][C]237[/C][C]258.999950156725[/C][C]-21.9999501567251[/C][/ROW]
[ROW][C]60[/C][C]231[/C][C]237.001096987199[/C][C]-6.00109698719874[/C][/ROW]
[ROW][C]61[/C][C]237[/C][C]231.000299233704[/C][C]5.999700766296[/C][/ROW]
[ROW][C]62[/C][C]236[/C][C]236.999700835916[/C][C]-0.999700835916002[/C][/ROW]
[ROW][C]63[/C][C]229[/C][C]236.00004984825[/C][C]-7.00004984825017[/C][/ROW]
[ROW][C]64[/C][C]243[/C][C]229.000349044658[/C][C]13.9996509553422[/C][/ROW]
[ROW][C]65[/C][C]271[/C][C]242.99930193306[/C][C]28.0006980669399[/C][/ROW]
[ROW][C]66[/C][C]262[/C][C]270.998603796503[/C][C]-8.99860379650335[/C][/ROW]
[ROW][C]67[/C][C]227[/C][C]262.000448698888[/C][C]-35.000448698888[/C][/ROW]
[ROW][C]68[/C][C]208[/C][C]227.001745233235[/C][C]-19.0017452332346[/C][/ROW]
[ROW][C]69[/C][C]212[/C][C]208.000947487205[/C][C]3.99905251279543[/C][/ROW]
[ROW][C]70[/C][C]222[/C][C]211.999800594575[/C][C]10.0001994054251[/C][/ROW]
[ROW][C]71[/C][C]200[/C][C]221.999501358382[/C][C]-21.9995013583824[/C][/ROW]
[ROW][C]72[/C][C]193[/C][C]200.001096964820[/C][C]-7.00109696482025[/C][/ROW]
[ROW][C]73[/C][C]204[/C][C]193.000349096870[/C][C]10.9996509031297[/C][/ROW]
[ROW][C]74[/C][C]203[/C][C]203.999451522565[/C][C]-0.99945152256504[/C][/ROW]
[ROW][C]75[/C][C]190[/C][C]203.000049835819[/C][C]-13.0000498358186[/C][/ROW]
[ROW][C]76[/C][C]209[/C][C]190.000648223662[/C][C]18.9993517763381[/C][/ROW]
[ROW][C]77[/C][C]240[/C][C]208.999052632141[/C][C]31.0009473678592[/C][/ROW]
[ROW][C]78[/C][C]234[/C][C]239.99845419457[/C][C]-5.99845419457006[/C][/ROW]
[ROW][C]79[/C][C]210[/C][C]234.000299101926[/C][C]-24.000299101926[/C][/ROW]
[ROW][C]80[/C][C]195[/C][C]210.001196730933[/C][C]-15.0011967309332[/C][/ROW]
[ROW][C]81[/C][C]202[/C][C]195.000748007185[/C][C]6.99925199281535[/C][/ROW]
[ROW][C]82[/C][C]204[/C][C]201.999650995126[/C][C]2.00034900487418[/C][/ROW]
[ROW][C]83[/C][C]180[/C][C]203.999900256263[/C][C]-23.9999002562626[/C][/ROW]
[ROW][C]84[/C][C]169[/C][C]180.001196711045[/C][C]-11.0011967110455[/C][/ROW]
[ROW][C]85[/C][C]178[/C][C]169.000548554514[/C][C]8.99945144548616[/C][/ROW]
[ROW][C]86[/C][C]181[/C][C]177.999551258846[/C][C]3.00044874115446[/C][/ROW]
[ROW][C]87[/C][C]163[/C][C]180.999850388122[/C][C]-17.999850388122[/C][/ROW]
[ROW][C]88[/C][C]174[/C][C]163.000897529554[/C][C]10.9991024704459[/C][/ROW]
[ROW][C]89[/C][C]194[/C][C]173.999451549912[/C][C]20.0005484500884[/C][/ROW]
[ROW][C]90[/C][C]187[/C][C]193.999002709303[/C][C]-6.9990027093034[/C][/ROW]
[ROW][C]91[/C][C]160[/C][C]187.000348992444[/C][C]-27.0003489924441[/C][/ROW]
[ROW][C]92[/C][C]143[/C][C]160.001346322923[/C][C]-17.0013463229232[/C][/ROW]
[ROW][C]93[/C][C]151[/C][C]143.000847740979[/C][C]7.99915225902132[/C][/ROW]
[ROW][C]94[/C][C]154[/C][C]150.999601136931[/C][C]3.00039886306860[/C][/ROW]
[ROW][C]95[/C][C]141[/C][C]153.999850390609[/C][C]-12.9998503906090[/C][/ROW]
[ROW][C]96[/C][C]127[/C][C]141.000648213717[/C][C]-14.0006482137169[/C][/ROW]
[ROW][C]97[/C][C]134[/C][C]127.000698116666[/C][C]6.9993018833336[/C][/ROW]
[ROW][C]98[/C][C]138[/C][C]133.999650992638[/C][C]4.00034900736190[/C][/ROW]
[ROW][C]99[/C][C]120[/C][C]137.999800529928[/C][C]-17.9998005299275[/C][/ROW]
[ROW][C]100[/C][C]129[/C][C]120.000897527068[/C][C]8.99910247293197[/C][/ROW]
[ROW][C]101[/C][C]151[/C][C]128.999551276246[/C][C]22.0004487237536[/C][/ROW]
