Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 08 Jul 2011 10:03:39 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jul/08/t13101339582btnm5badzjfful.htm/, Retrieved Thu, 16 May 2024 18:35:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123016, Retrieved Thu, 16 May 2024 18:35:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsLynn Pelgrims
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2011-07-08 14:03:39] [cedc01334dbefab590f7f4b747b64ab1] [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 time4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123016&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123016&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123016&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.140747053603334
beta0.189738233395024
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.140747053603334 \tabularnewline
beta & 0.189738233395024 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123016&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]0.140747053603334[/C][/ROW]
[ROW][C]beta[/C][C]0.189738233395024[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123016&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123016&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
alpha0.140747053603334
beta0.189738233395024
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
354540
45253-1
57251.832547849090420.1674521509096
67154.182925992820116.8170740071799
75656.510849882131-0.510849882131026
84656.3862772431474-10.3862772431474
94754.594400755599-7.59440075559902
104752.9926634465366-5.99266344653656
114851.4563312839078-3.4563312839078
125050.184678736869-0.18467873686901
134449.3685697826013-5.36856978260129
143847.6794752590063-9.67947525900628
153345.1251421625796-12.1251421625796
163341.9027855540759-8.90278555407592
175238.896216389360113.1037836106399
185439.336944810898214.6630551891018
193940.3887144285042-1.38871442850416
202239.1441590133688-17.1441590133688
213135.2242347600172-4.22423476001719
223133.0099431777924-2.00994317779241
233831.05363088344146.94636911655856
244230.543396618854511.4566033811455
254130.973914246161610.0260857538384
263131.4708383279547-0.47083832795472
273630.4777774899745.52222251002601
283430.47569379648163.5243062035184
295130.286526209604220.7134737903958
304733.069838647596713.9301613524033
313135.2704261606787-4.27042616067865
321934.7952924612846-15.7952924612846
333032.2762529647486-2.27625296474859
343331.59919088797991.40080911202013
353631.47707320807694.52292679192312
364031.91516959271058.08483040728952
373233.0704995991572-1.07049959915717
382532.9086560864685-7.9086560864685
392831.5731607657614-3.57316076576141
402930.7524520314144-1.75245203141435
415530.14120328487324.858796715127
425533.939265977306621.0607340226934
434037.76519148779652.23480851220347
443839.0011042301084-1.00110423010837
454439.75483720234364.2451627976564
464141.3603342867453-0.360334286745335
474942.30799846394856.69200153605154
485944.426968681425314.5730313185747
496148.04434483956212.955655160438
504751.7800621005985-4.78006210059846
514352.8918773900758-9.8918773900758
523953.0200561907513-14.0200561907513
536652.192799023670813.8072009763292
546855.65086895831912.349131041681
556359.23350459183363.76649540816644
566861.70874417415866.29125582584138
576764.70734494533342.29265505466662
585967.2043800157538-8.2043800157538
596868.0048895617835-0.00488956178350008
607869.9593226540358.04067734596501
618273.26087265405278.73912734594728
627076.8941066798025-6.89410667980246
636278.1429012884127-16.1429012884127
646877.6588575567664-9.65885755676643
659477.829483144863916.1705168551361
6610282.067352303962719.9326476960373
6710087.367033590482512.6329664095175
6810491.97667084091412.023329159086
6910396.8215876197196.17841238028103
