Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 14:07:03 +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/2014/Nov/29/t141727007196l0bpppv2ivj0i.htm/, Retrieved Fri, 17 May 2024 03:20:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261125, Retrieved Fri, 17 May 2024 03:20:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Werkloze beroepsb...] [2014-11-29 14:07:03] [30b408b6447afc100cbee3b5fe745b69] [Current]
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Dataseries X:
82
80
76
73
70
68
67
64
69
69
67
57
67
69
67
66
65
56
57
53
58
59
60
59
65
62
61
62
57
51
45
46
48
49
48
43
51
54
57
60
58
61
62
62
64
68
70
73
79
84
82
78
78
76
73
71
71
70
74
72
80
80
80
79
82
71
75
74
76
82
85
82
92
93
93
99
98
89
96
94
99
108
113
115
126
131
134
134
137
139
139
134
133
135
130
133




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' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261125&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261125&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99995515545583
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99995515545583 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261125&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]0.99995515545583[/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=261125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261125&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
alpha0.99995515545583
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
28082-2
37680.0000896890883-4.00008968908834
47376.0001793821987-3.00017938219874
57073.0001345416768-3.00013454167683
66870.000134539666-2.00013453966596
76768.0000896951217-1.00008969512172
86467.0000448485665-3.0000448485665
96964.00013453564374.99986546435628
106968.99977578331230.000224216687669809
116768.9999999899451-1.9999999899451
125767.0000896890879-10.0000896890879
136757.00044844946389.99955155053624
146966.99955157466882.00044842533119
156768.9999102908022-1.99991029080222
166667.0000896850654-1.00008968506536
176566.0000448485661-1.00004484856606
185665.0000448465554-9.00004484655538
195756.00040360290860.999596397091352
205356.9999551735552-3.99995517355522
215853.00017937616654.99982062383355
225957.99977578532321.00022421467681
236058.9999551454011.00004485459898
245959.9999551534443-0.99995515344434
256559.0000448425335.99995515746696
266264.9997309347459-2.99973093474593
276162.0001345215664-1.0001345215664
286261.00004485057670.999955149423272
295761.9999551574671-4.99995515746713
305157.0002242207099-6.0002242207099
314551.0002690773201-6.00026907732009
324645.00026907933170.999730920668334
334845.99995516752262.00004483247744
344947.99991030890121.00008969109883
354848.9999551514337-0.999955151433674
364348.000044842533-5.00004484253296
375143.00022422473187.99977577526821
385450.99964125370193.0003587462981
395753.99986545027973.00013454972032
406056.99986546033373.00013453966633
415859.9998654603341-1.99986546033412
426158.0000896830552.99991031694503
436260.99986547038931.00013452961071
446261.99995514942294.48505770833663e-05
456461.99999999798872.0000000020113
466863.99991031091164.00008968908843
477067.99982061780132.00017938219874
487369.99991030286733.00008969713265
