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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 08:40:20 -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/2013/Dec/13/t1386942053e2newv955lg5889.htm/, Retrieved Tue, 19 Nov 2019 08:24:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232296, Retrieved Tue, 19 Nov 2019 08:24:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 13:40:20] [6e7c8e41ae9c2cf944b21192a5249437] [Current]
- R PD    [Exponential Smoothing] [] [2013-12-18 08:43:39] [118d51f3b8c7238175a748a4b2235cf1]
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Dataseries X:
26,73
26,85
27,01
27,09
27,11
27,16
27,13
27,19
27,49
27,63
27,72
27,77
27,81
27,92
28,07
28,14
28,17
28,20
28,21
28,20
28,19
28,24
28,25
28,26
28,33
28,67
28,81
28,99
29,16
29,25
29,25
29,38
29,48
29,65
29,69
29,73
29,81
30,05
30,29
30,37
30,50
30,67
30,76
30,84
30,86
31,09
31,20
31,19
31,18
31,31
31,39
31,39
31,37
31,36
31,37
31,35
31,34
31,47
31,48
31,54
31,55
31,55
31,57
31,66
31,74
31,78
31,80
31,68
31,70
31,70
31,75
31,73
31,82
31,90
31,82
31,51
31,42
30,97
30,99
30,92
30,95
30,82
30,72
30,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 6 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232296&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232296&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 time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999954055201604
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999954055201604 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232296&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]0.999954055201604[/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=232296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232296&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
alpha0.999954055201604
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
226.8526.730.120000000000001
327.0126.84999448662420.160005513375808
427.0927.00999264857890.0800073514210524
527.1127.08999632407840.0200036759216324
627.1627.10999908093510.0500009190648569
727.1327.1599977027179-0.0299977027178535
827.1927.13000137823840.0599986217615971
927.4927.18999724337540.300002756624579
1027.6327.48998621643380.140013783566172
1127.7227.62999356709490.0900064329050601
1227.7727.71999586467260.0500041353274163
1327.8127.76999770257010.0400022974299148
1427.9227.80999816210250.110001837897492
1528.0727.91999494598770.150005054012265
1628.1428.0699931080480.0700068919519659
1728.1728.13999678354750.0300032164525383
1828.228.16999862150830.030001378491729
1928.2128.19999862159270.0100013784072885
2028.228.2099995404887-0.00999954048868545
2128.1928.2000004594269-0.0100004594268697
2228.2428.19000045946910.0499995405309051
2328.2528.23999770278120.0100022972188114
2428.2628.24999954044650.010000459553531
2528.3328.25999954053090.0700004594690959
2628.6728.3299967838430.340003216157001
2728.8128.66998437862080.140015621379217
2828.9928.80999356701050.180006432989497
2929.1628.98999172964070.170008270359276
3029.2529.15999218900430.0900078109957079
3129.2529.24999586460934.13539073207403e-06
