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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 computationTue, 26 Jan 2010 04:36:02 -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/2010/Jan/26/t1264505795u886cc1dx8w4g1w.htm/, Retrieved Thu, 02 May 2024 21:22:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72591, Retrieved Thu, 02 May 2024 21:22:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 opdracht 2] [2010-01-26 11:36:02] [2c3906e099e396db093769aeca236bf5] [Current]
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Dataseries X:
24.3
29.4
31.8
36.7
37.1
37.7
39.4
43.3
39.6
34.3
32
29.6
22.3
28.9
31.7
34.2
38.6
37.2
38.8
43.4
38.8
36.3
33
29.2
22.64
28.44
30.14
34.39
36.82
36.74
38.9
42.8
39.09
37.49
33.17
30.98
21.2
27.8
29
35.4
37.5
34.7
38.4
39.9
35.9
34.7
30.4
29
21.5
28
29.3
34.3
36.6
36.2
37.5
41.6
39.4
37.3
32.7
30.7
22.9
29.1
29.5
37.1
37.7
38.4
39.4
40.6
39.7
36.6
32.8
31.6
24.1
30.3
31.8
38.7
37.8
38.4
40.7
43.8
41.5
39.3
35.9
33.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72591&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72591&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.124974553803989
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.124974553803989 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72591&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.124974553803989[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72591&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
alpha1
beta0.124974553803989
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
331.834.5-2.7
436.736.56256870472920.137431295270773
537.141.4797441195344-4.3797441195344
637.741.33238755242-3.63238755241994
739.441.4784315388131-2.0784315388131
843.342.91868048463780.381319515362208
939.646.8663357209269-7.26633572092693
1034.342.2582286564141-7.95822865641411
113235.9636525810086-3.96365258100864
1229.633.1682968682631-3.56829686826305
1322.330.3223505593117-8.02235055931171
1428.922.01976087770266.88023912229745
1531.729.47961569207642.22038430792358
1634.232.55710723023251.64289276976746
1738.635.26242702108203.33757297891796
1837.240.0795387149106-2.87953871491056
1938.838.31966964885330.480330351146698
2043.439.97969872016643.42030127983363
2138.845.0071493464888-6.20714934648879
2236.339.6314136265166-3.33141362651664
233336.7150716950062-3.71507169500619
2429.232.9507822675730-3.75078226757296
2522.6428.6820299272671-6.04202992726712
2628.4421.36692993303667.07307006696344
2730.1428.05088370867972.08911629132033
2834.3930.01197008503214.37802991496793
2936.8234.80911242019572.01088757980430
3036.7437.4904221982317-0.750422198231725
3138.937.31663851884311.58336148115689
3242.839.67451841346113.12548158653888
3339.0943.9651240801614-4.87512408016138
3437.4939.6458576235041-2.15585762350415
3533.1737.7764302789418-4.60643027894179
3630.9832.8807437102019-1.90074371020185
3721.230.4531991131236-9.25319911312364
3827.819.51678468270158.28321531729845
