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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 22 May 2014 12:19:46 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/22/t1400775600zccjstel93d4qfa.htm/, Retrieved Wed, 15 May 2024 04:02:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235132, Retrieved Wed, 15 May 2024 04:02:41 +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] [] [2014-05-22 16:19:46] [de6881b70973343210d9b2d7428035f3] [Current]

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Dataseries X:

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6
6,7
-0,6
5,8
16,4
1,5
5,1
14,7
4,3
1,5
9,1
4,3
5,7
13
14,5
9,7
-4,7
7,3
5,2
-2,5
11,5
4,9
-2,4
-0,3
4,4
7,9
-9,7
-4,1
16,4
-4,9
3,5
3,8
-0,2
3,1
0,7
-2,8
5,9
-5,3
-2,9
6,6
-8,1
1,3
6,9
-7,2
-1,9
4
-5,7
3,9
-7,6
-0,9
7,3
-3,7
-2,5
9,3
1,3
9,5
11,3
-1,7
8
-4,8
1,6
1,9
-0,9
5,5
1,7
-5,4
1,9
0,2
-13,3
-8,2
0,2
5,7
-1,2
-2,8
5,5
-17,3
1,4
-2,2
-8,6
-5
4,1
0,7
-4,2
-2,3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235132&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]2 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=235132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235132&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0103060729385444
beta	0
gamma	0.244165532004629

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0103060729385444 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.244165532004629 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235132&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]0.0103060729385444[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.244165532004629[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235132&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	0.0103060729385444
beta	0
gamma	0.244165532004629

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	5.7	5.52903311965812	0.17096688034188
14	13	13.4212234384753	-0.42122343847532
15	14.5	15.21147726734	-0.711477267339959
16	9.7	9.84040638574029	-0.14040638574029
17	-4.7	-4.34561233103387	-0.354387668966133
18	7.3	8.1994969788129	-0.899496978812905
19	5.2	4.99732168568625	0.202678314313755
20	-2.5	14.2273388248549	-16.7273388248549
21	11.5	2.6412073058699	8.8587926941301
22	4.9	-0.981231675465295	5.88123167546529
23	-2.4	7.27397571549552	-9.67397571549552
24	-0.3	2.88970333784423	-3.18970333784423
25	4.4	3.93023901126212	0.469760988737876
26	7.9	11.6824064401949	-3.78240644019491
27	-9.7	13.3678800825315	-23.0678800825315
28	-4.1	7.90440127270408	-12.0044012727041
29	16.4	-6.45559703468884	22.8555970346888
30	-4.9	6.19699087218399	-11.096990872184
31	3.5	3.15605917956936	0.343940820430638
32	3.8	8.29640802707364	-4.49640802707364
33	-0.2	3.01919615852928	-3.21919615852928
34	3.1	-1.4472445289036	4.5472445289036
35	0.7	3.0353121389932	-2.3353121389932
36	-2.8	0.293591434399185	-3.09359143439918
37	5.9	2.21942406693635	3.68057593306365
38	-5.3	8.97714976858423	-14.2771497685842
39	-2.9	5.89414561910687	-8.79414561910687
40	6.6	3.2512531442858	3.3487468557142
41	-8.1	-2.52662574007273	-5.57337425992727
42	1.3	1.62835730322783	-0.328357303227829
43	6.9	1.46309928625414	5.43690071374587
44	-7.2	5.48627039315321	-12.6862703931532
