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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 28 May 2008 11:41:08 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/28/t12119965418pl9dsca2pyrtwk.htm/, Retrieved Tue, 14 May 2024 19:13:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13457, Retrieved Tue, 14 May 2024 19:13:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

181

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-28 17:41:08] [88615a9036e6e98ff64037322024b7ad] [Current]

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Dataseries X:

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Boxplots

8,16
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,43
8,68
8,68
8,68
8,68
8,68
8,68
8,68
8,68
8,68
8,68
8,68
8,68
8,92
8,92
8,92
8,92
8,92
8,92
8,92
8,92
8,92
8,92
8,92
8,92
9,3
9,3
9,3
9,3
9,3
9,3
9,3
9,3
9,3
9,3
9,3
9,3
9,6
9,6
9,6
9,6
9,6
9,6
9,6
9,6
9,6
9,6
9,6
9,6
9,9
9,9
9,9
9,9
9,9
9,9
9,9
9,9
9,9
9,9
9,9
9,9
10,2
10,2
10,2
10,2
10,2
10,2
10,2
10,2
10,2
10,2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13457&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13457&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.286867200485029
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.286867200485029 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13457&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.286867200485029[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13457&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
Parameter	Value
alpha	1
beta	0.286867200485029
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	8.43	8.7	-0.270000000000000
4	8.43	8.62254585586904	-0.192545855869042
5	8.43	8.5673107652309	-0.137310765230897
6	8.43	8.52792081041265	-0.0979208104126528
7	8.43	8.49983054166035	-0.06983054166035
8	8.43	8.47979844966589	-0.0497984496658912
9	8.43	8.46551290782174	-0.035512907821742
10	8.43	8.45532541937384	-0.0253254193738357
11	8.43	8.44806038721696	-0.0180603872169556
12	8.43	8.44287945449635	-0.0128794544963515
13	8.43	8.4391847614412	-0.00918476144120817
14	8.43	8.43654995463945	-0.0065499546394463
15	8.68	8.43467098748872	0.245329012511275
16	8.68	8.75504783450559	-0.0750478345055914
17	8.68	8.7335190723185	-0.0535190723185082
18	8.68	8.71816620586994	-0.0381662058699419
19	8.68	8.7072175732389	-0.0272175732388966
20	8.68	8.69940974419986	-0.0194097441998586
21	8.68	8.69384172521911	-0.0138417252191143
22	8.68	8.68987098825562	-0.00987098825562427
23	8.68	8.68703932548871	-0.00703932548871222
24	8.68	8.68501997389246	-0.00501997389246256
25	8.68	8.68357990803542	-0.00357990803542307
26	8.68	8.6825529498393	-0.00255294983930732
27	8.92	8.68182059226593	0.238179407734073
28	8.92	8.99014645217578	-0.0701464521757824
29	8.92	8.97002373581616	-0.0500237358161595
30	8.92	8.95567356676477	-0.0356735667647747
31	8.92	8.94543999053565	-0.0254399905356486
32	8.92	8.93814209167032	-0.0181420916703203
33	8.92	8.93293772062191	-0.0129377206219132
34	8.92	8.92922631292645	-0.00922631292644738
35	8.92	8.92657958636644	-0.0065795863664384
36	8.92	8.92469211884515	-0.0046921188451492
