Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Dec 2012 09:10:45 -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/Dec/29/t1356790285h5g2kwd3g0nv7av.htm/, Retrieved Thu, 02 May 2024 11:42:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204870, Retrieved Thu, 02 May 2024 11:42:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2012-12-13 18:51:07] [443e3dc6fee66d7ac3a3c54fbf520d20]
- RMP     [Exponential Smoothing] [] [2012-12-29 14:10:45] [acc52e68afa30ff76a44c134284f813d] [Current]
Feedback Forum

Post a new message
Dataseries X:
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204870&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]2 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=204870&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204870&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.81076580745604
beta0.0343226921710069
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.81076580745604 \tabularnewline
beta & 0.0343226921710069 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204870&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]0.81076580745604[/C][/ROW]
[ROW][C]beta[/C][C]0.0343226921710069[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204870&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204870&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
alpha0.81076580745604
beta0.0343226921710069
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-5-3-2
4-4-5.677186945376261.67718694537626
5-6-5.32636425097017-0.673635749029835
6-2-6.900253926692584.90025392669258
7-2-3.818661812982781.81866181298278
8-2-3.1849101054931.184910105493
9-2-3.032009331107041.03200933110704
102-2.974356866344324.97435686634432
1110.4180409187189670.581959081281033
12-80.265427329399959-8.26542732939996
13-1-7.290352191773156.29035219177315
141-2.869757561325623.86975756132562
15-1-0.304011973010718-0.695988026989282
162-1.45938451506543.4593845150654
1720.8505435114138591.14945648858614
1811.31964756670256-0.319647566702555
19-10.588757240889717-1.58875724088972
20-2-1.21529521930029-0.784704780699712
21-2-2.389285939310660.389285939310662
22-1-2.600612206467231.60061220646723
23-8-1.78529525389192-6.21470474610808
24-4-7.47931078408723.4793107840872
25-6-5.21692888971432-0.783071110285677
26-3-6.432131534328633.43213153432863
27-3-4.134283795821581.13428379582158
28-7-3.66788796468793-3.33211203531207
29-9-6.91541805423613-2.08458194576387
30-11-9.20950245194166-1.79049754805834
31-13-11.3149786418475-1.68502135815251
32-11-13.38182855374052.38182855374052
33-9-12.08513488538133.08513488538135
34-17-10.1323723903742-6.86762760962579
35-22-16.4400794581091-5.55992054189093
36-25-21.8422619567127-3.15773804328733
37-20-25.38470949933845.3847094993384
38-24-21.8513887690967-2.14861123090334
39-24-24.48561773758220.485617737582178
40-22-24.97059032157722.97059032157724
41-19-23.35816750899294.35816750899288
42-18-20.49946693118032.49946693118027
43-17-19.07818289913732.07818289913734
44-11-17.94063057749386.94063057749378
45-11-12.66763039348471.66763039348469
46-12-11.6233922010588-0.376607798941167
47-10-12.24703255310032.24703255310033
48-15-10.6809853469914-4.31901465300863
49-15-14.5586527996342-0.441347200365763
50-15-15.3047217311320.304721731132002
51-13-15.43742378864322.43742378864323
52-8-13.77317612721415.77317612721411
53-13-9.24376051493618-3.75623948506382
54-9-12.54499662105293.54499662105288
55-7-9.827991160947122.82799116094712
