Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 22:39:10 +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/2016/Nov/28/t14803727884jnar8h4jedqn71.htm/, Retrieved Sat, 04 May 2024 21:55:29 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 21:55:29 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
75,8
75,7
112,3
110,9
99,6
107,5
90
88,8
129,7
120,4
93,3
96
81,1
78
111,9
117,6
101
98,3
91
86,8
108,8
110,1
93,8
100,6
75,7
69
116
94,5
105,1
95,3
79,7
76,1
111,1
106,3
89,5
96,8
67,8
62,5
90,1
93,6
94,2
93,2
81
73,7
97,7
97,5
82,7
88,8
68,5
61,1
89,6
87,6
90,8
84,3
75
78,4
83,5
93
79,3
83,9
65
60,3
80,6
86,5
78,7
80,7
70,6
67,2
88
89,1
69
84,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0139967457219063
beta0.847436182319472
gamma0.541338263720888

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0139967457219063 \tabularnewline
beta & 0.847436182319472 \tabularnewline
gamma & 0.541338263720888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.0139967457219063[/C][/ROW]
[ROW][C]beta[/C][C]0.847436182319472[/C][/ROW]
[ROW][C]gamma[/C][C]0.541338263720888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.0139967457219063
beta0.847436182319472
gamma0.541338263720888







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1381.181.2302933216304-0.130293321630418
147877.95588066423670.0441193357632983
15111.9112.620478056834-0.720478056834409
16117.6119.595572747763-1.99557274776254
17101102.824770834374-1.8247708343736
1898.399.5280894658857-1.22808946588569
199188.8554068793222.14459312067804
2086.887.1664294673046-0.366429467304556
21108.8126.824045205571-18.0240452055706
22110.1116.638401480528-6.53840148052809
2393.889.52683579273584.2731642072642
24100.692.02658609433418.57341390566586
2575.777.7477073283794-2.04770732837945
266974.5587739469819-5.55877394698187
27116106.9363902689019.06360973109861
2894.5112.920850512344-18.4208505123442
29105.196.52655528131098.57344471868907
3095.393.66523654055181.63476345944822
3179.785.1619451307097-5.46194513070972
3276.181.9778720266608-5.87787202666077
33111.1109.9701760895791.12982391042125
34106.3106.2286921360860.0713078639142566
3589.586.17456345836873.32543654163126
3696.890.55669418770346.24330581229664
3767.871.7337317490812-3.93373174908125
3862.566.8464832183766-4.34648321837656
3990.1104.201390827916-14.1013908279162
4093.695.3749338024034-1.77493380240345
4194.293.49077261836560.709227381634363
4293.287.00274510984786.19725489015218
438175.5111360680735.48886393192699
4473.772.41358575674281.28641424325721
4597.7101.645975462185-3.94597546218451
4697.597.5188083476808-0.0188083476808174
4782.780.62184729978182.07815270021817
4888.885.94320014243542.85679985756458
4968.563.60309706546984.89690293453022
5061.159.03958581293812.06041418706186
5189.688.66413503112970.935864968870291
5287.687.04180208292010.558197917079895
5390.886.83557022993063.96442977006942
5484.383.89536280487660.404637195123371
557573.01651596604221.98348403395775
5678.468.170648395544710.2293516044553