37	8.92	8.9233461038477	-0.00334610384769896
38	8.92	8.92238621640438	-0.00238621640437664
39	9.3	8.9217016891847	0.3782983108153
40	9.3	9.4102230665565	-0.110223066556502
41	9.3	9.37860368402456	-0.0786036840245625
42	9.3	9.35605486524063	-0.0560548652406272
43	9.3	9.33997456297548	-0.0399745629754822
44	9.3	9.3285071720041	-0.0285071720040939
45	9.3	9.32032939937753	-0.0203293993775340
46	9.3	9.31449756149056	-0.0144975614905594
47	9.3	9.3103386866119	-0.0103386866119024
48	9.3	9.30737285652686	-0.00737285652685493
49	9.3	9.30525782581542	-0.00525782581541812
50	9.3	9.30374952804311	-0.00374952804311057
51	9.6	9.30267391143024	0.297326088569756
52	9.6	9.68796701408941	-0.0879670140894131
53	9.6	9.66273216302256	-0.0627321630225559
54	9.6	9.6447363630359	-0.0447363630359057
55	9.6	9.63190296781191	-0.0319029678119129
56	9.6	9.62275105274855	-0.0227510527485464
57	9.6	9.61622452193848	-0.0162245219384829
58	9.6	9.61157023875078	-0.0115702387507817
59	9.6	9.6082511167514	-0.00825111675140278
60	9.6	9.60588414198805	-0.00588414198805154
61	9.6	9.60419617464868	-0.00419617464868338
62	9.6	9.60299242977447	-0.00299242977446923
63	9.9	9.60213399982242	0.297866000177581
64	9.9	9.98758198541304	-0.0875819854130349
65	9.9	9.96245758644468	-0.0624575864446779
66	9.9	9.94454055347224	-0.0445405534722401
67	9.9	9.9317633295896	-0.0317633295896051
68	9.9	9.92265147215215	-0.0226514721521518
69	9.9	9.916153507749	-0.0161535077489994
70	9.9	9.91151959620303	-0.0115195962030317
71	9.9	9.90821500188955	-0.00821500188954971
72	9.9	9.90585838729552	-0.00585838729551469
73	9.9	9.9041778081327	-0.00417780813269353
74	9.9	9.9029793320095	-0.00297933200950418
75	10.2	9.90212465937662	0.297875340623376
76	10.2	10.2875753244348	-0.0875753244347752
77	10.2	10.2624528362826	-0.0624528362826027
78	10.2	10.2445371659759	-0.0445371659758624
79	10.2	10.2317609138548	-0.0317609138548303
80	10.2	10.2226497494124	-0.022649749412448
81	10.2	10.2161522792068	-0.0161522792068123
82	10.2	10.2115187200893	-0.0115187200893008
83	10.2	10.2082143771041	-0.0082143771041121
84	10.2	10.2058579417405	-0.005857941740528

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.43 & 8.7 & -0.270000000000000 \tabularnewline
4 & 8.43 & 8.62254585586904 & -0.192545855869042 \tabularnewline
5 & 8.43 & 8.5673107652309 & -0.137310765230897 \tabularnewline
6 & 8.43 & 8.52792081041265 & -0.0979208104126528 \tabularnewline
7 & 8.43 & 8.49983054166035 & -0.06983054166035 \tabularnewline
8 & 8.43 & 8.47979844966589 & -0.0497984496658912 \tabularnewline
9 & 8.43 & 8.46551290782174 & -0.035512907821742 \tabularnewline
10 & 8.43 & 8.45532541937384 & -0.0253254193738357 \tabularnewline
11 & 8.43 & 8.44806038721696 & -0.0180603872169556 \tabularnewline
12 & 8.43 & 8.44287945449635 & -0.0128794544963515 \tabularnewline
13 & 8.43 & 8.4391847614412 & -0.00918476144120817 \tabularnewline
14 & 8.43 & 8.43654995463945 & -0.0065499546394463 \tabularnewline
15 & 8.68 & 8.43467098748872 & 0.245329012511275 \tabularnewline
16 & 8.68 & 8.75504783450559 & -0.0750478345055914 \tabularnewline
