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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 16 Aug 2009 11:07:26 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Aug/16/t1250442516lqrx1ah9q834g63.htm/, Retrieved Sun, 19 May 2024 13:32:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42667, Retrieved Sun, 19 May 2024 13:32:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

147

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

-     [Exponential Smoothing] [Opdracht10 - smoo...] [2009-06-03 13:19:13] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [] [2009-08-16 17:07:26] [e921d89db97faa9283224ee60d8fb091] [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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42667&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42667&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42667&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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.929989159847248
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.929989159847248 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42667&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]0.929989159847248[/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=42667&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42667&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	0.929989159847248
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	131.5	113.305714174274	18.1942858257257
14	137.43	137.974551701713	-0.544551701712805
15	138.53	140.340439005924	-1.81043900592434
16	137.26	139.292529560728	-2.03252956072808
17	136.81	139.387640893203	-2.57764089320281
18	182.98	188.245230333321	-5.26523033332143
19	149.45	184.803288962658	-35.3532889626577
20	109.34	103.736795169832	5.60320483016845
21	93.37	93.3794968619423	-0.00949686194233834
22	84.09	81.665020226247	2.42497977375298
23	83.83	91.7655111862668	-7.93551118626677
24	82.94	97.1210791226548	-14.1810791226548
25	82.88	98.5752185079875	-15.6952185079875
26	81.41	88.5952534687052	-7.18525346870516
27	79.87	84.1426336785468	-4.27263367854684
28	79.66	81.119372501963	-1.45937250196295
29	76.07	81.4832106853364	-5.41321068533644
30	182.69	105.825899270878	76.8641007291216
31	165.78	176.216490802454	-10.4364908024540
32	142.5	115.847018188818	26.6529818111824
33	120.6	119.791116015651	0.808883984348782
34	105.73	105.369052697395	0.360947302604799
35	98.72	114.332266471431	-15.6122664714306
36	98.41	114.050955619058	-15.6409556190585
37	96.08	116.449692253561	-20.3696922535607
38	97.3	103.344233617483	-6.04423361748266
39	97.5	100.34415490479	-2.84415490479013
40	97.02	98.7867686268537	-1.76676862685372
41	98.75	98.5661583306535	0.183841669346549
42	232.81	140.93937568456	91.8706243154399
43	240.83	216.949158999637	23.8808410003633
44	193.4	168.759011032804	24.6409889671965
45	148.28	160.826969898315	-12.5469698983152
46	138.34	130.127155229314	8.21284477068582
47	135.34	147.037480061412	-11.6974800614124
48	134.02	155.141438975657	-21.1214389756574
49	133.86	157.497848228690	-23.6378482286904
50	131.67	144.560722945706	-12.8907229457061
51	132.43	135.931789495187	-3.5017894951867
