Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 13:53:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl.htm/, Retrieved Fri, 10 May 2024 02:54:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41909, Retrieved Fri, 10 May 2024 02:54:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [prijs bier] [2009-06-05 17:03:14] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [Eigen reeks: prij...] [2009-06-05 19:53:01] [43452a058b5967e58219044a1f0127ad] [Current]
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Dataseries X:
0.58
0.58
0.59
0.6
0.6
0.61
0.62
0.61
0.62
0.62
0.62
0.63
0.63
0.63
0.63
0.63
0.63
0.63
0.63
0.64
0.63
0.63
0.63
0.63
0.63
0.64
0.65
0.65
0.65
0.65
0.65
0.66
0.65
0.66
0.66
0.66
0.66
0.68
0.69
0.7
0.71
0.71
0.7
0.7
0.7
0.7
0.71
0.7
0.7
0.7
0.69
0.7
0.69
0.69
0.69
0.7
0.7
0.71
0.71
0.71
0.72
0.73
0.74
0.74
0.74
0.74
0.75
0.75
0.76
0.76
0.76
0.76
0.76
0.77
0.77
0.78
0.78
0.78
0.78
0.78
0.78
0.78
0.8
0.8
0.8
0.81
0.81
0.81
0.8
0.81
0.81
0.81
0.8
0.82
0.83
0.83




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41909&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41909&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.886472179761465
beta0.0337932685980229
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.886472179761465 \tabularnewline
beta & 0.0337932685980229 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41909&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]0.886472179761465[/C][/ROW]
[ROW][C]beta[/C][C]0.0337932685980229[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41909&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
alpha0.886472179761465
beta0.0337932685980229
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.590.580.01
40.60.5891642897223680.0108357102776319
50.60.5993940164803080.00060598351969221
60.610.6005735283833150.00942647161668464
70.620.609854544450220.0101454555497803
80.610.620076845077982-0.0100768450779816
90.620.6120707688316520.00792923116834776
100.620.620264112576957-0.000264112576957021
110.620.621186373067169-0.00118637306716851
120.630.6212555353585430.00874446464145717
130.630.630390065112912-0.000390065112912064
140.630.63141540326519-0.00141540326519018
150.630.631489406728742-0.00148940672874154
160.630.631453190332364-0.00145319033236435
170.630.631405545842613-0.00140554584261288
180.630.631358031222423-0.00135803122242328
190.630.631311954731659-0.00131195473165857
200.640.6312674218124640.00873257818753559
210.630.640388687917373-0.0103886879173729
220.630.632248271810432-0.00224827181043219
230.630.631256757101923-0.00125675710192319
240.630.631106544186638-0.00110654418663758
250.630.63105634232723-0.00105634232722962
260.640.6310189983916790.00898100160832072
270.650.6401485226150930.009851477384907
280.650.650344818061202-0.000344818061202123
290.650.651492051614606-0.00149205161460575
300.650.651577597458647-0.00157759745864694
310.650.651540049532173-0.00154004953217313
320.660.6514896518536890.00851034814631113
330.650.660603594846032-0.0106035948460322
340.660.6524559094398210.0075440905601788
350.660.660621639028606-0.000621639028606125
360.660.661530054198104-0.00153005419810348
370.660.66158734907608-0.00158734907607960
380.680.6615463017518290.018453698248171
390.690.6798238989426330.0101761010573672
400.70.6910684798561010.00893152014389886
410.710.7014773341097580.00852266589024209
420.710.711779062175382-0.00177906217538160
430.70.712895299910973-0.0128952999109733
440.70.703771000327008-0.00377100032700795