[ROW][C]102[/C][C]152[/C][C]150.998902987941[/C][C]1.00109701205884[/C][/ROW]
[ROW][C]103[/C][C]124[/C][C]151.999950082132[/C][C]-27.9999500821320[/C][/ROW]
[ROW][C]104[/C][C]99[/C][C]124.001396166200[/C][C]-25.0013961661998[/C][/ROW]
[ROW][C]105[/C][C]104[/C][C]99.0012466488037[/C][C]4.99875335119629[/C][/ROW]
[ROW][C]106[/C][C]109[/C][C]103.999750746325[/C][C]5.00024925367542[/C][/ROW]
[ROW][C]107[/C][C]96[/C][C]108.999750671734[/C][C]-12.9997506717341[/C][/ROW]
[ROW][C]108[/C][C]87[/C][C]96.0006482087447[/C][C]-9.00064820874466[/C][/ROW]
[ROW][C]109[/C][C]94[/C][C]87.0004488008289[/C][C]6.99955119917114[/C][/ROW]
[ROW][C]110[/C][C]89[/C][C]93.9996509802064[/C][C]-4.99965098020643[/C][/ROW]
[ROW][C]111[/C][C]63[/C][C]89.000249298434[/C][C]-26.0002492984341[/C][/ROW]
[ROW][C]112[/C][C]76[/C][C]63.0012964547847[/C][C]12.9987035452153[/C][/ROW]
[ROW][C]113[/C][C]100[/C][C]75.9993518434684[/C][C]24.0006481565316[/C][/ROW]
[ROW][C]114[/C][C]104[/C][C]99.9988032516619[/C][C]4.00119674833812[/C][/ROW]
[ROW][C]115[/C][C]80[/C][C]103.999800487657[/C][C]-23.9998004876565[/C][/ROW]
[ROW][C]116[/C][C]55[/C][C]80.0011967060707[/C][C]-25.0011967060707[/C][/ROW]
[ROW][C]117[/C][C]60[/C][C]55.001246638858[/C][C]4.998753361142[/C][/ROW]
[ROW][C]118[/C][C]71[/C][C]59.9997507463241[/C][C]11.0002492536759[/C][/ROW]
[ROW][C]119[/C][C]62[/C][C]70.9994514927294[/C][C]-8.9994514927294[/C][/ROW]
[ROW][C]120[/C][C]61[/C][C]62.0004487411568[/C][C]-1.00044874115681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78973&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78973&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
2332333-1
3331332.000049863167-1.00004986316748
4329331.000049865654-2.00004986565381
5349329.00009972882119.9999002711786
6348348.999002741624-0.999002741623599
7333348.000049813441-15.0000498134410
8323333.000747949996-10.0007479499957
9324323.000498668970.999501331030274
10324323.9999501616984.98383022318194e-05
11325323.9999999975151.00000000248508
12327324.9999501368322.00004986316759
13329326.9999002711792.00009972882128
14333328.9999002686924.00009973130773
15329332.999800542357-3.99980054235721
16333329.0001994427243.99980055727576
17355332.99980055727522.0001994427250
18358354.9989030003713.00109699962894
19338357.999850355798-19.9998503557977
20326338.000997255887-12.0009972558875
21320326.000598407736-6.00059840773582
22322320.0002992088431.99970079115678
23322321.9999002885859.97114154301926e-05
24324321.9999999950282.00000000497192
25326323.9999002736652.00009972633512
26330325.9999002686924.00009973130761
27331329.9998005423571.00019945764279
28333330.9999501268872.00004987311303
29364332.99990027117831.0000997288218
30363363.998454236836-0.998454236835983
31341363.000049786091-22.0000497860908
32327341.001096992167-14.0010969921666
33313327.000698139044-14.0006981390439
34321313.0006981191567.99930188084414
35312320.999601129471-8.99960112947082
36312312.000448748618-0.000448748618168793
37312312.000000022376-2.23760707740439e-08
38314312.0000000000011.99999999999886
39312313.999900273665-1.99990027366505
40319312.0000997213626.99990027863777
41356318.999650962837.0003490371998
42351355.9981550454-4.99815504539998
43329351.000249223842-22.000249223842
44313329.001097002111-16.0010970021112
45298313.000797865379-15.0007978653793
