Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 22:12:33 +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/May/02/t14937595652s1cfbzzsyvytp4.htm/, Retrieved Fri, 17 May 2024 04:29:59 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 04:29:59 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
90.33
90.62
91.22
91.39
91.72
91.32
91.1
91.05
91.45
91.53
91.63
91.78
92.32
92.8
92.65
93.35
93.63
93.76
93.83
93.37
93.41
93.84
94.66
94.65
94.91
95.81
95.87
95.84
96.31
96.17
96.16
96.48
96.61
97.68
97.83
97.88
98.63
99.25
99.64
100.47
101.12
101.33
100.5
99.93
99.81
99.74
99.72
99.87
100.39
100.09
100.03
101.2
99.96
99.94
100.01
98.69
98.19
98.08
98.46
98.75
99.25
99.68
99.64
101.46
100.99
101.12
100.6
100.24
100.16
101.25
100.74
100.61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 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]3 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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.897535358146864
beta0
gamma0.652859097529305

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.897535358146864 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.652859097529305 \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]0.897535358146864[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.652859097529305[/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
alpha0.897535358146864
beta0
gamma0.652859097529305







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.3291.28876335470091.0312366452991
1492.892.66930702582090.130692974179098
1592.6592.64366424388870.00633575611134063
1693.3593.3568231283665-0.00682312836650567
1793.6393.59358811541830.0364118845816535
1893.7693.69582472196780.0641752780322093
1993.8393.33714662246790.492853377532086
2093.3793.7411389411991-0.37113894119905
2193.4193.843000938035-0.433000938035036
2293.8493.57850627205180.261493727948221
2394.6693.93734512483290.72265487516708
2494.6594.7400924130466-0.0900924130465626
2594.9195.2381881543556-0.32818815435563
2695.8195.33835815593060.471641844069424
2795.8795.61041016722440.259589832775589
2895.8496.5499932768734-0.709993276873391
2996.3196.15853039789710.151469602102935
3096.1796.3658926056217-0.195892605621708
3196.1695.80247079517680.357529204823223
3296.4896.02720814072990.452791859270064
3396.6196.8644389070075-0.254438907007454
3497.6896.80666817984640.873331820153581
3597.8397.74550271661560.0844972833843514
3697.8897.9211122937387-0.0411122937386779
3798.6398.44724201564150.18275798435846
3899.2599.05950884945720.190491150542769
3999.6499.06503295864420.574967041355833
40100.47100.2228180276160.247181972384027
41101.12100.7480813153450.371918684654617
42101.33101.1300675836130.19993241638727
43100.5100.958933863464-0.458933863464409
4499.93100.457239329363-0.527239329363468
4599.81100.36754726831-0.557547268310159
4699.74100.11316826256-0.373168262560341
4799.7299.8804558356419-0.160455835641855
4899.8799.82780867800380.0421913219961567
49100.39100.443682136835-0.0536821368353202
50100.09100.844252911743-0.754252911742881
51100.03100.0275553251980.00244467480166577
52101.2100.649554153320.550445846680404
