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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Apr 2015 19:12:02 +0100

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/2015/Apr/02/t1427998353955tiloij8g0owg.htm/, Retrieved Thu, 09 May 2024 05:10:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278618, Retrieved Thu, 09 May 2024 05:10:52 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-04-02 18:12:02] [464dfecbd4863ecbf0b1962220ac611d] [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' @ 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278618&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278618&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' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0307829843001454
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0307829843001454 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278618&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0307829843001454[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278618&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	1
beta	0.0307829843001454
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	8.43	8.37	0.0599999999999987
4	8.44	8.41184697905801	0.0281530209419909
5	8.49	8.42271361305967	0.0672863869403333
6	8.47	8.47478488885247	-0.0047848888524662
7	8.53	8.45463759569404	0.075362404305956
8	8.52	8.51695747540261	0.00304252459738663
9	8.51	8.50705113338953	0.00294886661047222
10	8.53	8.4971419083041	0.032858091695898
11	8.54	8.51815337842491	0.0218466215750901
12	8.53	8.52882588263387	0.00117411736613349
13	8.47	8.51886202547031	-0.0488620254703136
14	8.63	8.45735790650739	0.172642093492611
15	8.67	8.62267234536092	0.0473276546390835
16	8.73	8.66412923181063	0.0658707681893667
17	8.57	8.72615693063365	-0.156156930633646
18	8.55	8.56134995428959	-0.0113499542895905
19	8.63	8.54100056882489	0.0889994311751128
20	8.65	8.62374023691747	0.0262597630825265
21	8.44	8.64454859079217	-0.204548590792168
22	8.62	8.42825197473319	0.191748025266804
23	8.37	8.61415455118457	-0.244154551184566
24	8.59	8.35663874546864	0.233361254531356
25	8.84	8.58382230130314	0.256177698696856
26	8.72	8.84170821538018	-0.121708215380176
27	8.8	8.71796167329693	0.0820383267030689
28	8.69	8.80048705781984	-0.110487057819842
29	8.68	8.6870859364536	-0.00708593645360445
30	8.57	8.676867810183	-0.106867810183001
31	8.85	8.56357810005995	0.286421899940052
32	8.85	8.85239502090902	-0.00239502090901844
33	8.85	8.85232129501798	-0.00232129501797829
34	8.93	8.85224983862988	0.0777501613701155
35	8.75	8.93464322062667	-0.184643220626674
36	8.78	8.748959351265	0.0310406487350043
37	8.77	8.77991487506767	-0.00991487506767008
38	9.03	8.76960966562412	0.260390334375876
39	9.01	9.03762525719913	-0.0276252571991265
40	9.07	9.01677486934048	0.0532251306595217
41	8.99	9.07841329770194	-0.0884132977019441
42	9.02	8.99569167254686	0.0243083274531379
43	8.99	9.02643995540921	-0.0364399554092127
44	8.98	8.99531822483395	-0.015318224833953
45	8.94	8.98484668415938	-0.0448466841593849
46	8.94	8.94346616938499	-0.00346616938499267
47	8.75	8.94335947034723	-0.193359470347232
48	8.86	8.74740728880725	0.11259271119275
49	8.87	8.86087322846821	0.00912677153179331
50	8.84	8.87115417773298	-0.0311541777329793
51	8.84	8.84019515916894	-0.000195159168942638
52	9.91	8.84018915158731	1.06981084841269
53	10.18	9.94312112213812	0.236878877861878
54	10.34	10.2204129609164	0.119587039083621
