Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 May 2020 00:27:22 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/May/16/t1589581660d8nv1jbgxvm40z6.htm/, Retrieved Wed, 21 Apr 2021 07:55:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319155, Retrieved Wed, 21 Apr 2021 07:55:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact38
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2020-05-15 22:27:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319155&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319155&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319155&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00321851640040526
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00321851640040526 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319155&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00321851640040526[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319155&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319155&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00321851640040526
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31321248
4129138.025748131203-9.02574813120324
5121134.996698612817-13.996698612817
6135126.951650008788.04834999121985
7148140.9775537552237.02244624477692
8148154.000155613633-6.00015561363287
9136153.980844014385-17.9808440143854
10119141.922972373032-22.922972373032
11104124.849194410503-20.8491944105033
12118109.7820909363588.2179090636421
13115123.808540411456-8.80854041145628
14126120.7801899796785.21981002032163
15141131.7969900238369.20300997616422
16135146.826610062377-11.8266100623771
17125140.78854592393-15.7885459239302
18149130.73773022993518.2622697700645
19170154.79650764469915.2034923553009
20170175.845440334188-5.84544033418803
21158175.826626688605-17.8266266886048
22133163.769251398244-30.7692513982437
23114138.67022005799-24.6702200579902
24140119.59081855013220.409181449868
25145145.656505835347-0.656505835347218
26150150.654392860549-0.654392860549194
27178155.65228668639522.3477133136048
28163183.724213168207-20.7242131682066
29172168.6575119482393.34248805176077
30178177.6682698008520.331730199148012
31199183.66933747993815.3306625200615
32199204.718679468688-5.71867946868835
33184204.70027380503-20.7002738050297
34162189.633649634295-27.6336496342954
35146167.544710279744-21.5447102797443
36166151.47536827636714.524631723633
37171171.522116041779-0.522116041779356
38180176.5204356027363.47956439726403
39193185.5316346378157.46836536218518
40181198.555671694217-17.5556716942172
41183186.499168476949-3.49916847694928
42218188.48790634581829.5120936541816
43230223.5828915032556.4171084967453
44242235.6035450721956.39645492780534
45209247.624132167284-38.6241321672842
46191214.499819764452-23.4998197644524
47172196.424185209134-24.424185209134
48194177.34557556847216.6544244315282
49196199.399178106644-3.39917810664403
50196201.38823779616-5.3882377961599
51236201.37089566444434.6291043355563
52235241.482350004679-6.48235000467901
53229240.461486454876-11.4614864548758
54243234.4245974727488.57540252725227
55264248.45219754642215.5478024535782
56272269.5022384036092.49776159639111
57237277.510277490271-40.5102774902712
58211242.379894497784-31.3798944977838
59180216.2788977927-36.2788977926996
60201185.16213356516515.8378664348348
61204206.213107998033-2.21310799803317
62188209.205985073646-21.2059850736456
63235193.13773326289941.8622667371006
64227240.272467654951-13.2724676549508
65234232.229750000131.77024999987046
66264239.23544757878724.7645524212131
67302269.31515269690332.6848473030967
68293307.420349413993-14.4203494139931
69259298.373937282905-39.3739372829045
70229264.247211620011-35.247211620011
71203234.133767891343-31.1337678913434
72229208.03356334877920.9664366512213
73242234.1010441689997.89895583100125
74233247.126467087887-14.1264670878869
75267238.08100082188528.9189991781153
76269272.174077095023-3.17407709502282
77270274.163861275836-4.16386127583633
78315275.15045982003139.8495401799689
79364320.27871621864943.7212837813511
80347369.419433887546-22.4194338875459
81312352.347276571891-40.3472765718911
82274317.217418200533-43.2174182005327
83237279.078322231271-42.0783222312712
84278241.94289246106836.0571075389317
85284283.0589428530330.9410571469665
86277289.061971660895-12.0619716608948
87317282.02315000728334.9768499927171
88313322.135723572619-9.13572357261899
89318318.106320096471-0.106320096470938
90374323.10597790349750.8940220965032
91413379.26978114829733.7302188517031
