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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Jan 2014 05:18:07 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/02/t1388657991vx0xzhfzzonvv06.htm/, Retrieved Tue, 21 Apr 2026 03:32:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232727, Retrieved Tue, 21 Apr 2026 03:32:57 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

402

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

-       [Exponential Smoothing] [ Exponential Smoo...] [2014-01-02 10:18:07] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Boxplots

1,26
1,26
1,28
1,34
1,39
1,47
1,57
1,63
1,72
1,43
1,35
1,41
1,44
1,43
1,43
1,42
1,45
1,51
1,48
1,48
1,45
1,38
1,46
1,45
1,41
1,45
1,47
1,47
1,53
1,56
1,66
1,79
1,78
1,46
1,41
1,43
1,43
1,45
1,35
1,35
1,29
1,29
1,26
1,3
1,3
1,16
1,24
1,15
1,21
1,22
1,17
1,13
1,15
1,2
1,23
1,25
1,38
1,28
1,26
1,25
1,26
1,28
1,31
1,22
1,23
1,36
1,54
1,58
1,44
1,29
1,28
1,23
1,2
1,22
1,19
1,17
1,22
1,29
1,39
1,53
1,82
1,77
1,63
1,57

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232727&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232727&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232727&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gertrude Mary Cox' @ cox.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=232727&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=232727&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232727&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	1.26	1.26	0
3	1.28	1.26	0.02
4	1.34	1.27999867786077	0.060001322139227
5	1.39	1.33999603349492	0.0500039665050835
6	1.47	1.38999669438972	0.0800033056102814
7	1.57	1.46999471122457	0.100005288775432
8	1.63	1.56999338895424	0.06000661104576
9	1.72	1.62999603314528	0.0900039668547172
10	1.43	1.71999405011124	-0.289994050111242
11	1.35	1.43001917062546	-0.0800191706254629
12	1.41	1.35000528982422	0.0599947101757798
13	1.44	1.40999603393201	0.0300039660679869
14	1.43	1.43999801652897	-0.00999801652897481
15	1.43	1.43000066093849	-6.60938492380581e-07
16	1.42	1.43000000004369	-0.0100000000436926
17	1.45	1.42000066106962	0.0299993389303836
18	1.51	1.44999801683486	0.0600019831651393
19	1.48	1.50999603345122	-0.0299960334512179
20	1.48	1.48000198294662	-1.98294662401288e-06
21	1.45	1.48000000013109	-0.0300000001310865
22	1.38	1.45000198320885	-0.0700019832088492
23	1.46	1.3800046276184	0.0799953723816016
24	1.45	1.45999471174901	-0.00999471174900957
25	1.41	1.45000066072002	-0.0400006607200234
26	1.45	1.41000264432213	0.0399973556778677
27	1.47	1.44999735589635	0.0200026441036461
28	1.47	1.46999867768598	1.32231402072414e-06
29	1.53	1.46999999991259	0.0600000000874141
30	1.56	1.52999603358231	0.030003966417687
31	1.66	1.55999801652895	0.100001983471048
32	1.79	1.65999338917274	0.130006610827257
33	1.78	1.789991405658	-0.00999140565800261
34	1.46	1.78000066050147	-0.320000660501468
35	1.41	1.4600211542713	-0.0500211542712965
36	1.43	1.41000330674651	0.0199966932534879
37	1.43	1.42999867807937	1.32192062807235e-06
38	1.45	1.42999999991261	0.0200000000873881
39	1.35	1.44999867786077	-0.0999986778607671
