Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Dec 2013 06:32:31 -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/14/t1387020768q4tcuuk0sukhrqr.htm/, Retrieved Thu, 25 Apr 2024 23:48:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232315, Retrieved Thu, 25 Apr 2024 23:48:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-14 11:32:31] [43b132fa6864a311b34d1147ccf52151] [Current]
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Dataseries X:
9
13
12
5
13
11
8
8
8
8
0
3
0
-1
-1
-4
1
-1
0
-1
6
0
-3
-3
4
1
0
-4
-2
3
2
5
6
6
3
4
7
5
6
1
3
6
0
3
4
7
6
6
6
6
2
2
2
3
-1
-4
4
5
3
-1
-4
0
-1
-1
3
2
-4
-3
-1
3
-2
-10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232315&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232315&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.449384645834359
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.449384645834359 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232315&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]0.449384645834359[/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=232315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232315&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
alpha0.449384645834359
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21394
31210.79753858333741.20246141666256
4511.3379062811938-6.33790628119382
5138.489748511688184.51025148831182
61110.51658627938710.483413720612923
7810.7338249830162-2.73382498301619
889.50528601125033-1.50528601125033
988.82883359020519-0.828833590205187
1088.45636850081521-0.456368500815209
1108.25128350370641-8.25128350370641
1234.54328338871442-1.54328338871442
1303.84975552965494-3.84975552965494
14-12.11973450441209-3.11973450441209
15-10.717773719049633-1.71777371904963
16-4-0.0541674153090562-3.94583258469094
171-1.827363993902072.82736399390207
18-1-0.556790026857569-0.443209973142431
190-0.7559617836684360.755961783668436
20-1-0.416244165250286-0.583755834749714
216-0.6785750743030276.67857507430303
2202.32267402014082-2.32267402014082
23-31.27889997821117-4.27889997821117
24-3-0.643971973057904-2.3560280269421
254-1.70273479352115.7027347935211
2610.8599866619526550.140013338047345
2700.922906506283148-0.922906506283148
28-40.50816649281887-4.50816649281887
29-2-1.51773430991886-0.482265690081138
303-1.734457106254044.73445710625404
3120.3931352236578981.6068647763421
3251.11523558207813.8847644179219
3362.860989064175853.13901093582415
3464.271612381841371.72838761815863
3535.04832323949208-2.04832323949208
3644.12783822595864-0.127838225958643
3774.070389690062132.92961030993787
3855.38691158162624-0.386911581626244
3965.213039457547920.786960542452078
4015.56668744220336-4.56668744220336
4133.51448822335259-0.514488223352591
4263.283285115315342.71671488468466
4304.50413507160229-4.50413507160229
4432.480045927660180.519954072339822
4542.713705304308741.28629469569126
4673.291746390570573.70825360942943
4764.9581786255081.041821374492
4865.426357154906750.573642845093248
4965.68414344168440.315856558315605
5065.826084529277510.173915470722487
5125.90423947149325-3.90423947149325
5224.14973419934373-2.14973419934373
5323.18367665753364-1.18367665753364
5432.651750542005490.348249457994513
55-12.80824850134836-3.80824850134836
56-41.0968800973207-5.0968800973207
574-1.193579560073965.19357956007396
5851.140335351142443.85966464885756
5932.874809382408690.125190617591307
