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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

Thu, 13 Jan 2011 08:56:05 +0000

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/Jan/13/t1294908838wf5zu9bv8doudub.htm/, Retrieved Tue, 10 Feb 2026 16:06:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117318, Retrieved Tue, 10 Feb 2026 16:06:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

531

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

-       [Exponential Smoothing] [werkloosheid] [2011-01-13 08:56:05] [d08a5fa9e4c562ec79e796d78c067f4f] [Current]

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Dataseries X:

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Boxplots

8,6
8,5
8,4
8,0
7,9
8,1
8,6
8,8
8,8
8,6
8,3
8,3
8,3
8,4
8,4
8,5
8,6
8,6
8,6
8,6
8,6
8,5
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,4
8,2
8,0
8,0
8,0
8,0
7,9
7,9
7,8
7,9
8,0
7,9
7,4
7,2
7,0
7,0
7,1
7,2
7,2
7,0
6,9
6,8
6,8
6,8
6,9
7,2
7,3
7,2
7,1
7,1
7,3
7,5
7,6
7,7
7,7
7,7
7,8
8,0
8,1
8,1
8,0
8,1
8,2
8,3
8,4
8,6
8,6
8,7
8,8
8,9

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	'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117318&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117318&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	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999938624722832
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999938624722832 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117318&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]0.999938624722832[/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=117318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117318&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	0.999938624722832
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	8.5	8.6	-0.0999999999999996
3	8.4	8.50000613752772	-0.100006137527716
4	8	8.4000061379044	-0.400006137904409
5	7.9	8.00002455048758	-0.100024550487582
6	8.1	7.90000613903451	0.199993860965489
7	8.6	8.09998772532135	0.50001227467865
8	8.8	8.59996931160805	0.200030688391946
9	8.8	8.79998772306106	1.22769389427901e-05
10	8.6	8.7999999992465	-0.199999999246501
11	8.3	8.60001227505539	-0.300012275055387
12	8.3	8.30001841333654	-1.84133365355166e-05
13	8.3	8.30000000113012	-1.13012355029696e-09
14	8.4	8.30000000000007	0.0999999999999304
15	8.4	8.39999386247228	6.13752771805309e-06
16	8.5	8.39999999962331	0.100000000376692
17	8.6	8.49999386247226	0.100006137527739
18	8.6	8.5999938620956	6.13790440873174e-06
19	8.6	8.59999999962328	3.7671554764529e-10
20	8.6	8.59999999999998	2.30926389122033e-14
21	8.6	8.6	0
22	8.5	8.6	-0.0999999999999996
23	8.4	8.50000613752772	-0.100006137527716
24	8.4	8.4000061379044	-6.13790440873174e-06
25	8.4	8.40000000037672	-3.7671554764529e-10
26	8.5	8.40000000000002	0.0999999999999766
27	8.5	8.49999386247228	6.13752771627674e-06
28	8.6	8.49999999962331	0.100000000376692
29	8.6	8.59999386247226	6.13752773936938e-06
30	8.4	8.59999999962331	-0.199999999623307
31	8.2	8.40001227505541	-0.200012275055411
32	8	8.20001227580882	-0.200012275808819
33	8	8.00001227580887	-1.22758088654251e-05
34	8	8.00000000075343	-7.5343109529058e-10
35	8	8.00000000000005	-4.61852778244065e-14
36	7.9	8	-0.0999999999999996
37	7.9	7.90000613752772	-6.13752771716491e-06
38	7.8	7.90000000037669	-0.100000000376693
39	7.9	7.80000613752774	0.0999938624722612
40	8	7.89999386284898	0.100006137151023
41	7.9	7.99999386209561	-0.0999938620956131
42	7.4	7.900006137151	-0.500006137151002
43	7.2	7.40003068801525	-0.200030688015254
44	7	7.20001227693892	-0.200012276938919
45	7	7.00001227580893	-1.22758089338149e-05
46	7.1	7.00000000075343	0.0999999992465685
47	7.2	7.09999386247233	0.100006137527671
48	7.2	7.1999938620956	6.13790440961992e-06
49	7	7.19999999962328	-0.199999999623285
50	6.9	7.00001227505541	-0.10001227505541
51	6.8	6.9000061382811	-0.100006138281103
52	6.8	6.80000613790445	-6.13790445491702e-06
53	6.8	6.80000000037672	-3.7671554764529e-10
54	6.9	6.80000000000002	0.0999999999999774
55	7.2	6.89999386247228	0.300006137527716
56	7.3	7.19998158704016	0.100018412959843
57	7.2	7.29999386134218	-0.099993861342182
58	7.1	7.20000613715096	-0.100006137150956
59	7.1	7.10000613790439	-6.13790438652728e-06
60	7.3	7.10000000037672	0.199999999623284
61	7.5	7.29998772494459	0.200012275055411
62	7.6	7.49998772419118	0.100012275808818
63	7.7	7.59999386171885	0.100006138281149
64	7.7	7.69999386209554	6.1379044558052e-06
65	7.7	7.69999999962328	3.7671554764529e-10
66	7.8	7.69999999999998	0.100000000000023
67	8	7.79999386247228	0.200006137527717
68	8.1	7.99998772456787	0.100012275432126
69	8.1	8.09999386171887	6.13828112605574e-06
70	8	8.09999999962326	-0.099999999623261
71	8.1	8.0000061375277	0.0999938624723065
72	8.2	8.09999386284898	0.100006137151023
73	8.3	8.19999386209561	0.100006137904387
74	8.4	8.29999386209557	0.100006137904431
75	8.6	8.39999386209557	0.200006137904433
76	8.6	8.59998772456785	1.22754321481011e-05
77	8.7	8.59999999924659	0.100000000753408
78	8.8	8.69999386247224	0.100006137527766
79	8.9	8.7999938620956	0.100006137904408

