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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 16 Dec 2013 06:26:11 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/16/t1387193185zimbdq4jw0nktwb.htm/, Retrieved Wed, 13 May 2026 07:31:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232389, Retrieved Wed, 13 May 2026 07:31:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

385

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

-       [Exponential Smoothing] [] [2013-12-16 11:26:11] [65fde7880dd4fc754cb993d7776a3fb6] [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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232389&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232389&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.567235557693194
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.567235557693194 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232389&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]0.567235557693194[/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=232389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232389&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	0.567235557693194
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.2	102.569738247863	1.63026175213678
14	104.2	103.414098980391	0.785901019609284
15	104.2	103.779508281909	0.42049171809127
16	104.2	103.937644434494	0.262355565506098
17	108.1	107.906080138376	0.193919861624039
18	109.2	109.0356966776	0.164303322399647
19	109.2	108.014763662681	1.1852363373191
20	109.2	108.875856822513	0.324143177486704
21	109.2	109.248507323602	-0.0485073236023794
22	109.2	109.409777209882	-0.209777209881523
23	109.2	109.390819082278	-0.190819082278026
24	109.2	109.248031345425	-0.0480313454251728
25	109.2	109.845923874762	-0.645923874762047
26	109.2	109.033741882284	0.166258117715685
27	109.2	108.889531544191	0.310468455809072
28	109.2	108.916822886354	0.283177113645834
29	112.1	112.867452773483	-0.767452773482916
30	112.1	113.438927584801	-1.33892758480094
31	112.1	112.007132054728	0.0928679452718626
32	112.1	111.875944519402	0.224055480597869
33	112.1	112.030551833649	0.0694481663509237
34	112.1	112.188938395658	-0.0889383956583742
35	112.1	112.246728743751	-0.14672874375124
36	112.1	112.190744069969	-0.0907440699688919
37	112.1	112.505661796161	-0.405661796160743
38	112.1	112.181248484857	-0.0812484848571984
39	112.1	111.95905270756	0.140947292439506
40	112.1	111.878374895608	0.221625104392089
41	114.81	115.339415037266	-0.529415037266318
42	114.81	115.798599338627	-0.98859933862677
43	114.81	115.185152640718	-0.375152640717587
44	114.81	114.845260487849	-0.0352604878489302
45	114.81	114.785866015989	0.0241339840114279
46	114.81	114.85000469033	-0.0400046903302638
47	114.81	114.910542368292	-0.100542368291784
48	114.81	114.904984425078	-0.0949844250781524
49	114.81	115.081211676927	-0.271211676926853
50	114.81	114.973457799732	-0.163457799732043
51	114.81	114.800788407509	0.00921159249053005
52	114.81	114.680299910624	0.129700089375575
53	115.57	117.764173447069	-2.19417344706918
54	115.57	117.080328945326	-1.51032894532636
55	115.57	116.436416581101	-0.866416581101504