450.70.702622171409816-0.00262217140981624
460.70.702413195522262-0.00241319552226182
470.710.7023171793478020.0076828206521975
480.70.711401153302326-0.0114011533023264
490.70.703226173283415-0.00322617328341501
500.70.702201439817833-0.00220143981783349
510.690.702019155985391-0.0120191559853908
520.70.6927736845400310.00722631545996899
530.690.700805265349972-0.0108052653499719
540.690.692528660323049-0.00252866032304933
550.690.691513284842829-0.00151328484282931
560.70.6913526783178440.00864732168215643
570.70.70045821282786-0.000458212827860405
580.710.7014782177262960.00852178227370437
590.710.710714023719756-0.000714023719755819
600.710.711741154781944-0.00174115478194403
610.720.7118056033200630.0081943966799366
620.730.720923119660530.00907688033947007
630.740.731094847434920.00890515256507995
640.740.741381113122175-0.00138111312217459
650.740.742507516724857-0.00250751672485694
660.740.742560277712423-0.0025602777124234
670.750.7424895698442250.00751043015577502
680.750.751571252729267-0.00157125272926661
690.760.7525552066993660.00744479330063397
700.760.76175465677435-0.00175465677435016
710.760.762746486399902-0.00274648639990160
720.760.76277681073222-0.00277681073222025
730.760.76269706904472-0.00269706904472
740.770.7626072206070920.00739277939290839
750.770.77168320606552-0.00168320606551986
760.780.7726631594563340.00733684054366612
770.780.781858921435934-0.00185892143593436
780.780.782847208925227-0.00284720892522661
790.780.782874113802748-0.00287411380274794
800.780.782791069024107-0.00279106902410720
810.780.782698029655867-0.00269802965586652
820.780.7826066427847-0.00260664278470057
830.80.782518181175460.0174818188245400
840.80.800761281135636-0.000761281135635894
850.80.802809574967513-0.00280957496751277
860.810.8029579474472080.007042052552792
870.810.81205047095595-0.00205047095595046
880.810.813021299797461-0.00302129979746135
890.80.813041007428625-0.0130410074286245
900.810.8037878562422090.006212143757791
910.810.811788183856672-0.00178818385667145
920.810.812642875359234-0.00264287535923347
930.80.812660734553821-0.0126607345538209
940.820.8034187652740250.0165812347259753
950.830.8205957088498780.00940429115012165
960.830.831692214008382-0.00169221400838204

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.59 & 0.58 & 0.01 \tabularnewline
4 & 0.6 & 0.589164289722368 & 0.0108357102776319 \tabularnewline
5 & 0.6 & 0.599394016480308 & 0.00060598351969221 \tabularnewline
6 & 0.61 & 0.600573528383315 & 0.00942647161668464 \tabularnewline
7 & 0.62 & 0.60985454445022 & 0.0101454555497803 \tabularnewline
8 & 0.61 & 0.620076845077982 & -0.0100768450779816 \tabularnewline
9 & 0.62 & 0.612070768831652 & 0.00792923116834776 \tabularnewline
10 & 0.62 & 0.620264112576957 & -0.000264112576957021 \tabularnewline
11 & 0.62 & 0.621186373067169 & -0.00118637306716851 \tabularnewline
12 & 0.63 & 0.621255535358543 & 0.00874446464145717 \tabularnewline
13 & 0.63 & 0.630390065112912 & -0.000390065112912064 \tabularnewline
14 & 0.63 & 0.63141540326519 & -0.00141540326519018 \tabularnewline
15 & 0.63 & 0.631489406728742 & -0.00148940672874154 \tabularnewline
16 & 0.63 & 0.631453190332364 & -0.00145319033236435 \tabularnewline
17 & 0.63 & 0.631405545842613 & -0.00140554584261288 \tabularnewline
18 & 0.63 & 0.631358031222423 & -0.00135803122242328 \tabularnewline
19 & 0.63 & 0.631311954731659 & -0.00131195473165857 \tabularnewline
20 & 0.64 & 0.631267421812464 & 0.00873257818753559 \tabularnewline
