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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 05:13:58 +0000
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/May/20/t1305868185r4a318h7dmcukkb.htm/, Retrieved Sun, 12 May 2024 12:48:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122407, Retrieved Sun, 12 May 2024 12:48:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-20 05:13:58] [e142b37b6acbb6a3ec873415888faca6] [Current]
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Dataseries X:
116
111
104
100
93
91
119
139
134
124
113
109
109
106
101
98
93
91
122
139
140
132
117
114
113
110
107
103
98
98
137
148
147
139
130
128
127
123
118
114
108
111
151
159
158
148
138
137
136
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122407&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122407&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.704179612610166
beta0.524677975873149
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.704179612610166 \tabularnewline
beta & 0.524677975873149 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122407&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]0.704179612610166[/C][/ROW]
[ROW][C]beta[/C][C]0.524677975873149[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122407&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
alpha0.704179612610166
beta0.524677975873149
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13109109.640224358974-0.640224358974436
14106105.9197782073310.0802217926689366
15101100.6112948955520.388705104447524
169897.33031982573940.669680174260606
179392.57796008748950.422039912510485
189190.93214717129220.0678528287077569
19122120.2703256822481.7296743177517
20139143.084450176702-4.08445017670226
21140135.1286483366214.87135166337885
22132130.1541458522211.84585414777933
23117122.606132879058-5.60613287905841
24114114.655965145873-0.655965145872997
25113113.634855366808-0.634855366807756
26110109.7965662946570.203433705343414
27107104.3768784391132.62312156088674
28103103.288772862142-0.288772862142409
299897.97043654236850.0295634576314967
309895.98067018453952.01932981546045
31137127.9428433069239.05715669307683
32148157.662365409917-9.6623654099169
33147149.83263003488-2.83263003487951
34139137.0963776204931.90362237950694
35130125.9641784203364.03582157966406
36128128.410012365075-0.41001236507546
37127129.801187176186-2.80118717618612
38123126.117850090049-3.1178500900493
39118119.280524046228-1.28052404622775
40114113.3452319156810.654768084318576
41108107.8971748480970.102825151903474
42111105.6863657346445.31363426535576
43151142.4061465004658.59385349953482
44159166.446521110303-7.4465211103028
45158163.200913059292-5.20091305929236
46148150.326440336971-2.32644033697068
47138135.4117906562812.58820934371946
48137133.5537569860833.44624301391727
49136136.408510850104-0.408510850104221
50133134.655829420832-1.65582942083194
51126130.27117331286-4.27117331285996
52120122.577104284392-2.57710428439202
53114113.2705591748470.729440825152636
54116111.8545843241564.14541567584354
55153147.1025869697095.89741303029055
56162161.883368002290.116631997709533
57161164.806469005864-3.80646900586419
58149154.458058981884-5.45805898188368
59139138.3288054426120.671194557387906
60135134.2031627433730.79683725662747
61130131.901564742916-1.90156474291572
62127126.026508436090.973491563910187
63122120.9891287541571.01087124584305
64117117.736686186467-0.73668618646721
65112111.6052223845550.39477761544515
66113111.7414052865671.25859471343276
67149145.1855631381673.81443686183283
68157155.7306090039131.26939099608742
69157157.671960226961-0.671960226960522
70147149.567366715528-2.56736671552824
71137138.879988156976-1.87998815697571
72132133.645593352486-1.64559335248589
73125128.574015451709-3.57401545170879
74123121.5020097490071.4979902509933
75117116.1690702836430.830929716357488
76114111.5305121519832.46948784801722
77111108.4336167224412.56638327755869
78112111.5990084778680.400991522131619
79144146.122947035791-2.12294703579136
