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 computationSun, 11 Nov 2012 12:12:40 -0500
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/Nov/11/t13526539711a7bab03ls1s665.htm/, Retrieved Fri, 03 May 2024 04:46:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187545, Retrieved Fri, 03 May 2024 04:46:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [test 4] [2012-11-11 17:12:40] [09a8c52255f1f9505addc8ea27636e79] [Current]
Feedback Forum

Post a new message
Dataseries X:
9.676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331
10.718
9.462
10.579
10.633
10.346
10.757
11.207
11.013
11.015
10.765
10.042
10.661




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187545&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187545&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0844128060248295
beta0
gamma0.573960908312786

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0844128060248295 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.573960908312786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187545&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]0.0844128060248295[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.573960908312786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187545&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
alpha0.0844128060248295
beta0
gamma0.573960908312786







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139.8299.746152243589740.0828477564102599
149.1259.037428580589120.0875714194108816
159.7829.687645321903760.0943546780962379
169.4419.357726323784690.0832736762153079
179.1629.075455280536620.0865447194633777
189.9159.819627021894420.0953729781055834
1910.44410.5044189813365-0.060418981336511
2010.2099.722851770992660.486148229007341
219.98510.0019634992218-0.0169634992217613
229.8429.807772821393710.0342271786062884
239.4299.171236625656770.257763374343225
2410.13210.02306974745010.108930252549895
259.84910.1551685431218-0.306168543121766
269.1729.41608926077168-0.244089260771682
2710.31310.04187427222570.271125727774344
289.8199.721053823201140.0979461767988656
299.9559.441740296949330.513259703050666
3010.04810.2265715967451-0.178571596745112
3110.08210.806368697415-0.724368697414983
3210.54110.25598285049010.285017149509907
3310.20810.2537256629586-0.0457256629585885
3410.23310.08400836765950.148991632340467
359.4399.57463054881125-0.135630548811246
369.96310.3150427046877-0.352042704687689
3710.15810.1900903894399-0.0320903894398921
389.2259.50677017484429-0.281770174844288
3910.47410.40012571111820.0738742888818429
409.7579.971646911039-0.214646911038995
4110.499.88419845853350.605801541466505
4210.28110.3132763382556-0.0322763382555777
4310.44410.6186001114933-0.174600111493323
4410.6410.6450653992841-0.00506539928406902
4510.69510.44451245854280.25048754145724
4610.78610.40212548171840.383874518281599
479.8329.763002626032020.0689973739679779
489.74710.4069609748898-0.659960974889772
4910.41110.4241549579517-0.0131549579517465
509.5119.61122359826276-0.100223598262765
5110.40210.7067991598434-0.304799159843419
529.70110.0947343328063-0.393734332806311
5310.5410.42332350649050.116676493509521
