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Author

*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 23 Dec 2011 07:47:29 -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/2011/Dec/23/t1324644463rci9dglwo6nrdgj.htm/, Retrieved Mon, 29 Apr 2024 18:56:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160356, Retrieved Mon, 29 Apr 2024 18:56:00 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2011-12-23 12:47:29] [aedc5b8e4f26bdca34b1a0cf88d6dfa2] [Current]

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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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160356&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160356&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160356&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	'AstonUniversity' @ aston.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160356&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160356&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160356&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	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.2262	1.2679	-0.0416999999999998
4	1.1985	1.2295	-0.0309999999999999
5	1.2007	1.2018	-0.00109999999999966
6	1.2138	1.204	0.00980000000000003
7	1.2266	1.2171	0.00950000000000006
8	1.2176	1.2299	-0.0122999999999998
9	1.2218	1.2209	0.000900000000000123
10	1.249	1.2251	0.0239000000000003
11	1.2991	1.2523	0.0468
12	1.3408	1.3024	0.0384000000000002
13	1.3119	1.3441	-0.0321999999999998
14	1.3014	1.3152	-0.0138
15	1.3201	1.3047	0.0154000000000003
16	1.2938	1.3234	-0.0295999999999998
17	1.2694	1.2971	-0.0276999999999998
18	1.2165	1.2727	-0.0562
19	1.2037	1.2198	-0.0160999999999998
20	1.2292	1.207	0.0222000000000002
21	1.2256	1.2325	-0.00689999999999991
22	1.2015	1.2289	-0.0273999999999999
23	1.1786	1.2048	-0.0261999999999998
24	1.1856	1.1819	0.00370000000000004
25	1.2103	1.1889	0.0214000000000001
26	1.1938	1.2136	-0.0197999999999998
27	1.202	1.1971	0.00490000000000013
28	1.2271	1.2053	0.0218000000000003
29	1.277	1.2304	0.0466
30	1.265	1.2803	-0.0152999999999999
31	1.2684	1.2683	0.000100000000000211
32	1.2811	1.2717	0.00940000000000007
33	1.2727	1.2844	-0.0116999999999998
34	1.2611	1.276	-0.0148999999999997
35	1.2881	1.2644	0.0237000000000001
36	1.3213	1.2914	0.0299
37	1.2999	1.3246	-0.0246999999999997
38	1.3074	1.3032	0.00419999999999998
39	1.3242	1.3107	0.0135000000000003
40	1.3516	1.3275	0.0241
41	1.3511	1.3549	-0.0037999999999998
42	1.3419	1.3544	-0.0124999999999997
43	1.3716	1.3452	0.0264
44	1.3622	1.3749	-0.0126999999999997
45	1.3896	1.3655	0.0241
46	1.4227	1.3929	0.0298000000000003
47	1.4684	1.426	0.0424
48	1.457	1.4717	-0.0146999999999997
49	1.4718	1.4603	0.0115000000000001
50	1.4748	1.4751	-0.000299999999999745
51	1.5527	1.4781	0.0746
52	1.575	1.556	0.0190000000000001
