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

Sun, 25 May 2008 10:19:18 -0600

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/2008/May/25/t1211732454hb4h9tpt4dm9fo8.htm/, Retrieved Thu, 16 May 2024 02:04:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13179, Retrieved Thu, 16 May 2024 02:04:47 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

Single Multiplicatief

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

172

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

-       [Exponential Smoothing] [ Gemiddelde consu...] [2008-05-25 16:19:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13179&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13179&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13179&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13179&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13179&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13179&T=1

As an alternative you can also use a QR Code:

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

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	4.07	4.07	0
3	4.08	4.07	0.00999999999999979
4	4.09	4.08	0.00999999999999979
5	4.08	4.09	-0.00999999999999979
6	4.09	4.08	0.00999999999999979
7	4.12	4.09	0.0300000000000002
8	4.14	4.12	0.0199999999999996
9	4.14	4.14	0
10	4.14	4.14	0
11	4.14	4.14	0
12	4.14	4.14	0
13	4.23	4.14	0.0900000000000007
14	4.29	4.23	0.0599999999999996
15	4.32	4.29	0.0300000000000002
16	4.33	4.32	0.00999999999999979
17	4.35	4.33	0.0199999999999996
18	4.35	4.35	0
19	4.35	4.35	0
20	4.35	4.35	0
21	4.36	4.35	0.0100000000000007
22	4.36	4.36	0
23	4.38	4.36	0.0199999999999996
24	4.4	4.38	0.0200000000000005
25	4.4	4.4	0
26	4.4	4.4	0
27	4.43	4.4	0.0299999999999994
28	4.44	4.43	0.0100000000000007
29	4.46	4.44	0.0199999999999996
30	4.47	4.46	0.00999999999999979
31	4.49	4.47	0.0200000000000005
32	4.49	4.49	0
33	4.57	4.49	0.08
34	4.62	4.57	0.0499999999999998
35	4.64	4.62	0.0199999999999996
36	4.66	4.64	0.0200000000000005
37	4.67	4.66	0.00999999999999979
38	4.68	4.67	0.00999999999999979
39	4.72	4.68	0.04
40	4.74	4.72	0.0200000000000005
41	4.75	4.74	0.00999999999999979
42	4.76	4.75	0.00999999999999979
43	4.77	4.76	0.00999999999999979
44	4.76	4.77	-0.00999999999999979
45	4.77	4.76	0.00999999999999979
46	4.77	4.77	0
47	4.78	4.77	0.0100000000000007
48	4.81	4.78	0.0299999999999994
49	4.81	4.81	0
50	4.85	4.81	0.04
51	4.92	4.85	0.0700000000000003
52	4.96	4.92	0.04
53	4.95	4.96	-0.00999999999999979
54	4.96	4.95	0.00999999999999979
55	4.97	4.96	0.00999999999999979
56	5	4.97	0.0300000000000002
57	5	5	0
58	5.01	5	0.00999999999999979
59	5.01	5.01	0
60	5.02	5.01	0.00999999999999979
61	5.04	5.02	0.0200000000000005
62	5.04	5.04	0
63	5.19	5.04	0.150000000000000
64	5.22	5.19	0.0299999999999994
65	5.22	5.22	0
66	5.22	5.22	0
67	5.24	5.22	0.0200000000000005
68	5.28	5.24	0.04
69	5.34	5.28	0.0599999999999996
70	5.36	5.34	0.0200000000000005
71	5.38	5.36	0.0199999999999996
72	5.39	5.38	0.00999999999999979
73	5.41	5.39	0.0200000000000005
74	5.44	5.41	0.0300000000000002
75	5.51	5.44	0.0699999999999994
76	5.55	5.51	0.04
77	5.56	5.55	0.00999999999999979
78	5.57	5.56	0.0100000000000007
79	5.58	5.57	0.00999999999999979
80	5.58	5.58	0
81	5.59	5.58	0.00999999999999979
82	5.61	5.59	0.0200000000000005
83	5.63	5.61	0.0199999999999996
84	5.64	5.63	0.00999999999999979
85	5.64	5.64	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4.07 & 4.07 & 0 \tabularnewline
3 & 4.08 & 4.07 & 0.00999999999999979 \tabularnewline
4 & 4.09 & 4.08 & 0.00999999999999979 \tabularnewline
5 & 4.08 & 4.09 & -0.00999999999999979 \tabularnewline
6 & 4.09 & 4.08 & 0.00999999999999979 \tabularnewline
7 & 4.12 & 4.09 & 0.0300000000000002 \tabularnewline
8 & 4.14 & 4.12 & 0.0199999999999996 \tabularnewline
9 & 4.14 & 4.14 & 0 \tabularnewline
10 & 4.14 & 4.14 & 0 \tabularnewline
11 & 4.14 & 4.14 & 0 \tabularnewline
12 & 4.14 & 4.14 & 0 \tabularnewline
13 & 4.23 & 4.14 & 0.0900000000000007 \tabularnewline
14 & 4.29 & 4.23 & 0.0599999999999996 \tabularnewline
15 & 4.32 & 4.29 & 0.0300000000000002 \tabularnewline
16 & 4.33 & 4.32 & 0.00999999999999979 \tabularnewline
17 & 4.35 & 4.33 & 0.0199999999999996 \tabularnewline
