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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 19 May 2011 14:45:39 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/19/t1305816153dr1oyfchkleh7lp.htm/, Retrieved Sat, 11 May 2024 12:32:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122055, Retrieved Sat, 11 May 2024 12:32:13 +0000

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No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [OlivierDeGroodtOp...] [2011-05-19 14:45:39] [461523bf9c5715e033e9a40193969321] [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	'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122055&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122055&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	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.629581570005306
beta	0.0178081048922574
gamma	0.529826221021731

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.629581570005306 \tabularnewline
beta & 0.0178081048922574 \tabularnewline
gamma & 0.529826221021731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122055&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]0.629581570005306[/C][/ROW]
[ROW][C]beta[/C][C]0.0178081048922574[/C][/ROW]
[ROW][C]gamma[/C][C]0.529826221021731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122055&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	0.629581570005306
beta	0.0178081048922574
gamma	0.529826221021731

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	12.51	12.6435229700855	-0.133522970085474
14	12.59	12.6349101993434	-0.0449101993434446
15	12.52	12.529082878283	-0.00908287828298882
16	12.5	12.4973766108371	0.00262338916289373
17	12.58	12.5747364728286	0.00526352717135481
18	12.51	12.5034008632347	0.00659913676526713
19	12.47	12.3846467827348	0.085353217265153
20	12.44	12.4947651040079	-0.054765104007867
21	12.51	12.3906368384883	0.11936316151165
22	12.27	12.4137247783001	-0.14372477830015
23	12.51	12.4283160073387	0.0816839926612918
24	12.41	12.5099029236739	-0.099902923673886
25	12.35	12.2548411165094	0.095158883490571
26	12.39	12.4080826322851	-0.0180826322850898
27	12.31	12.3269671055889	-0.0169671055889111
28	12.31	12.2932963960858	0.016703603914241
29	12.21	12.3808987914758	-0.170898791475841
30	12.1	12.197801427994	-0.0978014279940229
31	12.01	12.026488915786	-0.0164889157860362
32	11.85	12.0415624001407	-0.191562400140707
33	12.12	11.8805216643384	0.239478335661648
34	11.96	11.9239842657437	0.036015734256301
35	11.99	12.0943754519732	-0.104375451973196
36	11.93	12.0194994657449	-0.0894994657448507
37	11.91	11.8057009166806	0.104299083319377
38	11.83	11.9390060356676	-0.109006035667621
39	11.92	11.7963799254551	0.123620074544874
40	11.86	11.854918839424	0.00508116057597441
41	11.94	11.8953456941662	0.0446543058338378
42	11.87	11.8616792865318	0.0083207134681853
43	11.86	11.7737041056857	0.0862958943142864
44	11.92	11.820848538574	0.0991514614260236
45	11.82	11.9324092011001	-0.112409201100084
46	11.85	11.7154319887301	0.134568011269923
47	11.77	11.9224551321924	-0.152455132192408
48	11.82	11.8218276036797	-0.00182760367968093