40	1.35	1.35000661060873	-6.61060873263786e-06
41	1.29	1.35000000043701	-0.0600000004370074
42	1.29	1.29000396641771	-3.96641771005513e-06
43	1.26	1.29000000026221	-0.0300000002622078
44	1.3	1.26000198320886	0.0399980167911422
45	1.3	1.29999735585265	2.6441473501837e-06
46	1.16	1.2999999998252	-0.139999999825204
47	1.24	1.16000925497458	0.0799907450254225
48	1.15	1.23999471205491	-0.0899947120549103
49	1.21	1.15000594927695	0.0599940507230483
50	1.22	1.20999603397561	0.0100039660243925
51	1.17	1.2199993386682	-0.0499993386682047
52	1.13	1.17000330530435	-0.0400033053043489
53	1.15	1.13000264449696	0.0199973555030424
54	1.2	1.14999867803559	0.0500013219644073
55	1.23	1.19999669456454	0.0300033054354587
56	1.25	1.22999801657265	0.0200019834273528
57	1.38	1.24999867772965	0.130001322270345
58	1.28	1.37999140600761	-0.0999914060076128
59	1.26	1.28000661012801	-0.0200066101280125
60	1.25	1.2600013225762	-0.0100013225762026
61	1.26	1.25000066115705	0.0099993388429549
62	1.28	1.25999933897409	0.0200006610259065
63	1.31	1.27999867781707	0.0300013221829254
64	1.22	1.30999801670375	-0.089998016703754
65	1.23	1.22000594949541	0.00999405050458813
66	1.36	1.22999933932369	0.130000660676311
67	1.54	1.35999140605135	0.180008593948651
68	1.58	1.53998810017884	0.0400118998211632
69	1.44	1.57999735493488	-0.139997354934885
70	1.29	1.44000925479973	-0.150009254799732
71	1.28	1.29000991665601	-0.0100099166560095
72	1.23	1.28000066172517	-0.0500006617251736
73	1.2	1.23000330539181	-0.0300033053918123
74	1.22	1.20000198342735	0.0199980165726501
75	1.19	1.21999867799189	-0.0299986779918913
76	1.17	1.19000198312145	-0.0200019831214466
77	1.22	1.17000132227033	0.0499986777296748
78	1.29	1.21999669473934	0.0700033052606563
79	1.39	1.2899953722942	0.100004627705795
80	1.53	1.38999338899794	0.140006611002059
81	1.82	1.52999074458838	0.290009255411622
82	1.77	1.81998082836936	-0.0499808283693608
83	1.63	1.77000330408069	-0.140003304080689
84	1.57	1.63000925519301	-0.0600092551930118

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.26 & 1.26 & 0 \tabularnewline
3 & 1.28 & 1.26 & 0.02 \tabularnewline
4 & 1.34 & 1.27999867786077 & 0.060001322139227 \tabularnewline
5 & 1.39 & 1.33999603349492 & 0.0500039665050835 \tabularnewline
6 & 1.47 & 1.38999669438972 & 0.0800033056102814 \tabularnewline
7 & 1.57 & 1.46999471122457 & 0.100005288775432 \tabularnewline
8 & 1.63 & 1.56999338895424 & 0.06000661104576 \tabularnewline
9 & 1.72 & 1.62999603314528 & 0.0900039668547172 \tabularnewline
10 & 1.43 & 1.71999405011124 & -0.289994050111242 \tabularnewline
11 & 1.35 & 1.43001917062546 & -0.0800191706254629 \tabularnewline
12 & 1.41 & 1.35000528982422 & 0.0599947101757798 \tabularnewline
13 & 1.44 & 1.40999603393201 & 0.0300039660679869 \tabularnewline
14 & 1.43 & 1.43999801652897 & -0.00999801652897481 \tabularnewline
15 & 1.43 & 1.43000066093849 & -6.60938492380581e-07 \tabularnewline
16 & 1.42 & 1.43000000004369 & -0.0100000000436926 \tabularnewline
17 & 1.45 & 1.42000066106962 & 0.0299993389303836 \tabularnewline
18 & 1.51 & 1.44999801683486 & 0.0600019831651393 \tabularnewline
