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 Apr 2017 14:41:58 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/29/t149347341370ntmqlqnsvd893.htm/, Retrieved Mon, 13 May 2024 06:53:00 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 13 May 2024 06:53:00 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
74,16
73,21
77,14
80,9
82,76
83,33
81,94
82,38
82,81
83,17
84,07
87,33
90,75
92,82
97,78
99,32
98,33
98,66
98,13
97,8
99,36
100,37
103,22
101,68
104,39
103,99
106,71
106,06
103,5
100,17
101,1
105,93
108,09
107,27
104,9
102,7
102,06
103,05
102,08
100,13
97,56
97,38
99,66
99,58
102,7
98,92
97,85
99,01
97,71
97,95
97,24
96,69
96,41
96,99
98,36
97,8
96,79
94,73
92,67
87,15
79,54
82,35
86,38
84,75
87,54
86,73
84,74
80,75
79,28
78,52
78,54
77,33




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=&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=&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0791218719078013
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0791218719078013 \tabularnewline
gamma & 1 \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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0791218719078013[/C][/ROW]
[ROW][C]gamma[/C][C]1[/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
alpha1
beta0.0791218719078013
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1390.7582.12552884615388.62447115384617
1492.8293.5981593601822-0.778159360182201
1597.7898.481589934962-0.701589934962016
1699.3299.8919121593295-0.571912159329472
1798.3398.7483280653832-0.418328065383179
1898.6699.1639791657784-0.503979165778446
1998.1399.5957700574462-1.46577005744624
2097.898.805628920048-1.00562892004801
2199.3698.21731167744921.14268832255082
22100.3799.84730664986990.522693350130083
23103.22101.6499131261661.57008687383403
24101.68107.112891338682-5.4328913386816
25104.39105.27719747276-0.887197472760079
26103.99106.563250747963-2.57325074796344
27106.71108.834650331896-2.12465033189643
28106.06107.892377353821-1.83237735382056
29103.5104.459062894212-0.959062894211513
30100.17103.261930042744-3.09193004274414
31101.199.8289574166211.27104258337903
32105.93100.7153580184265.21464198157425
33108.09105.7792002533372.31079974666308
34107.27108.10161838823-0.831618388230325
35104.9107.967069184641-3.06706918464056
36102.7107.843146929481-5.14314692948111
37102.06105.37037818359-3.31037818359033
38103.05103.114704864982-0.064704864981934
39102.08106.974585294943-4.89458529494303
40100.13102.123149877528-1.99314987752805
4197.5697.37711479489190.182885205108079
4297.3896.26033501466431.11966498533572
4399.6696.31059167088043.34940832911964
4499.5898.71143646099720.868563539002793
45102.798.5214088340744.17859116592604
4698.92101.951610122393-3.03161012239278
4797.8598.6829934546144-0.83299345461441
4899.01100.035835453198-1.02583545319838
4997.71101.248836098539-3.53883609853861
5097.9598.3150867620473-0.365086762047312
5197.24101.401200414025-4.1612004140254
5296.6996.8677917812175-0.177791781217508
5396.4193.66539122934452.74460877065555
5496.9995.04129981293321.94870018706676
5598.3695.91715128618772.44284871381225
