Free Statistics

of Irreproducible Research!

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, 27 Nov 2012 16:41:16 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/27/t1354052534pq9jcd6o24p8x5c.htm/, Retrieved Sat, 04 May 2024 09:46:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194058, Retrieved Sat, 04 May 2024 09:46:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-11-27 21:41:16] [c394fd7c96c8a7cd973da7b3be872d6d] [Current]
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Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194058&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194058&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194058&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]0.999933893038648[/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=194058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194058&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21181126
3132117.99960335823214.0003966417681
4129131.99907447632-2.99907447632029
5121129.000198259701-8.00019825970051
6135121.00052886879713.9994711312028
7148134.99907453750313.000925462497
8148147.9991405483230.000859451677087009
9136147.999999943184-11.9999999431843
10119136.000793283532-17.0007932835325
11104119.001123870785-15.0011238707845
12118104.00099167871613.999008321284
13115117.999074568098-2.99907456809794
14126115.00019825970710.9998017402934
15141125.99927283653115.0007271634685
16135140.999008347509-5.99900834750915
17125135.000396576213-10.000396576213
18149125.0006610958323.99933890417
19170148.99841347663121.0015865233694
20170169.9986116489310.00138835106864121
21158169.99999990822-11.9999999082203
22133158.00079328353-25.0007932835302
23114133.001652726475-19.0016527264754
24140114.00125614152225.9987438584776
25145139.9982813020455.00171869795545
26150144.9996693515755.00033064842467
27178149.99966944333528.0003305566649
28163177.99814898323-14.99814898323
29172163.0009914820558.99900851794482
30178171.9994051028926.0005948971083
31199177.99960331890521.0003966810949
32199198.9986117275880.00138827241175932
33184198.999999908226-14.9999999082255
34162184.000991604414-22.0009916044142
35146162.001454418702-16.0014544187017
36166146.00105780752919.9989421924712
37171165.9986779307015.0013220692986
38180170.9996693777959.00033062220476
39193179.99940501549113.0005949845086
40181192.99914057017-11.9991405701698
41183181.0007932267221.99920677327808
42218182.99986783851535.0001321614849
43230217.99768624761612.0023137523841
44242229.99920656350912.0007934364914
45209241.999206664012-32.9992066640121
46191209.00218147728-18.0021814772796
47172191.001190069515-19.0011900695152
48194172.00125611093821.9987438890624
49196193.9985457298882.00145427011208
50196195.999867689940.000132310060081409
51236195.99999999125340.0000000087466
52235235.997355721545-0.997355721545347
53229235.000065932156-6.00006593215613
54243229.00039664612713.9996033538733
55264242.99907452876221.0009254712378
56272263.9986116926328.00138830736847
57237271.999471052532-34.9994710525324
58211237.00231370868-26.0023137086802
59180211.001718933947-31.0017189339474
60201180.00204942943520.9979505705646
61204200.9986118892933.00138811070684
62188203.999801587352-15.9998015873522
63235188.00105769826546.9989423017348
64227234.996893042738-7.99689304273767
65234227.0005286502996.99947134970068
66264233.99953728621830.000462713782
67302263.99801676057138.0019832394291
68293301.997487804363-8.99748780436272
69259293.000594796579-34.0005947965785
70229259.002247676006-30.0022476760062
71203229.001983357428-26.0019833574276
72229203.00171891210925.9982810878911
73242228.99828133263713.0017186673631
74233241.999140495887-8.99914049588654
75267233.00059490583333.999405094167
76269266.9977524026412.00224759735858
77270268.9998676374951.00013236250453
78315269.99993388428945.0000661157114
79364314.99702518236849.0029748176315
80347363.996760562238-16.9967605622376
81312347.001123604194-35.0011236041936
82274312.002313817925-38.0023138179254
83237274.002512217491-37.0025122174908
84278237.00244612364540.9975538763549
85284277.997289776296.00271022370964
86277283.999603179067-6.99960317906721
87317277.00046272249739.9995372775032
88313316.997355752135-3.99735575213509
89318313.0002642530424.99973574695781
90374317.99966948266256.0003305173378
91413373.99629798831539.0037020116852
92405412.997421583779-7.99742158377853
93355405.00052868524-50.0005286852395
94306355.003305383017-49.0033053830174
95271306.003239459615-35.0032394596151
