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Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 10 Nov 2012 09:54:36 -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/2012/Nov/10/t1352559292b25xgrwva6rd2sv.htm/, Retrieved Sat, 20 Apr 2024 12:07:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187362, Retrieved Sat, 20 Apr 2024 12:07:26 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

119

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

-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [Single smoothing] [2012-11-10 14:54:36] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
- R         [Exponential Smoothing] [double smoothing] [2012-11-10 14:57:27] [86dcce9422b96d4554cb918e531c1d5d] 
-             [Exponential Smoothing] [Triple smoothing] [2012-11-10 14:59:32] [86dcce9422b96d4554cb918e531c1d5d] 
-   P           [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:39:21] [74be16979710d4c4e7c6647856088456] 
-  M              [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:40:47] [74be16979710d4c4e7c6647856088456] 
-   P         [Exponential Smoothing] [Double Smoothing ...] [2012-11-11 17:31:29] [74be16979710d4c4e7c6647856088456] 
- R  D      [Exponential Smoothing] [Single smoothing] [2012-11-11 17:23:55] [74be16979710d4c4e7c6647856088456] 
- R         [Exponential Smoothing] [Single Smoothing] [2012-11-11 17:35:30] [74be16979710d4c4e7c6647856088456] 

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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	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=187362&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=187362&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187362&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	0.245575870418928
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.245575870418928 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187362&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]0.245575870418928[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187362&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187362&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	0.245575870418928
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	250580	236422	14158
3	279515	239898.863173391	39616.1368266088
4	264417	249627.630457221	14789.369542779
5	283706	253259.542755636	30446.4572443639
6	281288	260736.457994593	20551.5420054065
7	271146	265783.420811022	5362.57918897766
8	283944	267100.340863046	16843.6591369541
9	269155	271236.737116643	-2081.73711664317
10	270899	270725.51271224	173.487287759839
11	276507	270768.117003938	5738.88299606158
12	319957	272177.448190929	47779.5518090714
13	250746	283910.953214668	-33164.9532146676
14	247772	275766.440961573	-27994.4409615726
15	280449	268891.681755543	11557.3182444569
16	274925	271729.880243134	3195.11975686584
17	296013	272514.524558519	23498.4754414808
18	287881	278285.183118579	9595.81688142137
19	279098	280641.684201614	-1543.68420161435
20	294763	280262.592610151	14500.407389849
21	261924	283823.542776342	-21899.5427763422
22	291596	278445.543497265	13150.4565027346
23	287537	281674.978299331	5862.02170066925
24	326201	283114.549380887	43086.4506191128
25	255598	293695.541994938	-38097.541994938