49	11.61	11.7038420045317	-0.0938420045317052
50	11.56	11.6708989120675	-0.110898912067508
51	11.45	11.5730749274698	-0.123074927469792
52	11.4	11.4506084677555	-0.050608467755497
53	11.38	11.4606897001496	-0.0806897001496143
54	11.33	11.3365219852837	-0.0065219852836993
55	11.19	11.2498826147686	-0.0598826147685667
56	11.15	11.2012571434799	-0.0512571434799316
57	10.98	11.1686550370624	-0.188655037062434
58	10.92	10.9433431760111	-0.0233431760110587
59	10.99	10.9840447051869	0.00595529481313584
60	11	11.0039140455952	-0.00391404559521291
61	10.9	10.8577357787352	0.0422642212648281
62	10.99	10.8998405137788	0.0901594862211894
63	11.04	10.9211691559302	0.118830844069764
64	11.03	10.9628959521508	0.0671040478491758
65	10.99	11.0401746643781	-0.0501746643781242
66	11	10.949108254159	0.0508917458410192
67	10.87	10.888120433166	-0.018120433165965
68	10.88	10.8679260382209	0.0120739617791248
69	10.91	10.8493862859607	0.0606137140392669
70	10.92	10.8174034376877	0.102596562312346
71	10.83	10.9485066650829	-0.11850666508292
72	10.9	10.8920470122268	0.00795298777321207
73	10.82	10.766502780307	0.0534972196929662
74	10.79	10.8293052876537	-0.039305287653697
75	10.77	10.7775266294246	-0.00752662942463544
76	10.72	10.7309070155251	-0.010907015525083
77	10.71	10.7365376449181	-0.0265376449181165
78	10.63	10.6809357669128	-0.0509357669128097
79	10.61	10.5419014848566	0.0680985151433671
80	10.57	10.5824878960753	-0.0124878960753136
81	10.65	10.5583084291134	0.0916915708866348
82	10.57	10.5547771983643	0.0152228016357085
83	10.57	10.5871448951368	-0.0171448951367736
84	10.57	10.6201223426595	-0.0501223426595274
85	10.52	10.4671051807103	0.0528948192896781
86	10.43	10.5114603307166	-0.081460330716551
87	10.35	10.4390508846258	-0.0890508846258005
88	10.2	10.3392001081631	-0.139200108163061
89	10.2	10.2583121981844	-0.058312198184419
90	10.17	10.1748811437663	-0.00488114376633675
91	10.14	10.0856835191636	0.0543164808364267
92	10.05	10.0991029740418	-0.0491029740417837
93	10.12	10.0692324419545	0.0507675580455391
94	10.12	10.0213849415935	0.09861505840645

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12.51 & 12.6435229700855 & -0.133522970085474 \tabularnewline
14 & 12.59 & 12.6349101993434 & -0.0449101993434446 \tabularnewline
15 & 12.52 & 12.529082878283 & -0.00908287828298882 \tabularnewline
16 & 12.5 & 12.4973766108371 & 0.00262338916289373 \tabularnewline
17 & 12.58 & 12.5747364728286 & 0.00526352717135481 \tabularnewline
18 & 12.51 & 12.5034008632347 & 0.00659913676526713 \tabularnewline
19 & 12.47 & 12.3846467827348 & 0.085353217265153 \tabularnewline
20 & 12.44 & 12.4947651040079 & -0.054765104007867 \tabularnewline
21 & 12.51 & 12.3906368384883 & 0.11936316151165 \tabularnewline
22 & 12.27 & 12.4137247783001 & -0.14372477830015 \tabularnewline
23 & 12.51 & 12.4283160073387 & 0.0816839926612918 \tabularnewline
24 & 12.41 & 12.5099029236739 & -0.099902923673886 \tabularnewline
25 & 12.35 & 12.2548411165094 & 0.095158883490571 \tabularnewline
26 & 12.39 & 12.4080826322851 & -0.0180826322850898 \tabularnewline
27 & 12.31 & 12.3269671055889 & -0.0169671055889111 \tabularnewline
