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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 19 Jan 2010 03:33:53 -0700

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/2010/Jan/19/t1263897309wy3fw0z9lihkbd5.htm/, Retrieved Thu, 02 May 2024 00:05:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72283, Retrieved Thu, 02 May 2024 00:05:32 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

219

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

-       [Exponential Smoothing] [KDGP2W62] [2010-01-19 10:33:53] [3f12ab8801f7554f488f56dad3cd0b03] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72283&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72283&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.983484861538448
beta	0.23196686548946
gamma	0.942906046720505

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.983484861538448 \tabularnewline
beta & 0.23196686548946 \tabularnewline
gamma & 0.942906046720505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72283&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]0.983484861538448[/C][/ROW]
[ROW][C]beta[/C][C]0.23196686548946[/C][/ROW]
[ROW][C]gamma[/C][C]0.942906046720505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72283&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	0.983484861538448
beta	0.23196686548946
gamma	0.942906046720505

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	55.6	51.4044871794872	4.19551282051281
14	55.7	56.5915872243153	-0.89158722431533
15	56.1	56.922198331552	-0.822198331552023
16	56.8	57.487646074217	-0.687646074216943
17	57.5	58.0743805019632	-0.574380501963169
18	58.3	58.7831397589259	-0.483139758925937
19	58.9	58.8214113814092	0.0785886185908211
20	59.4	59.8800632447548	-0.480063244754845
21	59.8	60.6006031302821	-0.800603130282092
22	60	60.3315839080673	-0.331583908067337
23	60	60.3565251305174	-0.356525130517433
24	60.3	60.388100856527	-0.0881008565269639
25	60.1	60.4539022893204	-0.353902289320388
26	59.7	59.766336626544	-0.066336626543972
27	59.5	59.7767516741339	-0.276751674133855
28	59.4	59.8722711205326	-0.472271120532625
29	59.3	59.7132600061644	-0.413260006164435
30	59.2	59.6593296768512	-0.459329676851169
31	59.1	58.8126274731411	0.28737252685886
32	59	59.1984087610925	-0.198408761092544
33	59.3	59.3857086112982	-0.0857086112982515
34	59.5	59.1849226660486	0.315077333951415
35	59.5	59.3508253526875	0.149174647312513
36	59.5	59.5046657042383	-0.00466570423825630
37	59.7	59.2881563670693	0.411843632930747
38	59.7	59.172633539368	0.527366460632038
39	60.5	59.7135802195463	0.786419780453734
40	60.7	61.0441258657622	-0.344125865762223
41	61.3	61.2337549785384	0.0662450214615546
42	61.4	61.981777863726	-0.581777863725961
43	61.8	61.3294273944567	0.470572605543332
44	62.4	62.232762865013	0.167237134986983
45	62.4	63.2097862400401	-0.809786240040147
46	62.9	62.5662952642739	0.333704735726137
47	63.2	63.0153570513097	0.184642948690289
48	63.4	63.4771987033318	-0.077198703331824
49	63.9	63.4548072545878	0.445192745412186
50	64.5	63.6404568696413	0.859543130358681
51	65	64.8544848840001	0.145515115999856
52	65.4	65.7332485941135	-0.333248594113471
53	66.3	66.1385904314292	0.161409568570846
54	67.7	67.1904502054334	0.509549794566581
55	69	68.0970975772327	0.902902422767326
56	70	69.9888353955661	0.0111646044338727
57	71.4	71.329479750624	0.07052024937596
58	72.5	72.3027234698917	0.197276530108297
59	73.4	73.3173246785926	0.0826753214073932
60	74.6	74.3535784996001	0.246421500399862
61	75.2	75.4102000489749	-0.210200048974869
62	75.9	75.5608171342242	0.339182865775783
63	76.8	76.736330848968	0.0636691510320162
64	77.9	77.992844020204	-0.0928440202039553
65	79.2	79.1628671025947	0.0371328974053284
66	80.5	80.5901160574392	-0.0901160574392463
67	82.6	81.2685132958353	1.33148670416469
68	84.4	84.0210331656687	0.378966834331351
69	85.9	86.2614008780557	-0.361400878055647
70	87.6	87.250365001704	0.349634998296025