3229.3829.249999999810.130000000189998
3329.4829.37999402717620.100005972823801
3429.6529.47999540524570.170004594754257
3529.6929.64999218917320.040007810826836
3629.7329.68999816184920.0400018381508005
3729.8129.72999816212360.080001837876388
3830.0529.80999632433170.240003675668316
3930.2930.04998897307950.240011026920492
4030.3730.28998897274180.0800110272582479
4130.530.36999632390950.130003676090517
4230.6730.49999402700730.170005972992691
4330.7630.66999218910980.0900078108901567
4430.8430.75999586460930.0800041353907233
4530.8630.83999632422610.0200036757738715
4631.0930.85999908093520.23000091906485
4731.231.08998943265410.110010567345856
4831.1931.1999949455867-0.00999494558665859
4931.1831.1900004592158-0.0100004592157603
5031.3131.18000045946910.129999540530918
5131.3931.30999402719730.0800059728026845
5231.3931.38999632414173.67585829152972e-06
5331.3731.3899999998311-0.0199999998311142
5431.3631.370000918896-0.0100009188959618
5531.3731.36000045949020.00999954050979923
5631.3531.3699995405731-0.0199995405731279
5731.3431.3500009188749-0.0100009188748622
5831.4731.34000045949020.129999540509797
5931.4831.46999402719730.0100059728026807
6031.5431.47999954027760.0600004597224029
6131.5531.5399972432910.0100027567090279
6231.5531.54999954042544.59574639677385e-07
6331.5731.54999999997890.0200000000211134
6431.6631.5699990811040.0900009188959672
6531.7431.65999586492590.0800041350740734
6631.7831.73999632422610.0400036757738604
6731.831.77999816203920.0200018379608196
6831.6831.7999990810196-0.119999081019589
6931.731.68000551333360.0199944866664161
7031.731.69999908135739.18642658831459e-07
7131.7531.69999999995780.0500000000422069
7231.7331.7499977027601-0.0199977027600795
7331.8231.73000091879040.0899990812095766
7431.931.81999586501040.0800041349896397
7531.8231.8999963242261-0.0799963242261441
7631.5131.820003675415-0.310003675414986
7731.4231.5100142430564-0.0900142430563697
7830.9731.4200041356863-0.450004135686253
7930.9930.97002067534930.0199793246507092
8030.9230.989999082054-0.069999082053954
8130.9530.92000321609370.0299967839062845
8230.8230.9499986218038-0.129998621803811
8330.7230.8200059727605-0.100005972760471
8430.7330.72000459475430.00999540524574627

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 26.85 & 26.73 & 0.120000000000001 \tabularnewline
3 & 27.01 & 26.8499944866242 & 0.160005513375808 \tabularnewline
4 & 27.09 & 27.0099926485789 & 0.0800073514210524 \tabularnewline
5 & 27.11 & 27.0899963240784 & 0.0200036759216324 \tabularnewline
6 & 27.16 & 27.1099990809351 & 0.0500009190648569 \tabularnewline
7 & 27.13 & 27.1599977027179 & -0.0299977027178535 \tabularnewline
8 & 27.19 & 27.1300013782384 & 0.0599986217615971 \tabularnewline
9 & 27.49 & 27.1899972433754 & 0.300002756624579 \tabularnewline
10 & 27.63 & 27.4899862164338 & 0.140013783566172 \tabularnewline
11 & 27.72 & 27.6299935670949 & 0.0900064329050601 \tabularnewline
12 & 27.77 & 27.7199958646726 & 0.0500041353274163 \tabularnewline
13 & 27.81 & 27.7699977025701 & 0.0400022974299148 \tabularnewline
14 & 27.92 & 27.8099981621025 & 0.110001837897492 \tabularnewline