19 & 1.48 & 1.50999603345122 & -0.0299960334512179 \tabularnewline
20 & 1.48 & 1.48000198294662 & -1.98294662401288e-06 \tabularnewline
21 & 1.45 & 1.48000000013109 & -0.0300000001310865 \tabularnewline
22 & 1.38 & 1.45000198320885 & -0.0700019832088492 \tabularnewline
23 & 1.46 & 1.3800046276184 & 0.0799953723816016 \tabularnewline
24 & 1.45 & 1.45999471174901 & -0.00999471174900957 \tabularnewline
25 & 1.41 & 1.45000066072002 & -0.0400006607200234 \tabularnewline
26 & 1.45 & 1.41000264432213 & 0.0399973556778677 \tabularnewline
27 & 1.47 & 1.44999735589635 & 0.0200026441036461 \tabularnewline
28 & 1.47 & 1.46999867768598 & 1.32231402072414e-06 \tabularnewline
29 & 1.53 & 1.46999999991259 & 0.0600000000874141 \tabularnewline
30 & 1.56 & 1.52999603358231 & 0.030003966417687 \tabularnewline
31 & 1.66 & 1.55999801652895 & 0.100001983471048 \tabularnewline
32 & 1.79 & 1.65999338917274 & 0.130006610827257 \tabularnewline
33 & 1.78 & 1.789991405658 & -0.00999140565800261 \tabularnewline
34 & 1.46 & 1.78000066050147 & -0.320000660501468 \tabularnewline
35 & 1.41 & 1.4600211542713 & -0.0500211542712965 \tabularnewline
36 & 1.43 & 1.41000330674651 & 0.0199966932534879 \tabularnewline
37 & 1.43 & 1.42999867807937 & 1.32192062807235e-06 \tabularnewline
38 & 1.45 & 1.42999999991261 & 0.0200000000873881 \tabularnewline
39 & 1.35 & 1.44999867786077 & -0.0999986778607671 \tabularnewline
40 & 1.35 & 1.35000661060873 & -6.61060873263786e-06 \tabularnewline
41 & 1.29 & 1.35000000043701 & -0.0600000004370074 \tabularnewline
42 & 1.29 & 1.29000396641771 & -3.96641771005513e-06 \tabularnewline
43 & 1.26 & 1.29000000026221 & -0.0300000002622078 \tabularnewline
44 & 1.3 & 1.26000198320886 & 0.0399980167911422 \tabularnewline
45 & 1.3 & 1.29999735585265 & 2.6441473501837e-06 \tabularnewline
46 & 1.16 & 1.2999999998252 & -0.139999999825204 \tabularnewline
47 & 1.24 & 1.16000925497458 & 0.0799907450254225 \tabularnewline
48 & 1.15 & 1.23999471205491 & -0.0899947120549103 \tabularnewline
49 & 1.21 & 1.15000594927695 & 0.0599940507230483 \tabularnewline
50 & 1.22 & 1.20999603397561 & 0.0100039660243925 \tabularnewline
51 & 1.17 & 1.2199993386682 & -0.0499993386682047 \tabularnewline
52 & 1.13 & 1.17000330530435 & -0.0400033053043489 \tabularnewline
53 & 1.15 & 1.13000264449696 & 0.0199973555030424 \tabularnewline
54 & 1.2 & 1.14999867803559 & 0.0500013219644073 \tabularnewline
55 & 1.23 & 1.19999669456454 & 0.0300033054354587 \tabularnewline
56 & 1.25 & 1.22999801657265 & 0.0200019834273528 \tabularnewline
57 & 1.38 & 1.24999867772965 & 0.130001322270345 \tabularnewline
58 & 1.28 & 1.37999140600761 & -0.0999914060076128 \tabularnewline
59 & 1.26 & 1.28000661012801 & -0.0200066101280125 \tabularnewline
60 & 1.25 & 1.2600013225762 & -0.0100013225762026 \tabularnewline
61 & 1.26 & 1.25000066115705 & 0.0099993388429549 \tabularnewline
62 & 1.28 & 1.25999933897409 & 0.0200006610259065 \tabularnewline
63 & 1.31 & 1.27999867781707 & 0.0300013221829254 \tabularnewline
64 & 1.22 & 1.30999801670375 & -0.089998016703754 \tabularnewline
65 & 1.23 & 1.22000594949541 & 0.00999405050458813 \tabularnewline