497972.99986546234516.00013453765493
508478.99973092670175.0002690732983
518283.9997757652127-1.99977576521269
527882.0000896790326-4.00008967903264
537878.0001793821983-0.000179382198282951
547678.0000000080443-2.00000000804431
557376.0000896890887-3.0000896890887
567173.0001345376546-2.00013453765457
577171.0000896951216-8.96951216162734e-05
587071.0000000040223-1.00000000402233
597470.00004484454433.99995515545565
607273.9998206238344-1.99982062383435
618072.00008968104437.9999103189557
628079.99964124766840.000358752331649725
638079.99999998391191.60880802013708e-08
647979.9999999999993-0.999999999999289
658279.00004484454422.99995515545584
667181.9998654683785-10.9998654683785
677571.00049328395283.99950671604715
687474.9998206439444-0.999820643944417
697674.0000448365011.99995516349897
708275.99991031292236.00008968707768
718581.9997309287133.00026907128699
728284.9998654543011-2.9998654543011
739282.00013452759899.99986547240113
749391.99955156059111.00044843940887
759392.99995513534584.48646542281494e-05
769992.99999999798816.00000000201193
779898.9997309327349-0.999730932734892
788998.000044832478-9.00004483247797
799689.0004036029086.99959639709198
809495.9996861062902-1.9996861062902
819994.00008967501194.99991032498808
8210898.99977578130069.00022421869942
83113107.9995963890475.0004036109525
84115112.9997757591792.0002242408206
85126114.99991030085611.0000896991443
86131125.9995067059925.00049329400838
87134130.9997757551583.0002242448424
88134133.9998654563110.000134543688659505
89137133.9999999939663.00000000603356
90139136.9998654663672.00013453363277
91139138.9999103048798.96951214315322e-05
92134138.999999995978-4.99999999597765
93133134.000224222721-1.00022422272068
94135133.0000448545991.99995514540069
95130134.999910312923-4.99991031292313
96133130.0002242186992.99977578130114

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 80 & 82 & -2 \tabularnewline
3 & 76 & 80.0000896890883 & -4.00008968908834 \tabularnewline
4 & 73 & 76.0001793821987 & -3.00017938219874 \tabularnewline
5 & 70 & 73.0001345416768 & -3.00013454167683 \tabularnewline
6 & 68 & 70.000134539666 & -2.00013453966596 \tabularnewline
7 & 67 & 68.0000896951217 & -1.00008969512172 \tabularnewline
8 & 64 & 67.0000448485665 & -3.0000448485665 \tabularnewline
9 & 69 & 64.0001345356437 & 4.99986546435628 \tabularnewline
10 & 69 & 68.9997757833123 & 0.000224216687669809 \tabularnewline
11 & 67 & 68.9999999899451 & -1.9999999899451 \tabularnewline
12 & 57 & 67.0000896890879 & -10.0000896890879 \tabularnewline
13 & 67 & 57.0004484494638 & 9.99955155053624 \tabularnewline
14 & 69 & 66.9995515746688 & 2.00044842533119 \tabularnewline
15 & 67 & 68.9999102908022 & -1.99991029080222 \tabularnewline
16 & 66 & 67.0000896850654 & -1.00008968506536 \tabularnewline
17 & 65 & 66.0000448485661 & -1.00004484856606 \tabularnewline
18 & 56 & 65.0000448465554 & -9.00004484655538 \tabularnewline
19 & 57 & 56.0004036029086 & 0.999596397091352 \tabularnewline
20 & 53 & 56.9999551735552 & -3.99995517355522 \tabularnewline
21 & 58 & 53.0001793761665 & 4.99982062383355 \tabularnewline
22 & 59 & 57.9997757853232 & 1.00022421467681 \tabularnewline
23 & 60 & 58.999955145401 & 1.00004485459898 \tabularnewline