7093101.008844687164-8.00884468716397
71110102.9854101469727.01458985302835
72114107.2638050579036.7361949420975
73120111.6829074467848.31709255321572
74102116.546625282418-14.5466252824182
7595117.803873154624-22.8038731546241
76103117.289958066391-14.289958066391
77122117.592736720794.40726327920954
78139120.64479058487818.3552094151219
79135126.1501544249218.84984557507914
80135130.5540022982784.44599770172229
81137134.456752360192.54324763980986
82130138.15961363284-8.15961363283984
83148140.1381754401927.86182455980753
84148144.5816582575223.41834174247751
85145148.491021109435-3.49102110943517
86128151.334683439239-23.3346834392391
87131150.762253771568-19.7622537715683
88133150.164880143867-17.1648801438667
89146149.474689406879-3.47468940687898
90163150.6185607606712.3814392393298
91151154.324783042649-3.32478304264853
92157155.7316121605231.26838783947676
93152157.818788967429-5.81878896742901
94149158.753075194817-9.7530751948172
95172158.87316540555613.1268345944445
96167162.564088901014.43591109898981
97160165.150251958928-5.15025195892807
98150166.249652831368-16.249652831368
99160165.352897174195-5.35289717419519
100165165.846878129698-0.846878129697728
101171166.9524520263344.04754797366633
102179168.85499213858610.1450078614142
103171171.886655186615-0.886655186614746
104176173.3419659512532.6580340487468
105170175.367164339623-5.36716433962334
106169176.1195090543-7.1195090542999
107194176.43508923142117.5649107685795
108196180.6940014197715.3059985802303
109188185.0437265547142.95627344528552
110174187.734211834125-13.7342118341249
111186187.708787023794-1.7087870237936
112191189.3302720000991.6697279999012
113197191.4718632602565.52813673974407
114206194.304143611711.6958563882996
115197198.31685131406-1.31685131405999
116204200.4628921054313.53710789456878
117201203.386572164235-2.38657216423485
118190205.412778066399-15.4127780663988
119213205.193984130187.80601586982004
120213208.4516274420854.54837255791546

\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 & 51.8325478490904 & 20.1674521509096 \tabularnewline
6 & 71 & 54.1829259928201 & 16.8170740071799 \tabularnewline
7 & 56 & 56.510849882131 & -0.510849882131026 \tabularnewline
8 & 46 & 56.3862772431474 & -10.3862772431474 \tabularnewline
9 & 47 & 54.594400755599 & -7.59440075559902 \tabularnewline
10 & 47 & 52.9926634465366 & -5.99266344653656 \tabularnewline
11 & 48 & 51.4563312839078 & -3.4563312839078 \tabularnewline
12 & 50 & 50.184678736869 & -0.18467873686901 \tabularnewline
13 & 44 & 49.3685697826013 & -5.36856978260129 \tabularnewline
14 & 38 & 47.6794752590063 & -9.67947525900628 \tabularnewline
15 & 33 & 45.1251421625796 & -12.1251421625796 \tabularnewline
16 & 33 & 41.9027855540759 & -8.90278555407592 \tabularnewline
17 & 52 & 38.8962163893601 & 13.1037836106399 \tabularnewline
18 & 54 & 39.3369448108982 & 14.6630551891018 \tabularnewline
19 & 39 & 40.3887144285042 & -1.38871442850416 \tabularnewline
20 & 22 & 39.1441590133688 & -17.1441590133688 \tabularnewline
21 & 31 & 35.2242347600172 & -4.22423476001719 \tabularnewline
22 & 31 & 33.0099431777924 & -2.00994317779241 \tabularnewline
23 & 38 & 31.0536308834414 & 6.94636911655856 \tabularnewline
24 & 42 & 30.5433966188545 & 11.4566033811455 \tabularnewline
25 & 41 & 30.9739142461616 & 10.0260857538384 \tabularnewline
26 & 31 & 31.4708383279547 & -0.47083832795472 \tabularnewline
27 & 36 & 30.477777489974 & 5.52222251002601 \tabularnewline
28 & 34 & 30.4756937964816 & 3.5243062035184 \tabularnewline
29 & 51 & 30.2865262096042 & 20.7134737903958 \tabularnewline
30 & 47 & 33.0698386475967 & 13.9301613524033 \tabularnewline
31 & 31 & 35.2704261606787 & -4.27042616067865 \tabularnewline
32 & 19 & 34.7952924612846 & -15.7952924612846 \tabularnewline
33 & 30 & 32.2762529647486 & -2.27625296474859 \tabularnewline
