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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, 03 Jun 2010 18:00:21 +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/2010/Jun/03/t1275588133opfz08o5tm19zth.htm/, Retrieved Sun, 05 May 2024 10:16:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77406, Retrieved Sun, 05 May 2024 10:16:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

162

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

-       [Exponential Smoothing] [IKO - opgave 10 -...] [2010-06-03 18:00:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77406&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77406&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' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.384583602218265
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.384583602218265 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77406&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.384583602218265[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77406&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.384583602218265
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5107.4	5010.5	96.9000000000005
4	5202.1	5039.26615105495	162.833848945051
5	5307.5	5196.5893792453	110.910620754697
6	5266.1	5344.64378529941	-78.5437852994073
7	5329.8	5273.03713341710	56.7628665828961
8	5263.4	5358.56720111979	-95.1672011197888
9	5177.1	5255.56745610011	-78.4674561001093
10	5204.9	5139.09015917623	65.8098408237729
11	5185.2	5192.19954482164	-6.99954482164321
12	5189.8	5169.80763466025	19.9923653397527
13	5253.8	5182.09637053947	71.7036294605268
14	5372.3	5273.67241064953	98.6275893504735
15	5478.4	5430.10296424004	48.2970357599643
16	5590.5	5554.77721222907	35.7227877709338
17	5699.8	5680.61561063129	19.1843893687092
18	5797.9	5797.29361220107	0.606387798932701
19	5854.3	5895.62681900512	-41.3268190051213
20	5902.4	5936.13320208391	-33.7332020839103
21	5956.9	5971.25996571212	-14.3599657121231
22	6007.8	6020.23735837082	-12.4373583708229
23	6101.7	6066.35415428649	35.3458457135066
24	6148.6	6173.84758695444	-25.2475869544442
25	6207.4	6211.03777901619	-3.63777901618596
26	6232	6268.43874885807	-36.438748858066
27	6291.7	6279.0250035619	12.6749964380951
28	6323.4	6343.59959935017	-20.1995993501714
29	6365	6367.53116466872	-2.53116466871597
30	6435	6408.15772024261	26.8422797573858
31	6493.4	6488.48082088346	4.91917911653945
32	6606.8	6548.77265650806	58.0273434919445
33	6639.1	6684.48902129535	-45.3890212953447
34	6723.5	6699.33314798442	24.1668520155799
35	6759.4	6793.02732298685	-33.6273229868475
36	6848.6	6815.99480597961	32.6051940203924
37	6918.1	6917.734228947	0.365771053004210
38	6963.5	6987.37489849615	-23.8748984961476
39	7013.1	7023.5930040299	-10.4930040299032
40	7030.9	7069.15756674199	-38.2575667419933
41	7112.1	7072.24433391225	39.8556660877493
42	7130.3	7168.77216954509	-38.4721695450862
43	7130.8	7172.17640399629	-41.3764039962853
44	7076.9	7156.76371750056	-79.863717500556
45	7040.8	7072.14944133765	-31.3494413376493
46	7086.5	7023.99296026049	62.5070397395139
47	7120.7	7093.7321427675	26.9678572324910
48	7154.1	7138.30353844609	15.7964615539122
49	7228.2	7177.7785985328	50.4214014672052
50	7297.9	7271.26984273795	26.6301572620541
51	7369.5	7351.21136454542	18.2886354545753
52	7450.7	7429.8448738482	20.8551261517978
53	7459.7	7519.06541338838	-59.3654133883765
54	7497.5	7505.2344488603	-7.73444886029847
55	7536	7540.05990665643	-4.05990665643185
56	7637.4	7576.99853312983	60.4014668701684
57	7715.1	7701.62794683803	13.4720531619723
58	7815.7	7784.50907757234	31.1909224276642