5399.96101.455351750154-1.49535175015403
5499.94100.149891763081-0.209891763081501
55100.0199.5668515088340.443148491166042
5698.6999.8702384916356-1.18023849163558
5798.1999.1924291448268-1.00242914482678
5898.0898.5510869534282-0.471086953428241
5998.4698.24471843141740.215281568582625
6098.7598.54286495571130.207135044288734
6199.2599.3003677849064-0.0503677849063564
6299.6899.65704864436090.0229513556391083
6399.6499.58853863337610.051461366623883
64101.46100.2911901994781.1688098005223
65100.99101.515137732839-0.525137732839312
66101.12101.166469943187-0.0464699431869775
67100.6100.773791661161-0.173791661160934
68100.24100.414856614017-0.174856614017031
69100.16100.651307602373-0.491307602373155
70101.25100.5042591895080.745740810491796
71100.74101.335951214556-0.595951214556251
72100.61100.905442670767-0.295442670767471

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.32 & 91.2887633547009 & 1.0312366452991 \tabularnewline
14 & 92.8 & 92.6693070258209 & 0.130692974179098 \tabularnewline
15 & 92.65 & 92.6436642438887 & 0.00633575611134063 \tabularnewline
16 & 93.35 & 93.3568231283665 & -0.00682312836650567 \tabularnewline
17 & 93.63 & 93.5935881154183 & 0.0364118845816535 \tabularnewline
18 & 93.76 & 93.6958247219678 & 0.0641752780322093 \tabularnewline
19 & 93.83 & 93.3371466224679 & 0.492853377532086 \tabularnewline
20 & 93.37 & 93.7411389411991 & -0.37113894119905 \tabularnewline
21 & 93.41 & 93.843000938035 & -0.433000938035036 \tabularnewline
22 & 93.84 & 93.5785062720518 & 0.261493727948221 \tabularnewline
23 & 94.66 & 93.9373451248329 & 0.72265487516708 \tabularnewline
24 & 94.65 & 94.7400924130466 & -0.0900924130465626 \tabularnewline
25 & 94.91 & 95.2381881543556 & -0.32818815435563 \tabularnewline
26 & 95.81 & 95.3383581559306 & 0.471641844069424 \tabularnewline
27 & 95.87 & 95.6104101672244 & 0.259589832775589 \tabularnewline
28 & 95.84 & 96.5499932768734 & -0.709993276873391 \tabularnewline
29 & 96.31 & 96.1585303978971 & 0.151469602102935 \tabularnewline
30 & 96.17 & 96.3658926056217 & -0.195892605621708 \tabularnewline
31 & 96.16 & 95.8024707951768 & 0.357529204823223 \tabularnewline
32 & 96.48 & 96.0272081407299 & 0.452791859270064 \tabularnewline
33 & 96.61 & 96.8644389070075 & -0.254438907007454 \tabularnewline
34 & 97.68 & 96.8066681798464 & 0.873331820153581 \tabularnewline
35 & 97.83 & 97.7455027166156 & 0.0844972833843514 \tabularnewline
36 & 97.88 & 97.9211122937387 & -0.0411122937386779 \tabularnewline
37 & 98.63 & 98.4472420156415 & 0.18275798435846 \tabularnewline
38 & 99.25 & 99.0595088494572 & 0.190491150542769 \tabularnewline
39 & 99.64 & 99.0650329586442 & 0.574967041355833 \tabularnewline
40 & 100.47 & 100.222818027616 & 0.247181972384027 \tabularnewline
41 & 101.12 & 100.748081315345 & 0.371918684654617 \tabularnewline
42 & 101.33 & 101.130067583613 & 0.19993241638727 \tabularnewline
43 & 100.5 & 100.958933863464 & -0.458933863464409 \tabularnewline
44 & 99.93 & 100.457239329363 & -0.527239329363468 \tabularnewline
45 & 99.81 & 100.36754726831 & -0.557547268310159 \tabularnewline
46 & 99.74 & 100.11316826256 & -0.373168262560341 \tabularnewline
