Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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 05:28:19 -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/t138718976294h6qyqxe8bhz15.htm/, Retrieved Wed, 24 Apr 2024 16:55:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232385, Retrieved Wed, 24 Apr 2024 16:55:16 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [] [2013-12-16 10:28:19] [4e750cf741e4f7924818ee4654f0419a] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1.27
1.26
1.26
1.27
1.27
1.28
1.28
1.28
1.29
1.29
1.29
1.29
1.3
1.31
1.31
1.32
1.32
1.32
1.32
1.32
1.32
1.33
1.32
1.33
1.34
1.35
1.35
1.35
1.35
1.35
1.35
1.35
1.36
1.35
1.36
1.36
1.37
1.38
1.38
1.38
1.39
1.39
1.39
1.39
1.39
1.4
1.39
1.39
1.4
1.4
1.4
1.41
1.41
1.42
1.42
1.43
1.43
1.44
1.43
1.43
1.43
1.44
1.44
1.44
1.43
1.44
1.45
1.45
1.48
1.49
1.49
1.51
1.52
1.53
1.53
1.54
1.54
1.54
1.57
1.59
1.58
1.6
1.62
1.62

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' @ 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232385&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232385&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232385&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' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.790910936880998
beta	0.24611000085311
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.790910936880998 \tabularnewline
beta & 0.24611000085311 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232385&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]0.790910936880998[/C][/ROW]
[ROW][C]beta[/C][C]0.24611000085311[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232385&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232385&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	0.790910936880998
beta	0.24611000085311
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.26	1.25	0.01
4	1.27	1.24985562028232	0.020144379717685
5	1.27	1.26165566692785	0.00834433307215243
6	1.28	1.26574716116481	0.014252838835191
7	1.28	1.2772860878645	0.00271391213550487
8	1.28	1.28022701719654	-0.000227017196536616
9	1.29	1.28079774421021	0.00920225578978862
10	1.29	1.29061741548798	-0.000617415487976336
11	1.29	1.29255042075703	-0.00255042075702927
12	1.29	1.29245814883398	-0.00245814883398099
13	1.3	1.2919603744308	0.00803962556919768
14	1.31	1.3013303265071	0.00866967349289927
15	1.31	1.31288615178406	-0.00288615178405949
16	1.32	1.31474055587022	0.00525944412978485
17	1.32	1.3240611573918	-0.00406115739180324
18	1.32	1.3252194845132	-0.00521948451319698
19	1.32	1.32444569968901	-0.00444569968901343
20	1.32	1.32341854944879	-0.00341854944878617
21	1.32	1.32253835918633	-0.00253835918633283
22	1.33	1.32186022664313	0.00813977335686933
23	1.32	1.33121196168107	-0.0112119616810724
24	1.33	1.32307577725248	0.00692422274751814
25	1.34	1.33063150695631	0.00936849304368725
26	1.35	1.34194402416534	0.00805597583465922
27	1.35	1.35378656164701	-0.00378656164701385
28	1.35	1.35552564835695	-0.00552564835695124
29	1.35	1.35481369888472	-0.00481369888471517
30	1.35	1.35372784629523	-0.00372784629523459
31	1.35	1.35277517704486	-0.0027751770448603
32	1.35	1.35203579308336	-0.00203579308336432