392927.15197582104331.84802417895671
4035.428.58293181822746.81706818177262
4137.535.83489187249581.66510812750422
4234.738.142988017766-3.44298801776602
4338.434.91270212649323.48729787350676
4439.939.04852562221630.85147437778366
4535.940.6549382526554-4.75493825265538
4634.736.0606919661643-1.36069196616425
4730.434.6906400948282-4.29064009482821
482929.8544192634435-0.854419263443546
4921.528.3476385972332-6.84763859723316
502819.99185801893308.00814198106703
5129.327.49267198981581.80732801018419
5234.329.01854200146605.28145799853396
5336.634.67858985826731.92141014173268
5436.237.2187172334048-1.01871723340482
5537.536.69140350170760.808596498292374
5641.638.09245748828923.50754251171082
5739.442.6308110486388-3.23081104863876
5837.340.0270418794101-2.72704187941014
5932.737.5862310373261-4.88623103732606
6030.732.3755764936530-1.67557649365304
6122.930.1661720689943-7.2661720689943
6229.121.45808545680877.64191454319127
6329.528.61313031705230.88686968294773
6437.129.12396645996097.97603354003905
6537.737.720767692753-0.0207676927529761
6638.438.31817225961760.0818277403823586
6739.439.02839864496070.371601355039289
6840.640.07483935849970.5251606415003
6939.741.3404710753466-1.64047107534662
7036.640.2354539346768-3.63545393467682
7132.836.6811147013156-3.88111470131564
7231.632.3960741232566-0.79607412325661
7324.131.0965851149077-6.99658511490772
7430.322.72219001202057.5778099879795
7531.829.86922343407961.93077656592036
7638.731.61052137390077.08947862609926
7737.839.3965258019004-1.59652580190041
7838.438.29700070217130.102999297828653
7940.738.90987299345961.79012700654039
8043.841.43359331735452.36640668264553
8141.544.8293339366369-3.32933393663686
8239.342.1132519134412-2.8132519134412
8335.939.5616670108207-3.66166701082066
8433.435.7040518099646-2.30405180996457

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 31.8 & 34.5 & -2.7 \tabularnewline
4 & 36.7 & 36.5625687047292 & 0.137431295270773 \tabularnewline
5 & 37.1 & 41.4797441195344 & -4.3797441195344 \tabularnewline
6 & 37.7 & 41.33238755242 & -3.63238755241994 \tabularnewline
7 & 39.4 & 41.4784315388131 & -2.0784315388131 \tabularnewline
8 & 43.3 & 42.9186804846378 & 0.381319515362208 \tabularnewline
9 & 39.6 & 46.8663357209269 & -7.26633572092693 \tabularnewline
10 & 34.3 & 42.2582286564141 & -7.95822865641411 \tabularnewline
11 & 32 & 35.9636525810086 & -3.96365258100864 \tabularnewline
12 & 29.6 & 33.1682968682631 & -3.56829686826305 \tabularnewline
13 & 22.3 & 30.3223505593117 & -8.02235055931171 \tabularnewline
14 & 28.9 & 22.0197608777026 & 6.88023912229745 \tabularnewline
15 & 31.7 & 29.4796156920764 & 2.22038430792358 \tabularnewline
16 & 34.2 & 32.5571072302325 & 1.64289276976746 \tabularnewline
17 & 38.6 & 35.2624270210820 & 3.33757297891796 \tabularnewline
18 & 37.2 & 40.0795387149106 & -2.87953871491056 \tabularnewline
19 & 38.8 & 38.3196696488533 & 0.480330351146698 \tabularnewline