28 & 12.31 & 12.2932963960858 & 0.016703603914241 \tabularnewline
29 & 12.21 & 12.3808987914758 & -0.170898791475841 \tabularnewline
30 & 12.1 & 12.197801427994 & -0.0978014279940229 \tabularnewline
31 & 12.01 & 12.026488915786 & -0.0164889157860362 \tabularnewline
32 & 11.85 & 12.0415624001407 & -0.191562400140707 \tabularnewline
33 & 12.12 & 11.8805216643384 & 0.239478335661648 \tabularnewline
34 & 11.96 & 11.9239842657437 & 0.036015734256301 \tabularnewline
35 & 11.99 & 12.0943754519732 & -0.104375451973196 \tabularnewline
36 & 11.93 & 12.0194994657449 & -0.0894994657448507 \tabularnewline
37 & 11.91 & 11.8057009166806 & 0.104299083319377 \tabularnewline
38 & 11.83 & 11.9390060356676 & -0.109006035667621 \tabularnewline
39 & 11.92 & 11.7963799254551 & 0.123620074544874 \tabularnewline
40 & 11.86 & 11.854918839424 & 0.00508116057597441 \tabularnewline
41 & 11.94 & 11.8953456941662 & 0.0446543058338378 \tabularnewline
42 & 11.87 & 11.8616792865318 & 0.0083207134681853 \tabularnewline
43 & 11.86 & 11.7737041056857 & 0.0862958943142864 \tabularnewline
44 & 11.92 & 11.820848538574 & 0.0991514614260236 \tabularnewline
45 & 11.82 & 11.9324092011001 & -0.112409201100084 \tabularnewline
46 & 11.85 & 11.7154319887301 & 0.134568011269923 \tabularnewline
47 & 11.77 & 11.9224551321924 & -0.152455132192408 \tabularnewline
48 & 11.82 & 11.8218276036797 & -0.00182760367968093 \tabularnewline
49 & 11.61 & 11.7038420045317 & -0.0938420045317052 \tabularnewline
50 & 11.56 & 11.6708989120675 & -0.110898912067508 \tabularnewline
51 & 11.45 & 11.5730749274698 & -0.123074927469792 \tabularnewline
52 & 11.4 & 11.4506084677555 & -0.050608467755497 \tabularnewline
53 & 11.38 & 11.4606897001496 & -0.0806897001496143 \tabularnewline
54 & 11.33 & 11.3365219852837 & -0.0065219852836993 \tabularnewline
55 & 11.19 & 11.2498826147686 & -0.0598826147685667 \tabularnewline
56 & 11.15 & 11.2012571434799 & -0.0512571434799316 \tabularnewline
57 & 10.98 & 11.1686550370624 & -0.188655037062434 \tabularnewline
58 & 10.92 & 10.9433431760111 & -0.0233431760110587 \tabularnewline
59 & 10.99 & 10.9840447051869 & 0.00595529481313584 \tabularnewline
60 & 11 & 11.0039140455952 & -0.00391404559521291 \tabularnewline
61 & 10.9 & 10.8577357787352 & 0.0422642212648281 \tabularnewline
62 & 10.99 & 10.8998405137788 & 0.0901594862211894 \tabularnewline
63 & 11.04 & 10.9211691559302 & 0.118830844069764 \tabularnewline
64 & 11.03 & 10.9628959521508 & 0.0671040478491758 \tabularnewline
65 & 10.99 & 11.0401746643781 & -0.0501746643781242 \tabularnewline
66 & 11 & 10.949108254159 & 0.0508917458410192 \tabularnewline
67 & 10.87 & 10.888120433166 & -0.018120433165965 \tabularnewline
68 & 10.88 & 10.8679260382209 & 0.0120739617791248 \tabularnewline
69 & 10.91 & 10.8493862859607 & 0.0606137140392669 \tabularnewline
70 & 10.92 & 10.8174034376877 & 0.102596562312346 \tabularnewline
71 & 10.83 & 10.9485066650829 & -0.11850666508292 \tabularnewline
72 & 10.9 & 10.8920470122268 & 0.00795298777321207 \tabularnewline
73 & 10.82 & 10.766502780307 & 0.0534972196929662 \tabularnewline
74 & 10.79 & 10.8293052876537 & -0.039305287653697 \tabularnewline