92405418.37834241086-13.3783424108604
93355410.335283996401-55.3352839964008
94306360.157186477337-54.1571864773373
95271310.98288068446-39.9828806844602
96306275.85419512724230.1458048727582
97315310.9512198946284.04878010537175
98301319.964250959799-18.964250959799
99356305.90321420706450.0967857929365
100348361.064451533746-13.0644515337456
101355353.0224033822221.97759661777803
102422360.0287683093761.9712316906303
103465427.22822373491937.7717762650807
104467470.349792816301-3.34979281630092
105404472.339011453184-68.3390114531837
106347409.119061224034-62.1190612240341
107305351.919130006707-46.9191300067068
108336309.76812001728726.2318799827125
109340340.852547753225-0.852547753225281
110318344.849803814299-26.8498038142994
111362322.76338728037539.2366127196246
112348366.88967096191-18.8896709619099
113363352.82887424612110.1711257538793
114435367.8616101811767.1383898188299
115491440.07769618989950.9223038101011
116505496.2415904598588.75840954014194
117404510.269779544604-106.269779544604
118359408.927748516273-49.9277485162727
119310363.767055238838-53.7670552388378
120337314.5940050897522.4059949102499
121360341.66611915183618.3338808481639
122342364.725127048029-22.725127048029
123406346.65198585392459.3480141460764
124396410.842998410784-14.8429984107843
125420400.79522597696819.204774023032
126472424.85703685712747.1429631428728
127548477.00876725716670.9912327428337
128559553.2372537040345.76274629596594
129463564.255801197499-101.255801197499
130407467.929907740709-60.9299077407086
131362411.73380383337-49.73380383337
132405366.57373477007838.4262652299223
133417409.6974103349277.30258966507341
134391421.720913839529-30.720913839529
135419395.62203807450123.3779619254989
136461423.69728042836637.3027195716336
137472465.8173398430876.18266015691262
138535476.83723883620158.1627611637995
139622540.02443663689981.9755633631009
140606627.288276332016-21.2882763320157
141508611.219759665505-103.219759665505
142461512.887545176175-51.8875451761754
143390465.720544261049-75.7205442610491
144432394.47683644749737.5231635525027

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 132 & 124 & 8 \tabularnewline
4 & 129 & 138.025748131203 & -9.02574813120324 \tabularnewline
5 & 121 & 134.996698612817 & -13.996698612817 \tabularnewline
6 & 135 & 126.95165000878 & 8.04834999121985 \tabularnewline
7 & 148 & 140.977553755223 & 7.02244624477692 \tabularnewline
8 & 148 & 154.000155613633 & -6.00015561363287 \tabularnewline
9 & 136 & 153.980844014385 & -17.9808440143854 \tabularnewline
10 & 119 & 141.922972373032 & -22.922972373032 \tabularnewline
11 & 104 & 124.849194410503 & -20.8491944105033 \tabularnewline
12 & 118 & 109.782090936358 & 8.2179090636421 \tabularnewline
13 & 115 & 123.808540411456 & -8.80854041145628 \tabularnewline
14 & 126 & 120.780189979678 & 5.21981002032163 \tabularnewline
15 & 141 & 131.796990023836 & 9.20300997616422 \tabularnewline
16 & 135 & 146.826610062377 & -11.8266100623771 \tabularnewline
17 & 125 & 140.78854592393 & -15.7885459239302 \tabularnewline
18 & 149 & 130.737730229935 & 18.2622697700645 \tabularnewline
19 & 170 & 154.796507644699 & 15.2034923553009 \tabularnewline
20 & 170 & 175.845440334188 & -5.84544033418803 \tabularnewline
21 & 158 & 175.826626688605 & -17.8266266886048 \tabularnewline
22 & 133 & 163.769251398244 & -30.7692513982437 \tabularnewline
23 & 114 & 138.67022005799 & -24.6702200579902 \tabularnewline
24 & 140 & 119.590818550132 & 20.409181449868 \tabularnewline
25 & 145 & 145.656505835347 & -0.656505835347218 \tabularnewline
26 & 150 & 150.654392860549 & -0.654392860549194 \tabularnewline
27 & 178 & 155.652286686395 & 22.3477133136048 \tabularnewline
28 & 163 & 183.724213168207 & -20.7242131682066 \tabularnewline
29 & 172 & 168.657511948239 & 3.34248805176077 \tabularnewline
30 & 178 & 177.668269800852 & 0.331730199148012 \tabularnewline
31 & 199 & 183.669337479938 & 15.3306625200615 \tabularnewline
32 & 199 & 204.718679468688 & -5.71867946868835 \tabularnewline
33 & 184 & 204.70027380503 & -20.7002738050297 \tabularnewline
34 & 162 & 189.633649634295 & -27.6336496342954 \tabularnewline
35 & 146 & 167.544710279744 & -21.5447102797443 \tabularnewline
36 & 166 & 151.475368276367 & 14.524631723633 \tabularnewline
37 & 171 & 171.522116041779 & -0.522116041779356 \tabularnewline
38 & 180 & 176.520435602736 & 3.47956439726403 \tabularnewline
39 & 193 & 185.531634637815 & 7.46836536218518 \tabularnewline
40 & 181 & 198.555671694217 & -17.5556716942172 \tabularnewline
