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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 23 May 2012 08:16:48 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/23/t1337775459q5cpwdm7zdpl94i.htm/, Retrieved Mon, 29 Apr 2024 03:03:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167173, Retrieved Mon, 29 Apr 2024 03:03:31 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

104

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

-       [Exponential Smoothing] [iko opgave 10 opd...] [2012-05-23 12:16:48] [76c30f62b7052b57088120e90a652e05] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167173&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]1 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=167173&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167173&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999931422911231
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999931422911231 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167173&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]0.999931422911231[/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=167173&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167173&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	0.999931422911231
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	7.08	7.08	0
3	7.09	7.08	0.00999999999999979
4	7.07	7.08999931422911	-0.0199993142291115
5	7.06	7.07000137149475	-0.0100013714947478
6	6.99	7.06000068586494	-0.0700006858649402
7	6.99	6.99000480044325	-4.80044324824291e-06
8	6.99	6.9900000003292	-3.29200666726592e-10
9	6.98	6.99000000000002	-0.010000000000022
10	6.96	6.98000068577089	-0.0200006857708885
11	6.95	6.9600013715888	-0.0100013715888032
12	6.91	6.95000068586495	-0.0400006858649471
13	6.91	6.91000274313059	-2.74313058579168e-06
14	6.87	6.91000000018812	-0.0400000001881162
15	6.91	6.87000274308356	0.0399972569164362
16	6.89	6.90999725710456	-0.0199972571045626
17	6.88	6.89000137135368	-0.0100013713536757
18	6.9	6.88000068586493	0.0199993141350694
19	6.91	6.89999862850526	0.0100013714947407
20	6.85	6.90999931413506	-0.0599993141350597
21	6.86	6.85000411457829	0.00999588542170926
22	6.82	6.85999931451128	-0.0399993145112782
23	6.8	6.82000274303654	-0.0200027430365424
24	6.83	6.80000137172989	0.029998628270115
25	6.84	6.82999794278141	0.0100020572185935
26	6.89	6.83999931408803	0.0500006859119653
27	7.14	6.88999657109852	0.250003428901477
28	7.21	7.13998285549266	0.0700171445073368
29	7.25	7.20999519842807	0.0400048015719339
30	7.31	7.24999725658717	0.0600027434128281
31	7.3	7.30999588518654	-0.00999588518653827
32	7.48	7.30000068548871	0.179999314511295
33	7.49	7.47998765617103	0.0100123438289694
34	7.4	7.48999931338261	-0.0899993133826085
35	7.44	7.4000061718909	0.0399938281090968
36	7.42	7.4399972573397	-0.0199972573396998
37	7.14	7.42000137135369	-0.280001371353692
38	7.24	7.1400192016789	0.0999807983211021
39	7.33	7.23999314360792	0.0900068563920815
40	7.61	7.32999382759182	0.280006172408181
41	7.66	7.60998079799186	0.0500192020081407
42	7.69	7.65999656982874	0.0300034301712566