5410.11210.4757958594659-0.363795859465917
5510.91510.67834239462090.236657605379103
5611.18310.82861550009410.354384499905901
5710.38410.7927006812139-0.408700681213894
5810.83410.76476613473960.0692338652604256
599.8869.93361209457797-0.0476120945779677
6010.21610.1846512924180.0313487075819623
6110.94310.60010450892510.342895491074923
629.8679.771472816066740.0955271839332603
6310.20310.7760654898354-0.57306548983542
6410.83710.09461911454260.742380885457431
6510.57310.7873375969434-0.214337596943441
6610.64710.5593744913070.087625508693014
6711.50211.11557182622490.38642817377511
6810.65611.3403542940199-0.68435429401992
6910.86610.81574676571260.0502532342873607
7010.83511.0777137915992-0.242713791599188
719.94510.1588235071015-0.213823507101477
7210.33110.4373271236528-0.10632712365285
7310.71811.004880078885-0.286880078885012
749.4629.99309243285041-0.531092432850407
7510.57910.593437409713-0.0144374097130218
7610.63310.650428277033-0.017428277033039
7710.34610.7762428032309-0.430242803230918
7810.75710.6887395446560.0682604553439639
7911.20711.4003263853516-0.193326385351639
8011.01311.0134619028521-0.000461902852087803
8111.01510.93262817626730.0823718237327036
8210.76511.0433489522367-0.278348952236703
8310.04210.1366327735722-0.0946327735721741
8410.66110.4816881740350.179311825964991

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9.829 & 9.74615224358974 & 0.0828477564102599 \tabularnewline
14 & 9.125 & 9.03742858058912 & 0.0875714194108816 \tabularnewline
15 & 9.782 & 9.68764532190376 & 0.0943546780962379 \tabularnewline
16 & 9.441 & 9.35772632378469 & 0.0832736762153079 \tabularnewline
17 & 9.162 & 9.07545528053662 & 0.0865447194633777 \tabularnewline
18 & 9.915 & 9.81962702189442 & 0.0953729781055834 \tabularnewline
19 & 10.444 & 10.5044189813365 & -0.060418981336511 \tabularnewline
20 & 10.209 & 9.72285177099266 & 0.486148229007341 \tabularnewline
21 & 9.985 & 10.0019634992218 & -0.0169634992217613 \tabularnewline
22 & 9.842 & 9.80777282139371 & 0.0342271786062884 \tabularnewline
23 & 9.429 & 9.17123662565677 & 0.257763374343225 \tabularnewline
24 & 10.132 & 10.0230697474501 & 0.108930252549895 \tabularnewline
25 & 9.849 & 10.1551685431218 & -0.306168543121766 \tabularnewline
26 & 9.172 & 9.41608926077168 & -0.244089260771682 \tabularnewline
27 & 10.313 & 10.0418742722257 & 0.271125727774344 \tabularnewline
28 & 9.819 & 9.72105382320114 & 0.0979461767988656 \tabularnewline
29 & 9.955 & 9.44174029694933 & 0.513259703050666 \tabularnewline
30 & 10.048 & 10.2265715967451 & -0.178571596745112 \tabularnewline
31 & 10.082 & 10.806368697415 & -0.724368697414983 \tabularnewline
32 & 10.541 & 10.2559828504901 & 0.285017149509907 \tabularnewline
33 & 10.208 & 10.2537256629586 & -0.0457256629585885 \tabularnewline
34 & 10.233 & 10.0840083676595 & 0.148991632340467 \tabularnewline
35 & 9.439 & 9.57463054881125 & -0.135630548811246 \tabularnewline
36 & 9.963 & 10.3150427046877 & -0.352042704687689 \tabularnewline
37 & 10.158 & 10.1900903894399 & -0.0320903894398921 \tabularnewline
38 & 9.225 & 9.50677017484429 & -0.281770174844288 \tabularnewline
39 & 10.474 & 10.4001257111182 & 0.0738742888818429 \tabularnewline