45	-1.9	0.433290360732229	-2.33329036073223
46	4	-2.14726637115728	6.14726637115728
47	-5.7	0.688616309687475	-6.38861630968748
48	3.9	-2.27811558614848	6.17811558614848
49	-7.6	1.38024368237607	-8.98024368237607
50	-0.9	3.66801700561609	-4.56801700561609
51	7.3	2.01003914705467	5.28996085294533
52	-3.7	2.4466180757377	-6.1466180757377
53	-2.5	-5.58514366442861	3.08514366442861
54	9.3	-0.0734714448399174	9.37347144483992
55	1.3	1.25442795892606	0.0455720410739422
56	9.5	0.842586850704988	8.65741314929501
57	11.3	-1.48863485736097	12.788634857361
58	-1.7	-1.86402464818834	0.164024648188343
59	8	-2.11909101485189	10.1190910148519
60	-4.8	-1.87895326664799	-2.92104673335201
61	1.6	-1.97737517372722	3.57737517372722
62	1.9	1.5060286859339	0.393971314066097
63	-0.9	2.28136135420313	-3.18136135420313
64	5.5	-0.133005292618365	5.63300529261836
65	1.7	-5.81251805098266	7.51251805098266
66	-5.4	1.26435203868839	-6.66435203868839
67	1.9	0.172885555542042	1.72711444445796
68	0.2	1.85941857996309	-1.65941857996309
69	-13.3	0.420177041949132	-13.7201770419491
70	-8.2	-3.27914075101855	-4.92085924898145
71	0.2	-1.18097903382582	1.38097903382582
72	5.7	-4.18203503244329	9.88203503244329
73	-1.2	-2.57816935236227	1.37816935236227
74	-2.8	0.11330251329461	-2.91330251329461
75	5.5	-0.00942590332744031	5.50942590332744
76	-17.3	-0.204240505709835	-17.0957594942902
77	1.4	-5.66381492215663	7.06381492215663
78	-2.2	-2.01739772458457	-0.182602275415433
79	-8.6	-1.01427212747536	-7.58572787252464
80	-5	-0.242070742471592	-4.75792925752841
81	4.1	-4.62771771854514	8.72771771854514
82	0.7	-5.96933825638009	6.66933825638009
83	-4.2	-2.22889329025467	-1.97110670974533
84	-2.3	-3.21022322198638	0.910223221986382

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.7 & 5.52903311965812 & 0.17096688034188 \tabularnewline
14 & 13 & 13.4212234384753 & -0.42122343847532 \tabularnewline
15 & 14.5 & 15.21147726734 & -0.711477267339959 \tabularnewline
16 & 9.7 & 9.84040638574029 & -0.14040638574029 \tabularnewline
17 & -4.7 & -4.34561233103387 & -0.354387668966133 \tabularnewline
18 & 7.3 & 8.1994969788129 & -0.899496978812905 \tabularnewline
19 & 5.2 & 4.99732168568625 & 0.202678314313755 \tabularnewline
20 & -2.5 & 14.2273388248549 & -16.7273388248549 \tabularnewline
21 & 11.5 & 2.6412073058699 & 8.8587926941301 \tabularnewline
22 & 4.9 & -0.981231675465295 & 5.88123167546529 \tabularnewline
23 & -2.4 & 7.27397571549552 & -9.67397571549552 \tabularnewline
24 & -0.3 & 2.88970333784423 & -3.18970333784423 \tabularnewline
25 & 4.4 & 3.93023901126212 & 0.469760988737876 \tabularnewline
26 & 7.9 & 11.6824064401949 & -3.78240644019491 \tabularnewline
27 & -9.7 & 13.3678800825315 & -23.0678800825315 \tabularnewline
28 & -4.1 & 7.90440127270408 & -12.0044012727041 \tabularnewline
29 & 16.4 & -6.45559703468884 & 22.8555970346888 \tabularnewline
30 & -4.9 & 6.19699087218399 & -11.096990872184 \tabularnewline
31 & 3.5 & 3.15605917956936 & 0.343940820430638 \tabularnewline
32 & 3.8 & 8.29640802707364 & -4.49640802707364 \tabularnewline
33 & -0.2 & 3.01919615852928 & -3.21919615852928 \tabularnewline
34 & 3.1 & -1.4472445289036 & 4.5472445289036 \tabularnewline