17 & 8.68 & 8.7335190723185 & -0.0535190723185082 \tabularnewline
18 & 8.68 & 8.71816620586994 & -0.0381662058699419 \tabularnewline
19 & 8.68 & 8.7072175732389 & -0.0272175732388966 \tabularnewline
20 & 8.68 & 8.69940974419986 & -0.0194097441998586 \tabularnewline
21 & 8.68 & 8.69384172521911 & -0.0138417252191143 \tabularnewline
22 & 8.68 & 8.68987098825562 & -0.00987098825562427 \tabularnewline
23 & 8.68 & 8.68703932548871 & -0.00703932548871222 \tabularnewline
24 & 8.68 & 8.68501997389246 & -0.00501997389246256 \tabularnewline
25 & 8.68 & 8.68357990803542 & -0.00357990803542307 \tabularnewline
26 & 8.68 & 8.6825529498393 & -0.00255294983930732 \tabularnewline
27 & 8.92 & 8.68182059226593 & 0.238179407734073 \tabularnewline
28 & 8.92 & 8.99014645217578 & -0.0701464521757824 \tabularnewline
29 & 8.92 & 8.97002373581616 & -0.0500237358161595 \tabularnewline
30 & 8.92 & 8.95567356676477 & -0.0356735667647747 \tabularnewline
31 & 8.92 & 8.94543999053565 & -0.0254399905356486 \tabularnewline
32 & 8.92 & 8.93814209167032 & -0.0181420916703203 \tabularnewline
33 & 8.92 & 8.93293772062191 & -0.0129377206219132 \tabularnewline
34 & 8.92 & 8.92922631292645 & -0.00922631292644738 \tabularnewline
35 & 8.92 & 8.92657958636644 & -0.0065795863664384 \tabularnewline
36 & 8.92 & 8.92469211884515 & -0.0046921188451492 \tabularnewline
37 & 8.92 & 8.9233461038477 & -0.00334610384769896 \tabularnewline
38 & 8.92 & 8.92238621640438 & -0.00238621640437664 \tabularnewline
39 & 9.3 & 8.9217016891847 & 0.3782983108153 \tabularnewline
40 & 9.3 & 9.4102230665565 & -0.110223066556502 \tabularnewline
41 & 9.3 & 9.37860368402456 & -0.0786036840245625 \tabularnewline
42 & 9.3 & 9.35605486524063 & -0.0560548652406272 \tabularnewline
43 & 9.3 & 9.33997456297548 & -0.0399745629754822 \tabularnewline
44 & 9.3 & 9.3285071720041 & -0.0285071720040939 \tabularnewline
45 & 9.3 & 9.32032939937753 & -0.0203293993775340 \tabularnewline
46 & 9.3 & 9.31449756149056 & -0.0144975614905594 \tabularnewline
47 & 9.3 & 9.3103386866119 & -0.0103386866119024 \tabularnewline
48 & 9.3 & 9.30737285652686 & -0.00737285652685493 \tabularnewline
49 & 9.3 & 9.30525782581542 & -0.00525782581541812 \tabularnewline
50 & 9.3 & 9.30374952804311 & -0.00374952804311057 \tabularnewline
51 & 9.6 & 9.30267391143024 & 0.297326088569756 \tabularnewline
52 & 9.6 & 9.68796701408941 & -0.0879670140894131 \tabularnewline
53 & 9.6 & 9.66273216302256 & -0.0627321630225559 \tabularnewline
54 & 9.6 & 9.6447363630359 & -0.0447363630359057 \tabularnewline
55 & 9.6 & 9.63190296781191 & -0.0319029678119129 \tabularnewline
56 & 9.6 & 9.62275105274855 & -0.0227510527485464 \tabularnewline
57 & 9.6 & 9.61622452193848 & -0.0162245219384829 \tabularnewline
58 & 9.6 & 9.61157023875078 & -0.0115702387507817 \tabularnewline
59 & 9.6 & 9.6082511167514 & -0.00825111675140278 \tabularnewline
60 & 9.6 & 9.60588414198805 & -0.00588414198805154 \tabularnewline
61 & 9.6 & 9.60419617464868 & -0.00419617464868338 \tabularnewline
62 & 9.6 & 9.60299242977447 & -0.00299242977446923 \tabularnewline
63 & 9.9 & 9.60213399982242 & 0.297866000177581 \tabularnewline
