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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 03:28:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258626596flqsjjrmhccrp2p.htm/, Retrieved Thu, 28 Mar 2024 16:04:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57685, Retrieved Thu, 28 Mar 2024 16:04:53 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [multivariate line...] [2009-11-19 10:28:36] [a5b01ef1969ffd97a40c5fefe56a50d0] [Current]
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Dataseries X:
8.4	1.8
8.4	1.6
8.4	1.9
8.6	1.7
8.9	1.6
8.8	1.3
8.3	1.1
7.5	1.9
7.2	2.6
7.4	2.3
8.8	2.4
9.3	2.2
9.3	2
8.7	2.9
8.2	2.6
8.3	2.3
8.5	2.3
8.6	2.6
8.5	3.1
8.2	2.8
8.1	2.5
7.9	2.9
8.6	3.1
8.7	3.1
8.7	3.2
8.5	2.5
8.4	2.6
8.5	2.9
8.7	2.6
8.7	2.4
8.6	1.7
8.5	2
8.3	2.2
8	1.9
8.2	1.6
8.1	1.6
8.1	1.2
8	1.2
7.9	1.5
7.9	1.6
8	1.7
8	1.8
7.9	1.8
8	1.8
7.7	1.3
7.2	1.3
7.5	1.4
7.3	1.1
7	1.5
7	2.2
7	2.9
7.2	3.1
7.3	3.5
7.1	3.6
6.8	4.4
6.4	4.2
6.1	5.2
6.5	5.8
7.7	5.9
7.9	5.4
7.5	5.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&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]5 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=57685&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Twk[t] = + 8.8512487495832 -0.220615205068356Ncp[t] -0.125690230076687M1[t] -0.272369123041014M2[t] -0.363833777925975M3[t] -0.239421473824608M4[t] -0.0550091697232414M5[t] -0.095009169723241M6[t] -0.297359953317772M7[t] -0.57088612870957M8[t] -0.762350783594531M9[t] -0.824701567189063M10[t] -0.0558769589863286M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Twk[t] =  +  8.8512487495832 -0.220615205068356Ncp[t] -0.125690230076687M1[t] -0.272369123041014M2[t] -0.363833777925975M3[t] -0.239421473824608M4[t] -0.0550091697232414M5[t] -0.095009169723241M6[t] -0.297359953317772M7[t] -0.57088612870957M8[t] -0.762350783594531M9[t] -0.824701567189063M10[t] -0.0558769589863286M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Twk[t] =  +  8.8512487495832 -0.220615205068356Ncp[t] -0.125690230076687M1[t] -0.272369123041014M2[t] -0.363833777925975M3[t] -0.239421473824608M4[t] -0.0550091697232414M5[t] -0.095009169723241M6[t] -0.297359953317772M7[t] -0.57088612870957M8[t] -0.762350783594531M9[t] -0.824701567189063M10[t] -0.0558769589863286M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57685&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Twk[t] = + 8.8512487495832 -0.220615205068356Ncp[t] -0.125690230076687M1[t] -0.272369123041014M2[t] -0.363833777925975M3[t] -0.239421473824608M4[t] -0.0550091697232414M5[t] -0.095009169723241M6[t] -0.297359953317772M7[t] -0.57088612870957M8[t] -0.762350783594531M9[t] -0.824701567189063M10[t] -0.0558769589863286M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.85124874958320.35356825.034100
Ncp-0.2206152050683560.073442-3.00390.0042250.002113
M1-0.1256902300766870.397843-0.31590.7534260.376713
M2-0.2723691230410140.417712-0.65210.5174790.258739
M3-0.3638337779259750.416317-0.87390.3865060.193253
M4-0.2394214738246080.416221-0.57520.5678250.283913
M5-0.05500916972324140.416131-0.13220.8953850.447692
M6-0.0950091697232410.416131-0.22830.8203710.410185
M7-0.2973599533177720.415819-0.71510.4780.239
M8-0.570886128709570.415508-1.37390.175840.08792
M9-0.7623507835945310.415422-1.83510.0726880.036344
M10-0.8247015671890630.415547-1.98460.0529190.02646
M11-0.05587695898632860.41564-0.13440.893620.44681

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 8.8512487495832 & 0.353568 & 25.0341 & 0 & 0 \tabularnewline
Ncp & -0.220615205068356 & 0.073442 & -3.0039 & 0.004225 & 0.002113 \tabularnewline
M1 & -0.125690230076687 & 0.397843 & -0.3159 & 0.753426 & 0.376713 \tabularnewline
M2 & -0.272369123041014 & 0.417712 & -0.6521 & 0.517479 & 0.258739 \tabularnewline
M3 & -0.363833777925975 & 0.416317 & -0.8739 & 0.386506 & 0.193253 \tabularnewline
M4 & -0.239421473824608 & 0.416221 & -0.5752 & 0.567825 & 0.283913 \tabularnewline
M5 & -0.0550091697232414 & 0.416131 & -0.1322 & 0.895385 & 0.447692 \tabularnewline
