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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Dec 2015 10:36:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/12/t1449916667295qzv0iv2wlx8i.htm/, Retrieved Thu, 16 May 2024 07:23:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286048, Retrieved Thu, 16 May 2024 07:23:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-12-12 10:36:21] [aff7c5b01bb5e691e5ecdf00b98aae53] [Current]
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Dataseries X:
6.5
6.8
6.8
6.5
6.2
6.2
6.6
6.7
6.5
6.4
6.5
6.8
7.1
7.2
7.1
7
6.9
6.9
7.4
7.3
7
6.8
6.5
6.4
6.3
6
5.9
5.7
5.7
5.7
6.2
6.4
6.2
6.2
6.1
6.1
6.2
6.1
6.1
6.2
6.2
6.2
6.4
6.4
6.4
6.7
6.9
7.1
7.3
7.2
7.1
6.9
6.8
6.7
7.2
7.2
7.1
7.1
7
7.1
7.3
7.2
7.1
7
6.9
7
7.5
7.6
7.5
7.3
7.3
7.4
7.7
7.8
7.7
7.5
7.3
7.3
7.6
7.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286048&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286048&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286048&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286048&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286048&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286048&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26.86.50.3
36.86.799980167911591.98320884061687e-05
46.56.79999999868896-0.299999998688961
56.26.50001983208832-0.300019832088319
66.26.20001983339944-1.98333994445576e-05
76.66.200000001311130.399999998688874
86.76.599973557215550.100026442784454
96.56.69999338755581-0.199993387555812
106.46.50001322095514-0.100013220955142
116.56.400006611570130.0999933884298674
126.86.499993389740940.300006610259063
137.16.799980167474610.30001983252539
147.27.099980166600530.100019833399474
157.17.19999338799274-0.0999933879927397
1677.10000661025903-0.100006610259035
176.97.00000661113312-0.100006611133119
186.96.90000661113318-6.61113317779183e-06
197.46.900000000437040.499999999562958
207.37.39996694651935-0.0999669465193538
2177.30000660851107-0.30000660851107
226.87.00001983252527-0.200019832525275
236.56.80001322270334-0.300013222703338
246.46.50001983296252-0.100019832962518
256.36.40000661200723-0.100006612007232
2666.30000661113323-0.300006611133234
275.96.00001983252545-0.100019832525447
285.75.9000066120072-0.200006612007203
295.75.70001322182937-1.32218293700248e-05
305.75.70000000087406-8.74055494648474e-10
316.25.700000000000060.499999999999942
326.46.199966946519320.200033053480676
336.26.39998677642266-0.199986776422664
346.26.2000132205181-1.32205180998213e-05
356.16.20000000087397-0.100000000873969
366.16.10000661069619-6.61069619312116e-06
376.26.100000000437010.0999999995629874
386.16.19999338930389-0.0999933893038945
396.16.10000661025912-6.61025912229718e-06
406.26.100000000436980.0999999995630159
416.26.199993389303896.61069610607967e-06
426.26.199999999562994.37013092380312e-10
436.46.199999999999970.200000000000029
446.46.399986778607731.32213922707791e-05
456.46.399999999125978.74026184760623e-10
466.76.399999999999940.300000000000058
476.96.699980167911590.200019832088405
487.16.899986777296690.200013222703308
497.37.099986777733620.200013222266383
507.27.29998677773365-0.0999867777336449
517.17.20000660982205-0.100006609822052
526.97.10000661113309-0.20000661113309
