Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 14:42:19 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259962990l8xmx3rinc6qz7l.htm/, Retrieved Sun, 28 Apr 2024 11:18:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64170, Retrieved Sun, 28 Apr 2024 11:18:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [Exponential Smoot...] [2009-12-04 21:42:19] [d45d8d97b86162be82506c3c0ea6e4a6] [Current]
Feedback Forum

Post a new message
Dataseries X:
4.4
5
3.2
1.1
3.3
3.3
5.5
7
7.2
7.1
7.9
5
5.3
4.8
5.2
6.9
7.9
8.5
8.5
7.3
6
5.5
5
6.1
7
8
9.1
8.5
8.2
7.3
6.7
5.8
5.4
4.5
3.6
4.8
4.7
5.9
6
5.1
4.9
4.4
4.7
6.1
6.8
7.9
7.5
6
6
5.5
6.5
7.1
6.7
6.8
6.5
7
7.2
6.8
6.4
6
5.8 
5.1
2.5
0.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64170&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64170&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.820021630071807
beta0.0124549900483784
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.820021630071807 \tabularnewline
beta & 0.0124549900483784 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64170&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]0.820021630071807[/C][/ROW]
[ROW][C]beta[/C][C]0.0124549900483784[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64170&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
alpha0.820021630071807
beta0.0124549900483784
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135.33.732927639104061.56707236089594
144.84.572397012067250.227602987932749
155.25.31740170245888-0.117401702458880
166.97.22803758291348-0.328037582913476
177.98.40531663987926-0.505316639879263
188.58.91765786392155-0.417657863921553
198.57.192645654767481.30735434523252
207.310.6969905864318-3.39699058643176
2168.22562870564466-2.22562870564466
225.56.10724824393515-0.607248243935146
2355.95263181263204-0.952631812632037
246.13.155907554048422.94409244595158
2576.048298290884820.951701709115175
2685.90666661513452.0933333848655
279.18.352840459569720.747159540430284
288.512.2673081415784-3.76730814157836
298.210.9901444438420-2.79014444384196
307.39.69418385154293-2.39418385154293
316.76.70952034611903-0.00952034611902786
325.87.77345370352174-1.97345370352174
335.46.48727200764192-1.08727200764192
344.55.56251418522646-1.06251418522646
353.64.8941900750896-1.29419007508960
364.82.644975779293372.15502422070663
374.74.482733956073100.217266043926896
385.94.128707464424371.77129253557563
3965.91460429386270.0853957061372999
405.17.47383608329303-2.37383608329303
414.96.73722891691531-1.83722891691531
424.45.84340219746708-1.44340219746708
434.74.285548839248120.414451160751877
446.15.057357763321541.04264223667846
456.86.359931237643270.440068762356727
467.96.605811877950531.29418812204947
477.57.76913639712451-0.269136397124512
4865.966897937749820.0331020622501805
4965.620034863868090.379965136131913
505.55.485492591082630.0145074089173711
516.55.51476760877170.985232391228305
527.17.25070035191592-0.150700351915923
536.78.78485631735195-2.08485631735195
546.87.92663060946345-1.12663060946345
556.56.8853304602473-0.385330460247297
5677.2538735871291-0.253873587129096
577.27.40396259798497-0.203962597984967
586.87.22009198265402-0.420091982654015
596.46.70419509902575-0.304195099025745
6065.129805385601330.870194614398671
615.85.523481391502070.276518608497926
625.15.24850864902505-0.148508649025052
632.55.27413106632128-2.77413106632128
