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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Apr 2015 21:44:45 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1428007518pyaicr7kx4mfd66.htm/, Retrieved Thu, 09 May 2024 07:01:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278660, Retrieved Thu, 09 May 2024 07:01:57 +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] [] [2015-04-02 20:44:45] [efb69546851bccb1c0576f78d5afa44b] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278660&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278660&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.99993214474301
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99993214474301 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278660&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]0.99993214474301[/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=278660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278660&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	0.99993214474301
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	74	75.6	-1.59999999999999
3	75.3	74.0001085684112	1.29989143158882
4	83.1	75.2999117955329	7.80008820446714
5	84.9	83.0994707230103	1.80052927698968
6	83.5	84.8998778246232	-1.3998778246232
7	88.2	83.5000949890695	4.69990501093046
8	87.4	88.1996810867377	-0.79968108673765
9	77.8	87.4000542625657	-9.60005426256566
10	74.5	77.8006514141491	-3.3006514141491
11	75.3	74.5002239665499	0.799776033450058
12	78.7	75.2999457309917	3.40005426900829
13	71.4	78.6997692884438	-7.29976928844378
14	75.8	71.400495327721	4.39950467227897
15	79.2	75.7997014704798	3.40029852952017
16	84.4	79.1997692718694	5.20023072813056
17	84.4	84.3996471370075	0.000352862992471614
18	87.2	84.3999999760564	2.80000002394361
19	92.4	87.1998100052788	5.2001899947212
20	88.5	92.3996471397715	-3.89964713977153
21	94.8	88.5002646115588	6.29973538844116
22	100.9	94.7995725298363	6.10042747016375
23	110	100.899586053926	9.10041394607373
24	107.9	109.999382489073	-2.09938248907298
25	111.2	107.900142454138	3.29985754586168
26	116.7	111.199776087318	5.5002239126818
27	125.8	116.699626780893	9.1003732191071
28	131.5	125.799382491837	5.70061750816349
29	146.2	131.499613183134	14.700386816866
30	155.4	146.199002501475	9.20099749852531
31	157.5	155.39937566395	2.1006243360498
32	137.2	157.499857461596	-20.2998574615958
33	121.3	137.201377452045	-15.9013774520449
34	89.1	121.301078992053	-32.2010789920535
35	69.6	89.1021850124903	-19.5021850124903
36	56.7	69.6013233257759	-12.9013233257759
37	58.5	56.7008754226098	1.79912457739022
38	56.4	58.4998779199394	-2.09987791993944
39	60.5	56.4001424877559	4.0998575122441
40	64.6	60.4997218031149	4.10027819688511
41	73.2	64.5997217745692	8.6002782254308
42	84.6	73.1994164259108	11.4005835740892
43	80.4	84.5992264104717	-4.19922641047174
44	88.4	80.4002849395873	7.99971506041275
45	84.6	88.3994571772787	-3.79945717727874
46	90.8	84.6002578131432	6.19974218685682
47	94.9	90.7995793149006	4.10042068509937
48	93.1	94.8997217649006	-1.79972176490065
49	96.6	93.1001221205829	3.49987787941714
50	93.1	96.5997625148871	-3.49976251488707
51	98.3	93.1002374772848	5.19976252271516
52	105	98.2996471687777	6.70035283122228
53	95.6	104.999545345837	-9.39954534583673
54	94.3	95.600637808565	-1.30063780856503
