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 computationFri, 20 Dec 2013 10:56:18 -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/2013/Dec/20/t1387554993zcm62oe97efds68.htm/, Retrieved Thu, 18 Apr 2024 18:02:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232458, Retrieved Thu, 18 Apr 2024 18:02:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-20 15:56:18] [9e6a405f514733ea23d87e4507d39d29] [Current]
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Dataseries X:
56
55
54
52
72
71
56
46
47
47
48
50
44
38
33
33
52
54
39
22
31
31
38
42
41
31
36
34
51
47
31
19
30
33
36
40
32
25
28
29
55
55
40
38
44
41
49
59
61
47
43
39
66
68
63
68
67
59
68
78
82
70
62
68
94
102
100
104
103
93
110
114
120
102
95
103
122
139
135
135
137
130
148
148
145
128
131
133
146
163
151
157
152
149
172
167
160
150
160
165
171
179
171
176
170
169
194
196
188
174
186
191
197
206
197
204
201
190
213
213




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ yule.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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232458&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232458&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 time6 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.140747053607372
beta0.189738233389591
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.140747053607372 \tabularnewline
beta & 0.189738233389591 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232458&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]0.140747053607372[/C][/ROW]
[ROW][C]beta[/C][C]0.189738233389591[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232458&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
alpha0.140747053607372
beta0.189738233389591
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
354540
45253-1
57251.832547849086420.1674521509136
67154.182925992898216.8170740071018
75656.5108498822641-0.510849882264111
84656.3862772432542-10.3862772432542
94754.5944007556405-7.59440075564051
104752.9926634465321-5.99266344653208
114851.4563312838704-3.4563312838704
125050.1846787368146-0.184678736814554
134449.3685697825468-5.36856978254685
143847.6794752589324-9.67947525893236
153345.1251421624735-12.1251421624735
163341.9027855539351-8.9027855539351
175238.896216389206213.1037836107938
185439.336944810826114.6630551891739
193940.3887144285105-1.38871442851053
202239.1441590133776-17.1441590133776
213135.2242347599643-4.22423475996425
223133.00994317774-2.00994317773998
233831.05363088339986.94636911660021
244230.543396618859411.4566033811406
254130.973914246224610.0260857537754
263131.4708383280602-0.470838328060172
273630.47777749007075.52222250992926
283430.47569379659253.52430620340751
295130.286526209716220.7134737902838
304733.069838647776113.9301613522239
313135.2704261608838-4.27042616088384
321934.795292461433-15.795292461433
333032.2762529647976-2.27625296479758
343331.59919088799681.40080911200324
353631.47707320808064.5229267919194
364031.91516959271548.08483040728462
373233.0704995991774-1.07049959917735
382532.9086560864643-7.9086560864643
392831.5731607657088-3.57316076570877
402930.752452031339-1.75245203133898
415530.141203284787524.8587967152125
425533.939265977322121.0607340226779
434037.76519148788312.23480851211688
443839.0011042301777-1.00110423017773
454439.75483720238324.24516279761677
464141.3603342867795-0.360334286779548
474942.30799846395856.69200153604149
485944.426968681442814.5730313185572
496148.044344839617312.9556551603827
504751.7800621006782-4.78006210067823
514352.8918773901029-9.89187739010286
523953.0200561907116-14.0200561907116
536652.192799023558213.8072009764418
546855.650868958259212.3491310417408
556359.23350459181483.76649540818522
566861.7087441741416.29125582585905
576764.70734494532732.29265505467266
585967.2043800157418-8.20438001574176
596868.0048895617243-0.00488956172426924
607869.95932265396998.04067734603014
