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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 25 May 2013 13:22:22 -0400

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/2013/May/25/t1369502568z8exff6k7l4pgma.htm/, Retrieved Thu, 02 May 2024 14:56:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210539, Retrieved Thu, 02 May 2024 14:56:13 +0000

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User-defined keywords

Estimated Impact

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

-     [Variability] [] [2013-04-25 16:50:56] [a336235b4e17fb25709c82cf0b669eff]
- RMPD    [Exponential Smoothing] [] [2013-05-25 17:22:22] [08d4936d4ccd54ef409309ffdc209e97] [Current]

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Dataseries X:

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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	3 seconds
R Server	'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210539&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210539&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.382329654453277
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.382329654453277 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210539&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]0.382329654453277[/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=210539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210539&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	0.382329654453277
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	601962	579637.316239317	22324.6837606832
14	685640	672055.122116735	13584.8778832654
15	785923	779974.941033051	5948.05896694935
16	954888	954055.852611969	832.147388030775
17	1029140	1030738.42448471	-1598.42448470637
18	972811	974776.174986549	-1965.17498654942
19	951330	934359.830895752	16970.1691042477
20	1012865	1039934.19703481	-27069.1970348101
21	1005502	1036330.54920225	-30828.5492022474
22	987489	1001689.13122121	-14200.1312212069
23	828421	822548.167207629	5872.83279237116
24	817308	797151.525922549	20156.4740774513
25	625827	625292.531073677	534.468926323112
26	683491	703980.972726695	-20489.9727266951
27	848657	794155.929204839	54501.0707951607
28	978027	983640.150145967	-5613.15014596668
29	1019467	1056357.20147117	-36890.2014711723
30	980306	986675.328163535	-6369.32816353498
31	992574	956270.94623803	36303.0537619697
32	1080411	1042035.03698709	38375.9630129104
33	1047988	1061130.97422892	-13142.9742289186
34	1023560	1043522.15669648	-19962.1566964829
35	871245	874576.674092405	-3331.67409240536
36	824793	854483.458518877	-29690.4585188767
37	645999	651446.572452878	-5447.57245287811
38	736888	714861.728151714	22026.2718482856
39	874488	867611.649491916	6876.35050808394
40	992614	1001756.75596127	-9142.75596127321
41	1107708	1053805.42721503	53902.5727849659
42	955938	1037688.16227792	-81750.1622779166
43	1024122	1004820.91698229	19301.0830177113
44	1081598	1085365.02470499	-3767.02470498648
45	1028158	1056526.72824664	-28368.7282466427
46	1006457	1028884.64665073	-22427.6466507333
47	826725	869268.690061059	-42543.6900610586
48	839116	817902.518486928	21213.4815130718
49	591481	649301.83003709	-57820.83003709
50	671244	709662.915164159	-38418.9151641587
