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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Aug 2017 17:46:59 +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/14/t1502725638jbzeg0tqtbbfcyv.htm/, Retrieved Sun, 12 May 2024 20:44:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307246, Retrieved Sun, 12 May 2024 20:44:20 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-14 15:46:59] [b5765487180b26865894987d1ded8bd3] [Current]
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Dataseries X:
 228 768 
 227 916 
 227 052 
 225 264 
 242 952 
 242 016 
 228 768 
 219 960 
 220 812 
 220 812 
 221 760 
 223 464 
 226 116 
 226 116 
 224 412 
 219 960 
 242 952 
 246 456 
 241 164 
 228 768 
 234 072 
 226 116 
 229 704 
 231 420 
 233 208 
 228 768 
 229 704 
 223 464 
 242 952 
 249 108 
 243 816 
 234 072 
 244 668 
 233 208 
 243 816 
 242 952 
 245 604 
 235 860 
 246 456 
 245 604 
 261 504 
 257 916 
 243 816 
 236 712 
 246 456 
 233 208 
 242 952 
 244 668 
 248 256 
 240 312 
 244 668 
 247 320 
 257 064 
 249 108 
 238 512 
 227 052 
 237 660 
 208 500 
 222 612 
 230 556 
 238 512 
 227 052 
 227 052 
 227 052 
 233 208 
 224 412 
 212 868 
 203 208 
 210 216 
 182 856 
 199 620 
 209 364 
 211 152 
 201 408 
 202 260 
 199 620 
 208 500 
 202 260 
 189 960 
 181 068 
 196 104 
 163 452 
 184 656 
 194 316 
 194 316 
 182 856 
 172 260 
 171 408 
 181 068 
 172 260 
 155 508 
 143 964 
 156 360 
 127 212 
 153 708 
 167 808 
 172 260 
 162 516 
 150 204 
 159 012 
 162 516 
 159 864 
 133 356 
 121 056 
 129 852 
 103 356 
 130 716 
 140 460 
 148 404 
 135 156 
 122 760 
 129 852 
 133 356 
 126 348 
 99 852 
 88 308 
 98 904 
 69 756 
 101 556 
 121 056




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307246&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307246&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307246&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238429
beta0.0645195510984277
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238429 \tabularnewline
beta & 0.0645195510984277 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307246&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]0.405343002238429[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510984277[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307246&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307246&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
alpha0.405343002238429
beta0.0645195510984277
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13226116226106.1666666679.83333333331393
14226116225609.909706249506.090293750633
15224412223588.042583025823.957416975056
16219960219114.569260188845.430739812087
17242952242337.410166962614.589833037695
18246456245884.254417989571.745582010713
19241164232654.1846557658509.81534423455
20228768228174.809281841593.190718158759
21234072230161.4989634423910.50103655792
22226116232889.106737054-6773.10673705439
23229704231947.05485823-2243.0548582295
24231420233132.566207194-1712.56620719365
25233208234925.666908229-1717.66690822944
26228768234127.033922314-5359.03392231374
27229704229866.165138832-162.165138831508
28223464224929.317071126-1465.31707112599
29242952246941.383288701-3989.3832887013
30249108248339.297914568768.702085431636
31243816239657.3790360124158.62096398763
32234072228340.6936243045731.30637569632
33244668234151.21153430210516.7884656976
34233208233144.78802420963.2119757909095
35243816237787.6427637186028.35723628182
36242952242977.716035779-25.7160357786925
37245604245831.996036439-227.996036438708
38235860243891.24458187-8031.24458187039
39246456241987.1014207514468.89857924907
40245604238623.1414522826980.85854771765
41261504263249.38847531-1745.38847531023
42257916269136.541904585-11220.5419045846
43243816258047.379015118-14231.3790151181
44236712240167.371978457-3455.37197845665
45246456244815.3272570311640.67274296854