26	253086	284339.704958709	-31253.7049587094
27	285261	276664.549159658	8596.45084034197
28	284747	278775.630057289	5971.36994271149
29	300402	280242.054428563	20159.9455714367
30	288854	285192.850609867	3661.14939013292
31	295433	286091.940558083	9341.05944191728
32	307256	288385.879361167	18870.1206388335
33	273189	293019.925661958	-19830.9256619582
34	287540	288149.92883131	-609.928831309779
35	290705	288000.145027667	2704.85497233272
36	337006	288664.392141855	48341.6078581451
37	268335	300535.924569069	-32200.9245690693
38	259060	292628.154489726	-33568.1544897259
39	293703	284384.625732554	9318.37426744559
40	294262	286672.993604172	7589.00639582827
41	312404	288536.670455442	23867.329544558
42	301014	294397.910682922	6616.08931707777
43	309942	296022.662575733	13919.337424267
44	317079	299440.915979352	17638.0840206479
45	293912	303772.403815245	-9860.40381524485
46	304060	301350.926565634	2709.07343436603
47	301299	302016.209632307	-717.209632307175
48	357634	301840.080252581	55793.9197474195
49	281493	315541.720658637	-34048.7206586368
50	282478	307180.176446241	-24702.1764462412
51	319111	301113.917964214	17997.0820357865
52	315223	305533.567050153	9689.43294984737
53	328445	307913.057980677	20531.9420193228
54	321081	312955.207513463	8125.79248653661
55	328040	314950.706076188	13089.2939238118
56	326362	318165.120824697	8196.87917530257
57	313566	320178.076562891	-6612.07656289113
58	319768	318554.310105683	1213.68989431747
59	324315	318852.363057898	5462.63694210182
60	387243	320193.854879737	67049.1451202626
61	293308	336659.507053491	-43351.5070534909
62	295109	326013.422974858	-30904.4229748576
63	339190	318424.042403012	20765.9575969877
64	335678	323523.660514975	12154.3394850249
65	345401	326508.473013377	18892.5269866228
66	351002	331148.02177253	19853.9782274698
67	351889	336023.67975702	15865.3202429804
68	355773	339919.819585165	15853.1804148355
69	333363	343812.978164446	-10449.9781644461
70	336214	341246.715680853	-5032.71568085346
71	343910	340010.802146957	3899.19785304309
72	405788	340968.351053654	64819.6489463464

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 250580 & 236422 & 14158 \tabularnewline
3 & 279515 & 239898.863173391 & 39616.1368266088 \tabularnewline
4 & 264417 & 249627.630457221 & 14789.369542779 \tabularnewline
5 & 283706 & 253259.542755636 & 30446.4572443639 \tabularnewline
6 & 281288 & 260736.457994593 & 20551.5420054065 \tabularnewline
7 & 271146 & 265783.420811022 & 5362.57918897766 \tabularnewline
8 & 283944 & 267100.340863046 & 16843.6591369541 \tabularnewline
9 & 269155 & 271236.737116643 & -2081.73711664317 \tabularnewline
10 & 270899 & 270725.51271224 & 173.487287759839 \tabularnewline
11 & 276507 & 270768.117003938 & 5738.88299606158 \tabularnewline
12 & 319957 & 272177.448190929 & 47779.5518090714 \tabularnewline
13 & 250746 & 283910.953214668 & -33164.9532146676 \tabularnewline
14 & 247772 & 275766.440961573 & -27994.4409615726 \tabularnewline
15 & 280449 & 268891.681755543 & 11557.3182444569 \tabularnewline
16 & 274925 & 271729.880243134 & 3195.11975686584 \tabularnewline
17 & 296013 & 272514.524558519 & 23498.4754414808 \tabularnewline
18 & 287881 & 278285.183118579 & 9595.81688142137 \tabularnewline