35 & 0.7 & 3.0353121389932 & -2.3353121389932 \tabularnewline
36 & -2.8 & 0.293591434399185 & -3.09359143439918 \tabularnewline
37 & 5.9 & 2.21942406693635 & 3.68057593306365 \tabularnewline
38 & -5.3 & 8.97714976858423 & -14.2771497685842 \tabularnewline
39 & -2.9 & 5.89414561910687 & -8.79414561910687 \tabularnewline
40 & 6.6 & 3.2512531442858 & 3.3487468557142 \tabularnewline
41 & -8.1 & -2.52662574007273 & -5.57337425992727 \tabularnewline
42 & 1.3 & 1.62835730322783 & -0.328357303227829 \tabularnewline
43 & 6.9 & 1.46309928625414 & 5.43690071374587 \tabularnewline
44 & -7.2 & 5.48627039315321 & -12.6862703931532 \tabularnewline
45 & -1.9 & 0.433290360732229 & -2.33329036073223 \tabularnewline
46 & 4 & -2.14726637115728 & 6.14726637115728 \tabularnewline
47 & -5.7 & 0.688616309687475 & -6.38861630968748 \tabularnewline
48 & 3.9 & -2.27811558614848 & 6.17811558614848 \tabularnewline
49 & -7.6 & 1.38024368237607 & -8.98024368237607 \tabularnewline
50 & -0.9 & 3.66801700561609 & -4.56801700561609 \tabularnewline
51 & 7.3 & 2.01003914705467 & 5.28996085294533 \tabularnewline
52 & -3.7 & 2.4466180757377 & -6.1466180757377 \tabularnewline
53 & -2.5 & -5.58514366442861 & 3.08514366442861 \tabularnewline
54 & 9.3 & -0.0734714448399174 & 9.37347144483992 \tabularnewline
55 & 1.3 & 1.25442795892606 & 0.0455720410739422 \tabularnewline
56 & 9.5 & 0.842586850704988 & 8.65741314929501 \tabularnewline
57 & 11.3 & -1.48863485736097 & 12.788634857361 \tabularnewline
58 & -1.7 & -1.86402464818834 & 0.164024648188343 \tabularnewline
59 & 8 & -2.11909101485189 & 10.1190910148519 \tabularnewline
60 & -4.8 & -1.87895326664799 & -2.92104673335201 \tabularnewline
61 & 1.6 & -1.97737517372722 & 3.57737517372722 \tabularnewline
62 & 1.9 & 1.5060286859339 & 0.393971314066097 \tabularnewline
63 & -0.9 & 2.28136135420313 & -3.18136135420313 \tabularnewline
64 & 5.5 & -0.133005292618365 & 5.63300529261836 \tabularnewline
65 & 1.7 & -5.81251805098266 & 7.51251805098266 \tabularnewline
66 & -5.4 & 1.26435203868839 & -6.66435203868839 \tabularnewline
67 & 1.9 & 0.172885555542042 & 1.72711444445796 \tabularnewline
68 & 0.2 & 1.85941857996309 & -1.65941857996309 \tabularnewline
69 & -13.3 & 0.420177041949132 & -13.7201770419491 \tabularnewline
70 & -8.2 & -3.27914075101855 & -4.92085924898145 \tabularnewline
71 & 0.2 & -1.18097903382582 & 1.38097903382582 \tabularnewline
72 & 5.7 & -4.18203503244329 & 9.88203503244329 \tabularnewline
73 & -1.2 & -2.57816935236227 & 1.37816935236227 \tabularnewline
74 & -2.8 & 0.11330251329461 & -2.91330251329461 \tabularnewline
75 & 5.5 & -0.00942590332744031 & 5.50942590332744 \tabularnewline
76 & -17.3 & -0.204240505709835 & -17.0957594942902 \tabularnewline
77 & 1.4 & -5.66381492215663 & 7.06381492215663 \tabularnewline
78 & -2.2 & -2.01739772458457 & -0.182602275415433 \tabularnewline
79 & -8.6 & -1.01427212747536 & -7.58572787252464 \tabularnewline
80 & -5 & -0.242070742471592 & -4.75792925752841 \tabularnewline
81 & 4.1 & -4.62771771854514 & 8.72771771854514 \tabularnewline
82 & 0.7 & -5.96933825638009 & 6.66933825638009 \tabularnewline
83 & -4.2 & -2.22889329025467 & -1.97110670974533 \tabularnewline