80150150.468078343708-0.468078343708015
81149148.7036558863030.29634411369662
82134139.169987762389-5.16998776238887
83123124.341418228908-1.34141822890814
84116117.242777366841-1.242777366841
85117109.7203803443817.27961965561892
86111113.637744340642-2.6377443406417
87105105.513213568765-0.513213568765011
88102100.2342775177941.76572248220648
899596.2318715322436-1.23187153224357
909394.2401138450171-1.24011384501715
91124124.413523012446-0.413523012445992
92130128.6352524757461.36474752425391
93124127.248082740082-3.24808274008224
94115111.1523807903583.84761920964181
95106104.6890398885431.31096011145678
96105101.3499421657133.65005783428663
97105103.4644348924451.53556510755456
98101101.951308819141-0.951308819141275
999597.8140087446414-2.81400874464141
1009392.91018393325790.0898160667421024
1018487.5428249343067-3.54282493430665
1028783.76941601692463.23058398307543
103116118.835412855658-2.83541285565775
104120122.482826865252-2.48282686525222
105117116.2052319487740.794768051226427
106109105.7327060120883.2672939879122
10710598.57313472427826.42686527572175
108107101.8814850577855.11851494221469
109109107.3000516556131.69994834438724
110109108.1232735383210.876726461679084
111108108.353874353415-0.353874353414867
112107110.582036718822-3.58203671882218
11399104.738394300042-5.73839430004222
114103103.795400768742-0.795400768742255
115131135.117243154089-4.11724315408915
116137138.378033310129-1.37803331012915
117135134.6678890245320.332110975467685
118124125.249954354437-1.24995435443698
119118114.8240792431523.17592075684782
120121113.2350103303067.76498966969389
121121118.2625415801032.73745841989678
122118118.712810177377-0.712810177376781
123113116.012751793762-3.01275179376238
124107112.983958647061-5.98395864706129
125100101.493933084416-1.49393308441631
126102103.253127330707-1.25312733070673
127130131.351950659423-1.35195065942264
128136136.473974686256-0.47397468625627
129133133.344023063385-0.344023063384981
130120122.169829299251-2.16982929925145
131112111.2534650586580.746534941342077
132109107.2616371040541.73836289594612
133110102.2818762509647.7181237490357

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 109 & 109.640224358974 & -0.640224358974436 \tabularnewline
14 & 106 & 105.919778207331 & 0.0802217926689366 \tabularnewline
15 & 101 & 100.611294895552 & 0.388705104447524 \tabularnewline
16 & 98 & 97.3303198257394 & 0.669680174260606 \tabularnewline
17 & 93 & 92.5779600874895 & 0.422039912510485 \tabularnewline
18 & 91 & 90.9321471712922 & 0.0678528287077569 \tabularnewline
19 & 122 & 120.270325682248 & 1.7296743177517 \tabularnewline
20 & 139 & 143.084450176702 & -4.08445017670226 \tabularnewline
21 & 140 & 135.128648336621 & 4.87135166337885 \tabularnewline
22 & 132 & 130.154145852221 & 1.84585414777933 \tabularnewline
23 & 117 & 122.606132879058 & -5.60613287905841 \tabularnewline
24 & 114 & 114.655965145873 & -0.655965145872997 \tabularnewline
25 & 113 & 113.634855366808 & -0.634855366807756 \tabularnewline
26 & 110 & 109.796566294657 & 0.203433705343414 \tabularnewline
27 & 107 & 104.376878439113 & 2.62312156088674 \tabularnewline
28 & 103 & 103.288772862142 & -0.288772862142409 \tabularnewline
29 & 98 & 97.9704365423685 & 0.0295634576314967 \tabularnewline
30 & 98 & 95.9806701845395 & 2.01932981546045 \tabularnewline
31 & 137 & 127.942843306923 & 9.05715669307683 \tabularnewline
32 & 148 & 157.662365409917 & -9.6623654099169 \tabularnewline
33 & 147 & 149.83263003488 & -2.83263003487951 \tabularnewline
34 & 139 & 137.096377620493 & 1.90362237950694 \tabularnewline
35 & 130 & 125.964178420336 & 4.03582157966406 \tabularnewline
36 & 128 & 128.410012365075 & -0.41001236507546 \tabularnewline
37 & 127 & 129.801187176186 & -2.80118717618612 \tabularnewline
38 & 123 & 126.117850090049 & -3.1178500900493 \tabularnewline
39 & 118 & 119.280524046228 & -1.28052404622775 \tabularnewline
40 & 114 & 113.345231915681 & 0.654768084318576 \tabularnewline