M6 & -0.095009169723241 & 0.416131 & -0.2283 & 0.820371 & 0.410185 \tabularnewline
M7 & -0.297359953317772 & 0.415819 & -0.7151 & 0.478 & 0.239 \tabularnewline
M8 & -0.57088612870957 & 0.415508 & -1.3739 & 0.17584 & 0.08792 \tabularnewline
M9 & -0.762350783594531 & 0.415422 & -1.8351 & 0.072688 & 0.036344 \tabularnewline
M10 & -0.824701567189063 & 0.415547 & -1.9846 & 0.052919 & 0.02646 \tabularnewline
M11 & -0.0558769589863286 & 0.41564 & -0.1344 & 0.89362 & 0.44681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]8.8512487495832[/C][C]0.353568[/C][C]25.0341[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Ncp[/C][C]-0.220615205068356[/C][C]0.073442[/C][C]-3.0039[/C][C]0.004225[/C][C]0.002113[/C][/ROW]
[ROW][C]M1[/C][C]-0.125690230076687[/C][C]0.397843[/C][C]-0.3159[/C][C]0.753426[/C][C]0.376713[/C][/ROW]
[ROW][C]M2[/C][C]-0.272369123041014[/C][C]0.417712[/C][C]-0.6521[/C][C]0.517479[/C][C]0.258739[/C][/ROW]
[ROW][C]M3[/C][C]-0.363833777925975[/C][C]0.416317[/C][C]-0.8739[/C][C]0.386506[/C][C]0.193253[/C][/ROW]
[ROW][C]M4[/C][C]-0.239421473824608[/C][C]0.416221[/C][C]-0.5752[/C][C]0.567825[/C][C]0.283913[/C][/ROW]
[ROW][C]M5[/C][C]-0.0550091697232414[/C][C]0.416131[/C][C]-0.1322[/C][C]0.895385[/C][C]0.447692[/C][/ROW]
[ROW][C]M6[/C][C]-0.095009169723241[/C][C]0.416131[/C][C]-0.2283[/C][C]0.820371[/C][C]0.410185[/C][/ROW]
[ROW][C]M7[/C][C]-0.297359953317772[/C][C]0.415819[/C][C]-0.7151[/C][C]0.478[/C][C]0.239[/C][/ROW]
[ROW][C]M8[/C][C]-0.57088612870957[/C][C]0.415508[/C][C]-1.3739[/C][C]0.17584[/C][C]0.08792[/C][/ROW]
[ROW][C]M9[/C][C]-0.762350783594531[/C][C]0.415422[/C][C]-1.8351[/C][C]0.072688[/C][C]0.036344[/C][/ROW]
[ROW][C]M10[/C][C]-0.824701567189063[/C][C]0.415547[/C][C]-1.9846[/C][C]0.052919[/C][C]0.02646[/C][/ROW]
[ROW][C]M11[/C][C]-0.0558769589863286[/C][C]0.41564[/C][C]-0.1344[/C][C]0.89362[/C][C]0.44681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57685&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.85124874958320.35356825.034100
Ncp-0.2206152050683560.073442-3.00390.0042250.002113
M1-0.1256902300766870.397843-0.31590.7534260.376713
M2-0.2723691230410140.417712-0.65210.5174790.258739
M3-0.3638337779259750.416317-0.87390.3865060.193253
M4-0.2394214738246080.416221-0.57520.5678250.283913
M5-0.05500916972324140.416131-0.13220.8953850.447692
M6-0.0950091697232410.416131-0.22830.8203710.410185
M7-0.2973599533177720.415819-0.71510.4780.239
M8-0.570886128709570.415508-1.37390.175840.08792
M9-0.7623507835945310.415422-1.83510.0726880.036344
M10-0.8247015671890630.415547-1.98460.0529190.02646
M11-0.05587695898632860.41564-0.13440.893620.44681







Multiple Linear Regression - Regression Statistics
Multiple R0.547740927718233
R-squared0.300020123897631
Adjusted R-squared0.125025154872038
F-TEST (value)1.7144499957239
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.0931422593625605
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.656774722474512
Sum Squared Residuals20.7049457319106

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.547740927718233 \tabularnewline
R-squared & 0.300020123897631 \tabularnewline
Adjusted R-squared & 0.125025154872038 \tabularnewline
F-TEST (value) & 1.7144499957239 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.0931422593625605 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.656774722474512 \tabularnewline
Sum Squared Residuals & 20.7049457319106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.547740927718233[/C][/ROW]
[ROW][C]R-squared[/C][C]0.300020123897631[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.125025154872038[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.7144499957239[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.0931422593625605[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.656774722474512[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]20.7049457319106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57685&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.547740927718233
R-squared0.300020123897631
Adjusted R-squared0.125025154872038
F-TEST (value)1.7144499957239