536.86.90001322182931-0.100013221829313
546.76.80000661157019-0.10000661157019
557.26.700006611133210.499993388866794
567.27.199966946956373.30530436345455e-05
577.17.19999999781496-0.0999999978149644
587.17.10000661069599-6.61069599061648e-06
5977.10000000043701-0.100000000437013
607.17.000006610696160.0999933893038349
617.37.099993389740880.200006610259122
627.27.29998677817075-0.0999867781707451
637.17.20000660982208-0.10000660982208
6477.10000661113309-0.10000661113309
656.97.00000661113318-0.100006611133177
6676.900006611133180.0999933888668219
677.56.999993389740910.500006610259093
687.67.499966946082340.100033053917659
697.57.59999338711877-0.0999933871187704
707.37.50000661025898-0.200006610258978
717.37.30001322182925-1.32218292545616e-05
727.47.300000000874050.0999999991259459
737.77.399993389303920.300006610696077
747.87.699980167474580.100019832525419
757.77.7999933879928-0.0999933879927966
767.57.70000661025904-0.200006610259035
777.37.50001322182925-0.200013221829255
787.37.30001322226633-1.32222663253856e-05
797.67.300000000874080.299999999125917
807.67.599980167911651.98320883475489e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.8 & 6.5 & 0.3 \tabularnewline
3 & 6.8 & 6.79998016791159 & 1.98320884061687e-05 \tabularnewline
4 & 6.5 & 6.79999999868896 & -0.299999998688961 \tabularnewline
5 & 6.2 & 6.50001983208832 & -0.300019832088319 \tabularnewline
6 & 6.2 & 6.20001983339944 & -1.98333994445576e-05 \tabularnewline
7 & 6.6 & 6.20000000131113 & 0.399999998688874 \tabularnewline
8 & 6.7 & 6.59997355721555 & 0.100026442784454 \tabularnewline
9 & 6.5 & 6.69999338755581 & -0.199993387555812 \tabularnewline
10 & 6.4 & 6.50001322095514 & -0.100013220955142 \tabularnewline
11 & 6.5 & 6.40000661157013 & 0.0999933884298674 \tabularnewline
12 & 6.8 & 6.49999338974094 & 0.300006610259063 \tabularnewline
13 & 7.1 & 6.79998016747461 & 0.30001983252539 \tabularnewline
14 & 7.2 & 7.09998016660053 & 0.100019833399474 \tabularnewline
15 & 7.1 & 7.19999338799274 & -0.0999933879927397 \tabularnewline
16 & 7 & 7.10000661025903 & -0.100006610259035 \tabularnewline
17 & 6.9 & 7.00000661113312 & -0.100006611133119 \tabularnewline
18 & 6.9 & 6.90000661113318 & -6.61113317779183e-06 \tabularnewline
19 & 7.4 & 6.90000000043704 & 0.499999999562958 \tabularnewline
20 & 7.3 & 7.39996694651935 & -0.0999669465193538 \tabularnewline
21 & 7 & 7.30000660851107 & -0.30000660851107 \tabularnewline
22 & 6.8 & 7.00001983252527 & -0.200019832525275 \tabularnewline
23 & 6.5 & 6.80001322270334 & -0.300013222703338 \tabularnewline
24 & 6.4 & 6.50001983296252 & -0.100019832962518 \tabularnewline
25 & 6.3 & 6.40000661200723 & -0.100006612007232 \tabularnewline
26 & 6 & 6.30000661113323 & -0.300006611133234 \tabularnewline
27 & 5.9 & 6.00001983252545 & -0.100019832525447 \tabularnewline
28 & 5.7 & 5.9000066120072 & -0.200006612007203 \tabularnewline
29 & 5.7 & 5.70001322182937 & -1.32218293700248e-05 \tabularnewline
30 & 5.7 & 5.70000000087406 & -8.74055494648474e-10 \tabularnewline
31 & 6.2 & 5.70000000000006 & 0.499999999999942 \tabularnewline
32 & 6.4 & 6.19996694651932 & 0.200033053480676 \tabularnewline
33 & 6.2 & 6.39998677642266 & -0.199986776422664 \tabularnewline
34 & 6.2 & 6.2000132205181 & -1.32205180998213e-05 \tabularnewline