52	130.21	133.748952916699	-3.53895291669934
53	129.98	132.069884988681	-2.08988498868149
54	206.16	190.351485060288	15.8085149397118
55	195.17	192.644734398672	2.52526560132816
56	159.16	138.121713365665	21.0382866343348
57	136.33	130.557867088628	5.77213291137218
58	125.18	119.862731573144	5.31726842685615
59	121.21	131.954380405339	-10.7443804053388
60	119.38	138.391881533937	-19.0118815339374
61	119.26	140.253698745492	-20.9936987454921
62	119.75	129.628314538365	-9.87831453836537
63	118.78	124.229876447978	-5.44987644797848
64	116.97	120.260059049991	-3.29005904999086
65	121.69	118.880945098856	2.80905490114449
66	223.51	179.016840310821	44.4931596891794
67	228.58	206.002537173279	22.5774628267214
68	205.22	161.929461231110	43.2905387688905
69	189.4	166.052109338176	23.3478906618239
70	180.14	165.217018751686	14.9229812483140
71	177.59	187.194932773089	-9.6049327730889
72	176.39	200.763514177480	-24.3735141774796
73	171.16	206.059970511165	-34.8999705111648
74	173.11	186.989177727086	-13.8791777270861
75	171.74	179.381107528609	-7.64110752860947
76	175.97	173.449511924002	2.52048807599792
77	179.64	178.247833517453	1.39216648254717
78	254.62	266.870582063894	-12.2505820638935
79	240.5	236.833171960790	3.66682803921034
80	212.01	172.673712156756	39.3362878432438
81	176.36	170.770165824129	5.58983417587052
82	153.24	154.464255749855	-1.22425574985505
83	146.69	158.876839049809	-12.1868390498092
84	141.52	165.384332148669	-23.864332148669
85	142.6	165.15956205409	-22.5595620540901
86	143.19	156.848670740075	-13.6586707400753
87	142.32	149.137645674677	-6.81764567467673
88	142.03	144.599200734974	-2.56920073497403
89	144.92	144.398710283295	0.521289716704558
90	177.31	214.913996051311	-37.6039960513109
91	194.4	168.111082203988	26.2889177960116
92	189.19	140.347532800055	48.8424671999452
93	180.44	150.104225600533	30.3357743994673
94	175.84	156.079593518720	19.7604064812797
95	178.54	179.691595421468	-1.15159542146847
96	176.55	198.797301018429	-22.2473010184293

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 131.5 & 113.305714174274 & 18.1942858257257 \tabularnewline
14 & 137.43 & 137.974551701713 & -0.544551701712805 \tabularnewline
15 & 138.53 & 140.340439005924 & -1.81043900592434 \tabularnewline
16 & 137.26 & 139.292529560728 & -2.03252956072808 \tabularnewline
17 & 136.81 & 139.387640893203 & -2.57764089320281 \tabularnewline
18 & 182.98 & 188.245230333321 & -5.26523033332143 \tabularnewline
19 & 149.45 & 184.803288962658 & -35.3532889626577 \tabularnewline
20 & 109.34 & 103.736795169832 & 5.60320483016845 \tabularnewline
21 & 93.37 & 93.3794968619423 & -0.00949686194233834 \tabularnewline
22 & 84.09 & 81.665020226247 & 2.42497977375298 \tabularnewline
23 & 83.83 & 91.7655111862668 & -7.93551118626677 \tabularnewline
24 & 82.94 & 97.1210791226548 & -14.1810791226548 \tabularnewline
25 & 82.88 & 98.5752185079875 & -15.6952185079875 \tabularnewline
26 & 81.41 & 88.5952534687052 & -7.18525346870516 \tabularnewline
27 & 79.87 & 84.1426336785468 & -4.27263367854684 \tabularnewline
28 & 79.66 & 81.119372501963 & -1.45937250196295 \tabularnewline