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 55.6 & 51.4044871794872 & 4.19551282051281 \tabularnewline
14 & 55.7 & 56.5915872243153 & -0.89158722431533 \tabularnewline
15 & 56.1 & 56.922198331552 & -0.822198331552023 \tabularnewline
16 & 56.8 & 57.487646074217 & -0.687646074216943 \tabularnewline
17 & 57.5 & 58.0743805019632 & -0.574380501963169 \tabularnewline
18 & 58.3 & 58.7831397589259 & -0.483139758925937 \tabularnewline
19 & 58.9 & 58.8214113814092 & 0.0785886185908211 \tabularnewline
20 & 59.4 & 59.8800632447548 & -0.480063244754845 \tabularnewline
21 & 59.8 & 60.6006031302821 & -0.800603130282092 \tabularnewline
22 & 60 & 60.3315839080673 & -0.331583908067337 \tabularnewline
23 & 60 & 60.3565251305174 & -0.356525130517433 \tabularnewline
24 & 60.3 & 60.388100856527 & -0.0881008565269639 \tabularnewline
25 & 60.1 & 60.4539022893204 & -0.353902289320388 \tabularnewline
26 & 59.7 & 59.766336626544 & -0.066336626543972 \tabularnewline
27 & 59.5 & 59.7767516741339 & -0.276751674133855 \tabularnewline
28 & 59.4 & 59.8722711205326 & -0.472271120532625 \tabularnewline
29 & 59.3 & 59.7132600061644 & -0.413260006164435 \tabularnewline
30 & 59.2 & 59.6593296768512 & -0.459329676851169 \tabularnewline
31 & 59.1 & 58.8126274731411 & 0.28737252685886 \tabularnewline
32 & 59 & 59.1984087610925 & -0.198408761092544 \tabularnewline
33 & 59.3 & 59.3857086112982 & -0.0857086112982515 \tabularnewline
34 & 59.5 & 59.1849226660486 & 0.315077333951415 \tabularnewline
35 & 59.5 & 59.3508253526875 & 0.149174647312513 \tabularnewline
36 & 59.5 & 59.5046657042383 & -0.00466570423825630 \tabularnewline
37 & 59.7 & 59.2881563670693 & 0.411843632930747 \tabularnewline
38 & 59.7 & 59.172633539368 & 0.527366460632038 \tabularnewline
39 & 60.5 & 59.7135802195463 & 0.786419780453734 \tabularnewline
40 & 60.7 & 61.0441258657622 & -0.344125865762223 \tabularnewline
41 & 61.3 & 61.2337549785384 & 0.0662450214615546 \tabularnewline
42 & 61.4 & 61.981777863726 & -0.581777863725961 \tabularnewline
43 & 61.8 & 61.3294273944567 & 0.470572605543332 \tabularnewline
44 & 62.4 & 62.232762865013 & 0.167237134986983 \tabularnewline
45 & 62.4 & 63.2097862400401 & -0.809786240040147 \tabularnewline
46 & 62.9 & 62.5662952642739 & 0.333704735726137 \tabularnewline
47 & 63.2 & 63.0153570513097 & 0.184642948690289 \tabularnewline
48 & 63.4 & 63.4771987033318 & -0.077198703331824 \tabularnewline
49 & 63.9 & 63.4548072545878 & 0.445192745412186 \tabularnewline
50 & 64.5 & 63.6404568696413 & 0.859543130358681 \tabularnewline
51 & 65 & 64.8544848840001 & 0.145515115999856 \tabularnewline
52 & 65.4 & 65.7332485941135 & -0.333248594113471 \tabularnewline
53 & 66.3 & 66.1385904314292 & 0.161409568570846 \tabularnewline
54 & 67.7 & 67.1904502054334 & 0.509549794566581 \tabularnewline