75 & 10.77 & 10.7775266294246 & -0.00752662942463544 \tabularnewline
76 & 10.72 & 10.7309070155251 & -0.010907015525083 \tabularnewline
77 & 10.71 & 10.7365376449181 & -0.0265376449181165 \tabularnewline
78 & 10.63 & 10.6809357669128 & -0.0509357669128097 \tabularnewline
79 & 10.61 & 10.5419014848566 & 0.0680985151433671 \tabularnewline
80 & 10.57 & 10.5824878960753 & -0.0124878960753136 \tabularnewline
81 & 10.65 & 10.5583084291134 & 0.0916915708866348 \tabularnewline
82 & 10.57 & 10.5547771983643 & 0.0152228016357085 \tabularnewline
83 & 10.57 & 10.5871448951368 & -0.0171448951367736 \tabularnewline
84 & 10.57 & 10.6201223426595 & -0.0501223426595274 \tabularnewline
85 & 10.52 & 10.4671051807103 & 0.0528948192896781 \tabularnewline
86 & 10.43 & 10.5114603307166 & -0.081460330716551 \tabularnewline
87 & 10.35 & 10.4390508846258 & -0.0890508846258005 \tabularnewline
88 & 10.2 & 10.3392001081631 & -0.139200108163061 \tabularnewline
89 & 10.2 & 10.2583121981844 & -0.058312198184419 \tabularnewline
90 & 10.17 & 10.1748811437663 & -0.00488114376633675 \tabularnewline
91 & 10.14 & 10.0856835191636 & 0.0543164808364267 \tabularnewline
92 & 10.05 & 10.0991029740418 & -0.0491029740417837 \tabularnewline
93 & 10.12 & 10.0692324419545 & 0.0507675580455391 \tabularnewline
94 & 10.12 & 10.0213849415935 & 0.09861505840645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122055&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]12.51[/C][C]12.6435229700855[/C][C]-0.133522970085474[/C][/ROW]
[ROW][C]14[/C][C]12.59[/C][C]12.6349101993434[/C][C]-0.0449101993434446[/C][/ROW]
[ROW][C]15[/C][C]12.52[/C][C]12.529082878283[/C][C]-0.00908287828298882[/C][/ROW]
[ROW][C]16[/C][C]12.5[/C][C]12.4973766108371[/C][C]0.00262338916289373[/C][/ROW]
[ROW][C]17[/C][C]12.58[/C][C]12.5747364728286[/C][C]0.00526352717135481[/C][/ROW]
[ROW][C]18[/C][C]12.51[/C][C]12.5034008632347[/C][C]0.00659913676526713[/C][/ROW]
[ROW][C]19[/C][C]12.47[/C][C]12.3846467827348[/C][C]0.085353217265153[/C][/ROW]
[ROW][C]20[/C][C]12.44[/C][C]12.4947651040079[/C][C]-0.054765104007867[/C][/ROW]
[ROW][C]21[/C][C]12.51[/C][C]12.3906368384883[/C][C]0.11936316151165[/C][/ROW]
[ROW][C]22[/C][C]12.27[/C][C]12.4137247783001[/C][C]-0.14372477830015[/C][/ROW]
[ROW][C]23[/C][C]12.51[/C][C]12.4283160073387[/C][C]0.0816839926612918[/C][/ROW]
[ROW][C]24[/C][C]12.41[/C][C]12.5099029236739[/C][C]-0.099902923673886[/C][/ROW]
[ROW][C]25[/C][C]12.35[/C][C]12.2548411165094[/C][C]0.095158883490571[/C][/ROW]
[ROW][C]26[/C][C]12.39[/C][C]12.4080826322851[/C][C]-0.0180826322850898[/C][/ROW]
[ROW][C]27[/C][C]12.31[/C][C]12.3269671055889[/C][C]-0.0169671055889111[/C][/ROW]
[ROW][C]28[/C][C]12.31[/C][C]12.2932963960858[/C][C]0.016703603914241[/C][/ROW]
[ROW][C]29[/C][C]12.21[/C][C]12.3808987914758[/C][C]-0.170898791475841[/C][/ROW]
[ROW][C]30[/C][C]12.1[/C][C]12.197801427994[/C][C]-0.0978014279940229[/C][/ROW]
[ROW][C]31[/C][C]12.01[/C][C]12.026488915786[/C][C]-0.0164889157860362[/C][/ROW]
[ROW][C]32[/C][C]11.85[/C][C]12.0415624001407[/C][C]-0.191562400140707[/C][/ROW]
[ROW][C]33[/C][C]12.12[/C][C]11.8805216643384[/C][C]0.239478335661648[/C][/ROW]