41 & 183 & 186.499168476949 & -3.49916847694928 \tabularnewline
42 & 218 & 188.487906345818 & 29.5120936541816 \tabularnewline
43 & 230 & 223.582891503255 & 6.4171084967453 \tabularnewline
44 & 242 & 235.603545072195 & 6.39645492780534 \tabularnewline
45 & 209 & 247.624132167284 & -38.6241321672842 \tabularnewline
46 & 191 & 214.499819764452 & -23.4998197644524 \tabularnewline
47 & 172 & 196.424185209134 & -24.424185209134 \tabularnewline
48 & 194 & 177.345575568472 & 16.6544244315282 \tabularnewline
49 & 196 & 199.399178106644 & -3.39917810664403 \tabularnewline
50 & 196 & 201.38823779616 & -5.3882377961599 \tabularnewline
51 & 236 & 201.370895664444 & 34.6291043355563 \tabularnewline
52 & 235 & 241.482350004679 & -6.48235000467901 \tabularnewline
53 & 229 & 240.461486454876 & -11.4614864548758 \tabularnewline
54 & 243 & 234.424597472748 & 8.57540252725227 \tabularnewline
55 & 264 & 248.452197546422 & 15.5478024535782 \tabularnewline
56 & 272 & 269.502238403609 & 2.49776159639111 \tabularnewline
57 & 237 & 277.510277490271 & -40.5102774902712 \tabularnewline
58 & 211 & 242.379894497784 & -31.3798944977838 \tabularnewline
59 & 180 & 216.2788977927 & -36.2788977926996 \tabularnewline
60 & 201 & 185.162133565165 & 15.8378664348348 \tabularnewline
61 & 204 & 206.213107998033 & -2.21310799803317 \tabularnewline
62 & 188 & 209.205985073646 & -21.2059850736456 \tabularnewline
63 & 235 & 193.137733262899 & 41.8622667371006 \tabularnewline
64 & 227 & 240.272467654951 & -13.2724676549508 \tabularnewline
65 & 234 & 232.22975000013 & 1.77024999987046 \tabularnewline
66 & 264 & 239.235447578787 & 24.7645524212131 \tabularnewline
67 & 302 & 269.315152696903 & 32.6848473030967 \tabularnewline
68 & 293 & 307.420349413993 & -14.4203494139931 \tabularnewline
69 & 259 & 298.373937282905 & -39.3739372829045 \tabularnewline
70 & 229 & 264.247211620011 & -35.247211620011 \tabularnewline
71 & 203 & 234.133767891343 & -31.1337678913434 \tabularnewline
72 & 229 & 208.033563348779 & 20.9664366512213 \tabularnewline
73 & 242 & 234.101044168999 & 7.89895583100125 \tabularnewline
74 & 233 & 247.126467087887 & -14.1264670878869 \tabularnewline
75 & 267 & 238.081000821885 & 28.9189991781153 \tabularnewline
76 & 269 & 272.174077095023 & -3.17407709502282 \tabularnewline
77 & 270 & 274.163861275836 & -4.16386127583633 \tabularnewline
78 & 315 & 275.150459820031 & 39.8495401799689 \tabularnewline
79 & 364 & 320.278716218649 & 43.7212837813511 \tabularnewline
80 & 347 & 369.419433887546 & -22.4194338875459 \tabularnewline
81 & 312 & 352.347276571891 & -40.3472765718911 \tabularnewline
82 & 274 & 317.217418200533 & -43.2174182005327 \tabularnewline
83 & 237 & 279.078322231271 & -42.0783222312712 \tabularnewline
84 & 278 & 241.942892461068 & 36.0571075389317 \tabularnewline
85 & 284 & 283.058942853033 & 0.9410571469665 \tabularnewline
86 & 277 & 289.061971660895 & -12.0619716608948 \tabularnewline
87 & 317 & 282.023150007283 & 34.9768499927171 \tabularnewline
88 & 313 & 322.135723572619 & -9.13572357261899 \tabularnewline
89 & 318 & 318.106320096471 & -0.106320096470938 \tabularnewline
90 & 374 & 323.105977903497 & 50.8940220965032 \tabularnewline
91 & 413 & 379.269781148297 & 33.7302188517031 \tabularnewline
92 & 405 & 418.37834241086 & -13.3783424108604 \tabularnewline
93 & 355 & 410.335283996401 & -55.3352839964008 \tabularnewline
94 & 306 & 360.157186477337 & -54.1571864773373 \tabularnewline
95 & 271 & 310.98288068446 & -39.9828806844602 \tabularnewline
96 & 306 & 275.854195127242 & 30.1458048727582 \tabularnewline
97 & 315 & 310.951219894628 & 4.04878010537175 \tabularnewline
98 & 301 & 319.964250959799 & -18.964250959799 \tabularnewline
99 & 356 & 305.903214207064 & 50.0967857929365 \tabularnewline
100 & 348 & 361.064451533746 & -13.0644515337456 \tabularnewline
101 & 355 & 353.022403382222 & 1.97759661777803 \tabularnewline
102 & 422 & 360.02876830937 & 61.9712316906303 \tabularnewline
103 & 465 & 427.228223734919 & 37.7717762650807 \tabularnewline
104 & 467 & 470.349792816301 & -3.34979281630092 \tabularnewline
105 & 404 & 472.339011453184 & -68.3390114531837 \tabularnewline
106 & 347 & 409.119061224034 & -62.1190612240341 \tabularnewline
107 & 305 & 351.919130006707 & -46.9191300067068 \tabularnewline
108 & 336 & 309.768120017287 & 26.2318799827125 \tabularnewline
109 & 340 & 340.852547753225 & -0.852547753225281 \tabularnewline
110 & 318 & 344.849803814299 & -26.8498038142994 \tabularnewline
111 & 362 & 322.763387280375 & 39.2366127196246 \tabularnewline