18 & 4.35 & 4.35 & 0 \tabularnewline
19 & 4.35 & 4.35 & 0 \tabularnewline
20 & 4.35 & 4.35 & 0 \tabularnewline
21 & 4.36 & 4.35 & 0.0100000000000007 \tabularnewline
22 & 4.36 & 4.36 & 0 \tabularnewline
23 & 4.38 & 4.36 & 0.0199999999999996 \tabularnewline
24 & 4.4 & 4.38 & 0.0200000000000005 \tabularnewline
25 & 4.4 & 4.4 & 0 \tabularnewline
26 & 4.4 & 4.4 & 0 \tabularnewline
27 & 4.43 & 4.4 & 0.0299999999999994 \tabularnewline
28 & 4.44 & 4.43 & 0.0100000000000007 \tabularnewline
29 & 4.46 & 4.44 & 0.0199999999999996 \tabularnewline
30 & 4.47 & 4.46 & 0.00999999999999979 \tabularnewline
31 & 4.49 & 4.47 & 0.0200000000000005 \tabularnewline
32 & 4.49 & 4.49 & 0 \tabularnewline
33 & 4.57 & 4.49 & 0.08 \tabularnewline
34 & 4.62 & 4.57 & 0.0499999999999998 \tabularnewline
35 & 4.64 & 4.62 & 0.0199999999999996 \tabularnewline
36 & 4.66 & 4.64 & 0.0200000000000005 \tabularnewline
37 & 4.67 & 4.66 & 0.00999999999999979 \tabularnewline
38 & 4.68 & 4.67 & 0.00999999999999979 \tabularnewline
39 & 4.72 & 4.68 & 0.04 \tabularnewline
40 & 4.74 & 4.72 & 0.0200000000000005 \tabularnewline
41 & 4.75 & 4.74 & 0.00999999999999979 \tabularnewline
42 & 4.76 & 4.75 & 0.00999999999999979 \tabularnewline
43 & 4.77 & 4.76 & 0.00999999999999979 \tabularnewline
44 & 4.76 & 4.77 & -0.00999999999999979 \tabularnewline
45 & 4.77 & 4.76 & 0.00999999999999979 \tabularnewline
46 & 4.77 & 4.77 & 0 \tabularnewline
47 & 4.78 & 4.77 & 0.0100000000000007 \tabularnewline
48 & 4.81 & 4.78 & 0.0299999999999994 \tabularnewline
49 & 4.81 & 4.81 & 0 \tabularnewline
50 & 4.85 & 4.81 & 0.04 \tabularnewline
51 & 4.92 & 4.85 & 0.0700000000000003 \tabularnewline
52 & 4.96 & 4.92 & 0.04 \tabularnewline
53 & 4.95 & 4.96 & -0.00999999999999979 \tabularnewline
54 & 4.96 & 4.95 & 0.00999999999999979 \tabularnewline
55 & 4.97 & 4.96 & 0.00999999999999979 \tabularnewline
56 & 5 & 4.97 & 0.0300000000000002 \tabularnewline
57 & 5 & 5 & 0 \tabularnewline
58 & 5.01 & 5 & 0.00999999999999979 \tabularnewline
59 & 5.01 & 5.01 & 0 \tabularnewline
60 & 5.02 & 5.01 & 0.00999999999999979 \tabularnewline
61 & 5.04 & 5.02 & 0.0200000000000005 \tabularnewline
62 & 5.04 & 5.04 & 0 \tabularnewline
63 & 5.19 & 5.04 & 0.150000000000000 \tabularnewline
64 & 5.22 & 5.19 & 0.0299999999999994 \tabularnewline
65 & 5.22 & 5.22 & 0 \tabularnewline
66 & 5.22 & 5.22 & 0 \tabularnewline
67 & 5.24 & 5.22 & 0.0200000000000005 \tabularnewline
68 & 5.28 & 5.24 & 0.04 \tabularnewline
69 & 5.34 & 5.28 & 0.0599999999999996 \tabularnewline
70 & 5.36 & 5.34 & 0.0200000000000005 \tabularnewline
71 & 5.38 & 5.36 & 0.0199999999999996 \tabularnewline
72 & 5.39 & 5.38 & 0.00999999999999979 \tabularnewline
73 & 5.41 & 5.39 & 0.0200000000000005 \tabularnewline
74 & 5.44 & 5.41 & 0.0300000000000002 \tabularnewline
75 & 5.51 & 5.44 & 0.0699999999999994 \tabularnewline
76 & 5.55 & 5.51 & 0.04 \tabularnewline
77 & 5.56 & 5.55 & 0.00999999999999979 \tabularnewline
78 & 5.57 & 5.56 & 0.0100000000000007 \tabularnewline
79 & 5.58 & 5.57 & 0.00999999999999979 \tabularnewline
80 & 5.58 & 5.58 & 0 \tabularnewline
81 & 5.59 & 5.58 & 0.00999999999999979 \tabularnewline
82 & 5.61 & 5.59 & 0.0200000000000005 \tabularnewline
83 & 5.63 & 5.61 & 0.0199999999999996 \tabularnewline
84 & 5.64 & 5.63 & 0.00999999999999979 \tabularnewline
85 & 5.64 & 5.64 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13179&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]4.07[/C][C]4.07[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]4.08[/C][C]4.07[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]4.09[/C][C]4.08[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]5[/C][C]4.08[/C][C]4.09[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]6[/C][C]4.09[/C][C]4.08[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]7[/C][C]4.12[/C][C]4.09[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]8[/C][C]4.14[/C][C]4.12[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]9[/C][C]4.14[/C][C]4.14[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]4.14[/C][C]4.14[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]4.14[/C][C]4.14[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]4.14[/C][C]4.14[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]4.23[/C][C]4.14[/C][C]0.0900000000000007[/C][/ROW]