618273.26087265401688.73912734598322
627076.8941066797954-6.89410667979539
636278.1429012883675-16.1429012883675
646877.6588575566523-9.65885755665228
659477.829483144719716.1705168552803
6610282.067352303900919.9326476960991
6710087.367033590508412.6329664094916
6810491.976670840985112.0233291590149
6910396.82158761982456.17841238017553
7093101.008844687273-8.00884468727267
71110102.9854101470237.0145898529771
72114107.2638050579646.73619494203629
73120111.6829074468518.31709255314871
74102116.546625282495-14.5466252824948
7595117.803873154615-22.8038731546146
76103117.289958066274-14.2899580662743
77122117.5927367206194.40726327938083
78139120.6447905847418.35520941526
79135126.1501544248718.84984557512873
80135130.5540022982674.44599770173284
81137134.4567523601962.54324763980435
82130138.159613632851-8.15961363285132
83148140.1381754401667.86182455983445
84148144.5816582575283.41834174247202
85145148.49102110945-3.4910211094504
86128151.334683439234-23.3346834392345
87131150.762253771466-19.7622537714664
88133150.164880143698-17.1648801436985
89146149.474689406669-3.47468940666872
90163150.61856076048512.3814392395153
91151154.324783042553-3.32478304255329
92157155.7316121604451.26838783955529
93152157.818788967385-5.81878896738547
94149158.753075194776-9.75307519477622
95172158.87316540550213.126834594498
96167162.564088901044.43591109896033
97160165.150251958993-5.15025195899298
98150166.249652831423-16.2496528314229
99160165.352897174195-5.35289717419528
100165165.846878129695-0.84687812969463
101171166.9524520263464.04754797365388
102179168.85499213863110.1450078613689
103171171.886655186712-0.886655186711636
104176173.3419659513472.65803404865272
105170175.367164339727-5.36716433972686
106169176.119509054376-7.11950905437629
107194176.43508923146517.5649107685355
108196180.69400141988415.3059985801156
109188185.0437265548782.95627344512232
110174187.734211834276-13.7342118342757
111186187.708787023862-1.70878702386216
112191189.3302720001431.66972799985655
113197191.4718632602935.52813673970749
114206194.30414361174511.6958563882553
115197198.316851314135-1.3168513141346
116204200.4628921054773.53710789452265
117201203.386572164275-2.3865721642749
118190205.412778066409-15.4127780664086
119213205.1939841301117.80601586988908
120213208.4516274420434.54837255795661

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 54 & 54 & 0 \tabularnewline
4 & 52 & 53 & -1 \tabularnewline
5 & 72 & 51.8325478490864 & 20.1674521509136 \tabularnewline
6 & 71 & 54.1829259928982 & 16.8170740071018 \tabularnewline
7 & 56 & 56.5108498822641 & -0.510849882264111 \tabularnewline
8 & 46 & 56.3862772432542 & -10.3862772432542 \tabularnewline
9 & 47 & 54.5944007556405 & -7.59440075564051 \tabularnewline
10 & 47 & 52.9926634465321 & -5.99266344653208 \tabularnewline
11 & 48 & 51.4563312838704 & -3.4563312838704 \tabularnewline
12 & 50 & 50.1846787368146 & -0.184678736814554 \tabularnewline
13 & 44 & 49.3685697825468 & -5.36856978254685 \tabularnewline
14 & 38 & 47.6794752589324 & -9.67947525893236 \tabularnewline
15 & 33 & 45.1251421624735 & -12.1251421624735 \tabularnewline
16 & 33 & 41.9027855539351 & -8.9027855539351 \tabularnewline
17 & 52 & 38.8962163892062 & 13.1037836107938 \tabularnewline
18 & 54 & 39.3369448108261 & 14.6630551891739 \tabularnewline
19 & 39 & 40.3887144285105 & -1.38871442851053 \tabularnewline
20 & 22 & 39.1441590133776 & -17.1441590133776 \tabularnewline
21 & 31 & 35.2242347599643 & -4.22423475996425 \tabularnewline
22 & 31 & 33.00994317774 & -2.00994317773998 \tabularnewline
23 & 38 & 31.0536308833998 & 6.94636911660021 \tabularnewline
24 & 42 & 30.5433966188594 & 11.4566033811406 \tabularnewline
25 & 41 & 30.9739142462246 & 10.0260857537754 \tabularnewline
26 & 31 & 31.4708383280602 & -0.470838328060172 \tabularnewline
27 & 36 & 30.4777774900707 & 5.52222250992926 \tabularnewline