21 & 0.63 & 0.640388687917373 & -0.0103886879173729 \tabularnewline
22 & 0.63 & 0.632248271810432 & -0.00224827181043219 \tabularnewline
23 & 0.63 & 0.631256757101923 & -0.00125675710192319 \tabularnewline
24 & 0.63 & 0.631106544186638 & -0.00110654418663758 \tabularnewline
25 & 0.63 & 0.63105634232723 & -0.00105634232722962 \tabularnewline
26 & 0.64 & 0.631018998391679 & 0.00898100160832072 \tabularnewline
27 & 0.65 & 0.640148522615093 & 0.009851477384907 \tabularnewline
28 & 0.65 & 0.650344818061202 & -0.000344818061202123 \tabularnewline
29 & 0.65 & 0.651492051614606 & -0.00149205161460575 \tabularnewline
30 & 0.65 & 0.651577597458647 & -0.00157759745864694 \tabularnewline
31 & 0.65 & 0.651540049532173 & -0.00154004953217313 \tabularnewline
32 & 0.66 & 0.651489651853689 & 0.00851034814631113 \tabularnewline
33 & 0.65 & 0.660603594846032 & -0.0106035948460322 \tabularnewline
34 & 0.66 & 0.652455909439821 & 0.0075440905601788 \tabularnewline
35 & 0.66 & 0.660621639028606 & -0.000621639028606125 \tabularnewline
36 & 0.66 & 0.661530054198104 & -0.00153005419810348 \tabularnewline
37 & 0.66 & 0.66158734907608 & -0.00158734907607960 \tabularnewline
38 & 0.68 & 0.661546301751829 & 0.018453698248171 \tabularnewline
39 & 0.69 & 0.679823898942633 & 0.0101761010573672 \tabularnewline
40 & 0.7 & 0.691068479856101 & 0.00893152014389886 \tabularnewline
41 & 0.71 & 0.701477334109758 & 0.00852266589024209 \tabularnewline
42 & 0.71 & 0.711779062175382 & -0.00177906217538160 \tabularnewline
43 & 0.7 & 0.712895299910973 & -0.0128952999109733 \tabularnewline
44 & 0.7 & 0.703771000327008 & -0.00377100032700795 \tabularnewline
45 & 0.7 & 0.702622171409816 & -0.00262217140981624 \tabularnewline
46 & 0.7 & 0.702413195522262 & -0.00241319552226182 \tabularnewline
47 & 0.71 & 0.702317179347802 & 0.0076828206521975 \tabularnewline
48 & 0.7 & 0.711401153302326 & -0.0114011533023264 \tabularnewline
49 & 0.7 & 0.703226173283415 & -0.00322617328341501 \tabularnewline
50 & 0.7 & 0.702201439817833 & -0.00220143981783349 \tabularnewline
51 & 0.69 & 0.702019155985391 & -0.0120191559853908 \tabularnewline
52 & 0.7 & 0.692773684540031 & 0.00722631545996899 \tabularnewline
53 & 0.69 & 0.700805265349972 & -0.0108052653499719 \tabularnewline
54 & 0.69 & 0.692528660323049 & -0.00252866032304933 \tabularnewline
55 & 0.69 & 0.691513284842829 & -0.00151328484282931 \tabularnewline
56 & 0.7 & 0.691352678317844 & 0.00864732168215643 \tabularnewline
57 & 0.7 & 0.70045821282786 & -0.000458212827860405 \tabularnewline
58 & 0.71 & 0.701478217726296 & 0.00852178227370437 \tabularnewline
59 & 0.71 & 0.710714023719756 & -0.000714023719755819 \tabularnewline
60 & 0.71 & 0.711741154781944 & -0.00174115478194403 \tabularnewline
61 & 0.72 & 0.711805603320063 & 0.0081943966799366 \tabularnewline
62 & 0.73 & 0.72092311966053 & 0.00907688033947007 \tabularnewline
63 & 0.74 & 0.73109484743492 & 0.00890515256507995 \tabularnewline
64 & 0.74 & 0.741381113122175 & -0.00138111312217459 \tabularnewline
65 & 0.74 & 0.742507516724857 & -0.00250751672485694 \tabularnewline
66 & 0.74 & 0.742560277712423 & -0.0025602777124234 \tabularnewline
67 & 0.75 & 0.742489569844225 & 0.00751043015577502 \tabularnewline
68 & 0.75 & 0.751571252729267 & -0.00157125272926661 \tabularnewline
69 & 0.76 & 0.752555206699366 & 0.00744479330063397 \tabularnewline
70 & 0.76 & 0.76175465677435 & -0.00175465677435016 \tabularnewline
71 & 0.76 & 0.762746486399902 & -0.00274648639990160 \tabularnewline