55	95.3	94.3000882551127	0.999911744887257
56	97.1	95.2999321507316	1.80006784926842
57	98.1	97.0998778559335	1.00012214406651
58	104.4	98.0999321364549	6.30006786354512
59	107.8	104.399572507276	3.40042749272392
60	114.3	107.799769263119	6.50023073688139
61	118.7	114.299558925173	4.40044107482714
62	124.1	118.69970140694	5.40029859305999
63	134.2	124.099633561351	10.1003664386488
64	142.4	134.19931463704	8.2006853629604
65	133.8	142.399443540387	-8.5994435403872
66	131	133.800583517451	-2.80058351745143
67	133.2	131.000190034314	2.19980996568569
68	125.9	133.199850731329	-7.29985073132943
69	126.2	125.900495333247	0.29950466675264
70	122.7	126.199979677034	-3.49997967703386
71	126.6	122.70023749202	3.89976250797955
72	124.8	126.599735380613	-1.79973538061282
73	128	124.800122121507	3.19987787849324
74	134.1	127.999782871464	6.10021712853577
75	138.8	134.099586068199	4.70041393180097
76	134	138.799681052205	-4.7996810522047
77	124	134.000325683591	-10.0003256835913
78	110.4	124.000678574669	-13.6006785746692
79	116.7	110.40092287754	6.29907712246008
80	124.7	116.699572574503	8.00042742549695
81	126	124.699457128941	1.30054287105898
82	122.8	125.999911751329	-3.19991175132925
83	120.2	122.800217130834	-2.60021713083422
84	121.2	120.200176438402	0.999823561598348
85	125.4	121.199932156715	4.20006784328473
86	127.9	125.399715003317	2.50028499668288
87	122	127.899830342519	-5.89983034251901
88	117.5	122.000400334504	-4.50040033450408
89	117.9	117.500305375821	0.39969462417875
90	117.9	117.899972878619	2.71213814357907e-05
91	122.7	117.89999999816	4.80000000184033
92	125.7	122.699674294766	3.00032570523368
93	126.1	125.699796412128	0.400203587871786
94	123.2	126.099972844083	-2.89997284408268
95	120.6	123.200196778403	-2.6001967784026
96	123.5	120.600176437021	2.89982356297938

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 74 & 75.6 & -1.59999999999999 \tabularnewline
3 & 75.3 & 74.0001085684112 & 1.29989143158882 \tabularnewline
4 & 83.1 & 75.2999117955329 & 7.80008820446714 \tabularnewline
5 & 84.9 & 83.0994707230103 & 1.80052927698968 \tabularnewline
6 & 83.5 & 84.8998778246232 & -1.3998778246232 \tabularnewline
7 & 88.2 & 83.5000949890695 & 4.69990501093046 \tabularnewline
8 & 87.4 & 88.1996810867377 & -0.79968108673765 \tabularnewline
9 & 77.8 & 87.4000542625657 & -9.60005426256566 \tabularnewline
10 & 74.5 & 77.8006514141491 & -3.3006514141491 \tabularnewline
11 & 75.3 & 74.5002239665499 & 0.799776033450058 \tabularnewline
12 & 78.7 & 75.2999457309917 & 3.40005426900829 \tabularnewline
13 & 71.4 & 78.6997692884438 & -7.29976928844378 \tabularnewline
14 & 75.8 & 71.400495327721 & 4.39950467227897 \tabularnewline
15 & 79.2 & 75.7997014704798 & 3.40029852952017 \tabularnewline
16 & 84.4 & 79.1997692718694 & 5.20023072813056 \tabularnewline
17 & 84.4 & 84.3996471370075 & 0.000352862992471614 \tabularnewline
18 & 87.2 & 84.3999999760564 & 2.80000002394361 \tabularnewline
19 & 92.4 & 87.1998100052788 & 5.2001899947212 \tabularnewline
20 & 88.5 & 92.3996471397715 & -3.89964713977153 \tabularnewline
21 & 94.8 & 88.5002646115588 & 6.29973538844116 \tabularnewline
22 & 100.9 & 94.7995725298363 & 6.10042747016375 \tabularnewline
23 & 110 & 100.899586053926 & 9.10041394607373 \tabularnewline
24 & 107.9 & 109.999382489073 & -2.09938248907298 \tabularnewline