46233208233478.079633745-270.079633745423
47242952241007.6755918741944.32440812589
48244668240310.0331015734357.96689842676
49248256244303.3809681263952.61903187446
50240312239008.749844641303.25015536018
51244668248157.490856134-3489.49085613387
52247320242689.1902759044630.80972409551
53257064260740.060112588-3676.0601125884
54249108259725.99354444-10617.9935444398
55238512246622.242766559-8110.24276655939
56227052237323.095486361-10271.0954863609
57237660241752.167070487-4092.16707048731
58208500226318.405782708-17818.4057827078
59222612226956.283051875-4344.28305187469
60230556223884.9854760586671.01452394226
61238512227375.45870166511136.5412983348
62227052222405.7829668444646.21703315625
63227052229135.430842981-2083.43084298106
64227052228178.52808148-1126.52808148036
65233208237918.06166053-4710.0616605299
66224412231291.857342953-6879.85734295275
67212868220227.404088525-7359.40408852493
68203208209000.09279035-5792.09279034959
69210216218088.632099954-7872.63209995435
70182856192030.805373375-9174.80537337466
71199620203481.562641779-3861.56264177855
72209364206465.6562496572898.34375034337
73211152210293.095624508858.904375492217
74201408196239.8836448665168.11635513382
75202260198134.8452578094125.15474219091
76199620199381.546177059238.453822940763
77208500206697.0580919711802.94190802932
78202260200744.5674424181515.43255758201
79189960192341.476033823-2381.4760338229
80181068183737.6868354-2669.68683540015
81196104192610.0643287343493.93567126628
82163452170437.914613097-6985.91461309709
83184656186045.390231609-1389.39023160926
84194316194225.9507021590.0492978497932
85194316195803.420055279-1487.4200552793
86182856183401.401960183-545.401960183372
87172260182250.55843422-9990.55843422038
88171408174985.471971773-3577.47197177343
89181068181105.934747662-37.934747661755
90172260173609.520455684-1349.52045568422
91155508161026.122880253-5518.12288025318
92143964150195.804405577-6231.80440557704
93156360160412.660414589-4052.66041458934
94127212127875.388448004-663.388448004349
95153708148464.7723333265243.22766667383
96167808159478.1411287088329.85887129224
97172260162937.5624667829322.43753321774
98162516155240.1835021617275.81649783856
99150204151610.29389982-1406.29389982048
100159012151830.1722777867181.82772221425
101162516164889.84212022-2373.84212021981
102159864156078.7402179473785.25978205292
103133356143644.188583184-10288.1885831841
104121056130877.599573465-9821.59957346509
105129852141262.956093744-11410.9560937443
106103356107893.822211168-4537.82221116844
107130716130459.133225272256.866774727823
108140460141190.387463145-730.387463144783
109148404141234.1817573897169.81824261107
110135156131057.5561851334098.4438148669
111122760120504.1067823522255.89321764831
112129852126938.4329132252913.56708677516
113133356132097.0405535631258.95944643734
114126348128027.422728607-1679.42272860717
11599852104472.410688663-4620.41068866319
1168830893892.3880059626-5584.38800596258
11798904104772.672288151-5868.67228815114
1186975677604.6920494359-7848.69204943591
119101556101460.04334367595.9566563251283
120121056111315.6707831069740.32921689443

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 226116 & 226106.166666667 & 9.83333333331393 \tabularnewline
14 & 226116 & 225609.909706249 & 506.090293750633 \tabularnewline
15 & 224412 & 223588.042583025 & 823.957416975056 \tabularnewline
16 & 219960 & 219114.569260188 & 845.430739812087 \tabularnewline
17 & 242952 & 242337.410166962 & 614.589833037695 \tabularnewline
18 & 246456 & 245884.254417989 & 571.745582010713 \tabularnewline
19 & 241164 & 232654.184655765 & 8509.81534423455 \tabularnewline
20 & 228768 & 228174.809281841 & 593.190718158759 \tabularnewline
21 & 234072 & 230161.498963442 & 3910.50103655792 \tabularnewline
22 & 226116 & 232889.106737054 & -6773.10673705439 \tabularnewline
23 & 229704 & 231947.05485823 & -2243.0548582295 \tabularnewline