56	115.57	115.964955291015	-0.394955291015293
57	115.57	115.727232952372	-0.157232952372283
58	115.57	115.660736913775	-0.090736913775487
59	115.57	115.666298916236	-0.0962989162364636
60	115.57	115.665553290111	-0.0955532901111837
61	115.57	115.76519297312	-0.195192973120058
62	115.57	115.747191654345	-0.177191654344824
63	115.57	115.64145710467	-0.0714571046703441
64	117.3	115.527353591522	1.77264640847829
65	117.3	118.537474864552	-1.23747486455161
66	118.39	118.692247401229	-0.30224740122874
67	118.39	119.012264220607	-0.622264220607178
68	118.39	118.883326513161	-0.493326513161477
69	118.39	118.69268229477	-0.302682294770122
70	118.39	118.572459338381	-0.182459338381136
71	118.39	118.523586083275	-0.133586083274835
72	118.39	118.502012530634	-0.112012530634019
73	118.39	118.549195435317	-0.159195435316747
74	118.39	118.559403530654	-0.169403530653511
75	118.39	118.503844835087	-0.113844835086894
76	121.18	119.16375992246	2.01624007754015
77	123.21	121.009382732212	2.20061726778803
78	123.21	123.519096568572	-0.309096568572286
79	123.21	123.696736396326	-0.486736396325767
80	123.21	123.700474544924	-0.490474544924339
81	123.21	123.593952103178	-0.383952103177648
82	123.21	123.479658242367	-0.269658242367143
83	123.21	123.402473275318	-0.192473275317909
84	123.21	123.356833079935	-0.146833079934737

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.2 & 102.569738247863 & 1.63026175213678 \tabularnewline
14 & 104.2 & 103.414098980391 & 0.785901019609284 \tabularnewline
15 & 104.2 & 103.779508281909 & 0.42049171809127 \tabularnewline
16 & 104.2 & 103.937644434494 & 0.262355565506098 \tabularnewline
17 & 108.1 & 107.906080138376 & 0.193919861624039 \tabularnewline
18 & 109.2 & 109.0356966776 & 0.164303322399647 \tabularnewline
19 & 109.2 & 108.014763662681 & 1.1852363373191 \tabularnewline
20 & 109.2 & 108.875856822513 & 0.324143177486704 \tabularnewline
21 & 109.2 & 109.248507323602 & -0.0485073236023794 \tabularnewline
22 & 109.2 & 109.409777209882 & -0.209777209881523 \tabularnewline
23 & 109.2 & 109.390819082278 & -0.190819082278026 \tabularnewline
24 & 109.2 & 109.248031345425 & -0.0480313454251728 \tabularnewline
25 & 109.2 & 109.845923874762 & -0.645923874762047 \tabularnewline
26 & 109.2 & 109.033741882284 & 0.166258117715685 \tabularnewline
27 & 109.2 & 108.889531544191 & 0.310468455809072 \tabularnewline
28 & 109.2 & 108.916822886354 & 0.283177113645834 \tabularnewline
29 & 112.1 & 112.867452773483 & -0.767452773482916 \tabularnewline
30 & 112.1 & 113.438927584801 & -1.33892758480094 \tabularnewline
31 & 112.1 & 112.007132054728 & 0.0928679452718626 \tabularnewline
32 & 112.1 & 111.875944519402 & 0.224055480597869 \tabularnewline
33 & 112.1 & 112.030551833649 & 0.0694481663509237 \tabularnewline
34 & 112.1 & 112.188938395658 & -0.0889383956583742 \tabularnewline
35 & 112.1 & 112.246728743751 & -0.14672874375124 \tabularnewline
36 & 112.1 & 112.190744069969 & -0.0907440699688919 \tabularnewline
37 & 112.1 & 112.505661796161 & -0.405661796160743 \tabularnewline
38 & 112.1 & 112.181248484857 & -0.0812484848571984 \tabularnewline
39 & 112.1 & 111.95905270756 & 0.140947292439506 \tabularnewline
40 & 112.1 & 111.878374895608 & 0.221625104392089 \tabularnewline