43	7.7	7.68999794245211	0.0100020575478936
44	7.68	7.69999931408801	-0.0199993140880119
45	7.71	7.68000137149474	0.0299986285052629
46	7.71	7.70999794278139	2.05721860968566e-06
47	7.72	7.70999999985892	0.010000000141078
48	7.68	7.7199993142291	-0.0399993142291031
49	7.72	7.68000274303652	0.0399972569634777
50	7.74	7.71999725710456	0.0200027428954419
51	7.76	7.73999862827012	0.020001371729875
52	7.9	7.75999862836415	0.140001371635845
53	7.97	7.89999039911351	0.0700096008864897
54	7.96	7.96999519894539	-0.00999519894538548
55	7.95	7.96000068544165	-0.0100006854416455
56	7.97	7.95000068581789	0.0199993141821064
57	7.93	7.96999862850526	-0.0399986285052565
58	7.99	7.9300027429895	0.0599972570105027
59	7.96	7.98999588556278	-0.02999588556278
60	7.92	7.96000205703051	-0.0400020570305069
61	7.97	7.92000274322462	0.0499972567753835
62	7.98	7.96999657133368	0.0100034286663169
63	8	7.97999931399398	0.0200006860060151
64	8.04	7.99999862841118	0.0400013715888186
65	8.17	8.03999725682239	0.130002743177611
66	8.29	8.16999108479034	0.120008915209658
67	8.26	8.28999177013797	-0.0299917701379684
68	8.3	8.26000205674828	0.0399979432517181
69	8.32	8.2999972570575	0.0200027429425038
70	8.28	8.31999862827012	-0.0399986282701228
71	8.27	8.28000274298948	-0.0100027429894816
72	8.32	8.27000068595899	0.0499993140410062
73	8.31	8.3199965711926	-0.00999657119260178
74	8.34	8.31000068553575	0.0299993144642485
75	8.32	8.33999794273435	-0.0199979427343493
76	8.36	8.32000137140069	0.0399986285993048
77	8.33	8.35999725701049	-0.0299972570104945
78	8.35	8.33000205712456	0.0199979428754435
79	8.34	8.3499986285993	-0.00999862859929657
80	8.37	8.34000068567684	0.0299993143231578
81	8.31	8.36999794273436	-0.0599979427343573
82	8.33	8.31000411448425	0.0199958855157547
83	8.34	8.32999862874038	0.0100013712596159
84	8.25	8.33999931413508	-0.0899993141350759

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 7.08 & 7.08 & 0 \tabularnewline
3 & 7.09 & 7.08 & 0.00999999999999979 \tabularnewline
4 & 7.07 & 7.08999931422911 & -0.0199993142291115 \tabularnewline
5 & 7.06 & 7.07000137149475 & -0.0100013714947478 \tabularnewline
6 & 6.99 & 7.06000068586494 & -0.0700006858649402 \tabularnewline
7 & 6.99 & 6.99000480044325 & -4.80044324824291e-06 \tabularnewline
8 & 6.99 & 6.9900000003292 & -3.29200666726592e-10 \tabularnewline
9 & 6.98 & 6.99000000000002 & -0.010000000000022 \tabularnewline
10 & 6.96 & 6.98000068577089 & -0.0200006857708885 \tabularnewline
11 & 6.95 & 6.9600013715888 & -0.0100013715888032 \tabularnewline
12 & 6.91 & 6.95000068586495 & -0.0400006858649471 \tabularnewline
13 & 6.91 & 6.91000274313059 & -2.74313058579168e-06 \tabularnewline
14 & 6.87 & 6.91000000018812 & -0.0400000001881162 \tabularnewline
15 & 6.91 & 6.87000274308356 & 0.0399972569164362 \tabularnewline
16 & 6.89 & 6.90999725710456 & -0.0199972571045626 \tabularnewline
17 & 6.88 & 6.89000137135368 & -0.0100013713536757 \tabularnewline
18 & 6.9 & 6.88000068586493 & 0.0199993141350694 \tabularnewline
19 & 6.91 & 6.89999862850526 & 0.0100013714947407 \tabularnewline