5783.593.37569854674-9.87569854674004
589391.68726646967361.31273353032635
5979.377.13673565391152.16326434608845
6083.982.84890598952721.05109401047284
616562.91094667168812.08905332831195
6260.357.26781051801663.03218948198338
6380.685.1926904328103-4.59269043281026
6486.583.57195529616522.92804470383477
6578.785.3794124609319-6.6794124609319
6680.780.69677879761750.00322120238250534
6770.671.1495631168392-0.549563116839167
6867.270.7347790602851-3.53477906028509
698884.27574811500213.72425188499793
7089.188.58511849477960.514881505220359
716975.0677273225316-6.06772732253161
7284.179.7587557889974.34124421100304

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 81.1 & 81.2302933216304 & -0.130293321630418 \tabularnewline
14 & 78 & 77.9558806642367 & 0.0441193357632983 \tabularnewline
15 & 111.9 & 112.620478056834 & -0.720478056834409 \tabularnewline
16 & 117.6 & 119.595572747763 & -1.99557274776254 \tabularnewline
17 & 101 & 102.824770834374 & -1.8247708343736 \tabularnewline
18 & 98.3 & 99.5280894658857 & -1.22808946588569 \tabularnewline
19 & 91 & 88.855406879322 & 2.14459312067804 \tabularnewline
20 & 86.8 & 87.1664294673046 & -0.366429467304556 \tabularnewline
21 & 108.8 & 126.824045205571 & -18.0240452055706 \tabularnewline
22 & 110.1 & 116.638401480528 & -6.53840148052809 \tabularnewline
23 & 93.8 & 89.5268357927358 & 4.2731642072642 \tabularnewline
24 & 100.6 & 92.0265860943341 & 8.57341390566586 \tabularnewline
25 & 75.7 & 77.7477073283794 & -2.04770732837945 \tabularnewline
26 & 69 & 74.5587739469819 & -5.55877394698187 \tabularnewline
27 & 116 & 106.936390268901 & 9.06360973109861 \tabularnewline
28 & 94.5 & 112.920850512344 & -18.4208505123442 \tabularnewline
29 & 105.1 & 96.5265552813109 & 8.57344471868907 \tabularnewline
30 & 95.3 & 93.6652365405518 & 1.63476345944822 \tabularnewline
31 & 79.7 & 85.1619451307097 & -5.46194513070972 \tabularnewline
32 & 76.1 & 81.9778720266608 & -5.87787202666077 \tabularnewline
33 & 111.1 & 109.970176089579 & 1.12982391042125 \tabularnewline
34 & 106.3 & 106.228692136086 & 0.0713078639142566 \tabularnewline
35 & 89.5 & 86.1745634583687 & 3.32543654163126 \tabularnewline
36 & 96.8 & 90.5566941877034 & 6.24330581229664 \tabularnewline
37 & 67.8 & 71.7337317490812 & -3.93373174908125 \tabularnewline
38 & 62.5 & 66.8464832183766 & -4.34648321837656 \tabularnewline
39 & 90.1 & 104.201390827916 & -14.1013908279162 \tabularnewline
40 & 93.6 & 95.3749338024034 & -1.77493380240345 \tabularnewline
41 & 94.2 & 93.4907726183656 & 0.709227381634363 \tabularnewline
42 & 93.2 & 87.0027451098478 & 6.19725489015218 \tabularnewline
43 & 81 & 75.511136068073 & 5.48886393192699 \tabularnewline
44 & 73.7 & 72.4135857567428 & 1.28641424325721 \tabularnewline
45 & 97.7 & 101.645975462185 & -3.94597546218451 \tabularnewline
46 & 97.5 & 97.5188083476808 & -0.0188083476808174 \tabularnewline
47 & 82.7 & 80.6218472997818 & 2.07815270021817 \tabularnewline
48 & 88.8 & 85.9432001424354 & 2.85679985756458 \tabularnewline