112 & 348 & 366.88967096191 & -18.8896709619099 \tabularnewline
113 & 363 & 352.828874246121 & 10.1711257538793 \tabularnewline
114 & 435 & 367.86161018117 & 67.1383898188299 \tabularnewline
115 & 491 & 440.077696189899 & 50.9223038101011 \tabularnewline
116 & 505 & 496.241590459858 & 8.75840954014194 \tabularnewline
117 & 404 & 510.269779544604 & -106.269779544604 \tabularnewline
118 & 359 & 408.927748516273 & -49.9277485162727 \tabularnewline
119 & 310 & 363.767055238838 & -53.7670552388378 \tabularnewline
120 & 337 & 314.59400508975 & 22.4059949102499 \tabularnewline
121 & 360 & 341.666119151836 & 18.3338808481639 \tabularnewline
122 & 342 & 364.725127048029 & -22.725127048029 \tabularnewline
123 & 406 & 346.651985853924 & 59.3480141460764 \tabularnewline
124 & 396 & 410.842998410784 & -14.8429984107843 \tabularnewline
125 & 420 & 400.795225976968 & 19.204774023032 \tabularnewline
126 & 472 & 424.857036857127 & 47.1429631428728 \tabularnewline
127 & 548 & 477.008767257166 & 70.9912327428337 \tabularnewline
128 & 559 & 553.237253704034 & 5.76274629596594 \tabularnewline
129 & 463 & 564.255801197499 & -101.255801197499 \tabularnewline
130 & 407 & 467.929907740709 & -60.9299077407086 \tabularnewline
131 & 362 & 411.73380383337 & -49.73380383337 \tabularnewline
132 & 405 & 366.573734770078 & 38.4262652299223 \tabularnewline
133 & 417 & 409.697410334927 & 7.30258966507341 \tabularnewline
134 & 391 & 421.720913839529 & -30.720913839529 \tabularnewline
135 & 419 & 395.622038074501 & 23.3779619254989 \tabularnewline
136 & 461 & 423.697280428366 & 37.3027195716336 \tabularnewline
137 & 472 & 465.817339843087 & 6.18266015691262 \tabularnewline
138 & 535 & 476.837238836201 & 58.1627611637995 \tabularnewline
139 & 622 & 540.024436636899 & 81.9755633631009 \tabularnewline
140 & 606 & 627.288276332016 & -21.2882763320157 \tabularnewline
141 & 508 & 611.219759665505 & -103.219759665505 \tabularnewline
142 & 461 & 512.887545176175 & -51.8875451761754 \tabularnewline
143 & 390 & 465.720544261049 & -75.7205442610491 \tabularnewline
144 & 432 & 394.476836447497 & 37.5231635525027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319155&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]132[/C][C]124[/C][C]8[/C][/ROW]
[ROW][C]4[/C][C]129[/C][C]138.025748131203[/C][C]-9.02574813120324[/C][/ROW]
[ROW][C]5[/C][C]121[/C][C]134.996698612817[/C][C]-13.996698612817[/C][/ROW]
[ROW][C]6[/C][C]135[/C][C]126.95165000878[/C][C]8.04834999121985[/C][/ROW]
[ROW][C]7[/C][C]148[/C][C]140.977553755223[/C][C]7.02244624477692[/C][/ROW]
[ROW][C]8[/C][C]148[/C][C]154.000155613633[/C][C]-6.00015561363287[/C][/ROW]
[ROW][C]9[/C][C]136[/C][C]153.980844014385[/C][C]-17.9808440143854[/C][/ROW]
[ROW][C]10[/C][C]119[/C][C]141.922972373032[/C][C]-22.922972373032[/C][/ROW]
[ROW][C]11[/C][C]104[/C][C]124.849194410503[/C][C]-20.8491944105033[/C][/ROW]
[ROW][C]12[/C][C]118[/C][C]109.782090936358[/C][C]8.2179090636421[/C][/ROW]
[ROW][C]13[/C][C]115[/C][C]123.808540411456[/C][C]-8.80854041145628[/C][/ROW]
[ROW][C]14[/C][C]126[/C][C]120.780189979678[/C][C]5.21981002032163[/C][/ROW]
[ROW][C]15[/C][C]141[/C][C]131.796990023836[/C][C]9.20300997616422[/C][/ROW]
[ROW][C]16[/C][C]135[/C][C]146.826610062377[/C][C]-11.8266100623771[/C][/ROW]
[ROW][C]17[/C][C]125[/C][C]140.78854592393[/C][C]-15.7885459239302[/C][/ROW]
[ROW][C]18[/C][C]149[/C][C]130.737730229935[/C][C]18.2622697700645[/C][/ROW]
[ROW][C]19[/C][C]170[/C][C]154.796507644699[/C][C]15.2034923553009[/C][/ROW]
[ROW][C]20[/C][C]170[/C][C]175.845440334188[/C][C]-5.84544033418803[/C][/ROW]
[ROW][C]21[/C][C]158[/C][C]175.826626688605[/C][C]-17.8266266886048[/C][/ROW]
[ROW][C]22[/C][C]133[/C][C]163.769251398244[/C][C]-30.7692513982437[/C][/ROW]
[ROW][C]23[/C][C]114[/C][C]138.67022005799[/C][C]-24.6702200579902[/C][/ROW]
[ROW][C]24[/C][C]140[/C][C]119.590818550132[/C][C]20.409181449868[/C][/ROW]
[ROW][C]25[/C][C]145[/C][C]145.656505835347[/C][C]-0.656505835347218[/C][/ROW]
[ROW][C]26[/C][C]150[/C][C]150.654392860549[/C][C]-0.654392860549194[/C][/ROW]
[ROW][C]27[/C][C]178[/C][C]155.652286686395[/C][C]22.3477133136048[/C][/ROW]
[ROW][C]28[/C][C]163[/C][C]183.724213168207[/C][C]-20.7242131682066[/C][/ROW]
[ROW][C]29[/C][C]172[/C][C]168.657511948239[/C][C]3.34248805176077[/C][/ROW]
[ROW][C]30[/C][C]178[/C][C]177.668269800852[/C][C]0.331730199148012[/C][/ROW]
[ROW][C]31[/C][C]199[/C][C]183.669337479938[/C][C]15.3306625200615[/C][/ROW]
[ROW][C]32[/C][C]199[/C][C]204.718679468688[/C][C]-5.71867946868835[/C][/ROW]