51	788395	829945.191891321	-41550.1918913207
52	912291	935680.868110469	-23389.868110469
53	987428	1021223.67589107	-33795.675891067
54	873452	887788.098100836	-14336.0981008357
55	952046	943111.606266999	8934.39373300073
56	1037521	1005443.73518946	32077.2648105386
57	958597	975114.030828099	-16517.0308280988
58	965368	955672.834533173	9695.16546682734
59	780741	795913.298116184	-15172.298116184
60	814377	794392.935563518	19984.0644364825
61	594739	576505.053982372	18233.9460176278
62	668940	677928.122821794	-8988.12282179401
63	815882	807528.56743743	8353.43256257009
64	928023	943560.972614959	-15537.9726149593
65	1025552	1025678.43399962	-126.433999623987
66	945840	917135.209965337	28704.7900346626
67	1020639	1003288.01875176	17350.9812482438
68	1109899	1083132.723846	26766.2761539971
69	1033403	1020757.21564806	12645.7843519372
70	1050530	1028656.32474683	21873.6752531698
71	840420	858193.098944021	-17773.0989440206
72	820378	877393.415715617	-57015.4157156169
73	609379	628985.353246316	-19606.3532463158
74	678402	699126.688877203	-20724.6888772032
75	889241	834951.260754984	54289.7392450158
76	998445	973789.465701672	24655.5342983284
77	1054502	1080793.3470777	-26291.3470776998
78	1076699	980054.692979265	96644.3070207348
79	1093802	1085169.88282231	8632.11717768712
80	1134793	1167496.6560871	-32703.6560870996
81	1054084	1073662.22019439	-19578.2201943931
82	1068675	1074940.93133149	-6265.93133149296
83	857337	869230.462748527	-11893.4627485266
84	855380	866439.923434691	-11059.9234346913

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 601962 & 579637.316239317 & 22324.6837606832 \tabularnewline
14 & 685640 & 672055.122116735 & 13584.8778832654 \tabularnewline
15 & 785923 & 779974.941033051 & 5948.05896694935 \tabularnewline
16 & 954888 & 954055.852611969 & 832.147388030775 \tabularnewline
17 & 1029140 & 1030738.42448471 & -1598.42448470637 \tabularnewline
18 & 972811 & 974776.174986549 & -1965.17498654942 \tabularnewline
19 & 951330 & 934359.830895752 & 16970.1691042477 \tabularnewline
20 & 1012865 & 1039934.19703481 & -27069.1970348101 \tabularnewline
21 & 1005502 & 1036330.54920225 & -30828.5492022474 \tabularnewline
22 & 987489 & 1001689.13122121 & -14200.1312212069 \tabularnewline
23 & 828421 & 822548.167207629 & 5872.83279237116 \tabularnewline
24 & 817308 & 797151.525922549 & 20156.4740774513 \tabularnewline
25 & 625827 & 625292.531073677 & 534.468926323112 \tabularnewline
26 & 683491 & 703980.972726695 & -20489.9727266951 \tabularnewline
27 & 848657 & 794155.929204839 & 54501.0707951607 \tabularnewline
28 & 978027 & 983640.150145967 & -5613.15014596668 \tabularnewline
29 & 1019467 & 1056357.20147117 & -36890.2014711723 \tabularnewline
30 & 980306 & 986675.328163535 & -6369.32816353498 \tabularnewline
31 & 992574 & 956270.94623803 & 36303.0537619697 \tabularnewline
32 & 1080411 & 1042035.03698709 & 38375.9630129104 \tabularnewline
33 & 1047988 & 1061130.97422892 & -13142.9742289186 \tabularnewline
34 & 1023560 & 1043522.15669648 & -19962.1566964829 \tabularnewline
35 & 871245 & 874576.674092405 & -3331.67409240536 \tabularnewline
36 & 824793 & 854483.458518877 & -29690.4585188767 \tabularnewline