53	1.5557	1.5783	-0.0225999999999997
54	1.5553	1.559	-0.00370000000000004
55	1.577	1.5586	0.0184000000000002
56	1.4975	1.5803	-0.0827999999999998
57	1.437	1.5008	-0.0637999999999999
58	1.3322	1.4403	-0.1081
59	1.2732	1.3355	-0.0622999999999998
60	1.3449	1.2765	0.0684
61	1.3239	1.3482	-0.0242999999999998
62	1.2785	1.3272	-0.0487
63	1.305	1.2818	0.0232000000000001
64	1.319	1.3083	0.0107000000000002
65	1.365	1.3223	0.0427000000000002
66	1.4016	1.3683	0.0333000000000001
67	1.4088	1.4049	0.00390000000000024
68	1.4268	1.4121	0.0147000000000002
69	1.4562	1.4301	0.0261
70	1.4816	1.4595	0.0221000000000002
71	1.4914	1.4849	0.00650000000000017
72	1.4614	1.4947	-0.0332999999999999
73	1.4272	1.4647	-0.0374999999999999
74	1.3686	1.4305	-0.0618999999999998
75	1.3569	1.3719	-0.0149999999999999
76	1.3406	1.3602	-0.0195999999999998
77	1.2565	1.3439	-0.0874
78	1.2208	1.2598	-0.0389999999999997
79	1.277	1.2241	0.0529
80	1.2894	1.2803	0.00910000000000033
81	1.3067	1.2927	0.014
82	1.3898	1.31	0.0798000000000001
83	1.3661	1.3931	-0.0269999999999997
84	1.322	1.3694	-0.0473999999999999
85	1.336	1.3253	0.0107000000000002
86	1.3649	1.3393	0.0256000000000001
87	1.3999	1.3682	0.0317000000000001
88	1.4442	1.4032	0.0410000000000001
89	1.4349	1.4475	-0.0125999999999997
90	1.4388	1.4382	0.000600000000000156
91	1.4264	1.4421	-0.0157
92	1.4343	1.4297	0.00460000000000016
93	1.377	1.4376	-0.0605999999999998
94	1.3706	1.3803	-0.00969999999999982
95	1.3556	1.3739	-0.0183

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.2262 & 1.2679 & -0.0416999999999998 \tabularnewline
4 & 1.1985 & 1.2295 & -0.0309999999999999 \tabularnewline
5 & 1.2007 & 1.2018 & -0.00109999999999966 \tabularnewline
6 & 1.2138 & 1.204 & 0.00980000000000003 \tabularnewline
7 & 1.2266 & 1.2171 & 0.00950000000000006 \tabularnewline
8 & 1.2176 & 1.2299 & -0.0122999999999998 \tabularnewline
9 & 1.2218 & 1.2209 & 0.000900000000000123 \tabularnewline
10 & 1.249 & 1.2251 & 0.0239000000000003 \tabularnewline
11 & 1.2991 & 1.2523 & 0.0468 \tabularnewline
12 & 1.3408 & 1.3024 & 0.0384000000000002 \tabularnewline
13 & 1.3119 & 1.3441 & -0.0321999999999998 \tabularnewline
14 & 1.3014 & 1.3152 & -0.0138 \tabularnewline
15 & 1.3201 & 1.3047 & 0.0154000000000003 \tabularnewline
16 & 1.2938 & 1.3234 & -0.0295999999999998 \tabularnewline
17 & 1.2694 & 1.2971 & -0.0276999999999998 \tabularnewline
18 & 1.2165 & 1.2727 & -0.0562 \tabularnewline
19 & 1.2037 & 1.2198 & -0.0160999999999998 \tabularnewline
20 & 1.2292 & 1.207 & 0.0222000000000002 \tabularnewline
21 & 1.2256 & 1.2325 & -0.00689999999999991 \tabularnewline
22 & 1.2015 & 1.2289 & -0.0273999999999999 \tabularnewline
23 & 1.1786 & 1.2048 & -0.0261999999999998 \tabularnewline
24 & 1.1856 & 1.1819 & 0.00370000000000004 \tabularnewline
25 & 1.2103 & 1.1889 & 0.0214000000000001 \tabularnewline