59	7859.5	7897.10459487608	-37.6045948760766
60	7951.6	7926.44248431868	25.1575156813233
61	7973.7	8028.21765232226	-54.5176523222635
62	7988	8029.35105720768	-41.3510572076839
63	8053.1	8027.74811867122	25.351881328781
64	8112	8102.59803651565	9.40196348434802
65	8169.2	8165.11387750039	4.08612249961334
66	8303.1	8223.88533321039	79.2146667896068
67	8372.7	8388.24999511286	-15.5499951128604
68	8470.6	8451.86972197788	18.7302780221198
69	8536.1	8556.97307977018	-20.8730797701755
70	8665.8	8614.44563556277	51.3543644372257
71	8773.7	8763.89568202767	9.80431797232995
72	8838.4	8875.56626195076	-37.1662619507642
73	8936.2	8925.97272704875	10.2272729512515
74	8995.3	9027.70596852121	-32.4059685212142
75	9098.9	9074.34316441395	24.5568355860487
76	9237.1	9187.38732070272	49.7126792972849
77	9315.5	9344.70600198279	-29.2060019827877
78	9392.6	9411.87385253385	-19.2738525338518
79	9502.2	9481.56144489776	20.6385551022395
80	9671.1	9599.09869476356	72.0013052364393
81	9695.6	9795.6892160958	-100.089216095806
82	9847.9	9781.69654482648	66.2034551735196
83	9836.6	9959.4573080964	-122.857308096407
84	9887.7	9900.90840198985	-13.2084019898521
85	9875.6	9946.92866717305	-71.3286671730475
86	9905.9	9907.3968314102	-1.49683141020978
87	9871.1	9937.12117459456	-66.0211745945562
88	9910	9876.9305134463	33.0694865536989
89	9977.3	9928.54849570863	48.7515042913674
90	10031.6	10014.5975248426	17.0024751574365
91	10090.7	10075.4363979852	15.263602014762
92	10095.8	10140.4065290309	-44.6065290309034
93	10126	10128.3515894137	-2.35158941374175
94	10212.7	10157.6472066861	55.0527933139329
95	10398.7	10265.5196082509	133.180391749082
96	10467	10502.7386030546	-35.7386030546204
97	10543.6	10557.2941223536	-13.6941223536251
98	10634.2	10628.6275874497	5.57241255034933
99	10728.7	10721.3706459413	7.3293540586892
100	10796.4	10818.6893953271	-22.2893953271359
101	10875.8	10877.8172593810	-2.01725938095842
102	10946.1	10956.4414545016	-10.3414545016185
103	11050	11022.7643006772	27.2356993227877
104	11086.1	11137.1387040317	-51.0387040317019
105	11217.3	11153.6100553826	63.6899446173593
106	11291.7	11309.3041637087	-17.6041637086637
107	11314.1	11376.9338910155	-62.8338910155471
108	11356.4	11375.1690068674	-18.7690068673983
109	11357.8	11410.2507545963	-52.4507545962751
110	11491.4	11391.4790544546	99.9209455454275
111	11625.7	11563.5070116295	62.1929883705125
112	11620.7	11721.7254151297	-101.025415129739

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5107.4 & 5010.5 & 96.9000000000005 \tabularnewline
4 & 5202.1 & 5039.26615105495 & 162.833848945051 \tabularnewline
5 & 5307.5 & 5196.5893792453 & 110.910620754697 \tabularnewline
6 & 5266.1 & 5344.64378529941 & -78.5437852994073 \tabularnewline
7 & 5329.8 & 5273.03713341710 & 56.7628665828961 \tabularnewline
8 & 5263.4 & 5358.56720111979 & -95.1672011197888 \tabularnewline
9 & 5177.1 & 5255.56745610011 & -78.4674561001093 \tabularnewline
10 & 5204.9 & 5139.09015917623 & 65.8098408237729 \tabularnewline
11 & 5185.2 & 5192.19954482164 & -6.99954482164321 \tabularnewline
12 & 5189.8 & 5169.80763466025 & 19.9923653397527 \tabularnewline
13 & 5253.8 & 5182.09637053947 & 71.7036294605268 \tabularnewline
14 & 5372.3 & 5273.67241064953 & 98.6275893504735 \tabularnewline
15 & 5478.4 & 5430.10296424004 & 48.2970357599643 \tabularnewline
16 & 5590.5 & 5554.77721222907 & 35.7227877709338 \tabularnewline
17 & 5699.8 & 5680.61561063129 & 19.1843893687092 \tabularnewline
18 & 5797.9 & 5797.29361220107 & 0.606387798932701 \tabularnewline
19 & 5854.3 & 5895.62681900512 & -41.3268190051213 \tabularnewline
20 & 5902.4 & 5936.13320208391 & -33.7332020839103 \tabularnewline