72 & 0.76 & 0.76277681073222 & -0.00277681073222025 \tabularnewline
73 & 0.76 & 0.76269706904472 & -0.00269706904472 \tabularnewline
74 & 0.77 & 0.762607220607092 & 0.00739277939290839 \tabularnewline
75 & 0.77 & 0.77168320606552 & -0.00168320606551986 \tabularnewline
76 & 0.78 & 0.772663159456334 & 0.00733684054366612 \tabularnewline
77 & 0.78 & 0.781858921435934 & -0.00185892143593436 \tabularnewline
78 & 0.78 & 0.782847208925227 & -0.00284720892522661 \tabularnewline
79 & 0.78 & 0.782874113802748 & -0.00287411380274794 \tabularnewline
80 & 0.78 & 0.782791069024107 & -0.00279106902410720 \tabularnewline
81 & 0.78 & 0.782698029655867 & -0.00269802965586652 \tabularnewline
82 & 0.78 & 0.7826066427847 & -0.00260664278470057 \tabularnewline
83 & 0.8 & 0.78251818117546 & 0.0174818188245400 \tabularnewline
84 & 0.8 & 0.800761281135636 & -0.000761281135635894 \tabularnewline
85 & 0.8 & 0.802809574967513 & -0.00280957496751277 \tabularnewline
86 & 0.81 & 0.802957947447208 & 0.007042052552792 \tabularnewline
87 & 0.81 & 0.81205047095595 & -0.00205047095595046 \tabularnewline
88 & 0.81 & 0.813021299797461 & -0.00302129979746135 \tabularnewline
89 & 0.8 & 0.813041007428625 & -0.0130410074286245 \tabularnewline
90 & 0.81 & 0.803787856242209 & 0.006212143757791 \tabularnewline
91 & 0.81 & 0.811788183856672 & -0.00178818385667145 \tabularnewline
92 & 0.81 & 0.812642875359234 & -0.00264287535923347 \tabularnewline
93 & 0.8 & 0.812660734553821 & -0.0126607345538209 \tabularnewline
94 & 0.82 & 0.803418765274025 & 0.0165812347259753 \tabularnewline
95 & 0.83 & 0.820595708849878 & 0.00940429115012165 \tabularnewline
96 & 0.83 & 0.831692214008382 & -0.00169221400838204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41909&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]0.59[/C][C]0.58[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]0.6[/C][C]0.589164289722368[/C][C]0.0108357102776319[/C][/ROW]
[ROW][C]5[/C][C]0.6[/C][C]0.599394016480308[/C][C]0.00060598351969221[/C][/ROW]
[ROW][C]6[/C][C]0.61[/C][C]0.600573528383315[/C][C]0.00942647161668464[/C][/ROW]
[ROW][C]7[/C][C]0.62[/C][C]0.60985454445022[/C][C]0.0101454555497803[/C][/ROW]
[ROW][C]8[/C][C]0.61[/C][C]0.620076845077982[/C][C]-0.0100768450779816[/C][/ROW]
[ROW][C]9[/C][C]0.62[/C][C]0.612070768831652[/C][C]0.00792923116834776[/C][/ROW]
[ROW][C]10[/C][C]0.62[/C][C]0.620264112576957[/C][C]-0.000264112576957021[/C][/ROW]
[ROW][C]11[/C][C]0.62[/C][C]0.621186373067169[/C][C]-0.00118637306716851[/C][/ROW]
[ROW][C]12[/C][C]0.63[/C][C]0.621255535358543[/C][C]0.00874446464145717[/C][/ROW]
[ROW][C]13[/C][C]0.63[/C][C]0.630390065112912[/C][C]-0.000390065112912064[/C][/ROW]
[ROW][C]14[/C][C]0.63[/C][C]0.63141540326519[/C][C]-0.00141540326519018[/C][/ROW]
[ROW][C]15[/C][C]0.63[/C][C]0.631489406728742[/C][C]-0.00148940672874154[/C][/ROW]
[ROW][C]16[/C][C]0.63[/C][C]0.631453190332364[/C][C]-0.00145319033236435[/C][/ROW]
[ROW][C]17[/C][C]0.63[/C][C]0.631405545842613[/C][C]-0.00140554584261288[/C][/ROW]
[ROW][C]18[/C][C]0.63[/C][C]0.631358031222423[/C][C]-0.00135803122242328[/C][/ROW]
[ROW][C]19[/C][C]0.63[/C][C]0.631311954731659[/C][C]-0.00131195473165857[/C][/ROW]
[ROW][C]20[/C][C]0.64[/C][C]0.631267421812464[/C][C]0.00873257818753559[/C][/ROW]
[ROW][C]21[/C][C]0.63[/C][C]0.640388687917373[/C][C]-0.0103886879173729[/C][/ROW]
[ROW][C]22[/C][C]0.63[/C][C]0.632248271810432[/C][C]-0.00224827181043219[/C][/ROW]
[ROW][C]23[/C][C]0.63[/C][C]0.631256757101923[/C][C]-0.00125675710192319[/C][/ROW]
