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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Jun 2009 06:59:01 -0600
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/Jun/04/t1244120430fuv5238oylxr45o.htm/, Retrieved Tue, 14 May 2024 10:30:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41645, Retrieved Tue, 14 May 2024 10:30:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [voorspellen datar...] [2009-06-04 12:59:01] [267e4485b61217b9c165d444603a8c11] [Current]
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Dataseries X:
1
-1
3
4
3
2
1
4
3
5
6
6
6
6
6
5
6
5
6
5
7
4
5
6
6
5
3
2
3
3
2
0
4
4
5
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41645&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41645&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.632874910581782
beta0.230201372346766
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.632874910581782 \tabularnewline
beta & 0.230201372346766 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41645&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]0.632874910581782[/C][/ROW]
[ROW][C]beta[/C][C]0.230201372346766[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41645&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
alpha0.632874910581782
beta0.230201372346766
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33-36
44-0.3286184988707334.32861849887073
531.915618268946291.08438173105371
622.26464111778233-0.264641117782325
711.72134603853347-0.721346038533472
840.783921926317683.21607807368232
932.806940893668450.193059106331545
1052.944893527370462.05510647262954
1164.560694956264661.43930504373534
1265.996461552688620.00353844731137798
1366.52408300447752-0.524083004477522
1466.64143311971188-0.641433119711878
1566.5910657512701-0.591065751270094
1656.48646304170446-1.48646304170446
1765.598625024100080.40137497589992
1855.96402811067005-0.964028110670049
1965.324853864798810.675146135201186
2055.82143301768917-0.821433017689166
2175.251191286759441.74880871324056
2246.56237268212294-2.56237268212294
2354.771806861758330.228193138241669
2464.780565290913941.21943470908606
2565.594313465086070.405686534913929
2655.95216476919407-0.952164769194068
2735.31194642898748-2.31194642898748
2823.47433198528138-1.47433198528138
2931.952029237329501.04797076267050
3032.178706085140980.821293914859019
3122.38157806371213-0.381578063712125
3201.76759094467858-1.76759094467858
3340.01891306850762993.98108693149237
3442.488428461088791.51157153891121
3553.615268371967311.38473162803269
3664.863574198856181.13642580114382
3766.12029786461897-0.120297864618973
3856.5641466165323-1.56414661653230
3955.86634127383906-0.866341273839057
4035.48394331450773-2.48394331450773
4153.715923203183081.28407679681692
4254.519663927364380.480336072635623
4354.884716837585880.115283162414121
4435.03553237083774-2.03553237083774
4563.528596705971642.47140329402836
4665.234043013211470.765956986788529
4745.97174639818902-1.97174639818902
4864.689564882073551.31043511792645
4955.6755092527872-0.675509252787198
5045.30618521086796-1.30618521086796
5154.347425788387380.652574211612621
5254.723388731144970.276611268855026
5344.90171328880246-0.901713288802465
5434.20293638497837-1.20293638497837
5523.13826873553833-1.13826873553833
5631.948694757425791.05130524257421
5722.29801048056867-0.298010480568670
58-11.74996138464472-2.74996138464472