41 & 108 & 107.897174848097 & 0.102825151903474 \tabularnewline
42 & 111 & 105.686365734644 & 5.31363426535576 \tabularnewline
43 & 151 & 142.406146500465 & 8.59385349953482 \tabularnewline
44 & 159 & 166.446521110303 & -7.4465211103028 \tabularnewline
45 & 158 & 163.200913059292 & -5.20091305929236 \tabularnewline
46 & 148 & 150.326440336971 & -2.32644033697068 \tabularnewline
47 & 138 & 135.411790656281 & 2.58820934371946 \tabularnewline
48 & 137 & 133.553756986083 & 3.44624301391727 \tabularnewline
49 & 136 & 136.408510850104 & -0.408510850104221 \tabularnewline
50 & 133 & 134.655829420832 & -1.65582942083194 \tabularnewline
51 & 126 & 130.27117331286 & -4.27117331285996 \tabularnewline
52 & 120 & 122.577104284392 & -2.57710428439202 \tabularnewline
53 & 114 & 113.270559174847 & 0.729440825152636 \tabularnewline
54 & 116 & 111.854584324156 & 4.14541567584354 \tabularnewline
55 & 153 & 147.102586969709 & 5.89741303029055 \tabularnewline
56 & 162 & 161.88336800229 & 0.116631997709533 \tabularnewline
57 & 161 & 164.806469005864 & -3.80646900586419 \tabularnewline
58 & 149 & 154.458058981884 & -5.45805898188368 \tabularnewline
59 & 139 & 138.328805442612 & 0.671194557387906 \tabularnewline
60 & 135 & 134.203162743373 & 0.79683725662747 \tabularnewline
61 & 130 & 131.901564742916 & -1.90156474291572 \tabularnewline
62 & 127 & 126.02650843609 & 0.973491563910187 \tabularnewline
63 & 122 & 120.989128754157 & 1.01087124584305 \tabularnewline
64 & 117 & 117.736686186467 & -0.73668618646721 \tabularnewline
65 & 112 & 111.605222384555 & 0.39477761544515 \tabularnewline
66 & 113 & 111.741405286567 & 1.25859471343276 \tabularnewline
67 & 149 & 145.185563138167 & 3.81443686183283 \tabularnewline
68 & 157 & 155.730609003913 & 1.26939099608742 \tabularnewline
69 & 157 & 157.671960226961 & -0.671960226960522 \tabularnewline
70 & 147 & 149.567366715528 & -2.56736671552824 \tabularnewline
71 & 137 & 138.879988156976 & -1.87998815697571 \tabularnewline
72 & 132 & 133.645593352486 & -1.64559335248589 \tabularnewline
73 & 125 & 128.574015451709 & -3.57401545170879 \tabularnewline
74 & 123 & 121.502009749007 & 1.4979902509933 \tabularnewline
75 & 117 & 116.169070283643 & 0.830929716357488 \tabularnewline
76 & 114 & 111.530512151983 & 2.46948784801722 \tabularnewline
77 & 111 & 108.433616722441 & 2.56638327755869 \tabularnewline
78 & 112 & 111.599008477868 & 0.400991522131619 \tabularnewline
79 & 144 & 146.122947035791 & -2.12294703579136 \tabularnewline
80 & 150 & 150.468078343708 & -0.468078343708015 \tabularnewline
81 & 149 & 148.703655886303 & 0.29634411369662 \tabularnewline
82 & 134 & 139.169987762389 & -5.16998776238887 \tabularnewline
83 & 123 & 124.341418228908 & -1.34141822890814 \tabularnewline
84 & 116 & 117.242777366841 & -1.242777366841 \tabularnewline
85 & 117 & 109.720380344381 & 7.27961965561892 \tabularnewline
86 & 111 & 113.637744340642 & -2.6377443406417 \tabularnewline
87 & 105 & 105.513213568765 & -0.513213568765011 \tabularnewline
88 & 102 & 100.234277517794 & 1.76572248220648 \tabularnewline
89 & 95 & 96.2318715322436 & -1.23187153224357 \tabularnewline
90 & 93 & 94.2401138450171 & -1.24011384501715 \tabularnewline
91 & 124 & 124.413523012446 & -0.413523012445992 \tabularnewline
92 & 130 & 128.635252475746 & 1.36474752425391 \tabularnewline
93 & 124 & 127.248082740082 & -3.24808274008224 \tabularnewline
94 & 115 & 111.152380790358 & 3.84761920964181 \tabularnewline
95 & 106 & 104.689039888543 & 1.31096011145678 \tabularnewline
96 & 105 & 101.349942165713 & 3.65005783428663 \tabularnewline
97 & 105 & 103.464434892445 & 1.53556510755456 \tabularnewline
98 & 101 & 101.951308819141 & -0.951308819141275 \tabularnewline
99 & 95 & 97.8140087446414 & -2.81400874464141 \tabularnewline
100 & 93 & 92.9101839332579 & 0.0898160667421024 \tabularnewline
101 & 84 & 87.5428249343067 & -3.54282493430665 \tabularnewline
102 & 87 & 83.7694160169246 & 3.23058398307543 \tabularnewline
103 & 116 & 118.835412855658 & -2.83541285565775 \tabularnewline
