Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 06:14:28 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/28/t13382001599jslwv8t20wja9k.htm/, Retrieved Thu, 02 May 2024 12:40:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167770, Retrieved Thu, 02 May 2024 12:40:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-28 10:14:28] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
100,17
102,01
100,3
99,94
100,16
100,18
99,98
100,04
100,05
100,11
100,11
101,03
100,84
102,68
101,27
100,28
100,82
100,87
101,23
101,09
101,22
101,33
101,3
102,39
101,69
103,75
102,99
100,8
102,21
102,45
102,49
102,4
102,99
103,19
103,35
104,44
103,42
105,81
104,25
103,78
104,53
105,01
104,83
104,55
105,16
105,06
105,2
105,87
105,41
107,89
106,06
105,5
106,71
106,34
106,11
106,15
106,61
106,63
106,27
105,59
107,09
108,53
108,01
106,52
107,27
107,58
107,36
107,23
107,54
107,64
108,23
108,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167770&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167770&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167770&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.312724386625416
beta0.0542931337928069
gamma0.338534322419725

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.312724386625416 \tabularnewline
beta & 0.0542931337928069 \tabularnewline
gamma & 0.338534322419725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167770&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]0.312724386625416[/C][/ROW]
[ROW][C]beta[/C][C]0.0542931337928069[/C][/ROW]
[ROW][C]gamma[/C][C]0.338534322419725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167770&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167770&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
alpha0.312724386625416
beta0.0542931337928069
gamma0.338534322419725







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.84100.499165257990.340834742009534
14102.68102.4278381904860.252161809513609
15101.27101.0931317480150.176868251985127
16100.28100.149654071510.130345928489618
17100.82100.7212754113130.0987245886874604
18100.87100.7893055318730.0806944681267083
19101.23100.8676864659910.362313534008564
20101.09101.0859037374320.00409626256788442
21101.22101.1290448838350.0909551161647926
22101.33101.2652554760720.0647445239283826
23101.3101.346654176889-0.0466541768887225
24102.39102.3093376079060.0806623920944816
25101.69102.244954970182-0.554954970182038
26103.75103.909251470311-0.159251470310735
27102.99102.4149053823230.575094617677351
28100.8101.582209326248-0.782209326248037
29102.21101.8627310777660.347268922234306
30102.45102.0046211122610.445378887739452
31102.49102.2700305812380.219969418761963
32102.4102.3642080776620.0357919223379497
33102.99102.4423251396290.547674860370961
34103.19102.728360747190.461639252810429
35103.35102.9267345274670.423265472532506
36104.44104.1095476012790.330452398721349
37103.42104.001151028744-0.581151028744159
38105.81105.815366826904-0.00536682690410828
39104.25104.548013638874-0.298013638874437
40103.78103.1213574530960.658642546904105
41104.53104.1742815978950.3557184021046
42105.01104.3848747137330.62512528626678
43104.83104.7006176341990.129382365801092
44104.55104.766441608197-0.216441608196789
45105.16104.9277657627650.232234237235048
46105.06105.130554262132-0.0705542621321911