20 & 6.85 & 6.90999931413506 & -0.0599993141350597 \tabularnewline
21 & 6.86 & 6.85000411457829 & 0.00999588542170926 \tabularnewline
22 & 6.82 & 6.85999931451128 & -0.0399993145112782 \tabularnewline
23 & 6.8 & 6.82000274303654 & -0.0200027430365424 \tabularnewline
24 & 6.83 & 6.80000137172989 & 0.029998628270115 \tabularnewline
25 & 6.84 & 6.82999794278141 & 0.0100020572185935 \tabularnewline
26 & 6.89 & 6.83999931408803 & 0.0500006859119653 \tabularnewline
27 & 7.14 & 6.88999657109852 & 0.250003428901477 \tabularnewline
28 & 7.21 & 7.13998285549266 & 0.0700171445073368 \tabularnewline
29 & 7.25 & 7.20999519842807 & 0.0400048015719339 \tabularnewline
30 & 7.31 & 7.24999725658717 & 0.0600027434128281 \tabularnewline
31 & 7.3 & 7.30999588518654 & -0.00999588518653827 \tabularnewline
32 & 7.48 & 7.30000068548871 & 0.179999314511295 \tabularnewline
33 & 7.49 & 7.47998765617103 & 0.0100123438289694 \tabularnewline
34 & 7.4 & 7.48999931338261 & -0.0899993133826085 \tabularnewline
35 & 7.44 & 7.4000061718909 & 0.0399938281090968 \tabularnewline
36 & 7.42 & 7.4399972573397 & -0.0199972573396998 \tabularnewline
37 & 7.14 & 7.42000137135369 & -0.280001371353692 \tabularnewline
38 & 7.24 & 7.1400192016789 & 0.0999807983211021 \tabularnewline
39 & 7.33 & 7.23999314360792 & 0.0900068563920815 \tabularnewline
40 & 7.61 & 7.32999382759182 & 0.280006172408181 \tabularnewline
41 & 7.66 & 7.60998079799186 & 0.0500192020081407 \tabularnewline
42 & 7.69 & 7.65999656982874 & 0.0300034301712566 \tabularnewline
43 & 7.7 & 7.68999794245211 & 0.0100020575478936 \tabularnewline
44 & 7.68 & 7.69999931408801 & -0.0199993140880119 \tabularnewline
45 & 7.71 & 7.68000137149474 & 0.0299986285052629 \tabularnewline
46 & 7.71 & 7.70999794278139 & 2.05721860968566e-06 \tabularnewline
47 & 7.72 & 7.70999999985892 & 0.010000000141078 \tabularnewline
48 & 7.68 & 7.7199993142291 & -0.0399993142291031 \tabularnewline
49 & 7.72 & 7.68000274303652 & 0.0399972569634777 \tabularnewline
50 & 7.74 & 7.71999725710456 & 0.0200027428954419 \tabularnewline
51 & 7.76 & 7.73999862827012 & 0.020001371729875 \tabularnewline
52 & 7.9 & 7.75999862836415 & 0.140001371635845 \tabularnewline
53 & 7.97 & 7.89999039911351 & 0.0700096008864897 \tabularnewline
54 & 7.96 & 7.96999519894539 & -0.00999519894538548 \tabularnewline
55 & 7.95 & 7.96000068544165 & -0.0100006854416455 \tabularnewline
56 & 7.97 & 7.95000068581789 & 0.0199993141821064 \tabularnewline
57 & 7.93 & 7.96999862850526 & -0.0399986285052565 \tabularnewline
58 & 7.99 & 7.9300027429895 & 0.0599972570105027 \tabularnewline
59 & 7.96 & 7.98999588556278 & -0.02999588556278 \tabularnewline
60 & 7.92 & 7.96000205703051 & -0.0400020570305069 \tabularnewline
61 & 7.97 & 7.92000274322462 & 0.0499972567753835 \tabularnewline
62 & 7.98 & 7.96999657133368 & 0.0100034286663169 \tabularnewline
63 & 8 & 7.97999931399398 & 0.0200006860060151 \tabularnewline
64 & 8.04 & 7.99999862841118 & 0.0400013715888186 \tabularnewline
65 & 8.17 & 8.03999725682239 & 0.130002743177611 \tabularnewline
66 & 8.29 & 8.16999108479034 & 0.120008915209658 \tabularnewline