20 & 43.4 & 39.9796987201664 & 3.42030127983363 \tabularnewline
21 & 38.8 & 45.0071493464888 & -6.20714934648879 \tabularnewline
22 & 36.3 & 39.6314136265166 & -3.33141362651664 \tabularnewline
23 & 33 & 36.7150716950062 & -3.71507169500619 \tabularnewline
24 & 29.2 & 32.9507822675730 & -3.75078226757296 \tabularnewline
25 & 22.64 & 28.6820299272671 & -6.04202992726712 \tabularnewline
26 & 28.44 & 21.3669299330366 & 7.07307006696344 \tabularnewline
27 & 30.14 & 28.0508837086797 & 2.08911629132033 \tabularnewline
28 & 34.39 & 30.0119700850321 & 4.37802991496793 \tabularnewline
29 & 36.82 & 34.8091124201957 & 2.01088757980430 \tabularnewline
30 & 36.74 & 37.4904221982317 & -0.750422198231725 \tabularnewline
31 & 38.9 & 37.3166385188431 & 1.58336148115689 \tabularnewline
32 & 42.8 & 39.6745184134611 & 3.12548158653888 \tabularnewline
33 & 39.09 & 43.9651240801614 & -4.87512408016138 \tabularnewline
34 & 37.49 & 39.6458576235041 & -2.15585762350415 \tabularnewline
35 & 33.17 & 37.7764302789418 & -4.60643027894179 \tabularnewline
36 & 30.98 & 32.8807437102019 & -1.90074371020185 \tabularnewline
37 & 21.2 & 30.4531991131236 & -9.25319911312364 \tabularnewline
38 & 27.8 & 19.5167846827015 & 8.28321531729845 \tabularnewline
39 & 29 & 27.1519758210433 & 1.84802417895671 \tabularnewline
40 & 35.4 & 28.5829318182274 & 6.81706818177262 \tabularnewline
41 & 37.5 & 35.8348918724958 & 1.66510812750422 \tabularnewline
42 & 34.7 & 38.142988017766 & -3.44298801776602 \tabularnewline
43 & 38.4 & 34.9127021264932 & 3.48729787350676 \tabularnewline
44 & 39.9 & 39.0485256222163 & 0.85147437778366 \tabularnewline
45 & 35.9 & 40.6549382526554 & -4.75493825265538 \tabularnewline
46 & 34.7 & 36.0606919661643 & -1.36069196616425 \tabularnewline
47 & 30.4 & 34.6906400948282 & -4.29064009482821 \tabularnewline
48 & 29 & 29.8544192634435 & -0.854419263443546 \tabularnewline
49 & 21.5 & 28.3476385972332 & -6.84763859723316 \tabularnewline
50 & 28 & 19.9918580189330 & 8.00814198106703 \tabularnewline
51 & 29.3 & 27.4926719898158 & 1.80732801018419 \tabularnewline
52 & 34.3 & 29.0185420014660 & 5.28145799853396 \tabularnewline
53 & 36.6 & 34.6785898582673 & 1.92141014173268 \tabularnewline
54 & 36.2 & 37.2187172334048 & -1.01871723340482 \tabularnewline
55 & 37.5 & 36.6914035017076 & 0.808596498292374 \tabularnewline
56 & 41.6 & 38.0924574882892 & 3.50754251171082 \tabularnewline
57 & 39.4 & 42.6308110486388 & -3.23081104863876 \tabularnewline
58 & 37.3 & 40.0270418794101 & -2.72704187941014 \tabularnewline
59 & 32.7 & 37.5862310373261 & -4.88623103732606 \tabularnewline
60 & 30.7 & 32.3755764936530 & -1.67557649365304 \tabularnewline
61 & 22.9 & 30.1661720689943 & -7.2661720689943 \tabularnewline
62 & 29.1 & 21.4580854568087 & 7.64191454319127 \tabularnewline
63 & 29.5 & 28.6131303170523 & 0.88686968294773 \tabularnewline
64 & 37.1 & 29.1239664599609 & 7.97603354003905 \tabularnewline
65 & 37.7 & 37.720767692753 & -0.0207676927529761 \tabularnewline