590-0.7505041452117640.750504145211764
60-2-0.926272912914023-1.07372708708598
611-2.412981733054243.41298173305424
62-2-0.562932330385403-1.43706766961460
63-2-1.99172199145862-0.00827800854138205
64-2-2.517472535618930.517472535618926
65-6-2.63509886415836-3.36490113584164
66-4-5.700010063922731.70001006392273
67-2-5.311793830834423.31179383083442
680-3.421029242120343.42102924212034
69-5-0.96272709188369-4.03727290811631
70-4-3.81278218034909-0.187217819650909
71-5-4.25350951466263-0.746490485337366
72-1-5.156941695434294.15694169543429

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3 & -3 & 6 \tabularnewline
4 & 4 & -0.328618498870733 & 4.32861849887073 \tabularnewline
5 & 3 & 1.91561826894629 & 1.08438173105371 \tabularnewline
6 & 2 & 2.26464111778233 & -0.264641117782325 \tabularnewline
7 & 1 & 1.72134603853347 & -0.721346038533472 \tabularnewline
8 & 4 & 0.78392192631768 & 3.21607807368232 \tabularnewline
9 & 3 & 2.80694089366845 & 0.193059106331545 \tabularnewline
10 & 5 & 2.94489352737046 & 2.05510647262954 \tabularnewline
11 & 6 & 4.56069495626466 & 1.43930504373534 \tabularnewline
12 & 6 & 5.99646155268862 & 0.00353844731137798 \tabularnewline
13 & 6 & 6.52408300447752 & -0.524083004477522 \tabularnewline
14 & 6 & 6.64143311971188 & -0.641433119711878 \tabularnewline
15 & 6 & 6.5910657512701 & -0.591065751270094 \tabularnewline
16 & 5 & 6.48646304170446 & -1.48646304170446 \tabularnewline
17 & 6 & 5.59862502410008 & 0.40137497589992 \tabularnewline
18 & 5 & 5.96402811067005 & -0.964028110670049 \tabularnewline
19 & 6 & 5.32485386479881 & 0.675146135201186 \tabularnewline
20 & 5 & 5.82143301768917 & -0.821433017689166 \tabularnewline
21 & 7 & 5.25119128675944 & 1.74880871324056 \tabularnewline
22 & 4 & 6.56237268212294 & -2.56237268212294 \tabularnewline
23 & 5 & 4.77180686175833 & 0.228193138241669 \tabularnewline
24 & 6 & 4.78056529091394 & 1.21943470908606 \tabularnewline
25 & 6 & 5.59431346508607 & 0.405686534913929 \tabularnewline
26 & 5 & 5.95216476919407 & -0.952164769194068 \tabularnewline
27 & 3 & 5.31194642898748 & -2.31194642898748 \tabularnewline
28 & 2 & 3.47433198528138 & -1.47433198528138 \tabularnewline
29 & 3 & 1.95202923732950 & 1.04797076267050 \tabularnewline
30 & 3 & 2.17870608514098 & 0.821293914859019 \tabularnewline
31 & 2 & 2.38157806371213 & -0.381578063712125 \tabularnewline
32 & 0 & 1.76759094467858 & -1.76759094467858 \tabularnewline
33 & 4 & 0.0189130685076299 & 3.98108693149237 \tabularnewline
34 & 4 & 2.48842846108879 & 1.51157153891121 \tabularnewline
35 & 5 & 3.61526837196731 & 1.38473162803269 \tabularnewline
36 & 6 & 4.86357419885618 & 1.13642580114382 \tabularnewline
37 & 6 & 6.12029786461897 & -0.120297864618973 \tabularnewline
38 & 5 & 6.5641466165323 & -1.56414661653230 \tabularnewline
39 & 5 & 5.86634127383906 & -0.866341273839057 \tabularnewline
40 & 3 & 5.48394331450773 & -2.48394331450773 \tabularnewline
41 & 5 & 3.71592320318308 & 1.28407679681692 \tabularnewline
42 & 5 & 4.51966392736438 & 0.480336072635623 \tabularnewline
43 & 5 & 4.88471683758588 & 0.115283162414121 \tabularnewline
44 & 3 & 5.03553237083774 & -2.03553237083774 \tabularnewline
45 & 6 & 3.52859670597164 & 2.47140329402836 \tabularnewline
46 & 6 & 5.23404301321147 & 0.765956986788529 \tabularnewline
47 & 4 & 5.97174639818902 & -1.97174639818902 \tabularnewline
48 & 6 & 4.68956488207355 & 1.31043511792645 \tabularnewline
