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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 28 May 2008 14:16:37 -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/2008/May/28/t1212005911bbc02srrbhmkwjk.htm/, Retrieved Tue, 14 May 2024 19:29:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13479, Retrieved Tue, 14 May 2024 19:29:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

150

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

-       [Exponential Smoothing] [aankoopprijs nieu...] [2008-05-28 20:16:37] [d41d8cd98f00b204e9800998ecf8427e] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13479&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13479&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.963580582065361
beta	0.0293940647936531
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.963580582065361 \tabularnewline
beta & 0.0293940647936531 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13479&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]0.963580582065361[/C][/ROW]
[ROW][C]beta[/C][C]0.0293940647936531[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13479&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	0.963580582065361
beta	0.0293940647936531
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	103.1	101.902722222222	1.19727777777773
14	103.1	103.267319678465	-0.167319678465049
15	103.3	103.312278436247	-0.0122784362469446
16	103.5	103.506284155546	-0.00628415554575668
17	103.3	103.705887857737	-0.405887857737483
18	103.5	103.508945006917	-0.00894500691718747
19	103.8	103.694235224986	0.105764775014251
20	103.9	103.993053195396	-0.0930531953964362
21	103.9	104.097658433315	-0.197658433315397
22	104.2	104.095869706662	0.104130293338088
23	104.6	104.387828076474	0.212171923525588
24	104.9	104.789902725288	0.110097274711791
25	105.2	105.096738570256	0.103261429743966
26	105.2	105.399912258026	-0.199912258025790
27	105.6	105.405291442419	0.194708557580952
28	105.6	105.796434419588	-0.196434419588115
29	106.2	105.805115899029	0.394884100971495
30	106.3	106.394764942299	-0.0947649422987666
31	106.4	106.509913595859	-0.109913595859467
32	106.9	106.607352157770	0.292647842230295
33	107.2	107.100979930322	0.0990200696781613
34	107.3	107.410836340995	-0.110836340994950
35	107.3	107.515339910669	-0.215339910668519
36	107.4	107.513046679108	-0.113046679107711
37	107.55	107.606119335880	-0.056119335880453
38	107.87	107.752456576356	0.117543423643795
39	108.37	108.069461126782	0.3005388732184
40	108.38	108.571308866845	-0.191308866844935
41	107.92	108.593803128983	-0.673803128982883
42	108.03	108.132290792510	-0.102290792510303
43	108.14	108.218579407491	-0.0785794074908495
44	108.3	108.325490204868	-0.0254902048680208
45	108.64	108.482834753916	0.157165246083821
46	108.66	108.820634026426	-0.160634026425569
47	109.04	108.847658365061	0.192341634938913
48	109.03	109.220250994856	-0.190250994855532
49	109.03	109.218796212161	-0.188796212161364
50	109.54	109.213395850856	0.326604149144458
51	109.75	109.713875858663	0.0361241413373961
52	109.83	109.935478135394	-0.105478135394250
53	109.65	110.017647692643	-0.367647692642620
54	109.82	109.836782667490	-0.0167826674896503
55	109.95	109.993529022777	-0.0435290227770935
56	110.12	110.123270213013	-0.00327021301272623
57	110.15	110.291711386552	-0.141711386552387
58	110.2	110.322739563959	-0.122739563959357
59	109.99	110.368572201039	-0.378572201038821
60	110.14	110.157166968081	-0.0171669680812983
61	110.14	110.293518570379	-0.15351857037858
62	110.81	110.294136225455	0.515863774545039