33	1.36	1.35148492663813	0.00851507336187085
34	1.35	1.36093632418082	-0.0109363241808191
35	1.36	1.35287463123222	0.00712536876778413
36	1.36	1.36048508958217	-0.000485089582173526
37	1.37	1.3619819299719	0.00801807002810073
38	1.38	1.37176473837693	0.0082352616230692
39	1.38	1.38332232865231	-0.00332232865230853
40	1.38	1.3850921994769	-0.00509219947690376
41	1.39	1.38447105792391	0.00552894207609378
42	1.39	1.39332650799646	-0.00332650799646106
43	1.39	1.39453057734373	-0.00453057734373141
44	1.39	1.39390045325108	-0.00390045325107691
45	1.39	1.39300947371281	-0.00300947371281146
46	1.4	1.39223738229331	0.00776261770669207
47	1.39	1.40149605779892	-0.011496057798916
48	1.39	1.39328511602051	-0.00328511602050896
49	1.4	1.39092884647813	0.00907115352186794
50	1.4	1.40011099558871	-0.000110995588710194
51	1.4	1.40200927713118	-0.00200927713118237
52	1.41	1.40201507905402	0.00798492094597636
53	1.41	1.41147967511793	-0.0014796751179269
54	1.42	1.41317059826518	0.00682940173482049
55	1.42	1.42276261167161	-0.00276261167160863
56	1.43	1.42423045139133	0.0057695486086724
57	1.43	1.43356951892522	-0.00356951892522028
58	1.44	1.4348274050519	0.0051725949481034
59	1.43	1.44400637590421	-0.0140063759042062
60	1.43	1.43529013259568	-0.00529013259568289
61	1.43	1.43243793136525	-0.00243793136524806
62	1.44	1.43136702128127	0.00863297871873381
63	1.44	1.44073263379314	-0.000732633793139259
64	1.44	1.44254827297139	-0.00254827297138727
65	1.43	1.44243187915119	-0.0124318791511899
66	1.44	1.43207855426325	0.00792144573675468
67	1.45	1.4393648146888	0.0106351853111986
68	1.45	1.45086755185117	-0.000867551851171822
69	1.48	1.45310377847312	0.026896221526878
70	1.49	1.48253405598227	0.00746594401773049
71	1.49	1.49804996865381	-0.00804996865381247
72	1.51	1.49972724111394	0.0102727588860603
73	1.52	1.5178957629072	0.00210423709280483
74	1.53	1.53001330352259	-1.33035225888811e-05
75	1.53	1.54045346856079	-0.0104534685607873
76	1.54	1.54060161382368	-0.000601613823676406
77	1.54	1.54842459395936	-0.00842459395935902
78	1.54	1.54842043713835	-0.00842043713835339
79	1.57	1.54678052071391	0.0232194792860854
80	1.59	1.57468465721519	0.0153153427848074
81	1.58	1.59931847389848	-0.0193184738984797
82	1.6	1.59279966415346	0.00720033584654245
83	1.62	1.60865642429946	0.0113435757005402
84	1.62	1.62999815755004	-0.00999815755003719

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.26 & 1.25 & 0.01 \tabularnewline
4 & 1.27 & 1.24985562028232 & 0.020144379717685 \tabularnewline
5 & 1.27 & 1.26165566692785 & 0.00834433307215243 \tabularnewline
6 & 1.28 & 1.26574716116481 & 0.014252838835191 \tabularnewline
7 & 1.28 & 1.2772860878645 & 0.00271391213550487 \tabularnewline
8 & 1.28 & 1.28022701719654 & -0.000227017196536616 \tabularnewline
9 & 1.29 & 1.28079774421021 & 0.00920225578978862 \tabularnewline
10 & 1.29 & 1.29061741548798 & -0.000617415487976336 \tabularnewline
11 & 1.29 & 1.29255042075703 & -0.00255042075702927 \tabularnewline
12 & 1.29 & 1.29245814883398 & -0.00245814883398099 \tabularnewline
13 & 1.3 & 1.2919603744308 & 0.00803962556919768 \tabularnewline
14 & 1.31 & 1.3013303265071 & 0.00866967349289927 \tabularnewline