[ROW][C]24[/C][C]0.63[/C][C]0.631106544186638[/C][C]-0.00110654418663758[/C][/ROW]
[ROW][C]25[/C][C]0.63[/C][C]0.63105634232723[/C][C]-0.00105634232722962[/C][/ROW]
[ROW][C]26[/C][C]0.64[/C][C]0.631018998391679[/C][C]0.00898100160832072[/C][/ROW]
[ROW][C]27[/C][C]0.65[/C][C]0.640148522615093[/C][C]0.009851477384907[/C][/ROW]
[ROW][C]28[/C][C]0.65[/C][C]0.650344818061202[/C][C]-0.000344818061202123[/C][/ROW]
[ROW][C]29[/C][C]0.65[/C][C]0.651492051614606[/C][C]-0.00149205161460575[/C][/ROW]
[ROW][C]30[/C][C]0.65[/C][C]0.651577597458647[/C][C]-0.00157759745864694[/C][/ROW]
[ROW][C]31[/C][C]0.65[/C][C]0.651540049532173[/C][C]-0.00154004953217313[/C][/ROW]
[ROW][C]32[/C][C]0.66[/C][C]0.651489651853689[/C][C]0.00851034814631113[/C][/ROW]
[ROW][C]33[/C][C]0.65[/C][C]0.660603594846032[/C][C]-0.0106035948460322[/C][/ROW]
[ROW][C]34[/C][C]0.66[/C][C]0.652455909439821[/C][C]0.0075440905601788[/C][/ROW]
[ROW][C]35[/C][C]0.66[/C][C]0.660621639028606[/C][C]-0.000621639028606125[/C][/ROW]
[ROW][C]36[/C][C]0.66[/C][C]0.661530054198104[/C][C]-0.00153005419810348[/C][/ROW]
[ROW][C]37[/C][C]0.66[/C][C]0.66158734907608[/C][C]-0.00158734907607960[/C][/ROW]
[ROW][C]38[/C][C]0.68[/C][C]0.661546301751829[/C][C]0.018453698248171[/C][/ROW]
[ROW][C]39[/C][C]0.69[/C][C]0.679823898942633[/C][C]0.0101761010573672[/C][/ROW]
[ROW][C]40[/C][C]0.7[/C][C]0.691068479856101[/C][C]0.00893152014389886[/C][/ROW]
[ROW][C]41[/C][C]0.71[/C][C]0.701477334109758[/C][C]0.00852266589024209[/C][/ROW]
[ROW][C]42[/C][C]0.71[/C][C]0.711779062175382[/C][C]-0.00177906217538160[/C][/ROW]
[ROW][C]43[/C][C]0.7[/C][C]0.712895299910973[/C][C]-0.0128952999109733[/C][/ROW]
[ROW][C]44[/C][C]0.7[/C][C]0.703771000327008[/C][C]-0.00377100032700795[/C][/ROW]
[ROW][C]45[/C][C]0.7[/C][C]0.702622171409816[/C][C]-0.00262217140981624[/C][/ROW]
[ROW][C]46[/C][C]0.7[/C][C]0.702413195522262[/C][C]-0.00241319552226182[/C][/ROW]
[ROW][C]47[/C][C]0.71[/C][C]0.702317179347802[/C][C]0.0076828206521975[/C][/ROW]
[ROW][C]48[/C][C]0.7[/C][C]0.711401153302326[/C][C]-0.0114011533023264[/C][/ROW]
[ROW][C]49[/C][C]0.7[/C][C]0.703226173283415[/C][C]-0.00322617328341501[/C][/ROW]
[ROW][C]50[/C][C]0.7[/C][C]0.702201439817833[/C][C]-0.00220143981783349[/C][/ROW]
[ROW][C]51[/C][C]0.69[/C][C]0.702019155985391[/C][C]-0.0120191559853908[/C][/ROW]
[ROW][C]52[/C][C]0.7[/C][C]0.692773684540031[/C][C]0.00722631545996899[/C][/ROW]
[ROW][C]53[/C][C]0.69[/C][C]0.700805265349972[/C][C]-0.0108052653499719[/C][/ROW]
[ROW][C]54[/C][C]0.69[/C][C]0.692528660323049[/C][C]-0.00252866032304933[/C][/ROW]
[ROW][C]55[/C][C]0.69[/C][C]0.691513284842829[/C][C]-0.00151328484282931[/C][/ROW]
[ROW][C]56[/C][C]0.7[/C][C]0.691352678317844[/C][C]0.00864732168215643[/C][/ROW]
[ROW][C]57[/C][C]0.7[/C][C]0.70045821282786[/C][C]-0.000458212827860405[/C][/ROW]
[ROW][C]58[/C][C]0.71[/C][C]0.701478217726296[/C][C]0.00852178227370437[/C][/ROW]
[ROW][C]59[/C][C]0.71[/C][C]0.710714023719756[/C][C]-0.000714023719755819[/C][/ROW]
[ROW][C]60[/C][C]0.71[/C][C]0.711741154781944[/C][C]-0.00174115478194403[/C][/ROW]
[ROW][C]61[/C][C]0.72[/C][C]0.711805603320063[/C][C]0.0081943966799366[/C][/ROW]
[ROW][C]62[/C][C]0.73[/C][C]0.72092311966053[/C][C]0.00907688033947007[/C][/ROW]
[ROW][C]63[/C][C]0.74[/C][C]0.73109484743492[/C][C]0.00890515256507995[/C][/ROW]
[ROW][C]64[/C][C]0.74[/C][C]0.741381113122175[/C][C]-0.00138111312217459[/C][/ROW]
[ROW][C]65[/C][C]0.74[/C][C]0.742507516724857[/C][C]-0.00250751672485694[/C][/ROW]
[ROW][C]66[/C][C]0.74[/C][C]0.742560277712423[/C][C]-0.0025602777124234[/C][/ROW]