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 8.5 & 8.6 & -0.0999999999999996 \tabularnewline
3 & 8.4 & 8.50000613752772 & -0.100006137527716 \tabularnewline
4 & 8 & 8.4000061379044 & -0.400006137904409 \tabularnewline
5 & 7.9 & 8.00002455048758 & -0.100024550487582 \tabularnewline
6 & 8.1 & 7.90000613903451 & 0.199993860965489 \tabularnewline
7 & 8.6 & 8.09998772532135 & 0.50001227467865 \tabularnewline
8 & 8.8 & 8.59996931160805 & 0.200030688391946 \tabularnewline
9 & 8.8 & 8.79998772306106 & 1.22769389427901e-05 \tabularnewline
10 & 8.6 & 8.7999999992465 & -0.199999999246501 \tabularnewline
11 & 8.3 & 8.60001227505539 & -0.300012275055387 \tabularnewline
12 & 8.3 & 8.30001841333654 & -1.84133365355166e-05 \tabularnewline
13 & 8.3 & 8.30000000113012 & -1.13012355029696e-09 \tabularnewline
14 & 8.4 & 8.30000000000007 & 0.0999999999999304 \tabularnewline
15 & 8.4 & 8.39999386247228 & 6.13752771805309e-06 \tabularnewline
16 & 8.5 & 8.39999999962331 & 0.100000000376692 \tabularnewline
17 & 8.6 & 8.49999386247226 & 0.100006137527739 \tabularnewline
18 & 8.6 & 8.5999938620956 & 6.13790440873174e-06 \tabularnewline
19 & 8.6 & 8.59999999962328 & 3.7671554764529e-10 \tabularnewline
20 & 8.6 & 8.59999999999998 & 2.30926389122033e-14 \tabularnewline
21 & 8.6 & 8.6 & 0 \tabularnewline
22 & 8.5 & 8.6 & -0.0999999999999996 \tabularnewline
23 & 8.4 & 8.50000613752772 & -0.100006137527716 \tabularnewline
24 & 8.4 & 8.4000061379044 & -6.13790440873174e-06 \tabularnewline
25 & 8.4 & 8.40000000037672 & -3.7671554764529e-10 \tabularnewline
26 & 8.5 & 8.40000000000002 & 0.0999999999999766 \tabularnewline
27 & 8.5 & 8.49999386247228 & 6.13752771627674e-06 \tabularnewline
28 & 8.6 & 8.49999999962331 & 0.100000000376692 \tabularnewline
29 & 8.6 & 8.59999386247226 & 6.13752773936938e-06 \tabularnewline
30 & 8.4 & 8.59999999962331 & -0.199999999623307 \tabularnewline
31 & 8.2 & 8.40001227505541 & -0.200012275055411 \tabularnewline
32 & 8 & 8.20001227580882 & -0.200012275808819 \tabularnewline
33 & 8 & 8.00001227580887 & -1.22758088654251e-05 \tabularnewline
34 & 8 & 8.00000000075343 & -7.5343109529058e-10 \tabularnewline
35 & 8 & 8.00000000000005 & -4.61852778244065e-14 \tabularnewline
36 & 7.9 & 8 & -0.0999999999999996 \tabularnewline
37 & 7.9 & 7.90000613752772 & -6.13752771716491e-06 \tabularnewline
38 & 7.8 & 7.90000000037669 & -0.100000000376693 \tabularnewline
39 & 7.9 & 7.80000613752774 & 0.0999938624722612 \tabularnewline
40 & 8 & 7.89999386284898 & 0.100006137151023 \tabularnewline
41 & 7.9 & 7.99999386209561 & -0.0999938620956131 \tabularnewline
42 & 7.4 & 7.900006137151 & -0.500006137151002 \tabularnewline
43 & 7.2 & 7.40003068801525 & -0.200030688015254 \tabularnewline
44 & 7 & 7.20001227693892 & -0.200012276938919 \tabularnewline
45 & 7 & 7.00001227580893 & -1.22758089338149e-05 \tabularnewline
46 & 7.1 & 7.00000000075343 & 0.0999999992465685 \tabularnewline
47 & 7.2 & 7.09999386247233 & 0.100006137527671 \tabularnewline