84 & -2.3 & -3.21022322198638 & 0.910223221986382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235132&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]13[/C][C]5.7[/C][C]5.52903311965812[/C][C]0.17096688034188[/C][/ROW]
[ROW][C]14[/C][C]13[/C][C]13.4212234384753[/C][C]-0.42122343847532[/C][/ROW]
[ROW][C]15[/C][C]14.5[/C][C]15.21147726734[/C][C]-0.711477267339959[/C][/ROW]
[ROW][C]16[/C][C]9.7[/C][C]9.84040638574029[/C][C]-0.14040638574029[/C][/ROW]
[ROW][C]17[/C][C]-4.7[/C][C]-4.34561233103387[/C][C]-0.354387668966133[/C][/ROW]
[ROW][C]18[/C][C]7.3[/C][C]8.1994969788129[/C][C]-0.899496978812905[/C][/ROW]
[ROW][C]19[/C][C]5.2[/C][C]4.99732168568625[/C][C]0.202678314313755[/C][/ROW]
[ROW][C]20[/C][C]-2.5[/C][C]14.2273388248549[/C][C]-16.7273388248549[/C][/ROW]
[ROW][C]21[/C][C]11.5[/C][C]2.6412073058699[/C][C]8.8587926941301[/C][/ROW]
[ROW][C]22[/C][C]4.9[/C][C]-0.981231675465295[/C][C]5.88123167546529[/C][/ROW]
[ROW][C]23[/C][C]-2.4[/C][C]7.27397571549552[/C][C]-9.67397571549552[/C][/ROW]
[ROW][C]24[/C][C]-0.3[/C][C]2.88970333784423[/C][C]-3.18970333784423[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]3.93023901126212[/C][C]0.469760988737876[/C][/ROW]
[ROW][C]26[/C][C]7.9[/C][C]11.6824064401949[/C][C]-3.78240644019491[/C][/ROW]
[ROW][C]27[/C][C]-9.7[/C][C]13.3678800825315[/C][C]-23.0678800825315[/C][/ROW]
[ROW][C]28[/C][C]-4.1[/C][C]7.90440127270408[/C][C]-12.0044012727041[/C][/ROW]
[ROW][C]29[/C][C]16.4[/C][C]-6.45559703468884[/C][C]22.8555970346888[/C][/ROW]
[ROW][C]30[/C][C]-4.9[/C][C]6.19699087218399[/C][C]-11.096990872184[/C][/ROW]
[ROW][C]31[/C][C]3.5[/C][C]3.15605917956936[/C][C]0.343940820430638[/C][/ROW]
[ROW][C]32[/C][C]3.8[/C][C]8.29640802707364[/C][C]-4.49640802707364[/C][/ROW]
[ROW][C]33[/C][C]-0.2[/C][C]3.01919615852928[/C][C]-3.21919615852928[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]-1.4472445289036[/C][C]4.5472445289036[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]3.0353121389932[/C][C]-2.3353121389932[/C][/ROW]
[ROW][C]36[/C][C]-2.8[/C][C]0.293591434399185[/C][C]-3.09359143439918[/C][/ROW]
[ROW][C]37[/C][C]5.9[/C][C]2.21942406693635[/C][C]3.68057593306365[/C][/ROW]
[ROW][C]38[/C][C]-5.3[/C][C]8.97714976858423[/C][C]-14.2771497685842[/C][/ROW]
[ROW][C]39[/C][C]-2.9[/C][C]5.89414561910687[/C][C]-8.79414561910687[/C][/ROW]
[ROW][C]40[/C][C]6.6[/C][C]3.2512531442858[/C][C]3.3487468557142[/C][/ROW]
[ROW][C]41[/C][C]-8.1[/C][C]-2.52662574007273[/C][C]-5.57337425992727[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]1.62835730322783[/C][C]-0.328357303227829[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]1.46309928625414[/C][C]5.43690071374587[/C][/ROW]
[ROW][C]44[/C][C]-7.2[/C][C]5.48627039315321[/C][C]-12.6862703931532[/C][/ROW]
[ROW][C]45[/C][C]-1.9[/C][C]0.433290360732229[/C][C]-2.33329036073223[/C][/ROW]
[ROW][C]46[/C][C]4[/C][C]-2.14726637115728[/C][C]6.14726637115728[/C][/ROW]
[ROW][C]47[/C][C]-5.7[/C][C]0.688616309687475[/C][C]-6.38861630968748[/C][/ROW]
[ROW][C]48[/C][C]3.9[/C][C]-2.27811558614848[/C][C]6.17811558614848[/C][/ROW]
[ROW][C]49[/C][C]-7.6[/C][C]1.38024368237607[/C][C]-8.98024368237607[/C][/ROW]
[ROW][C]50[/C][C]-0.9[/C][C]3.66801700561609[/C][C]-4.56801700561609[/C][/ROW]
[ROW][C]51[/C][C]7.3[/C][C]2.01003914705467[/C][C]5.28996085294533[/C][/ROW]