28 & 34 & 30.4756937965925 & 3.52430620340751 \tabularnewline
29 & 51 & 30.2865262097162 & 20.7134737902838 \tabularnewline
30 & 47 & 33.0698386477761 & 13.9301613522239 \tabularnewline
31 & 31 & 35.2704261608838 & -4.27042616088384 \tabularnewline
32 & 19 & 34.795292461433 & -15.795292461433 \tabularnewline
33 & 30 & 32.2762529647976 & -2.27625296479758 \tabularnewline
34 & 33 & 31.5991908879968 & 1.40080911200324 \tabularnewline
35 & 36 & 31.4770732080806 & 4.5229267919194 \tabularnewline
36 & 40 & 31.9151695927154 & 8.08483040728462 \tabularnewline
37 & 32 & 33.0704995991774 & -1.07049959917735 \tabularnewline
38 & 25 & 32.9086560864643 & -7.9086560864643 \tabularnewline
39 & 28 & 31.5731607657088 & -3.57316076570877 \tabularnewline
40 & 29 & 30.752452031339 & -1.75245203133898 \tabularnewline
41 & 55 & 30.1412032847875 & 24.8587967152125 \tabularnewline
42 & 55 & 33.9392659773221 & 21.0607340226779 \tabularnewline
43 & 40 & 37.7651914878831 & 2.23480851211688 \tabularnewline
44 & 38 & 39.0011042301777 & -1.00110423017773 \tabularnewline
45 & 44 & 39.7548372023832 & 4.24516279761677 \tabularnewline
46 & 41 & 41.3603342867795 & -0.360334286779548 \tabularnewline
47 & 49 & 42.3079984639585 & 6.69200153604149 \tabularnewline
48 & 59 & 44.4269686814428 & 14.5730313185572 \tabularnewline
49 & 61 & 48.0443448396173 & 12.9556551603827 \tabularnewline
50 & 47 & 51.7800621006782 & -4.78006210067823 \tabularnewline
51 & 43 & 52.8918773901029 & -9.89187739010286 \tabularnewline
52 & 39 & 53.0200561907116 & -14.0200561907116 \tabularnewline
53 & 66 & 52.1927990235582 & 13.8072009764418 \tabularnewline
54 & 68 & 55.6508689582592 & 12.3491310417408 \tabularnewline
55 & 63 & 59.2335045918148 & 3.76649540818522 \tabularnewline
56 & 68 & 61.708744174141 & 6.29125582585905 \tabularnewline
57 & 67 & 64.7073449453273 & 2.29265505467266 \tabularnewline
58 & 59 & 67.2043800157418 & -8.20438001574176 \tabularnewline
59 & 68 & 68.0048895617243 & -0.00488956172426924 \tabularnewline
60 & 78 & 69.9593226539699 & 8.04067734603014 \tabularnewline
61 & 82 & 73.2608726540168 & 8.73912734598322 \tabularnewline
62 & 70 & 76.8941066797954 & -6.89410667979539 \tabularnewline
63 & 62 & 78.1429012883675 & -16.1429012883675 \tabularnewline
64 & 68 & 77.6588575566523 & -9.65885755665228 \tabularnewline
65 & 94 & 77.8294831447197 & 16.1705168552803 \tabularnewline
66 & 102 & 82.0673523039009 & 19.9326476960991 \tabularnewline
67 & 100 & 87.3670335905084 & 12.6329664094916 \tabularnewline
68 & 104 & 91.9766708409851 & 12.0233291590149 \tabularnewline
69 & 103 & 96.8215876198245 & 6.17841238017553 \tabularnewline
70 & 93 & 101.008844687273 & -8.00884468727267 \tabularnewline
71 & 110 & 102.985410147023 & 7.0145898529771 \tabularnewline
72 & 114 & 107.263805057964 & 6.73619494203629 \tabularnewline
73 & 120 & 111.682907446851 & 8.31709255314871 \tabularnewline
74 & 102 & 116.546625282495 & -14.5466252824948 \tabularnewline
75 & 95 & 117.803873154615 & -22.8038731546146 \tabularnewline
76 & 103 & 117.289958066274 & -14.2899580662743 \tabularnewline
77 & 122 & 117.592736720619 & 4.40726327938083 \tabularnewline
78 & 139 & 120.64479058474 & 18.35520941526 \tabularnewline
79 & 135 & 126.150154424871 & 8.84984557512873 \tabularnewline
80 & 135 & 130.554002298267 & 4.44599770173284 \tabularnewline
81 & 137 & 134.456752360196 & 2.54324763980435 \tabularnewline
82 & 130 & 138.159613632851 & -8.15961363285132 \tabularnewline
83 & 148 & 140.138175440166 & 7.86182455983445 \tabularnewline
84 & 148 & 144.581658257528 & 3.41834174247202 \tabularnewline
85 & 145 & 148.49102110945 & -3.4910211094504 \tabularnewline
86 & 128 & 151.334683439234 & -23.3346834392345 \tabularnewline
87 & 131 & 150.762253771466 & -19.7622537714664 \tabularnewline
88 & 133 & 150.164880143698 & -17.1648801436985 \tabularnewline
89 & 146 & 149.474689406669 & -3.47468940666872 \tabularnewline
90 & 163 & 150.618560760485 & 12.3814392395153 \tabularnewline