[ROW][C]67[/C][C]0.75[/C][C]0.742489569844225[/C][C]0.00751043015577502[/C][/ROW]
[ROW][C]68[/C][C]0.75[/C][C]0.751571252729267[/C][C]-0.00157125272926661[/C][/ROW]
[ROW][C]69[/C][C]0.76[/C][C]0.752555206699366[/C][C]0.00744479330063397[/C][/ROW]
[ROW][C]70[/C][C]0.76[/C][C]0.76175465677435[/C][C]-0.00175465677435016[/C][/ROW]
[ROW][C]71[/C][C]0.76[/C][C]0.762746486399902[/C][C]-0.00274648639990160[/C][/ROW]
[ROW][C]72[/C][C]0.76[/C][C]0.76277681073222[/C][C]-0.00277681073222025[/C][/ROW]
[ROW][C]73[/C][C]0.76[/C][C]0.76269706904472[/C][C]-0.00269706904472[/C][/ROW]
[ROW][C]74[/C][C]0.77[/C][C]0.762607220607092[/C][C]0.00739277939290839[/C][/ROW]
[ROW][C]75[/C][C]0.77[/C][C]0.77168320606552[/C][C]-0.00168320606551986[/C][/ROW]
[ROW][C]76[/C][C]0.78[/C][C]0.772663159456334[/C][C]0.00733684054366612[/C][/ROW]
[ROW][C]77[/C][C]0.78[/C][C]0.781858921435934[/C][C]-0.00185892143593436[/C][/ROW]
[ROW][C]78[/C][C]0.78[/C][C]0.782847208925227[/C][C]-0.00284720892522661[/C][/ROW]
[ROW][C]79[/C][C]0.78[/C][C]0.782874113802748[/C][C]-0.00287411380274794[/C][/ROW]
[ROW][C]80[/C][C]0.78[/C][C]0.782791069024107[/C][C]-0.00279106902410720[/C][/ROW]
[ROW][C]81[/C][C]0.78[/C][C]0.782698029655867[/C][C]-0.00269802965586652[/C][/ROW]
[ROW][C]82[/C][C]0.78[/C][C]0.7826066427847[/C][C]-0.00260664278470057[/C][/ROW]
[ROW][C]83[/C][C]0.8[/C][C]0.78251818117546[/C][C]0.0174818188245400[/C][/ROW]
[ROW][C]84[/C][C]0.8[/C][C]0.800761281135636[/C][C]-0.000761281135635894[/C][/ROW]
[ROW][C]85[/C][C]0.8[/C][C]0.802809574967513[/C][C]-0.00280957496751277[/C][/ROW]
[ROW][C]86[/C][C]0.81[/C][C]0.802957947447208[/C][C]0.007042052552792[/C][/ROW]
[ROW][C]87[/C][C]0.81[/C][C]0.81205047095595[/C][C]-0.00205047095595046[/C][/ROW]
[ROW][C]88[/C][C]0.81[/C][C]0.813021299797461[/C][C]-0.00302129979746135[/C][/ROW]
[ROW][C]89[/C][C]0.8[/C][C]0.813041007428625[/C][C]-0.0130410074286245[/C][/ROW]
[ROW][C]90[/C][C]0.81[/C][C]0.803787856242209[/C][C]0.006212143757791[/C][/ROW]
[ROW][C]91[/C][C]0.81[/C][C]0.811788183856672[/C][C]-0.00178818385667145[/C][/ROW]
[ROW][C]92[/C][C]0.81[/C][C]0.812642875359234[/C][C]-0.00264287535923347[/C][/ROW]
[ROW][C]93[/C][C]0.8[/C][C]0.812660734553821[/C][C]-0.0126607345538209[/C][/ROW]
[ROW][C]94[/C][C]0.82[/C][C]0.803418765274025[/C][C]0.0165812347259753[/C][/ROW]
[ROW][C]95[/C][C]0.83[/C][C]0.820595708849878[/C][C]0.00940429115012165[/C][/ROW]
[ROW][C]96[/C][C]0.83[/C][C]0.831692214008382[/C][C]-0.00169221400838204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41909&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41909&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
30.590.580.01
40.60.5891642897223680.0108357102776319
50.60.5993940164803080.00060598351969221
60.610.6005735283833150.00942647161668464
70.620.609854544450220.0101454555497803
80.610.620076845077982-0.0100768450779816
90.620.6120707688316520.00792923116834776
100.620.620264112576957-0.000264112576957021
110.620.621186373067169-0.00118637306716851
120.630.6212555353585430.00874446464145717
130.630.630390065112912-0.000390065112912064
140.630.63141540326519-0.00141540326519018
150.630.631489406728742-0.00148940672874154
160.630.631453190332364-0.00145319033236435
170.630.631405545842613-0.00140554584261288
180.630.631358031222423-0.00135803122242328
190.630.631311954731659-0.00131195473165857
200.640.6312674218124640.00873257818753559
210.630.640388687917373-0.0103886879173729
220.630.632248271810432-0.00224827181043219
230.630.631256757101923-0.00125675710192319
