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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 17 Aug 2017 09:18:19 +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/2017/Aug/17/t1502954336bqst3ogl6rsybxm.htm/, Retrieved Fri, 10 May 2024 15:43:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307545, Retrieved Fri, 10 May 2024 15:43:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2017-08-17 07:18:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
209704
208923
208131
206492
222706
221848
209704
201630
202411
202411
203280
204842
207273
207273
205711
201630
222706
225918
221067
209704
214566
207273
210562
212135
213774
209704
210562
204842
222706
228349
223498
214566
224279
213774
223498
222706
225137
216205
225918
225137
239712
236423
223498
216986
225918
213774
222706
224279
227568
220286
224279
226710
235642
228349
218636
208131
217855
191125
204061
211343
218636
208131
208131
208131
213774
205711
195129
186274
192698
167618
182985
191917
193556
184624
185405
182985
191125
185405
174130
165979
179762
149831
169268
178123
178123
167618
157905
157124
165979
157905
142549
131967
143330
116611
140899
153824
157905
148973
137687
145761
148973
146542
122243
110968
119031
94743
119823
128755
136037
123893
112530
119031
122243
115819
91531
80949
90662
63943
93093
110968




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=307545&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=307545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307545&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
alpha0.405343002238528
beta0.0645195510983345
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238528 \tabularnewline
beta & 0.0645195510983345 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307545&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]0.405343002238528[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983345[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307545&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
alpha0.405343002238528
beta0.0645195510983345
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13207273207263.9861111119.01388888887595
14207273206809.083897395463.916102604737
15205711204955.705701106755.294298893743
16201630200855.021821839774.978178160993
17222706222142.625986382563.374013617809
18225918225393.899883157524.100116843154
19221067213266.3359344527800.66406554831
20209704209160.241841688543.758158311772
21214566210981.3740498223584.62595017813
22207273213481.681175633-6208.68117563307
23210562212618.133620043-2056.13362004279
24212135213704.852356593-1569.8523565933
25213774215348.52799921-1574.52799920953
26209704214616.44776212-4912.44776212019
27210562210710.651377261-148.651377261413
28204842206185.207315199-1343.20731519852
29222706226362.934681309-3656.93468130942
30228349227644.356421688704.643578312389
31223498219685.9307830113812.06921698895
32214566209312.3024889465253.69751105405
33224279214638.6105731129640.38942688843
34213774213716.05568886157.9443111393484
35223498217972.0058667435525.99413325725
36222706222729.573032798-23.5730327977217
37225137225345.996366735-208.996366735228
38216205223566.974200047-7361.97420004732
39225918221821.5096356874096.49036431347
40225137218737.8796645916399.12033540904
41239712241311.9394357-1599.93943570048
42236423246708.496745868-10285.4967458678
43223498236543.430763855-13045.4307638554
44216986220153.424313582-3167.42431358225
45225918224414.049985611503.95001438993
46213774214021.572997601-247.572997600626
47222706220923.7026258861782.29737411431
48224279220284.1970097783994.80299022247
49227568223944.7658874513623.23411254922
50220286219091.3540242561194.64597574389
51224279227477.699951457-3198.69995145701
52226710222465.0910862454244.90891375465
53235642239011.721769873-3369.72176987323
54228349238082.160749071-9733.16074907075
55218636226070.38920268-7434.38920267959