24 & 59 & 59.9999551534443 & -0.99995515344434 \tabularnewline
25 & 65 & 59.000044842533 & 5.99995515746696 \tabularnewline
26 & 62 & 64.9997309347459 & -2.99973093474593 \tabularnewline
27 & 61 & 62.0001345215664 & -1.0001345215664 \tabularnewline
28 & 62 & 61.0000448505767 & 0.999955149423272 \tabularnewline
29 & 57 & 61.9999551574671 & -4.99995515746713 \tabularnewline
30 & 51 & 57.0002242207099 & -6.0002242207099 \tabularnewline
31 & 45 & 51.0002690773201 & -6.00026907732009 \tabularnewline
32 & 46 & 45.0002690793317 & 0.999730920668334 \tabularnewline
33 & 48 & 45.9999551675226 & 2.00004483247744 \tabularnewline
34 & 49 & 47.9999103089012 & 1.00008969109883 \tabularnewline
35 & 48 & 48.9999551514337 & -0.999955151433674 \tabularnewline
36 & 43 & 48.000044842533 & -5.00004484253296 \tabularnewline
37 & 51 & 43.0002242247318 & 7.99977577526821 \tabularnewline
38 & 54 & 50.9996412537019 & 3.0003587462981 \tabularnewline
39 & 57 & 53.9998654502797 & 3.00013454972032 \tabularnewline
40 & 60 & 56.9998654603337 & 3.00013453966633 \tabularnewline
41 & 58 & 59.9998654603341 & -1.99986546033412 \tabularnewline
42 & 61 & 58.000089683055 & 2.99991031694503 \tabularnewline
43 & 62 & 60.9998654703893 & 1.00013452961071 \tabularnewline
44 & 62 & 61.9999551494229 & 4.48505770833663e-05 \tabularnewline
45 & 64 & 61.9999999979887 & 2.0000000020113 \tabularnewline
46 & 68 & 63.9999103109116 & 4.00008968908843 \tabularnewline
47 & 70 & 67.9998206178013 & 2.00017938219874 \tabularnewline
48 & 73 & 69.9999103028673 & 3.00008969713265 \tabularnewline
49 & 79 & 72.9998654623451 & 6.00013453765493 \tabularnewline
50 & 84 & 78.9997309267017 & 5.0002690732983 \tabularnewline
51 & 82 & 83.9997757652127 & -1.99977576521269 \tabularnewline
52 & 78 & 82.0000896790326 & -4.00008967903264 \tabularnewline
53 & 78 & 78.0001793821983 & -0.000179382198282951 \tabularnewline
54 & 76 & 78.0000000080443 & -2.00000000804431 \tabularnewline
55 & 73 & 76.0000896890887 & -3.0000896890887 \tabularnewline
56 & 71 & 73.0001345376546 & -2.00013453765457 \tabularnewline
57 & 71 & 71.0000896951216 & -8.96951216162734e-05 \tabularnewline
58 & 70 & 71.0000000040223 & -1.00000000402233 \tabularnewline
59 & 74 & 70.0000448445443 & 3.99995515545565 \tabularnewline
60 & 72 & 73.9998206238344 & -1.99982062383435 \tabularnewline
61 & 80 & 72.0000896810443 & 7.9999103189557 \tabularnewline
62 & 80 & 79.9996412476684 & 0.000358752331649725 \tabularnewline
63 & 80 & 79.9999999839119 & 1.60880802013708e-08 \tabularnewline
64 & 79 & 79.9999999999993 & -0.999999999999289 \tabularnewline
65 & 82 & 79.0000448445442 & 2.99995515545584 \tabularnewline
66 & 71 & 81.9998654683785 & -10.9998654683785 \tabularnewline
67 & 75 & 71.0004932839528 & 3.99950671604715 \tabularnewline
68 & 74 & 74.9998206439444 & -0.999820643944417 \tabularnewline
69 & 76 & 74.000044836501 & 1.99995516349897 \tabularnewline
70 & 82 & 75.9999103129223 & 6.00008968707768 \tabularnewline
71 & 85 & 81.999730928713 & 3.00026907128699 \tabularnewline
72 & 82 & 84.9998654543011 & -2.9998654543011 \tabularnewline
73 & 92 & 82.0001345275989 & 9.99986547240113 \tabularnewline
74 & 93 & 91.9995515605911 & 1.00044843940887 \tabularnewline
75 & 93 & 92.9999551353458 & 4.48646542281494e-05 \tabularnewline