96306271.00231395779834.9976860422018
97315305.9976864093219.00231359067863
98301314.999404884403-13.9994048844034
99356301.00092545811854.9990745418824
100348355.996364178305-7.99636417830487
101355348.0005286153386.99947138466229
102422354.99953728621667.0004627137843
103465421.99557080300143.0044291969992
104467464.9971571078612.00284289213886
105404466.999867598142-62.9998675981423
106347404.004164729812-57.0041647298125
107305347.003768372115-42.0037683721147
108336305.00277674149230.9972232585076
109340335.997950867764.00204913223996
110318339.999735436693-21.9997354366927
111362318.0014543356643.9985456643398
112348361.997091389842-13.9970913898422
113363348.0009253051814.9990746948205
114435362.99900845674972.0009915432512
115491434.99524023323556.0047597667652
116505490.99629769551114.0037023044894
117404504.999074257793-100.999074257793
118359404.006676741899-45.0066767418986
119310359.00297525464-49.00297525464
120337310.00323943779126.9967605622087
121360336.99821532619323.0017846738071
122342359.99847942191-17.9984794219096
123406342.00118982478463.9988101752165
124396405.995769233129-9.99576923312918
125420396.0006607899323.9993392100696
126472419.9984134766152.0015865233896
127548471.99656233312976.0034376668705
128559547.99497564368411.0050243563164
129463558.99927249128-95.9992724912802
130407463.006346220196-56.0063462201964
131362407.003702409365-45.003702409365
132405362.00297505801642.9970249419841
133417404.99715759733412.0028424026661
134391416.999206528561-25.9992065285612
135419391.00171872854127.9982812714588
136461418.99814911870242.0018508812979
137472460.99722338526711.0027766147329
138535471.99927263987263.0007273601285
139622534.99583521335187.0041647866487
140606621.994248419041-15.994248419041
141508606.001057331162-98.0010573311621
142461508.006478552109-47.0064785521095
143390461.003107455461-71.0031074554609
144432390.0046937996841.9953062003196

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 118 & 112 & 6 \tabularnewline
3 & 132 & 117.999603358232 & 14.0003966417681 \tabularnewline
4 & 129 & 131.99907447632 & -2.99907447632029 \tabularnewline
5 & 121 & 129.000198259701 & -8.00019825970051 \tabularnewline
6 & 135 & 121.000528868797 & 13.9994711312028 \tabularnewline
7 & 148 & 134.999074537503 & 13.000925462497 \tabularnewline
8 & 148 & 147.999140548323 & 0.000859451677087009 \tabularnewline
9 & 136 & 147.999999943184 & -11.9999999431843 \tabularnewline
10 & 119 & 136.000793283532 & -17.0007932835325 \tabularnewline
11 & 104 & 119.001123870785 & -15.0011238707845 \tabularnewline
12 & 118 & 104.000991678716 & 13.999008321284 \tabularnewline
13 & 115 & 117.999074568098 & -2.99907456809794 \tabularnewline
14 & 126 & 115.000198259707 & 10.9998017402934 \tabularnewline
15 & 141 & 125.999272836531 & 15.0007271634685 \tabularnewline
16 & 135 & 140.999008347509 & -5.99900834750915 \tabularnewline
17 & 125 & 135.000396576213 & -10.000396576213 \tabularnewline
18 & 149 & 125.00066109583 & 23.99933890417 \tabularnewline
19 & 170 & 148.998413476631 & 21.0015865233694 \tabularnewline
20 & 170 & 169.998611648931 & 0.00138835106864121 \tabularnewline
21 & 158 & 169.99999990822 & -11.9999999082203 \tabularnewline
22 & 133 & 158.00079328353 & -25.0007932835302 \tabularnewline
23 & 114 & 133.001652726475 & -19.0016527264754 \tabularnewline
24 & 140 & 114.001256141522 & 25.9987438584776 \tabularnewline
25 & 145 & 139.998281302045 & 5.00171869795545 \tabularnewline
26 & 150 & 144.999669351575 & 5.00033064842467 \tabularnewline
27 & 178 & 149.999669443335 & 28.0003305566649 \tabularnewline
28 & 163 & 177.99814898323 & -14.99814898323 \tabularnewline
29 & 172 & 163.000991482055 & 8.99900851794482 \tabularnewline
30 & 178 & 171.999405102892 & 6.0005948971083 \tabularnewline
31 & 199 & 177.999603318905 & 21.0003966810949 \tabularnewline
32 & 199 & 198.998611727588 & 0.00138827241175932 \tabularnewline
33 & 184 & 198.999999908226 & -14.9999999082255 \tabularnewline
34 & 162 & 184.000991604414 & -22.0009916044142 \tabularnewline
35 & 146 & 162.001454418702 & -16.0014544187017 \tabularnewline
36 & 166 & 146.001057807529 & 19.9989421924712 \tabularnewline
37 & 171 & 165.998677930701 & 5.0013220692986 \tabularnewline
38 & 180 & 170.999669377795 & 9.00033062220476 \tabularnewline
39 & 193 & 179.999405015491 & 13.0005949845086 \tabularnewline
40 & 181 & 192.99914057017 & -11.9991405701698 \tabularnewline
41 & 183 & 181.000793226722 & 1.99920677327808 \tabularnewline
42 & 218 & 182.999867838515 & 35.0001321614849 \tabularnewline