34 & 33 & 31.5991908879799 & 1.40080911202013 \tabularnewline
35 & 36 & 31.4770732080769 & 4.52292679192312 \tabularnewline
36 & 40 & 31.9151695927105 & 8.08483040728952 \tabularnewline
37 & 32 & 33.0704995991572 & -1.07049959915717 \tabularnewline
38 & 25 & 32.9086560864685 & -7.9086560864685 \tabularnewline
39 & 28 & 31.5731607657614 & -3.57316076576141 \tabularnewline
40 & 29 & 30.7524520314144 & -1.75245203141435 \tabularnewline
41 & 55 & 30.141203284873 & 24.858796715127 \tabularnewline
42 & 55 & 33.9392659773066 & 21.0607340226934 \tabularnewline
43 & 40 & 37.7651914877965 & 2.23480851220347 \tabularnewline
44 & 38 & 39.0011042301084 & -1.00110423010837 \tabularnewline
45 & 44 & 39.7548372023436 & 4.2451627976564 \tabularnewline
46 & 41 & 41.3603342867453 & -0.360334286745335 \tabularnewline
47 & 49 & 42.3079984639485 & 6.69200153605154 \tabularnewline
48 & 59 & 44.4269686814253 & 14.5730313185747 \tabularnewline
49 & 61 & 48.044344839562 & 12.955655160438 \tabularnewline
50 & 47 & 51.7800621005985 & -4.78006210059846 \tabularnewline
51 & 43 & 52.8918773900758 & -9.8918773900758 \tabularnewline
52 & 39 & 53.0200561907513 & -14.0200561907513 \tabularnewline
53 & 66 & 52.1927990236708 & 13.8072009763292 \tabularnewline
54 & 68 & 55.650868958319 & 12.349131041681 \tabularnewline
55 & 63 & 59.2335045918336 & 3.76649540816644 \tabularnewline
56 & 68 & 61.7087441741586 & 6.29125582584138 \tabularnewline
57 & 67 & 64.7073449453334 & 2.29265505466662 \tabularnewline
58 & 59 & 67.2043800157538 & -8.2043800157538 \tabularnewline
59 & 68 & 68.0048895617835 & -0.00488956178350008 \tabularnewline
60 & 78 & 69.959322654035 & 8.04067734596501 \tabularnewline
61 & 82 & 73.2608726540527 & 8.73912734594728 \tabularnewline
62 & 70 & 76.8941066798025 & -6.89410667980246 \tabularnewline
63 & 62 & 78.1429012884127 & -16.1429012884127 \tabularnewline
64 & 68 & 77.6588575567664 & -9.65885755676643 \tabularnewline
65 & 94 & 77.8294831448639 & 16.1705168551361 \tabularnewline
66 & 102 & 82.0673523039627 & 19.9326476960373 \tabularnewline
67 & 100 & 87.3670335904825 & 12.6329664095175 \tabularnewline
68 & 104 & 91.976670840914 & 12.023329159086 \tabularnewline
69 & 103 & 96.821587619719 & 6.17841238028103 \tabularnewline
70 & 93 & 101.008844687164 & -8.00884468716397 \tabularnewline
71 & 110 & 102.985410146972 & 7.01458985302835 \tabularnewline
72 & 114 & 107.263805057903 & 6.7361949420975 \tabularnewline
73 & 120 & 111.682907446784 & 8.31709255321572 \tabularnewline
74 & 102 & 116.546625282418 & -14.5466252824182 \tabularnewline
75 & 95 & 117.803873154624 & -22.8038731546241 \tabularnewline
76 & 103 & 117.289958066391 & -14.289958066391 \tabularnewline
77 & 122 & 117.59273672079 & 4.40726327920954 \tabularnewline
78 & 139 & 120.644790584878 & 18.3552094151219 \tabularnewline
79 & 135 & 126.150154424921 & 8.84984557507914 \tabularnewline
80 & 135 & 130.554002298278 & 4.44599770172229 \tabularnewline
81 & 137 & 134.45675236019 & 2.54324763980986 \tabularnewline
82 & 130 & 138.15961363284 & -8.15961363283984 \tabularnewline
83 & 148 & 140.138175440192 & 7.86182455980753 \tabularnewline
84 & 148 & 144.581658257522 & 3.41834174247751 \tabularnewline
85 & 145 & 148.491021109435 & -3.49102110943517 \tabularnewline
86 & 128 & 151.334683439239 & -23.3346834392391 \tabularnewline
87 & 131 & 150.762253771568 & -19.7622537715683 \tabularnewline
88 & 133 & 150.164880143867 & -17.1648801438667 \tabularnewline
89 & 146 & 149.474689406879 & -3.47468940687898 \tabularnewline
90 & 163 & 150.61856076067 & 12.3814392393298 \tabularnewline
91 & 151 & 154.324783042649 & -3.32478304264853 \tabularnewline
92 & 157 & 155.731612160523 & 1.26838783947676 \tabularnewline
93 & 152 & 157.818788967429 & -5.81878896742901 \tabularnewline
94 & 149 & 158.753075194817 & -9.7530751948172 \tabularnewline