25 & 111.2 & 107.900142454138 & 3.29985754586168 \tabularnewline
26 & 116.7 & 111.199776087318 & 5.5002239126818 \tabularnewline
27 & 125.8 & 116.699626780893 & 9.1003732191071 \tabularnewline
28 & 131.5 & 125.799382491837 & 5.70061750816349 \tabularnewline
29 & 146.2 & 131.499613183134 & 14.700386816866 \tabularnewline
30 & 155.4 & 146.199002501475 & 9.20099749852531 \tabularnewline
31 & 157.5 & 155.39937566395 & 2.1006243360498 \tabularnewline
32 & 137.2 & 157.499857461596 & -20.2998574615958 \tabularnewline
33 & 121.3 & 137.201377452045 & -15.9013774520449 \tabularnewline
34 & 89.1 & 121.301078992053 & -32.2010789920535 \tabularnewline
35 & 69.6 & 89.1021850124903 & -19.5021850124903 \tabularnewline
36 & 56.7 & 69.6013233257759 & -12.9013233257759 \tabularnewline
37 & 58.5 & 56.7008754226098 & 1.79912457739022 \tabularnewline
38 & 56.4 & 58.4998779199394 & -2.09987791993944 \tabularnewline
39 & 60.5 & 56.4001424877559 & 4.0998575122441 \tabularnewline
40 & 64.6 & 60.4997218031149 & 4.10027819688511 \tabularnewline
41 & 73.2 & 64.5997217745692 & 8.6002782254308 \tabularnewline
42 & 84.6 & 73.1994164259108 & 11.4005835740892 \tabularnewline
43 & 80.4 & 84.5992264104717 & -4.19922641047174 \tabularnewline
44 & 88.4 & 80.4002849395873 & 7.99971506041275 \tabularnewline
45 & 84.6 & 88.3994571772787 & -3.79945717727874 \tabularnewline
46 & 90.8 & 84.6002578131432 & 6.19974218685682 \tabularnewline
47 & 94.9 & 90.7995793149006 & 4.10042068509937 \tabularnewline
48 & 93.1 & 94.8997217649006 & -1.79972176490065 \tabularnewline
49 & 96.6 & 93.1001221205829 & 3.49987787941714 \tabularnewline
50 & 93.1 & 96.5997625148871 & -3.49976251488707 \tabularnewline
51 & 98.3 & 93.1002374772848 & 5.19976252271516 \tabularnewline
52 & 105 & 98.2996471687777 & 6.70035283122228 \tabularnewline
53 & 95.6 & 104.999545345837 & -9.39954534583673 \tabularnewline
54 & 94.3 & 95.600637808565 & -1.30063780856503 \tabularnewline
55 & 95.3 & 94.3000882551127 & 0.999911744887257 \tabularnewline
56 & 97.1 & 95.2999321507316 & 1.80006784926842 \tabularnewline
57 & 98.1 & 97.0998778559335 & 1.00012214406651 \tabularnewline
58 & 104.4 & 98.0999321364549 & 6.30006786354512 \tabularnewline
59 & 107.8 & 104.399572507276 & 3.40042749272392 \tabularnewline
60 & 114.3 & 107.799769263119 & 6.50023073688139 \tabularnewline
61 & 118.7 & 114.299558925173 & 4.40044107482714 \tabularnewline
62 & 124.1 & 118.69970140694 & 5.40029859305999 \tabularnewline
63 & 134.2 & 124.099633561351 & 10.1003664386488 \tabularnewline
64 & 142.4 & 134.19931463704 & 8.2006853629604 \tabularnewline
65 & 133.8 & 142.399443540387 & -8.5994435403872 \tabularnewline
66 & 131 & 133.800583517451 & -2.80058351745143 \tabularnewline
67 & 133.2 & 131.000190034314 & 2.19980996568569 \tabularnewline
68 & 125.9 & 133.199850731329 & -7.29985073132943 \tabularnewline
69 & 126.2 & 125.900495333247 & 0.29950466675264 \tabularnewline
70 & 122.7 & 126.199979677034 & -3.49997967703386 \tabularnewline
71 & 126.6 & 122.70023749202 & 3.89976250797955 \tabularnewline
72 & 124.8 & 126.599735380613 & -1.79973538061282 \tabularnewline
73 & 128 & 124.800122121507 & 3.19987787849324 \tabularnewline
74 & 134.1 & 127.999782871464 & 6.10021712853577 \tabularnewline
75 & 138.8 & 134.099586068199 & 4.70041393180097 \tabularnewline
76 & 134 & 138.799681052205 & -4.7996810522047 \tabularnewline