55	10.36	10.384094206863	-0.0240942068629924
56	10.26	10.4033525152714	-0.143352515271404
57	10.16	10.2989396970444	-0.138939697044417
58	10.31	10.1946627185316	0.115337281468367
59	10.46	10.3482131442563	0.111786855743706
60	10.54	10.5016542772816	0.0383457227183825
61	10.47	10.582834673062	-0.112834673062032
62	10.48	10.5093612850927	-0.0293612850926532
63	10.46	10.5184574571146	-0.0584574571146135
64	11.3	10.49665796213	0.803342037869971
65	11.58	11.3613872274694	0.218612772530573
66	11.69	11.648116781014	0.0418832189859533
67	11.63	11.7594060714865	-0.12940607148653
68	11.51	11.6954225664196	-0.185422566419618
69	11.37	11.5697147064686	-0.19971470646863
70	11.42	11.4235668917949	-0.00356689179489678
71	11.7	11.4734570922208	0.226542907779224
72	11.75	11.7604307589943	-0.0104307589942518
73	11.43	11.8101096691039	-0.380109669103893
74	11.36	11.4784087591275	-0.118408759127535
75	11.3	11.4047637841543	-0.104763784154311
76	11.85	11.3415388422315	0.508461157768533
77	11.99	11.9071907940683	0.0828092059317118
78	12.07	12.0497399085544	0.0202600914456088
79	12.21	12.1303635746313	0.0796364253687187
80	12.13	12.2728150214631	-0.142815021463127
81	12.3	12.1884187488996	0.111581251100398
82	12.27	12.3618535528004	-0.0918535528004174
83	12.32	12.3290260263266	-0.00902602632664795
84	12.38	12.3787481782999	0.00125182170005722
85	12.4	12.4387867131077	-0.0387867131076831
86	12.33	12.457592742327	-0.127592742327034
87	12.25	12.3836650569432	-0.133665056943169
88	12.41	12.2995504475938	0.110449552406191
89	12.38	12.4629504144315	-0.0829504144314868
90	12.58	12.4303969531264	0.149603046873647
91	12.45	12.6350021813695	-0.185002181369518
92	12.43	12.4993072621249	-0.0693072621249264
93	12.38	12.477173777763	-0.0971737777630484
94	12.34	12.4241824788878	-0.0841824788877847
95	11.98	12.3815910909618	-0.401591090961833
96	12.24	12.0092289187137	0.230771081286322

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.43 & 8.37 & 0.0599999999999987 \tabularnewline
4 & 8.44 & 8.41184697905801 & 0.0281530209419909 \tabularnewline
5 & 8.49 & 8.42271361305967 & 0.0672863869403333 \tabularnewline
6 & 8.47 & 8.47478488885247 & -0.0047848888524662 \tabularnewline
7 & 8.53 & 8.45463759569404 & 0.075362404305956 \tabularnewline
8 & 8.52 & 8.51695747540261 & 0.00304252459738663 \tabularnewline
9 & 8.51 & 8.50705113338953 & 0.00294886661047222 \tabularnewline
10 & 8.53 & 8.4971419083041 & 0.032858091695898 \tabularnewline
11 & 8.54 & 8.51815337842491 & 0.0218466215750901 \tabularnewline
12 & 8.53 & 8.52882588263387 & 0.00117411736613349 \tabularnewline
13 & 8.47 & 8.51886202547031 & -0.0488620254703136 \tabularnewline
14 & 8.63 & 8.45735790650739 & 0.172642093492611 \tabularnewline
15 & 8.67 & 8.62267234536092 & 0.0473276546390835 \tabularnewline
16 & 8.73 & 8.66412923181063 & 0.0658707681893667 \tabularnewline
17 & 8.57 & 8.72615693063365 & -0.156156930633646 \tabularnewline
18 & 8.55 & 8.56134995428959 & -0.0113499542895905 \tabularnewline
19 & 8.63 & 8.54100056882489 & 0.0889994311751128 \tabularnewline
20 & 8.65 & 8.62374023691747 & 0.0262597630825265 \tabularnewline
21 & 8.44 & 8.64454859079217 & -0.204548590792168 \tabularnewline
22 & 8.62 & 8.42825197473319 & 0.191748025266804 \tabularnewline
23 & 8.37 & 8.61415455118457 & -0.244154551184566 \tabularnewline
24 & 8.59 & 8.35663874546864 & 0.233361254531356 \tabularnewline