66 & 38.4 & 38.3181722596176 & 0.0818277403823586 \tabularnewline
67 & 39.4 & 39.0283986449607 & 0.371601355039289 \tabularnewline
68 & 40.6 & 40.0748393584997 & 0.5251606415003 \tabularnewline
69 & 39.7 & 41.3404710753466 & -1.64047107534662 \tabularnewline
70 & 36.6 & 40.2354539346768 & -3.63545393467682 \tabularnewline
71 & 32.8 & 36.6811147013156 & -3.88111470131564 \tabularnewline
72 & 31.6 & 32.3960741232566 & -0.79607412325661 \tabularnewline
73 & 24.1 & 31.0965851149077 & -6.99658511490772 \tabularnewline
74 & 30.3 & 22.7221900120205 & 7.5778099879795 \tabularnewline
75 & 31.8 & 29.8692234340796 & 1.93077656592036 \tabularnewline
76 & 38.7 & 31.6105213739007 & 7.08947862609926 \tabularnewline
77 & 37.8 & 39.3965258019004 & -1.59652580190041 \tabularnewline
78 & 38.4 & 38.2970007021713 & 0.102999297828653 \tabularnewline
79 & 40.7 & 38.9098729934596 & 1.79012700654039 \tabularnewline
80 & 43.8 & 41.4335933173545 & 2.36640668264553 \tabularnewline
81 & 41.5 & 44.8293339366369 & -3.32933393663686 \tabularnewline
82 & 39.3 & 42.1132519134412 & -2.8132519134412 \tabularnewline
83 & 35.9 & 39.5616670108207 & -3.66166701082066 \tabularnewline
84 & 33.4 & 35.7040518099646 & -2.30405180996457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72591&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]31.8[/C][C]34.5[/C][C]-2.7[/C][/ROW]
[ROW][C]4[/C][C]36.7[/C][C]36.5625687047292[/C][C]0.137431295270773[/C][/ROW]
[ROW][C]5[/C][C]37.1[/C][C]41.4797441195344[/C][C]-4.3797441195344[/C][/ROW]
[ROW][C]6[/C][C]37.7[/C][C]41.33238755242[/C][C]-3.63238755241994[/C][/ROW]
[ROW][C]7[/C][C]39.4[/C][C]41.4784315388131[/C][C]-2.0784315388131[/C][/ROW]
[ROW][C]8[/C][C]43.3[/C][C]42.9186804846378[/C][C]0.381319515362208[/C][/ROW]
[ROW][C]9[/C][C]39.6[/C][C]46.8663357209269[/C][C]-7.26633572092693[/C][/ROW]
[ROW][C]10[/C][C]34.3[/C][C]42.2582286564141[/C][C]-7.95822865641411[/C][/ROW]
[ROW][C]11[/C][C]32[/C][C]35.9636525810086[/C][C]-3.96365258100864[/C][/ROW]
[ROW][C]12[/C][C]29.6[/C][C]33.1682968682631[/C][C]-3.56829686826305[/C][/ROW]
[ROW][C]13[/C][C]22.3[/C][C]30.3223505593117[/C][C]-8.02235055931171[/C][/ROW]
[ROW][C]14[/C][C]28.9[/C][C]22.0197608777026[/C][C]6.88023912229745[/C][/ROW]
[ROW][C]15[/C][C]31.7[/C][C]29.4796156920764[/C][C]2.22038430792358[/C][/ROW]
[ROW][C]16[/C][C]34.2[/C][C]32.5571072302325[/C][C]1.64289276976746[/C][/ROW]
[ROW][C]17[/C][C]38.6[/C][C]35.2624270210820[/C][C]3.33757297891796[/C][/ROW]
[ROW][C]18[/C][C]37.2[/C][C]40.0795387149106[/C][C]-2.87953871491056[/C][/ROW]
[ROW][C]19[/C][C]38.8[/C][C]38.3196696488533[/C][C]0.480330351146698[/C][/ROW]
[ROW][C]20[/C][C]43.4[/C][C]39.9796987201664[/C][C]3.42030127983363[/C][/ROW]
[ROW][C]21[/C][C]38.8[/C][C]45.0071493464888[/C][C]-6.20714934648879[/C][/ROW]
[ROW][C]22[/C][C]36.3[/C][C]39.6314136265166[/C][C]-3.33141362651664[/C][/ROW]
[ROW][C]23[/C][C]33[/C][C]36.7150716950062[/C][C]-3.71507169500619[/C][/ROW]