35 & 6.1 & 6.20000000087397 & -0.100000000873969 \tabularnewline
36 & 6.1 & 6.10000661069619 & -6.61069619312116e-06 \tabularnewline
37 & 6.2 & 6.10000000043701 & 0.0999999995629874 \tabularnewline
38 & 6.1 & 6.19999338930389 & -0.0999933893038945 \tabularnewline
39 & 6.1 & 6.10000661025912 & -6.61025912229718e-06 \tabularnewline
40 & 6.2 & 6.10000000043698 & 0.0999999995630159 \tabularnewline
41 & 6.2 & 6.19999338930389 & 6.61069610607967e-06 \tabularnewline
42 & 6.2 & 6.19999999956299 & 4.37013092380312e-10 \tabularnewline
43 & 6.4 & 6.19999999999997 & 0.200000000000029 \tabularnewline
44 & 6.4 & 6.39998677860773 & 1.32213922707791e-05 \tabularnewline
45 & 6.4 & 6.39999999912597 & 8.74026184760623e-10 \tabularnewline
46 & 6.7 & 6.39999999999994 & 0.300000000000058 \tabularnewline
47 & 6.9 & 6.69998016791159 & 0.200019832088405 \tabularnewline
48 & 7.1 & 6.89998677729669 & 0.200013222703308 \tabularnewline
49 & 7.3 & 7.09998677773362 & 0.200013222266383 \tabularnewline
50 & 7.2 & 7.29998677773365 & -0.0999867777336449 \tabularnewline
51 & 7.1 & 7.20000660982205 & -0.100006609822052 \tabularnewline
52 & 6.9 & 7.10000661113309 & -0.20000661113309 \tabularnewline
53 & 6.8 & 6.90001322182931 & -0.100013221829313 \tabularnewline
54 & 6.7 & 6.80000661157019 & -0.10000661157019 \tabularnewline
55 & 7.2 & 6.70000661113321 & 0.499993388866794 \tabularnewline
56 & 7.2 & 7.19996694695637 & 3.30530436345455e-05 \tabularnewline
57 & 7.1 & 7.19999999781496 & -0.0999999978149644 \tabularnewline
58 & 7.1 & 7.10000661069599 & -6.61069599061648e-06 \tabularnewline
59 & 7 & 7.10000000043701 & -0.100000000437013 \tabularnewline
60 & 7.1 & 7.00000661069616 & 0.0999933893038349 \tabularnewline
61 & 7.3 & 7.09999338974088 & 0.200006610259122 \tabularnewline
62 & 7.2 & 7.29998677817075 & -0.0999867781707451 \tabularnewline
63 & 7.1 & 7.20000660982208 & -0.10000660982208 \tabularnewline
64 & 7 & 7.10000661113309 & -0.10000661113309 \tabularnewline
65 & 6.9 & 7.00000661113318 & -0.100006611133177 \tabularnewline
66 & 7 & 6.90000661113318 & 0.0999933888668219 \tabularnewline
67 & 7.5 & 6.99999338974091 & 0.500006610259093 \tabularnewline
68 & 7.6 & 7.49996694608234 & 0.100033053917659 \tabularnewline
69 & 7.5 & 7.59999338711877 & -0.0999933871187704 \tabularnewline
70 & 7.3 & 7.50000661025898 & -0.200006610258978 \tabularnewline
71 & 7.3 & 7.30001322182925 & -1.32218292545616e-05 \tabularnewline
72 & 7.4 & 7.30000000087405 & 0.0999999991259459 \tabularnewline
73 & 7.7 & 7.39999338930392 & 0.300006610696077 \tabularnewline
74 & 7.8 & 7.69998016747458 & 0.100019832525419 \tabularnewline
75 & 7.7 & 7.7999933879928 & -0.0999933879927966 \tabularnewline
76 & 7.5 & 7.70000661025904 & -0.200006610259035 \tabularnewline
77 & 7.3 & 7.50001322182925 & -0.200013221829255 \tabularnewline
78 & 7.3 & 7.30001322226633 & -1.32222663253856e-05 \tabularnewline
79 & 7.6 & 7.30000000087408 & 0.299999999125917 \tabularnewline
80 & 7.6 & 7.59998016791165 & 1.98320883475489e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286048&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]2[/C][C]6.8[/C][C]6.5[/C][C]0.3[/C][/ROW]
[ROW][C]3[/C][C]6.8[/C][C]6.79998016791159[/C][C]1.98320884061687e-05[/C][/ROW]
[ROW][C]4[/C][C]6.5[/C][C]6.79999999868896[/C][C]-0.299999998688961[/C][/ROW]