[ROW][C]34[/C][C]11.96[/C][C]11.9239842657437[/C][C]0.036015734256301[/C][/ROW]
[ROW][C]35[/C][C]11.99[/C][C]12.0943754519732[/C][C]-0.104375451973196[/C][/ROW]
[ROW][C]36[/C][C]11.93[/C][C]12.0194994657449[/C][C]-0.0894994657448507[/C][/ROW]
[ROW][C]37[/C][C]11.91[/C][C]11.8057009166806[/C][C]0.104299083319377[/C][/ROW]
[ROW][C]38[/C][C]11.83[/C][C]11.9390060356676[/C][C]-0.109006035667621[/C][/ROW]
[ROW][C]39[/C][C]11.92[/C][C]11.7963799254551[/C][C]0.123620074544874[/C][/ROW]
[ROW][C]40[/C][C]11.86[/C][C]11.854918839424[/C][C]0.00508116057597441[/C][/ROW]
[ROW][C]41[/C][C]11.94[/C][C]11.8953456941662[/C][C]0.0446543058338378[/C][/ROW]
[ROW][C]42[/C][C]11.87[/C][C]11.8616792865318[/C][C]0.0083207134681853[/C][/ROW]
[ROW][C]43[/C][C]11.86[/C][C]11.7737041056857[/C][C]0.0862958943142864[/C][/ROW]
[ROW][C]44[/C][C]11.92[/C][C]11.820848538574[/C][C]0.0991514614260236[/C][/ROW]
[ROW][C]45[/C][C]11.82[/C][C]11.9324092011001[/C][C]-0.112409201100084[/C][/ROW]
[ROW][C]46[/C][C]11.85[/C][C]11.7154319887301[/C][C]0.134568011269923[/C][/ROW]
[ROW][C]47[/C][C]11.77[/C][C]11.9224551321924[/C][C]-0.152455132192408[/C][/ROW]
[ROW][C]48[/C][C]11.82[/C][C]11.8218276036797[/C][C]-0.00182760367968093[/C][/ROW]
[ROW][C]49[/C][C]11.61[/C][C]11.7038420045317[/C][C]-0.0938420045317052[/C][/ROW]
[ROW][C]50[/C][C]11.56[/C][C]11.6708989120675[/C][C]-0.110898912067508[/C][/ROW]
[ROW][C]51[/C][C]11.45[/C][C]11.5730749274698[/C][C]-0.123074927469792[/C][/ROW]
[ROW][C]52[/C][C]11.4[/C][C]11.4506084677555[/C][C]-0.050608467755497[/C][/ROW]
[ROW][C]53[/C][C]11.38[/C][C]11.4606897001496[/C][C]-0.0806897001496143[/C][/ROW]
[ROW][C]54[/C][C]11.33[/C][C]11.3365219852837[/C][C]-0.0065219852836993[/C][/ROW]
[ROW][C]55[/C][C]11.19[/C][C]11.2498826147686[/C][C]-0.0598826147685667[/C][/ROW]
[ROW][C]56[/C][C]11.15[/C][C]11.2012571434799[/C][C]-0.0512571434799316[/C][/ROW]
[ROW][C]57[/C][C]10.98[/C][C]11.1686550370624[/C][C]-0.188655037062434[/C][/ROW]
[ROW][C]58[/C][C]10.92[/C][C]10.9433431760111[/C][C]-0.0233431760110587[/C][/ROW]
[ROW][C]59[/C][C]10.99[/C][C]10.9840447051869[/C][C]0.00595529481313584[/C][/ROW]
[ROW][C]60[/C][C]11[/C][C]11.0039140455952[/C][C]-0.00391404559521291[/C][/ROW]
[ROW][C]61[/C][C]10.9[/C][C]10.8577357787352[/C][C]0.0422642212648281[/C][/ROW]
[ROW][C]62[/C][C]10.99[/C][C]10.8998405137788[/C][C]0.0901594862211894[/C][/ROW]
[ROW][C]63[/C][C]11.04[/C][C]10.9211691559302[/C][C]0.118830844069764[/C][/ROW]
[ROW][C]64[/C][C]11.03[/C][C]10.9628959521508[/C][C]0.0671040478491758[/C][/ROW]
[ROW][C]65[/C][C]10.99[/C][C]11.0401746643781[/C][C]-0.0501746643781242[/C][/ROW]
[ROW][C]66[/C][C]11[/C][C]10.949108254159[/C][C]0.0508917458410192[/C][/ROW]
[ROW][C]67[/C][C]10.87[/C][C]10.888120433166[/C][C]-0.018120433165965[/C][/ROW]
[ROW][C]68[/C][C]10.88[/C][C]10.8679260382209[/C][C]0.0120739617791248[/C][/ROW]
[ROW][C]69[/C][C]10.91[/C][C]10.8493862859607[/C][C]0.0606137140392669[/C][/ROW]
[ROW][C]70[/C][C]10.92[/C][C]10.8174034376877[/C][C]0.102596562312346[/C][/ROW]
[ROW][C]71[/C][C]10.83[/C][C]10.9485066650829[/C][C]-0.11850666508292[/C][/ROW]
[ROW][C]72[/C][C]10.9[/C][C]10.8920470122268[/C][C]0.00795298777321207[/C][/ROW]
