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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 29 Nov 2015 14:56:36 +0000

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/Nov/29/t14488090176g37s25j6nvxbso.htm/, Retrieved Wed, 15 May 2024 11:28:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284473, Retrieved Wed, 15 May 2024 11:28:30 +0000

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No (this computation is public)

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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] [Consumptieprijzen...] [2015-11-29 14:56:36] [c53767938e2c856c14b03e8e32322294] [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	1 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284473&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284473&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284473&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	1 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284473&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[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284473&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284473&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
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.32	99.1514877136752	0.168512286324784
14	99.17	99.1669391025641	0.00306089743590121
15	99.13	99.1252724358974	0.00472756410256636
16	99.12	99.1169391025641	0.003060897435887
17	99.23	99.2306891025641	-0.000689102564081168
18	99.25	99.2506891025641	-0.000689102564081168
19	99.25	99.2098557692308	0.040144230769215
20	99.36	99.3577724358974	0.00222756410256864
21	99.43	99.3961057692308	0.0338942307692491
22	99.57	99.6594391025641	-0.0894391025641141
23	99.64	99.6548557692308	-0.0148557692307634
24	99.68	99.6677724358974	0.0122275641026022
25	99.68	99.6769391025641	0.00306089743590121
26	99.52	99.5269391025641	-0.00693910256411812
27	99.69	99.4752724358974	0.214727564102574
28	99.7	99.6769391025641	0.023060897435883
29	99.85	99.8106891025641	0.0393108974359109
30	99.94	99.8706891025641	0.0693108974359262
31	99.94	99.8998557692308	0.040144230769215
32	99.93	100.047772435897	-0.117772435897422
33	100.19	99.9661057692308	0.223894230769233
34	100.57	100.419439102564	0.150560897435895
35	100.76	100.654855769231	0.105144230769241
36	100.86	100.787772435897	0.0722275641025902
37	100.86	100.856939102564	0.00306089743590121
38	100.39	100.706939102564	-0.316939102564106
39	100.61	100.345272435897	0.264727564102571
40	100.67	100.596939102564	0.0730608974358802
41	100.81	100.780689102564	0.02931089743592
42	100.86	100.830689102564	0.02931089743592
43	100.86	100.819855769231	0.040144230769215
44	100.98	100.967772435897	0.0122275641025738
45	101.03	101.016105769231	0.0138942307692389
46	101.37	101.259439102564	0.110560897435903
47	101.64	101.454855769231	0.185144230769225
48	101.68	101.667772435897	0.0122275641026022
49	101.68	101.676939102564	0.00306089743590121
50	101.25	101.526939102564	-0.276939102564114
51	101.24	101.205272435897	0.0347275641025675
52	101.11	101.226939102564	-0.116939102564118
53	101.08	101.220689102564	-0.140689102564082
54	101.09	101.100689102564	-0.0106891025640721
55	101.09	101.049855769231	0.040144230769215
56	101.62	101.197772435897	0.42222756410257
57	101.66	101.656105769231	0.00389423076923379
58	101.96	101.889439102564	0.0705608974358967
59	102.04	102.044855769231	-0.00485576923075826
60	102.02	102.067772435897	-0.0477724358974143
61	102.02	102.016939102564	0.00306089743590121
62	101.51	101.866939102564	-0.356939102564098