[ROW][C]33[/C][C]184[/C][C]204.70027380503[/C][C]-20.7002738050297[/C][/ROW]
[ROW][C]34[/C][C]162[/C][C]189.633649634295[/C][C]-27.6336496342954[/C][/ROW]
[ROW][C]35[/C][C]146[/C][C]167.544710279744[/C][C]-21.5447102797443[/C][/ROW]
[ROW][C]36[/C][C]166[/C][C]151.475368276367[/C][C]14.524631723633[/C][/ROW]
[ROW][C]37[/C][C]171[/C][C]171.522116041779[/C][C]-0.522116041779356[/C][/ROW]
[ROW][C]38[/C][C]180[/C][C]176.520435602736[/C][C]3.47956439726403[/C][/ROW]
[ROW][C]39[/C][C]193[/C][C]185.531634637815[/C][C]7.46836536218518[/C][/ROW]
[ROW][C]40[/C][C]181[/C][C]198.555671694217[/C][C]-17.5556716942172[/C][/ROW]
[ROW][C]41[/C][C]183[/C][C]186.499168476949[/C][C]-3.49916847694928[/C][/ROW]
[ROW][C]42[/C][C]218[/C][C]188.487906345818[/C][C]29.5120936541816[/C][/ROW]
[ROW][C]43[/C][C]230[/C][C]223.582891503255[/C][C]6.4171084967453[/C][/ROW]
[ROW][C]44[/C][C]242[/C][C]235.603545072195[/C][C]6.39645492780534[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]247.624132167284[/C][C]-38.6241321672842[/C][/ROW]
[ROW][C]46[/C][C]191[/C][C]214.499819764452[/C][C]-23.4998197644524[/C][/ROW]
[ROW][C]47[/C][C]172[/C][C]196.424185209134[/C][C]-24.424185209134[/C][/ROW]
[ROW][C]48[/C][C]194[/C][C]177.345575568472[/C][C]16.6544244315282[/C][/ROW]
[ROW][C]49[/C][C]196[/C][C]199.399178106644[/C][C]-3.39917810664403[/C][/ROW]
[ROW][C]50[/C][C]196[/C][C]201.38823779616[/C][C]-5.3882377961599[/C][/ROW]
[ROW][C]51[/C][C]236[/C][C]201.370895664444[/C][C]34.6291043355563[/C][/ROW]
[ROW][C]52[/C][C]235[/C][C]241.482350004679[/C][C]-6.48235000467901[/C][/ROW]
[ROW][C]53[/C][C]229[/C][C]240.461486454876[/C][C]-11.4614864548758[/C][/ROW]
[ROW][C]54[/C][C]243[/C][C]234.424597472748[/C][C]8.57540252725227[/C][/ROW]
[ROW][C]55[/C][C]264[/C][C]248.452197546422[/C][C]15.5478024535782[/C][/ROW]
[ROW][C]56[/C][C]272[/C][C]269.502238403609[/C][C]2.49776159639111[/C][/ROW]
[ROW][C]57[/C][C]237[/C][C]277.510277490271[/C][C]-40.5102774902712[/C][/ROW]
[ROW][C]58[/C][C]211[/C][C]242.379894497784[/C][C]-31.3798944977838[/C][/ROW]
[ROW][C]59[/C][C]180[/C][C]216.2788977927[/C][C]-36.2788977926996[/C][/ROW]
[ROW][C]60[/C][C]201[/C][C]185.162133565165[/C][C]15.8378664348348[/C][/ROW]
[ROW][C]61[/C][C]204[/C][C]206.213107998033[/C][C]-2.21310799803317[/C][/ROW]
[ROW][C]62[/C][C]188[/C][C]209.205985073646[/C][C]-21.2059850736456[/C][/ROW]
[ROW][C]63[/C][C]235[/C][C]193.137733262899[/C][C]41.8622667371006[/C][/ROW]
[ROW][C]64[/C][C]227[/C][C]240.272467654951[/C][C]-13.2724676549508[/C][/ROW]
[ROW][C]65[/C][C]234[/C][C]232.22975000013[/C][C]1.77024999987046[/C][/ROW]
[ROW][C]66[/C][C]264[/C][C]239.235447578787[/C][C]24.7645524212131[/C][/ROW]
[ROW][C]67[/C][C]302[/C][C]269.315152696903[/C][C]32.6848473030967[/C][/ROW]
[ROW][C]68[/C][C]293[/C][C]307.420349413993[/C][C]-14.4203494139931[/C][/ROW]
[ROW][C]69[/C][C]259[/C][C]298.373937282905[/C][C]-39.3739372829045[/C][/ROW]
[ROW][C]70[/C][C]229[/C][C]264.247211620011[/C][C]-35.247211620011[/C][/ROW]
[ROW][C]71[/C][C]203[/C][C]234.133767891343[/C][C]-31.1337678913434[/C][/ROW]
[ROW][C]72[/C][C]229[/C][C]208.033563348779[/C][C]20.9664366512213[/C][/ROW]
[ROW][C]73[/C][C]242[/C][C]234.101044168999[/C][C]7.89895583100125[/C][/ROW]
[ROW][C]74[/C][C]233[/C][C]247.126467087887[/C][C]-14.1264670878869[/C][/ROW]
[ROW][C]75[/C][C]267[/C][C]238.081000821885[/C][C]28.9189991781153[/C][/ROW]
[ROW][C]76[/C][C]269[/C][C]272.174077095023[/C][C]-3.17407709502282[/C][/ROW]
[ROW][C]77[/C][C]270[/C][C]274.163861275836[/C][C]-4.16386127583633[/C][/ROW]
[ROW][C]78[/C][C]315[/C][C]275.150459820031[/C][C]39.8495401799689[/C][/ROW]
[ROW][C]79[/C][C]364[/C][C]320.278716218649[/C][C]43.7212837813511[/C][/ROW]
[ROW][C]80[/C][C]347[/C][C]369.419433887546[/C][C]-22.4194338875459[/C][/ROW]
[ROW][C]81[/C][C]312[/C][C]352.347276571891[/C][C]-40.3472765718911[/C][/ROW]
[ROW][C]82[/C][C]274[/C][C]317.217418200533[/C][C]-43.2174182005327[/C][/ROW]
[ROW][C]83[/C][C]237[/C][C]279.078322231271[/C][C]-42.0783222312712[/C][/ROW]
[ROW][C]84[/C][C]278[/C][C]241.942892461068[/C][C]36.0571075389317[/C][/ROW]
[ROW][C]85[/C][C]284[/C][C]283.058942853033[/C][C]0.9410571469665[/C][/ROW]
[ROW][C]86[/C][C]277[/C][C]289.061971660895[/C][C]-12.0619716608948[/C][/ROW]
[ROW][C]87[/C][C]317[/C][C]282.023150007283[/C][C]34.9768499927171[/C][/ROW]
[ROW][C]88[/C][C]313[/C][C]322.135723572619[/C][C]-9.13572357261899[/C][/ROW]
[ROW][C]89[/C][C]318[/C][C]318.106320096471[/C][C]-0.106320096470938[/C][/ROW]
[ROW][C]90[/C][C]374[/C][C]323.105977903497[/C][C]50.8940220965032[/C][/ROW]