104 & 120 & 122.482826865252 & -2.48282686525222 \tabularnewline
105 & 117 & 116.205231948774 & 0.794768051226427 \tabularnewline
106 & 109 & 105.732706012088 & 3.2672939879122 \tabularnewline
107 & 105 & 98.5731347242782 & 6.42686527572175 \tabularnewline
108 & 107 & 101.881485057785 & 5.11851494221469 \tabularnewline
109 & 109 & 107.300051655613 & 1.69994834438724 \tabularnewline
110 & 109 & 108.123273538321 & 0.876726461679084 \tabularnewline
111 & 108 & 108.353874353415 & -0.353874353414867 \tabularnewline
112 & 107 & 110.582036718822 & -3.58203671882218 \tabularnewline
113 & 99 & 104.738394300042 & -5.73839430004222 \tabularnewline
114 & 103 & 103.795400768742 & -0.795400768742255 \tabularnewline
115 & 131 & 135.117243154089 & -4.11724315408915 \tabularnewline
116 & 137 & 138.378033310129 & -1.37803331012915 \tabularnewline
117 & 135 & 134.667889024532 & 0.332110975467685 \tabularnewline
118 & 124 & 125.249954354437 & -1.24995435443698 \tabularnewline
119 & 118 & 114.824079243152 & 3.17592075684782 \tabularnewline
120 & 121 & 113.235010330306 & 7.76498966969389 \tabularnewline
121 & 121 & 118.262541580103 & 2.73745841989678 \tabularnewline
122 & 118 & 118.712810177377 & -0.712810177376781 \tabularnewline
123 & 113 & 116.012751793762 & -3.01275179376238 \tabularnewline
124 & 107 & 112.983958647061 & -5.98395864706129 \tabularnewline
125 & 100 & 101.493933084416 & -1.49393308441631 \tabularnewline
126 & 102 & 103.253127330707 & -1.25312733070673 \tabularnewline
127 & 130 & 131.351950659423 & -1.35195065942264 \tabularnewline
128 & 136 & 136.473974686256 & -0.47397468625627 \tabularnewline
129 & 133 & 133.344023063385 & -0.344023063384981 \tabularnewline
130 & 120 & 122.169829299251 & -2.16982929925145 \tabularnewline
131 & 112 & 111.253465058658 & 0.746534941342077 \tabularnewline
132 & 109 & 107.261637104054 & 1.73836289594612 \tabularnewline
133 & 110 & 102.281876250964 & 7.7181237490357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122407&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]109[/C][C]109.640224358974[/C][C]-0.640224358974436[/C][/ROW]
[ROW][C]14[/C][C]106[/C][C]105.919778207331[/C][C]0.0802217926689366[/C][/ROW]
[ROW][C]15[/C][C]101[/C][C]100.611294895552[/C][C]0.388705104447524[/C][/ROW]
[ROW][C]16[/C][C]98[/C][C]97.3303198257394[/C][C]0.669680174260606[/C][/ROW]
[ROW][C]17[/C][C]93[/C][C]92.5779600874895[/C][C]0.422039912510485[/C][/ROW]
[ROW][C]18[/C][C]91[/C][C]90.9321471712922[/C][C]0.0678528287077569[/C][/ROW]
[ROW][C]19[/C][C]122[/C][C]120.270325682248[/C][C]1.7296743177517[/C][/ROW]
[ROW][C]20[/C][C]139[/C][C]143.084450176702[/C][C]-4.08445017670226[/C][/ROW]
[ROW][C]21[/C][C]140[/C][C]135.128648336621[/C][C]4.87135166337885[/C][/ROW]
[ROW][C]22[/C][C]132[/C][C]130.154145852221[/C][C]1.84585414777933[/C][/ROW]
[ROW][C]23[/C][C]117[/C][C]122.606132879058[/C][C]-5.60613287905841[/C][/ROW]
[ROW][C]24[/C][C]114[/C][C]114.655965145873[/C][C]-0.655965145872997[/C][/ROW]
[ROW][C]25[/C][C]113[/C][C]113.634855366808[/C][C]-0.634855366807756[/C][/ROW]
[ROW][C]26[/C][C]110[/C][C]109.796566294657[/C][C]0.203433705343414[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]104.376878439113[/C][C]2.62312156088674[/C][/ROW]
[ROW][C]28[/C][C]103[/C][C]103.288772862142[/C][C]-0.288772862142409[/C][/ROW]
[ROW][C]29[/C][C]98[/C][C]97.9704365423685[/C][C]0.0295634576314967[/C][/ROW]
[ROW][C]30[/C][C]98[/C][C]95.9806701845395[/C][C]2.01932981546045[/C][/ROW]
[ROW][C]31[/C][C]137[/C][C]127.942843306923[/C][C]9.05715669307683[/C][/ROW]
[ROW][C]32[/C][C]148[/C][C]157.662365409917[/C][C]-9.6623654099169[/C][/ROW]
[ROW][C]33[/C][C]147[/C][C]149.83263003488[/C][C]-2.83263003487951[/C][/ROW]
[ROW][C]34[/C][C]139[/C][C]137.096377620493[/C][C]1.90362237950694[/C][/ROW]
[ROW][C]35[/C][C]130[/C][C]125.964178420336[/C][C]4.03582157966406[/C][/ROW]
[ROW][C]36[/C][C]128[/C][C]128.410012365075[/C][C]-0.41001236507546[/C][/ROW]
[ROW][C]37[/C][C]127[/C][C]129.801187176186[/C][C]-2.80118717618612[/C][/ROW]