56208131217546.170862496-9415.1708624961
57217855221606.153147944-3751.15314794425
58191125207458.538634148-16333.5386341478
59204061208043.259464218-3982.25946421755
60211343205227.9033530546115.09664694627
61218636208427.50380986310208.4961901373
62208131203871.9677196124259.03228038832
63208131210040.811606071-1909.81160607096
64208131209163.65074136-1032.65074135998
65213774218091.556522155-4317.55652215544
66205711212017.53589771-6306.53589771019
67195129201875.120414484-6746.120414484
68186274191583.418391156-5309.41839115572
69192698199914.579424958-7216.57942495847
70167618176028.238258928-8410.2382589278
71182985186524.765754964-3539.7657549635
72191917189260.1848955182656.81510448214
73193556192768.670989132787.329010867688
74184624179886.5600077964737.43999220378
75185405181623.6081529963781.3918470038
76182985182766.417328976218.582671024284
77191125189472.3032509781652.69674902203
78185405184015.8534888881389.14651111167
79174130176313.019697676-2183.01969767586
80165979168426.212932454-2447.21293245372
81179762176559.2256346753202.7743653252
82149831156234.755062008-6403.75506200767
83169268170541.607712308-1273.60771230832
84178123178040.45481030282.5451896975283
85178123179486.468384004-1363.46838400397
86167618168117.951796833-499.951796833018
87157905167063.011898035-9158.01189803524
88157124160403.34930746-3279.3493074599
89165979166013.773518692-34.7735186921491
90157905159142.060417714-1237.06041771412
91142549147607.279306903-5058.27930690334
92131967137679.487371783-5712.48737178338
93143330147044.938713377-3714.93871337682
94116611117219.106077341-608.10607734113
95140899136092.7079722184806.29202778151
96153824146188.296034657635.70396534953
97157905149359.4322612188545.56773878195
98148973142303.5015436486669.49845635166
99137687138976.102741503-1289.1027415031
100145761139177.6579213046583.34207869624
101148973151149.021943535-2176.02194353519
102146542143072.1785331193469.82146688143
103122243131673.839534587-9430.83953458717
104110968119971.132942344-9003.13294234447
105119031129491.043085933-10460.0430859332
1069474398902.6703602382-4159.67036023825
107119823119587.538789833235.461210166919
108128755129424.521841216-669.521841216017
109136037129464.6666109396572.33338906053
110123893120136.0931697053756.90683029451
111112530110462.0978838242067.90211617624
112119031116360.2301704572670.76982954323
113122243121088.9538407671154.04615923282
114115819117358.470834558-1539.47083455756
1159153195766.3764646103-4235.37646461034
1168094986068.0223388017-5119.02233880169
1179066296041.616264141-5379.61626414103
1186394371137.6343786509-7194.63437865094
1199309393005.03973170287.9602682979748
120110968102039.3648845138928.63511548654

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 207273 & 207263.986111111 & 9.01388888887595 \tabularnewline
14 & 207273 & 206809.083897395 & 463.916102604737 \tabularnewline
15 & 205711 & 204955.705701106 & 755.294298893743 \tabularnewline
16 & 201630 & 200855.021821839 & 774.978178160993 \tabularnewline
17 & 222706 & 222142.625986382 & 563.374013617809 \tabularnewline
18 & 225918 & 225393.899883157 & 524.100116843154 \tabularnewline
19 & 221067 & 213266.335934452 & 7800.66406554831 \tabularnewline
20 & 209704 & 209160.241841688 & 543.758158311772 \tabularnewline
21 & 214566 & 210981.374049822 & 3584.62595017813 \tabularnewline
22 & 207273 & 213481.681175633 & -6208.68117563307 \tabularnewline
23 & 210562 & 212618.133620043 & -2056.13362004279 \tabularnewline
24 & 212135 & 213704.852356593 & -1569.8523565933 \tabularnewline
25 & 213774 & 215348.52799921 & -1574.52799920953 \tabularnewline
26 & 209704 & 214616.44776212 & -4912.44776212019 \tabularnewline
27 & 210562 & 210710.651377261 & -148.651377261413 \tabularnewline
28 & 204842 & 206185.207315199 & -1343.20731519852 \tabularnewline
29 & 222706 & 226362.934681309 & -3656.93468130942 \tabularnewline