40 & 9.757 & 9.971646911039 & -0.214646911038995 \tabularnewline
41 & 10.49 & 9.8841984585335 & 0.605801541466505 \tabularnewline
42 & 10.281 & 10.3132763382556 & -0.0322763382555777 \tabularnewline
43 & 10.444 & 10.6186001114933 & -0.174600111493323 \tabularnewline
44 & 10.64 & 10.6450653992841 & -0.00506539928406902 \tabularnewline
45 & 10.695 & 10.4445124585428 & 0.25048754145724 \tabularnewline
46 & 10.786 & 10.4021254817184 & 0.383874518281599 \tabularnewline
47 & 9.832 & 9.76300262603202 & 0.0689973739679779 \tabularnewline
48 & 9.747 & 10.4069609748898 & -0.659960974889772 \tabularnewline
49 & 10.411 & 10.4241549579517 & -0.0131549579517465 \tabularnewline
50 & 9.511 & 9.61122359826276 & -0.100223598262765 \tabularnewline
51 & 10.402 & 10.7067991598434 & -0.304799159843419 \tabularnewline
52 & 9.701 & 10.0947343328063 & -0.393734332806311 \tabularnewline
53 & 10.54 & 10.4233235064905 & 0.116676493509521 \tabularnewline
54 & 10.112 & 10.4757958594659 & -0.363795859465917 \tabularnewline
55 & 10.915 & 10.6783423946209 & 0.236657605379103 \tabularnewline
56 & 11.183 & 10.8286155000941 & 0.354384499905901 \tabularnewline
57 & 10.384 & 10.7927006812139 & -0.408700681213894 \tabularnewline
58 & 10.834 & 10.7647661347396 & 0.0692338652604256 \tabularnewline
59 & 9.886 & 9.93361209457797 & -0.0476120945779677 \tabularnewline
60 & 10.216 & 10.184651292418 & 0.0313487075819623 \tabularnewline
61 & 10.943 & 10.6001045089251 & 0.342895491074923 \tabularnewline
62 & 9.867 & 9.77147281606674 & 0.0955271839332603 \tabularnewline
63 & 10.203 & 10.7760654898354 & -0.57306548983542 \tabularnewline
64 & 10.837 & 10.0946191145426 & 0.742380885457431 \tabularnewline
65 & 10.573 & 10.7873375969434 & -0.214337596943441 \tabularnewline
66 & 10.647 & 10.559374491307 & 0.087625508693014 \tabularnewline
67 & 11.502 & 11.1155718262249 & 0.38642817377511 \tabularnewline
68 & 10.656 & 11.3403542940199 & -0.68435429401992 \tabularnewline
69 & 10.866 & 10.8157467657126 & 0.0502532342873607 \tabularnewline
70 & 10.835 & 11.0777137915992 & -0.242713791599188 \tabularnewline
71 & 9.945 & 10.1588235071015 & -0.213823507101477 \tabularnewline
72 & 10.331 & 10.4373271236528 & -0.10632712365285 \tabularnewline
73 & 10.718 & 11.004880078885 & -0.286880078885012 \tabularnewline
74 & 9.462 & 9.99309243285041 & -0.531092432850407 \tabularnewline
75 & 10.579 & 10.593437409713 & -0.0144374097130218 \tabularnewline
76 & 10.633 & 10.650428277033 & -0.017428277033039 \tabularnewline
77 & 10.346 & 10.7762428032309 & -0.430242803230918 \tabularnewline
78 & 10.757 & 10.688739544656 & 0.0682604553439639 \tabularnewline
79 & 11.207 & 11.4003263853516 & -0.193326385351639 \tabularnewline
80 & 11.013 & 11.0134619028521 & -0.000461902852087803 \tabularnewline
81 & 11.015 & 10.9326281762673 & 0.0823718237327036 \tabularnewline
82 & 10.765 & 11.0433489522367 & -0.278348952236703 \tabularnewline
83 & 10.042 & 10.1366327735722 & -0.0946327735721741 \tabularnewline
84 & 10.661 & 10.481688174035 & 0.179311825964991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187545&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]9.829[/C][C]9.74615224358974[/C][C]0.0828477564102599[/C][/ROW]