64 & 9.9 & 9.98758198541304 & -0.0875819854130349 \tabularnewline
65 & 9.9 & 9.96245758644468 & -0.0624575864446779 \tabularnewline
66 & 9.9 & 9.94454055347224 & -0.0445405534722401 \tabularnewline
67 & 9.9 & 9.9317633295896 & -0.0317633295896051 \tabularnewline
68 & 9.9 & 9.92265147215215 & -0.0226514721521518 \tabularnewline
69 & 9.9 & 9.916153507749 & -0.0161535077489994 \tabularnewline
70 & 9.9 & 9.91151959620303 & -0.0115195962030317 \tabularnewline
71 & 9.9 & 9.90821500188955 & -0.00821500188954971 \tabularnewline
72 & 9.9 & 9.90585838729552 & -0.00585838729551469 \tabularnewline
73 & 9.9 & 9.9041778081327 & -0.00417780813269353 \tabularnewline
74 & 9.9 & 9.9029793320095 & -0.00297933200950418 \tabularnewline
75 & 10.2 & 9.90212465937662 & 0.297875340623376 \tabularnewline
76 & 10.2 & 10.2875753244348 & -0.0875753244347752 \tabularnewline
77 & 10.2 & 10.2624528362826 & -0.0624528362826027 \tabularnewline
78 & 10.2 & 10.2445371659759 & -0.0445371659758624 \tabularnewline
79 & 10.2 & 10.2317609138548 & -0.0317609138548303 \tabularnewline
80 & 10.2 & 10.2226497494124 & -0.022649749412448 \tabularnewline
81 & 10.2 & 10.2161522792068 & -0.0161522792068123 \tabularnewline
82 & 10.2 & 10.2115187200893 & -0.0115187200893008 \tabularnewline
83 & 10.2 & 10.2082143771041 & -0.0082143771041121 \tabularnewline
84 & 10.2 & 10.2058579417405 & -0.005857941740528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13457&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]8.43[/C][C]8.7[/C][C]-0.270000000000000[/C][/ROW]
[ROW][C]4[/C][C]8.43[/C][C]8.62254585586904[/C][C]-0.192545855869042[/C][/ROW]
[ROW][C]5[/C][C]8.43[/C][C]8.5673107652309[/C][C]-0.137310765230897[/C][/ROW]
[ROW][C]6[/C][C]8.43[/C][C]8.52792081041265[/C][C]-0.0979208104126528[/C][/ROW]
[ROW][C]7[/C][C]8.43[/C][C]8.49983054166035[/C][C]-0.06983054166035[/C][/ROW]
[ROW][C]8[/C][C]8.43[/C][C]8.47979844966589[/C][C]-0.0497984496658912[/C][/ROW]
[ROW][C]9[/C][C]8.43[/C][C]8.46551290782174[/C][C]-0.035512907821742[/C][/ROW]
[ROW][C]10[/C][C]8.43[/C][C]8.45532541937384[/C][C]-0.0253254193738357[/C][/ROW]
[ROW][C]11[/C][C]8.43[/C][C]8.44806038721696[/C][C]-0.0180603872169556[/C][/ROW]
[ROW][C]12[/C][C]8.43[/C][C]8.44287945449635[/C][C]-0.0128794544963515[/C][/ROW]
[ROW][C]13[/C][C]8.43[/C][C]8.4391847614412[/C][C]-0.00918476144120817[/C][/ROW]
[ROW][C]14[/C][C]8.43[/C][C]8.43654995463945[/C][C]-0.0065499546394463[/C][/ROW]
[ROW][C]15[/C][C]8.68[/C][C]8.43467098748872[/C][C]0.245329012511275[/C][/ROW]
[ROW][C]16[/C][C]8.68[/C][C]8.75504783450559[/C][C]-0.0750478345055914[/C][/ROW]
[ROW][C]17[/C][C]8.68[/C][C]8.7335190723185[/C][C]-0.0535190723185082[/C][/ROW]
[ROW][C]18[/C][C]8.68[/C][C]8.71816620586994[/C][C]-0.0381662058699419[/C][/ROW]
[ROW][C]19[/C][C]8.68[/C][C]8.7072175732389[/C][C]-0.0272175732388966[/C][/ROW]
[ROW][C]20[/C][C]8.68[/C][C]8.69940974419986[/C][C]-0.0194097441998586[/C][/ROW]
[ROW][C]21[/C][C]8.68[/C][C]8.69384172521911[/C][C]-0.0138417252191143[/C][/ROW]
[ROW][C]22[/C][C]8.68[/C][C]8.68987098825562[/C][C]-0.00987098825562427[/C][/ROW]
[ROW][C]23[/C][C]8.68[/C][C]8.68703932548871[/C][C]-0.00703932548871222[/C][/ROW]