[ROW][C]5[/C][C]6.2[/C][C]6.50001983208832[/C][C]-0.300019832088319[/C][/ROW]
[ROW][C]6[/C][C]6.2[/C][C]6.20001983339944[/C][C]-1.98333994445576e-05[/C][/ROW]
[ROW][C]7[/C][C]6.6[/C][C]6.20000000131113[/C][C]0.399999998688874[/C][/ROW]
[ROW][C]8[/C][C]6.7[/C][C]6.59997355721555[/C][C]0.100026442784454[/C][/ROW]
[ROW][C]9[/C][C]6.5[/C][C]6.69999338755581[/C][C]-0.199993387555812[/C][/ROW]
[ROW][C]10[/C][C]6.4[/C][C]6.50001322095514[/C][C]-0.100013220955142[/C][/ROW]
[ROW][C]11[/C][C]6.5[/C][C]6.40000661157013[/C][C]0.0999933884298674[/C][/ROW]
[ROW][C]12[/C][C]6.8[/C][C]6.49999338974094[/C][C]0.300006610259063[/C][/ROW]
[ROW][C]13[/C][C]7.1[/C][C]6.79998016747461[/C][C]0.30001983252539[/C][/ROW]
[ROW][C]14[/C][C]7.2[/C][C]7.09998016660053[/C][C]0.100019833399474[/C][/ROW]
[ROW][C]15[/C][C]7.1[/C][C]7.19999338799274[/C][C]-0.0999933879927397[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]7.10000661025903[/C][C]-0.100006610259035[/C][/ROW]
[ROW][C]17[/C][C]6.9[/C][C]7.00000661113312[/C][C]-0.100006611133119[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.90000661113318[/C][C]-6.61113317779183e-06[/C][/ROW]
[ROW][C]19[/C][C]7.4[/C][C]6.90000000043704[/C][C]0.499999999562958[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]7.39996694651935[/C][C]-0.0999669465193538[/C][/ROW]
[ROW][C]21[/C][C]7[/C][C]7.30000660851107[/C][C]-0.30000660851107[/C][/ROW]
[ROW][C]22[/C][C]6.8[/C][C]7.00001983252527[/C][C]-0.200019832525275[/C][/ROW]
[ROW][C]23[/C][C]6.5[/C][C]6.80001322270334[/C][C]-0.300013222703338[/C][/ROW]
[ROW][C]24[/C][C]6.4[/C][C]6.50001983296252[/C][C]-0.100019832962518[/C][/ROW]
[ROW][C]25[/C][C]6.3[/C][C]6.40000661200723[/C][C]-0.100006612007232[/C][/ROW]
[ROW][C]26[/C][C]6[/C][C]6.30000661113323[/C][C]-0.300006611133234[/C][/ROW]
[ROW][C]27[/C][C]5.9[/C][C]6.00001983252545[/C][C]-0.100019832525447[/C][/ROW]
[ROW][C]28[/C][C]5.7[/C][C]5.9000066120072[/C][C]-0.200006612007203[/C][/ROW]
[ROW][C]29[/C][C]5.7[/C][C]5.70001322182937[/C][C]-1.32218293700248e-05[/C][/ROW]
[ROW][C]30[/C][C]5.7[/C][C]5.70000000087406[/C][C]-8.74055494648474e-10[/C][/ROW]
[ROW][C]31[/C][C]6.2[/C][C]5.70000000000006[/C][C]0.499999999999942[/C][/ROW]
[ROW][C]32[/C][C]6.4[/C][C]6.19996694651932[/C][C]0.200033053480676[/C][/ROW]
[ROW][C]33[/C][C]6.2[/C][C]6.39998677642266[/C][C]-0.199986776422664[/C][/ROW]
[ROW][C]34[/C][C]6.2[/C][C]6.2000132205181[/C][C]-1.32205180998213e-05[/C][/ROW]
[ROW][C]35[/C][C]6.1[/C][C]6.20000000087397[/C][C]-0.100000000873969[/C][/ROW]
[ROW][C]36[/C][C]6.1[/C][C]6.10000661069619[/C][C]-6.61069619312116e-06[/C][/ROW]
[ROW][C]37[/C][C]6.2[/C][C]6.10000000043701[/C][C]0.0999999995629874[/C][/ROW]
[ROW][C]38[/C][C]6.1[/C][C]6.19999338930389[/C][C]-0.0999933893038945[/C][/ROW]
[ROW][C]39[/C][C]6.1[/C][C]6.10000661025912[/C][C]-6.61025912229718e-06[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]6.10000000043698[/C][C]0.0999999995630159[/C][/ROW]
[ROW][C]41[/C][C]6.2[/C][C]6.19999338930389[/C][C]6.61069610607967e-06[/C][/ROW]
[ROW][C]42[/C][C]6.2[/C][C]6.19999999956299[/C][C]4.37013092380312e-10[/C][/ROW]
[ROW][C]43[/C][C]6.4[/C][C]6.19999999999997[/C][C]0.200000000000029[/C][/ROW]
[ROW][C]44[/C][C]6.4[/C][C]6.39998677860773[/C][C]1.32213922707791e-05[/C][/ROW]