25 & 8.84 & 8.58382230130314 & 0.256177698696856 \tabularnewline
26 & 8.72 & 8.84170821538018 & -0.121708215380176 \tabularnewline
27 & 8.8 & 8.71796167329693 & 0.0820383267030689 \tabularnewline
28 & 8.69 & 8.80048705781984 & -0.110487057819842 \tabularnewline
29 & 8.68 & 8.6870859364536 & -0.00708593645360445 \tabularnewline
30 & 8.57 & 8.676867810183 & -0.106867810183001 \tabularnewline
31 & 8.85 & 8.56357810005995 & 0.286421899940052 \tabularnewline
32 & 8.85 & 8.85239502090902 & -0.00239502090901844 \tabularnewline
33 & 8.85 & 8.85232129501798 & -0.00232129501797829 \tabularnewline
34 & 8.93 & 8.85224983862988 & 0.0777501613701155 \tabularnewline
35 & 8.75 & 8.93464322062667 & -0.184643220626674 \tabularnewline
36 & 8.78 & 8.748959351265 & 0.0310406487350043 \tabularnewline
37 & 8.77 & 8.77991487506767 & -0.00991487506767008 \tabularnewline
38 & 9.03 & 8.76960966562412 & 0.260390334375876 \tabularnewline
39 & 9.01 & 9.03762525719913 & -0.0276252571991265 \tabularnewline
40 & 9.07 & 9.01677486934048 & 0.0532251306595217 \tabularnewline
41 & 8.99 & 9.07841329770194 & -0.0884132977019441 \tabularnewline
42 & 9.02 & 8.99569167254686 & 0.0243083274531379 \tabularnewline
43 & 8.99 & 9.02643995540921 & -0.0364399554092127 \tabularnewline
44 & 8.98 & 8.99531822483395 & -0.015318224833953 \tabularnewline
45 & 8.94 & 8.98484668415938 & -0.0448466841593849 \tabularnewline
46 & 8.94 & 8.94346616938499 & -0.00346616938499267 \tabularnewline
47 & 8.75 & 8.94335947034723 & -0.193359470347232 \tabularnewline
48 & 8.86 & 8.74740728880725 & 0.11259271119275 \tabularnewline
49 & 8.87 & 8.86087322846821 & 0.00912677153179331 \tabularnewline
50 & 8.84 & 8.87115417773298 & -0.0311541777329793 \tabularnewline
51 & 8.84 & 8.84019515916894 & -0.000195159168942638 \tabularnewline
52 & 9.91 & 8.84018915158731 & 1.06981084841269 \tabularnewline
53 & 10.18 & 9.94312112213812 & 0.236878877861878 \tabularnewline
54 & 10.34 & 10.2204129609164 & 0.119587039083621 \tabularnewline
55 & 10.36 & 10.384094206863 & -0.0240942068629924 \tabularnewline
56 & 10.26 & 10.4033525152714 & -0.143352515271404 \tabularnewline
57 & 10.16 & 10.2989396970444 & -0.138939697044417 \tabularnewline
58 & 10.31 & 10.1946627185316 & 0.115337281468367 \tabularnewline
59 & 10.46 & 10.3482131442563 & 0.111786855743706 \tabularnewline
60 & 10.54 & 10.5016542772816 & 0.0383457227183825 \tabularnewline
61 & 10.47 & 10.582834673062 & -0.112834673062032 \tabularnewline
62 & 10.48 & 10.5093612850927 & -0.0293612850926532 \tabularnewline
63 & 10.46 & 10.5184574571146 & -0.0584574571146135 \tabularnewline
64 & 11.3 & 10.49665796213 & 0.803342037869971 \tabularnewline
65 & 11.58 & 11.3613872274694 & 0.218612772530573 \tabularnewline
66 & 11.69 & 11.648116781014 & 0.0418832189859533 \tabularnewline
67 & 11.63 & 11.7594060714865 & -0.12940607148653 \tabularnewline
68 & 11.51 & 11.6954225664196 & -0.185422566419618 \tabularnewline
69 & 11.37 & 11.5697147064686 & -0.19971470646863 \tabularnewline
70 & 11.42 & 11.4235668917949 & -0.00356689179489678 \tabularnewline
71 & 11.7 & 11.4734570922208 & 0.226542907779224 \tabularnewline
72 & 11.75 & 11.7604307589943 & -0.0104307589942518 \tabularnewline
73 & 11.43 & 11.8101096691039 & -0.380109669103893 \tabularnewline
74 & 11.36 & 11.4784087591275 & -0.118408759127535 \tabularnewline
75 & 11.3 & 11.4047637841543 & -0.104763784154311 \tabularnewline
76 & 11.85 & 11.3415388422315 & 0.508461157768533 \tabularnewline