21 & 5956.9 & 5971.25996571212 & -14.3599657121231 \tabularnewline
22 & 6007.8 & 6020.23735837082 & -12.4373583708229 \tabularnewline
23 & 6101.7 & 6066.35415428649 & 35.3458457135066 \tabularnewline
24 & 6148.6 & 6173.84758695444 & -25.2475869544442 \tabularnewline
25 & 6207.4 & 6211.03777901619 & -3.63777901618596 \tabularnewline
26 & 6232 & 6268.43874885807 & -36.438748858066 \tabularnewline
27 & 6291.7 & 6279.0250035619 & 12.6749964380951 \tabularnewline
28 & 6323.4 & 6343.59959935017 & -20.1995993501714 \tabularnewline
29 & 6365 & 6367.53116466872 & -2.53116466871597 \tabularnewline
30 & 6435 & 6408.15772024261 & 26.8422797573858 \tabularnewline
31 & 6493.4 & 6488.48082088346 & 4.91917911653945 \tabularnewline
32 & 6606.8 & 6548.77265650806 & 58.0273434919445 \tabularnewline
33 & 6639.1 & 6684.48902129535 & -45.3890212953447 \tabularnewline
34 & 6723.5 & 6699.33314798442 & 24.1668520155799 \tabularnewline
35 & 6759.4 & 6793.02732298685 & -33.6273229868475 \tabularnewline
36 & 6848.6 & 6815.99480597961 & 32.6051940203924 \tabularnewline
37 & 6918.1 & 6917.734228947 & 0.365771053004210 \tabularnewline
38 & 6963.5 & 6987.37489849615 & -23.8748984961476 \tabularnewline
39 & 7013.1 & 7023.5930040299 & -10.4930040299032 \tabularnewline
40 & 7030.9 & 7069.15756674199 & -38.2575667419933 \tabularnewline
41 & 7112.1 & 7072.24433391225 & 39.8556660877493 \tabularnewline
42 & 7130.3 & 7168.77216954509 & -38.4721695450862 \tabularnewline
43 & 7130.8 & 7172.17640399629 & -41.3764039962853 \tabularnewline
44 & 7076.9 & 7156.76371750056 & -79.863717500556 \tabularnewline
45 & 7040.8 & 7072.14944133765 & -31.3494413376493 \tabularnewline
46 & 7086.5 & 7023.99296026049 & 62.5070397395139 \tabularnewline
47 & 7120.7 & 7093.7321427675 & 26.9678572324910 \tabularnewline
48 & 7154.1 & 7138.30353844609 & 15.7964615539122 \tabularnewline
49 & 7228.2 & 7177.7785985328 & 50.4214014672052 \tabularnewline
50 & 7297.9 & 7271.26984273795 & 26.6301572620541 \tabularnewline
51 & 7369.5 & 7351.21136454542 & 18.2886354545753 \tabularnewline
52 & 7450.7 & 7429.8448738482 & 20.8551261517978 \tabularnewline
53 & 7459.7 & 7519.06541338838 & -59.3654133883765 \tabularnewline
54 & 7497.5 & 7505.2344488603 & -7.73444886029847 \tabularnewline
55 & 7536 & 7540.05990665643 & -4.05990665643185 \tabularnewline
56 & 7637.4 & 7576.99853312983 & 60.4014668701684 \tabularnewline
57 & 7715.1 & 7701.62794683803 & 13.4720531619723 \tabularnewline
58 & 7815.7 & 7784.50907757234 & 31.1909224276642 \tabularnewline
59 & 7859.5 & 7897.10459487608 & -37.6045948760766 \tabularnewline
60 & 7951.6 & 7926.44248431868 & 25.1575156813233 \tabularnewline
61 & 7973.7 & 8028.21765232226 & -54.5176523222635 \tabularnewline
62 & 7988 & 8029.35105720768 & -41.3510572076839 \tabularnewline
63 & 8053.1 & 8027.74811867122 & 25.351881328781 \tabularnewline
64 & 8112 & 8102.59803651565 & 9.40196348434802 \tabularnewline
65 & 8169.2 & 8165.11387750039 & 4.08612249961334 \tabularnewline
66 & 8303.1 & 8223.88533321039 & 79.2146667896068 \tabularnewline
67 & 8372.7 & 8388.24999511286 & -15.5499951128604 \tabularnewline
68 & 8470.6 & 8451.86972197788 & 18.7302780221198 \tabularnewline
69 & 8536.1 & 8556.97307977018 & -20.8730797701755 \tabularnewline
70 & 8665.8 & 8614.44563556277 & 51.3543644372257 \tabularnewline
71 & 8773.7 & 8763.89568202767 & 9.80431797232995 \tabularnewline
72 & 8838.4 & 8875.56626195076 & -37.1662619507642 \tabularnewline
73 & 8936.2 & 8925.97272704875 & 10.2272729512515 \tabularnewline
74 & 8995.3 & 9027.70596852121 & -32.4059685212142 \tabularnewline
75 & 9098.9 & 9074.34316441395 & 24.5568355860487 \tabularnewline
