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 05:19:30 -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/t1387189235f0c521wg9ljgxdr.htm/, Retrieved Thu, 12 Feb 2026 15:48:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232380, Retrieved Thu, 12 Feb 2026 15:48:27 +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

361

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

-       [Exponential Smoothing] [] [2013-12-16 10:19:30] [996f793b29251b773cdee78c11137970] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1,41
1,42
1,43
1,43
1,43
1,43
1,43
1,44
1,44
1,45
1,46
1,46
1,47
1,47
1,47
1,49
1,49
1,49
1,49
1,5
1,52
1,54
1,56
1,56
1,57
1,58
1,59
1,6
1,59
1,6
1,61
1,61
1,61
1,62
1,62
1,61
1,62
1,62
1,63
1,64
1,64
1,64
1,64
1,64
1,65
1,65
1,65
1,65
1,65
1,66
1,66
1,67
1,67
1,67
1,67
1,67
1,67
1,69
1,69
1,69
1,7
1,71
1,72
1,71
1,71
1,71
1,72
1,72
1,72
1,73
1,73
1,73
1,74
1,74
1,75
1,76
1,76
1,77
1,78
1,79
1,8
1,8
1,8
1,81

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=232380&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=232380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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	1
beta	0.0812546799739967
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0812546799739967 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]0.0812546799739967[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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	0.0812546799739967
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.43	1.43	0
4	1.43	1.44	-0.01
5	1.43	1.43918745320026	-0.00918745320026004
6	1.43	1.4384409296307	-0.00844092963069687
7	1.43	1.43775506459487	-0.00775506459487163
8	1.44	1.43712492930304	0.00287507069696247
9	1.44	1.44735854225242	-0.00735854225242183
10	1.45	1.44676062625663	0.0032393737433738
11	1.46	1.45702384053346	0.00297615946653984
12	1.46	1.46726566741847	-0.00726566741846546
13	1.47	1.46667529793758	0.00332470206241942
14	1.47	1.47694544553967	-0.00694544553967136
15	1.47	1.47638109558507	-0.0063810955850685
16	1.49	1.47586260170542	0.0141373982945796
17	1.49	1.49701133147951	-0.00701133147951127
18	1.49	1.49644162798395	-0.00644162798395209
19	1.49	1.4959182155636	-0.00591821556360439
20	1.5	1.49543733285197	0.00456266714803344
21	1.52	1.50580807091091	0.0141919290890919
22	1.54	1.52696123156726	0.0130387684327442
23	1.56	1.54802069252351	0.0119793074764865
24	1.56	1.56899406731883	-0.00899406731882557
25	1.57	1.56826325725717	0.00173674274283031
26	1.58	1.57840437573294	0.0015956242670645
27	1.59	1.58853402767211	0.00146597232788537
28	1.6	1.59865314478447	0.00134685521553224
29	1.59	1.60876258307398	-0.018762583073977
30	1.6	1.59723803539082	0.00276196460918454
31	1.61	1.60746245794123	0.00253754205876566
32	1.61	1.61766864510914	-0.00766864510913989
33	1.61	1.61704553180496	-0.00704553180496248
34	1.62	1.6164730493729	0.00352695062709629
35	1.62	1.62675963061739	-0.00675963061739249
36	1.61	1.62621037899483	-0.0162103789948338
37	1.62	1.61489320983735	0.00510679016264848
38	1.62	1.62530816043771	-0.00530816043771187