43 & 230 & 217.997686247616 & 12.0023137523841 \tabularnewline
44 & 242 & 229.999206563509 & 12.0007934364914 \tabularnewline
45 & 209 & 241.999206664012 & -32.9992066640121 \tabularnewline
46 & 191 & 209.00218147728 & -18.0021814772796 \tabularnewline
47 & 172 & 191.001190069515 & -19.0011900695152 \tabularnewline
48 & 194 & 172.001256110938 & 21.9987438890624 \tabularnewline
49 & 196 & 193.998545729888 & 2.00145427011208 \tabularnewline
50 & 196 & 195.99986768994 & 0.000132310060081409 \tabularnewline
51 & 236 & 195.999999991253 & 40.0000000087466 \tabularnewline
52 & 235 & 235.997355721545 & -0.997355721545347 \tabularnewline
53 & 229 & 235.000065932156 & -6.00006593215613 \tabularnewline
54 & 243 & 229.000396646127 & 13.9996033538733 \tabularnewline
55 & 264 & 242.999074528762 & 21.0009254712378 \tabularnewline
56 & 272 & 263.998611692632 & 8.00138830736847 \tabularnewline
57 & 237 & 271.999471052532 & -34.9994710525324 \tabularnewline
58 & 211 & 237.00231370868 & -26.0023137086802 \tabularnewline
59 & 180 & 211.001718933947 & -31.0017189339474 \tabularnewline
60 & 201 & 180.002049429435 & 20.9979505705646 \tabularnewline
61 & 204 & 200.998611889293 & 3.00138811070684 \tabularnewline
62 & 188 & 203.999801587352 & -15.9998015873522 \tabularnewline
63 & 235 & 188.001057698265 & 46.9989423017348 \tabularnewline
64 & 227 & 234.996893042738 & -7.99689304273767 \tabularnewline
65 & 234 & 227.000528650299 & 6.99947134970068 \tabularnewline
66 & 264 & 233.999537286218 & 30.000462713782 \tabularnewline
67 & 302 & 263.998016760571 & 38.0019832394291 \tabularnewline
68 & 293 & 301.997487804363 & -8.99748780436272 \tabularnewline
69 & 259 & 293.000594796579 & -34.0005947965785 \tabularnewline
70 & 229 & 259.002247676006 & -30.0022476760062 \tabularnewline
71 & 203 & 229.001983357428 & -26.0019833574276 \tabularnewline
72 & 229 & 203.001718912109 & 25.9982810878911 \tabularnewline
73 & 242 & 228.998281332637 & 13.0017186673631 \tabularnewline
74 & 233 & 241.999140495887 & -8.99914049588654 \tabularnewline
75 & 267 & 233.000594905833 & 33.999405094167 \tabularnewline
76 & 269 & 266.997752402641 & 2.00224759735858 \tabularnewline
77 & 270 & 268.999867637495 & 1.00013236250453 \tabularnewline
78 & 315 & 269.999933884289 & 45.0000661157114 \tabularnewline
79 & 364 & 314.997025182368 & 49.0029748176315 \tabularnewline
80 & 347 & 363.996760562238 & -16.9967605622376 \tabularnewline
81 & 312 & 347.001123604194 & -35.0011236041936 \tabularnewline
82 & 274 & 312.002313817925 & -38.0023138179254 \tabularnewline
83 & 237 & 274.002512217491 & -37.0025122174908 \tabularnewline
84 & 278 & 237.002446123645 & 40.9975538763549 \tabularnewline
85 & 284 & 277.99728977629 & 6.00271022370964 \tabularnewline
86 & 277 & 283.999603179067 & -6.99960317906721 \tabularnewline
87 & 317 & 277.000462722497 & 39.9995372775032 \tabularnewline
88 & 313 & 316.997355752135 & -3.99735575213509 \tabularnewline
89 & 318 & 313.000264253042 & 4.99973574695781 \tabularnewline
90 & 374 & 317.999669482662 & 56.0003305173378 \tabularnewline
91 & 413 & 373.996297988315 & 39.0037020116852 \tabularnewline
92 & 405 & 412.997421583779 & -7.99742158377853 \tabularnewline
93 & 355 & 405.00052868524 & -50.0005286852395 \tabularnewline
94 & 306 & 355.003305383017 & -49.0033053830174 \tabularnewline
95 & 271 & 306.003239459615 & -35.0032394596151 \tabularnewline
96 & 306 & 271.002313957798 & 34.9976860422018 \tabularnewline
97 & 315 & 305.997686409321 & 9.00231359067863 \tabularnewline
98 & 301 & 314.999404884403 & -13.9994048844034 \tabularnewline
99 & 356 & 301.000925458118 & 54.9990745418824 \tabularnewline
100 & 348 & 355.996364178305 & -7.99636417830487 \tabularnewline
101 & 355 & 348.000528615338 & 6.99947138466229 \tabularnewline
102 & 422 & 354.999537286216 & 67.0004627137843 \tabularnewline
103 & 465 & 421.995570803001 & 43.0044291969992 \tabularnewline
104 & 467 & 464.997157107861 & 2.00284289213886 \tabularnewline
105 & 404 & 466.999867598142 & -62.9998675981423 \tabularnewline
106 & 347 & 404.004164729812 & -57.0041647298125 \tabularnewline
107 & 305 & 347.003768372115 & -42.0037683721147 \tabularnewline
108 & 336 & 305.002776741492 & 30.9972232585076 \tabularnewline
109 & 340 & 335.99795086776 & 4.00204913223996 \tabularnewline
110 & 318 & 339.999735436693 & -21.9997354366927 \tabularnewline
111 & 362 & 318.00145433566 & 43.9985456643398 \tabularnewline
112 & 348 & 361.997091389842 & -13.9970913898422 \tabularnewline