49 & 68.5 & 63.6030970654698 & 4.89690293453022 \tabularnewline
50 & 61.1 & 59.0395858129381 & 2.06041418706186 \tabularnewline
51 & 89.6 & 88.6641350311297 & 0.935864968870291 \tabularnewline
52 & 87.6 & 87.0418020829201 & 0.558197917079895 \tabularnewline
53 & 90.8 & 86.8355702299306 & 3.96442977006942 \tabularnewline
54 & 84.3 & 83.8953628048766 & 0.404637195123371 \tabularnewline
55 & 75 & 73.0165159660422 & 1.98348403395775 \tabularnewline
56 & 78.4 & 68.1706483955447 & 10.2293516044553 \tabularnewline
57 & 83.5 & 93.37569854674 & -9.87569854674004 \tabularnewline
58 & 93 & 91.6872664696736 & 1.31273353032635 \tabularnewline
59 & 79.3 & 77.1367356539115 & 2.16326434608845 \tabularnewline
60 & 83.9 & 82.8489059895272 & 1.05109401047284 \tabularnewline
61 & 65 & 62.9109466716881 & 2.08905332831195 \tabularnewline
62 & 60.3 & 57.2678105180166 & 3.03218948198338 \tabularnewline
63 & 80.6 & 85.1926904328103 & -4.59269043281026 \tabularnewline
64 & 86.5 & 83.5719552961652 & 2.92804470383477 \tabularnewline
65 & 78.7 & 85.3794124609319 & -6.6794124609319 \tabularnewline
66 & 80.7 & 80.6967787976175 & 0.00322120238250534 \tabularnewline
67 & 70.6 & 71.1495631168392 & -0.549563116839167 \tabularnewline
68 & 67.2 & 70.7347790602851 & -3.53477906028509 \tabularnewline
69 & 88 & 84.2757481150021 & 3.72425188499793 \tabularnewline
70 & 89.1 & 88.5851184947796 & 0.514881505220359 \tabularnewline
71 & 69 & 75.0677273225316 & -6.06772732253161 \tabularnewline
72 & 84.1 & 79.758755788997 & 4.34124421100304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]81.1[/C][C]81.2302933216304[/C][C]-0.130293321630418[/C][/ROW]
[ROW][C]14[/C][C]78[/C][C]77.9558806642367[/C][C]0.0441193357632983[/C][/ROW]
[ROW][C]15[/C][C]111.9[/C][C]112.620478056834[/C][C]-0.720478056834409[/C][/ROW]
[ROW][C]16[/C][C]117.6[/C][C]119.595572747763[/C][C]-1.99557274776254[/C][/ROW]
[ROW][C]17[/C][C]101[/C][C]102.824770834374[/C][C]-1.8247708343736[/C][/ROW]
[ROW][C]18[/C][C]98.3[/C][C]99.5280894658857[/C][C]-1.22808946588569[/C][/ROW]
[ROW][C]19[/C][C]91[/C][C]88.855406879322[/C][C]2.14459312067804[/C][/ROW]
[ROW][C]20[/C][C]86.8[/C][C]87.1664294673046[/C][C]-0.366429467304556[/C][/ROW]
[ROW][C]21[/C][C]108.8[/C][C]126.824045205571[/C][C]-18.0240452055706[/C][/ROW]
[ROW][C]22[/C][C]110.1[/C][C]116.638401480528[/C][C]-6.53840148052809[/C][/ROW]
[ROW][C]23[/C][C]93.8[/C][C]89.5268357927358[/C][C]4.2731642072642[/C][/ROW]
[ROW][C]24[/C][C]100.6[/C][C]92.0265860943341[/C][C]8.57341390566586[/C][/ROW]
[ROW][C]25[/C][C]75.7[/C][C]77.7477073283794[/C][C]-2.04770732837945[/C][/ROW]
[ROW][C]26[/C][C]69[/C][C]74.5587739469819[/C][C]-5.55877394698187[/C][/ROW]
[ROW][C]27[/C][C]116[/C][C]106.936390268901[/C][C]9.06360973109861[/C][/ROW]
[ROW][C]28[/C][C]94.5[/C][C]112.920850512344[/C][C]-18.4208505123442[/C][/ROW]
[ROW][C]29[/C][C]105.1[/C][C]96.5265552813109[/C][C]8.57344471868907[/C][/ROW]
[ROW][C]30[/C][C]95.3[/C][C]93.6652365405518[/C][C]1.63476345944822[/C][/ROW]
[ROW][C]31[/C][C]79.7[/C][C]85.1619451307097[/C][C]-5.46194513070972[/C][/ROW]