24 & 231420 & 233132.566207194 & -1712.56620719365 \tabularnewline
25 & 233208 & 234925.666908229 & -1717.66690822944 \tabularnewline
26 & 228768 & 234127.033922314 & -5359.03392231374 \tabularnewline
27 & 229704 & 229866.165138832 & -162.165138831508 \tabularnewline
28 & 223464 & 224929.317071126 & -1465.31707112599 \tabularnewline
29 & 242952 & 246941.383288701 & -3989.3832887013 \tabularnewline
30 & 249108 & 248339.297914568 & 768.702085431636 \tabularnewline
31 & 243816 & 239657.379036012 & 4158.62096398763 \tabularnewline
32 & 234072 & 228340.693624304 & 5731.30637569632 \tabularnewline
33 & 244668 & 234151.211534302 & 10516.7884656976 \tabularnewline
34 & 233208 & 233144.788024209 & 63.2119757909095 \tabularnewline
35 & 243816 & 237787.642763718 & 6028.35723628182 \tabularnewline
36 & 242952 & 242977.716035779 & -25.7160357786925 \tabularnewline
37 & 245604 & 245831.996036439 & -227.996036438708 \tabularnewline
38 & 235860 & 243891.24458187 & -8031.24458187039 \tabularnewline
39 & 246456 & 241987.101420751 & 4468.89857924907 \tabularnewline
40 & 245604 & 238623.141452282 & 6980.85854771765 \tabularnewline
41 & 261504 & 263249.38847531 & -1745.38847531023 \tabularnewline
42 & 257916 & 269136.541904585 & -11220.5419045846 \tabularnewline
43 & 243816 & 258047.379015118 & -14231.3790151181 \tabularnewline
44 & 236712 & 240167.371978457 & -3455.37197845665 \tabularnewline
45 & 246456 & 244815.327257031 & 1640.67274296854 \tabularnewline
46 & 233208 & 233478.079633745 & -270.079633745423 \tabularnewline
47 & 242952 & 241007.675591874 & 1944.32440812589 \tabularnewline
48 & 244668 & 240310.033101573 & 4357.96689842676 \tabularnewline
49 & 248256 & 244303.380968126 & 3952.61903187446 \tabularnewline
50 & 240312 & 239008.74984464 & 1303.25015536018 \tabularnewline
51 & 244668 & 248157.490856134 & -3489.49085613387 \tabularnewline
52 & 247320 & 242689.190275904 & 4630.80972409551 \tabularnewline
53 & 257064 & 260740.060112588 & -3676.0601125884 \tabularnewline
54 & 249108 & 259725.99354444 & -10617.9935444398 \tabularnewline
55 & 238512 & 246622.242766559 & -8110.24276655939 \tabularnewline
56 & 227052 & 237323.095486361 & -10271.0954863609 \tabularnewline
57 & 237660 & 241752.167070487 & -4092.16707048731 \tabularnewline
58 & 208500 & 226318.405782708 & -17818.4057827078 \tabularnewline
59 & 222612 & 226956.283051875 & -4344.28305187469 \tabularnewline
60 & 230556 & 223884.985476058 & 6671.01452394226 \tabularnewline
61 & 238512 & 227375.458701665 & 11136.5412983348 \tabularnewline
62 & 227052 & 222405.782966844 & 4646.21703315625 \tabularnewline
63 & 227052 & 229135.430842981 & -2083.43084298106 \tabularnewline
64 & 227052 & 228178.52808148 & -1126.52808148036 \tabularnewline
65 & 233208 & 237918.06166053 & -4710.0616605299 \tabularnewline
66 & 224412 & 231291.857342953 & -6879.85734295275 \tabularnewline
67 & 212868 & 220227.404088525 & -7359.40408852493 \tabularnewline
68 & 203208 & 209000.09279035 & -5792.09279034959 \tabularnewline
69 & 210216 & 218088.632099954 & -7872.63209995435 \tabularnewline
70 & 182856 & 192030.805373375 & -9174.80537337466 \tabularnewline
71 & 199620 & 203481.562641779 & -3861.56264177855 \tabularnewline
72 & 209364 & 206465.656249657 & 2898.34375034337 \tabularnewline
73 & 211152 & 210293.095624508 & 858.904375492217 \tabularnewline
74 & 201408 & 196239.883644866 & 5168.11635513382 \tabularnewline
75 & 202260 & 198134.845257809 & 4125.15474219091 \tabularnewline
76 & 199620 & 199381.546177059 & 238.453822940763 \tabularnewline
77 & 208500 & 206697.058091971 & 1802.94190802932 \tabularnewline
78 & 202260 & 200744.567442418 & 1515.43255758201 \tabularnewline
79 & 189960 & 192341.476033823 & -2381.4760338229 \tabularnewline
80 & 181068 & 183737.6868354 & -2669.68683540015 \tabularnewline
81 & 196104 & 192610.064328734 & 3493.93567126628 \tabularnewline
82 & 163452 & 170437.914613097 & -6985.91461309709 \tabularnewline