19 & 279098 & 280641.684201614 & -1543.68420161435 \tabularnewline
20 & 294763 & 280262.592610151 & 14500.407389849 \tabularnewline
21 & 261924 & 283823.542776342 & -21899.5427763422 \tabularnewline
22 & 291596 & 278445.543497265 & 13150.4565027346 \tabularnewline
23 & 287537 & 281674.978299331 & 5862.02170066925 \tabularnewline
24 & 326201 & 283114.549380887 & 43086.4506191128 \tabularnewline
25 & 255598 & 293695.541994938 & -38097.541994938 \tabularnewline
26 & 253086 & 284339.704958709 & -31253.7049587094 \tabularnewline
27 & 285261 & 276664.549159658 & 8596.45084034197 \tabularnewline
28 & 284747 & 278775.630057289 & 5971.36994271149 \tabularnewline
29 & 300402 & 280242.054428563 & 20159.9455714367 \tabularnewline
30 & 288854 & 285192.850609867 & 3661.14939013292 \tabularnewline
31 & 295433 & 286091.940558083 & 9341.05944191728 \tabularnewline
32 & 307256 & 288385.879361167 & 18870.1206388335 \tabularnewline
33 & 273189 & 293019.925661958 & -19830.9256619582 \tabularnewline
34 & 287540 & 288149.92883131 & -609.928831309779 \tabularnewline
35 & 290705 & 288000.145027667 & 2704.85497233272 \tabularnewline
36 & 337006 & 288664.392141855 & 48341.6078581451 \tabularnewline
37 & 268335 & 300535.924569069 & -32200.9245690693 \tabularnewline
38 & 259060 & 292628.154489726 & -33568.1544897259 \tabularnewline
39 & 293703 & 284384.625732554 & 9318.37426744559 \tabularnewline
40 & 294262 & 286672.993604172 & 7589.00639582827 \tabularnewline
41 & 312404 & 288536.670455442 & 23867.329544558 \tabularnewline
42 & 301014 & 294397.910682922 & 6616.08931707777 \tabularnewline
43 & 309942 & 296022.662575733 & 13919.337424267 \tabularnewline
44 & 317079 & 299440.915979352 & 17638.0840206479 \tabularnewline
45 & 293912 & 303772.403815245 & -9860.40381524485 \tabularnewline
46 & 304060 & 301350.926565634 & 2709.07343436603 \tabularnewline
47 & 301299 & 302016.209632307 & -717.209632307175 \tabularnewline
48 & 357634 & 301840.080252581 & 55793.9197474195 \tabularnewline
49 & 281493 & 315541.720658637 & -34048.7206586368 \tabularnewline
50 & 282478 & 307180.176446241 & -24702.1764462412 \tabularnewline
51 & 319111 & 301113.917964214 & 17997.0820357865 \tabularnewline
52 & 315223 & 305533.567050153 & 9689.43294984737 \tabularnewline
53 & 328445 & 307913.057980677 & 20531.9420193228 \tabularnewline
54 & 321081 & 312955.207513463 & 8125.79248653661 \tabularnewline
55 & 328040 & 314950.706076188 & 13089.2939238118 \tabularnewline
56 & 326362 & 318165.120824697 & 8196.87917530257 \tabularnewline
57 & 313566 & 320178.076562891 & -6612.07656289113 \tabularnewline
58 & 319768 & 318554.310105683 & 1213.68989431747 \tabularnewline
59 & 324315 & 318852.363057898 & 5462.63694210182 \tabularnewline
60 & 387243 & 320193.854879737 & 67049.1451202626 \tabularnewline
61 & 293308 & 336659.507053491 & -43351.5070534909 \tabularnewline
62 & 295109 & 326013.422974858 & -30904.4229748576 \tabularnewline
63 & 339190 & 318424.042403012 & 20765.9575969877 \tabularnewline
64 & 335678 & 323523.660514975 & 12154.3394850249 \tabularnewline
65 & 345401 & 326508.473013377 & 18892.5269866228 \tabularnewline
66 & 351002 & 331148.02177253 & 19853.9782274698 \tabularnewline
67 & 351889 & 336023.67975702 & 15865.3202429804 \tabularnewline