240.630.631106544186638-0.00110654418663758
250.630.63105634232723-0.00105634232722962
260.640.6310189983916790.00898100160832072
270.650.6401485226150930.009851477384907
280.650.650344818061202-0.000344818061202123
290.650.651492051614606-0.00149205161460575
300.650.651577597458647-0.00157759745864694
310.650.651540049532173-0.00154004953217313
320.660.6514896518536890.00851034814631113
330.650.660603594846032-0.0106035948460322
340.660.6524559094398210.0075440905601788
350.660.660621639028606-0.000621639028606125
360.660.661530054198104-0.00153005419810348
370.660.66158734907608-0.00158734907607960
380.680.6615463017518290.018453698248171
390.690.6798238989426330.0101761010573672
400.70.6910684798561010.00893152014389886
410.710.7014773341097580.00852266589024209
420.710.711779062175382-0.00177906217538160
430.70.712895299910973-0.0128952999109733
440.70.703771000327008-0.00377100032700795
450.70.702622171409816-0.00262217140981624
460.70.702413195522262-0.00241319552226182
470.710.7023171793478020.0076828206521975
480.70.711401153302326-0.0114011533023264
490.70.703226173283415-0.00322617328341501
500.70.702201439817833-0.00220143981783349
510.690.702019155985391-0.0120191559853908
520.70.6927736845400310.00722631545996899
530.690.700805265349972-0.0108052653499719
540.690.692528660323049-0.00252866032304933
550.690.691513284842829-0.00151328484282931
560.70.6913526783178440.00864732168215643
570.70.70045821282786-0.000458212827860405
580.710.7014782177262960.00852178227370437
590.710.710714023719756-0.000714023719755819
600.710.711741154781944-0.00174115478194403
610.720.7118056033200630.0081943966799366
620.730.720923119660530.00907688033947007
630.740.731094847434920.00890515256507995
640.740.741381113122175-0.00138111312217459
650.740.742507516724857-0.00250751672485694
660.740.742560277712423-0.0025602777124234
670.750.7424895698442250.00751043015577502
680.750.751571252729267-0.00157125272926661
690.760.7525552066993660.00744479330063397
700.760.76175465677435-0.00175465677435016
710.760.762746486399902-0.00274648639990160
720.760.76277681073222-0.00277681073222025
730.760.76269706904472-0.00269706904472
740.770.7626072206070920.00739277939290839
750.770.77168320606552-0.00168320606551986
760.780.7726631594563340.00733684054366612
770.780.781858921435934-0.00185892143593436
780.780.782847208925227-0.00284720892522661
790.780.782874113802748-0.00287411380274794
800.780.782791069024107-0.00279106902410720
810.780.782698029655867-0.00269802965586652
820.780.7826066427847-0.00260664278470057
830.80.782518181175460.0174818188245400
840.80.800761281135636-0.000761281135635894
850.80.802809574967513-0.00280957496751277
860.810.8029579474472080.007042052552792
870.810.81205047095595-0.00205047095595046
880.810.813021299797461-0.00302129979746135
890.80.813041007428625-0.0130410074286245
900.810.8037878562422090.006212143757791
910.810.811788183856672-0.00178818385667145
920.810.812642875359234-0.00264287535923347
930.80.812660734553821-0.0126607345538209
940.820.8034187652740250.0165812347259753
950.830.8205957088498780.00940429115012165
960.830.831692214008382-0.00169221400838204







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
970.832901282747420.8195255526749470.846277012819892
980.835610452127090.8174675078157440.853753396438437
990.8383196215067610.8161970855819570.860442157431566
1000.8410287908864320.8153392644473210.866718317325543
1010.8437379602661030.8147358386477740.872740081884432