67 & 8.26 & 8.28999177013797 & -0.0299917701379684 \tabularnewline
68 & 8.3 & 8.26000205674828 & 0.0399979432517181 \tabularnewline
69 & 8.32 & 8.2999972570575 & 0.0200027429425038 \tabularnewline
70 & 8.28 & 8.31999862827012 & -0.0399986282701228 \tabularnewline
71 & 8.27 & 8.28000274298948 & -0.0100027429894816 \tabularnewline
72 & 8.32 & 8.27000068595899 & 0.0499993140410062 \tabularnewline
73 & 8.31 & 8.3199965711926 & -0.00999657119260178 \tabularnewline
74 & 8.34 & 8.31000068553575 & 0.0299993144642485 \tabularnewline
75 & 8.32 & 8.33999794273435 & -0.0199979427343493 \tabularnewline
76 & 8.36 & 8.32000137140069 & 0.0399986285993048 \tabularnewline
77 & 8.33 & 8.35999725701049 & -0.0299972570104945 \tabularnewline
78 & 8.35 & 8.33000205712456 & 0.0199979428754435 \tabularnewline
79 & 8.34 & 8.3499986285993 & -0.00999862859929657 \tabularnewline
80 & 8.37 & 8.34000068567684 & 0.0299993143231578 \tabularnewline
81 & 8.31 & 8.36999794273436 & -0.0599979427343573 \tabularnewline
82 & 8.33 & 8.31000411448425 & 0.0199958855157547 \tabularnewline
83 & 8.34 & 8.32999862874038 & 0.0100013712596159 \tabularnewline
84 & 8.25 & 8.33999931413508 & -0.0899993141350759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167173&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]7.08[/C][C]7.08[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]7.09[/C][C]7.08[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]7.07[/C][C]7.08999931422911[/C][C]-0.0199993142291115[/C][/ROW]
[ROW][C]5[/C][C]7.06[/C][C]7.07000137149475[/C][C]-0.0100013714947478[/C][/ROW]
[ROW][C]6[/C][C]6.99[/C][C]7.06000068586494[/C][C]-0.0700006858649402[/C][/ROW]
[ROW][C]7[/C][C]6.99[/C][C]6.99000480044325[/C][C]-4.80044324824291e-06[/C][/ROW]
[ROW][C]8[/C][C]6.99[/C][C]6.9900000003292[/C][C]-3.29200666726592e-10[/C][/ROW]
[ROW][C]9[/C][C]6.98[/C][C]6.99000000000002[/C][C]-0.010000000000022[/C][/ROW]
[ROW][C]10[/C][C]6.96[/C][C]6.98000068577089[/C][C]-0.0200006857708885[/C][/ROW]
[ROW][C]11[/C][C]6.95[/C][C]6.9600013715888[/C][C]-0.0100013715888032[/C][/ROW]
[ROW][C]12[/C][C]6.91[/C][C]6.95000068586495[/C][C]-0.0400006858649471[/C][/ROW]
[ROW][C]13[/C][C]6.91[/C][C]6.91000274313059[/C][C]-2.74313058579168e-06[/C][/ROW]
[ROW][C]14[/C][C]6.87[/C][C]6.91000000018812[/C][C]-0.0400000001881162[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.87000274308356[/C][C]0.0399972569164362[/C][/ROW]
[ROW][C]16[/C][C]6.89[/C][C]6.90999725710456[/C][C]-0.0199972571045626[/C][/ROW]
[ROW][C]17[/C][C]6.88[/C][C]6.89000137135368[/C][C]-0.0100013713536757[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.88000068586493[/C][C]0.0199993141350694[/C][/ROW]
[ROW][C]19[/C][C]6.91[/C][C]6.89999862850526[/C][C]0.0100013714947407[/C][/ROW]
[ROW][C]20[/C][C]6.85[/C][C]6.90999931413506[/C][C]-0.0599993141350597[/C][/ROW]
[ROW][C]21[/C][C]6.86[/C][C]6.85000411457829[/C][C]0.00999588542170926[/C][/ROW]
[ROW][C]22[/C][C]6.82[/C][C]6.85999931451128[/C][C]-0.0399993145112782[/C][/ROW]
[ROW][C]23[/C][C]6.8[/C][C]6.82000274303654[/C][C]-0.0200027430365424[/C][/ROW]