[ROW][C]24[/C][C]8.68[/C][C]8.68501997389246[/C][C]-0.00501997389246256[/C][/ROW]
[ROW][C]25[/C][C]8.68[/C][C]8.68357990803542[/C][C]-0.00357990803542307[/C][/ROW]
[ROW][C]26[/C][C]8.68[/C][C]8.6825529498393[/C][C]-0.00255294983930732[/C][/ROW]
[ROW][C]27[/C][C]8.92[/C][C]8.68182059226593[/C][C]0.238179407734073[/C][/ROW]
[ROW][C]28[/C][C]8.92[/C][C]8.99014645217578[/C][C]-0.0701464521757824[/C][/ROW]
[ROW][C]29[/C][C]8.92[/C][C]8.97002373581616[/C][C]-0.0500237358161595[/C][/ROW]
[ROW][C]30[/C][C]8.92[/C][C]8.95567356676477[/C][C]-0.0356735667647747[/C][/ROW]
[ROW][C]31[/C][C]8.92[/C][C]8.94543999053565[/C][C]-0.0254399905356486[/C][/ROW]
[ROW][C]32[/C][C]8.92[/C][C]8.93814209167032[/C][C]-0.0181420916703203[/C][/ROW]
[ROW][C]33[/C][C]8.92[/C][C]8.93293772062191[/C][C]-0.0129377206219132[/C][/ROW]
[ROW][C]34[/C][C]8.92[/C][C]8.92922631292645[/C][C]-0.00922631292644738[/C][/ROW]
[ROW][C]35[/C][C]8.92[/C][C]8.92657958636644[/C][C]-0.0065795863664384[/C][/ROW]
[ROW][C]36[/C][C]8.92[/C][C]8.92469211884515[/C][C]-0.0046921188451492[/C][/ROW]
[ROW][C]37[/C][C]8.92[/C][C]8.9233461038477[/C][C]-0.00334610384769896[/C][/ROW]
[ROW][C]38[/C][C]8.92[/C][C]8.92238621640438[/C][C]-0.00238621640437664[/C][/ROW]
[ROW][C]39[/C][C]9.3[/C][C]8.9217016891847[/C][C]0.3782983108153[/C][/ROW]
[ROW][C]40[/C][C]9.3[/C][C]9.4102230665565[/C][C]-0.110223066556502[/C][/ROW]
[ROW][C]41[/C][C]9.3[/C][C]9.37860368402456[/C][C]-0.0786036840245625[/C][/ROW]
[ROW][C]42[/C][C]9.3[/C][C]9.35605486524063[/C][C]-0.0560548652406272[/C][/ROW]
[ROW][C]43[/C][C]9.3[/C][C]9.33997456297548[/C][C]-0.0399745629754822[/C][/ROW]
[ROW][C]44[/C][C]9.3[/C][C]9.3285071720041[/C][C]-0.0285071720040939[/C][/ROW]
[ROW][C]45[/C][C]9.3[/C][C]9.32032939937753[/C][C]-0.0203293993775340[/C][/ROW]
[ROW][C]46[/C][C]9.3[/C][C]9.31449756149056[/C][C]-0.0144975614905594[/C][/ROW]
[ROW][C]47[/C][C]9.3[/C][C]9.3103386866119[/C][C]-0.0103386866119024[/C][/ROW]
[ROW][C]48[/C][C]9.3[/C][C]9.30737285652686[/C][C]-0.00737285652685493[/C][/ROW]
[ROW][C]49[/C][C]9.3[/C][C]9.30525782581542[/C][C]-0.00525782581541812[/C][/ROW]
[ROW][C]50[/C][C]9.3[/C][C]9.30374952804311[/C][C]-0.00374952804311057[/C][/ROW]
[ROW][C]51[/C][C]9.6[/C][C]9.30267391143024[/C][C]0.297326088569756[/C][/ROW]
[ROW][C]52[/C][C]9.6[/C][C]9.68796701408941[/C][C]-0.0879670140894131[/C][/ROW]
[ROW][C]53[/C][C]9.6[/C][C]9.66273216302256[/C][C]-0.0627321630225559[/C][/ROW]
[ROW][C]54[/C][C]9.6[/C][C]9.6447363630359[/C][C]-0.0447363630359057[/C][/ROW]
[ROW][C]55[/C][C]9.6[/C][C]9.63190296781191[/C][C]-0.0319029678119129[/C][/ROW]
[ROW][C]56[/C][C]9.6[/C][C]9.62275105274855[/C][C]-0.0227510527485464[/C][/ROW]
[ROW][C]57[/C][C]9.6[/C][C]9.61622452193848[/C][C]-0.0162245219384829[/C][/ROW]
[ROW][C]58[/C][C]9.6[/C][C]9.61157023875078[/C][C]-0.0115702387507817[/C][/ROW]
[ROW][C]59[/C][C]9.6[/C][C]9.6082511167514[/C][C]-0.00825111675140278[/C][/ROW]
[ROW][C]60[/C][C]9.6[/C][C]9.60588414198805[/C][C]-0.00588414198805154[/C][/ROW]
[ROW][C]61[/C][C]9.6[/C][C]9.60419617464868[/C][C]-0.00419617464868338[/C][/ROW]
