Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 22 Dec 2011 11:47:54 -0500

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/2011/Dec/22/t1324572529q41enzfdlmb83hy.htm/, Retrieved Fri, 03 May 2024 09:56:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159714, Retrieved Fri, 03 May 2024 09:56:06 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

115

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

-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-22 13:45:12] [5a05da414fd67612c3b80d44effe0727]
- RM D    [(Partial) Autocorrelation Function] [] [2011-12-22 15:18:49] [5a05da414fd67612c3b80d44effe0727]
- R         [(Partial) Autocorrelation Function] [] [2011-12-22 15:20:17] [5a05da414fd67612c3b80d44effe0727]
-             [(Partial) Autocorrelation Function] [] [2011-12-22 15:29:46] [5a05da414fd67612c3b80d44effe0727]
- RM              [Exponential Smoothing] [] [2011-12-22 16:47:54] [95610e892c4b5c84ff80f4c898567a9d] [Current]
- RM                [Classical Decomposition] [] [2011-12-22 16:54:59] [5a05da414fd67612c3b80d44effe0727] 
- RM                  [Decomposition by Loess] [] [2011-12-22 17:21:01] [5a05da414fd67612c3b80d44effe0727] 
- RM                  [Structural Time Series Models] [] [2011-12-22 18:01:39] [5a05da414fd67612c3b80d44effe0727] 
- RM D                [Kendall tau Correlation Matrix] [] [2011-12-22 19:00:08] [5a05da414fd67612c3b80d44effe0727] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8.0
8.0
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9
6.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=159714&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=159714&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159714&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.783408091932541
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.783408091932541 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159714&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]0.783408091932541[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159714&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159714&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	0.783408091932541
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	7	7.55016025641025	-0.550160256410255
14	7.2	7.35511597063449	-0.15511597063449
15	7.3	7.29455257500717	0.00544742499282869
16	7.1	7.00560917611579	0.0943908238842059
17	6.8	6.6738447556399	0.126155244360096
18	6.4	6.29613150586704	0.10386849413296
19	6.1	7.07595863562336	-0.97595863562336
20	6.5	5.81817378737362	0.68182621262638
21	7.7	6.65077767059255	1.04922232940745
22	7.9	7.2795359779757	0.620464022024299
23	7.5	7.48906822453826	0.0109317754617422
24	6.9	7.55025464351655	-0.650254643516553
25	6.6	6.99513534524591	-0.395135345245908
26	6.9	7.00710222495474	-0.107102224954736
27	7.7	7.01892991844164	0.681070081558361
28	8	7.27853919627255	0.721460803727452
29	8	7.44490638865336	0.555093611346638
30	7.7	7.39839979676177	0.301600203238233
31	7.3	8.09924972904588	-0.79924972904588
32	7.4	7.33896285157322	0.0610371484267755
33	8.1	7.76481058446515	0.335189415534853
34	8.3	7.74132414931844	0.558675850681557
35	8.1	7.77043129015375	0.329568709846247
36	7.9	7.93803283384265	-0.0380328338426486
37	7.9	7.91778983092539	-0.0177898309253939
38	8.3	8.28775788311785	0.0122421168821525
39	8.6	8.56379264347973	0.036207356520265
40	8.7	8.32695954791296	0.373040452087043
41	8.5	8.18433762978711	0.315662370212895
42	8.3	7.89535404518516	0.404645954814838