63	110.97	110.954368803521	0.0156311964787932
64	110.99	111.133029713822	-0.143029713822330
65	109.73	111.154756942565	-1.4247569425645
66	109.81	109.901082527596	-0.0910825275957592
67	110.02	109.929931101158	0.0900688988419489
68	110.18	110.135884742615	0.0441152573853856
69	110.21	110.298807848190	-0.0888078481895747
70	110.25	110.331133476790	-0.0811334767904697
71	110.36	110.368555992559	-0.00855599255943673
72	110.51	110.475670426745	0.0343295732550217
73	110.64	110.625080894787	0.0149191052130391
74	110.95	110.756210374758	0.193789625241720
75	111.18	111.065184824685	0.114815175314590
76	111.19	111.301313001550	-0.111313001549519
77	111.69	111.316395678757	0.373604321242553
78	111.7	111.809317072811	-0.10931707281145
79	111.83	111.833808541307	-0.0038085413065545
80	111.77	111.959858110592	-0.189858110591643
81	111.73	111.901256471912	-0.171256471911761
82	112.01	111.855728419803	0.154271580197417
83	111.86	112.128242396448	-0.268242396448429
84	112.04	111.986032532602	0.0539674673977686

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 103.1 & 101.902722222222 & 1.19727777777773 \tabularnewline
14 & 103.1 & 103.267319678465 & -0.167319678465049 \tabularnewline
15 & 103.3 & 103.312278436247 & -0.0122784362469446 \tabularnewline
16 & 103.5 & 103.506284155546 & -0.00628415554575668 \tabularnewline
17 & 103.3 & 103.705887857737 & -0.405887857737483 \tabularnewline
18 & 103.5 & 103.508945006917 & -0.00894500691718747 \tabularnewline
19 & 103.8 & 103.694235224986 & 0.105764775014251 \tabularnewline
20 & 103.9 & 103.993053195396 & -0.0930531953964362 \tabularnewline
21 & 103.9 & 104.097658433315 & -0.197658433315397 \tabularnewline
22 & 104.2 & 104.095869706662 & 0.104130293338088 \tabularnewline
23 & 104.6 & 104.387828076474 & 0.212171923525588 \tabularnewline
24 & 104.9 & 104.789902725288 & 0.110097274711791 \tabularnewline
25 & 105.2 & 105.096738570256 & 0.103261429743966 \tabularnewline
26 & 105.2 & 105.399912258026 & -0.199912258025790 \tabularnewline
27 & 105.6 & 105.405291442419 & 0.194708557580952 \tabularnewline
28 & 105.6 & 105.796434419588 & -0.196434419588115 \tabularnewline
29 & 106.2 & 105.805115899029 & 0.394884100971495 \tabularnewline
30 & 106.3 & 106.394764942299 & -0.0947649422987666 \tabularnewline
31 & 106.4 & 106.509913595859 & -0.109913595859467 \tabularnewline
32 & 106.9 & 106.607352157770 & 0.292647842230295 \tabularnewline
33 & 107.2 & 107.100979930322 & 0.0990200696781613 \tabularnewline
34 & 107.3 & 107.410836340995 & -0.110836340994950 \tabularnewline
35 & 107.3 & 107.515339910669 & -0.215339910668519 \tabularnewline
36 & 107.4 & 107.513046679108 & -0.113046679107711 \tabularnewline
37 & 107.55 & 107.606119335880 & -0.056119335880453 \tabularnewline
38 & 107.87 & 107.752456576356 & 0.117543423643795 \tabularnewline
39 & 108.37 & 108.069461126782 & 0.3005388732184 \tabularnewline
40 & 108.38 & 108.571308866845 & -0.191308866844935 \tabularnewline
41 & 107.92 & 108.593803128983 & -0.673803128982883 \tabularnewline
42 & 108.03 & 108.132290792510 & -0.102290792510303 \tabularnewline
43 & 108.14 & 108.218579407491 & -0.0785794074908495 \tabularnewline
44 & 108.3 & 108.325490204868 & -0.0254902048680208 \tabularnewline
45 & 108.64 & 108.482834753916 & 0.157165246083821 \tabularnewline
46 & 108.66 & 108.820634026426 & -0.160634026425569 \tabularnewline
47 & 109.04 & 108.847658365061 & 0.192341634938913 \tabularnewline
48 & 109.03 & 109.220250994856 & -0.190250994855532 \tabularnewline
49 & 109.03 & 109.218796212161 & -0.188796212161364 \tabularnewline