47 & 99.72 & 99.8804558356419 & -0.160455835641855 \tabularnewline
48 & 99.87 & 99.8278086780038 & 0.0421913219961567 \tabularnewline
49 & 100.39 & 100.443682136835 & -0.0536821368353202 \tabularnewline
50 & 100.09 & 100.844252911743 & -0.754252911742881 \tabularnewline
51 & 100.03 & 100.027555325198 & 0.00244467480166577 \tabularnewline
52 & 101.2 & 100.64955415332 & 0.550445846680404 \tabularnewline
53 & 99.96 & 101.455351750154 & -1.49535175015403 \tabularnewline
54 & 99.94 & 100.149891763081 & -0.209891763081501 \tabularnewline
55 & 100.01 & 99.566851508834 & 0.443148491166042 \tabularnewline
56 & 98.69 & 99.8702384916356 & -1.18023849163558 \tabularnewline
57 & 98.19 & 99.1924291448268 & -1.00242914482678 \tabularnewline
58 & 98.08 & 98.5510869534282 & -0.471086953428241 \tabularnewline
59 & 98.46 & 98.2447184314174 & 0.215281568582625 \tabularnewline
60 & 98.75 & 98.5428649557113 & 0.207135044288734 \tabularnewline
61 & 99.25 & 99.3003677849064 & -0.0503677849063564 \tabularnewline
62 & 99.68 & 99.6570486443609 & 0.0229513556391083 \tabularnewline
63 & 99.64 & 99.5885386333761 & 0.051461366623883 \tabularnewline
64 & 101.46 & 100.291190199478 & 1.1688098005223 \tabularnewline
65 & 100.99 & 101.515137732839 & -0.525137732839312 \tabularnewline
66 & 101.12 & 101.166469943187 & -0.0464699431869775 \tabularnewline
67 & 100.6 & 100.773791661161 & -0.173791661160934 \tabularnewline
68 & 100.24 & 100.414856614017 & -0.174856614017031 \tabularnewline
69 & 100.16 & 100.651307602373 & -0.491307602373155 \tabularnewline
70 & 101.25 & 100.504259189508 & 0.745740810491796 \tabularnewline
71 & 100.74 & 101.335951214556 & -0.595951214556251 \tabularnewline
72 & 100.61 & 100.905442670767 & -0.295442670767471 \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]92.32[/C][C]91.2887633547009[/C][C]1.0312366452991[/C][/ROW]
[ROW][C]14[/C][C]92.8[/C][C]92.6693070258209[/C][C]0.130692974179098[/C][/ROW]
[ROW][C]15[/C][C]92.65[/C][C]92.6436642438887[/C][C]0.00633575611134063[/C][/ROW]
[ROW][C]16[/C][C]93.35[/C][C]93.3568231283665[/C][C]-0.00682312836650567[/C][/ROW]
[ROW][C]17[/C][C]93.63[/C][C]93.5935881154183[/C][C]0.0364118845816535[/C][/ROW]
[ROW][C]18[/C][C]93.76[/C][C]93.6958247219678[/C][C]0.0641752780322093[/C][/ROW]
[ROW][C]19[/C][C]93.83[/C][C]93.3371466224679[/C][C]0.492853377532086[/C][/ROW]
[ROW][C]20[/C][C]93.37[/C][C]93.7411389411991[/C][C]-0.37113894119905[/C][/ROW]
[ROW][C]21[/C][C]93.41[/C][C]93.843000938035[/C][C]-0.433000938035036[/C][/ROW]
[ROW][C]22[/C][C]93.84[/C][C]93.5785062720518[/C][C]0.261493727948221[/C][/ROW]
[ROW][C]23[/C][C]94.66[/C][C]93.9373451248329[/C][C]0.72265487516708[/C][/ROW]
[ROW][C]24[/C][C]94.65[/C][C]94.7400924130466[/C][C]-0.0900924130465626[/C][/ROW]
[ROW][C]25[/C][C]94.91[/C][C]95.2381881543556[/C][C]-0.32818815435563[/C][/ROW]
[ROW][C]26[/C][C]95.81[/C][C]95.3383581559306[/C][C]0.471641844069424[/C][/ROW]
[ROW][C]27[/C][C]95.87[/C][C]95.6104101672244[/C][C]0.259589832775589[/C][/ROW]
[ROW][C]28[/C][C]95.84[/C][C]96.5499932768734[/C][C]-0.709993276873391[/C][/ROW]
[ROW][C]29[/C][C]96.31[/C][C]96.1585303978971[/C][C]0.151469602102935[/C][/ROW]