60-12.93106812375675-3.93106812375675
61-41.16450646721158-5.16450646721158
620-1.156343442465551.15634344246555
63-1-0.636700454110286-0.363299545889714
64-1-0.799961691871718-0.200038308128282
653-0.8898558361232513.88985583612325
6620.8581856511397111.14181434886029
67-41.37129948791088-5.37129948791088
68-3-1.04248003013422-1.95751996986578
69-1-1.922159448506040.922159448506041
703-1.507755151336354.50775515133635
71-20.517960800854945-2.51796080085495
72-10-0.613572121862053-9.38642787813795

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 13 & 9 & 4 \tabularnewline
3 & 12 & 10.7975385833374 & 1.20246141666256 \tabularnewline
4 & 5 & 11.3379062811938 & -6.33790628119382 \tabularnewline
5 & 13 & 8.48974851168818 & 4.51025148831182 \tabularnewline
6 & 11 & 10.5165862793871 & 0.483413720612923 \tabularnewline
7 & 8 & 10.7338249830162 & -2.73382498301619 \tabularnewline
8 & 8 & 9.50528601125033 & -1.50528601125033 \tabularnewline
9 & 8 & 8.82883359020519 & -0.828833590205187 \tabularnewline
10 & 8 & 8.45636850081521 & -0.456368500815209 \tabularnewline
11 & 0 & 8.25128350370641 & -8.25128350370641 \tabularnewline
12 & 3 & 4.54328338871442 & -1.54328338871442 \tabularnewline
13 & 0 & 3.84975552965494 & -3.84975552965494 \tabularnewline
14 & -1 & 2.11973450441209 & -3.11973450441209 \tabularnewline
15 & -1 & 0.717773719049633 & -1.71777371904963 \tabularnewline
16 & -4 & -0.0541674153090562 & -3.94583258469094 \tabularnewline
17 & 1 & -1.82736399390207 & 2.82736399390207 \tabularnewline
18 & -1 & -0.556790026857569 & -0.443209973142431 \tabularnewline
19 & 0 & -0.755961783668436 & 0.755961783668436 \tabularnewline
20 & -1 & -0.416244165250286 & -0.583755834749714 \tabularnewline
21 & 6 & -0.678575074303027 & 6.67857507430303 \tabularnewline
22 & 0 & 2.32267402014082 & -2.32267402014082 \tabularnewline
23 & -3 & 1.27889997821117 & -4.27889997821117 \tabularnewline
24 & -3 & -0.643971973057904 & -2.3560280269421 \tabularnewline
25 & 4 & -1.7027347935211 & 5.7027347935211 \tabularnewline
26 & 1 & 0.859986661952655 & 0.140013338047345 \tabularnewline
27 & 0 & 0.922906506283148 & -0.922906506283148 \tabularnewline
28 & -4 & 0.50816649281887 & -4.50816649281887 \tabularnewline
29 & -2 & -1.51773430991886 & -0.482265690081138 \tabularnewline
30 & 3 & -1.73445710625404 & 4.73445710625404 \tabularnewline
31 & 2 & 0.393135223657898 & 1.6068647763421 \tabularnewline
32 & 5 & 1.1152355820781 & 3.8847644179219 \tabularnewline
33 & 6 & 2.86098906417585 & 3.13901093582415 \tabularnewline
34 & 6 & 4.27161238184137 & 1.72838761815863 \tabularnewline
35 & 3 & 5.04832323949208 & -2.04832323949208 \tabularnewline
36 & 4 & 4.12783822595864 & -0.127838225958643 \tabularnewline
37 & 7 & 4.07038969006213 & 2.92961030993787 \tabularnewline
38 & 5 & 5.38691158162624 & -0.386911581626244 \tabularnewline
39 & 6 & 5.21303945754792 & 0.786960542452078 \tabularnewline
40 & 1 & 5.56668744220336 & -4.56668744220336 \tabularnewline
41 & 3 & 3.51448822335259 & -0.514488223352591 \tabularnewline
42 & 6 & 3.28328511531534 & 2.71671488468466 \tabularnewline
43 & 0 & 4.50413507160229 & -4.50413507160229 \tabularnewline
44 & 3 & 2.48004592766018 & 0.519954072339822 \tabularnewline
45 & 4 & 2.71370530430874 & 1.28629469569126 \tabularnewline
46 & 7 & 3.29174639057057 & 3.70825360942943 \tabularnewline
47 & 6 & 4.958178625508 & 1.041821374492 \tabularnewline