76 & 9237.1 & 9187.38732070272 & 49.7126792972849 \tabularnewline
77 & 9315.5 & 9344.70600198279 & -29.2060019827877 \tabularnewline
78 & 9392.6 & 9411.87385253385 & -19.2738525338518 \tabularnewline
79 & 9502.2 & 9481.56144489776 & 20.6385551022395 \tabularnewline
80 & 9671.1 & 9599.09869476356 & 72.0013052364393 \tabularnewline
81 & 9695.6 & 9795.6892160958 & -100.089216095806 \tabularnewline
82 & 9847.9 & 9781.69654482648 & 66.2034551735196 \tabularnewline
83 & 9836.6 & 9959.4573080964 & -122.857308096407 \tabularnewline
84 & 9887.7 & 9900.90840198985 & -13.2084019898521 \tabularnewline
85 & 9875.6 & 9946.92866717305 & -71.3286671730475 \tabularnewline
86 & 9905.9 & 9907.3968314102 & -1.49683141020978 \tabularnewline
87 & 9871.1 & 9937.12117459456 & -66.0211745945562 \tabularnewline
88 & 9910 & 9876.9305134463 & 33.0694865536989 \tabularnewline
89 & 9977.3 & 9928.54849570863 & 48.7515042913674 \tabularnewline
90 & 10031.6 & 10014.5975248426 & 17.0024751574365 \tabularnewline
91 & 10090.7 & 10075.4363979852 & 15.263602014762 \tabularnewline
92 & 10095.8 & 10140.4065290309 & -44.6065290309034 \tabularnewline
93 & 10126 & 10128.3515894137 & -2.35158941374175 \tabularnewline
94 & 10212.7 & 10157.6472066861 & 55.0527933139329 \tabularnewline
95 & 10398.7 & 10265.5196082509 & 133.180391749082 \tabularnewline
96 & 10467 & 10502.7386030546 & -35.7386030546204 \tabularnewline
97 & 10543.6 & 10557.2941223536 & -13.6941223536251 \tabularnewline
98 & 10634.2 & 10628.6275874497 & 5.57241255034933 \tabularnewline
99 & 10728.7 & 10721.3706459413 & 7.3293540586892 \tabularnewline
100 & 10796.4 & 10818.6893953271 & -22.2893953271359 \tabularnewline
101 & 10875.8 & 10877.8172593810 & -2.01725938095842 \tabularnewline
102 & 10946.1 & 10956.4414545016 & -10.3414545016185 \tabularnewline
103 & 11050 & 11022.7643006772 & 27.2356993227877 \tabularnewline
104 & 11086.1 & 11137.1387040317 & -51.0387040317019 \tabularnewline
105 & 11217.3 & 11153.6100553826 & 63.6899446173593 \tabularnewline
106 & 11291.7 & 11309.3041637087 & -17.6041637086637 \tabularnewline
107 & 11314.1 & 11376.9338910155 & -62.8338910155471 \tabularnewline
108 & 11356.4 & 11375.1690068674 & -18.7690068673983 \tabularnewline
109 & 11357.8 & 11410.2507545963 & -52.4507545962751 \tabularnewline
110 & 11491.4 & 11391.4790544546 & 99.9209455454275 \tabularnewline
111 & 11625.7 & 11563.5070116295 & 62.1929883705125 \tabularnewline
112 & 11620.7 & 11721.7254151297 & -101.025415129739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77406&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]5107.4[/C][C]5010.5[/C][C]96.9000000000005[/C][/ROW]
[ROW][C]4[/C][C]5202.1[/C][C]5039.26615105495[/C][C]162.833848945051[/C][/ROW]
[ROW][C]5[/C][C]5307.5[/C][C]5196.5893792453[/C][C]110.910620754697[/C][/ROW]
[ROW][C]6[/C][C]5266.1[/C][C]5344.64378529941[/C][C]-78.5437852994073[/C][/ROW]
[ROW][C]7[/C][C]5329.8[/C][C]5273.03713341710[/C][C]56.7628665828961[/C][/ROW]
[ROW][C]8[/C][C]5263.4[/C][C]5358.56720111979[/C][C]-95.1672011197888[/C][/ROW]
[ROW][C]9[/C][C]5177.1[/C][C]5255.56745610011[/C][C]-78.4674561001093[/C][/ROW]
[ROW][C]10[/C][C]5204.9[/C][C]5139.09015917623[/C][C]65.8098408237729[/C][/ROW]
[ROW][C]11[/C][C]5185.2[/C][C]5192.19954482164[/C][C]-6.99954482164321[/C][/ROW]
[ROW][C]12[/C][C]5189.8[/C][C]5169.80763466025[/C][C]19.9923653397527[/C][/ROW]
[ROW][C]13[/C][C]5253.8[/C][C]5182.09637053947[/C][C]71.7036294605268[/C][/ROW]
[ROW][C]14[/C][C]5372.3[/C][C]5273.67241064953[/C][C]98.6275893504735[/C][/ROW]
[ROW][C]15[/C][C]5478.4[/C][C]5430.10296424004[/C][C]48.2970357599643[/C][/ROW]