91 & 151 & 154.324783042553 & -3.32478304255329 \tabularnewline
92 & 157 & 155.731612160445 & 1.26838783955529 \tabularnewline
93 & 152 & 157.818788967385 & -5.81878896738547 \tabularnewline
94 & 149 & 158.753075194776 & -9.75307519477622 \tabularnewline
95 & 172 & 158.873165405502 & 13.126834594498 \tabularnewline
96 & 167 & 162.56408890104 & 4.43591109896033 \tabularnewline
97 & 160 & 165.150251958993 & -5.15025195899298 \tabularnewline
98 & 150 & 166.249652831423 & -16.2496528314229 \tabularnewline
99 & 160 & 165.352897174195 & -5.35289717419528 \tabularnewline
100 & 165 & 165.846878129695 & -0.84687812969463 \tabularnewline
101 & 171 & 166.952452026346 & 4.04754797365388 \tabularnewline
102 & 179 & 168.854992138631 & 10.1450078613689 \tabularnewline
103 & 171 & 171.886655186712 & -0.886655186711636 \tabularnewline
104 & 176 & 173.341965951347 & 2.65803404865272 \tabularnewline
105 & 170 & 175.367164339727 & -5.36716433972686 \tabularnewline
106 & 169 & 176.119509054376 & -7.11950905437629 \tabularnewline
107 & 194 & 176.435089231465 & 17.5649107685355 \tabularnewline
108 & 196 & 180.694001419884 & 15.3059985801156 \tabularnewline
109 & 188 & 185.043726554878 & 2.95627344512232 \tabularnewline
110 & 174 & 187.734211834276 & -13.7342118342757 \tabularnewline
111 & 186 & 187.708787023862 & -1.70878702386216 \tabularnewline
112 & 191 & 189.330272000143 & 1.66972799985655 \tabularnewline
113 & 197 & 191.471863260293 & 5.52813673970749 \tabularnewline
114 & 206 & 194.304143611745 & 11.6958563882553 \tabularnewline
115 & 197 & 198.316851314135 & -1.3168513141346 \tabularnewline
116 & 204 & 200.462892105477 & 3.53710789452265 \tabularnewline
117 & 201 & 203.386572164275 & -2.3865721642749 \tabularnewline
118 & 190 & 205.412778066409 & -15.4127780664086 \tabularnewline
119 & 213 & 205.193984130111 & 7.80601586988908 \tabularnewline
120 & 213 & 208.451627442043 & 4.54837255795661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232458&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]54[/C][C]54[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]52[/C][C]53[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]72[/C][C]51.8325478490864[/C][C]20.1674521509136[/C][/ROW]
[ROW][C]6[/C][C]71[/C][C]54.1829259928982[/C][C]16.8170740071018[/C][/ROW]
[ROW][C]7[/C][C]56[/C][C]56.5108498822641[/C][C]-0.510849882264111[/C][/ROW]
[ROW][C]8[/C][C]46[/C][C]56.3862772432542[/C][C]-10.3862772432542[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]54.5944007556405[/C][C]-7.59440075564051[/C][/ROW]
[ROW][C]10[/C][C]47[/C][C]52.9926634465321[/C][C]-5.99266344653208[/C][/ROW]
[ROW][C]11[/C][C]48[/C][C]51.4563312838704[/C][C]-3.4563312838704[/C][/ROW]
[ROW][C]12[/C][C]50[/C][C]50.1846787368146[/C][C]-0.184678736814554[/C][/ROW]
[ROW][C]13[/C][C]44[/C][C]49.3685697825468[/C][C]-5.36856978254685[/C][/ROW]
[ROW][C]14[/C][C]38[/C][C]47.6794752589324[/C][C]-9.67947525893236[/C][/ROW]
[ROW][C]15[/C][C]33[/C][C]45.1251421624735[/C][C]-12.1251421624735[/C][/ROW]
[ROW][C]16[/C][C]33[/C][C]41.9027855539351[/C][C]-8.9027855539351[/C][/ROW]
[ROW][C]17[/C][C]52[/C][C]38.8962163892062[/C][C]13.1037836107938[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]39.3369448108261[/C][C]14.6630551891739[/C][/ROW]
[ROW][C]19[/C][C]39[/C][C]40.3887144285105[/C][C]-1.38871442851053[/C][/ROW]
[ROW][C]20[/C][C]22[/C][C]39.1441590133776[/C][C]-17.1441590133776[/C][/ROW]
[ROW][C]21[/C][C]31[/C][C]35.2242347599643[/C][C]-4.22423475996425[/C][/ROW]
[ROW][C]22[/C][C]31[/C][C]33.00994317774[/C][C]-2.00994317773998[/C][/ROW]
[ROW][C]23[/C][C]38[/C][C]31.0536308833998[/C][C]6.94636911660021[/C][/ROW]
[ROW][C]24[/C][C]42[/C][C]30.5433966188594[/C][C]11.4566033811406[/C][/ROW]
[ROW][C]25[/C][C]41[/C][C]30.9739142462246[/C][C]10.0260857537754[/C][/ROW]
[ROW][C]26[/C][C]31[/C][C]31.4708383280602[/C][C]-0.470838328060172[/C][/ROW]