640.33.33308215302075-3.03308215302075

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.3 & 3.73292763910406 & 1.56707236089594 \tabularnewline
14 & 4.8 & 4.57239701206725 & 0.227602987932749 \tabularnewline
15 & 5.2 & 5.31740170245888 & -0.117401702458880 \tabularnewline
16 & 6.9 & 7.22803758291348 & -0.328037582913476 \tabularnewline
17 & 7.9 & 8.40531663987926 & -0.505316639879263 \tabularnewline
18 & 8.5 & 8.91765786392155 & -0.417657863921553 \tabularnewline
19 & 8.5 & 7.19264565476748 & 1.30735434523252 \tabularnewline
20 & 7.3 & 10.6969905864318 & -3.39699058643176 \tabularnewline
21 & 6 & 8.22562870564466 & -2.22562870564466 \tabularnewline
22 & 5.5 & 6.10724824393515 & -0.607248243935146 \tabularnewline
23 & 5 & 5.95263181263204 & -0.952631812632037 \tabularnewline
24 & 6.1 & 3.15590755404842 & 2.94409244595158 \tabularnewline
25 & 7 & 6.04829829088482 & 0.951701709115175 \tabularnewline
26 & 8 & 5.9066666151345 & 2.0933333848655 \tabularnewline
27 & 9.1 & 8.35284045956972 & 0.747159540430284 \tabularnewline
28 & 8.5 & 12.2673081415784 & -3.76730814157836 \tabularnewline
29 & 8.2 & 10.9901444438420 & -2.79014444384196 \tabularnewline
30 & 7.3 & 9.69418385154293 & -2.39418385154293 \tabularnewline
31 & 6.7 & 6.70952034611903 & -0.00952034611902786 \tabularnewline
32 & 5.8 & 7.77345370352174 & -1.97345370352174 \tabularnewline
33 & 5.4 & 6.48727200764192 & -1.08727200764192 \tabularnewline
34 & 4.5 & 5.56251418522646 & -1.06251418522646 \tabularnewline
35 & 3.6 & 4.8941900750896 & -1.29419007508960 \tabularnewline
36 & 4.8 & 2.64497577929337 & 2.15502422070663 \tabularnewline
37 & 4.7 & 4.48273395607310 & 0.217266043926896 \tabularnewline
38 & 5.9 & 4.12870746442437 & 1.77129253557563 \tabularnewline
39 & 6 & 5.9146042938627 & 0.0853957061372999 \tabularnewline
40 & 5.1 & 7.47383608329303 & -2.37383608329303 \tabularnewline
41 & 4.9 & 6.73722891691531 & -1.83722891691531 \tabularnewline
42 & 4.4 & 5.84340219746708 & -1.44340219746708 \tabularnewline
43 & 4.7 & 4.28554883924812 & 0.414451160751877 \tabularnewline
44 & 6.1 & 5.05735776332154 & 1.04264223667846 \tabularnewline
45 & 6.8 & 6.35993123764327 & 0.440068762356727 \tabularnewline
46 & 7.9 & 6.60581187795053 & 1.29418812204947 \tabularnewline
47 & 7.5 & 7.76913639712451 & -0.269136397124512 \tabularnewline
48 & 6 & 5.96689793774982 & 0.0331020622501805 \tabularnewline
49 & 6 & 5.62003486386809 & 0.379965136131913 \tabularnewline
50 & 5.5 & 5.48549259108263 & 0.0145074089173711 \tabularnewline
51 & 6.5 & 5.5147676087717 & 0.985232391228305 \tabularnewline
52 & 7.1 & 7.25070035191592 & -0.150700351915923 \tabularnewline
53 & 6.7 & 8.78485631735195 & -2.08485631735195 \tabularnewline
54 & 6.8 & 7.92663060946345 & -1.12663060946345 \tabularnewline
55 & 6.5 & 6.8853304602473 & -0.385330460247297 \tabularnewline
56 & 7 & 7.2538735871291 & -0.253873587129096 \tabularnewline
57 & 7.2 & 7.40396259798497 & -0.203962597984967 \tabularnewline
58 & 6.8 & 7.22009198265402 & -0.420091982654015 \tabularnewline
59 & 6.4 & 6.70419509902575 & -0.304195099025745 \tabularnewline
60 & 6 & 5.12980538560133 & 0.870194614398671 \tabularnewline
61 & 5.8 & 5.52348139150207 & 0.276518608497926 \tabularnewline
62 & 5.1 & 5.24850864902505 & -0.148508649025052 \tabularnewline
63 & 2.5 & 5.27413106632128 & -2.77413106632128 \tabularnewline