63	101.62	101.465272435897	0.154727564102572
64	101.83	101.606939102564	0.223060897435872
65	102.06	101.940689102564	0.119310897435923
66	102.14	102.080689102564	0.0593108974359211
67	102.14	102.099855769231	0.040144230769215
68	102.59	102.247772435897	0.342227564102572
69	102.92	102.626105769231	0.29389423076924
70	103.31	103.149439102564	0.1605608974359
71	103.54	103.394855769231	0.145144230769233
72	103.58	103.567772435897	0.012227564102588
73	103.58	103.576939102564	0.00306089743590121
74	102.83	103.426939102564	-0.596939102564107
75	102.86	102.785272435897	0.0747275641025738
76	103.03	102.846939102564	0.18306089743588
77	103.2	103.140689102564	0.0593108974359211
78	103.28	103.220689102564	0.0593108974359211
79	103.28	103.239855769231	0.040144230769215
80	103.79	103.387772435897	0.402227564102574
81	103.92	103.826105769231	0.0938942307692372
82	104.26	104.149439102564	0.110560897435903
83	104.41	104.344855769231	0.0651442307692207
84	104.45	104.437772435897	0.0122275641026022
85	99.92	104.446939102564	-4.5269391025641
86	99.18	99.7669391025641	-0.586939102564102
87	99.18	99.1352724358974	0.0447275641025726
88	99.35	99.1669391025641	0.183060897435865
89	99.62	99.4606891025641	0.15931089743593
90	99.67	99.6406891025641	0.02931089743592
91	99.72	99.6298557692308	0.0901442307692122
92	100.08	99.8277724358974	0.252227564102569
93	100.39	100.116105769231	0.273894230769244
94	100.77	100.619439102564	0.150560897435895
95	101.03	100.854855769231	0.175144230769234
96	101.07	101.057772435897	0.012227564102588
97	101.29	101.066939102564	0.223060897435914
98	101.1	101.136939102564	-0.0369391025641193
99	101.2	101.055272435897	0.144727564102581
100	101.15	101.186939102564	-0.0369391025641193
101	101.24	101.260689102564	-0.0206891025640914
102	101.16	101.260689102564	-0.100689102564075
103	100.81	101.119855769231	-0.309855769230779
104	101.02	100.917772435897	0.102227564102563
105	101.15	101.056105769231	0.0938942307692514
106	101.06	101.379439102564	-0.319439102564104
107	101.17	101.144855769231	0.0251442307692287
108	101.22	101.197772435897	0.0222275641025931

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.32 & 99.1514877136752 & 0.168512286324784 \tabularnewline
14 & 99.17 & 99.1669391025641 & 0.00306089743590121 \tabularnewline
15 & 99.13 & 99.1252724358974 & 0.00472756410256636 \tabularnewline
16 & 99.12 & 99.1169391025641 & 0.003060897435887 \tabularnewline
17 & 99.23 & 99.2306891025641 & -0.000689102564081168 \tabularnewline
18 & 99.25 & 99.2506891025641 & -0.000689102564081168 \tabularnewline
19 & 99.25 & 99.2098557692308 & 0.040144230769215 \tabularnewline
20 & 99.36 & 99.3577724358974 & 0.00222756410256864 \tabularnewline
21 & 99.43 & 99.3961057692308 & 0.0338942307692491 \tabularnewline
22 & 99.57 & 99.6594391025641 & -0.0894391025641141 \tabularnewline
23 & 99.64 & 99.6548557692308 & -0.0148557692307634 \tabularnewline
24 & 99.68 & 99.6677724358974 & 0.0122275641026022 \tabularnewline
25 & 99.68 & 99.6769391025641 & 0.00306089743590121 \tabularnewline
26 & 99.52 & 99.5269391025641 & -0.00693910256411812 \tabularnewline
27 & 99.69 & 99.4752724358974 & 0.214727564102574 \tabularnewline
28 & 99.7 & 99.6769391025641 & 0.023060897435883 \tabularnewline
29 & 99.85 & 99.8106891025641 & 0.0393108974359109 \tabularnewline
30 & 99.94 & 99.8706891025641 & 0.0693108974359262 \tabularnewline
31 & 99.94 & 99.8998557692308 & 0.040144230769215 \tabularnewline
32 & 99.93 & 100.047772435897 & -0.117772435897422 \tabularnewline
33 & 100.19 & 99.9661057692308 & 0.223894230769233 \tabularnewline