[ROW][C]52[/C][C]-3.7[/C][C]2.4466180757377[/C][C]-6.1466180757377[/C][/ROW]
[ROW][C]53[/C][C]-2.5[/C][C]-5.58514366442861[/C][C]3.08514366442861[/C][/ROW]
[ROW][C]54[/C][C]9.3[/C][C]-0.0734714448399174[/C][C]9.37347144483992[/C][/ROW]
[ROW][C]55[/C][C]1.3[/C][C]1.25442795892606[/C][C]0.0455720410739422[/C][/ROW]
[ROW][C]56[/C][C]9.5[/C][C]0.842586850704988[/C][C]8.65741314929501[/C][/ROW]
[ROW][C]57[/C][C]11.3[/C][C]-1.48863485736097[/C][C]12.788634857361[/C][/ROW]
[ROW][C]58[/C][C]-1.7[/C][C]-1.86402464818834[/C][C]0.164024648188343[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]-2.11909101485189[/C][C]10.1190910148519[/C][/ROW]
[ROW][C]60[/C][C]-4.8[/C][C]-1.87895326664799[/C][C]-2.92104673335201[/C][/ROW]
[ROW][C]61[/C][C]1.6[/C][C]-1.97737517372722[/C][C]3.57737517372722[/C][/ROW]
[ROW][C]62[/C][C]1.9[/C][C]1.5060286859339[/C][C]0.393971314066097[/C][/ROW]
[ROW][C]63[/C][C]-0.9[/C][C]2.28136135420313[/C][C]-3.18136135420313[/C][/ROW]
[ROW][C]64[/C][C]5.5[/C][C]-0.133005292618365[/C][C]5.63300529261836[/C][/ROW]
[ROW][C]65[/C][C]1.7[/C][C]-5.81251805098266[/C][C]7.51251805098266[/C][/ROW]
[ROW][C]66[/C][C]-5.4[/C][C]1.26435203868839[/C][C]-6.66435203868839[/C][/ROW]
[ROW][C]67[/C][C]1.9[/C][C]0.172885555542042[/C][C]1.72711444445796[/C][/ROW]
[ROW][C]68[/C][C]0.2[/C][C]1.85941857996309[/C][C]-1.65941857996309[/C][/ROW]
[ROW][C]69[/C][C]-13.3[/C][C]0.420177041949132[/C][C]-13.7201770419491[/C][/ROW]
[ROW][C]70[/C][C]-8.2[/C][C]-3.27914075101855[/C][C]-4.92085924898145[/C][/ROW]
[ROW][C]71[/C][C]0.2[/C][C]-1.18097903382582[/C][C]1.38097903382582[/C][/ROW]
[ROW][C]72[/C][C]5.7[/C][C]-4.18203503244329[/C][C]9.88203503244329[/C][/ROW]
[ROW][C]73[/C][C]-1.2[/C][C]-2.57816935236227[/C][C]1.37816935236227[/C][/ROW]
[ROW][C]74[/C][C]-2.8[/C][C]0.11330251329461[/C][C]-2.91330251329461[/C][/ROW]
[ROW][C]75[/C][C]5.5[/C][C]-0.00942590332744031[/C][C]5.50942590332744[/C][/ROW]
[ROW][C]76[/C][C]-17.3[/C][C]-0.204240505709835[/C][C]-17.0957594942902[/C][/ROW]
[ROW][C]77[/C][C]1.4[/C][C]-5.66381492215663[/C][C]7.06381492215663[/C][/ROW]
[ROW][C]78[/C][C]-2.2[/C][C]-2.01739772458457[/C][C]-0.182602275415433[/C][/ROW]
[ROW][C]79[/C][C]-8.6[/C][C]-1.01427212747536[/C][C]-7.58572787252464[/C][/ROW]
[ROW][C]80[/C][C]-5[/C][C]-0.242070742471592[/C][C]-4.75792925752841[/C][/ROW]
[ROW][C]81[/C][C]4.1[/C][C]-4.62771771854514[/C][C]8.72771771854514[/C][/ROW]
[ROW][C]82[/C][C]0.7[/C][C]-5.96933825638009[/C][C]6.66933825638009[/C][/ROW]
[ROW][C]83[/C][C]-4.2[/C][C]-2.22889329025467[/C][C]-1.97110670974533[/C][/ROW]
[ROW][C]84[/C][C]-2.3[/C][C]-3.21022322198638[/C][C]0.910223221986382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235132&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
13	5.7	5.52903311965812	0.17096688034188
14	13	13.4212234384753	-0.42122343847532
15	14.5	15.21147726734	-0.711477267339959
16	9.7	9.84040638574029	-0.14040638574029
17	-4.7	-4.34561233103387	-0.354387668966133
18	7.3	8.1994969788129	-0.899496978812905
19	5.2	4.99732168568625	0.202678314313755
20	-2.5	14.2273388248549	-16.7273388248549
21	11.5	2.6412073058699	8.8587926941301
22	4.9	-0.981231675465295	5.88123167546529
23	-2.4	7.27397571549552	-9.67397571549552