[ROW][C]45[/C][C]6.4[/C][C]6.39999999912597[/C][C]8.74026184760623e-10[/C][/ROW]
[ROW][C]46[/C][C]6.7[/C][C]6.39999999999994[/C][C]0.300000000000058[/C][/ROW]
[ROW][C]47[/C][C]6.9[/C][C]6.69998016791159[/C][C]0.200019832088405[/C][/ROW]
[ROW][C]48[/C][C]7.1[/C][C]6.89998677729669[/C][C]0.200013222703308[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.09998677773362[/C][C]0.200013222266383[/C][/ROW]
[ROW][C]50[/C][C]7.2[/C][C]7.29998677773365[/C][C]-0.0999867777336449[/C][/ROW]
[ROW][C]51[/C][C]7.1[/C][C]7.20000660982205[/C][C]-0.100006609822052[/C][/ROW]
[ROW][C]52[/C][C]6.9[/C][C]7.10000661113309[/C][C]-0.20000661113309[/C][/ROW]
[ROW][C]53[/C][C]6.8[/C][C]6.90001322182931[/C][C]-0.100013221829313[/C][/ROW]
[ROW][C]54[/C][C]6.7[/C][C]6.80000661157019[/C][C]-0.10000661157019[/C][/ROW]
[ROW][C]55[/C][C]7.2[/C][C]6.70000661113321[/C][C]0.499993388866794[/C][/ROW]
[ROW][C]56[/C][C]7.2[/C][C]7.19996694695637[/C][C]3.30530436345455e-05[/C][/ROW]
[ROW][C]57[/C][C]7.1[/C][C]7.19999999781496[/C][C]-0.0999999978149644[/C][/ROW]
[ROW][C]58[/C][C]7.1[/C][C]7.10000661069599[/C][C]-6.61069599061648e-06[/C][/ROW]
[ROW][C]59[/C][C]7[/C][C]7.10000000043701[/C][C]-0.100000000437013[/C][/ROW]
[ROW][C]60[/C][C]7.1[/C][C]7.00000661069616[/C][C]0.0999933893038349[/C][/ROW]
[ROW][C]61[/C][C]7.3[/C][C]7.09999338974088[/C][C]0.200006610259122[/C][/ROW]
[ROW][C]62[/C][C]7.2[/C][C]7.29998677817075[/C][C]-0.0999867781707451[/C][/ROW]
[ROW][C]63[/C][C]7.1[/C][C]7.20000660982208[/C][C]-0.10000660982208[/C][/ROW]
[ROW][C]64[/C][C]7[/C][C]7.10000661113309[/C][C]-0.10000661113309[/C][/ROW]
[ROW][C]65[/C][C]6.9[/C][C]7.00000661113318[/C][C]-0.100006611133177[/C][/ROW]
[ROW][C]66[/C][C]7[/C][C]6.90000661113318[/C][C]0.0999933888668219[/C][/ROW]
[ROW][C]67[/C][C]7.5[/C][C]6.99999338974091[/C][C]0.500006610259093[/C][/ROW]
[ROW][C]68[/C][C]7.6[/C][C]7.49996694608234[/C][C]0.100033053917659[/C][/ROW]
[ROW][C]69[/C][C]7.5[/C][C]7.59999338711877[/C][C]-0.0999933871187704[/C][/ROW]
[ROW][C]70[/C][C]7.3[/C][C]7.50000661025898[/C][C]-0.200006610258978[/C][/ROW]
[ROW][C]71[/C][C]7.3[/C][C]7.30001322182925[/C][C]-1.32218292545616e-05[/C][/ROW]
[ROW][C]72[/C][C]7.4[/C][C]7.30000000087405[/C][C]0.0999999991259459[/C][/ROW]
[ROW][C]73[/C][C]7.7[/C][C]7.39999338930392[/C][C]0.300006610696077[/C][/ROW]
[ROW][C]74[/C][C]7.8[/C][C]7.69998016747458[/C][C]0.100019832525419[/C][/ROW]
[ROW][C]75[/C][C]7.7[/C][C]7.7999933879928[/C][C]-0.0999933879927966[/C][/ROW]
[ROW][C]76[/C][C]7.5[/C][C]7.70000661025904[/C][C]-0.200006610259035[/C][/ROW]
[ROW][C]77[/C][C]7.3[/C][C]7.50001322182925[/C][C]-0.200013221829255[/C][/ROW]
[ROW][C]78[/C][C]7.3[/C][C]7.30001322226633[/C][C]-1.32222663253856e-05[/C][/ROW]
[ROW][C]79[/C][C]7.6[/C][C]7.30000000087408[/C][C]0.299999999125917[/C][/ROW]
[ROW][C]80[/C][C]7.6[/C][C]7.59998016791165[/C][C]1.98320883475489e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286048&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286048&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
26.86.50.3
36.86.799980167911591.98320884061687e-05
46.56.79999999868896-0.299999998688961
56.26.50001983208832-0.300019832088319
66.26.20001983339944-1.98333994445576e-05
76.66.200000001311130.399999998688874
86.76.599973557215550.100026442784454