[ROW][C]16[/C][C]5590.5[/C][C]5554.77721222907[/C][C]35.7227877709338[/C][/ROW]
[ROW][C]17[/C][C]5699.8[/C][C]5680.61561063129[/C][C]19.1843893687092[/C][/ROW]
[ROW][C]18[/C][C]5797.9[/C][C]5797.29361220107[/C][C]0.606387798932701[/C][/ROW]
[ROW][C]19[/C][C]5854.3[/C][C]5895.62681900512[/C][C]-41.3268190051213[/C][/ROW]
[ROW][C]20[/C][C]5902.4[/C][C]5936.13320208391[/C][C]-33.7332020839103[/C][/ROW]
[ROW][C]21[/C][C]5956.9[/C][C]5971.25996571212[/C][C]-14.3599657121231[/C][/ROW]
[ROW][C]22[/C][C]6007.8[/C][C]6020.23735837082[/C][C]-12.4373583708229[/C][/ROW]
[ROW][C]23[/C][C]6101.7[/C][C]6066.35415428649[/C][C]35.3458457135066[/C][/ROW]
[ROW][C]24[/C][C]6148.6[/C][C]6173.84758695444[/C][C]-25.2475869544442[/C][/ROW]
[ROW][C]25[/C][C]6207.4[/C][C]6211.03777901619[/C][C]-3.63777901618596[/C][/ROW]
[ROW][C]26[/C][C]6232[/C][C]6268.43874885807[/C][C]-36.438748858066[/C][/ROW]
[ROW][C]27[/C][C]6291.7[/C][C]6279.0250035619[/C][C]12.6749964380951[/C][/ROW]
[ROW][C]28[/C][C]6323.4[/C][C]6343.59959935017[/C][C]-20.1995993501714[/C][/ROW]
[ROW][C]29[/C][C]6365[/C][C]6367.53116466872[/C][C]-2.53116466871597[/C][/ROW]
[ROW][C]30[/C][C]6435[/C][C]6408.15772024261[/C][C]26.8422797573858[/C][/ROW]
[ROW][C]31[/C][C]6493.4[/C][C]6488.48082088346[/C][C]4.91917911653945[/C][/ROW]
[ROW][C]32[/C][C]6606.8[/C][C]6548.77265650806[/C][C]58.0273434919445[/C][/ROW]
[ROW][C]33[/C][C]6639.1[/C][C]6684.48902129535[/C][C]-45.3890212953447[/C][/ROW]
[ROW][C]34[/C][C]6723.5[/C][C]6699.33314798442[/C][C]24.1668520155799[/C][/ROW]
[ROW][C]35[/C][C]6759.4[/C][C]6793.02732298685[/C][C]-33.6273229868475[/C][/ROW]
[ROW][C]36[/C][C]6848.6[/C][C]6815.99480597961[/C][C]32.6051940203924[/C][/ROW]
[ROW][C]37[/C][C]6918.1[/C][C]6917.734228947[/C][C]0.365771053004210[/C][/ROW]
[ROW][C]38[/C][C]6963.5[/C][C]6987.37489849615[/C][C]-23.8748984961476[/C][/ROW]
[ROW][C]39[/C][C]7013.1[/C][C]7023.5930040299[/C][C]-10.4930040299032[/C][/ROW]
[ROW][C]40[/C][C]7030.9[/C][C]7069.15756674199[/C][C]-38.2575667419933[/C][/ROW]
[ROW][C]41[/C][C]7112.1[/C][C]7072.24433391225[/C][C]39.8556660877493[/C][/ROW]
[ROW][C]42[/C][C]7130.3[/C][C]7168.77216954509[/C][C]-38.4721695450862[/C][/ROW]
[ROW][C]43[/C][C]7130.8[/C][C]7172.17640399629[/C][C]-41.3764039962853[/C][/ROW]
[ROW][C]44[/C][C]7076.9[/C][C]7156.76371750056[/C][C]-79.863717500556[/C][/ROW]
[ROW][C]45[/C][C]7040.8[/C][C]7072.14944133765[/C][C]-31.3494413376493[/C][/ROW]
[ROW][C]46[/C][C]7086.5[/C][C]7023.99296026049[/C][C]62.5070397395139[/C][/ROW]
[ROW][C]47[/C][C]7120.7[/C][C]7093.7321427675[/C][C]26.9678572324910[/C][/ROW]
[ROW][C]48[/C][C]7154.1[/C][C]7138.30353844609[/C][C]15.7964615539122[/C][/ROW]
[ROW][C]49[/C][C]7228.2[/C][C]7177.7785985328[/C][C]50.4214014672052[/C][/ROW]
[ROW][C]50[/C][C]7297.9[/C][C]7271.26984273795[/C][C]26.6301572620541[/C][/ROW]
[ROW][C]51[/C][C]7369.5[/C][C]7351.21136454542[/C][C]18.2886354545753[/C][/ROW]
[ROW][C]52[/C][C]7450.7[/C][C]7429.8448738482[/C][C]20.8551261517978[/C][/ROW]
[ROW][C]53[/C][C]7459.7[/C][C]7519.06541338838[/C][C]-59.3654133883765[/C][/ROW]
[ROW][C]54[/C][C]7497.5[/C][C]7505.2344488603[/C][C]-7.73444886029847[/C][/ROW]
[ROW][C]55[/C][C]7536[/C][C]7540.05990665643[/C][C]-4.05990665643185[/C][/ROW]
[ROW][C]56[/C][C]7637.4[/C][C]7576.99853312983[/C][C]60.4014668701684[/C][/ROW]
[ROW][C]57[/C][C]7715.1[/C][C]7701.62794683803[/C][C]13.4720531619723[/C][/ROW]
[ROW][C]58[/C][C]7815.7[/C][C]7784.50907757234[/C][C]31.1909224276642[/C][/ROW]
[ROW][C]59[/C][C]7859.5[/C][C]7897.10459487608[/C][C]-37.6045948760766[/C][/ROW]
[ROW][C]60[/C][C]7951.6[/C][C]7926.44248431868[/C][C]25.1575156813233[/C][/ROW]