49 & 5 & 5.6755092527872 & -0.675509252787198 \tabularnewline
50 & 4 & 5.30618521086796 & -1.30618521086796 \tabularnewline
51 & 5 & 4.34742578838738 & 0.652574211612621 \tabularnewline
52 & 5 & 4.72338873114497 & 0.276611268855026 \tabularnewline
53 & 4 & 4.90171328880246 & -0.901713288802465 \tabularnewline
54 & 3 & 4.20293638497837 & -1.20293638497837 \tabularnewline
55 & 2 & 3.13826873553833 & -1.13826873553833 \tabularnewline
56 & 3 & 1.94869475742579 & 1.05130524257421 \tabularnewline
57 & 2 & 2.29801048056867 & -0.298010480568670 \tabularnewline
58 & -1 & 1.74996138464472 & -2.74996138464472 \tabularnewline
59 & 0 & -0.750504145211764 & 0.750504145211764 \tabularnewline
60 & -2 & -0.926272912914023 & -1.07372708708598 \tabularnewline
61 & 1 & -2.41298173305424 & 3.41298173305424 \tabularnewline
62 & -2 & -0.562932330385403 & -1.43706766961460 \tabularnewline
63 & -2 & -1.99172199145862 & -0.00827800854138205 \tabularnewline
64 & -2 & -2.51747253561893 & 0.517472535618926 \tabularnewline
65 & -6 & -2.63509886415836 & -3.36490113584164 \tabularnewline
66 & -4 & -5.70001006392273 & 1.70001006392273 \tabularnewline
67 & -2 & -5.31179383083442 & 3.31179383083442 \tabularnewline
68 & 0 & -3.42102924212034 & 3.42102924212034 \tabularnewline
69 & -5 & -0.96272709188369 & -4.03727290811631 \tabularnewline
70 & -4 & -3.81278218034909 & -0.187217819650909 \tabularnewline
71 & -5 & -4.25350951466263 & -0.746490485337366 \tabularnewline
72 & -1 & -5.15694169543429 & 4.15694169543429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41645&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]3[/C][C]3[/C][C]-3[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]4[/C][C]-0.328618498870733[/C][C]4.32861849887073[/C][/ROW]
[ROW][C]5[/C][C]3[/C][C]1.91561826894629[/C][C]1.08438173105371[/C][/ROW]
[ROW][C]6[/C][C]2[/C][C]2.26464111778233[/C][C]-0.264641117782325[/C][/ROW]
[ROW][C]7[/C][C]1[/C][C]1.72134603853347[/C][C]-0.721346038533472[/C][/ROW]
[ROW][C]8[/C][C]4[/C][C]0.78392192631768[/C][C]3.21607807368232[/C][/ROW]
[ROW][C]9[/C][C]3[/C][C]2.80694089366845[/C][C]0.193059106331545[/C][/ROW]
[ROW][C]10[/C][C]5[/C][C]2.94489352737046[/C][C]2.05510647262954[/C][/ROW]
[ROW][C]11[/C][C]6[/C][C]4.56069495626466[/C][C]1.43930504373534[/C][/ROW]
[ROW][C]12[/C][C]6[/C][C]5.99646155268862[/C][C]0.00353844731137798[/C][/ROW]
[ROW][C]13[/C][C]6[/C][C]6.52408300447752[/C][C]-0.524083004477522[/C][/ROW]
[ROW][C]14[/C][C]6[/C][C]6.64143311971188[/C][C]-0.641433119711878[/C][/ROW]
[ROW][C]15[/C][C]6[/C][C]6.5910657512701[/C][C]-0.591065751270094[/C][/ROW]
[ROW][C]16[/C][C]5[/C][C]6.48646304170446[/C][C]-1.48646304170446[/C][/ROW]
[ROW][C]17[/C][C]6[/C][C]5.59862502410008[/C][C]0.40137497589992[/C][/ROW]
[ROW][C]18[/C][C]5[/C][C]5.96402811067005[/C][C]-0.964028110670049[/C][/ROW]
[ROW][C]19[/C][C]6[/C][C]5.32485386479881[/C][C]0.675146135201186[/C][/ROW]
[ROW][C]20[/C][C]5[/C][C]5.82143301768917[/C][C]-0.821433017689166[/C][/ROW]
[ROW][C]21[/C][C]7[/C][C]5.25119128675944[/C][C]1.74880871324056[/C][/ROW]
[ROW][C]22[/C][C]4[/C][C]6.56237268212294[/C][C]-2.56237268212294[/C][/ROW]
[ROW][C]23[/C][C]5[/C][C]4.77180686175833[/C][C]0.228193138241669[/C][/ROW]
[ROW][C]24[/C][C]6[/C][C]4.78056529091394[/C][C]1.21943470908606[/C][/ROW]
[ROW][C]25[/C][C]6[/C][C]5.59431346508607[/C][C]0.405686534913929[/C][/ROW]