5697.897.33626738254550.463732617454525
5796.7996.63420877530320.155791224696841
5894.7395.6161186019613-0.886118601961329
5992.6794.2372572394418-1.56725723944182
6087.1594.5420029128961-7.39200291289613
6179.5488.5713004719465-9.03130047194652
6282.3578.89297707284433.45702292715568
6386.3884.85150319806911.52849680193093
6484.7585.5082740595762-0.758274059576237
6587.5481.17994466323016.36005533676986
6686.7385.91191414691250.818085853087467
6784.7485.3083092976568-0.568309297656825
6880.7583.1291769355369-2.37917693553692
6979.2878.77218200279740.507817997202636
7078.5277.32194484665781.19805515334215
7178.5477.4079872130391.13201278696096
7277.3380.006304183767-2.676304183767

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 90.75 & 82.1255288461538 & 8.62447115384617 \tabularnewline
14 & 92.82 & 93.5981593601822 & -0.778159360182201 \tabularnewline
15 & 97.78 & 98.481589934962 & -0.701589934962016 \tabularnewline
16 & 99.32 & 99.8919121593295 & -0.571912159329472 \tabularnewline
17 & 98.33 & 98.7483280653832 & -0.418328065383179 \tabularnewline
18 & 98.66 & 99.1639791657784 & -0.503979165778446 \tabularnewline
19 & 98.13 & 99.5957700574462 & -1.46577005744624 \tabularnewline
20 & 97.8 & 98.805628920048 & -1.00562892004801 \tabularnewline
21 & 99.36 & 98.2173116774492 & 1.14268832255082 \tabularnewline
22 & 100.37 & 99.8473066498699 & 0.522693350130083 \tabularnewline
23 & 103.22 & 101.649913126166 & 1.57008687383403 \tabularnewline
24 & 101.68 & 107.112891338682 & -5.4328913386816 \tabularnewline
25 & 104.39 & 105.27719747276 & -0.887197472760079 \tabularnewline
26 & 103.99 & 106.563250747963 & -2.57325074796344 \tabularnewline
27 & 106.71 & 108.834650331896 & -2.12465033189643 \tabularnewline
28 & 106.06 & 107.892377353821 & -1.83237735382056 \tabularnewline
29 & 103.5 & 104.459062894212 & -0.959062894211513 \tabularnewline
30 & 100.17 & 103.261930042744 & -3.09193004274414 \tabularnewline
31 & 101.1 & 99.828957416621 & 1.27104258337903 \tabularnewline
32 & 105.93 & 100.715358018426 & 5.21464198157425 \tabularnewline
33 & 108.09 & 105.779200253337 & 2.31079974666308 \tabularnewline
34 & 107.27 & 108.10161838823 & -0.831618388230325 \tabularnewline
35 & 104.9 & 107.967069184641 & -3.06706918464056 \tabularnewline
36 & 102.7 & 107.843146929481 & -5.14314692948111 \tabularnewline
37 & 102.06 & 105.37037818359 & -3.31037818359033 \tabularnewline
38 & 103.05 & 103.114704864982 & -0.064704864981934 \tabularnewline
39 & 102.08 & 106.974585294943 & -4.89458529494303 \tabularnewline
40 & 100.13 & 102.123149877528 & -1.99314987752805 \tabularnewline
41 & 97.56 & 97.3771147948919 & 0.182885205108079 \tabularnewline
42 & 97.38 & 96.2603350146643 & 1.11966498533572 \tabularnewline
43 & 99.66 & 96.3105916708804 & 3.34940832911964 \tabularnewline
44 & 99.58 & 98.7114364609972 & 0.868563539002793 \tabularnewline
45 & 102.7 & 98.521408834074 & 4.17859116592604 \tabularnewline
46 & 98.92 & 101.951610122393 & -3.03161012239278 \tabularnewline
47 & 97.85 & 98.6829934546144 & -0.83299345461441 \tabularnewline