24	-0.3	2.88970333784423	-3.18970333784423
25	4.4	3.93023901126212	0.469760988737876
26	7.9	11.6824064401949	-3.78240644019491
27	-9.7	13.3678800825315	-23.0678800825315
28	-4.1	7.90440127270408	-12.0044012727041
29	16.4	-6.45559703468884	22.8555970346888
30	-4.9	6.19699087218399	-11.096990872184
31	3.5	3.15605917956936	0.343940820430638
32	3.8	8.29640802707364	-4.49640802707364
33	-0.2	3.01919615852928	-3.21919615852928
34	3.1	-1.4472445289036	4.5472445289036
35	0.7	3.0353121389932	-2.3353121389932
36	-2.8	0.293591434399185	-3.09359143439918
37	5.9	2.21942406693635	3.68057593306365
38	-5.3	8.97714976858423	-14.2771497685842
39	-2.9	5.89414561910687	-8.79414561910687
40	6.6	3.2512531442858	3.3487468557142
41	-8.1	-2.52662574007273	-5.57337425992727
42	1.3	1.62835730322783	-0.328357303227829
43	6.9	1.46309928625414	5.43690071374587
44	-7.2	5.48627039315321	-12.6862703931532
45	-1.9	0.433290360732229	-2.33329036073223
46	4	-2.14726637115728	6.14726637115728
47	-5.7	0.688616309687475	-6.38861630968748
48	3.9	-2.27811558614848	6.17811558614848
49	-7.6	1.38024368237607	-8.98024368237607
50	-0.9	3.66801700561609	-4.56801700561609
51	7.3	2.01003914705467	5.28996085294533
52	-3.7	2.4466180757377	-6.1466180757377
53	-2.5	-5.58514366442861	3.08514366442861
54	9.3	-0.0734714448399174	9.37347144483992
55	1.3	1.25442795892606	0.0455720410739422
56	9.5	0.842586850704988	8.65741314929501
57	11.3	-1.48863485736097	12.788634857361
58	-1.7	-1.86402464818834	0.164024648188343
59	8	-2.11909101485189	10.1190910148519
60	-4.8	-1.87895326664799	-2.92104673335201
61	1.6	-1.97737517372722	3.57737517372722
62	1.9	1.5060286859339	0.393971314066097
63	-0.9	2.28136135420313	-3.18136135420313
64	5.5	-0.133005292618365	5.63300529261836
65	1.7	-5.81251805098266	7.51251805098266
66	-5.4	1.26435203868839	-6.66435203868839
67	1.9	0.172885555542042	1.72711444445796
68	0.2	1.85941857996309	-1.65941857996309
69	-13.3	0.420177041949132	-13.7201770419491
70	-8.2	-3.27914075101855	-4.92085924898145
71	0.2	-1.18097903382582	1.38097903382582
72	5.7	-4.18203503244329	9.88203503244329
73	-1.2	-2.57816935236227	1.37816935236227
74	-2.8	0.11330251329461	-2.91330251329461
75	5.5	-0.00942590332744031	5.50942590332744
76	-17.3	-0.204240505709835	-17.0957594942902
77	1.4	-5.66381492215663	7.06381492215663
78	-2.2	-2.01739772458457	-0.182602275415433
79	-8.6	-1.01427212747536	-7.58572787252464
80	-5	-0.242070742471592	-4.75792925752841
81	4.1	-4.62771771854514	8.72771771854514
82	0.7	-5.96933825638009	6.66933825638009
83	-4.2	-2.22889329025467	-1.97110670974533
84	-2.3	-3.21022322198638	0.910223221986382

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	-3.75377355299129	-18.8014706810249	11.2939235750423
86	-2.11353570499335	-17.1620319584318	12.9349605484451
87	-0.17089429952431	-15.2201896359337	14.8784010368851
88	-5.88501315344592	-20.9351075303991	9.16508122350725
89	-5.33025694308548	-20.3811503181619	9.72063643199096
90	-3.50773045179956	-18.5594227825856	11.5439618789864
91	-4.29168190743586	-19.3441731515245	10.7608093366528
92	-2.7579663423379	-17.811256457329	12.2953237726532
93	-3.83578270138917	-18.8898716448892	11.2183062421109
94	-5.76475737013626	-20.8196450997586	9.29013035948606