30 & 228349 & 227644.356421688 & 704.643578312389 \tabularnewline
31 & 223498 & 219685.930783011 & 3812.06921698895 \tabularnewline
32 & 214566 & 209312.302488946 & 5253.69751105405 \tabularnewline
33 & 224279 & 214638.610573112 & 9640.38942688843 \tabularnewline
34 & 213774 & 213716.055688861 & 57.9443111393484 \tabularnewline
35 & 223498 & 217972.005866743 & 5525.99413325725 \tabularnewline
36 & 222706 & 222729.573032798 & -23.5730327977217 \tabularnewline
37 & 225137 & 225345.996366735 & -208.996366735228 \tabularnewline
38 & 216205 & 223566.974200047 & -7361.97420004732 \tabularnewline
39 & 225918 & 221821.509635687 & 4096.49036431347 \tabularnewline
40 & 225137 & 218737.879664591 & 6399.12033540904 \tabularnewline
41 & 239712 & 241311.9394357 & -1599.93943570048 \tabularnewline
42 & 236423 & 246708.496745868 & -10285.4967458678 \tabularnewline
43 & 223498 & 236543.430763855 & -13045.4307638554 \tabularnewline
44 & 216986 & 220153.424313582 & -3167.42431358225 \tabularnewline
45 & 225918 & 224414.04998561 & 1503.95001438993 \tabularnewline
46 & 213774 & 214021.572997601 & -247.572997600626 \tabularnewline
47 & 222706 & 220923.702625886 & 1782.29737411431 \tabularnewline
48 & 224279 & 220284.197009778 & 3994.80299022247 \tabularnewline
49 & 227568 & 223944.765887451 & 3623.23411254922 \tabularnewline
50 & 220286 & 219091.354024256 & 1194.64597574389 \tabularnewline
51 & 224279 & 227477.699951457 & -3198.69995145701 \tabularnewline
52 & 226710 & 222465.091086245 & 4244.90891375465 \tabularnewline
53 & 235642 & 239011.721769873 & -3369.72176987323 \tabularnewline
54 & 228349 & 238082.160749071 & -9733.16074907075 \tabularnewline
55 & 218636 & 226070.38920268 & -7434.38920267959 \tabularnewline
56 & 208131 & 217546.170862496 & -9415.1708624961 \tabularnewline
57 & 217855 & 221606.153147944 & -3751.15314794425 \tabularnewline
58 & 191125 & 207458.538634148 & -16333.5386341478 \tabularnewline
59 & 204061 & 208043.259464218 & -3982.25946421755 \tabularnewline
60 & 211343 & 205227.903353054 & 6115.09664694627 \tabularnewline
61 & 218636 & 208427.503809863 & 10208.4961901373 \tabularnewline
62 & 208131 & 203871.967719612 & 4259.03228038832 \tabularnewline
63 & 208131 & 210040.811606071 & -1909.81160607096 \tabularnewline
64 & 208131 & 209163.65074136 & -1032.65074135998 \tabularnewline
65 & 213774 & 218091.556522155 & -4317.55652215544 \tabularnewline
66 & 205711 & 212017.53589771 & -6306.53589771019 \tabularnewline
67 & 195129 & 201875.120414484 & -6746.120414484 \tabularnewline
68 & 186274 & 191583.418391156 & -5309.41839115572 \tabularnewline
69 & 192698 & 199914.579424958 & -7216.57942495847 \tabularnewline
70 & 167618 & 176028.238258928 & -8410.2382589278 \tabularnewline
71 & 182985 & 186524.765754964 & -3539.7657549635 \tabularnewline
72 & 191917 & 189260.184895518 & 2656.81510448214 \tabularnewline
73 & 193556 & 192768.670989132 & 787.329010867688 \tabularnewline
74 & 184624 & 179886.560007796 & 4737.43999220378 \tabularnewline
75 & 185405 & 181623.608152996 & 3781.3918470038 \tabularnewline
76 & 182985 & 182766.417328976 & 218.582671024284 \tabularnewline
77 & 191125 & 189472.303250978 & 1652.69674902203 \tabularnewline
78 & 185405 & 184015.853488888 & 1389.14651111167 \tabularnewline
79 & 174130 & 176313.019697676 & -2183.01969767586 \tabularnewline
80 & 165979 & 168426.212932454 & -2447.21293245372 \tabularnewline
81 & 179762 & 176559.225634675 & 3202.7743653252 \tabularnewline
82 & 149831 & 156234.755062008 & -6403.75506200767 \tabularnewline
83 & 169268 & 170541.607712308 & -1273.60771230832 \tabularnewline
84 & 178123 & 178040.454810302 & 82.5451896975283 \tabularnewline
85 & 178123 & 179486.468384004 & -1363.46838400397 \tabularnewline
86 & 167618 & 168117.951796833 & -499.951796833018 \tabularnewline
87 & 157905 & 167063.011898035 & -9158.01189803524 \tabularnewline