26 & 1.1938 & 1.2136 & -0.0197999999999998 \tabularnewline
27 & 1.202 & 1.1971 & 0.00490000000000013 \tabularnewline
28 & 1.2271 & 1.2053 & 0.0218000000000003 \tabularnewline
29 & 1.277 & 1.2304 & 0.0466 \tabularnewline
30 & 1.265 & 1.2803 & -0.0152999999999999 \tabularnewline
31 & 1.2684 & 1.2683 & 0.000100000000000211 \tabularnewline
32 & 1.2811 & 1.2717 & 0.00940000000000007 \tabularnewline
33 & 1.2727 & 1.2844 & -0.0116999999999998 \tabularnewline
34 & 1.2611 & 1.276 & -0.0148999999999997 \tabularnewline
35 & 1.2881 & 1.2644 & 0.0237000000000001 \tabularnewline
36 & 1.3213 & 1.2914 & 0.0299 \tabularnewline
37 & 1.2999 & 1.3246 & -0.0246999999999997 \tabularnewline
38 & 1.3074 & 1.3032 & 0.00419999999999998 \tabularnewline
39 & 1.3242 & 1.3107 & 0.0135000000000003 \tabularnewline
40 & 1.3516 & 1.3275 & 0.0241 \tabularnewline
41 & 1.3511 & 1.3549 & -0.0037999999999998 \tabularnewline
42 & 1.3419 & 1.3544 & -0.0124999999999997 \tabularnewline
43 & 1.3716 & 1.3452 & 0.0264 \tabularnewline
44 & 1.3622 & 1.3749 & -0.0126999999999997 \tabularnewline
45 & 1.3896 & 1.3655 & 0.0241 \tabularnewline
46 & 1.4227 & 1.3929 & 0.0298000000000003 \tabularnewline
47 & 1.4684 & 1.426 & 0.0424 \tabularnewline
48 & 1.457 & 1.4717 & -0.0146999999999997 \tabularnewline
49 & 1.4718 & 1.4603 & 0.0115000000000001 \tabularnewline
50 & 1.4748 & 1.4751 & -0.000299999999999745 \tabularnewline
51 & 1.5527 & 1.4781 & 0.0746 \tabularnewline
52 & 1.575 & 1.556 & 0.0190000000000001 \tabularnewline
53 & 1.5557 & 1.5783 & -0.0225999999999997 \tabularnewline
54 & 1.5553 & 1.559 & -0.00370000000000004 \tabularnewline
55 & 1.577 & 1.5586 & 0.0184000000000002 \tabularnewline
56 & 1.4975 & 1.5803 & -0.0827999999999998 \tabularnewline
57 & 1.437 & 1.5008 & -0.0637999999999999 \tabularnewline
58 & 1.3322 & 1.4403 & -0.1081 \tabularnewline
59 & 1.2732 & 1.3355 & -0.0622999999999998 \tabularnewline
60 & 1.3449 & 1.2765 & 0.0684 \tabularnewline
61 & 1.3239 & 1.3482 & -0.0242999999999998 \tabularnewline
62 & 1.2785 & 1.3272 & -0.0487 \tabularnewline
63 & 1.305 & 1.2818 & 0.0232000000000001 \tabularnewline
64 & 1.319 & 1.3083 & 0.0107000000000002 \tabularnewline
65 & 1.365 & 1.3223 & 0.0427000000000002 \tabularnewline
66 & 1.4016 & 1.3683 & 0.0333000000000001 \tabularnewline
67 & 1.4088 & 1.4049 & 0.00390000000000024 \tabularnewline
68 & 1.4268 & 1.4121 & 0.0147000000000002 \tabularnewline
69 & 1.4562 & 1.4301 & 0.0261 \tabularnewline
70 & 1.4816 & 1.4595 & 0.0221000000000002 \tabularnewline
71 & 1.4914 & 1.4849 & 0.00650000000000017 \tabularnewline
72 & 1.4614 & 1.4947 & -0.0332999999999999 \tabularnewline
73 & 1.4272 & 1.4647 & -0.0374999999999999 \tabularnewline
74 & 1.3686 & 1.4305 & -0.0618999999999998 \tabularnewline
75 & 1.3569 & 1.3719 & -0.0149999999999999 \tabularnewline
76 & 1.3406 & 1.3602 & -0.0195999999999998 \tabularnewline