77 & 11.99 & 11.9071907940683 & 0.0828092059317118 \tabularnewline
78 & 12.07 & 12.0497399085544 & 0.0202600914456088 \tabularnewline
79 & 12.21 & 12.1303635746313 & 0.0796364253687187 \tabularnewline
80 & 12.13 & 12.2728150214631 & -0.142815021463127 \tabularnewline
81 & 12.3 & 12.1884187488996 & 0.111581251100398 \tabularnewline
82 & 12.27 & 12.3618535528004 & -0.0918535528004174 \tabularnewline
83 & 12.32 & 12.3290260263266 & -0.00902602632664795 \tabularnewline
84 & 12.38 & 12.3787481782999 & 0.00125182170005722 \tabularnewline
85 & 12.4 & 12.4387867131077 & -0.0387867131076831 \tabularnewline
86 & 12.33 & 12.457592742327 & -0.127592742327034 \tabularnewline
87 & 12.25 & 12.3836650569432 & -0.133665056943169 \tabularnewline
88 & 12.41 & 12.2995504475938 & 0.110449552406191 \tabularnewline
89 & 12.38 & 12.4629504144315 & -0.0829504144314868 \tabularnewline
90 & 12.58 & 12.4303969531264 & 0.149603046873647 \tabularnewline
91 & 12.45 & 12.6350021813695 & -0.185002181369518 \tabularnewline
92 & 12.43 & 12.4993072621249 & -0.0693072621249264 \tabularnewline
93 & 12.38 & 12.477173777763 & -0.0971737777630484 \tabularnewline
94 & 12.34 & 12.4241824788878 & -0.0841824788877847 \tabularnewline
95 & 11.98 & 12.3815910909618 & -0.401591090961833 \tabularnewline
96 & 12.24 & 12.0092289187137 & 0.230771081286322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278618&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]3[/C][C]8.43[/C][C]8.37[/C][C]0.0599999999999987[/C][/ROW]
[ROW][C]4[/C][C]8.44[/C][C]8.41184697905801[/C][C]0.0281530209419909[/C][/ROW]
[ROW][C]5[/C][C]8.49[/C][C]8.42271361305967[/C][C]0.0672863869403333[/C][/ROW]
[ROW][C]6[/C][C]8.47[/C][C]8.47478488885247[/C][C]-0.0047848888524662[/C][/ROW]
[ROW][C]7[/C][C]8.53[/C][C]8.45463759569404[/C][C]0.075362404305956[/C][/ROW]
[ROW][C]8[/C][C]8.52[/C][C]8.51695747540261[/C][C]0.00304252459738663[/C][/ROW]
[ROW][C]9[/C][C]8.51[/C][C]8.50705113338953[/C][C]0.00294886661047222[/C][/ROW]
[ROW][C]10[/C][C]8.53[/C][C]8.4971419083041[/C][C]0.032858091695898[/C][/ROW]
[ROW][C]11[/C][C]8.54[/C][C]8.51815337842491[/C][C]0.0218466215750901[/C][/ROW]
[ROW][C]12[/C][C]8.53[/C][C]8.52882588263387[/C][C]0.00117411736613349[/C][/ROW]
[ROW][C]13[/C][C]8.47[/C][C]8.51886202547031[/C][C]-0.0488620254703136[/C][/ROW]
[ROW][C]14[/C][C]8.63[/C][C]8.45735790650739[/C][C]0.172642093492611[/C][/ROW]
[ROW][C]15[/C][C]8.67[/C][C]8.62267234536092[/C][C]0.0473276546390835[/C][/ROW]
[ROW][C]16[/C][C]8.73[/C][C]8.66412923181063[/C][C]0.0658707681893667[/C][/ROW]
[ROW][C]17[/C][C]8.57[/C][C]8.72615693063365[/C][C]-0.156156930633646[/C][/ROW]
[ROW][C]18[/C][C]8.55[/C][C]8.56134995428959[/C][C]-0.0113499542895905[/C][/ROW]
[ROW][C]19[/C][C]8.63[/C][C]8.54100056882489[/C][C]0.0889994311751128[/C][/ROW]
[ROW][C]20[/C][C]8.65[/C][C]8.62374023691747[/C][C]0.0262597630825265[/C][/ROW]
[ROW][C]21[/C][C]8.44[/C][C]8.64454859079217[/C][C]-0.204548590792168[/C][/ROW]
[ROW][C]22[/C][C]8.62[/C][C]8.42825197473319[/C][C]0.191748025266804[/C][/ROW]
[ROW][C]23[/C][C]8.37[/C][C]8.61415455118457[/C][C]-0.244154551184566[/C][/ROW]
[ROW][C]24[/C][C]8.59[/C][C]8.35663874546864[/C][C]0.233361254531356[/C][/ROW]
[ROW][C]25[/C][C]8.84[/C][C]8.58382230130314[/C][C]0.256177698696856[/C][/ROW]
[ROW][C]26[/C][C]8.72[/C][C]8.84170821538018[/C][C]-0.121708215380176[/C][/ROW]
[ROW][C]27[/C][C]8.8[/C][C]8.71796167329693[/C][C]0.0820383267030689[/C][/ROW]