113 & 363 & 348.00092530518 & 14.9990746948205 \tabularnewline
114 & 435 & 362.999008456749 & 72.0009915432512 \tabularnewline
115 & 491 & 434.995240233235 & 56.0047597667652 \tabularnewline
116 & 505 & 490.996297695511 & 14.0037023044894 \tabularnewline
117 & 404 & 504.999074257793 & -100.999074257793 \tabularnewline
118 & 359 & 404.006676741899 & -45.0066767418986 \tabularnewline
119 & 310 & 359.00297525464 & -49.00297525464 \tabularnewline
120 & 337 & 310.003239437791 & 26.9967605622087 \tabularnewline
121 & 360 & 336.998215326193 & 23.0017846738071 \tabularnewline
122 & 342 & 359.99847942191 & -17.9984794219096 \tabularnewline
123 & 406 & 342.001189824784 & 63.9988101752165 \tabularnewline
124 & 396 & 405.995769233129 & -9.99576923312918 \tabularnewline
125 & 420 & 396.00066078993 & 23.9993392100696 \tabularnewline
126 & 472 & 419.99841347661 & 52.0015865233896 \tabularnewline
127 & 548 & 471.996562333129 & 76.0034376668705 \tabularnewline
128 & 559 & 547.994975643684 & 11.0050243563164 \tabularnewline
129 & 463 & 558.99927249128 & -95.9992724912802 \tabularnewline
130 & 407 & 463.006346220196 & -56.0063462201964 \tabularnewline
131 & 362 & 407.003702409365 & -45.003702409365 \tabularnewline
132 & 405 & 362.002975058016 & 42.9970249419841 \tabularnewline
133 & 417 & 404.997157597334 & 12.0028424026661 \tabularnewline
134 & 391 & 416.999206528561 & -25.9992065285612 \tabularnewline
135 & 419 & 391.001718728541 & 27.9982812714588 \tabularnewline
136 & 461 & 418.998149118702 & 42.0018508812979 \tabularnewline
137 & 472 & 460.997223385267 & 11.0027766147329 \tabularnewline
138 & 535 & 471.999272639872 & 63.0007273601285 \tabularnewline
139 & 622 & 534.995835213351 & 87.0041647866487 \tabularnewline
140 & 606 & 621.994248419041 & -15.994248419041 \tabularnewline
141 & 508 & 606.001057331162 & -98.0010573311621 \tabularnewline
142 & 461 & 508.006478552109 & -47.0064785521095 \tabularnewline
143 & 390 & 461.003107455461 & -71.0031074554609 \tabularnewline
144 & 432 & 390.00469379968 & 41.9953062003196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194058&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]118[/C][C]112[/C][C]6[/C][/ROW]
[ROW][C]3[/C][C]132[/C][C]117.999603358232[/C][C]14.0003966417681[/C][/ROW]
[ROW][C]4[/C][C]129[/C][C]131.99907447632[/C][C]-2.99907447632029[/C][/ROW]
[ROW][C]5[/C][C]121[/C][C]129.000198259701[/C][C]-8.00019825970051[/C][/ROW]
[ROW][C]6[/C][C]135[/C][C]121.000528868797[/C][C]13.9994711312028[/C][/ROW]
[ROW][C]7[/C][C]148[/C][C]134.999074537503[/C][C]13.000925462497[/C][/ROW]
[ROW][C]8[/C][C]148[/C][C]147.999140548323[/C][C]0.000859451677087009[/C][/ROW]
[ROW][C]9[/C][C]136[/C][C]147.999999943184[/C][C]-11.9999999431843[/C][/ROW]
[ROW][C]10[/C][C]119[/C][C]136.000793283532[/C][C]-17.0007932835325[/C][/ROW]
[ROW][C]11[/C][C]104[/C][C]119.001123870785[/C][C]-15.0011238707845[/C][/ROW]
[ROW][C]12[/C][C]118[/C][C]104.000991678716[/C][C]13.999008321284[/C][/ROW]
[ROW][C]13[/C][C]115[/C][C]117.999074568098[/C][C]-2.99907456809794[/C][/ROW]
[ROW][C]14[/C][C]126[/C][C]115.000198259707[/C][C]10.9998017402934[/C][/ROW]
[ROW][C]15[/C][C]141[/C][C]125.999272836531[/C][C]15.0007271634685[/C][/ROW]
[ROW][C]16[/C][C]135[/C][C]140.999008347509[/C][C]-5.99900834750915[/C][/ROW]
[ROW][C]17[/C][C]125[/C][C]135.000396576213[/C][C]-10.000396576213[/C][/ROW]
[ROW][C]18[/C][C]149[/C][C]125.00066109583[/C][C]23.99933890417[/C][/ROW]
[ROW][C]19[/C][C]170[/C][C]148.998413476631[/C][C]21.0015865233694[/C][/ROW]
[ROW][C]20[/C][C]170[/C][C]169.998611648931[/C][C]0.00138835106864121[/C][/ROW]
[ROW][C]21[/C][C]158[/C][C]169.99999990822[/C][C]-11.9999999082203[/C][/ROW]
[ROW][C]22[/C][C]133[/C][C]158.00079328353[/C][C]-25.0007932835302[/C][/ROW]
[ROW][C]23[/C][C]114[/C][C]133.001652726475[/C][C]-19.0016527264754[/C][/ROW]
[ROW][C]24[/C][C]140[/C][C]114.001256141522[/C][C]25.9987438584776[/C][/ROW]
[ROW][C]25[/C][C]145[/C][C]139.998281302045[/C][C]5.00171869795545[/C][/ROW]
[ROW][C]26[/C][C]150[/C][C]144.999669351575[/C][C]5.00033064842467[/C][/ROW]
[ROW][C]27[/C][C]178[/C][C]149.999669443335[/C][C]28.0003305566649[/C][/ROW]
[ROW][C]28[/C][C]163[/C][C]177.99814898323[/C][C]-14.99814898323[/C][/ROW]
[ROW][C]29[/C][C]172[/C][C]163.000991482055[/C][C]8.99900851794482[/C][/ROW]
[ROW][C]30[/C][C]178[/C][C]171.999405102892[/C][C]6.0005948971083[/C][/ROW]
[ROW][C]31[/C][C]199[/C][C]177.999603318905[/C][C]21.0003966810949[/C][/ROW]
[ROW][C]32[/C][C]199[/C][C]198.998611727588[/C][C]0.00138827241175932[/C][/ROW]