[ROW][C]24[/C][C]29.2[/C][C]32.9507822675730[/C][C]-3.75078226757296[/C][/ROW]
[ROW][C]25[/C][C]22.64[/C][C]28.6820299272671[/C][C]-6.04202992726712[/C][/ROW]
[ROW][C]26[/C][C]28.44[/C][C]21.3669299330366[/C][C]7.07307006696344[/C][/ROW]
[ROW][C]27[/C][C]30.14[/C][C]28.0508837086797[/C][C]2.08911629132033[/C][/ROW]
[ROW][C]28[/C][C]34.39[/C][C]30.0119700850321[/C][C]4.37802991496793[/C][/ROW]
[ROW][C]29[/C][C]36.82[/C][C]34.8091124201957[/C][C]2.01088757980430[/C][/ROW]
[ROW][C]30[/C][C]36.74[/C][C]37.4904221982317[/C][C]-0.750422198231725[/C][/ROW]
[ROW][C]31[/C][C]38.9[/C][C]37.3166385188431[/C][C]1.58336148115689[/C][/ROW]
[ROW][C]32[/C][C]42.8[/C][C]39.6745184134611[/C][C]3.12548158653888[/C][/ROW]
[ROW][C]33[/C][C]39.09[/C][C]43.9651240801614[/C][C]-4.87512408016138[/C][/ROW]
[ROW][C]34[/C][C]37.49[/C][C]39.6458576235041[/C][C]-2.15585762350415[/C][/ROW]
[ROW][C]35[/C][C]33.17[/C][C]37.7764302789418[/C][C]-4.60643027894179[/C][/ROW]
[ROW][C]36[/C][C]30.98[/C][C]32.8807437102019[/C][C]-1.90074371020185[/C][/ROW]
[ROW][C]37[/C][C]21.2[/C][C]30.4531991131236[/C][C]-9.25319911312364[/C][/ROW]
[ROW][C]38[/C][C]27.8[/C][C]19.5167846827015[/C][C]8.28321531729845[/C][/ROW]
[ROW][C]39[/C][C]29[/C][C]27.1519758210433[/C][C]1.84802417895671[/C][/ROW]
[ROW][C]40[/C][C]35.4[/C][C]28.5829318182274[/C][C]6.81706818177262[/C][/ROW]
[ROW][C]41[/C][C]37.5[/C][C]35.8348918724958[/C][C]1.66510812750422[/C][/ROW]
[ROW][C]42[/C][C]34.7[/C][C]38.142988017766[/C][C]-3.44298801776602[/C][/ROW]
[ROW][C]43[/C][C]38.4[/C][C]34.9127021264932[/C][C]3.48729787350676[/C][/ROW]
[ROW][C]44[/C][C]39.9[/C][C]39.0485256222163[/C][C]0.85147437778366[/C][/ROW]
[ROW][C]45[/C][C]35.9[/C][C]40.6549382526554[/C][C]-4.75493825265538[/C][/ROW]
[ROW][C]46[/C][C]34.7[/C][C]36.0606919661643[/C][C]-1.36069196616425[/C][/ROW]
[ROW][C]47[/C][C]30.4[/C][C]34.6906400948282[/C][C]-4.29064009482821[/C][/ROW]
[ROW][C]48[/C][C]29[/C][C]29.8544192634435[/C][C]-0.854419263443546[/C][/ROW]
[ROW][C]49[/C][C]21.5[/C][C]28.3476385972332[/C][C]-6.84763859723316[/C][/ROW]
[ROW][C]50[/C][C]28[/C][C]19.9918580189330[/C][C]8.00814198106703[/C][/ROW]
[ROW][C]51[/C][C]29.3[/C][C]27.4926719898158[/C][C]1.80732801018419[/C][/ROW]
[ROW][C]52[/C][C]34.3[/C][C]29.0185420014660[/C][C]5.28145799853396[/C][/ROW]
[ROW][C]53[/C][C]36.6[/C][C]34.6785898582673[/C][C]1.92141014173268[/C][/ROW]
[ROW][C]54[/C][C]36.2[/C][C]37.2187172334048[/C][C]-1.01871723340482[/C][/ROW]
[ROW][C]55[/C][C]37.5[/C][C]36.6914035017076[/C][C]0.808596498292374[/C][/ROW]
[ROW][C]56[/C][C]41.6[/C][C]38.0924574882892[/C][C]3.50754251171082[/C][/ROW]
[ROW][C]57[/C][C]39.4[/C][C]42.6308110486388[/C][C]-3.23081104863876[/C][/ROW]
[ROW][C]58[/C][C]37.3[/C][C]40.0270418794101[/C][C]-2.72704187941014[/C][/ROW]
[ROW][C]59[/C][C]32.7[/C][C]37.5862310373261[/C][C]-4.88623103732606[/C][/ROW]
[ROW][C]60[/C][C]30.7[/C][C]32.3755764936530[/C][C]-1.67557649365304[/C][/ROW]
[ROW][C]61[/C][C]22.9[/C][C]30.1661720689943[/C][C]-7.2661720689943[/C][/ROW]