[ROW][C]24[/C][C]6.83[/C][C]6.80000137172989[/C][C]0.029998628270115[/C][/ROW]
[ROW][C]25[/C][C]6.84[/C][C]6.82999794278141[/C][C]0.0100020572185935[/C][/ROW]
[ROW][C]26[/C][C]6.89[/C][C]6.83999931408803[/C][C]0.0500006859119653[/C][/ROW]
[ROW][C]27[/C][C]7.14[/C][C]6.88999657109852[/C][C]0.250003428901477[/C][/ROW]
[ROW][C]28[/C][C]7.21[/C][C]7.13998285549266[/C][C]0.0700171445073368[/C][/ROW]
[ROW][C]29[/C][C]7.25[/C][C]7.20999519842807[/C][C]0.0400048015719339[/C][/ROW]
[ROW][C]30[/C][C]7.31[/C][C]7.24999725658717[/C][C]0.0600027434128281[/C][/ROW]
[ROW][C]31[/C][C]7.3[/C][C]7.30999588518654[/C][C]-0.00999588518653827[/C][/ROW]
[ROW][C]32[/C][C]7.48[/C][C]7.30000068548871[/C][C]0.179999314511295[/C][/ROW]
[ROW][C]33[/C][C]7.49[/C][C]7.47998765617103[/C][C]0.0100123438289694[/C][/ROW]
[ROW][C]34[/C][C]7.4[/C][C]7.48999931338261[/C][C]-0.0899993133826085[/C][/ROW]
[ROW][C]35[/C][C]7.44[/C][C]7.4000061718909[/C][C]0.0399938281090968[/C][/ROW]
[ROW][C]36[/C][C]7.42[/C][C]7.4399972573397[/C][C]-0.0199972573396998[/C][/ROW]
[ROW][C]37[/C][C]7.14[/C][C]7.42000137135369[/C][C]-0.280001371353692[/C][/ROW]
[ROW][C]38[/C][C]7.24[/C][C]7.1400192016789[/C][C]0.0999807983211021[/C][/ROW]
[ROW][C]39[/C][C]7.33[/C][C]7.23999314360792[/C][C]0.0900068563920815[/C][/ROW]
[ROW][C]40[/C][C]7.61[/C][C]7.32999382759182[/C][C]0.280006172408181[/C][/ROW]
[ROW][C]41[/C][C]7.66[/C][C]7.60998079799186[/C][C]0.0500192020081407[/C][/ROW]
[ROW][C]42[/C][C]7.69[/C][C]7.65999656982874[/C][C]0.0300034301712566[/C][/ROW]
[ROW][C]43[/C][C]7.7[/C][C]7.68999794245211[/C][C]0.0100020575478936[/C][/ROW]
[ROW][C]44[/C][C]7.68[/C][C]7.69999931408801[/C][C]-0.0199993140880119[/C][/ROW]
[ROW][C]45[/C][C]7.71[/C][C]7.68000137149474[/C][C]0.0299986285052629[/C][/ROW]
[ROW][C]46[/C][C]7.71[/C][C]7.70999794278139[/C][C]2.05721860968566e-06[/C][/ROW]
[ROW][C]47[/C][C]7.72[/C][C]7.70999999985892[/C][C]0.010000000141078[/C][/ROW]
[ROW][C]48[/C][C]7.68[/C][C]7.7199993142291[/C][C]-0.0399993142291031[/C][/ROW]
[ROW][C]49[/C][C]7.72[/C][C]7.68000274303652[/C][C]0.0399972569634777[/C][/ROW]
[ROW][C]50[/C][C]7.74[/C][C]7.71999725710456[/C][C]0.0200027428954419[/C][/ROW]
[ROW][C]51[/C][C]7.76[/C][C]7.73999862827012[/C][C]0.020001371729875[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.75999862836415[/C][C]0.140001371635845[/C][/ROW]
[ROW][C]53[/C][C]7.97[/C][C]7.89999039911351[/C][C]0.0700096008864897[/C][/ROW]
[ROW][C]54[/C][C]7.96[/C][C]7.96999519894539[/C][C]-0.00999519894538548[/C][/ROW]
[ROW][C]55[/C][C]7.95[/C][C]7.96000068544165[/C][C]-0.0100006854416455[/C][/ROW]
[ROW][C]56[/C][C]7.97[/C][C]7.95000068581789[/C][C]0.0199993141821064[/C][/ROW]
[ROW][C]57[/C][C]7.93[/C][C]7.96999862850526[/C][C]-0.0399986285052565[/C][/ROW]
[ROW][C]58[/C][C]7.99[/C][C]7.9300027429895[/C][C]0.0599972570105027[/C][/ROW]
[ROW][C]59[/C][C]7.96[/C][C]7.98999588556278[/C][C]-0.02999588556278[/C][/ROW]
[ROW][C]60[/C][C]7.92[/C][C]7.96000205703051[/C][C]-0.0400020570305069[/C][/ROW]
[ROW][C]61[/C][C]7.97[/C][C]7.92000274322462[/C][C]0.0499972567753835[/C][/ROW]
[ROW][C]62[/C][C]7.98[/C][C]7.96999657133368[/C][C]0.0100034286663169[/C][/ROW]