95 & 172 & 158.873165405556 & 13.1268345944445 \tabularnewline
96 & 167 & 162.56408890101 & 4.43591109898981 \tabularnewline
97 & 160 & 165.150251958928 & -5.15025195892807 \tabularnewline
98 & 150 & 166.249652831368 & -16.249652831368 \tabularnewline
99 & 160 & 165.352897174195 & -5.35289717419519 \tabularnewline
100 & 165 & 165.846878129698 & -0.846878129697728 \tabularnewline
101 & 171 & 166.952452026334 & 4.04754797366633 \tabularnewline
102 & 179 & 168.854992138586 & 10.1450078614142 \tabularnewline
103 & 171 & 171.886655186615 & -0.886655186614746 \tabularnewline
104 & 176 & 173.341965951253 & 2.6580340487468 \tabularnewline
105 & 170 & 175.367164339623 & -5.36716433962334 \tabularnewline
106 & 169 & 176.1195090543 & -7.1195090542999 \tabularnewline
107 & 194 & 176.435089231421 & 17.5649107685795 \tabularnewline
108 & 196 & 180.69400141977 & 15.3059985802303 \tabularnewline
109 & 188 & 185.043726554714 & 2.95627344528552 \tabularnewline
110 & 174 & 187.734211834125 & -13.7342118341249 \tabularnewline
111 & 186 & 187.708787023794 & -1.7087870237936 \tabularnewline
112 & 191 & 189.330272000099 & 1.6697279999012 \tabularnewline
113 & 197 & 191.471863260256 & 5.52813673974407 \tabularnewline
114 & 206 & 194.3041436117 & 11.6958563882996 \tabularnewline
115 & 197 & 198.31685131406 & -1.31685131405999 \tabularnewline
116 & 204 & 200.462892105431 & 3.53710789456878 \tabularnewline
117 & 201 & 203.386572164235 & -2.38657216423485 \tabularnewline
118 & 190 & 205.412778066399 & -15.4127780663988 \tabularnewline
119 & 213 & 205.19398413018 & 7.80601586982004 \tabularnewline
120 & 213 & 208.451627442085 & 4.54837255791546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123016&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]51.8325478490904[/C][C]20.1674521509096[/C][/ROW]
[ROW][C]6[/C][C]71[/C][C]54.1829259928201[/C][C]16.8170740071799[/C][/ROW]
[ROW][C]7[/C][C]56[/C][C]56.510849882131[/C][C]-0.510849882131026[/C][/ROW]
[ROW][C]8[/C][C]46[/C][C]56.3862772431474[/C][C]-10.3862772431474[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]54.594400755599[/C][C]-7.59440075559902[/C][/ROW]
[ROW][C]10[/C][C]47[/C][C]52.9926634465366[/C][C]-5.99266344653656[/C][/ROW]
[ROW][C]11[/C][C]48[/C][C]51.4563312839078[/C][C]-3.4563312839078[/C][/ROW]
[ROW][C]12[/C][C]50[/C][C]50.184678736869[/C][C]-0.18467873686901[/C][/ROW]
[ROW][C]13[/C][C]44[/C][C]49.3685697826013[/C][C]-5.36856978260129[/C][/ROW]
[ROW][C]14[/C][C]38[/C][C]47.6794752590063[/C][C]-9.67947525900628[/C][/ROW]
[ROW][C]15[/C][C]33[/C][C]45.1251421625796[/C][C]-12.1251421625796[/C][/ROW]
[ROW][C]16[/C][C]33[/C][C]41.9027855540759[/C][C]-8.90278555407592[/C][/ROW]
[ROW][C]17[/C][C]52[/C][C]38.8962163893601[/C][C]13.1037836106399[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]39.3369448108982[/C][C]14.6630551891018[/C][/ROW]
[ROW][C]19[/C][C]39[/C][C]40.3887144285042[/C][C]-1.38871442850416[/C][/ROW]
[ROW][C]20[/C][C]22[/C][C]39.1441590133688[/C][C]-17.1441590133688[/C][/ROW]
[ROW][C]21[/C][C]31[/C][C]35.2242347600172[/C][C]-4.22423476001719[/C][/ROW]
[ROW][C]22[/C][C]31[/C][C]33.0099431777924[/C][C]-2.00994317779241[/C][/ROW]
[ROW][C]23[/C][C]38[/C][C]31.0536308834414[/C][C]6.94636911655856[/C][/ROW]
[ROW][C]24[/C][C]42[/C][C]30.5433966188545[/C][C]11.4566033811455[/C][/ROW]
[ROW][C]25[/C][C]41[/C][C]30.9739142461616[/C][C]10.0260857538384[/C][/ROW]
[ROW][C]26[/C][C]31[/C][C]31.4708383279547[/C][C]-0.47083832795472[/C][/ROW]
[ROW][C]27[/C][C]36[/C][C]30.477777489974[/C][C]5.52222251002601[/C][/ROW]
[ROW][C]28[/C][C]34[/C][C]30.4756937964816[/C][C]3.5243062035184[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]30.2865262096042[/C][C]20.7134737903958[/C][/ROW]
[ROW][C]30[/C][C]47[/C][C]33.0698386475967[/C][C]13.9301613524033[/C][/ROW]