[ROW][C]38[/C][C]123[/C][C]126.117850090049[/C][C]-3.1178500900493[/C][/ROW]
[ROW][C]39[/C][C]118[/C][C]119.280524046228[/C][C]-1.28052404622775[/C][/ROW]
[ROW][C]40[/C][C]114[/C][C]113.345231915681[/C][C]0.654768084318576[/C][/ROW]
[ROW][C]41[/C][C]108[/C][C]107.897174848097[/C][C]0.102825151903474[/C][/ROW]
[ROW][C]42[/C][C]111[/C][C]105.686365734644[/C][C]5.31363426535576[/C][/ROW]
[ROW][C]43[/C][C]151[/C][C]142.406146500465[/C][C]8.59385349953482[/C][/ROW]
[ROW][C]44[/C][C]159[/C][C]166.446521110303[/C][C]-7.4465211103028[/C][/ROW]
[ROW][C]45[/C][C]158[/C][C]163.200913059292[/C][C]-5.20091305929236[/C][/ROW]
[ROW][C]46[/C][C]148[/C][C]150.326440336971[/C][C]-2.32644033697068[/C][/ROW]
[ROW][C]47[/C][C]138[/C][C]135.411790656281[/C][C]2.58820934371946[/C][/ROW]
[ROW][C]48[/C][C]137[/C][C]133.553756986083[/C][C]3.44624301391727[/C][/ROW]
[ROW][C]49[/C][C]136[/C][C]136.408510850104[/C][C]-0.408510850104221[/C][/ROW]
[ROW][C]50[/C][C]133[/C][C]134.655829420832[/C][C]-1.65582942083194[/C][/ROW]
[ROW][C]51[/C][C]126[/C][C]130.27117331286[/C][C]-4.27117331285996[/C][/ROW]
[ROW][C]52[/C][C]120[/C][C]122.577104284392[/C][C]-2.57710428439202[/C][/ROW]
[ROW][C]53[/C][C]114[/C][C]113.270559174847[/C][C]0.729440825152636[/C][/ROW]
[ROW][C]54[/C][C]116[/C][C]111.854584324156[/C][C]4.14541567584354[/C][/ROW]
[ROW][C]55[/C][C]153[/C][C]147.102586969709[/C][C]5.89741303029055[/C][/ROW]
[ROW][C]56[/C][C]162[/C][C]161.88336800229[/C][C]0.116631997709533[/C][/ROW]
[ROW][C]57[/C][C]161[/C][C]164.806469005864[/C][C]-3.80646900586419[/C][/ROW]
[ROW][C]58[/C][C]149[/C][C]154.458058981884[/C][C]-5.45805898188368[/C][/ROW]
[ROW][C]59[/C][C]139[/C][C]138.328805442612[/C][C]0.671194557387906[/C][/ROW]
[ROW][C]60[/C][C]135[/C][C]134.203162743373[/C][C]0.79683725662747[/C][/ROW]
[ROW][C]61[/C][C]130[/C][C]131.901564742916[/C][C]-1.90156474291572[/C][/ROW]
[ROW][C]62[/C][C]127[/C][C]126.02650843609[/C][C]0.973491563910187[/C][/ROW]
[ROW][C]63[/C][C]122[/C][C]120.989128754157[/C][C]1.01087124584305[/C][/ROW]
[ROW][C]64[/C][C]117[/C][C]117.736686186467[/C][C]-0.73668618646721[/C][/ROW]
[ROW][C]65[/C][C]112[/C][C]111.605222384555[/C][C]0.39477761544515[/C][/ROW]
[ROW][C]66[/C][C]113[/C][C]111.741405286567[/C][C]1.25859471343276[/C][/ROW]
[ROW][C]67[/C][C]149[/C][C]145.185563138167[/C][C]3.81443686183283[/C][/ROW]
[ROW][C]68[/C][C]157[/C][C]155.730609003913[/C][C]1.26939099608742[/C][/ROW]
[ROW][C]69[/C][C]157[/C][C]157.671960226961[/C][C]-0.671960226960522[/C][/ROW]
[ROW][C]70[/C][C]147[/C][C]149.567366715528[/C][C]-2.56736671552824[/C][/ROW]
[ROW][C]71[/C][C]137[/C][C]138.879988156976[/C][C]-1.87998815697571[/C][/ROW]
[ROW][C]72[/C][C]132[/C][C]133.645593352486[/C][C]-1.64559335248589[/C][/ROW]
[ROW][C]73[/C][C]125[/C][C]128.574015451709[/C][C]-3.57401545170879[/C][/ROW]
[ROW][C]74[/C][C]123[/C][C]121.502009749007[/C][C]1.4979902509933[/C][/ROW]
[ROW][C]75[/C][C]117[/C][C]116.169070283643[/C][C]0.830929716357488[/C][/ROW]
[ROW][C]76[/C][C]114[/C][C]111.530512151983[/C][C]2.46948784801722[/C][/ROW]
[ROW][C]77[/C][C]111[/C][C]108.433616722441[/C][C]2.56638327755869[/C][/ROW]
[ROW][C]78[/C][C]112[/C][C]111.599008477868[/C][C]0.400991522131619[/C][/ROW]
[ROW][C]79[/C][C]144[/C][C]146.122947035791[/C][C]-2.12294703579136[/C][/ROW]
[ROW][C]80[/C][C]150[/C][C]150.468078343708[/C][C]-0.468078343708015[/C][/ROW]
[ROW][C]81[/C][C]149[/C][C]148.703655886303[/C][C]0.29634411369662[/C][/ROW]
[ROW][C]82[/C][C]134[/C][C]139.169987762389[/C][C]-5.16998776238887[/C][/ROW]
[ROW][C]83[/C][C]123[/C][C]124.341418228908[/C][C]-1.34141822890814[/C][/ROW]
[ROW][C]84[/C][C]116[/C][C]117.242777366841[/C][C]-1.242777366841[/C][/ROW]
[ROW][C]85[/C][C]117[/C][C]109.720380344381[/C][C]7.27961965561892[/C][/ROW]
[ROW][C]86[/C][C]111[/C][C]113.637744340642[/C][C]-2.6377443406417[/C][/ROW]
[ROW][C]87[/C][C]105[/C][C]105.513213568765[/C][C]-0.513213568765011[/C][/ROW]
[ROW][C]88[/C][C]102[/C][C]100.234277517794[/C][C]1.76572248220648[/C][/ROW]
[ROW][C]89[/C][C]95[/C][C]96.2318715322436[/C][C]-1.23187153224357[/C][/ROW]