56-4-7.613612820348253.61361282034825
57-4-4.661720892867020.661720892867024
58-2-4.08470786000932.0847078600093
590-2.295973097301992.29597309730199
60-2-0.272060133160077-1.72793986683992
61-3-1.55868274467912-1.44131725532088
621-2.653030037209073.65303003720907
63-20.484600563308747-2.48460056330875
64-1-1.423090498580390.423090498580388
651-0.9615514480868941.96155144808689
66-30.801904533405716-3.80190453340572
67-4-2.21325065427386-1.78674934572614
68-9-3.6443079817117-5.3556920182883
69-9-8.11797840140483-0.882021598595166
70-7-8.989094412756441.98909441275644
71-14-7.47705587943139-6.52294412056861
72-12-13.04780544598941.04780544598937

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -5 & -3 & -2 \tabularnewline
4 & -4 & -5.67718694537626 & 1.67718694537626 \tabularnewline
5 & -6 & -5.32636425097017 & -0.673635749029835 \tabularnewline
6 & -2 & -6.90025392669258 & 4.90025392669258 \tabularnewline
7 & -2 & -3.81866181298278 & 1.81866181298278 \tabularnewline
8 & -2 & -3.184910105493 & 1.184910105493 \tabularnewline
9 & -2 & -3.03200933110704 & 1.03200933110704 \tabularnewline
10 & 2 & -2.97435686634432 & 4.97435686634432 \tabularnewline
11 & 1 & 0.418040918718967 & 0.581959081281033 \tabularnewline
12 & -8 & 0.265427329399959 & -8.26542732939996 \tabularnewline
13 & -1 & -7.29035219177315 & 6.29035219177315 \tabularnewline
14 & 1 & -2.86975756132562 & 3.86975756132562 \tabularnewline
15 & -1 & -0.304011973010718 & -0.695988026989282 \tabularnewline
16 & 2 & -1.4593845150654 & 3.4593845150654 \tabularnewline
17 & 2 & 0.850543511413859 & 1.14945648858614 \tabularnewline
18 & 1 & 1.31964756670256 & -0.319647566702555 \tabularnewline
19 & -1 & 0.588757240889717 & -1.58875724088972 \tabularnewline
20 & -2 & -1.21529521930029 & -0.784704780699712 \tabularnewline
21 & -2 & -2.38928593931066 & 0.389285939310662 \tabularnewline
22 & -1 & -2.60061220646723 & 1.60061220646723 \tabularnewline
23 & -8 & -1.78529525389192 & -6.21470474610808 \tabularnewline
24 & -4 & -7.4793107840872 & 3.4793107840872 \tabularnewline
25 & -6 & -5.21692888971432 & -0.783071110285677 \tabularnewline
26 & -3 & -6.43213153432863 & 3.43213153432863 \tabularnewline
27 & -3 & -4.13428379582158 & 1.13428379582158 \tabularnewline
28 & -7 & -3.66788796468793 & -3.33211203531207 \tabularnewline
29 & -9 & -6.91541805423613 & -2.08458194576387 \tabularnewline
30 & -11 & -9.20950245194166 & -1.79049754805834 \tabularnewline
31 & -13 & -11.3149786418475 & -1.68502135815251 \tabularnewline
32 & -11 & -13.3818285537405 & 2.38182855374052 \tabularnewline
33 & -9 & -12.0851348853813 & 3.08513488538135 \tabularnewline
34 & -17 & -10.1323723903742 & -6.86762760962579 \tabularnewline
35 & -22 & -16.4400794581091 & -5.55992054189093 \tabularnewline
36 & -25 & -21.8422619567127 & -3.15773804328733 \tabularnewline
37 & -20 & -25.3847094993384 & 5.3847094993384 \tabularnewline
38 & -24 & -21.8513887690967 & -2.14861123090334 \tabularnewline
39 & -24 & -24.4856177375822 & 0.485617737582178 \tabularnewline
40 & -22 & -24.9705903215772 & 2.97059032157724 \tabularnewline
41 & -19 & -23.3581675089929 & 4.35816750899288 \tabularnewline
42 & -18 & -20.4994669311803 & 2.49946693118027 \tabularnewline
43 & -17 & -19.0781828991373 & 2.07818289913734 \tabularnewline
44 & -11 & -17.9406305774938 & 6.94063057749378 \tabularnewline
45 & -11 & -12.6676303934847 & 1.66763039348469 \tabularnewline
46 & -12 & -11.6233922010588 & -0.376607798941167 \tabularnewline