15 & 28.07 & 27.9199949459877 & 0.150005054012265 \tabularnewline
16 & 28.14 & 28.069993108048 & 0.0700068919519659 \tabularnewline
17 & 28.17 & 28.1399967835475 & 0.0300032164525383 \tabularnewline
18 & 28.2 & 28.1699986215083 & 0.030001378491729 \tabularnewline
19 & 28.21 & 28.1999986215927 & 0.0100013784072885 \tabularnewline
20 & 28.2 & 28.2099995404887 & -0.00999954048868545 \tabularnewline
21 & 28.19 & 28.2000004594269 & -0.0100004594268697 \tabularnewline
22 & 28.24 & 28.1900004594691 & 0.0499995405309051 \tabularnewline
23 & 28.25 & 28.2399977027812 & 0.0100022972188114 \tabularnewline
24 & 28.26 & 28.2499995404465 & 0.010000459553531 \tabularnewline
25 & 28.33 & 28.2599995405309 & 0.0700004594690959 \tabularnewline
26 & 28.67 & 28.329996783843 & 0.340003216157001 \tabularnewline
27 & 28.81 & 28.6699843786208 & 0.140015621379217 \tabularnewline
28 & 28.99 & 28.8099935670105 & 0.180006432989497 \tabularnewline
29 & 29.16 & 28.9899917296407 & 0.170008270359276 \tabularnewline
30 & 29.25 & 29.1599921890043 & 0.0900078109957079 \tabularnewline
31 & 29.25 & 29.2499958646093 & 4.13539073207403e-06 \tabularnewline
32 & 29.38 & 29.24999999981 & 0.130000000189998 \tabularnewline
33 & 29.48 & 29.3799940271762 & 0.100005972823801 \tabularnewline
34 & 29.65 & 29.4799954052457 & 0.170004594754257 \tabularnewline
35 & 29.69 & 29.6499921891732 & 0.040007810826836 \tabularnewline
36 & 29.73 & 29.6899981618492 & 0.0400018381508005 \tabularnewline
37 & 29.81 & 29.7299981621236 & 0.080001837876388 \tabularnewline
38 & 30.05 & 29.8099963243317 & 0.240003675668316 \tabularnewline
39 & 30.29 & 30.0499889730795 & 0.240011026920492 \tabularnewline
40 & 30.37 & 30.2899889727418 & 0.0800110272582479 \tabularnewline
41 & 30.5 & 30.3699963239095 & 0.130003676090517 \tabularnewline
42 & 30.67 & 30.4999940270073 & 0.170005972992691 \tabularnewline
43 & 30.76 & 30.6699921891098 & 0.0900078108901567 \tabularnewline
44 & 30.84 & 30.7599958646093 & 0.0800041353907233 \tabularnewline
45 & 30.86 & 30.8399963242261 & 0.0200036757738715 \tabularnewline
46 & 31.09 & 30.8599990809352 & 0.23000091906485 \tabularnewline
47 & 31.2 & 31.0899894326541 & 0.110010567345856 \tabularnewline
48 & 31.19 & 31.1999949455867 & -0.00999494558665859 \tabularnewline
49 & 31.18 & 31.1900004592158 & -0.0100004592157603 \tabularnewline
50 & 31.31 & 31.1800004594691 & 0.129999540530918 \tabularnewline
51 & 31.39 & 31.3099940271973 & 0.0800059728026845 \tabularnewline
52 & 31.39 & 31.3899963241417 & 3.67585829152972e-06 \tabularnewline
53 & 31.37 & 31.3899999998311 & -0.0199999998311142 \tabularnewline
54 & 31.36 & 31.370000918896 & -0.0100009188959618 \tabularnewline
55 & 31.37 & 31.3600004594902 & 0.00999954050979923 \tabularnewline
56 & 31.35 & 31.3699995405731 & -0.0199995405731279 \tabularnewline
57 & 31.34 & 31.3500009188749 & -0.0100009188748622 \tabularnewline
58 & 31.47 & 31.3400004594902 & 0.129999540509797 \tabularnewline
59 & 31.48 & 31.4699940271973 & 0.0100059728026807 \tabularnewline
60 & 31.54 & 31.4799995402776 & 0.0600004597224029 \tabularnewline