[ROW][C]14[/C][C]4.29[/C][C]4.23[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]15[/C][C]4.32[/C][C]4.29[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]16[/C][C]4.33[/C][C]4.32[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]17[/C][C]4.35[/C][C]4.33[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]18[/C][C]4.35[/C][C]4.35[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]4.35[/C][C]4.35[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]4.35[/C][C]4.35[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]4.36[/C][C]4.35[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]22[/C][C]4.36[/C][C]4.36[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]4.38[/C][C]4.36[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]24[/C][C]4.4[/C][C]4.38[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]4.4[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]4.4[/C][C]4.4[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]4.43[/C][C]4.4[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]28[/C][C]4.44[/C][C]4.43[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]29[/C][C]4.46[/C][C]4.44[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]30[/C][C]4.47[/C][C]4.46[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]31[/C][C]4.49[/C][C]4.47[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]32[/C][C]4.49[/C][C]4.49[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]4.57[/C][C]4.49[/C][C]0.08[/C][/ROW]
[ROW][C]34[/C][C]4.62[/C][C]4.57[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]35[/C][C]4.64[/C][C]4.62[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]36[/C][C]4.66[/C][C]4.64[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]37[/C][C]4.67[/C][C]4.66[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]38[/C][C]4.68[/C][C]4.67[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]39[/C][C]4.72[/C][C]4.68[/C][C]0.04[/C][/ROW]
[ROW][C]40[/C][C]4.74[/C][C]4.72[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]41[/C][C]4.75[/C][C]4.74[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]42[/C][C]4.76[/C][C]4.75[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]43[/C][C]4.77[/C][C]4.76[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]44[/C][C]4.76[/C][C]4.77[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]45[/C][C]4.77[/C][C]4.76[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]46[/C][C]4.77[/C][C]4.77[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]4.78[/C][C]4.77[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]48[/C][C]4.81[/C][C]4.78[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]49[/C][C]4.81[/C][C]4.81[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]4.85[/C][C]4.81[/C][C]0.04[/C][/ROW]
[ROW][C]51[/C][C]4.92[/C][C]4.85[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]52[/C][C]4.96[/C][C]4.92[/C][C]0.04[/C][/ROW]
[ROW][C]53[/C][C]4.95[/C][C]4.96[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]54[/C][C]4.96[/C][C]4.95[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]55[/C][C]4.97[/C][C]4.96[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]56[/C][C]5[/C][C]4.97[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]5[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]5.01[/C][C]5[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]59[/C][C]5.01[/C][C]5.01[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]5.02[/C][C]5.01[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]61[/C][C]5.04[/C][C]5.02[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]62[/C][C]5.04[/C][C]5.04[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]5.19[/C][C]5.04[/C][C]0.150000000000000[/C][/ROW]
[ROW][C]64[/C][C]5.22[/C][C]5.19[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]65[/C][C]5.22[/C][C]5.22[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]5.22[/C][C]5.22[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]5.24[/C][C]5.22[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]68[/C][C]5.28[/C][C]5.24[/C][C]0.04[/C][/ROW]
