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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 26 Dec 2012 10:27:54 -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/2012/Dec/26/t135653595513swxzv6ev2bq8h.htm/, Retrieved Thu, 25 Apr 2024 04:09:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204733, Retrieved Thu, 25 Apr 2024 04:09:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

118

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

-       [Exponential Smoothing] [] [2012-12-26 15:27:54] [f207e3c1cee24707935f474931b4ba78] [Current]

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Dataseries X:

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Histogram

Boxplots

1,44
1,45
1,45
1,47
1,49
1,5
1,5
1,5
1,5
1,5
1,5
1,51
1,52
1,51
1,51
1,51
1,52
1,52
1,52
1,52
1,52
1,53
1,53
1,53
1,53
1,54
1,54
1,55
1,56
1,55
1,56
1,56
1,56
1,56
1,57
1,56
1,57
1,58
1,58
1,58
1,6
1,61
1,61
1,61
1,6
1,59
1,56
1,57
1,55
1,59
1,62
1,63
1,62
1,56
1,56
1,54
1,54
1,52
1,56
1,59
1,61
1,56
1,51
1,48
1,49
1,48
1,47
1,47
1,46
1,45
1,45
1,45

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204733&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204733&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933893038648
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204733&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204733&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	0.999933893038648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.45	1.44	0.01
3	1.45	1.44999933893039	6.61069613494547e-07
4	1.47	1.4499999999563	0.0200000000437013
5	1.49	1.46999867786077	0.0200013221392299
6	1.5	1.48999867777337	0.0100013222266297
7	1.5	1.49999933884298	6.61157021797365e-07
8	1.5	1.49999999995629	4.37070379888382e-11
9	1.5	1.5	2.88657986402541e-15
10	1.5	1.5	0
11	1.5	1.5	0
12	1.51	1.5	0.01
13	1.52	1.50999933893039	0.0100006610696135
14	1.51	1.51999933888669	-0.00999933888668525
15	1.51	1.51000066102591	-6.61025909343138e-07
16	1.51	1.5100000000437	-4.36983782492462e-11
17	1.52	1.51	0.00999999999999712
18	1.52	1.51999933893039	6.61069613494547e-07
19	1.52	1.5199999999563	4.37012648291102e-11
20	1.52	1.52	2.88657986402541e-15
21	1.52	1.52	0
22	1.53	1.52	0.01
23	1.53	1.52999933893039	6.61069613494547e-07
24	1.53	1.5299999999563	4.37012648291102e-11
25	1.53	1.53	2.88657986402541e-15
26	1.54	1.53	0.01
27	1.54	1.53999933893039	6.61069613494547e-07
28	1.55	1.5399999999563	0.0100000000437013
29	1.56	1.54999933893038	0.0100006610696164
30	1.55	1.55999933888669	-0.00999933888668525
31	1.56	1.55000066102591	0.00999933897409067
32	1.56	1.55999933897408	6.61025915116298e-07
33	1.56	1.5599999999563	4.36983782492462e-11
34	1.56	1.56	2.88657986402541e-15
35	1.57	1.56	0.01
36	1.56	1.56999933893039	-0.00999933893038651
37	1.57	1.56000066102591	0.00999933897408778
38	1.58	1.56999933897408	0.0100006610259151
39	1.58	1.57999933888669	6.61113311872796e-07
40	1.58	1.5799999999563	4.37041514089742e-11