83 & 184656 & 186045.390231609 & -1389.39023160926 \tabularnewline
84 & 194316 & 194225.95070215 & 90.0492978497932 \tabularnewline
85 & 194316 & 195803.420055279 & -1487.4200552793 \tabularnewline
86 & 182856 & 183401.401960183 & -545.401960183372 \tabularnewline
87 & 172260 & 182250.55843422 & -9990.55843422038 \tabularnewline
88 & 171408 & 174985.471971773 & -3577.47197177343 \tabularnewline
89 & 181068 & 181105.934747662 & -37.934747661755 \tabularnewline
90 & 172260 & 173609.520455684 & -1349.52045568422 \tabularnewline
91 & 155508 & 161026.122880253 & -5518.12288025318 \tabularnewline
92 & 143964 & 150195.804405577 & -6231.80440557704 \tabularnewline
93 & 156360 & 160412.660414589 & -4052.66041458934 \tabularnewline
94 & 127212 & 127875.388448004 & -663.388448004349 \tabularnewline
95 & 153708 & 148464.772333326 & 5243.22766667383 \tabularnewline
96 & 167808 & 159478.141128708 & 8329.85887129224 \tabularnewline
97 & 172260 & 162937.562466782 & 9322.43753321774 \tabularnewline
98 & 162516 & 155240.183502161 & 7275.81649783856 \tabularnewline
99 & 150204 & 151610.29389982 & -1406.29389982048 \tabularnewline
100 & 159012 & 151830.172277786 & 7181.82772221425 \tabularnewline
101 & 162516 & 164889.84212022 & -2373.84212021981 \tabularnewline
102 & 159864 & 156078.740217947 & 3785.25978205292 \tabularnewline
103 & 133356 & 143644.188583184 & -10288.1885831841 \tabularnewline
104 & 121056 & 130877.599573465 & -9821.59957346509 \tabularnewline
105 & 129852 & 141262.956093744 & -11410.9560937443 \tabularnewline
106 & 103356 & 107893.822211168 & -4537.82221116844 \tabularnewline
107 & 130716 & 130459.133225272 & 256.866774727823 \tabularnewline
108 & 140460 & 141190.387463145 & -730.387463144783 \tabularnewline
109 & 148404 & 141234.181757389 & 7169.81824261107 \tabularnewline
110 & 135156 & 131057.556185133 & 4098.4438148669 \tabularnewline
111 & 122760 & 120504.106782352 & 2255.89321764831 \tabularnewline
112 & 129852 & 126938.432913225 & 2913.56708677516 \tabularnewline
113 & 133356 & 132097.040553563 & 1258.95944643734 \tabularnewline
114 & 126348 & 128027.422728607 & -1679.42272860717 \tabularnewline
115 & 99852 & 104472.410688663 & -4620.41068866319 \tabularnewline
116 & 88308 & 93892.3880059626 & -5584.38800596258 \tabularnewline
117 & 98904 & 104772.672288151 & -5868.67228815114 \tabularnewline
118 & 69756 & 77604.6920494359 & -7848.69204943591 \tabularnewline
119 & 101556 & 101460.043343675 & 95.9566563251283 \tabularnewline
120 & 121056 & 111315.670783106 & 9740.32921689443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307246&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]226116[/C][C]226106.166666667[/C][C]9.83333333331393[/C][/ROW]
[ROW][C]14[/C][C]226116[/C][C]225609.909706249[/C][C]506.090293750633[/C][/ROW]
[ROW][C]15[/C][C]224412[/C][C]223588.042583025[/C][C]823.957416975056[/C][/ROW]
[ROW][C]16[/C][C]219960[/C][C]219114.569260188[/C][C]845.430739812087[/C][/ROW]
[ROW][C]17[/C][C]242952[/C][C]242337.410166962[/C][C]614.589833037695[/C][/ROW]
[ROW][C]18[/C][C]246456[/C][C]245884.254417989[/C][C]571.745582010713[/C][/ROW]
[ROW][C]19[/C][C]241164[/C][C]232654.184655765[/C][C]8509.81534423455[/C][/ROW]
[ROW][C]20[/C][C]228768[/C][C]228174.809281841[/C][C]593.190718158759[/C][/ROW]
[ROW][C]21[/C][C]234072[/C][C]230161.498963442[/C][C]3910.50103655792[/C][/ROW]
[ROW][C]22[/C][C]226116[/C][C]232889.106737054[/C][C]-6773.10673705439[/C][/ROW]
[ROW][C]23[/C][C]229704[/C][C]231947.05485823[/C][C]-2243.0548582295[/C][/ROW]
[ROW][C]24[/C][C]231420[/C][C]233132.566207194[/C][C]-1712.56620719365[/C][/ROW]
[ROW][C]25[/C][C]233208[/C][C]234925.666908229[/C][C]-1717.66690822944[/C][/ROW]
[ROW][C]26[/C][C]228768[/C][C]234127.033922314[/C][C]-5359.03392231374[/C][/ROW]
[ROW][C]27[/C][C]229704[/C][C]229866.165138832[/C][C]-162.165138831508[/C][/ROW]
[ROW][C]28[/C][C]223464[/C][C]224929.317071126[/C][C]-1465.31707112599[/C][/ROW]
[ROW][C]29[/C][C]242952[/C][C]246941.383288701[/C][C]-3989.3832887013[/C][/ROW]