[ROW][C]31[/C][C]31[/C][C]35.2704261606787[/C][C]-4.27042616067865[/C][/ROW]
[ROW][C]32[/C][C]19[/C][C]34.7952924612846[/C][C]-15.7952924612846[/C][/ROW]
[ROW][C]33[/C][C]30[/C][C]32.2762529647486[/C][C]-2.27625296474859[/C][/ROW]
[ROW][C]34[/C][C]33[/C][C]31.5991908879799[/C][C]1.40080911202013[/C][/ROW]
[ROW][C]35[/C][C]36[/C][C]31.4770732080769[/C][C]4.52292679192312[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]31.9151695927105[/C][C]8.08483040728952[/C][/ROW]
[ROW][C]37[/C][C]32[/C][C]33.0704995991572[/C][C]-1.07049959915717[/C][/ROW]
[ROW][C]38[/C][C]25[/C][C]32.9086560864685[/C][C]-7.9086560864685[/C][/ROW]
[ROW][C]39[/C][C]28[/C][C]31.5731607657614[/C][C]-3.57316076576141[/C][/ROW]
[ROW][C]40[/C][C]29[/C][C]30.7524520314144[/C][C]-1.75245203141435[/C][/ROW]
[ROW][C]41[/C][C]55[/C][C]30.141203284873[/C][C]24.858796715127[/C][/ROW]
[ROW][C]42[/C][C]55[/C][C]33.9392659773066[/C][C]21.0607340226934[/C][/ROW]
[ROW][C]43[/C][C]40[/C][C]37.7651914877965[/C][C]2.23480851220347[/C][/ROW]
[ROW][C]44[/C][C]38[/C][C]39.0011042301084[/C][C]-1.00110423010837[/C][/ROW]
[ROW][C]45[/C][C]44[/C][C]39.7548372023436[/C][C]4.2451627976564[/C][/ROW]
[ROW][C]46[/C][C]41[/C][C]41.3603342867453[/C][C]-0.360334286745335[/C][/ROW]
[ROW][C]47[/C][C]49[/C][C]42.3079984639485[/C][C]6.69200153605154[/C][/ROW]
[ROW][C]48[/C][C]59[/C][C]44.4269686814253[/C][C]14.5730313185747[/C][/ROW]
[ROW][C]49[/C][C]61[/C][C]48.044344839562[/C][C]12.955655160438[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]51.7800621005985[/C][C]-4.78006210059846[/C][/ROW]
[ROW][C]51[/C][C]43[/C][C]52.8918773900758[/C][C]-9.8918773900758[/C][/ROW]
[ROW][C]52[/C][C]39[/C][C]53.0200561907513[/C][C]-14.0200561907513[/C][/ROW]
[ROW][C]53[/C][C]66[/C][C]52.1927990236708[/C][C]13.8072009763292[/C][/ROW]
[ROW][C]54[/C][C]68[/C][C]55.650868958319[/C][C]12.349131041681[/C][/ROW]
[ROW][C]55[/C][C]63[/C][C]59.2335045918336[/C][C]3.76649540816644[/C][/ROW]
[ROW][C]56[/C][C]68[/C][C]61.7087441741586[/C][C]6.29125582584138[/C][/ROW]
[ROW][C]57[/C][C]67[/C][C]64.7073449453334[/C][C]2.29265505466662[/C][/ROW]
[ROW][C]58[/C][C]59[/C][C]67.2043800157538[/C][C]-8.2043800157538[/C][/ROW]
[ROW][C]59[/C][C]68[/C][C]68.0048895617835[/C][C]-0.00488956178350008[/C][/ROW]
[ROW][C]60[/C][C]78[/C][C]69.959322654035[/C][C]8.04067734596501[/C][/ROW]
[ROW][C]61[/C][C]82[/C][C]73.2608726540527[/C][C]8.73912734594728[/C][/ROW]
[ROW][C]62[/C][C]70[/C][C]76.8941066798025[/C][C]-6.89410667980246[/C][/ROW]
[ROW][C]63[/C][C]62[/C][C]78.1429012884127[/C][C]-16.1429012884127[/C][/ROW]
[ROW][C]64[/C][C]68[/C][C]77.6588575567664[/C][C]-9.65885755676643[/C][/ROW]
[ROW][C]65[/C][C]94[/C][C]77.8294831448639[/C][C]16.1705168551361[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]82.0673523039627[/C][C]19.9326476960373[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]87.3670335904825[/C][C]12.6329664095175[/C][/ROW]
[ROW][C]68[/C][C]104[/C][C]91.976670840914[/C][C]12.023329159086[/C][/ROW]
[ROW][C]69[/C][C]103[/C][C]96.821587619719[/C][C]6.17841238028103[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]101.008844687164[/C][C]-8.00884468716397[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]102.985410146972[/C][C]7.01458985302835[/C][/ROW]
[ROW][C]72[/C][C]114[/C][C]107.263805057903[/C][C]6.7361949420975[/C][/ROW]
[ROW][C]73[/C][C]120[/C][C]111.682907446784[/C][C]8.31709255321572[/C][/ROW]
[ROW][C]74[/C][C]102[/C][C]116.546625282418[/C][C]-14.5466252824182[/C][/ROW]
[ROW][C]75[/C][C]95[/C][C]117.803873154624[/C][C]-22.8038731546241[/C][/ROW]
[ROW][C]76[/C][C]103[/C][C]117.289958066391[/C][C]-14.289958066391[/C][/ROW]
[ROW][C]77[/C][C]122[/C][C]117.59273672079[/C][C]4.40726327920954[/C][/ROW]
[ROW][C]78[/C][C]139[/C][C]120.644790584878[/C][C]18.3552094151219[/C][/ROW]
[ROW][C]79[/C][C]135[/C][C]126.150154424921[/C][C]8.84984557507914[/C][/ROW]