[ROW][C]27[/C][C]36[/C][C]30.4777774900707[/C][C]5.52222250992926[/C][/ROW]
[ROW][C]28[/C][C]34[/C][C]30.4756937965925[/C][C]3.52430620340751[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]30.2865262097162[/C][C]20.7134737902838[/C][/ROW]
[ROW][C]30[/C][C]47[/C][C]33.0698386477761[/C][C]13.9301613522239[/C][/ROW]
[ROW][C]31[/C][C]31[/C][C]35.2704261608838[/C][C]-4.27042616088384[/C][/ROW]
[ROW][C]32[/C][C]19[/C][C]34.795292461433[/C][C]-15.795292461433[/C][/ROW]
[ROW][C]33[/C][C]30[/C][C]32.2762529647976[/C][C]-2.27625296479758[/C][/ROW]
[ROW][C]34[/C][C]33[/C][C]31.5991908879968[/C][C]1.40080911200324[/C][/ROW]
[ROW][C]35[/C][C]36[/C][C]31.4770732080806[/C][C]4.5229267919194[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]31.9151695927154[/C][C]8.08483040728462[/C][/ROW]
[ROW][C]37[/C][C]32[/C][C]33.0704995991774[/C][C]-1.07049959917735[/C][/ROW]
[ROW][C]38[/C][C]25[/C][C]32.9086560864643[/C][C]-7.9086560864643[/C][/ROW]
[ROW][C]39[/C][C]28[/C][C]31.5731607657088[/C][C]-3.57316076570877[/C][/ROW]
[ROW][C]40[/C][C]29[/C][C]30.752452031339[/C][C]-1.75245203133898[/C][/ROW]
[ROW][C]41[/C][C]55[/C][C]30.1412032847875[/C][C]24.8587967152125[/C][/ROW]
[ROW][C]42[/C][C]55[/C][C]33.9392659773221[/C][C]21.0607340226779[/C][/ROW]
[ROW][C]43[/C][C]40[/C][C]37.7651914878831[/C][C]2.23480851211688[/C][/ROW]
[ROW][C]44[/C][C]38[/C][C]39.0011042301777[/C][C]-1.00110423017773[/C][/ROW]
[ROW][C]45[/C][C]44[/C][C]39.7548372023832[/C][C]4.24516279761677[/C][/ROW]
[ROW][C]46[/C][C]41[/C][C]41.3603342867795[/C][C]-0.360334286779548[/C][/ROW]
[ROW][C]47[/C][C]49[/C][C]42.3079984639585[/C][C]6.69200153604149[/C][/ROW]
[ROW][C]48[/C][C]59[/C][C]44.4269686814428[/C][C]14.5730313185572[/C][/ROW]
[ROW][C]49[/C][C]61[/C][C]48.0443448396173[/C][C]12.9556551603827[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]51.7800621006782[/C][C]-4.78006210067823[/C][/ROW]
[ROW][C]51[/C][C]43[/C][C]52.8918773901029[/C][C]-9.89187739010286[/C][/ROW]
[ROW][C]52[/C][C]39[/C][C]53.0200561907116[/C][C]-14.0200561907116[/C][/ROW]
[ROW][C]53[/C][C]66[/C][C]52.1927990235582[/C][C]13.8072009764418[/C][/ROW]
[ROW][C]54[/C][C]68[/C][C]55.6508689582592[/C][C]12.3491310417408[/C][/ROW]
[ROW][C]55[/C][C]63[/C][C]59.2335045918148[/C][C]3.76649540818522[/C][/ROW]
[ROW][C]56[/C][C]68[/C][C]61.708744174141[/C][C]6.29125582585905[/C][/ROW]
[ROW][C]57[/C][C]67[/C][C]64.7073449453273[/C][C]2.29265505467266[/C][/ROW]
[ROW][C]58[/C][C]59[/C][C]67.2043800157418[/C][C]-8.20438001574176[/C][/ROW]
[ROW][C]59[/C][C]68[/C][C]68.0048895617243[/C][C]-0.00488956172426924[/C][/ROW]
[ROW][C]60[/C][C]78[/C][C]69.9593226539699[/C][C]8.04067734603014[/C][/ROW]
[ROW][C]61[/C][C]82[/C][C]73.2608726540168[/C][C]8.73912734598322[/C][/ROW]
[ROW][C]62[/C][C]70[/C][C]76.8941066797954[/C][C]-6.89410667979539[/C][/ROW]
[ROW][C]63[/C][C]62[/C][C]78.1429012883675[/C][C]-16.1429012883675[/C][/ROW]
[ROW][C]64[/C][C]68[/C][C]77.6588575566523[/C][C]-9.65885755665228[/C][/ROW]
[ROW][C]65[/C][C]94[/C][C]77.8294831447197[/C][C]16.1705168552803[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]82.0673523039009[/C][C]19.9326476960991[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]87.3670335905084[/C][C]12.6329664094916[/C][/ROW]
[ROW][C]68[/C][C]104[/C][C]91.9766708409851[/C][C]12.0233291590149[/C][/ROW]
[ROW][C]69[/C][C]103[/C][C]96.8215876198245[/C][C]6.17841238017553[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]101.008844687273[/C][C]-8.00884468727267[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]102.985410147023[/C][C]7.0145898529771[/C][/ROW]
[ROW][C]72[/C][C]114[/C][C]107.263805057964[/C][C]6.73619494203629[/C][/ROW]
[ROW][C]73[/C][C]120[/C][C]111.682907446851[/C][C]8.31709255314871[/C][/ROW]
[ROW][C]74[/C][C]102[/C][C]116.546625282495[/C][C]-14.5466252824948[/C][/ROW]
[ROW][C]75[/C][C]95[/C][C]117.803873154615[/C][C]-22.8038731546146[/C][/ROW]
[ROW][C]76[/C][C]103[/C][C]117.289958066274[/C][C]-14.2899580662743[/C][/ROW]