37 & 645999 & 651446.572452878 & -5447.57245287811 \tabularnewline
38 & 736888 & 714861.728151714 & 22026.2718482856 \tabularnewline
39 & 874488 & 867611.649491916 & 6876.35050808394 \tabularnewline
40 & 992614 & 1001756.75596127 & -9142.75596127321 \tabularnewline
41 & 1107708 & 1053805.42721503 & 53902.5727849659 \tabularnewline
42 & 955938 & 1037688.16227792 & -81750.1622779166 \tabularnewline
43 & 1024122 & 1004820.91698229 & 19301.0830177113 \tabularnewline
44 & 1081598 & 1085365.02470499 & -3767.02470498648 \tabularnewline
45 & 1028158 & 1056526.72824664 & -28368.7282466427 \tabularnewline
46 & 1006457 & 1028884.64665073 & -22427.6466507333 \tabularnewline
47 & 826725 & 869268.690061059 & -42543.6900610586 \tabularnewline
48 & 839116 & 817902.518486928 & 21213.4815130718 \tabularnewline
49 & 591481 & 649301.83003709 & -57820.83003709 \tabularnewline
50 & 671244 & 709662.915164159 & -38418.9151641587 \tabularnewline
51 & 788395 & 829945.191891321 & -41550.1918913207 \tabularnewline
52 & 912291 & 935680.868110469 & -23389.868110469 \tabularnewline
53 & 987428 & 1021223.67589107 & -33795.675891067 \tabularnewline
54 & 873452 & 887788.098100836 & -14336.0981008357 \tabularnewline
55 & 952046 & 943111.606266999 & 8934.39373300073 \tabularnewline
56 & 1037521 & 1005443.73518946 & 32077.2648105386 \tabularnewline
57 & 958597 & 975114.030828099 & -16517.0308280988 \tabularnewline
58 & 965368 & 955672.834533173 & 9695.16546682734 \tabularnewline
59 & 780741 & 795913.298116184 & -15172.298116184 \tabularnewline
60 & 814377 & 794392.935563518 & 19984.0644364825 \tabularnewline
61 & 594739 & 576505.053982372 & 18233.9460176278 \tabularnewline
62 & 668940 & 677928.122821794 & -8988.12282179401 \tabularnewline
63 & 815882 & 807528.56743743 & 8353.43256257009 \tabularnewline
64 & 928023 & 943560.972614959 & -15537.9726149593 \tabularnewline
65 & 1025552 & 1025678.43399962 & -126.433999623987 \tabularnewline
66 & 945840 & 917135.209965337 & 28704.7900346626 \tabularnewline
67 & 1020639 & 1003288.01875176 & 17350.9812482438 \tabularnewline
68 & 1109899 & 1083132.723846 & 26766.2761539971 \tabularnewline
69 & 1033403 & 1020757.21564806 & 12645.7843519372 \tabularnewline
70 & 1050530 & 1028656.32474683 & 21873.6752531698 \tabularnewline
71 & 840420 & 858193.098944021 & -17773.0989440206 \tabularnewline
72 & 820378 & 877393.415715617 & -57015.4157156169 \tabularnewline
73 & 609379 & 628985.353246316 & -19606.3532463158 \tabularnewline
74 & 678402 & 699126.688877203 & -20724.6888772032 \tabularnewline
75 & 889241 & 834951.260754984 & 54289.7392450158 \tabularnewline
76 & 998445 & 973789.465701672 & 24655.5342983284 \tabularnewline
77 & 1054502 & 1080793.3470777 & -26291.3470776998 \tabularnewline
78 & 1076699 & 980054.692979265 & 96644.3070207348 \tabularnewline
79 & 1093802 & 1085169.88282231 & 8632.11717768712 \tabularnewline
80 & 1134793 & 1167496.6560871 & -32703.6560870996 \tabularnewline
81 & 1054084 & 1073662.22019439 & -19578.2201943931 \tabularnewline
82 & 1068675 & 1074940.93133149 & -6265.93133149296 \tabularnewline
83 & 857337 & 869230.462748527 & -11893.4627485266 \tabularnewline
84 & 855380 & 866439.923434691 & -11059.9234346913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210539&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]601962[/C][C]579637.316239317[/C][C]22324.6837606832[/C][/ROW]
