Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Aug 2010 08:58:58 +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/2010/Aug/18/t1282121916ckqvrf9em3p9e51.htm/, Retrieved Thu, 16 May 2024 18:13:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79181, Retrieved Thu, 16 May 2024 18:13:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPatrick Fieremans
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2010-08-18 08:58:58] [bffa0fb6afa860209dcefcd4361c2008] [Current]
Feedback Forum

Post a new message
Dataseries X:
136
135
134
132
152
151
136
126
127
127
128
130
125
118
111
104
126
131
122
116
115
115
113
122
114
106
93
89
114
122
115
116
120
120
120
121
118
112
99
96
120
135
128
134
134
132
130
125
124
114
101
101
123
143
133
136
137
135
141
136
133
124
110
104
130
160
142
142
137
135
139
135
134
120
103
101
127
159
141
140
135
127
130
128
126
110
101
102
129
169
146
145
138
123
124
137
132
112
105
106
137
175
151
142
140
122
127
135
128
117
107
108
134
171
154
146
148
122
124
135




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79181&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79181&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79181&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79181&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2135136-1
3134135.000066106961-1.00006610696136
4132134.000066111331-2.00006611133148
5152132.00013221829319.9998677817069
6151151.998677869514-0.9986778695135
7136151.000066019559-15.0000660195593
8126136.000991608785-10.0009916087846
9127126.0006611351660.999338864834243
10127126.9999339367446.60632557156760e-05
11128126.9999999956331.00000000436724
12130127.9999338930382.00006610696164
13125129.999867781707-4.99986778170717
14118125.000330526066-7.00033052606621
15111118.000462770580-7.00046277057953
16104111.000462779322-7.00046277932181
17126104.00046277932221.9995372206776
18131125.9985456774435.00145432255681
19122130.999669369052-8.99966936905238
20116122.000594940795-6.00059494079515
21115116.000396681098-1.00039668109784
22115115.000066133185-6.61331847453539e-05
23113115.000000004372-2.00000000437187
24122113.0001322139238.999867786077
25114121.999405046088-7.99940504608809
26106114.000528816360-8.00052881636022
2793106.000528890649-13.0005288906492
288993.000859425461-4.00085942546093
2911489.000264484659424.9997355153406
30122113.9983473434508.00165265654952
31115121.999471035057-6.99947103505707
32116115.0004627137610.999537286238791
33120115.9999339236274.00006607637275
34120119.9997355677860.000264432213512578
35120119.9999999825191.74808150177341e-08
36121119.9999999999991.00000000000115
37118120.999933893039-2.99993389303864
38112118.000198316514-6.00019831651392
3999112.000396654878-13.0003966548782
409699.0008594167192-3.00085941671922
4112096.000198377697523.9998016223025
42135119.99841344604215.0015865539583
43128134.999008290697-6.99900829069747
44134128.0004626831715.99953731682942
45134133.9996033888180.000396611181514572
46132133.999999973781-1.99999997378126
47130132.000132213921-2.00013221392098
48125130.000132222663-5.00013222266296
49124125.000330543548-1.00033054354759
50114124.000066128813-10.0000661288126
51101114.000661073985-13.0006610739851
52101101.000859434199-0.000859434199171005
53123101.00000005681521.9999999431854
54143122.99854564685420.001454353146
55133142.99867776463-9.99867776463009
56136133.0006609822052.99933901779542
57137135.9998017228111.00019827718853
58135136.999933879931-1.99993387993115
59141135.0001322095525.99986779044829
60136140.999603366972-4.99960336697185
61133136.000330508587-3.00033050858656
62124133.000198342733-9.00019834273297
63110124.000594975764-14.000594975764
64104110.000925536791-6.00092553679096
65130104.00039670295325.9996032970475
66160129.99828124523030.0017187547703
67142159.998016677538-17.9980166775378
68142142.001189794193-0.00118979419292486
69137142.000000078654-5.00000007865367