15 & 1.31 & 1.31288615178406 & -0.00288615178405949 \tabularnewline
16 & 1.32 & 1.31474055587022 & 0.00525944412978485 \tabularnewline
17 & 1.32 & 1.3240611573918 & -0.00406115739180324 \tabularnewline
18 & 1.32 & 1.3252194845132 & -0.00521948451319698 \tabularnewline
19 & 1.32 & 1.32444569968901 & -0.00444569968901343 \tabularnewline
20 & 1.32 & 1.32341854944879 & -0.00341854944878617 \tabularnewline
21 & 1.32 & 1.32253835918633 & -0.00253835918633283 \tabularnewline
22 & 1.33 & 1.32186022664313 & 0.00813977335686933 \tabularnewline
23 & 1.32 & 1.33121196168107 & -0.0112119616810724 \tabularnewline
24 & 1.33 & 1.32307577725248 & 0.00692422274751814 \tabularnewline
25 & 1.34 & 1.33063150695631 & 0.00936849304368725 \tabularnewline
26 & 1.35 & 1.34194402416534 & 0.00805597583465922 \tabularnewline
27 & 1.35 & 1.35378656164701 & -0.00378656164701385 \tabularnewline
28 & 1.35 & 1.35552564835695 & -0.00552564835695124 \tabularnewline
29 & 1.35 & 1.35481369888472 & -0.00481369888471517 \tabularnewline
30 & 1.35 & 1.35372784629523 & -0.00372784629523459 \tabularnewline
31 & 1.35 & 1.35277517704486 & -0.0027751770448603 \tabularnewline
32 & 1.35 & 1.35203579308336 & -0.00203579308336432 \tabularnewline
33 & 1.36 & 1.35148492663813 & 0.00851507336187085 \tabularnewline
34 & 1.35 & 1.36093632418082 & -0.0109363241808191 \tabularnewline
35 & 1.36 & 1.35287463123222 & 0.00712536876778413 \tabularnewline
36 & 1.36 & 1.36048508958217 & -0.000485089582173526 \tabularnewline
37 & 1.37 & 1.3619819299719 & 0.00801807002810073 \tabularnewline
38 & 1.38 & 1.37176473837693 & 0.0082352616230692 \tabularnewline
39 & 1.38 & 1.38332232865231 & -0.00332232865230853 \tabularnewline
40 & 1.38 & 1.3850921994769 & -0.00509219947690376 \tabularnewline
41 & 1.39 & 1.38447105792391 & 0.00552894207609378 \tabularnewline
42 & 1.39 & 1.39332650799646 & -0.00332650799646106 \tabularnewline
43 & 1.39 & 1.39453057734373 & -0.00453057734373141 \tabularnewline
44 & 1.39 & 1.39390045325108 & -0.00390045325107691 \tabularnewline
45 & 1.39 & 1.39300947371281 & -0.00300947371281146 \tabularnewline
46 & 1.4 & 1.39223738229331 & 0.00776261770669207 \tabularnewline
47 & 1.39 & 1.40149605779892 & -0.011496057798916 \tabularnewline
48 & 1.39 & 1.39328511602051 & -0.00328511602050896 \tabularnewline
49 & 1.4 & 1.39092884647813 & 0.00907115352186794 \tabularnewline
50 & 1.4 & 1.40011099558871 & -0.000110995588710194 \tabularnewline
51 & 1.4 & 1.40200927713118 & -0.00200927713118237 \tabularnewline
52 & 1.41 & 1.40201507905402 & 0.00798492094597636 \tabularnewline
53 & 1.41 & 1.41147967511793 & -0.0014796751179269 \tabularnewline
54 & 1.42 & 1.41317059826518 & 0.00682940173482049 \tabularnewline
55 & 1.42 & 1.42276261167161 & -0.00276261167160863 \tabularnewline
56 & 1.43 & 1.42423045139133 & 0.0057695486086724 \tabularnewline
57 & 1.43 & 1.43356951892522 & -0.00356951892522028 \tabularnewline
58 & 1.44 & 1.4348274050519 & 0.0051725949481034 \tabularnewline
59 & 1.43 & 1.44400637590421 & -0.0140063759042062 \tabularnewline
60 & 1.43 & 1.43529013259568 & -0.00529013259568289 \tabularnewline
61 & 1.43 & 1.43243793136525 & -0.00243793136524806 \tabularnewline