47105.2105.1787870798960.0212129201044036
48105.87106.252138235754-0.382138235753715
49105.41105.706812186666-0.296812186666074
50107.89107.7943755326210.0956244673789115
51106.06106.477405525427-0.417405525427426
52105.5105.2250919844790.274908015521376
53106.71106.1048856648310.605114335168594
54106.34106.466592273033-0.12659227303331
55106.11106.427068428748-0.31706842874766
56106.15106.259668689902-0.109668689902136
57106.61106.5532830553980.0567169446017459
58106.63106.618180601550.0118193984496031
59106.27106.702850619722-0.432850619722217
60105.59107.533339337999-1.94333933799889
61107.09106.4710485732320.618951426768078
62108.53108.929904058402-0.399904058402413
63108.01107.2873599632290.722640036770898
64106.52106.522275375096-0.00227537509630338
65107.27107.3777552369-0.107755236899706
66107.58107.3107833507370.269216649262802
67107.36107.321393459960.0386065400399644
68107.23107.290431820381-0.0604318203814813
69107.54107.619836502148-0.0798365021475433
70107.64107.6076958721810.0323041278188327
71108.23107.5711429748550.658857025144584
72108.42108.39090019020.0290998097998028

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.84 & 100.49916525799 & 0.340834742009534 \tabularnewline
14 & 102.68 & 102.427838190486 & 0.252161809513609 \tabularnewline
15 & 101.27 & 101.093131748015 & 0.176868251985127 \tabularnewline
16 & 100.28 & 100.14965407151 & 0.130345928489618 \tabularnewline
17 & 100.82 & 100.721275411313 & 0.0987245886874604 \tabularnewline
18 & 100.87 & 100.789305531873 & 0.0806944681267083 \tabularnewline
19 & 101.23 & 100.867686465991 & 0.362313534008564 \tabularnewline
20 & 101.09 & 101.085903737432 & 0.00409626256788442 \tabularnewline
21 & 101.22 & 101.129044883835 & 0.0909551161647926 \tabularnewline
22 & 101.33 & 101.265255476072 & 0.0647445239283826 \tabularnewline
23 & 101.3 & 101.346654176889 & -0.0466541768887225 \tabularnewline
24 & 102.39 & 102.309337607906 & 0.0806623920944816 \tabularnewline
25 & 101.69 & 102.244954970182 & -0.554954970182038 \tabularnewline
26 & 103.75 & 103.909251470311 & -0.159251470310735 \tabularnewline
27 & 102.99 & 102.414905382323 & 0.575094617677351 \tabularnewline
28 & 100.8 & 101.582209326248 & -0.782209326248037 \tabularnewline
29 & 102.21 & 101.862731077766 & 0.347268922234306 \tabularnewline
30 & 102.45 & 102.004621112261 & 0.445378887739452 \tabularnewline
31 & 102.49 & 102.270030581238 & 0.219969418761963 \tabularnewline
32 & 102.4 & 102.364208077662 & 0.0357919223379497 \tabularnewline
33 & 102.99 & 102.442325139629 & 0.547674860370961 \tabularnewline
34 & 103.19 & 102.72836074719 & 0.461639252810429 \tabularnewline
35 & 103.35 & 102.926734527467 & 0.423265472532506 \tabularnewline
36 & 104.44 & 104.109547601279 & 0.330452398721349 \tabularnewline
37 & 103.42 & 104.001151028744 & -0.581151028744159 \tabularnewline
38 & 105.81 & 105.815366826904 & -0.00536682690410828 \tabularnewline
39 & 104.25 & 104.548013638874 & -0.298013638874437 \tabularnewline
40 & 103.78 & 103.121357453096 & 0.658642546904105 \tabularnewline
41 & 104.53 & 104.174281597895 & 0.3557184021046 \tabularnewline
42 & 105.01 & 104.384874713733 & 0.62512528626678 \tabularnewline
43 & 104.83 & 104.700617634199 & 0.129382365801092 \tabularnewline
44 & 104.55 & 104.766441608197 & -0.216441608196789 \tabularnewline