70135137.000330534812-2.00033053481195
71139135.0001322357733.99986776422665
72135138.999735580896-3.99973558089627
73134135.000264410365-1.00026441036547
74120134.000066124441-14.0000661244407
75103120.000925501830-17.0009255018302
76101103.001123879525-2.00112387952510
77127101.00013228821925.9998677117810
78159126.9982812277532.00171877225
79141158.997884463614-17.9978844636139
80140141.001189785453-1.00118978545265
81135140.000066185614-5.00006618561446
82127135.000330539182-8.0003305391821
83130127.0005288775422.99947112245825
84128129.999801714078-1.99980171407842
85126128.000132200815-2.00013220081462
86110126.000132222662-16.0001322226621
87101110.001057720122-9.00105772012246
88102101.0005950325750.999404967425164
89129101.99993393237427.0000660676256
90169128.99821510767640.001784892324
91146168.997355603552-22.9973556035521
92145146.001520285298-1.00152028529806
93138145.000066207463-7.00006620746279
94123138.000462753106-15.0004627531062
95124123.0009916350110.999008364988512
96137123.99993395859313.0000660414074
97132136.999140605137-4.99914060513663
98112132.000330477995-20.0003304779948
99105112.001322161074-7.00132216107394
100106105.0004628361340.999537163866478
101137105.99993392363531.0000660763647
102175136.9979506798338.00204932017
103151174.997487799994-23.9974877999943
104142151.001586400999-9.00158640099855
105140142.000595067524-2.00059506752433
106122140.000132253261-18.0001322532608
107127122.0011899340474.99881006595281
108135126.9996695438568.00033045614383
109128134.999471122464-6.99947112246375
110117128.000462713767-11.0004627137670
111107117.000727207163-10.0007272071635
112108107.0006611176870.999338882313026
113134107.99993393674326.0000660632569
114171133.99828121463837.0017187853624
115154170.997553928806-16.9975539288063
116146154.001123656641-8.00112365664063
117148146.0005289299721.99947107002768
118122147.999867821043-25.9998678210433
119124122.0017187722571.99828122774281
120135123.999867899711.0001321002999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 135 & 136 & -1 \tabularnewline
3 & 134 & 135.000066106961 & -1.00006610696136 \tabularnewline
4 & 132 & 134.000066111331 & -2.00006611133148 \tabularnewline
5 & 152 & 132.000132218293 & 19.9998677817069 \tabularnewline
6 & 151 & 151.998677869514 & -0.9986778695135 \tabularnewline
7 & 136 & 151.000066019559 & -15.0000660195593 \tabularnewline
8 & 126 & 136.000991608785 & -10.0009916087846 \tabularnewline
9 & 127 & 126.000661135166 & 0.999338864834243 \tabularnewline
10 & 127 & 126.999933936744 & 6.60632557156760e-05 \tabularnewline
11 & 128 & 126.999999995633 & 1.00000000436724 \tabularnewline
12 & 130 & 127.999933893038 & 2.00006610696164 \tabularnewline
13 & 125 & 129.999867781707 & -4.99986778170717 \tabularnewline
14 & 118 & 125.000330526066 & -7.00033052606621 \tabularnewline
15 & 111 & 118.000462770580 & -7.00046277057953 \tabularnewline
16 & 104 & 111.000462779322 & -7.00046277932181 \tabularnewline
17 & 126 & 104.000462779322 & 21.9995372206776 \tabularnewline
18 & 131 & 125.998545677443 & 5.00145432255681 \tabularnewline
19 & 122 & 130.999669369052 & -8.99966936905238 \tabularnewline
20 & 116 & 122.000594940795 & -6.00059494079515 \tabularnewline
21 & 115 & 116.000396681098 & -1.00039668109784 \tabularnewline
22 & 115 & 115.000066133185 & -6.61331847453539e-05 \tabularnewline
23 & 113 & 115.000000004372 & -2.00000000437187 \tabularnewline
24 & 122 & 113.000132213923 & 8.999867786077 \tabularnewline
25 & 114 & 121.999405046088 & -7.99940504608809 \tabularnewline
26 & 106 & 114.000528816360 & -8.00052881636022 \tabularnewline
27 & 93 & 106.000528890649 & -13.0005288906492 \tabularnewline
28 & 89 & 93.000859425461 & -4.00085942546093 \tabularnewline
29 & 114 & 89.0002644846594 & 24.9997355153406 \tabularnewline
30 & 122 & 113.998347343450 & 8.00165265654952 \tabularnewline
31 & 115 & 121.999471035057 & -6.99947103505707 \tabularnewline