[ROW][C]62[/C][C]9.6[/C][C]9.60299242977447[/C][C]-0.00299242977446923[/C][/ROW]
[ROW][C]63[/C][C]9.9[/C][C]9.60213399982242[/C][C]0.297866000177581[/C][/ROW]
[ROW][C]64[/C][C]9.9[/C][C]9.98758198541304[/C][C]-0.0875819854130349[/C][/ROW]
[ROW][C]65[/C][C]9.9[/C][C]9.96245758644468[/C][C]-0.0624575864446779[/C][/ROW]
[ROW][C]66[/C][C]9.9[/C][C]9.94454055347224[/C][C]-0.0445405534722401[/C][/ROW]
[ROW][C]67[/C][C]9.9[/C][C]9.9317633295896[/C][C]-0.0317633295896051[/C][/ROW]
[ROW][C]68[/C][C]9.9[/C][C]9.92265147215215[/C][C]-0.0226514721521518[/C][/ROW]
[ROW][C]69[/C][C]9.9[/C][C]9.916153507749[/C][C]-0.0161535077489994[/C][/ROW]
[ROW][C]70[/C][C]9.9[/C][C]9.91151959620303[/C][C]-0.0115195962030317[/C][/ROW]
[ROW][C]71[/C][C]9.9[/C][C]9.90821500188955[/C][C]-0.00821500188954971[/C][/ROW]
[ROW][C]72[/C][C]9.9[/C][C]9.90585838729552[/C][C]-0.00585838729551469[/C][/ROW]
[ROW][C]73[/C][C]9.9[/C][C]9.9041778081327[/C][C]-0.00417780813269353[/C][/ROW]
[ROW][C]74[/C][C]9.9[/C][C]9.9029793320095[/C][C]-0.00297933200950418[/C][/ROW]
[ROW][C]75[/C][C]10.2[/C][C]9.90212465937662[/C][C]0.297875340623376[/C][/ROW]
[ROW][C]76[/C][C]10.2[/C][C]10.2875753244348[/C][C]-0.0875753244347752[/C][/ROW]
[ROW][C]77[/C][C]10.2[/C][C]10.2624528362826[/C][C]-0.0624528362826027[/C][/ROW]
[ROW][C]78[/C][C]10.2[/C][C]10.2445371659759[/C][C]-0.0445371659758624[/C][/ROW]
[ROW][C]79[/C][C]10.2[/C][C]10.2317609138548[/C][C]-0.0317609138548303[/C][/ROW]
[ROW][C]80[/C][C]10.2[/C][C]10.2226497494124[/C][C]-0.022649749412448[/C][/ROW]
[ROW][C]81[/C][C]10.2[/C][C]10.2161522792068[/C][C]-0.0161522792068123[/C][/ROW]
[ROW][C]82[/C][C]10.2[/C][C]10.2115187200893[/C][C]-0.0115187200893008[/C][/ROW]
[ROW][C]83[/C][C]10.2[/C][C]10.2082143771041[/C][C]-0.0082143771041121[/C][/ROW]
[ROW][C]84[/C][C]10.2[/C][C]10.2058579417405[/C][C]-0.005857941740528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13457&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13457&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
t	Observed	Fitted	Residuals
3	8.43	8.7	-0.270000000000000
4	8.43	8.62254585586904	-0.192545855869042
5	8.43	8.5673107652309	-0.137310765230897
6	8.43	8.52792081041265	-0.0979208104126528
7	8.43	8.49983054166035	-0.06983054166035
8	8.43	8.47979844966589	-0.0497984496658912
9	8.43	8.46551290782174	-0.035512907821742
10	8.43	8.45532541937384	-0.0253254193738357
11	8.43	8.44806038721696	-0.0180603872169556
12	8.43	8.44287945449635	-0.0128794544963515
13	8.43	8.4391847614412	-0.00918476144120817
14	8.43	8.43654995463945	-0.0065499546394463
15	8.68	8.43467098748872	0.245329012511275
16	8.68	8.75504783450559	-0.0750478345055914
17	8.68	8.7335190723185	-0.0535190723185082
18	8.68	8.71816620586994	-0.0381662058699419
19	8.68	8.7072175732389	-0.0272175732388966
20	8.68	8.69940974419986	-0.0194097441998586
21	8.68	8.69384172521911	-0.0138417252191143
22	8.68	8.68987098825562	-0.00987098825562427
23	8.68	8.68703932548871	-0.00703932548871222
24	8.68	8.68501997389246	-0.00501997389246256
25	8.68	8.68357990803542	-0.00357990803542307
26	8.68	8.6825529498393	-0.00255294983930732
27	8.92	8.68182059226593	0.238179407734073