[ROW][C]91[/C][C]413[/C][C]379.269781148297[/C][C]33.7302188517031[/C][/ROW]
[ROW][C]92[/C][C]405[/C][C]418.37834241086[/C][C]-13.3783424108604[/C][/ROW]
[ROW][C]93[/C][C]355[/C][C]410.335283996401[/C][C]-55.3352839964008[/C][/ROW]
[ROW][C]94[/C][C]306[/C][C]360.157186477337[/C][C]-54.1571864773373[/C][/ROW]
[ROW][C]95[/C][C]271[/C][C]310.98288068446[/C][C]-39.9828806844602[/C][/ROW]
[ROW][C]96[/C][C]306[/C][C]275.854195127242[/C][C]30.1458048727582[/C][/ROW]
[ROW][C]97[/C][C]315[/C][C]310.951219894628[/C][C]4.04878010537175[/C][/ROW]
[ROW][C]98[/C][C]301[/C][C]319.964250959799[/C][C]-18.964250959799[/C][/ROW]
[ROW][C]99[/C][C]356[/C][C]305.903214207064[/C][C]50.0967857929365[/C][/ROW]
[ROW][C]100[/C][C]348[/C][C]361.064451533746[/C][C]-13.0644515337456[/C][/ROW]
[ROW][C]101[/C][C]355[/C][C]353.022403382222[/C][C]1.97759661777803[/C][/ROW]
[ROW][C]102[/C][C]422[/C][C]360.02876830937[/C][C]61.9712316906303[/C][/ROW]
[ROW][C]103[/C][C]465[/C][C]427.228223734919[/C][C]37.7717762650807[/C][/ROW]
[ROW][C]104[/C][C]467[/C][C]470.349792816301[/C][C]-3.34979281630092[/C][/ROW]
[ROW][C]105[/C][C]404[/C][C]472.339011453184[/C][C]-68.3390114531837[/C][/ROW]
[ROW][C]106[/C][C]347[/C][C]409.119061224034[/C][C]-62.1190612240341[/C][/ROW]
[ROW][C]107[/C][C]305[/C][C]351.919130006707[/C][C]-46.9191300067068[/C][/ROW]
[ROW][C]108[/C][C]336[/C][C]309.768120017287[/C][C]26.2318799827125[/C][/ROW]
[ROW][C]109[/C][C]340[/C][C]340.852547753225[/C][C]-0.852547753225281[/C][/ROW]
[ROW][C]110[/C][C]318[/C][C]344.849803814299[/C][C]-26.8498038142994[/C][/ROW]
[ROW][C]111[/C][C]362[/C][C]322.763387280375[/C][C]39.2366127196246[/C][/ROW]
[ROW][C]112[/C][C]348[/C][C]366.88967096191[/C][C]-18.8896709619099[/C][/ROW]
[ROW][C]113[/C][C]363[/C][C]352.828874246121[/C][C]10.1711257538793[/C][/ROW]
[ROW][C]114[/C][C]435[/C][C]367.86161018117[/C][C]67.1383898188299[/C][/ROW]
[ROW][C]115[/C][C]491[/C][C]440.077696189899[/C][C]50.9223038101011[/C][/ROW]
[ROW][C]116[/C][C]505[/C][C]496.241590459858[/C][C]8.75840954014194[/C][/ROW]
[ROW][C]117[/C][C]404[/C][C]510.269779544604[/C][C]-106.269779544604[/C][/ROW]
[ROW][C]118[/C][C]359[/C][C]408.927748516273[/C][C]-49.9277485162727[/C][/ROW]
[ROW][C]119[/C][C]310[/C][C]363.767055238838[/C][C]-53.7670552388378[/C][/ROW]
[ROW][C]120[/C][C]337[/C][C]314.59400508975[/C][C]22.4059949102499[/C][/ROW]
[ROW][C]121[/C][C]360[/C][C]341.666119151836[/C][C]18.3338808481639[/C][/ROW]
[ROW][C]122[/C][C]342[/C][C]364.725127048029[/C][C]-22.725127048029[/C][/ROW]
[ROW][C]123[/C][C]406[/C][C]346.651985853924[/C][C]59.3480141460764[/C][/ROW]
[ROW][C]124[/C][C]396[/C][C]410.842998410784[/C][C]-14.8429984107843[/C][/ROW]
[ROW][C]125[/C][C]420[/C][C]400.795225976968[/C][C]19.204774023032[/C][/ROW]
[ROW][C]126[/C][C]472[/C][C]424.857036857127[/C][C]47.1429631428728[/C][/ROW]
[ROW][C]127[/C][C]548[/C][C]477.008767257166[/C][C]70.9912327428337[/C][/ROW]
[ROW][C]128[/C][C]559[/C][C]553.237253704034[/C][C]5.76274629596594[/C][/ROW]
[ROW][C]129[/C][C]463[/C][C]564.255801197499[/C][C]-101.255801197499[/C][/ROW]
[ROW][C]130[/C][C]407[/C][C]467.929907740709[/C][C]-60.9299077407086[/C][/ROW]
[ROW][C]131[/C][C]362[/C][C]411.73380383337[/C][C]-49.73380383337[/C][/ROW]
[ROW][C]132[/C][C]405[/C][C]366.573734770078[/C][C]38.4262652299223[/C][/ROW]
[ROW][C]133[/C][C]417[/C][C]409.697410334927[/C][C]7.30258966507341[/C][/ROW]
[ROW][C]134[/C][C]391[/C][C]421.720913839529[/C][C]-30.720913839529[/C][/ROW]
[ROW][C]135[/C][C]419[/C][C]395.622038074501[/C][C]23.3779619254989[/C][/ROW]
[ROW][C]136[/C][C]461[/C][C]423.697280428366[/C][C]37.3027195716336[/C][/ROW]
[ROW][C]137[/C][C]472[/C][C]465.817339843087[/C][C]6.18266015691262[/C][/ROW]
[ROW][C]138[/C][C]535[/C][C]476.837238836201[/C][C]58.1627611637995[/C][/ROW]
[ROW][C]139[/C][C]622[/C][C]540.024436636899[/C][C]81.9755633631009[/C][/ROW]
[ROW][C]140[/C][C]606[/C][C]627.288276332016[/C][C]-21.2882763320157[/C][/ROW]
[ROW][C]141[/C][C]508[/C][C]611.219759665505[/C][C]-103.219759665505[/C][/ROW]
[ROW][C]142[/C][C]461[/C][C]512.887545176175[/C][C]-51.8875451761754[/C][/ROW]
[ROW][C]143[/C][C]390[/C][C]465.720544261049[/C][C]-75.7205442610491[/C][/ROW]
[ROW][C]144[/C][C]432[/C][C]394.476836447497[/C][C]37.5231635525027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319155&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319155&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
31321248
4129138.025748131203-9.02574813120324
5121134.996698612817-13.996698612817
6135126.951650008788.04834999121985