77 & 1.2565 & 1.3439 & -0.0874 \tabularnewline
78 & 1.2208 & 1.2598 & -0.0389999999999997 \tabularnewline
79 & 1.277 & 1.2241 & 0.0529 \tabularnewline
80 & 1.2894 & 1.2803 & 0.00910000000000033 \tabularnewline
81 & 1.3067 & 1.2927 & 0.014 \tabularnewline
82 & 1.3898 & 1.31 & 0.0798000000000001 \tabularnewline
83 & 1.3661 & 1.3931 & -0.0269999999999997 \tabularnewline
84 & 1.322 & 1.3694 & -0.0473999999999999 \tabularnewline
85 & 1.336 & 1.3253 & 0.0107000000000002 \tabularnewline
86 & 1.3649 & 1.3393 & 0.0256000000000001 \tabularnewline
87 & 1.3999 & 1.3682 & 0.0317000000000001 \tabularnewline
88 & 1.4442 & 1.4032 & 0.0410000000000001 \tabularnewline
89 & 1.4349 & 1.4475 & -0.0125999999999997 \tabularnewline
90 & 1.4388 & 1.4382 & 0.000600000000000156 \tabularnewline
91 & 1.4264 & 1.4421 & -0.0157 \tabularnewline
92 & 1.4343 & 1.4297 & 0.00460000000000016 \tabularnewline
93 & 1.377 & 1.4376 & -0.0605999999999998 \tabularnewline
94 & 1.3706 & 1.3803 & -0.00969999999999982 \tabularnewline
95 & 1.3556 & 1.3739 & -0.0183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160356&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]1.2262[/C][C]1.2679[/C][C]-0.0416999999999998[/C][/ROW]
[ROW][C]4[/C][C]1.1985[/C][C]1.2295[/C][C]-0.0309999999999999[/C][/ROW]
[ROW][C]5[/C][C]1.2007[/C][C]1.2018[/C][C]-0.00109999999999966[/C][/ROW]
[ROW][C]6[/C][C]1.2138[/C][C]1.204[/C][C]0.00980000000000003[/C][/ROW]
[ROW][C]7[/C][C]1.2266[/C][C]1.2171[/C][C]0.00950000000000006[/C][/ROW]
[ROW][C]8[/C][C]1.2176[/C][C]1.2299[/C][C]-0.0122999999999998[/C][/ROW]
[ROW][C]9[/C][C]1.2218[/C][C]1.2209[/C][C]0.000900000000000123[/C][/ROW]
[ROW][C]10[/C][C]1.249[/C][C]1.2251[/C][C]0.0239000000000003[/C][/ROW]
[ROW][C]11[/C][C]1.2991[/C][C]1.2523[/C][C]0.0468[/C][/ROW]
[ROW][C]12[/C][C]1.3408[/C][C]1.3024[/C][C]0.0384000000000002[/C][/ROW]
[ROW][C]13[/C][C]1.3119[/C][C]1.3441[/C][C]-0.0321999999999998[/C][/ROW]
[ROW][C]14[/C][C]1.3014[/C][C]1.3152[/C][C]-0.0138[/C][/ROW]
[ROW][C]15[/C][C]1.3201[/C][C]1.3047[/C][C]0.0154000000000003[/C][/ROW]
[ROW][C]16[/C][C]1.2938[/C][C]1.3234[/C][C]-0.0295999999999998[/C][/ROW]
[ROW][C]17[/C][C]1.2694[/C][C]1.2971[/C][C]-0.0276999999999998[/C][/ROW]
[ROW][C]18[/C][C]1.2165[/C][C]1.2727[/C][C]-0.0562[/C][/ROW]
[ROW][C]19[/C][C]1.2037[/C][C]1.2198[/C][C]-0.0160999999999998[/C][/ROW]
[ROW][C]20[/C][C]1.2292[/C][C]1.207[/C][C]0.0222000000000002[/C][/ROW]
[ROW][C]21[/C][C]1.2256[/C][C]1.2325[/C][C]-0.00689999999999991[/C][/ROW]
[ROW][C]22[/C][C]1.2015[/C][C]1.2289[/C][C]-0.0273999999999999[/C][/ROW]
[ROW][C]23[/C][C]1.1786[/C][C]1.2048[/C][C]-0.0261999999999998[/C][/ROW]
[ROW][C]24[/C][C]1.1856[/C][C]1.1819[/C][C]0.00370000000000004[/C][/ROW]
[ROW][C]25[/C][C]1.2103[/C][C]1.1889[/C][C]0.0214000000000001[/C][/ROW]
[ROW][C]26[/C][C]1.1938[/C][C]1.2136[/C][C]-0.0197999999999998[/C][/ROW]