[ROW][C]30[/C][C]96.17[/C][C]96.3658926056217[/C][C]-0.195892605621708[/C][/ROW]
[ROW][C]31[/C][C]96.16[/C][C]95.8024707951768[/C][C]0.357529204823223[/C][/ROW]
[ROW][C]32[/C][C]96.48[/C][C]96.0272081407299[/C][C]0.452791859270064[/C][/ROW]
[ROW][C]33[/C][C]96.61[/C][C]96.8644389070075[/C][C]-0.254438907007454[/C][/ROW]
[ROW][C]34[/C][C]97.68[/C][C]96.8066681798464[/C][C]0.873331820153581[/C][/ROW]
[ROW][C]35[/C][C]97.83[/C][C]97.7455027166156[/C][C]0.0844972833843514[/C][/ROW]
[ROW][C]36[/C][C]97.88[/C][C]97.9211122937387[/C][C]-0.0411122937386779[/C][/ROW]
[ROW][C]37[/C][C]98.63[/C][C]98.4472420156415[/C][C]0.18275798435846[/C][/ROW]
[ROW][C]38[/C][C]99.25[/C][C]99.0595088494572[/C][C]0.190491150542769[/C][/ROW]
[ROW][C]39[/C][C]99.64[/C][C]99.0650329586442[/C][C]0.574967041355833[/C][/ROW]
[ROW][C]40[/C][C]100.47[/C][C]100.222818027616[/C][C]0.247181972384027[/C][/ROW]
[ROW][C]41[/C][C]101.12[/C][C]100.748081315345[/C][C]0.371918684654617[/C][/ROW]
[ROW][C]42[/C][C]101.33[/C][C]101.130067583613[/C][C]0.19993241638727[/C][/ROW]
[ROW][C]43[/C][C]100.5[/C][C]100.958933863464[/C][C]-0.458933863464409[/C][/ROW]
[ROW][C]44[/C][C]99.93[/C][C]100.457239329363[/C][C]-0.527239329363468[/C][/ROW]
[ROW][C]45[/C][C]99.81[/C][C]100.36754726831[/C][C]-0.557547268310159[/C][/ROW]
[ROW][C]46[/C][C]99.74[/C][C]100.11316826256[/C][C]-0.373168262560341[/C][/ROW]
[ROW][C]47[/C][C]99.72[/C][C]99.8804558356419[/C][C]-0.160455835641855[/C][/ROW]
[ROW][C]48[/C][C]99.87[/C][C]99.8278086780038[/C][C]0.0421913219961567[/C][/ROW]
[ROW][C]49[/C][C]100.39[/C][C]100.443682136835[/C][C]-0.0536821368353202[/C][/ROW]
[ROW][C]50[/C][C]100.09[/C][C]100.844252911743[/C][C]-0.754252911742881[/C][/ROW]
[ROW][C]51[/C][C]100.03[/C][C]100.027555325198[/C][C]0.00244467480166577[/C][/ROW]
[ROW][C]52[/C][C]101.2[/C][C]100.64955415332[/C][C]0.550445846680404[/C][/ROW]
[ROW][C]53[/C][C]99.96[/C][C]101.455351750154[/C][C]-1.49535175015403[/C][/ROW]
[ROW][C]54[/C][C]99.94[/C][C]100.149891763081[/C][C]-0.209891763081501[/C][/ROW]
[ROW][C]55[/C][C]100.01[/C][C]99.566851508834[/C][C]0.443148491166042[/C][/ROW]
[ROW][C]56[/C][C]98.69[/C][C]99.8702384916356[/C][C]-1.18023849163558[/C][/ROW]
[ROW][C]57[/C][C]98.19[/C][C]99.1924291448268[/C][C]-1.00242914482678[/C][/ROW]
[ROW][C]58[/C][C]98.08[/C][C]98.5510869534282[/C][C]-0.471086953428241[/C][/ROW]
[ROW][C]59[/C][C]98.46[/C][C]98.2447184314174[/C][C]0.215281568582625[/C][/ROW]
[ROW][C]60[/C][C]98.75[/C][C]98.5428649557113[/C][C]0.207135044288734[/C][/ROW]
[ROW][C]61[/C][C]99.25[/C][C]99.3003677849064[/C][C]-0.0503677849063564[/C][/ROW]
[ROW][C]62[/C][C]99.68[/C][C]99.6570486443609[/C][C]0.0229513556391083[/C][/ROW]
[ROW][C]63[/C][C]99.64[/C][C]99.5885386333761[/C][C]0.051461366623883[/C][/ROW]
[ROW][C]64[/C][C]101.46[/C][C]100.291190199478[/C][C]1.1688098005223[/C][/ROW]
[ROW][C]65[/C][C]100.99[/C][C]101.515137732839[/C][C]-0.525137732839312[/C][/ROW]
[ROW][C]66[/C][C]101.12[/C][C]101.166469943187[/C][C]-0.0464699431869775[/C][/ROW]
[ROW][C]67[/C][C]100.6[/C][C]100.773791661161[/C][C]-0.173791661160934[/C][/ROW]
[ROW][C]68[/C][C]100.24[/C][C]100.414856614017[/C][C]-0.174856614017031[/C][/ROW]