[ROW][C]28[/C][C]8.69[/C][C]8.80048705781984[/C][C]-0.110487057819842[/C][/ROW]
[ROW][C]29[/C][C]8.68[/C][C]8.6870859364536[/C][C]-0.00708593645360445[/C][/ROW]
[ROW][C]30[/C][C]8.57[/C][C]8.676867810183[/C][C]-0.106867810183001[/C][/ROW]
[ROW][C]31[/C][C]8.85[/C][C]8.56357810005995[/C][C]0.286421899940052[/C][/ROW]
[ROW][C]32[/C][C]8.85[/C][C]8.85239502090902[/C][C]-0.00239502090901844[/C][/ROW]
[ROW][C]33[/C][C]8.85[/C][C]8.85232129501798[/C][C]-0.00232129501797829[/C][/ROW]
[ROW][C]34[/C][C]8.93[/C][C]8.85224983862988[/C][C]0.0777501613701155[/C][/ROW]
[ROW][C]35[/C][C]8.75[/C][C]8.93464322062667[/C][C]-0.184643220626674[/C][/ROW]
[ROW][C]36[/C][C]8.78[/C][C]8.748959351265[/C][C]0.0310406487350043[/C][/ROW]
[ROW][C]37[/C][C]8.77[/C][C]8.77991487506767[/C][C]-0.00991487506767008[/C][/ROW]
[ROW][C]38[/C][C]9.03[/C][C]8.76960966562412[/C][C]0.260390334375876[/C][/ROW]
[ROW][C]39[/C][C]9.01[/C][C]9.03762525719913[/C][C]-0.0276252571991265[/C][/ROW]
[ROW][C]40[/C][C]9.07[/C][C]9.01677486934048[/C][C]0.0532251306595217[/C][/ROW]
[ROW][C]41[/C][C]8.99[/C][C]9.07841329770194[/C][C]-0.0884132977019441[/C][/ROW]
[ROW][C]42[/C][C]9.02[/C][C]8.99569167254686[/C][C]0.0243083274531379[/C][/ROW]
[ROW][C]43[/C][C]8.99[/C][C]9.02643995540921[/C][C]-0.0364399554092127[/C][/ROW]
[ROW][C]44[/C][C]8.98[/C][C]8.99531822483395[/C][C]-0.015318224833953[/C][/ROW]
[ROW][C]45[/C][C]8.94[/C][C]8.98484668415938[/C][C]-0.0448466841593849[/C][/ROW]
[ROW][C]46[/C][C]8.94[/C][C]8.94346616938499[/C][C]-0.00346616938499267[/C][/ROW]
[ROW][C]47[/C][C]8.75[/C][C]8.94335947034723[/C][C]-0.193359470347232[/C][/ROW]
[ROW][C]48[/C][C]8.86[/C][C]8.74740728880725[/C][C]0.11259271119275[/C][/ROW]
[ROW][C]49[/C][C]8.87[/C][C]8.86087322846821[/C][C]0.00912677153179331[/C][/ROW]
[ROW][C]50[/C][C]8.84[/C][C]8.87115417773298[/C][C]-0.0311541777329793[/C][/ROW]
[ROW][C]51[/C][C]8.84[/C][C]8.84019515916894[/C][C]-0.000195159168942638[/C][/ROW]
[ROW][C]52[/C][C]9.91[/C][C]8.84018915158731[/C][C]1.06981084841269[/C][/ROW]
[ROW][C]53[/C][C]10.18[/C][C]9.94312112213812[/C][C]0.236878877861878[/C][/ROW]
[ROW][C]54[/C][C]10.34[/C][C]10.2204129609164[/C][C]0.119587039083621[/C][/ROW]
[ROW][C]55[/C][C]10.36[/C][C]10.384094206863[/C][C]-0.0240942068629924[/C][/ROW]
[ROW][C]56[/C][C]10.26[/C][C]10.4033525152714[/C][C]-0.143352515271404[/C][/ROW]
[ROW][C]57[/C][C]10.16[/C][C]10.2989396970444[/C][C]-0.138939697044417[/C][/ROW]
[ROW][C]58[/C][C]10.31[/C][C]10.1946627185316[/C][C]0.115337281468367[/C][/ROW]
[ROW][C]59[/C][C]10.46[/C][C]10.3482131442563[/C][C]0.111786855743706[/C][/ROW]
[ROW][C]60[/C][C]10.54[/C][C]10.5016542772816[/C][C]0.0383457227183825[/C][/ROW]
[ROW][C]61[/C][C]10.47[/C][C]10.582834673062[/C][C]-0.112834673062032[/C][/ROW]
[ROW][C]62[/C][C]10.48[/C][C]10.5093612850927[/C][C]-0.0293612850926532[/C][/ROW]
[ROW][C]63[/C][C]10.46[/C][C]10.5184574571146[/C][C]-0.0584574571146135[/C][/ROW]
[ROW][C]64[/C][C]11.3[/C][C]10.49665796213[/C][C]0.803342037869971[/C][/ROW]
[ROW][C]65[/C][C]11.58[/C][C]11.3613872274694[/C][C]0.218612772530573[/C][/ROW]
[ROW][C]66[/C][C]11.69[/C][C]11.648116781014[/C][C]0.0418832189859533[/C][/ROW]
[ROW][C]67[/C][C]11.63[/C][C]11.7594060714865[/C][C]-0.12940607148653[/C][/ROW]
[ROW][C]68[/C][C]11.51[/C][C]11.6954225664196[/C][C]-0.185422566419618[/C][/ROW]
[ROW][C]69[/C][C]11.37[/C][C]11.5697147064686[/C][C]-0.19971470646863[/C][/ROW]