45 & 105.16 & 104.927765762765 & 0.232234237235048 \tabularnewline
46 & 105.06 & 105.130554262132 & -0.0705542621321911 \tabularnewline
47 & 105.2 & 105.178787079896 & 0.0212129201044036 \tabularnewline
48 & 105.87 & 106.252138235754 & -0.382138235753715 \tabularnewline
49 & 105.41 & 105.706812186666 & -0.296812186666074 \tabularnewline
50 & 107.89 & 107.794375532621 & 0.0956244673789115 \tabularnewline
51 & 106.06 & 106.477405525427 & -0.417405525427426 \tabularnewline
52 & 105.5 & 105.225091984479 & 0.274908015521376 \tabularnewline
53 & 106.71 & 106.104885664831 & 0.605114335168594 \tabularnewline
54 & 106.34 & 106.466592273033 & -0.12659227303331 \tabularnewline
55 & 106.11 & 106.427068428748 & -0.31706842874766 \tabularnewline
56 & 106.15 & 106.259668689902 & -0.109668689902136 \tabularnewline
57 & 106.61 & 106.553283055398 & 0.0567169446017459 \tabularnewline
58 & 106.63 & 106.61818060155 & 0.0118193984496031 \tabularnewline
59 & 106.27 & 106.702850619722 & -0.432850619722217 \tabularnewline
60 & 105.59 & 107.533339337999 & -1.94333933799889 \tabularnewline
61 & 107.09 & 106.471048573232 & 0.618951426768078 \tabularnewline
62 & 108.53 & 108.929904058402 & -0.399904058402413 \tabularnewline
63 & 108.01 & 107.287359963229 & 0.722640036770898 \tabularnewline
64 & 106.52 & 106.522275375096 & -0.00227537509630338 \tabularnewline
65 & 107.27 & 107.3777552369 & -0.107755236899706 \tabularnewline
66 & 107.58 & 107.310783350737 & 0.269216649262802 \tabularnewline
67 & 107.36 & 107.32139345996 & 0.0386065400399644 \tabularnewline
68 & 107.23 & 107.290431820381 & -0.0604318203814813 \tabularnewline
69 & 107.54 & 107.619836502148 & -0.0798365021475433 \tabularnewline
70 & 107.64 & 107.607695872181 & 0.0323041278188327 \tabularnewline
71 & 108.23 & 107.571142974855 & 0.658857025144584 \tabularnewline
72 & 108.42 & 108.3909001902 & 0.0290998097998028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167770&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]100.84[/C][C]100.49916525799[/C][C]0.340834742009534[/C][/ROW]
[ROW][C]14[/C][C]102.68[/C][C]102.427838190486[/C][C]0.252161809513609[/C][/ROW]
[ROW][C]15[/C][C]101.27[/C][C]101.093131748015[/C][C]0.176868251985127[/C][/ROW]
[ROW][C]16[/C][C]100.28[/C][C]100.14965407151[/C][C]0.130345928489618[/C][/ROW]
[ROW][C]17[/C][C]100.82[/C][C]100.721275411313[/C][C]0.0987245886874604[/C][/ROW]
[ROW][C]18[/C][C]100.87[/C][C]100.789305531873[/C][C]0.0806944681267083[/C][/ROW]
[ROW][C]19[/C][C]101.23[/C][C]100.867686465991[/C][C]0.362313534008564[/C][/ROW]
[ROW][C]20[/C][C]101.09[/C][C]101.085903737432[/C][C]0.00409626256788442[/C][/ROW]
[ROW][C]21[/C][C]101.22[/C][C]101.129044883835[/C][C]0.0909551161647926[/C][/ROW]
[ROW][C]22[/C][C]101.33[/C][C]101.265255476072[/C][C]0.0647445239283826[/C][/ROW]
[ROW][C]23[/C][C]101.3[/C][C]101.346654176889[/C][C]-0.0466541768887225[/C][/ROW]
[ROW][C]24[/C][C]102.39[/C][C]102.309337607906[/C][C]0.0806623920944816[/C][/ROW]
[ROW][C]25[/C][C]101.69[/C][C]102.244954970182[/C][C]-0.554954970182038[/C][/ROW]
[ROW][C]26[/C][C]103.75[/C][C]103.909251470311[/C][C]-0.159251470310735[/C][/ROW]
[ROW][C]27[/C][C]102.99[/C][C]102.414905382323[/C][C]0.575094617677351[/C][/ROW]
[ROW][C]28[/C][C]100.8[/C][C]101.582209326248[/C][C]-0.782209326248037[/C][/ROW]