7148140.9775537552237.02244624477692
8148154.000155613633-6.00015561363287
9136153.980844014385-17.9808440143854
10119141.922972373032-22.922972373032
11104124.849194410503-20.8491944105033
12118109.7820909363588.2179090636421
13115123.808540411456-8.80854041145628
14126120.7801899796785.21981002032163
15141131.7969900238369.20300997616422
16135146.826610062377-11.8266100623771
17125140.78854592393-15.7885459239302
18149130.73773022993518.2622697700645
19170154.79650764469915.2034923553009
20170175.845440334188-5.84544033418803
21158175.826626688605-17.8266266886048
22133163.769251398244-30.7692513982437
23114138.67022005799-24.6702200579902
24140119.59081855013220.409181449868
25145145.656505835347-0.656505835347218
26150150.654392860549-0.654392860549194
27178155.65228668639522.3477133136048
28163183.724213168207-20.7242131682066
29172168.6575119482393.34248805176077
30178177.6682698008520.331730199148012
31199183.66933747993815.3306625200615
32199204.718679468688-5.71867946868835
33184204.70027380503-20.7002738050297
34162189.633649634295-27.6336496342954
35146167.544710279744-21.5447102797443
36166151.47536827636714.524631723633
37171171.522116041779-0.522116041779356
38180176.5204356027363.47956439726403
39193185.5316346378157.46836536218518
40181198.555671694217-17.5556716942172
41183186.499168476949-3.49916847694928
42218188.48790634581829.5120936541816
43230223.5828915032556.4171084967453
44242235.6035450721956.39645492780534
45209247.624132167284-38.6241321672842
46191214.499819764452-23.4998197644524
47172196.424185209134-24.424185209134
48194177.34557556847216.6544244315282
49196199.399178106644-3.39917810664403
50196201.38823779616-5.3882377961599
51236201.37089566444434.6291043355563
52235241.482350004679-6.48235000467901
53229240.461486454876-11.4614864548758
54243234.4245974727488.57540252725227
55264248.45219754642215.5478024535782
56272269.5022384036092.49776159639111
57237277.510277490271-40.5102774902712
58211242.379894497784-31.3798944977838
59180216.2788977927-36.2788977926996
60201185.16213356516515.8378664348348
61204206.213107998033-2.21310799803317
62188209.205985073646-21.2059850736456
63235193.13773326289941.8622667371006
64227240.272467654951-13.2724676549508
65234232.229750000131.77024999987046
66264239.23544757878724.7645524212131
67302269.31515269690332.6848473030967
68293307.420349413993-14.4203494139931
69259298.373937282905-39.3739372829045
70229264.247211620011-35.247211620011
71203234.133767891343-31.1337678913434
72229208.03356334877920.9664366512213
73242234.1010441689997.89895583100125
74233247.126467087887-14.1264670878869
75267238.08100082188528.9189991781153
76269272.174077095023-3.17407709502282
77270274.163861275836-4.16386127583633
78315275.15045982003139.8495401799689
79364320.27871621864943.7212837813511
80347369.419433887546-22.4194338875459
81312352.347276571891-40.3472765718911
82274317.217418200533-43.2174182005327
83237279.078322231271-42.0783222312712
84278241.94289246106836.0571075389317
85284283.0589428530330.9410571469665
86277289.061971660895-12.0619716608948
87317282.02315000728334.9768499927171
88313322.135723572619-9.13572357261899
89318318.106320096471-0.106320096470938
90374323.10597790349750.8940220965032
91413379.26978114829733.7302188517031
92405418.37834241086-13.3783424108604
93355410.335283996401-55.3352839964008
94306360.157186477337-54.1571864773373
95271310.98288068446-39.9828806844602
96306275.85419512724230.1458048727582
97315310.9512198946284.04878010537175
98301319.964250959799-18.964250959799
99356305.90321420706450.0967857929365
100348361.064451533746-13.0644515337456
101355353.0224033822221.97759661777803
102422360.0287683093761.9712316906303
103465427.22822373491937.7717762650807
104467470.349792816301-3.34979281630092
105404472.339011453184-68.3390114531837
106347409.119061224034-62.1190612240341
107305351.919130006707-46.9191300067068
108336309.76812001728726.2318799827125
109340340.852547753225-0.852547753225281
110318344.849803814299-26.8498038142994
111362322.76338728037539.2366127196246
112348366.88967096191-18.8896709619099
113363352.82887424612110.1711257538793
114435367.8616101811767.1383898188299
115491440.07769618989950.9223038101011
116505496.2415904598588.75840954014194
117404510.269779544604-106.269779544604
118359408.927748516273-49.9277485162727
119310363.767055238838-53.7670552388378
120337314.5940050897522.4059949102499
121360341.66611915183618.3338808481639
122342364.725127048029-22.725127048029
123406346.65198585392459.3480141460764