[ROW][C]26[/C][C]5[/C][C]5.95216476919407[/C][C]-0.952164769194068[/C][/ROW]
[ROW][C]27[/C][C]3[/C][C]5.31194642898748[/C][C]-2.31194642898748[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]3.47433198528138[/C][C]-1.47433198528138[/C][/ROW]
[ROW][C]29[/C][C]3[/C][C]1.95202923732950[/C][C]1.04797076267050[/C][/ROW]
[ROW][C]30[/C][C]3[/C][C]2.17870608514098[/C][C]0.821293914859019[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]2.38157806371213[/C][C]-0.381578063712125[/C][/ROW]
[ROW][C]32[/C][C]0[/C][C]1.76759094467858[/C][C]-1.76759094467858[/C][/ROW]
[ROW][C]33[/C][C]4[/C][C]0.0189130685076299[/C][C]3.98108693149237[/C][/ROW]
[ROW][C]34[/C][C]4[/C][C]2.48842846108879[/C][C]1.51157153891121[/C][/ROW]
[ROW][C]35[/C][C]5[/C][C]3.61526837196731[/C][C]1.38473162803269[/C][/ROW]
[ROW][C]36[/C][C]6[/C][C]4.86357419885618[/C][C]1.13642580114382[/C][/ROW]
[ROW][C]37[/C][C]6[/C][C]6.12029786461897[/C][C]-0.120297864618973[/C][/ROW]
[ROW][C]38[/C][C]5[/C][C]6.5641466165323[/C][C]-1.56414661653230[/C][/ROW]
[ROW][C]39[/C][C]5[/C][C]5.86634127383906[/C][C]-0.866341273839057[/C][/ROW]
[ROW][C]40[/C][C]3[/C][C]5.48394331450773[/C][C]-2.48394331450773[/C][/ROW]
[ROW][C]41[/C][C]5[/C][C]3.71592320318308[/C][C]1.28407679681692[/C][/ROW]
[ROW][C]42[/C][C]5[/C][C]4.51966392736438[/C][C]0.480336072635623[/C][/ROW]
[ROW][C]43[/C][C]5[/C][C]4.88471683758588[/C][C]0.115283162414121[/C][/ROW]
[ROW][C]44[/C][C]3[/C][C]5.03553237083774[/C][C]-2.03553237083774[/C][/ROW]
[ROW][C]45[/C][C]6[/C][C]3.52859670597164[/C][C]2.47140329402836[/C][/ROW]
[ROW][C]46[/C][C]6[/C][C]5.23404301321147[/C][C]0.765956986788529[/C][/ROW]
[ROW][C]47[/C][C]4[/C][C]5.97174639818902[/C][C]-1.97174639818902[/C][/ROW]
[ROW][C]48[/C][C]6[/C][C]4.68956488207355[/C][C]1.31043511792645[/C][/ROW]
[ROW][C]49[/C][C]5[/C][C]5.6755092527872[/C][C]-0.675509252787198[/C][/ROW]
[ROW][C]50[/C][C]4[/C][C]5.30618521086796[/C][C]-1.30618521086796[/C][/ROW]
[ROW][C]51[/C][C]5[/C][C]4.34742578838738[/C][C]0.652574211612621[/C][/ROW]
[ROW][C]52[/C][C]5[/C][C]4.72338873114497[/C][C]0.276611268855026[/C][/ROW]
[ROW][C]53[/C][C]4[/C][C]4.90171328880246[/C][C]-0.901713288802465[/C][/ROW]
[ROW][C]54[/C][C]3[/C][C]4.20293638497837[/C][C]-1.20293638497837[/C][/ROW]
[ROW][C]55[/C][C]2[/C][C]3.13826873553833[/C][C]-1.13826873553833[/C][/ROW]
[ROW][C]56[/C][C]3[/C][C]1.94869475742579[/C][C]1.05130524257421[/C][/ROW]
[ROW][C]57[/C][C]2[/C][C]2.29801048056867[/C][C]-0.298010480568670[/C][/ROW]
[ROW][C]58[/C][C]-1[/C][C]1.74996138464472[/C][C]-2.74996138464472[/C][/ROW]
[ROW][C]59[/C][C]0[/C][C]-0.750504145211764[/C][C]0.750504145211764[/C][/ROW]
[ROW][C]60[/C][C]-2[/C][C]-0.926272912914023[/C][C]-1.07372708708598[/C][/ROW]
[ROW][C]61[/C][C]1[/C][C]-2.41298173305424[/C][C]3.41298173305424[/C][/ROW]
[ROW][C]62[/C][C]-2[/C][C]-0.562932330385403[/C][C]-1.43706766961460[/C][/ROW]
[ROW][C]63[/C][C]-2[/C][C]-1.99172199145862[/C][C]-0.00827800854138205[/C][/ROW]
[ROW][C]64[/C][C]-2[/C][C]-2.51747253561893[/C][C]0.517472535618926[/C][/ROW]
[ROW][C]65[/C][C]-6[/C][C]-2.63509886415836[/C][C]-3.36490113584164[/C][/ROW]
[ROW][C]66[/C][C]-4[/C][C]-5.70001006392273[/C][C]1.70001006392273[/C][/ROW]
[ROW][C]67[/C][C]-2[/C][C]-5.31179383083442[/C][C]3.31179383083442[/C][/ROW]
[ROW][C]68[/C][C]0[/C][C]-3.42102924212034[/C][C]3.42102924212034[/C][/ROW]
[ROW][C]69[/C][C]-5[/C][C]-0.96272709188369[/C][C]-4.03727290811631[/C][/ROW]