50 & 109.54 & 109.213395850856 & 0.326604149144458 \tabularnewline
51 & 109.75 & 109.713875858663 & 0.0361241413373961 \tabularnewline
52 & 109.83 & 109.935478135394 & -0.105478135394250 \tabularnewline
53 & 109.65 & 110.017647692643 & -0.367647692642620 \tabularnewline
54 & 109.82 & 109.836782667490 & -0.0167826674896503 \tabularnewline
55 & 109.95 & 109.993529022777 & -0.0435290227770935 \tabularnewline
56 & 110.12 & 110.123270213013 & -0.00327021301272623 \tabularnewline
57 & 110.15 & 110.291711386552 & -0.141711386552387 \tabularnewline
58 & 110.2 & 110.322739563959 & -0.122739563959357 \tabularnewline
59 & 109.99 & 110.368572201039 & -0.378572201038821 \tabularnewline
60 & 110.14 & 110.157166968081 & -0.0171669680812983 \tabularnewline
61 & 110.14 & 110.293518570379 & -0.15351857037858 \tabularnewline
62 & 110.81 & 110.294136225455 & 0.515863774545039 \tabularnewline
63 & 110.97 & 110.954368803521 & 0.0156311964787932 \tabularnewline
64 & 110.99 & 111.133029713822 & -0.143029713822330 \tabularnewline
65 & 109.73 & 111.154756942565 & -1.4247569425645 \tabularnewline
66 & 109.81 & 109.901082527596 & -0.0910825275957592 \tabularnewline
67 & 110.02 & 109.929931101158 & 0.0900688988419489 \tabularnewline
68 & 110.18 & 110.135884742615 & 0.0441152573853856 \tabularnewline
69 & 110.21 & 110.298807848190 & -0.0888078481895747 \tabularnewline
70 & 110.25 & 110.331133476790 & -0.0811334767904697 \tabularnewline
71 & 110.36 & 110.368555992559 & -0.00855599255943673 \tabularnewline
72 & 110.51 & 110.475670426745 & 0.0343295732550217 \tabularnewline
73 & 110.64 & 110.625080894787 & 0.0149191052130391 \tabularnewline
74 & 110.95 & 110.756210374758 & 0.193789625241720 \tabularnewline
75 & 111.18 & 111.065184824685 & 0.114815175314590 \tabularnewline
76 & 111.19 & 111.301313001550 & -0.111313001549519 \tabularnewline
77 & 111.69 & 111.316395678757 & 0.373604321242553 \tabularnewline
78 & 111.7 & 111.809317072811 & -0.10931707281145 \tabularnewline
79 & 111.83 & 111.833808541307 & -0.0038085413065545 \tabularnewline
80 & 111.77 & 111.959858110592 & -0.189858110591643 \tabularnewline
81 & 111.73 & 111.901256471912 & -0.171256471911761 \tabularnewline
82 & 112.01 & 111.855728419803 & 0.154271580197417 \tabularnewline
83 & 111.86 & 112.128242396448 & -0.268242396448429 \tabularnewline
84 & 112.04 & 111.986032532602 & 0.0539674673977686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13479&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]103.1[/C][C]101.902722222222[/C][C]1.19727777777773[/C][/ROW]
[ROW][C]14[/C][C]103.1[/C][C]103.267319678465[/C][C]-0.167319678465049[/C][/ROW]
[ROW][C]15[/C][C]103.3[/C][C]103.312278436247[/C][C]-0.0122784362469446[/C][/ROW]
[ROW][C]16[/C][C]103.5[/C][C]103.506284155546[/C][C]-0.00628415554575668[/C][/ROW]
[ROW][C]17[/C][C]103.3[/C][C]103.705887857737[/C][C]-0.405887857737483[/C][/ROW]
[ROW][C]18[/C][C]103.5[/C][C]103.508945006917[/C][C]-0.00894500691718747[/C][/ROW]
[ROW][C]19[/C][C]103.8[/C][C]103.694235224986[/C][C]0.105764775014251[/C][/ROW]
[ROW][C]20[/C][C]103.9[/C][C]103.993053195396[/C][C]-0.0930531953964362[/C][/ROW]
[ROW][C]21[/C][C]103.9[/C][C]104.097658433315[/C][C]-0.197658433315397[/C][/ROW]
[ROW][C]22[/C][C]104.2[/C][C]104.095869706662[/C][C]0.104130293338088[/C][/ROW]
[ROW][C]23[/C][C]104.6[/C][C]104.387828076474[/C][C]0.212171923525588[/C][/ROW]
[ROW][C]24[/C][C]104.9[/C][C]104.789902725288[/C][C]0.110097274711791[/C][/ROW]
[ROW][C]25[/C][C]105.2[/C][C]105.096738570256[/C][C]0.103261429743966[/C][/ROW]
[ROW][C]26[/C][C]105.2[/C][C]105.399912258026[/C][C]-0.199912258025790[/C][/ROW]