48 & 6 & 5.42635715490675 & 0.573642845093248 \tabularnewline
49 & 6 & 5.6841434416844 & 0.315856558315605 \tabularnewline
50 & 6 & 5.82608452927751 & 0.173915470722487 \tabularnewline
51 & 2 & 5.90423947149325 & -3.90423947149325 \tabularnewline
52 & 2 & 4.14973419934373 & -2.14973419934373 \tabularnewline
53 & 2 & 3.18367665753364 & -1.18367665753364 \tabularnewline
54 & 3 & 2.65175054200549 & 0.348249457994513 \tabularnewline
55 & -1 & 2.80824850134836 & -3.80824850134836 \tabularnewline
56 & -4 & 1.0968800973207 & -5.0968800973207 \tabularnewline
57 & 4 & -1.19357956007396 & 5.19357956007396 \tabularnewline
58 & 5 & 1.14033535114244 & 3.85966464885756 \tabularnewline
59 & 3 & 2.87480938240869 & 0.125190617591307 \tabularnewline
60 & -1 & 2.93106812375675 & -3.93106812375675 \tabularnewline
61 & -4 & 1.16450646721158 & -5.16450646721158 \tabularnewline
62 & 0 & -1.15634344246555 & 1.15634344246555 \tabularnewline
63 & -1 & -0.636700454110286 & -0.363299545889714 \tabularnewline
64 & -1 & -0.799961691871718 & -0.200038308128282 \tabularnewline
65 & 3 & -0.889855836123251 & 3.88985583612325 \tabularnewline
66 & 2 & 0.858185651139711 & 1.14181434886029 \tabularnewline
67 & -4 & 1.37129948791088 & -5.37129948791088 \tabularnewline
68 & -3 & -1.04248003013422 & -1.95751996986578 \tabularnewline
69 & -1 & -1.92215944850604 & 0.922159448506041 \tabularnewline
70 & 3 & -1.50775515133635 & 4.50775515133635 \tabularnewline
71 & -2 & 0.517960800854945 & -2.51796080085495 \tabularnewline
72 & -10 & -0.613572121862053 & -9.38642787813795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232315&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]13[/C][C]9[/C][C]4[/C][/ROW]
[ROW][C]3[/C][C]12[/C][C]10.7975385833374[/C][C]1.20246141666256[/C][/ROW]
[ROW][C]4[/C][C]5[/C][C]11.3379062811938[/C][C]-6.33790628119382[/C][/ROW]
[ROW][C]5[/C][C]13[/C][C]8.48974851168818[/C][C]4.51025148831182[/C][/ROW]
[ROW][C]6[/C][C]11[/C][C]10.5165862793871[/C][C]0.483413720612923[/C][/ROW]
[ROW][C]7[/C][C]8[/C][C]10.7338249830162[/C][C]-2.73382498301619[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]9.50528601125033[/C][C]-1.50528601125033[/C][/ROW]
[ROW][C]9[/C][C]8[/C][C]8.82883359020519[/C][C]-0.828833590205187[/C][/ROW]
[ROW][C]10[/C][C]8[/C][C]8.45636850081521[/C][C]-0.456368500815209[/C][/ROW]
[ROW][C]11[/C][C]0[/C][C]8.25128350370641[/C][C]-8.25128350370641[/C][/ROW]
[ROW][C]12[/C][C]3[/C][C]4.54328338871442[/C][C]-1.54328338871442[/C][/ROW]
[ROW][C]13[/C][C]0[/C][C]3.84975552965494[/C][C]-3.84975552965494[/C][/ROW]
[ROW][C]14[/C][C]-1[/C][C]2.11973450441209[/C][C]-3.11973450441209[/C][/ROW]
[ROW][C]15[/C][C]-1[/C][C]0.717773719049633[/C][C]-1.71777371904963[/C][/ROW]
[ROW][C]16[/C][C]-4[/C][C]-0.0541674153090562[/C][C]-3.94583258469094[/C][/ROW]
[ROW][C]17[/C][C]1[/C][C]-1.82736399390207[/C][C]2.82736399390207[/C][/ROW]
[ROW][C]18[/C][C]-1[/C][C]-0.556790026857569[/C][C]-0.443209973142431[/C][/ROW]
[ROW][C]19[/C][C]0[/C][C]-0.755961783668436[/C][C]0.755961783668436[/C][/ROW]
[ROW][C]20[/C][C]-1[/C][C]-0.416244165250286[/C][C]-0.583755834749714[/C][/ROW]
[ROW][C]21[/C][C]6[/C][C]-0.678575074303027[/C][C]6.67857507430303[/C][/ROW]
[ROW][C]22[/C][C]0[/C][C]2.32267402014082[/C][C]-2.32267402014082[/C][/ROW]
[ROW][C]23[/C][C]-3[/C][C]1.27889997821117[/C][C]-4.27889997821117[/C][/ROW]
[ROW][C]24[/C][C]-3[/C][C]-0.643971973057904[/C][C]-2.3560280269421[/C][/ROW]