[ROW][C]69[/C][C]100.16[/C][C]100.651307602373[/C][C]-0.491307602373155[/C][/ROW]
[ROW][C]70[/C][C]101.25[/C][C]100.504259189508[/C][C]0.745740810491796[/C][/ROW]
[ROW][C]71[/C][C]100.74[/C][C]101.335951214556[/C][C]-0.595951214556251[/C][/ROW]
[ROW][C]72[/C][C]100.61[/C][C]100.905442670767[/C][C]-0.295442670767471[/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
1392.3291.28876335470091.0312366452991
1492.892.66930702582090.130692974179098
1592.6592.64366424388870.00633575611134063
1693.3593.3568231283665-0.00682312836650567
1793.6393.59358811541830.0364118845816535
1893.7693.69582472196780.0641752780322093
1993.8393.33714662246790.492853377532086
2093.3793.7411389411991-0.37113894119905
2193.4193.843000938035-0.433000938035036
2293.8493.57850627205180.261493727948221
2394.6693.93734512483290.72265487516708
2494.6594.7400924130466-0.0900924130465626
2594.9195.2381881543556-0.32818815435563
2695.8195.33835815593060.471641844069424
2795.8795.61041016722440.259589832775589
2895.8496.5499932768734-0.709993276873391
2996.3196.15853039789710.151469602102935
3096.1796.3658926056217-0.195892605621708
3196.1695.80247079517680.357529204823223
3296.4896.02720814072990.452791859270064
3396.6196.8644389070075-0.254438907007454
3497.6896.80666817984640.873331820153581
3597.8397.74550271661560.0844972833843514
3697.8897.9211122937387-0.0411122937386779
3798.6398.44724201564150.18275798435846
3899.2599.05950884945720.190491150542769
3999.6499.06503295864420.574967041355833
40100.47100.2228180276160.247181972384027
41101.12100.7480813153450.371918684654617
42101.33101.1300675836130.19993241638727
43100.5100.958933863464-0.458933863464409
4499.93100.457239329363-0.527239329363468
4599.81100.36754726831-0.557547268310159
4699.74100.11316826256-0.373168262560341
4799.7299.8804558356419-0.160455835641855
4899.8799.82780867800380.0421913219961567
49100.39100.443682136835-0.0536821368353202
50100.09100.844252911743-0.754252911742881
51100.03100.0275553251980.00244467480166577
52101.2100.649554153320.550445846680404
5399.96101.455351750154-1.49535175015403
5499.94100.149891763081-0.209891763081501
55100.0199.5668515088340.443148491166042
5698.6999.8702384916356-1.18023849163558
5798.1999.1924291448268-1.00242914482678
5898.0898.5510869534282-0.471086953428241
5998.4698.24471843141740.215281568582625
6098.7598.54286495571130.207135044288734
6199.2599.3003677849064-0.0503677849063564
6299.6899.65704864436090.0229513556391083
6399.6499.58853863337610.051461366623883
64101.46100.2911901994781.1688098005223
65100.99101.515137732839-0.525137732839312
66101.12101.166469943187-0.0464699431869775
67100.6100.773791661161-0.173791661160934
68100.24100.414856614017-0.174856614017031
69100.16100.651307602373-0.491307602373155
70101.25100.5042591895080.745740810491796
71100.74101.335951214556-0.595951214556251
72100.61100.905442670767-0.295442670767471







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.19463858552100.207430266948102.181846904092
74101.601430994811100.274904472649102.927957516973
75101.51422850705599.9189965603648103.109460453746
76102.245436671031100.420647008225104.070226333837