[ROW][C]70[/C][C]-4[/C][C]-3.81278218034909[/C][C]-0.187217819650909[/C][/ROW]
[ROW][C]71[/C][C]-5[/C][C]-4.25350951466263[/C][C]-0.746490485337366[/C][/ROW]
[ROW][C]72[/C][C]-1[/C][C]-5.15694169543429[/C][C]4.15694169543429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41645&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
33-36
44-0.3286184988707334.32861849887073
531.915618268946291.08438173105371
622.26464111778233-0.264641117782325
711.72134603853347-0.721346038533472
840.783921926317683.21607807368232
932.806940893668450.193059106331545
1052.944893527370462.05510647262954
1164.560694956264661.43930504373534
1265.996461552688620.00353844731137798
1366.52408300447752-0.524083004477522
1466.64143311971188-0.641433119711878
1566.5910657512701-0.591065751270094
1656.48646304170446-1.48646304170446
1765.598625024100080.40137497589992
1855.96402811067005-0.964028110670049
1965.324853864798810.675146135201186
2055.82143301768917-0.821433017689166
2175.251191286759441.74880871324056
2246.56237268212294-2.56237268212294
2354.771806861758330.228193138241669
2464.780565290913941.21943470908606
2565.594313465086070.405686534913929
2655.95216476919407-0.952164769194068
2735.31194642898748-2.31194642898748
2823.47433198528138-1.47433198528138
2931.952029237329501.04797076267050
3032.178706085140980.821293914859019
3122.38157806371213-0.381578063712125
3201.76759094467858-1.76759094467858
3340.01891306850762993.98108693149237
3442.488428461088791.51157153891121
3553.615268371967311.38473162803269
3664.863574198856181.13642580114382
3766.12029786461897-0.120297864618973
3856.5641466165323-1.56414661653230
3955.86634127383906-0.866341273839057
4035.48394331450773-2.48394331450773
4153.715923203183081.28407679681692
4254.519663927364380.480336072635623
4354.884716837585880.115283162414121
4435.03553237083774-2.03553237083774
4563.528596705971642.47140329402836
4665.234043013211470.765956986788529
4745.97174639818902-1.97174639818902
4864.689564882073551.31043511792645
4955.6755092527872-0.675509252787198
5045.30618521086796-1.30618521086796
5154.347425788387380.652574211612621
5254.723388731144970.276611268855026
5344.90171328880246-0.901713288802465
5434.20293638497837-1.20293638497837
5523.13826873553833-1.13826873553833
5631.948694757425791.05130524257421
5722.29801048056867-0.298010480568670
58-11.74996138464472-2.74996138464472
590-0.7505041452117640.750504145211764
60-2-0.926272912914023-1.07372708708598
611-2.412981733054243.41298173305424
62-2-0.562932330385403-1.43706766961460
63-2-1.99172199145862-0.00827800854138205
64-2-2.517472535618930.517472535618926
65-6-2.63509886415836-3.36490113584164
66-4-5.700010063922731.70001006392273
67-2-5.311793830834423.31179383083442
680-3.421029242120343.42102924212034
69-5-0.96272709188369-4.03727290811631
70-4-3.81278218034909-0.187217819650909
71-5-4.25350951466263-0.746490485337366
72-1-5.156941695434294.15694169543429







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-2.35149535416046-6.090038626878681.38704791855776
74-2.17687311667829-6.91489414997062.56114791661402
75-2.00225087919612-7.866407740520143.8619059821279
76-1.82762864171395-8.926114353834415.27085707040651
77-1.65300640423178-10.08168666279706.77567385433342
78-1.47838416674961-11.32440400414438.36763567064512
79-1.30376192926744-12.647755188839710.0402313303049