32 & 116 & 115.000462713761 & 0.999537286238791 \tabularnewline
33 & 120 & 115.999933923627 & 4.00006607637275 \tabularnewline
34 & 120 & 119.999735567786 & 0.000264432213512578 \tabularnewline
35 & 120 & 119.999999982519 & 1.74808150177341e-08 \tabularnewline
36 & 121 & 119.999999999999 & 1.00000000000115 \tabularnewline
37 & 118 & 120.999933893039 & -2.99993389303864 \tabularnewline
38 & 112 & 118.000198316514 & -6.00019831651392 \tabularnewline
39 & 99 & 112.000396654878 & -13.0003966548782 \tabularnewline
40 & 96 & 99.0008594167192 & -3.00085941671922 \tabularnewline
41 & 120 & 96.0001983776975 & 23.9998016223025 \tabularnewline
42 & 135 & 119.998413446042 & 15.0015865539583 \tabularnewline
43 & 128 & 134.999008290697 & -6.99900829069747 \tabularnewline
44 & 134 & 128.000462683171 & 5.99953731682942 \tabularnewline
45 & 134 & 133.999603388818 & 0.000396611181514572 \tabularnewline
46 & 132 & 133.999999973781 & -1.99999997378126 \tabularnewline
47 & 130 & 132.000132213921 & -2.00013221392098 \tabularnewline
48 & 125 & 130.000132222663 & -5.00013222266296 \tabularnewline
49 & 124 & 125.000330543548 & -1.00033054354759 \tabularnewline
50 & 114 & 124.000066128813 & -10.0000661288126 \tabularnewline
51 & 101 & 114.000661073985 & -13.0006610739851 \tabularnewline
52 & 101 & 101.000859434199 & -0.000859434199171005 \tabularnewline
53 & 123 & 101.000000056815 & 21.9999999431854 \tabularnewline
54 & 143 & 122.998545646854 & 20.001454353146 \tabularnewline
55 & 133 & 142.99867776463 & -9.99867776463009 \tabularnewline
56 & 136 & 133.000660982205 & 2.99933901779542 \tabularnewline
57 & 137 & 135.999801722811 & 1.00019827718853 \tabularnewline
58 & 135 & 136.999933879931 & -1.99993387993115 \tabularnewline
59 & 141 & 135.000132209552 & 5.99986779044829 \tabularnewline
60 & 136 & 140.999603366972 & -4.99960336697185 \tabularnewline
61 & 133 & 136.000330508587 & -3.00033050858656 \tabularnewline
62 & 124 & 133.000198342733 & -9.00019834273297 \tabularnewline
63 & 110 & 124.000594975764 & -14.000594975764 \tabularnewline
64 & 104 & 110.000925536791 & -6.00092553679096 \tabularnewline
65 & 130 & 104.000396702953 & 25.9996032970475 \tabularnewline
66 & 160 & 129.998281245230 & 30.0017187547703 \tabularnewline
67 & 142 & 159.998016677538 & -17.9980166775378 \tabularnewline
68 & 142 & 142.001189794193 & -0.00118979419292486 \tabularnewline
69 & 137 & 142.000000078654 & -5.00000007865367 \tabularnewline
70 & 135 & 137.000330534812 & -2.00033053481195 \tabularnewline
71 & 139 & 135.000132235773 & 3.99986776422665 \tabularnewline
72 & 135 & 138.999735580896 & -3.99973558089627 \tabularnewline
73 & 134 & 135.000264410365 & -1.00026441036547 \tabularnewline
74 & 120 & 134.000066124441 & -14.0000661244407 \tabularnewline
75 & 103 & 120.000925501830 & -17.0009255018302 \tabularnewline
76 & 101 & 103.001123879525 & -2.00112387952510 \tabularnewline
77 & 127 & 101.000132288219 & 25.9998677117810 \tabularnewline
78 & 159 & 126.99828122775 & 32.00171877225 \tabularnewline
79 & 141 & 158.997884463614 & -17.9978844636139 \tabularnewline
80 & 140 & 141.001189785453 & -1.00118978545265 \tabularnewline
81 & 135 & 140.000066185614 & -5.00006618561446 \tabularnewline
82 & 127 & 135.000330539182 & -8.0003305391821 \tabularnewline
83 & 130 & 127.000528877542 & 2.99947112245825 \tabularnewline
84 & 128 & 129.999801714078 & -1.99980171407842 \tabularnewline
85 & 126 & 128.000132200815 & -2.00013220081462 \tabularnewline
86 & 110 & 126.000132222662 & -16.0001322226621 \tabularnewline
87 & 101 & 110.001057720122 & -9.00105772012246 \tabularnewline
88 & 102 & 101.000595032575 & 0.999404967425164 \tabularnewline
89 & 129 & 101.999933932374 & 27.0000660676256 \tabularnewline
90 & 169 & 128.998215107676 & 40.001784892324 \tabularnewline
91 & 146 & 168.997355603552 & -22.9973556035521 \tabularnewline
92 & 145 & 146.001520285298 & -1.00152028529806 \tabularnewline