[ROW][C]73[/C][C]10.82[/C][C]10.766502780307[/C][C]0.0534972196929662[/C][/ROW]
[ROW][C]74[/C][C]10.79[/C][C]10.8293052876537[/C][C]-0.039305287653697[/C][/ROW]
[ROW][C]75[/C][C]10.77[/C][C]10.7775266294246[/C][C]-0.00752662942463544[/C][/ROW]
[ROW][C]76[/C][C]10.72[/C][C]10.7309070155251[/C][C]-0.010907015525083[/C][/ROW]
[ROW][C]77[/C][C]10.71[/C][C]10.7365376449181[/C][C]-0.0265376449181165[/C][/ROW]
[ROW][C]78[/C][C]10.63[/C][C]10.6809357669128[/C][C]-0.0509357669128097[/C][/ROW]
[ROW][C]79[/C][C]10.61[/C][C]10.5419014848566[/C][C]0.0680985151433671[/C][/ROW]
[ROW][C]80[/C][C]10.57[/C][C]10.5824878960753[/C][C]-0.0124878960753136[/C][/ROW]
[ROW][C]81[/C][C]10.65[/C][C]10.5583084291134[/C][C]0.0916915708866348[/C][/ROW]
[ROW][C]82[/C][C]10.57[/C][C]10.5547771983643[/C][C]0.0152228016357085[/C][/ROW]
[ROW][C]83[/C][C]10.57[/C][C]10.5871448951368[/C][C]-0.0171448951367736[/C][/ROW]
[ROW][C]84[/C][C]10.57[/C][C]10.6201223426595[/C][C]-0.0501223426595274[/C][/ROW]
[ROW][C]85[/C][C]10.52[/C][C]10.4671051807103[/C][C]0.0528948192896781[/C][/ROW]
[ROW][C]86[/C][C]10.43[/C][C]10.5114603307166[/C][C]-0.081460330716551[/C][/ROW]
[ROW][C]87[/C][C]10.35[/C][C]10.4390508846258[/C][C]-0.0890508846258005[/C][/ROW]
[ROW][C]88[/C][C]10.2[/C][C]10.3392001081631[/C][C]-0.139200108163061[/C][/ROW]
[ROW][C]89[/C][C]10.2[/C][C]10.2583121981844[/C][C]-0.058312198184419[/C][/ROW]
[ROW][C]90[/C][C]10.17[/C][C]10.1748811437663[/C][C]-0.00488114376633675[/C][/ROW]
[ROW][C]91[/C][C]10.14[/C][C]10.0856835191636[/C][C]0.0543164808364267[/C][/ROW]
[ROW][C]92[/C][C]10.05[/C][C]10.0991029740418[/C][C]-0.0491029740417837[/C][/ROW]
[ROW][C]93[/C][C]10.12[/C][C]10.0692324419545[/C][C]0.0507675580455391[/C][/ROW]
[ROW][C]94[/C][C]10.12[/C][C]10.0213849415935[/C][C]0.09861505840645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122055&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122055&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	12.51	12.6435229700855	-0.133522970085474
14	12.59	12.6349101993434	-0.0449101993434446
15	12.52	12.529082878283	-0.00908287828298882
16	12.5	12.4973766108371	0.00262338916289373
17	12.58	12.5747364728286	0.00526352717135481
18	12.51	12.5034008632347	0.00659913676526713
19	12.47	12.3846467827348	0.085353217265153
20	12.44	12.4947651040079	-0.054765104007867
21	12.51	12.3906368384883	0.11936316151165
22	12.27	12.4137247783001	-0.14372477830015
23	12.51	12.4283160073387	0.0816839926612918
24	12.41	12.5099029236739	-0.099902923673886
25	12.35	12.2548411165094	0.095158883490571
26	12.39	12.4080826322851	-0.0180826322850898
27	12.31	12.3269671055889	-0.0169671055889111
28	12.31	12.2932963960858	0.016703603914241
29	12.21	12.3808987914758	-0.170898791475841
30	12.1	12.197801427994	-0.0978014279940229
31	12.01	12.026488915786	-0.0164889157860362
32	11.85	12.0415624001407	-0.191562400140707
33	12.12	11.8805216643384	0.239478335661648
34	11.96	11.9239842657437	0.036015734256301
35	11.99	12.0943754519732	-0.104375451973196
36	11.93	12.0194994657449	-0.0894994657448507
37	11.91	11.8057009166806	0.104299083319377