[ROW][C]32[/C][C]76.1[/C][C]81.9778720266608[/C][C]-5.87787202666077[/C][/ROW]
[ROW][C]33[/C][C]111.1[/C][C]109.970176089579[/C][C]1.12982391042125[/C][/ROW]
[ROW][C]34[/C][C]106.3[/C][C]106.228692136086[/C][C]0.0713078639142566[/C][/ROW]
[ROW][C]35[/C][C]89.5[/C][C]86.1745634583687[/C][C]3.32543654163126[/C][/ROW]
[ROW][C]36[/C][C]96.8[/C][C]90.5566941877034[/C][C]6.24330581229664[/C][/ROW]
[ROW][C]37[/C][C]67.8[/C][C]71.7337317490812[/C][C]-3.93373174908125[/C][/ROW]
[ROW][C]38[/C][C]62.5[/C][C]66.8464832183766[/C][C]-4.34648321837656[/C][/ROW]
[ROW][C]39[/C][C]90.1[/C][C]104.201390827916[/C][C]-14.1013908279162[/C][/ROW]
[ROW][C]40[/C][C]93.6[/C][C]95.3749338024034[/C][C]-1.77493380240345[/C][/ROW]
[ROW][C]41[/C][C]94.2[/C][C]93.4907726183656[/C][C]0.709227381634363[/C][/ROW]
[ROW][C]42[/C][C]93.2[/C][C]87.0027451098478[/C][C]6.19725489015218[/C][/ROW]
[ROW][C]43[/C][C]81[/C][C]75.511136068073[/C][C]5.48886393192699[/C][/ROW]
[ROW][C]44[/C][C]73.7[/C][C]72.4135857567428[/C][C]1.28641424325721[/C][/ROW]
[ROW][C]45[/C][C]97.7[/C][C]101.645975462185[/C][C]-3.94597546218451[/C][/ROW]
[ROW][C]46[/C][C]97.5[/C][C]97.5188083476808[/C][C]-0.0188083476808174[/C][/ROW]
[ROW][C]47[/C][C]82.7[/C][C]80.6218472997818[/C][C]2.07815270021817[/C][/ROW]
[ROW][C]48[/C][C]88.8[/C][C]85.9432001424354[/C][C]2.85679985756458[/C][/ROW]
[ROW][C]49[/C][C]68.5[/C][C]63.6030970654698[/C][C]4.89690293453022[/C][/ROW]
[ROW][C]50[/C][C]61.1[/C][C]59.0395858129381[/C][C]2.06041418706186[/C][/ROW]
[ROW][C]51[/C][C]89.6[/C][C]88.6641350311297[/C][C]0.935864968870291[/C][/ROW]
[ROW][C]52[/C][C]87.6[/C][C]87.0418020829201[/C][C]0.558197917079895[/C][/ROW]
[ROW][C]53[/C][C]90.8[/C][C]86.8355702299306[/C][C]3.96442977006942[/C][/ROW]
[ROW][C]54[/C][C]84.3[/C][C]83.8953628048766[/C][C]0.404637195123371[/C][/ROW]
[ROW][C]55[/C][C]75[/C][C]73.0165159660422[/C][C]1.98348403395775[/C][/ROW]
[ROW][C]56[/C][C]78.4[/C][C]68.1706483955447[/C][C]10.2293516044553[/C][/ROW]
[ROW][C]57[/C][C]83.5[/C][C]93.37569854674[/C][C]-9.87569854674004[/C][/ROW]
[ROW][C]58[/C][C]93[/C][C]91.6872664696736[/C][C]1.31273353032635[/C][/ROW]
[ROW][C]59[/C][C]79.3[/C][C]77.1367356539115[/C][C]2.16326434608845[/C][/ROW]
[ROW][C]60[/C][C]83.9[/C][C]82.8489059895272[/C][C]1.05109401047284[/C][/ROW]
[ROW][C]61[/C][C]65[/C][C]62.9109466716881[/C][C]2.08905332831195[/C][/ROW]
[ROW][C]62[/C][C]60.3[/C][C]57.2678105180166[/C][C]3.03218948198338[/C][/ROW]
[ROW][C]63[/C][C]80.6[/C][C]85.1926904328103[/C][C]-4.59269043281026[/C][/ROW]
[ROW][C]64[/C][C]86.5[/C][C]83.5719552961652[/C][C]2.92804470383477[/C][/ROW]
[ROW][C]65[/C][C]78.7[/C][C]85.3794124609319[/C][C]-6.6794124609319[/C][/ROW]
[ROW][C]66[/C][C]80.7[/C][C]80.6967787976175[/C][C]0.00322120238250534[/C][/ROW]
[ROW][C]67[/C][C]70.6[/C][C]71.1495631168392[/C][C]-0.549563116839167[/C][/ROW]
[ROW][C]68[/C][C]67.2[/C][C]70.7347790602851[/C][C]-3.53477906028509[/C][/ROW]
[ROW][C]69[/C][C]88[/C][C]84.2757481150021[/C][C]3.72425188499793[/C][/ROW]