[ROW][C]14[/C][C]9.125[/C][C]9.03742858058912[/C][C]0.0875714194108816[/C][/ROW]
[ROW][C]15[/C][C]9.782[/C][C]9.68764532190376[/C][C]0.0943546780962379[/C][/ROW]
[ROW][C]16[/C][C]9.441[/C][C]9.35772632378469[/C][C]0.0832736762153079[/C][/ROW]
[ROW][C]17[/C][C]9.162[/C][C]9.07545528053662[/C][C]0.0865447194633777[/C][/ROW]
[ROW][C]18[/C][C]9.915[/C][C]9.81962702189442[/C][C]0.0953729781055834[/C][/ROW]
[ROW][C]19[/C][C]10.444[/C][C]10.5044189813365[/C][C]-0.060418981336511[/C][/ROW]
[ROW][C]20[/C][C]10.209[/C][C]9.72285177099266[/C][C]0.486148229007341[/C][/ROW]
[ROW][C]21[/C][C]9.985[/C][C]10.0019634992218[/C][C]-0.0169634992217613[/C][/ROW]
[ROW][C]22[/C][C]9.842[/C][C]9.80777282139371[/C][C]0.0342271786062884[/C][/ROW]
[ROW][C]23[/C][C]9.429[/C][C]9.17123662565677[/C][C]0.257763374343225[/C][/ROW]
[ROW][C]24[/C][C]10.132[/C][C]10.0230697474501[/C][C]0.108930252549895[/C][/ROW]
[ROW][C]25[/C][C]9.849[/C][C]10.1551685431218[/C][C]-0.306168543121766[/C][/ROW]
[ROW][C]26[/C][C]9.172[/C][C]9.41608926077168[/C][C]-0.244089260771682[/C][/ROW]
[ROW][C]27[/C][C]10.313[/C][C]10.0418742722257[/C][C]0.271125727774344[/C][/ROW]
[ROW][C]28[/C][C]9.819[/C][C]9.72105382320114[/C][C]0.0979461767988656[/C][/ROW]
[ROW][C]29[/C][C]9.955[/C][C]9.44174029694933[/C][C]0.513259703050666[/C][/ROW]
[ROW][C]30[/C][C]10.048[/C][C]10.2265715967451[/C][C]-0.178571596745112[/C][/ROW]
[ROW][C]31[/C][C]10.082[/C][C]10.806368697415[/C][C]-0.724368697414983[/C][/ROW]
[ROW][C]32[/C][C]10.541[/C][C]10.2559828504901[/C][C]0.285017149509907[/C][/ROW]
[ROW][C]33[/C][C]10.208[/C][C]10.2537256629586[/C][C]-0.0457256629585885[/C][/ROW]
[ROW][C]34[/C][C]10.233[/C][C]10.0840083676595[/C][C]0.148991632340467[/C][/ROW]
[ROW][C]35[/C][C]9.439[/C][C]9.57463054881125[/C][C]-0.135630548811246[/C][/ROW]
[ROW][C]36[/C][C]9.963[/C][C]10.3150427046877[/C][C]-0.352042704687689[/C][/ROW]
[ROW][C]37[/C][C]10.158[/C][C]10.1900903894399[/C][C]-0.0320903894398921[/C][/ROW]
[ROW][C]38[/C][C]9.225[/C][C]9.50677017484429[/C][C]-0.281770174844288[/C][/ROW]
[ROW][C]39[/C][C]10.474[/C][C]10.4001257111182[/C][C]0.0738742888818429[/C][/ROW]
[ROW][C]40[/C][C]9.757[/C][C]9.971646911039[/C][C]-0.214646911038995[/C][/ROW]
[ROW][C]41[/C][C]10.49[/C][C]9.8841984585335[/C][C]0.605801541466505[/C][/ROW]
[ROW][C]42[/C][C]10.281[/C][C]10.3132763382556[/C][C]-0.0322763382555777[/C][/ROW]
[ROW][C]43[/C][C]10.444[/C][C]10.6186001114933[/C][C]-0.174600111493323[/C][/ROW]
[ROW][C]44[/C][C]10.64[/C][C]10.6450653992841[/C][C]-0.00506539928406902[/C][/ROW]
[ROW][C]45[/C][C]10.695[/C][C]10.4445124585428[/C][C]0.25048754145724[/C][/ROW]
[ROW][C]46[/C][C]10.786[/C][C]10.4021254817184[/C][C]0.383874518281599[/C][/ROW]
[ROW][C]47[/C][C]9.832[/C][C]9.76300262603202[/C][C]0.0689973739679779[/C][/ROW]
[ROW][C]48[/C][C]9.747[/C][C]10.4069609748898[/C][C]-0.659960974889772[/C][/ROW]
[ROW][C]49[/C][C]10.411[/C][C]10.4241549579517[/C][C]-0.0131549579517465[/C][/ROW]
[ROW][C]50[/C][C]9.511[/C][C]9.61122359826276[/C][C]-0.100223598262765[/C][/ROW]
[ROW][C]51[/C][C]10.402[/C][C]10.7067991598434[/C][C]-0.304799159843419[/C][/ROW]