[ROW][C]30[/C][C]249108[/C][C]248339.297914568[/C][C]768.702085431636[/C][/ROW]
[ROW][C]31[/C][C]243816[/C][C]239657.379036012[/C][C]4158.62096398763[/C][/ROW]
[ROW][C]32[/C][C]234072[/C][C]228340.693624304[/C][C]5731.30637569632[/C][/ROW]
[ROW][C]33[/C][C]244668[/C][C]234151.211534302[/C][C]10516.7884656976[/C][/ROW]
[ROW][C]34[/C][C]233208[/C][C]233144.788024209[/C][C]63.2119757909095[/C][/ROW]
[ROW][C]35[/C][C]243816[/C][C]237787.642763718[/C][C]6028.35723628182[/C][/ROW]
[ROW][C]36[/C][C]242952[/C][C]242977.716035779[/C][C]-25.7160357786925[/C][/ROW]
[ROW][C]37[/C][C]245604[/C][C]245831.996036439[/C][C]-227.996036438708[/C][/ROW]
[ROW][C]38[/C][C]235860[/C][C]243891.24458187[/C][C]-8031.24458187039[/C][/ROW]
[ROW][C]39[/C][C]246456[/C][C]241987.101420751[/C][C]4468.89857924907[/C][/ROW]
[ROW][C]40[/C][C]245604[/C][C]238623.141452282[/C][C]6980.85854771765[/C][/ROW]
[ROW][C]41[/C][C]261504[/C][C]263249.38847531[/C][C]-1745.38847531023[/C][/ROW]
[ROW][C]42[/C][C]257916[/C][C]269136.541904585[/C][C]-11220.5419045846[/C][/ROW]
[ROW][C]43[/C][C]243816[/C][C]258047.379015118[/C][C]-14231.3790151181[/C][/ROW]
[ROW][C]44[/C][C]236712[/C][C]240167.371978457[/C][C]-3455.37197845665[/C][/ROW]
[ROW][C]45[/C][C]246456[/C][C]244815.327257031[/C][C]1640.67274296854[/C][/ROW]
[ROW][C]46[/C][C]233208[/C][C]233478.079633745[/C][C]-270.079633745423[/C][/ROW]
[ROW][C]47[/C][C]242952[/C][C]241007.675591874[/C][C]1944.32440812589[/C][/ROW]
[ROW][C]48[/C][C]244668[/C][C]240310.033101573[/C][C]4357.96689842676[/C][/ROW]
[ROW][C]49[/C][C]248256[/C][C]244303.380968126[/C][C]3952.61903187446[/C][/ROW]
[ROW][C]50[/C][C]240312[/C][C]239008.74984464[/C][C]1303.25015536018[/C][/ROW]
[ROW][C]51[/C][C]244668[/C][C]248157.490856134[/C][C]-3489.49085613387[/C][/ROW]
[ROW][C]52[/C][C]247320[/C][C]242689.190275904[/C][C]4630.80972409551[/C][/ROW]
[ROW][C]53[/C][C]257064[/C][C]260740.060112588[/C][C]-3676.0601125884[/C][/ROW]
[ROW][C]54[/C][C]249108[/C][C]259725.99354444[/C][C]-10617.9935444398[/C][/ROW]
[ROW][C]55[/C][C]238512[/C][C]246622.242766559[/C][C]-8110.24276655939[/C][/ROW]
[ROW][C]56[/C][C]227052[/C][C]237323.095486361[/C][C]-10271.0954863609[/C][/ROW]
[ROW][C]57[/C][C]237660[/C][C]241752.167070487[/C][C]-4092.16707048731[/C][/ROW]
[ROW][C]58[/C][C]208500[/C][C]226318.405782708[/C][C]-17818.4057827078[/C][/ROW]
[ROW][C]59[/C][C]222612[/C][C]226956.283051875[/C][C]-4344.28305187469[/C][/ROW]
[ROW][C]60[/C][C]230556[/C][C]223884.985476058[/C][C]6671.01452394226[/C][/ROW]
[ROW][C]61[/C][C]238512[/C][C]227375.458701665[/C][C]11136.5412983348[/C][/ROW]
[ROW][C]62[/C][C]227052[/C][C]222405.782966844[/C][C]4646.21703315625[/C][/ROW]
[ROW][C]63[/C][C]227052[/C][C]229135.430842981[/C][C]-2083.43084298106[/C][/ROW]
[ROW][C]64[/C][C]227052[/C][C]228178.52808148[/C][C]-1126.52808148036[/C][/ROW]
[ROW][C]65[/C][C]233208[/C][C]237918.06166053[/C][C]-4710.0616605299[/C][/ROW]
[ROW][C]66[/C][C]224412[/C][C]231291.857342953[/C][C]-6879.85734295275[/C][/ROW]
[ROW][C]67[/C][C]212868[/C][C]220227.404088525[/C][C]-7359.40408852493[/C][/ROW]
[ROW][C]68[/C][C]203208[/C][C]209000.09279035[/C][C]-5792.09279034959[/C][/ROW]
[ROW][C]69[/C][C]210216[/C][C]218088.632099954[/C][C]-7872.63209995435[/C][/ROW]
[ROW][C]70[/C][C]182856[/C][C]192030.805373375[/C][C]-9174.80537337466[/C][/ROW]
[ROW][C]71[/C][C]199620[/C][C]203481.562641779[/C][C]-3861.56264177855[/C][/ROW]
[ROW][C]72[/C][C]209364[/C][C]206465.656249657[/C][C]2898.34375034337[/C][/ROW]
[ROW][C]73[/C][C]211152[/C][C]210293.095624508[/C][C]858.904375492217[/C][/ROW]
[ROW][C]74[/C][C]201408[/C][C]196239.883644866[/C][C]5168.11635513382[/C][/ROW]
[ROW][C]75[/C][C]202260[/C][C]198134.845257809[/C][C]4125.15474219091[/C][/ROW]
[ROW][C]76[/C][C]199620[/C][C]199381.546177059[/C][C]238.453822940763[/C][/ROW]
[ROW][C]77[/C][C]208500[/C][C]206697.058091971[/C][C]1802.94190802932[/C][/ROW]