41	1.6	1.58	0.0200000000000029
42	1.61	1.59999867786077	0.010001322139227
43	1.61	1.60999933884298	6.61157016024205e-07
44	1.61	1.60999999995629	4.37070379888382e-11
45	1.6	1.61	-0.00999999999999712
46	1.59	1.60000066106961	-0.0100006610696135
47	1.56	1.59000066111331	-0.0300006611133148
48	1.57	1.56000198325254	0.00999801674745515
49	1.55	1.56999933906149	-0.0199993390614932
50	1.59	1.55000132209553	0.0399986779044657
51	1.62	1.58999735580895	0.0300026441910544
52	1.63	1.61999801661636	0.0100019833836398
53	1.62	1.62999933879927	-0.00999933879927073
54	1.56	1.6200006610259	-0.0600006610259036
55	1.56	1.56000396646138	-3.96646137956758e-06
56	1.54	1.56000000026221	-0.0200000002622107
57	1.54	1.54000132213924	-1.32213924430857e-06
58	1.52	1.5400000000874	-0.0200000000874025
59	1.56	1.52000132213923	0.0399986778607673
60	1.59	1.55999735580895	0.0300026441910515
61	1.61	1.58999801661636	0.02000198338364
62	1.56	1.60999867772966	-0.0499986777296575
63	1.51	1.56000330526066	-0.0500033052606563
64	1.48	1.51000330556657	-0.0300033055665683
65	1.49	1.48000198342736	0.00999801657263855
66	1.48	1.4899993390615	-0.00999933906150474
67	1.47	1.48000066102592	-0.0100006610259209
68	1.47	1.47000066111331	-6.61113311872796e-07
69	1.46	1.4700000000437	-0.0100000000437042
70	1.45	1.46000066106962	-0.0100006610696164
71	1.45	1.45000066111331	-6.61113314759376e-07
72	1.45	1.4500000000437	-4.37041514089742e-11

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.45 & 1.44 & 0.01 \tabularnewline
3 & 1.45 & 1.44999933893039 & 6.61069613494547e-07 \tabularnewline
4 & 1.47 & 1.4499999999563 & 0.0200000000437013 \tabularnewline
5 & 1.49 & 1.46999867786077 & 0.0200013221392299 \tabularnewline
6 & 1.5 & 1.48999867777337 & 0.0100013222266297 \tabularnewline
7 & 1.5 & 1.49999933884298 & 6.61157021797365e-07 \tabularnewline
8 & 1.5 & 1.49999999995629 & 4.37070379888382e-11 \tabularnewline
9 & 1.5 & 1.5 & 2.88657986402541e-15 \tabularnewline
10 & 1.5 & 1.5 & 0 \tabularnewline
11 & 1.5 & 1.5 & 0 \tabularnewline
12 & 1.51 & 1.5 & 0.01 \tabularnewline
13 & 1.52 & 1.50999933893039 & 0.0100006610696135 \tabularnewline
14 & 1.51 & 1.51999933888669 & -0.00999933888668525 \tabularnewline
15 & 1.51 & 1.51000066102591 & -6.61025909343138e-07 \tabularnewline
16 & 1.51 & 1.5100000000437 & -4.36983782492462e-11 \tabularnewline
17 & 1.52 & 1.51 & 0.00999999999999712 \tabularnewline
18 & 1.52 & 1.51999933893039 & 6.61069613494547e-07 \tabularnewline
19 & 1.52 & 1.5199999999563 & 4.37012648291102e-11 \tabularnewline
20 & 1.52 & 1.52 & 2.88657986402541e-15 \tabularnewline
21 & 1.52 & 1.52 & 0 \tabularnewline
22 & 1.53 & 1.52 & 0.01 \tabularnewline
23 & 1.53 & 1.52999933893039 & 6.61069613494547e-07 \tabularnewline
24 & 1.53 & 1.5299999999563 & 4.37012648291102e-11 \tabularnewline
25 & 1.53 & 1.53 & 2.88657986402541e-15 \tabularnewline
26 & 1.54 & 1.53 & 0.01 \tabularnewline
27 & 1.54 & 1.53999933893039 & 6.61069613494547e-07 \tabularnewline