[ROW][C]52[/C][C]9.701[/C][C]10.0947343328063[/C][C]-0.393734332806311[/C][/ROW]
[ROW][C]53[/C][C]10.54[/C][C]10.4233235064905[/C][C]0.116676493509521[/C][/ROW]
[ROW][C]54[/C][C]10.112[/C][C]10.4757958594659[/C][C]-0.363795859465917[/C][/ROW]
[ROW][C]55[/C][C]10.915[/C][C]10.6783423946209[/C][C]0.236657605379103[/C][/ROW]
[ROW][C]56[/C][C]11.183[/C][C]10.8286155000941[/C][C]0.354384499905901[/C][/ROW]
[ROW][C]57[/C][C]10.384[/C][C]10.7927006812139[/C][C]-0.408700681213894[/C][/ROW]
[ROW][C]58[/C][C]10.834[/C][C]10.7647661347396[/C][C]0.0692338652604256[/C][/ROW]
[ROW][C]59[/C][C]9.886[/C][C]9.93361209457797[/C][C]-0.0476120945779677[/C][/ROW]
[ROW][C]60[/C][C]10.216[/C][C]10.184651292418[/C][C]0.0313487075819623[/C][/ROW]
[ROW][C]61[/C][C]10.943[/C][C]10.6001045089251[/C][C]0.342895491074923[/C][/ROW]
[ROW][C]62[/C][C]9.867[/C][C]9.77147281606674[/C][C]0.0955271839332603[/C][/ROW]
[ROW][C]63[/C][C]10.203[/C][C]10.7760654898354[/C][C]-0.57306548983542[/C][/ROW]
[ROW][C]64[/C][C]10.837[/C][C]10.0946191145426[/C][C]0.742380885457431[/C][/ROW]
[ROW][C]65[/C][C]10.573[/C][C]10.7873375969434[/C][C]-0.214337596943441[/C][/ROW]
[ROW][C]66[/C][C]10.647[/C][C]10.559374491307[/C][C]0.087625508693014[/C][/ROW]
[ROW][C]67[/C][C]11.502[/C][C]11.1155718262249[/C][C]0.38642817377511[/C][/ROW]
[ROW][C]68[/C][C]10.656[/C][C]11.3403542940199[/C][C]-0.68435429401992[/C][/ROW]
[ROW][C]69[/C][C]10.866[/C][C]10.8157467657126[/C][C]0.0502532342873607[/C][/ROW]
[ROW][C]70[/C][C]10.835[/C][C]11.0777137915992[/C][C]-0.242713791599188[/C][/ROW]
[ROW][C]71[/C][C]9.945[/C][C]10.1588235071015[/C][C]-0.213823507101477[/C][/ROW]
[ROW][C]72[/C][C]10.331[/C][C]10.4373271236528[/C][C]-0.10632712365285[/C][/ROW]
[ROW][C]73[/C][C]10.718[/C][C]11.004880078885[/C][C]-0.286880078885012[/C][/ROW]
[ROW][C]74[/C][C]9.462[/C][C]9.99309243285041[/C][C]-0.531092432850407[/C][/ROW]
[ROW][C]75[/C][C]10.579[/C][C]10.593437409713[/C][C]-0.0144374097130218[/C][/ROW]
[ROW][C]76[/C][C]10.633[/C][C]10.650428277033[/C][C]-0.017428277033039[/C][/ROW]
[ROW][C]77[/C][C]10.346[/C][C]10.7762428032309[/C][C]-0.430242803230918[/C][/ROW]
[ROW][C]78[/C][C]10.757[/C][C]10.688739544656[/C][C]0.0682604553439639[/C][/ROW]
[ROW][C]79[/C][C]11.207[/C][C]11.4003263853516[/C][C]-0.193326385351639[/C][/ROW]
[ROW][C]80[/C][C]11.013[/C][C]11.0134619028521[/C][C]-0.000461902852087803[/C][/ROW]
[ROW][C]81[/C][C]11.015[/C][C]10.9326281762673[/C][C]0.0823718237327036[/C][/ROW]
[ROW][C]82[/C][C]10.765[/C][C]11.0433489522367[/C][C]-0.278348952236703[/C][/ROW]
[ROW][C]83[/C][C]10.042[/C][C]10.1366327735722[/C][C]-0.0946327735721741[/C][/ROW]
[ROW][C]84[/C][C]10.661[/C][C]10.481688174035[/C][C]0.179311825964991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187545&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187545&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
139.8299.746152243589740.0828477564102599
149.1259.037428580589120.0875714194108816
159.7829.687645321903760.0943546780962379
169.4419.357726323784690.0832736762153079
179.1629.075455280536620.0865447194633777
189.9159.819627021894420.0953729781055834
1910.44410.5044189813365-0.060418981336511
2010.2099.722851770992660.486148229007341