34 & 100.57 & 100.419439102564 & 0.150560897435895 \tabularnewline
35 & 100.76 & 100.654855769231 & 0.105144230769241 \tabularnewline
36 & 100.86 & 100.787772435897 & 0.0722275641025902 \tabularnewline
37 & 100.86 & 100.856939102564 & 0.00306089743590121 \tabularnewline
38 & 100.39 & 100.706939102564 & -0.316939102564106 \tabularnewline
39 & 100.61 & 100.345272435897 & 0.264727564102571 \tabularnewline
40 & 100.67 & 100.596939102564 & 0.0730608974358802 \tabularnewline
41 & 100.81 & 100.780689102564 & 0.02931089743592 \tabularnewline
42 & 100.86 & 100.830689102564 & 0.02931089743592 \tabularnewline
43 & 100.86 & 100.819855769231 & 0.040144230769215 \tabularnewline
44 & 100.98 & 100.967772435897 & 0.0122275641025738 \tabularnewline
45 & 101.03 & 101.016105769231 & 0.0138942307692389 \tabularnewline
46 & 101.37 & 101.259439102564 & 0.110560897435903 \tabularnewline
47 & 101.64 & 101.454855769231 & 0.185144230769225 \tabularnewline
48 & 101.68 & 101.667772435897 & 0.0122275641026022 \tabularnewline
49 & 101.68 & 101.676939102564 & 0.00306089743590121 \tabularnewline
50 & 101.25 & 101.526939102564 & -0.276939102564114 \tabularnewline
51 & 101.24 & 101.205272435897 & 0.0347275641025675 \tabularnewline
52 & 101.11 & 101.226939102564 & -0.116939102564118 \tabularnewline
53 & 101.08 & 101.220689102564 & -0.140689102564082 \tabularnewline
54 & 101.09 & 101.100689102564 & -0.0106891025640721 \tabularnewline
55 & 101.09 & 101.049855769231 & 0.040144230769215 \tabularnewline
56 & 101.62 & 101.197772435897 & 0.42222756410257 \tabularnewline
57 & 101.66 & 101.656105769231 & 0.00389423076923379 \tabularnewline
58 & 101.96 & 101.889439102564 & 0.0705608974358967 \tabularnewline
59 & 102.04 & 102.044855769231 & -0.00485576923075826 \tabularnewline
60 & 102.02 & 102.067772435897 & -0.0477724358974143 \tabularnewline
61 & 102.02 & 102.016939102564 & 0.00306089743590121 \tabularnewline
62 & 101.51 & 101.866939102564 & -0.356939102564098 \tabularnewline
63 & 101.62 & 101.465272435897 & 0.154727564102572 \tabularnewline
64 & 101.83 & 101.606939102564 & 0.223060897435872 \tabularnewline
65 & 102.06 & 101.940689102564 & 0.119310897435923 \tabularnewline
66 & 102.14 & 102.080689102564 & 0.0593108974359211 \tabularnewline
67 & 102.14 & 102.099855769231 & 0.040144230769215 \tabularnewline
68 & 102.59 & 102.247772435897 & 0.342227564102572 \tabularnewline
69 & 102.92 & 102.626105769231 & 0.29389423076924 \tabularnewline
70 & 103.31 & 103.149439102564 & 0.1605608974359 \tabularnewline
71 & 103.54 & 103.394855769231 & 0.145144230769233 \tabularnewline
72 & 103.58 & 103.567772435897 & 0.012227564102588 \tabularnewline
73 & 103.58 & 103.576939102564 & 0.00306089743590121 \tabularnewline
74 & 102.83 & 103.426939102564 & -0.596939102564107 \tabularnewline
75 & 102.86 & 102.785272435897 & 0.0747275641025738 \tabularnewline
76 & 103.03 & 102.846939102564 & 0.18306089743588 \tabularnewline
77 & 103.2 & 103.140689102564 & 0.0593108974359211 \tabularnewline
78 & 103.28 & 103.220689102564 & 0.0593108974359211 \tabularnewline
79 & 103.28 & 103.239855769231 & 0.040144230769215 \tabularnewline
80 & 103.79 & 103.387772435897 & 0.402227564102574 \tabularnewline
81 & 103.92 & 103.826105769231 & 0.0938942307692372 \tabularnewline
82 & 104.26 & 104.149439102564 & 0.110560897435903 \tabularnewline
83 & 104.41 & 104.344855769231 & 0.0651442307692207 \tabularnewline
84 & 104.45 & 104.437772435897 & 0.0122275641026022 \tabularnewline
85 & 99.92 & 104.446939102564 & -4.5269391025641 \tabularnewline