43	8	8.43849566576431	-0.438495665764307
44	8	8.14715761694118	-0.147157616941179
45	8.8	8.46928304857981	0.330716951420193
46	8.7	8.49069820227042	0.209301797729578
47	8.5	8.19648013012648	0.303519869873517
48	8.1	8.26405528203917	-0.164055282039167
49	7.8	8.14946974406647	-0.349469744066474
50	7.6	8.26610174525134	-0.666101745251344
51	7.4	8.01590711188559	-0.615907111885589
52	7.1	7.34115758777246	-0.241157587772457
53	6.9	6.7049403269372	0.195059673062804
54	6.7	6.3407487378546	0.359251262145401
55	6.6	6.66571013649339	-0.0657101364933901
56	6.5	6.7295167517437	-0.229516751743705
57	7.1	7.09062513531177	0.00937486468822524
58	7.2	6.83400075817192	0.36599924182808
59	6.9	6.68294760373999	0.217052396260013
60	6.7	6.58151044281719	0.118489557182813

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7 & 7.55016025641025 & -0.550160256410255 \tabularnewline
14 & 7.2 & 7.35511597063449 & -0.15511597063449 \tabularnewline
15 & 7.3 & 7.29455257500717 & 0.00544742499282869 \tabularnewline
16 & 7.1 & 7.00560917611579 & 0.0943908238842059 \tabularnewline
17 & 6.8 & 6.6738447556399 & 0.126155244360096 \tabularnewline
18 & 6.4 & 6.29613150586704 & 0.10386849413296 \tabularnewline
19 & 6.1 & 7.07595863562336 & -0.97595863562336 \tabularnewline
20 & 6.5 & 5.81817378737362 & 0.68182621262638 \tabularnewline
21 & 7.7 & 6.65077767059255 & 1.04922232940745 \tabularnewline
22 & 7.9 & 7.2795359779757 & 0.620464022024299 \tabularnewline
23 & 7.5 & 7.48906822453826 & 0.0109317754617422 \tabularnewline
24 & 6.9 & 7.55025464351655 & -0.650254643516553 \tabularnewline
25 & 6.6 & 6.99513534524591 & -0.395135345245908 \tabularnewline
26 & 6.9 & 7.00710222495474 & -0.107102224954736 \tabularnewline
27 & 7.7 & 7.01892991844164 & 0.681070081558361 \tabularnewline
28 & 8 & 7.27853919627255 & 0.721460803727452 \tabularnewline
29 & 8 & 7.44490638865336 & 0.555093611346638 \tabularnewline
30 & 7.7 & 7.39839979676177 & 0.301600203238233 \tabularnewline
31 & 7.3 & 8.09924972904588 & -0.79924972904588 \tabularnewline
32 & 7.4 & 7.33896285157322 & 0.0610371484267755 \tabularnewline
33 & 8.1 & 7.76481058446515 & 0.335189415534853 \tabularnewline
34 & 8.3 & 7.74132414931844 & 0.558675850681557 \tabularnewline
35 & 8.1 & 7.77043129015375 & 0.329568709846247 \tabularnewline
36 & 7.9 & 7.93803283384265 & -0.0380328338426486 \tabularnewline
37 & 7.9 & 7.91778983092539 & -0.0177898309253939 \tabularnewline
38 & 8.3 & 8.28775788311785 & 0.0122421168821525 \tabularnewline
39 & 8.6 & 8.56379264347973 & 0.036207356520265 \tabularnewline
40 & 8.7 & 8.32695954791296 & 0.373040452087043 \tabularnewline
41 & 8.5 & 8.18433762978711 & 0.315662370212895 \tabularnewline
42 & 8.3 & 7.89535404518516 & 0.404645954814838 \tabularnewline
43 & 8 & 8.43849566576431 & -0.438495665764307 \tabularnewline
44 & 8 & 8.14715761694118 & -0.147157616941179 \tabularnewline
45 & 8.8 & 8.46928304857981 & 0.330716951420193 \tabularnewline
46 & 8.7 & 8.49069820227042 & 0.209301797729578 \tabularnewline
47 & 8.5 & 8.19648013012648 & 0.303519869873517 \tabularnewline
48 & 8.1 & 8.26405528203917 & -0.164055282039167 \tabularnewline
49 & 7.8 & 8.14946974406647 & -0.349469744066474 \tabularnewline
50 & 7.6 & 8.26610174525134 & -0.666101745251344 \tabularnewline
51 & 7.4 & 8.01590711188559 & -0.615907111885589 \tabularnewline
52 & 7.1 & 7.34115758777246 & -0.241157587772457 \tabularnewline
53 & 6.9 & 6.7049403269372 & 0.195059673062804 \tabularnewline