76 & 99 & 92.9999999979881 & 6.00000000201193 \tabularnewline
77 & 98 & 98.9997309327349 & -0.999730932734892 \tabularnewline
78 & 89 & 98.000044832478 & -9.00004483247797 \tabularnewline
79 & 96 & 89.000403602908 & 6.99959639709198 \tabularnewline
80 & 94 & 95.9996861062902 & -1.9996861062902 \tabularnewline
81 & 99 & 94.0000896750119 & 4.99991032498808 \tabularnewline
82 & 108 & 98.9997757813006 & 9.00022421869942 \tabularnewline
83 & 113 & 107.999596389047 & 5.0004036109525 \tabularnewline
84 & 115 & 112.999775759179 & 2.0002242408206 \tabularnewline
85 & 126 & 114.999910300856 & 11.0000896991443 \tabularnewline
86 & 131 & 125.999506705992 & 5.00049329400838 \tabularnewline
87 & 134 & 130.999775755158 & 3.0002242448424 \tabularnewline
88 & 134 & 133.999865456311 & 0.000134543688659505 \tabularnewline
89 & 137 & 133.999999993966 & 3.00000000603356 \tabularnewline
90 & 139 & 136.999865466367 & 2.00013453363277 \tabularnewline
91 & 139 & 138.999910304879 & 8.96951214315322e-05 \tabularnewline
92 & 134 & 138.999999995978 & -4.99999999597765 \tabularnewline
93 & 133 & 134.000224222721 & -1.00022422272068 \tabularnewline
94 & 135 & 133.000044854599 & 1.99995514540069 \tabularnewline
95 & 130 & 134.999910312923 & -4.99991031292313 \tabularnewline
96 & 133 & 130.000224218699 & 2.99977578130114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261125&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]80[/C][C]82[/C][C]-2[/C][/ROW]
[ROW][C]3[/C][C]76[/C][C]80.0000896890883[/C][C]-4.00008968908834[/C][/ROW]
[ROW][C]4[/C][C]73[/C][C]76.0001793821987[/C][C]-3.00017938219874[/C][/ROW]
[ROW][C]5[/C][C]70[/C][C]73.0001345416768[/C][C]-3.00013454167683[/C][/ROW]
[ROW][C]6[/C][C]68[/C][C]70.000134539666[/C][C]-2.00013453966596[/C][/ROW]
[ROW][C]7[/C][C]67[/C][C]68.0000896951217[/C][C]-1.00008969512172[/C][/ROW]
[ROW][C]8[/C][C]64[/C][C]67.0000448485665[/C][C]-3.0000448485665[/C][/ROW]
[ROW][C]9[/C][C]69[/C][C]64.0001345356437[/C][C]4.99986546435628[/C][/ROW]
[ROW][C]10[/C][C]69[/C][C]68.9997757833123[/C][C]0.000224216687669809[/C][/ROW]
[ROW][C]11[/C][C]67[/C][C]68.9999999899451[/C][C]-1.9999999899451[/C][/ROW]
[ROW][C]12[/C][C]57[/C][C]67.0000896890879[/C][C]-10.0000896890879[/C][/ROW]
[ROW][C]13[/C][C]67[/C][C]57.0004484494638[/C][C]9.99955155053624[/C][/ROW]
[ROW][C]14[/C][C]69[/C][C]66.9995515746688[/C][C]2.00044842533119[/C][/ROW]
[ROW][C]15[/C][C]67[/C][C]68.9999102908022[/C][C]-1.99991029080222[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]67.0000896850654[/C][C]-1.00008968506536[/C][/ROW]
[ROW][C]17[/C][C]65[/C][C]66.0000448485661[/C][C]-1.00004484856606[/C][/ROW]
[ROW][C]18[/C][C]56[/C][C]65.0000448465554[/C][C]-9.00004484655538[/C][/ROW]
[ROW][C]19[/C][C]57[/C][C]56.0004036029086[/C][C]0.999596397091352[/C][/ROW]
[ROW][C]20[/C][C]53[/C][C]56.9999551735552[/C][C]-3.99995517355522[/C][/ROW]
[ROW][C]21[/C][C]58[/C][C]53.0001793761665[/C][C]4.99982062383355[/C][/ROW]
[ROW][C]22[/C][C]59[/C][C]57.9997757853232[/C][C]1.00022421467681[/C][/ROW]
[ROW][C]23[/C][C]60[/C][C]58.999955145401[/C][C]1.00004485459898[/C][/ROW]
[ROW][C]24[/C][C]59[/C][C]59.9999551534443[/C][C]-0.99995515344434[/C][/ROW]