38	11.83	11.9390060356676	-0.109006035667621
39	11.92	11.7963799254551	0.123620074544874
40	11.86	11.854918839424	0.00508116057597441
41	11.94	11.8953456941662	0.0446543058338378
42	11.87	11.8616792865318	0.0083207134681853
43	11.86	11.7737041056857	0.0862958943142864
44	11.92	11.820848538574	0.0991514614260236
45	11.82	11.9324092011001	-0.112409201100084
46	11.85	11.7154319887301	0.134568011269923
47	11.77	11.9224551321924	-0.152455132192408
48	11.82	11.8218276036797	-0.00182760367968093
49	11.61	11.7038420045317	-0.0938420045317052
50	11.56	11.6708989120675	-0.110898912067508
51	11.45	11.5730749274698	-0.123074927469792
52	11.4	11.4506084677555	-0.050608467755497
53	11.38	11.4606897001496	-0.0806897001496143
54	11.33	11.3365219852837	-0.0065219852836993
55	11.19	11.2498826147686	-0.0598826147685667
56	11.15	11.2012571434799	-0.0512571434799316
57	10.98	11.1686550370624	-0.188655037062434
58	10.92	10.9433431760111	-0.0233431760110587
59	10.99	10.9840447051869	0.00595529481313584
60	11	11.0039140455952	-0.00391404559521291
61	10.9	10.8577357787352	0.0422642212648281
62	10.99	10.8998405137788	0.0901594862211894
63	11.04	10.9211691559302	0.118830844069764
64	11.03	10.9628959521508	0.0671040478491758
65	10.99	11.0401746643781	-0.0501746643781242
66	11	10.949108254159	0.0508917458410192
67	10.87	10.888120433166	-0.018120433165965
68	10.88	10.8679260382209	0.0120739617791248
69	10.91	10.8493862859607	0.0606137140392669
70	10.92	10.8174034376877	0.102596562312346
71	10.83	10.9485066650829	-0.11850666508292
72	10.9	10.8920470122268	0.00795298777321207
73	10.82	10.766502780307	0.0534972196929662
74	10.79	10.8293052876537	-0.039305287653697
75	10.77	10.7775266294246	-0.00752662942463544
76	10.72	10.7309070155251	-0.010907015525083
77	10.71	10.7365376449181	-0.0265376449181165
78	10.63	10.6809357669128	-0.0509357669128097
79	10.61	10.5419014848566	0.0680985151433671
80	10.57	10.5824878960753	-0.0124878960753136
81	10.65	10.5583084291134	0.0916915708866348
82	10.57	10.5547771983643	0.0152228016357085
83	10.57	10.5871448951368	-0.0171448951367736
84	10.57	10.6201223426595	-0.0501223426595274
85	10.52	10.4671051807103	0.0528948192896781
86	10.43	10.5114603307166	-0.081460330716551
87	10.35	10.4390508846258	-0.0890508846258005
88	10.2	10.3392001081631	-0.139200108163061
89	10.2	10.2583121981844	-0.058312198184419
90	10.17	10.1748811437663	-0.00488114376633675
91	10.14	10.0856835191636	0.0543164808364267
92	10.05	10.0991029740418	-0.0491029740417837
93	10.12	10.0692324419545	0.0507675580455391
94	10.12	10.0213849415935	0.09861505840645

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
95	10.0972937278237	9.93145618606037	10.2631312695871
96	10.132176701406	9.93521252354106	10.3291408792709
97	10.0290789611536	9.80438737046983	10.2537705518373
98	10.0113167157982	9.76115022116802	10.2614832104284
99	9.98716919537647	9.7131387339526	10.2611996568003
100	9.93300517147437	9.636321027521	10.2296893154277
101	9.95665471121269	9.63825786515024	10.2750515572751
102	9.92210073437888	9.5827413101585	10.2614601585993
103	9.8493274379848	9.48961477899316	10.2090400969764
104	9.80937770528916	9.42981400790893	10.1889414026694