[ROW][C]33[/C][C]184[/C][C]198.999999908226[/C][C]-14.9999999082255[/C][/ROW]
[ROW][C]34[/C][C]162[/C][C]184.000991604414[/C][C]-22.0009916044142[/C][/ROW]
[ROW][C]35[/C][C]146[/C][C]162.001454418702[/C][C]-16.0014544187017[/C][/ROW]
[ROW][C]36[/C][C]166[/C][C]146.001057807529[/C][C]19.9989421924712[/C][/ROW]
[ROW][C]37[/C][C]171[/C][C]165.998677930701[/C][C]5.0013220692986[/C][/ROW]
[ROW][C]38[/C][C]180[/C][C]170.999669377795[/C][C]9.00033062220476[/C][/ROW]
[ROW][C]39[/C][C]193[/C][C]179.999405015491[/C][C]13.0005949845086[/C][/ROW]
[ROW][C]40[/C][C]181[/C][C]192.99914057017[/C][C]-11.9991405701698[/C][/ROW]
[ROW][C]41[/C][C]183[/C][C]181.000793226722[/C][C]1.99920677327808[/C][/ROW]
[ROW][C]42[/C][C]218[/C][C]182.999867838515[/C][C]35.0001321614849[/C][/ROW]
[ROW][C]43[/C][C]230[/C][C]217.997686247616[/C][C]12.0023137523841[/C][/ROW]
[ROW][C]44[/C][C]242[/C][C]229.999206563509[/C][C]12.0007934364914[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]241.999206664012[/C][C]-32.9992066640121[/C][/ROW]
[ROW][C]46[/C][C]191[/C][C]209.00218147728[/C][C]-18.0021814772796[/C][/ROW]
[ROW][C]47[/C][C]172[/C][C]191.001190069515[/C][C]-19.0011900695152[/C][/ROW]
[ROW][C]48[/C][C]194[/C][C]172.001256110938[/C][C]21.9987438890624[/C][/ROW]
[ROW][C]49[/C][C]196[/C][C]193.998545729888[/C][C]2.00145427011208[/C][/ROW]
[ROW][C]50[/C][C]196[/C][C]195.99986768994[/C][C]0.000132310060081409[/C][/ROW]
[ROW][C]51[/C][C]236[/C][C]195.999999991253[/C][C]40.0000000087466[/C][/ROW]
[ROW][C]52[/C][C]235[/C][C]235.997355721545[/C][C]-0.997355721545347[/C][/ROW]
[ROW][C]53[/C][C]229[/C][C]235.000065932156[/C][C]-6.00006593215613[/C][/ROW]
[ROW][C]54[/C][C]243[/C][C]229.000396646127[/C][C]13.9996033538733[/C][/ROW]
[ROW][C]55[/C][C]264[/C][C]242.999074528762[/C][C]21.0009254712378[/C][/ROW]
[ROW][C]56[/C][C]272[/C][C]263.998611692632[/C][C]8.00138830736847[/C][/ROW]
[ROW][C]57[/C][C]237[/C][C]271.999471052532[/C][C]-34.9994710525324[/C][/ROW]
[ROW][C]58[/C][C]211[/C][C]237.00231370868[/C][C]-26.0023137086802[/C][/ROW]
[ROW][C]59[/C][C]180[/C][C]211.001718933947[/C][C]-31.0017189339474[/C][/ROW]
[ROW][C]60[/C][C]201[/C][C]180.002049429435[/C][C]20.9979505705646[/C][/ROW]
[ROW][C]61[/C][C]204[/C][C]200.998611889293[/C][C]3.00138811070684[/C][/ROW]
[ROW][C]62[/C][C]188[/C][C]203.999801587352[/C][C]-15.9998015873522[/C][/ROW]
[ROW][C]63[/C][C]235[/C][C]188.001057698265[/C][C]46.9989423017348[/C][/ROW]
[ROW][C]64[/C][C]227[/C][C]234.996893042738[/C][C]-7.99689304273767[/C][/ROW]
[ROW][C]65[/C][C]234[/C][C]227.000528650299[/C][C]6.99947134970068[/C][/ROW]
[ROW][C]66[/C][C]264[/C][C]233.999537286218[/C][C]30.000462713782[/C][/ROW]
[ROW][C]67[/C][C]302[/C][C]263.998016760571[/C][C]38.0019832394291[/C][/ROW]
[ROW][C]68[/C][C]293[/C][C]301.997487804363[/C][C]-8.99748780436272[/C][/ROW]
[ROW][C]69[/C][C]259[/C][C]293.000594796579[/C][C]-34.0005947965785[/C][/ROW]
[ROW][C]70[/C][C]229[/C][C]259.002247676006[/C][C]-30.0022476760062[/C][/ROW]
[ROW][C]71[/C][C]203[/C][C]229.001983357428[/C][C]-26.0019833574276[/C][/ROW]
[ROW][C]72[/C][C]229[/C][C]203.001718912109[/C][C]25.9982810878911[/C][/ROW]
[ROW][C]73[/C][C]242[/C][C]228.998281332637[/C][C]13.0017186673631[/C][/ROW]
[ROW][C]74[/C][C]233[/C][C]241.999140495887[/C][C]-8.99914049588654[/C][/ROW]
[ROW][C]75[/C][C]267[/C][C]233.000594905833[/C][C]33.999405094167[/C][/ROW]
[ROW][C]76[/C][C]269[/C][C]266.997752402641[/C][C]2.00224759735858[/C][/ROW]
[ROW][C]77[/C][C]270[/C][C]268.999867637495[/C][C]1.00013236250453[/C][/ROW]
[ROW][C]78[/C][C]315[/C][C]269.999933884289[/C][C]45.0000661157114[/C][/ROW]
[ROW][C]79[/C][C]364[/C][C]314.997025182368[/C][C]49.0029748176315[/C][/ROW]
[ROW][C]80[/C][C]347[/C][C]363.996760562238[/C][C]-16.9967605622376[/C][/ROW]
[ROW][C]81[/C][C]312[/C][C]347.001123604194[/C][C]-35.0011236041936[/C][/ROW]
[ROW][C]82[/C][C]274[/C][C]312.002313817925[/C][C]-38.0023138179254[/C][/ROW]
[ROW][C]83[/C][C]237[/C][C]274.002512217491[/C][C]-37.0025122174908[/C][/ROW]
[ROW][C]84[/C][C]278[/C][C]237.002446123645[/C][C]40.9975538763549[/C][/ROW]
[ROW][C]85[/C][C]284[/C][C]277.99728977629[/C][C]6.00271022370964[/C][/ROW]
[ROW][C]86[/C][C]277[/C][C]283.999603179067[/C][C]-6.99960317906721[/C][/ROW]
[ROW][C]87[/C][C]317[/C][C]277.000462722497[/C][C]39.9995372775032[/C][/ROW]
[ROW][C]88[/C][C]313[/C][C]316.997355752135[/C][C]-3.99735575213509[/C][/ROW]
[ROW][C]89[/C][C]318[/C][C]313.000264253042[/C][C]4.99973574695781[/C][/ROW]
[ROW][C]90[/C][C]374[/C][C]317.999669482662[/C][C]56.0003305173378[/C][/ROW]