[ROW][C]90[/C][C]93[/C][C]94.2401138450171[/C][C]-1.24011384501715[/C][/ROW]
[ROW][C]91[/C][C]124[/C][C]124.413523012446[/C][C]-0.413523012445992[/C][/ROW]
[ROW][C]92[/C][C]130[/C][C]128.635252475746[/C][C]1.36474752425391[/C][/ROW]
[ROW][C]93[/C][C]124[/C][C]127.248082740082[/C][C]-3.24808274008224[/C][/ROW]
[ROW][C]94[/C][C]115[/C][C]111.152380790358[/C][C]3.84761920964181[/C][/ROW]
[ROW][C]95[/C][C]106[/C][C]104.689039888543[/C][C]1.31096011145678[/C][/ROW]
[ROW][C]96[/C][C]105[/C][C]101.349942165713[/C][C]3.65005783428663[/C][/ROW]
[ROW][C]97[/C][C]105[/C][C]103.464434892445[/C][C]1.53556510755456[/C][/ROW]
[ROW][C]98[/C][C]101[/C][C]101.951308819141[/C][C]-0.951308819141275[/C][/ROW]
[ROW][C]99[/C][C]95[/C][C]97.8140087446414[/C][C]-2.81400874464141[/C][/ROW]
[ROW][C]100[/C][C]93[/C][C]92.9101839332579[/C][C]0.0898160667421024[/C][/ROW]
[ROW][C]101[/C][C]84[/C][C]87.5428249343067[/C][C]-3.54282493430665[/C][/ROW]
[ROW][C]102[/C][C]87[/C][C]83.7694160169246[/C][C]3.23058398307543[/C][/ROW]
[ROW][C]103[/C][C]116[/C][C]118.835412855658[/C][C]-2.83541285565775[/C][/ROW]
[ROW][C]104[/C][C]120[/C][C]122.482826865252[/C][C]-2.48282686525222[/C][/ROW]
[ROW][C]105[/C][C]117[/C][C]116.205231948774[/C][C]0.794768051226427[/C][/ROW]
[ROW][C]106[/C][C]109[/C][C]105.732706012088[/C][C]3.2672939879122[/C][/ROW]
[ROW][C]107[/C][C]105[/C][C]98.5731347242782[/C][C]6.42686527572175[/C][/ROW]
[ROW][C]108[/C][C]107[/C][C]101.881485057785[/C][C]5.11851494221469[/C][/ROW]
[ROW][C]109[/C][C]109[/C][C]107.300051655613[/C][C]1.69994834438724[/C][/ROW]
[ROW][C]110[/C][C]109[/C][C]108.123273538321[/C][C]0.876726461679084[/C][/ROW]
[ROW][C]111[/C][C]108[/C][C]108.353874353415[/C][C]-0.353874353414867[/C][/ROW]
[ROW][C]112[/C][C]107[/C][C]110.582036718822[/C][C]-3.58203671882218[/C][/ROW]
[ROW][C]113[/C][C]99[/C][C]104.738394300042[/C][C]-5.73839430004222[/C][/ROW]
[ROW][C]114[/C][C]103[/C][C]103.795400768742[/C][C]-0.795400768742255[/C][/ROW]
[ROW][C]115[/C][C]131[/C][C]135.117243154089[/C][C]-4.11724315408915[/C][/ROW]
[ROW][C]116[/C][C]137[/C][C]138.378033310129[/C][C]-1.37803331012915[/C][/ROW]
[ROW][C]117[/C][C]135[/C][C]134.667889024532[/C][C]0.332110975467685[/C][/ROW]
[ROW][C]118[/C][C]124[/C][C]125.249954354437[/C][C]-1.24995435443698[/C][/ROW]
[ROW][C]119[/C][C]118[/C][C]114.824079243152[/C][C]3.17592075684782[/C][/ROW]
[ROW][C]120[/C][C]121[/C][C]113.235010330306[/C][C]7.76498966969389[/C][/ROW]
[ROW][C]121[/C][C]121[/C][C]118.262541580103[/C][C]2.73745841989678[/C][/ROW]
[ROW][C]122[/C][C]118[/C][C]118.712810177377[/C][C]-0.712810177376781[/C][/ROW]
[ROW][C]123[/C][C]113[/C][C]116.012751793762[/C][C]-3.01275179376238[/C][/ROW]
[ROW][C]124[/C][C]107[/C][C]112.983958647061[/C][C]-5.98395864706129[/C][/ROW]
[ROW][C]125[/C][C]100[/C][C]101.493933084416[/C][C]-1.49393308441631[/C][/ROW]
[ROW][C]126[/C][C]102[/C][C]103.253127330707[/C][C]-1.25312733070673[/C][/ROW]
[ROW][C]127[/C][C]130[/C][C]131.351950659423[/C][C]-1.35195065942264[/C][/ROW]
[ROW][C]128[/C][C]136[/C][C]136.473974686256[/C][C]-0.47397468625627[/C][/ROW]
[ROW][C]129[/C][C]133[/C][C]133.344023063385[/C][C]-0.344023063384981[/C][/ROW]
[ROW][C]130[/C][C]120[/C][C]122.169829299251[/C][C]-2.16982929925145[/C][/ROW]
[ROW][C]131[/C][C]112[/C][C]111.253465058658[/C][C]0.746534941342077[/C][/ROW]
[ROW][C]132[/C][C]109[/C][C]107.261637104054[/C][C]1.73836289594612[/C][/ROW]
[ROW][C]133[/C][C]110[/C][C]102.281876250964[/C][C]7.7181237490357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122407&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122407&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
13109109.640224358974-0.640224358974436
14106105.9197782073310.0802217926689366
15101100.6112948955520.388705104447524
169897.33031982573940.669680174260606
179392.57796008748950.422039912510485
189190.93214717129220.0678528287077569
19122120.2703256822481.7296743177517
20139143.084450176702-4.08445017670226
21140135.1286483366214.87135166337885
22132130.1541458522211.84585414777933