[ROW][C]77[/C][C]122[/C][C]117.592736720619[/C][C]4.40726327938083[/C][/ROW]
[ROW][C]78[/C][C]139[/C][C]120.64479058474[/C][C]18.35520941526[/C][/ROW]
[ROW][C]79[/C][C]135[/C][C]126.150154424871[/C][C]8.84984557512873[/C][/ROW]
[ROW][C]80[/C][C]135[/C][C]130.554002298267[/C][C]4.44599770173284[/C][/ROW]
[ROW][C]81[/C][C]137[/C][C]134.456752360196[/C][C]2.54324763980435[/C][/ROW]
[ROW][C]82[/C][C]130[/C][C]138.159613632851[/C][C]-8.15961363285132[/C][/ROW]
[ROW][C]83[/C][C]148[/C][C]140.138175440166[/C][C]7.86182455983445[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]144.581658257528[/C][C]3.41834174247202[/C][/ROW]
[ROW][C]85[/C][C]145[/C][C]148.49102110945[/C][C]-3.4910211094504[/C][/ROW]
[ROW][C]86[/C][C]128[/C][C]151.334683439234[/C][C]-23.3346834392345[/C][/ROW]
[ROW][C]87[/C][C]131[/C][C]150.762253771466[/C][C]-19.7622537714664[/C][/ROW]
[ROW][C]88[/C][C]133[/C][C]150.164880143698[/C][C]-17.1648801436985[/C][/ROW]
[ROW][C]89[/C][C]146[/C][C]149.474689406669[/C][C]-3.47468940666872[/C][/ROW]
[ROW][C]90[/C][C]163[/C][C]150.618560760485[/C][C]12.3814392395153[/C][/ROW]
[ROW][C]91[/C][C]151[/C][C]154.324783042553[/C][C]-3.32478304255329[/C][/ROW]
[ROW][C]92[/C][C]157[/C][C]155.731612160445[/C][C]1.26838783955529[/C][/ROW]
[ROW][C]93[/C][C]152[/C][C]157.818788967385[/C][C]-5.81878896738547[/C][/ROW]
[ROW][C]94[/C][C]149[/C][C]158.753075194776[/C][C]-9.75307519477622[/C][/ROW]
[ROW][C]95[/C][C]172[/C][C]158.873165405502[/C][C]13.126834594498[/C][/ROW]
[ROW][C]96[/C][C]167[/C][C]162.56408890104[/C][C]4.43591109896033[/C][/ROW]
[ROW][C]97[/C][C]160[/C][C]165.150251958993[/C][C]-5.15025195899298[/C][/ROW]
[ROW][C]98[/C][C]150[/C][C]166.249652831423[/C][C]-16.2496528314229[/C][/ROW]
[ROW][C]99[/C][C]160[/C][C]165.352897174195[/C][C]-5.35289717419528[/C][/ROW]
[ROW][C]100[/C][C]165[/C][C]165.846878129695[/C][C]-0.84687812969463[/C][/ROW]
[ROW][C]101[/C][C]171[/C][C]166.952452026346[/C][C]4.04754797365388[/C][/ROW]
[ROW][C]102[/C][C]179[/C][C]168.854992138631[/C][C]10.1450078613689[/C][/ROW]
[ROW][C]103[/C][C]171[/C][C]171.886655186712[/C][C]-0.886655186711636[/C][/ROW]
[ROW][C]104[/C][C]176[/C][C]173.341965951347[/C][C]2.65803404865272[/C][/ROW]
[ROW][C]105[/C][C]170[/C][C]175.367164339727[/C][C]-5.36716433972686[/C][/ROW]
[ROW][C]106[/C][C]169[/C][C]176.119509054376[/C][C]-7.11950905437629[/C][/ROW]
[ROW][C]107[/C][C]194[/C][C]176.435089231465[/C][C]17.5649107685355[/C][/ROW]
[ROW][C]108[/C][C]196[/C][C]180.694001419884[/C][C]15.3059985801156[/C][/ROW]
[ROW][C]109[/C][C]188[/C][C]185.043726554878[/C][C]2.95627344512232[/C][/ROW]
[ROW][C]110[/C][C]174[/C][C]187.734211834276[/C][C]-13.7342118342757[/C][/ROW]
[ROW][C]111[/C][C]186[/C][C]187.708787023862[/C][C]-1.70878702386216[/C][/ROW]
[ROW][C]112[/C][C]191[/C][C]189.330272000143[/C][C]1.66972799985655[/C][/ROW]
[ROW][C]113[/C][C]197[/C][C]191.471863260293[/C][C]5.52813673970749[/C][/ROW]
[ROW][C]114[/C][C]206[/C][C]194.304143611745[/C][C]11.6958563882553[/C][/ROW]
[ROW][C]115[/C][C]197[/C][C]198.316851314135[/C][C]-1.3168513141346[/C][/ROW]
[ROW][C]116[/C][C]204[/C][C]200.462892105477[/C][C]3.53710789452265[/C][/ROW]
[ROW][C]117[/C][C]201[/C][C]203.386572164275[/C][C]-2.3865721642749[/C][/ROW]
[ROW][C]118[/C][C]190[/C][C]205.412778066409[/C][C]-15.4127780664086[/C][/ROW]
[ROW][C]119[/C][C]213[/C][C]205.193984130111[/C][C]7.80601586988908[/C][/ROW]
[ROW][C]120[/C][C]213[/C][C]208.451627442043[/C][C]4.54837255795661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232458&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232458&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
354540
45253-1
57251.832547849086420.1674521509136
67154.182925992898216.8170740071018
75656.5108498822641-0.510849882264111
84656.3862772432542-10.3862772432542
94754.5944007556405-7.59440075564051
104752.9926634465321-5.99266344653208
114851.4563312838704-3.4563312838704