48 & 99.01 & 100.035835453198 & -1.02583545319838 \tabularnewline
49 & 97.71 & 101.248836098539 & -3.53883609853861 \tabularnewline
50 & 97.95 & 98.3150867620473 & -0.365086762047312 \tabularnewline
51 & 97.24 & 101.401200414025 & -4.1612004140254 \tabularnewline
52 & 96.69 & 96.8677917812175 & -0.177791781217508 \tabularnewline
53 & 96.41 & 93.6653912293445 & 2.74460877065555 \tabularnewline
54 & 96.99 & 95.0412998129332 & 1.94870018706676 \tabularnewline
55 & 98.36 & 95.9171512861877 & 2.44284871381225 \tabularnewline
56 & 97.8 & 97.3362673825455 & 0.463732617454525 \tabularnewline
57 & 96.79 & 96.6342087753032 & 0.155791224696841 \tabularnewline
58 & 94.73 & 95.6161186019613 & -0.886118601961329 \tabularnewline
59 & 92.67 & 94.2372572394418 & -1.56725723944182 \tabularnewline
60 & 87.15 & 94.5420029128961 & -7.39200291289613 \tabularnewline
61 & 79.54 & 88.5713004719465 & -9.03130047194652 \tabularnewline
62 & 82.35 & 78.8929770728443 & 3.45702292715568 \tabularnewline
63 & 86.38 & 84.8515031980691 & 1.52849680193093 \tabularnewline
64 & 84.75 & 85.5082740595762 & -0.758274059576237 \tabularnewline
65 & 87.54 & 81.1799446632301 & 6.36005533676986 \tabularnewline
66 & 86.73 & 85.9119141469125 & 0.818085853087467 \tabularnewline
67 & 84.74 & 85.3083092976568 & -0.568309297656825 \tabularnewline
68 & 80.75 & 83.1291769355369 & -2.37917693553692 \tabularnewline
69 & 79.28 & 78.7721820027974 & 0.507817997202636 \tabularnewline
70 & 78.52 & 77.3219448466578 & 1.19805515334215 \tabularnewline
71 & 78.54 & 77.407987213039 & 1.13201278696096 \tabularnewline
72 & 77.33 & 80.006304183767 & -2.676304183767 \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]90.75[/C][C]82.1255288461538[/C][C]8.62447115384617[/C][/ROW]
[ROW][C]14[/C][C]92.82[/C][C]93.5981593601822[/C][C]-0.778159360182201[/C][/ROW]
[ROW][C]15[/C][C]97.78[/C][C]98.481589934962[/C][C]-0.701589934962016[/C][/ROW]
[ROW][C]16[/C][C]99.32[/C][C]99.8919121593295[/C][C]-0.571912159329472[/C][/ROW]
[ROW][C]17[/C][C]98.33[/C][C]98.7483280653832[/C][C]-0.418328065383179[/C][/ROW]
[ROW][C]18[/C][C]98.66[/C][C]99.1639791657784[/C][C]-0.503979165778446[/C][/ROW]
[ROW][C]19[/C][C]98.13[/C][C]99.5957700574462[/C][C]-1.46577005744624[/C][/ROW]
[ROW][C]20[/C][C]97.8[/C][C]98.805628920048[/C][C]-1.00562892004801[/C][/ROW]
[ROW][C]21[/C][C]99.36[/C][C]98.2173116774492[/C][C]1.14268832255082[/C][/ROW]
[ROW][C]22[/C][C]100.37[/C][C]99.8473066498699[/C][C]0.522693350130083[/C][/ROW]
[ROW][C]23[/C][C]103.22[/C][C]101.649913126166[/C][C]1.57008687383403[/C][/ROW]
[ROW][C]24[/C][C]101.68[/C][C]107.112891338682[/C][C]-5.4328913386816[/C][/ROW]
[ROW][C]25[/C][C]104.39[/C][C]105.27719747276[/C][C]-0.887197472760079[/C][/ROW]
[ROW][C]26[/C][C]103.99[/C][C]106.563250747963[/C][C]-2.57325074796344[/C][/ROW]
[ROW][C]27[/C][C]106.71[/C][C]108.834650331896[/C][C]-2.12465033189643[/C][/ROW]
[ROW][C]28[/C][C]106.06[/C][C]107.892377353821[/C][C]-1.83237735382056[/C][/ROW]
[ROW][C]29[/C][C]103.5[/C][C]104.459062894212[/C][C]-0.959062894211513[/C][/ROW]
[ROW][C]30[/C][C]100.17[/C][C]103.261930042744[/C][C]-3.09193004274414[/C][/ROW]