28 & 1.55 & 1.5399999999563 & 0.0100000000437013 \tabularnewline
29 & 1.56 & 1.54999933893038 & 0.0100006610696164 \tabularnewline
30 & 1.55 & 1.55999933888669 & -0.00999933888668525 \tabularnewline
31 & 1.56 & 1.55000066102591 & 0.00999933897409067 \tabularnewline
32 & 1.56 & 1.55999933897408 & 6.61025915116298e-07 \tabularnewline
33 & 1.56 & 1.5599999999563 & 4.36983782492462e-11 \tabularnewline
34 & 1.56 & 1.56 & 2.88657986402541e-15 \tabularnewline
35 & 1.57 & 1.56 & 0.01 \tabularnewline
36 & 1.56 & 1.56999933893039 & -0.00999933893038651 \tabularnewline
37 & 1.57 & 1.56000066102591 & 0.00999933897408778 \tabularnewline
38 & 1.58 & 1.56999933897408 & 0.0100006610259151 \tabularnewline
39 & 1.58 & 1.57999933888669 & 6.61113311872796e-07 \tabularnewline
40 & 1.58 & 1.5799999999563 & 4.37041514089742e-11 \tabularnewline
41 & 1.6 & 1.58 & 0.0200000000000029 \tabularnewline
42 & 1.61 & 1.59999867786077 & 0.010001322139227 \tabularnewline
43 & 1.61 & 1.60999933884298 & 6.61157016024205e-07 \tabularnewline
44 & 1.61 & 1.60999999995629 & 4.37070379888382e-11 \tabularnewline
45 & 1.6 & 1.61 & -0.00999999999999712 \tabularnewline
46 & 1.59 & 1.60000066106961 & -0.0100006610696135 \tabularnewline
47 & 1.56 & 1.59000066111331 & -0.0300006611133148 \tabularnewline
48 & 1.57 & 1.56000198325254 & 0.00999801674745515 \tabularnewline
49 & 1.55 & 1.56999933906149 & -0.0199993390614932 \tabularnewline
50 & 1.59 & 1.55000132209553 & 0.0399986779044657 \tabularnewline
51 & 1.62 & 1.58999735580895 & 0.0300026441910544 \tabularnewline
52 & 1.63 & 1.61999801661636 & 0.0100019833836398 \tabularnewline
53 & 1.62 & 1.62999933879927 & -0.00999933879927073 \tabularnewline
54 & 1.56 & 1.6200006610259 & -0.0600006610259036 \tabularnewline
55 & 1.56 & 1.56000396646138 & -3.96646137956758e-06 \tabularnewline
56 & 1.54 & 1.56000000026221 & -0.0200000002622107 \tabularnewline
57 & 1.54 & 1.54000132213924 & -1.32213924430857e-06 \tabularnewline
58 & 1.52 & 1.5400000000874 & -0.0200000000874025 \tabularnewline
59 & 1.56 & 1.52000132213923 & 0.0399986778607673 \tabularnewline
60 & 1.59 & 1.55999735580895 & 0.0300026441910515 \tabularnewline
61 & 1.61 & 1.58999801661636 & 0.02000198338364 \tabularnewline
62 & 1.56 & 1.60999867772966 & -0.0499986777296575 \tabularnewline
63 & 1.51 & 1.56000330526066 & -0.0500033052606563 \tabularnewline
64 & 1.48 & 1.51000330556657 & -0.0300033055665683 \tabularnewline
65 & 1.49 & 1.48000198342736 & 0.00999801657263855 \tabularnewline
66 & 1.48 & 1.4899993390615 & -0.00999933906150474 \tabularnewline
67 & 1.47 & 1.48000066102592 & -0.0100006610259209 \tabularnewline
68 & 1.47 & 1.47000066111331 & -6.61113311872796e-07 \tabularnewline
69 & 1.46 & 1.4700000000437 & -0.0100000000437042 \tabularnewline
70 & 1.45 & 1.46000066106962 & -0.0100006610696164 \tabularnewline
71 & 1.45 & 1.45000066111331 & -6.61113314759376e-07 \tabularnewline