29 & 76.07 & 81.4832106853364 & -5.41321068533644 \tabularnewline
30 & 182.69 & 105.825899270878 & 76.8641007291216 \tabularnewline
31 & 165.78 & 176.216490802454 & -10.4364908024540 \tabularnewline
32 & 142.5 & 115.847018188818 & 26.6529818111824 \tabularnewline
33 & 120.6 & 119.791116015651 & 0.808883984348782 \tabularnewline
34 & 105.73 & 105.369052697395 & 0.360947302604799 \tabularnewline
35 & 98.72 & 114.332266471431 & -15.6122664714306 \tabularnewline
36 & 98.41 & 114.050955619058 & -15.6409556190585 \tabularnewline
37 & 96.08 & 116.449692253561 & -20.3696922535607 \tabularnewline
38 & 97.3 & 103.344233617483 & -6.04423361748266 \tabularnewline
39 & 97.5 & 100.34415490479 & -2.84415490479013 \tabularnewline
40 & 97.02 & 98.7867686268537 & -1.76676862685372 \tabularnewline
41 & 98.75 & 98.5661583306535 & 0.183841669346549 \tabularnewline
42 & 232.81 & 140.93937568456 & 91.8706243154399 \tabularnewline
43 & 240.83 & 216.949158999637 & 23.8808410003633 \tabularnewline
44 & 193.4 & 168.759011032804 & 24.6409889671965 \tabularnewline
45 & 148.28 & 160.826969898315 & -12.5469698983152 \tabularnewline
46 & 138.34 & 130.127155229314 & 8.21284477068582 \tabularnewline
47 & 135.34 & 147.037480061412 & -11.6974800614124 \tabularnewline
48 & 134.02 & 155.141438975657 & -21.1214389756574 \tabularnewline
49 & 133.86 & 157.497848228690 & -23.6378482286904 \tabularnewline
50 & 131.67 & 144.560722945706 & -12.8907229457061 \tabularnewline
51 & 132.43 & 135.931789495187 & -3.5017894951867 \tabularnewline
52 & 130.21 & 133.748952916699 & -3.53895291669934 \tabularnewline
53 & 129.98 & 132.069884988681 & -2.08988498868149 \tabularnewline
54 & 206.16 & 190.351485060288 & 15.8085149397118 \tabularnewline
55 & 195.17 & 192.644734398672 & 2.52526560132816 \tabularnewline
56 & 159.16 & 138.121713365665 & 21.0382866343348 \tabularnewline
57 & 136.33 & 130.557867088628 & 5.77213291137218 \tabularnewline
58 & 125.18 & 119.862731573144 & 5.31726842685615 \tabularnewline
59 & 121.21 & 131.954380405339 & -10.7443804053388 \tabularnewline
60 & 119.38 & 138.391881533937 & -19.0118815339374 \tabularnewline
61 & 119.26 & 140.253698745492 & -20.9936987454921 \tabularnewline
62 & 119.75 & 129.628314538365 & -9.87831453836537 \tabularnewline
63 & 118.78 & 124.229876447978 & -5.44987644797848 \tabularnewline
64 & 116.97 & 120.260059049991 & -3.29005904999086 \tabularnewline
65 & 121.69 & 118.880945098856 & 2.80905490114449 \tabularnewline
66 & 223.51 & 179.016840310821 & 44.4931596891794 \tabularnewline
67 & 228.58 & 206.002537173279 & 22.5774628267214 \tabularnewline
68 & 205.22 & 161.929461231110 & 43.2905387688905 \tabularnewline
69 & 189.4 & 166.052109338176 & 23.3478906618239 \tabularnewline
70 & 180.14 & 165.217018751686 & 14.9229812483140 \tabularnewline
71 & 177.59 & 187.194932773089 & -9.6049327730889 \tabularnewline
72 & 176.39 & 200.763514177480 & -24.3735141774796 \tabularnewline
73 & 171.16 & 206.059970511165 & -34.8999705111648 \tabularnewline
74 & 173.11 & 186.989177727086 & -13.8791777270861 \tabularnewline
75 & 171.74 & 179.381107528609 & -7.64110752860947 \tabularnewline
76 & 175.97 & 173.449511924002 & 2.52048807599792 \tabularnewline