39	1.63	1.62487684756009	0.00512315243990491
40	1.64	1.63529312767206	0.00470687232794265
41	1.64	1.64567558307674	-0.00567558307674276
42	1.64	1.64521441539018	-0.00521441539017631
43	1.64	1.6447907197364	-0.00479071973639589
44	1.64	1.64440145133737	-0.00440145133737002
45	1.65	1.64404381281753	0.00595618718246915
46	1.65	1.65452778090091	-0.00452778090090766
47	1.65	1.65415987751281	-0.00415987751281199
48	1.65	1.65382186799678	-0.00382186799677742
49	1.65	1.6535113233358	-0.0035113233357964
50	1.66	1.65322601188186	0.00677398811813901
51	1.66	1.66377643011855	-0.00377643011854811
52	1.67	1.66346957749782	0.00653042250217872
53	1.67	1.67400020488833	-0.00400020488833075
54	1.67	1.6736751695203	-0.003675169520299
55	1.67	1.67337654479708	-0.00337654479707705
56	1.67	1.67310218473017	-0.00310218473017265
57	1.67	1.6728501177027	-0.00285011770270227
58	1.69	1.67261853230088	0.0173814676991191
59	1.69	1.69403085789625	-0.00403085789625135
60	1.69	1.69370333182787	-0.00370333182787075
61	1.7	1.69340241878536	0.00659758121464038
62	1.71	1.70393850313556	0.00606149686444235
63	1.72	1.71443102812344	0.0055689718765588
64	1.71	1.72488353315106	-0.0148835331510553
65	1.71	1.71367417642798	-0.00367417642798396
66	1.71	1.71337563239816	-0.00337563239815997
67	1.72	1.71310134646794	0.00689865353206232
68	1.72	1.72366189435294	-0.00366189435293696
69	1.72	1.72336434829919	-0.00336434829919052
70	1.73	1.72309097925482	0.0069090207451814
71	1.73	1.7336523695244	-0.00365236952440195
72	1.73	1.73335559740755	-0.00335559740755009
73	1.74	1.73308293941408	0.00691706058592212
74	1.74	1.74364498295835	-0.00364498295834781
75	1.75	1.74334881103456	0.00665118896544348
76	1.76	1.75388925126539	0.00611074873460971
77	1.76	1.76438577819822	-0.00438577819822239
78	1.77	1.76402941319429	0.00597058680571094
79	1.78	1.77451455131444	0.005485448685556
80	1.79	1.7849602696919	0.00503973030809735
81	1.8	1.79536977136524	0.0046302286347577
82	1.8	1.80574599911117	-0.00574599911116591
83	1.8	1.80527910979226	-0.00527910979225732
84	1.81	1.80485015741554	0.00514984258446005

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.43 & 1.43 & 0 \tabularnewline
4 & 1.43 & 1.44 & -0.01 \tabularnewline
5 & 1.43 & 1.43918745320026 & -0.00918745320026004 \tabularnewline
6 & 1.43 & 1.4384409296307 & -0.00844092963069687 \tabularnewline
7 & 1.43 & 1.43775506459487 & -0.00775506459487163 \tabularnewline
8 & 1.44 & 1.43712492930304 & 0.00287507069696247 \tabularnewline
9 & 1.44 & 1.44735854225242 & -0.00735854225242183 \tabularnewline
10 & 1.45 & 1.44676062625663 & 0.0032393737433738 \tabularnewline
11 & 1.46 & 1.45702384053346 & 0.00297615946653984 \tabularnewline
12 & 1.46 & 1.46726566741847 & -0.00726566741846546 \tabularnewline
13 & 1.47 & 1.46667529793758 & 0.00332470206241942 \tabularnewline
14 & 1.47 & 1.47694544553967 & -0.00694544553967136 \tabularnewline
15 & 1.47 & 1.47638109558507 & -0.0063810955850685 \tabularnewline
16 & 1.49 & 1.47586260170542 & 0.0141373982945796 \tabularnewline
17 & 1.49 & 1.49701133147951 & -0.00701133147951127 \tabularnewline