86 & 99.18 & 99.7669391025641 & -0.586939102564102 \tabularnewline
87 & 99.18 & 99.1352724358974 & 0.0447275641025726 \tabularnewline
88 & 99.35 & 99.1669391025641 & 0.183060897435865 \tabularnewline
89 & 99.62 & 99.4606891025641 & 0.15931089743593 \tabularnewline
90 & 99.67 & 99.6406891025641 & 0.02931089743592 \tabularnewline
91 & 99.72 & 99.6298557692308 & 0.0901442307692122 \tabularnewline
92 & 100.08 & 99.8277724358974 & 0.252227564102569 \tabularnewline
93 & 100.39 & 100.116105769231 & 0.273894230769244 \tabularnewline
94 & 100.77 & 100.619439102564 & 0.150560897435895 \tabularnewline
95 & 101.03 & 100.854855769231 & 0.175144230769234 \tabularnewline
96 & 101.07 & 101.057772435897 & 0.012227564102588 \tabularnewline
97 & 101.29 & 101.066939102564 & 0.223060897435914 \tabularnewline
98 & 101.1 & 101.136939102564 & -0.0369391025641193 \tabularnewline
99 & 101.2 & 101.055272435897 & 0.144727564102581 \tabularnewline
100 & 101.15 & 101.186939102564 & -0.0369391025641193 \tabularnewline
101 & 101.24 & 101.260689102564 & -0.0206891025640914 \tabularnewline
102 & 101.16 & 101.260689102564 & -0.100689102564075 \tabularnewline
103 & 100.81 & 101.119855769231 & -0.309855769230779 \tabularnewline
104 & 101.02 & 100.917772435897 & 0.102227564102563 \tabularnewline
105 & 101.15 & 101.056105769231 & 0.0938942307692514 \tabularnewline
106 & 101.06 & 101.379439102564 & -0.319439102564104 \tabularnewline
107 & 101.17 & 101.144855769231 & 0.0251442307692287 \tabularnewline
108 & 101.22 & 101.197772435897 & 0.0222275641025931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284473&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]99.32[/C][C]99.1514877136752[/C][C]0.168512286324784[/C][/ROW]
[ROW][C]14[/C][C]99.17[/C][C]99.1669391025641[/C][C]0.00306089743590121[/C][/ROW]
[ROW][C]15[/C][C]99.13[/C][C]99.1252724358974[/C][C]0.00472756410256636[/C][/ROW]
[ROW][C]16[/C][C]99.12[/C][C]99.1169391025641[/C][C]0.003060897435887[/C][/ROW]
[ROW][C]17[/C][C]99.23[/C][C]99.2306891025641[/C][C]-0.000689102564081168[/C][/ROW]
[ROW][C]18[/C][C]99.25[/C][C]99.2506891025641[/C][C]-0.000689102564081168[/C][/ROW]
[ROW][C]19[/C][C]99.25[/C][C]99.2098557692308[/C][C]0.040144230769215[/C][/ROW]
[ROW][C]20[/C][C]99.36[/C][C]99.3577724358974[/C][C]0.00222756410256864[/C][/ROW]
[ROW][C]21[/C][C]99.43[/C][C]99.3961057692308[/C][C]0.0338942307692491[/C][/ROW]
[ROW][C]22[/C][C]99.57[/C][C]99.6594391025641[/C][C]-0.0894391025641141[/C][/ROW]
[ROW][C]23[/C][C]99.64[/C][C]99.6548557692308[/C][C]-0.0148557692307634[/C][/ROW]
[ROW][C]24[/C][C]99.68[/C][C]99.6677724358974[/C][C]0.0122275641026022[/C][/ROW]
[ROW][C]25[/C][C]99.68[/C][C]99.6769391025641[/C][C]0.00306089743590121[/C][/ROW]
[ROW][C]26[/C][C]99.52[/C][C]99.5269391025641[/C][C]-0.00693910256411812[/C][/ROW]
[ROW][C]27[/C][C]99.69[/C][C]99.4752724358974[/C][C]0.214727564102574[/C][/ROW]
[ROW][C]28[/C][C]99.7[/C][C]99.6769391025641[/C][C]0.023060897435883[/C][/ROW]
[ROW][C]29[/C][C]99.85[/C][C]99.8106891025641[/C][C]0.0393108974359109[/C][/ROW]
[ROW][C]30[/C][C]99.94[/C][C]99.8706891025641[/C][C]0.0693108974359262[/C][/ROW]
[ROW][C]31[/C][C]99.94[/C][C]99.8998557692308[/C][C]0.040144230769215[/C][/ROW]
[ROW][C]32[/C][C]99.93[/C][C]100.047772435897[/C][C]-0.117772435897422[/C][/ROW]
[ROW][C]33[/C][C]100.19[/C][C]99.9661057692308[/C][C]0.223894230769233[/C][/ROW]
[ROW][C]34[/C][C]100.57[/C][C]100.419439102564[/C][C]0.150560897435895[/C][/ROW]
[ROW][C]35[/C][C]100.76[/C][C]100.654855769231[/C][C]0.105144230769241[/C][/ROW]