1020.8464471296457740.8143030543572370.87859120493431
1030.8491562990254450.8139905709176230.884322027133266
1040.8518654684051160.8137655374173320.8899653993929
1050.8545746377847860.8136052393118740.895544036257699
1060.8572838071644570.8134932813107580.901074333018157
1070.8599929765441280.8134174305728480.906568522515408
1080.8627021459237990.8133683166938950.912035975153703

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 0.83290128274742 & 0.819525552674947 & 0.846277012819892 \tabularnewline
98 & 0.83561045212709 & 0.817467507815744 & 0.853753396438437 \tabularnewline
99 & 0.838319621506761 & 0.816197085581957 & 0.860442157431566 \tabularnewline
100 & 0.841028790886432 & 0.815339264447321 & 0.866718317325543 \tabularnewline
101 & 0.843737960266103 & 0.814735838647774 & 0.872740081884432 \tabularnewline
102 & 0.846447129645774 & 0.814303054357237 & 0.87859120493431 \tabularnewline
103 & 0.849156299025445 & 0.813990570917623 & 0.884322027133266 \tabularnewline
104 & 0.851865468405116 & 0.813765537417332 & 0.8899653993929 \tabularnewline
105 & 0.854574637784786 & 0.813605239311874 & 0.895544036257699 \tabularnewline
106 & 0.857283807164457 & 0.813493281310758 & 0.901074333018157 \tabularnewline
107 & 0.859992976544128 & 0.813417430572848 & 0.906568522515408 \tabularnewline
108 & 0.862702145923799 & 0.813368316693895 & 0.912035975153703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41909&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]97[/C][C]0.83290128274742[/C][C]0.819525552674947[/C][C]0.846277012819892[/C][/ROW]
[ROW][C]98[/C][C]0.83561045212709[/C][C]0.817467507815744[/C][C]0.853753396438437[/C][/ROW]
[ROW][C]99[/C][C]0.838319621506761[/C][C]0.816197085581957[/C][C]0.860442157431566[/C][/ROW]
[ROW][C]100[/C][C]0.841028790886432[/C][C]0.815339264447321[/C][C]0.866718317325543[/C][/ROW]
[ROW][C]101[/C][C]0.843737960266103[/C][C]0.814735838647774[/C][C]0.872740081884432[/C][/ROW]
[ROW][C]102[/C][C]0.846447129645774[/C][C]0.814303054357237[/C][C]0.87859120493431[/C][/ROW]
[ROW][C]103[/C][C]0.849156299025445[/C][C]0.813990570917623[/C][C]0.884322027133266[/C][/ROW]
[ROW][C]104[/C][C]0.851865468405116[/C][C]0.813765537417332[/C][C]0.8899653993929[/C][/ROW]
[ROW][C]105[/C][C]0.854574637784786[/C][C]0.813605239311874[/C][C]0.895544036257699[/C][/ROW]
[ROW][C]106[/C][C]0.857283807164457[/C][C]0.813493281310758[/C][C]0.901074333018157[/C][/ROW]
[ROW][C]107[/C][C]0.859992976544128[/C][C]0.813417430572848[/C][C]0.906568522515408[/C][/ROW]
[ROW][C]108[/C][C]0.862702145923799[/C][C]0.813368316693895[/C][C]0.912035975153703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41909&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41909&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
970.832901282747420.8195255526749470.846277012819892
980.835610452127090.8174675078157440.853753396438437
990.8383196215067610.8161970855819570.860442157431566
1000.8410287908864320.8153392644473210.866718317325543
1010.8437379602661030.8147358386477740.872740081884432
1020.8464471296457740.8143030543572370.87859120493431
1030.8491562990254450.8139905709176230.884322027133266
1040.8518654684051160.8137655374173320.8899653993929
1050.8545746377847860.8136052393118740.895544036257699
1060.8572838071644570.8134932813107580.901074333018157
1070.8599929765441280.8134174305728480.906568522515408
1080.8627021459237990.8133683166938950.912035975153703



Parameters (Session):
par1 = 12 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')