47 & -10 & -12.2470325531003 & 2.24703255310033 \tabularnewline
48 & -15 & -10.6809853469914 & -4.31901465300863 \tabularnewline
49 & -15 & -14.5586527996342 & -0.441347200365763 \tabularnewline
50 & -15 & -15.304721731132 & 0.304721731132002 \tabularnewline
51 & -13 & -15.4374237886432 & 2.43742378864323 \tabularnewline
52 & -8 & -13.7731761272141 & 5.77317612721411 \tabularnewline
53 & -13 & -9.24376051493618 & -3.75623948506382 \tabularnewline
54 & -9 & -12.5449966210529 & 3.54499662105288 \tabularnewline
55 & -7 & -9.82799116094712 & 2.82799116094712 \tabularnewline
56 & -4 & -7.61361282034825 & 3.61361282034825 \tabularnewline
57 & -4 & -4.66172089286702 & 0.661720892867024 \tabularnewline
58 & -2 & -4.0847078600093 & 2.0847078600093 \tabularnewline
59 & 0 & -2.29597309730199 & 2.29597309730199 \tabularnewline
60 & -2 & -0.272060133160077 & -1.72793986683992 \tabularnewline
61 & -3 & -1.55868274467912 & -1.44131725532088 \tabularnewline
62 & 1 & -2.65303003720907 & 3.65303003720907 \tabularnewline
63 & -2 & 0.484600563308747 & -2.48460056330875 \tabularnewline
64 & -1 & -1.42309049858039 & 0.423090498580388 \tabularnewline
65 & 1 & -0.961551448086894 & 1.96155144808689 \tabularnewline
66 & -3 & 0.801904533405716 & -3.80190453340572 \tabularnewline
67 & -4 & -2.21325065427386 & -1.78674934572614 \tabularnewline
68 & -9 & -3.6443079817117 & -5.3556920182883 \tabularnewline
69 & -9 & -8.11797840140483 & -0.882021598595166 \tabularnewline
70 & -7 & -8.98909441275644 & 1.98909441275644 \tabularnewline
71 & -14 & -7.47705587943139 & -6.52294412056861 \tabularnewline
72 & -12 & -13.0478054459894 & 1.04780544598937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204870&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]-5[/C][C]-3[/C][C]-2[/C][/ROW]
[ROW][C]4[/C][C]-4[/C][C]-5.67718694537626[/C][C]1.67718694537626[/C][/ROW]
[ROW][C]5[/C][C]-6[/C][C]-5.32636425097017[/C][C]-0.673635749029835[/C][/ROW]
[ROW][C]6[/C][C]-2[/C][C]-6.90025392669258[/C][C]4.90025392669258[/C][/ROW]
[ROW][C]7[/C][C]-2[/C][C]-3.81866181298278[/C][C]1.81866181298278[/C][/ROW]
[ROW][C]8[/C][C]-2[/C][C]-3.184910105493[/C][C]1.184910105493[/C][/ROW]
[ROW][C]9[/C][C]-2[/C][C]-3.03200933110704[/C][C]1.03200933110704[/C][/ROW]
[ROW][C]10[/C][C]2[/C][C]-2.97435686634432[/C][C]4.97435686634432[/C][/ROW]
[ROW][C]11[/C][C]1[/C][C]0.418040918718967[/C][C]0.581959081281033[/C][/ROW]
[ROW][C]12[/C][C]-8[/C][C]0.265427329399959[/C][C]-8.26542732939996[/C][/ROW]
[ROW][C]13[/C][C]-1[/C][C]-7.29035219177315[/C][C]6.29035219177315[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]-2.86975756132562[/C][C]3.86975756132562[/C][/ROW]
[ROW][C]15[/C][C]-1[/C][C]-0.304011973010718[/C][C]-0.695988026989282[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]-1.4593845150654[/C][C]3.4593845150654[/C][/ROW]
[ROW][C]17[/C][C]2[/C][C]0.850543511413859[/C][C]1.14945648858614[/C][/ROW]
[ROW][C]18[/C][C]1[/C][C]1.31964756670256[/C][C]-0.319647566702555[/C][/ROW]
[ROW][C]19[/C][C]-1[/C][C]0.588757240889717[/C][C]-1.58875724088972[/C][/ROW]
[ROW][C]20[/C][C]-2[/C][C]-1.21529521930029[/C][C]-0.784704780699712[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-2.38928593931066[/C][C]0.389285939310662[/C][/ROW]
[ROW][C]22[/C][C]-1[/C][C]-2.60061220646723[/C][C]1.60061220646723[/C][/ROW]
[ROW][C]23[/C][C]-8[/C][C]-1.78529525389192[/C][C]-6.21470474610808[/C][/ROW]
[ROW][C]24[/C][C]-4[/C][C]-7.4793107840872[/C][C]3.4793107840872[/C][/ROW]