[ROW][C]36[/C][C]100.86[/C][C]100.787772435897[/C][C]0.0722275641025902[/C][/ROW]
[ROW][C]37[/C][C]100.86[/C][C]100.856939102564[/C][C]0.00306089743590121[/C][/ROW]
[ROW][C]38[/C][C]100.39[/C][C]100.706939102564[/C][C]-0.316939102564106[/C][/ROW]
[ROW][C]39[/C][C]100.61[/C][C]100.345272435897[/C][C]0.264727564102571[/C][/ROW]
[ROW][C]40[/C][C]100.67[/C][C]100.596939102564[/C][C]0.0730608974358802[/C][/ROW]
[ROW][C]41[/C][C]100.81[/C][C]100.780689102564[/C][C]0.02931089743592[/C][/ROW]
[ROW][C]42[/C][C]100.86[/C][C]100.830689102564[/C][C]0.02931089743592[/C][/ROW]
[ROW][C]43[/C][C]100.86[/C][C]100.819855769231[/C][C]0.040144230769215[/C][/ROW]
[ROW][C]44[/C][C]100.98[/C][C]100.967772435897[/C][C]0.0122275641025738[/C][/ROW]
[ROW][C]45[/C][C]101.03[/C][C]101.016105769231[/C][C]0.0138942307692389[/C][/ROW]
[ROW][C]46[/C][C]101.37[/C][C]101.259439102564[/C][C]0.110560897435903[/C][/ROW]
[ROW][C]47[/C][C]101.64[/C][C]101.454855769231[/C][C]0.185144230769225[/C][/ROW]
[ROW][C]48[/C][C]101.68[/C][C]101.667772435897[/C][C]0.0122275641026022[/C][/ROW]
[ROW][C]49[/C][C]101.68[/C][C]101.676939102564[/C][C]0.00306089743590121[/C][/ROW]
[ROW][C]50[/C][C]101.25[/C][C]101.526939102564[/C][C]-0.276939102564114[/C][/ROW]
[ROW][C]51[/C][C]101.24[/C][C]101.205272435897[/C][C]0.0347275641025675[/C][/ROW]
[ROW][C]52[/C][C]101.11[/C][C]101.226939102564[/C][C]-0.116939102564118[/C][/ROW]
[ROW][C]53[/C][C]101.08[/C][C]101.220689102564[/C][C]-0.140689102564082[/C][/ROW]
[ROW][C]54[/C][C]101.09[/C][C]101.100689102564[/C][C]-0.0106891025640721[/C][/ROW]
[ROW][C]55[/C][C]101.09[/C][C]101.049855769231[/C][C]0.040144230769215[/C][/ROW]
[ROW][C]56[/C][C]101.62[/C][C]101.197772435897[/C][C]0.42222756410257[/C][/ROW]
[ROW][C]57[/C][C]101.66[/C][C]101.656105769231[/C][C]0.00389423076923379[/C][/ROW]
[ROW][C]58[/C][C]101.96[/C][C]101.889439102564[/C][C]0.0705608974358967[/C][/ROW]
[ROW][C]59[/C][C]102.04[/C][C]102.044855769231[/C][C]-0.00485576923075826[/C][/ROW]
[ROW][C]60[/C][C]102.02[/C][C]102.067772435897[/C][C]-0.0477724358974143[/C][/ROW]
[ROW][C]61[/C][C]102.02[/C][C]102.016939102564[/C][C]0.00306089743590121[/C][/ROW]
[ROW][C]62[/C][C]101.51[/C][C]101.866939102564[/C][C]-0.356939102564098[/C][/ROW]
[ROW][C]63[/C][C]101.62[/C][C]101.465272435897[/C][C]0.154727564102572[/C][/ROW]
[ROW][C]64[/C][C]101.83[/C][C]101.606939102564[/C][C]0.223060897435872[/C][/ROW]
[ROW][C]65[/C][C]102.06[/C][C]101.940689102564[/C][C]0.119310897435923[/C][/ROW]
[ROW][C]66[/C][C]102.14[/C][C]102.080689102564[/C][C]0.0593108974359211[/C][/ROW]
[ROW][C]67[/C][C]102.14[/C][C]102.099855769231[/C][C]0.040144230769215[/C][/ROW]
[ROW][C]68[/C][C]102.59[/C][C]102.247772435897[/C][C]0.342227564102572[/C][/ROW]
[ROW][C]69[/C][C]102.92[/C][C]102.626105769231[/C][C]0.29389423076924[/C][/ROW]
[ROW][C]70[/C][C]103.31[/C][C]103.149439102564[/C][C]0.1605608974359[/C][/ROW]
[ROW][C]71[/C][C]103.54[/C][C]103.394855769231[/C][C]0.145144230769233[/C][/ROW]
[ROW][C]72[/C][C]103.58[/C][C]103.567772435897[/C][C]0.012227564102588[/C][/ROW]
[ROW][C]73[/C][C]103.58[/C][C]103.576939102564[/C][C]0.00306089743590121[/C][/ROW]
[ROW][C]74[/C][C]102.83[/C][C]103.426939102564[/C][C]-0.596939102564107[/C][/ROW]
[ROW][C]75[/C][C]102.86[/C][C]102.785272435897[/C][C]0.0747275641025738[/C][/ROW]
[ROW][C]76[/C][C]103.03[/C][C]102.846939102564[/C][C]0.18306089743588[/C][/ROW]
[ROW][C]77[/C][C]103.2[/C][C]103.140689102564[/C][C]0.0593108974359211[/C][/ROW]
[ROW][C]78[/C][C]103.28[/C][C]103.220689102564[/C][C]0.0593108974359211[/C][/ROW]
[ROW][C]79[/C][C]103.28[/C][C]103.239855769231[/C][C]0.040144230769215[/C][/ROW]