[ROW][C]25[/C][C]4[/C][C]-1.7027347935211[/C][C]5.7027347935211[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]0.859986661952655[/C][C]0.140013338047345[/C][/ROW]
[ROW][C]27[/C][C]0[/C][C]0.922906506283148[/C][C]-0.922906506283148[/C][/ROW]
[ROW][C]28[/C][C]-4[/C][C]0.50816649281887[/C][C]-4.50816649281887[/C][/ROW]
[ROW][C]29[/C][C]-2[/C][C]-1.51773430991886[/C][C]-0.482265690081138[/C][/ROW]
[ROW][C]30[/C][C]3[/C][C]-1.73445710625404[/C][C]4.73445710625404[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]0.393135223657898[/C][C]1.6068647763421[/C][/ROW]
[ROW][C]32[/C][C]5[/C][C]1.1152355820781[/C][C]3.8847644179219[/C][/ROW]
[ROW][C]33[/C][C]6[/C][C]2.86098906417585[/C][C]3.13901093582415[/C][/ROW]
[ROW][C]34[/C][C]6[/C][C]4.27161238184137[/C][C]1.72838761815863[/C][/ROW]
[ROW][C]35[/C][C]3[/C][C]5.04832323949208[/C][C]-2.04832323949208[/C][/ROW]
[ROW][C]36[/C][C]4[/C][C]4.12783822595864[/C][C]-0.127838225958643[/C][/ROW]
[ROW][C]37[/C][C]7[/C][C]4.07038969006213[/C][C]2.92961030993787[/C][/ROW]
[ROW][C]38[/C][C]5[/C][C]5.38691158162624[/C][C]-0.386911581626244[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]5.21303945754792[/C][C]0.786960542452078[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]5.56668744220336[/C][C]-4.56668744220336[/C][/ROW]
[ROW][C]41[/C][C]3[/C][C]3.51448822335259[/C][C]-0.514488223352591[/C][/ROW]
[ROW][C]42[/C][C]6[/C][C]3.28328511531534[/C][C]2.71671488468466[/C][/ROW]
[ROW][C]43[/C][C]0[/C][C]4.50413507160229[/C][C]-4.50413507160229[/C][/ROW]
[ROW][C]44[/C][C]3[/C][C]2.48004592766018[/C][C]0.519954072339822[/C][/ROW]
[ROW][C]45[/C][C]4[/C][C]2.71370530430874[/C][C]1.28629469569126[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]3.29174639057057[/C][C]3.70825360942943[/C][/ROW]
[ROW][C]47[/C][C]6[/C][C]4.958178625508[/C][C]1.041821374492[/C][/ROW]
[ROW][C]48[/C][C]6[/C][C]5.42635715490675[/C][C]0.573642845093248[/C][/ROW]
[ROW][C]49[/C][C]6[/C][C]5.6841434416844[/C][C]0.315856558315605[/C][/ROW]
[ROW][C]50[/C][C]6[/C][C]5.82608452927751[/C][C]0.173915470722487[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]5.90423947149325[/C][C]-3.90423947149325[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]4.14973419934373[/C][C]-2.14973419934373[/C][/ROW]
[ROW][C]53[/C][C]2[/C][C]3.18367665753364[/C][C]-1.18367665753364[/C][/ROW]
[ROW][C]54[/C][C]3[/C][C]2.65175054200549[/C][C]0.348249457994513[/C][/ROW]
[ROW][C]55[/C][C]-1[/C][C]2.80824850134836[/C][C]-3.80824850134836[/C][/ROW]
[ROW][C]56[/C][C]-4[/C][C]1.0968800973207[/C][C]-5.0968800973207[/C][/ROW]
[ROW][C]57[/C][C]4[/C][C]-1.19357956007396[/C][C]5.19357956007396[/C][/ROW]
[ROW][C]58[/C][C]5[/C][C]1.14033535114244[/C][C]3.85966464885756[/C][/ROW]
[ROW][C]59[/C][C]3[/C][C]2.87480938240869[/C][C]0.125190617591307[/C][/ROW]
[ROW][C]60[/C][C]-1[/C][C]2.93106812375675[/C][C]-3.93106812375675[/C][/ROW]
[ROW][C]61[/C][C]-4[/C][C]1.16450646721158[/C][C]-5.16450646721158[/C][/ROW]
[ROW][C]62[/C][C]0[/C][C]-1.15634344246555[/C][C]1.15634344246555[/C][/ROW]
[ROW][C]63[/C][C]-1[/C][C]-0.636700454110286[/C][C]-0.363299545889714[/C][/ROW]
[ROW][C]64[/C][C]-1[/C][C]-0.799961691871718[/C][C]-0.200038308128282[/C][/ROW]
[ROW][C]65[/C][C]3[/C][C]-0.889855836123251[/C][C]3.88985583612325[/C][/ROW]
[ROW][C]66[/C][C]2[/C][C]0.858185651139711[/C][C]1.14181434886029[/C][/ROW]
[ROW][C]67[/C][C]-4[/C][C]1.37129948791088[/C][C]-5.37129948791088[/C][/ROW]