72 & 1.45 & 1.4500000000437 & -4.37041514089742e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204733&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]2[/C][C]1.45[/C][C]1.44[/C][C]0.01[/C][/ROW]
[ROW][C]3[/C][C]1.45[/C][C]1.44999933893039[/C][C]6.61069613494547e-07[/C][/ROW]
[ROW][C]4[/C][C]1.47[/C][C]1.4499999999563[/C][C]0.0200000000437013[/C][/ROW]
[ROW][C]5[/C][C]1.49[/C][C]1.46999867786077[/C][C]0.0200013221392299[/C][/ROW]
[ROW][C]6[/C][C]1.5[/C][C]1.48999867777337[/C][C]0.0100013222266297[/C][/ROW]
[ROW][C]7[/C][C]1.5[/C][C]1.49999933884298[/C][C]6.61157021797365e-07[/C][/ROW]
[ROW][C]8[/C][C]1.5[/C][C]1.49999999995629[/C][C]4.37070379888382e-11[/C][/ROW]
[ROW][C]9[/C][C]1.5[/C][C]1.5[/C][C]2.88657986402541e-15[/C][/ROW]
[ROW][C]10[/C][C]1.5[/C][C]1.5[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]1.5[/C][C]1.5[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]1.51[/C][C]1.5[/C][C]0.01[/C][/ROW]
[ROW][C]13[/C][C]1.52[/C][C]1.50999933893039[/C][C]0.0100006610696135[/C][/ROW]
[ROW][C]14[/C][C]1.51[/C][C]1.51999933888669[/C][C]-0.00999933888668525[/C][/ROW]
[ROW][C]15[/C][C]1.51[/C][C]1.51000066102591[/C][C]-6.61025909343138e-07[/C][/ROW]
[ROW][C]16[/C][C]1.51[/C][C]1.5100000000437[/C][C]-4.36983782492462e-11[/C][/ROW]
[ROW][C]17[/C][C]1.52[/C][C]1.51[/C][C]0.00999999999999712[/C][/ROW]
[ROW][C]18[/C][C]1.52[/C][C]1.51999933893039[/C][C]6.61069613494547e-07[/C][/ROW]
[ROW][C]19[/C][C]1.52[/C][C]1.5199999999563[/C][C]4.37012648291102e-11[/C][/ROW]
[ROW][C]20[/C][C]1.52[/C][C]1.52[/C][C]2.88657986402541e-15[/C][/ROW]
[ROW][C]21[/C][C]1.52[/C][C]1.52[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]1.53[/C][C]1.52[/C][C]0.01[/C][/ROW]
[ROW][C]23[/C][C]1.53[/C][C]1.52999933893039[/C][C]6.61069613494547e-07[/C][/ROW]
[ROW][C]24[/C][C]1.53[/C][C]1.5299999999563[/C][C]4.37012648291102e-11[/C][/ROW]
[ROW][C]25[/C][C]1.53[/C][C]1.53[/C][C]2.88657986402541e-15[/C][/ROW]
[ROW][C]26[/C][C]1.54[/C][C]1.53[/C][C]0.01[/C][/ROW]
[ROW][C]27[/C][C]1.54[/C][C]1.53999933893039[/C][C]6.61069613494547e-07[/C][/ROW]
[ROW][C]28[/C][C]1.55[/C][C]1.5399999999563[/C][C]0.0100000000437013[/C][/ROW]
[ROW][C]29[/C][C]1.56[/C][C]1.54999933893038[/C][C]0.0100006610696164[/C][/ROW]
[ROW][C]30[/C][C]1.55[/C][C]1.55999933888669[/C][C]-0.00999933888668525[/C][/ROW]
[ROW][C]31[/C][C]1.56[/C][C]1.55000066102591[/C][C]0.00999933897409067[/C][/ROW]
[ROW][C]32[/C][C]1.56[/C][C]1.55999933897408[/C][C]6.61025915116298e-07[/C][/ROW]
[ROW][C]33[/C][C]1.56[/C][C]1.5599999999563[/C][C]4.36983782492462e-11[/C][/ROW]
[ROW][C]34[/C][C]1.56[/C][C]1.56[/C][C]2.88657986402541e-15[/C][/ROW]
[ROW][C]35[/C][C]1.57[/C][C]1.56[/C][C]0.01[/C][/ROW]
[ROW][C]36[/C][C]1.56[/C][C]1.56999933893039[/C][C]-0.00999933893038651[/C][/ROW]
[ROW][C]37[/C][C]1.57[/C][C]1.56000066102591[/C][C]0.00999933897408778[/C][/ROW]
[ROW][C]38[/C][C]1.58[/C][C]1.56999933897408[/C][C]0.0100006610259151[/C][/ROW]
[ROW][C]39[/C][C]1.58[/C][C]1.57999933888669[/C][C]6.61113311872796e-07[/C][/ROW]