[ROW][C]27[/C][C]105.6[/C][C]105.405291442419[/C][C]0.194708557580952[/C][/ROW]
[ROW][C]28[/C][C]105.6[/C][C]105.796434419588[/C][C]-0.196434419588115[/C][/ROW]
[ROW][C]29[/C][C]106.2[/C][C]105.805115899029[/C][C]0.394884100971495[/C][/ROW]
[ROW][C]30[/C][C]106.3[/C][C]106.394764942299[/C][C]-0.0947649422987666[/C][/ROW]
[ROW][C]31[/C][C]106.4[/C][C]106.509913595859[/C][C]-0.109913595859467[/C][/ROW]
[ROW][C]32[/C][C]106.9[/C][C]106.607352157770[/C][C]0.292647842230295[/C][/ROW]
[ROW][C]33[/C][C]107.2[/C][C]107.100979930322[/C][C]0.0990200696781613[/C][/ROW]
[ROW][C]34[/C][C]107.3[/C][C]107.410836340995[/C][C]-0.110836340994950[/C][/ROW]
[ROW][C]35[/C][C]107.3[/C][C]107.515339910669[/C][C]-0.215339910668519[/C][/ROW]
[ROW][C]36[/C][C]107.4[/C][C]107.513046679108[/C][C]-0.113046679107711[/C][/ROW]
[ROW][C]37[/C][C]107.55[/C][C]107.606119335880[/C][C]-0.056119335880453[/C][/ROW]
[ROW][C]38[/C][C]107.87[/C][C]107.752456576356[/C][C]0.117543423643795[/C][/ROW]
[ROW][C]39[/C][C]108.37[/C][C]108.069461126782[/C][C]0.3005388732184[/C][/ROW]
[ROW][C]40[/C][C]108.38[/C][C]108.571308866845[/C][C]-0.191308866844935[/C][/ROW]
[ROW][C]41[/C][C]107.92[/C][C]108.593803128983[/C][C]-0.673803128982883[/C][/ROW]
[ROW][C]42[/C][C]108.03[/C][C]108.132290792510[/C][C]-0.102290792510303[/C][/ROW]
[ROW][C]43[/C][C]108.14[/C][C]108.218579407491[/C][C]-0.0785794074908495[/C][/ROW]
[ROW][C]44[/C][C]108.3[/C][C]108.325490204868[/C][C]-0.0254902048680208[/C][/ROW]
[ROW][C]45[/C][C]108.64[/C][C]108.482834753916[/C][C]0.157165246083821[/C][/ROW]
[ROW][C]46[/C][C]108.66[/C][C]108.820634026426[/C][C]-0.160634026425569[/C][/ROW]
[ROW][C]47[/C][C]109.04[/C][C]108.847658365061[/C][C]0.192341634938913[/C][/ROW]
[ROW][C]48[/C][C]109.03[/C][C]109.220250994856[/C][C]-0.190250994855532[/C][/ROW]
[ROW][C]49[/C][C]109.03[/C][C]109.218796212161[/C][C]-0.188796212161364[/C][/ROW]
[ROW][C]50[/C][C]109.54[/C][C]109.213395850856[/C][C]0.326604149144458[/C][/ROW]
[ROW][C]51[/C][C]109.75[/C][C]109.713875858663[/C][C]0.0361241413373961[/C][/ROW]
[ROW][C]52[/C][C]109.83[/C][C]109.935478135394[/C][C]-0.105478135394250[/C][/ROW]
[ROW][C]53[/C][C]109.65[/C][C]110.017647692643[/C][C]-0.367647692642620[/C][/ROW]
[ROW][C]54[/C][C]109.82[/C][C]109.836782667490[/C][C]-0.0167826674896503[/C][/ROW]
[ROW][C]55[/C][C]109.95[/C][C]109.993529022777[/C][C]-0.0435290227770935[/C][/ROW]
[ROW][C]56[/C][C]110.12[/C][C]110.123270213013[/C][C]-0.00327021301272623[/C][/ROW]
[ROW][C]57[/C][C]110.15[/C][C]110.291711386552[/C][C]-0.141711386552387[/C][/ROW]
[ROW][C]58[/C][C]110.2[/C][C]110.322739563959[/C][C]-0.122739563959357[/C][/ROW]
[ROW][C]59[/C][C]109.99[/C][C]110.368572201039[/C][C]-0.378572201038821[/C][/ROW]
[ROW][C]60[/C][C]110.14[/C][C]110.157166968081[/C][C]-0.0171669680812983[/C][/ROW]
[ROW][C]61[/C][C]110.14[/C][C]110.293518570379[/C][C]-0.15351857037858[/C][/ROW]
[ROW][C]62[/C][C]110.81[/C][C]110.294136225455[/C][C]0.515863774545039[/C][/ROW]
[ROW][C]63[/C][C]110.97[/C][C]110.954368803521[/C][C]0.0156311964787932[/C][/ROW]
[ROW][C]64[/C][C]110.99[/C][C]111.133029713822[/C][C]-0.143029713822330[/C][/ROW]
[ROW][C]65[/C][C]109.73[/C][C]111.154756942565[/C][C]-1.4247569425645[/C][/ROW]
[ROW][C]66[/C][C]109.81[/C][C]109.901082527596[/C][C]-0.0910825275957592[/C][/ROW]
[ROW][C]67[/C][C]110.02[/C][C]109.929931101158[/C][C]0.0900688988419489[/C][/ROW]
[ROW][C]68[/C][C]110.18[/C][C]110.135884742615[/C][C]0.0441152573853856[/C][/ROW]
[ROW][C]69[/C][C]110.21[/C][C]110.298807848190[/C][C]-0.0888078481895747[/C][/ROW]