[ROW][C]31[/C][C]101.1[/C][C]99.828957416621[/C][C]1.27104258337903[/C][/ROW]
[ROW][C]32[/C][C]105.93[/C][C]100.715358018426[/C][C]5.21464198157425[/C][/ROW]
[ROW][C]33[/C][C]108.09[/C][C]105.779200253337[/C][C]2.31079974666308[/C][/ROW]
[ROW][C]34[/C][C]107.27[/C][C]108.10161838823[/C][C]-0.831618388230325[/C][/ROW]
[ROW][C]35[/C][C]104.9[/C][C]107.967069184641[/C][C]-3.06706918464056[/C][/ROW]
[ROW][C]36[/C][C]102.7[/C][C]107.843146929481[/C][C]-5.14314692948111[/C][/ROW]
[ROW][C]37[/C][C]102.06[/C][C]105.37037818359[/C][C]-3.31037818359033[/C][/ROW]
[ROW][C]38[/C][C]103.05[/C][C]103.114704864982[/C][C]-0.064704864981934[/C][/ROW]
[ROW][C]39[/C][C]102.08[/C][C]106.974585294943[/C][C]-4.89458529494303[/C][/ROW]
[ROW][C]40[/C][C]100.13[/C][C]102.123149877528[/C][C]-1.99314987752805[/C][/ROW]
[ROW][C]41[/C][C]97.56[/C][C]97.3771147948919[/C][C]0.182885205108079[/C][/ROW]
[ROW][C]42[/C][C]97.38[/C][C]96.2603350146643[/C][C]1.11966498533572[/C][/ROW]
[ROW][C]43[/C][C]99.66[/C][C]96.3105916708804[/C][C]3.34940832911964[/C][/ROW]
[ROW][C]44[/C][C]99.58[/C][C]98.7114364609972[/C][C]0.868563539002793[/C][/ROW]
[ROW][C]45[/C][C]102.7[/C][C]98.521408834074[/C][C]4.17859116592604[/C][/ROW]
[ROW][C]46[/C][C]98.92[/C][C]101.951610122393[/C][C]-3.03161012239278[/C][/ROW]
[ROW][C]47[/C][C]97.85[/C][C]98.6829934546144[/C][C]-0.83299345461441[/C][/ROW]
[ROW][C]48[/C][C]99.01[/C][C]100.035835453198[/C][C]-1.02583545319838[/C][/ROW]
[ROW][C]49[/C][C]97.71[/C][C]101.248836098539[/C][C]-3.53883609853861[/C][/ROW]
[ROW][C]50[/C][C]97.95[/C][C]98.3150867620473[/C][C]-0.365086762047312[/C][/ROW]
[ROW][C]51[/C][C]97.24[/C][C]101.401200414025[/C][C]-4.1612004140254[/C][/ROW]
[ROW][C]52[/C][C]96.69[/C][C]96.8677917812175[/C][C]-0.177791781217508[/C][/ROW]
[ROW][C]53[/C][C]96.41[/C][C]93.6653912293445[/C][C]2.74460877065555[/C][/ROW]
[ROW][C]54[/C][C]96.99[/C][C]95.0412998129332[/C][C]1.94870018706676[/C][/ROW]
[ROW][C]55[/C][C]98.36[/C][C]95.9171512861877[/C][C]2.44284871381225[/C][/ROW]
[ROW][C]56[/C][C]97.8[/C][C]97.3362673825455[/C][C]0.463732617454525[/C][/ROW]
[ROW][C]57[/C][C]96.79[/C][C]96.6342087753032[/C][C]0.155791224696841[/C][/ROW]
[ROW][C]58[/C][C]94.73[/C][C]95.6161186019613[/C][C]-0.886118601961329[/C][/ROW]
[ROW][C]59[/C][C]92.67[/C][C]94.2372572394418[/C][C]-1.56725723944182[/C][/ROW]
[ROW][C]60[/C][C]87.15[/C][C]94.5420029128961[/C][C]-7.39200291289613[/C][/ROW]
[ROW][C]61[/C][C]79.54[/C][C]88.5713004719465[/C][C]-9.03130047194652[/C][/ROW]
[ROW][C]62[/C][C]82.35[/C][C]78.8929770728443[/C][C]3.45702292715568[/C][/ROW]
[ROW][C]63[/C][C]86.38[/C][C]84.8515031980691[/C][C]1.52849680193093[/C][/ROW]
[ROW][C]64[/C][C]84.75[/C][C]85.5082740595762[/C][C]-0.758274059576237[/C][/ROW]
[ROW][C]65[/C][C]87.54[/C][C]81.1799446632301[/C][C]6.36005533676986[/C][/ROW]
[ROW][C]66[/C][C]86.73[/C][C]85.9119141469125[/C][C]0.818085853087467[/C][/ROW]
[ROW][C]67[/C][C]84.74[/C][C]85.3083092976568[/C][C]-0.568309297656825[/C][/ROW]
[ROW][C]68[/C][C]80.75[/C][C]83.1291769355369[/C][C]-2.37917693553692[/C][/ROW]
[ROW][C]69[/C][C]79.28[/C][C]78.7721820027974[/C][C]0.507817997202636[/C][/ROW]