[ROW][C]63[/C][C]8[/C][C]7.97999931399398[/C][C]0.0200006860060151[/C][/ROW]
[ROW][C]64[/C][C]8.04[/C][C]7.99999862841118[/C][C]0.0400013715888186[/C][/ROW]
[ROW][C]65[/C][C]8.17[/C][C]8.03999725682239[/C][C]0.130002743177611[/C][/ROW]
[ROW][C]66[/C][C]8.29[/C][C]8.16999108479034[/C][C]0.120008915209658[/C][/ROW]
[ROW][C]67[/C][C]8.26[/C][C]8.28999177013797[/C][C]-0.0299917701379684[/C][/ROW]
[ROW][C]68[/C][C]8.3[/C][C]8.26000205674828[/C][C]0.0399979432517181[/C][/ROW]
[ROW][C]69[/C][C]8.32[/C][C]8.2999972570575[/C][C]0.0200027429425038[/C][/ROW]
[ROW][C]70[/C][C]8.28[/C][C]8.31999862827012[/C][C]-0.0399986282701228[/C][/ROW]
[ROW][C]71[/C][C]8.27[/C][C]8.28000274298948[/C][C]-0.0100027429894816[/C][/ROW]
[ROW][C]72[/C][C]8.32[/C][C]8.27000068595899[/C][C]0.0499993140410062[/C][/ROW]
[ROW][C]73[/C][C]8.31[/C][C]8.3199965711926[/C][C]-0.00999657119260178[/C][/ROW]
[ROW][C]74[/C][C]8.34[/C][C]8.31000068553575[/C][C]0.0299993144642485[/C][/ROW]
[ROW][C]75[/C][C]8.32[/C][C]8.33999794273435[/C][C]-0.0199979427343493[/C][/ROW]
[ROW][C]76[/C][C]8.36[/C][C]8.32000137140069[/C][C]0.0399986285993048[/C][/ROW]
[ROW][C]77[/C][C]8.33[/C][C]8.35999725701049[/C][C]-0.0299972570104945[/C][/ROW]
[ROW][C]78[/C][C]8.35[/C][C]8.33000205712456[/C][C]0.0199979428754435[/C][/ROW]
[ROW][C]79[/C][C]8.34[/C][C]8.3499986285993[/C][C]-0.00999862859929657[/C][/ROW]
[ROW][C]80[/C][C]8.37[/C][C]8.34000068567684[/C][C]0.0299993143231578[/C][/ROW]
[ROW][C]81[/C][C]8.31[/C][C]8.36999794273436[/C][C]-0.0599979427343573[/C][/ROW]
[ROW][C]82[/C][C]8.33[/C][C]8.31000411448425[/C][C]0.0199958855157547[/C][/ROW]
[ROW][C]83[/C][C]8.34[/C][C]8.32999862874038[/C][C]0.0100013712596159[/C][/ROW]
[ROW][C]84[/C][C]8.25[/C][C]8.33999931413508[/C][C]-0.0899993141350759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167173&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167173&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	7.08	7.08	0
3	7.09	7.08	0.00999999999999979
4	7.07	7.08999931422911	-0.0199993142291115
5	7.06	7.07000137149475	-0.0100013714947478
6	6.99	7.06000068586494	-0.0700006858649402
7	6.99	6.99000480044325	-4.80044324824291e-06
8	6.99	6.9900000003292	-3.29200666726592e-10
9	6.98	6.99000000000002	-0.010000000000022
10	6.96	6.98000068577089	-0.0200006857708885
11	6.95	6.9600013715888	-0.0100013715888032
12	6.91	6.95000068586495	-0.0400006858649471
13	6.91	6.91000274313059	-2.74313058579168e-06
14	6.87	6.91000000018812	-0.0400000001881162
15	6.91	6.87000274308356	0.0399972569164362
16	6.89	6.90999725710456	-0.0199972571045626
17	6.88	6.89000137135368	-0.0100013713536757
18	6.9	6.88000068586493	0.0199993141350694
19	6.91	6.89999862850526	0.0100013714947407
20	6.85	6.90999931413506	-0.0599993141350597
21	6.86	6.85000411457829	0.00999588542170926
22	6.82	6.85999931451128	-0.0399993145112782
23	6.8	6.82000274303654	-0.0200027430365424
24	6.83	6.80000137172989	0.029998628270115
25	6.84	6.82999794278141	0.0100020572185935
26	6.89	6.83999931408803	0.0500006859119653
27	7.14	6.88999657109852	0.250003428901477
28	7.21	7.13998285549266	0.0700171445073368