46303298.0007479872964.99925201270406
47278302.99975072146-24.9997507214597
48275278.001246566757-3.00124656675661
49276275.000149651660.999850348339862
50276275.9999501442954.98557053560944e-05
51273275.999999997514-2.99999999751401
52287273.00014958950213.9998504104978
53320286.99930192311533.0006980768854
54313319.998354480666-6.99835448066557
55281313.000348960121-32.0003489601214
56266281.001595638759-15.0015956387589
57258266.000748027075-8.00074802707547
58259258.0003989426390.999601057361303
59237258.999950156725-21.9999501567251
60231237.001096987199-6.00109698719874
61237231.0002992337045.999700766296
62236236.999700835916-0.999700835916002
63229236.00004984825-7.00004984825017
64243229.00034904465813.9996509553422
65271242.9993019330628.0006980669399
66262270.998603796503-8.99860379650335
67227262.000448698888-35.000448698888
68208227.001745233235-19.0017452332346
69212208.0009474872053.99905251279543
70222211.99980059457510.0001994054251
71200221.999501358382-21.9995013583824
72193200.001096964820-7.00109696482025
73204193.00034909687010.9996509031297
74203203.999451522565-0.99945152256504
75190203.000049835819-13.0000498358186
76209190.00064822366218.9993517763381
77240208.99905263214131.0009473678592
78234239.99845419457-5.99845419457006
79210234.000299101926-24.000299101926
80195210.001196730933-15.0011967309332
81202195.0007480071856.99925199281535
82204201.9996509951262.00034900487418
83180203.999900256263-23.9999002562626
84169180.001196711045-11.0011967110455
85178169.0005485545148.99945144548616
86181177.9995512588463.00044874115446
87163180.999850388122-17.999850388122
88174163.00089752955410.9991024704459
89194173.99945154991220.0005484500884
90187193.999002709303-6.9990027093034
91160187.000348992444-27.0003489924441
92143160.001346322923-17.0013463229232
93151143.0008477409797.99915225902132
94154150.9996011369313.00039886306860
95141153.999850390609-12.9998503906090
96127141.000648213717-14.0006482137169
97134127.0006981166666.9993018833336
98138133.9996509926384.00034900736190
99120137.999800529928-17.9998005299275
100129120.0008975270688.99910247293197
101151128.99955127624622.0004487237536
102152150.9989029879411.00109701205884
103124151.999950082132-27.9999500821320
10499124.001396166200-25.0013961661998
10510499.00124664880374.99875335119629
106109103.9997507463255.00024925367542
10796108.999750671734-12.9997506717341
1088796.0006482087447-9.00064820874466
1099487.00044880082896.99955119917114
1108993.9996509802064-4.99965098020643
1116389.000249298434-26.0002492984341
1127663.001296454784712.9987035452153
11310075.999351843468424.0006481565316
11410499.99880325166194.00119674833812
11580103.999800487657-23.9998004876565
1165580.0011967060707-25.0011967060707
1176055.0012466388584.998753361142
1187159.999750746324111.0002492536759
1196270.9994514927294-8.9994514927294
1206162.0004487411568-1.00044874115681







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12161.000049885543132.968520171933789.0315795991525
12261.000049885543121.358468730212100.641631040874
12361.000049885543112.4496301664054109.550469604681
12461.00004988554314.93908705654619117.06101271454
12561.0000498855431-1.67785572499808123.677955496084
12661.0000498855431-7.66004150773751129.660141278824
12761.0000498855431-13.1612368383493135.161336609436