124396410.842998410784-14.8429984107843
125420400.79522597696819.204774023032
126472424.85703685712747.1429631428728
127548477.00876725716670.9912327428337
128559553.2372537040345.76274629596594
129463564.255801197499-101.255801197499
130407467.929907740709-60.9299077407086
131362411.73380383337-49.73380383337
132405366.57373477007838.4262652299223
133417409.6974103349277.30258966507341
134391421.720913839529-30.720913839529
135419395.62203807450123.3779619254989
136461423.69728042836637.3027195716336
137472465.8173398430876.18266015691262
138535476.83723883620158.1627611637995
139622540.02443663689981.9755633631009
140606627.288276332016-21.2882763320157
141508611.219759665505-103.219759665505
142461512.887545176175-51.8875451761754
143390465.720544261049-75.7205442610491
144432394.47683644749737.5231635525027







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
145436.597605364786370.101864270584503.093346458988
146441.195210729572347.004576942849535.385844516295
147445.792816094358330.247728204276561.337903984441
148450.390421459145316.756029486461584.024813431828
149454.988026823931305.340383182659604.635670465203
150459.585632188717295.391970523443623.779293853991
151464.183237553503286.549721076461641.816754030545
152468.780842918289278.578761464571658.982924372007
153473.378448283075271.316212874953675.440683691197
154477.976053647861264.643676007955691.308431287768
155482.573659012648258.471913123583706.675404901712
156487.171264377434252.731706989362721.610821765505

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
145 & 436.597605364786 & 370.101864270584 & 503.093346458988 \tabularnewline
146 & 441.195210729572 & 347.004576942849 & 535.385844516295 \tabularnewline
147 & 445.792816094358 & 330.247728204276 & 561.337903984441 \tabularnewline
148 & 450.390421459145 & 316.756029486461 & 584.024813431828 \tabularnewline
149 & 454.988026823931 & 305.340383182659 & 604.635670465203 \tabularnewline
150 & 459.585632188717 & 295.391970523443 & 623.779293853991 \tabularnewline
151 & 464.183237553503 & 286.549721076461 & 641.816754030545 \tabularnewline
152 & 468.780842918289 & 278.578761464571 & 658.982924372007 \tabularnewline
153 & 473.378448283075 & 271.316212874953 & 675.440683691197 \tabularnewline
154 & 477.976053647861 & 264.643676007955 & 691.308431287768 \tabularnewline
155 & 482.573659012648 & 258.471913123583 & 706.675404901712 \tabularnewline
156 & 487.171264377434 & 252.731706989362 & 721.610821765505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319155&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]145[/C][C]436.597605364786[/C][C]370.101864270584[/C][C]503.093346458988[/C][/ROW]
[ROW][C]146[/C][C]441.195210729572[/C][C]347.004576942849[/C][C]535.385844516295[/C][/ROW]
[ROW][C]147[/C][C]445.792816094358[/C][C]330.247728204276[/C][C]561.337903984441[/C][/ROW]
[ROW][C]148[/C][C]450.390421459145[/C][C]316.756029486461[/C][C]584.024813431828[/C][/ROW]
[ROW][C]149[/C][C]454.988026823931[/C][C]305.340383182659[/C][C]604.635670465203[/C][/ROW]
[ROW][C]150[/C][C]459.585632188717[/C][C]295.391970523443[/C][C]623.779293853991[/C][/ROW]
[ROW][C]151[/C][C]464.183237553503[/C][C]286.549721076461[/C][C]641.816754030545[/C][/ROW]
[ROW][C]152[/C][C]468.780842918289[/C][C]278.578761464571[/C][C]658.982924372007[/C][/ROW]
[ROW][C]153[/C][C]473.378448283075[/C][C]271.316212874953[/C][C]675.440683691197[/C][/ROW]
[ROW][C]154[/C][C]477.976053647861[/C][C]264.643676007955[/C][C]691.308431287768[/C][/ROW]
[ROW][C]155[/C][C]482.573659012648[/C][C]258.471913123583[/C][C]706.675404901712[/C][/ROW]
[ROW][C]156[/C][C]487.171264377434[/C][C]252.731706989362[/C][C]721.610821765505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319155&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319155&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
145436.597605364786370.101864270584503.093346458988
146441.195210729572347.004576942849535.385844516295
147445.792816094358330.247728204276561.337903984441
148450.390421459145316.756029486461584.024813431828
149454.988026823931305.340383182659604.635670465203
150459.585632188717295.391970523443623.779293853991
151464.183237553503286.549721076461641.816754030545
152468.780842918289278.578761464571658.982924372007
153473.378448283075271.316212874953675.440683691197
154477.976053647861264.643676007955691.308431287768
155482.573659012648258.471913123583706.675404901712
156487.171264377434252.731706989362721.610821765505



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')