29	7.25	7.20999519842807	0.0400048015719339
30	7.31	7.24999725658717	0.0600027434128281
31	7.3	7.30999588518654	-0.00999588518653827
32	7.48	7.30000068548871	0.179999314511295
33	7.49	7.47998765617103	0.0100123438289694
34	7.4	7.48999931338261	-0.0899993133826085
35	7.44	7.4000061718909	0.0399938281090968
36	7.42	7.4399972573397	-0.0199972573396998
37	7.14	7.42000137135369	-0.280001371353692
38	7.24	7.1400192016789	0.0999807983211021
39	7.33	7.23999314360792	0.0900068563920815
40	7.61	7.32999382759182	0.280006172408181
41	7.66	7.60998079799186	0.0500192020081407
42	7.69	7.65999656982874	0.0300034301712566
43	7.7	7.68999794245211	0.0100020575478936
44	7.68	7.69999931408801	-0.0199993140880119
45	7.71	7.68000137149474	0.0299986285052629
46	7.71	7.70999794278139	2.05721860968566e-06
47	7.72	7.70999999985892	0.010000000141078
48	7.68	7.7199993142291	-0.0399993142291031
49	7.72	7.68000274303652	0.0399972569634777
50	7.74	7.71999725710456	0.0200027428954419
51	7.76	7.73999862827012	0.020001371729875
52	7.9	7.75999862836415	0.140001371635845
53	7.97	7.89999039911351	0.0700096008864897
54	7.96	7.96999519894539	-0.00999519894538548
55	7.95	7.96000068544165	-0.0100006854416455
56	7.97	7.95000068581789	0.0199993141821064
57	7.93	7.96999862850526	-0.0399986285052565
58	7.99	7.9300027429895	0.0599972570105027
59	7.96	7.98999588556278	-0.02999588556278
60	7.92	7.96000205703051	-0.0400020570305069
61	7.97	7.92000274322462	0.0499972567753835
62	7.98	7.96999657133368	0.0100034286663169
63	8	7.97999931399398	0.0200006860060151
64	8.04	7.99999862841118	0.0400013715888186
65	8.17	8.03999725682239	0.130002743177611
66	8.29	8.16999108479034	0.120008915209658
67	8.26	8.28999177013797	-0.0299917701379684
68	8.3	8.26000205674828	0.0399979432517181
69	8.32	8.2999972570575	0.0200027429425038
70	8.28	8.31999862827012	-0.0399986282701228
71	8.27	8.28000274298948	-0.0100027429894816
72	8.32	8.27000068595899	0.0499993140410062
73	8.31	8.3199965711926	-0.00999657119260178
74	8.34	8.31000068553575	0.0299993144642485
75	8.32	8.33999794273435	-0.0199979427343493
76	8.36	8.32000137140069	0.0399986285993048
77	8.33	8.35999725701049	-0.0299972570104945
78	8.35	8.33000205712456	0.0199979428754435
79	8.34	8.3499986285993	-0.00999862859929657
80	8.37	8.34000068567684	0.0299993143231578
81	8.31	8.36999794273436	-0.0599979427343573
82	8.33	8.31000411448425	0.0199958855157547
83	8.34	8.32999862874038	0.0100013712596159
84	8.25	8.33999931413508	-0.0899993141350759

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	8.25000617189095	8.11362819862611	8.38638414515579
86	8.25000617189095	8.05714520552604	8.44286713825587
87	8.25000617189095	8.01380339226592	8.48620895151599
88	8.25000617189095	7.97726425384758	8.52274808993433
89	8.25000617189095	7.94507248301194	8.55493986076997
90	8.25000617189095	7.91596881564356	8.58404352813834
91	8.25000617189095	7.88920517948083	8.61080716430108
92	8.25000617189095	7.86429415901151	8.6357181847704
93	8.25000617189095	7.84089719174642	8.65911515203549
94	8.25000617189095	7.81876777101473	8.68124457276718