[ROW][C]70[/C][C]78.52[/C][C]77.3219448466578[/C][C]1.19805515334215[/C][/ROW]
[ROW][C]71[/C][C]78.54[/C][C]77.407987213039[/C][C]1.13201278696096[/C][/ROW]
[ROW][C]72[/C][C]77.33[/C][C]80.006304183767[/C][C]-2.676304183767[/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
1390.7582.12552884615388.62447115384617
1492.8293.5981593601822-0.778159360182201
1597.7898.481589934962-0.701589934962016
1699.3299.8919121593295-0.571912159329472
1798.3398.7483280653832-0.418328065383179
1898.6699.1639791657784-0.503979165778446
1998.1399.5957700574462-1.46577005744624
2097.898.805628920048-1.00562892004801
2199.3698.21731167744921.14268832255082
22100.3799.84730664986990.522693350130083
23103.22101.6499131261661.57008687383403
24101.68107.112891338682-5.4328913386816
25104.39105.27719747276-0.887197472760079
26103.99106.563250747963-2.57325074796344
27106.71108.834650331896-2.12465033189643
28106.06107.892377353821-1.83237735382056
29103.5104.459062894212-0.959062894211513
30100.17103.261930042744-3.09193004274414
31101.199.8289574166211.27104258337903
32105.93100.7153580184265.21464198157425
33108.09105.7792002533372.31079974666308
34107.27108.10161838823-0.831618388230325
35104.9107.967069184641-3.06706918464056
36102.7107.843146929481-5.14314692948111
37102.06105.37037818359-3.31037818359033
38103.05103.114704864982-0.064704864981934
39102.08106.974585294943-4.89458529494303
40100.13102.123149877528-1.99314987752805
4197.5697.37711479489190.182885205108079
4297.3896.26033501466431.11966498533572
4399.6696.31059167088043.34940832911964
4499.5898.71143646099720.868563539002793
45102.798.5214088340744.17859116592604
4698.92101.951610122393-3.03161012239278
4797.8598.6829934546144-0.83299345461441
4899.01100.035835453198-1.02583545319838
4997.71101.248836098539-3.53883609853861
5097.9598.3150867620473-0.365086762047312
5197.24101.401200414025-4.1612004140254
5296.6996.8677917812175-0.177791781217508
5396.4193.66539122934452.74460877065555
5496.9995.04129981293321.94870018706676
5598.3695.91715128618772.44284871381225
5697.897.33626738254550.463732617454525
5796.7996.63420877530320.155791224696841
5894.7395.6161186019613-0.886118601961329
5992.6794.2372572394418-1.56725723944182
6087.1594.5420029128961-7.39200291289613
6179.5488.5713004719465-9.03130047194652
6282.3578.89297707284433.45702292715568
6386.3884.85150319806911.52849680193093
6484.7585.5082740595762-0.758274059576237
6587.5481.17994466323016.36005533676986
6686.7385.91191414691250.818085853087467
6784.7485.3083092976568-0.568309297656825
6880.7583.1291769355369-2.37917693553692
6979.2878.77218200279740.507817997202636
7078.5277.32194484665781.19805515334215
7178.5477.4079872130391.13201278696096
7277.3380.006304183767-2.676304183767







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7378.718716653619372.80587699010184.6315563171376
7478.753683307238670.054563736043187.4528028784342
7581.66364996085870.592210833570492.7350890881455
7681.079449947810667.808969132893194.3499307627281
7777.856916601429962.471887823090793.2419453797692
7876.073133255049258.614758423189393.5315080869092