219.98510.0019634992218-0.0169634992217613
229.8429.807772821393710.0342271786062884
239.4299.171236625656770.257763374343225
2410.13210.02306974745010.108930252549895
259.84910.1551685431218-0.306168543121766
269.1729.41608926077168-0.244089260771682
2710.31310.04187427222570.271125727774344
289.8199.721053823201140.0979461767988656
299.9559.441740296949330.513259703050666
3010.04810.2265715967451-0.178571596745112
3110.08210.806368697415-0.724368697414983
3210.54110.25598285049010.285017149509907
3310.20810.2537256629586-0.0457256629585885
3410.23310.08400836765950.148991632340467
359.4399.57463054881125-0.135630548811246
369.96310.3150427046877-0.352042704687689
3710.15810.1900903894399-0.0320903894398921
389.2259.50677017484429-0.281770174844288
3910.47410.40012571111820.0738742888818429
409.7579.971646911039-0.214646911038995
4110.499.88419845853350.605801541466505
4210.28110.3132763382556-0.0322763382555777
4310.44410.6186001114933-0.174600111493323
4410.6410.6450653992841-0.00506539928406902
4510.69510.44451245854280.25048754145724
4610.78610.40212548171840.383874518281599
479.8329.763002626032020.0689973739679779
489.74710.4069609748898-0.659960974889772
4910.41110.4241549579517-0.0131549579517465
509.5119.61122359826276-0.100223598262765
5110.40210.7067991598434-0.304799159843419
529.70110.0947343328063-0.393734332806311
5310.5410.42332350649050.116676493509521
5410.11210.4757958594659-0.363795859465917
5510.91510.67834239462090.236657605379103
5611.18310.82861550009410.354384499905901
5710.38410.7927006812139-0.408700681213894
5810.83410.76476613473960.0692338652604256
599.8869.93361209457797-0.0476120945779677
6010.21610.1846512924180.0313487075819623
6110.94310.60010450892510.342895491074923
629.8679.771472816066740.0955271839332603
6310.20310.7760654898354-0.57306548983542
6410.83710.09461911454260.742380885457431
6510.57310.7873375969434-0.214337596943441
6610.64710.5593744913070.087625508693014
6711.50211.11557182622490.38642817377511
6810.65611.3403542940199-0.68435429401992
6910.86610.81574676571260.0502532342873607
7010.83511.0777137915992-0.242713791599188
719.94510.1588235071015-0.213823507101477
7210.33110.4373271236528-0.10632712365285
7310.71811.004880078885-0.286880078885012
749.4629.99309243285041-0.531092432850407
7510.57910.593437409713-0.0144374097130218
7610.63310.650428277033-0.017428277033039
7710.34610.7762428032309-0.430242803230918
7810.75710.6887395446560.0682604553439639
7911.20711.4003263853516-0.193326385351639
8011.01311.0134619028521-0.000461902852087803
8111.01510.93262817626730.0823718237327036
8210.76511.0433489522367-0.278348952236703
8310.04210.1366327735722-0.0946327735721741
8410.66110.4816881740350.179311825964991







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8510.978470103966210.405415206472911.5515250014594
869.862562469155069.2874695381421310.437655400168
8710.779246479432410.202122711891111.3563702469737
8810.835884314571710.256736831782511.4150317973609
8910.746231329764310.165067178614911.3273954809136
9010.957015147760410.373841302032511.5401889934884
9111.525373102282210.940196463906112.1105497406583
9211.25618029917310.669007699453611.8433528988923