28	8.92	8.99014645217578	-0.0701464521757824
29	8.92	8.97002373581616	-0.0500237358161595
30	8.92	8.95567356676477	-0.0356735667647747
31	8.92	8.94543999053565	-0.0254399905356486
32	8.92	8.93814209167032	-0.0181420916703203
33	8.92	8.93293772062191	-0.0129377206219132
34	8.92	8.92922631292645	-0.00922631292644738
35	8.92	8.92657958636644	-0.0065795863664384
36	8.92	8.92469211884515	-0.0046921188451492
37	8.92	8.9233461038477	-0.00334610384769896
38	8.92	8.92238621640438	-0.00238621640437664
39	9.3	8.9217016891847	0.3782983108153
40	9.3	9.4102230665565	-0.110223066556502
41	9.3	9.37860368402456	-0.0786036840245625
42	9.3	9.35605486524063	-0.0560548652406272
43	9.3	9.33997456297548	-0.0399745629754822
44	9.3	9.3285071720041	-0.0285071720040939
45	9.3	9.32032939937753	-0.0203293993775340
46	9.3	9.31449756149056	-0.0144975614905594
47	9.3	9.3103386866119	-0.0103386866119024
48	9.3	9.30737285652686	-0.00737285652685493
49	9.3	9.30525782581542	-0.00525782581541812
50	9.3	9.30374952804311	-0.00374952804311057
51	9.6	9.30267391143024	0.297326088569756
52	9.6	9.68796701408941	-0.0879670140894131
53	9.6	9.66273216302256	-0.0627321630225559
54	9.6	9.6447363630359	-0.0447363630359057
55	9.6	9.63190296781191	-0.0319029678119129
56	9.6	9.62275105274855	-0.0227510527485464
57	9.6	9.61622452193848	-0.0162245219384829
58	9.6	9.61157023875078	-0.0115702387507817
59	9.6	9.6082511167514	-0.00825111675140278
60	9.6	9.60588414198805	-0.00588414198805154
61	9.6	9.60419617464868	-0.00419617464868338
62	9.6	9.60299242977447	-0.00299242977446923
63	9.9	9.60213399982242	0.297866000177581
64	9.9	9.98758198541304	-0.0875819854130349
65	9.9	9.96245758644468	-0.0624575864446779
66	9.9	9.94454055347224	-0.0445405534722401
67	9.9	9.9317633295896	-0.0317633295896051
68	9.9	9.92265147215215	-0.0226514721521518
69	9.9	9.916153507749	-0.0161535077489994
70	9.9	9.91151959620303	-0.0115195962030317
71	9.9	9.90821500188955	-0.00821500188954971
72	9.9	9.90585838729552	-0.00585838729551469
73	9.9	9.9041778081327	-0.00417780813269353
74	9.9	9.9029793320095	-0.00297933200950418
75	10.2	9.90212465937662	0.297875340623376
76	10.2	10.2875753244348	-0.0875753244347752
77	10.2	10.2624528362826	-0.0624528362826027
78	10.2	10.2445371659759	-0.0445371659758624
79	10.2	10.2317609138548	-0.0317609138548303
80	10.2	10.2226497494124	-0.022649749412448
81	10.2	10.2161522792068	-0.0161522792068123
82	10.2	10.2115187200893	-0.0115187200893008
83	10.2	10.2082143771041	-0.0082143771041121
84	10.2	10.2058579417405	-0.005857941740528

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	10.2041774903928	10.0147294817858	10.3936254989998
86	10.2083549807856	9.89960545233274	10.5171045092385
87	10.2125324711785	9.78333061101376	10.6417343313431
88	10.2167099615713	9.6613168476271	10.7721030755154
89	10.2208874519641	9.5324289123498	10.9093459915784
90	10.2250649423569	9.3964140793711	11.0537158053427
91	10.2292424327497	9.25331730570405	11.2051675597954
92	10.2334199231425	9.10329381067171	11.3635460356134
93	10.2375974135354	8.94653782974394	11.5286569973268
94	10.2417749039282	8.78325292029629	11.7002968875601