[ROW][C]80[/C][C]103.79[/C][C]103.387772435897[/C][C]0.402227564102574[/C][/ROW]
[ROW][C]81[/C][C]103.92[/C][C]103.826105769231[/C][C]0.0938942307692372[/C][/ROW]
[ROW][C]82[/C][C]104.26[/C][C]104.149439102564[/C][C]0.110560897435903[/C][/ROW]
[ROW][C]83[/C][C]104.41[/C][C]104.344855769231[/C][C]0.0651442307692207[/C][/ROW]
[ROW][C]84[/C][C]104.45[/C][C]104.437772435897[/C][C]0.0122275641026022[/C][/ROW]
[ROW][C]85[/C][C]99.92[/C][C]104.446939102564[/C][C]-4.5269391025641[/C][/ROW]
[ROW][C]86[/C][C]99.18[/C][C]99.7669391025641[/C][C]-0.586939102564102[/C][/ROW]
[ROW][C]87[/C][C]99.18[/C][C]99.1352724358974[/C][C]0.0447275641025726[/C][/ROW]
[ROW][C]88[/C][C]99.35[/C][C]99.1669391025641[/C][C]0.183060897435865[/C][/ROW]
[ROW][C]89[/C][C]99.62[/C][C]99.4606891025641[/C][C]0.15931089743593[/C][/ROW]
[ROW][C]90[/C][C]99.67[/C][C]99.6406891025641[/C][C]0.02931089743592[/C][/ROW]
[ROW][C]91[/C][C]99.72[/C][C]99.6298557692308[/C][C]0.0901442307692122[/C][/ROW]
[ROW][C]92[/C][C]100.08[/C][C]99.8277724358974[/C][C]0.252227564102569[/C][/ROW]
[ROW][C]93[/C][C]100.39[/C][C]100.116105769231[/C][C]0.273894230769244[/C][/ROW]
[ROW][C]94[/C][C]100.77[/C][C]100.619439102564[/C][C]0.150560897435895[/C][/ROW]
[ROW][C]95[/C][C]101.03[/C][C]100.854855769231[/C][C]0.175144230769234[/C][/ROW]
[ROW][C]96[/C][C]101.07[/C][C]101.057772435897[/C][C]0.012227564102588[/C][/ROW]
[ROW][C]97[/C][C]101.29[/C][C]101.066939102564[/C][C]0.223060897435914[/C][/ROW]
[ROW][C]98[/C][C]101.1[/C][C]101.136939102564[/C][C]-0.0369391025641193[/C][/ROW]
[ROW][C]99[/C][C]101.2[/C][C]101.055272435897[/C][C]0.144727564102581[/C][/ROW]
[ROW][C]100[/C][C]101.15[/C][C]101.186939102564[/C][C]-0.0369391025641193[/C][/ROW]
[ROW][C]101[/C][C]101.24[/C][C]101.260689102564[/C][C]-0.0206891025640914[/C][/ROW]
[ROW][C]102[/C][C]101.16[/C][C]101.260689102564[/C][C]-0.100689102564075[/C][/ROW]
[ROW][C]103[/C][C]100.81[/C][C]101.119855769231[/C][C]-0.309855769230779[/C][/ROW]
[ROW][C]104[/C][C]101.02[/C][C]100.917772435897[/C][C]0.102227564102563[/C][/ROW]
[ROW][C]105[/C][C]101.15[/C][C]101.056105769231[/C][C]0.0938942307692514[/C][/ROW]
[ROW][C]106[/C][C]101.06[/C][C]101.379439102564[/C][C]-0.319439102564104[/C][/ROW]
[ROW][C]107[/C][C]101.17[/C][C]101.144855769231[/C][C]0.0251442307692287[/C][/ROW]
[ROW][C]108[/C][C]101.22[/C][C]101.197772435897[/C][C]0.0222275641025931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284473&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284473&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	99.32	99.1514877136752	0.168512286324784
14	99.17	99.1669391025641	0.00306089743590121
15	99.13	99.1252724358974	0.00472756410256636
16	99.12	99.1169391025641	0.003060897435887
17	99.23	99.2306891025641	-0.000689102564081168
18	99.25	99.2506891025641	-0.000689102564081168
19	99.25	99.2098557692308	0.040144230769215
20	99.36	99.3577724358974	0.00222756410256864
21	99.43	99.3961057692308	0.0338942307692491
22	99.57	99.6594391025641	-0.0894391025641141
23	99.64	99.6548557692308	-0.0148557692307634
24	99.68	99.6677724358974	0.0122275641026022
25	99.68	99.6769391025641	0.00306089743590121
26	99.52	99.5269391025641	-0.00693910256411812
27	99.69	99.4752724358974	0.214727564102574
28	99.7	99.6769391025641	0.023060897435883
29	99.85	99.8106891025641	0.0393108974359109
30	99.94	99.8706891025641	0.0693108974359262
31	99.94	99.8998557692308	0.040144230769215
32	99.93	100.047772435897	-0.117772435897422
33	100.19	99.9661057692308	0.223894230769233
34	100.57	100.419439102564	0.150560897435895