9311.218915618924510.629753819737511.8080774181115
9411.133120329531510.541976024491511.7242646345715
9510.34644528705139.7533251026524810.93956547145
9610.843449876459610.248360373190311.4385393797289

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 10.9784701039662 & 10.4054152064729 & 11.5515250014594 \tabularnewline
86 & 9.86256246915506 & 9.28746953814213 & 10.437655400168 \tabularnewline
87 & 10.7792464794324 & 10.2021227118911 & 11.3563702469737 \tabularnewline
88 & 10.8358843145717 & 10.2567368317825 & 11.4150317973609 \tabularnewline
89 & 10.7462313297643 & 10.1650671786149 & 11.3273954809136 \tabularnewline
90 & 10.9570151477604 & 10.3738413020325 & 11.5401889934884 \tabularnewline
91 & 11.5253731022822 & 10.9401964639061 & 12.1105497406583 \tabularnewline
92 & 11.256180299173 & 10.6690076994536 & 11.8433528988923 \tabularnewline
93 & 11.2189156189245 & 10.6297538197375 & 11.8080774181115 \tabularnewline
94 & 11.1331203295315 & 10.5419760244915 & 11.7242646345715 \tabularnewline
95 & 10.3464452870513 & 9.75332510265248 & 10.93956547145 \tabularnewline
96 & 10.8434498764596 & 10.2483603731903 & 11.4385393797289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187545&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]85[/C][C]10.9784701039662[/C][C]10.4054152064729[/C][C]11.5515250014594[/C][/ROW]
[ROW][C]86[/C][C]9.86256246915506[/C][C]9.28746953814213[/C][C]10.437655400168[/C][/ROW]
[ROW][C]87[/C][C]10.7792464794324[/C][C]10.2021227118911[/C][C]11.3563702469737[/C][/ROW]
[ROW][C]88[/C][C]10.8358843145717[/C][C]10.2567368317825[/C][C]11.4150317973609[/C][/ROW]
[ROW][C]89[/C][C]10.7462313297643[/C][C]10.1650671786149[/C][C]11.3273954809136[/C][/ROW]
[ROW][C]90[/C][C]10.9570151477604[/C][C]10.3738413020325[/C][C]11.5401889934884[/C][/ROW]
[ROW][C]91[/C][C]11.5253731022822[/C][C]10.9401964639061[/C][C]12.1105497406583[/C][/ROW]
[ROW][C]92[/C][C]11.256180299173[/C][C]10.6690076994536[/C][C]11.8433528988923[/C][/ROW]
[ROW][C]93[/C][C]11.2189156189245[/C][C]10.6297538197375[/C][C]11.8080774181115[/C][/ROW]
[ROW][C]94[/C][C]11.1331203295315[/C][C]10.5419760244915[/C][C]11.7242646345715[/C][/ROW]
[ROW][C]95[/C][C]10.3464452870513[/C][C]9.75332510265248[/C][C]10.93956547145[/C][/ROW]
[ROW][C]96[/C][C]10.8434498764596[/C][C]10.2483603731903[/C][C]11.4385393797289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187545&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187545&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
8510.978470103966210.405415206472911.5515250014594
869.862562469155069.2874695381421310.437655400168
8710.779246479432410.202122711891111.3563702469737
8810.835884314571710.256736831782511.4150317973609
8910.746231329764310.165067178614911.3273954809136
9010.957015147760410.373841302032511.5401889934884
9111.525373102282210.940196463906112.1105497406583
9211.25618029917310.669007699453611.8433528988923
9311.218915618924510.629753819737511.8080774181115
9411.133120329531510.541976024491511.7242646345715
9510.34644528705139.7533251026524810.93956547145
9610.843449876459610.248360373190311.4385393797289



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')