66 & 1.36 & 1.22999933932369 & 0.130000660676311 \tabularnewline
67 & 1.54 & 1.35999140605135 & 0.180008593948651 \tabularnewline
68 & 1.58 & 1.53998810017884 & 0.0400118998211632 \tabularnewline
69 & 1.44 & 1.57999735493488 & -0.139997354934885 \tabularnewline
70 & 1.29 & 1.44000925479973 & -0.150009254799732 \tabularnewline
71 & 1.28 & 1.29000991665601 & -0.0100099166560095 \tabularnewline
72 & 1.23 & 1.28000066172517 & -0.0500006617251736 \tabularnewline
73 & 1.2 & 1.23000330539181 & -0.0300033053918123 \tabularnewline
74 & 1.22 & 1.20000198342735 & 0.0199980165726501 \tabularnewline
75 & 1.19 & 1.21999867799189 & -0.0299986779918913 \tabularnewline
76 & 1.17 & 1.19000198312145 & -0.0200019831214466 \tabularnewline
77 & 1.22 & 1.17000132227033 & 0.0499986777296748 \tabularnewline
78 & 1.29 & 1.21999669473934 & 0.0700033052606563 \tabularnewline
79 & 1.39 & 1.2899953722942 & 0.100004627705795 \tabularnewline
80 & 1.53 & 1.38999338899794 & 0.140006611002059 \tabularnewline
81 & 1.82 & 1.52999074458838 & 0.290009255411622 \tabularnewline
82 & 1.77 & 1.81998082836936 & -0.0499808283693608 \tabularnewline
83 & 1.63 & 1.77000330408069 & -0.140003304080689 \tabularnewline
84 & 1.57 & 1.63000925519301 & -0.0600092551930118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232727&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]1.26[/C][C]1.26[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]1.28[/C][C]1.26[/C][C]0.02[/C][/ROW]
[ROW][C]4[/C][C]1.34[/C][C]1.27999867786077[/C][C]0.060001322139227[/C][/ROW]
[ROW][C]5[/C][C]1.39[/C][C]1.33999603349492[/C][C]0.0500039665050835[/C][/ROW]
[ROW][C]6[/C][C]1.47[/C][C]1.38999669438972[/C][C]0.0800033056102814[/C][/ROW]
[ROW][C]7[/C][C]1.57[/C][C]1.46999471122457[/C][C]0.100005288775432[/C][/ROW]
[ROW][C]8[/C][C]1.63[/C][C]1.56999338895424[/C][C]0.06000661104576[/C][/ROW]
[ROW][C]9[/C][C]1.72[/C][C]1.62999603314528[/C][C]0.0900039668547172[/C][/ROW]
[ROW][C]10[/C][C]1.43[/C][C]1.71999405011124[/C][C]-0.289994050111242[/C][/ROW]
[ROW][C]11[/C][C]1.35[/C][C]1.43001917062546[/C][C]-0.0800191706254629[/C][/ROW]
[ROW][C]12[/C][C]1.41[/C][C]1.35000528982422[/C][C]0.0599947101757798[/C][/ROW]
[ROW][C]13[/C][C]1.44[/C][C]1.40999603393201[/C][C]0.0300039660679869[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43999801652897[/C][C]-0.00999801652897481[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.43000066093849[/C][C]-6.60938492380581e-07[/C][/ROW]
[ROW][C]16[/C][C]1.42[/C][C]1.43000000004369[/C][C]-0.0100000000436926[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.42000066106962[/C][C]0.0299993389303836[/C][/ROW]
[ROW][C]18[/C][C]1.51[/C][C]1.44999801683486[/C][C]0.0600019831651393[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.50999603345122[/C][C]-0.0299960334512179[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.48000198294662[/C][C]-1.98294662401288e-06[/C][/ROW]
[ROW][C]21[/C][C]1.45[/C][C]1.48000000013109[/C][C]-0.0300000001310865[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.45000198320885[/C][C]-0.0700019832088492[/C][/ROW]