18 & 1.49 & 1.49644162798395 & -0.00644162798395209 \tabularnewline
19 & 1.49 & 1.4959182155636 & -0.00591821556360439 \tabularnewline
20 & 1.5 & 1.49543733285197 & 0.00456266714803344 \tabularnewline
21 & 1.52 & 1.50580807091091 & 0.0141919290890919 \tabularnewline
22 & 1.54 & 1.52696123156726 & 0.0130387684327442 \tabularnewline
23 & 1.56 & 1.54802069252351 & 0.0119793074764865 \tabularnewline
24 & 1.56 & 1.56899406731883 & -0.00899406731882557 \tabularnewline
25 & 1.57 & 1.56826325725717 & 0.00173674274283031 \tabularnewline
26 & 1.58 & 1.57840437573294 & 0.0015956242670645 \tabularnewline
27 & 1.59 & 1.58853402767211 & 0.00146597232788537 \tabularnewline
28 & 1.6 & 1.59865314478447 & 0.00134685521553224 \tabularnewline
29 & 1.59 & 1.60876258307398 & -0.018762583073977 \tabularnewline
30 & 1.6 & 1.59723803539082 & 0.00276196460918454 \tabularnewline
31 & 1.61 & 1.60746245794123 & 0.00253754205876566 \tabularnewline
32 & 1.61 & 1.61766864510914 & -0.00766864510913989 \tabularnewline
33 & 1.61 & 1.61704553180496 & -0.00704553180496248 \tabularnewline
34 & 1.62 & 1.6164730493729 & 0.00352695062709629 \tabularnewline
35 & 1.62 & 1.62675963061739 & -0.00675963061739249 \tabularnewline
36 & 1.61 & 1.62621037899483 & -0.0162103789948338 \tabularnewline
37 & 1.62 & 1.61489320983735 & 0.00510679016264848 \tabularnewline
38 & 1.62 & 1.62530816043771 & -0.00530816043771187 \tabularnewline
39 & 1.63 & 1.62487684756009 & 0.00512315243990491 \tabularnewline
40 & 1.64 & 1.63529312767206 & 0.00470687232794265 \tabularnewline
41 & 1.64 & 1.64567558307674 & -0.00567558307674276 \tabularnewline
42 & 1.64 & 1.64521441539018 & -0.00521441539017631 \tabularnewline
43 & 1.64 & 1.6447907197364 & -0.00479071973639589 \tabularnewline
44 & 1.64 & 1.64440145133737 & -0.00440145133737002 \tabularnewline
45 & 1.65 & 1.64404381281753 & 0.00595618718246915 \tabularnewline
46 & 1.65 & 1.65452778090091 & -0.00452778090090766 \tabularnewline
47 & 1.65 & 1.65415987751281 & -0.00415987751281199 \tabularnewline
48 & 1.65 & 1.65382186799678 & -0.00382186799677742 \tabularnewline
49 & 1.65 & 1.6535113233358 & -0.0035113233357964 \tabularnewline
50 & 1.66 & 1.65322601188186 & 0.00677398811813901 \tabularnewline
51 & 1.66 & 1.66377643011855 & -0.00377643011854811 \tabularnewline
52 & 1.67 & 1.66346957749782 & 0.00653042250217872 \tabularnewline
53 & 1.67 & 1.67400020488833 & -0.00400020488833075 \tabularnewline
54 & 1.67 & 1.6736751695203 & -0.003675169520299 \tabularnewline
55 & 1.67 & 1.67337654479708 & -0.00337654479707705 \tabularnewline
56 & 1.67 & 1.67310218473017 & -0.00310218473017265 \tabularnewline
57 & 1.67 & 1.6728501177027 & -0.00285011770270227 \tabularnewline
58 & 1.69 & 1.67261853230088 & 0.0173814676991191 \tabularnewline
59 & 1.69 & 1.69403085789625 & -0.00403085789625135 \tabularnewline
60 & 1.69 & 1.69370333182787 & -0.00370333182787075 \tabularnewline
61 & 1.7 & 1.69340241878536 & 0.00659758121464038 \tabularnewline
62 & 1.71 & 1.70393850313556 & 0.00606149686444235 \tabularnewline
63 & 1.72 & 1.71443102812344 & 0.0055689718765588 \tabularnewline