88 & 157124 & 160403.34930746 & -3279.3493074599 \tabularnewline
89 & 165979 & 166013.773518692 & -34.7735186921491 \tabularnewline
90 & 157905 & 159142.060417714 & -1237.06041771412 \tabularnewline
91 & 142549 & 147607.279306903 & -5058.27930690334 \tabularnewline
92 & 131967 & 137679.487371783 & -5712.48737178338 \tabularnewline
93 & 143330 & 147044.938713377 & -3714.93871337682 \tabularnewline
94 & 116611 & 117219.106077341 & -608.10607734113 \tabularnewline
95 & 140899 & 136092.707972218 & 4806.29202778151 \tabularnewline
96 & 153824 & 146188.29603465 & 7635.70396534953 \tabularnewline
97 & 157905 & 149359.432261218 & 8545.56773878195 \tabularnewline
98 & 148973 & 142303.501543648 & 6669.49845635166 \tabularnewline
99 & 137687 & 138976.102741503 & -1289.1027415031 \tabularnewline
100 & 145761 & 139177.657921304 & 6583.34207869624 \tabularnewline
101 & 148973 & 151149.021943535 & -2176.02194353519 \tabularnewline
102 & 146542 & 143072.178533119 & 3469.82146688143 \tabularnewline
103 & 122243 & 131673.839534587 & -9430.83953458717 \tabularnewline
104 & 110968 & 119971.132942344 & -9003.13294234447 \tabularnewline
105 & 119031 & 129491.043085933 & -10460.0430859332 \tabularnewline
106 & 94743 & 98902.6703602382 & -4159.67036023825 \tabularnewline
107 & 119823 & 119587.538789833 & 235.461210166919 \tabularnewline
108 & 128755 & 129424.521841216 & -669.521841216017 \tabularnewline
109 & 136037 & 129464.666610939 & 6572.33338906053 \tabularnewline
110 & 123893 & 120136.093169705 & 3756.90683029451 \tabularnewline
111 & 112530 & 110462.097883824 & 2067.90211617624 \tabularnewline
112 & 119031 & 116360.230170457 & 2670.76982954323 \tabularnewline
113 & 122243 & 121088.953840767 & 1154.04615923282 \tabularnewline
114 & 115819 & 117358.470834558 & -1539.47083455756 \tabularnewline
115 & 91531 & 95766.3764646103 & -4235.37646461034 \tabularnewline
116 & 80949 & 86068.0223388017 & -5119.02233880169 \tabularnewline
117 & 90662 & 96041.616264141 & -5379.61626414103 \tabularnewline
118 & 63943 & 71137.6343786509 & -7194.63437865094 \tabularnewline
119 & 93093 & 93005.039731702 & 87.9602682979748 \tabularnewline
120 & 110968 & 102039.364884513 & 8928.63511548654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307545&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]207273[/C][C]207263.986111111[/C][C]9.01388888887595[/C][/ROW]
[ROW][C]14[/C][C]207273[/C][C]206809.083897395[/C][C]463.916102604737[/C][/ROW]
[ROW][C]15[/C][C]205711[/C][C]204955.705701106[/C][C]755.294298893743[/C][/ROW]
[ROW][C]16[/C][C]201630[/C][C]200855.021821839[/C][C]774.978178160993[/C][/ROW]
[ROW][C]17[/C][C]222706[/C][C]222142.625986382[/C][C]563.374013617809[/C][/ROW]
[ROW][C]18[/C][C]225918[/C][C]225393.899883157[/C][C]524.100116843154[/C][/ROW]
[ROW][C]19[/C][C]221067[/C][C]213266.335934452[/C][C]7800.66406554831[/C][/ROW]
[ROW][C]20[/C][C]209704[/C][C]209160.241841688[/C][C]543.758158311772[/C][/ROW]
[ROW][C]21[/C][C]214566[/C][C]210981.374049822[/C][C]3584.62595017813[/C][/ROW]
[ROW][C]22[/C][C]207273[/C][C]213481.681175633[/C][C]-6208.68117563307[/C][/ROW]
[ROW][C]23[/C][C]210562[/C][C]212618.133620043[/C][C]-2056.13362004279[/C][/ROW]
[ROW][C]24[/C][C]212135[/C][C]213704.852356593[/C][C]-1569.8523565933[/C][/ROW]
[ROW][C]25[/C][C]213774[/C][C]215348.52799921[/C][C]-1574.52799920953[/C][/ROW]
[ROW][C]26[/C][C]209704[/C][C]214616.44776212[/C][C]-4912.44776212019[/C][/ROW]
[ROW][C]27[/C][C]210562[/C][C]210710.651377261[/C][C]-148.651377261413[/C][/ROW]
[ROW][C]28[/C][C]204842[/C][C]206185.207315199[/C][C]-1343.20731519852[/C][/ROW]
[ROW][C]29[/C][C]222706[/C][C]226362.934681309[/C][C]-3656.93468130942[/C][/ROW]
[ROW][C]30[/C][C]228349[/C][C]227644.356421688[/C][C]704.643578312389[/C][/ROW]
[ROW][C]31[/C][C]223498[/C][C]219685.930783011[/C][C]3812.06921698895[/C][/ROW]
[ROW][C]32[/C][C]214566[/C][C]209312.302488946[/C][C]5253.69751105405[/C][/ROW]