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.0931422593625605
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.656774722474512
Sum Squared Residuals20.7049457319106







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.48.328451150383440.0715488496165638
28.48.225895298432810.174104701567189
38.48.068246082027340.331753917972658
48.68.236781427142380.363218572857618
58.98.443255251750580.456744748249417
68.88.46943981327110.33056018672891
78.38.31121207069023-0.0112120706902295
87.57.86119373124375-0.361193731243749
97.27.51529843281094-0.315298432810937
107.47.51913221073691-0.119132210736913
118.88.265895298432810.53410470156719
129.38.365895298432810.93410470156719
139.38.28432810936981.01567189063021
148.77.939095531843950.760904468156052
158.27.91381543847950.286184561520506
168.38.104412304101370.195587695898633
178.58.288824608202730.211175391797266
188.68.182640046682230.417359953317772
198.57.869981660553520.630018339446482
208.27.662640046682230.537359953317772
218.17.537359953317770.562640046682227
227.97.38676308769590.513236912304102
238.68.111464654884960.488535345115038
248.78.167341613871290.532658386128709
258.78.019589863287770.680410136712232
268.58.027341613871290.47265838612871
278.47.91381543847950.486184561520507
288.57.972043181060350.527956818939647
298.78.222640046682230.477359953317772
308.78.22676308769590.473236912304101
318.68.178842947649220.421157052350783
328.57.839132210736910.660867789263087
338.37.603544514838280.696455485161721
3487.607378292764260.392621707235745
358.28.4423874624875-0.242387462487497
368.18.49826442147383-0.398264421473825
378.18.46082027342448-0.360820273424481
3888.31414138046015-0.314141380460154
397.98.15649216405469-0.256492164054685
407.98.25884294764922-0.358842947649217
4188.42119373124375-0.421193731243748
4288.35913221073691-0.359132210736912
437.98.15678142714238-0.256781427142381
4487.883255251750580.116744748249416
457.77.8020981993998-0.102098199399801
467.27.73974741580527-0.539747415805269
477.58.48651050350117-0.986510503501167
487.38.608572024008-1.30857202400800
4978.39463571190397-1.39463571190397
5078.0935261753918-1.09352617539180
5177.84763087695899-0.847630876958986
527.27.92792014004668-0.727920140046683
537.38.0240863621207-0.724086362120706
547.17.96202484161387-0.862024841613871
556.87.58318189396465-0.783181893964655
566.47.35377875958653-0.953778759586528
576.16.94169889963321-0.84169889963321
586.56.74697899299766-0.246978992997665
597.77.493742080693560.206257919306437
607.97.659926642214070.24007335778593
617.57.51217489163055-0.0121748916305475

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.4 & 8.32845115038344 & 0.0715488496165638 \tabularnewline
2 & 8.4 & 8.22589529843281 & 0.174104701567189 \tabularnewline
3 & 8.4 & 8.06824608202734 & 0.331753917972658 \tabularnewline
4 & 8.6 & 8.23678142714238 & 0.363218572857618 \tabularnewline
5 & 8.9 & 8.44325525175058 & 0.456744748249417 \tabularnewline
6 & 8.8 & 8.4694398132711 & 0.33056018672891 \tabularnewline
7 & 8.3 & 8.31121207069023 & -0.0112120706902295 \tabularnewline
8 & 7.5 & 7.86119373124375 & -0.361193731243749 \tabularnewline
9 & 7.2 & 7.51529843281094 & -0.315298432810937 \tabularnewline
10 & 7.4 & 7.51913221073691 & -0.119132210736913 \tabularnewline
11 & 8.8 & 8.26589529843281 & 0.53410470156719 \tabularnewline
12 & 9.3 & 8.36589529843281 & 0.93410470156719 \tabularnewline
13 & 9.3 & 8.2843281093698 & 1.01567189063021 \tabularnewline
14 & 8.7 & 7.93909553184395 & 0.760904468156052 \tabularnewline
15 & 8.2 & 7.9138154384795 & 0.286184561520506 \tabularnewline
16 & 8.3 & 8.10441230410137 & 0.195587695898633 \tabularnewline
17 & 8.5 & 8.28882460820273 & 0.211175391797266 \tabularnewline
18 & 8.6 & 8.18264004668223 & 0.417359953317772 \tabularnewline
19 & 8.5 & 7.86998166055352 & 0.630018339446482 \tabularnewline
20 & 8.2 & 7.66264004668223 & 0.537359953317772 \tabularnewline
21 & 8.1 & 7.53735995331777 & 0.562640046682227 \tabularnewline
22 & 7.9 & 7.3867630876959 & 0.513236912304102 \tabularnewline