[ROW][C]23[/C][C]1.46[/C][C]1.3800046276184[/C][C]0.0799953723816016[/C][/ROW]
[ROW][C]24[/C][C]1.45[/C][C]1.45999471174901[/C][C]-0.00999471174900957[/C][/ROW]
[ROW][C]25[/C][C]1.41[/C][C]1.45000066072002[/C][C]-0.0400006607200234[/C][/ROW]
[ROW][C]26[/C][C]1.45[/C][C]1.41000264432213[/C][C]0.0399973556778677[/C][/ROW]
[ROW][C]27[/C][C]1.47[/C][C]1.44999735589635[/C][C]0.0200026441036461[/C][/ROW]
[ROW][C]28[/C][C]1.47[/C][C]1.46999867768598[/C][C]1.32231402072414e-06[/C][/ROW]
[ROW][C]29[/C][C]1.53[/C][C]1.46999999991259[/C][C]0.0600000000874141[/C][/ROW]
[ROW][C]30[/C][C]1.56[/C][C]1.52999603358231[/C][C]0.030003966417687[/C][/ROW]
[ROW][C]31[/C][C]1.66[/C][C]1.55999801652895[/C][C]0.100001983471048[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.65999338917274[/C][C]0.130006610827257[/C][/ROW]
[ROW][C]33[/C][C]1.78[/C][C]1.789991405658[/C][C]-0.00999140565800261[/C][/ROW]
[ROW][C]34[/C][C]1.46[/C][C]1.78000066050147[/C][C]-0.320000660501468[/C][/ROW]
[ROW][C]35[/C][C]1.41[/C][C]1.4600211542713[/C][C]-0.0500211542712965[/C][/ROW]
[ROW][C]36[/C][C]1.43[/C][C]1.41000330674651[/C][C]0.0199966932534879[/C][/ROW]
[ROW][C]37[/C][C]1.43[/C][C]1.42999867807937[/C][C]1.32192062807235e-06[/C][/ROW]
[ROW][C]38[/C][C]1.45[/C][C]1.42999999991261[/C][C]0.0200000000873881[/C][/ROW]
[ROW][C]39[/C][C]1.35[/C][C]1.44999867786077[/C][C]-0.0999986778607671[/C][/ROW]
[ROW][C]40[/C][C]1.35[/C][C]1.35000661060873[/C][C]-6.61060873263786e-06[/C][/ROW]
[ROW][C]41[/C][C]1.29[/C][C]1.35000000043701[/C][C]-0.0600000004370074[/C][/ROW]
[ROW][C]42[/C][C]1.29[/C][C]1.29000396641771[/C][C]-3.96641771005513e-06[/C][/ROW]
[ROW][C]43[/C][C]1.26[/C][C]1.29000000026221[/C][C]-0.0300000002622078[/C][/ROW]
[ROW][C]44[/C][C]1.3[/C][C]1.26000198320886[/C][C]0.0399980167911422[/C][/ROW]
[ROW][C]45[/C][C]1.3[/C][C]1.29999735585265[/C][C]2.6441473501837e-06[/C][/ROW]
[ROW][C]46[/C][C]1.16[/C][C]1.2999999998252[/C][C]-0.139999999825204[/C][/ROW]
[ROW][C]47[/C][C]1.24[/C][C]1.16000925497458[/C][C]0.0799907450254225[/C][/ROW]
[ROW][C]48[/C][C]1.15[/C][C]1.23999471205491[/C][C]-0.0899947120549103[/C][/ROW]
[ROW][C]49[/C][C]1.21[/C][C]1.15000594927695[/C][C]0.0599940507230483[/C][/ROW]
[ROW][C]50[/C][C]1.22[/C][C]1.20999603397561[/C][C]0.0100039660243925[/C][/ROW]
[ROW][C]51[/C][C]1.17[/C][C]1.2199993386682[/C][C]-0.0499993386682047[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.17000330530435[/C][C]-0.0400033053043489[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.13000264449696[/C][C]0.0199973555030424[/C][/ROW]
[ROW][C]54[/C][C]1.2[/C][C]1.14999867803559[/C][C]0.0500013219644073[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.19999669456454[/C][C]0.0300033054354587[/C][/ROW]
[ROW][C]56[/C][C]1.25[/C][C]1.22999801657265[/C][C]0.0200019834273528[/C][/ROW]
[ROW][C]57[/C][C]1.38[/C][C]1.24999867772965[/C][C]0.130001322270345[/C][/ROW]
[ROW][C]58[/C][C]1.28[/C][C]1.37999140600761[/C][C]-0.0999914060076128[/C][/ROW]
[ROW][C]59[/C][C]1.26[/C][C]1.28000661012801[/C][C]-0.0200066101280125[/C][/ROW]
[ROW][C]60[/C][C]1.25[/C][C]1.2600013225762[/C][C]-0.0100013225762026[/C][/ROW]
[ROW][C]61[/C][C]1.26[/C][C]1.25000066115705[/C][C]0.0099993388429549[/C][/ROW]
