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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 27 Nov 2009 02:27:31 -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/27/t1259314098m7v5rtkitngm3hx.htm/, Retrieved Tue, 10 Feb 2026 14:13:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60495, Retrieved Tue, 10 Feb 2026 14:13:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact511

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
F    D    [Multiple Regression] [ws7777] [2009-11-20 12:13:23] [b8b64ced21f32e31669b267b64eede7f]
-    D      [Multiple Regression] [w7] [2009-11-22 13:32:33] [0a7d38ad9c7f1a2c46637c75a8a0e083]
-    D          [Multiple Regression] [verbetering] [2009-11-27 09:27:31] [9be6fbb216efe5bb8ca600257c6e1971] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,6	0	7,5	7,7	8,1	8
7,8	0	7,6	7,5	7,7	8,1
7,8	0	7,8	7,6	7,5	7,7
7,8	0	7,8	7,8	7,6	7,5
7,5	0	7,8	7,8	7,8	7,6
7,5	0	7,5	7,8	7,8	7,8
7,1	0	7,5	7,5	7,8	7,8
7,5	0	7,1	7,5	7,5	7,8
7,5	0	7,5	7,1	7,5	7,5
7,6	0	7,5	7,5	7,1	7,5
7,7	0	7,6	7,5	7,5	7,1
7,7	0	7,7	7,6	7,5	7,5
7,9	0	7,7	7,7	7,6	7,5
8,1	0	7,9	7,7	7,7	7,6
8,2	0	8,1	7,9	7,7	7,7
8,2	0	8,2	8,1	7,9	7,7
8,2	0	8,2	8,2	8,1	7,9
7,9	0	8,2	8,2	8,2	8,1
7,3	0	7,9	8,2	8,2	8,2
6,9	0	7,3	7,9	8,2	8,2
6,6	0	6,9	7,3	7,9	8,2
6,7	0	6,6	6,9	7,3	7,9
6,9	0	6,7	6,6	6,9	7,3
7	0	6,9	6,7	6,6	6,9
7,1	0	7	6,9	6,7	6,6
7,2	0	7,1	7	6,9	6,7
7,1	0	7,2	7,1	7	6,9
6,9	0	7,1	7,2	7,1	7
7	0	6,9	7,1	7,2	7,1
6,8	0	7	6,9	7,1	7,2
6,4	0	6,8	7	6,9	7,1
6,7	0	6,4	6,8	7	6,9
6,6	0	6,7	6,4	6,8	7
6,4	0	6,6	6,7	6,4	6,8
6,3	0	6,4	6,6	6,7	6,4
6,2	0	6,3	6,4	6,6	6,7
6,5	0	6,2	6,3	6,4	6,6
6,8	1	6,5	6,2	6,3	6,4
6,8	1	6,8	6,5	6,2	6,3
6,4	1	6,8	6,8	6,5	6,2
6,1	1	6,4	6,8	6,8	6,5
5,8	1	6,1	6,4	6,8	6,8
6,1	1	5,8	6,1	6,4	6,8
7,2	1	6,1	5,8	6,1	6,4
7,3	1	7,2	6,1	5,8	6,1
6,9	1	7,3	7,2	6,1	5,8
6,1	1	6,9	7,3	7,2	6,1
5,8	1	6,1	6,9	7,3	7,2
6,2	1	5,8	6,1	6,9	7,3
7,1	1	6,2	5,8	6,1	6,9
7,7	1	7,1	6,2	5,8	6,1
7,9	1	7,7	7,1	6,2	5,8
7,7	1	7,9	7,7	7,1	6,2
7,4	1	7,7	7,9	7,7	7,1
7,5	1	7,4	7,7	7,9	7,7
8	1	7,5	7,4	7,7	7,9
8,1	1	8	7,5	7,4	7,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&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]3 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=60495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.206618878764414 + 0.0835818229950486X[t] + 1.52890254510051`Y-1`[t] -0.711924325810514`Y-2`[t] -0.264801000441926`Y-3`[t] + 0.461488266484942`Y-4`[t] + 0.266355376773095M1[t] + 0.155434228591892M2[t] -0.0233346187909136M3[t] + 0.0582735063385753M4[t] + 0.113138663587701M5[t] -0.0762817036946616M6[t] -0.117538108379314M7[t] + 0.410083083239657M8[t] -0.348315498829714M9[t] -0.068081760433958M10[t] + 0.0996209060985931M11[t] + 0.00138288697974347t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.206618878764414 +  0.0835818229950486X[t] +  1.52890254510051`Y-1`[t] -0.711924325810514`Y-2`[t] -0.264801000441926`Y-3`[t] +  0.461488266484942`Y-4`[t] +  0.266355376773095M1[t] +  0.155434228591892M2[t] -0.0233346187909136M3[t] +  0.0582735063385753M4[t] +  0.113138663587701M5[t] -0.0762817036946616M6[t] -0.117538108379314M7[t] +  0.410083083239657M8[t] -0.348315498829714M9[t] -0.068081760433958M10[t] +  0.0996209060985931M11[t] +  0.00138288697974347t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.206618878764414 +  0.0835818229950486X[t] +  1.52890254510051`Y-1`[t] -0.711924325810514`Y-2`[t] -0.264801000441926`Y-3`[t] +  0.461488266484942`Y-4`[t] +  0.266355376773095M1[t] +  0.155434228591892M2[t] -0.0233346187909136M3[t] +  0.0582735063385753M4[t] +  0.113138663587701M5[t] -0.0762817036946616M6[t] -0.117538108379314M7[t] +  