62 & 1.44 & 1.43136702128127 & 0.00863297871873381 \tabularnewline
63 & 1.44 & 1.44073263379314 & -0.000732633793139259 \tabularnewline
64 & 1.44 & 1.44254827297139 & -0.00254827297138727 \tabularnewline
65 & 1.43 & 1.44243187915119 & -0.0124318791511899 \tabularnewline
66 & 1.44 & 1.43207855426325 & 0.00792144573675468 \tabularnewline
67 & 1.45 & 1.4393648146888 & 0.0106351853111986 \tabularnewline
68 & 1.45 & 1.45086755185117 & -0.000867551851171822 \tabularnewline
69 & 1.48 & 1.45310377847312 & 0.026896221526878 \tabularnewline
70 & 1.49 & 1.48253405598227 & 0.00746594401773049 \tabularnewline
71 & 1.49 & 1.49804996865381 & -0.00804996865381247 \tabularnewline
72 & 1.51 & 1.49972724111394 & 0.0102727588860603 \tabularnewline
73 & 1.52 & 1.5178957629072 & 0.00210423709280483 \tabularnewline
74 & 1.53 & 1.53001330352259 & -1.33035225888811e-05 \tabularnewline
75 & 1.53 & 1.54045346856079 & -0.0104534685607873 \tabularnewline
76 & 1.54 & 1.54060161382368 & -0.000601613823676406 \tabularnewline
77 & 1.54 & 1.54842459395936 & -0.00842459395935902 \tabularnewline
78 & 1.54 & 1.54842043713835 & -0.00842043713835339 \tabularnewline
79 & 1.57 & 1.54678052071391 & 0.0232194792860854 \tabularnewline
80 & 1.59 & 1.57468465721519 & 0.0153153427848074 \tabularnewline
81 & 1.58 & 1.59931847389848 & -0.0193184738984797 \tabularnewline
82 & 1.6 & 1.59279966415346 & 0.00720033584654245 \tabularnewline
83 & 1.62 & 1.60865642429946 & 0.0113435757005402 \tabularnewline
84 & 1.62 & 1.62999815755004 & -0.00999815755003719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232385&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1.26[/C][C]1.25[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]1.27[/C][C]1.24985562028232[/C][C]0.020144379717685[/C][/ROW]
[ROW][C]5[/C][C]1.27[/C][C]1.26165566692785[/C][C]0.00834433307215243[/C][/ROW]
[ROW][C]6[/C][C]1.28[/C][C]1.26574716116481[/C][C]0.014252838835191[/C][/ROW]
[ROW][C]7[/C][C]1.28[/C][C]1.2772860878645[/C][C]0.00271391213550487[/C][/ROW]
[ROW][C]8[/C][C]1.28[/C][C]1.28022701719654[/C][C]-0.000227017196536616[/C][/ROW]
[ROW][C]9[/C][C]1.29[/C][C]1.28079774421021[/C][C]0.00920225578978862[/C][/ROW]
[ROW][C]10[/C][C]1.29[/C][C]1.29061741548798[/C][C]-0.000617415487976336[/C][/ROW]
[ROW][C]11[/C][C]1.29[/C][C]1.29255042075703[/C][C]-0.00255042075702927[/C][/ROW]
[ROW][C]12[/C][C]1.29[/C][C]1.29245814883398[/C][C]-0.00245814883398099[/C][/ROW]
[ROW][C]13[/C][C]1.3[/C][C]1.2919603744308[/C][C]0.00803962556919768[/C][/ROW]
[ROW][C]14[/C][C]1.31[/C][C]1.3013303265071[/C][C]0.00866967349289927[/C][/ROW]
[ROW][C]15[/C][C]1.31[/C][C]1.31288615178406[/C][C]-0.00288615178405949[/C][/ROW]
[ROW][C]16[/C][C]1.32[/C][C]1.31474055587022[/C][C]0.00525944412978485[/C][/ROW]
[ROW][C]17[/C][C]1.32[/C][C]1.3240611573918[/C][C]-0.00406115739180324[/C][/ROW]
[ROW][C]18[/C][C]1.32[/C][C]1.3252194845132[/C][C]-0.00521948451319698[/C][/ROW]
[ROW][C]19[/C][C]1.32[/C][C]1.32444569968901[/C][C]-0.00444569968901343[/C][/ROW]
[ROW][C]20[/C][C]1.32[/C][C]1.32341854944879[/C][C]-0.00341854944878617[/C][/ROW]
[ROW][C]21[/C][C]1.32[/C][C]1.32253835918633[/C][C]-0.00253835918633283[/C][/ROW]