64 & 1.71 & 1.72488353315106 & -0.0148835331510553 \tabularnewline
65 & 1.71 & 1.71367417642798 & -0.00367417642798396 \tabularnewline
66 & 1.71 & 1.71337563239816 & -0.00337563239815997 \tabularnewline
67 & 1.72 & 1.71310134646794 & 0.00689865353206232 \tabularnewline
68 & 1.72 & 1.72366189435294 & -0.00366189435293696 \tabularnewline
69 & 1.72 & 1.72336434829919 & -0.00336434829919052 \tabularnewline
70 & 1.73 & 1.72309097925482 & 0.0069090207451814 \tabularnewline
71 & 1.73 & 1.7336523695244 & -0.00365236952440195 \tabularnewline
72 & 1.73 & 1.73335559740755 & -0.00335559740755009 \tabularnewline
73 & 1.74 & 1.73308293941408 & 0.00691706058592212 \tabularnewline
74 & 1.74 & 1.74364498295835 & -0.00364498295834781 \tabularnewline
75 & 1.75 & 1.74334881103456 & 0.00665118896544348 \tabularnewline
76 & 1.76 & 1.75388925126539 & 0.00611074873460971 \tabularnewline
77 & 1.76 & 1.76438577819822 & -0.00438577819822239 \tabularnewline
78 & 1.77 & 1.76402941319429 & 0.00597058680571094 \tabularnewline
79 & 1.78 & 1.77451455131444 & 0.005485448685556 \tabularnewline
80 & 1.79 & 1.7849602696919 & 0.00503973030809735 \tabularnewline
81 & 1.8 & 1.79536977136524 & 0.0046302286347577 \tabularnewline
82 & 1.8 & 1.80574599911117 & -0.00574599911116591 \tabularnewline
83 & 1.8 & 1.80527910979226 & -0.00527910979225732 \tabularnewline
84 & 1.81 & 1.80485015741554 & 0.00514984258446005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]1.43[/C][C]1.44[/C][C]-0.01[/C][/ROW]
[ROW][C]5[/C][C]1.43[/C][C]1.43918745320026[/C][C]-0.00918745320026004[/C][/ROW]
[ROW][C]6[/C][C]1.43[/C][C]1.4384409296307[/C][C]-0.00844092963069687[/C][/ROW]
[ROW][C]7[/C][C]1.43[/C][C]1.43775506459487[/C][C]-0.00775506459487163[/C][/ROW]
[ROW][C]8[/C][C]1.44[/C][C]1.43712492930304[/C][C]0.00287507069696247[/C][/ROW]
[ROW][C]9[/C][C]1.44[/C][C]1.44735854225242[/C][C]-0.00735854225242183[/C][/ROW]
[ROW][C]10[/C][C]1.45[/C][C]1.44676062625663[/C][C]0.0032393737433738[/C][/ROW]
[ROW][C]11[/C][C]1.46[/C][C]1.45702384053346[/C][C]0.00297615946653984[/C][/ROW]
[ROW][C]12[/C][C]1.46[/C][C]1.46726566741847[/C][C]-0.00726566741846546[/C][/ROW]
[ROW][C]13[/C][C]1.47[/C][C]1.46667529793758[/C][C]0.00332470206241942[/C][/ROW]
[ROW][C]14[/C][C]1.47[/C][C]1.47694544553967[/C][C]-0.00694544553967136[/C][/ROW]
[ROW][C]15[/C][C]1.47[/C][C]1.47638109558507[/C][C]-0.0063810955850685[/C][/ROW]
[ROW][C]16[/C][C]1.49[/C][C]1.47586260170542[/C][C]0.0141373982945796[/C][/ROW]
[ROW][C]17[/C][C]1.49[/C][C]1.49701133147951[/C][C]-0.00701133147951127[/C][/ROW]
[ROW][C]18[/C][C]1.49[/C][C]1.49644162798395[/C][C]-0.00644162798395209[/C][/ROW]
[ROW][C]19[/C][C]1.49[/C][C]1.4959182155636[/C][C]-0.00591821556360439[/C][/ROW]
[ROW][C]20[/C][C]1.5[/C][C]1.49543733285197[/C][C]0.00456266714803344[/C][/ROW]
[ROW][C]21[/C][C]1.52[/C][C]1.50580807091091[/C][C]0.0141919290890919[/C][/ROW]
[ROW][C]22[/C][C]1.54[/C][C]1.52696123156726[/C][C]0.0130387684327442[/C][/ROW]
[ROW][C]23[/C][C]1.56[/C][C]1.54802069252351[/C][C]0.0119793074764865[/C][/ROW]
[ROW][C]24[/C][C]1.56[/C][C]1.56899406731883[/C][C]-0.00899406731882557[/C][/ROW]