125050.1846787368146-0.184678736814554
134449.3685697825468-5.36856978254685
143847.6794752589324-9.67947525893236
153345.1251421624735-12.1251421624735
163341.9027855539351-8.9027855539351
175238.896216389206213.1037836107938
185439.336944810826114.6630551891739
193940.3887144285105-1.38871442851053
202239.1441590133776-17.1441590133776
213135.2242347599643-4.22423475996425
223133.00994317774-2.00994317773998
233831.05363088339986.94636911660021
244230.543396618859411.4566033811406
254130.973914246224610.0260857537754
263131.4708383280602-0.470838328060172
273630.47777749007075.52222250992926
283430.47569379659253.52430620340751
295130.286526209716220.7134737902838
304733.069838647776113.9301613522239
313135.2704261608838-4.27042616088384
321934.795292461433-15.795292461433
333032.2762529647976-2.27625296479758
343331.59919088799681.40080911200324
353631.47707320808064.5229267919194
364031.91516959271548.08483040728462
373233.0704995991774-1.07049959917735
382532.9086560864643-7.9086560864643
392831.5731607657088-3.57316076570877
402930.752452031339-1.75245203133898
415530.141203284787524.8587967152125
425533.939265977322121.0607340226779
434037.76519148788312.23480851211688
443839.0011042301777-1.00110423017773
454439.75483720238324.24516279761677
464141.3603342867795-0.360334286779548
474942.30799846395856.69200153604149
485944.426968681442814.5730313185572
496148.044344839617312.9556551603827
504751.7800621006782-4.78006210067823
514352.8918773901029-9.89187739010286
523953.0200561907116-14.0200561907116
536652.192799023558213.8072009764418
546855.650868958259212.3491310417408
556359.23350459181483.76649540818522
566861.7087441741416.29125582585905
576764.70734494532732.29265505467266
585967.2043800157418-8.20438001574176
596868.0048895617243-0.00488956172426924
607869.95932265396998.04067734603014
618273.26087265401688.73912734598322
627076.8941066797954-6.89410667979539
636278.1429012883675-16.1429012883675
646877.6588575566523-9.65885755665228
659477.829483144719716.1705168552803
6610282.067352303900919.9326476960991
6710087.367033590508412.6329664094916
6810491.976670840985112.0233291590149
6910396.82158761982456.17841238017553
7093101.008844687273-8.00884468727267
71110102.9854101470237.0145898529771
72114107.2638050579646.73619494203629
73120111.6829074468518.31709255314871
74102116.546625282495-14.5466252824948
7595117.803873154615-22.8038731546146
76103117.289958066274-14.2899580662743
77122117.5927367206194.40726327938083
78139120.6447905847418.35520941526
79135126.1501544248718.84984557512873
80135130.5540022982674.44599770173284
81137134.4567523601962.54324763980435
82130138.159613632851-8.15961363285132
83148140.1381754401667.86182455983445
84148144.5816582575283.41834174247202
85145148.49102110945-3.4910211094504
86128151.334683439234-23.3346834392345
87131150.762253771466-19.7622537714664
88133150.164880143698-17.1648801436985
89146149.474689406669-3.47468940666872
90163150.61856076048512.3814392395153
91151154.324783042553-3.32478304255329
92157155.7316121604451.26838783955529
93152157.818788967385-5.81878896738547
94149158.753075194776-9.75307519477622
95172158.87316540550213.126834594498
96167162.564088901044.43591109896033
97160165.150251958993-5.15025195899298
98150166.249652831423-16.2496528314229
99160165.352897174195-5.35289717419528
100165165.846878129695-0.84687812969463
101171166.9524520263464.04754797365388
102179168.85499213863110.1450078613689
103171171.886655186712-0.886655186711636
104176173.3419659513472.65803404865272
105170175.367164339727-5.36716433972686
106169176.119509054376-7.11950905437629
107194176.43508923146517.5649107685355
108196180.69400141988415.3059985801156
109188185.0437265548782.95627344512232
110174187.734211834276-13.7342118342757
111186187.708787023862-1.70878702386216
112191189.3302720001431.66972799985655
113197191.4718632602935.52813673970749
114206194.30414361174511.6958563882553