77 & 124 & 134.000325683591 & -10.0003256835913 \tabularnewline
78 & 110.4 & 124.000678574669 & -13.6006785746692 \tabularnewline
79 & 116.7 & 110.40092287754 & 6.29907712246008 \tabularnewline
80 & 124.7 & 116.699572574503 & 8.00042742549695 \tabularnewline
81 & 126 & 124.699457128941 & 1.30054287105898 \tabularnewline
82 & 122.8 & 125.999911751329 & -3.19991175132925 \tabularnewline
83 & 120.2 & 122.800217130834 & -2.60021713083422 \tabularnewline
84 & 121.2 & 120.200176438402 & 0.999823561598348 \tabularnewline
85 & 125.4 & 121.199932156715 & 4.20006784328473 \tabularnewline
86 & 127.9 & 125.399715003317 & 2.50028499668288 \tabularnewline
87 & 122 & 127.899830342519 & -5.89983034251901 \tabularnewline
88 & 117.5 & 122.000400334504 & -4.50040033450408 \tabularnewline
89 & 117.9 & 117.500305375821 & 0.39969462417875 \tabularnewline
90 & 117.9 & 117.899972878619 & 2.71213814357907e-05 \tabularnewline
91 & 122.7 & 117.89999999816 & 4.80000000184033 \tabularnewline
92 & 125.7 & 122.699674294766 & 3.00032570523368 \tabularnewline
93 & 126.1 & 125.699796412128 & 0.400203587871786 \tabularnewline
94 & 123.2 & 126.099972844083 & -2.89997284408268 \tabularnewline
95 & 120.6 & 123.200196778403 & -2.6001967784026 \tabularnewline
96 & 123.5 & 120.600176437021 & 2.89982356297938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278660&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]74[/C][C]75.6[/C][C]-1.59999999999999[/C][/ROW]
[ROW][C]3[/C][C]75.3[/C][C]74.0001085684112[/C][C]1.29989143158882[/C][/ROW]
[ROW][C]4[/C][C]83.1[/C][C]75.2999117955329[/C][C]7.80008820446714[/C][/ROW]
[ROW][C]5[/C][C]84.9[/C][C]83.0994707230103[/C][C]1.80052927698968[/C][/ROW]
[ROW][C]6[/C][C]83.5[/C][C]84.8998778246232[/C][C]-1.3998778246232[/C][/ROW]
[ROW][C]7[/C][C]88.2[/C][C]83.5000949890695[/C][C]4.69990501093046[/C][/ROW]
[ROW][C]8[/C][C]87.4[/C][C]88.1996810867377[/C][C]-0.79968108673765[/C][/ROW]
[ROW][C]9[/C][C]77.8[/C][C]87.4000542625657[/C][C]-9.60005426256566[/C][/ROW]
[ROW][C]10[/C][C]74.5[/C][C]77.8006514141491[/C][C]-3.3006514141491[/C][/ROW]
[ROW][C]11[/C][C]75.3[/C][C]74.5002239665499[/C][C]0.799776033450058[/C][/ROW]
[ROW][C]12[/C][C]78.7[/C][C]75.2999457309917[/C][C]3.40005426900829[/C][/ROW]
[ROW][C]13[/C][C]71.4[/C][C]78.6997692884438[/C][C]-7.29976928844378[/C][/ROW]
[ROW][C]14[/C][C]75.8[/C][C]71.400495327721[/C][C]4.39950467227897[/C][/ROW]
[ROW][C]15[/C][C]79.2[/C][C]75.7997014704798[/C][C]3.40029852952017[/C][/ROW]
[ROW][C]16[/C][C]84.4[/C][C]79.1997692718694[/C][C]5.20023072813056[/C][/ROW]
[ROW][C]17[/C][C]84.4[/C][C]84.3996471370075[/C][C]0.000352862992471614[/C][/ROW]
[ROW][C]18[/C][C]87.2[/C][C]84.3999999760564[/C][C]2.80000002394361[/C][/ROW]
[ROW][C]19[/C][C]92.4[/C][C]87.1998100052788[/C][C]5.2001899947212[/C][/ROW]
[ROW][C]20[/C][C]88.5[/C][C]92.3996471397715[/C][C]-3.89964713977153[/C][/ROW]
[ROW][C]21[/C][C]94.8[/C][C]88.5002646115588[/C][C]6.29973538844116[/C][/ROW]
[ROW][C]22[/C][C]100.9[/C][C]94.7995725298363[/C][C]6.10042747016375[/C][/ROW]
[ROW][C]23[/C][C]110[/C][C]100.899586053926[/C][C]9.10041394607373[/C][/ROW]
[ROW][C]24[/C][C]107.9[/C][C]109.999382489073[/C][C]-2.09938248907298[/C][/ROW]
[ROW][C]25[/C][C]111.2[/C][C]107.900142454138[/C][C]3.29985754586168[/C][/ROW]
[ROW][C]26[/C][C]116.7[/C][C]111.199776087318[/C][C]5.5002239126818[/C][/ROW]