[ROW][C]22[/C][C]1.33[/C][C]1.32186022664313[/C][C]0.00813977335686933[/C][/ROW]
[ROW][C]23[/C][C]1.32[/C][C]1.33121196168107[/C][C]-0.0112119616810724[/C][/ROW]
[ROW][C]24[/C][C]1.33[/C][C]1.32307577725248[/C][C]0.00692422274751814[/C][/ROW]
[ROW][C]25[/C][C]1.34[/C][C]1.33063150695631[/C][C]0.00936849304368725[/C][/ROW]
[ROW][C]26[/C][C]1.35[/C][C]1.34194402416534[/C][C]0.00805597583465922[/C][/ROW]
[ROW][C]27[/C][C]1.35[/C][C]1.35378656164701[/C][C]-0.00378656164701385[/C][/ROW]
[ROW][C]28[/C][C]1.35[/C][C]1.35552564835695[/C][C]-0.00552564835695124[/C][/ROW]
[ROW][C]29[/C][C]1.35[/C][C]1.35481369888472[/C][C]-0.00481369888471517[/C][/ROW]
[ROW][C]30[/C][C]1.35[/C][C]1.35372784629523[/C][C]-0.00372784629523459[/C][/ROW]
[ROW][C]31[/C][C]1.35[/C][C]1.35277517704486[/C][C]-0.0027751770448603[/C][/ROW]
[ROW][C]32[/C][C]1.35[/C][C]1.35203579308336[/C][C]-0.00203579308336432[/C][/ROW]
[ROW][C]33[/C][C]1.36[/C][C]1.35148492663813[/C][C]0.00851507336187085[/C][/ROW]
[ROW][C]34[/C][C]1.35[/C][C]1.36093632418082[/C][C]-0.0109363241808191[/C][/ROW]
[ROW][C]35[/C][C]1.36[/C][C]1.35287463123222[/C][C]0.00712536876778413[/C][/ROW]
[ROW][C]36[/C][C]1.36[/C][C]1.36048508958217[/C][C]-0.000485089582173526[/C][/ROW]
[ROW][C]37[/C][C]1.37[/C][C]1.3619819299719[/C][C]0.00801807002810073[/C][/ROW]
[ROW][C]38[/C][C]1.38[/C][C]1.37176473837693[/C][C]0.0082352616230692[/C][/ROW]
[ROW][C]39[/C][C]1.38[/C][C]1.38332232865231[/C][C]-0.00332232865230853[/C][/ROW]
[ROW][C]40[/C][C]1.38[/C][C]1.3850921994769[/C][C]-0.00509219947690376[/C][/ROW]
[ROW][C]41[/C][C]1.39[/C][C]1.38447105792391[/C][C]0.00552894207609378[/C][/ROW]
[ROW][C]42[/C][C]1.39[/C][C]1.39332650799646[/C][C]-0.00332650799646106[/C][/ROW]
[ROW][C]43[/C][C]1.39[/C][C]1.39453057734373[/C][C]-0.00453057734373141[/C][/ROW]
[ROW][C]44[/C][C]1.39[/C][C]1.39390045325108[/C][C]-0.00390045325107691[/C][/ROW]
[ROW][C]45[/C][C]1.39[/C][C]1.39300947371281[/C][C]-0.00300947371281146[/C][/ROW]
[ROW][C]46[/C][C]1.4[/C][C]1.39223738229331[/C][C]0.00776261770669207[/C][/ROW]
[ROW][C]47[/C][C]1.39[/C][C]1.40149605779892[/C][C]-0.011496057798916[/C][/ROW]
[ROW][C]48[/C][C]1.39[/C][C]1.39328511602051[/C][C]-0.00328511602050896[/C][/ROW]
[ROW][C]49[/C][C]1.4[/C][C]1.39092884647813[/C][C]0.00907115352186794[/C][/ROW]
[ROW][C]50[/C][C]1.4[/C][C]1.40011099558871[/C][C]-0.000110995588710194[/C][/ROW]
[ROW][C]51[/C][C]1.4[/C][C]1.40200927713118[/C][C]-0.00200927713118237[/C][/ROW]
[ROW][C]52[/C][C]1.41[/C][C]1.40201507905402[/C][C]0.00798492094597636[/C][/ROW]
[ROW][C]53[/C][C]1.41[/C][C]1.41147967511793[/C][C]-0.0014796751179269[/C][/ROW]
[ROW][C]54[/C][C]1.42[/C][C]1.41317059826518[/C][C]0.00682940173482049[/C][/ROW]
[ROW][C]55[/C][C]1.42[/C][C]1.42276261167161[/C][C]-0.00276261167160863[/C][/ROW]
[ROW][C]56[/C][C]1.43[/C][C]1.42423045139133[/C][C]0.0057695486086724[/C][/ROW]
[ROW][C]57[/C][C]1.43[/C][C]1.43356951892522[/C][C]-0.00356951892522028[/C][/ROW]
[ROW][C]58[/C][C]1.44[/C][C]1.4348274050519[/C][C]0.0051725949481034[/C][/ROW]
[ROW][C]59[/C][C]1.43[/C][C]1.44400637590421[/C][C]-0.0140063759042062[/C][/ROW]
[ROW][C]60[/C][C]1.43[/C][C]1.43529013259568[/C][C]-0.00529013259568289[/C][/ROW]