68 & 355773 & 339919.819585165 & 15853.1804148355 \tabularnewline
69 & 333363 & 343812.978164446 & -10449.9781644461 \tabularnewline
70 & 336214 & 341246.715680853 & -5032.71568085346 \tabularnewline
71 & 343910 & 340010.802146957 & 3899.19785304309 \tabularnewline
72 & 405788 & 340968.351053654 & 64819.6489463464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187362&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]250580[/C][C]236422[/C][C]14158[/C][/ROW]
[ROW][C]3[/C][C]279515[/C][C]239898.863173391[/C][C]39616.1368266088[/C][/ROW]
[ROW][C]4[/C][C]264417[/C][C]249627.630457221[/C][C]14789.369542779[/C][/ROW]
[ROW][C]5[/C][C]283706[/C][C]253259.542755636[/C][C]30446.4572443639[/C][/ROW]
[ROW][C]6[/C][C]281288[/C][C]260736.457994593[/C][C]20551.5420054065[/C][/ROW]
[ROW][C]7[/C][C]271146[/C][C]265783.420811022[/C][C]5362.57918897766[/C][/ROW]
[ROW][C]8[/C][C]283944[/C][C]267100.340863046[/C][C]16843.6591369541[/C][/ROW]
[ROW][C]9[/C][C]269155[/C][C]271236.737116643[/C][C]-2081.73711664317[/C][/ROW]
[ROW][C]10[/C][C]270899[/C][C]270725.51271224[/C][C]173.487287759839[/C][/ROW]
[ROW][C]11[/C][C]276507[/C][C]270768.117003938[/C][C]5738.88299606158[/C][/ROW]
[ROW][C]12[/C][C]319957[/C][C]272177.448190929[/C][C]47779.5518090714[/C][/ROW]
[ROW][C]13[/C][C]250746[/C][C]283910.953214668[/C][C]-33164.9532146676[/C][/ROW]
[ROW][C]14[/C][C]247772[/C][C]275766.440961573[/C][C]-27994.4409615726[/C][/ROW]
[ROW][C]15[/C][C]280449[/C][C]268891.681755543[/C][C]11557.3182444569[/C][/ROW]
[ROW][C]16[/C][C]274925[/C][C]271729.880243134[/C][C]3195.11975686584[/C][/ROW]
[ROW][C]17[/C][C]296013[/C][C]272514.524558519[/C][C]23498.4754414808[/C][/ROW]
[ROW][C]18[/C][C]287881[/C][C]278285.183118579[/C][C]9595.81688142137[/C][/ROW]
[ROW][C]19[/C][C]279098[/C][C]280641.684201614[/C][C]-1543.68420161435[/C][/ROW]
[ROW][C]20[/C][C]294763[/C][C]280262.592610151[/C][C]14500.407389849[/C][/ROW]
[ROW][C]21[/C][C]261924[/C][C]283823.542776342[/C][C]-21899.5427763422[/C][/ROW]
[ROW][C]22[/C][C]291596[/C][C]278445.543497265[/C][C]13150.4565027346[/C][/ROW]
[ROW][C]23[/C][C]287537[/C][C]281674.978299331[/C][C]5862.02170066925[/C][/ROW]
[ROW][C]24[/C][C]326201[/C][C]283114.549380887[/C][C]43086.4506191128[/C][/ROW]
[ROW][C]25[/C][C]255598[/C][C]293695.541994938[/C][C]-38097.541994938[/C][/ROW]
[ROW][C]26[/C][C]253086[/C][C]284339.704958709[/C][C]-31253.7049587094[/C][/ROW]
[ROW][C]27[/C][C]285261[/C][C]276664.549159658[/C][C]8596.45084034197[/C][/ROW]
[ROW][C]28[/C][C]284747[/C][C]278775.630057289[/C][C]5971.36994271149[/C][/ROW]
[ROW][C]29[/C][C]300402[/C][C]280242.054428563[/C][C]20159.9455714367[/C][/ROW]
[ROW][C]30[/C][C]288854[/C][C]285192.850609867[/C][C]3661.14939013292[/C][/ROW]
[ROW][C]31[/C][C]295433[/C][C]286091.940558083[/C][C]9341.05944191728[/C][/ROW]
[ROW][C]32[/C][C]307256[/C][C]288385.879361167[/C][C]18870.1206388335[/C][/ROW]
[ROW][C]33[/C][C]273189[/C][C]293019.925661958[/C][C]-19830.9256619582[/C][/ROW]
[ROW][C]34[/C][C]287540[/C][C]288149.92883131[/C][C]-609.928831309779[/C][/ROW]
[ROW][C]35[/C][C]290705[/C][C]288000.145027667[/C][C]2704.85497233272[/C][/ROW]
[ROW][C]36[/C][C]337006[/C][C]288664.392141855[/C][C]48341.6078581451[/C][/ROW]
[ROW][C]37[/C][C]268335[/C][C]300535.924569069[/C][C]-32200.9245690693[/C][/ROW]