[ROW][C]27[/C][C]125.8[/C][C]116.699626780893[/C][C]9.1003732191071[/C][/ROW]
[ROW][C]28[/C][C]131.5[/C][C]125.799382491837[/C][C]5.70061750816349[/C][/ROW]
[ROW][C]29[/C][C]146.2[/C][C]131.499613183134[/C][C]14.700386816866[/C][/ROW]
[ROW][C]30[/C][C]155.4[/C][C]146.199002501475[/C][C]9.20099749852531[/C][/ROW]
[ROW][C]31[/C][C]157.5[/C][C]155.39937566395[/C][C]2.1006243360498[/C][/ROW]
[ROW][C]32[/C][C]137.2[/C][C]157.499857461596[/C][C]-20.2998574615958[/C][/ROW]
[ROW][C]33[/C][C]121.3[/C][C]137.201377452045[/C][C]-15.9013774520449[/C][/ROW]
[ROW][C]34[/C][C]89.1[/C][C]121.301078992053[/C][C]-32.2010789920535[/C][/ROW]
[ROW][C]35[/C][C]69.6[/C][C]89.1021850124903[/C][C]-19.5021850124903[/C][/ROW]
[ROW][C]36[/C][C]56.7[/C][C]69.6013233257759[/C][C]-12.9013233257759[/C][/ROW]
[ROW][C]37[/C][C]58.5[/C][C]56.7008754226098[/C][C]1.79912457739022[/C][/ROW]
[ROW][C]38[/C][C]56.4[/C][C]58.4998779199394[/C][C]-2.09987791993944[/C][/ROW]
[ROW][C]39[/C][C]60.5[/C][C]56.4001424877559[/C][C]4.0998575122441[/C][/ROW]
[ROW][C]40[/C][C]64.6[/C][C]60.4997218031149[/C][C]4.10027819688511[/C][/ROW]
[ROW][C]41[/C][C]73.2[/C][C]64.5997217745692[/C][C]8.6002782254308[/C][/ROW]
[ROW][C]42[/C][C]84.6[/C][C]73.1994164259108[/C][C]11.4005835740892[/C][/ROW]
[ROW][C]43[/C][C]80.4[/C][C]84.5992264104717[/C][C]-4.19922641047174[/C][/ROW]
[ROW][C]44[/C][C]88.4[/C][C]80.4002849395873[/C][C]7.99971506041275[/C][/ROW]
[ROW][C]45[/C][C]84.6[/C][C]88.3994571772787[/C][C]-3.79945717727874[/C][/ROW]
[ROW][C]46[/C][C]90.8[/C][C]84.6002578131432[/C][C]6.19974218685682[/C][/ROW]
[ROW][C]47[/C][C]94.9[/C][C]90.7995793149006[/C][C]4.10042068509937[/C][/ROW]
[ROW][C]48[/C][C]93.1[/C][C]94.8997217649006[/C][C]-1.79972176490065[/C][/ROW]
[ROW][C]49[/C][C]96.6[/C][C]93.1001221205829[/C][C]3.49987787941714[/C][/ROW]
[ROW][C]50[/C][C]93.1[/C][C]96.5997625148871[/C][C]-3.49976251488707[/C][/ROW]
[ROW][C]51[/C][C]98.3[/C][C]93.1002374772848[/C][C]5.19976252271516[/C][/ROW]
[ROW][C]52[/C][C]105[/C][C]98.2996471687777[/C][C]6.70035283122228[/C][/ROW]
[ROW][C]53[/C][C]95.6[/C][C]104.999545345837[/C][C]-9.39954534583673[/C][/ROW]
[ROW][C]54[/C][C]94.3[/C][C]95.600637808565[/C][C]-1.30063780856503[/C][/ROW]
[ROW][C]55[/C][C]95.3[/C][C]94.3000882551127[/C][C]0.999911744887257[/C][/ROW]
[ROW][C]56[/C][C]97.1[/C][C]95.2999321507316[/C][C]1.80006784926842[/C][/ROW]
[ROW][C]57[/C][C]98.1[/C][C]97.0998778559335[/C][C]1.00012214406651[/C][/ROW]
[ROW][C]58[/C][C]104.4[/C][C]98.0999321364549[/C][C]6.30006786354512[/C][/ROW]
[ROW][C]59[/C][C]107.8[/C][C]104.399572507276[/C][C]3.40042749272392[/C][/ROW]
[ROW][C]60[/C][C]114.3[/C][C]107.799769263119[/C][C]6.50023073688139[/C][/ROW]
[ROW][C]61[/C][C]118.7[/C][C]114.299558925173[/C][C]4.40044107482714[/C][/ROW]
[ROW][C]62[/C][C]124.1[/C][C]118.69970140694[/C][C]5.40029859305999[/C][/ROW]
[ROW][C]63[/C][C]134.2[/C][C]124.099633561351[/C][C]10.1003664386488[/C][/ROW]
[ROW][C]64[/C][C]142.4[/C][C]134.19931463704[/C][C]8.2006853629604[/C][/ROW]
[ROW][C]65[/C][C]133.8[/C][C]142.399443540387[/C][C]-8.5994435403872[/C][/ROW]
[ROW][C]66[/C][C]131[/C][C]133.800583517451[/C][C]-2.80058351745143[/C][/ROW]
[ROW][C]67[/C][C]133.2[/C][C]131.000190034314[/C][C]2.19980996568569[/C][/ROW]
[ROW][C]68[/C][C]125.9[/C][C]133.199850731329[/C][C]-7.29985073132943[/C][/ROW]