41 & 114.81 & 115.339415037266 & -0.529415037266318 \tabularnewline
42 & 114.81 & 115.798599338627 & -0.98859933862677 \tabularnewline
43 & 114.81 & 115.185152640718 & -0.375152640717587 \tabularnewline
44 & 114.81 & 114.845260487849 & -0.0352604878489302 \tabularnewline
45 & 114.81 & 114.785866015989 & 0.0241339840114279 \tabularnewline
46 & 114.81 & 114.85000469033 & -0.0400046903302638 \tabularnewline
47 & 114.81 & 114.910542368292 & -0.100542368291784 \tabularnewline
48 & 114.81 & 114.904984425078 & -0.0949844250781524 \tabularnewline
49 & 114.81 & 115.081211676927 & -0.271211676926853 \tabularnewline
50 & 114.81 & 114.973457799732 & -0.163457799732043 \tabularnewline
51 & 114.81 & 114.800788407509 & 0.00921159249053005 \tabularnewline
52 & 114.81 & 114.680299910624 & 0.129700089375575 \tabularnewline
53 & 115.57 & 117.764173447069 & -2.19417344706918 \tabularnewline
54 & 115.57 & 117.080328945326 & -1.51032894532636 \tabularnewline
55 & 115.57 & 116.436416581101 & -0.866416581101504 \tabularnewline
56 & 115.57 & 115.964955291015 & -0.394955291015293 \tabularnewline
57 & 115.57 & 115.727232952372 & -0.157232952372283 \tabularnewline
58 & 115.57 & 115.660736913775 & -0.090736913775487 \tabularnewline
59 & 115.57 & 115.666298916236 & -0.0962989162364636 \tabularnewline
60 & 115.57 & 115.665553290111 & -0.0955532901111837 \tabularnewline
61 & 115.57 & 115.76519297312 & -0.195192973120058 \tabularnewline
62 & 115.57 & 115.747191654345 & -0.177191654344824 \tabularnewline
63 & 115.57 & 115.64145710467 & -0.0714571046703441 \tabularnewline
64 & 117.3 & 115.527353591522 & 1.77264640847829 \tabularnewline
65 & 117.3 & 118.537474864552 & -1.23747486455161 \tabularnewline
66 & 118.39 & 118.692247401229 & -0.30224740122874 \tabularnewline
67 & 118.39 & 119.012264220607 & -0.622264220607178 \tabularnewline
68 & 118.39 & 118.883326513161 & -0.493326513161477 \tabularnewline
69 & 118.39 & 118.69268229477 & -0.302682294770122 \tabularnewline
70 & 118.39 & 118.572459338381 & -0.182459338381136 \tabularnewline
71 & 118.39 & 118.523586083275 & -0.133586083274835 \tabularnewline
72 & 118.39 & 118.502012530634 & -0.112012530634019 \tabularnewline
73 & 118.39 & 118.549195435317 & -0.159195435316747 \tabularnewline
74 & 118.39 & 118.559403530654 & -0.169403530653511 \tabularnewline
75 & 118.39 & 118.503844835087 & -0.113844835086894 \tabularnewline
76 & 121.18 & 119.16375992246 & 2.01624007754015 \tabularnewline
77 & 123.21 & 121.009382732212 & 2.20061726778803 \tabularnewline
78 & 123.21 & 123.519096568572 & -0.309096568572286 \tabularnewline
79 & 123.21 & 123.696736396326 & -0.486736396325767 \tabularnewline
80 & 123.21 & 123.700474544924 & -0.490474544924339 \tabularnewline
81 & 123.21 & 123.593952103178 & -0.383952103177648 \tabularnewline
82 & 123.21 & 123.479658242367 & -0.269658242367143 \tabularnewline
83 & 123.21 & 123.402473275318 & -0.192473275317909 \tabularnewline
84 & 123.21 & 123.356833079935 & -0.146833079934737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232389&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]104.2[/C][C]102.569738247863[/C][C]1.63026175213678[/C][/ROW]