[ROW][C]40[/C][C]1.58[/C][C]1.5799999999563[/C][C]4.37041514089742e-11[/C][/ROW]
[ROW][C]41[/C][C]1.6[/C][C]1.58[/C][C]0.0200000000000029[/C][/ROW]
[ROW][C]42[/C][C]1.61[/C][C]1.59999867786077[/C][C]0.010001322139227[/C][/ROW]
[ROW][C]43[/C][C]1.61[/C][C]1.60999933884298[/C][C]6.61157016024205e-07[/C][/ROW]
[ROW][C]44[/C][C]1.61[/C][C]1.60999999995629[/C][C]4.37070379888382e-11[/C][/ROW]
[ROW][C]45[/C][C]1.6[/C][C]1.61[/C][C]-0.00999999999999712[/C][/ROW]
[ROW][C]46[/C][C]1.59[/C][C]1.60000066106961[/C][C]-0.0100006610696135[/C][/ROW]
[ROW][C]47[/C][C]1.56[/C][C]1.59000066111331[/C][C]-0.0300006611133148[/C][/ROW]
[ROW][C]48[/C][C]1.57[/C][C]1.56000198325254[/C][C]0.00999801674745515[/C][/ROW]
[ROW][C]49[/C][C]1.55[/C][C]1.56999933906149[/C][C]-0.0199993390614932[/C][/ROW]
[ROW][C]50[/C][C]1.59[/C][C]1.55000132209553[/C][C]0.0399986779044657[/C][/ROW]
[ROW][C]51[/C][C]1.62[/C][C]1.58999735580895[/C][C]0.0300026441910544[/C][/ROW]
[ROW][C]52[/C][C]1.63[/C][C]1.61999801661636[/C][C]0.0100019833836398[/C][/ROW]
[ROW][C]53[/C][C]1.62[/C][C]1.62999933879927[/C][C]-0.00999933879927073[/C][/ROW]
[ROW][C]54[/C][C]1.56[/C][C]1.6200006610259[/C][C]-0.0600006610259036[/C][/ROW]
[ROW][C]55[/C][C]1.56[/C][C]1.56000396646138[/C][C]-3.96646137956758e-06[/C][/ROW]
[ROW][C]56[/C][C]1.54[/C][C]1.56000000026221[/C][C]-0.0200000002622107[/C][/ROW]
[ROW][C]57[/C][C]1.54[/C][C]1.54000132213924[/C][C]-1.32213924430857e-06[/C][/ROW]
[ROW][C]58[/C][C]1.52[/C][C]1.5400000000874[/C][C]-0.0200000000874025[/C][/ROW]
[ROW][C]59[/C][C]1.56[/C][C]1.52000132213923[/C][C]0.0399986778607673[/C][/ROW]
[ROW][C]60[/C][C]1.59[/C][C]1.55999735580895[/C][C]0.0300026441910515[/C][/ROW]
[ROW][C]61[/C][C]1.61[/C][C]1.58999801661636[/C][C]0.02000198338364[/C][/ROW]
[ROW][C]62[/C][C]1.56[/C][C]1.60999867772966[/C][C]-0.0499986777296575[/C][/ROW]
[ROW][C]63[/C][C]1.51[/C][C]1.56000330526066[/C][C]-0.0500033052606563[/C][/ROW]
[ROW][C]64[/C][C]1.48[/C][C]1.51000330556657[/C][C]-0.0300033055665683[/C][/ROW]
[ROW][C]65[/C][C]1.49[/C][C]1.48000198342736[/C][C]0.00999801657263855[/C][/ROW]
[ROW][C]66[/C][C]1.48[/C][C]1.4899993390615[/C][C]-0.00999933906150474[/C][/ROW]
[ROW][C]67[/C][C]1.47[/C][C]1.48000066102592[/C][C]-0.0100006610259209[/C][/ROW]
[ROW][C]68[/C][C]1.47[/C][C]1.47000066111331[/C][C]-6.61113311872796e-07[/C][/ROW]
[ROW][C]69[/C][C]1.46[/C][C]1.4700000000437[/C][C]-0.0100000000437042[/C][/ROW]
[ROW][C]70[/C][C]1.45[/C][C]1.46000066106962[/C][C]-0.0100006610696164[/C][/ROW]
[ROW][C]71[/C][C]1.45[/C][C]1.45000066111331[/C][C]-6.61113314759376e-07[/C][/ROW]
[ROW][C]72[/C][C]1.45[/C][C]1.4500000000437[/C][C]-4.37041514089742e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204733&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204733&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
2	1.45	1.44	0.01
3	1.45	1.44999933893039	6.61069613494547e-07
4	1.47	1.4499999999563	0.0200000000437013
5	1.49	1.46999867786077	0.0200013221392299