[ROW][C]25[/C][C]65[/C][C]59.000044842533[/C][C]5.99995515746696[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]64.9997309347459[/C][C]-2.99973093474593[/C][/ROW]
[ROW][C]27[/C][C]61[/C][C]62.0001345215664[/C][C]-1.0001345215664[/C][/ROW]
[ROW][C]28[/C][C]62[/C][C]61.0000448505767[/C][C]0.999955149423272[/C][/ROW]
[ROW][C]29[/C][C]57[/C][C]61.9999551574671[/C][C]-4.99995515746713[/C][/ROW]
[ROW][C]30[/C][C]51[/C][C]57.0002242207099[/C][C]-6.0002242207099[/C][/ROW]
[ROW][C]31[/C][C]45[/C][C]51.0002690773201[/C][C]-6.00026907732009[/C][/ROW]
[ROW][C]32[/C][C]46[/C][C]45.0002690793317[/C][C]0.999730920668334[/C][/ROW]
[ROW][C]33[/C][C]48[/C][C]45.9999551675226[/C][C]2.00004483247744[/C][/ROW]
[ROW][C]34[/C][C]49[/C][C]47.9999103089012[/C][C]1.00008969109883[/C][/ROW]
[ROW][C]35[/C][C]48[/C][C]48.9999551514337[/C][C]-0.999955151433674[/C][/ROW]
[ROW][C]36[/C][C]43[/C][C]48.000044842533[/C][C]-5.00004484253296[/C][/ROW]
[ROW][C]37[/C][C]51[/C][C]43.0002242247318[/C][C]7.99977577526821[/C][/ROW]
[ROW][C]38[/C][C]54[/C][C]50.9996412537019[/C][C]3.0003587462981[/C][/ROW]
[ROW][C]39[/C][C]57[/C][C]53.9998654502797[/C][C]3.00013454972032[/C][/ROW]
[ROW][C]40[/C][C]60[/C][C]56.9998654603337[/C][C]3.00013453966633[/C][/ROW]
[ROW][C]41[/C][C]58[/C][C]59.9998654603341[/C][C]-1.99986546033412[/C][/ROW]
[ROW][C]42[/C][C]61[/C][C]58.000089683055[/C][C]2.99991031694503[/C][/ROW]
[ROW][C]43[/C][C]62[/C][C]60.9998654703893[/C][C]1.00013452961071[/C][/ROW]
[ROW][C]44[/C][C]62[/C][C]61.9999551494229[/C][C]4.48505770833663e-05[/C][/ROW]
[ROW][C]45[/C][C]64[/C][C]61.9999999979887[/C][C]2.0000000020113[/C][/ROW]
[ROW][C]46[/C][C]68[/C][C]63.9999103109116[/C][C]4.00008968908843[/C][/ROW]
[ROW][C]47[/C][C]70[/C][C]67.9998206178013[/C][C]2.00017938219874[/C][/ROW]
[ROW][C]48[/C][C]73[/C][C]69.9999103028673[/C][C]3.00008969713265[/C][/ROW]
[ROW][C]49[/C][C]79[/C][C]72.9998654623451[/C][C]6.00013453765493[/C][/ROW]
[ROW][C]50[/C][C]84[/C][C]78.9997309267017[/C][C]5.0002690732983[/C][/ROW]
[ROW][C]51[/C][C]82[/C][C]83.9997757652127[/C][C]-1.99977576521269[/C][/ROW]
[ROW][C]52[/C][C]78[/C][C]82.0000896790326[/C][C]-4.00008967903264[/C][/ROW]
[ROW][C]53[/C][C]78[/C][C]78.0001793821983[/C][C]-0.000179382198282951[/C][/ROW]
[ROW][C]54[/C][C]76[/C][C]78.0000000080443[/C][C]-2.00000000804431[/C][/ROW]
[ROW][C]55[/C][C]73[/C][C]76.0000896890887[/C][C]-3.0000896890887[/C][/ROW]
[ROW][C]56[/C][C]71[/C][C]73.0001345376546[/C][C]-2.00013453765457[/C][/ROW]
[ROW][C]57[/C][C]71[/C][C]71.0000896951216[/C][C]-8.96951216162734e-05[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]71.0000000040223[/C][C]-1.00000000402233[/C][/ROW]
[ROW][C]59[/C][C]74[/C][C]70.0000448445443[/C][C]3.99995515545565[/C][/ROW]
[ROW][C]60[/C][C]72[/C][C]73.9998206238344[/C][C]-1.99982062383435[/C][/ROW]
[ROW][C]61[/C][C]80[/C][C]72.0000896810443[/C][C]7.9999103189557[/C][/ROW]
[ROW][C]62[/C][C]80[/C][C]79.9996412476684[/C][C]0.000358752331649725[/C][/ROW]
[ROW][C]63[/C][C]80[/C][C]79.9999999839119[/C][C]1.60880802013708e-08[/C][/ROW]
[ROW][C]64[/C][C]79[/C][C]79.9999999999993[/C][C]-0.999999999999289[/C][/ROW]
[ROW][C]65[/C][C]82[/C][C]79.0000448445442[/C][C]2.99995515545584[/C][/ROW]
[ROW][C]66[/C][C]71[/C][C]81.9998654683785[/C][C]-10.9998654683785[/C][/ROW]