93 & 138 & 145.000066207463 & -7.00006620746279 \tabularnewline
94 & 123 & 138.000462753106 & -15.0004627531062 \tabularnewline
95 & 124 & 123.000991635011 & 0.999008364988512 \tabularnewline
96 & 137 & 123.999933958593 & 13.0000660414074 \tabularnewline
97 & 132 & 136.999140605137 & -4.99914060513663 \tabularnewline
98 & 112 & 132.000330477995 & -20.0003304779948 \tabularnewline
99 & 105 & 112.001322161074 & -7.00132216107394 \tabularnewline
100 & 106 & 105.000462836134 & 0.999537163866478 \tabularnewline
101 & 137 & 105.999933923635 & 31.0000660763647 \tabularnewline
102 & 175 & 136.99795067983 & 38.00204932017 \tabularnewline
103 & 151 & 174.997487799994 & -23.9974877999943 \tabularnewline
104 & 142 & 151.001586400999 & -9.00158640099855 \tabularnewline
105 & 140 & 142.000595067524 & -2.00059506752433 \tabularnewline
106 & 122 & 140.000132253261 & -18.0001322532608 \tabularnewline
107 & 127 & 122.001189934047 & 4.99881006595281 \tabularnewline
108 & 135 & 126.999669543856 & 8.00033045614383 \tabularnewline
109 & 128 & 134.999471122464 & -6.99947112246375 \tabularnewline
110 & 117 & 128.000462713767 & -11.0004627137670 \tabularnewline
111 & 107 & 117.000727207163 & -10.0007272071635 \tabularnewline
112 & 108 & 107.000661117687 & 0.999338882313026 \tabularnewline
113 & 134 & 107.999933936743 & 26.0000660632569 \tabularnewline
114 & 171 & 133.998281214638 & 37.0017187853624 \tabularnewline
115 & 154 & 170.997553928806 & -16.9975539288063 \tabularnewline
116 & 146 & 154.001123656641 & -8.00112365664063 \tabularnewline
117 & 148 & 146.000528929972 & 1.99947107002768 \tabularnewline
118 & 122 & 147.999867821043 & -25.9998678210433 \tabularnewline
119 & 124 & 122.001718772257 & 1.99828122774281 \tabularnewline
120 & 135 & 123.9998678997 & 11.0001321002999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79181&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]2[/C][C]135[/C][C]136[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]134[/C][C]135.000066106961[/C][C]-1.00006610696136[/C][/ROW]
[ROW][C]4[/C][C]132[/C][C]134.000066111331[/C][C]-2.00006611133148[/C][/ROW]
[ROW][C]5[/C][C]152[/C][C]132.000132218293[/C][C]19.9998677817069[/C][/ROW]
[ROW][C]6[/C][C]151[/C][C]151.998677869514[/C][C]-0.9986778695135[/C][/ROW]
[ROW][C]7[/C][C]136[/C][C]151.000066019559[/C][C]-15.0000660195593[/C][/ROW]
[ROW][C]8[/C][C]126[/C][C]136.000991608785[/C][C]-10.0009916087846[/C][/ROW]
[ROW][C]9[/C][C]127[/C][C]126.000661135166[/C][C]0.999338864834243[/C][/ROW]
[ROW][C]10[/C][C]127[/C][C]126.999933936744[/C][C]6.60632557156760e-05[/C][/ROW]
[ROW][C]11[/C][C]128[/C][C]126.999999995633[/C][C]1.00000000436724[/C][/ROW]
[ROW][C]12[/C][C]130[/C][C]127.999933893038[/C][C]2.00006610696164[/C][/ROW]
[ROW][C]13[/C][C]125[/C][C]129.999867781707[/C][C]-4.99986778170717[/C][/ROW]
[ROW][C]14[/C][C]118[/C][C]125.000330526066[/C][C]-7.00033052606621[/C][/ROW]
[ROW][C]15[/C][C]111[/C][C]118.000462770580[/C][C]-7.00046277057953[/C][/ROW]
[ROW][C]16[/C][C]104[/C][C]111.000462779322[/C][C]-7.00046277932181[/C][/ROW]
[ROW][C]17[/C][C]126[/C][C]104.000462779322[/C][C]21.9995372206776[/C][/ROW]
[ROW][C]18[/C][C]131[/C][C]125.998545677443[/C][C]5.00145432255681[/C][/ROW]
[ROW][C]19[/C][C]122[/C][C]130.999669369052[/C][C]-8.99966936905238[/C][/ROW]
[ROW][C]20[/C][C]116[/C][C]122.000594940795[/C][C]-6.00059494079515[/C][/ROW]
[ROW][C]21[/C][C]115[/C][C]116.000396681098[/C][C]-1.00039668109784[/C][/ROW]
[ROW][C]22[/C][C]115[/C][C]115.000066133185[/C][C]-6.61331847453539e-05[/C][/ROW]
[ROW][C]23[/C][C]113[/C][C]115.000000004372[/C][C]-2.00000000437187[/C][/ROW]
[ROW][C]24[/C][C]122[/C][C]113.000132213923[/C][C]8.999867786077[/C][/ROW]
[ROW][C]25[/C][C]114[/C][C]121.999405046088[/C][C]-7.99940504608809[/C][/ROW]
[ROW][C]26[/C][C]106[/C][C]114.000528816360[/C][C]-8.00052881636022[/C][/ROW]
[ROW][C]27[/C][C]93[/C][C]106.000528890649[/C][C]-13.0005288906492[/C][/ROW]