[ROW][C]61[/C][C]1.43[/C][C]1.43243793136525[/C][C]-0.00243793136524806[/C][/ROW]
[ROW][C]62[/C][C]1.44[/C][C]1.43136702128127[/C][C]0.00863297871873381[/C][/ROW]
[ROW][C]63[/C][C]1.44[/C][C]1.44073263379314[/C][C]-0.000732633793139259[/C][/ROW]
[ROW][C]64[/C][C]1.44[/C][C]1.44254827297139[/C][C]-0.00254827297138727[/C][/ROW]
[ROW][C]65[/C][C]1.43[/C][C]1.44243187915119[/C][C]-0.0124318791511899[/C][/ROW]
[ROW][C]66[/C][C]1.44[/C][C]1.43207855426325[/C][C]0.00792144573675468[/C][/ROW]
[ROW][C]67[/C][C]1.45[/C][C]1.4393648146888[/C][C]0.0106351853111986[/C][/ROW]
[ROW][C]68[/C][C]1.45[/C][C]1.45086755185117[/C][C]-0.000867551851171822[/C][/ROW]
[ROW][C]69[/C][C]1.48[/C][C]1.45310377847312[/C][C]0.026896221526878[/C][/ROW]
[ROW][C]70[/C][C]1.49[/C][C]1.48253405598227[/C][C]0.00746594401773049[/C][/ROW]
[ROW][C]71[/C][C]1.49[/C][C]1.49804996865381[/C][C]-0.00804996865381247[/C][/ROW]
[ROW][C]72[/C][C]1.51[/C][C]1.49972724111394[/C][C]0.0102727588860603[/C][/ROW]
[ROW][C]73[/C][C]1.52[/C][C]1.5178957629072[/C][C]0.00210423709280483[/C][/ROW]
[ROW][C]74[/C][C]1.53[/C][C]1.53001330352259[/C][C]-1.33035225888811e-05[/C][/ROW]
[ROW][C]75[/C][C]1.53[/C][C]1.54045346856079[/C][C]-0.0104534685607873[/C][/ROW]
[ROW][C]76[/C][C]1.54[/C][C]1.54060161382368[/C][C]-0.000601613823676406[/C][/ROW]
[ROW][C]77[/C][C]1.54[/C][C]1.54842459395936[/C][C]-0.00842459395935902[/C][/ROW]
[ROW][C]78[/C][C]1.54[/C][C]1.54842043713835[/C][C]-0.00842043713835339[/C][/ROW]
[ROW][C]79[/C][C]1.57[/C][C]1.54678052071391[/C][C]0.0232194792860854[/C][/ROW]
[ROW][C]80[/C][C]1.59[/C][C]1.57468465721519[/C][C]0.0153153427848074[/C][/ROW]
[ROW][C]81[/C][C]1.58[/C][C]1.59931847389848[/C][C]-0.0193184738984797[/C][/ROW]
[ROW][C]82[/C][C]1.6[/C][C]1.59279966415346[/C][C]0.00720033584654245[/C][/ROW]
[ROW][C]83[/C][C]1.62[/C][C]1.60865642429946[/C][C]0.0113435757005402[/C][/ROW]
[ROW][C]84[/C][C]1.62[/C][C]1.62999815755004[/C][C]-0.00999815755003719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232385&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232385&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.26	1.25	0.01
4	1.27	1.24985562028232	0.020144379717685
5	1.27	1.26165566692785	0.00834433307215243
6	1.28	1.26574716116481	0.014252838835191
7	1.28	1.2772860878645	0.00271391213550487
8	1.28	1.28022701719654	-0.000227017196536616
9	1.29	1.28079774421021	0.00920225578978862
10	1.29	1.29061741548798	-0.000617415487976336
11	1.29	1.29255042075703	-0.00255042075702927
12	1.29	1.29245814883398	-0.00245814883398099
13	1.3	1.2919603744308	0.00803962556919768
14	1.31	1.3013303265071	0.00866967349289927
15	1.31	1.31288615178406	-0.00288615178405949
16	1.32	1.31474055587022	0.00525944412978485
17	1.32	1.3240611573918	-0.00406115739180324
18	1.32	1.3252194845132	-0.00521948451319698
19	1.32	1.32444569968901	-0.00444569968901343
20	1.32	1.32341854944879	-0.00341854944878617
21	1.32	1.32253835918633	-0.00253835918633283
22	1.33	1.32186022664313	0.00813977335686933
23	1.32	1.33121196168107	-0.0112119616810724
24	1.33	1.32307577725248	0.00692422274751814
25	1.34	1.33063150695631	0.00936849304368725
26	1.35	1.34194402416534	0.00805597583465922