[ROW][C]61[/C][C]7973.7[/C][C]8028.21765232226[/C][C]-54.5176523222635[/C][/ROW]
[ROW][C]62[/C][C]7988[/C][C]8029.35105720768[/C][C]-41.3510572076839[/C][/ROW]
[ROW][C]63[/C][C]8053.1[/C][C]8027.74811867122[/C][C]25.351881328781[/C][/ROW]
[ROW][C]64[/C][C]8112[/C][C]8102.59803651565[/C][C]9.40196348434802[/C][/ROW]
[ROW][C]65[/C][C]8169.2[/C][C]8165.11387750039[/C][C]4.08612249961334[/C][/ROW]
[ROW][C]66[/C][C]8303.1[/C][C]8223.88533321039[/C][C]79.2146667896068[/C][/ROW]
[ROW][C]67[/C][C]8372.7[/C][C]8388.24999511286[/C][C]-15.5499951128604[/C][/ROW]
[ROW][C]68[/C][C]8470.6[/C][C]8451.86972197788[/C][C]18.7302780221198[/C][/ROW]
[ROW][C]69[/C][C]8536.1[/C][C]8556.97307977018[/C][C]-20.8730797701755[/C][/ROW]
[ROW][C]70[/C][C]8665.8[/C][C]8614.44563556277[/C][C]51.3543644372257[/C][/ROW]
[ROW][C]71[/C][C]8773.7[/C][C]8763.89568202767[/C][C]9.80431797232995[/C][/ROW]
[ROW][C]72[/C][C]8838.4[/C][C]8875.56626195076[/C][C]-37.1662619507642[/C][/ROW]
[ROW][C]73[/C][C]8936.2[/C][C]8925.97272704875[/C][C]10.2272729512515[/C][/ROW]
[ROW][C]74[/C][C]8995.3[/C][C]9027.70596852121[/C][C]-32.4059685212142[/C][/ROW]
[ROW][C]75[/C][C]9098.9[/C][C]9074.34316441395[/C][C]24.5568355860487[/C][/ROW]
[ROW][C]76[/C][C]9237.1[/C][C]9187.38732070272[/C][C]49.7126792972849[/C][/ROW]
[ROW][C]77[/C][C]9315.5[/C][C]9344.70600198279[/C][C]-29.2060019827877[/C][/ROW]
[ROW][C]78[/C][C]9392.6[/C][C]9411.87385253385[/C][C]-19.2738525338518[/C][/ROW]
[ROW][C]79[/C][C]9502.2[/C][C]9481.56144489776[/C][C]20.6385551022395[/C][/ROW]
[ROW][C]80[/C][C]9671.1[/C][C]9599.09869476356[/C][C]72.0013052364393[/C][/ROW]
[ROW][C]81[/C][C]9695.6[/C][C]9795.6892160958[/C][C]-100.089216095806[/C][/ROW]
[ROW][C]82[/C][C]9847.9[/C][C]9781.69654482648[/C][C]66.2034551735196[/C][/ROW]
[ROW][C]83[/C][C]9836.6[/C][C]9959.4573080964[/C][C]-122.857308096407[/C][/ROW]
[ROW][C]84[/C][C]9887.7[/C][C]9900.90840198985[/C][C]-13.2084019898521[/C][/ROW]
[ROW][C]85[/C][C]9875.6[/C][C]9946.92866717305[/C][C]-71.3286671730475[/C][/ROW]
[ROW][C]86[/C][C]9905.9[/C][C]9907.3968314102[/C][C]-1.49683141020978[/C][/ROW]
[ROW][C]87[/C][C]9871.1[/C][C]9937.12117459456[/C][C]-66.0211745945562[/C][/ROW]
[ROW][C]88[/C][C]9910[/C][C]9876.9305134463[/C][C]33.0694865536989[/C][/ROW]
[ROW][C]89[/C][C]9977.3[/C][C]9928.54849570863[/C][C]48.7515042913674[/C][/ROW]
[ROW][C]90[/C][C]10031.6[/C][C]10014.5975248426[/C][C]17.0024751574365[/C][/ROW]
[ROW][C]91[/C][C]10090.7[/C][C]10075.4363979852[/C][C]15.263602014762[/C][/ROW]
[ROW][C]92[/C][C]10095.8[/C][C]10140.4065290309[/C][C]-44.6065290309034[/C][/ROW]
[ROW][C]93[/C][C]10126[/C][C]10128.3515894137[/C][C]-2.35158941374175[/C][/ROW]
[ROW][C]94[/C][C]10212.7[/C][C]10157.6472066861[/C][C]55.0527933139329[/C][/ROW]
[ROW][C]95[/C][C]10398.7[/C][C]10265.5196082509[/C][C]133.180391749082[/C][/ROW]
[ROW][C]96[/C][C]10467[/C][C]10502.7386030546[/C][C]-35.7386030546204[/C][/ROW]
[ROW][C]97[/C][C]10543.6[/C][C]10557.2941223536[/C][C]-13.6941223536251[/C][/ROW]
[ROW][C]98[/C][C]10634.2[/C][C]10628.6275874497[/C][C]5.57241255034933[/C][/ROW]
[ROW][C]99[/C][C]10728.7[/C][C]10721.3706459413[/C][C]7.3293540586892[/C][/ROW]
[ROW][C]100[/C][C]10796.4[/C][C]10818.6893953271[/C][C]-22.2893953271359[/C][/ROW]
[ROW][C]101[/C][C]10875.8[/C][C]10877.8172593810[/C][C]-2.01725938095842[/C][/ROW]
[ROW][C]102[/C][C]10946.1[/C][C]10956.4414545016[/C][C]-10.3414545016185[/C][/ROW]
[ROW][C]103[/C][C]11050[/C][C]11022.7643006772[/C][C]27.2356993227877[/C][/ROW]
[ROW][C]104[/C][C]11086.1[/C][C]11137.1387040317[/C][C]-51.0387040317019[/C][/ROW]
[ROW][C]105[/C][C]11217.3[/C][C]11153.6100553826[/C][C]63.6899446173593[/C][/ROW]