[ROW][C]14[/C][C]104.2[/C][C]103.414098980391[/C][C]0.785901019609284[/C][/ROW]
[ROW][C]15[/C][C]104.2[/C][C]103.779508281909[/C][C]0.42049171809127[/C][/ROW]
[ROW][C]16[/C][C]104.2[/C][C]103.937644434494[/C][C]0.262355565506098[/C][/ROW]
[ROW][C]17[/C][C]108.1[/C][C]107.906080138376[/C][C]0.193919861624039[/C][/ROW]
[ROW][C]18[/C][C]109.2[/C][C]109.0356966776[/C][C]0.164303322399647[/C][/ROW]
[ROW][C]19[/C][C]109.2[/C][C]108.014763662681[/C][C]1.1852363373191[/C][/ROW]
[ROW][C]20[/C][C]109.2[/C][C]108.875856822513[/C][C]0.324143177486704[/C][/ROW]
[ROW][C]21[/C][C]109.2[/C][C]109.248507323602[/C][C]-0.0485073236023794[/C][/ROW]
[ROW][C]22[/C][C]109.2[/C][C]109.409777209882[/C][C]-0.209777209881523[/C][/ROW]
[ROW][C]23[/C][C]109.2[/C][C]109.390819082278[/C][C]-0.190819082278026[/C][/ROW]
[ROW][C]24[/C][C]109.2[/C][C]109.248031345425[/C][C]-0.0480313454251728[/C][/ROW]
[ROW][C]25[/C][C]109.2[/C][C]109.845923874762[/C][C]-0.645923874762047[/C][/ROW]
[ROW][C]26[/C][C]109.2[/C][C]109.033741882284[/C][C]0.166258117715685[/C][/ROW]
[ROW][C]27[/C][C]109.2[/C][C]108.889531544191[/C][C]0.310468455809072[/C][/ROW]
[ROW][C]28[/C][C]109.2[/C][C]108.916822886354[/C][C]0.283177113645834[/C][/ROW]
[ROW][C]29[/C][C]112.1[/C][C]112.867452773483[/C][C]-0.767452773482916[/C][/ROW]
[ROW][C]30[/C][C]112.1[/C][C]113.438927584801[/C][C]-1.33892758480094[/C][/ROW]
[ROW][C]31[/C][C]112.1[/C][C]112.007132054728[/C][C]0.0928679452718626[/C][/ROW]
[ROW][C]32[/C][C]112.1[/C][C]111.875944519402[/C][C]0.224055480597869[/C][/ROW]
[ROW][C]33[/C][C]112.1[/C][C]112.030551833649[/C][C]0.0694481663509237[/C][/ROW]
[ROW][C]34[/C][C]112.1[/C][C]112.188938395658[/C][C]-0.0889383956583742[/C][/ROW]
[ROW][C]35[/C][C]112.1[/C][C]112.246728743751[/C][C]-0.14672874375124[/C][/ROW]
[ROW][C]36[/C][C]112.1[/C][C]112.190744069969[/C][C]-0.0907440699688919[/C][/ROW]
[ROW][C]37[/C][C]112.1[/C][C]112.505661796161[/C][C]-0.405661796160743[/C][/ROW]
[ROW][C]38[/C][C]112.1[/C][C]112.181248484857[/C][C]-0.0812484848571984[/C][/ROW]
[ROW][C]39[/C][C]112.1[/C][C]111.95905270756[/C][C]0.140947292439506[/C][/ROW]
[ROW][C]40[/C][C]112.1[/C][C]111.878374895608[/C][C]0.221625104392089[/C][/ROW]
[ROW][C]41[/C][C]114.81[/C][C]115.339415037266[/C][C]-0.529415037266318[/C][/ROW]
[ROW][C]42[/C][C]114.81[/C][C]115.798599338627[/C][C]-0.98859933862677[/C][/ROW]
[ROW][C]43[/C][C]114.81[/C][C]115.185152640718[/C][C]-0.375152640717587[/C][/ROW]
[ROW][C]44[/C][C]114.81[/C][C]114.845260487849[/C][C]-0.0352604878489302[/C][/ROW]
[ROW][C]45[/C][C]114.81[/C][C]114.785866015989[/C][C]0.0241339840114279[/C][/ROW]
[ROW][C]46[/C][C]114.81[/C][C]114.85000469033[/C][C]-0.0400046903302638[/C][/ROW]
[ROW][C]47[/C][C]114.81[/C][C]114.910542368292[/C][C]-0.100542368291784[/C][/ROW]
[ROW][C]48[/C][C]114.81[/C][C]114.904984425078[/C][C]-0.0949844250781524[/C][/ROW]
[ROW][C]49[/C][C]114.81[/C][C]115.081211676927[/C][C]-0.271211676926853[/C][/ROW]
[ROW][C]50[/C][C]114.81[/C][C]114.973457799732[/C][C]-0.163457799732043[/C][/ROW]
[ROW][C]51[/C][C]114.81[/C][C]114.800788407509[/C][C]0.00921159249053005[/C][/ROW]
[ROW][C]52[/C][C]114.81[/C][C]114.680299910624[/C][C]0.129700089375575[/C][/ROW]
[ROW][C]53[/C][C]115.57[/C][C]117.764173447069[/C][C]-2.19417344706918[/C][/ROW]