95	8.25000617189095	7.79771980337465	8.70229254040726
96	8.25000617189095	7.77760871222267	8.72240363155924

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 8.25000617189095 & 8.11362819862611 & 8.38638414515579 \tabularnewline
86 & 8.25000617189095 & 8.05714520552604 & 8.44286713825587 \tabularnewline
87 & 8.25000617189095 & 8.01380339226592 & 8.48620895151599 \tabularnewline
88 & 8.25000617189095 & 7.97726425384758 & 8.52274808993433 \tabularnewline
89 & 8.25000617189095 & 7.94507248301194 & 8.55493986076997 \tabularnewline
90 & 8.25000617189095 & 7.91596881564356 & 8.58404352813834 \tabularnewline
91 & 8.25000617189095 & 7.88920517948083 & 8.61080716430108 \tabularnewline
92 & 8.25000617189095 & 7.86429415901151 & 8.6357181847704 \tabularnewline
93 & 8.25000617189095 & 7.84089719174642 & 8.65911515203549 \tabularnewline
94 & 8.25000617189095 & 7.81876777101473 & 8.68124457276718 \tabularnewline
95 & 8.25000617189095 & 7.79771980337465 & 8.70229254040726 \tabularnewline
96 & 8.25000617189095 & 7.77760871222267 & 8.72240363155924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167173&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]8.25000617189095[/C][C]8.11362819862611[/C][C]8.38638414515579[/C][/ROW]
[ROW][C]86[/C][C]8.25000617189095[/C][C]8.05714520552604[/C][C]8.44286713825587[/C][/ROW]
[ROW][C]87[/C][C]8.25000617189095[/C][C]8.01380339226592[/C][C]8.48620895151599[/C][/ROW]
[ROW][C]88[/C][C]8.25000617189095[/C][C]7.97726425384758[/C][C]8.52274808993433[/C][/ROW]
[ROW][C]89[/C][C]8.25000617189095[/C][C]7.94507248301194[/C][C]8.55493986076997[/C][/ROW]
[ROW][C]90[/C][C]8.25000617189095[/C][C]7.91596881564356[/C][C]8.58404352813834[/C][/ROW]
[ROW][C]91[/C][C]8.25000617189095[/C][C]7.88920517948083[/C][C]8.61080716430108[/C][/ROW]
[ROW][C]92[/C][C]8.25000617189095[/C][C]7.86429415901151[/C][C]8.6357181847704[/C][/ROW]
[ROW][C]93[/C][C]8.25000617189095[/C][C]7.84089719174642[/C][C]8.65911515203549[/C][/ROW]
[ROW][C]94[/C][C]8.25000617189095[/C][C]7.81876777101473[/C][C]8.68124457276718[/C][/ROW]
[ROW][C]95[/C][C]8.25000617189095[/C][C]7.79771980337465[/C][C]8.70229254040726[/C][/ROW]
[ROW][C]96[/C][C]8.25000617189095[/C][C]7.77760871222267[/C][C]8.72240363155924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167173&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167173&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	8.25000617189095	8.11362819862611	8.38638414515579
86	8.25000617189095	8.05714520552604	8.44286713825587
87	8.25000617189095	8.01380339226592	8.48620895151599
88	8.25000617189095	7.97726425384758	8.52274808993433
89	8.25000617189095	7.94507248301194	8.55493986076997
90	8.25000617189095	7.91596881564356	8.58404352813834
91	8.25000617189095	7.88920517948083	8.61080716430108
92	8.25000617189095	7.86429415901151	8.6357181847704
93	8.25000617189095	7.84089719174642	8.65911515203549
94	8.25000617189095	7.81876777101473	8.68124457276718
95	8.25000617189095	7.79771980337465	8.70229254040726
96	8.25000617189095	7.77760871222267	8.72240363155924

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