[ROW][C]70[/C][C]11.42[/C][C]11.4235668917949[/C][C]-0.00356689179489678[/C][/ROW]
[ROW][C]71[/C][C]11.7[/C][C]11.4734570922208[/C][C]0.226542907779224[/C][/ROW]
[ROW][C]72[/C][C]11.75[/C][C]11.7604307589943[/C][C]-0.0104307589942518[/C][/ROW]
[ROW][C]73[/C][C]11.43[/C][C]11.8101096691039[/C][C]-0.380109669103893[/C][/ROW]
[ROW][C]74[/C][C]11.36[/C][C]11.4784087591275[/C][C]-0.118408759127535[/C][/ROW]
[ROW][C]75[/C][C]11.3[/C][C]11.4047637841543[/C][C]-0.104763784154311[/C][/ROW]
[ROW][C]76[/C][C]11.85[/C][C]11.3415388422315[/C][C]0.508461157768533[/C][/ROW]
[ROW][C]77[/C][C]11.99[/C][C]11.9071907940683[/C][C]0.0828092059317118[/C][/ROW]
[ROW][C]78[/C][C]12.07[/C][C]12.0497399085544[/C][C]0.0202600914456088[/C][/ROW]
[ROW][C]79[/C][C]12.21[/C][C]12.1303635746313[/C][C]0.0796364253687187[/C][/ROW]
[ROW][C]80[/C][C]12.13[/C][C]12.2728150214631[/C][C]-0.142815021463127[/C][/ROW]
[ROW][C]81[/C][C]12.3[/C][C]12.1884187488996[/C][C]0.111581251100398[/C][/ROW]
[ROW][C]82[/C][C]12.27[/C][C]12.3618535528004[/C][C]-0.0918535528004174[/C][/ROW]
[ROW][C]83[/C][C]12.32[/C][C]12.3290260263266[/C][C]-0.00902602632664795[/C][/ROW]
[ROW][C]84[/C][C]12.38[/C][C]12.3787481782999[/C][C]0.00125182170005722[/C][/ROW]
[ROW][C]85[/C][C]12.4[/C][C]12.4387867131077[/C][C]-0.0387867131076831[/C][/ROW]
[ROW][C]86[/C][C]12.33[/C][C]12.457592742327[/C][C]-0.127592742327034[/C][/ROW]
[ROW][C]87[/C][C]12.25[/C][C]12.3836650569432[/C][C]-0.133665056943169[/C][/ROW]
[ROW][C]88[/C][C]12.41[/C][C]12.2995504475938[/C][C]0.110449552406191[/C][/ROW]
[ROW][C]89[/C][C]12.38[/C][C]12.4629504144315[/C][C]-0.0829504144314868[/C][/ROW]
[ROW][C]90[/C][C]12.58[/C][C]12.4303969531264[/C][C]0.149603046873647[/C][/ROW]
[ROW][C]91[/C][C]12.45[/C][C]12.6350021813695[/C][C]-0.185002181369518[/C][/ROW]
[ROW][C]92[/C][C]12.43[/C][C]12.4993072621249[/C][C]-0.0693072621249264[/C][/ROW]
[ROW][C]93[/C][C]12.38[/C][C]12.477173777763[/C][C]-0.0971737777630484[/C][/ROW]
[ROW][C]94[/C][C]12.34[/C][C]12.4241824788878[/C][C]-0.0841824788877847[/C][/ROW]
[ROW][C]95[/C][C]11.98[/C][C]12.3815910909618[/C][C]-0.401591090961833[/C][/ROW]
[ROW][C]96[/C][C]12.24[/C][C]12.0092289187137[/C][C]0.230771081286322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278618&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278618&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
3	8.43	8.37	0.0599999999999987
4	8.44	8.41184697905801	0.0281530209419909
5	8.49	8.42271361305967	0.0672863869403333
6	8.47	8.47478488885247	-0.0047848888524662
7	8.53	8.45463759569404	0.075362404305956
8	8.52	8.51695747540261	0.00304252459738663
9	8.51	8.50705113338953	0.00294886661047222
10	8.53	8.4971419083041	0.032858091695898
11	8.54	8.51815337842491	0.0218466215750901
12	8.53	8.52882588263387	0.00117411736613349
13	8.47	8.51886202547031	-0.0488620254703136
14	8.63	8.45735790650739	0.172642093492611
15	8.67	8.62267234536092	0.0473276546390835
16	8.73	8.66412923181063	0.0658707681893667
17	8.57	8.72615693063365	-0.156156930633646
18	8.55	8.56134995428959	-0.0113499542895905
19	8.63	8.54100056882489	0.0889994311751128
20	8.65	8.62374023691747	0.0262597630825265
21	8.44	8.64454859079217	-0.204548590792168
22	8.62	8.42825197473319	0.191748025266804
23	8.37	8.61415455118457	-0.244154551184566
24	8.59	8.35663874546864	0.233361254531356
25	8.84	8.58382230130314	0.256177698696856
26	8.72	8.84170821538018	-0.121708215380176
27	8.8	8.71796167329693	0.0820383267030689