[ROW][C]70[/C][C]110.25[/C][C]110.331133476790[/C][C]-0.0811334767904697[/C][/ROW]
[ROW][C]71[/C][C]110.36[/C][C]110.368555992559[/C][C]-0.00855599255943673[/C][/ROW]
[ROW][C]72[/C][C]110.51[/C][C]110.475670426745[/C][C]0.0343295732550217[/C][/ROW]
[ROW][C]73[/C][C]110.64[/C][C]110.625080894787[/C][C]0.0149191052130391[/C][/ROW]
[ROW][C]74[/C][C]110.95[/C][C]110.756210374758[/C][C]0.193789625241720[/C][/ROW]
[ROW][C]75[/C][C]111.18[/C][C]111.065184824685[/C][C]0.114815175314590[/C][/ROW]
[ROW][C]76[/C][C]111.19[/C][C]111.301313001550[/C][C]-0.111313001549519[/C][/ROW]
[ROW][C]77[/C][C]111.69[/C][C]111.316395678757[/C][C]0.373604321242553[/C][/ROW]
[ROW][C]78[/C][C]111.7[/C][C]111.809317072811[/C][C]-0.10931707281145[/C][/ROW]
[ROW][C]79[/C][C]111.83[/C][C]111.833808541307[/C][C]-0.0038085413065545[/C][/ROW]
[ROW][C]80[/C][C]111.77[/C][C]111.959858110592[/C][C]-0.189858110591643[/C][/ROW]
[ROW][C]81[/C][C]111.73[/C][C]111.901256471912[/C][C]-0.171256471911761[/C][/ROW]
[ROW][C]82[/C][C]112.01[/C][C]111.855728419803[/C][C]0.154271580197417[/C][/ROW]
[ROW][C]83[/C][C]111.86[/C][C]112.128242396448[/C][C]-0.268242396448429[/C][/ROW]
[ROW][C]84[/C][C]112.04[/C][C]111.986032532602[/C][C]0.0539674673977686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13479&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	103.1	101.902722222222	1.19727777777773
14	103.1	103.267319678465	-0.167319678465049
15	103.3	103.312278436247	-0.0122784362469446
16	103.5	103.506284155546	-0.00628415554575668
17	103.3	103.705887857737	-0.405887857737483
18	103.5	103.508945006917	-0.00894500691718747
19	103.8	103.694235224986	0.105764775014251
20	103.9	103.993053195396	-0.0930531953964362
21	103.9	104.097658433315	-0.197658433315397
22	104.2	104.095869706662	0.104130293338088
23	104.6	104.387828076474	0.212171923525588
24	104.9	104.789902725288	0.110097274711791
25	105.2	105.096738570256	0.103261429743966
26	105.2	105.399912258026	-0.199912258025790
27	105.6	105.405291442419	0.194708557580952
28	105.6	105.796434419588	-0.196434419588115
29	106.2	105.805115899029	0.394884100971495
30	106.3	106.394764942299	-0.0947649422987666
31	106.4	106.509913595859	-0.109913595859467
32	106.9	106.607352157770	0.292647842230295
33	107.2	107.100979930322	0.0990200696781613
34	107.3	107.410836340995	-0.110836340994950
35	107.3	107.515339910669	-0.215339910668519
36	107.4	107.513046679108	-0.113046679107711
37	107.55	107.606119335880	-0.056119335880453
38	107.87	107.752456576356	0.117543423643795
39	108.37	108.069461126782	0.3005388732184
40	108.38	108.571308866845	-0.191308866844935
41	107.92	108.593803128983	-0.673803128982883
42	108.03	108.132290792510	-0.102290792510303
43	108.14	108.218579407491	-0.0785794074908495
44	108.3	108.325490204868	-0.0254902048680208
45	108.64	108.482834753916	0.157165246083821
46	108.66	108.820634026426	-0.160634026425569
47	109.04	108.847658365061	0.192341634938913
48	109.03	109.220250994856	-0.190250994855532
49	109.03	109.218796212161	-0.188796212161364
50	109.54	109.213395850856	0.326604149144458
51	109.75	109.713875858663	0.0361241413373961
52	109.83	109.935478135394	-0.105478135394250
53	109.65	110.017647692643	-0.367647692642620
54	109.82	109.836782667490	-0.0167826674896503
55	109.95	109.993529022777	-0.0435290227770935
56	110.12	110.123270213013	-0.00327021301272623
57	110.15	110.291711386552	-0.141711386552387
58	110.2	110.322739563959	-0.122739563959357
59	109.99	110.368572201039	-0.378572201038821
60	110.14	110.157166968081	-0.0171669680812983
61	110.14	110.293518570379	-0.15351857037858