23 & 8.6 & 8.11146465488496 & 0.488535345115038 \tabularnewline
24 & 8.7 & 8.16734161387129 & 0.532658386128709 \tabularnewline
25 & 8.7 & 8.01958986328777 & 0.680410136712232 \tabularnewline
26 & 8.5 & 8.02734161387129 & 0.47265838612871 \tabularnewline
27 & 8.4 & 7.9138154384795 & 0.486184561520507 \tabularnewline
28 & 8.5 & 7.97204318106035 & 0.527956818939647 \tabularnewline
29 & 8.7 & 8.22264004668223 & 0.477359953317772 \tabularnewline
30 & 8.7 & 8.2267630876959 & 0.473236912304101 \tabularnewline
31 & 8.6 & 8.17884294764922 & 0.421157052350783 \tabularnewline
32 & 8.5 & 7.83913221073691 & 0.660867789263087 \tabularnewline
33 & 8.3 & 7.60354451483828 & 0.696455485161721 \tabularnewline
34 & 8 & 7.60737829276426 & 0.392621707235745 \tabularnewline
35 & 8.2 & 8.4423874624875 & -0.242387462487497 \tabularnewline
36 & 8.1 & 8.49826442147383 & -0.398264421473825 \tabularnewline
37 & 8.1 & 8.46082027342448 & -0.360820273424481 \tabularnewline
38 & 8 & 8.31414138046015 & -0.314141380460154 \tabularnewline
39 & 7.9 & 8.15649216405469 & -0.256492164054685 \tabularnewline
40 & 7.9 & 8.25884294764922 & -0.358842947649217 \tabularnewline
41 & 8 & 8.42119373124375 & -0.421193731243748 \tabularnewline
42 & 8 & 8.35913221073691 & -0.359132210736912 \tabularnewline
43 & 7.9 & 8.15678142714238 & -0.256781427142381 \tabularnewline
44 & 8 & 7.88325525175058 & 0.116744748249416 \tabularnewline
45 & 7.7 & 7.8020981993998 & -0.102098199399801 \tabularnewline
46 & 7.2 & 7.73974741580527 & -0.539747415805269 \tabularnewline
47 & 7.5 & 8.48651050350117 & -0.986510503501167 \tabularnewline
48 & 7.3 & 8.608572024008 & -1.30857202400800 \tabularnewline
49 & 7 & 8.39463571190397 & -1.39463571190397 \tabularnewline
50 & 7 & 8.0935261753918 & -1.09352617539180 \tabularnewline
51 & 7 & 7.84763087695899 & -0.847630876958986 \tabularnewline
52 & 7.2 & 7.92792014004668 & -0.727920140046683 \tabularnewline
53 & 7.3 & 8.0240863621207 & -0.724086362120706 \tabularnewline
54 & 7.1 & 7.96202484161387 & -0.862024841613871 \tabularnewline
55 & 6.8 & 7.58318189396465 & -0.783181893964655 \tabularnewline
56 & 6.4 & 7.35377875958653 & -0.953778759586528 \tabularnewline
57 & 6.1 & 6.94169889963321 & -0.84169889963321 \tabularnewline
58 & 6.5 & 6.74697899299766 & -0.246978992997665 \tabularnewline
59 & 7.7 & 7.49374208069356 & 0.206257919306437 \tabularnewline
60 & 7.9 & 7.65992664221407 & 0.24007335778593 \tabularnewline
61 & 7.5 & 7.51217489163055 & -0.0121748916305475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]8.4[/C][C]8.32845115038344[/C][C]0.0715488496165638[/C][/ROW]
[ROW][C]2[/C][C]8.4[/C][C]8.22589529843281[/C][C]0.174104701567189[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.06824608202734[/C][C]0.331753917972658[/C][/ROW]
[ROW][C]4[/C][C]8.6[/C][C]8.23678142714238[/C][C]0.363218572857618[/C][/ROW]
[ROW][C]5[/C][C]8.9[/C][C]8.44325525175058[/C][C]0.456744748249417[/C][/ROW]
[ROW][C]6[/C][C]8.8[/C][C]8.4694398132711[/C][C]0.33056018672891[/C][/ROW]
[ROW][C]7[/C][C]8.3[/C][C]8.31121207069023[/C][C]-0.0112120706902295[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]7.86119373124375[/C][C]-0.361193731243749[/C][/ROW]
[ROW][C]9[/C][C]7.2[/C][C]7.51529843281094[/C][C]-0.315298432810937[/C][/ROW]
[ROW][C]10[/C][C]7.4[/C][C]7.51913221073691[/C][C]-0.119132210736913[/C][/ROW]
[ROW][C]11[/C][C]8.8[/C][C]8.26589529843281[/C][C]0.53410470156719[/C][/ROW]
[ROW][C]12[/C][C]9.3[/C][C]8.36589529843281[/C][C]0.93410470156719[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]8.2843281093698[/C][C]1.01567189063021[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]7.93909553184395[/C][C]0.760904468156052[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]7.9138154384795[/C][C]0.286184561520506[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.10441230410137[/C][C]0.195587695898633[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.28882460820273[/C][C]0.211175391797266[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.18264004668223[/C][C]0.417359953317772[