77 & 179.64 & 178.247833517453 & 1.39216648254717 \tabularnewline
78 & 254.62 & 266.870582063894 & -12.2505820638935 \tabularnewline
79 & 240.5 & 236.833171960790 & 3.66682803921034 \tabularnewline
80 & 212.01 & 172.673712156756 & 39.3362878432438 \tabularnewline
81 & 176.36 & 170.770165824129 & 5.58983417587052 \tabularnewline
82 & 153.24 & 154.464255749855 & -1.22425574985505 \tabularnewline
83 & 146.69 & 158.876839049809 & -12.1868390498092 \tabularnewline
84 & 141.52 & 165.384332148669 & -23.864332148669 \tabularnewline
85 & 142.6 & 165.15956205409 & -22.5595620540901 \tabularnewline
86 & 143.19 & 156.848670740075 & -13.6586707400753 \tabularnewline
87 & 142.32 & 149.137645674677 & -6.81764567467673 \tabularnewline
88 & 142.03 & 144.599200734974 & -2.56920073497403 \tabularnewline
89 & 144.92 & 144.398710283295 & 0.521289716704558 \tabularnewline
90 & 177.31 & 214.913996051311 & -37.6039960513109 \tabularnewline
91 & 194.4 & 168.111082203988 & 26.2889177960116 \tabularnewline
92 & 189.19 & 140.347532800055 & 48.8424671999452 \tabularnewline
93 & 180.44 & 150.104225600533 & 30.3357743994673 \tabularnewline
94 & 175.84 & 156.079593518720 & 19.7604064812797 \tabularnewline
95 & 178.54 & 179.691595421468 & -1.15159542146847 \tabularnewline
96 & 176.55 & 198.797301018429 & -22.2473010184293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42667&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]131.5[/C][C]113.305714174274[/C][C]18.1942858257257[/C][/ROW]
[ROW][C]14[/C][C]137.43[/C][C]137.974551701713[/C][C]-0.544551701712805[/C][/ROW]
[ROW][C]15[/C][C]138.53[/C][C]140.340439005924[/C][C]-1.81043900592434[/C][/ROW]
[ROW][C]16[/C][C]137.26[/C][C]139.292529560728[/C][C]-2.03252956072808[/C][/ROW]
[ROW][C]17[/C][C]136.81[/C][C]139.387640893203[/C][C]-2.57764089320281[/C][/ROW]
[ROW][C]18[/C][C]182.98[/C][C]188.245230333321[/C][C]-5.26523033332143[/C][/ROW]
[ROW][C]19[/C][C]149.45[/C][C]184.803288962658[/C][C]-35.3532889626577[/C][/ROW]
[ROW][C]20[/C][C]109.34[/C][C]103.736795169832[/C][C]5.60320483016845[/C][/ROW]
[ROW][C]21[/C][C]93.37[/C][C]93.3794968619423[/C][C]-0.00949686194233834[/C][/ROW]
[ROW][C]22[/C][C]84.09[/C][C]81.665020226247[/C][C]2.42497977375298[/C][/ROW]
[ROW][C]23[/C][C]83.83[/C][C]91.7655111862668[/C][C]-7.93551118626677[/C][/ROW]
[ROW][C]24[/C][C]82.94[/C][C]97.1210791226548[/C][C]-14.1810791226548[/C][/ROW]
[ROW][C]25[/C][C]82.88[/C][C]98.5752185079875[/C][C]-15.6952185079875[/C][/ROW]
[ROW][C]26[/C][C]81.41[/C][C]88.5952534687052[/C][C]-7.18525346870516[/C][/ROW]
[ROW][C]27[/C][C]79.87[/C][C]84.1426336785468[/C][C]-4.27263367854684[/C][/ROW]
[ROW][C]28[/C][C]79.66[/C][C]81.119372501963[/C][C]-1.45937250196295[/C][/ROW]
[ROW][C]29[/C][C]76.07[/C][C]81.4832106853364[/C][C]-5.41321068533644[/C][/ROW]
[ROW][C]30[/C][C]182.69[/C][C]105.825899270878[/C][C]76.8641007291216[/C][/ROW]
[ROW][C]31[/C][C]165.78[/C][C]176.216490802454[/C][C]-10.4364908024540[/C][/ROW]
[ROW][C]32[/C][C]142.5[/C][C]115.847018188818[/C][C]26.6529818111824[/C][/ROW]
[ROW][C]33[/C][C]120.6[/C][C]119.791116015651[/C][C]0.808883984348782[/C][/ROW]
[ROW][C]34[/C][C]105.73[/C][C]105.369052697395[/C][C]0.360947302604799[/C][/ROW]