[ROW][C]91[/C][C]413[/C][C]373.996297988315[/C][C]39.0037020116852[/C][/ROW]
[ROW][C]92[/C][C]405[/C][C]412.997421583779[/C][C]-7.99742158377853[/C][/ROW]
[ROW][C]93[/C][C]355[/C][C]405.00052868524[/C][C]-50.0005286852395[/C][/ROW]
[ROW][C]94[/C][C]306[/C][C]355.003305383017[/C][C]-49.0033053830174[/C][/ROW]
[ROW][C]95[/C][C]271[/C][C]306.003239459615[/C][C]-35.0032394596151[/C][/ROW]
[ROW][C]96[/C][C]306[/C][C]271.002313957798[/C][C]34.9976860422018[/C][/ROW]
[ROW][C]97[/C][C]315[/C][C]305.997686409321[/C][C]9.00231359067863[/C][/ROW]
[ROW][C]98[/C][C]301[/C][C]314.999404884403[/C][C]-13.9994048844034[/C][/ROW]
[ROW][C]99[/C][C]356[/C][C]301.000925458118[/C][C]54.9990745418824[/C][/ROW]
[ROW][C]100[/C][C]348[/C][C]355.996364178305[/C][C]-7.99636417830487[/C][/ROW]
[ROW][C]101[/C][C]355[/C][C]348.000528615338[/C][C]6.99947138466229[/C][/ROW]
[ROW][C]102[/C][C]422[/C][C]354.999537286216[/C][C]67.0004627137843[/C][/ROW]
[ROW][C]103[/C][C]465[/C][C]421.995570803001[/C][C]43.0044291969992[/C][/ROW]
[ROW][C]104[/C][C]467[/C][C]464.997157107861[/C][C]2.00284289213886[/C][/ROW]
[ROW][C]105[/C][C]404[/C][C]466.999867598142[/C][C]-62.9998675981423[/C][/ROW]
[ROW][C]106[/C][C]347[/C][C]404.004164729812[/C][C]-57.0041647298125[/C][/ROW]
[ROW][C]107[/C][C]305[/C][C]347.003768372115[/C][C]-42.0037683721147[/C][/ROW]
[ROW][C]108[/C][C]336[/C][C]305.002776741492[/C][C]30.9972232585076[/C][/ROW]
[ROW][C]109[/C][C]340[/C][C]335.99795086776[/C][C]4.00204913223996[/C][/ROW]
[ROW][C]110[/C][C]318[/C][C]339.999735436693[/C][C]-21.9997354366927[/C][/ROW]
[ROW][C]111[/C][C]362[/C][C]318.00145433566[/C][C]43.9985456643398[/C][/ROW]
[ROW][C]112[/C][C]348[/C][C]361.997091389842[/C][C]-13.9970913898422[/C][/ROW]
[ROW][C]113[/C][C]363[/C][C]348.00092530518[/C][C]14.9990746948205[/C][/ROW]
[ROW][C]114[/C][C]435[/C][C]362.999008456749[/C][C]72.0009915432512[/C][/ROW]
[ROW][C]115[/C][C]491[/C][C]434.995240233235[/C][C]56.0047597667652[/C][/ROW]
[ROW][C]116[/C][C]505[/C][C]490.996297695511[/C][C]14.0037023044894[/C][/ROW]
[ROW][C]117[/C][C]404[/C][C]504.999074257793[/C][C]-100.999074257793[/C][/ROW]
[ROW][C]118[/C][C]359[/C][C]404.006676741899[/C][C]-45.0066767418986[/C][/ROW]
[ROW][C]119[/C][C]310[/C][C]359.00297525464[/C][C]-49.00297525464[/C][/ROW]
[ROW][C]120[/C][C]337[/C][C]310.003239437791[/C][C]26.9967605622087[/C][/ROW]
[ROW][C]121[/C][C]360[/C][C]336.998215326193[/C][C]23.0017846738071[/C][/ROW]
[ROW][C]122[/C][C]342[/C][C]359.99847942191[/C][C]-17.9984794219096[/C][/ROW]
[ROW][C]123[/C][C]406[/C][C]342.001189824784[/C][C]63.9988101752165[/C][/ROW]
[ROW][C]124[/C][C]396[/C][C]405.995769233129[/C][C]-9.99576923312918[/C][/ROW]
[ROW][C]125[/C][C]420[/C][C]396.00066078993[/C][C]23.9993392100696[/C][/ROW]
[ROW][C]126[/C][C]472[/C][C]419.99841347661[/C][C]52.0015865233896[/C][/ROW]
[ROW][C]127[/C][C]548[/C][C]471.996562333129[/C][C]76.0034376668705[/C][/ROW]
[ROW][C]128[/C][C]559[/C][C]547.994975643684[/C][C]11.0050243563164[/C][/ROW]
[ROW][C]129[/C][C]463[/C][C]558.99927249128[/C][C]-95.9992724912802[/C][/ROW]
[ROW][C]130[/C][C]407[/C][C]463.006346220196[/C][C]-56.0063462201964[/C][/ROW]
[ROW][C]131[/C][C]362[/C][C]407.003702409365[/C][C]-45.003702409365[/C][/ROW]
[ROW][C]132[/C][C]405[/C][C]362.002975058016[/C][C]42.9970249419841[/C][/ROW]
[ROW][C]133[/C][C]417[/C][C]404.997157597334[/C][C]12.0028424026661[/C][/ROW]
[ROW][C]134[/C][C]391[/C][C]416.999206528561[/C][C]-25.9992065285612[/C][/ROW]
[ROW][C]135[/C][C]419[/C][C]391.001718728541[/C][C]27.9982812714588[/C][/ROW]
[ROW][C]136[/C][C]461[/C][C]418.998149118702[/C][C]42.0018508812979[/C][/ROW]
[ROW][C]137[/C][C]472[/C][C]460.997223385267[/C][C]11.0027766147329[/C][/ROW]
[ROW][C]138[/C][C]535[/C][C]471.999272639872[/C][C]63.0007273601285[/C][/ROW]
[ROW][C]139[/C][C]622[/C][C]534.995835213351[/C][C]87.0041647866487[/C][/ROW]
[ROW][C]140[/C][C]606[/C][C]621.994248419041[/C][C]-15.994248419041[/C][/ROW]
[ROW][C]141[/C][C]508[/C][C]606.001057331162[/C][C]-98.0010573311621[/C][/ROW]
[ROW][C]142[/C][C]461[/C][C]508.006478552109[/C][C]-47.0064785521095[/C][/ROW]
[ROW][C]143[/C][C]390[/C][C]461.003107455461[/C][C]-71.0031074554609[/C][/ROW]
[ROW][C]144[/C][C]432[/C][C]390.00469379968[/C][C]41.9953062003196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194058&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
21181126
3132117.99960335823214.0003966417681
4129131.99907447632-2.99907447632029
5121129.000198259701-8.00019825970051
6135121.00052886879713.9994711312028
7148134.99907453750313.000925462497