[ROW][C]33[/C][C]224279[/C][C]214638.610573112[/C][C]9640.38942688843[/C][/ROW]
[ROW][C]34[/C][C]213774[/C][C]213716.055688861[/C][C]57.9443111393484[/C][/ROW]
[ROW][C]35[/C][C]223498[/C][C]217972.005866743[/C][C]5525.99413325725[/C][/ROW]
[ROW][C]36[/C][C]222706[/C][C]222729.573032798[/C][C]-23.5730327977217[/C][/ROW]
[ROW][C]37[/C][C]225137[/C][C]225345.996366735[/C][C]-208.996366735228[/C][/ROW]
[ROW][C]38[/C][C]216205[/C][C]223566.974200047[/C][C]-7361.97420004732[/C][/ROW]
[ROW][C]39[/C][C]225918[/C][C]221821.509635687[/C][C]4096.49036431347[/C][/ROW]
[ROW][C]40[/C][C]225137[/C][C]218737.879664591[/C][C]6399.12033540904[/C][/ROW]
[ROW][C]41[/C][C]239712[/C][C]241311.9394357[/C][C]-1599.93943570048[/C][/ROW]
[ROW][C]42[/C][C]236423[/C][C]246708.496745868[/C][C]-10285.4967458678[/C][/ROW]
[ROW][C]43[/C][C]223498[/C][C]236543.430763855[/C][C]-13045.4307638554[/C][/ROW]
[ROW][C]44[/C][C]216986[/C][C]220153.424313582[/C][C]-3167.42431358225[/C][/ROW]
[ROW][C]45[/C][C]225918[/C][C]224414.04998561[/C][C]1503.95001438993[/C][/ROW]
[ROW][C]46[/C][C]213774[/C][C]214021.572997601[/C][C]-247.572997600626[/C][/ROW]
[ROW][C]47[/C][C]222706[/C][C]220923.702625886[/C][C]1782.29737411431[/C][/ROW]
[ROW][C]48[/C][C]224279[/C][C]220284.197009778[/C][C]3994.80299022247[/C][/ROW]
[ROW][C]49[/C][C]227568[/C][C]223944.765887451[/C][C]3623.23411254922[/C][/ROW]
[ROW][C]50[/C][C]220286[/C][C]219091.354024256[/C][C]1194.64597574389[/C][/ROW]
[ROW][C]51[/C][C]224279[/C][C]227477.699951457[/C][C]-3198.69995145701[/C][/ROW]
[ROW][C]52[/C][C]226710[/C][C]222465.091086245[/C][C]4244.90891375465[/C][/ROW]
[ROW][C]53[/C][C]235642[/C][C]239011.721769873[/C][C]-3369.72176987323[/C][/ROW]
[ROW][C]54[/C][C]228349[/C][C]238082.160749071[/C][C]-9733.16074907075[/C][/ROW]
[ROW][C]55[/C][C]218636[/C][C]226070.38920268[/C][C]-7434.38920267959[/C][/ROW]
[ROW][C]56[/C][C]208131[/C][C]217546.170862496[/C][C]-9415.1708624961[/C][/ROW]
[ROW][C]57[/C][C]217855[/C][C]221606.153147944[/C][C]-3751.15314794425[/C][/ROW]
[ROW][C]58[/C][C]191125[/C][C]207458.538634148[/C][C]-16333.5386341478[/C][/ROW]
[ROW][C]59[/C][C]204061[/C][C]208043.259464218[/C][C]-3982.25946421755[/C][/ROW]
[ROW][C]60[/C][C]211343[/C][C]205227.903353054[/C][C]6115.09664694627[/C][/ROW]
[ROW][C]61[/C][C]218636[/C][C]208427.503809863[/C][C]10208.4961901373[/C][/ROW]
[ROW][C]62[/C][C]208131[/C][C]203871.967719612[/C][C]4259.03228038832[/C][/ROW]
[ROW][C]63[/C][C]208131[/C][C]210040.811606071[/C][C]-1909.81160607096[/C][/ROW]
[ROW][C]64[/C][C]208131[/C][C]209163.65074136[/C][C]-1032.65074135998[/C][/ROW]
[ROW][C]65[/C][C]213774[/C][C]218091.556522155[/C][C]-4317.55652215544[/C][/ROW]
[ROW][C]66[/C][C]205711[/C][C]212017.53589771[/C][C]-6306.53589771019[/C][/ROW]
[ROW][C]67[/C][C]195129[/C][C]201875.120414484[/C][C]-6746.120414484[/C][/ROW]
[ROW][C]68[/C][C]186274[/C][C]191583.418391156[/C][C]-5309.41839115572[/C][/ROW]
[ROW][C]69[/C][C]192698[/C][C]199914.579424958[/C][C]-7216.57942495847[/C][/ROW]
[ROW][C]70[/C][C]167618[/C][C]176028.238258928[/C][C]-8410.2382589278[/C][/ROW]
[ROW][C]71[/C][C]182985[/C][C]186524.765754964[/C][C]-3539.7657549635[/C][/ROW]
[ROW][C]72[/C][C]191917[/C][C]189260.184895518[/C][C]2656.81510448214[/C][/ROW]
[ROW][C]73[/C][C]193556[/C][C]192768.670989132[/C][C]787.329010867688[/C][/ROW]
[ROW][C]74[/C][C]184624[/C][C]179886.560007796[/C][C]4737.43999220378[/C][/ROW]
[ROW][C]75[/C][C]185405[/C][C]181623.608152996[/C][C]3781.3918470038[/C][/ROW]
[ROW][C]76[/C][C]182985[/C][C]182766.417328976[/C][C]218.582671024284[/C][/ROW]
[ROW][C]77[/C][C]191125[/C][C]189472.303250978[/C][C]1652.69674902203[/C][/ROW]
[ROW][C]78[/C][C]185405[/C][C]184015.853488888[/C][C]1389.14651111167[/C][/ROW]
[ROW][C]79[/C][C]174130[/C][C]176313.019697676[/C][C]-2183.01969767586[/C][/ROW]
[ROW][C]80[/C][C]165979[/C][C]168426.212932454[/C][C]-2447.21293245372[/C][/ROW]