[ROW][C]14[/C][C]685640[/C][C]672055.122116735[/C][C]13584.8778832654[/C][/ROW]
[ROW][C]15[/C][C]785923[/C][C]779974.941033051[/C][C]5948.05896694935[/C][/ROW]
[ROW][C]16[/C][C]954888[/C][C]954055.852611969[/C][C]832.147388030775[/C][/ROW]
[ROW][C]17[/C][C]1029140[/C][C]1030738.42448471[/C][C]-1598.42448470637[/C][/ROW]
[ROW][C]18[/C][C]972811[/C][C]974776.174986549[/C][C]-1965.17498654942[/C][/ROW]
[ROW][C]19[/C][C]951330[/C][C]934359.830895752[/C][C]16970.1691042477[/C][/ROW]
[ROW][C]20[/C][C]1012865[/C][C]1039934.19703481[/C][C]-27069.1970348101[/C][/ROW]
[ROW][C]21[/C][C]1005502[/C][C]1036330.54920225[/C][C]-30828.5492022474[/C][/ROW]
[ROW][C]22[/C][C]987489[/C][C]1001689.13122121[/C][C]-14200.1312212069[/C][/ROW]
[ROW][C]23[/C][C]828421[/C][C]822548.167207629[/C][C]5872.83279237116[/C][/ROW]
[ROW][C]24[/C][C]817308[/C][C]797151.525922549[/C][C]20156.4740774513[/C][/ROW]
[ROW][C]25[/C][C]625827[/C][C]625292.531073677[/C][C]534.468926323112[/C][/ROW]
[ROW][C]26[/C][C]683491[/C][C]703980.972726695[/C][C]-20489.9727266951[/C][/ROW]
[ROW][C]27[/C][C]848657[/C][C]794155.929204839[/C][C]54501.0707951607[/C][/ROW]
[ROW][C]28[/C][C]978027[/C][C]983640.150145967[/C][C]-5613.15014596668[/C][/ROW]
[ROW][C]29[/C][C]1019467[/C][C]1056357.20147117[/C][C]-36890.2014711723[/C][/ROW]
[ROW][C]30[/C][C]980306[/C][C]986675.328163535[/C][C]-6369.32816353498[/C][/ROW]
[ROW][C]31[/C][C]992574[/C][C]956270.94623803[/C][C]36303.0537619697[/C][/ROW]
[ROW][C]32[/C][C]1080411[/C][C]1042035.03698709[/C][C]38375.9630129104[/C][/ROW]
[ROW][C]33[/C][C]1047988[/C][C]1061130.97422892[/C][C]-13142.9742289186[/C][/ROW]
[ROW][C]34[/C][C]1023560[/C][C]1043522.15669648[/C][C]-19962.1566964829[/C][/ROW]
[ROW][C]35[/C][C]871245[/C][C]874576.674092405[/C][C]-3331.67409240536[/C][/ROW]
[ROW][C]36[/C][C]824793[/C][C]854483.458518877[/C][C]-29690.4585188767[/C][/ROW]
[ROW][C]37[/C][C]645999[/C][C]651446.572452878[/C][C]-5447.57245287811[/C][/ROW]
[ROW][C]38[/C][C]736888[/C][C]714861.728151714[/C][C]22026.2718482856[/C][/ROW]
[ROW][C]39[/C][C]874488[/C][C]867611.649491916[/C][C]6876.35050808394[/C][/ROW]
[ROW][C]40[/C][C]992614[/C][C]1001756.75596127[/C][C]-9142.75596127321[/C][/ROW]
[ROW][C]41[/C][C]1107708[/C][C]1053805.42721503[/C][C]53902.5727849659[/C][/ROW]
[ROW][C]42[/C][C]955938[/C][C]1037688.16227792[/C][C]-81750.1622779166[/C][/ROW]
[ROW][C]43[/C][C]1024122[/C][C]1004820.91698229[/C][C]19301.0830177113[/C][/ROW]
[ROW][C]44[/C][C]1081598[/C][C]1085365.02470499[/C][C]-3767.02470498648[/C][/ROW]
[ROW][C]45[/C][C]1028158[/C][C]1056526.72824664[/C][C]-28368.7282466427[/C][/ROW]
[ROW][C]46[/C][C]1006457[/C][C]1028884.64665073[/C][C]-22427.6466507333[/C][/ROW]
[ROW][C]47[/C][C]826725[/C][C]869268.690061059[/C][C]-42543.6900610586[/C][/ROW]
[ROW][C]48[/C][C]839116[/C][C]817902.518486928[/C][C]21213.4815130718[/C][/ROW]
[ROW][C]49[/C][C]591481[/C][C]649301.83003709[/C][C]-57820.83003709[/C][/ROW]
[ROW][C]50[/C][C]671244[/C][C]709662.915164159[/C][C]-38418.9151641587[/C][/ROW]
[ROW][C]51[/C][C]788395[/C][C]829945.191891321[/C][C]-41550.1918913207[/C][/ROW]
[ROW][C]52[/C][C]912291[/C][C]935680.868110469[/C][C]-23389.868110469[/C][/ROW]