61 & 31.55 & 31.539997243291 & 0.0100027567090279 \tabularnewline
62 & 31.55 & 31.5499995404254 & 4.59574639677385e-07 \tabularnewline
63 & 31.57 & 31.5499999999789 & 0.0200000000211134 \tabularnewline
64 & 31.66 & 31.569999081104 & 0.0900009188959672 \tabularnewline
65 & 31.74 & 31.6599958649259 & 0.0800041350740734 \tabularnewline
66 & 31.78 & 31.7399963242261 & 0.0400036757738604 \tabularnewline
67 & 31.8 & 31.7799981620392 & 0.0200018379608196 \tabularnewline
68 & 31.68 & 31.7999990810196 & -0.119999081019589 \tabularnewline
69 & 31.7 & 31.6800055133336 & 0.0199944866664161 \tabularnewline
70 & 31.7 & 31.6999990813573 & 9.18642658831459e-07 \tabularnewline
71 & 31.75 & 31.6999999999578 & 0.0500000000422069 \tabularnewline
72 & 31.73 & 31.7499977027601 & -0.0199977027600795 \tabularnewline
73 & 31.82 & 31.7300009187904 & 0.0899990812095766 \tabularnewline
74 & 31.9 & 31.8199958650104 & 0.0800041349896397 \tabularnewline
75 & 31.82 & 31.8999963242261 & -0.0799963242261441 \tabularnewline
76 & 31.51 & 31.820003675415 & -0.310003675414986 \tabularnewline
77 & 31.42 & 31.5100142430564 & -0.0900142430563697 \tabularnewline
78 & 30.97 & 31.4200041356863 & -0.450004135686253 \tabularnewline
79 & 30.99 & 30.9700206753493 & 0.0199793246507092 \tabularnewline
80 & 30.92 & 30.989999082054 & -0.069999082053954 \tabularnewline
81 & 30.95 & 30.9200032160937 & 0.0299967839062845 \tabularnewline
82 & 30.82 & 30.9499986218038 & -0.129998621803811 \tabularnewline
83 & 30.72 & 30.8200059727605 & -0.100005972760471 \tabularnewline
84 & 30.73 & 30.7200045947543 & 0.00999540524574627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232296&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]26.85[/C][C]26.73[/C][C]0.120000000000001[/C][/ROW]
[ROW][C]3[/C][C]27.01[/C][C]26.8499944866242[/C][C]0.160005513375808[/C][/ROW]
[ROW][C]4[/C][C]27.09[/C][C]27.0099926485789[/C][C]0.0800073514210524[/C][/ROW]
[ROW][C]5[/C][C]27.11[/C][C]27.0899963240784[/C][C]0.0200036759216324[/C][/ROW]
[ROW][C]6[/C][C]27.16[/C][C]27.1099990809351[/C][C]0.0500009190648569[/C][/ROW]
[ROW][C]7[/C][C]27.13[/C][C]27.1599977027179[/C][C]-0.0299977027178535[/C][/ROW]
[ROW][C]8[/C][C]27.19[/C][C]27.1300013782384[/C][C]0.0599986217615971[/C][/ROW]
[ROW][C]9[/C][C]27.49[/C][C]27.1899972433754[/C][C]0.300002756624579[/C][/ROW]
[ROW][C]10[/C][C]27.63[/C][C]27.4899862164338[/C][C]0.140013783566172[/C][/ROW]
[ROW][C]11[/C][C]27.72[/C][C]27.6299935670949[/C][C]0.0900064329050601[/C][/ROW]
[ROW][C]12[/C][C]27.77[/C][C]27.7199958646726[/C][C]0.0500041353274163[/C][/ROW]
[ROW][C]13[/C][C]27.81[/C][C]27.7699977025701[/C][C]0.0400022974299148[/C][/ROW]
[ROW][C]14[/C][C]27.92[/C][C]27.8099981621025[/C][C]0.110001837897492[/C][/ROW]
[ROW][C]15[/C][C]28.07[/C][C]27.9199949459877[/C][C]0.150005054012265[/C][/ROW]
[ROW][C]16[/C][C]28.14[/C][C]28.069993108048[/C][C]0.0700068919519659[/C][/ROW]
[ROW][C]17[/C][C]28.17[/C][C]28.1399967835475[/C][C]0.0300032164525383[/C][/ROW]
[ROW][C]18[/C][C]28.2[/C][C]28.1699986215083[/C][C]0.030001378491729[/C][/ROW]
[ROW][C]19[/C][C]28.21[/C][C]28.1999986215927[/C][C]0.0100013784072885[/C][/ROW]