[ROW][C]81[/C][C]179762[/C][C]176559.225634675[/C][C]3202.7743653252[/C][/ROW]
[ROW][C]82[/C][C]149831[/C][C]156234.755062008[/C][C]-6403.75506200767[/C][/ROW]
[ROW][C]83[/C][C]169268[/C][C]170541.607712308[/C][C]-1273.60771230832[/C][/ROW]
[ROW][C]84[/C][C]178123[/C][C]178040.454810302[/C][C]82.5451896975283[/C][/ROW]
[ROW][C]85[/C][C]178123[/C][C]179486.468384004[/C][C]-1363.46838400397[/C][/ROW]
[ROW][C]86[/C][C]167618[/C][C]168117.951796833[/C][C]-499.951796833018[/C][/ROW]
[ROW][C]87[/C][C]157905[/C][C]167063.011898035[/C][C]-9158.01189803524[/C][/ROW]
[ROW][C]88[/C][C]157124[/C][C]160403.34930746[/C][C]-3279.3493074599[/C][/ROW]
[ROW][C]89[/C][C]165979[/C][C]166013.773518692[/C][C]-34.7735186921491[/C][/ROW]
[ROW][C]90[/C][C]157905[/C][C]159142.060417714[/C][C]-1237.06041771412[/C][/ROW]
[ROW][C]91[/C][C]142549[/C][C]147607.279306903[/C][C]-5058.27930690334[/C][/ROW]
[ROW][C]92[/C][C]131967[/C][C]137679.487371783[/C][C]-5712.48737178338[/C][/ROW]
[ROW][C]93[/C][C]143330[/C][C]147044.938713377[/C][C]-3714.93871337682[/C][/ROW]
[ROW][C]94[/C][C]116611[/C][C]117219.106077341[/C][C]-608.10607734113[/C][/ROW]
[ROW][C]95[/C][C]140899[/C][C]136092.707972218[/C][C]4806.29202778151[/C][/ROW]
[ROW][C]96[/C][C]153824[/C][C]146188.29603465[/C][C]7635.70396534953[/C][/ROW]
[ROW][C]97[/C][C]157905[/C][C]149359.432261218[/C][C]8545.56773878195[/C][/ROW]
[ROW][C]98[/C][C]148973[/C][C]142303.501543648[/C][C]6669.49845635166[/C][/ROW]
[ROW][C]99[/C][C]137687[/C][C]138976.102741503[/C][C]-1289.1027415031[/C][/ROW]
[ROW][C]100[/C][C]145761[/C][C]139177.657921304[/C][C]6583.34207869624[/C][/ROW]
[ROW][C]101[/C][C]148973[/C][C]151149.021943535[/C][C]-2176.02194353519[/C][/ROW]
[ROW][C]102[/C][C]146542[/C][C]143072.178533119[/C][C]3469.82146688143[/C][/ROW]
[ROW][C]103[/C][C]122243[/C][C]131673.839534587[/C][C]-9430.83953458717[/C][/ROW]
[ROW][C]104[/C][C]110968[/C][C]119971.132942344[/C][C]-9003.13294234447[/C][/ROW]
[ROW][C]105[/C][C]119031[/C][C]129491.043085933[/C][C]-10460.0430859332[/C][/ROW]
[ROW][C]106[/C][C]94743[/C][C]98902.6703602382[/C][C]-4159.67036023825[/C][/ROW]
[ROW][C]107[/C][C]119823[/C][C]119587.538789833[/C][C]235.461210166919[/C][/ROW]
[ROW][C]108[/C][C]128755[/C][C]129424.521841216[/C][C]-669.521841216017[/C][/ROW]
[ROW][C]109[/C][C]136037[/C][C]129464.666610939[/C][C]6572.33338906053[/C][/ROW]
[ROW][C]110[/C][C]123893[/C][C]120136.093169705[/C][C]3756.90683029451[/C][/ROW]
[ROW][C]111[/C][C]112530[/C][C]110462.097883824[/C][C]2067.90211617624[/C][/ROW]
[ROW][C]112[/C][C]119031[/C][C]116360.230170457[/C][C]2670.76982954323[/C][/ROW]
[ROW][C]113[/C][C]122243[/C][C]121088.953840767[/C][C]1154.04615923282[/C][/ROW]
[ROW][C]114[/C][C]115819[/C][C]117358.470834558[/C][C]-1539.47083455756[/C][/ROW]
[ROW][C]115[/C][C]91531[/C][C]95766.3764646103[/C][C]-4235.37646461034[/C][/ROW]
[ROW][C]116[/C][C]80949[/C][C]86068.0223388017[/C][C]-5119.02233880169[/C][/ROW]
[ROW][C]117[/C][C]90662[/C][C]96041.616264141[/C][C]-5379.61626414103[/C][/ROW]
[ROW][C]118[/C][C]63943[/C][C]71137.6343786509[/C][C]-7194.63437865094[/C][/ROW]
[ROW][C]119[/C][C]93093[/C][C]93005.039731702[/C][C]87.9602682979748[/C][/ROW]
[ROW][C]120[/C][C]110968[/C][C]102039.364884513[/C][C]8928.63511548654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307545&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307545&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
13207273207263.9861111119.01388888887595
14207273206809.083897395463.916102604737
15205711204955.705701106755.294298893743
16201630200855.021821839774.978178160993
17222706222142.625986382563.374013617809
18225918225393.899883157524.100116843154
19221067213266.3359344527800.66406554831
20209704209160.241841688543.758158311772
21214566210981.3740498223584.62595017813
22207273213481.681175633-6208.68117563307
23210562212618.133620043-2056.13362004279