[ROW][C]27[/C][C]1.202[/C][C]1.1971[/C][C]0.00490000000000013[/C][/ROW]
[ROW][C]28[/C][C]1.2271[/C][C]1.2053[/C][C]0.0218000000000003[/C][/ROW]
[ROW][C]29[/C][C]1.277[/C][C]1.2304[/C][C]0.0466[/C][/ROW]
[ROW][C]30[/C][C]1.265[/C][C]1.2803[/C][C]-0.0152999999999999[/C][/ROW]
[ROW][C]31[/C][C]1.2684[/C][C]1.2683[/C][C]0.000100000000000211[/C][/ROW]
[ROW][C]32[/C][C]1.2811[/C][C]1.2717[/C][C]0.00940000000000007[/C][/ROW]
[ROW][C]33[/C][C]1.2727[/C][C]1.2844[/C][C]-0.0116999999999998[/C][/ROW]
[ROW][C]34[/C][C]1.2611[/C][C]1.276[/C][C]-0.0148999999999997[/C][/ROW]
[ROW][C]35[/C][C]1.2881[/C][C]1.2644[/C][C]0.0237000000000001[/C][/ROW]
[ROW][C]36[/C][C]1.3213[/C][C]1.2914[/C][C]0.0299[/C][/ROW]
[ROW][C]37[/C][C]1.2999[/C][C]1.3246[/C][C]-0.0246999999999997[/C][/ROW]
[ROW][C]38[/C][C]1.3074[/C][C]1.3032[/C][C]0.00419999999999998[/C][/ROW]
[ROW][C]39[/C][C]1.3242[/C][C]1.3107[/C][C]0.0135000000000003[/C][/ROW]
[ROW][C]40[/C][C]1.3516[/C][C]1.3275[/C][C]0.0241[/C][/ROW]
[ROW][C]41[/C][C]1.3511[/C][C]1.3549[/C][C]-0.0037999999999998[/C][/ROW]
[ROW][C]42[/C][C]1.3419[/C][C]1.3544[/C][C]-0.0124999999999997[/C][/ROW]
[ROW][C]43[/C][C]1.3716[/C][C]1.3452[/C][C]0.0264[/C][/ROW]
[ROW][C]44[/C][C]1.3622[/C][C]1.3749[/C][C]-0.0126999999999997[/C][/ROW]
[ROW][C]45[/C][C]1.3896[/C][C]1.3655[/C][C]0.0241[/C][/ROW]
[ROW][C]46[/C][C]1.4227[/C][C]1.3929[/C][C]0.0298000000000003[/C][/ROW]
[ROW][C]47[/C][C]1.4684[/C][C]1.426[/C][C]0.0424[/C][/ROW]
[ROW][C]48[/C][C]1.457[/C][C]1.4717[/C][C]-0.0146999999999997[/C][/ROW]
[ROW][C]49[/C][C]1.4718[/C][C]1.4603[/C][C]0.0115000000000001[/C][/ROW]
[ROW][C]50[/C][C]1.4748[/C][C]1.4751[/C][C]-0.000299999999999745[/C][/ROW]
[ROW][C]51[/C][C]1.5527[/C][C]1.4781[/C][C]0.0746[/C][/ROW]
[ROW][C]52[/C][C]1.575[/C][C]1.556[/C][C]0.0190000000000001[/C][/ROW]
[ROW][C]53[/C][C]1.5557[/C][C]1.5783[/C][C]-0.0225999999999997[/C][/ROW]
[ROW][C]54[/C][C]1.5553[/C][C]1.559[/C][C]-0.00370000000000004[/C][/ROW]
[ROW][C]55[/C][C]1.577[/C][C]1.5586[/C][C]0.0184000000000002[/C][/ROW]
[ROW][C]56[/C][C]1.4975[/C][C]1.5803[/C][C]-0.0827999999999998[/C][/ROW]
[ROW][C]57[/C][C]1.437[/C][C]1.5008[/C][C]-0.0637999999999999[/C][/ROW]
[ROW][C]58[/C][C]1.3322[/C][C]1.4403[/C][C]-0.1081[/C][/ROW]
[ROW][C]59[/C][C]1.2732[/C][C]1.3355[/C][C]-0.0622999999999998[/C][/ROW]
[ROW][C]60[/C][C]1.3449[/C][C]1.2765[/C][C]0.0684[/C][/ROW]
[ROW][C]61[/C][C]1.3239[/C][C]1.3482[/C][C]-0.0242999999999998[/C][/ROW]
[ROW][C]62[/C][C]1.2785[/C][C]1.3272[/C][C]-0.0487[/C][/ROW]
[ROW][C]63[/C][C]1.305[/C][C]1.2818[/C][C]0.0232000000000001[/C][/ROW]
[ROW][C]64[/C][C]1.319[/C][C]1.3083[/C][C]0.0107000000000002[/C][/ROW]
[ROW][C]65[/C][C]1.365[/C][C]1.3223[/C][C]0.0427000000000002[/C][/ROW]
[ROW][C]66[/C][C]1.4016[/C][C]1.3683[/C][C]0.0333000000000001[/C][/ROW]
[ROW][C]67[/C][C]1.4088[/C][C]1.4049[/C][C]0.00390000000000024[/C][/ROW]