[ROW][C]62[/C][C]1.28[/C][C]1.25999933897409[/C][C]0.0200006610259065[/C][/ROW]
[ROW][C]63[/C][C]1.31[/C][C]1.27999867781707[/C][C]0.0300013221829254[/C][/ROW]
[ROW][C]64[/C][C]1.22[/C][C]1.30999801670375[/C][C]-0.089998016703754[/C][/ROW]
[ROW][C]65[/C][C]1.23[/C][C]1.22000594949541[/C][C]0.00999405050458813[/C][/ROW]
[ROW][C]66[/C][C]1.36[/C][C]1.22999933932369[/C][C]0.130000660676311[/C][/ROW]
[ROW][C]67[/C][C]1.54[/C][C]1.35999140605135[/C][C]0.180008593948651[/C][/ROW]
[ROW][C]68[/C][C]1.58[/C][C]1.53998810017884[/C][C]0.0400118998211632[/C][/ROW]
[ROW][C]69[/C][C]1.44[/C][C]1.57999735493488[/C][C]-0.139997354934885[/C][/ROW]
[ROW][C]70[/C][C]1.29[/C][C]1.44000925479973[/C][C]-0.150009254799732[/C][/ROW]
[ROW][C]71[/C][C]1.28[/C][C]1.29000991665601[/C][C]-0.0100099166560095[/C][/ROW]
[ROW][C]72[/C][C]1.23[/C][C]1.28000066172517[/C][C]-0.0500006617251736[/C][/ROW]
[ROW][C]73[/C][C]1.2[/C][C]1.23000330539181[/C][C]-0.0300033053918123[/C][/ROW]
[ROW][C]74[/C][C]1.22[/C][C]1.20000198342735[/C][C]0.0199980165726501[/C][/ROW]
[ROW][C]75[/C][C]1.19[/C][C]1.21999867799189[/C][C]-0.0299986779918913[/C][/ROW]
[ROW][C]76[/C][C]1.17[/C][C]1.19000198312145[/C][C]-0.0200019831214466[/C][/ROW]
[ROW][C]77[/C][C]1.22[/C][C]1.17000132227033[/C][C]0.0499986777296748[/C][/ROW]
[ROW][C]78[/C][C]1.29[/C][C]1.21999669473934[/C][C]0.0700033052606563[/C][/ROW]
[ROW][C]79[/C][C]1.39[/C][C]1.2899953722942[/C][C]0.100004627705795[/C][/ROW]
[ROW][C]80[/C][C]1.53[/C][C]1.38999338899794[/C][C]0.140006611002059[/C][/ROW]
[ROW][C]81[/C][C]1.82[/C][C]1.52999074458838[/C][C]0.290009255411622[/C][/ROW]
[ROW][C]82[/C][C]1.77[/C][C]1.81998082836936[/C][C]-0.0499808283693608[/C][/ROW]
[ROW][C]83[/C][C]1.63[/C][C]1.77000330408069[/C][C]-0.140003304080689[/C][/ROW]
[ROW][C]84[/C][C]1.57[/C][C]1.63000925519301[/C][C]-0.0600092551930118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232727&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232727&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	1.26	1.26	0
3	1.28	1.26	0.02
4	1.34	1.27999867786077	0.060001322139227
5	1.39	1.33999603349492	0.0500039665050835
6	1.47	1.38999669438972	0.0800033056102814
7	1.57	1.46999471122457	0.100005288775432
8	1.63	1.56999338895424	0.06000661104576
9	1.72	1.62999603314528	0.0900039668547172
10	1.43	1.71999405011124	-0.289994050111242
11	1.35	1.43001917062546	-0.0800191706254629
12	1.41	1.35000528982422	0.0599947101757798
13	1.44	1.40999603393201	0.0300039660679869
14	1.43	1.43999801652897	-0.00999801652897481
15	1.43	1.43000066093849	-6.60938492380581e-07
16	1.42	1.43000000004369	-0.0100000000436926
17	1.45	1.42000066106962	0.0299993389303836
18	1.51	1.44999801683486	0.0600019831651393
19	1.48	1.50999603345122	-0.0299960334512179
20	1.48	1.48000198294662	-1.98294662401288e-06
21	1.45	1.48000000013109	-0.0300000001310865
22	1.38	1.45000198320885	-0.0700019832088492
23	1.46	1.3800046276184	0.0799953723816016
24	1.45	1.45999471174901	-0.00999471174900957
25	1.41	1.45000066072002	-0.0400006607200234
26	1.45	1.41000264432213	0.0399973556778677
27	1.47	1.44999735589635	0.0200026441036461