[ROW][C]25[/C][C]-6[/C][C]-5.21692888971432[/C][C]-0.783071110285677[/C][/ROW]
[ROW][C]26[/C][C]-3[/C][C]-6.43213153432863[/C][C]3.43213153432863[/C][/ROW]
[ROW][C]27[/C][C]-3[/C][C]-4.13428379582158[/C][C]1.13428379582158[/C][/ROW]
[ROW][C]28[/C][C]-7[/C][C]-3.66788796468793[/C][C]-3.33211203531207[/C][/ROW]
[ROW][C]29[/C][C]-9[/C][C]-6.91541805423613[/C][C]-2.08458194576387[/C][/ROW]
[ROW][C]30[/C][C]-11[/C][C]-9.20950245194166[/C][C]-1.79049754805834[/C][/ROW]
[ROW][C]31[/C][C]-13[/C][C]-11.3149786418475[/C][C]-1.68502135815251[/C][/ROW]
[ROW][C]32[/C][C]-11[/C][C]-13.3818285537405[/C][C]2.38182855374052[/C][/ROW]
[ROW][C]33[/C][C]-9[/C][C]-12.0851348853813[/C][C]3.08513488538135[/C][/ROW]
[ROW][C]34[/C][C]-17[/C][C]-10.1323723903742[/C][C]-6.86762760962579[/C][/ROW]
[ROW][C]35[/C][C]-22[/C][C]-16.4400794581091[/C][C]-5.55992054189093[/C][/ROW]
[ROW][C]36[/C][C]-25[/C][C]-21.8422619567127[/C][C]-3.15773804328733[/C][/ROW]
[ROW][C]37[/C][C]-20[/C][C]-25.3847094993384[/C][C]5.3847094993384[/C][/ROW]
[ROW][C]38[/C][C]-24[/C][C]-21.8513887690967[/C][C]-2.14861123090334[/C][/ROW]
[ROW][C]39[/C][C]-24[/C][C]-24.4856177375822[/C][C]0.485617737582178[/C][/ROW]
[ROW][C]40[/C][C]-22[/C][C]-24.9705903215772[/C][C]2.97059032157724[/C][/ROW]
[ROW][C]41[/C][C]-19[/C][C]-23.3581675089929[/C][C]4.35816750899288[/C][/ROW]
[ROW][C]42[/C][C]-18[/C][C]-20.4994669311803[/C][C]2.49946693118027[/C][/ROW]
[ROW][C]43[/C][C]-17[/C][C]-19.0781828991373[/C][C]2.07818289913734[/C][/ROW]
[ROW][C]44[/C][C]-11[/C][C]-17.9406305774938[/C][C]6.94063057749378[/C][/ROW]
[ROW][C]45[/C][C]-11[/C][C]-12.6676303934847[/C][C]1.66763039348469[/C][/ROW]
[ROW][C]46[/C][C]-12[/C][C]-11.6233922010588[/C][C]-0.376607798941167[/C][/ROW]
[ROW][C]47[/C][C]-10[/C][C]-12.2470325531003[/C][C]2.24703255310033[/C][/ROW]
[ROW][C]48[/C][C]-15[/C][C]-10.6809853469914[/C][C]-4.31901465300863[/C][/ROW]
[ROW][C]49[/C][C]-15[/C][C]-14.5586527996342[/C][C]-0.441347200365763[/C][/ROW]
[ROW][C]50[/C][C]-15[/C][C]-15.304721731132[/C][C]0.304721731132002[/C][/ROW]
[ROW][C]51[/C][C]-13[/C][C]-15.4374237886432[/C][C]2.43742378864323[/C][/ROW]
[ROW][C]52[/C][C]-8[/C][C]-13.7731761272141[/C][C]5.77317612721411[/C][/ROW]
[ROW][C]53[/C][C]-13[/C][C]-9.24376051493618[/C][C]-3.75623948506382[/C][/ROW]
[ROW][C]54[/C][C]-9[/C][C]-12.5449966210529[/C][C]3.54499662105288[/C][/ROW]
[ROW][C]55[/C][C]-7[/C][C]-9.82799116094712[/C][C]2.82799116094712[/C][/ROW]
[ROW][C]56[/C][C]-4[/C][C]-7.61361282034825[/C][C]3.61361282034825[/C][/ROW]
[ROW][C]57[/C][C]-4[/C][C]-4.66172089286702[/C][C]0.661720892867024[/C][/ROW]
[ROW][C]58[/C][C]-2[/C][C]-4.0847078600093[/C][C]2.0847078600093[/C][/ROW]
[ROW][C]59[/C][C]0[/C][C]-2.29597309730199[/C][C]2.29597309730199[/C][/ROW]
[ROW][C]60[/C][C]-2[/C][C]-0.272060133160077[/C][C]-1.72793986683992[/C][/ROW]
[ROW][C]61[/C][C]-3[/C][C]-1.55868274467912[/C][C]-1.44131725532088[/C][/ROW]
[ROW][C]62[/C][C]1[/C][C]-2.65303003720907[/C][C]3.65303003720907[/C][/ROW]
[ROW][C]63[/C][C]-2[/C][C]0.484600563308747[/C][C]-2.48460056330875[/C][/ROW]
[ROW][C]64[/C][C]-1[/C][C]-1.42309049858039[/C][C]0.423090498580388[/C][/ROW]
[ROW][C]65[/C][C]1[/C][C]-0.961551448086894[/C][C]1.96155144808689[/C][/ROW]
[ROW][C]66[/C][C]-3[/C][C]0.801904533405716[/C][C]-3.80190453340572[/C][/ROW]
[ROW][C]67[/C][C]-4[/C][C]-2.21325065427386[/C][C]-1.78674934572614[/C][/ROW]
[ROW][C]68[/C][C]-9[/C][C]-3.6443079817117[/C][C]-5.3556920182883[/C][/ROW]