[ROW][C]69[/C][C]126.2[/C][C]125.900495333247[/C][C]0.29950466675264[/C][/ROW]
[ROW][C]70[/C][C]122.7[/C][C]126.199979677034[/C][C]-3.49997967703386[/C][/ROW]
[ROW][C]71[/C][C]126.6[/C][C]122.70023749202[/C][C]3.89976250797955[/C][/ROW]
[ROW][C]72[/C][C]124.8[/C][C]126.599735380613[/C][C]-1.79973538061282[/C][/ROW]
[ROW][C]73[/C][C]128[/C][C]124.800122121507[/C][C]3.19987787849324[/C][/ROW]
[ROW][C]74[/C][C]134.1[/C][C]127.999782871464[/C][C]6.10021712853577[/C][/ROW]
[ROW][C]75[/C][C]138.8[/C][C]134.099586068199[/C][C]4.70041393180097[/C][/ROW]
[ROW][C]76[/C][C]134[/C][C]138.799681052205[/C][C]-4.7996810522047[/C][/ROW]
[ROW][C]77[/C][C]124[/C][C]134.000325683591[/C][C]-10.0003256835913[/C][/ROW]
[ROW][C]78[/C][C]110.4[/C][C]124.000678574669[/C][C]-13.6006785746692[/C][/ROW]
[ROW][C]79[/C][C]116.7[/C][C]110.40092287754[/C][C]6.29907712246008[/C][/ROW]
[ROW][C]80[/C][C]124.7[/C][C]116.699572574503[/C][C]8.00042742549695[/C][/ROW]
[ROW][C]81[/C][C]126[/C][C]124.699457128941[/C][C]1.30054287105898[/C][/ROW]
[ROW][C]82[/C][C]122.8[/C][C]125.999911751329[/C][C]-3.19991175132925[/C][/ROW]
[ROW][C]83[/C][C]120.2[/C][C]122.800217130834[/C][C]-2.60021713083422[/C][/ROW]
[ROW][C]84[/C][C]121.2[/C][C]120.200176438402[/C][C]0.999823561598348[/C][/ROW]
[ROW][C]85[/C][C]125.4[/C][C]121.199932156715[/C][C]4.20006784328473[/C][/ROW]
[ROW][C]86[/C][C]127.9[/C][C]125.399715003317[/C][C]2.50028499668288[/C][/ROW]
[ROW][C]87[/C][C]122[/C][C]127.899830342519[/C][C]-5.89983034251901[/C][/ROW]
[ROW][C]88[/C][C]117.5[/C][C]122.000400334504[/C][C]-4.50040033450408[/C][/ROW]
[ROW][C]89[/C][C]117.9[/C][C]117.500305375821[/C][C]0.39969462417875[/C][/ROW]
[ROW][C]90[/C][C]117.9[/C][C]117.899972878619[/C][C]2.71213814357907e-05[/C][/ROW]
[ROW][C]91[/C][C]122.7[/C][C]117.89999999816[/C][C]4.80000000184033[/C][/ROW]
[ROW][C]92[/C][C]125.7[/C][C]122.699674294766[/C][C]3.00032570523368[/C][/ROW]
[ROW][C]93[/C][C]126.1[/C][C]125.699796412128[/C][C]0.400203587871786[/C][/ROW]
[ROW][C]94[/C][C]123.2[/C][C]126.099972844083[/C][C]-2.89997284408268[/C][/ROW]
[ROW][C]95[/C][C]120.6[/C][C]123.200196778403[/C][C]-2.6001967784026[/C][/ROW]
[ROW][C]96[/C][C]123.5[/C][C]120.600176437021[/C][C]2.89982356297938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278660&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	74	75.6	-1.59999999999999
3	75.3	74.0001085684112	1.29989143158882
4	83.1	75.2999117955329	7.80008820446714
5	84.9	83.0994707230103	1.80052927698968
6	83.5	84.8998778246232	-1.3998778246232
7	88.2	83.5000949890695	4.69990501093046
8	87.4	88.1996810867377	-0.79968108673765
9	77.8	87.4000542625657	-9.60005426256566
10	74.5	77.8006514141491	-3.3006514141491
11	75.3	74.5002239665499	0.799776033450058
12	78.7	75.2999457309917	3.40005426900829
13	71.4	78.6997692884438	-7.29976928844378
14	75.8	71.400495327721	4.39950467227897
15	79.2	75.7997014704798	3.40029852952017
16	84.4	79.1997692718694	5.20023072813056
17	84.4	84.3996471370075	0.000352862992471614
18	87.2	84.3999999760564	2.80000002394361
19	92.4	87.1998100052788	5.2001899947212
20	88.5	92.3996471397715	-3.89964713977153
21	94.8	88.5002646115588	6.29973538844116
22	100.9	94.7995725298363	6.10042747016375
23	110	100.899586053926	9.10041394607373
24	107.9	109.999382489073	-2.09938248907298
25	111.2	107.900142454138	3.29985754586168
26	116.7	111.199776087318	5.5002239126818