[ROW][C]53[/C][C]987428[/C][C]1021223.67589107[/C][C]-33795.675891067[/C][/ROW]
[ROW][C]54[/C][C]873452[/C][C]887788.098100836[/C][C]-14336.0981008357[/C][/ROW]
[ROW][C]55[/C][C]952046[/C][C]943111.606266999[/C][C]8934.39373300073[/C][/ROW]
[ROW][C]56[/C][C]1037521[/C][C]1005443.73518946[/C][C]32077.2648105386[/C][/ROW]
[ROW][C]57[/C][C]958597[/C][C]975114.030828099[/C][C]-16517.0308280988[/C][/ROW]
[ROW][C]58[/C][C]965368[/C][C]955672.834533173[/C][C]9695.16546682734[/C][/ROW]
[ROW][C]59[/C][C]780741[/C][C]795913.298116184[/C][C]-15172.298116184[/C][/ROW]
[ROW][C]60[/C][C]814377[/C][C]794392.935563518[/C][C]19984.0644364825[/C][/ROW]
[ROW][C]61[/C][C]594739[/C][C]576505.053982372[/C][C]18233.9460176278[/C][/ROW]
[ROW][C]62[/C][C]668940[/C][C]677928.122821794[/C][C]-8988.12282179401[/C][/ROW]
[ROW][C]63[/C][C]815882[/C][C]807528.56743743[/C][C]8353.43256257009[/C][/ROW]
[ROW][C]64[/C][C]928023[/C][C]943560.972614959[/C][C]-15537.9726149593[/C][/ROW]
[ROW][C]65[/C][C]1025552[/C][C]1025678.43399962[/C][C]-126.433999623987[/C][/ROW]
[ROW][C]66[/C][C]945840[/C][C]917135.209965337[/C][C]28704.7900346626[/C][/ROW]
[ROW][C]67[/C][C]1020639[/C][C]1003288.01875176[/C][C]17350.9812482438[/C][/ROW]
[ROW][C]68[/C][C]1109899[/C][C]1083132.723846[/C][C]26766.2761539971[/C][/ROW]
[ROW][C]69[/C][C]1033403[/C][C]1020757.21564806[/C][C]12645.7843519372[/C][/ROW]
[ROW][C]70[/C][C]1050530[/C][C]1028656.32474683[/C][C]21873.6752531698[/C][/ROW]
[ROW][C]71[/C][C]840420[/C][C]858193.098944021[/C][C]-17773.0989440206[/C][/ROW]
[ROW][C]72[/C][C]820378[/C][C]877393.415715617[/C][C]-57015.4157156169[/C][/ROW]
[ROW][C]73[/C][C]609379[/C][C]628985.353246316[/C][C]-19606.3532463158[/C][/ROW]
[ROW][C]74[/C][C]678402[/C][C]699126.688877203[/C][C]-20724.6888772032[/C][/ROW]
[ROW][C]75[/C][C]889241[/C][C]834951.260754984[/C][C]54289.7392450158[/C][/ROW]
[ROW][C]76[/C][C]998445[/C][C]973789.465701672[/C][C]24655.5342983284[/C][/ROW]
[ROW][C]77[/C][C]1054502[/C][C]1080793.3470777[/C][C]-26291.3470776998[/C][/ROW]
[ROW][C]78[/C][C]1076699[/C][C]980054.692979265[/C][C]96644.3070207348[/C][/ROW]
[ROW][C]79[/C][C]1093802[/C][C]1085169.88282231[/C][C]8632.11717768712[/C][/ROW]
[ROW][C]80[/C][C]1134793[/C][C]1167496.6560871[/C][C]-32703.6560870996[/C][/ROW]
[ROW][C]81[/C][C]1054084[/C][C]1073662.22019439[/C][C]-19578.2201943931[/C][/ROW]
[ROW][C]82[/C][C]1068675[/C][C]1074940.93133149[/C][C]-6265.93133149296[/C][/ROW]
[ROW][C]83[/C][C]857337[/C][C]869230.462748527[/C][C]-11893.4627485266[/C][/ROW]
[ROW][C]84[/C][C]855380[/C][C]866439.923434691[/C][C]-11059.9234346913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210539&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210539&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	601962	579637.316239317	22324.6837606832
14	685640	672055.122116735	13584.8778832654
15	785923	779974.941033051	5948.05896694935
16	954888	954055.852611969	832.147388030775
17	1029140	1030738.42448471	-1598.42448470637
18	972811	974776.174986549	-1965.17498654942
19	951330	934359.830895752	16970.1691042477
20	1012865	1039934.19703481	-27069.1970348101
21	1005502	1036330.54920225	-30828.5492022474
22	987489	1001689.13122121	-14200.1312212069