64 & 0.3 & 3.33308215302075 & -3.03308215302075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64170&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]5.3[/C][C]3.73292763910406[/C][C]1.56707236089594[/C][/ROW]
[ROW][C]14[/C][C]4.8[/C][C]4.57239701206725[/C][C]0.227602987932749[/C][/ROW]
[ROW][C]15[/C][C]5.2[/C][C]5.31740170245888[/C][C]-0.117401702458880[/C][/ROW]
[ROW][C]16[/C][C]6.9[/C][C]7.22803758291348[/C][C]-0.328037582913476[/C][/ROW]
[ROW][C]17[/C][C]7.9[/C][C]8.40531663987926[/C][C]-0.505316639879263[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.91765786392155[/C][C]-0.417657863921553[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]7.19264565476748[/C][C]1.30735434523252[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]10.6969905864318[/C][C]-3.39699058643176[/C][/ROW]
[ROW][C]21[/C][C]6[/C][C]8.22562870564466[/C][C]-2.22562870564466[/C][/ROW]
[ROW][C]22[/C][C]5.5[/C][C]6.10724824393515[/C][C]-0.607248243935146[/C][/ROW]
[ROW][C]23[/C][C]5[/C][C]5.95263181263204[/C][C]-0.952631812632037[/C][/ROW]
[ROW][C]24[/C][C]6.1[/C][C]3.15590755404842[/C][C]2.94409244595158[/C][/ROW]
[ROW][C]25[/C][C]7[/C][C]6.04829829088482[/C][C]0.951701709115175[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]5.9066666151345[/C][C]2.0933333848655[/C][/ROW]
[ROW][C]27[/C][C]9.1[/C][C]8.35284045956972[/C][C]0.747159540430284[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]12.2673081415784[/C][C]-3.76730814157836[/C][/ROW]
[ROW][C]29[/C][C]8.2[/C][C]10.9901444438420[/C][C]-2.79014444384196[/C][/ROW]
[ROW][C]30[/C][C]7.3[/C][C]9.69418385154293[/C][C]-2.39418385154293[/C][/ROW]
[ROW][C]31[/C][C]6.7[/C][C]6.70952034611903[/C][C]-0.00952034611902786[/C][/ROW]
[ROW][C]32[/C][C]5.8[/C][C]7.77345370352174[/C][C]-1.97345370352174[/C][/ROW]
[ROW][C]33[/C][C]5.4[/C][C]6.48727200764192[/C][C]-1.08727200764192[/C][/ROW]
[ROW][C]34[/C][C]4.5[/C][C]5.56251418522646[/C][C]-1.06251418522646[/C][/ROW]
[ROW][C]35[/C][C]3.6[/C][C]4.8941900750896[/C][C]-1.29419007508960[/C][/ROW]
[ROW][C]36[/C][C]4.8[/C][C]2.64497577929337[/C][C]2.15502422070663[/C][/ROW]
[ROW][C]37[/C][C]4.7[/C][C]4.48273395607310[/C][C]0.217266043926896[/C][/ROW]
[ROW][C]38[/C][C]5.9[/C][C]4.12870746442437[/C][C]1.77129253557563[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]5.9146042938627[/C][C]0.0853957061372999[/C][/ROW]
[ROW][C]40[/C][C]5.1[/C][C]7.47383608329303[/C][C]-2.37383608329303[/C][/ROW]
[ROW][C]41[/C][C]4.9[/C][C]6.73722891691531[/C][C]-1.83722891691531[/C][/ROW]
[ROW][C]42[/C][C]4.4[/C][C]5.84340219746708[/C][C]-1.44340219746708[/C][/ROW]
[ROW][C]43[/C][C]4.7[/C][C]4.28554883924812[/C][C]0.414451160751877[/C][/ROW]
[ROW][C]44[/C][C]6.1[/C][C]5.05735776332154[/C][C]1.04264223667846[/C][/ROW]
[ROW][C]45[/C][C]6.8[/C][C]6.35993123764327[/C][C]0.440068762356727[/C][/ROW]
[ROW][C]46[/C][C]7.9[/C][C]6.60581187795053[/C][C]1.29418812204947[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]7.76913639712451[/C][C]-0.269136397124512[/C][/ROW]
[ROW][C]48[/C][C]6[/C][C]5.96689793774982[/C][C]0.0331020622501805[/C][/ROW]
[ROW][C]49[/C][C]6[/C][C]5.62003486386809[/C][C]0.379965136131913[/C][/ROW]
[ROW][C]50[/C][C]5.5[/C][C]5.48549259108263[/C][C]0.0145074089173711[/C][/ROW]
[ROW][C]51[/C][C]6.5[/C][C]5.5147676087717[/C][C]0.985232391228305[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]7.25070035191592[/C][C]-0.150700351915923[/C][/ROW]