[ROW][C]38[/C][C]259060[/C][C]292628.154489726[/C][C]-33568.1544897259[/C][/ROW]
[ROW][C]39[/C][C]293703[/C][C]284384.625732554[/C][C]9318.37426744559[/C][/ROW]
[ROW][C]40[/C][C]294262[/C][C]286672.993604172[/C][C]7589.00639582827[/C][/ROW]
[ROW][C]41[/C][C]312404[/C][C]288536.670455442[/C][C]23867.329544558[/C][/ROW]
[ROW][C]42[/C][C]301014[/C][C]294397.910682922[/C][C]6616.08931707777[/C][/ROW]
[ROW][C]43[/C][C]309942[/C][C]296022.662575733[/C][C]13919.337424267[/C][/ROW]
[ROW][C]44[/C][C]317079[/C][C]299440.915979352[/C][C]17638.0840206479[/C][/ROW]
[ROW][C]45[/C][C]293912[/C][C]303772.403815245[/C][C]-9860.40381524485[/C][/ROW]
[ROW][C]46[/C][C]304060[/C][C]301350.926565634[/C][C]2709.07343436603[/C][/ROW]
[ROW][C]47[/C][C]301299[/C][C]302016.209632307[/C][C]-717.209632307175[/C][/ROW]
[ROW][C]48[/C][C]357634[/C][C]301840.080252581[/C][C]55793.9197474195[/C][/ROW]
[ROW][C]49[/C][C]281493[/C][C]315541.720658637[/C][C]-34048.7206586368[/C][/ROW]
[ROW][C]50[/C][C]282478[/C][C]307180.176446241[/C][C]-24702.1764462412[/C][/ROW]
[ROW][C]51[/C][C]319111[/C][C]301113.917964214[/C][C]17997.0820357865[/C][/ROW]
[ROW][C]52[/C][C]315223[/C][C]305533.567050153[/C][C]9689.43294984737[/C][/ROW]
[ROW][C]53[/C][C]328445[/C][C]307913.057980677[/C][C]20531.9420193228[/C][/ROW]
[ROW][C]54[/C][C]321081[/C][C]312955.207513463[/C][C]8125.79248653661[/C][/ROW]
[ROW][C]55[/C][C]328040[/C][C]314950.706076188[/C][C]13089.2939238118[/C][/ROW]
[ROW][C]56[/C][C]326362[/C][C]318165.120824697[/C][C]8196.87917530257[/C][/ROW]
[ROW][C]57[/C][C]313566[/C][C]320178.076562891[/C][C]-6612.07656289113[/C][/ROW]
[ROW][C]58[/C][C]319768[/C][C]318554.310105683[/C][C]1213.68989431747[/C][/ROW]
[ROW][C]59[/C][C]324315[/C][C]318852.363057898[/C][C]5462.63694210182[/C][/ROW]
[ROW][C]60[/C][C]387243[/C][C]320193.854879737[/C][C]67049.1451202626[/C][/ROW]
[ROW][C]61[/C][C]293308[/C][C]336659.507053491[/C][C]-43351.5070534909[/C][/ROW]
[ROW][C]62[/C][C]295109[/C][C]326013.422974858[/C][C]-30904.4229748576[/C][/ROW]
[ROW][C]63[/C][C]339190[/C][C]318424.042403012[/C][C]20765.9575969877[/C][/ROW]
[ROW][C]64[/C][C]335678[/C][C]323523.660514975[/C][C]12154.3394850249[/C][/ROW]
[ROW][C]65[/C][C]345401[/C][C]326508.473013377[/C][C]18892.5269866228[/C][/ROW]
[ROW][C]66[/C][C]351002[/C][C]331148.02177253[/C][C]19853.9782274698[/C][/ROW]
[ROW][C]67[/C][C]351889[/C][C]336023.67975702[/C][C]15865.3202429804[/C][/ROW]
[ROW][C]68[/C][C]355773[/C][C]339919.819585165[/C][C]15853.1804148355[/C][/ROW]
[ROW][C]69[/C][C]333363[/C][C]343812.978164446[/C][C]-10449.9781644461[/C][/ROW]
[ROW][C]70[/C][C]336214[/C][C]341246.715680853[/C][C]-5032.71568085346[/C][/ROW]
[ROW][C]71[/C][C]343910[/C][C]340010.802146957[/C][C]3899.19785304309[/C][/ROW]
[ROW][C]72[/C][C]405788[/C][C]340968.351053654[/C][C]64819.6489463464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187362&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187362&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
2	250580	236422	14158
3	279515	239898.863173391	39616.1368266088
4	264417	249627.630457221	14789.369542779
5	283706	253259.542755636	30446.4572443639
6	281288	260736.457994593	20551.5420054065
7	271146	265783.420811022	5362.57918897766
8	283944	267100.340863046	16843.6591369541