[ROW][C]20[/C][C]28.2[/C][C]28.2099995404887[/C][C]-0.00999954048868545[/C][/ROW]
[ROW][C]21[/C][C]28.19[/C][C]28.2000004594269[/C][C]-0.0100004594268697[/C][/ROW]
[ROW][C]22[/C][C]28.24[/C][C]28.1900004594691[/C][C]0.0499995405309051[/C][/ROW]
[ROW][C]23[/C][C]28.25[/C][C]28.2399977027812[/C][C]0.0100022972188114[/C][/ROW]
[ROW][C]24[/C][C]28.26[/C][C]28.2499995404465[/C][C]0.010000459553531[/C][/ROW]
[ROW][C]25[/C][C]28.33[/C][C]28.2599995405309[/C][C]0.0700004594690959[/C][/ROW]
[ROW][C]26[/C][C]28.67[/C][C]28.329996783843[/C][C]0.340003216157001[/C][/ROW]
[ROW][C]27[/C][C]28.81[/C][C]28.6699843786208[/C][C]0.140015621379217[/C][/ROW]
[ROW][C]28[/C][C]28.99[/C][C]28.8099935670105[/C][C]0.180006432989497[/C][/ROW]
[ROW][C]29[/C][C]29.16[/C][C]28.9899917296407[/C][C]0.170008270359276[/C][/ROW]
[ROW][C]30[/C][C]29.25[/C][C]29.1599921890043[/C][C]0.0900078109957079[/C][/ROW]
[ROW][C]31[/C][C]29.25[/C][C]29.2499958646093[/C][C]4.13539073207403e-06[/C][/ROW]
[ROW][C]32[/C][C]29.38[/C][C]29.24999999981[/C][C]0.130000000189998[/C][/ROW]
[ROW][C]33[/C][C]29.48[/C][C]29.3799940271762[/C][C]0.100005972823801[/C][/ROW]
[ROW][C]34[/C][C]29.65[/C][C]29.4799954052457[/C][C]0.170004594754257[/C][/ROW]
[ROW][C]35[/C][C]29.69[/C][C]29.6499921891732[/C][C]0.040007810826836[/C][/ROW]
[ROW][C]36[/C][C]29.73[/C][C]29.6899981618492[/C][C]0.0400018381508005[/C][/ROW]
[ROW][C]37[/C][C]29.81[/C][C]29.7299981621236[/C][C]0.080001837876388[/C][/ROW]
[ROW][C]38[/C][C]30.05[/C][C]29.8099963243317[/C][C]0.240003675668316[/C][/ROW]
[ROW][C]39[/C][C]30.29[/C][C]30.0499889730795[/C][C]0.240011026920492[/C][/ROW]
[ROW][C]40[/C][C]30.37[/C][C]30.2899889727418[/C][C]0.0800110272582479[/C][/ROW]
[ROW][C]41[/C][C]30.5[/C][C]30.3699963239095[/C][C]0.130003676090517[/C][/ROW]
[ROW][C]42[/C][C]30.67[/C][C]30.4999940270073[/C][C]0.170005972992691[/C][/ROW]
[ROW][C]43[/C][C]30.76[/C][C]30.6699921891098[/C][C]0.0900078108901567[/C][/ROW]
[ROW][C]44[/C][C]30.84[/C][C]30.7599958646093[/C][C]0.0800041353907233[/C][/ROW]
[ROW][C]45[/C][C]30.86[/C][C]30.8399963242261[/C][C]0.0200036757738715[/C][/ROW]
[ROW][C]46[/C][C]31.09[/C][C]30.8599990809352[/C][C]0.23000091906485[/C][/ROW]
[ROW][C]47[/C][C]31.2[/C][C]31.0899894326541[/C][C]0.110010567345856[/C][/ROW]
[ROW][C]48[/C][C]31.19[/C][C]31.1999949455867[/C][C]-0.00999494558665859[/C][/ROW]
[ROW][C]49[/C][C]31.18[/C][C]31.1900004592158[/C][C]-0.0100004592157603[/C][/ROW]
[ROW][C]50[/C][C]31.31[/C][C]31.1800004594691[/C][C]0.129999540530918[/C][/ROW]
[ROW][C]51[/C][C]31.39[/C][C]31.3099940271973[/C][C]0.0800059728026845[/C][/ROW]
[ROW][C]52[/C][C]31.39[/C][C]31.3899963241417[/C][C]3.67585829152972e-06[/C][/ROW]
[ROW][C]53[/C][C]31.37[/C][C]31.3899999998311[/C][C]-0.0199999998311142[/C][/ROW]
[ROW][C]54[/C][C]31.36[/C][C]31.370000918896[/C][C]-0.0100009188959618[/C][/ROW]
[ROW][C]55[/C][C]31.37[/C][C]31.3600004594902[/C][C]0.00999954050979923[/C][/ROW]
[ROW][C]56[/C][C]31.35[/C][C]31.3699995405731[/C][C]-0.0199995405731279[/C][/ROW]
[ROW][C]57[/C][C]31.34[/C][C]31.3500009188749[/C][C]-0.0100009188748622[/C][/ROW]