48 & 7.2 & 7.1999938620956 & 6.13790440961992e-06 \tabularnewline
49 & 7 & 7.19999999962328 & -0.199999999623285 \tabularnewline
50 & 6.9 & 7.00001227505541 & -0.10001227505541 \tabularnewline
51 & 6.8 & 6.9000061382811 & -0.100006138281103 \tabularnewline
52 & 6.8 & 6.80000613790445 & -6.13790445491702e-06 \tabularnewline
53 & 6.8 & 6.80000000037672 & -3.7671554764529e-10 \tabularnewline
54 & 6.9 & 6.80000000000002 & 0.0999999999999774 \tabularnewline
55 & 7.2 & 6.89999386247228 & 0.300006137527716 \tabularnewline
56 & 7.3 & 7.19998158704016 & 0.100018412959843 \tabularnewline
57 & 7.2 & 7.29999386134218 & -0.099993861342182 \tabularnewline
58 & 7.1 & 7.20000613715096 & -0.100006137150956 \tabularnewline
59 & 7.1 & 7.10000613790439 & -6.13790438652728e-06 \tabularnewline
60 & 7.3 & 7.10000000037672 & 0.199999999623284 \tabularnewline
61 & 7.5 & 7.29998772494459 & 0.200012275055411 \tabularnewline
62 & 7.6 & 7.49998772419118 & 0.100012275808818 \tabularnewline
63 & 7.7 & 7.59999386171885 & 0.100006138281149 \tabularnewline
64 & 7.7 & 7.69999386209554 & 6.1379044558052e-06 \tabularnewline
65 & 7.7 & 7.69999999962328 & 3.7671554764529e-10 \tabularnewline
66 & 7.8 & 7.69999999999998 & 0.100000000000023 \tabularnewline
67 & 8 & 7.79999386247228 & 0.200006137527717 \tabularnewline
68 & 8.1 & 7.99998772456787 & 0.100012275432126 \tabularnewline
69 & 8.1 & 8.09999386171887 & 6.13828112605574e-06 \tabularnewline
70 & 8 & 8.09999999962326 & -0.099999999623261 \tabularnewline
71 & 8.1 & 8.0000061375277 & 0.0999938624723065 \tabularnewline
72 & 8.2 & 8.09999386284898 & 0.100006137151023 \tabularnewline
73 & 8.3 & 8.19999386209561 & 0.100006137904387 \tabularnewline
74 & 8.4 & 8.29999386209557 & 0.100006137904431 \tabularnewline
75 & 8.6 & 8.39999386209557 & 0.200006137904433 \tabularnewline
76 & 8.6 & 8.59998772456785 & 1.22754321481011e-05 \tabularnewline
77 & 8.7 & 8.59999999924659 & 0.100000000753408 \tabularnewline
78 & 8.8 & 8.69999386247224 & 0.100006137527766 \tabularnewline
79 & 8.9 & 8.7999938620956 & 0.100006137904408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117318&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]8.5[/C][C]8.6[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.50000613752772[/C][C]-0.100006137527716[/C][/ROW]
[ROW][C]4[/C][C]8[/C][C]8.4000061379044[/C][C]-0.400006137904409[/C][/ROW]
[ROW][C]5[/C][C]7.9[/C][C]8.00002455048758[/C][C]-0.100024550487582[/C][/ROW]
[ROW][C]6[/C][C]8.1[/C][C]7.90000613903451[/C][C]0.199993860965489[/C][/ROW]
[ROW][C]7[/C][C]8.6[/C][C]8.09998772532135[/C][C]0.50001227467865[/C][/ROW]
[ROW][C]8[/C][C]8.8[/C][C]8.59996931160805[/C][C]0.200030688391946[/C][/ROW]
[ROW][C]9[/C][C]8.8[/C][C]8.79998772306106[/C][C]1.22769389427901e-05[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.7999999992465[/C][C]-0.199999999246501[/C][/ROW]
[ROW][C]11[/C][C]8.3[/C][C]8.60001227505539[/C][C]-0.300012275055387[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.30001841333654[/C][C]-1.84133365355166e-05[/C][/ROW]