[ROW][C]35[/C][C]98.72[/C][C]114.332266471431[/C][C]-15.6122664714306[/C][/ROW]
[ROW][C]36[/C][C]98.41[/C][C]114.050955619058[/C][C]-15.6409556190585[/C][/ROW]
[ROW][C]37[/C][C]96.08[/C][C]116.449692253561[/C][C]-20.3696922535607[/C][/ROW]
[ROW][C]38[/C][C]97.3[/C][C]103.344233617483[/C][C]-6.04423361748266[/C][/ROW]
[ROW][C]39[/C][C]97.5[/C][C]100.34415490479[/C][C]-2.84415490479013[/C][/ROW]
[ROW][C]40[/C][C]97.02[/C][C]98.7867686268537[/C][C]-1.76676862685372[/C][/ROW]
[ROW][C]41[/C][C]98.75[/C][C]98.5661583306535[/C][C]0.183841669346549[/C][/ROW]
[ROW][C]42[/C][C]232.81[/C][C]140.93937568456[/C][C]91.8706243154399[/C][/ROW]
[ROW][C]43[/C][C]240.83[/C][C]216.949158999637[/C][C]23.8808410003633[/C][/ROW]
[ROW][C]44[/C][C]193.4[/C][C]168.759011032804[/C][C]24.6409889671965[/C][/ROW]
[ROW][C]45[/C][C]148.28[/C][C]160.826969898315[/C][C]-12.5469698983152[/C][/ROW]
[ROW][C]46[/C][C]138.34[/C][C]130.127155229314[/C][C]8.21284477068582[/C][/ROW]
[ROW][C]47[/C][C]135.34[/C][C]147.037480061412[/C][C]-11.6974800614124[/C][/ROW]
[ROW][C]48[/C][C]134.02[/C][C]155.141438975657[/C][C]-21.1214389756574[/C][/ROW]
[ROW][C]49[/C][C]133.86[/C][C]157.497848228690[/C][C]-23.6378482286904[/C][/ROW]
[ROW][C]50[/C][C]131.67[/C][C]144.560722945706[/C][C]-12.8907229457061[/C][/ROW]
[ROW][C]51[/C][C]132.43[/C][C]135.931789495187[/C][C]-3.5017894951867[/C][/ROW]
[ROW][C]52[/C][C]130.21[/C][C]133.748952916699[/C][C]-3.53895291669934[/C][/ROW]
[ROW][C]53[/C][C]129.98[/C][C]132.069884988681[/C][C]-2.08988498868149[/C][/ROW]
[ROW][C]54[/C][C]206.16[/C][C]190.351485060288[/C][C]15.8085149397118[/C][/ROW]
[ROW][C]55[/C][C]195.17[/C][C]192.644734398672[/C][C]2.52526560132816[/C][/ROW]
[ROW][C]56[/C][C]159.16[/C][C]138.121713365665[/C][C]21.0382866343348[/C][/ROW]
[ROW][C]57[/C][C]136.33[/C][C]130.557867088628[/C][C]5.77213291137218[/C][/ROW]
[ROW][C]58[/C][C]125.18[/C][C]119.862731573144[/C][C]5.31726842685615[/C][/ROW]
[ROW][C]59[/C][C]121.21[/C][C]131.954380405339[/C][C]-10.7443804053388[/C][/ROW]
[ROW][C]60[/C][C]119.38[/C][C]138.391881533937[/C][C]-19.0118815339374[/C][/ROW]
[ROW][C]61[/C][C]119.26[/C][C]140.253698745492[/C][C]-20.9936987454921[/C][/ROW]
[ROW][C]62[/C][C]119.75[/C][C]129.628314538365[/C][C]-9.87831453836537[/C][/ROW]
[ROW][C]63[/C][C]118.78[/C][C]124.229876447978[/C][C]-5.44987644797848[/C][/ROW]
[ROW][C]64[/C][C]116.97[/C][C]120.260059049991[/C][C]-3.29005904999086[/C][/ROW]
[ROW][C]65[/C][C]121.69[/C][C]118.880945098856[/C][C]2.80905490114449[/C][/ROW]
[ROW][C]66[/C][C]223.51[/C][C]179.016840310821[/C][C]44.4931596891794[/C][/ROW]
[ROW][C]67[/C][C]228.58[/C][C]206.002537173279[/C][C]22.5774628267214[/C][/ROW]
[ROW][C]68[/C][C]205.22[/C][C]161.929461231110[/C][C]43.2905387688905[/C][/ROW]
[ROW][C]69[/C][C]189.4[/C][C]166.052109338176[/C][C]23.3478906618239[/C][/ROW]
[ROW][C]70[/C][C]180.14[/C][C]165.217018751686[/C][C]14.9229812483140[/C][/ROW]
[ROW][C]71[/C][C]177.59[/C][C]187.194932773089[/C][C]-9.6049327730889[/C][/ROW]
[ROW][C]72[/C][C]176.39[/C][C]200.763514177480[/C][C]-24.3735141774796[/C][/ROW]
[ROW][C]73[/C][C]171.16[/C][C]206.059970511165[/C][C]-34.8999705111648[/C][/ROW]