[ROW][C]62[/C][C]29.1[/C][C]21.4580854568087[/C][C]7.64191454319127[/C][/ROW]
[ROW][C]63[/C][C]29.5[/C][C]28.6131303170523[/C][C]0.88686968294773[/C][/ROW]
[ROW][C]64[/C][C]37.1[/C][C]29.1239664599609[/C][C]7.97603354003905[/C][/ROW]
[ROW][C]65[/C][C]37.7[/C][C]37.720767692753[/C][C]-0.0207676927529761[/C][/ROW]
[ROW][C]66[/C][C]38.4[/C][C]38.3181722596176[/C][C]0.0818277403823586[/C][/ROW]
[ROW][C]67[/C][C]39.4[/C][C]39.0283986449607[/C][C]0.371601355039289[/C][/ROW]
[ROW][C]68[/C][C]40.6[/C][C]40.0748393584997[/C][C]0.5251606415003[/C][/ROW]
[ROW][C]69[/C][C]39.7[/C][C]41.3404710753466[/C][C]-1.64047107534662[/C][/ROW]
[ROW][C]70[/C][C]36.6[/C][C]40.2354539346768[/C][C]-3.63545393467682[/C][/ROW]
[ROW][C]71[/C][C]32.8[/C][C]36.6811147013156[/C][C]-3.88111470131564[/C][/ROW]
[ROW][C]72[/C][C]31.6[/C][C]32.3960741232566[/C][C]-0.79607412325661[/C][/ROW]
[ROW][C]73[/C][C]24.1[/C][C]31.0965851149077[/C][C]-6.99658511490772[/C][/ROW]
[ROW][C]74[/C][C]30.3[/C][C]22.7221900120205[/C][C]7.5778099879795[/C][/ROW]
[ROW][C]75[/C][C]31.8[/C][C]29.8692234340796[/C][C]1.93077656592036[/C][/ROW]
[ROW][C]76[/C][C]38.7[/C][C]31.6105213739007[/C][C]7.08947862609926[/C][/ROW]
[ROW][C]77[/C][C]37.8[/C][C]39.3965258019004[/C][C]-1.59652580190041[/C][/ROW]
[ROW][C]78[/C][C]38.4[/C][C]38.2970007021713[/C][C]0.102999297828653[/C][/ROW]
[ROW][C]79[/C][C]40.7[/C][C]38.9098729934596[/C][C]1.79012700654039[/C][/ROW]
[ROW][C]80[/C][C]43.8[/C][C]41.4335933173545[/C][C]2.36640668264553[/C][/ROW]
[ROW][C]81[/C][C]41.5[/C][C]44.8293339366369[/C][C]-3.32933393663686[/C][/ROW]
[ROW][C]82[/C][C]39.3[/C][C]42.1132519134412[/C][C]-2.8132519134412[/C][/ROW]
[ROW][C]83[/C][C]35.9[/C][C]39.5616670108207[/C][C]-3.66166701082066[/C][/ROW]
[ROW][C]84[/C][C]33.4[/C][C]35.7040518099646[/C][C]-2.30405180996457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72591&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72591&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
331.834.5-2.7
436.736.56256870472920.137431295270773
537.141.4797441195344-4.3797441195344
637.741.33238755242-3.63238755241994
739.441.4784315388131-2.0784315388131
843.342.91868048463780.381319515362208
939.646.8663357209269-7.26633572092693
1034.342.2582286564141-7.95822865641411
113235.9636525810086-3.96365258100864
1229.633.1682968682631-3.56829686826305
1322.330.3223505593117-8.02235055931171
1428.922.01976087770266.88023912229745
1531.729.47961569207642.22038430792358
1634.232.55710723023251.64289276976746
1738.635.26242702108203.33757297891796
1837.240.0795387149106-2.87953871491056
1938.838.31966964885330.480330351146698
2043.439.97969872016643.42030127983363
2138.845.0071493464888-6.20714934648879
2236.339.6314136265166-3.33141362651664
233336.7150716950062-3.71507169500619
2429.232.9507822675730-3.75078226757296
2522.6428.6820299272671-6.04202992726712
2628.4421.36692993303667.07307006696344
2730.1428.05088370867972.08911629132033
2834.3930.01197008503214.37802991496793