[ROW][C]13[/C][C]8.3[/C][C]8.30000000113012[/C][C]-1.13012355029696e-09[/C][/ROW]
[ROW][C]14[/C][C]8.4[/C][C]8.30000000000007[/C][C]0.0999999999999304[/C][/ROW]
[ROW][C]15[/C][C]8.4[/C][C]8.39999386247228[/C][C]6.13752771805309e-06[/C][/ROW]
[ROW][C]16[/C][C]8.5[/C][C]8.39999999962331[/C][C]0.100000000376692[/C][/ROW]
[ROW][C]17[/C][C]8.6[/C][C]8.49999386247226[/C][C]0.100006137527739[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.5999938620956[/C][C]6.13790440873174e-06[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]8.59999999962328[/C][C]3.7671554764529e-10[/C][/ROW]
[ROW][C]20[/C][C]8.6[/C][C]8.59999999999998[/C][C]2.30926389122033e-14[/C][/ROW]
[ROW][C]21[/C][C]8.6[/C][C]8.6[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.6[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]8.50000613752772[/C][C]-0.100006137527716[/C][/ROW]
[ROW][C]24[/C][C]8.4[/C][C]8.4000061379044[/C][C]-6.13790440873174e-06[/C][/ROW]
[ROW][C]25[/C][C]8.4[/C][C]8.40000000037672[/C][C]-3.7671554764529e-10[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.40000000000002[/C][C]0.0999999999999766[/C][/ROW]
[ROW][C]27[/C][C]8.5[/C][C]8.49999386247228[/C][C]6.13752771627674e-06[/C][/ROW]
[ROW][C]28[/C][C]8.6[/C][C]8.49999999962331[/C][C]0.100000000376692[/C][/ROW]
[ROW][C]29[/C][C]8.6[/C][C]8.59999386247226[/C][C]6.13752773936938e-06[/C][/ROW]
[ROW][C]30[/C][C]8.4[/C][C]8.59999999962331[/C][C]-0.199999999623307[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.40001227505541[/C][C]-0.200012275055411[/C][/ROW]
[ROW][C]32[/C][C]8[/C][C]8.20001227580882[/C][C]-0.200012275808819[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]8.00001227580887[/C][C]-1.22758088654251e-05[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.00000000075343[/C][C]-7.5343109529058e-10[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]8.00000000000005[/C][C]-4.61852778244065e-14[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]7.90000613752772[/C][C]-6.13752771716491e-06[/C][/ROW]
[ROW][C]38[/C][C]7.8[/C][C]7.90000000037669[/C][C]-0.100000000376693[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.80000613752774[/C][C]0.0999938624722612[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.89999386284898[/C][C]0.100006137151023[/C][/ROW]
[ROW][C]41[/C][C]7.9[/C][C]7.99999386209561[/C][C]-0.0999938620956131[/C][/ROW]
[ROW][C]42[/C][C]7.4[/C][C]7.900006137151[/C][C]-0.500006137151002[/C][/ROW]
[ROW][C]43[/C][C]7.2[/C][C]7.40003068801525[/C][C]-0.200030688015254[/C][/ROW]
[ROW][C]44[/C][C]7[/C][C]7.20001227693892[/C][C]-0.200012276938919[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.00001227580893[/C][C]-1.22758089338149e-05[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.00000000075343[/C][C]0.0999999992465685[/C][/ROW]
[ROW][C]47[/C][C]7.2[/C][C]7.09999386247233[/C][C]0.100006137527671[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.1999938620956[/C][C]6.13790440961992e-06[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.19999999962328[/C][C]-0.199999999623285[/C][/ROW]