[ROW][C]58[/C][C]31.47[/C][C]31.3400004594902[/C][C]0.129999540509797[/C][/ROW]
[ROW][C]59[/C][C]31.48[/C][C]31.4699940271973[/C][C]0.0100059728026807[/C][/ROW]
[ROW][C]60[/C][C]31.54[/C][C]31.4799995402776[/C][C]0.0600004597224029[/C][/ROW]
[ROW][C]61[/C][C]31.55[/C][C]31.539997243291[/C][C]0.0100027567090279[/C][/ROW]
[ROW][C]62[/C][C]31.55[/C][C]31.5499995404254[/C][C]4.59574639677385e-07[/C][/ROW]
[ROW][C]63[/C][C]31.57[/C][C]31.5499999999789[/C][C]0.0200000000211134[/C][/ROW]
[ROW][C]64[/C][C]31.66[/C][C]31.569999081104[/C][C]0.0900009188959672[/C][/ROW]
[ROW][C]65[/C][C]31.74[/C][C]31.6599958649259[/C][C]0.0800041350740734[/C][/ROW]
[ROW][C]66[/C][C]31.78[/C][C]31.7399963242261[/C][C]0.0400036757738604[/C][/ROW]
[ROW][C]67[/C][C]31.8[/C][C]31.7799981620392[/C][C]0.0200018379608196[/C][/ROW]
[ROW][C]68[/C][C]31.68[/C][C]31.7999990810196[/C][C]-0.119999081019589[/C][/ROW]
[ROW][C]69[/C][C]31.7[/C][C]31.6800055133336[/C][C]0.0199944866664161[/C][/ROW]
[ROW][C]70[/C][C]31.7[/C][C]31.6999990813573[/C][C]9.18642658831459e-07[/C][/ROW]
[ROW][C]71[/C][C]31.75[/C][C]31.6999999999578[/C][C]0.0500000000422069[/C][/ROW]
[ROW][C]72[/C][C]31.73[/C][C]31.7499977027601[/C][C]-0.0199977027600795[/C][/ROW]
[ROW][C]73[/C][C]31.82[/C][C]31.7300009187904[/C][C]0.0899990812095766[/C][/ROW]
[ROW][C]74[/C][C]31.9[/C][C]31.8199958650104[/C][C]0.0800041349896397[/C][/ROW]
[ROW][C]75[/C][C]31.82[/C][C]31.8999963242261[/C][C]-0.0799963242261441[/C][/ROW]
[ROW][C]76[/C][C]31.51[/C][C]31.820003675415[/C][C]-0.310003675414986[/C][/ROW]
[ROW][C]77[/C][C]31.42[/C][C]31.5100142430564[/C][C]-0.0900142430563697[/C][/ROW]
[ROW][C]78[/C][C]30.97[/C][C]31.4200041356863[/C][C]-0.450004135686253[/C][/ROW]
[ROW][C]79[/C][C]30.99[/C][C]30.9700206753493[/C][C]0.0199793246507092[/C][/ROW]
[ROW][C]80[/C][C]30.92[/C][C]30.989999082054[/C][C]-0.069999082053954[/C][/ROW]
[ROW][C]81[/C][C]30.95[/C][C]30.9200032160937[/C][C]0.0299967839062845[/C][/ROW]
[ROW][C]82[/C][C]30.82[/C][C]30.9499986218038[/C][C]-0.129998621803811[/C][/ROW]
[ROW][C]83[/C][C]30.72[/C][C]30.8200059727605[/C][C]-0.100005972760471[/C][/ROW]
[ROW][C]84[/C][C]30.73[/C][C]30.7200045947543[/C][C]0.00999540524574627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232296&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
226.8526.730.120000000000001
327.0126.84999448662420.160005513375808
427.0927.00999264857890.0800073514210524
527.1127.08999632407840.0200036759216324
627.1627.10999908093510.0500009190648569
727.1327.1599977027179-0.0299977027178535
827.1927.13000137823840.0599986217615971
927.4927.18999724337540.300002756624579
1027.6327.48998621643380.140013783566172
1127.7227.62999356709490.0900064329050601
1227.7727.71999586467260.0500041353274163
1327.8127.76999770257010.0400022974299148
1427.9227.80999816210250.110001837897492
1528.0727.91999494598770.150005054012265
1628.1428.0699931080480.0700068919519659
1728.1728.13999678354750.0300032164525383
1828.228.16999862150830.030001378491729
1928.2128.19999862159270.0100013784072885
2028.228.2099995404887-0.00999954048868545
2128.1928.2000004594269-0.0100004594268697