[ROW][C]54[/C][C]115.57[/C][C]117.080328945326[/C][C]-1.51032894532636[/C][/ROW]
[ROW][C]55[/C][C]115.57[/C][C]116.436416581101[/C][C]-0.866416581101504[/C][/ROW]
[ROW][C]56[/C][C]115.57[/C][C]115.964955291015[/C][C]-0.394955291015293[/C][/ROW]
[ROW][C]57[/C][C]115.57[/C][C]115.727232952372[/C][C]-0.157232952372283[/C][/ROW]
[ROW][C]58[/C][C]115.57[/C][C]115.660736913775[/C][C]-0.090736913775487[/C][/ROW]
[ROW][C]59[/C][C]115.57[/C][C]115.666298916236[/C][C]-0.0962989162364636[/C][/ROW]
[ROW][C]60[/C][C]115.57[/C][C]115.665553290111[/C][C]-0.0955532901111837[/C][/ROW]
[ROW][C]61[/C][C]115.57[/C][C]115.76519297312[/C][C]-0.195192973120058[/C][/ROW]
[ROW][C]62[/C][C]115.57[/C][C]115.747191654345[/C][C]-0.177191654344824[/C][/ROW]
[ROW][C]63[/C][C]115.57[/C][C]115.64145710467[/C][C]-0.0714571046703441[/C][/ROW]
[ROW][C]64[/C][C]117.3[/C][C]115.527353591522[/C][C]1.77264640847829[/C][/ROW]
[ROW][C]65[/C][C]117.3[/C][C]118.537474864552[/C][C]-1.23747486455161[/C][/ROW]
[ROW][C]66[/C][C]118.39[/C][C]118.692247401229[/C][C]-0.30224740122874[/C][/ROW]
[ROW][C]67[/C][C]118.39[/C][C]119.012264220607[/C][C]-0.622264220607178[/C][/ROW]
[ROW][C]68[/C][C]118.39[/C][C]118.883326513161[/C][C]-0.493326513161477[/C][/ROW]
[ROW][C]69[/C][C]118.39[/C][C]118.69268229477[/C][C]-0.302682294770122[/C][/ROW]
[ROW][C]70[/C][C]118.39[/C][C]118.572459338381[/C][C]-0.182459338381136[/C][/ROW]
[ROW][C]71[/C][C]118.39[/C][C]118.523586083275[/C][C]-0.133586083274835[/C][/ROW]
[ROW][C]72[/C][C]118.39[/C][C]118.502012530634[/C][C]-0.112012530634019[/C][/ROW]
[ROW][C]73[/C][C]118.39[/C][C]118.549195435317[/C][C]-0.159195435316747[/C][/ROW]
[ROW][C]74[/C][C]118.39[/C][C]118.559403530654[/C][C]-0.169403530653511[/C][/ROW]
[ROW][C]75[/C][C]118.39[/C][C]118.503844835087[/C][C]-0.113844835086894[/C][/ROW]
[ROW][C]76[/C][C]121.18[/C][C]119.16375992246[/C][C]2.01624007754015[/C][/ROW]
[ROW][C]77[/C][C]123.21[/C][C]121.009382732212[/C][C]2.20061726778803[/C][/ROW]
[ROW][C]78[/C][C]123.21[/C][C]123.519096568572[/C][C]-0.309096568572286[/C][/ROW]
[ROW][C]79[/C][C]123.21[/C][C]123.696736396326[/C][C]-0.486736396325767[/C][/ROW]
[ROW][C]80[/C][C]123.21[/C][C]123.700474544924[/C][C]-0.490474544924339[/C][/ROW]
[ROW][C]81[/C][C]123.21[/C][C]123.593952103178[/C][C]-0.383952103177648[/C][/ROW]
[ROW][C]82[/C][C]123.21[/C][C]123.479658242367[/C][C]-0.269658242367143[/C][/ROW]
[ROW][C]83[/C][C]123.21[/C][C]123.402473275318[/C][C]-0.192473275317909[/C][/ROW]
[ROW][C]84[/C][C]123.21[/C][C]123.356833079935[/C][C]-0.146833079934737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232389&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	104.2	102.569738247863	1.63026175213678
14	104.2	103.414098980391	0.785901019609284
15	104.2	103.779508281909	0.42049171809127
16	104.2	103.937644434494	0.262355565506098
17	108.1	107.906080138376	0.193919861624039
18	109.2	109.0356966776	0.164303322399647
19	109.2	108.014763662681	1.1852363373191
20	109.2	108.875856822513	0.324143177486704
21	109.2	109.248507323602	-0.0485073236023794
22	109.2	109.409777209882	-0.209777209881523
23	109.2	109.390819082278	-0.190819082278026
24	109.2	109.248031345425	-0.0480313454251728