[ROW][C]78[/C][C]202260[/C][C]200744.567442418[/C][C]1515.43255758201[/C][/ROW]
[ROW][C]79[/C][C]189960[/C][C]192341.476033823[/C][C]-2381.4760338229[/C][/ROW]
[ROW][C]80[/C][C]181068[/C][C]183737.6868354[/C][C]-2669.68683540015[/C][/ROW]
[ROW][C]81[/C][C]196104[/C][C]192610.064328734[/C][C]3493.93567126628[/C][/ROW]
[ROW][C]82[/C][C]163452[/C][C]170437.914613097[/C][C]-6985.91461309709[/C][/ROW]
[ROW][C]83[/C][C]184656[/C][C]186045.390231609[/C][C]-1389.39023160926[/C][/ROW]
[ROW][C]84[/C][C]194316[/C][C]194225.95070215[/C][C]90.0492978497932[/C][/ROW]
[ROW][C]85[/C][C]194316[/C][C]195803.420055279[/C][C]-1487.4200552793[/C][/ROW]
[ROW][C]86[/C][C]182856[/C][C]183401.401960183[/C][C]-545.401960183372[/C][/ROW]
[ROW][C]87[/C][C]172260[/C][C]182250.55843422[/C][C]-9990.55843422038[/C][/ROW]
[ROW][C]88[/C][C]171408[/C][C]174985.471971773[/C][C]-3577.47197177343[/C][/ROW]
[ROW][C]89[/C][C]181068[/C][C]181105.934747662[/C][C]-37.934747661755[/C][/ROW]
[ROW][C]90[/C][C]172260[/C][C]173609.520455684[/C][C]-1349.52045568422[/C][/ROW]
[ROW][C]91[/C][C]155508[/C][C]161026.122880253[/C][C]-5518.12288025318[/C][/ROW]
[ROW][C]92[/C][C]143964[/C][C]150195.804405577[/C][C]-6231.80440557704[/C][/ROW]
[ROW][C]93[/C][C]156360[/C][C]160412.660414589[/C][C]-4052.66041458934[/C][/ROW]
[ROW][C]94[/C][C]127212[/C][C]127875.388448004[/C][C]-663.388448004349[/C][/ROW]
[ROW][C]95[/C][C]153708[/C][C]148464.772333326[/C][C]5243.22766667383[/C][/ROW]
[ROW][C]96[/C][C]167808[/C][C]159478.141128708[/C][C]8329.85887129224[/C][/ROW]
[ROW][C]97[/C][C]172260[/C][C]162937.562466782[/C][C]9322.43753321774[/C][/ROW]
[ROW][C]98[/C][C]162516[/C][C]155240.183502161[/C][C]7275.81649783856[/C][/ROW]
[ROW][C]99[/C][C]150204[/C][C]151610.29389982[/C][C]-1406.29389982048[/C][/ROW]
[ROW][C]100[/C][C]159012[/C][C]151830.172277786[/C][C]7181.82772221425[/C][/ROW]
[ROW][C]101[/C][C]162516[/C][C]164889.84212022[/C][C]-2373.84212021981[/C][/ROW]
[ROW][C]102[/C][C]159864[/C][C]156078.740217947[/C][C]3785.25978205292[/C][/ROW]
[ROW][C]103[/C][C]133356[/C][C]143644.188583184[/C][C]-10288.1885831841[/C][/ROW]
[ROW][C]104[/C][C]121056[/C][C]130877.599573465[/C][C]-9821.59957346509[/C][/ROW]
[ROW][C]105[/C][C]129852[/C][C]141262.956093744[/C][C]-11410.9560937443[/C][/ROW]
[ROW][C]106[/C][C]103356[/C][C]107893.822211168[/C][C]-4537.82221116844[/C][/ROW]
[ROW][C]107[/C][C]130716[/C][C]130459.133225272[/C][C]256.866774727823[/C][/ROW]
[ROW][C]108[/C][C]140460[/C][C]141190.387463145[/C][C]-730.387463144783[/C][/ROW]
[ROW][C]109[/C][C]148404[/C][C]141234.181757389[/C][C]7169.81824261107[/C][/ROW]
[ROW][C]110[/C][C]135156[/C][C]131057.556185133[/C][C]4098.4438148669[/C][/ROW]
[ROW][C]111[/C][C]122760[/C][C]120504.106782352[/C][C]2255.89321764831[/C][/ROW]
[ROW][C]112[/C][C]129852[/C][C]126938.432913225[/C][C]2913.56708677516[/C][/ROW]
[ROW][C]113[/C][C]133356[/C][C]132097.040553563[/C][C]1258.95944643734[/C][/ROW]
[ROW][C]114[/C][C]126348[/C][C]128027.422728607[/C][C]-1679.42272860717[/C][/ROW]
[ROW][C]115[/C][C]99852[/C][C]104472.410688663[/C][C]-4620.41068866319[/C][/ROW]
[ROW][C]116[/C][C]88308[/C][C]93892.3880059626[/C][C]-5584.38800596258[/C][/ROW]
[ROW][C]117[/C][C]98904[/C][C]104772.672288151[/C][C]-5868.67228815114[/C][/ROW]
[ROW][C]118[/C][C]69756[/C][C]77604.6920494359[/C][C]-7848.69204943591[/C][/ROW]
[ROW][C]119[/C][C]101556[/C][C]101460.043343675[/C][C]95.9566563251283[/C][/ROW]
[ROW][C]120[/C][C]121056[/C][C]111315.670783106[/C][C]9740.32921689443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307246&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307246&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
13226116226106.1666666679.83333333331393
14226116225609.909706249506.090293750633
15224412223588.042583025823.957416975056
16219960219114.569260188845.430739812087
17242952242337.410166962614.589833037695
18246456245884.254417989571.745582010713
19241164232654.1846557658509.81534423455