[ROW][C]68[/C][C]-3[/C][C]-1.04248003013422[/C][C]-1.95751996986578[/C][/ROW]
[ROW][C]69[/C][C]-1[/C][C]-1.92215944850604[/C][C]0.922159448506041[/C][/ROW]
[ROW][C]70[/C][C]3[/C][C]-1.50775515133635[/C][C]4.50775515133635[/C][/ROW]
[ROW][C]71[/C][C]-2[/C][C]0.517960800854945[/C][C]-2.51796080085495[/C][/ROW]
[ROW][C]72[/C][C]-10[/C][C]-0.613572121862053[/C][C]-9.38642787813795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232315&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
21394
31210.79753858333741.20246141666256
4511.3379062811938-6.33790628119382
5138.489748511688184.51025148831182
61110.51658627938710.483413720612923
7810.7338249830162-2.73382498301619
889.50528601125033-1.50528601125033
988.82883359020519-0.828833590205187
1088.45636850081521-0.456368500815209
1108.25128350370641-8.25128350370641
1234.54328338871442-1.54328338871442
1303.84975552965494-3.84975552965494
14-12.11973450441209-3.11973450441209
15-10.717773719049633-1.71777371904963
16-4-0.0541674153090562-3.94583258469094
171-1.827363993902072.82736399390207
18-1-0.556790026857569-0.443209973142431
190-0.7559617836684360.755961783668436
20-1-0.416244165250286-0.583755834749714
216-0.6785750743030276.67857507430303
2202.32267402014082-2.32267402014082
23-31.27889997821117-4.27889997821117
24-3-0.643971973057904-2.3560280269421
254-1.70273479352115.7027347935211
2610.8599866619526550.140013338047345
2700.922906506283148-0.922906506283148
28-40.50816649281887-4.50816649281887
29-2-1.51773430991886-0.482265690081138
303-1.734457106254044.73445710625404
3120.3931352236578981.6068647763421
3251.11523558207813.8847644179219
3362.860989064175853.13901093582415
3464.271612381841371.72838761815863
3535.04832323949208-2.04832323949208
3644.12783822595864-0.127838225958643
3774.070389690062132.92961030993787
3855.38691158162624-0.386911581626244
3965.213039457547920.786960542452078
4015.56668744220336-4.56668744220336
4133.51448822335259-0.514488223352591
4263.283285115315342.71671488468466
4304.50413507160229-4.50413507160229
4432.480045927660180.519954072339822
4542.713705304308741.28629469569126
4673.291746390570573.70825360942943
4764.9581786255081.041821374492
4865.426357154906750.573642845093248
4965.68414344168440.315856558315605
5065.826084529277510.173915470722487
5125.90423947149325-3.90423947149325
5224.14973419934373-2.14973419934373
5323.18367665753364-1.18367665753364
5432.651750542005490.348249457994513
55-12.80824850134836-3.80824850134836
56-41.0968800973207-5.0968800973207
574-1.193579560073965.19357956007396
5851.140335351142443.85966464885756
5932.874809382408690.125190617591307
60-12.93106812375675-3.93106812375675
61-41.16450646721158-5.16450646721158
620-1.156343442465551.15634344246555
63-1-0.636700454110286-0.363299545889714
64-1-0.799961691871718-0.200038308128282
653-0.8898558361232513.88985583612325
6620.8581856511397111.14181434886029
67-41.37129948791088-5.37129948791088
68-3-1.04248003013422-1.95751996986578
69-1-1.922159448506040.922159448506041
703-1.507755151336354.50775515133635
71-20.517960800854945-2.51796080085495
72-10-0.613572121862053-9.38642787813795







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-4.83168868952883-11.33448734465491.67110996559728
74-4.83168868952883-11.96092296897252.29754558991485
75-4.83168868952883-12.53659443024232.87321705118466
76-4.83168868952883-13.07214762913683.40877025007912
77-4.83168868952883-13.57495779195553.91158041289787