[ROW][C]74[/C][C]173.11[/C][C]186.989177727086[/C][C]-13.8791777270861[/C][/ROW]
[ROW][C]75[/C][C]171.74[/C][C]179.381107528609[/C][C]-7.64110752860947[/C][/ROW]
[ROW][C]76[/C][C]175.97[/C][C]173.449511924002[/C][C]2.52048807599792[/C][/ROW]
[ROW][C]77[/C][C]179.64[/C][C]178.247833517453[/C][C]1.39216648254717[/C][/ROW]
[ROW][C]78[/C][C]254.62[/C][C]266.870582063894[/C][C]-12.2505820638935[/C][/ROW]
[ROW][C]79[/C][C]240.5[/C][C]236.833171960790[/C][C]3.66682803921034[/C][/ROW]
[ROW][C]80[/C][C]212.01[/C][C]172.673712156756[/C][C]39.3362878432438[/C][/ROW]
[ROW][C]81[/C][C]176.36[/C][C]170.770165824129[/C][C]5.58983417587052[/C][/ROW]
[ROW][C]82[/C][C]153.24[/C][C]154.464255749855[/C][C]-1.22425574985505[/C][/ROW]
[ROW][C]83[/C][C]146.69[/C][C]158.876839049809[/C][C]-12.1868390498092[/C][/ROW]
[ROW][C]84[/C][C]141.52[/C][C]165.384332148669[/C][C]-23.864332148669[/C][/ROW]
[ROW][C]85[/C][C]142.6[/C][C]165.15956205409[/C][C]-22.5595620540901[/C][/ROW]
[ROW][C]86[/C][C]143.19[/C][C]156.848670740075[/C][C]-13.6586707400753[/C][/ROW]
[ROW][C]87[/C][C]142.32[/C][C]149.137645674677[/C][C]-6.81764567467673[/C][/ROW]
[ROW][C]88[/C][C]142.03[/C][C]144.599200734974[/C][C]-2.56920073497403[/C][/ROW]
[ROW][C]89[/C][C]144.92[/C][C]144.398710283295[/C][C]0.521289716704558[/C][/ROW]
[ROW][C]90[/C][C]177.31[/C][C]214.913996051311[/C][C]-37.6039960513109[/C][/ROW]
[ROW][C]91[/C][C]194.4[/C][C]168.111082203988[/C][C]26.2889177960116[/C][/ROW]
[ROW][C]92[/C][C]189.19[/C][C]140.347532800055[/C][C]48.8424671999452[/C][/ROW]
[ROW][C]93[/C][C]180.44[/C][C]150.104225600533[/C][C]30.3357743994673[/C][/ROW]
[ROW][C]94[/C][C]175.84[/C][C]156.079593518720[/C][C]19.7604064812797[/C][/ROW]
[ROW][C]95[/C][C]178.54[/C][C]179.691595421468[/C][C]-1.15159542146847[/C][/ROW]
[ROW][C]96[/C][C]176.55[/C][C]198.797301018429[/C][C]-22.2473010184293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42667&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42667&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	131.5	113.305714174274	18.1942858257257
14	137.43	137.974551701713	-0.544551701712805
15	138.53	140.340439005924	-1.81043900592434
16	137.26	139.292529560728	-2.03252956072808
17	136.81	139.387640893203	-2.57764089320281
18	182.98	188.245230333321	-5.26523033332143
19	149.45	184.803288962658	-35.3532889626577
20	109.34	103.736795169832	5.60320483016845
21	93.37	93.3794968619423	-0.00949686194233834
22	84.09	81.665020226247	2.42497977375298
23	83.83	91.7655111862668	-7.93551118626677
24	82.94	97.1210791226548	-14.1810791226548
25	82.88	98.5752185079875	-15.6952185079875
26	81.41	88.5952534687052	-7.18525346870516
27	79.87	84.1426336785468	-4.27263367854684
28	79.66	81.119372501963	-1.45937250196295
29	76.07	81.4832106853364	-5.41321068533644
30	182.69	105.825899270878	76.8641007291216
31	165.78	176.216490802454	-10.4364908024540
32	142.5	115.847018188818	26.6529818111824
33	120.6	119.791116015651	0.808883984348782
34	105.73	105.369052697395	0.360947302604799
35	98.72	114.332266471431	-15.6122664714306
36	98.41	114.050955619058	-15.6409556190585
37	96.08	116.449692253561	-20.3696922535607
38	97.3	103.344233617483	-6.04423361748266