25	109.2	109.845923874762	-0.645923874762047
26	109.2	109.033741882284	0.166258117715685
27	109.2	108.889531544191	0.310468455809072
28	109.2	108.916822886354	0.283177113645834
29	112.1	112.867452773483	-0.767452773482916
30	112.1	113.438927584801	-1.33892758480094
31	112.1	112.007132054728	0.0928679452718626
32	112.1	111.875944519402	0.224055480597869
33	112.1	112.030551833649	0.0694481663509237
34	112.1	112.188938395658	-0.0889383956583742
35	112.1	112.246728743751	-0.14672874375124
36	112.1	112.190744069969	-0.0907440699688919
37	112.1	112.505661796161	-0.405661796160743
38	112.1	112.181248484857	-0.0812484848571984
39	112.1	111.95905270756	0.140947292439506
40	112.1	111.878374895608	0.221625104392089
41	114.81	115.339415037266	-0.529415037266318
42	114.81	115.798599338627	-0.98859933862677
43	114.81	115.185152640718	-0.375152640717587
44	114.81	114.845260487849	-0.0352604878489302
45	114.81	114.785866015989	0.0241339840114279
46	114.81	114.85000469033	-0.0400046903302638
47	114.81	114.910542368292	-0.100542368291784
48	114.81	114.904984425078	-0.0949844250781524
49	114.81	115.081211676927	-0.271211676926853
50	114.81	114.973457799732	-0.163457799732043
51	114.81	114.800788407509	0.00921159249053005
52	114.81	114.680299910624	0.129700089375575
53	115.57	117.764173447069	-2.19417344706918
54	115.57	117.080328945326	-1.51032894532636
55	115.57	116.436416581101	-0.866416581101504
56	115.57	115.964955291015	-0.394955291015293
57	115.57	115.727232952372	-0.157232952372283
58	115.57	115.660736913775	-0.090736913775487
59	115.57	115.666298916236	-0.0962989162364636
60	115.57	115.665553290111	-0.0955532901111837
61	115.57	115.76519297312	-0.195192973120058
62	115.57	115.747191654345	-0.177191654344824
63	115.57	115.64145710467	-0.0714571046703441
64	117.3	115.527353591522	1.77264640847829
65	117.3	118.537474864552	-1.23747486455161
66	118.39	118.692247401229	-0.30224740122874
67	118.39	119.012264220607	-0.622264220607178
68	118.39	118.883326513161	-0.493326513161477
69	118.39	118.69268229477	-0.302682294770122
70	118.39	118.572459338381	-0.182459338381136
71	118.39	118.523586083275	-0.133586083274835
72	118.39	118.502012530634	-0.112012530634019
73	118.39	118.549195435317	-0.159195435316747
74	118.39	118.559403530654	-0.169403530653511
75	118.39	118.503844835087	-0.113844835086894
76	121.18	119.16375992246	2.01624007754015
77	123.21	121.009382732212	2.20061726778803
78	123.21	123.519096568572	-0.309096568572286
79	123.21	123.696736396326	-0.486736396325767
80	123.21	123.700474544924	-0.490474544924339
81	123.21	123.593952103178	-0.383952103177648
82	123.21	123.479658242367	-0.269658242367143
83	123.21	123.402473275318	-0.192473275317909
84	123.21	123.356833079935	-0.146833079934737

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	123.363845447484	122.026205029727	124.701485865242
86	123.45993715367	121.922083328218	124.997790979121
87	123.524513992191	121.809665051411	125.239362932971
88	125.170830927364	123.295619101747	127.04604275298
89	125.952562564201	123.929660714834	127.975464413567
90	126.127893128656	123.967373655611	128.288412601701
91	126.403987319875	124.114105904901	128.69386873485
92	126.6822019219	124.269885732864	129.094518110936