78-4.83168868952883-14.05038413191844.38700675286075
79-4.83168868952883-14.5024661516374.83908877257934
80-4.83168868952883-14.93433823228275.270960853225
81-4.83168868952883-15.34849042987695.68511305081928
82-4.83168868952883-15.74693994215126.08356256309353
83-4.83168868952883-16.13134801934756.46797064028987
84-4.83168868952883-16.50310214429276.83972476523506

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -4.83168868952883 & -11.3344873446549 & 1.67110996559728 \tabularnewline
74 & -4.83168868952883 & -11.9609229689725 & 2.29754558991485 \tabularnewline
75 & -4.83168868952883 & -12.5365944302423 & 2.87321705118466 \tabularnewline
76 & -4.83168868952883 & -13.0721476291368 & 3.40877025007912 \tabularnewline
77 & -4.83168868952883 & -13.5749577919555 & 3.91158041289787 \tabularnewline
78 & -4.83168868952883 & -14.0503841319184 & 4.38700675286075 \tabularnewline
79 & -4.83168868952883 & -14.502466151637 & 4.83908877257934 \tabularnewline
80 & -4.83168868952883 & -14.9343382322827 & 5.270960853225 \tabularnewline
81 & -4.83168868952883 & -15.3484904298769 & 5.68511305081928 \tabularnewline
82 & -4.83168868952883 & -15.7469399421512 & 6.08356256309353 \tabularnewline
83 & -4.83168868952883 & -16.1313480193475 & 6.46797064028987 \tabularnewline
84 & -4.83168868952883 & -16.5031021442927 & 6.83972476523506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232315&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]-4.83168868952883[/C][C]-11.3344873446549[/C][C]1.67110996559728[/C][/ROW]
[ROW][C]74[/C][C]-4.83168868952883[/C][C]-11.9609229689725[/C][C]2.29754558991485[/C][/ROW]
[ROW][C]75[/C][C]-4.83168868952883[/C][C]-12.5365944302423[/C][C]2.87321705118466[/C][/ROW]
[ROW][C]76[/C][C]-4.83168868952883[/C][C]-13.0721476291368[/C][C]3.40877025007912[/C][/ROW]
[ROW][C]77[/C][C]-4.83168868952883[/C][C]-13.5749577919555[/C][C]3.91158041289787[/C][/ROW]
[ROW][C]78[/C][C]-4.83168868952883[/C][C]-14.0503841319184[/C][C]4.38700675286075[/C][/ROW]
[ROW][C]79[/C][C]-4.83168868952883[/C][C]-14.502466151637[/C][C]4.83908877257934[/C][/ROW]
[ROW][C]80[/C][C]-4.83168868952883[/C][C]-14.9343382322827[/C][C]5.270960853225[/C][/ROW]
[ROW][C]81[/C][C]-4.83168868952883[/C][C]-15.3484904298769[/C][C]5.68511305081928[/C][/ROW]
[ROW][C]82[/C][C]-4.83168868952883[/C][C]-15.7469399421512[/C][C]6.08356256309353[/C][/ROW]
[ROW][C]83[/C][C]-4.83168868952883[/C][C]-16.1313480193475[/C][C]6.46797064028987[/C][/ROW]
[ROW][C]84[/C][C]-4.83168868952883[/C][C]-16.5031021442927[/C][C]6.83972476523506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232315&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232315&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
73-4.83168868952883-11.33448734465491.67110996559728
74-4.83168868952883-11.96092296897252.29754558991485
75-4.83168868952883-12.53659443024232.87321705118466
76-4.83168868952883-13.07214762913683.40877025007912
77-4.83168868952883-13.57495779195553.91158041289787
78-4.83168868952883-14.05038413191844.38700675286075
79-4.83168868952883-14.5024661516374.83908877257934
80-4.83168868952883-14.93433823228275.270960853225
81-4.83168868952883-15.34849042987695.68511305081928
82-4.83168868952883-15.74693994215126.08356256309353
83-4.83168868952883-16.13134801934756.46797064028987
84-4.83168868952883-16.50310214429276.83972476523506



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')