115197198.316851314135-1.3168513141346
116204200.4628921054773.53710789452265
117201203.386572164275-2.3865721642749
118190205.412778066409-15.4127780664086
119213205.1939841301117.80601586988908
120213208.4516274420434.54837255795661







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121211.372231787863191.242391792533231.502071783193
122213.652666097441193.242554638022234.062777556861
123215.93310040702195.152150394145236.714050419895
124218.213534716598196.962320144855239.464749288342
125220.493969026177198.666249874199242.321688178155
126222.774403335755200.259265032177245.289541639334
127225.054837645334201.73878157423248.370893716438
128227.335271954913203.104127974404251.566415935421
129229.615706264491204.356272025168254.875140503814
130231.89614057407205.497495329433258.294785818706
131234.176574883648206.531057016004261.822092751293
132236.457009193227207.460879418262265.453138968192

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 211.372231787863 & 191.242391792533 & 231.502071783193 \tabularnewline
122 & 213.652666097441 & 193.242554638022 & 234.062777556861 \tabularnewline
123 & 215.93310040702 & 195.152150394145 & 236.714050419895 \tabularnewline
124 & 218.213534716598 & 196.962320144855 & 239.464749288342 \tabularnewline
125 & 220.493969026177 & 198.666249874199 & 242.321688178155 \tabularnewline
126 & 222.774403335755 & 200.259265032177 & 245.289541639334 \tabularnewline
127 & 225.054837645334 & 201.73878157423 & 248.370893716438 \tabularnewline
128 & 227.335271954913 & 203.104127974404 & 251.566415935421 \tabularnewline
129 & 229.615706264491 & 204.356272025168 & 254.875140503814 \tabularnewline
130 & 231.89614057407 & 205.497495329433 & 258.294785818706 \tabularnewline
131 & 234.176574883648 & 206.531057016004 & 261.822092751293 \tabularnewline
132 & 236.457009193227 & 207.460879418262 & 265.453138968192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232458&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]211.372231787863[/C][C]191.242391792533[/C][C]231.502071783193[/C][/ROW]
[ROW][C]122[/C][C]213.652666097441[/C][C]193.242554638022[/C][C]234.062777556861[/C][/ROW]
[ROW][C]123[/C][C]215.93310040702[/C][C]195.152150394145[/C][C]236.714050419895[/C][/ROW]
[ROW][C]124[/C][C]218.213534716598[/C][C]196.962320144855[/C][C]239.464749288342[/C][/ROW]
[ROW][C]125[/C][C]220.493969026177[/C][C]198.666249874199[/C][C]242.321688178155[/C][/ROW]
[ROW][C]126[/C][C]222.774403335755[/C][C]200.259265032177[/C][C]245.289541639334[/C][/ROW]
[ROW][C]127[/C][C]225.054837645334[/C][C]201.73878157423[/C][C]248.370893716438[/C][/ROW]
[ROW][C]128[/C][C]227.335271954913[/C][C]203.104127974404[/C][C]251.566415935421[/C][/ROW]
[ROW][C]129[/C][C]229.615706264491[/C][C]204.356272025168[/C][C]254.875140503814[/C][/ROW]
[ROW][C]130[/C][C]231.89614057407[/C][C]205.497495329433[/C][C]258.294785818706[/C][/ROW]
[ROW][C]131[/C][C]234.176574883648[/C][C]206.531057016004[/C][C]261.822092751293[/C][/ROW]
[ROW][C]132[/C][C]236.457009193227[/C][C]207.460879418262[/C][C]265.453138968192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232458&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232458&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
121211.372231787863191.242391792533231.502071783193
122213.652666097441193.242554638022234.062777556861
123215.93310040702195.152150394145236.714050419895
124218.213534716598196.962320144855239.464749288342
125220.493969026177198.666249874199242.321688178155
126222.774403335755200.259265032177245.289541639334
127225.054837645334201.73878157423248.370893716438
128227.335271954913203.104127974404251.566415935421
129229.615706264491204.356272025168254.875140503814
130231.89614057407205.497495329433258.294785818706
131234.176574883648206.531057016004261.822092751293
132236.457009193227207.460879418262265.453138968192



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