20228768228174.809281841593.190718158759
21234072230161.4989634423910.50103655792
22226116232889.106737054-6773.10673705439
23229704231947.05485823-2243.0548582295
24231420233132.566207194-1712.56620719365
25233208234925.666908229-1717.66690822944
26228768234127.033922314-5359.03392231374
27229704229866.165138832-162.165138831508
28223464224929.317071126-1465.31707112599
29242952246941.383288701-3989.3832887013
30249108248339.297914568768.702085431636
31243816239657.3790360124158.62096398763
32234072228340.6936243045731.30637569632
33244668234151.21153430210516.7884656976
34233208233144.78802420963.2119757909095
35243816237787.6427637186028.35723628182
36242952242977.716035779-25.7160357786925
37245604245831.996036439-227.996036438708
38235860243891.24458187-8031.24458187039
39246456241987.1014207514468.89857924907
40245604238623.1414522826980.85854771765
41261504263249.38847531-1745.38847531023
42257916269136.541904585-11220.5419045846
43243816258047.379015118-14231.3790151181
44236712240167.371978457-3455.37197845665
45246456244815.3272570311640.67274296854
46233208233478.079633745-270.079633745423
47242952241007.6755918741944.32440812589
48244668240310.0331015734357.96689842676
49248256244303.3809681263952.61903187446
50240312239008.749844641303.25015536018
51244668248157.490856134-3489.49085613387
52247320242689.1902759044630.80972409551
53257064260740.060112588-3676.0601125884
54249108259725.99354444-10617.9935444398
55238512246622.242766559-8110.24276655939
56227052237323.095486361-10271.0954863609
57237660241752.167070487-4092.16707048731
58208500226318.405782708-17818.4057827078
59222612226956.283051875-4344.28305187469
60230556223884.9854760586671.01452394226
61238512227375.45870166511136.5412983348
62227052222405.7829668444646.21703315625
63227052229135.430842981-2083.43084298106
64227052228178.52808148-1126.52808148036
65233208237918.06166053-4710.0616605299
66224412231291.857342953-6879.85734295275
67212868220227.404088525-7359.40408852493
68203208209000.09279035-5792.09279034959
69210216218088.632099954-7872.63209995435
70182856192030.805373375-9174.80537337466
71199620203481.562641779-3861.56264177855
72209364206465.6562496572898.34375034337
73211152210293.095624508858.904375492217
74201408196239.8836448665168.11635513382
75202260198134.8452578094125.15474219091
76199620199381.546177059238.453822940763
77208500206697.0580919711802.94190802932
78202260200744.5674424181515.43255758201
79189960192341.476033823-2381.4760338229
80181068183737.6868354-2669.68683540015
81196104192610.0643287343493.93567126628
82163452170437.914613097-6985.91461309709
83184656186045.390231609-1389.39023160926
84194316194225.9507021590.0492978497932
85194316195803.420055279-1487.4200552793
86182856183401.401960183-545.401960183372
87172260182250.55843422-9990.55843422038
88171408174985.471971773-3577.47197177343
89181068181105.934747662-37.934747661755
90172260173609.520455684-1349.52045568422
91155508161026.122880253-5518.12288025318
92143964150195.804405577-6231.80440557704
93156360160412.660414589-4052.66041458934
94127212127875.388448004-663.388448004349
95153708148464.7723333265243.22766667383
96167808159478.1411287088329.85887129224
97172260162937.5624667829322.43753321774
98162516155240.1835021617275.81649783856
99150204151610.29389982-1406.29389982048
100159012151830.1722777867181.82772221425
101162516164889.84212022-2373.84212021981
102159864156078.7402179473785.25978205292
103133356143644.188583184-10288.1885831841
104121056130877.599573465-9821.59957346509
105129852141262.956093744-11410.9560937443
106103356107893.822211168-4537.82221116844
107130716130459.133225272256.866774727823
108140460141190.387463145-730.387463144783
109148404141234.1817573897169.81824261107
110135156131057.5561851334098.4438148669
111122760120504.1067823522255.89321764831
112129852126938.4329132252913.56708677516
113133356132097.0405535631258.95944643734
114126348128027.422728607-1679.42272860717