[ROW][C]25[/C][C]1.57[/C][C]1.56826325725717[/C][C]0.00173674274283031[/C][/ROW]
[ROW][C]26[/C][C]1.58[/C][C]1.57840437573294[/C][C]0.0015956242670645[/C][/ROW]
[ROW][C]27[/C][C]1.59[/C][C]1.58853402767211[/C][C]0.00146597232788537[/C][/ROW]
[ROW][C]28[/C][C]1.6[/C][C]1.59865314478447[/C][C]0.00134685521553224[/C][/ROW]
[ROW][C]29[/C][C]1.59[/C][C]1.60876258307398[/C][C]-0.018762583073977[/C][/ROW]
[ROW][C]30[/C][C]1.6[/C][C]1.59723803539082[/C][C]0.00276196460918454[/C][/ROW]
[ROW][C]31[/C][C]1.61[/C][C]1.60746245794123[/C][C]0.00253754205876566[/C][/ROW]
[ROW][C]32[/C][C]1.61[/C][C]1.61766864510914[/C][C]-0.00766864510913989[/C][/ROW]
[ROW][C]33[/C][C]1.61[/C][C]1.61704553180496[/C][C]-0.00704553180496248[/C][/ROW]
[ROW][C]34[/C][C]1.62[/C][C]1.6164730493729[/C][C]0.00352695062709629[/C][/ROW]
[ROW][C]35[/C][C]1.62[/C][C]1.62675963061739[/C][C]-0.00675963061739249[/C][/ROW]
[ROW][C]36[/C][C]1.61[/C][C]1.62621037899483[/C][C]-0.0162103789948338[/C][/ROW]
[ROW][C]37[/C][C]1.62[/C][C]1.61489320983735[/C][C]0.00510679016264848[/C][/ROW]
[ROW][C]38[/C][C]1.62[/C][C]1.62530816043771[/C][C]-0.00530816043771187[/C][/ROW]
[ROW][C]39[/C][C]1.63[/C][C]1.62487684756009[/C][C]0.00512315243990491[/C][/ROW]
[ROW][C]40[/C][C]1.64[/C][C]1.63529312767206[/C][C]0.00470687232794265[/C][/ROW]
[ROW][C]41[/C][C]1.64[/C][C]1.64567558307674[/C][C]-0.00567558307674276[/C][/ROW]
[ROW][C]42[/C][C]1.64[/C][C]1.64521441539018[/C][C]-0.00521441539017631[/C][/ROW]
[ROW][C]43[/C][C]1.64[/C][C]1.6447907197364[/C][C]-0.00479071973639589[/C][/ROW]
[ROW][C]44[/C][C]1.64[/C][C]1.64440145133737[/C][C]-0.00440145133737002[/C][/ROW]
[ROW][C]45[/C][C]1.65[/C][C]1.64404381281753[/C][C]0.00595618718246915[/C][/ROW]
[ROW][C]46[/C][C]1.65[/C][C]1.65452778090091[/C][C]-0.00452778090090766[/C][/ROW]
[ROW][C]47[/C][C]1.65[/C][C]1.65415987751281[/C][C]-0.00415987751281199[/C][/ROW]
[ROW][C]48[/C][C]1.65[/C][C]1.65382186799678[/C][C]-0.00382186799677742[/C][/ROW]
[ROW][C]49[/C][C]1.65[/C][C]1.6535113233358[/C][C]-0.0035113233357964[/C][/ROW]
[ROW][C]50[/C][C]1.66[/C][C]1.65322601188186[/C][C]0.00677398811813901[/C][/ROW]
[ROW][C]51[/C][C]1.66[/C][C]1.66377643011855[/C][C]-0.00377643011854811[/C][/ROW]
[ROW][C]52[/C][C]1.67[/C][C]1.66346957749782[/C][C]0.00653042250217872[/C][/ROW]
[ROW][C]53[/C][C]1.67[/C][C]1.67400020488833[/C][C]-0.00400020488833075[/C][/ROW]
[ROW][C]54[/C][C]1.67[/C][C]1.6736751695203[/C][C]-0.003675169520299[/C][/ROW]
[ROW][C]55[/C][C]1.67[/C][C]1.67337654479708[/C][C]-0.00337654479707705[/C][/ROW]
[ROW][C]56[/C][C]1.67[/C][C]1.67310218473017[/C][C]-0.00310218473017265[/C][/ROW]
[ROW][C]57[/C][C]1.67[/C][C]1.6728501177027[/C][C]-0.00285011770270227[/C][/ROW]
[ROW][C]58[/C][C]1.69[/C][C]1.67261853230088[/C][C]0.0173814676991191[/C][/ROW]
[ROW][C]59[/C][C]1.69[/C][C]1.69403085789625[/C][C]-0.00403085789625135[/C][/ROW]
[ROW][C]60[/C][C]1.69[/C][C]1.69370333182787[/C][C]-0.00370333182787075[/C][/ROW]
[ROW][C]61[/C][C]1.7[/C][C]1.69340241878536[/C][C]0.00659758121464038[/C][/ROW]
[ROW][C]62[/C][C]1.71[/C][C]1.70393850313556[/C][C]0.00606149686444235[/C][/ROW]