[ROW][C]69[/C][C]5.34[/C][C]5.28[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]70[/C][C]5.36[/C][C]5.34[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]71[/C][C]5.38[/C][C]5.36[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]72[/C][C]5.39[/C][C]5.38[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]73[/C][C]5.41[/C][C]5.39[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]74[/C][C]5.44[/C][C]5.41[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]75[/C][C]5.51[/C][C]5.44[/C][C]0.0699999999999994[/C][/ROW]
[ROW][C]76[/C][C]5.55[/C][C]5.51[/C][C]0.04[/C][/ROW]
[ROW][C]77[/C][C]5.56[/C][C]5.55[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]78[/C][C]5.57[/C][C]5.56[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]79[/C][C]5.58[/C][C]5.57[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]80[/C][C]5.58[/C][C]5.58[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]5.59[/C][C]5.58[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]82[/C][C]5.61[/C][C]5.59[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]83[/C][C]5.63[/C][C]5.61[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]84[/C][C]5.64[/C][C]5.63[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]85[/C][C]5.64[/C][C]5.64[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13179&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13179&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	4.07	4.07	0
3	4.08	4.07	0.00999999999999979
4	4.09	4.08	0.00999999999999979
5	4.08	4.09	-0.00999999999999979
6	4.09	4.08	0.00999999999999979
7	4.12	4.09	0.0300000000000002
8	4.14	4.12	0.0199999999999996
9	4.14	4.14	0
10	4.14	4.14	0
11	4.14	4.14	0
12	4.14	4.14	0
13	4.23	4.14	0.0900000000000007
14	4.29	4.23	0.0599999999999996
15	4.32	4.29	0.0300000000000002
16	4.33	4.32	0.00999999999999979
17	4.35	4.33	0.0199999999999996
18	4.35	4.35	0
19	4.35	4.35	0
20	4.35	4.35	0
21	4.36	4.35	0.0100000000000007
22	4.36	4.36	0
23	4.38	4.36	0.0199999999999996
24	4.4	4.38	0.0200000000000005
25	4.4	4.4	0
26	4.4	4.4	0
27	4.43	4.4	0.0299999999999994
28	4.44	4.43	0.0100000000000007
29	4.46	4.44	0.0199999999999996
30	4.47	4.46	0.00999999999999979
31	4.49	4.47	0.0200000000000005
32	4.49	4.49	0
33	4.57	4.49	0.08
34	4.62	4.57	0.0499999999999998
35	4.64	4.62	0.0199999999999996
36	4.66	4.64	0.0200000000000005
37	4.67	4.66	0.00999999999999979
38	4.68	4.67	0.00999999999999979
39	4.72	4.68	0.04
40	4.74	4.72	0.0200000000000005
41	4.75	4.74	0.00999999999999979
42	4.76	4.75	0.00999999999999979
43	4.77	4.76	0.00999999999999979
44	4.76	4.77	-0.00999999999999979
45	4.77	4.76	0.00999999999999979
46	4.77	4.77	0
47	4.78	4.77	0.0100000000000007
48	4.81	4.78	0.0299999999999994
49	4.81	4.81	0
50	4.85	4.81	0.04
51	4.92	4.85	0.0700000000000003
52	4.96	4.92	0.04
53	4.95	4.96	-0.00999999999999979
54	4.96	4.95	0.00999999999999979
55	4.97	4.96	0.00999999999999979
56	5	4.97	0.0300000000000002
57	5	5	0
58	5.01	5	0.00999999999999979
59	5.01	5.01	0
60	5.02	5.01	0.00999999999999979
61	5.04	5.02	0.0200000000000005
62	5.04	5.04	0
63	5.19	5.04	0.150000000000000
64	5.22	5.19	0.0299999999999994
65	5.22	5.22	0
66	5.22	5.22	0
67	5.24	5.22	0.0200000000000005
68	5.28	5.24	0.04
69	5.34	5.28	0.0599999999999996
70	5.36	5.34	0.0200000000000005
71	5.38	5.36	0.0199999999999996
72	5.39	5.38	0.00999999999999979
73	5.41	5.39	0.0200000000000005
74	5.44	5.41	0.0300000000000002
75	5.51	5.44	0.0699999999999994
76	5.55	5.51	0.04
77	5.56	5.55	0.00999999999999979
78	5.57	5.56	0.0100000000000007
79	5.58	5.57	0.00999999999999979
80	5.58	5.58	0
81	5.59	5.58	0.00999999999999979
82	5.61	5.59	0.0200000000000005
83	5.63	5.61	0.0199999999999996
84	5.64	5.63	0.00999999999999979
85	5.64	5.64	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	5.64	5.59162787205843	5.68837212794157
87	5.64	5.57159148062419	5.70840851937581
88	5.64	5.55621701673499	5.72378298326501
89	5.64	5.54325574411687	5.73674425588313
90	5.64	5.53183663370634	5.74816336629366
91	5.64	5.52151296877054	5.75848703122946
92	5.64	5.51201937907962	5.76798062092038
93	5.64	5.50318296124838	5.77681703875162
94	5.64	5.4948836161753	5.7851163838247
95	5.64	5.48703390043558	5.79296609956442
96	5.64	5.47956780130676	5.80043219869324
97	5.64	5.47243403346997	5.80756596653003