55 & 69 & 68.0970975772327 & 0.902902422767326 \tabularnewline
56 & 70 & 69.9888353955661 & 0.0111646044338727 \tabularnewline
57 & 71.4 & 71.329479750624 & 0.07052024937596 \tabularnewline
58 & 72.5 & 72.3027234698917 & 0.197276530108297 \tabularnewline
59 & 73.4 & 73.3173246785926 & 0.0826753214073932 \tabularnewline
60 & 74.6 & 74.3535784996001 & 0.246421500399862 \tabularnewline
61 & 75.2 & 75.4102000489749 & -0.210200048974869 \tabularnewline
62 & 75.9 & 75.5608171342242 & 0.339182865775783 \tabularnewline
63 & 76.8 & 76.736330848968 & 0.0636691510320162 \tabularnewline
64 & 77.9 & 77.992844020204 & -0.0928440202039553 \tabularnewline
65 & 79.2 & 79.1628671025947 & 0.0371328974053284 \tabularnewline
66 & 80.5 & 80.5901160574392 & -0.0901160574392463 \tabularnewline
67 & 82.6 & 81.2685132958353 & 1.33148670416469 \tabularnewline
68 & 84.4 & 84.0210331656687 & 0.378966834331351 \tabularnewline
69 & 85.9 & 86.2614008780557 & -0.361400878055647 \tabularnewline
70 & 87.6 & 87.250365001704 & 0.349634998296025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72283&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]55.6[/C][C]51.4044871794872[/C][C]4.19551282051281[/C][/ROW]
[ROW][C]14[/C][C]55.7[/C][C]56.5915872243153[/C][C]-0.89158722431533[/C][/ROW]
[ROW][C]15[/C][C]56.1[/C][C]56.922198331552[/C][C]-0.822198331552023[/C][/ROW]
[ROW][C]16[/C][C]56.8[/C][C]57.487646074217[/C][C]-0.687646074216943[/C][/ROW]
[ROW][C]17[/C][C]57.5[/C][C]58.0743805019632[/C][C]-0.574380501963169[/C][/ROW]
[ROW][C]18[/C][C]58.3[/C][C]58.7831397589259[/C][C]-0.483139758925937[/C][/ROW]
[ROW][C]19[/C][C]58.9[/C][C]58.8214113814092[/C][C]0.0785886185908211[/C][/ROW]
[ROW][C]20[/C][C]59.4[/C][C]59.8800632447548[/C][C]-0.480063244754845[/C][/ROW]
[ROW][C]21[/C][C]59.8[/C][C]60.6006031302821[/C][C]-0.800603130282092[/C][/ROW]
[ROW][C]22[/C][C]60[/C][C]60.3315839080673[/C][C]-0.331583908067337[/C][/ROW]
[ROW][C]23[/C][C]60[/C][C]60.3565251305174[/C][C]-0.356525130517433[/C][/ROW]
[ROW][C]24[/C][C]60.3[/C][C]60.388100856527[/C][C]-0.0881008565269639[/C][/ROW]
[ROW][C]25[/C][C]60.1[/C][C]60.4539022893204[/C][C]-0.353902289320388[/C][/ROW]
[ROW][C]26[/C][C]59.7[/C][C]59.766336626544[/C][C]-0.066336626543972[/C][/ROW]
[ROW][C]27[/C][C]59.5[/C][C]59.7767516741339[/C][C]-0.276751674133855[/C][/ROW]
[ROW][C]28[/C][C]59.4[/C][C]59.8722711205326[/C][C]-0.472271120532625[/C][/ROW]
[ROW][C]29[/C][C]59.3[/C][C]59.7132600061644[/C][C]-0.413260006164435[/C][/ROW]
[ROW][C]30[/C][C]59.2[/C][C]59.6593296768512[/C][C]-0.459329676851169[/C][/ROW]
[ROW][C]31[/C][C]59.1[/C][C]58.8126274731411[/C][C]0.28737252685886[/C][/ROW]
[ROW][C]32[/C][C]59[/C][C]59.1984087610925[/C][C]-0.198408761092544[/C][/ROW]
[ROW][C]33[/C][C]59.3[/C][C]59.3857086112982[/C][C]-0.0857086112982515[/C][/ROW]