[ROW][C]63[/C][C]1.72[/C][C]1.71443102812344[/C][C]0.0055689718765588[/C][/ROW]
[ROW][C]64[/C][C]1.71[/C][C]1.72488353315106[/C][C]-0.0148835331510553[/C][/ROW]
[ROW][C]65[/C][C]1.71[/C][C]1.71367417642798[/C][C]-0.00367417642798396[/C][/ROW]
[ROW][C]66[/C][C]1.71[/C][C]1.71337563239816[/C][C]-0.00337563239815997[/C][/ROW]
[ROW][C]67[/C][C]1.72[/C][C]1.71310134646794[/C][C]0.00689865353206232[/C][/ROW]
[ROW][C]68[/C][C]1.72[/C][C]1.72366189435294[/C][C]-0.00366189435293696[/C][/ROW]
[ROW][C]69[/C][C]1.72[/C][C]1.72336434829919[/C][C]-0.00336434829919052[/C][/ROW]
[ROW][C]70[/C][C]1.73[/C][C]1.72309097925482[/C][C]0.0069090207451814[/C][/ROW]
[ROW][C]71[/C][C]1.73[/C][C]1.7336523695244[/C][C]-0.00365236952440195[/C][/ROW]
[ROW][C]72[/C][C]1.73[/C][C]1.73335559740755[/C][C]-0.00335559740755009[/C][/ROW]
[ROW][C]73[/C][C]1.74[/C][C]1.73308293941408[/C][C]0.00691706058592212[/C][/ROW]
[ROW][C]74[/C][C]1.74[/C][C]1.74364498295835[/C][C]-0.00364498295834781[/C][/ROW]
[ROW][C]75[/C][C]1.75[/C][C]1.74334881103456[/C][C]0.00665118896544348[/C][/ROW]
[ROW][C]76[/C][C]1.76[/C][C]1.75388925126539[/C][C]0.00611074873460971[/C][/ROW]
[ROW][C]77[/C][C]1.76[/C][C]1.76438577819822[/C][C]-0.00438577819822239[/C][/ROW]
[ROW][C]78[/C][C]1.77[/C][C]1.76402941319429[/C][C]0.00597058680571094[/C][/ROW]
[ROW][C]79[/C][C]1.78[/C][C]1.77451455131444[/C][C]0.005485448685556[/C][/ROW]
[ROW][C]80[/C][C]1.79[/C][C]1.7849602696919[/C][C]0.00503973030809735[/C][/ROW]
[ROW][C]81[/C][C]1.8[/C][C]1.79536977136524[/C][C]0.0046302286347577[/C][/ROW]
[ROW][C]82[/C][C]1.8[/C][C]1.80574599911117[/C][C]-0.00574599911116591[/C][/ROW]
[ROW][C]83[/C][C]1.8[/C][C]1.80527910979226[/C][C]-0.00527910979225732[/C][/ROW]
[ROW][C]84[/C][C]1.81[/C][C]1.80485015741554[/C][C]0.00514984258446005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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	1.43	1.43	0
4	1.43	1.44	-0.01
5	1.43	1.43918745320026	-0.00918745320026004
6	1.43	1.4384409296307	-0.00844092963069687
7	1.43	1.43775506459487	-0.00775506459487163
8	1.44	1.43712492930304	0.00287507069696247
9	1.44	1.44735854225242	-0.00735854225242183
10	1.45	1.44676062625663	0.0032393737433738
11	1.46	1.45702384053346	0.00297615946653984
12	1.46	1.46726566741847	-0.00726566741846546
13	1.47	1.46667529793758	0.00332470206241942
14	1.47	1.47694544553967	-0.00694544553967136
15	1.47	1.47638109558507	-0.0063810955850685
16	1.49	1.47586260170542	0.0141373982945796
17	1.49	1.49701133147951	-0.00701133147951127
18	1.49	1.49644162798395	-0.00644162798395209
19	1.49	1.4959182155636	-0.00591821556360439
20	1.5	1.49543733285197	0.00456266714803344
21	1.52	1.50580807091091	0.0141919290890919
22	1.54	1.52696123156726	0.0130387684327442
23	1.56	1.54802069252351	0.0119793074764865
24	1.56	1.56899406731883	-0.00899406731882557
25	1.57	1.56826325725717	0.00173674274283031
26	1.58	1.57840437573294	0.0015956242670645
27	1.59	1.58853402767211	0.00146597232788537
28	1.6	1.59865314478447	0.00134685521553224
29	1.59	1.60876258307398	-0.018762583073977
30	1.6	1.59723803539082	0.00276196460918454