24212135213704.852356593-1569.8523565933
25213774215348.52799921-1574.52799920953
26209704214616.44776212-4912.44776212019
27210562210710.651377261-148.651377261413
28204842206185.207315199-1343.20731519852
29222706226362.934681309-3656.93468130942
30228349227644.356421688704.643578312389
31223498219685.9307830113812.06921698895
32214566209312.3024889465253.69751105405
33224279214638.6105731129640.38942688843
34213774213716.05568886157.9443111393484
35223498217972.0058667435525.99413325725
36222706222729.573032798-23.5730327977217
37225137225345.996366735-208.996366735228
38216205223566.974200047-7361.97420004732
39225918221821.5096356874096.49036431347
40225137218737.8796645916399.12033540904
41239712241311.9394357-1599.93943570048
42236423246708.496745868-10285.4967458678
43223498236543.430763855-13045.4307638554
44216986220153.424313582-3167.42431358225
45225918224414.049985611503.95001438993
46213774214021.572997601-247.572997600626
47222706220923.7026258861782.29737411431
48224279220284.1970097783994.80299022247
49227568223944.7658874513623.23411254922
50220286219091.3540242561194.64597574389
51224279227477.699951457-3198.69995145701
52226710222465.0910862454244.90891375465
53235642239011.721769873-3369.72176987323
54228349238082.160749071-9733.16074907075
55218636226070.38920268-7434.38920267959
56208131217546.170862496-9415.1708624961
57217855221606.153147944-3751.15314794425
58191125207458.538634148-16333.5386341478
59204061208043.259464218-3982.25946421755
60211343205227.9033530546115.09664694627
61218636208427.50380986310208.4961901373
62208131203871.9677196124259.03228038832
63208131210040.811606071-1909.81160607096
64208131209163.65074136-1032.65074135998
65213774218091.556522155-4317.55652215544
66205711212017.53589771-6306.53589771019
67195129201875.120414484-6746.120414484
68186274191583.418391156-5309.41839115572
69192698199914.579424958-7216.57942495847
70167618176028.238258928-8410.2382589278
71182985186524.765754964-3539.7657549635
72191917189260.1848955182656.81510448214
73193556192768.670989132787.329010867688
74184624179886.5600077964737.43999220378
75185405181623.6081529963781.3918470038
76182985182766.417328976218.582671024284
77191125189472.3032509781652.69674902203
78185405184015.8534888881389.14651111167
79174130176313.019697676-2183.01969767586
80165979168426.212932454-2447.21293245372
81179762176559.2256346753202.7743653252
82149831156234.755062008-6403.75506200767
83169268170541.607712308-1273.60771230832
84178123178040.45481030282.5451896975283
85178123179486.468384004-1363.46838400397
86167618168117.951796833-499.951796833018
87157905167063.011898035-9158.01189803524
88157124160403.34930746-3279.3493074599
89165979166013.773518692-34.7735186921491
90157905159142.060417714-1237.06041771412
91142549147607.279306903-5058.27930690334
92131967137679.487371783-5712.48737178338
93143330147044.938713377-3714.93871337682
94116611117219.106077341-608.10607734113
95140899136092.7079722184806.29202778151
96153824146188.296034657635.70396534953
97157905149359.4322612188545.56773878195
98148973142303.5015436486669.49845635166
99137687138976.102741503-1289.1027415031
100145761139177.6579213046583.34207869624
101148973151149.021943535-2176.02194353519
102146542143072.1785331193469.82146688143
103122243131673.839534587-9430.83953458717
104110968119971.132942344-9003.13294234447
105119031129491.043085933-10460.0430859332
1069474398902.6703602382-4159.67036023825
107119823119587.538789833235.461210166919
108128755129424.521841216-669.521841216017
109136037129464.6666109396572.33338906053
110123893120136.0931697053756.90683029451
111112530110462.0978838242067.90211617624
112119031116360.2301704572670.76982954323
113122243121088.9538407671154.04615923282
114115819117358.470834558-1539.47083455756
1159153195766.3764646103-4235.37646461034
1168094986068.0223388017-5119.02233880169