35	100.76	100.654855769231	0.105144230769241
36	100.86	100.787772435897	0.0722275641025902
37	100.86	100.856939102564	0.00306089743590121
38	100.39	100.706939102564	-0.316939102564106
39	100.61	100.345272435897	0.264727564102571
40	100.67	100.596939102564	0.0730608974358802
41	100.81	100.780689102564	0.02931089743592
42	100.86	100.830689102564	0.02931089743592
43	100.86	100.819855769231	0.040144230769215
44	100.98	100.967772435897	0.0122275641025738
45	101.03	101.016105769231	0.0138942307692389
46	101.37	101.259439102564	0.110560897435903
47	101.64	101.454855769231	0.185144230769225
48	101.68	101.667772435897	0.0122275641026022
49	101.68	101.676939102564	0.00306089743590121
50	101.25	101.526939102564	-0.276939102564114
51	101.24	101.205272435897	0.0347275641025675
52	101.11	101.226939102564	-0.116939102564118
53	101.08	101.220689102564	-0.140689102564082
54	101.09	101.100689102564	-0.0106891025640721
55	101.09	101.049855769231	0.040144230769215
56	101.62	101.197772435897	0.42222756410257
57	101.66	101.656105769231	0.00389423076923379
58	101.96	101.889439102564	0.0705608974358967
59	102.04	102.044855769231	-0.00485576923075826
60	102.02	102.067772435897	-0.0477724358974143
61	102.02	102.016939102564	0.00306089743590121
62	101.51	101.866939102564	-0.356939102564098
63	101.62	101.465272435897	0.154727564102572
64	101.83	101.606939102564	0.223060897435872
65	102.06	101.940689102564	0.119310897435923
66	102.14	102.080689102564	0.0593108974359211
67	102.14	102.099855769231	0.040144230769215
68	102.59	102.247772435897	0.342227564102572
69	102.92	102.626105769231	0.29389423076924
70	103.31	103.149439102564	0.1605608974359
71	103.54	103.394855769231	0.145144230769233
72	103.58	103.567772435897	0.012227564102588
73	103.58	103.576939102564	0.00306089743590121
74	102.83	103.426939102564	-0.596939102564107
75	102.86	102.785272435897	0.0747275641025738
76	103.03	102.846939102564	0.18306089743588
77	103.2	103.140689102564	0.0593108974359211
78	103.28	103.220689102564	0.0593108974359211
79	103.28	103.239855769231	0.040144230769215
80	103.79	103.387772435897	0.402227564102574
81	103.92	103.826105769231	0.0938942307692372
82	104.26	104.149439102564	0.110560897435903
83	104.41	104.344855769231	0.0651442307692207
84	104.45	104.437772435897	0.0122275641026022
85	99.92	104.446939102564	-4.5269391025641
86	99.18	99.7669391025641	-0.586939102564102
87	99.18	99.1352724358974	0.0447275641025726
88	99.35	99.1669391025641	0.183060897435865
89	99.62	99.4606891025641	0.15931089743593
90	99.67	99.6406891025641	0.02931089743592
91	99.72	99.6298557692308	0.0901442307692122
92	100.08	99.8277724358974	0.252227564102569
93	100.39	100.116105769231	0.273894230769244
94	100.77	100.619439102564	0.150560897435895
95	101.03	100.854855769231	0.175144230769234
96	101.07	101.057772435897	0.012227564102588
97	101.29	101.066939102564	0.223060897435914
98	101.1	101.136939102564	-0.0369391025641193
99	101.2	101.055272435897	0.144727564102581
100	101.15	101.186939102564	-0.0369391025641193
101	101.24	101.260689102564	-0.0206891025640914
102	101.16	101.260689102564	-0.100689102564075
103	100.81	101.119855769231	-0.309855769230779
104	101.02	100.917772435897	0.102227564102563
105	101.15	101.056105769231	0.0938942307692514
106	101.06	101.379439102564	-0.319439102564104
107	101.17	101.144855769231	0.0251442307692287
108	101.22	101.197772435897	0.0222275641025931

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	101.216939102564	100.248807299349	102.18507090578
110	101.063878205128	99.6947330788562	102.4330233314