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 5.64 & 5.59162787205843 & 5.68837212794157 \tabularnewline
87 & 5.64 & 5.57159148062419 & 5.70840851937581 \tabularnewline
88 & 5.64 & 5.55621701673499 & 5.72378298326501 \tabularnewline
89 & 5.64 & 5.54325574411687 & 5.73674425588313 \tabularnewline
90 & 5.64 & 5.53183663370634 & 5.74816336629366 \tabularnewline
91 & 5.64 & 5.52151296877054 & 5.75848703122946 \tabularnewline
92 & 5.64 & 5.51201937907962 & 5.76798062092038 \tabularnewline
93 & 5.64 & 5.50318296124838 & 5.77681703875162 \tabularnewline
94 & 5.64 & 5.4948836161753 & 5.7851163838247 \tabularnewline
95 & 5.64 & 5.48703390043558 & 5.79296609956442 \tabularnewline
96 & 5.64 & 5.47956780130676 & 5.80043219869324 \tabularnewline
97 & 5.64 & 5.47243403346997 & 5.80756596653003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13179&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]86[/C][C]5.64[/C][C]5.59162787205843[/C][C]5.68837212794157[/C][/ROW]
[ROW][C]87[/C][C]5.64[/C][C]5.57159148062419[/C][C]5.70840851937581[/C][/ROW]
[ROW][C]88[/C][C]5.64[/C][C]5.55621701673499[/C][C]5.72378298326501[/C][/ROW]
[ROW][C]89[/C][C]5.64[/C][C]5.54325574411687[/C][C]5.73674425588313[/C][/ROW]
[ROW][C]90[/C][C]5.64[/C][C]5.53183663370634[/C][C]5.74816336629366[/C][/ROW]
[ROW][C]91[/C][C]5.64[/C][C]5.52151296877054[/C][C]5.75848703122946[/C][/ROW]
[ROW][C]92[/C][C]5.64[/C][C]5.51201937907962[/C][C]5.76798062092038[/C][/ROW]
[ROW][C]93[/C][C]5.64[/C][C]5.50318296124838[/C][C]5.77681703875162[/C][/ROW]
[ROW][C]94[/C][C]5.64[/C][C]5.4948836161753[/C][C]5.7851163838247[/C][/ROW]
[ROW][C]95[/C][C]5.64[/C][C]5.48703390043558[/C][C]5.79296609956442[/C][/ROW]
[ROW][C]96[/C][C]5.64[/C][C]5.47956780130676[/C][C]5.80043219869324[/C][/ROW]
[ROW][C]97[/C][C]5.64[/C][C]5.47243403346997[/C][C]5.80756596653003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13179&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13179&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
86	5.64	5.59162787205843	5.68837212794157
87	5.64	5.57159148062419	5.70840851937581
88	5.64	5.55621701673499	5.72378298326501
89	5.64	5.54325574411687	5.73674425588313
90	5.64	5.53183663370634	5.74816336629366
91	5.64	5.52151296877054	5.75848703122946
92	5.64	5.51201937907962	5.76798062092038
93	5.64	5.50318296124838	5.77681703875162
94	5.64	5.4948836161753	5.7851163838247
95	5.64	5.48703390043558	5.79296609956442
96	5.64	5.47956780130676	5.80043219869324
97	5.64	5.47243403346997	5.80756596653003

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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