[ROW][C]29[/C][C]102.21[/C][C]101.862731077766[/C][C]0.347268922234306[/C][/ROW]
[ROW][C]30[/C][C]102.45[/C][C]102.004621112261[/C][C]0.445378887739452[/C][/ROW]
[ROW][C]31[/C][C]102.49[/C][C]102.270030581238[/C][C]0.219969418761963[/C][/ROW]
[ROW][C]32[/C][C]102.4[/C][C]102.364208077662[/C][C]0.0357919223379497[/C][/ROW]
[ROW][C]33[/C][C]102.99[/C][C]102.442325139629[/C][C]0.547674860370961[/C][/ROW]
[ROW][C]34[/C][C]103.19[/C][C]102.72836074719[/C][C]0.461639252810429[/C][/ROW]
[ROW][C]35[/C][C]103.35[/C][C]102.926734527467[/C][C]0.423265472532506[/C][/ROW]
[ROW][C]36[/C][C]104.44[/C][C]104.109547601279[/C][C]0.330452398721349[/C][/ROW]
[ROW][C]37[/C][C]103.42[/C][C]104.001151028744[/C][C]-0.581151028744159[/C][/ROW]
[ROW][C]38[/C][C]105.81[/C][C]105.815366826904[/C][C]-0.00536682690410828[/C][/ROW]
[ROW][C]39[/C][C]104.25[/C][C]104.548013638874[/C][C]-0.298013638874437[/C][/ROW]
[ROW][C]40[/C][C]103.78[/C][C]103.121357453096[/C][C]0.658642546904105[/C][/ROW]
[ROW][C]41[/C][C]104.53[/C][C]104.174281597895[/C][C]0.3557184021046[/C][/ROW]
[ROW][C]42[/C][C]105.01[/C][C]104.384874713733[/C][C]0.62512528626678[/C][/ROW]
[ROW][C]43[/C][C]104.83[/C][C]104.700617634199[/C][C]0.129382365801092[/C][/ROW]
[ROW][C]44[/C][C]104.55[/C][C]104.766441608197[/C][C]-0.216441608196789[/C][/ROW]
[ROW][C]45[/C][C]105.16[/C][C]104.927765762765[/C][C]0.232234237235048[/C][/ROW]
[ROW][C]46[/C][C]105.06[/C][C]105.130554262132[/C][C]-0.0705542621321911[/C][/ROW]
[ROW][C]47[/C][C]105.2[/C][C]105.178787079896[/C][C]0.0212129201044036[/C][/ROW]
[ROW][C]48[/C][C]105.87[/C][C]106.252138235754[/C][C]-0.382138235753715[/C][/ROW]
[ROW][C]49[/C][C]105.41[/C][C]105.706812186666[/C][C]-0.296812186666074[/C][/ROW]
[ROW][C]50[/C][C]107.89[/C][C]107.794375532621[/C][C]0.0956244673789115[/C][/ROW]
[ROW][C]51[/C][C]106.06[/C][C]106.477405525427[/C][C]-0.417405525427426[/C][/ROW]
[ROW][C]52[/C][C]105.5[/C][C]105.225091984479[/C][C]0.274908015521376[/C][/ROW]
[ROW][C]53[/C][C]106.71[/C][C]106.104885664831[/C][C]0.605114335168594[/C][/ROW]
[ROW][C]54[/C][C]106.34[/C][C]106.466592273033[/C][C]-0.12659227303331[/C][/ROW]
[ROW][C]55[/C][C]106.11[/C][C]106.427068428748[/C][C]-0.31706842874766[/C][/ROW]
[ROW][C]56[/C][C]106.15[/C][C]106.259668689902[/C][C]-0.109668689902136[/C][/ROW]
[ROW][C]57[/C][C]106.61[/C][C]106.553283055398[/C][C]0.0567169446017459[/C][/ROW]
[ROW][C]58[/C][C]106.63[/C][C]106.61818060155[/C][C]0.0118193984496031[/C][/ROW]
[ROW][C]59[/C][C]106.27[/C][C]106.702850619722[/C][C]-0.432850619722217[/C][/ROW]
[ROW][C]60[/C][C]105.59[/C][C]107.533339337999[/C][C]-1.94333933799889[/C][/ROW]
[ROW][C]61[/C][C]107.09[/C][C]106.471048573232[/C][C]0.618951426768078[/C][/ROW]
[ROW][C]62[/C][C]108.53[/C][C]108.929904058402[/C][C]-0.399904058402413[/C][/ROW]
[ROW][C]63[/C][C]108.01[/C][C]107.287359963229[/C][C]0.722640036770898[/C][/ROW]
[ROW][C]64[/C][C]106.52[/C][C]106.522275375096[/C][C]-0.00227537509630338[/C][/ROW]
[ROW][C]65[/C][C]107.27[/C][C]107.3777552369[/C][C]-0.107755236899706[/C][/ROW]
[ROW][C]66[/C][C]107.58[/C][C]107.310783350737[/C][C]0.269216649262802[/C][/ROW]
[ROW][C]67[/C][C]107.36[/C][C]107.32139345996[/C][C]0.0386065400399644[/C][/ROW]
[ROW][C]68[/C][C]107.23[/C][C]107.290431820381[/C][C]-0.0604318203814813[/C][/ROW]
[ROW][C]69[/C][C]107.54[/C][C]107.619836502148[/C][C]-0.0798365021475433[/C][/ROW]