62	110.81	110.294136225455	0.515863774545039
63	110.97	110.954368803521	0.0156311964787932
64	110.99	111.133029713822	-0.143029713822330
65	109.73	111.154756942565	-1.4247569425645
66	109.81	109.901082527596	-0.0910825275957592
67	110.02	109.929931101158	0.0900688988419489
68	110.18	110.135884742615	0.0441152573853856
69	110.21	110.298807848190	-0.0888078481895747
70	110.25	110.331133476790	-0.0811334767904697
71	110.36	110.368555992559	-0.00855599255943673
72	110.51	110.475670426745	0.0343295732550217
73	110.64	110.625080894787	0.0149191052130391
74	110.95	110.756210374758	0.193789625241720
75	111.18	111.065184824685	0.114815175314590
76	111.19	111.301313001550	-0.111313001549519
77	111.69	111.316395678757	0.373604321242553
78	111.7	111.809317072811	-0.10931707281145
79	111.83	111.833808541307	-0.0038085413065545
80	111.77	111.959858110592	-0.189858110591643
81	111.73	111.901256471912	-0.171256471911761
82	112.01	111.855728419803	0.154271580197417
83	111.86	112.128242396448	-0.268242396448429
84	112.04	111.986032532602	0.0539674673977686

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	112.155826387173	NA	NA
86	112.273618238096	NA	NA
87	112.391410089018	NA	NA
88	112.509201939941	NA	NA
89	112.626993790864	NA	NA
90	112.744785641787	NA	NA
91	112.862577492710	NA	NA
92	112.980369343633	NA	NA
93	113.098161194555	NA	NA
94	113.215953045478	NA	NA
95	113.333744896401	NA	NA
96	113.451536747324	NA	NA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 112.155826387173 & NA & NA \tabularnewline
86 & 112.273618238096 & NA & NA \tabularnewline
87 & 112.391410089018 & NA & NA \tabularnewline
88 & 112.509201939941 & NA & NA \tabularnewline
89 & 112.626993790864 & NA & NA \tabularnewline
90 & 112.744785641787 & NA & NA \tabularnewline
91 & 112.862577492710 & NA & NA \tabularnewline
92 & 112.980369343633 & NA & NA \tabularnewline
93 & 113.098161194555 & NA & NA \tabularnewline
94 & 113.215953045478 & NA & NA \tabularnewline
95 & 113.333744896401 & NA & NA \tabularnewline
96 & 113.451536747324 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13479&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]112.155826387173[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]86[/C][C]112.273618238096[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]87[/C][C]112.391410089018[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]88[/C][C]112.509201939941[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]89[/C][C]112.626993790864[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]90[/C][C]112.744785641787[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]91[/C][C]112.862577492710[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]92[/C][C]112.980369343633[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]93[/C][C]113.098161194555[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]94[/C][C]113.215953045478[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]95[/C][C]113.333744896401[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]96[/C][C]113.451536747324[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13479&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	112.155826387173	NA	NA
86	112.273618238096	NA	NA
87	112.391410089018	NA	NA
88	112.509201939941	NA	NA
89	112.626993790864	NA	NA
90	112.744785641787	NA	NA
91	112.862577492710	NA	NA
92	112.980369343633	NA	NA
93	113.098161194555	NA	NA
94	113.215953045478	NA	NA
95	113.333744896401	NA	NA
96	113.451536747324	NA	NA

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 = multiplicative ;

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