23117122.606132879058-5.60613287905841
24114114.655965145873-0.655965145872997
25113113.634855366808-0.634855366807756
26110109.7965662946570.203433705343414
27107104.3768784391132.62312156088674
28103103.288772862142-0.288772862142409
299897.97043654236850.0295634576314967
309895.98067018453952.01932981546045
31137127.9428433069239.05715669307683
32148157.662365409917-9.6623654099169
33147149.83263003488-2.83263003487951
34139137.0963776204931.90362237950694
35130125.9641784203364.03582157966406
36128128.410012365075-0.41001236507546
37127129.801187176186-2.80118717618612
38123126.117850090049-3.1178500900493
39118119.280524046228-1.28052404622775
40114113.3452319156810.654768084318576
41108107.8971748480970.102825151903474
42111105.6863657346445.31363426535576
43151142.4061465004658.59385349953482
44159166.446521110303-7.4465211103028
45158163.200913059292-5.20091305929236
46148150.326440336971-2.32644033697068
47138135.4117906562812.58820934371946
48137133.5537569860833.44624301391727
49136136.408510850104-0.408510850104221
50133134.655829420832-1.65582942083194
51126130.27117331286-4.27117331285996
52120122.577104284392-2.57710428439202
53114113.2705591748470.729440825152636
54116111.8545843241564.14541567584354
55153147.1025869697095.89741303029055
56162161.883368002290.116631997709533
57161164.806469005864-3.80646900586419
58149154.458058981884-5.45805898188368
59139138.3288054426120.671194557387906
60135134.2031627433730.79683725662747
61130131.901564742916-1.90156474291572
62127126.026508436090.973491563910187
63122120.9891287541571.01087124584305
64117117.736686186467-0.73668618646721
65112111.6052223845550.39477761544515
66113111.7414052865671.25859471343276
67149145.1855631381673.81443686183283
68157155.7306090039131.26939099608742
69157157.671960226961-0.671960226960522
70147149.567366715528-2.56736671552824
71137138.879988156976-1.87998815697571
72132133.645593352486-1.64559335248589
73125128.574015451709-3.57401545170879
74123121.5020097490071.4979902509933
75117116.1690702836430.830929716357488
76114111.5305121519832.46948784801722
77111108.4336167224412.56638327755869
78112111.5990084778680.400991522131619
79144146.122947035791-2.12294703579136
80150150.468078343708-0.468078343708015
81149148.7036558863030.29634411369662
82134139.169987762389-5.16998776238887
83123124.341418228908-1.34141822890814
84116117.242777366841-1.242777366841
85117109.7203803443817.27961965561892
86111113.637744340642-2.6377443406417
87105105.513213568765-0.513213568765011
88102100.2342775177941.76572248220648
899596.2318715322436-1.23187153224357
909394.2401138450171-1.24011384501715
91124124.413523012446-0.413523012445992
92130128.6352524757461.36474752425391
93124127.248082740082-3.24808274008224
94115111.1523807903583.84761920964181
95106104.6890398885431.31096011145678
96105101.3499421657133.65005783428663
97105103.4644348924451.53556510755456
98101101.951308819141-0.951308819141275
999597.8140087446414-2.81400874464141
1009392.91018393325790.0898160667421024
1018487.5428249343067-3.54282493430665
1028783.76941601692463.23058398307543
103116118.835412855658-2.83541285565775
104120122.482826865252-2.48282686525222
105117116.2052319487740.794768051226427
106109105.7327060120883.2672939879122
10710598.57313472427826.42686527572175
108107101.8814850577855.11851494221469
109109107.3000516556131.69994834438724
110109108.1232735383210.876726461679084
111108108.353874353415-0.353874353414867
112107110.582036718822-3.58203671882218
11399104.738394300042-5.73839430004222
114103103.795400768742-0.795400768742255
115131135.117243154089-4.11724315408915
116137138.378033310129-1.37803331012915
117135134.6678890245320.332110975467685
118124125.249954354437-1.24995435443698
119118114.8240792431523.17592075684782
120121113.2350103303067.76498966969389
121121118.2625415801032.73745841989678
122118118.712810177377-0.712810177376781
123113116.012751793762-3.01275179376238
124107112.983958647061-5.98395864706129
125100101.493933084416-1.49393308441631