[ROW][C]50[/C][C]6.9[/C][C]7.00001227505541[/C][C]-0.10001227505541[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]6.9000061382811[/C][C]-0.100006138281103[/C][/ROW]
[ROW][C]52[/C][C]6.8[/C][C]6.80000613790445[/C][C]-6.13790445491702e-06[/C][/ROW]
[ROW][C]53[/C][C]6.8[/C][C]6.80000000037672[/C][C]-3.7671554764529e-10[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.80000000000002[/C][C]0.0999999999999774[/C][/ROW]
[ROW][C]55[/C][C]7.2[/C][C]6.89999386247228[/C][C]0.300006137527716[/C][/ROW]
[ROW][C]56[/C][C]7.3[/C][C]7.19998158704016[/C][C]0.100018412959843[/C][/ROW]
[ROW][C]57[/C][C]7.2[/C][C]7.29999386134218[/C][C]-0.099993861342182[/C][/ROW]
[ROW][C]58[/C][C]7.1[/C][C]7.20000613715096[/C][C]-0.100006137150956[/C][/ROW]
[ROW][C]59[/C][C]7.1[/C][C]7.10000613790439[/C][C]-6.13790438652728e-06[/C][/ROW]
[ROW][C]60[/C][C]7.3[/C][C]7.10000000037672[/C][C]0.199999999623284[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.29998772494459[/C][C]0.200012275055411[/C][/ROW]
[ROW][C]62[/C][C]7.6[/C][C]7.49998772419118[/C][C]0.100012275808818[/C][/ROW]
[ROW][C]63[/C][C]7.7[/C][C]7.59999386171885[/C][C]0.100006138281149[/C][/ROW]
[ROW][C]64[/C][C]7.7[/C][C]7.69999386209554[/C][C]6.1379044558052e-06[/C][/ROW]
[ROW][C]65[/C][C]7.7[/C][C]7.69999999962328[/C][C]3.7671554764529e-10[/C][/ROW]
[ROW][C]66[/C][C]7.8[/C][C]7.69999999999998[/C][C]0.100000000000023[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]7.79999386247228[/C][C]0.200006137527717[/C][/ROW]
[ROW][C]68[/C][C]8.1[/C][C]7.99998772456787[/C][C]0.100012275432126[/C][/ROW]
[ROW][C]69[/C][C]8.1[/C][C]8.09999386171887[/C][C]6.13828112605574e-06[/C][/ROW]
[ROW][C]70[/C][C]8[/C][C]8.09999999962326[/C][C]-0.099999999623261[/C][/ROW]
[ROW][C]71[/C][C]8.1[/C][C]8.0000061375277[/C][C]0.0999938624723065[/C][/ROW]
[ROW][C]72[/C][C]8.2[/C][C]8.09999386284898[/C][C]0.100006137151023[/C][/ROW]
[ROW][C]73[/C][C]8.3[/C][C]8.19999386209561[/C][C]0.100006137904387[/C][/ROW]
[ROW][C]74[/C][C]8.4[/C][C]8.29999386209557[/C][C]0.100006137904431[/C][/ROW]
[ROW][C]75[/C][C]8.6[/C][C]8.39999386209557[/C][C]0.200006137904433[/C][/ROW]
[ROW][C]76[/C][C]8.6[/C][C]8.59998772456785[/C][C]1.22754321481011e-05[/C][/ROW]
[ROW][C]77[/C][C]8.7[/C][C]8.59999999924659[/C][C]0.100000000753408[/C][/ROW]
[ROW][C]78[/C][C]8.8[/C][C]8.69999386247224[/C][C]0.100006137527766[/C][/ROW]
[ROW][C]79[/C][C]8.9[/C][C]8.7999938620956[/C][C]0.100006137904408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117318&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117318&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	8.5	8.6	-0.0999999999999996
3	8.4	8.50000613752772	-0.100006137527716
4	8	8.4000061379044	-0.400006137904409
5	7.9	8.00002455048758	-0.100024550487582
6	8.1	7.90000613903451	0.199993860965489
7	8.6	8.09998772532135	0.50001227467865
8	8.8	8.59996931160805	0.200030688391946
9	8.8	8.79998772306106	1.22769389427901e-05