95	10.245952394321	8.61363910321953	11.8782656854225
96	10.2501298847138	8.43788739919723	12.0623723702304

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 10.2041774903928 & 10.0147294817858 & 10.3936254989998 \tabularnewline
86 & 10.2083549807856 & 9.89960545233274 & 10.5171045092385 \tabularnewline
87 & 10.2125324711785 & 9.78333061101376 & 10.6417343313431 \tabularnewline
88 & 10.2167099615713 & 9.6613168476271 & 10.7721030755154 \tabularnewline
89 & 10.2208874519641 & 9.5324289123498 & 10.9093459915784 \tabularnewline
90 & 10.2250649423569 & 9.3964140793711 & 11.0537158053427 \tabularnewline
91 & 10.2292424327497 & 9.25331730570405 & 11.2051675597954 \tabularnewline
92 & 10.2334199231425 & 9.10329381067171 & 11.3635460356134 \tabularnewline
93 & 10.2375974135354 & 8.94653782974394 & 11.5286569973268 \tabularnewline
94 & 10.2417749039282 & 8.78325292029629 & 11.7002968875601 \tabularnewline
95 & 10.245952394321 & 8.61363910321953 & 11.8782656854225 \tabularnewline
96 & 10.2501298847138 & 8.43788739919723 & 12.0623723702304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13457&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]10.2041774903928[/C][C]10.0147294817858[/C][C]10.3936254989998[/C][/ROW]
[ROW][C]86[/C][C]10.2083549807856[/C][C]9.89960545233274[/C][C]10.5171045092385[/C][/ROW]
[ROW][C]87[/C][C]10.2125324711785[/C][C]9.78333061101376[/C][C]10.6417343313431[/C][/ROW]
[ROW][C]88[/C][C]10.2167099615713[/C][C]9.6613168476271[/C][C]10.7721030755154[/C][/ROW]
[ROW][C]89[/C][C]10.2208874519641[/C][C]9.5324289123498[/C][C]10.9093459915784[/C][/ROW]
[ROW][C]90[/C][C]10.2250649423569[/C][C]9.3964140793711[/C][C]11.0537158053427[/C][/ROW]
[ROW][C]91[/C][C]10.2292424327497[/C][C]9.25331730570405[/C][C]11.2051675597954[/C][/ROW]
[ROW][C]92[/C][C]10.2334199231425[/C][C]9.10329381067171[/C][C]11.3635460356134[/C][/ROW]
[ROW][C]93[/C][C]10.2375974135354[/C][C]8.94653782974394[/C][C]11.5286569973268[/C][/ROW]
[ROW][C]94[/C][C]10.2417749039282[/C][C]8.78325292029629[/C][C]11.7002968875601[/C][/ROW]
[ROW][C]95[/C][C]10.245952394321[/C][C]8.61363910321953[/C][C]11.8782656854225[/C][/ROW]
[ROW][C]96[/C][C]10.2501298847138[/C][C]8.43788739919723[/C][C]12.0623723702304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13457&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13457&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
t	Forecast	95% Lower Bound	95% Upper Bound
85	10.2041774903928	10.0147294817858	10.3936254989998
86	10.2083549807856	9.89960545233274	10.5171045092385
87	10.2125324711785	9.78333061101376	10.6417343313431
88	10.2167099615713	9.6613168476271	10.7721030755154
89	10.2208874519641	9.5324289123498	10.9093459915784
90	10.2250649423569	9.3964140793711	11.0537158053427
91	10.2292424327497	9.25331730570405	11.2051675597954
92	10.2334199231425	9.10329381067171	11.3635460356134
93	10.2375974135354	8.94653782974394	11.5286569973268
94	10.2417749039282	8.78325292029629	11.7002968875601
95	10.245952394321	8.61363910321953	11.8782656854225
96	10.2501298847138	8.43788739919723	12.0623723702304

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code