23	828421	822548.167207629	5872.83279237116
24	817308	797151.525922549	20156.4740774513
25	625827	625292.531073677	534.468926323112
26	683491	703980.972726695	-20489.9727266951
27	848657	794155.929204839	54501.0707951607
28	978027	983640.150145967	-5613.15014596668
29	1019467	1056357.20147117	-36890.2014711723
30	980306	986675.328163535	-6369.32816353498
31	992574	956270.94623803	36303.0537619697
32	1080411	1042035.03698709	38375.9630129104
33	1047988	1061130.97422892	-13142.9742289186
34	1023560	1043522.15669648	-19962.1566964829
35	871245	874576.674092405	-3331.67409240536
36	824793	854483.458518877	-29690.4585188767
37	645999	651446.572452878	-5447.57245287811
38	736888	714861.728151714	22026.2718482856
39	874488	867611.649491916	6876.35050808394
40	992614	1001756.75596127	-9142.75596127321
41	1107708	1053805.42721503	53902.5727849659
42	955938	1037688.16227792	-81750.1622779166
43	1024122	1004820.91698229	19301.0830177113
44	1081598	1085365.02470499	-3767.02470498648
45	1028158	1056526.72824664	-28368.7282466427
46	1006457	1028884.64665073	-22427.6466507333
47	826725	869268.690061059	-42543.6900610586
48	839116	817902.518486928	21213.4815130718
49	591481	649301.83003709	-57820.83003709
50	671244	709662.915164159	-38418.9151641587
51	788395	829945.191891321	-41550.1918913207
52	912291	935680.868110469	-23389.868110469
53	987428	1021223.67589107	-33795.675891067
54	873452	887788.098100836	-14336.0981008357
55	952046	943111.606266999	8934.39373300073
56	1037521	1005443.73518946	32077.2648105386
57	958597	975114.030828099	-16517.0308280988
58	965368	955672.834533173	9695.16546682734
59	780741	795913.298116184	-15172.298116184
60	814377	794392.935563518	19984.0644364825
61	594739	576505.053982372	18233.9460176278
62	668940	677928.122821794	-8988.12282179401
63	815882	807528.56743743	8353.43256257009
64	928023	943560.972614959	-15537.9726149593
65	1025552	1025678.43399962	-126.433999623987
66	945840	917135.209965337	28704.7900346626
67	1020639	1003288.01875176	17350.9812482438
68	1109899	1083132.723846	26766.2761539971
69	1033403	1020757.21564806	12645.7843519372
70	1050530	1028656.32474683	21873.6752531698
71	840420	858193.098944021	-17773.0989440206
72	820378	877393.415715617	-57015.4157156169
73	609379	628985.353246316	-19606.3532463158
74	678402	699126.688877203	-20724.6888772032
75	889241	834951.260754984	54289.7392450158
76	998445	973789.465701672	24655.5342983284
77	1054502	1080793.3470777	-26291.3470776998
78	1076699	980054.692979265	96644.3070207348
79	1093802	1085169.88282231	8632.11717768712
80	1134793	1167496.6560871	-32703.6560870996
81	1054084	1073662.22019439	-19578.2201943931
82	1068675	1074940.93133149	-6265.93133149296
83	857337	869230.462748527	-11893.4627485266
84	855380	866439.923434691	-11059.9234346913

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	658708.476991379	601840.368147599	715576.585835159
86	735655.140128452	674772.365772076	796537.914484827
87	925737.562882546	861088.954056133	990386.17170896
88	1025515.02097391	957308.180898647	1093721.86104916
89	1091623.98261723	1020035.55168798	1163212.41354649
90	1076870.99810912	1002053.66153013	1151688.33468811
91	1090673.68373137	1012761.1413352	1168586.22612755