2936.8234.80911242019572.01088757980430
3036.7437.4904221982317-0.750422198231725
3138.937.31663851884311.58336148115689
3242.839.67451841346113.12548158653888
3339.0943.9651240801614-4.87512408016138
3437.4939.6458576235041-2.15585762350415
3533.1737.7764302789418-4.60643027894179
3630.9832.8807437102019-1.90074371020185
3721.230.4531991131236-9.25319911312364
3827.819.51678468270158.28321531729845
392927.15197582104331.84802417895671
4035.428.58293181822746.81706818177262
4137.535.83489187249581.66510812750422
4234.738.142988017766-3.44298801776602
4338.434.91270212649323.48729787350676
4439.939.04852562221630.85147437778366
4535.940.6549382526554-4.75493825265538
4634.736.0606919661643-1.36069196616425
4730.434.6906400948282-4.29064009482821
482929.8544192634435-0.854419263443546
4921.528.3476385972332-6.84763859723316
502819.99185801893308.00814198106703
5129.327.49267198981581.80732801018419
5234.329.01854200146605.28145799853396
5336.634.67858985826731.92141014173268
5436.237.2187172334048-1.01871723340482
5537.536.69140350170760.808596498292374
5641.638.09245748828923.50754251171082
5739.442.6308110486388-3.23081104863876
5837.340.0270418794101-2.72704187941014
5932.737.5862310373261-4.88623103732606
6030.732.3755764936530-1.67557649365304
6122.930.1661720689943-7.2661720689943
6229.121.45808545680877.64191454319127
6329.528.61313031705230.88686968294773
6437.129.12396645996097.97603354003905
6537.737.720767692753-0.0207676927529761
6638.438.31817225961760.0818277403823586
6739.439.02839864496070.371601355039289
6840.640.07483935849970.5251606415003
6939.741.3404710753466-1.64047107534662
7036.640.2354539346768-3.63545393467682
7132.836.6811147013156-3.88111470131564
7231.632.3960741232566-0.79607412325661
7324.131.0965851149077-6.99658511490772
7430.322.72219001202057.5778099879795
7531.829.86922343407961.93077656592036
7638.731.61052137390077.08947862609926
7737.839.3965258019004-1.59652580190041
7838.438.29700070217130.102999297828653
7940.738.90987299345961.79012700654039
8043.841.43359331735452.36640668264553
8141.544.8293339366369-3.32933393663686
8239.342.1132519134412-2.8132519134412
8335.939.5616670108207-3.66166701082066
8433.435.7040518099646-2.30405180996457







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8532.91610396307324.567989222429541.2642187037164
8632.432207926145919.866790045335244.9976258069567
8731.948311889218915.615122422361348.2815013560765
8831.464415852291911.501499421657951.4273322829259
8930.98051981536497.4156827257743254.5453569049554
9030.49662377843783.3065413979339857.6867061589417
9130.0127277415108-0.85298282193364460.8784383049553
9229.5288317045838-5.0782922876390264.1359556968066
9329.0449356676568-9.378499432679867.4683707679933
9428.5610396307297-13.759062543619170.8811418050785
9528.0771435938027-18.223202389749574.3774895773549
9627.5932475568757-22.772716080571577.9592111943229

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 32.916103963073 & 24.5679892224295 & 41.2642187037164 \tabularnewline