2228.2428.19000045946910.0499995405309051
2328.2528.23999770278120.0100022972188114
2428.2628.24999954044650.010000459553531
2528.3328.25999954053090.0700004594690959
2628.6728.3299967838430.340003216157001
2728.8128.66998437862080.140015621379217
2828.9928.80999356701050.180006432989497
2929.1628.98999172964070.170008270359276
3029.2529.15999218900430.0900078109957079
3129.2529.24999586460934.13539073207403e-06
3229.3829.249999999810.130000000189998
3329.4829.37999402717620.100005972823801
3429.6529.47999540524570.170004594754257
3529.6929.64999218917320.040007810826836
3629.7329.68999816184920.0400018381508005
3729.8129.72999816212360.080001837876388
3830.0529.80999632433170.240003675668316
3930.2930.04998897307950.240011026920492
4030.3730.28998897274180.0800110272582479
4130.530.36999632390950.130003676090517
4230.6730.49999402700730.170005972992691
4330.7630.66999218910980.0900078108901567
4430.8430.75999586460930.0800041353907233
4530.8630.83999632422610.0200036757738715
4631.0930.85999908093520.23000091906485
4731.231.08998943265410.110010567345856
4831.1931.1999949455867-0.00999494558665859
4931.1831.1900004592158-0.0100004592157603
5031.3131.18000045946910.129999540530918
5131.3931.30999402719730.0800059728026845
5231.3931.38999632414173.67585829152972e-06
5331.3731.3899999998311-0.0199999998311142
5431.3631.370000918896-0.0100009188959618
5531.3731.36000045949020.00999954050979923
5631.3531.3699995405731-0.0199995405731279
5731.3431.3500009188749-0.0100009188748622
5831.4731.34000045949020.129999540509797
5931.4831.46999402719730.0100059728026807
6031.5431.47999954027760.0600004597224029
6131.5531.5399972432910.0100027567090279
6231.5531.54999954042544.59574639677385e-07
6331.5731.54999999997890.0200000000211134
6431.6631.5699990811040.0900009188959672
6531.7431.65999586492590.0800041350740734
6631.7831.73999632422610.0400036757738604
6731.831.77999816203920.0200018379608196
6831.6831.7999990810196-0.119999081019589
6931.731.68000551333360.0199944866664161
7031.731.69999908135739.18642658831459e-07
7131.7531.69999999995780.0500000000422069
7231.7331.7499977027601-0.0199977027600795
7331.8231.73000091879040.0899990812095766
7431.931.81999586501040.0800041349896397
7531.8231.8999963242261-0.0799963242261441
7631.5131.820003675415-0.310003675414986
7731.4231.5100142430564-0.0900142430563697
7830.9731.4200041356863-0.450004135686253
7930.9930.97002067534930.0199793246507092
8030.9230.989999082054-0.069999082053954
8130.9530.92000321609370.0299967839062845
8230.8230.9499986218038-0.129998621803811
8330.7230.8200059727605-0.100005972760471
8430.7330.72000459475430.00999540524574627







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8530.729999540763130.514635266039630.9453638154866
8630.729999540763130.425435459246631.0345636222797
8730.729999540763130.35698910032931.1030099811973
8830.729999540763130.299285833533231.1607132479931
8930.729999540763130.248448082953531.2115509985728
9030.729999540763130.202487156603831.2575119249225
9130.729999540763130.160221667935231.2997774135911
9230.729999540763130.12088187291331.3391172086133