28	8.69	8.80048705781984	-0.110487057819842
29	8.68	8.6870859364536	-0.00708593645360445
30	8.57	8.676867810183	-0.106867810183001
31	8.85	8.56357810005995	0.286421899940052
32	8.85	8.85239502090902	-0.00239502090901844
33	8.85	8.85232129501798	-0.00232129501797829
34	8.93	8.85224983862988	0.0777501613701155
35	8.75	8.93464322062667	-0.184643220626674
36	8.78	8.748959351265	0.0310406487350043
37	8.77	8.77991487506767	-0.00991487506767008
38	9.03	8.76960966562412	0.260390334375876
39	9.01	9.03762525719913	-0.0276252571991265
40	9.07	9.01677486934048	0.0532251306595217
41	8.99	9.07841329770194	-0.0884132977019441
42	9.02	8.99569167254686	0.0243083274531379
43	8.99	9.02643995540921	-0.0364399554092127
44	8.98	8.99531822483395	-0.015318224833953
45	8.94	8.98484668415938	-0.0448466841593849
46	8.94	8.94346616938499	-0.00346616938499267
47	8.75	8.94335947034723	-0.193359470347232
48	8.86	8.74740728880725	0.11259271119275
49	8.87	8.86087322846821	0.00912677153179331
50	8.84	8.87115417773298	-0.0311541777329793
51	8.84	8.84019515916894	-0.000195159168942638
52	9.91	8.84018915158731	1.06981084841269
53	10.18	9.94312112213812	0.236878877861878
54	10.34	10.2204129609164	0.119587039083621
55	10.36	10.384094206863	-0.0240942068629924
56	10.26	10.4033525152714	-0.143352515271404
57	10.16	10.2989396970444	-0.138939697044417
58	10.31	10.1946627185316	0.115337281468367
59	10.46	10.3482131442563	0.111786855743706
60	10.54	10.5016542772816	0.0383457227183825
61	10.47	10.582834673062	-0.112834673062032
62	10.48	10.5093612850927	-0.0293612850926532
63	10.46	10.5184574571146	-0.0584574571146135
64	11.3	10.49665796213	0.803342037869971
65	11.58	11.3613872274694	0.218612772530573
66	11.69	11.648116781014	0.0418832189859533
67	11.63	11.7594060714865	-0.12940607148653
68	11.51	11.6954225664196	-0.185422566419618
69	11.37	11.5697147064686	-0.19971470646863
70	11.42	11.4235668917949	-0.00356689179489678
71	11.7	11.4734570922208	0.226542907779224
72	11.75	11.7604307589943	-0.0104307589942518
73	11.43	11.8101096691039	-0.380109669103893
74	11.36	11.4784087591275	-0.118408759127535
75	11.3	11.4047637841543	-0.104763784154311
76	11.85	11.3415388422315	0.508461157768533
77	11.99	11.9071907940683	0.0828092059317118
78	12.07	12.0497399085544	0.0202600914456088
79	12.21	12.1303635746313	0.0796364253687187
80	12.13	12.2728150214631	-0.142815021463127
81	12.3	12.1884187488996	0.111581251100398
82	12.27	12.3618535528004	-0.0918535528004174
83	12.32	12.3290260263266	-0.00902602632664795
84	12.38	12.3787481782999	0.00125182170005722
85	12.4	12.4387867131077	-0.0387867131076831
86	12.33	12.457592742327	-0.127592742327034
87	12.25	12.3836650569432	-0.133665056943169
88	12.41	12.2995504475938	0.110449552406191
89	12.38	12.4629504144315	-0.0829504144314868
90	12.58	12.4303969531264	0.149603046873647
91	12.45	12.6350021813695	-0.185002181369518
92	12.43	12.4993072621249	-0.0693072621249264
93	12.38	12.477173777763	-0.0971737777630484
94	12.34	12.4241824788878	-0.0841824788877847
95	11.98	12.3815910909618	-0.401591090961833
96	12.24	12.0092289187137	0.230771081286322

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	12.2763327412858	11.8917371115772	12.6609283709944
98	12.3126654825717	11.7603302446959	12.8650007204475
99	12.3489982238575	11.6621492057135	13.0358472420016
100	12.3853309651434	11.5801873764155	13.1904745538713
101	12.4216637064292	11.5079687829825	13.3353586298759