10	8.6	8.7999999992465	-0.199999999246501
11	8.3	8.60001227505539	-0.300012275055387
12	8.3	8.30001841333654	-1.84133365355166e-05
13	8.3	8.30000000113012	-1.13012355029696e-09
14	8.4	8.30000000000007	0.0999999999999304
15	8.4	8.39999386247228	6.13752771805309e-06
16	8.5	8.39999999962331	0.100000000376692
17	8.6	8.49999386247226	0.100006137527739
18	8.6	8.5999938620956	6.13790440873174e-06
19	8.6	8.59999999962328	3.7671554764529e-10
20	8.6	8.59999999999998	2.30926389122033e-14
21	8.6	8.6	0
22	8.5	8.6	-0.0999999999999996
23	8.4	8.50000613752772	-0.100006137527716
24	8.4	8.4000061379044	-6.13790440873174e-06
25	8.4	8.40000000037672	-3.7671554764529e-10
26	8.5	8.40000000000002	0.0999999999999766
27	8.5	8.49999386247228	6.13752771627674e-06
28	8.6	8.49999999962331	0.100000000376692
29	8.6	8.59999386247226	6.13752773936938e-06
30	8.4	8.59999999962331	-0.199999999623307
31	8.2	8.40001227505541	-0.200012275055411
32	8	8.20001227580882	-0.200012275808819
33	8	8.00001227580887	-1.22758088654251e-05
34	8	8.00000000075343	-7.5343109529058e-10
35	8	8.00000000000005	-4.61852778244065e-14
36	7.9	8	-0.0999999999999996
37	7.9	7.90000613752772	-6.13752771716491e-06
38	7.8	7.90000000037669	-0.100000000376693
39	7.9	7.80000613752774	0.0999938624722612
40	8	7.89999386284898	0.100006137151023
41	7.9	7.99999386209561	-0.0999938620956131
42	7.4	7.900006137151	-0.500006137151002
43	7.2	7.40003068801525	-0.200030688015254
44	7	7.20001227693892	-0.200012276938919
45	7	7.00001227580893	-1.22758089338149e-05
46	7.1	7.00000000075343	0.0999999992465685
47	7.2	7.09999386247233	0.100006137527671
48	7.2	7.1999938620956	6.13790440961992e-06
49	7	7.19999999962328	-0.199999999623285
50	6.9	7.00001227505541	-0.10001227505541
51	6.8	6.9000061382811	-0.100006138281103
52	6.8	6.80000613790445	-6.13790445491702e-06
53	6.8	6.80000000037672	-3.7671554764529e-10
54	6.9	6.80000000000002	0.0999999999999774
55	7.2	6.89999386247228	0.300006137527716
56	7.3	7.19998158704016	0.100018412959843
57	7.2	7.29999386134218	-0.099993861342182
58	7.1	7.20000613715096	-0.100006137150956
59	7.1	7.10000613790439	-6.13790438652728e-06
60	7.3	7.10000000037672	0.199999999623284
61	7.5	7.29998772494459	0.200012275055411
62	7.6	7.49998772419118	0.100012275808818
63	7.7	7.59999386171885	0.100006138281149
64	7.7	7.69999386209554	6.1379044558052e-06
65	7.7	7.69999999962328	3.7671554764529e-10
66	7.8	7.69999999999998	0.100000000000023
67	8	7.79999386247228	0.200006137527717
68	8.1	7.99998772456787	0.100012275432126
69	8.1	8.09999386171887	6.13828112605574e-06
70	8	8.09999999962326	-0.099999999623261
71	8.1	8.0000061375277	0.0999938624723065
72	8.2	8.09999386284898	0.100006137151023
73	8.3	8.19999386209561	0.100006137904387
74	8.4	8.29999386209557	0.100006137904431
75	8.6	8.39999386209557	0.200006137904433
76	8.6	8.59998772456785	1.22754321481011e-05
77	8.7	8.59999999924659	0.100000000753408
78	8.8	8.69999386247224	0.100006137527766
79	8.9	8.7999938620956	0.100006137904408