[ROW][C]53[/C][C]6.7[/C][C]8.78485631735195[/C][C]-2.08485631735195[/C][/ROW]
[ROW][C]54[/C][C]6.8[/C][C]7.92663060946345[/C][C]-1.12663060946345[/C][/ROW]
[ROW][C]55[/C][C]6.5[/C][C]6.8853304602473[/C][C]-0.385330460247297[/C][/ROW]
[ROW][C]56[/C][C]7[/C][C]7.2538735871291[/C][C]-0.253873587129096[/C][/ROW]
[ROW][C]57[/C][C]7.2[/C][C]7.40396259798497[/C][C]-0.203962597984967[/C][/ROW]
[ROW][C]58[/C][C]6.8[/C][C]7.22009198265402[/C][C]-0.420091982654015[/C][/ROW]
[ROW][C]59[/C][C]6.4[/C][C]6.70419509902575[/C][C]-0.304195099025745[/C][/ROW]
[ROW][C]60[/C][C]6[/C][C]5.12980538560133[/C][C]0.870194614398671[/C][/ROW]
[ROW][C]61[/C][C]5.8[/C][C]5.52348139150207[/C][C]0.276518608497926[/C][/ROW]
[ROW][C]62[/C][C]5.1[/C][C]5.24850864902505[/C][C]-0.148508649025052[/C][/ROW]
[ROW][C]63[/C][C]2.5[/C][C]5.27413106632128[/C][C]-2.77413106632128[/C][/ROW]
[ROW][C]64[/C][C]0.3[/C][C]3.33308215302075[/C][C]-3.03308215302075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64170&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64170&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
135.33.732927639104061.56707236089594
144.84.572397012067250.227602987932749
155.25.31740170245888-0.117401702458880
166.97.22803758291348-0.328037582913476
177.98.40531663987926-0.505316639879263
188.58.91765786392155-0.417657863921553
198.57.192645654767481.30735434523252
207.310.6969905864318-3.39699058643176
2168.22562870564466-2.22562870564466
225.56.10724824393515-0.607248243935146
2355.95263181263204-0.952631812632037
246.13.155907554048422.94409244595158
2576.048298290884820.951701709115175
2685.90666661513452.0933333848655
279.18.352840459569720.747159540430284
288.512.2673081415784-3.76730814157836
298.210.9901444438420-2.79014444384196
307.39.69418385154293-2.39418385154293
316.76.70952034611903-0.00952034611902786
325.87.77345370352174-1.97345370352174
335.46.48727200764192-1.08727200764192
344.55.56251418522646-1.06251418522646
353.64.8941900750896-1.29419007508960
364.82.644975779293372.15502422070663
374.74.482733956073100.217266043926896
385.94.128707464424371.77129253557563
3965.91460429386270.0853957061372999
405.17.47383608329303-2.37383608329303
414.96.73722891691531-1.83722891691531
424.45.84340219746708-1.44340219746708
434.74.285548839248120.414451160751877
446.15.057357763321541.04264223667846
456.86.359931237643270.440068762356727
467.96.605811877950531.29418812204947
477.57.76913639712451-0.269136397124512
4865.966897937749820.0331020622501805
4965.620034863868090.379965136131913
505.55.485492591082630.0145074089173711
516.55.51476760877170.985232391228305
527.17.25070035191592-0.150700351915923
536.78.78485631735195-2.08485631735195
546.87.92663060946345-1.12663060946345
556.56.8853304602473-0.385330460247297
5677.2538735871291-0.253873587129096
577.27.40396259798497-0.203962597984967
586.87.22009198265402-0.420091982654015
596.46.70419509902575-0.304195099025745
6065.129805385601330.870194614398671
615.85.523481391502070.276518608497926
625.15.24850864902505-0.148508649025052
632.55.27413106632128-2.77413106632128
640.33.33308215302075-3.03308215302075







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
651.00036988744781-1.906331952597383.90707172749301
661.15872781150093-2.827774057826895.14522968082874
671.16955537973946-3.469249193768895.80835995324781
681.30582134192355-4.290451257969876.90209394181696
691.38328711931787-4.927192593380217.69376683201596