27	125.8	116.699626780893	9.1003732191071
28	131.5	125.799382491837	5.70061750816349
29	146.2	131.499613183134	14.700386816866
30	155.4	146.199002501475	9.20099749852531
31	157.5	155.39937566395	2.1006243360498
32	137.2	157.499857461596	-20.2998574615958
33	121.3	137.201377452045	-15.9013774520449
34	89.1	121.301078992053	-32.2010789920535
35	69.6	89.1021850124903	-19.5021850124903
36	56.7	69.6013233257759	-12.9013233257759
37	58.5	56.7008754226098	1.79912457739022
38	56.4	58.4998779199394	-2.09987791993944
39	60.5	56.4001424877559	4.0998575122441
40	64.6	60.4997218031149	4.10027819688511
41	73.2	64.5997217745692	8.6002782254308
42	84.6	73.1994164259108	11.4005835740892
43	80.4	84.5992264104717	-4.19922641047174
44	88.4	80.4002849395873	7.99971506041275
45	84.6	88.3994571772787	-3.79945717727874
46	90.8	84.6002578131432	6.19974218685682
47	94.9	90.7995793149006	4.10042068509937
48	93.1	94.8997217649006	-1.79972176490065
49	96.6	93.1001221205829	3.49987787941714
50	93.1	96.5997625148871	-3.49976251488707
51	98.3	93.1002374772848	5.19976252271516
52	105	98.2996471687777	6.70035283122228
53	95.6	104.999545345837	-9.39954534583673
54	94.3	95.600637808565	-1.30063780856503
55	95.3	94.3000882551127	0.999911744887257
56	97.1	95.2999321507316	1.80006784926842
57	98.1	97.0998778559335	1.00012214406651
58	104.4	98.0999321364549	6.30006786354512
59	107.8	104.399572507276	3.40042749272392
60	114.3	107.799769263119	6.50023073688139
61	118.7	114.299558925173	4.40044107482714
62	124.1	118.69970140694	5.40029859305999
63	134.2	124.099633561351	10.1003664386488
64	142.4	134.19931463704	8.2006853629604
65	133.8	142.399443540387	-8.5994435403872
66	131	133.800583517451	-2.80058351745143
67	133.2	131.000190034314	2.19980996568569
68	125.9	133.199850731329	-7.29985073132943
69	126.2	125.900495333247	0.29950466675264
70	122.7	126.199979677034	-3.49997967703386
71	126.6	122.70023749202	3.89976250797955
72	124.8	126.599735380613	-1.79973538061282
73	128	124.800122121507	3.19987787849324
74	134.1	127.999782871464	6.10021712853577
75	138.8	134.099586068199	4.70041393180097
76	134	138.799681052205	-4.7996810522047
77	124	134.000325683591	-10.0003256835913
78	110.4	124.000678574669	-13.6006785746692
79	116.7	110.40092287754	6.29907712246008
80	124.7	116.699572574503	8.00042742549695
81	126	124.699457128941	1.30054287105898
82	122.8	125.999911751329	-3.19991175132925
83	120.2	122.800217130834	-2.60021713083422
84	121.2	120.200176438402	0.999823561598348
85	125.4	121.199932156715	4.20006784328473
86	127.9	125.399715003317	2.50028499668288
87	122	127.899830342519	-5.89983034251901
88	117.5	122.000400334504	-4.50040033450408
89	117.9	117.500305375821	0.39969462417875
90	117.9	117.899972878619	2.71213814357907e-05
91	122.7	117.89999999816	4.80000000184033
92	125.7	122.699674294766	3.00032570523368
93	126.1	125.699796412128	0.400203587871786
94	123.2	126.099972844083	-2.89997284408268
95	120.6	123.200196778403	-2.6001967784026
96	123.5	120.600176437021	2.89982356297938

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	123.499803231727	109.306917796863	137.692688666591
98	123.499803231727	103.428713136574	143.57089332688
99	123.499803231727	98.918116588042	148.081489875412
100	123.499803231727	95.1154769425777	151.884129520876
101	123.499803231727	91.7652693682927	155.234337095161