8148147.9991405483230.000859451677087009
9136147.999999943184-11.9999999431843
10119136.000793283532-17.0007932835325
11104119.001123870785-15.0011238707845
12118104.00099167871613.999008321284
13115117.999074568098-2.99907456809794
14126115.00019825970710.9998017402934
15141125.99927283653115.0007271634685
16135140.999008347509-5.99900834750915
17125135.000396576213-10.000396576213
18149125.0006610958323.99933890417
19170148.99841347663121.0015865233694
20170169.9986116489310.00138835106864121
21158169.99999990822-11.9999999082203
22133158.00079328353-25.0007932835302
23114133.001652726475-19.0016527264754
24140114.00125614152225.9987438584776
25145139.9982813020455.00171869795545
26150144.9996693515755.00033064842467
27178149.99966944333528.0003305566649
28163177.99814898323-14.99814898323
29172163.0009914820558.99900851794482
30178171.9994051028926.0005948971083
31199177.99960331890521.0003966810949
32199198.9986117275880.00138827241175932
33184198.999999908226-14.9999999082255
34162184.000991604414-22.0009916044142
35146162.001454418702-16.0014544187017
36166146.00105780752919.9989421924712
37171165.9986779307015.0013220692986
38180170.9996693777959.00033062220476
39193179.99940501549113.0005949845086
40181192.99914057017-11.9991405701698
41183181.0007932267221.99920677327808
42218182.99986783851535.0001321614849
43230217.99768624761612.0023137523841
44242229.99920656350912.0007934364914
45209241.999206664012-32.9992066640121
46191209.00218147728-18.0021814772796
47172191.001190069515-19.0011900695152
48194172.00125611093821.9987438890624
49196193.9985457298882.00145427011208
50196195.999867689940.000132310060081409
51236195.99999999125340.0000000087466
52235235.997355721545-0.997355721545347
53229235.000065932156-6.00006593215613
54243229.00039664612713.9996033538733
55264242.99907452876221.0009254712378
56272263.9986116926328.00138830736847
57237271.999471052532-34.9994710525324
58211237.00231370868-26.0023137086802
59180211.001718933947-31.0017189339474
60201180.00204942943520.9979505705646
61204200.9986118892933.00138811070684
62188203.999801587352-15.9998015873522
63235188.00105769826546.9989423017348
64227234.996893042738-7.99689304273767
65234227.0005286502996.99947134970068
66264233.99953728621830.000462713782
67302263.99801676057138.0019832394291
68293301.997487804363-8.99748780436272
69259293.000594796579-34.0005947965785
70229259.002247676006-30.0022476760062
71203229.001983357428-26.0019833574276
72229203.00171891210925.9982810878911
73242228.99828133263713.0017186673631
74233241.999140495887-8.99914049588654
75267233.00059490583333.999405094167
76269266.9977524026412.00224759735858
77270268.9998676374951.00013236250453
78315269.99993388428945.0000661157114
79364314.99702518236849.0029748176315
80347363.996760562238-16.9967605622376
81312347.001123604194-35.0011236041936
82274312.002313817925-38.0023138179254
83237274.002512217491-37.0025122174908
84278237.00244612364540.9975538763549
85284277.997289776296.00271022370964
86277283.999603179067-6.99960317906721
87317277.00046272249739.9995372775032
88313316.997355752135-3.99735575213509
89318313.0002642530424.99973574695781
90374317.99966948266256.0003305173378
91413373.99629798831539.0037020116852
92405412.997421583779-7.99742158377853
93355405.00052868524-50.0005286852395
94306355.003305383017-49.0033053830174
95271306.003239459615-35.0032394596151
96306271.00231395779834.9976860422018
97315305.9976864093219.00231359067863
98301314.999404884403-13.9994048844034
99356301.00092545811854.9990745418824
100348355.996364178305-7.99636417830487
101355348.0005286153386.99947138466229
102422354.99953728621667.0004627137843
103465421.99557080300143.0044291969992
104467464.9971571078612.00284289213886
105404466.999867598142-62.9998675981423
106347404.004164729812-57.0041647298125
107305347.003768372115-42.0037683721147
108336305.00277674149230.9972232585076
109340335.997950867764.00204913223996
110318339.999735436693-21.9997354366927
111362318.0014543356643.9985456643398
112348361.997091389842-13.9970913898422
113363348.0009253051814.9990746948205
114435362.99900845674972.0009915432512
115491434.99524023323556.0047597667652
116505490.99629769551114.0037023044894
117404504.999074257793-100.999074257793
118359404.006676741899-45.0066767418986
119310359.00297525464-49.00297525464
120337310.00323943779126.9967605622087
121360336.99821532619323.0017846738071
122342359.99847942191-17.9984794219096
123406342.00118982478463.9988101752165
124396405.995769233129-9.99576923312918