[ROW][C]70[/C][C]89.1[/C][C]88.5851184947796[/C][C]0.514881505220359[/C][/ROW]
[ROW][C]71[/C][C]69[/C][C]75.0677273225316[/C][C]-6.06772732253161[/C][/ROW]
[ROW][C]72[/C][C]84.1[/C][C]79.758755788997[/C][C]4.34124421100304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1381.181.2302933216304-0.130293321630418
147877.95588066423670.0441193357632983
15111.9112.620478056834-0.720478056834409
16117.6119.595572747763-1.99557274776254
17101102.824770834374-1.8247708343736
1898.399.5280894658857-1.22808946588569
199188.8554068793222.14459312067804
2086.887.1664294673046-0.366429467304556
21108.8126.824045205571-18.0240452055706
22110.1116.638401480528-6.53840148052809
2393.889.52683579273584.2731642072642
24100.692.02658609433418.57341390566586
2575.777.7477073283794-2.04770732837945
266974.5587739469819-5.55877394698187
27116106.9363902689019.06360973109861
2894.5112.920850512344-18.4208505123442
29105.196.52655528131098.57344471868907
3095.393.66523654055181.63476345944822
3179.785.1619451307097-5.46194513070972
3276.181.9778720266608-5.87787202666077
33111.1109.9701760895791.12982391042125
34106.3106.2286921360860.0713078639142566
3589.586.17456345836873.32543654163126
3696.890.55669418770346.24330581229664
3767.871.7337317490812-3.93373174908125
3862.566.8464832183766-4.34648321837656
3990.1104.201390827916-14.1013908279162
4093.695.3749338024034-1.77493380240345
4194.293.49077261836560.709227381634363
4293.287.00274510984786.19725489015218
438175.5111360680735.48886393192699
4473.772.41358575674281.28641424325721
4597.7101.645975462185-3.94597546218451
4697.597.5188083476808-0.0188083476808174
4782.780.62184729978182.07815270021817
4888.885.94320014243542.85679985756458
4968.563.60309706546984.89690293453022
5061.159.03958581293812.06041418706186
5189.688.66413503112970.935864968870291
5287.687.04180208292010.558197917079895
5390.886.83557022993063.96442977006942
5484.383.89536280487660.404637195123371
557573.01651596604221.98348403395775
5678.468.170648395544710.2293516044553
5783.593.37569854674-9.87569854674004
589391.68726646967361.31273353032635
5979.377.13673565391152.16326434608845
6083.982.84890598952721.05109401047284
616562.91094667168812.08905332831195
6260.357.26781051801663.03218948198338
6380.685.1926904328103-4.59269043281026
6486.583.57195529616522.92804470383477
6578.785.3794124609319-6.6794124609319
6680.780.69677879761750.00322120238250534
6770.671.1495631168392-0.549563116839167
6867.270.7347790602851-3.53477906028509
698884.27574811500213.72425188499793
7089.188.58511849477960.514881505220359
716975.0677273225316-6.06772732253161
7284.179.7587557889974.34124421100304







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7361.21555226132155.153495968146467.2776085544955
7456.212367473556150.144569545998962.2801654011133
7578.787819625449372.688277351846384.8873618990522
7681.038927523342174.895174143595387.182680903089
7777.71700554696671.523562005997183.9104490879348
7876.697536883080970.432561647632882.9625121185289
7967.30126385476961.006580829506173.5959468800319