[ROW][C]70[/C][C]107.64[/C][C]107.607695872181[/C][C]0.0323041278188327[/C][/ROW]
[ROW][C]71[/C][C]108.23[/C][C]107.571142974855[/C][C]0.658857025144584[/C][/ROW]
[ROW][C]72[/C][C]108.42[/C][C]108.3909001902[/C][C]0.0290998097998028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167770&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167770&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
13100.84100.499165257990.340834742009534
14102.68102.4278381904860.252161809513609
15101.27101.0931317480150.176868251985127
16100.28100.149654071510.130345928489618
17100.82100.7212754113130.0987245886874604
18100.87100.7893055318730.0806944681267083
19101.23100.8676864659910.362313534008564
20101.09101.0859037374320.00409626256788442
21101.22101.1290448838350.0909551161647926
22101.33101.2652554760720.0647445239283826
23101.3101.346654176889-0.0466541768887225
24102.39102.3093376079060.0806623920944816
25101.69102.244954970182-0.554954970182038
26103.75103.909251470311-0.159251470310735
27102.99102.4149053823230.575094617677351
28100.8101.582209326248-0.782209326248037
29102.21101.8627310777660.347268922234306
30102.45102.0046211122610.445378887739452
31102.49102.2700305812380.219969418761963
32102.4102.3642080776620.0357919223379497
33102.99102.4423251396290.547674860370961
34103.19102.728360747190.461639252810429
35103.35102.9267345274670.423265472532506
36104.44104.1095476012790.330452398721349
37103.42104.001151028744-0.581151028744159
38105.81105.815366826904-0.00536682690410828
39104.25104.548013638874-0.298013638874437
40103.78103.1213574530960.658642546904105
41104.53104.1742815978950.3557184021046
42105.01104.3848747137330.62512528626678
43104.83104.7006176341990.129382365801092
44104.55104.766441608197-0.216441608196789
45105.16104.9277657627650.232234237235048
46105.06105.130554262132-0.0705542621321911
47105.2105.1787870798960.0212129201044036
48105.87106.252138235754-0.382138235753715
49105.41105.706812186666-0.296812186666074
50107.89107.7943755326210.0956244673789115
51106.06106.477405525427-0.417405525427426
52105.5105.2250919844790.274908015521376
53106.71106.1048856648310.605114335168594
54106.34106.466592273033-0.12659227303331
55106.11106.427068428748-0.31706842874766
56106.15106.259668689902-0.109668689902136
57106.61106.5532830553980.0567169446017459
58106.63106.618180601550.0118193984496031
59106.27106.702850619722-0.432850619722217
60105.59107.533339337999-1.94333933799889
61107.09106.4710485732320.618951426768078
62108.53108.929904058402-0.399904058402413
63108.01107.2873599632290.722640036770898
64106.52106.522275375096-0.00227537509630338
65107.27107.3777552369-0.107755236899706
66107.58107.3107833507370.269216649262802
67107.36107.321393459960.0386065400399644
68107.23107.290431820381-0.0604318203814813
69107.54107.619836502148-0.0798365021475433
70107.64107.6076958721810.0323041278188327
71108.23107.5711429748550.658857025144584
72108.42108.39090019020.0290998097998028







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73108.571422142245108.115487526665109.027356757826
74110.650324455271110.114979691957111.185669218586
75109.395005775587108.78934770543110.000663845745
76108.228146246091107.554933194476108.901359297707
77109.084548936368108.337273931748109.831823940989