9330.729999540763130.083933102840531.3760659786858
9430.729999540763130.048986067230531.4110130142957
9530.729999540763130.015746882346131.4442521991801
9630.729999540763129.983987229216831.4760118523094

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 30.7299995407631 & 30.5146352660396 & 30.9453638154866 \tabularnewline
86 & 30.7299995407631 & 30.4254354592466 & 31.0345636222797 \tabularnewline
87 & 30.7299995407631 & 30.356989100329 & 31.1030099811973 \tabularnewline
88 & 30.7299995407631 & 30.2992858335332 & 31.1607132479931 \tabularnewline
89 & 30.7299995407631 & 30.2484480829535 & 31.2115509985728 \tabularnewline
90 & 30.7299995407631 & 30.2024871566038 & 31.2575119249225 \tabularnewline
91 & 30.7299995407631 & 30.1602216679352 & 31.2997774135911 \tabularnewline
92 & 30.7299995407631 & 30.120881872913 & 31.3391172086133 \tabularnewline
93 & 30.7299995407631 & 30.0839331028405 & 31.3760659786858 \tabularnewline
94 & 30.7299995407631 & 30.0489860672305 & 31.4110130142957 \tabularnewline
95 & 30.7299995407631 & 30.0157468823461 & 31.4442521991801 \tabularnewline
96 & 30.7299995407631 & 29.9839872292168 & 31.4760118523094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232296&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]30.7299995407631[/C][C]30.5146352660396[/C][C]30.9453638154866[/C][/ROW]
[ROW][C]86[/C][C]30.7299995407631[/C][C]30.4254354592466[/C][C]31.0345636222797[/C][/ROW]
[ROW][C]87[/C][C]30.7299995407631[/C][C]30.356989100329[/C][C]31.1030099811973[/C][/ROW]
[ROW][C]88[/C][C]30.7299995407631[/C][C]30.2992858335332[/C][C]31.1607132479931[/C][/ROW]
[ROW][C]89[/C][C]30.7299995407631[/C][C]30.2484480829535[/C][C]31.2115509985728[/C][/ROW]
[ROW][C]90[/C][C]30.7299995407631[/C][C]30.2024871566038[/C][C]31.2575119249225[/C][/ROW]
[ROW][C]91[/C][C]30.7299995407631[/C][C]30.1602216679352[/C][C]31.2997774135911[/C][/ROW]
[ROW][C]92[/C][C]30.7299995407631[/C][C]30.120881872913[/C][C]31.3391172086133[/C][/ROW]
[ROW][C]93[/C][C]30.7299995407631[/C][C]30.0839331028405[/C][C]31.3760659786858[/C][/ROW]
[ROW][C]94[/C][C]30.7299995407631[/C][C]30.0489860672305[/C][C]31.4110130142957[/C][/ROW]
[ROW][C]95[/C][C]30.7299995407631[/C][C]30.0157468823461[/C][C]31.4442521991801[/C][/ROW]
[ROW][C]96[/C][C]30.7299995407631[/C][C]29.9839872292168[/C][C]31.4760118523094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232296&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
8530.729999540763130.514635266039630.9453638154866
8630.729999540763130.425435459246631.0345636222797
8730.729999540763130.35698910032931.1030099811973
8830.729999540763130.299285833533231.1607132479931
8930.729999540763130.248448082953531.2115509985728
9030.729999540763130.202487156603831.2575119249225
9130.729999540763130.160221667935231.2997774135911
9230.729999540763130.12088187291331.3391172086133
9330.729999540763130.083933102840531.3760659786858
9430.729999540763130.048986067230531.4110130142957
9530.729999540763130.015746882346131.4442521991801
9630.729999540763129.983987229216831.4760118523094



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')