105	9.83169665765596	9.43270048864053	10.2306928266714
106	9.76238290224417	9.3443061883621	10.1804596161262

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
95 & 10.0972937278237 & 9.93145618606037 & 10.2631312695871 \tabularnewline
96 & 10.132176701406 & 9.93521252354106 & 10.3291408792709 \tabularnewline
97 & 10.0290789611536 & 9.80438737046983 & 10.2537705518373 \tabularnewline
98 & 10.0113167157982 & 9.76115022116802 & 10.2614832104284 \tabularnewline
99 & 9.98716919537647 & 9.7131387339526 & 10.2611996568003 \tabularnewline
100 & 9.93300517147437 & 9.636321027521 & 10.2296893154277 \tabularnewline
101 & 9.95665471121269 & 9.63825786515024 & 10.2750515572751 \tabularnewline
102 & 9.92210073437888 & 9.5827413101585 & 10.2614601585993 \tabularnewline
103 & 9.8493274379848 & 9.48961477899316 & 10.2090400969764 \tabularnewline
104 & 9.80937770528916 & 9.42981400790893 & 10.1889414026694 \tabularnewline
105 & 9.83169665765596 & 9.43270048864053 & 10.2306928266714 \tabularnewline
106 & 9.76238290224417 & 9.3443061883621 & 10.1804596161262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122055&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]95[/C][C]10.0972937278237[/C][C]9.93145618606037[/C][C]10.2631312695871[/C][/ROW]
[ROW][C]96[/C][C]10.132176701406[/C][C]9.93521252354106[/C][C]10.3291408792709[/C][/ROW]
[ROW][C]97[/C][C]10.0290789611536[/C][C]9.80438737046983[/C][C]10.2537705518373[/C][/ROW]
[ROW][C]98[/C][C]10.0113167157982[/C][C]9.76115022116802[/C][C]10.2614832104284[/C][/ROW]
[ROW][C]99[/C][C]9.98716919537647[/C][C]9.7131387339526[/C][C]10.2611996568003[/C][/ROW]
[ROW][C]100[/C][C]9.93300517147437[/C][C]9.636321027521[/C][C]10.2296893154277[/C][/ROW]
[ROW][C]101[/C][C]9.95665471121269[/C][C]9.63825786515024[/C][C]10.2750515572751[/C][/ROW]
[ROW][C]102[/C][C]9.92210073437888[/C][C]9.5827413101585[/C][C]10.2614601585993[/C][/ROW]
[ROW][C]103[/C][C]9.8493274379848[/C][C]9.48961477899316[/C][C]10.2090400969764[/C][/ROW]
[ROW][C]104[/C][C]9.80937770528916[/C][C]9.42981400790893[/C][C]10.1889414026694[/C][/ROW]
[ROW][C]105[/C][C]9.83169665765596[/C][C]9.43270048864053[/C][C]10.2306928266714[/C][/ROW]
[ROW][C]106[/C][C]9.76238290224417[/C][C]9.3443061883621[/C][C]10.1804596161262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122055&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122055&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
95	10.0972937278237	9.93145618606037	10.2631312695871
96	10.132176701406	9.93521252354106	10.3291408792709
97	10.0290789611536	9.80438737046983	10.2537705518373
98	10.0113167157982	9.76115022116802	10.2614832104284
99	9.98716919537647	9.7131387339526	10.2611996568003
100	9.93300517147437	9.636321027521	10.2296893154277
101	9.95665471121269	9.63825786515024	10.2750515572751
102	9.92210073437888	9.5827413101585	10.2614601585993
103	9.8493274379848	9.48961477899316	10.2090400969764
104	9.80937770528916	9.42981400790893	10.1889414026694
105	9.83169665765596	9.43270048864053	10.2306928266714
106	9.76238290224417	9.3443061883621	10.1804596161262

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