[ROW][C]69[/C][C]-9[/C][C]-8.11797840140483[/C][C]-0.882021598595166[/C][/ROW]
[ROW][C]70[/C][C]-7[/C][C]-8.98909441275644[/C][C]1.98909441275644[/C][/ROW]
[ROW][C]71[/C][C]-14[/C][C]-7.47705587943139[/C][C]-6.52294412056861[/C][/ROW]
[ROW][C]72[/C][C]-12[/C][C]-13.0478054459894[/C][C]1.04780544598937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204870&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204870&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
3-5-3-2
4-4-5.677186945376261.67718694537626
5-6-5.32636425097017-0.673635749029835
6-2-6.900253926692584.90025392669258
7-2-3.818661812982781.81866181298278
8-2-3.1849101054931.184910105493
9-2-3.032009331107041.03200933110704
102-2.974356866344324.97435686634432
1110.4180409187189670.581959081281033
12-80.265427329399959-8.26542732939996
13-1-7.290352191773156.29035219177315
141-2.869757561325623.86975756132562
15-1-0.304011973010718-0.695988026989282
162-1.45938451506543.4593845150654
1720.8505435114138591.14945648858614
1811.31964756670256-0.319647566702555
19-10.588757240889717-1.58875724088972
20-2-1.21529521930029-0.784704780699712
21-2-2.389285939310660.389285939310662
22-1-2.600612206467231.60061220646723
23-8-1.78529525389192-6.21470474610808
24-4-7.47931078408723.4793107840872
25-6-5.21692888971432-0.783071110285677
26-3-6.432131534328633.43213153432863
27-3-4.134283795821581.13428379582158
28-7-3.66788796468793-3.33211203531207
29-9-6.91541805423613-2.08458194576387
30-11-9.20950245194166-1.79049754805834
31-13-11.3149786418475-1.68502135815251
32-11-13.38182855374052.38182855374052
33-9-12.08513488538133.08513488538135
34-17-10.1323723903742-6.86762760962579
35-22-16.4400794581091-5.55992054189093
36-25-21.8422619567127-3.15773804328733
37-20-25.38470949933845.3847094993384
38-24-21.8513887690967-2.14861123090334
39-24-24.48561773758220.485617737582178
40-22-24.97059032157722.97059032157724
41-19-23.35816750899294.35816750899288
42-18-20.49946693118032.49946693118027
43-17-19.07818289913732.07818289913734
44-11-17.94063057749386.94063057749378
45-11-12.66763039348471.66763039348469
46-12-11.6233922010588-0.376607798941167
47-10-12.24703255310032.24703255310033
48-15-10.6809853469914-4.31901465300863
49-15-14.5586527996342-0.441347200365763
50-15-15.3047217311320.304721731132002
51-13-15.43742378864322.43742378864323
52-8-13.77317612721415.77317612721411
53-13-9.24376051493618-3.75623948506382
54-9-12.54499662105293.54499662105288
55-7-9.827991160947122.82799116094712
56-4-7.613612820348253.61361282034825
57-4-4.661720892867020.661720892867024
58-2-4.08470786000932.0847078600093
590-2.295973097301992.29597309730199
60-2-0.272060133160077-1.72793986683992
61-3-1.55868274467912-1.44131725532088
621-2.653030037209073.65303003720907
63-20.484600563308747-2.48460056330875
64-1-1.423090498580390.423090498580388
651-0.9615514480868941.96155144808689
66-30.801904533405716-3.80190453340572
67-4-2.21325065427386-1.78674934572614
68-9-3.6443079817117-5.3556920182883
69-9-8.11797840140483-0.882021598595166
70-7-8.989094412756441.98909441275644
71-14-7.47705587943139-6.52294412056861
72-12-13.04780544598941.04780544598937







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-12.4512921479902-18.918569791855-5.98401450412532
74-12.7043036784653-21.1446312850718-4.26397607185885
75-12.9573152089405-23.0883104904112-2.82631992746985
76-13.2103267394157-24.8758427517723-1.54481072705908