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]7.86998166055352[/C][C]0.630018339446482[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]7.66264004668223[/C][C]0.537359953317772[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.53735995331777[/C][C]0.562640046682227[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.3867630876959[/C][C]0.513236912304102[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.11146465488496[/C][C]0.488535345115038[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.16734161387129[/C][C]0.532658386128709[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.01958986328777[/C][C]0.680410136712232[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.02734161387129[/C][C]0.47265838612871[/C][/ROW]
[ROW][C]27[/C][C]8.4[/C][C]7.9138154384795[/C][C]0.486184561520507[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]7.97204318106035[/C][C]0.527956818939647[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.22264004668223[/C][C]0.477359953317772[/C][/ROW]
[ROW][C]30[/C][C]8.7[/C][C]8.2267630876959[/C][C]0.473236912304101[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]8.17884294764922[/C][C]0.421157052350783[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]7.83913221073691[/C][C]0.660867789263087[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]7.60354451483828[/C][C]0.696455485161721[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.60737829276426[/C][C]0.392621707235745[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]8.4423874624875[/C][C]-0.242387462487497[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.49826442147383[/C][C]-0.398264421473825[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]8.46082027342448[/C][C]-0.360820273424481[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]8.31414138046015[/C][C]-0.314141380460154[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]8.15649216405469[/C][C]-0.256492164054685[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]8.25884294764922[/C][C]-0.358842947649217[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]8.42119373124375[/C][C]-0.421193731243748[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]8.35913221073691[/C][C]-0.359132210736912[/C][/ROW]
[ROW][C]43[/C][C]7.9[/C][C]8.15678142714238[/C][C]-0.256781427142381[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]7.88325525175058[/C][C]0.116744748249416[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.8020981993998[/C][C]-0.102098199399801[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]7.73974741580527[/C][C]-0.539747415805269[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]8.48651050350117[/C][C]-0.986510503501167[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]8.608572024008[/C][C]-1.30857202400800[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]8.39463571190397[/C][C]-1.39463571190397[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]8.0935261753918[/C][C]-1.09352617539180[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]7.84763087695899[/C][C]-0.847630876958986[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.92792014004668[/C][C]-0.727920140046683[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]8.0240863621207[/C][C]-0.724086362120706[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.96202484161387[/C][C]-0.862024841613871[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]7.58318189396465[/C][C]-0.783181893964655[/C][/ROW]
[ROW][C]56[/C][C]6.4[/C][C]7.35377875958653[/C][C]-0.953778759586528[/C][/ROW]
[ROW][C]57[/C][C]6.1[/C][C]6.94169889963321[/C][C]-0.84169889963321[/C][/ROW]
[ROW][C]58[/C][C]6.5[/C][C]6.74697899299766[/C][C]-0.246978992997665[/C][/ROW]
[ROW][C]59[/C][C]7.7[/C][C]7.49374208069356[/C][C]0.206257919306437[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.65992664221407[/C][C]0.24007335778593[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.51217489163055[/C][C]-0.0121748916305475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57685&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.48.328451150383440.0715488496165638