[ROW][C]34[/C][C]59.5[/C][C]59.1849226660486[/C][C]0.315077333951415[/C][/ROW]
[ROW][C]35[/C][C]59.5[/C][C]59.3508253526875[/C][C]0.149174647312513[/C][/ROW]
[ROW][C]36[/C][C]59.5[/C][C]59.5046657042383[/C][C]-0.00466570423825630[/C][/ROW]
[ROW][C]37[/C][C]59.7[/C][C]59.2881563670693[/C][C]0.411843632930747[/C][/ROW]
[ROW][C]38[/C][C]59.7[/C][C]59.172633539368[/C][C]0.527366460632038[/C][/ROW]
[ROW][C]39[/C][C]60.5[/C][C]59.7135802195463[/C][C]0.786419780453734[/C][/ROW]
[ROW][C]40[/C][C]60.7[/C][C]61.0441258657622[/C][C]-0.344125865762223[/C][/ROW]
[ROW][C]41[/C][C]61.3[/C][C]61.2337549785384[/C][C]0.0662450214615546[/C][/ROW]
[ROW][C]42[/C][C]61.4[/C][C]61.981777863726[/C][C]-0.581777863725961[/C][/ROW]
[ROW][C]43[/C][C]61.8[/C][C]61.3294273944567[/C][C]0.470572605543332[/C][/ROW]
[ROW][C]44[/C][C]62.4[/C][C]62.232762865013[/C][C]0.167237134986983[/C][/ROW]
[ROW][C]45[/C][C]62.4[/C][C]63.2097862400401[/C][C]-0.809786240040147[/C][/ROW]
[ROW][C]46[/C][C]62.9[/C][C]62.5662952642739[/C][C]0.333704735726137[/C][/ROW]
[ROW][C]47[/C][C]63.2[/C][C]63.0153570513097[/C][C]0.184642948690289[/C][/ROW]
[ROW][C]48[/C][C]63.4[/C][C]63.4771987033318[/C][C]-0.077198703331824[/C][/ROW]
[ROW][C]49[/C][C]63.9[/C][C]63.4548072545878[/C][C]0.445192745412186[/C][/ROW]
[ROW][C]50[/C][C]64.5[/C][C]63.6404568696413[/C][C]0.859543130358681[/C][/ROW]
[ROW][C]51[/C][C]65[/C][C]64.8544848840001[/C][C]0.145515115999856[/C][/ROW]
[ROW][C]52[/C][C]65.4[/C][C]65.7332485941135[/C][C]-0.333248594113471[/C][/ROW]
[ROW][C]53[/C][C]66.3[/C][C]66.1385904314292[/C][C]0.161409568570846[/C][/ROW]
[ROW][C]54[/C][C]67.7[/C][C]67.1904502054334[/C][C]0.509549794566581[/C][/ROW]
[ROW][C]55[/C][C]69[/C][C]68.0970975772327[/C][C]0.902902422767326[/C][/ROW]
[ROW][C]56[/C][C]70[/C][C]69.9888353955661[/C][C]0.0111646044338727[/C][/ROW]
[ROW][C]57[/C][C]71.4[/C][C]71.329479750624[/C][C]0.07052024937596[/C][/ROW]
[ROW][C]58[/C][C]72.5[/C][C]72.3027234698917[/C][C]0.197276530108297[/C][/ROW]
[ROW][C]59[/C][C]73.4[/C][C]73.3173246785926[/C][C]0.0826753214073932[/C][/ROW]
[ROW][C]60[/C][C]74.6[/C][C]74.3535784996001[/C][C]0.246421500399862[/C][/ROW]
[ROW][C]61[/C][C]75.2[/C][C]75.4102000489749[/C][C]-0.210200048974869[/C][/ROW]
[ROW][C]62[/C][C]75.9[/C][C]75.5608171342242[/C][C]0.339182865775783[/C][/ROW]
[ROW][C]63[/C][C]76.8[/C][C]76.736330848968[/C][C]0.0636691510320162[/C][/ROW]
[ROW][C]64[/C][C]77.9[/C][C]77.992844020204[/C][C]-0.0928440202039553[/C][/ROW]
[ROW][C]65[/C][C]79.2[/C][C]79.1628671025947[/C][C]0.0371328974053284[/C][/ROW]
[ROW][C]66[/C][C]80.5[/C][C]80.5901160574392[/C][C]-0.0901160574392463[/C][/ROW]
[ROW][C]67[/C][C]82.6[/C][C]81.2685132958353[/C][C]1.33148670416469[/C][/ROW]
[ROW][C]68[/C][C]84.4[/C][C]84.0210331656687[/C][C]0.378966834331351[/C][/ROW]