77-13.4633382698909-26.5646932869741-0.361983252807725
78-13.7163498003661-28.18651087732680.753811276594618
79-13.9693613308413-29.7607899114311.82206724974845
80-14.2223728613165-31.30046544229242.85571971965949
81-14.4753843917916-32.81458906951563.86382028593228
82-14.7283959222668-34.30975288468814.85296104015445
83-14.981407452742-35.79090915009245.82809424460838
84-15.2344189832172-37.26187156564146.79303359920702

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -12.4512921479902 & -18.918569791855 & -5.98401450412532 \tabularnewline
74 & -12.7043036784653 & -21.1446312850718 & -4.26397607185885 \tabularnewline
75 & -12.9573152089405 & -23.0883104904112 & -2.82631992746985 \tabularnewline
76 & -13.2103267394157 & -24.8758427517723 & -1.54481072705908 \tabularnewline
77 & -13.4633382698909 & -26.5646932869741 & -0.361983252807725 \tabularnewline
78 & -13.7163498003661 & -28.1865108773268 & 0.753811276594618 \tabularnewline
79 & -13.9693613308413 & -29.760789911431 & 1.82206724974845 \tabularnewline
80 & -14.2223728613165 & -31.3004654422924 & 2.85571971965949 \tabularnewline
81 & -14.4753843917916 & -32.8145890695156 & 3.86382028593228 \tabularnewline
82 & -14.7283959222668 & -34.3097528846881 & 4.85296104015445 \tabularnewline
83 & -14.981407452742 & -35.7909091500924 & 5.82809424460838 \tabularnewline
84 & -15.2344189832172 & -37.2618715656414 & 6.79303359920702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204870&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]-12.4512921479902[/C][C]-18.918569791855[/C][C]-5.98401450412532[/C][/ROW]
[ROW][C]74[/C][C]-12.7043036784653[/C][C]-21.1446312850718[/C][C]-4.26397607185885[/C][/ROW]
[ROW][C]75[/C][C]-12.9573152089405[/C][C]-23.0883104904112[/C][C]-2.82631992746985[/C][/ROW]
[ROW][C]76[/C][C]-13.2103267394157[/C][C]-24.8758427517723[/C][C]-1.54481072705908[/C][/ROW]
[ROW][C]77[/C][C]-13.4633382698909[/C][C]-26.5646932869741[/C][C]-0.361983252807725[/C][/ROW]
[ROW][C]78[/C][C]-13.7163498003661[/C][C]-28.1865108773268[/C][C]0.753811276594618[/C][/ROW]
[ROW][C]79[/C][C]-13.9693613308413[/C][C]-29.760789911431[/C][C]1.82206724974845[/C][/ROW]
[ROW][C]80[/C][C]-14.2223728613165[/C][C]-31.3004654422924[/C][C]2.85571971965949[/C][/ROW]
[ROW][C]81[/C][C]-14.4753843917916[/C][C]-32.8145890695156[/C][C]3.86382028593228[/C][/ROW]
[ROW][C]82[/C][C]-14.7283959222668[/C][C]-34.3097528846881[/C][C]4.85296104015445[/C][/ROW]
[ROW][C]83[/C][C]-14.981407452742[/C][C]-35.7909091500924[/C][C]5.82809424460838[/C][/ROW]
[ROW][C]84[/C][C]-15.2344189832172[/C][C]-37.2618715656414[/C][C]6.79303359920702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204870&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204870&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
73-12.4512921479902-18.918569791855-5.98401450412532
74-12.7043036784653-21.1446312850718-4.26397607185885
75-12.9573152089405-23.0883104904112-2.82631992746985
76-13.2103267394157-24.8758427517723-1.54481072705908
77-13.4633382698909-26.5646932869741-0.361983252807725
78-13.7163498003661-28.18651087732680.753811276594618
79-13.9693613308413-29.7607899114311.82206724974845
80-14.2223728613165-31.30046544229242.85571971965949
81-14.4753843917916-32.81458906951563.86382028593228
82-14.7283959222668-34.30975288468814.85296104015445
83-14.981407452742-35.79090915009245.82809424460838
84-15.2344189832172-37.26187156564146.79303359920702



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')