102	123.499803231727	88.7364417692616	158.263164694192
103	123.499803231727	85.9511419931343	161.04846447032
104	123.499803231727	83.3586445358054	163.640961927648
105	123.499803231727	80.9237150824885	166.075891380965
106	123.499803231727	78.6206996006127	168.378906862841
107	123.499803231727	76.4302312836748	170.569375179779
108	123.499803231727	74.3372639969251	172.662342466529

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 123.499803231727 & 109.306917796863 & 137.692688666591 \tabularnewline
98 & 123.499803231727 & 103.428713136574 & 143.57089332688 \tabularnewline
99 & 123.499803231727 & 98.918116588042 & 148.081489875412 \tabularnewline
100 & 123.499803231727 & 95.1154769425777 & 151.884129520876 \tabularnewline
101 & 123.499803231727 & 91.7652693682927 & 155.234337095161 \tabularnewline
102 & 123.499803231727 & 88.7364417692616 & 158.263164694192 \tabularnewline
103 & 123.499803231727 & 85.9511419931343 & 161.04846447032 \tabularnewline
104 & 123.499803231727 & 83.3586445358054 & 163.640961927648 \tabularnewline
105 & 123.499803231727 & 80.9237150824885 & 166.075891380965 \tabularnewline
106 & 123.499803231727 & 78.6206996006127 & 168.378906862841 \tabularnewline
107 & 123.499803231727 & 76.4302312836748 & 170.569375179779 \tabularnewline
108 & 123.499803231727 & 74.3372639969251 & 172.662342466529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278660&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]97[/C][C]123.499803231727[/C][C]109.306917796863[/C][C]137.692688666591[/C][/ROW]
[ROW][C]98[/C][C]123.499803231727[/C][C]103.428713136574[/C][C]143.57089332688[/C][/ROW]
[ROW][C]99[/C][C]123.499803231727[/C][C]98.918116588042[/C][C]148.081489875412[/C][/ROW]
[ROW][C]100[/C][C]123.499803231727[/C][C]95.1154769425777[/C][C]151.884129520876[/C][/ROW]
[ROW][C]101[/C][C]123.499803231727[/C][C]91.7652693682927[/C][C]155.234337095161[/C][/ROW]
[ROW][C]102[/C][C]123.499803231727[/C][C]88.7364417692616[/C][C]158.263164694192[/C][/ROW]
[ROW][C]103[/C][C]123.499803231727[/C][C]85.9511419931343[/C][C]161.04846447032[/C][/ROW]
[ROW][C]104[/C][C]123.499803231727[/C][C]83.3586445358054[/C][C]163.640961927648[/C][/ROW]
[ROW][C]105[/C][C]123.499803231727[/C][C]80.9237150824885[/C][C]166.075891380965[/C][/ROW]
[ROW][C]106[/C][C]123.499803231727[/C][C]78.6206996006127[/C][C]168.378906862841[/C][/ROW]
[ROW][C]107[/C][C]123.499803231727[/C][C]76.4302312836748[/C][C]170.569375179779[/C][/ROW]
[ROW][C]108[/C][C]123.499803231727[/C][C]74.3372639969251[/C][C]172.662342466529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278660&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
97	123.499803231727	109.306917796863	137.692688666591
98	123.499803231727	103.428713136574	143.57089332688
99	123.499803231727	98.918116588042	148.081489875412
100	123.499803231727	95.1154769425777	151.884129520876
101	123.499803231727	91.7652693682927	155.234337095161
102	123.499803231727	88.7364417692616	158.263164694192
103	123.499803231727	85.9511419931343	161.04846447032
104	123.499803231727	83.3586445358054	163.640961927648
105	123.499803231727	80.9237150824885	166.075891380965
106	123.499803231727	78.6206996006127	168.378906862841
107	123.499803231727	76.4302312836748	170.569375179779
108	123.499803231727	74.3372639969251	172.662342466529

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