77102.307019505936100.278485635569104.335553376303
78102.46170186856100.248098016701104.67530572042
79102.10221482067299.7178628410537104.48656680029
80101.89919269437899.355528661442104.442856727314
81102.27141469590699.5778447483836104.964984643428
82102.64808454882899.8125226271036105.483646470553
83102.7206953758499.7499204328871105.691470318793
84102.84517662995299.74508048444105.945272775464

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.19463858552 & 100.207430266948 & 102.181846904092 \tabularnewline
74 & 101.601430994811 & 100.274904472649 & 102.927957516973 \tabularnewline
75 & 101.514228507055 & 99.9189965603648 & 103.109460453746 \tabularnewline
76 & 102.245436671031 & 100.420647008225 & 104.070226333837 \tabularnewline
77 & 102.307019505936 & 100.278485635569 & 104.335553376303 \tabularnewline
78 & 102.46170186856 & 100.248098016701 & 104.67530572042 \tabularnewline
79 & 102.102214820672 & 99.7178628410537 & 104.48656680029 \tabularnewline
80 & 101.899192694378 & 99.355528661442 & 104.442856727314 \tabularnewline
81 & 102.271414695906 & 99.5778447483836 & 104.964984643428 \tabularnewline
82 & 102.648084548828 & 99.8125226271036 & 105.483646470553 \tabularnewline
83 & 102.72069537584 & 99.7499204328871 & 105.691470318793 \tabularnewline
84 & 102.845176629952 & 99.74508048444 & 105.945272775464 \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]101.19463858552[/C][C]100.207430266948[/C][C]102.181846904092[/C][/ROW]
[ROW][C]74[/C][C]101.601430994811[/C][C]100.274904472649[/C][C]102.927957516973[/C][/ROW]
[ROW][C]75[/C][C]101.514228507055[/C][C]99.9189965603648[/C][C]103.109460453746[/C][/ROW]
[ROW][C]76[/C][C]102.245436671031[/C][C]100.420647008225[/C][C]104.070226333837[/C][/ROW]
[ROW][C]77[/C][C]102.307019505936[/C][C]100.278485635569[/C][C]104.335553376303[/C][/ROW]
[ROW][C]78[/C][C]102.46170186856[/C][C]100.248098016701[/C][C]104.67530572042[/C][/ROW]
[ROW][C]79[/C][C]102.102214820672[/C][C]99.7178628410537[/C][C]104.48656680029[/C][/ROW]
[ROW][C]80[/C][C]101.899192694378[/C][C]99.355528661442[/C][C]104.442856727314[/C][/ROW]
[ROW][C]81[/C][C]102.271414695906[/C][C]99.5778447483836[/C][C]104.964984643428[/C][/ROW]
[ROW][C]82[/C][C]102.648084548828[/C][C]99.8125226271036[/C][C]105.483646470553[/C][/ROW]
[ROW][C]83[/C][C]102.72069537584[/C][C]99.7499204328871[/C][C]105.691470318793[/C][/ROW]
[ROW][C]84[/C][C]102.845176629952[/C][C]99.74508048444[/C][C]105.945272775464[/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
73101.19463858552100.207430266948102.181846904092
74101.601430994811100.274904472649102.927957516973
75101.51422850705599.9189965603648103.109460453746
76102.245436671031100.420647008225104.070226333837
77102.307019505936100.278485635569104.335553376303
78102.46170186856100.248098016701104.67530572042
79102.10221482067299.7178628410537104.48656680029
80101.89919269437899.355528661442104.442856727314
81102.27141469590699.5778447483836104.964984643428
82102.64808454882899.8125226271036105.483646470553
83102.7206953758499.7499204328871105.691470318793
84102.84517662995299.74508048444105.945272775464



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')