[ROW][C]67[/C][C]75[/C][C]71.0004932839528[/C][C]3.99950671604715[/C][/ROW]
[ROW][C]68[/C][C]74[/C][C]74.9998206439444[/C][C]-0.999820643944417[/C][/ROW]
[ROW][C]69[/C][C]76[/C][C]74.000044836501[/C][C]1.99995516349897[/C][/ROW]
[ROW][C]70[/C][C]82[/C][C]75.9999103129223[/C][C]6.00008968707768[/C][/ROW]
[ROW][C]71[/C][C]85[/C][C]81.999730928713[/C][C]3.00026907128699[/C][/ROW]
[ROW][C]72[/C][C]82[/C][C]84.9998654543011[/C][C]-2.9998654543011[/C][/ROW]
[ROW][C]73[/C][C]92[/C][C]82.0001345275989[/C][C]9.99986547240113[/C][/ROW]
[ROW][C]74[/C][C]93[/C][C]91.9995515605911[/C][C]1.00044843940887[/C][/ROW]
[ROW][C]75[/C][C]93[/C][C]92.9999551353458[/C][C]4.48646542281494e-05[/C][/ROW]
[ROW][C]76[/C][C]99[/C][C]92.9999999979881[/C][C]6.00000000201193[/C][/ROW]
[ROW][C]77[/C][C]98[/C][C]98.9997309327349[/C][C]-0.999730932734892[/C][/ROW]
[ROW][C]78[/C][C]89[/C][C]98.000044832478[/C][C]-9.00004483247797[/C][/ROW]
[ROW][C]79[/C][C]96[/C][C]89.000403602908[/C][C]6.99959639709198[/C][/ROW]
[ROW][C]80[/C][C]94[/C][C]95.9996861062902[/C][C]-1.9996861062902[/C][/ROW]
[ROW][C]81[/C][C]99[/C][C]94.0000896750119[/C][C]4.99991032498808[/C][/ROW]
[ROW][C]82[/C][C]108[/C][C]98.9997757813006[/C][C]9.00022421869942[/C][/ROW]
[ROW][C]83[/C][C]113[/C][C]107.999596389047[/C][C]5.0004036109525[/C][/ROW]
[ROW][C]84[/C][C]115[/C][C]112.999775759179[/C][C]2.0002242408206[/C][/ROW]
[ROW][C]85[/C][C]126[/C][C]114.999910300856[/C][C]11.0000896991443[/C][/ROW]
[ROW][C]86[/C][C]131[/C][C]125.999506705992[/C][C]5.00049329400838[/C][/ROW]
[ROW][C]87[/C][C]134[/C][C]130.999775755158[/C][C]3.0002242448424[/C][/ROW]
[ROW][C]88[/C][C]134[/C][C]133.999865456311[/C][C]0.000134543688659505[/C][/ROW]
[ROW][C]89[/C][C]137[/C][C]133.999999993966[/C][C]3.00000000603356[/C][/ROW]
[ROW][C]90[/C][C]139[/C][C]136.999865466367[/C][C]2.00013453363277[/C][/ROW]
[ROW][C]91[/C][C]139[/C][C]138.999910304879[/C][C]8.96951214315322e-05[/C][/ROW]
[ROW][C]92[/C][C]134[/C][C]138.999999995978[/C][C]-4.99999999597765[/C][/ROW]
[ROW][C]93[/C][C]133[/C][C]134.000224222721[/C][C]-1.00022422272068[/C][/ROW]
[ROW][C]94[/C][C]135[/C][C]133.000044854599[/C][C]1.99995514540069[/C][/ROW]
[ROW][C]95[/C][C]130[/C][C]134.999910312923[/C][C]-4.99991031292313[/C][/ROW]
[ROW][C]96[/C][C]133[/C][C]130.000224218699[/C][C]2.99977578130114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261125&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261125&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
28082-2
37680.0000896890883-4.00008968908834
47376.0001793821987-3.00017938219874
57073.0001345416768-3.00013454167683
66870.000134539666-2.00013453966596
76768.0000896951217-1.00008969512172
86467.0000448485665-3.0000448485665
96964.00013453564374.99986546435628
106968.99977578331230.000224216687669809
116768.9999999899451-1.9999999899451
125767.0000896890879-10.0000896890879
136757.00044844946389.99955155053624
146966.99955157466882.00044842533119
156768.9999102908022-1.99991029080222
166667.0000896850654-1.00008968506536
176566.0000448485661-1.00004484856606
185665.0000448465554-9.00004484655538
195756.00040360290860.999596397091352
205356.9999551735552-3.99995517355522
215853.00017937616654.99982062383355
225957.99977578532321.00022421467681