93	126.899993207273	124.37116306329	129.428823351257
94	127.052952950769	124.412745686489	129.693160215049
95	127.162130636435	124.415058213	129.90920305987
96	127.24541958042	124.395486352985	130.095352807854

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 123.363845447484 & 122.026205029727 & 124.701485865242 \tabularnewline
86 & 123.45993715367 & 121.922083328218 & 124.997790979121 \tabularnewline
87 & 123.524513992191 & 121.809665051411 & 125.239362932971 \tabularnewline
88 & 125.170830927364 & 123.295619101747 & 127.04604275298 \tabularnewline
89 & 125.952562564201 & 123.929660714834 & 127.975464413567 \tabularnewline
90 & 126.127893128656 & 123.967373655611 & 128.288412601701 \tabularnewline
91 & 126.403987319875 & 124.114105904901 & 128.69386873485 \tabularnewline
92 & 126.6822019219 & 124.269885732864 & 129.094518110936 \tabularnewline
93 & 126.899993207273 & 124.37116306329 & 129.428823351257 \tabularnewline
94 & 127.052952950769 & 124.412745686489 & 129.693160215049 \tabularnewline
95 & 127.162130636435 & 124.415058213 & 129.90920305987 \tabularnewline
96 & 127.24541958042 & 124.395486352985 & 130.095352807854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232389&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]123.363845447484[/C][C]122.026205029727[/C][C]124.701485865242[/C][/ROW]
[ROW][C]86[/C][C]123.45993715367[/C][C]121.922083328218[/C][C]124.997790979121[/C][/ROW]
[ROW][C]87[/C][C]123.524513992191[/C][C]121.809665051411[/C][C]125.239362932971[/C][/ROW]
[ROW][C]88[/C][C]125.170830927364[/C][C]123.295619101747[/C][C]127.04604275298[/C][/ROW]
[ROW][C]89[/C][C]125.952562564201[/C][C]123.929660714834[/C][C]127.975464413567[/C][/ROW]
[ROW][C]90[/C][C]126.127893128656[/C][C]123.967373655611[/C][C]128.288412601701[/C][/ROW]
[ROW][C]91[/C][C]126.403987319875[/C][C]124.114105904901[/C][C]128.69386873485[/C][/ROW]
[ROW][C]92[/C][C]126.6822019219[/C][C]124.269885732864[/C][C]129.094518110936[/C][/ROW]
[ROW][C]93[/C][C]126.899993207273[/C][C]124.37116306329[/C][C]129.428823351257[/C][/ROW]
[ROW][C]94[/C][C]127.052952950769[/C][C]124.412745686489[/C][C]129.693160215049[/C][/ROW]
[ROW][C]95[/C][C]127.162130636435[/C][C]124.415058213[/C][C]129.90920305987[/C][/ROW]
[ROW][C]96[/C][C]127.24541958042[/C][C]124.395486352985[/C][C]130.095352807854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232389&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232389&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	123.363845447484	122.026205029727	124.701485865242
86	123.45993715367	121.922083328218	124.997790979121
87	123.524513992191	121.809665051411	125.239362932971
88	125.170830927364	123.295619101747	127.04604275298
89	125.952562564201	123.929660714834	127.975464413567
90	126.127893128656	123.967373655611	128.288412601701
91	126.403987319875	124.114105904901	128.69386873485
92	126.6822019219	124.269885732864	129.094518110936
93	126.899993207273	124.37116306329	129.428823351257
94	127.052952950769	124.412745686489	129.693160215049
95	127.162130636435	124.415058213	129.90920305987
96	127.24541958042	124.395486352985	130.095352807854

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code