6	1.5	1.48999867777337	0.0100013222266297
7	1.5	1.49999933884298	6.61157021797365e-07
8	1.5	1.49999999995629	4.37070379888382e-11
9	1.5	1.5	2.88657986402541e-15
10	1.5	1.5	0
11	1.5	1.5	0
12	1.51	1.5	0.01
13	1.52	1.50999933893039	0.0100006610696135
14	1.51	1.51999933888669	-0.00999933888668525
15	1.51	1.51000066102591	-6.61025909343138e-07
16	1.51	1.5100000000437	-4.36983782492462e-11
17	1.52	1.51	0.00999999999999712
18	1.52	1.51999933893039	6.61069613494547e-07
19	1.52	1.5199999999563	4.37012648291102e-11
20	1.52	1.52	2.88657986402541e-15
21	1.52	1.52	0
22	1.53	1.52	0.01
23	1.53	1.52999933893039	6.61069613494547e-07
24	1.53	1.5299999999563	4.37012648291102e-11
25	1.53	1.53	2.88657986402541e-15
26	1.54	1.53	0.01
27	1.54	1.53999933893039	6.61069613494547e-07
28	1.55	1.5399999999563	0.0100000000437013
29	1.56	1.54999933893038	0.0100006610696164
30	1.55	1.55999933888669	-0.00999933888668525
31	1.56	1.55000066102591	0.00999933897409067
32	1.56	1.55999933897408	6.61025915116298e-07
33	1.56	1.5599999999563	4.36983782492462e-11
34	1.56	1.56	2.88657986402541e-15
35	1.57	1.56	0.01
36	1.56	1.56999933893039	-0.00999933893038651
37	1.57	1.56000066102591	0.00999933897408778
38	1.58	1.56999933897408	0.0100006610259151
39	1.58	1.57999933888669	6.61113311872796e-07
40	1.58	1.5799999999563	4.37041514089742e-11
41	1.6	1.58	0.0200000000000029
42	1.61	1.59999867786077	0.010001322139227
43	1.61	1.60999933884298	6.61157016024205e-07
44	1.61	1.60999999995629	4.37070379888382e-11
45	1.6	1.61	-0.00999999999999712
46	1.59	1.60000066106961	-0.0100006610696135
47	1.56	1.59000066111331	-0.0300006611133148
48	1.57	1.56000198325254	0.00999801674745515
49	1.55	1.56999933906149	-0.0199993390614932
50	1.59	1.55000132209553	0.0399986779044657
51	1.62	1.58999735580895	0.0300026441910544
52	1.63	1.61999801661636	0.0100019833836398
53	1.62	1.62999933879927	-0.00999933879927073
54	1.56	1.6200006610259	-0.0600006610259036
55	1.56	1.56000396646138	-3.96646137956758e-06
56	1.54	1.56000000026221	-0.0200000002622107
57	1.54	1.54000132213924	-1.32213924430857e-06
58	1.52	1.5400000000874	-0.0200000000874025
59	1.56	1.52000132213923	0.0399986778607673
60	1.59	1.55999735580895	0.0300026441910515
61	1.61	1.58999801661636	0.02000198338364
62	1.56	1.60999867772966	-0.0499986777296575
63	1.51	1.56000330526066	-0.0500033052606563
64	1.48	1.51000330556657	-0.0300033055665683
65	1.49	1.48000198342736	0.00999801657263855
66	1.48	1.4899993390615	-0.00999933906150474
67	1.47	1.48000066102592	-0.0100006610259209
68	1.47	1.47000066111331	-6.61113311872796e-07
69	1.46	1.4700000000437	-0.0100000000437042
70	1.45	1.46000066106962	-0.0100006610696164
71	1.45	1.45000066111331	-6.61113314759376e-07
72	1.45	1.4500000000437	-4.37041514089742e-11

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.45	1.41613390402981	1.4838660959702
74	1.45	1.402107690808	1.497892309192
75	1.45	1.39134478622303	1.50865521377697
76	1.45	1.38227116620891	1.5177288337911