28.48.225895298432810.174104701567189
38.48.068246082027340.331753917972658
48.68.236781427142380.363218572857618
58.98.443255251750580.456744748249417
68.88.46943981327110.33056018672891
78.38.31121207069023-0.0112120706902295
87.57.86119373124375-0.361193731243749
97.27.51529843281094-0.315298432810937
107.47.51913221073691-0.119132210736913
118.88.265895298432810.53410470156719
129.38.365895298432810.93410470156719
139.38.28432810936981.01567189063021
148.77.939095531843950.760904468156052
158.27.91381543847950.286184561520506
168.38.104412304101370.195587695898633
178.58.288824608202730.211175391797266
188.68.182640046682230.417359953317772
198.57.869981660553520.630018339446482
208.27.662640046682230.537359953317772
218.17.537359953317770.562640046682227
227.97.38676308769590.513236912304102
238.68.111464654884960.488535345115038
248.78.167341613871290.532658386128709
258.78.019589863287770.680410136712232
268.58.027341613871290.47265838612871
278.47.91381543847950.486184561520507
288.57.972043181060350.527956818939647
298.78.222640046682230.477359953317772
308.78.22676308769590.473236912304101
318.68.178842947649220.421157052350783
328.57.839132210736910.660867789263087
338.37.603544514838280.696455485161721
3487.607378292764260.392621707235745
358.28.4423874624875-0.242387462487497
368.18.49826442147383-0.398264421473825
378.18.46082027342448-0.360820273424481
3888.31414138046015-0.314141380460154
397.98.15649216405469-0.256492164054685
407.98.25884294764922-0.358842947649217
4188.42119373124375-0.421193731243748
4288.35913221073691-0.359132210736912
437.98.15678142714238-0.256781427142381
4487.883255251750580.116744748249416
457.77.8020981993998-0.102098199399801
467.27.73974741580527-0.539747415805269
477.58.48651050350117-0.986510503501167
487.38.608572024008-1.30857202400800
4978.39463571190397-1.39463571190397
5078.0935261753918-1.09352617539180
5177.84763087695899-0.847630876958986
527.27.92792014004668-0.727920140046683
537.38.0240863621207-0.724086362120706
547.17.96202484161387-0.862024841613871
556.87.58318189396465-0.783181893964655
566.47.35377875958653-0.953778759586528
576.16.94169889963321-0.84169889963321
586.56.74697899299766-0.246978992997665
597.77.493742080693560.206257919306437
607.97.659926642214070.24007335778593
617.57.51217489163055-0.0121748916305475







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.2050802732942860.4101605465885720.794919726705714
170.1222956698526840.2445913397053690.877704330147316
180.05813842105071020.1162768421014200.94186157894929
190.02883275849622670.05766551699245340.971167241503773
200.02741586012248980.05483172024497960.97258413987751
210.04135679328907650.0827135865781530.958643206710923
220.02734137262077310.05468274524154610.972658627379227
230.01606071104559240.03212142209118480.983939288954408
240.01604397150022480.03208794300044970.983956028499775
250.01205671704361390.02411343408722790.987943282956386
260.008268237419510240.01653647483902050.99173176258049
270.005484241902256360.01096848380451270.994515758097744
280.003809229982754230.007618459965508450.996190770017246
290.002717461618823290.005434923237646580.997282538381177
300.002132402622187190.004264805244374390.997867597377813
310.001713276115793020.003426552231586040.998286723884207
320.004074992896808260.008149985793616530.995925007103192
330.01095766522485060.02191533044970120.98904233477515
340.01152426744116940.02304853488233870.98847573255883
350.009738801393521740.01947760278704350.990261198606478
360.01443693371992230.02887386743984470.985563066280078
370.01474322916579280.02948645833158550.985256770834207
380.01474333430893350.0294866686178670.985256665691067
390.01192447255511410.02384894511022820.988075527444886
400.009004278546112230.01800855709222450.990995721453888
410.007717970186400550.01543594037280110.9922820298136
420.007900066458759480.01580013291751900.99209993354124
430.008468719792087380.01693743958417480.991531280207913
440.02967522021598320.05935044043196650.970324779784017