78109.153064062258108.335688574532109.970439549984
79109.032466391367108.146337918312109.918594864422
80108.973316724881108.018153190804109.928480258957
81109.331602336911108.304160643382110.35904403044
82109.381488069186108.283736313577110.479239824794
83109.4917049052108.322675830906110.660733979494
84109.96427935254106.262994328608113.665564376472

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 108.571422142245 & 108.115487526665 & 109.027356757826 \tabularnewline
74 & 110.650324455271 & 110.114979691957 & 111.185669218586 \tabularnewline
75 & 109.395005775587 & 108.78934770543 & 110.000663845745 \tabularnewline
76 & 108.228146246091 & 107.554933194476 & 108.901359297707 \tabularnewline
77 & 109.084548936368 & 108.337273931748 & 109.831823940989 \tabularnewline
78 & 109.153064062258 & 108.335688574532 & 109.970439549984 \tabularnewline
79 & 109.032466391367 & 108.146337918312 & 109.918594864422 \tabularnewline
80 & 108.973316724881 & 108.018153190804 & 109.928480258957 \tabularnewline
81 & 109.331602336911 & 108.304160643382 & 110.35904403044 \tabularnewline
82 & 109.381488069186 & 108.283736313577 & 110.479239824794 \tabularnewline
83 & 109.4917049052 & 108.322675830906 & 110.660733979494 \tabularnewline
84 & 109.96427935254 & 106.262994328608 & 113.665564376472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167770&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]108.571422142245[/C][C]108.115487526665[/C][C]109.027356757826[/C][/ROW]
[ROW][C]74[/C][C]110.650324455271[/C][C]110.114979691957[/C][C]111.185669218586[/C][/ROW]
[ROW][C]75[/C][C]109.395005775587[/C][C]108.78934770543[/C][C]110.000663845745[/C][/ROW]
[ROW][C]76[/C][C]108.228146246091[/C][C]107.554933194476[/C][C]108.901359297707[/C][/ROW]
[ROW][C]77[/C][C]109.084548936368[/C][C]108.337273931748[/C][C]109.831823940989[/C][/ROW]
[ROW][C]78[/C][C]109.153064062258[/C][C]108.335688574532[/C][C]109.970439549984[/C][/ROW]
[ROW][C]79[/C][C]109.032466391367[/C][C]108.146337918312[/C][C]109.918594864422[/C][/ROW]
[ROW][C]80[/C][C]108.973316724881[/C][C]108.018153190804[/C][C]109.928480258957[/C][/ROW]
[ROW][C]81[/C][C]109.331602336911[/C][C]108.304160643382[/C][C]110.35904403044[/C][/ROW]
[ROW][C]82[/C][C]109.381488069186[/C][C]108.283736313577[/C][C]110.479239824794[/C][/ROW]
[ROW][C]83[/C][C]109.4917049052[/C][C]108.322675830906[/C][C]110.660733979494[/C][/ROW]
[ROW][C]84[/C][C]109.96427935254[/C][C]106.262994328608[/C][C]113.665564376472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167770&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167770&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
73108.571422142245108.115487526665109.027356757826
74110.650324455271110.114979691957111.185669218586
75109.395005775587108.78934770543110.000663845745
76108.228146246091107.554933194476108.901359297707
77109.084548936368108.337273931748109.831823940989
78109.153064062258108.335688574532109.970439549984
79109.032466391367108.146337918312109.918594864422
80108.973316724881108.018153190804109.928480258957
81109.331602336911108.304160643382110.35904403044
82109.381488069186108.283736313577110.479239824794
83109.4917049052108.322675830906110.660733979494
84109.96427935254106.262994328608113.665564376472



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