[ROW][C]69[/C][C]85.9[/C][C]86.2614008780557[/C][C]-0.361400878055647[/C][/ROW]
[ROW][C]70[/C][C]87.6[/C][C]87.250365001704[/C][C]0.349634998296025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72283&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	55.6	51.4044871794872	4.19551282051281
14	55.7	56.5915872243153	-0.89158722431533
15	56.1	56.922198331552	-0.822198331552023
16	56.8	57.487646074217	-0.687646074216943
17	57.5	58.0743805019632	-0.574380501963169
18	58.3	58.7831397589259	-0.483139758925937
19	58.9	58.8214113814092	0.0785886185908211
20	59.4	59.8800632447548	-0.480063244754845
21	59.8	60.6006031302821	-0.800603130282092
22	60	60.3315839080673	-0.331583908067337
23	60	60.3565251305174	-0.356525130517433
24	60.3	60.388100856527	-0.0881008565269639
25	60.1	60.4539022893204	-0.353902289320388
26	59.7	59.766336626544	-0.066336626543972
27	59.5	59.7767516741339	-0.276751674133855
28	59.4	59.8722711205326	-0.472271120532625
29	59.3	59.7132600061644	-0.413260006164435
30	59.2	59.6593296768512	-0.459329676851169
31	59.1	58.8126274731411	0.28737252685886
32	59	59.1984087610925	-0.198408761092544
33	59.3	59.3857086112982	-0.0857086112982515
34	59.5	59.1849226660486	0.315077333951415
35	59.5	59.3508253526875	0.149174647312513
36	59.5	59.5046657042383	-0.00466570423825630
37	59.7	59.2881563670693	0.411843632930747
38	59.7	59.172633539368	0.527366460632038
39	60.5	59.7135802195463	0.786419780453734
40	60.7	61.0441258657622	-0.344125865762223
41	61.3	61.2337549785384	0.0662450214615546
42	61.4	61.981777863726	-0.581777863725961
43	61.8	61.3294273944567	0.470572605543332
44	62.4	62.232762865013	0.167237134986983
45	62.4	63.2097862400401	-0.809786240040147
46	62.9	62.5662952642739	0.333704735726137
47	63.2	63.0153570513097	0.184642948690289
48	63.4	63.4771987033318	-0.077198703331824
49	63.9	63.4548072545878	0.445192745412186
50	64.5	63.6404568696413	0.859543130358681
51	65	64.8544848840001	0.145515115999856
52	65.4	65.7332485941135	-0.333248594113471
53	66.3	66.1385904314292	0.161409568570846
54	67.7	67.1904502054334	0.509549794566581
55	69	68.0970975772327	0.902902422767326
56	70	69.9888353955661	0.0111646044338727
57	71.4	71.329479750624	0.07052024937596
58	72.5	72.3027234698917	0.197276530108297
59	73.4	73.3173246785926	0.0826753214073932
60	74.6	74.3535784996001	0.246421500399862
61	75.2	75.4102000489749	-0.210200048974869
62	75.9	75.5608171342242	0.339182865775783
63	76.8	76.736330848968	0.0636691510320162
64	77.9	77.992844020204	-0.0928440202039553
65	79.2	79.1628671025947	0.0371328974053284
66	80.5	80.5901160574392	-0.0901160574392463
67	82.6	81.2685132958353	1.33148670416469
68	84.4	84.0210331656687	0.378966834331351
69	85.9	86.2614008780557	-0.361400878055647
70	87.6	87.250365001704	0.349634998296025