31	1.61	1.60746245794123	0.00253754205876566
32	1.61	1.61766864510914	-0.00766864510913989
33	1.61	1.61704553180496	-0.00704553180496248
34	1.62	1.6164730493729	0.00352695062709629
35	1.62	1.62675963061739	-0.00675963061739249
36	1.61	1.62621037899483	-0.0162103789948338
37	1.62	1.61489320983735	0.00510679016264848
38	1.62	1.62530816043771	-0.00530816043771187
39	1.63	1.62487684756009	0.00512315243990491
40	1.64	1.63529312767206	0.00470687232794265
41	1.64	1.64567558307674	-0.00567558307674276
42	1.64	1.64521441539018	-0.00521441539017631
43	1.64	1.6447907197364	-0.00479071973639589
44	1.64	1.64440145133737	-0.00440145133737002
45	1.65	1.64404381281753	0.00595618718246915
46	1.65	1.65452778090091	-0.00452778090090766
47	1.65	1.65415987751281	-0.00415987751281199
48	1.65	1.65382186799678	-0.00382186799677742
49	1.65	1.6535113233358	-0.0035113233357964
50	1.66	1.65322601188186	0.00677398811813901
51	1.66	1.66377643011855	-0.00377643011854811
52	1.67	1.66346957749782	0.00653042250217872
53	1.67	1.67400020488833	-0.00400020488833075
54	1.67	1.6736751695203	-0.003675169520299
55	1.67	1.67337654479708	-0.00337654479707705
56	1.67	1.67310218473017	-0.00310218473017265
57	1.67	1.6728501177027	-0.00285011770270227
58	1.69	1.67261853230088	0.0173814676991191
59	1.69	1.69403085789625	-0.00403085789625135
60	1.69	1.69370333182787	-0.00370333182787075
61	1.7	1.69340241878536	0.00659758121464038
62	1.71	1.70393850313556	0.00606149686444235
63	1.72	1.71443102812344	0.0055689718765588
64	1.71	1.72488353315106	-0.0148835331510553
65	1.71	1.71367417642798	-0.00367417642798396
66	1.71	1.71337563239816	-0.00337563239815997
67	1.72	1.71310134646794	0.00689865353206232
68	1.72	1.72366189435294	-0.00366189435293696
69	1.72	1.72336434829919	-0.00336434829919052
70	1.73	1.72309097925482	0.0069090207451814
71	1.73	1.7336523695244	-0.00365236952440195
72	1.73	1.73335559740755	-0.00335559740755009
73	1.74	1.73308293941408	0.00691706058592212
74	1.74	1.74364498295835	-0.00364498295834781
75	1.75	1.74334881103456	0.00665118896544348
76	1.76	1.75388925126539	0.00611074873460971
77	1.76	1.76438577819822	-0.00438577819822239
78	1.77	1.76402941319429	0.00597058680571094
79	1.78	1.77451455131444	0.005485448685556
80	1.79	1.7849602696919	0.00503973030809735
81	1.8	1.79536977136524	0.0046302286347577
82	1.8	1.80574599911117	-0.00574599911116591
83	1.8	1.80527910979226	-0.00527910979225732
84	1.81	1.80485015741554	0.00514984258446005

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.81526860622666	1.80163626328387	1.82890094916944
86	1.82053721245331	1.80045962807937	1.84061479682725
87	1.82580581867997	1.80022731555352	1.85138432180642
88	1.83107442490663	1.80038654424597	1.86176230556729
89	1.83634303113328	1.80073373532879	1.87195232693778
90	1.84161163735994	1.80116980791839	1.88205346680149
91	1.8468802435866	1.80163912463774	1.89212136253545
92	1.85214884981325	1.8021075894891	1.90219011013741
93	1.85741745603991	1.80255305771572	1.9122818543641
94	1.86268606226657	1.80296055505798	1.92241156947515
95	1.86795466849322	1.80331966466392	1.93258967232252