[ROW][C]68[/C][C]1.4268[/C][C]1.4121[/C][C]0.0147000000000002[/C][/ROW]
[ROW][C]69[/C][C]1.4562[/C][C]1.4301[/C][C]0.0261[/C][/ROW]
[ROW][C]70[/C][C]1.4816[/C][C]1.4595[/C][C]0.0221000000000002[/C][/ROW]
[ROW][C]71[/C][C]1.4914[/C][C]1.4849[/C][C]0.00650000000000017[/C][/ROW]
[ROW][C]72[/C][C]1.4614[/C][C]1.4947[/C][C]-0.0332999999999999[/C][/ROW]
[ROW][C]73[/C][C]1.4272[/C][C]1.4647[/C][C]-0.0374999999999999[/C][/ROW]
[ROW][C]74[/C][C]1.3686[/C][C]1.4305[/C][C]-0.0618999999999998[/C][/ROW]
[ROW][C]75[/C][C]1.3569[/C][C]1.3719[/C][C]-0.0149999999999999[/C][/ROW]
[ROW][C]76[/C][C]1.3406[/C][C]1.3602[/C][C]-0.0195999999999998[/C][/ROW]
[ROW][C]77[/C][C]1.2565[/C][C]1.3439[/C][C]-0.0874[/C][/ROW]
[ROW][C]78[/C][C]1.2208[/C][C]1.2598[/C][C]-0.0389999999999997[/C][/ROW]
[ROW][C]79[/C][C]1.277[/C][C]1.2241[/C][C]0.0529[/C][/ROW]
[ROW][C]80[/C][C]1.2894[/C][C]1.2803[/C][C]0.00910000000000033[/C][/ROW]
[ROW][C]81[/C][C]1.3067[/C][C]1.2927[/C][C]0.014[/C][/ROW]
[ROW][C]82[/C][C]1.3898[/C][C]1.31[/C][C]0.0798000000000001[/C][/ROW]
[ROW][C]83[/C][C]1.3661[/C][C]1.3931[/C][C]-0.0269999999999997[/C][/ROW]
[ROW][C]84[/C][C]1.322[/C][C]1.3694[/C][C]-0.0473999999999999[/C][/ROW]
[ROW][C]85[/C][C]1.336[/C][C]1.3253[/C][C]0.0107000000000002[/C][/ROW]
[ROW][C]86[/C][C]1.3649[/C][C]1.3393[/C][C]0.0256000000000001[/C][/ROW]
[ROW][C]87[/C][C]1.3999[/C][C]1.3682[/C][C]0.0317000000000001[/C][/ROW]
[ROW][C]88[/C][C]1.4442[/C][C]1.4032[/C][C]0.0410000000000001[/C][/ROW]
[ROW][C]89[/C][C]1.4349[/C][C]1.4475[/C][C]-0.0125999999999997[/C][/ROW]
[ROW][C]90[/C][C]1.4388[/C][C]1.4382[/C][C]0.000600000000000156[/C][/ROW]
[ROW][C]91[/C][C]1.4264[/C][C]1.4421[/C][C]-0.0157[/C][/ROW]
[ROW][C]92[/C][C]1.4343[/C][C]1.4297[/C][C]0.00460000000000016[/C][/ROW]
[ROW][C]93[/C][C]1.377[/C][C]1.4376[/C][C]-0.0605999999999998[/C][/ROW]
[ROW][C]94[/C][C]1.3706[/C][C]1.3803[/C][C]-0.00969999999999982[/C][/ROW]
[ROW][C]95[/C][C]1.3556[/C][C]1.3739[/C][C]-0.0183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160356&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160356&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	1.2262	1.2679	-0.0416999999999998
4	1.1985	1.2295	-0.0309999999999999
5	1.2007	1.2018	-0.00109999999999966
6	1.2138	1.204	0.00980000000000003
7	1.2266	1.2171	0.00950000000000006
8	1.2176	1.2299	-0.0122999999999998
9	1.2218	1.2209	0.000900000000000123
10	1.249	1.2251	0.0239000000000003
11	1.2991	1.2523	0.0468
12	1.3408	1.3024	0.0384000000000002
13	1.3119	1.3441	-0.0321999999999998
14	1.3014	1.3152	-0.0138
15	1.3201	1.3047	0.0154000000000003
16	1.2938	1.3234	-0.0295999999999998
17	1.2694	1.2971	-0.0276999999999998
18	1.2165	1.2727	-0.0562
19	1.2037	1.2198	-0.0160999999999998
20	1.2292	1.207	0.0222000000000002
21	1.2256	1.2325	-0.00689999999999991
22	1.2015	1.2289	-0.0273999999999999
23	1.1786	1.2048	-0.0261999999999998