[ROW][C]80[/C][C]135[/C][C]130.554002298278[/C][C]4.44599770172229[/C][/ROW]
[ROW][C]81[/C][C]137[/C][C]134.45675236019[/C][C]2.54324763980986[/C][/ROW]
[ROW][C]82[/C][C]130[/C][C]138.15961363284[/C][C]-8.15961363283984[/C][/ROW]
[ROW][C]83[/C][C]148[/C][C]140.138175440192[/C][C]7.86182455980753[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]144.581658257522[/C][C]3.41834174247751[/C][/ROW]
[ROW][C]85[/C][C]145[/C][C]148.491021109435[/C][C]-3.49102110943517[/C][/ROW]
[ROW][C]86[/C][C]128[/C][C]151.334683439239[/C][C]-23.3346834392391[/C][/ROW]
[ROW][C]87[/C][C]131[/C][C]150.762253771568[/C][C]-19.7622537715683[/C][/ROW]
[ROW][C]88[/C][C]133[/C][C]150.164880143867[/C][C]-17.1648801438667[/C][/ROW]
[ROW][C]89[/C][C]146[/C][C]149.474689406879[/C][C]-3.47468940687898[/C][/ROW]
[ROW][C]90[/C][C]163[/C][C]150.61856076067[/C][C]12.3814392393298[/C][/ROW]
[ROW][C]91[/C][C]151[/C][C]154.324783042649[/C][C]-3.32478304264853[/C][/ROW]
[ROW][C]92[/C][C]157[/C][C]155.731612160523[/C][C]1.26838783947676[/C][/ROW]
[ROW][C]93[/C][C]152[/C][C]157.818788967429[/C][C]-5.81878896742901[/C][/ROW]
[ROW][C]94[/C][C]149[/C][C]158.753075194817[/C][C]-9.7530751948172[/C][/ROW]
[ROW][C]95[/C][C]172[/C][C]158.873165405556[/C][C]13.1268345944445[/C][/ROW]
[ROW][C]96[/C][C]167[/C][C]162.56408890101[/C][C]4.43591109898981[/C][/ROW]
[ROW][C]97[/C][C]160[/C][C]165.150251958928[/C][C]-5.15025195892807[/C][/ROW]
[ROW][C]98[/C][C]150[/C][C]166.249652831368[/C][C]-16.249652831368[/C][/ROW]
[ROW][C]99[/C][C]160[/C][C]165.352897174195[/C][C]-5.35289717419519[/C][/ROW]
[ROW][C]100[/C][C]165[/C][C]165.846878129698[/C][C]-0.846878129697728[/C][/ROW]
[ROW][C]101[/C][C]171[/C][C]166.952452026334[/C][C]4.04754797366633[/C][/ROW]
[ROW][C]102[/C][C]179[/C][C]168.854992138586[/C][C]10.1450078614142[/C][/ROW]
[ROW][C]103[/C][C]171[/C][C]171.886655186615[/C][C]-0.886655186614746[/C][/ROW]
[ROW][C]104[/C][C]176[/C][C]173.341965951253[/C][C]2.6580340487468[/C][/ROW]
[ROW][C]105[/C][C]170[/C][C]175.367164339623[/C][C]-5.36716433962334[/C][/ROW]
[ROW][C]106[/C][C]169[/C][C]176.1195090543[/C][C]-7.1195090542999[/C][/ROW]
[ROW][C]107[/C][C]194[/C][C]176.435089231421[/C][C]17.5649107685795[/C][/ROW]
[ROW][C]108[/C][C]196[/C][C]180.69400141977[/C][C]15.3059985802303[/C][/ROW]
[ROW][C]109[/C][C]188[/C][C]185.043726554714[/C][C]2.95627344528552[/C][/ROW]
[ROW][C]110[/C][C]174[/C][C]187.734211834125[/C][C]-13.7342118341249[/C][/ROW]
[ROW][C]111[/C][C]186[/C][C]187.708787023794[/C][C]-1.7087870237936[/C][/ROW]
[ROW][C]112[/C][C]191[/C][C]189.330272000099[/C][C]1.6697279999012[/C][/ROW]
[ROW][C]113[/C][C]197[/C][C]191.471863260256[/C][C]5.52813673974407[/C][/ROW]
[ROW][C]114[/C][C]206[/C][C]194.3041436117[/C][C]11.6958563882996[/C][/ROW]
[ROW][C]115[/C][C]197[/C][C]198.31685131406[/C][C]-1.31685131405999[/C][/ROW]
[ROW][C]116[/C][C]204[/C][C]200.462892105431[/C][C]3.53710789456878[/C][/ROW]
[ROW][C]117[/C][C]201[/C][C]203.386572164235[/C][C]-2.38657216423485[/C][/ROW]
[ROW][C]118[/C][C]190[/C][C]205.412778066399[/C][C]-15.4127780663988[/C][/ROW]
[ROW][C]119[/C][C]213[/C][C]205.19398413018[/C][C]7.80601586982004[/C][/ROW]
[ROW][C]120[/C][C]213[/C][C]208.451627442085[/C][C]4.54837255791546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123016&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123016&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
57251.832547849090420.1674521509096
67154.182925992820116.8170740071799
75656.510849882131-0.510849882131026
84656.3862772431474-10.3862772431474
94754.594400755599-7.59440075559902
104752.9926634465366-5.99266344653656
114851.4563312839078-3.4563312839078
125050.184678736869-0.18467873686901
134449.3685697826013-5.36856978260129
143847.6794752590063-9.67947525900628
153345.1251421625796-12.1251421625796
163341.9027855540759-8.90278555407592