77	1.45	1.37427711211146	1.52572288788855
78	1.45	1.36704991516785	1.53295008483215
79	1.45	1.36040380924872	1.53959619075129
80	1.45	1.3542177562352	1.54578224376481
81	1.45	1.34840768216002	1.55159231783999
82	1.45	1.34291237294823	1.55708762705178
83	1.45	1.33768561672226	1.56231438327775
84	1.45	1.33269151132787	1.56730848867213

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.45 & 1.41613390402981 & 1.4838660959702 \tabularnewline
74 & 1.45 & 1.402107690808 & 1.497892309192 \tabularnewline
75 & 1.45 & 1.39134478622303 & 1.50865521377697 \tabularnewline
76 & 1.45 & 1.38227116620891 & 1.5177288337911 \tabularnewline
77 & 1.45 & 1.37427711211146 & 1.52572288788855 \tabularnewline
78 & 1.45 & 1.36704991516785 & 1.53295008483215 \tabularnewline
79 & 1.45 & 1.36040380924872 & 1.53959619075129 \tabularnewline
80 & 1.45 & 1.3542177562352 & 1.54578224376481 \tabularnewline
81 & 1.45 & 1.34840768216002 & 1.55159231783999 \tabularnewline
82 & 1.45 & 1.34291237294823 & 1.55708762705178 \tabularnewline
83 & 1.45 & 1.33768561672226 & 1.56231438327775 \tabularnewline
84 & 1.45 & 1.33269151132787 & 1.56730848867213 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204733&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]73[/C][C]1.45[/C][C]1.41613390402981[/C][C]1.4838660959702[/C][/ROW]
[ROW][C]74[/C][C]1.45[/C][C]1.402107690808[/C][C]1.497892309192[/C][/ROW]
[ROW][C]75[/C][C]1.45[/C][C]1.39134478622303[/C][C]1.50865521377697[/C][/ROW]
[ROW][C]76[/C][C]1.45[/C][C]1.38227116620891[/C][C]1.5177288337911[/C][/ROW]
[ROW][C]77[/C][C]1.45[/C][C]1.37427711211146[/C][C]1.52572288788855[/C][/ROW]
[ROW][C]78[/C][C]1.45[/C][C]1.36704991516785[/C][C]1.53295008483215[/C][/ROW]
[ROW][C]79[/C][C]1.45[/C][C]1.36040380924872[/C][C]1.53959619075129[/C][/ROW]
[ROW][C]80[/C][C]1.45[/C][C]1.3542177562352[/C][C]1.54578224376481[/C][/ROW]
[ROW][C]81[/C][C]1.45[/C][C]1.34840768216002[/C][C]1.55159231783999[/C][/ROW]
[ROW][C]82[/C][C]1.45[/C][C]1.34291237294823[/C][C]1.55708762705178[/C][/ROW]
[ROW][C]83[/C][C]1.45[/C][C]1.33768561672226[/C][C]1.56231438327775[/C][/ROW]
[ROW][C]84[/C][C]1.45[/C][C]1.33269151132787[/C][C]1.56730848867213[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204733&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204733&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
73	1.45	1.41613390402981	1.4838660959702
74	1.45	1.402107690808	1.497892309192
75	1.45	1.39134478622303	1.50865521377697
76	1.45	1.38227116620891	1.5177288337911
77	1.45	1.37427711211146	1.52572288788855
78	1.45	1.36704991516785	1.53295008483215
79	1.45	1.36040380924872	1.53959619075129
80	1.45	1.3542177562352	1.54578224376481
81	1.45	1.34840768216002	1.55159231783999
82	1.45	1.34291237294823	1.55708762705178
83	1.45	1.33768561672226	1.56231438327775
84	1.45	1.33269151132787	1.56730848867213

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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