92	1144168.26126251	1063278.86348693	1225057.6590381
93	1070944.59542425	987184.073205493	1154705.117643
94	1087931.24678504	1001394.80652882	1174467.68704127
95	881140.470287941	791914.432036314	970366.508539568
96	883412.006993006	791575.106392311	975248.907593702

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 658708.476991379 & 601840.368147599 & 715576.585835159 \tabularnewline
86 & 735655.140128452 & 674772.365772076 & 796537.914484827 \tabularnewline
87 & 925737.562882546 & 861088.954056133 & 990386.17170896 \tabularnewline
88 & 1025515.02097391 & 957308.180898647 & 1093721.86104916 \tabularnewline
89 & 1091623.98261723 & 1020035.55168798 & 1163212.41354649 \tabularnewline
90 & 1076870.99810912 & 1002053.66153013 & 1151688.33468811 \tabularnewline
91 & 1090673.68373137 & 1012761.1413352 & 1168586.22612755 \tabularnewline
92 & 1144168.26126251 & 1063278.86348693 & 1225057.6590381 \tabularnewline
93 & 1070944.59542425 & 987184.073205493 & 1154705.117643 \tabularnewline
94 & 1087931.24678504 & 1001394.80652882 & 1174467.68704127 \tabularnewline
95 & 881140.470287941 & 791914.432036314 & 970366.508539568 \tabularnewline
96 & 883412.006993006 & 791575.106392311 & 975248.907593702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210539&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]658708.476991379[/C][C]601840.368147599[/C][C]715576.585835159[/C][/ROW]
[ROW][C]86[/C][C]735655.140128452[/C][C]674772.365772076[/C][C]796537.914484827[/C][/ROW]
[ROW][C]87[/C][C]925737.562882546[/C][C]861088.954056133[/C][C]990386.17170896[/C][/ROW]
[ROW][C]88[/C][C]1025515.02097391[/C][C]957308.180898647[/C][C]1093721.86104916[/C][/ROW]
[ROW][C]89[/C][C]1091623.98261723[/C][C]1020035.55168798[/C][C]1163212.41354649[/C][/ROW]
[ROW][C]90[/C][C]1076870.99810912[/C][C]1002053.66153013[/C][C]1151688.33468811[/C][/ROW]
[ROW][C]91[/C][C]1090673.68373137[/C][C]1012761.1413352[/C][C]1168586.22612755[/C][/ROW]
[ROW][C]92[/C][C]1144168.26126251[/C][C]1063278.86348693[/C][C]1225057.6590381[/C][/ROW]
[ROW][C]93[/C][C]1070944.59542425[/C][C]987184.073205493[/C][C]1154705.117643[/C][/ROW]
[ROW][C]94[/C][C]1087931.24678504[/C][C]1001394.80652882[/C][C]1174467.68704127[/C][/ROW]
[ROW][C]95[/C][C]881140.470287941[/C][C]791914.432036314[/C][C]970366.508539568[/C][/ROW]
[ROW][C]96[/C][C]883412.006993006[/C][C]791575.106392311[/C][C]975248.907593702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210539&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210539&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	658708.476991379	601840.368147599	715576.585835159
86	735655.140128452	674772.365772076	796537.914484827
87	925737.562882546	861088.954056133	990386.17170896
88	1025515.02097391	957308.180898647	1093721.86104916
89	1091623.98261723	1020035.55168798	1163212.41354649
90	1076870.99810912	1002053.66153013	1151688.33468811
91	1090673.68373137	1012761.1413352	1168586.22612755
92	1144168.26126251	1063278.86348693	1225057.6590381
93	1070944.59542425	987184.073205493	1154705.117643
94	1087931.24678504	1001394.80652882	1174467.68704127
95	881140.470287941	791914.432036314	970366.508539568
96	883412.006993006	791575.106392311	975248.907593702

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