28	1.47	1.46999867768598	1.32231402072414e-06
29	1.53	1.46999999991259	0.0600000000874141
30	1.56	1.52999603358231	0.030003966417687
31	1.66	1.55999801652895	0.100001983471048
32	1.79	1.65999338917274	0.130006610827257
33	1.78	1.789991405658	-0.00999140565800261
34	1.46	1.78000066050147	-0.320000660501468
35	1.41	1.4600211542713	-0.0500211542712965
36	1.43	1.41000330674651	0.0199966932534879
37	1.43	1.42999867807937	1.32192062807235e-06
38	1.45	1.42999999991261	0.0200000000873881
39	1.35	1.44999867786077	-0.0999986778607671
40	1.35	1.35000661060873	-6.61060873263786e-06
41	1.29	1.35000000043701	-0.0600000004370074
42	1.29	1.29000396641771	-3.96641771005513e-06
43	1.26	1.29000000026221	-0.0300000002622078
44	1.3	1.26000198320886	0.0399980167911422
45	1.3	1.29999735585265	2.6441473501837e-06
46	1.16	1.2999999998252	-0.139999999825204
47	1.24	1.16000925497458	0.0799907450254225
48	1.15	1.23999471205491	-0.0899947120549103
49	1.21	1.15000594927695	0.0599940507230483
50	1.22	1.20999603397561	0.0100039660243925
51	1.17	1.2199993386682	-0.0499993386682047
52	1.13	1.17000330530435	-0.0400033053043489
53	1.15	1.13000264449696	0.0199973555030424
54	1.2	1.14999867803559	0.0500013219644073
55	1.23	1.19999669456454	0.0300033054354587
56	1.25	1.22999801657265	0.0200019834273528
57	1.38	1.24999867772965	0.130001322270345
58	1.28	1.37999140600761	-0.0999914060076128
59	1.26	1.28000661012801	-0.0200066101280125
60	1.25	1.2600013225762	-0.0100013225762026
61	1.26	1.25000066115705	0.0099993388429549
62	1.28	1.25999933897409	0.0200006610259065
63	1.31	1.27999867781707	0.0300013221829254
64	1.22	1.30999801670375	-0.089998016703754
65	1.23	1.22000594949541	0.00999405050458813
66	1.36	1.22999933932369	0.130000660676311
67	1.54	1.35999140605135	0.180008593948651
68	1.58	1.53998810017884	0.0400118998211632
69	1.44	1.57999735493488	-0.139997354934885
70	1.29	1.44000925479973	-0.150009254799732
71	1.28	1.29000991665601	-0.0100099166560095
72	1.23	1.28000066172517	-0.0500006617251736
73	1.2	1.23000330539181	-0.0300033053918123
74	1.22	1.20000198342735	0.0199980165726501
75	1.19	1.21999867799189	-0.0299986779918913
76	1.17	1.19000198312145	-0.0200019831214466
77	1.22	1.17000132227033	0.0499986777296748
78	1.29	1.21999669473934	0.0700033052606563
79	1.39	1.2899953722942	0.100004627705795
80	1.53	1.38999338899794	0.140006611002059
81	1.82	1.52999074458838	0.290009255411622
82	1.77	1.81998082836936	-0.0499808283693608
83	1.63	1.77000330408069	-0.140003304080689
84	1.57	1.63000925519301	-0.0600092551930118

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.57000396702951	1.39802333867659	1.74198459538244
86	1.57000396702951	1.32679466899405	1.81321326506498
87	1.57000396702951	1.27213790858522	1.86787002547381
88	1.57000396702951	1.22605976385787	1.91394817020116
89	1.57000396702951	1.18546392877912	1.95454400527991
90	1.57000396702951	1.14876238890616	1.99124554515287
91	1.57000396702951	1.11501177669863	2.02499615736039
92	1.57000396702951	1.08359742987738	2.05641050418165
93	1.57000396702951	1.05409239950406	2.08591553455496
94	1.57000396702951	1.02618582497391	2.11382210908511