7974.431016575335254.916134461828593.945898688842
8072.644733228954651.075213856002794.2142526019064
8170.679699882573947.047661945384694.3117378197632
8268.694249869526542.985194728882594.4033050101706
8367.460049856479239.654856051603495.265243661355
8468.714599843431938.790849827138498.6383498597253

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 78.7187166536193 & 72.805876990101 & 84.6315563171376 \tabularnewline
74 & 78.7536833072386 & 70.0545637360431 & 87.4528028784342 \tabularnewline
75 & 81.663649960858 & 70.5922108335704 & 92.7350890881455 \tabularnewline
76 & 81.0794499478106 & 67.8089691328931 & 94.3499307627281 \tabularnewline
77 & 77.8569166014299 & 62.4718878230907 & 93.2419453797692 \tabularnewline
78 & 76.0731332550492 & 58.6147584231893 & 93.5315080869092 \tabularnewline
79 & 74.4310165753352 & 54.9161344618285 & 93.945898688842 \tabularnewline
80 & 72.6447332289546 & 51.0752138560027 & 94.2142526019064 \tabularnewline
81 & 70.6796998825739 & 47.0476619453846 & 94.3117378197632 \tabularnewline
82 & 68.6942498695265 & 42.9851947288825 & 94.4033050101706 \tabularnewline
83 & 67.4600498564792 & 39.6548560516034 & 95.265243661355 \tabularnewline
84 & 68.7145998434319 & 38.7908498271384 & 98.6383498597253 \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]78.7187166536193[/C][C]72.805876990101[/C][C]84.6315563171376[/C][/ROW]
[ROW][C]74[/C][C]78.7536833072386[/C][C]70.0545637360431[/C][C]87.4528028784342[/C][/ROW]
[ROW][C]75[/C][C]81.663649960858[/C][C]70.5922108335704[/C][C]92.7350890881455[/C][/ROW]
[ROW][C]76[/C][C]81.0794499478106[/C][C]67.8089691328931[/C][C]94.3499307627281[/C][/ROW]
[ROW][C]77[/C][C]77.8569166014299[/C][C]62.4718878230907[/C][C]93.2419453797692[/C][/ROW]
[ROW][C]78[/C][C]76.0731332550492[/C][C]58.6147584231893[/C][C]93.5315080869092[/C][/ROW]
[ROW][C]79[/C][C]74.4310165753352[/C][C]54.9161344618285[/C][C]93.945898688842[/C][/ROW]
[ROW][C]80[/C][C]72.6447332289546[/C][C]51.0752138560027[/C][C]94.2142526019064[/C][/ROW]
[ROW][C]81[/C][C]70.6796998825739[/C][C]47.0476619453846[/C][C]94.3117378197632[/C][/ROW]
[ROW][C]82[/C][C]68.6942498695265[/C][C]42.9851947288825[/C][C]94.4033050101706[/C][/ROW]
[ROW][C]83[/C][C]67.4600498564792[/C][C]39.6548560516034[/C][C]95.265243661355[/C][/ROW]
[ROW][C]84[/C][C]68.7145998434319[/C][C]38.7908498271384[/C][C]98.6383498597253[/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
7378.718716653619372.80587699010184.6315563171376
7478.753683307238670.054563736043187.4528028784342
7581.66364996085870.592210833570492.7350890881455
7681.079449947810667.808969132893194.3499307627281
7777.856916601429962.471887823090793.2419453797692
7876.073133255049258.614758423189393.5315080869092
7974.431016575335254.916134461828593.945898688842
8072.644733228954651.075213856002794.2142526019064
8170.679699882573947.047661945384694.3117378197632
8268.694249869526542.985194728882594.4033050101706
8367.460049856479239.654856051603495.265243661355
8468.714599843431938.790849827138498.6383498597253



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')