12861.0000498855431-18.2816298831974140.281729654284
12961.0000498855431-23.0908119566503145.090911727737
13061.0000498855431-27.6394522778411149.639552048927
13161.0000498855431-31.9658021364888153.965901907575
13261.0000498855431-36.0995790560345158.099678827121

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 61.0000498855431 & 32.9685201719337 & 89.0315795991525 \tabularnewline
122 & 61.0000498855431 & 21.358468730212 & 100.641631040874 \tabularnewline
123 & 61.0000498855431 & 12.4496301664054 & 109.550469604681 \tabularnewline
124 & 61.0000498855431 & 4.93908705654619 & 117.06101271454 \tabularnewline
125 & 61.0000498855431 & -1.67785572499808 & 123.677955496084 \tabularnewline
126 & 61.0000498855431 & -7.66004150773751 & 129.660141278824 \tabularnewline
127 & 61.0000498855431 & -13.1612368383493 & 135.161336609436 \tabularnewline
128 & 61.0000498855431 & -18.2816298831974 & 140.281729654284 \tabularnewline
129 & 61.0000498855431 & -23.0908119566503 & 145.090911727737 \tabularnewline
130 & 61.0000498855431 & -27.6394522778411 & 149.639552048927 \tabularnewline
131 & 61.0000498855431 & -31.9658021364888 & 153.965901907575 \tabularnewline
132 & 61.0000498855431 & -36.0995790560345 & 158.099678827121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78973&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]121[/C][C]61.0000498855431[/C][C]32.9685201719337[/C][C]89.0315795991525[/C][/ROW]
[ROW][C]122[/C][C]61.0000498855431[/C][C]21.358468730212[/C][C]100.641631040874[/C][/ROW]
[ROW][C]123[/C][C]61.0000498855431[/C][C]12.4496301664054[/C][C]109.550469604681[/C][/ROW]
[ROW][C]124[/C][C]61.0000498855431[/C][C]4.93908705654619[/C][C]117.06101271454[/C][/ROW]
[ROW][C]125[/C][C]61.0000498855431[/C][C]-1.67785572499808[/C][C]123.677955496084[/C][/ROW]
[ROW][C]126[/C][C]61.0000498855431[/C][C]-7.66004150773751[/C][C]129.660141278824[/C][/ROW]
[ROW][C]127[/C][C]61.0000498855431[/C][C]-13.1612368383493[/C][C]135.161336609436[/C][/ROW]
[ROW][C]128[/C][C]61.0000498855431[/C][C]-18.2816298831974[/C][C]140.281729654284[/C][/ROW]
[ROW][C]129[/C][C]61.0000498855431[/C][C]-23.0908119566503[/C][C]145.090911727737[/C][/ROW]
[ROW][C]130[/C][C]61.0000498855431[/C][C]-27.6394522778411[/C][C]149.639552048927[/C][/ROW]
[ROW][C]131[/C][C]61.0000498855431[/C][C]-31.9658021364888[/C][C]153.965901907575[/C][/ROW]
[ROW][C]132[/C][C]61.0000498855431[/C][C]-36.0995790560345[/C][C]158.099678827121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78973&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78973&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
12161.000049885543132.968520171933789.0315795991525
12261.000049885543121.358468730212100.641631040874
12361.000049885543112.4496301664054109.550469604681
12461.00004988554314.93908705654619117.06101271454
12561.0000498855431-1.67785572499808123.677955496084
12661.0000498855431-7.66004150773751129.660141278824
12761.0000498855431-13.1612368383493135.161336609436
12861.0000498855431-18.2816298831974140.281729654284
12961.0000498855431-23.0908119566503145.090911727737
13061.0000498855431-27.6394522778411149.639552048927
13161.0000498855431-31.9658021364888153.965901907575
13261.0000498855431-36.0995790560345158.099678827121



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')