450.2954932918790330.5909865837580670.704506708120967

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.205080273294286 & 0.410160546588572 & 0.794919726705714 \tabularnewline
17 & 0.122295669852684 & 0.244591339705369 & 0.877704330147316 \tabularnewline
18 & 0.0581384210507102 & 0.116276842101420 & 0.94186157894929 \tabularnewline
19 & 0.0288327584962267 & 0.0576655169924534 & 0.971167241503773 \tabularnewline
20 & 0.0274158601224898 & 0.0548317202449796 & 0.97258413987751 \tabularnewline
21 & 0.0413567932890765 & 0.082713586578153 & 0.958643206710923 \tabularnewline
22 & 0.0273413726207731 & 0.0546827452415461 & 0.972658627379227 \tabularnewline
23 & 0.0160607110455924 & 0.0321214220911848 & 0.983939288954408 \tabularnewline
24 & 0.0160439715002248 & 0.0320879430004497 & 0.983956028499775 \tabularnewline
25 & 0.0120567170436139 & 0.0241134340872279 & 0.987943282956386 \tabularnewline
26 & 0.00826823741951024 & 0.0165364748390205 & 0.99173176258049 \tabularnewline
27 & 0.00548424190225636 & 0.0109684838045127 & 0.994515758097744 \tabularnewline
28 & 0.00380922998275423 & 0.00761845996550845 & 0.996190770017246 \tabularnewline
29 & 0.00271746161882329 & 0.00543492323764658 & 0.997282538381177 \tabularnewline
30 & 0.00213240262218719 & 0.00426480524437439 & 0.997867597377813 \tabularnewline
31 & 0.00171327611579302 & 0.00342655223158604 & 0.998286723884207 \tabularnewline
32 & 0.00407499289680826 & 0.00814998579361653 & 0.995925007103192 \tabularnewline
33 & 0.0109576652248506 & 0.0219153304497012 & 0.98904233477515 \tabularnewline
34 & 0.0115242674411694 & 0.0230485348823387 & 0.98847573255883 \tabularnewline
35 & 0.00973880139352174 & 0.0194776027870435 & 0.990261198606478 \tabularnewline
36 & 0.0144369337199223 & 0.0288738674398447 & 0.985563066280078 \tabularnewline
37 & 0.0147432291657928 & 0.0294864583315855 & 0.985256770834207 \tabularnewline
38 & 0.0147433343089335 & 0.029486668617867 & 0.985256665691067 \tabularnewline
39 & 0.0119244725551141 & 0.0238489451102282 & 0.988075527444886 \tabularnewline
40 & 0.00900427854611223 & 0.0180085570922245 & 0.990995721453888 \tabularnewline
41 & 0.00771797018640055 & 0.0154359403728011 & 0.9922820298136 \tabularnewline
42 & 0.00790006645875948 & 0.0158001329175190 & 0.99209993354124 \tabularnewline
43 & 0.00846871979208738 & 0.0169374395841748 & 0.991531280207913 \tabularnewline
44 & 0.0296752202159832 & 0.0593504404319665 & 0.970324779784017 \tabularnewline
45 & 0.295493291879033 & 0.590986583758067 & 0.704506708120967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]16[/C][C]0.205080273294286[/C][C]0.410160546588572[/C][C]0.794919726705714[/C][/ROW]
[ROW][C]17[/C][C]0.122295669852684[/C][C]0.244591339705369[/C][C]0.877704330147316[/C][/ROW]
[ROW][C]18[/C][C]0.0581384210507102[/C][C]0.116276842101420[/C][C]0.94186157894929[/C][/ROW]
[ROW][C]19[/C][C]0.0288327584962267[/C][C]0.0576655169924534[/C][C]0.971167241503773[/C][/ROW]
[ROW][C]20[/C][C]0.0274158601224898[/C][C]0.0548317202449796[/C][C]0.97258413987751[/C][/ROW]
[ROW][C]21[/C][C]0.0413567932890765[/C][C]0.082713586578153[/C][C]0.958643206710923[/C][/ROW]
[ROW][C]22[/C][C]0.0273413726207731[/C][C]0.0546827452415461[/C][C]0.972658627379227[/C][/ROW]
[ROW][C]23[/C][C]0.0160607110455924[/C][C]0.0321214220911848[/C][C]0.983939288954408[/C][/ROW]
[ROW][C]24[/C][C]0.0160439715002248[/C][C]0.0320879430004497[/C][C]0.983956028499775[/C][/ROW]
[ROW][C]25[/C][C]0.0120567170436139[/C][C]0.0241134340872279[/C][C]0.987943282956386[/C][/ROW]
[ROW][C]26[/C][C]0.00826823741951024[/C][C]0.0165364748390205[/C][C]0.99173176258049[/C][/ROW]
[ROW][C]27[/C][C]0.00548424190225636[/C][C]0.0109684838045127[/C][C]0.994515758097744[/C][/ROW]
[ROW][C]28[/C][C]0.00380922998275423[/C][C]0.00761845996550845[/C][C]0.996190770017246[/C][/ROW]
[ROW][C]29[/C][C]0.00271746161882329[/C][C]0.00543492323764658[/C][C]0.997282538381177[/C][/ROW]
[ROW][C]30[/C][C]0.00213240262218719[/C][C]0.00426480524437439[/C][C]0.997867597377813[/C][/ROW]
[ROW][C]31[/C][C]0.00171327611579302[/C][C]0.00342655223158604[/C][C]0.998286723884207[/C][/ROW]