9	269155	271236.737116643	-2081.73711664317
10	270899	270725.51271224	173.487287759839
11	276507	270768.117003938	5738.88299606158
12	319957	272177.448190929	47779.5518090714
13	250746	283910.953214668	-33164.9532146676
14	247772	275766.440961573	-27994.4409615726
15	280449	268891.681755543	11557.3182444569
16	274925	271729.880243134	3195.11975686584
17	296013	272514.524558519	23498.4754414808
18	287881	278285.183118579	9595.81688142137
19	279098	280641.684201614	-1543.68420161435
20	294763	280262.592610151	14500.407389849
21	261924	283823.542776342	-21899.5427763422
22	291596	278445.543497265	13150.4565027346
23	287537	281674.978299331	5862.02170066925
24	326201	283114.549380887	43086.4506191128
25	255598	293695.541994938	-38097.541994938
26	253086	284339.704958709	-31253.7049587094
27	285261	276664.549159658	8596.45084034197
28	284747	278775.630057289	5971.36994271149
29	300402	280242.054428563	20159.9455714367
30	288854	285192.850609867	3661.14939013292
31	295433	286091.940558083	9341.05944191728
32	307256	288385.879361167	18870.1206388335
33	273189	293019.925661958	-19830.9256619582
34	287540	288149.92883131	-609.928831309779
35	290705	288000.145027667	2704.85497233272
36	337006	288664.392141855	48341.6078581451
37	268335	300535.924569069	-32200.9245690693
38	259060	292628.154489726	-33568.1544897259
39	293703	284384.625732554	9318.37426744559
40	294262	286672.993604172	7589.00639582827
41	312404	288536.670455442	23867.329544558
42	301014	294397.910682922	6616.08931707777
43	309942	296022.662575733	13919.337424267
44	317079	299440.915979352	17638.0840206479
45	293912	303772.403815245	-9860.40381524485
46	304060	301350.926565634	2709.07343436603
47	301299	302016.209632307	-717.209632307175
48	357634	301840.080252581	55793.9197474195
49	281493	315541.720658637	-34048.7206586368
50	282478	307180.176446241	-24702.1764462412
51	319111	301113.917964214	17997.0820357865
52	315223	305533.567050153	9689.43294984737
53	328445	307913.057980677	20531.9420193228
54	321081	312955.207513463	8125.79248653661
55	328040	314950.706076188	13089.2939238118
56	326362	318165.120824697	8196.87917530257
57	313566	320178.076562891	-6612.07656289113
58	319768	318554.310105683	1213.68989431747
59	324315	318852.363057898	5462.63694210182
60	387243	320193.854879737	67049.1451202626
61	293308	336659.507053491	-43351.5070534909
62	295109	326013.422974858	-30904.4229748576
63	339190	318424.042403012	20765.9575969877
64	335678	323523.660514975	12154.3394850249
65	345401	326508.473013377	18892.5269866228
66	351002	331148.02177253	19853.9782274698
67	351889	336023.67975702	15865.3202429804
68	355773	339919.819585165	15853.1804148355
69	333363	343812.978164446	-10449.9781644461
70	336214	341246.715680853	-5032.71568085346
71	343910	340010.802146957	3899.19785304309
72	405788	340968.351053654	64819.6489463464

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	356886.492763902	311646.165149274	402126.82037853
74	356886.492763902	310301.969043997	403471.016483807
75	356886.492763902	308995.4867425	404777.498785304
76	356886.492763902	307723.711462663	406049.274065141
77	356886.492763902	306484.015912015	407288.969615789
78	356886.492763902	305274.08843765	408498.897090154
79	356886.492763902	304091.882358406	409681.103169398