96.56.69999338755581-0.199993387555812
106.46.50001322095514-0.100013220955142
116.56.400006611570130.0999933884298674
126.86.499993389740940.300006610259063
137.16.799980167474610.30001983252539
147.27.099980166600530.100019833399474
157.17.19999338799274-0.0999933879927397
1677.10000661025903-0.100006610259035
176.97.00000661113312-0.100006611133119
186.96.90000661113318-6.61113317779183e-06
197.46.900000000437040.499999999562958
207.37.39996694651935-0.0999669465193538
2177.30000660851107-0.30000660851107
226.87.00001983252527-0.200019832525275
236.56.80001322270334-0.300013222703338
246.46.50001983296252-0.100019832962518
256.36.40000661200723-0.100006612007232
2666.30000661113323-0.300006611133234
275.96.00001983252545-0.100019832525447
285.75.9000066120072-0.200006612007203
295.75.70001322182937-1.32218293700248e-05
305.75.70000000087406-8.74055494648474e-10
316.25.700000000000060.499999999999942
326.46.199966946519320.200033053480676
336.26.39998677642266-0.199986776422664
346.26.2000132205181-1.32205180998213e-05
356.16.20000000087397-0.100000000873969
366.16.10000661069619-6.61069619312116e-06
376.26.100000000437010.0999999995629874
386.16.19999338930389-0.0999933893038945
396.16.10000661025912-6.61025912229718e-06
406.26.100000000436980.0999999995630159
416.26.199993389303896.61069610607967e-06
426.26.199999999562994.37013092380312e-10
436.46.199999999999970.200000000000029
446.46.399986778607731.32213922707791e-05
456.46.399999999125978.74026184760623e-10
466.76.399999999999940.300000000000058
476.96.699980167911590.200019832088405
487.16.899986777296690.200013222703308
497.37.099986777733620.200013222266383
507.27.29998677773365-0.0999867777336449
517.17.20000660982205-0.100006609822052
526.97.10000661113309-0.20000661113309
536.86.90001322182931-0.100013221829313
546.76.80000661157019-0.10000661157019
557.26.700006611133210.499993388866794
567.27.199966946956373.30530436345455e-05
577.17.19999999781496-0.0999999978149644
587.17.10000661069599-6.61069599061648e-06
5977.10000000043701-0.100000000437013
607.17.000006610696160.0999933893038349
617.37.099993389740880.200006610259122
627.27.29998677817075-0.0999867781707451
637.17.20000660982208-0.10000660982208
6477.10000661113309-0.10000661113309
656.97.00000661113318-0.100006611133177
6676.900006611133180.0999933888668219
677.56.999993389740910.500006610259093
687.67.499966946082340.100033053917659
697.57.59999338711877-0.0999933871187704
707.37.50000661025898-0.200006610258978
717.37.30001322182925-1.32218292545616e-05
727.47.300000000874050.0999999991259459
737.77.399993389303920.300006610696077
747.87.699980167474580.100019832525419
757.77.7999933879928-0.0999933879927966
767.57.70000661025904-0.200006610259035
777.37.50001322182925-0.200013221829255
787.37.30001322226633-1.32222663253856e-05
797.67.300000000874080.299999999125917
807.67.599980167911651.98320883475489e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
817.599999998688967.214672347102767.98532765027516
827.599999998688967.055082419578718.14491757779921
837.599999998688966.932622341758638.26737765561929
847.599999998688966.829382904461068.37061709291686
857.599999998688966.738426743032378.46157325434555
867.599999998688966.656195864448638.54380413292929