236058.9999551454011.00004485459898
245959.9999551534443-0.99995515344434
256559.0000448425335.99995515746696
266264.9997309347459-2.99973093474593
276162.0001345215664-1.0001345215664
286261.00004485057670.999955149423272
295761.9999551574671-4.99995515746713
305157.0002242207099-6.0002242207099
314551.0002690773201-6.00026907732009
324645.00026907933170.999730920668334
334845.99995516752262.00004483247744
344947.99991030890121.00008969109883
354848.9999551514337-0.999955151433674
364348.000044842533-5.00004484253296
375143.00022422473187.99977577526821
385450.99964125370193.0003587462981
395753.99986545027973.00013454972032
406056.99986546033373.00013453966633
415859.9998654603341-1.99986546033412
426158.0000896830552.99991031694503
436260.99986547038931.00013452961071
446261.99995514942294.48505770833663e-05
456461.99999999798872.0000000020113
466863.99991031091164.00008968908843
477067.99982061780132.00017938219874
487369.99991030286733.00008969713265
497972.99986546234516.00013453765493
508478.99973092670175.0002690732983
518283.9997757652127-1.99977576521269
527882.0000896790326-4.00008967903264
537878.0001793821983-0.000179382198282951
547678.0000000080443-2.00000000804431
557376.0000896890887-3.0000896890887
567173.0001345376546-2.00013453765457
577171.0000896951216-8.96951216162734e-05
587071.0000000040223-1.00000000402233
597470.00004484454433.99995515545565
607273.9998206238344-1.99982062383435
618072.00008968104437.9999103189557
628079.99964124766840.000358752331649725
638079.99999998391191.60880802013708e-08
647979.9999999999993-0.999999999999289
658279.00004484454422.99995515545584
667181.9998654683785-10.9998654683785
677571.00049328395283.99950671604715
687474.9998206439444-0.999820643944417
697674.0000448365011.99995516349897
708275.99991031292236.00008968707768
718581.9997309287133.00026907128699
728284.9998654543011-2.9998654543011
739282.00013452759899.99986547240113
749391.99955156059111.00044843940887
759392.99995513534584.48646542281494e-05
769992.99999999798816.00000000201193
779898.9997309327349-0.999730932734892
788998.000044832478-9.00004483247797
799689.0004036029086.99959639709198
809495.9996861062902-1.9996861062902
819994.00008967501194.99991032498808
8210898.99977578130069.00022421869942
83113107.9995963890475.0004036109525
84115112.9997757591792.0002242408206
85126114.99991030085611.0000896991443
86131125.9995067059925.00049329400838
87134130.9997757551583.0002242448424
88134133.9998654563110.000134543688659505
89137133.9999999939663.00000000603356
90139136.9998654663672.00013453363277
91139138.9999103048798.96951214315322e-05
92134138.999999995978-4.99999999597765
93133134.000224222721-1.00022422272068
94135133.0000448545991.99995514540069
95130134.999910312923-4.99991031292313
96133130.0002242186992.99977578130114







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97132.999865476422124.587643366435141.41208758641
98132.999865476422121.103453626357144.896277326488
99132.999865476422118.429904975961147.569825976883
100132.999865476422116.175987116674149.823743836171
101132.999865476422114.190239825118151.809491127727
102132.999865476422112.394983743667153.604747209178
103132.999865476422110.744073302261155.255657650584