8065.364696937983758.991332750225271.7380611257423
8181.961663654105275.243277650573388.6800496576371
8284.337900275009277.367152283856791.3086482661617
8368.127650462827861.287318374330374.9679825513254
8477.969849862389457.014997392793598.9247023319854

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 61.215552261321 & 55.1534959681464 & 67.2776085544955 \tabularnewline
74 & 56.2123674735561 & 50.1445695459989 & 62.2801654011133 \tabularnewline
75 & 78.7878196254493 & 72.6882773518463 & 84.8873618990522 \tabularnewline
76 & 81.0389275233421 & 74.8951741435953 & 87.182680903089 \tabularnewline
77 & 77.717005546966 & 71.5235620059971 & 83.9104490879348 \tabularnewline
78 & 76.6975368830809 & 70.4325616476328 & 82.9625121185289 \tabularnewline
79 & 67.301263854769 & 61.0065808295061 & 73.5959468800319 \tabularnewline
80 & 65.3646969379837 & 58.9913327502252 & 71.7380611257423 \tabularnewline
81 & 81.9616636541052 & 75.2432776505733 & 88.6800496576371 \tabularnewline
82 & 84.3379002750092 & 77.3671522838567 & 91.3086482661617 \tabularnewline
83 & 68.1276504628278 & 61.2873183743303 & 74.9679825513254 \tabularnewline
84 & 77.9698498623894 & 57.0149973927935 & 98.9247023319854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]61.215552261321[/C][C]55.1534959681464[/C][C]67.2776085544955[/C][/ROW]
[ROW][C]74[/C][C]56.2123674735561[/C][C]50.1445695459989[/C][C]62.2801654011133[/C][/ROW]
[ROW][C]75[/C][C]78.7878196254493[/C][C]72.6882773518463[/C][C]84.8873618990522[/C][/ROW]
[ROW][C]76[/C][C]81.0389275233421[/C][C]74.8951741435953[/C][C]87.182680903089[/C][/ROW]
[ROW][C]77[/C][C]77.717005546966[/C][C]71.5235620059971[/C][C]83.9104490879348[/C][/ROW]
[ROW][C]78[/C][C]76.6975368830809[/C][C]70.4325616476328[/C][C]82.9625121185289[/C][/ROW]
[ROW][C]79[/C][C]67.301263854769[/C][C]61.0065808295061[/C][C]73.5959468800319[/C][/ROW]
[ROW][C]80[/C][C]65.3646969379837[/C][C]58.9913327502252[/C][C]71.7380611257423[/C][/ROW]
[ROW][C]81[/C][C]81.9616636541052[/C][C]75.2432776505733[/C][C]88.6800496576371[/C][/ROW]
[ROW][C]82[/C][C]84.3379002750092[/C][C]77.3671522838567[/C][C]91.3086482661617[/C][/ROW]
[ROW][C]83[/C][C]68.1276504628278[/C][C]61.2873183743303[/C][C]74.9679825513254[/C][/ROW]
[ROW][C]84[/C][C]77.9698498623894[/C][C]57.0149973927935[/C][C]98.9247023319854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7361.21555226132155.153495968146467.2776085544955
7456.212367473556150.144569545998962.2801654011133
7578.787819625449372.688277351846384.8873618990522
7681.038927523342174.895174143595387.182680903089
7777.71700554696671.523562005997183.9104490879348
7876.697536883080970.432561647632882.9625121185289
7967.30126385476961.006580829506173.5959468800319
8065.364696937983758.991332750225271.7380611257423
8181.961663654105275.243277650573388.6800496576371
8284.337900275009277.367152283856791.3086482661617
8368.127650462827861.287318374330374.9679825513254
8477.969849862389457.014997392793598.9247023319854



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