54 & 6.7 & 6.3407487378546 & 0.359251262145401 \tabularnewline
55 & 6.6 & 6.66571013649339 & -0.0657101364933901 \tabularnewline
56 & 6.5 & 6.7295167517437 & -0.229516751743705 \tabularnewline
57 & 7.1 & 7.09062513531177 & 0.00937486468822524 \tabularnewline
58 & 7.2 & 6.83400075817192 & 0.36599924182808 \tabularnewline
59 & 6.9 & 6.68294760373999 & 0.217052396260013 \tabularnewline
60 & 6.7 & 6.58151044281719 & 0.118489557182813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159714&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]13[/C][C]7[/C][C]7.55016025641025[/C][C]-0.550160256410255[/C][/ROW]
[ROW][C]14[/C][C]7.2[/C][C]7.35511597063449[/C][C]-0.15511597063449[/C][/ROW]
[ROW][C]15[/C][C]7.3[/C][C]7.29455257500717[/C][C]0.00544742499282869[/C][/ROW]
[ROW][C]16[/C][C]7.1[/C][C]7.00560917611579[/C][C]0.0943908238842059[/C][/ROW]
[ROW][C]17[/C][C]6.8[/C][C]6.6738447556399[/C][C]0.126155244360096[/C][/ROW]
[ROW][C]18[/C][C]6.4[/C][C]6.29613150586704[/C][C]0.10386849413296[/C][/ROW]
[ROW][C]19[/C][C]6.1[/C][C]7.07595863562336[/C][C]-0.97595863562336[/C][/ROW]
[ROW][C]20[/C][C]6.5[/C][C]5.81817378737362[/C][C]0.68182621262638[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]6.65077767059255[/C][C]1.04922232940745[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.2795359779757[/C][C]0.620464022024299[/C][/ROW]
[ROW][C]23[/C][C]7.5[/C][C]7.48906822453826[/C][C]0.0109317754617422[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]7.55025464351655[/C][C]-0.650254643516553[/C][/ROW]
[ROW][C]25[/C][C]6.6[/C][C]6.99513534524591[/C][C]-0.395135345245908[/C][/ROW]
[ROW][C]26[/C][C]6.9[/C][C]7.00710222495474[/C][C]-0.107102224954736[/C][/ROW]
[ROW][C]27[/C][C]7.7[/C][C]7.01892991844164[/C][C]0.681070081558361[/C][/ROW]
[ROW][C]28[/C][C]8[/C][C]7.27853919627255[/C][C]0.721460803727452[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]7.44490638865336[/C][C]0.555093611346638[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.39839979676177[/C][C]0.301600203238233[/C][/ROW]
[ROW][C]31[/C][C]7.3[/C][C]8.09924972904588[/C][C]-0.79924972904588[/C][/ROW]
[ROW][C]32[/C][C]7.4[/C][C]7.33896285157322[/C][C]0.0610371484267755[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]7.76481058446515[/C][C]0.335189415534853[/C][/ROW]
[ROW][C]34[/C][C]8.3[/C][C]7.74132414931844[/C][C]0.558675850681557[/C][/ROW]
[ROW][C]35[/C][C]8.1[/C][C]7.77043129015375[/C][C]0.329568709846247[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.93803283384265[/C][C]-0.0380328338426486[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]7.91778983092539[/C][C]-0.0177898309253939[/C][/ROW]
[ROW][C]38[/C][C]8.3[/C][C]8.28775788311785[/C][C]0.0122421168821525[/C][/ROW]
[ROW][C]39[/C][C]8.6[/C][C]8.56379264347973[/C][C]0.036207356520265[/C][/ROW]
[ROW][C]40[/C][C]8.7[/C][C]8.32695954791296[/C][C]0.373040452087043[/C][/ROW]
[ROW][C]41[/C][C]8.5[/C][C]8.18433762978711[/C][C]0.315662370212895[/C][/ROW]
[ROW][C]42[/C][C]8.3[/C][C]7.89535404518516[/C][C]0.404645954814838[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]8.43849566576431[/C][C]-0.438495665764307[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]8.14715761694118[/C][C]-0.147157616941179[/C][/ROW]
[ROW][C]45[/C][C]8.8[/C][C]8.46928304857981[/C][C]0.330716951420193[/C][/ROW]
[ROW][C]46[/C][C]8.7[/C][C]8.49069820227042[/C][C]0.209301797729578[/C][/ROW]
[ROW][C]47[/C][C]8.5[/C][C]8.19648013012648[/C][C]0.303519869873517[/C][/ROW]
[ROW][C]48[/C][C]8.1[/C][C]8.26405528203917[/C][C]-0.164055282039167[/C][/ROW]