80	356886.492763902	302935.57529812	410837.410229684
81	356886.492763902	301803.536208074	411969.44931973
82	356886.492763902	300694.298373019	413078.687154785
83	356886.492763902	299606.537125003	414166.448402801
84	356886.492763902	298539.05129878	415233.934229024

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 356886.492763902 & 311646.165149274 & 402126.82037853 \tabularnewline
74 & 356886.492763902 & 310301.969043997 & 403471.016483807 \tabularnewline
75 & 356886.492763902 & 308995.4867425 & 404777.498785304 \tabularnewline
76 & 356886.492763902 & 307723.711462663 & 406049.274065141 \tabularnewline
77 & 356886.492763902 & 306484.015912015 & 407288.969615789 \tabularnewline
78 & 356886.492763902 & 305274.08843765 & 408498.897090154 \tabularnewline
79 & 356886.492763902 & 304091.882358406 & 409681.103169398 \tabularnewline
80 & 356886.492763902 & 302935.57529812 & 410837.410229684 \tabularnewline
81 & 356886.492763902 & 301803.536208074 & 411969.44931973 \tabularnewline
82 & 356886.492763902 & 300694.298373019 & 413078.687154785 \tabularnewline
83 & 356886.492763902 & 299606.537125003 & 414166.448402801 \tabularnewline
84 & 356886.492763902 & 298539.05129878 & 415233.934229024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187362&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]356886.492763902[/C][C]311646.165149274[/C][C]402126.82037853[/C][/ROW]
[ROW][C]74[/C][C]356886.492763902[/C][C]310301.969043997[/C][C]403471.016483807[/C][/ROW]
[ROW][C]75[/C][C]356886.492763902[/C][C]308995.4867425[/C][C]404777.498785304[/C][/ROW]
[ROW][C]76[/C][C]356886.492763902[/C][C]307723.711462663[/C][C]406049.274065141[/C][/ROW]
[ROW][C]77[/C][C]356886.492763902[/C][C]306484.015912015[/C][C]407288.969615789[/C][/ROW]
[ROW][C]78[/C][C]356886.492763902[/C][C]305274.08843765[/C][C]408498.897090154[/C][/ROW]
[ROW][C]79[/C][C]356886.492763902[/C][C]304091.882358406[/C][C]409681.103169398[/C][/ROW]
[ROW][C]80[/C][C]356886.492763902[/C][C]302935.57529812[/C][C]410837.410229684[/C][/ROW]
[ROW][C]81[/C][C]356886.492763902[/C][C]301803.536208074[/C][C]411969.44931973[/C][/ROW]
[ROW][C]82[/C][C]356886.492763902[/C][C]300694.298373019[/C][C]413078.687154785[/C][/ROW]
[ROW][C]83[/C][C]356886.492763902[/C][C]299606.537125003[/C][C]414166.448402801[/C][/ROW]
[ROW][C]84[/C][C]356886.492763902[/C][C]298539.05129878[/C][C]415233.934229024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187362&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187362&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
73	356886.492763902	311646.165149274	402126.82037853
74	356886.492763902	310301.969043997	403471.016483807
75	356886.492763902	308995.4867425	404777.498785304
76	356886.492763902	307723.711462663	406049.274065141
77	356886.492763902	306484.015912015	407288.969615789
78	356886.492763902	305274.08843765	408498.897090154
79	356886.492763902	304091.882358406	409681.103169398
80	356886.492763902	302935.57529812	410837.410229684
81	356886.492763902	301803.536208074	411969.44931973
82	356886.492763902	300694.298373019	413078.687154785
83	356886.492763902	299606.537125003	414166.448402801
84	356886.492763902	298539.05129878	415233.934229024

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code