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
80	8.89999386209557	8.60800389717144	9.19198382701969
81	8.89999386209557	8.48707036546448	9.31291735872666
82	8.89999386209557	8.39427310068301	9.40571462350812
83	8.89999386209557	8.31604081348862	9.48394691070252
84	8.89999386209557	8.2471165095775	9.55287121461363
85	8.89999386209557	8.18480401884788	9.61518370534326
86	8.89999386209557	8.1275016703303	9.67248605386084
87	8.89999386209557	8.07416587710598	9.72582184708515
88	8.89999386209557	8.02407175640031	9.77591596779082
89	8.89999386209557	7.97669152282676	9.82329620136438
90	8.89999386209557	7.93162673948508	9.86836098470606
91	8.89999386209557	7.88856785955926	9.91141986463187

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
80 & 8.89999386209557 & 8.60800389717144 & 9.19198382701969 \tabularnewline
81 & 8.89999386209557 & 8.48707036546448 & 9.31291735872666 \tabularnewline
82 & 8.89999386209557 & 8.39427310068301 & 9.40571462350812 \tabularnewline
83 & 8.89999386209557 & 8.31604081348862 & 9.48394691070252 \tabularnewline
84 & 8.89999386209557 & 8.2471165095775 & 9.55287121461363 \tabularnewline
85 & 8.89999386209557 & 8.18480401884788 & 9.61518370534326 \tabularnewline
86 & 8.89999386209557 & 8.1275016703303 & 9.67248605386084 \tabularnewline
87 & 8.89999386209557 & 8.07416587710598 & 9.72582184708515 \tabularnewline
88 & 8.89999386209557 & 8.02407175640031 & 9.77591596779082 \tabularnewline
89 & 8.89999386209557 & 7.97669152282676 & 9.82329620136438 \tabularnewline
90 & 8.89999386209557 & 7.93162673948508 & 9.86836098470606 \tabularnewline
91 & 8.89999386209557 & 7.88856785955926 & 9.91141986463187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117318&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]80[/C][C]8.89999386209557[/C][C]8.60800389717144[/C][C]9.19198382701969[/C][/ROW]
[ROW][C]81[/C][C]8.89999386209557[/C][C]8.48707036546448[/C][C]9.31291735872666[/C][/ROW]
[ROW][C]82[/C][C]8.89999386209557[/C][C]8.39427310068301[/C][C]9.40571462350812[/C][/ROW]
[ROW][C]83[/C][C]8.89999386209557[/C][C]8.31604081348862[/C][C]9.48394691070252[/C][/ROW]
[ROW][C]84[/C][C]8.89999386209557[/C][C]8.2471165095775[/C][C]9.55287121461363[/C][/ROW]
[ROW][C]85[/C][C]8.89999386209557[/C][C]8.18480401884788[/C][C]9.61518370534326[/C][/ROW]
[ROW][C]86[/C][C]8.89999386209557[/C][C]8.1275016703303[/C][C]9.67248605386084[/C][/ROW]
[ROW][C]87[/C][C]8.89999386209557[/C][C]8.07416587710598[/C][C]9.72582184708515[/C][/ROW]
[ROW][C]88[/C][C]8.89999386209557[/C][C]8.02407175640031[/C][C]9.77591596779082[/C][/ROW]
[ROW][C]89[/C][C]8.89999386209557[/C][C]7.97669152282676[/C][C]9.82329620136438[/C][/ROW]
[ROW][C]90[/C][C]8.89999386209557[/C][C]7.93162673948508[/C][C]9.86836098470606[/C][/ROW]
[ROW][C]91[/C][C]8.89999386209557[/C][C]7.88856785955926[/C][C]9.91141986463187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117318&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117318&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
80	8.89999386209557	8.60800389717144	9.19198382701969
81	8.89999386209557	8.48707036546448	9.31291735872666
82	8.89999386209557	8.39427310068301	9.40571462350812
83	8.89999386209557	8.31604081348862	9.48394691070252
84	8.89999386209557	8.2471165095775	9.55287121461363
85	8.89999386209557	8.18480401884788	9.61518370534326
86	8.89999386209557	8.1275016703303	9.67248605386084
87	8.89999386209557	8.07416587710598	9.72582184708515
88	8.89999386209557	8.02407175640031	9.77591596779082
89	8.89999386209557	7.97669152282676	9.82329620136438
90	8.89999386209557	7.93162673948508	9.86836098470606
91	8.89999386209557	7.88856785955926	9.91141986463187

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 ;

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