27	1.35	1.35378656164701	-0.00378656164701385
28	1.35	1.35552564835695	-0.00552564835695124
29	1.35	1.35481369888472	-0.00481369888471517
30	1.35	1.35372784629523	-0.00372784629523459
31	1.35	1.35277517704486	-0.0027751770448603
32	1.35	1.35203579308336	-0.00203579308336432
33	1.36	1.35148492663813	0.00851507336187085
34	1.35	1.36093632418082	-0.0109363241808191
35	1.36	1.35287463123222	0.00712536876778413
36	1.36	1.36048508958217	-0.000485089582173526
37	1.37	1.3619819299719	0.00801807002810073
38	1.38	1.37176473837693	0.0082352616230692
39	1.38	1.38332232865231	-0.00332232865230853
40	1.38	1.3850921994769	-0.00509219947690376
41	1.39	1.38447105792391	0.00552894207609378
42	1.39	1.39332650799646	-0.00332650799646106
43	1.39	1.39453057734373	-0.00453057734373141
44	1.39	1.39390045325108	-0.00390045325107691
45	1.39	1.39300947371281	-0.00300947371281146
46	1.4	1.39223738229331	0.00776261770669207
47	1.39	1.40149605779892	-0.011496057798916
48	1.39	1.39328511602051	-0.00328511602050896
49	1.4	1.39092884647813	0.00907115352186794
50	1.4	1.40011099558871	-0.000110995588710194
51	1.4	1.40200927713118	-0.00200927713118237
52	1.41	1.40201507905402	0.00798492094597636
53	1.41	1.41147967511793	-0.0014796751179269
54	1.42	1.41317059826518	0.00682940173482049
55	1.42	1.42276261167161	-0.00276261167160863
56	1.43	1.42423045139133	0.0057695486086724
57	1.43	1.43356951892522	-0.00356951892522028
58	1.44	1.4348274050519	0.0051725949481034
59	1.43	1.44400637590421	-0.0140063759042062
60	1.43	1.43529013259568	-0.00529013259568289
61	1.43	1.43243793136525	-0.00243793136524806
62	1.44	1.43136702128127	0.00863297871873381
63	1.44	1.44073263379314	-0.000732633793139259
64	1.44	1.44254827297139	-0.00254827297138727
65	1.43	1.44243187915119	-0.0124318791511899
66	1.44	1.43207855426325	0.00792144573675468
67	1.45	1.4393648146888	0.0106351853111986
68	1.45	1.45086755185117	-0.000867551851171822
69	1.48	1.45310377847312	0.026896221526878
70	1.49	1.48253405598227	0.00746594401773049
71	1.49	1.49804996865381	-0.00804996865381247
72	1.51	1.49972724111394	0.0102727588860603
73	1.52	1.5178957629072	0.00210423709280483
74	1.53	1.53001330352259	-1.33035225888811e-05
75	1.53	1.54045346856079	-0.0104534685607873
76	1.54	1.54060161382368	-0.000601613823676406
77	1.54	1.54842459395936	-0.00842459395935902
78	1.54	1.54842043713835	-0.00842043713835339
79	1.57	1.54678052071391	0.0232194792860854
80	1.59	1.57468465721519	0.0153153427848074
81	1.58	1.59931847389848	-0.0193184738984797
82	1.6	1.59279966415346	0.00720033584654245
83	1.62	1.60865642429946	0.0113435757005402
84	1.62	1.62999815755004	-0.00999815755003719

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.63251432828213	1.61600091158277	1.64902774498148
86	1.6429381511692	1.61975262894725	1.66612367339115
87	1.65336197405627	1.6230733087741	1.68365063933845
88	1.66378579694335	1.6259326399619	1.7016389539248
89	1.67420961983042	1.62833362024318	1.72008561941766
90	1.6846334427175	1.63028912443732	1.73897776099767
91	1.69505726560457	1.6318147291449	1.75829980206424
92	1.70548108849164	1.63292619923917	1.77803597774411
93	1.71590491137872	1.63363857749992	1.79817124525751