24	1.1856	1.1819	0.00370000000000004
25	1.2103	1.1889	0.0214000000000001
26	1.1938	1.2136	-0.0197999999999998
27	1.202	1.1971	0.00490000000000013
28	1.2271	1.2053	0.0218000000000003
29	1.277	1.2304	0.0466
30	1.265	1.2803	-0.0152999999999999
31	1.2684	1.2683	0.000100000000000211
32	1.2811	1.2717	0.00940000000000007
33	1.2727	1.2844	-0.0116999999999998
34	1.2611	1.276	-0.0148999999999997
35	1.2881	1.2644	0.0237000000000001
36	1.3213	1.2914	0.0299
37	1.2999	1.3246	-0.0246999999999997
38	1.3074	1.3032	0.00419999999999998
39	1.3242	1.3107	0.0135000000000003
40	1.3516	1.3275	0.0241
41	1.3511	1.3549	-0.0037999999999998
42	1.3419	1.3544	-0.0124999999999997
43	1.3716	1.3452	0.0264
44	1.3622	1.3749	-0.0126999999999997
45	1.3896	1.3655	0.0241
46	1.4227	1.3929	0.0298000000000003
47	1.4684	1.426	0.0424
48	1.457	1.4717	-0.0146999999999997
49	1.4718	1.4603	0.0115000000000001
50	1.4748	1.4751	-0.000299999999999745
51	1.5527	1.4781	0.0746
52	1.575	1.556	0.0190000000000001
53	1.5557	1.5783	-0.0225999999999997
54	1.5553	1.559	-0.00370000000000004
55	1.577	1.5586	0.0184000000000002
56	1.4975	1.5803	-0.0827999999999998
57	1.437	1.5008	-0.0637999999999999
58	1.3322	1.4403	-0.1081
59	1.2732	1.3355	-0.0622999999999998
60	1.3449	1.2765	0.0684
61	1.3239	1.3482	-0.0242999999999998
62	1.2785	1.3272	-0.0487
63	1.305	1.2818	0.0232000000000001
64	1.319	1.3083	0.0107000000000002
65	1.365	1.3223	0.0427000000000002
66	1.4016	1.3683	0.0333000000000001
67	1.4088	1.4049	0.00390000000000024
68	1.4268	1.4121	0.0147000000000002
69	1.4562	1.4301	0.0261
70	1.4816	1.4595	0.0221000000000002
71	1.4914	1.4849	0.00650000000000017
72	1.4614	1.4947	-0.0332999999999999
73	1.4272	1.4647	-0.0374999999999999
74	1.3686	1.4305	-0.0618999999999998
75	1.3569	1.3719	-0.0149999999999999
76	1.3406	1.3602	-0.0195999999999998
77	1.2565	1.3439	-0.0874
78	1.2208	1.2598	-0.0389999999999997
79	1.277	1.2241	0.0529
80	1.2894	1.2803	0.00910000000000033
81	1.3067	1.2927	0.014
82	1.3898	1.31	0.0798000000000001
83	1.3661	1.3931	-0.0269999999999997
84	1.322	1.3694	-0.0473999999999999
85	1.336	1.3253	0.0107000000000002
86	1.3649	1.3393	0.0256000000000001
87	1.3999	1.3682	0.0317000000000001
88	1.4442	1.4032	0.0410000000000001
89	1.4349	1.4475	-0.0125999999999997
90	1.4388	1.4382	0.000600000000000156
91	1.4264	1.4421	-0.0157
92	1.4343	1.4297	0.00460000000000016
93	1.377	1.4376	-0.0605999999999998
94	1.3706	1.3803	-0.00969999999999982
95	1.3556	1.3739	-0.0183

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
96	1.3589	1.29129590464457	1.42650409535543
97	1.3622	1.26659337147639	1.45780662852361
98	1.3655	1.24840627204467	1.48259372795533
99	1.3688	1.23359180928914	1.50400819071086
100	1.3721	1.22093264722788	1.52326735277212
101	1.3754	1.20980446185674	1.54099553814326
102	1.3787	1.19983637608004	1.55756362391996
103	1.382	1.19078674295278	1.57321325704722