[ROW][C]28[/C][C]89[/C][C]93.000859425461[/C][C]-4.00085942546093[/C][/ROW]
[ROW][C]29[/C][C]114[/C][C]89.0002644846594[/C][C]24.9997355153406[/C][/ROW]
[ROW][C]30[/C][C]122[/C][C]113.998347343450[/C][C]8.00165265654952[/C][/ROW]
[ROW][C]31[/C][C]115[/C][C]121.999471035057[/C][C]-6.99947103505707[/C][/ROW]
[ROW][C]32[/C][C]116[/C][C]115.000462713761[/C][C]0.999537286238791[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]115.999933923627[/C][C]4.00006607637275[/C][/ROW]
[ROW][C]34[/C][C]120[/C][C]119.999735567786[/C][C]0.000264432213512578[/C][/ROW]
[ROW][C]35[/C][C]120[/C][C]119.999999982519[/C][C]1.74808150177341e-08[/C][/ROW]
[ROW][C]36[/C][C]121[/C][C]119.999999999999[/C][C]1.00000000000115[/C][/ROW]
[ROW][C]37[/C][C]118[/C][C]120.999933893039[/C][C]-2.99993389303864[/C][/ROW]
[ROW][C]38[/C][C]112[/C][C]118.000198316514[/C][C]-6.00019831651392[/C][/ROW]
[ROW][C]39[/C][C]99[/C][C]112.000396654878[/C][C]-13.0003966548782[/C][/ROW]
[ROW][C]40[/C][C]96[/C][C]99.0008594167192[/C][C]-3.00085941671922[/C][/ROW]
[ROW][C]41[/C][C]120[/C][C]96.0001983776975[/C][C]23.9998016223025[/C][/ROW]
[ROW][C]42[/C][C]135[/C][C]119.998413446042[/C][C]15.0015865539583[/C][/ROW]
[ROW][C]43[/C][C]128[/C][C]134.999008290697[/C][C]-6.99900829069747[/C][/ROW]
[ROW][C]44[/C][C]134[/C][C]128.000462683171[/C][C]5.99953731682942[/C][/ROW]
[ROW][C]45[/C][C]134[/C][C]133.999603388818[/C][C]0.000396611181514572[/C][/ROW]
[ROW][C]46[/C][C]132[/C][C]133.999999973781[/C][C]-1.99999997378126[/C][/ROW]
[ROW][C]47[/C][C]130[/C][C]132.000132213921[/C][C]-2.00013221392098[/C][/ROW]
[ROW][C]48[/C][C]125[/C][C]130.000132222663[/C][C]-5.00013222266296[/C][/ROW]
[ROW][C]49[/C][C]124[/C][C]125.000330543548[/C][C]-1.00033054354759[/C][/ROW]
[ROW][C]50[/C][C]114[/C][C]124.000066128813[/C][C]-10.0000661288126[/C][/ROW]
[ROW][C]51[/C][C]101[/C][C]114.000661073985[/C][C]-13.0006610739851[/C][/ROW]
[ROW][C]52[/C][C]101[/C][C]101.000859434199[/C][C]-0.000859434199171005[/C][/ROW]
[ROW][C]53[/C][C]123[/C][C]101.000000056815[/C][C]21.9999999431854[/C][/ROW]
[ROW][C]54[/C][C]143[/C][C]122.998545646854[/C][C]20.001454353146[/C][/ROW]
[ROW][C]55[/C][C]133[/C][C]142.99867776463[/C][C]-9.99867776463009[/C][/ROW]
[ROW][C]56[/C][C]136[/C][C]133.000660982205[/C][C]2.99933901779542[/C][/ROW]
[ROW][C]57[/C][C]137[/C][C]135.999801722811[/C][C]1.00019827718853[/C][/ROW]
[ROW][C]58[/C][C]135[/C][C]136.999933879931[/C][C]-1.99993387993115[/C][/ROW]
[ROW][C]59[/C][C]141[/C][C]135.000132209552[/C][C]5.99986779044829[/C][/ROW]
[ROW][C]60[/C][C]136[/C][C]140.999603366972[/C][C]-4.99960336697185[/C][/ROW]
[ROW][C]61[/C][C]133[/C][C]136.000330508587[/C][C]-3.00033050858656[/C][/ROW]
[ROW][C]62[/C][C]124[/C][C]133.000198342733[/C][C]-9.00019834273297[/C][/ROW]
[ROW][C]63[/C][C]110[/C][C]124.000594975764[/C][C]-14.000594975764[/C][/ROW]
[ROW][C]64[/C][C]104[/C][C]110.000925536791[/C][C]-6.00092553679096[/C][/ROW]
[ROW][C]65[/C][C]130[/C][C]104.000396702953[/C][C]25.9996032970475[/C][/ROW]
[ROW][C]66[/C][C]160[/C][C]129.998281245230[/C][C]30.0017187547703[/C][/ROW]
[ROW][C]67[/C][C]142[/C][C]159.998016677538[/C][C]-17.9980166775378[/C][/ROW]
[ROW][C]68[/C][C]142[/C][C]142.001189794193[/C][C]-0.00118979419292486[/C][/ROW]
[ROW][C]69[/C][C]137[/C][C]142.000000078654[/C][C]-5.00000007865367[/C][/ROW]
[ROW][C]70[/C][C]135[/C][C]137.000330534812[/C][C]-2.00033053481195[/C][/ROW]
[ROW][C]71[/C][C]139[/C][C]135.000132235773[/C][C]3.99986776422665[/C][/ROW]
[ROW][C]72[/C][C]135[/C][C]138.999735580896[/C][C]-3.99973558089627[/C][/ROW]
[ROW][C]73[/C][C]134[/C][C]135.000264410365[/C][C]-1.00026441036547[/C][/ROW]
[ROW][C]74[/C][C]120[/C][C]134.000066124441[/C][C]-14.0000661244407[/C][/ROW]
[ROW][C]75[/C][C]103[/C][C]120.000925501830[/C][C]-17.0009255018302[/C][/ROW]
[ROW][C]76[/C][C]101[/C][C]103.001123879525[/C][C]-2.00112387952510[/C][/ROW]
[ROW][C]77[/C][C]127[/C][C]101.000132288219[/C][C]25.9998677117810[/C][/ROW]