877.599999998688966.580576626014218.61942337136371
887.599999998688966.510191858830388.68980813854754
897.599999998688966.444084971254668.75591502612327
907.599999998688966.38155947096728.81844052641072
917.599999998688966.322089560300848.87791043707708
927.599999998688966.265266745380368.93473325199756

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 7.59999999868896 & 7.21467234710276 & 7.98532765027516 \tabularnewline
82 & 7.59999999868896 & 7.05508241957871 & 8.14491757779921 \tabularnewline
83 & 7.59999999868896 & 6.93262234175863 & 8.26737765561929 \tabularnewline
84 & 7.59999999868896 & 6.82938290446106 & 8.37061709291686 \tabularnewline
85 & 7.59999999868896 & 6.73842674303237 & 8.46157325434555 \tabularnewline
86 & 7.59999999868896 & 6.65619586444863 & 8.54380413292929 \tabularnewline
87 & 7.59999999868896 & 6.58057662601421 & 8.61942337136371 \tabularnewline
88 & 7.59999999868896 & 6.51019185883038 & 8.68980813854754 \tabularnewline
89 & 7.59999999868896 & 6.44408497125466 & 8.75591502612327 \tabularnewline
90 & 7.59999999868896 & 6.3815594709672 & 8.81844052641072 \tabularnewline
91 & 7.59999999868896 & 6.32208956030084 & 8.87791043707708 \tabularnewline
92 & 7.59999999868896 & 6.26526674538036 & 8.93473325199756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286048&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]81[/C][C]7.59999999868896[/C][C]7.21467234710276[/C][C]7.98532765027516[/C][/ROW]
[ROW][C]82[/C][C]7.59999999868896[/C][C]7.05508241957871[/C][C]8.14491757779921[/C][/ROW]
[ROW][C]83[/C][C]7.59999999868896[/C][C]6.93262234175863[/C][C]8.26737765561929[/C][/ROW]
[ROW][C]84[/C][C]7.59999999868896[/C][C]6.82938290446106[/C][C]8.37061709291686[/C][/ROW]
[ROW][C]85[/C][C]7.59999999868896[/C][C]6.73842674303237[/C][C]8.46157325434555[/C][/ROW]
[ROW][C]86[/C][C]7.59999999868896[/C][C]6.65619586444863[/C][C]8.54380413292929[/C][/ROW]
[ROW][C]87[/C][C]7.59999999868896[/C][C]6.58057662601421[/C][C]8.61942337136371[/C][/ROW]
[ROW][C]88[/C][C]7.59999999868896[/C][C]6.51019185883038[/C][C]8.68980813854754[/C][/ROW]
[ROW][C]89[/C][C]7.59999999868896[/C][C]6.44408497125466[/C][C]8.75591502612327[/C][/ROW]
[ROW][C]90[/C][C]7.59999999868896[/C][C]6.3815594709672[/C][C]8.81844052641072[/C][/ROW]
[ROW][C]91[/C][C]7.59999999868896[/C][C]6.32208956030084[/C][C]8.87791043707708[/C][/ROW]
[ROW][C]92[/C][C]7.59999999868896[/C][C]6.26526674538036[/C][C]8.93473325199756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286048&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286048&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
817.599999998688967.214672347102767.98532765027516
827.599999998688967.055082419578718.14491757779921
837.599999998688966.932622341758638.26737765561929
847.599999998688966.829382904461068.37061709291686
857.599999998688966.738426743032378.46157325434555
867.599999998688966.656195864448638.54380413292929
877.599999998688966.580576626014218.61942337136371
887.599999998688966.510191858830388.68980813854754
897.599999998688966.444084971254668.75591502612327
907.599999998688966.38155947096728.81844052641072
917.599999998688966.322089560300848.87791043707708
927.599999998688966.265266745380368.93473325199756



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