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
71	88.8863167154654	87.480718230571	90.2919152003597
72	90.298242146459	88.0900541420414	92.5064301508767
73	91.5036153215507	88.5083630740932	94.4988675690082
74	92.3156843180334	88.5120429508068	96.1193256852599
75	93.5221149005942	88.8777414878298	98.1664883133585
76	95.0678363912434	89.5465374927368	100.589135289750
77	96.7066384695665	90.2710379304204	103.142239008713
78	98.462359163651	91.0750390828492	105.849679244453
79	99.6390533356885	91.2630741202454	108.015032551132
80	101.151015056405	91.7501534424879	110.551876670322
81	103.004461232828	92.5433108641415	113.465611601514
82	104.439694354084	92.883696477012	115.995692231156

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 88.8863167154654 & 87.480718230571 & 90.2919152003597 \tabularnewline
72 & 90.298242146459 & 88.0900541420414 & 92.5064301508767 \tabularnewline
73 & 91.5036153215507 & 88.5083630740932 & 94.4988675690082 \tabularnewline
74 & 92.3156843180334 & 88.5120429508068 & 96.1193256852599 \tabularnewline
75 & 93.5221149005942 & 88.8777414878298 & 98.1664883133585 \tabularnewline
76 & 95.0678363912434 & 89.5465374927368 & 100.589135289750 \tabularnewline
77 & 96.7066384695665 & 90.2710379304204 & 103.142239008713 \tabularnewline
78 & 98.462359163651 & 91.0750390828492 & 105.849679244453 \tabularnewline
79 & 99.6390533356885 & 91.2630741202454 & 108.015032551132 \tabularnewline
80 & 101.151015056405 & 91.7501534424879 & 110.551876670322 \tabularnewline
81 & 103.004461232828 & 92.5433108641415 & 113.465611601514 \tabularnewline
82 & 104.439694354084 & 92.883696477012 & 115.995692231156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72283&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]71[/C][C]88.8863167154654[/C][C]87.480718230571[/C][C]90.2919152003597[/C][/ROW]
[ROW][C]72[/C][C]90.298242146459[/C][C]88.0900541420414[/C][C]92.5064301508767[/C][/ROW]
[ROW][C]73[/C][C]91.5036153215507[/C][C]88.5083630740932[/C][C]94.4988675690082[/C][/ROW]
[ROW][C]74[/C][C]92.3156843180334[/C][C]88.5120429508068[/C][C]96.1193256852599[/C][/ROW]
[ROW][C]75[/C][C]93.5221149005942[/C][C]88.8777414878298[/C][C]98.1664883133585[/C][/ROW]
[ROW][C]76[/C][C]95.0678363912434[/C][C]89.5465374927368[/C][C]100.589135289750[/C][/ROW]
[ROW][C]77[/C][C]96.7066384695665[/C][C]90.2710379304204[/C][C]103.142239008713[/C][/ROW]
[ROW][C]78[/C][C]98.462359163651[/C][C]91.0750390828492[/C][C]105.849679244453[/C][/ROW]
[ROW][C]79[/C][C]99.6390533356885[/C][C]91.2630741202454[/C][C]108.015032551132[/C][/ROW]
[ROW][C]80[/C][C]101.151015056405[/C][C]91.7501534424879[/C][C]110.551876670322[/C][/ROW]
[ROW][C]81[/C][C]103.004461232828[/C][C]92.5433108641415[/C][C]113.465611601514[/C][/ROW]
[ROW][C]82[/C][C]104.439694354084[/C][C]92.883696477012[/C][C]115.995692231156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72283&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
71	88.8863167154654	87.480718230571	90.2919152003597
72	90.298242146459	88.0900541420414	92.5064301508767
73	91.5036153215507	88.5083630740932	94.4988675690082
74	92.3156843180334	88.5120429508068	96.1193256852599
75	93.5221149005942	88.8777414878298	98.1664883133585
76	95.0678363912434	89.5465374927368	100.589135289750
77	96.7066384695665	90.2710379304204	103.142239008713
78	98.462359163651	91.0750390828492	105.849679244453
79	99.6390533356885	91.2630741202454	108.015032551132
80	101.151015056405	91.7501534424879	110.551876670322
81	103.004461232828	92.5433108641415	113.465611601514
82	104.439694354084	92.883696477012	115.995692231156

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 = Triple ; par3 = additive ;

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