[ROW][C]78[/C][C]159[/C][C]126.99828122775[/C][C]32.00171877225[/C][/ROW]
[ROW][C]79[/C][C]141[/C][C]158.997884463614[/C][C]-17.9978844636139[/C][/ROW]
[ROW][C]80[/C][C]140[/C][C]141.001189785453[/C][C]-1.00118978545265[/C][/ROW]
[ROW][C]81[/C][C]135[/C][C]140.000066185614[/C][C]-5.00006618561446[/C][/ROW]
[ROW][C]82[/C][C]127[/C][C]135.000330539182[/C][C]-8.0003305391821[/C][/ROW]
[ROW][C]83[/C][C]130[/C][C]127.000528877542[/C][C]2.99947112245825[/C][/ROW]
[ROW][C]84[/C][C]128[/C][C]129.999801714078[/C][C]-1.99980171407842[/C][/ROW]
[ROW][C]85[/C][C]126[/C][C]128.000132200815[/C][C]-2.00013220081462[/C][/ROW]
[ROW][C]86[/C][C]110[/C][C]126.000132222662[/C][C]-16.0001322226621[/C][/ROW]
[ROW][C]87[/C][C]101[/C][C]110.001057720122[/C][C]-9.00105772012246[/C][/ROW]
[ROW][C]88[/C][C]102[/C][C]101.000595032575[/C][C]0.999404967425164[/C][/ROW]
[ROW][C]89[/C][C]129[/C][C]101.999933932374[/C][C]27.0000660676256[/C][/ROW]
[ROW][C]90[/C][C]169[/C][C]128.998215107676[/C][C]40.001784892324[/C][/ROW]
[ROW][C]91[/C][C]146[/C][C]168.997355603552[/C][C]-22.9973556035521[/C][/ROW]
[ROW][C]92[/C][C]145[/C][C]146.001520285298[/C][C]-1.00152028529806[/C][/ROW]
[ROW][C]93[/C][C]138[/C][C]145.000066207463[/C][C]-7.00006620746279[/C][/ROW]
[ROW][C]94[/C][C]123[/C][C]138.000462753106[/C][C]-15.0004627531062[/C][/ROW]
[ROW][C]95[/C][C]124[/C][C]123.000991635011[/C][C]0.999008364988512[/C][/ROW]
[ROW][C]96[/C][C]137[/C][C]123.999933958593[/C][C]13.0000660414074[/C][/ROW]
[ROW][C]97[/C][C]132[/C][C]136.999140605137[/C][C]-4.99914060513663[/C][/ROW]
[ROW][C]98[/C][C]112[/C][C]132.000330477995[/C][C]-20.0003304779948[/C][/ROW]
[ROW][C]99[/C][C]105[/C][C]112.001322161074[/C][C]-7.00132216107394[/C][/ROW]
[ROW][C]100[/C][C]106[/C][C]105.000462836134[/C][C]0.999537163866478[/C][/ROW]
[ROW][C]101[/C][C]137[/C][C]105.999933923635[/C][C]31.0000660763647[/C][/ROW]
[ROW][C]102[/C][C]175[/C][C]136.99795067983[/C][C]38.00204932017[/C][/ROW]
[ROW][C]103[/C][C]151[/C][C]174.997487799994[/C][C]-23.9974877999943[/C][/ROW]
[ROW][C]104[/C][C]142[/C][C]151.001586400999[/C][C]-9.00158640099855[/C][/ROW]
[ROW][C]105[/C][C]140[/C][C]142.000595067524[/C][C]-2.00059506752433[/C][/ROW]
[ROW][C]106[/C][C]122[/C][C]140.000132253261[/C][C]-18.0001322532608[/C][/ROW]
[ROW][C]107[/C][C]127[/C][C]122.001189934047[/C][C]4.99881006595281[/C][/ROW]
[ROW][C]108[/C][C]135[/C][C]126.999669543856[/C][C]8.00033045614383[/C][/ROW]
[ROW][C]109[/C][C]128[/C][C]134.999471122464[/C][C]-6.99947112246375[/C][/ROW]
[ROW][C]110[/C][C]117[/C][C]128.000462713767[/C][C]-11.0004627137670[/C][/ROW]
[ROW][C]111[/C][C]107[/C][C]117.000727207163[/C][C]-10.0007272071635[/C][/ROW]
[ROW][C]112[/C][C]108[/C][C]107.000661117687[/C][C]0.999338882313026[/C][/ROW]
[ROW][C]113[/C][C]134[/C][C]107.999933936743[/C][C]26.0000660632569[/C][/ROW]
[ROW][C]114[/C][C]171[/C][C]133.998281214638[/C][C]37.0017187853624[/C][/ROW]
[ROW][C]115[/C][C]154[/C][C]170.997553928806[/C][C]-16.9975539288063[/C][/ROW]
[ROW][C]116[/C][C]146[/C][C]154.001123656641[/C][C]-8.00112365664063[/C][/ROW]
[ROW][C]117[/C][C]148[/C][C]146.000528929972[/C][C]1.99947107002768[/C][/ROW]
[ROW][C]118[/C][C]122[/C][C]147.999867821043[/C][C]-25.9998678210433[/C][/ROW]
[ROW][C]119[/C][C]124[/C][C]122.001718772257[/C][C]1.99828122774281[/C][/ROW]
[ROW][C]120[/C][C]135[/C][C]123.9998678997[/C][C]11.0001321002999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79181&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
2135136-1
3134135.000066106961-1.00006610696136
4132134.000066111331-2.00006611133148
5152132.00013221829319.9998677817069
6151151.998677869514-0.9986778695135
7136151.000066019559-15.0000660195593
8126136.000991608785-10.0009916087846
9127126.0006611351660.999338864834243
10127126.9999339367446.60632557156760e-05
11128126.9999999956331.00000000436724
12130127.9999338930382.00006610696164
13125129.999867781707-4.99986778170717