111	101.019150641026	99.3422971694332	102.696004112618
112	101.00608974359	99.0698261371589	102.942353350021
113	101.116778846154	98.9519703229847	103.281587369323
114	101.137467948718	98.7660390270795	103.508896870356
115	101.097323717949	98.5358877303081	103.658759705589
116	101.205096153846	98.4668059013022	103.94338640639
117	101.241201923077	98.3368065134306	104.145597332723
118	101.470641025641	98.4091394522343	104.532142599048
119	101.555496794872	98.344566855996	104.766426733748
120	101.583269230769	98.2295622875844	104.936976173954

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.216939102564 & 100.248807299349 & 102.18507090578 \tabularnewline
110 & 101.063878205128 & 99.6947330788562 & 102.4330233314 \tabularnewline
111 & 101.019150641026 & 99.3422971694332 & 102.696004112618 \tabularnewline
112 & 101.00608974359 & 99.0698261371589 & 102.942353350021 \tabularnewline
113 & 101.116778846154 & 98.9519703229847 & 103.281587369323 \tabularnewline
114 & 101.137467948718 & 98.7660390270795 & 103.508896870356 \tabularnewline
115 & 101.097323717949 & 98.5358877303081 & 103.658759705589 \tabularnewline
116 & 101.205096153846 & 98.4668059013022 & 103.94338640639 \tabularnewline
117 & 101.241201923077 & 98.3368065134306 & 104.145597332723 \tabularnewline
118 & 101.470641025641 & 98.4091394522343 & 104.532142599048 \tabularnewline
119 & 101.555496794872 & 98.344566855996 & 104.766426733748 \tabularnewline
120 & 101.583269230769 & 98.2295622875844 & 104.936976173954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284473&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]109[/C][C]101.216939102564[/C][C]100.248807299349[/C][C]102.18507090578[/C][/ROW]
[ROW][C]110[/C][C]101.063878205128[/C][C]99.6947330788562[/C][C]102.4330233314[/C][/ROW]
[ROW][C]111[/C][C]101.019150641026[/C][C]99.3422971694332[/C][C]102.696004112618[/C][/ROW]
[ROW][C]112[/C][C]101.00608974359[/C][C]99.0698261371589[/C][C]102.942353350021[/C][/ROW]
[ROW][C]113[/C][C]101.116778846154[/C][C]98.9519703229847[/C][C]103.281587369323[/C][/ROW]
[ROW][C]114[/C][C]101.137467948718[/C][C]98.7660390270795[/C][C]103.508896870356[/C][/ROW]
[ROW][C]115[/C][C]101.097323717949[/C][C]98.5358877303081[/C][C]103.658759705589[/C][/ROW]
[ROW][C]116[/C][C]101.205096153846[/C][C]98.4668059013022[/C][C]103.94338640639[/C][/ROW]
[ROW][C]117[/C][C]101.241201923077[/C][C]98.3368065134306[/C][C]104.145597332723[/C][/ROW]
[ROW][C]118[/C][C]101.470641025641[/C][C]98.4091394522343[/C][C]104.532142599048[/C][/ROW]
[ROW][C]119[/C][C]101.555496794872[/C][C]98.344566855996[/C][C]104.766426733748[/C][/ROW]
[ROW][C]120[/C][C]101.583269230769[/C][C]98.2295622875844[/C][C]104.936976173954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284473&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284473&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
109	101.216939102564	100.248807299349	102.18507090578
110	101.063878205128	99.6947330788562	102.4330233314
111	101.019150641026	99.3422971694332	102.696004112618
112	101.00608974359	99.0698261371589	102.942353350021
113	101.116778846154	98.9519703229847	103.281587369323
114	101.137467948718	98.7660390270795	103.508896870356
115	101.097323717949	98.5358877303081	103.658759705589
116	101.205096153846	98.4668059013022	103.94338640639
117	101.241201923077	98.3368065134306	104.145597332723
118	101.470641025641	98.4091394522343	104.532142599048
119	101.555496794872	98.344566855996	104.766426733748
120	101.583269230769	98.2295622875844	104.936976173954

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