80-1.12913969178527-14.046654803523811.7883754199532
81-0.954517454303094-15.516985097563113.6079501889569
82-0.779895216820923-17.055315368895115.4955249352532
83-0.605272979338753-18.658722093426117.4481761347486
84-0.430650741856581-20.324668729244419.4633672455313

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -2.35149535416046 & -6.09003862687868 & 1.38704791855776 \tabularnewline
74 & -2.17687311667829 & -6.9148941499706 & 2.56114791661402 \tabularnewline
75 & -2.00225087919612 & -7.86640774052014 & 3.8619059821279 \tabularnewline
76 & -1.82762864171395 & -8.92611435383441 & 5.27085707040651 \tabularnewline
77 & -1.65300640423178 & -10.0816866627970 & 6.77567385433342 \tabularnewline
78 & -1.47838416674961 & -11.3244040041443 & 8.36763567064512 \tabularnewline
79 & -1.30376192926744 & -12.6477551888397 & 10.0402313303049 \tabularnewline
80 & -1.12913969178527 & -14.0466548035238 & 11.7883754199532 \tabularnewline
81 & -0.954517454303094 & -15.5169850975631 & 13.6079501889569 \tabularnewline
82 & -0.779895216820923 & -17.0553153688951 & 15.4955249352532 \tabularnewline
83 & -0.605272979338753 & -18.6587220934261 & 17.4481761347486 \tabularnewline
84 & -0.430650741856581 & -20.3246687292444 & 19.4633672455313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41645&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]-2.35149535416046[/C][C]-6.09003862687868[/C][C]1.38704791855776[/C][/ROW]
[ROW][C]74[/C][C]-2.17687311667829[/C][C]-6.9148941499706[/C][C]2.56114791661402[/C][/ROW]
[ROW][C]75[/C][C]-2.00225087919612[/C][C]-7.86640774052014[/C][C]3.8619059821279[/C][/ROW]
[ROW][C]76[/C][C]-1.82762864171395[/C][C]-8.92611435383441[/C][C]5.27085707040651[/C][/ROW]
[ROW][C]77[/C][C]-1.65300640423178[/C][C]-10.0816866627970[/C][C]6.77567385433342[/C][/ROW]
[ROW][C]78[/C][C]-1.47838416674961[/C][C]-11.3244040041443[/C][C]8.36763567064512[/C][/ROW]
[ROW][C]79[/C][C]-1.30376192926744[/C][C]-12.6477551888397[/C][C]10.0402313303049[/C][/ROW]
[ROW][C]80[/C][C]-1.12913969178527[/C][C]-14.0466548035238[/C][C]11.7883754199532[/C][/ROW]
[ROW][C]81[/C][C]-0.954517454303094[/C][C]-15.5169850975631[/C][C]13.6079501889569[/C][/ROW]
[ROW][C]82[/C][C]-0.779895216820923[/C][C]-17.0553153688951[/C][C]15.4955249352532[/C][/ROW]
[ROW][C]83[/C][C]-0.605272979338753[/C][C]-18.6587220934261[/C][C]17.4481761347486[/C][/ROW]
[ROW][C]84[/C][C]-0.430650741856581[/C][C]-20.3246687292444[/C][C]19.4633672455313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41645&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41645&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
73-2.35149535416046-6.090038626878681.38704791855776
74-2.17687311667829-6.91489414997062.56114791661402
75-2.00225087919612-7.866407740520143.8619059821279
76-1.82762864171395-8.926114353834415.27085707040651
77-1.65300640423178-10.08168666279706.77567385433342
78-1.47838416674961-11.32440400414438.36763567064512
79-1.30376192926744-12.647755188839710.0402313303049
80-1.12913969178527-14.046654803523811.7883754199532
81-0.954517454303094-15.516985097563113.6079501889569
82-0.779895216820923-17.055315368895115.4955249352532
83-0.605272979338753-18.658722093426117.4481761347486
84-0.430650741856581-20.324668729244419.4633672455313



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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=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')