14118125.000330526066-7.00033052606621
15111118.000462770580-7.00046277057953
16104111.000462779322-7.00046277932181
17126104.00046277932221.9995372206776
18131125.9985456774435.00145432255681
19122130.999669369052-8.99966936905238
20116122.000594940795-6.00059494079515
21115116.000396681098-1.00039668109784
22115115.000066133185-6.61331847453539e-05
23113115.000000004372-2.00000000437187
24122113.0001322139238.999867786077
25114121.999405046088-7.99940504608809
26106114.000528816360-8.00052881636022
2793106.000528890649-13.0005288906492
288993.000859425461-4.00085942546093
2911489.000264484659424.9997355153406
30122113.9983473434508.00165265654952
31115121.999471035057-6.99947103505707
32116115.0004627137610.999537286238791
33120115.9999339236274.00006607637275
34120119.9997355677860.000264432213512578
35120119.9999999825191.74808150177341e-08
36121119.9999999999991.00000000000115
37118120.999933893039-2.99993389303864
38112118.000198316514-6.00019831651392
3999112.000396654878-13.0003966548782
409699.0008594167192-3.00085941671922
4112096.000198377697523.9998016223025
42135119.99841344604215.0015865539583
43128134.999008290697-6.99900829069747
44134128.0004626831715.99953731682942
45134133.9996033888180.000396611181514572
46132133.999999973781-1.99999997378126
47130132.000132213921-2.00013221392098
48125130.000132222663-5.00013222266296
49124125.000330543548-1.00033054354759
50114124.000066128813-10.0000661288126
51101114.000661073985-13.0006610739851
52101101.000859434199-0.000859434199171005
53123101.00000005681521.9999999431854
54143122.99854564685420.001454353146
55133142.99867776463-9.99867776463009
56136133.0006609822052.99933901779542
57137135.9998017228111.00019827718853
58135136.999933879931-1.99993387993115
59141135.0001322095525.99986779044829
60136140.999603366972-4.99960336697185
61133136.000330508587-3.00033050858656
62124133.000198342733-9.00019834273297
63110124.000594975764-14.000594975764
64104110.000925536791-6.00092553679096
65130104.00039670295325.9996032970475
66160129.99828124523030.0017187547703
67142159.998016677538-17.9980166775378
68142142.001189794193-0.00118979419292486
69137142.000000078654-5.00000007865367
70135137.000330534812-2.00033053481195
71139135.0001322357733.99986776422665
72135138.999735580896-3.99973558089627
73134135.000264410365-1.00026441036547
74120134.000066124441-14.0000661244407
75103120.000925501830-17.0009255018302
76101103.001123879525-2.00112387952510
77127101.00013228821925.9998677117810
78159126.9982812277532.00171877225
79141158.997884463614-17.9978844636139
80140141.001189785453-1.00118978545265
81135140.000066185614-5.00006618561446
82127135.000330539182-8.0003305391821
83130127.0005288775422.99947112245825
84128129.999801714078-1.99980171407842
85126128.000132200815-2.00013220081462
86110126.000132222662-16.0001322226621
87101110.001057720122-9.00105772012246
88102101.0005950325750.999404967425164
89129101.99993393237427.0000660676256
90169128.99821510767640.001784892324
91146168.997355603552-22.9973556035521
92145146.001520285298-1.00152028529806
93138145.000066207463-7.00006620746279
94123138.000462753106-15.0004627531062
95124123.0009916350110.999008364988512
96137123.99993395859313.0000660414074
97132136.999140605137-4.99914060513663
98112132.000330477995-20.0003304779948
99105112.001322161074-7.00132216107394
100106105.0004628361340.999537163866478
101137105.99993392363531.0000660763647
102175136.9979506798338.00204932017
103151174.997487799994-23.9974877999943
104142151.001586400999-9.00158640099855
105140142.000595067524-2.00059506752433
106122140.000132253261-18.0001322532608
107127122.0011899340474.99881006595281
108135126.9996695438568.00033045614383
109128134.999471122464-6.99947112246375
110117128.000462713767-11.0004627137670
111107117.000727207163-10.0007272071635
112108107.0006611176870.999338882313026
113134107.99993393674326.0000660632569
114171133.99828121463837.0017187853624