96	1.87322327471988	1.8036229967665	1.94282355267326

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.81526860622666 & 1.80163626328387 & 1.82890094916944 \tabularnewline
86 & 1.82053721245331 & 1.80045962807937 & 1.84061479682725 \tabularnewline
87 & 1.82580581867997 & 1.80022731555352 & 1.85138432180642 \tabularnewline
88 & 1.83107442490663 & 1.80038654424597 & 1.86176230556729 \tabularnewline
89 & 1.83634303113328 & 1.80073373532879 & 1.87195232693778 \tabularnewline
90 & 1.84161163735994 & 1.80116980791839 & 1.88205346680149 \tabularnewline
91 & 1.8468802435866 & 1.80163912463774 & 1.89212136253545 \tabularnewline
92 & 1.85214884981325 & 1.8021075894891 & 1.90219011013741 \tabularnewline
93 & 1.85741745603991 & 1.80255305771572 & 1.9122818543641 \tabularnewline
94 & 1.86268606226657 & 1.80296055505798 & 1.92241156947515 \tabularnewline
95 & 1.86795466849322 & 1.80331966466392 & 1.93258967232252 \tabularnewline
96 & 1.87322327471988 & 1.8036229967665 & 1.94282355267326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232380&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]1.81526860622666[/C][C]1.80163626328387[/C][C]1.82890094916944[/C][/ROW]
[ROW][C]86[/C][C]1.82053721245331[/C][C]1.80045962807937[/C][C]1.84061479682725[/C][/ROW]
[ROW][C]87[/C][C]1.82580581867997[/C][C]1.80022731555352[/C][C]1.85138432180642[/C][/ROW]
[ROW][C]88[/C][C]1.83107442490663[/C][C]1.80038654424597[/C][C]1.86176230556729[/C][/ROW]
[ROW][C]89[/C][C]1.83634303113328[/C][C]1.80073373532879[/C][C]1.87195232693778[/C][/ROW]
[ROW][C]90[/C][C]1.84161163735994[/C][C]1.80116980791839[/C][C]1.88205346680149[/C][/ROW]
[ROW][C]91[/C][C]1.8468802435866[/C][C]1.80163912463774[/C][C]1.89212136253545[/C][/ROW]
[ROW][C]92[/C][C]1.85214884981325[/C][C]1.8021075894891[/C][C]1.90219011013741[/C][/ROW]
[ROW][C]93[/C][C]1.85741745603991[/C][C]1.80255305771572[/C][C]1.9122818543641[/C][/ROW]
[ROW][C]94[/C][C]1.86268606226657[/C][C]1.80296055505798[/C][C]1.92241156947515[/C][/ROW]
[ROW][C]95[/C][C]1.86795466849322[/C][C]1.80331966466392[/C][C]1.93258967232252[/C][/ROW]
[ROW][C]96[/C][C]1.87322327471988[/C][C]1.8036229967665[/C][C]1.94282355267326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232380&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232380&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	1.81526860622666	1.80163626328387	1.82890094916944
86	1.82053721245331	1.80045962807937	1.84061479682725
87	1.82580581867997	1.80022731555352	1.85138432180642
88	1.83107442490663	1.80038654424597	1.86176230556729
89	1.83634303113328	1.80073373532879	1.87195232693778
90	1.84161163735994	1.80116980791839	1.88205346680149
91	1.8468802435866	1.80163912463774	1.89212136253545
92	1.85214884981325	1.8021075894891	1.90219011013741
93	1.85741745603991	1.80255305771572	1.9122818543641
94	1.86268606226657	1.80296055505798	1.92241156947515
95	1.86795466849322	1.80331966466392	1.93258967232252
96	1.87322327471988	1.8036229967665	1.94282355267326

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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