104	1.3853	1.18248771393371	1.58811228606628
105	1.3886	1.17481707952163	1.60238292047836
106	1.3919	1.16768258141463	1.61611741858536
107	1.3952	1.16101254408933	1.62938745591066

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
96 & 1.3589 & 1.29129590464457 & 1.42650409535543 \tabularnewline
97 & 1.3622 & 1.26659337147639 & 1.45780662852361 \tabularnewline
98 & 1.3655 & 1.24840627204467 & 1.48259372795533 \tabularnewline
99 & 1.3688 & 1.23359180928914 & 1.50400819071086 \tabularnewline
100 & 1.3721 & 1.22093264722788 & 1.52326735277212 \tabularnewline
101 & 1.3754 & 1.20980446185674 & 1.54099553814326 \tabularnewline
102 & 1.3787 & 1.19983637608004 & 1.55756362391996 \tabularnewline
103 & 1.382 & 1.19078674295278 & 1.57321325704722 \tabularnewline
104 & 1.3853 & 1.18248771393371 & 1.58811228606628 \tabularnewline
105 & 1.3886 & 1.17481707952163 & 1.60238292047836 \tabularnewline
106 & 1.3919 & 1.16768258141463 & 1.61611741858536 \tabularnewline
107 & 1.3952 & 1.16101254408933 & 1.62938745591066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160356&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]96[/C][C]1.3589[/C][C]1.29129590464457[/C][C]1.42650409535543[/C][/ROW]
[ROW][C]97[/C][C]1.3622[/C][C]1.26659337147639[/C][C]1.45780662852361[/C][/ROW]
[ROW][C]98[/C][C]1.3655[/C][C]1.24840627204467[/C][C]1.48259372795533[/C][/ROW]
[ROW][C]99[/C][C]1.3688[/C][C]1.23359180928914[/C][C]1.50400819071086[/C][/ROW]
[ROW][C]100[/C][C]1.3721[/C][C]1.22093264722788[/C][C]1.52326735277212[/C][/ROW]
[ROW][C]101[/C][C]1.3754[/C][C]1.20980446185674[/C][C]1.54099553814326[/C][/ROW]
[ROW][C]102[/C][C]1.3787[/C][C]1.19983637608004[/C][C]1.55756362391996[/C][/ROW]
[ROW][C]103[/C][C]1.382[/C][C]1.19078674295278[/C][C]1.57321325704722[/C][/ROW]
[ROW][C]104[/C][C]1.3853[/C][C]1.18248771393371[/C][C]1.58811228606628[/C][/ROW]
[ROW][C]105[/C][C]1.3886[/C][C]1.17481707952163[/C][C]1.60238292047836[/C][/ROW]
[ROW][C]106[/C][C]1.3919[/C][C]1.16768258141463[/C][C]1.61611741858536[/C][/ROW]
[ROW][C]107[/C][C]1.3952[/C][C]1.16101254408933[/C][C]1.62938745591066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160356&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160356&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
96	1.3589	1.29129590464457	1.42650409535543
97	1.3622	1.26659337147639	1.45780662852361
98	1.3655	1.24840627204467	1.48259372795533
99	1.3688	1.23359180928914	1.50400819071086
100	1.3721	1.22093264722788	1.52326735277212
101	1.3754	1.20980446185674	1.54099553814326
102	1.3787	1.19983637608004	1.55756362391996
103	1.382	1.19078674295278	1.57321325704722
104	1.3853	1.18248771393371	1.58811228606628
105	1.3886	1.17481707952163	1.60238292047836
106	1.3919	1.16768258141463	1.61611741858536
107	1.3952	1.16101254408933	1.62938745591066

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