115154170.997553928806-16.9975539288063
116146154.001123656641-8.00112365664063
117148146.0005289299721.99947107002768
118122147.999867821043-25.9998678210433
119124122.0017187722571.99828122774281
120135123.999867899711.0001321002999







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121134.999272814692108.768390807580161.230154821805
122134.99927281469297.904429861163172.094115768222
123134.99927281469289.5680547303954180.430490898989
124134.99927281469282.540109844827187.458435784558
125134.99927281469276.3483394685398193.650206160845
126134.99927281469270.7505359769087199.248009652476
127134.99927281469265.6028147773637204.395730852021
128134.99927281469260.8114261617354209.187119467649
129134.99927281469256.3112508934456213.687294735939
130134.99927281469252.0548757962406217.943669833144
131134.99927281469248.0065076003914221.992038028993
132134.99927281469244.1383384011259225.860207228259

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 134.999272814692 & 108.768390807580 & 161.230154821805 \tabularnewline
122 & 134.999272814692 & 97.904429861163 & 172.094115768222 \tabularnewline
123 & 134.999272814692 & 89.5680547303954 & 180.430490898989 \tabularnewline
124 & 134.999272814692 & 82.540109844827 & 187.458435784558 \tabularnewline
125 & 134.999272814692 & 76.3483394685398 & 193.650206160845 \tabularnewline
126 & 134.999272814692 & 70.7505359769087 & 199.248009652476 \tabularnewline
127 & 134.999272814692 & 65.6028147773637 & 204.395730852021 \tabularnewline
128 & 134.999272814692 & 60.8114261617354 & 209.187119467649 \tabularnewline
129 & 134.999272814692 & 56.3112508934456 & 213.687294735939 \tabularnewline
130 & 134.999272814692 & 52.0548757962406 & 217.943669833144 \tabularnewline
131 & 134.999272814692 & 48.0065076003914 & 221.992038028993 \tabularnewline
132 & 134.999272814692 & 44.1383384011259 & 225.860207228259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79181&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]134.999272814692[/C][C]108.768390807580[/C][C]161.230154821805[/C][/ROW]
[ROW][C]122[/C][C]134.999272814692[/C][C]97.904429861163[/C][C]172.094115768222[/C][/ROW]
[ROW][C]123[/C][C]134.999272814692[/C][C]89.5680547303954[/C][C]180.430490898989[/C][/ROW]
[ROW][C]124[/C][C]134.999272814692[/C][C]82.540109844827[/C][C]187.458435784558[/C][/ROW]
[ROW][C]125[/C][C]134.999272814692[/C][C]76.3483394685398[/C][C]193.650206160845[/C][/ROW]
[ROW][C]126[/C][C]134.999272814692[/C][C]70.7505359769087[/C][C]199.248009652476[/C][/ROW]
[ROW][C]127[/C][C]134.999272814692[/C][C]65.6028147773637[/C][C]204.395730852021[/C][/ROW]
[ROW][C]128[/C][C]134.999272814692[/C][C]60.8114261617354[/C][C]209.187119467649[/C][/ROW]
[ROW][C]129[/C][C]134.999272814692[/C][C]56.3112508934456[/C][C]213.687294735939[/C][/ROW]
[ROW][C]130[/C][C]134.999272814692[/C][C]52.0548757962406[/C][C]217.943669833144[/C][/ROW]
[ROW][C]131[/C][C]134.999272814692[/C][C]48.0065076003914[/C][C]221.992038028993[/C][/ROW]
[ROW][C]132[/C][C]134.999272814692[/C][C]44.1383384011259[/C][C]225.860207228259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79181&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79181&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
121134.999272814692108.768390807580161.230154821805
122134.99927281469297.904429861163172.094115768222
123134.99927281469289.5680547303954180.430490898989
124134.99927281469282.540109844827187.458435784558
125134.99927281469276.3483394685398193.650206160845
126134.99927281469270.7505359769087199.248009652476
127134.99927281469265.6028147773637204.395730852021
128134.99927281469260.8114261617354209.187119467649
129134.99927281469256.3112508934456213.687294735939
130134.99927281469252.0548757962406217.943669833144
131134.99927281469248.0065076003914221.992038028993
132134.99927281469244.1383384011259225.860207228259



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