701.38054243745398-5.299289121761538.06037399666948
711.35752240873118-5.580895696711148.2959405141735
721.12348725627180-5.11787055640687.3648450689504
731.04920100662204-5.231904542711587.33030655595566
740.949811950078959-5.215045603888817.11466950404673
750.823146115435996-5.04952073597516.6958129668471
760.390666440950698-30.651252525784531.4325854076859

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
65 & 1.00036988744781 & -1.90633195259738 & 3.90707172749301 \tabularnewline
66 & 1.15872781150093 & -2.82777405782689 & 5.14522968082874 \tabularnewline
67 & 1.16955537973946 & -3.46924919376889 & 5.80835995324781 \tabularnewline
68 & 1.30582134192355 & -4.29045125796987 & 6.90209394181696 \tabularnewline
69 & 1.38328711931787 & -4.92719259338021 & 7.69376683201596 \tabularnewline
70 & 1.38054243745398 & -5.29928912176153 & 8.06037399666948 \tabularnewline
71 & 1.35752240873118 & -5.58089569671114 & 8.2959405141735 \tabularnewline
72 & 1.12348725627180 & -5.1178705564068 & 7.3648450689504 \tabularnewline
73 & 1.04920100662204 & -5.23190454271158 & 7.33030655595566 \tabularnewline
74 & 0.949811950078959 & -5.21504560388881 & 7.11466950404673 \tabularnewline
75 & 0.823146115435996 & -5.0495207359751 & 6.6958129668471 \tabularnewline
76 & 0.390666440950698 & -30.6512525257845 & 31.4325854076859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64170&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]65[/C][C]1.00036988744781[/C][C]-1.90633195259738[/C][C]3.90707172749301[/C][/ROW]
[ROW][C]66[/C][C]1.15872781150093[/C][C]-2.82777405782689[/C][C]5.14522968082874[/C][/ROW]
[ROW][C]67[/C][C]1.16955537973946[/C][C]-3.46924919376889[/C][C]5.80835995324781[/C][/ROW]
[ROW][C]68[/C][C]1.30582134192355[/C][C]-4.29045125796987[/C][C]6.90209394181696[/C][/ROW]
[ROW][C]69[/C][C]1.38328711931787[/C][C]-4.92719259338021[/C][C]7.69376683201596[/C][/ROW]
[ROW][C]70[/C][C]1.38054243745398[/C][C]-5.29928912176153[/C][C]8.06037399666948[/C][/ROW]
[ROW][C]71[/C][C]1.35752240873118[/C][C]-5.58089569671114[/C][C]8.2959405141735[/C][/ROW]
[ROW][C]72[/C][C]1.12348725627180[/C][C]-5.1178705564068[/C][C]7.3648450689504[/C][/ROW]
[ROW][C]73[/C][C]1.04920100662204[/C][C]-5.23190454271158[/C][C]7.33030655595566[/C][/ROW]
[ROW][C]74[/C][C]0.949811950078959[/C][C]-5.21504560388881[/C][C]7.11466950404673[/C][/ROW]
[ROW][C]75[/C][C]0.823146115435996[/C][C]-5.0495207359751[/C][C]6.6958129668471[/C][/ROW]
[ROW][C]76[/C][C]0.390666440950698[/C][C]-30.6512525257845[/C][C]31.4325854076859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64170&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64170&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
651.00036988744781-1.906331952597383.90707172749301
661.15872781150093-2.827774057826895.14522968082874
671.16955537973946-3.469249193768895.80835995324781
681.30582134192355-4.290451257969876.90209394181696
691.38328711931787-4.927192593380217.69376683201596
701.38054243745398-5.299289121761538.06037399666948
711.35752240873118-5.580895696711148.2959405141735
721.12348725627180-5.11787055640687.3648450689504
731.04920100662204-5.231904542711587.33030655595566
740.949811950078959-5.215045603888817.11466950404673
750.823146115435996-5.04952073597516.6958129668471
760.390666440950698-30.651252525784531.4325854076859



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')