[ROW][C]106[/C][C]11291.7[/C][C]11309.3041637087[/C][C]-17.6041637086637[/C][/ROW]
[ROW][C]107[/C][C]11314.1[/C][C]11376.9338910155[/C][C]-62.8338910155471[/C][/ROW]
[ROW][C]108[/C][C]11356.4[/C][C]11375.1690068674[/C][C]-18.7690068673983[/C][/ROW]
[ROW][C]109[/C][C]11357.8[/C][C]11410.2507545963[/C][C]-52.4507545962751[/C][/ROW]
[ROW][C]110[/C][C]11491.4[/C][C]11391.4790544546[/C][C]99.9209455454275[/C][/ROW]
[ROW][C]111[/C][C]11625.7[/C][C]11563.5070116295[/C][C]62.1929883705125[/C][/ROW]
[ROW][C]112[/C][C]11620.7[/C][C]11721.7254151297[/C][C]-101.025415129739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77406&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77406&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5107.4	5010.5	96.9000000000005
4	5202.1	5039.26615105495	162.833848945051
5	5307.5	5196.5893792453	110.910620754697
6	5266.1	5344.64378529941	-78.5437852994073
7	5329.8	5273.03713341710	56.7628665828961
8	5263.4	5358.56720111979	-95.1672011197888
9	5177.1	5255.56745610011	-78.4674561001093
10	5204.9	5139.09015917623	65.8098408237729
11	5185.2	5192.19954482164	-6.99954482164321
12	5189.8	5169.80763466025	19.9923653397527
13	5253.8	5182.09637053947	71.7036294605268
14	5372.3	5273.67241064953	98.6275893504735
15	5478.4	5430.10296424004	48.2970357599643
16	5590.5	5554.77721222907	35.7227877709338
17	5699.8	5680.61561063129	19.1843893687092
18	5797.9	5797.29361220107	0.606387798932701
19	5854.3	5895.62681900512	-41.3268190051213
20	5902.4	5936.13320208391	-33.7332020839103
21	5956.9	5971.25996571212	-14.3599657121231
22	6007.8	6020.23735837082	-12.4373583708229
23	6101.7	6066.35415428649	35.3458457135066
24	6148.6	6173.84758695444	-25.2475869544442
25	6207.4	6211.03777901619	-3.63777901618596
26	6232	6268.43874885807	-36.438748858066
27	6291.7	6279.0250035619	12.6749964380951
28	6323.4	6343.59959935017	-20.1995993501714
29	6365	6367.53116466872	-2.53116466871597
30	6435	6408.15772024261	26.8422797573858
31	6493.4	6488.48082088346	4.91917911653945
32	6606.8	6548.77265650806	58.0273434919445
33	6639.1	6684.48902129535	-45.3890212953447
34	6723.5	6699.33314798442	24.1668520155799
35	6759.4	6793.02732298685	-33.6273229868475
36	6848.6	6815.99480597961	32.6051940203924
37	6918.1	6917.734228947	0.365771053004210
38	6963.5	6987.37489849615	-23.8748984961476
39	7013.1	7023.5930040299	-10.4930040299032
40	7030.9	7069.15756674199	-38.2575667419933
41	7112.1	7072.24433391225	39.8556660877493
42	7130.3	7168.77216954509	-38.4721695450862
43	7130.8	7172.17640399629	-41.3764039962853
44	7076.9	7156.76371750056	-79.863717500556
45	7040.8	7072.14944133765	-31.3494413376493
46	7086.5	7023.99296026049	62.5070397395139
47	7120.7	7093.7321427675	26.9678572324910
48	7154.1	7138.30353844609	15.7964615539122
49	7228.2	7177.7785985328	50.4214014672052
50	7297.9	7271.26984273795	26.6301572620541
51	7369.5	7351.21136454542	18.2886354545753
52	7450.7	7429.8448738482	20.8551261517978
53	7459.7	7519.06541338838	-59.3654133883765
54	7497.5	7505.2344488603	-7.73444886029847
55	7536	7540.05990665643	-4.05990665643185
56	7637.4	7576.99853312983	60.4014668701684
57	7715.1	7701.62794683803	13.4720531619723
58	7815.7	7784.50907757234	31.1909224276642
59	7859.5	7897.10459487608	-37.6045948760766
60	7951.6	7926.44248431868	25.1575156813233
61	7973.7	8028.21765232226	-54.5176523222635
62	7988	8029.35105720768	-41.3510572076839
63	8053.1	8027.74811867122	25.351881328781
64	8112	8102.59803651565	9.40196348434802
65	8169.2	8165.11387750039	4.08612249961334
66	8303.1	8223.88533321039	79.2146667896068
67	8372.7	8388.24999511286	-15.5499951128604
68	8470.6	8451.86972197788	18.7302780221198
69	8536.1	8556.97307977018	-20.8730797701755