175238.896216389360113.1037836106399
185439.336944810898214.6630551891018
193940.3887144285042-1.38871442850416
202239.1441590133688-17.1441590133688
213135.2242347600172-4.22423476001719
223133.0099431777924-2.00994317779241
233831.05363088344146.94636911655856
244230.543396618854511.4566033811455
254130.973914246161610.0260857538384
263131.4708383279547-0.47083832795472
273630.4777774899745.52222251002601
283430.47569379648163.5243062035184
295130.286526209604220.7134737903958
304733.069838647596713.9301613524033
313135.2704261606787-4.27042616067865
321934.7952924612846-15.7952924612846
333032.2762529647486-2.27625296474859
343331.59919088797991.40080911202013
353631.47707320807694.52292679192312
364031.91516959271058.08483040728952
373233.0704995991572-1.07049959915717
382532.9086560864685-7.9086560864685
392831.5731607657614-3.57316076576141
402930.7524520314144-1.75245203141435
415530.14120328487324.858796715127
425533.939265977306621.0607340226934
434037.76519148779652.23480851220347
443839.0011042301084-1.00110423010837
454439.75483720234364.2451627976564
464141.3603342867453-0.360334286745335
474942.30799846394856.69200153605154
485944.426968681425314.5730313185747
496148.04434483956212.955655160438
504751.7800621005985-4.78006210059846
514352.8918773900758-9.8918773900758
523953.0200561907513-14.0200561907513
536652.192799023670813.8072009763292
546855.65086895831912.349131041681
556359.23350459183363.76649540816644
566861.70874417415866.29125582584138
576764.70734494533342.29265505466662
585967.2043800157538-8.2043800157538
596868.0048895617835-0.00488956178350008
607869.9593226540358.04067734596501
618273.26087265405278.73912734594728
627076.8941066798025-6.89410667980246
636278.1429012884127-16.1429012884127
646877.6588575567664-9.65885755676643
659477.829483144863916.1705168551361
6610282.067352303962719.9326476960373
6710087.367033590482512.6329664095175
6810491.97667084091412.023329159086
6910396.8215876197196.17841238028103
7093101.008844687164-8.00884468716397
71110102.9854101469727.01458985302835
72114107.2638050579036.7361949420975
73120111.6829074467848.31709255321572
74102116.546625282418-14.5466252824182
7595117.803873154624-22.8038731546241
76103117.289958066391-14.289958066391
77122117.592736720794.40726327920954
78139120.64479058487818.3552094151219
79135126.1501544249218.84984557507914
80135130.5540022982784.44599770172229
81137134.456752360192.54324763980986
82130138.15961363284-8.15961363283984
83148140.1381754401927.86182455980753
84148144.5816582575223.41834174247751
85145148.491021109435-3.49102110943517
86128151.334683439239-23.3346834392391
87131150.762253771568-19.7622537715683
88133150.164880143867-17.1648801438667
89146149.474689406879-3.47468940687898
90163150.6185607606712.3814392393298
91151154.324783042649-3.32478304264853
92157155.7316121605231.26838783947676
93152157.818788967429-5.81878896742901
94149158.753075194817-9.7530751948172
95172158.87316540555613.1268345944445
96167162.564088901014.43591109898981
97160165.150251958928-5.15025195892807
98150166.249652831368-16.249652831368
99160165.352897174195-5.35289717419519
100165165.846878129698-0.846878129697728
101171166.9524520263344.04754797366633
102179168.85499213858610.1450078614142
103171171.886655186615-0.886655186614746
104176173.3419659512532.6580340487468
105170175.367164339623-5.36716433962334
106169176.1195090543-7.1195090542999
107194176.43508923142117.5649107685795
108196180.6940014197715.3059985802303
109188185.0437265547142.95627344528552
110174187.734211834125-13.7342118341249
111186187.708787023794-1.7087870237936
112191189.3302720000991.6697279999012
113197191.4718632602565.52813673974407
114206194.304143611711.6958563882996
115197198.31685131406-1.31685131405999
116204200.4628921054313.53710789456878