125420396.0006607899323.9993392100696
126472419.9984134766152.0015865233896
127548471.99656233312976.0034376668705
128559547.99497564368411.0050243563164
129463558.99927249128-95.9992724912802
130407463.006346220196-56.0063462201964
131362407.003702409365-45.003702409365
132405362.00297505801642.9970249419841
133417404.99715759733412.0028424026661
134391416.999206528561-25.9992065285612
135419391.00171872854127.9982812714588
136461418.99814911870242.0018508812979
137472460.99722338526711.0027766147329
138535471.99927263987263.0007273601285
139622534.99583521335187.0041647866487
140606621.994248419041-15.994248419041
141508606.001057331162-98.0010573311621
142461508.006478552109-47.0064785521095
143390461.003107455461-71.0031074554609
144432390.0046937996841.9953062003196







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
145431.997223817916365.838723296861498.155724338972
146431.997223817916338.43806762164525.556380014192
147431.997223817916317.412389633265546.582058002567
148431.997223817916299.686783027748564.307664608084
149431.997223817916284.070142933268579.924304702565
150431.997223817916269.951582790402594.04286484543
151431.997223817916256.968202530066607.026245105766
152431.997223817916244.883550319832619.110897316
153431.997223817916233.533384978413630.461062657419
154431.997223817916222.798122854559641.196324781273
155431.997223817916212.587487568948651.406960066884
156431.997223817916202.831343116171661.163104519661

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
145 & 431.997223817916 & 365.838723296861 & 498.155724338972 \tabularnewline
146 & 431.997223817916 & 338.43806762164 & 525.556380014192 \tabularnewline
147 & 431.997223817916 & 317.412389633265 & 546.582058002567 \tabularnewline
148 & 431.997223817916 & 299.686783027748 & 564.307664608084 \tabularnewline
149 & 431.997223817916 & 284.070142933268 & 579.924304702565 \tabularnewline
150 & 431.997223817916 & 269.951582790402 & 594.04286484543 \tabularnewline
151 & 431.997223817916 & 256.968202530066 & 607.026245105766 \tabularnewline
152 & 431.997223817916 & 244.883550319832 & 619.110897316 \tabularnewline
153 & 431.997223817916 & 233.533384978413 & 630.461062657419 \tabularnewline
154 & 431.997223817916 & 222.798122854559 & 641.196324781273 \tabularnewline
155 & 431.997223817916 & 212.587487568948 & 651.406960066884 \tabularnewline
156 & 431.997223817916 & 202.831343116171 & 661.163104519661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194058&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]431.997223817916[/C][C]365.838723296861[/C][C]498.155724338972[/C][/ROW]
[ROW][C]146[/C][C]431.997223817916[/C][C]338.43806762164[/C][C]525.556380014192[/C][/ROW]
[ROW][C]147[/C][C]431.997223817916[/C][C]317.412389633265[/C][C]546.582058002567[/C][/ROW]
[ROW][C]148[/C][C]431.997223817916[/C][C]299.686783027748[/C][C]564.307664608084[/C][/ROW]
[ROW][C]149[/C][C]431.997223817916[/C][C]284.070142933268[/C][C]579.924304702565[/C][/ROW]
[ROW][C]150[/C][C]431.997223817916[/C][C]269.951582790402[/C][C]594.04286484543[/C][/ROW]
[ROW][C]151[/C][C]431.997223817916[/C][C]256.968202530066[/C][C]607.026245105766[/C][/ROW]
[ROW][C]152[/C][C]431.997223817916[/C][C]244.883550319832[/C][C]619.110897316[/C][/ROW]
[ROW][C]153[/C][C]431.997223817916[/C][C]233.533384978413[/C][C]630.461062657419[/C][/ROW]
[ROW][C]154[/C][C]431.997223817916[/C][C]222.798122854559[/C][C]641.196324781273[/C][/ROW]
[ROW][C]155[/C][C]431.997223817916[/C][C]212.587487568948[/C][C]651.406960066884[/C][/ROW]
[ROW][C]156[/C][C]431.997223817916[/C][C]202.831343116171[/C][C]661.163104519661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194058&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194058&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
145431.997223817916365.838723296861498.155724338972
146431.997223817916338.43806762164525.556380014192
147431.997223817916317.412389633265546.582058002567
148431.997223817916299.686783027748564.307664608084
149431.997223817916284.070142933268579.924304702565
150431.997223817916269.951582790402594.04286484543
151431.997223817916256.968202530066607.026245105766
152431.997223817916244.883550319832619.110897316
153431.997223817916233.533384978413630.461062657419
154431.997223817916222.798122854559641.196324781273
155431.997223817916212.587487568948651.406960066884
156431.997223817916202.831343116171661.163104519661



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
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')