95	-4.18100322230055	-19.2366896956652	10.8746832510641
96	-4.44574787228573	-19.5022330470195	10.610737302448

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & -3.75377355299129 & -18.8014706810249 & 11.2939235750423 \tabularnewline
86 & -2.11353570499335 & -17.1620319584318 & 12.9349605484451 \tabularnewline
87 & -0.17089429952431 & -15.2201896359337 & 14.8784010368851 \tabularnewline
88 & -5.88501315344592 & -20.9351075303991 & 9.16508122350725 \tabularnewline
89 & -5.33025694308548 & -20.3811503181619 & 9.72063643199096 \tabularnewline
90 & -3.50773045179956 & -18.5594227825856 & 11.5439618789864 \tabularnewline
91 & -4.29168190743586 & -19.3441731515245 & 10.7608093366528 \tabularnewline
92 & -2.7579663423379 & -17.811256457329 & 12.2953237726532 \tabularnewline
93 & -3.83578270138917 & -18.8898716448892 & 11.2183062421109 \tabularnewline
94 & -5.76475737013626 & -20.8196450997586 & 9.29013035948606 \tabularnewline
95 & -4.18100322230055 & -19.2366896956652 & 10.8746832510641 \tabularnewline
96 & -4.44574787228573 & -19.5022330470195 & 10.610737302448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235132&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]-3.75377355299129[/C][C]-18.8014706810249[/C][C]11.2939235750423[/C][/ROW]
[ROW][C]86[/C][C]-2.11353570499335[/C][C]-17.1620319584318[/C][C]12.9349605484451[/C][/ROW]
[ROW][C]87[/C][C]-0.17089429952431[/C][C]-15.2201896359337[/C][C]14.8784010368851[/C][/ROW]
[ROW][C]88[/C][C]-5.88501315344592[/C][C]-20.9351075303991[/C][C]9.16508122350725[/C][/ROW]
[ROW][C]89[/C][C]-5.33025694308548[/C][C]-20.3811503181619[/C][C]9.72063643199096[/C][/ROW]
[ROW][C]90[/C][C]-3.50773045179956[/C][C]-18.5594227825856[/C][C]11.5439618789864[/C][/ROW]
[ROW][C]91[/C][C]-4.29168190743586[/C][C]-19.3441731515245[/C][C]10.7608093366528[/C][/ROW]
[ROW][C]92[/C][C]-2.7579663423379[/C][C]-17.811256457329[/C][C]12.2953237726532[/C][/ROW]
[ROW][C]93[/C][C]-3.83578270138917[/C][C]-18.8898716448892[/C][C]11.2183062421109[/C][/ROW]
[ROW][C]94[/C][C]-5.76475737013626[/C][C]-20.8196450997586[/C][C]9.29013035948606[/C][/ROW]
[ROW][C]95[/C][C]-4.18100322230055[/C][C]-19.2366896956652[/C][C]10.8746832510641[/C][/ROW]
[ROW][C]96[/C][C]-4.44574787228573[/C][C]-19.5022330470195[/C][C]10.610737302448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235132&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235132&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	-3.75377355299129	-18.8014706810249	11.2939235750423
86	-2.11353570499335	-17.1620319584318	12.9349605484451
87	-0.17089429952431	-15.2201896359337	14.8784010368851
88	-5.88501315344592	-20.9351075303991	9.16508122350725
89	-5.33025694308548	-20.3811503181619	9.72063643199096
90	-3.50773045179956	-18.5594227825856	11.5439618789864
91	-4.29168190743586	-19.3441731515245	10.7608093366528
92	-2.7579663423379	-17.811256457329	12.2953237726532
93	-3.83578270138917	-18.8898716448892	11.2183062421109
94	-5.76475737013626	-20.8196450997586	9.29013035948606
95	-4.18100322230055	-19.2366896956652	10.8746832510641
96	-4.44574787228573	-19.5022330470195	10.610737302448

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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