95	1.57000396702951	0.999643030647084	2.14036490341194
96	1.57000396702951	0.974281696274693	2.16572623778433

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.57000396702951 & 1.39802333867659 & 1.74198459538244 \tabularnewline
86 & 1.57000396702951 & 1.32679466899405 & 1.81321326506498 \tabularnewline
87 & 1.57000396702951 & 1.27213790858522 & 1.86787002547381 \tabularnewline
88 & 1.57000396702951 & 1.22605976385787 & 1.91394817020116 \tabularnewline
89 & 1.57000396702951 & 1.18546392877912 & 1.95454400527991 \tabularnewline
90 & 1.57000396702951 & 1.14876238890616 & 1.99124554515287 \tabularnewline
91 & 1.57000396702951 & 1.11501177669863 & 2.02499615736039 \tabularnewline
92 & 1.57000396702951 & 1.08359742987738 & 2.05641050418165 \tabularnewline
93 & 1.57000396702951 & 1.05409239950406 & 2.08591553455496 \tabularnewline
94 & 1.57000396702951 & 1.02618582497391 & 2.11382210908511 \tabularnewline
95 & 1.57000396702951 & 0.999643030647084 & 2.14036490341194 \tabularnewline
96 & 1.57000396702951 & 0.974281696274693 & 2.16572623778433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232727&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]1.57000396702951[/C][C]1.39802333867659[/C][C]1.74198459538244[/C][/ROW]
[ROW][C]86[/C][C]1.57000396702951[/C][C]1.32679466899405[/C][C]1.81321326506498[/C][/ROW]
[ROW][C]87[/C][C]1.57000396702951[/C][C]1.27213790858522[/C][C]1.86787002547381[/C][/ROW]
[ROW][C]88[/C][C]1.57000396702951[/C][C]1.22605976385787[/C][C]1.91394817020116[/C][/ROW]
[ROW][C]89[/C][C]1.57000396702951[/C][C]1.18546392877912[/C][C]1.95454400527991[/C][/ROW]
[ROW][C]90[/C][C]1.57000396702951[/C][C]1.14876238890616[/C][C]1.99124554515287[/C][/ROW]
[ROW][C]91[/C][C]1.57000396702951[/C][C]1.11501177669863[/C][C]2.02499615736039[/C][/ROW]
[ROW][C]92[/C][C]1.57000396702951[/C][C]1.08359742987738[/C][C]2.05641050418165[/C][/ROW]
[ROW][C]93[/C][C]1.57000396702951[/C][C]1.05409239950406[/C][C]2.08591553455496[/C][/ROW]
[ROW][C]94[/C][C]1.57000396702951[/C][C]1.02618582497391[/C][C]2.11382210908511[/C][/ROW]
[ROW][C]95[/C][C]1.57000396702951[/C][C]0.999643030647084[/C][C]2.14036490341194[/C][/ROW]
[ROW][C]96[/C][C]1.57000396702951[/C][C]0.974281696274693[/C][C]2.16572623778433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232727&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232727&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	1.57000396702951	1.39802333867659	1.74198459538244
86	1.57000396702951	1.32679466899405	1.81321326506498
87	1.57000396702951	1.27213790858522	1.86787002547381
88	1.57000396702951	1.22605976385787	1.91394817020116
89	1.57000396702951	1.18546392877912	1.95454400527991
90	1.57000396702951	1.14876238890616	1.99124554515287
91	1.57000396702951	1.11501177669863	2.02499615736039
92	1.57000396702951	1.08359742987738	2.05641050418165
93	1.57000396702951	1.05409239950406	2.08591553455496
94	1.57000396702951	1.02618582497391	2.11382210908511
95	1.57000396702951	0.999643030647084	2.14036490341194
96	1.57000396702951	0.974281696274693	2.16572623778433

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