39	97.5	100.34415490479	-2.84415490479013
40	97.02	98.7867686268537	-1.76676862685372
41	98.75	98.5661583306535	0.183841669346549
42	232.81	140.93937568456	91.8706243154399
43	240.83	216.949158999637	23.8808410003633
44	193.4	168.759011032804	24.6409889671965
45	148.28	160.826969898315	-12.5469698983152
46	138.34	130.127155229314	8.21284477068582
47	135.34	147.037480061412	-11.6974800614124
48	134.02	155.141438975657	-21.1214389756574
49	133.86	157.497848228690	-23.6378482286904
50	131.67	144.560722945706	-12.8907229457061
51	132.43	135.931789495187	-3.5017894951867
52	130.21	133.748952916699	-3.53895291669934
53	129.98	132.069884988681	-2.08988498868149
54	206.16	190.351485060288	15.8085149397118
55	195.17	192.644734398672	2.52526560132816
56	159.16	138.121713365665	21.0382866343348
57	136.33	130.557867088628	5.77213291137218
58	125.18	119.862731573144	5.31726842685615
59	121.21	131.954380405339	-10.7443804053388
60	119.38	138.391881533937	-19.0118815339374
61	119.26	140.253698745492	-20.9936987454921
62	119.75	129.628314538365	-9.87831453836537
63	118.78	124.229876447978	-5.44987644797848
64	116.97	120.260059049991	-3.29005904999086
65	121.69	118.880945098856	2.80905490114449
66	223.51	179.016840310821	44.4931596891794
67	228.58	206.002537173279	22.5774628267214
68	205.22	161.929461231110	43.2905387688905
69	189.4	166.052109338176	23.3478906618239
70	180.14	165.217018751686	14.9229812483140
71	177.59	187.194932773089	-9.6049327730889
72	176.39	200.763514177480	-24.3735141774796
73	171.16	206.059970511165	-34.8999705111648
74	173.11	186.989177727086	-13.8791777270861
75	171.74	179.381107528609	-7.64110752860947
76	175.97	173.449511924002	2.52048807599792
77	179.64	178.247833517453	1.39216648254717
78	254.62	266.870582063894	-12.2505820638935
79	240.5	236.833171960790	3.66682803921034
80	212.01	172.673712156756	39.3362878432438
81	176.36	170.770165824129	5.58983417587052
82	153.24	154.464255749855	-1.22425574985505
83	146.69	158.876839049809	-12.1868390498092
84	141.52	165.384332148669	-23.864332148669
85	142.6	165.15956205409	-22.5595620540901
86	143.19	156.848670740075	-13.6586707400753
87	142.32	149.137645674677	-6.81764567467673
88	142.03	144.599200734974	-2.56920073497403
89	144.92	144.398710283295	0.521289716704558
90	177.31	214.913996051311	-37.6039960513109
91	194.4	168.111082203988	26.2889177960116
92	189.19	140.347532800055	48.8424671999452
93	180.44	150.104225600533	30.3357743994673
94	175.84	156.079593518720	19.7604064812797
95	178.54	179.691595421468	-1.15159542146847
96	176.55	198.797301018429	-22.2473010184293

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	205.259082949355	162.400179191347	248.117986707364
98	223.676991638419	162.843328577126	284.510654699713
99	231.407744271001	157.327138946502	305.488349595499
100	233.941863898399	149.512909719481	318.370818077318
101	236.993026804595	143.110132423085	330.875921186105
102	345.021288263484	204.387210569578	485.65536595739
103	328.425851119435	189.407657235446	467.444045003424
104	240.505297334114	131.195733644992	349.814861023237
105	192.787573944479	96.5167579893626	289.058389899595