117201203.386572164235-2.38657216423485
118190205.412778066399-15.4127780663988
119213205.193984130187.80601586982004
120213208.4516274420854.54837255791546







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121211.372231787892191.242391792563231.502071783221
122213.652666097483193.242554638078234.062777556888
123215.933100407074195.152150394228236.714050419919
124218.213534716665196.962320144967239.464749288362
125220.493969026255198.666249874341242.32168817817
126222.774403335846200.259265032349245.289541639343
127225.054837645437201.738781574432248.370893716441
128227.335271955028203.104127974638251.566415935418
129229.615706264618204.356272025432254.875140503805
130231.896140574209205.497495329727258.294785818691
131234.1765748838206.531057016327261.822092751273
132236.457009193391207.460879418614265.453138968167

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 211.372231787892 & 191.242391792563 & 231.502071783221 \tabularnewline
122 & 213.652666097483 & 193.242554638078 & 234.062777556888 \tabularnewline
123 & 215.933100407074 & 195.152150394228 & 236.714050419919 \tabularnewline
124 & 218.213534716665 & 196.962320144967 & 239.464749288362 \tabularnewline
125 & 220.493969026255 & 198.666249874341 & 242.32168817817 \tabularnewline
126 & 222.774403335846 & 200.259265032349 & 245.289541639343 \tabularnewline
127 & 225.054837645437 & 201.738781574432 & 248.370893716441 \tabularnewline
128 & 227.335271955028 & 203.104127974638 & 251.566415935418 \tabularnewline
129 & 229.615706264618 & 204.356272025432 & 254.875140503805 \tabularnewline
130 & 231.896140574209 & 205.497495329727 & 258.294785818691 \tabularnewline
131 & 234.1765748838 & 206.531057016327 & 261.822092751273 \tabularnewline
132 & 236.457009193391 & 207.460879418614 & 265.453138968167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123016&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]211.372231787892[/C][C]191.242391792563[/C][C]231.502071783221[/C][/ROW]
[ROW][C]122[/C][C]213.652666097483[/C][C]193.242554638078[/C][C]234.062777556888[/C][/ROW]
[ROW][C]123[/C][C]215.933100407074[/C][C]195.152150394228[/C][C]236.714050419919[/C][/ROW]
[ROW][C]124[/C][C]218.213534716665[/C][C]196.962320144967[/C][C]239.464749288362[/C][/ROW]
[ROW][C]125[/C][C]220.493969026255[/C][C]198.666249874341[/C][C]242.32168817817[/C][/ROW]
[ROW][C]126[/C][C]222.774403335846[/C][C]200.259265032349[/C][C]245.289541639343[/C][/ROW]
[ROW][C]127[/C][C]225.054837645437[/C][C]201.738781574432[/C][C]248.370893716441[/C][/ROW]
[ROW][C]128[/C][C]227.335271955028[/C][C]203.104127974638[/C][C]251.566415935418[/C][/ROW]
[ROW][C]129[/C][C]229.615706264618[/C][C]204.356272025432[/C][C]254.875140503805[/C][/ROW]
[ROW][C]130[/C][C]231.896140574209[/C][C]205.497495329727[/C][C]258.294785818691[/C][/ROW]
[ROW][C]131[/C][C]234.1765748838[/C][C]206.531057016327[/C][C]261.822092751273[/C][/ROW]
[ROW][C]132[/C][C]236.457009193391[/C][C]207.460879418614[/C][C]265.453138968167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123016&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123016&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
121211.372231787892191.242391792563231.502071783221
122213.652666097483193.242554638078234.062777556888
123215.933100407074195.152150394228236.714050419919
124218.213534716665196.962320144967239.464749288362
125220.493969026255198.666249874341242.32168817817
126222.774403335846200.259265032349245.289541639343
127225.054837645437201.738781574432248.370893716441
128227.335271955028203.104127974638251.566415935418
129229.615706264618204.356272025432254.875140503805
130231.896140574209205.497495329727258.294785818691
131234.1765748838206.531057016327261.822092751273
132236.457009193391207.460879418614265.453138968167



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')