[ROW][C]32[/C][C]0.00407499289680826[/C][C]0.00814998579361653[/C][C]0.995925007103192[/C][/ROW]
[ROW][C]33[/C][C]0.0109576652248506[/C][C]0.0219153304497012[/C][C]0.98904233477515[/C][/ROW]
[ROW][C]34[/C][C]0.0115242674411694[/C][C]0.0230485348823387[/C][C]0.98847573255883[/C][/ROW]
[ROW][C]35[/C][C]0.00973880139352174[/C][C]0.0194776027870435[/C][C]0.990261198606478[/C][/ROW]
[ROW][C]36[/C][C]0.0144369337199223[/C][C]0.0288738674398447[/C][C]0.985563066280078[/C][/ROW]
[ROW][C]37[/C][C]0.0147432291657928[/C][C]0.0294864583315855[/C][C]0.985256770834207[/C][/ROW]
[ROW][C]38[/C][C]0.0147433343089335[/C][C]0.029486668617867[/C][C]0.985256665691067[/C][/ROW]
[ROW][C]39[/C][C]0.0119244725551141[/C][C]0.0238489451102282[/C][C]0.988075527444886[/C][/ROW]
[ROW][C]40[/C][C]0.00900427854611223[/C][C]0.0180085570922245[/C][C]0.990995721453888[/C][/ROW]
[ROW][C]41[/C][C]0.00771797018640055[/C][C]0.0154359403728011[/C][C]0.9922820298136[/C][/ROW]
[ROW][C]42[/C][C]0.00790006645875948[/C][C]0.0158001329175190[/C][C]0.99209993354124[/C][/ROW]
[ROW][C]43[/C][C]0.00846871979208738[/C][C]0.0169374395841748[/C][C]0.991531280207913[/C][/ROW]
[ROW][C]44[/C][C]0.0296752202159832[/C][C]0.0593504404319665[/C][C]0.970324779784017[/C][/ROW]
[ROW][C]45[/C][C]0.295493291879033[/C][C]0.590986583758067[/C][C]0.704506708120967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57685&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.2050802732942860.4101605465885720.794919726705714
170.1222956698526840.2445913397053690.877704330147316
180.05813842105071020.1162768421014200.94186157894929
190.02883275849622670.05766551699245340.971167241503773
200.02741586012248980.05483172024497960.97258413987751
210.04135679328907650.0827135865781530.958643206710923
220.02734137262077310.05468274524154610.972658627379227
230.01606071104559240.03212142209118480.983939288954408
240.01604397150022480.03208794300044970.983956028499775
250.01205671704361390.02411343408722790.987943282956386
260.008268237419510240.01653647483902050.99173176258049
270.005484241902256360.01096848380451270.994515758097744
280.003809229982754230.007618459965508450.996190770017246
290.002717461618823290.005434923237646580.997282538381177
300.002132402622187190.004264805244374390.997867597377813
310.001713276115793020.003426552231586040.998286723884207
320.004074992896808260.008149985793616530.995925007103192
330.01095766522485060.02191533044970120.98904233477515
340.01152426744116940.02304853488233870.98847573255883
350.009738801393521740.01947760278704350.990261198606478
360.01443693371992230.02887386743984470.985563066280078
370.01474322916579280.02948645833158550.985256770834207
380.01474333430893350.0294866686178670.985256665691067
390.01192447255511410.02384894511022820.988075527444886
400.009004278546112230.01800855709222450.990995721453888
410.007717970186400550.01543594037280110.9922820298136
420.007900066458759480.01580013291751900.99209993354124
430.008468719792087380.01693743958417480.991531280207913
440.02967522021598320.05935044043196650.970324779784017
450.2954932918790330.5909865837580670.704506708120967







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.166666666666667NOK
5% type I error level210.7NOK
10% type I error level260.866666666666667NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 5 & 0.166666666666667 & NOK \tabularnewline
5% type I error level & 21 & 0.7 & NOK \tabularnewline
10% type I error level & 26 & 0.866666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57685&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]5[/C][C]0.166666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]21[/C][C]0.7[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]26[/C][C]0.866666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57685&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57685&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.166666666666667NOK
5% type I error level210.7NOK
10% type I error level260.866666666666667NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}