94	1.72632873426579	1.63396588580997	1.81869158272161
95	1.73675255715286	1.63392107189543	1.83958404241029
96	1.74717638003994	1.63351605452241	1.86083670555746

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.63251432828213 & 1.61600091158277 & 1.64902774498148 \tabularnewline
86 & 1.6429381511692 & 1.61975262894725 & 1.66612367339115 \tabularnewline
87 & 1.65336197405627 & 1.6230733087741 & 1.68365063933845 \tabularnewline
88 & 1.66378579694335 & 1.6259326399619 & 1.7016389539248 \tabularnewline
89 & 1.67420961983042 & 1.62833362024318 & 1.72008561941766 \tabularnewline
90 & 1.6846334427175 & 1.63028912443732 & 1.73897776099767 \tabularnewline
91 & 1.69505726560457 & 1.6318147291449 & 1.75829980206424 \tabularnewline
92 & 1.70548108849164 & 1.63292619923917 & 1.77803597774411 \tabularnewline
93 & 1.71590491137872 & 1.63363857749992 & 1.79817124525751 \tabularnewline
94 & 1.72632873426579 & 1.63396588580997 & 1.81869158272161 \tabularnewline
95 & 1.73675255715286 & 1.63392107189543 & 1.83958404241029 \tabularnewline
96 & 1.74717638003994 & 1.63351605452241 & 1.86083670555746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232385&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]1.63251432828213[/C][C]1.61600091158277[/C][C]1.64902774498148[/C][/ROW]
[ROW][C]86[/C][C]1.6429381511692[/C][C]1.61975262894725[/C][C]1.66612367339115[/C][/ROW]
[ROW][C]87[/C][C]1.65336197405627[/C][C]1.6230733087741[/C][C]1.68365063933845[/C][/ROW]
[ROW][C]88[/C][C]1.66378579694335[/C][C]1.6259326399619[/C][C]1.7016389539248[/C][/ROW]
[ROW][C]89[/C][C]1.67420961983042[/C][C]1.62833362024318[/C][C]1.72008561941766[/C][/ROW]
[ROW][C]90[/C][C]1.6846334427175[/C][C]1.63028912443732[/C][C]1.73897776099767[/C][/ROW]
[ROW][C]91[/C][C]1.69505726560457[/C][C]1.6318147291449[/C][C]1.75829980206424[/C][/ROW]
[ROW][C]92[/C][C]1.70548108849164[/C][C]1.63292619923917[/C][C]1.77803597774411[/C][/ROW]
[ROW][C]93[/C][C]1.71590491137872[/C][C]1.63363857749992[/C][C]1.79817124525751[/C][/ROW]
[ROW][C]94[/C][C]1.72632873426579[/C][C]1.63396588580997[/C][C]1.81869158272161[/C][/ROW]
[ROW][C]95[/C][C]1.73675255715286[/C][C]1.63392107189543[/C][C]1.83958404241029[/C][/ROW]
[ROW][C]96[/C][C]1.74717638003994[/C][C]1.63351605452241[/C][C]1.86083670555746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232385&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232385&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	1.63251432828213	1.61600091158277	1.64902774498148
86	1.6429381511692	1.61975262894725	1.66612367339115
87	1.65336197405627	1.6230733087741	1.68365063933845
88	1.66378579694335	1.6259326399619	1.7016389539248
89	1.67420961983042	1.62833362024318	1.72008561941766
90	1.6846334427175	1.63028912443732	1.73897776099767
91	1.69505726560457	1.6318147291449	1.75829980206424
92	1.70548108849164	1.63292619923917	1.77803597774411
93	1.71590491137872	1.63363857749992	1.79817124525751
94	1.72632873426579	1.63396588580997	1.81869158272161
95	1.73675255715286	1.63392107189543	1.83958404241029
96	1.74717638003994	1.63351605452241	1.86083670555746

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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