[ROW][C]49[/C][C]7.8[/C][C]8.14946974406647[/C][C]-0.349469744066474[/C][/ROW]
[ROW][C]50[/C][C]7.6[/C][C]8.26610174525134[/C][C]-0.666101745251344[/C][/ROW]
[ROW][C]51[/C][C]7.4[/C][C]8.01590711188559[/C][C]-0.615907111885589[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]7.34115758777246[/C][C]-0.241157587772457[/C][/ROW]
[ROW][C]53[/C][C]6.9[/C][C]6.7049403269372[/C][C]0.195059673062804[/C][/ROW]
[ROW][C]54[/C][C]6.7[/C][C]6.3407487378546[/C][C]0.359251262145401[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.66571013649339[/C][C]-0.0657101364933901[/C][/ROW]
[ROW][C]56[/C][C]6.5[/C][C]6.7295167517437[/C][C]-0.229516751743705[/C][/ROW]
[ROW][C]57[/C][C]7.1[/C][C]7.09062513531177[/C][C]0.00937486468822524[/C][/ROW]
[ROW][C]58[/C][C]7.2[/C][C]6.83400075817192[/C][C]0.36599924182808[/C][/ROW]
[ROW][C]59[/C][C]6.9[/C][C]6.68294760373999[/C][C]0.217052396260013[/C][/ROW]
[ROW][C]60[/C][C]6.7[/C][C]6.58151044281719[/C][C]0.118489557182813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159714&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159714&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
13	7	7.55016025641025	-0.550160256410255
14	7.2	7.35511597063449	-0.15511597063449
15	7.3	7.29455257500717	0.00544742499282869
16	7.1	7.00560917611579	0.0943908238842059
17	6.8	6.6738447556399	0.126155244360096
18	6.4	6.29613150586704	0.10386849413296
19	6.1	7.07595863562336	-0.97595863562336
20	6.5	5.81817378737362	0.68182621262638
21	7.7	6.65077767059255	1.04922232940745
22	7.9	7.2795359779757	0.620464022024299
23	7.5	7.48906822453826	0.0109317754617422
24	6.9	7.55025464351655	-0.650254643516553
25	6.6	6.99513534524591	-0.395135345245908
26	6.9	7.00710222495474	-0.107102224954736
27	7.7	7.01892991844164	0.681070081558361
28	8	7.27853919627255	0.721460803727452
29	8	7.44490638865336	0.555093611346638
30	7.7	7.39839979676177	0.301600203238233
31	7.3	8.09924972904588	-0.79924972904588
32	7.4	7.33896285157322	0.0610371484267755
33	8.1	7.76481058446515	0.335189415534853
34	8.3	7.74132414931844	0.558675850681557
35	8.1	7.77043129015375	0.329568709846247
36	7.9	7.93803283384265	-0.0380328338426486
37	7.9	7.91778983092539	-0.0177898309253939
38	8.3	8.28775788311785	0.0122421168821525
39	8.6	8.56379264347973	0.036207356520265
40	8.7	8.32695954791296	0.373040452087043
41	8.5	8.18433762978711	0.315662370212895
42	8.3	7.89535404518516	0.404645954814838
43	8	8.43849566576431	-0.438495665764307
44	8	8.14715761694118	-0.147157616941179
45	8.8	8.46928304857981	0.330716951420193
46	8.7	8.49069820227042	0.209301797729578
47	8.5	8.19648013012648	0.303519869873517
48	8.1	8.26405528203917	-0.164055282039167
49	7.8	8.14946974406647	-0.349469744066474
50	7.6	8.26610174525134	-0.666101745251344
51	7.4	8.01590711188559	-0.615907111885589
52	7.1	7.34115758777246	-0.241157587772457
53	6.9	6.7049403269372	0.195059673062804
54	6.7	6.3407487378546	0.359251262145401
55	6.6	6.66571013649339	-0.0657101364933901
56	6.5	6.7295167517437	-0.229516751743705
57	7.1	7.09062513531177	0.00937486468822524
58	7.2	6.83400075817192	0.36599924182808
59	6.9	6.68294760373999	0.217052396260013
60	6.7	6.58151044281719	0.118489557182813

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	6.64811354611097	5.81182074263352	7.48440634958843
62	6.96994304339126	5.90757852116231	8.03230756562022
63	7.25244965872124	6.00431060275298	8.5005887146895
64	7.14137446441311	5.73173485515977	8.55101407366645