70	8665.8	8614.44563556277	51.3543644372257
71	8773.7	8763.89568202767	9.80431797232995
72	8838.4	8875.56626195076	-37.1662619507642
73	8936.2	8925.97272704875	10.2272729512515
74	8995.3	9027.70596852121	-32.4059685212142
75	9098.9	9074.34316441395	24.5568355860487
76	9237.1	9187.38732070272	49.7126792972849
77	9315.5	9344.70600198279	-29.2060019827877
78	9392.6	9411.87385253385	-19.2738525338518
79	9502.2	9481.56144489776	20.6385551022395
80	9671.1	9599.09869476356	72.0013052364393
81	9695.6	9795.6892160958	-100.089216095806
82	9847.9	9781.69654482648	66.2034551735196
83	9836.6	9959.4573080964	-122.857308096407
84	9887.7	9900.90840198985	-13.2084019898521
85	9875.6	9946.92866717305	-71.3286671730475
86	9905.9	9907.3968314102	-1.49683141020978
87	9871.1	9937.12117459456	-66.0211745945562
88	9910	9876.9305134463	33.0694865536989
89	9977.3	9928.54849570863	48.7515042913674
90	10031.6	10014.5975248426	17.0024751574365
91	10090.7	10075.4363979852	15.263602014762
92	10095.8	10140.4065290309	-44.6065290309034
93	10126	10128.3515894137	-2.35158941374175
94	10212.7	10157.6472066861	55.0527933139329
95	10398.7	10265.5196082509	133.180391749082
96	10467	10502.7386030546	-35.7386030546204
97	10543.6	10557.2941223536	-13.6941223536251
98	10634.2	10628.6275874497	5.57241255034933
99	10728.7	10721.3706459413	7.3293540586892
100	10796.4	10818.6893953271	-22.2893953271359
101	10875.8	10877.8172593810	-2.01725938095842
102	10946.1	10956.4414545016	-10.3414545016185
103	11050	11022.7643006772	27.2356993227877
104	11086.1	11137.1387040317	-51.0387040317019
105	11217.3	11153.6100553826	63.6899446173593
106	11291.7	11309.3041637087	-17.6041637086637
107	11314.1	11376.9338910155	-62.8338910155471
108	11356.4	11375.1690068674	-18.7690068673983
109	11357.8	11410.2507545963	-52.4507545962751
110	11491.4	11391.4790544546	99.9209455454275
111	11625.7	11563.5070116295	62.1929883705125
112	11620.7	11721.7254151297	-101.025415129739

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
113	11677.8726970635	11578.6811236784	11777.0642704487
114	11735.0453941271	11565.6317692625	11904.4590189917
115	11792.2180911906	11548.2990873031	12036.1370950782
116	11849.3907882542	11525.144065813	12173.6375106954

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
113 & 11677.8726970635 & 11578.6811236784 & 11777.0642704487 \tabularnewline
114 & 11735.0453941271 & 11565.6317692625 & 11904.4590189917 \tabularnewline
115 & 11792.2180911906 & 11548.2990873031 & 12036.1370950782 \tabularnewline
116 & 11849.3907882542 & 11525.144065813 & 12173.6375106954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77406&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]113[/C][C]11677.8726970635[/C][C]11578.6811236784[/C][C]11777.0642704487[/C][/ROW]
[ROW][C]114[/C][C]11735.0453941271[/C][C]11565.6317692625[/C][C]11904.4590189917[/C][/ROW]
[ROW][C]115[/C][C]11792.2180911906[/C][C]11548.2990873031[/C][C]12036.1370950782[/C][/ROW]
[ROW][C]116[/C][C]11849.3907882542[/C][C]11525.144065813[/C][C]12173.6375106954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77406&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77406&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
113	11677.8726970635	11578.6811236784	11777.0642704487
114	11735.0453941271	11565.6317692625	11904.4590189917
115	11792.2180911906	11548.2990873031	12036.1370950782
116	11849.3907882542	11525.144065813	12173.6375106954

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 = 4 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 4 ; par2 = Double ; par3 = multiplicative ;

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