106	168.016308700406	75.2316744704573	260.800942930354
107	171.662811817287	69.36537295357	273.960250681004
108	189.509901875503	75.7845693001444	303.235234450861

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 205.259082949355 & 162.400179191347 & 248.117986707364 \tabularnewline
98 & 223.676991638419 & 162.843328577126 & 284.510654699713 \tabularnewline
99 & 231.407744271001 & 157.327138946502 & 305.488349595499 \tabularnewline
100 & 233.941863898399 & 149.512909719481 & 318.370818077318 \tabularnewline
101 & 236.993026804595 & 143.110132423085 & 330.875921186105 \tabularnewline
102 & 345.021288263484 & 204.387210569578 & 485.65536595739 \tabularnewline
103 & 328.425851119435 & 189.407657235446 & 467.444045003424 \tabularnewline
104 & 240.505297334114 & 131.195733644992 & 349.814861023237 \tabularnewline
105 & 192.787573944479 & 96.5167579893626 & 289.058389899595 \tabularnewline
106 & 168.016308700406 & 75.2316744704573 & 260.800942930354 \tabularnewline
107 & 171.662811817287 & 69.36537295357 & 273.960250681004 \tabularnewline
108 & 189.509901875503 & 75.7845693001444 & 303.235234450861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42667&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]97[/C][C]205.259082949355[/C][C]162.400179191347[/C][C]248.117986707364[/C][/ROW]
[ROW][C]98[/C][C]223.676991638419[/C][C]162.843328577126[/C][C]284.510654699713[/C][/ROW]
[ROW][C]99[/C][C]231.407744271001[/C][C]157.327138946502[/C][C]305.488349595499[/C][/ROW]
[ROW][C]100[/C][C]233.941863898399[/C][C]149.512909719481[/C][C]318.370818077318[/C][/ROW]
[ROW][C]101[/C][C]236.993026804595[/C][C]143.110132423085[/C][C]330.875921186105[/C][/ROW]
[ROW][C]102[/C][C]345.021288263484[/C][C]204.387210569578[/C][C]485.65536595739[/C][/ROW]
[ROW][C]103[/C][C]328.425851119435[/C][C]189.407657235446[/C][C]467.444045003424[/C][/ROW]
[ROW][C]104[/C][C]240.505297334114[/C][C]131.195733644992[/C][C]349.814861023237[/C][/ROW]
[ROW][C]105[/C][C]192.787573944479[/C][C]96.5167579893626[/C][C]289.058389899595[/C][/ROW]
[ROW][C]106[/C][C]168.016308700406[/C][C]75.2316744704573[/C][C]260.800942930354[/C][/ROW]
[ROW][C]107[/C][C]171.662811817287[/C][C]69.36537295357[/C][C]273.960250681004[/C][/ROW]
[ROW][C]108[/C][C]189.509901875503[/C][C]75.7845693001444[/C][C]303.235234450861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42667&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42667&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
97	205.259082949355	162.400179191347	248.117986707364
98	223.676991638419	162.843328577126	284.510654699713
99	231.407744271001	157.327138946502	305.488349595499
100	233.941863898399	149.512909719481	318.370818077318
101	236.993026804595	143.110132423085	330.875921186105
102	345.021288263484	204.387210569578	485.65536595739
103	328.425851119435	189.407657235446	467.444045003424
104	240.505297334114	131.195733644992	349.814861023237
105	192.787573944479	96.5167579893626	289.058389899595
106	168.016308700406	75.2316744704573	260.800942930354
107	171.662811817287	69.36537295357	273.960250681004
108	189.509901875503	75.7845693001444	303.235234450861

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code