65	6.78856313812599	5.23411257509143	8.34301370116057
66	6.30712279232431	4.62024719588542	7.9939983887632
67	6.25860064497522	4.44896476922462	8.06823652072582
68	6.33840592552531	4.41382422350635	8.26298762754428
69	6.93106158066778	4.8980226108768	8.96410055045877
70	6.74433481297849	4.60833851671968	8.88033110923731
71	6.27429420937505	4.04008005165115	8.50850836709896
72	5.98146853146853	3.65317610406245	8.30976095887462

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 6.64811354611097 & 5.81182074263352 & 7.48440634958843 \tabularnewline
62 & 6.96994304339126 & 5.90757852116231 & 8.03230756562022 \tabularnewline
63 & 7.25244965872124 & 6.00431060275298 & 8.5005887146895 \tabularnewline
64 & 7.14137446441311 & 5.73173485515977 & 8.55101407366645 \tabularnewline
65 & 6.78856313812599 & 5.23411257509143 & 8.34301370116057 \tabularnewline
66 & 6.30712279232431 & 4.62024719588542 & 7.9939983887632 \tabularnewline
67 & 6.25860064497522 & 4.44896476922462 & 8.06823652072582 \tabularnewline
68 & 6.33840592552531 & 4.41382422350635 & 8.26298762754428 \tabularnewline
69 & 6.93106158066778 & 4.8980226108768 & 8.96410055045877 \tabularnewline
70 & 6.74433481297849 & 4.60833851671968 & 8.88033110923731 \tabularnewline
71 & 6.27429420937505 & 4.04008005165115 & 8.50850836709896 \tabularnewline
72 & 5.98146853146853 & 3.65317610406245 & 8.30976095887462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159714&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]61[/C][C]6.64811354611097[/C][C]5.81182074263352[/C][C]7.48440634958843[/C][/ROW]
[ROW][C]62[/C][C]6.96994304339126[/C][C]5.90757852116231[/C][C]8.03230756562022[/C][/ROW]
[ROW][C]63[/C][C]7.25244965872124[/C][C]6.00431060275298[/C][C]8.5005887146895[/C][/ROW]
[ROW][C]64[/C][C]7.14137446441311[/C][C]5.73173485515977[/C][C]8.55101407366645[/C][/ROW]
[ROW][C]65[/C][C]6.78856313812599[/C][C]5.23411257509143[/C][C]8.34301370116057[/C][/ROW]
[ROW][C]66[/C][C]6.30712279232431[/C][C]4.62024719588542[/C][C]7.9939983887632[/C][/ROW]
[ROW][C]67[/C][C]6.25860064497522[/C][C]4.44896476922462[/C][C]8.06823652072582[/C][/ROW]
[ROW][C]68[/C][C]6.33840592552531[/C][C]4.41382422350635[/C][C]8.26298762754428[/C][/ROW]
[ROW][C]69[/C][C]6.93106158066778[/C][C]4.8980226108768[/C][C]8.96410055045877[/C][/ROW]
[ROW][C]70[/C][C]6.74433481297849[/C][C]4.60833851671968[/C][C]8.88033110923731[/C][/ROW]
[ROW][C]71[/C][C]6.27429420937505[/C][C]4.04008005165115[/C][C]8.50850836709896[/C][/ROW]
[ROW][C]72[/C][C]5.98146853146853[/C][C]3.65317610406245[/C][C]8.30976095887462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159714&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159714&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
61	6.64811354611097	5.81182074263352	7.48440634958843
62	6.96994304339126	5.90757852116231	8.03230756562022
63	7.25244965872124	6.00431060275298	8.5005887146895
64	7.14137446441311	5.73173485515977	8.55101407366645
65	6.78856313812599	5.23411257509143	8.34301370116057
66	6.30712279232431	4.62024719588542	7.9939983887632
67	6.25860064497522	4.44896476922462	8.06823652072582
68	6.33840592552531	4.41382422350635	8.26298762754428
69	6.93106158066778	4.8980226108768	8.96410055045877
70	6.74433481297849	4.60833851671968	8.88033110923731
71	6.27429420937505	4.04008005165115	8.50850836709896
72	5.98146853146853	3.65317610406245	8.30976095887462

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 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code