104132.999865476422109.207441905502156.792289047342
105132.999865476422107.764205123329158.235525829516
106132.999865476422106.399157073538159.600573879307
107132.999865476422105.100818510372160.898912442473
108132.999865476422103.860271181159162.139459771686

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 132.999865476422 & 124.587643366435 & 141.41208758641 \tabularnewline
98 & 132.999865476422 & 121.103453626357 & 144.896277326488 \tabularnewline
99 & 132.999865476422 & 118.429904975961 & 147.569825976883 \tabularnewline
100 & 132.999865476422 & 116.175987116674 & 149.823743836171 \tabularnewline
101 & 132.999865476422 & 114.190239825118 & 151.809491127727 \tabularnewline
102 & 132.999865476422 & 112.394983743667 & 153.604747209178 \tabularnewline
103 & 132.999865476422 & 110.744073302261 & 155.255657650584 \tabularnewline
104 & 132.999865476422 & 109.207441905502 & 156.792289047342 \tabularnewline
105 & 132.999865476422 & 107.764205123329 & 158.235525829516 \tabularnewline
106 & 132.999865476422 & 106.399157073538 & 159.600573879307 \tabularnewline
107 & 132.999865476422 & 105.100818510372 & 160.898912442473 \tabularnewline
108 & 132.999865476422 & 103.860271181159 & 162.139459771686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261125&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]132.999865476422[/C][C]124.587643366435[/C][C]141.41208758641[/C][/ROW]
[ROW][C]98[/C][C]132.999865476422[/C][C]121.103453626357[/C][C]144.896277326488[/C][/ROW]
[ROW][C]99[/C][C]132.999865476422[/C][C]118.429904975961[/C][C]147.569825976883[/C][/ROW]
[ROW][C]100[/C][C]132.999865476422[/C][C]116.175987116674[/C][C]149.823743836171[/C][/ROW]
[ROW][C]101[/C][C]132.999865476422[/C][C]114.190239825118[/C][C]151.809491127727[/C][/ROW]
[ROW][C]102[/C][C]132.999865476422[/C][C]112.394983743667[/C][C]153.604747209178[/C][/ROW]
[ROW][C]103[/C][C]132.999865476422[/C][C]110.744073302261[/C][C]155.255657650584[/C][/ROW]
[ROW][C]104[/C][C]132.999865476422[/C][C]109.207441905502[/C][C]156.792289047342[/C][/ROW]
[ROW][C]105[/C][C]132.999865476422[/C][C]107.764205123329[/C][C]158.235525829516[/C][/ROW]
[ROW][C]106[/C][C]132.999865476422[/C][C]106.399157073538[/C][C]159.600573879307[/C][/ROW]
[ROW][C]107[/C][C]132.999865476422[/C][C]105.100818510372[/C][C]160.898912442473[/C][/ROW]
[ROW][C]108[/C][C]132.999865476422[/C][C]103.860271181159[/C][C]162.139459771686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261125&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261125&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
97132.999865476422124.587643366435141.41208758641
98132.999865476422121.103453626357144.896277326488
99132.999865476422118.429904975961147.569825976883
100132.999865476422116.175987116674149.823743836171
101132.999865476422114.190239825118151.809491127727
102132.999865476422112.394983743667153.604747209178
103132.999865476422110.744073302261155.255657650584
104132.999865476422109.207441905502156.792289047342
105132.999865476422107.764205123329158.235525829516
106132.999865476422106.399157073538159.600573879307
107132.999865476422105.100818510372160.898912442473
108132.999865476422103.860271181159162.139459771686



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')