1179066296041.616264141-5379.61626414103
1186394371137.6343786509-7194.63437865094
1199309393005.03973170287.9602682979748
120110968102039.3648845138928.63511548654







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121110322.776646637100280.090297887120365.462995387
12296530.358831056585592.6404464582107468.077215655
12384105.314568832172241.206955050395969.422182614
12489245.821187238776425.3840415782102066.258332899
12591642.273694114777836.792089379105447.75529885
12685464.343217631470646.1735551998100282.512880063
12762555.440308720346697.885027461678412.995589979
12853821.482959967836898.687509037970744.2784108976
12965622.031015497347608.898230034283635.1638009605
13041866.974638182622739.092852921160994.8564234441
13171217.127507440650950.709622642891483.5453922384
13285706.474307137864278.3056711511107134.642943124

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 110322.776646637 & 100280.090297887 & 120365.462995387 \tabularnewline
122 & 96530.3588310565 & 85592.6404464582 & 107468.077215655 \tabularnewline
123 & 84105.3145688321 & 72241.2069550503 & 95969.422182614 \tabularnewline
124 & 89245.8211872387 & 76425.3840415782 & 102066.258332899 \tabularnewline
125 & 91642.2736941147 & 77836.792089379 & 105447.75529885 \tabularnewline
126 & 85464.3432176314 & 70646.1735551998 & 100282.512880063 \tabularnewline
127 & 62555.4403087203 & 46697.8850274616 & 78412.995589979 \tabularnewline
128 & 53821.4829599678 & 36898.6875090379 & 70744.2784108976 \tabularnewline
129 & 65622.0310154973 & 47608.8982300342 & 83635.1638009605 \tabularnewline
130 & 41866.9746381826 & 22739.0928529211 & 60994.8564234441 \tabularnewline
131 & 71217.1275074406 & 50950.7096226428 & 91483.5453922384 \tabularnewline
132 & 85706.4743071378 & 64278.3056711511 & 107134.642943124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307545&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]110322.776646637[/C][C]100280.090297887[/C][C]120365.462995387[/C][/ROW]
[ROW][C]122[/C][C]96530.3588310565[/C][C]85592.6404464582[/C][C]107468.077215655[/C][/ROW]
[ROW][C]123[/C][C]84105.3145688321[/C][C]72241.2069550503[/C][C]95969.422182614[/C][/ROW]
[ROW][C]124[/C][C]89245.8211872387[/C][C]76425.3840415782[/C][C]102066.258332899[/C][/ROW]
[ROW][C]125[/C][C]91642.2736941147[/C][C]77836.792089379[/C][C]105447.75529885[/C][/ROW]
[ROW][C]126[/C][C]85464.3432176314[/C][C]70646.1735551998[/C][C]100282.512880063[/C][/ROW]
[ROW][C]127[/C][C]62555.4403087203[/C][C]46697.8850274616[/C][C]78412.995589979[/C][/ROW]
[ROW][C]128[/C][C]53821.4829599678[/C][C]36898.6875090379[/C][C]70744.2784108976[/C][/ROW]
[ROW][C]129[/C][C]65622.0310154973[/C][C]47608.8982300342[/C][C]83635.1638009605[/C][/ROW]
[ROW][C]130[/C][C]41866.9746381826[/C][C]22739.0928529211[/C][C]60994.8564234441[/C][/ROW]
[ROW][C]131[/C][C]71217.1275074406[/C][C]50950.7096226428[/C][C]91483.5453922384[/C][/ROW]
[ROW][C]132[/C][C]85706.4743071378[/C][C]64278.3056711511[/C][C]107134.642943124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307545&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307545&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
121110322.776646637100280.090297887120365.462995387
12296530.358831056585592.6404464582107468.077215655
12384105.314568832172241.206955050395969.422182614
12489245.821187238776425.3840415782102066.258332899
12591642.273694114777836.792089379105447.75529885
12685464.343217631470646.1735551998100282.512880063
12762555.440308720346697.885027461678412.995589979
12853821.482959967836898.687509037970744.2784108976
12965622.031015497347608.898230034283635.1638009605
13041866.974638182622739.092852921160994.8564234441
13171217.127507440650950.709622642891483.5453922384
13285706.474307137864278.3056711511107134.642943124



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; 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')