11599852104472.410688663-4620.41068866319
1168830893892.3880059626-5584.38800596258
11798904104772.672288151-5868.67228815114
1186975677604.6920494359-7848.69204943591
119101556101460.04334367595.9566563251283
120121056111315.6707831069740.32921689443







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121120352.11997815109396.46214315131307.777813151
122105305.84599751793373.7895779552117237.902417079
12391751.252256908478808.5894055101104693.915108307
12497359.077658806483373.1462271768111345.009090436
12599973.389484488784912.8640975041115033.914871473
12693233.82896468877068.5529693076109399.104960068
12768242.298518601350943.147302681985541.4497345207
12858714.345047233240253.113646217577175.5764482488
12971587.670198718351936.97988730291238.3605101345
13045673.063241646424806.283112267766539.843371025
13177691.411826291755582.592315699800.2313369835
13293497.971971417270121.7880048823116874.155937952

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 120352.11997815 & 109396.46214315 & 131307.777813151 \tabularnewline
122 & 105305.845997517 & 93373.7895779552 & 117237.902417079 \tabularnewline
123 & 91751.2522569084 & 78808.5894055101 & 104693.915108307 \tabularnewline
124 & 97359.0776588064 & 83373.1462271768 & 111345.009090436 \tabularnewline
125 & 99973.3894844887 & 84912.8640975041 & 115033.914871473 \tabularnewline
126 & 93233.828964688 & 77068.5529693076 & 109399.104960068 \tabularnewline
127 & 68242.2985186013 & 50943.1473026819 & 85541.4497345207 \tabularnewline
128 & 58714.3450472332 & 40253.1136462175 & 77175.5764482488 \tabularnewline
129 & 71587.6701987183 & 51936.979887302 & 91238.3605101345 \tabularnewline
130 & 45673.0632416464 & 24806.2831122677 & 66539.843371025 \tabularnewline
131 & 77691.4118262917 & 55582.5923156 & 99800.2313369835 \tabularnewline
132 & 93497.9719714172 & 70121.7880048823 & 116874.155937952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307246&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]120352.11997815[/C][C]109396.46214315[/C][C]131307.777813151[/C][/ROW]
[ROW][C]122[/C][C]105305.845997517[/C][C]93373.7895779552[/C][C]117237.902417079[/C][/ROW]
[ROW][C]123[/C][C]91751.2522569084[/C][C]78808.5894055101[/C][C]104693.915108307[/C][/ROW]
[ROW][C]124[/C][C]97359.0776588064[/C][C]83373.1462271768[/C][C]111345.009090436[/C][/ROW]
[ROW][C]125[/C][C]99973.3894844887[/C][C]84912.8640975041[/C][C]115033.914871473[/C][/ROW]
[ROW][C]126[/C][C]93233.828964688[/C][C]77068.5529693076[/C][C]109399.104960068[/C][/ROW]
[ROW][C]127[/C][C]68242.2985186013[/C][C]50943.1473026819[/C][C]85541.4497345207[/C][/ROW]
[ROW][C]128[/C][C]58714.3450472332[/C][C]40253.1136462175[/C][C]77175.5764482488[/C][/ROW]
[ROW][C]129[/C][C]71587.6701987183[/C][C]51936.979887302[/C][C]91238.3605101345[/C][/ROW]
[ROW][C]130[/C][C]45673.0632416464[/C][C]24806.2831122677[/C][C]66539.843371025[/C][/ROW]
[ROW][C]131[/C][C]77691.4118262917[/C][C]55582.5923156[/C][C]99800.2313369835[/C][/ROW]
[ROW][C]132[/C][C]93497.9719714172[/C][C]70121.7880048823[/C][C]116874.155937952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307246&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307246&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
121120352.11997815109396.46214315131307.777813151
122105305.84599751793373.7895779552117237.902417079
12391751.252256908478808.5894055101104693.915108307
12497359.077658806483373.1462271768111345.009090436
12599973.389484488784912.8640975041115033.914871473
12693233.82896468877068.5529693076109399.104960068
12768242.298518601350943.147302681985541.4497345207
12858714.345047233240253.113646217577175.5764482488
12971587.670198718351936.97988730291238.3605101345
13045673.063241646424806.283112267766539.843371025
13177691.411826291755582.592315699800.2313369835
13293497.971971417270121.7880048823116874.155937952



Parameters (Session):
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')