126102103.253127330707-1.25312733070673
127130131.351950659423-1.35195065942264
128136136.473974686256-0.47397468625627
129133133.344023063385-0.344023063384981
130120122.169829299251-2.16982929925145
131112111.2534650586580.746534941342077
132109107.2616371040541.73836289594612
133110102.2818762509647.7181237490357







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
134102.78274401895196.4486997256334109.116788312269
13597.731598610017188.4381973980278107.024999822006
13694.885830467202881.8504686086489107.921192325757
13790.08915630673972.7186793600399107.459633253438
13894.674871416268572.476695095659116.873047736878
139125.79316576353898.3350041215887153.251327405487
140134.792709206092101.68286792142167.902550490764
141134.87586162360795.7524009696718173.999322277542
142126.37181492179380.8959456519968171.84768419159
143121.6158054587669.4675224480622173.764088469457
144120.88555054720761.7605585974631180.010542496952
145119.30220130261852.909643464552185.694759140685

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
134 & 102.782744018951 & 96.4486997256334 & 109.116788312269 \tabularnewline
135 & 97.7315986100171 & 88.4381973980278 & 107.024999822006 \tabularnewline
136 & 94.8858304672028 & 81.8504686086489 & 107.921192325757 \tabularnewline
137 & 90.089156306739 & 72.7186793600399 & 107.459633253438 \tabularnewline
138 & 94.6748714162685 & 72.476695095659 & 116.873047736878 \tabularnewline
139 & 125.793165763538 & 98.3350041215887 & 153.251327405487 \tabularnewline
140 & 134.792709206092 & 101.68286792142 & 167.902550490764 \tabularnewline
141 & 134.875861623607 & 95.7524009696718 & 173.999322277542 \tabularnewline
142 & 126.371814921793 & 80.8959456519968 & 171.84768419159 \tabularnewline
143 & 121.61580545876 & 69.4675224480622 & 173.764088469457 \tabularnewline
144 & 120.885550547207 & 61.7605585974631 & 180.010542496952 \tabularnewline
145 & 119.302201302618 & 52.909643464552 & 185.694759140685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122407&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]134[/C][C]102.782744018951[/C][C]96.4486997256334[/C][C]109.116788312269[/C][/ROW]
[ROW][C]135[/C][C]97.7315986100171[/C][C]88.4381973980278[/C][C]107.024999822006[/C][/ROW]
[ROW][C]136[/C][C]94.8858304672028[/C][C]81.8504686086489[/C][C]107.921192325757[/C][/ROW]
[ROW][C]137[/C][C]90.089156306739[/C][C]72.7186793600399[/C][C]107.459633253438[/C][/ROW]
[ROW][C]138[/C][C]94.6748714162685[/C][C]72.476695095659[/C][C]116.873047736878[/C][/ROW]
[ROW][C]139[/C][C]125.793165763538[/C][C]98.3350041215887[/C][C]153.251327405487[/C][/ROW]
[ROW][C]140[/C][C]134.792709206092[/C][C]101.68286792142[/C][C]167.902550490764[/C][/ROW]
[ROW][C]141[/C][C]134.875861623607[/C][C]95.7524009696718[/C][C]173.999322277542[/C][/ROW]
[ROW][C]142[/C][C]126.371814921793[/C][C]80.8959456519968[/C][C]171.84768419159[/C][/ROW]
[ROW][C]143[/C][C]121.61580545876[/C][C]69.4675224480622[/C][C]173.764088469457[/C][/ROW]
[ROW][C]144[/C][C]120.885550547207[/C][C]61.7605585974631[/C][C]180.010542496952[/C][/ROW]
[ROW][C]145[/C][C]119.302201302618[/C][C]52.909643464552[/C][C]185.694759140685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122407&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122407&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
134102.78274401895196.4486997256334109.116788312269
13597.731598610017188.4381973980278107.024999822006
13694.885830467202881.8504686086489107.921192325757
13790.08915630673972.7186793600399107.459633253438
13894.674871416268572.476695095659116.873047736878
139125.79316576353898.3350041215887153.251327405487
140134.792709206092101.68286792142167.902550490764
141134.87586162360795.7524009696718173.999322277542
142126.37181492179380.8959456519968171.84768419159
143121.6158054587669.4675224480622173.764088469457
144120.88555054720761.7605585974631180.010542496952
145119.30220130261852.909643464552185.694759140685



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