86 & 32.4322079261459 & 19.8667900453352 & 44.9976258069567 \tabularnewline
87 & 31.9483118892189 & 15.6151224223613 & 48.2815013560765 \tabularnewline
88 & 31.4644158522919 & 11.5014994216579 & 51.4273322829259 \tabularnewline
89 & 30.9805198153649 & 7.41568272577432 & 54.5453569049554 \tabularnewline
90 & 30.4966237784378 & 3.30654139793398 & 57.6867061589417 \tabularnewline
91 & 30.0127277415108 & -0.852982821933644 & 60.8784383049553 \tabularnewline
92 & 29.5288317045838 & -5.07829228763902 & 64.1359556968066 \tabularnewline
93 & 29.0449356676568 & -9.3784994326798 & 67.4683707679933 \tabularnewline
94 & 28.5610396307297 & -13.7590625436191 & 70.8811418050785 \tabularnewline
95 & 28.0771435938027 & -18.2232023897495 & 74.3774895773549 \tabularnewline
96 & 27.5932475568757 & -22.7727160805715 & 77.9592111943229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72591&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]32.916103963073[/C][C]24.5679892224295[/C][C]41.2642187037164[/C][/ROW]
[ROW][C]86[/C][C]32.4322079261459[/C][C]19.8667900453352[/C][C]44.9976258069567[/C][/ROW]
[ROW][C]87[/C][C]31.9483118892189[/C][C]15.6151224223613[/C][C]48.2815013560765[/C][/ROW]
[ROW][C]88[/C][C]31.4644158522919[/C][C]11.5014994216579[/C][C]51.4273322829259[/C][/ROW]
[ROW][C]89[/C][C]30.9805198153649[/C][C]7.41568272577432[/C][C]54.5453569049554[/C][/ROW]
[ROW][C]90[/C][C]30.4966237784378[/C][C]3.30654139793398[/C][C]57.6867061589417[/C][/ROW]
[ROW][C]91[/C][C]30.0127277415108[/C][C]-0.852982821933644[/C][C]60.8784383049553[/C][/ROW]
[ROW][C]92[/C][C]29.5288317045838[/C][C]-5.07829228763902[/C][C]64.1359556968066[/C][/ROW]
[ROW][C]93[/C][C]29.0449356676568[/C][C]-9.3784994326798[/C][C]67.4683707679933[/C][/ROW]
[ROW][C]94[/C][C]28.5610396307297[/C][C]-13.7590625436191[/C][C]70.8811418050785[/C][/ROW]
[ROW][C]95[/C][C]28.0771435938027[/C][C]-18.2232023897495[/C][C]74.3774895773549[/C][/ROW]
[ROW][C]96[/C][C]27.5932475568757[/C][C]-22.7727160805715[/C][C]77.9592111943229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72591&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72591&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
8532.91610396307324.567989222429541.2642187037164
8632.432207926145919.866790045335244.9976258069567
8731.948311889218915.615122422361348.2815013560765
8831.464415852291911.501499421657951.4273322829259
8930.98051981536497.4156827257743254.5453569049554
9030.49662377843783.3065413979339857.6867061589417
9130.0127277415108-0.85298282193364460.8784383049553
9229.5288317045838-5.0782922876390264.1359556968066
9329.0449356676568-9.378499432679867.4683707679933
9428.5610396307297-13.759062543619170.8811418050785
9528.0771435938027-18.223202389749574.3774895773549
9627.5932475568757-22.772716080571577.9592111943229



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=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')