102	12.457996447715	11.442226522184	13.4737663732461
103	12.4943291890009	11.381051636989	13.6076067410128
104	12.5306619302867	11.3232209024792	13.7381029580943
105	12.5669946715726	11.2678989672567	13.8660903758885
106	12.6033274128584	11.2144880874752	13.9921667382417
107	12.6396601541443	11.1625449833434	14.1167753249451
108	12.6759928954301	11.1117315230534	14.2402542678068

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 12.2763327412858 & 11.8917371115772 & 12.6609283709944 \tabularnewline
98 & 12.3126654825717 & 11.7603302446959 & 12.8650007204475 \tabularnewline
99 & 12.3489982238575 & 11.6621492057135 & 13.0358472420016 \tabularnewline
100 & 12.3853309651434 & 11.5801873764155 & 13.1904745538713 \tabularnewline
101 & 12.4216637064292 & 11.5079687829825 & 13.3353586298759 \tabularnewline
102 & 12.457996447715 & 11.442226522184 & 13.4737663732461 \tabularnewline
103 & 12.4943291890009 & 11.381051636989 & 13.6076067410128 \tabularnewline
104 & 12.5306619302867 & 11.3232209024792 & 13.7381029580943 \tabularnewline
105 & 12.5669946715726 & 11.2678989672567 & 13.8660903758885 \tabularnewline
106 & 12.6033274128584 & 11.2144880874752 & 13.9921667382417 \tabularnewline
107 & 12.6396601541443 & 11.1625449833434 & 14.1167753249451 \tabularnewline
108 & 12.6759928954301 & 11.1117315230534 & 14.2402542678068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278618&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]12.2763327412858[/C][C]11.8917371115772[/C][C]12.6609283709944[/C][/ROW]
[ROW][C]98[/C][C]12.3126654825717[/C][C]11.7603302446959[/C][C]12.8650007204475[/C][/ROW]
[ROW][C]99[/C][C]12.3489982238575[/C][C]11.6621492057135[/C][C]13.0358472420016[/C][/ROW]
[ROW][C]100[/C][C]12.3853309651434[/C][C]11.5801873764155[/C][C]13.1904745538713[/C][/ROW]
[ROW][C]101[/C][C]12.4216637064292[/C][C]11.5079687829825[/C][C]13.3353586298759[/C][/ROW]
[ROW][C]102[/C][C]12.457996447715[/C][C]11.442226522184[/C][C]13.4737663732461[/C][/ROW]
[ROW][C]103[/C][C]12.4943291890009[/C][C]11.381051636989[/C][C]13.6076067410128[/C][/ROW]
[ROW][C]104[/C][C]12.5306619302867[/C][C]11.3232209024792[/C][C]13.7381029580943[/C][/ROW]
[ROW][C]105[/C][C]12.5669946715726[/C][C]11.2678989672567[/C][C]13.8660903758885[/C][/ROW]
[ROW][C]106[/C][C]12.6033274128584[/C][C]11.2144880874752[/C][C]13.9921667382417[/C][/ROW]
[ROW][C]107[/C][C]12.6396601541443[/C][C]11.1625449833434[/C][C]14.1167753249451[/C][/ROW]
[ROW][C]108[/C][C]12.6759928954301[/C][C]11.1117315230534[/C][C]14.2402542678068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278618&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278618&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	12.2763327412858	11.8917371115772	12.6609283709944
98	12.3126654825717	11.7603302446959	12.8650007204475
99	12.3489982238575	11.6621492057135	13.0358472420016
100	12.3853309651434	11.5801873764155	13.1904745538713
101	12.4216637064292	11.5079687829825	13.3353586298759
102	12.457996447715	11.442226522184	13.4737663732461
103	12.4943291890009	11.381051636989	13.6076067410128
104	12.5306619302867	11.3232209024792	13.7381029580943
105	12.5669946715726	11.2678989672567	13.8660903758885
106	12.6033274128584	11.2144880874752	13.9921667382417
107	12.6396601541443	11.1625449833434	14.1167753249451
108	12.6759928954301	11.1117315230534	14.2402542678068

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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