0.410083083239657M8[t] -0.348315498829714M9[t] -0.068081760433958M10[t] +  0.0996209060985931M11[t] +  0.00138288697974347t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.206618878764414 + 0.0835818229950486X[t] + 1.52890254510051`Y-1`[t] -0.711924325810514`Y-2`[t] -0.264801000441926`Y-3`[t] + 0.461488266484942`Y-4`[t] + 0.266355376773095M1[t] + 0.155434228591892M2[t] -0.0233346187909136M3[t] + 0.0582735063385753M4[t] + 0.113138663587701M5[t] -0.0762817036946616M6[t] -0.117538108379314M7[t] + 0.410083083239657M8[t] -0.348315498829714M9[t] -0.068081760433958M10[t] + 0.0996209060985931M11[t] + 0.00138288697974347t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.2066188787644140.544443-0.37950.7063710.353186
X0.08358182299504860.1056950.79080.4338550.216927
`Y-1`1.528902545100510.14563810.49800
`Y-2`-0.7119243258105140.278027-2.56060.0144330.007217
`Y-3`-0.2648010004419260.277183-0.95530.3452960.172648
`Y-4`0.4614882664849420.1531933.01250.0045340.002267
M10.2663553767730950.1386431.92120.0620420.031021
M20.1554342285918920.1460751.06410.2938410.14692
M3-0.02333461879091360.148041-0.15760.8755680.437784
M40.05827350633857530.1461480.39870.6922670.346133
M50.1131386635877010.1452240.77910.4406430.220322
M6-0.07628170369466160.141797-0.5380.5936580.296829
M7-0.1175381083793140.140423-0.8370.4076770.203839
M80.4100830832396570.1392882.94410.0054330.002717
M9-0.3483154988297140.159101-2.18930.0346260.017313
M10-0.0680817604339580.16833-0.40450.6880880.344044
M110.09962090609859310.1574380.63280.5305810.26529
t0.001382886979743470.0033850.40850.6851570.342579

\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) & -0.206618878764414 & 0.544443 & -0.3795 & 0.706371 & 0.353186 \tabularnewline
X & 0.0835818229950486 & 0.105695 & 0.7908 & 0.433855 & 0.216927 \tabularnewline
`Y-1` & 1.52890254510051 & 0.145638 & 10.498 & 0 & 0 \tabularnewline
`Y-2` & -0.711924325810514 & 0.278027 & -2.5606 & 0.014433 & 0.007217 \tabularnewline
`Y-3` & -0.264801000441926 & 0.277183 & -0.9553 & 0.345296 & 0.172648 \tabularnewline
`Y-4` & 0.461488266484942 & 0.153193 & 3.0125 & 0.004534 & 0.002267 \tabularnewline
M1 & 0.266355376773095 & 0.138643 & 1.9212 & 0.062042 & 0.031021 \tabularnewline
M2 & 0.155434228591892 & 0.146075 & 1.0641 & 0.293841 & 0.14692 \tabularnewline
M3 & -0.0233346187909136 & 0.148041 & -0.1576 & 0.875568 & 0.437784 \tabularnewline
M4 & 0.0582735063385753 & 0.146148 & 0.3987 & 0.692267 & 0.346133 \tabularnewline
M5 & 0.113138663587701 & 0.145224 & 0.7791 & 0.440643 & 0.220322 \tabularnewline
M6 & -0.0762817036946616 & 0.141797 & -0.538 & 0.593658 & 0.296829 \tabularnewline
M7 & -0.117538108379314 & 0.140423 & -0.837 & 0.407677 & 0.203839 \tabularnewline
M8 & 0.410083083239657 & 0.139288 & 2.9441 & 0.005433 & 0.002717 \tabularnewline
M9 & -0.348315498829714 & 0.159101 & -2.1893 & 0.034626 & 0.017313 \tabularnewline
M10 & -0.068081760433958 & 0.16833 & -0.4045 & 0.688088 & 0.344044 \tabularnewline
M11 & 0.0996209060985931 & 0.157438 & 0.6328 & 0.530581 & 0.26529 \tabularnewline
t & 0.00138288697974347 & 0.003385 & 0.4085 & 0.685157 & 0.342579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&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]-0.206618878764414[/C][C]0.544443[/C][C]-0.3795[/C][C]0.706371[/C][C]0.353186[/C][/ROW]
[ROW][C]X[/C][C]0.0835818229950486[/C][C]0.105695[/C][C]0.7908[/C][C]0.433855[/C][C]0.216927[/C][/ROW]
[ROW][C]`Y-1`[/C][C]1.52890254510051[/C][C]0.145638[/C][C]10.498[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y-2`[/C][C]-0.711924325810514[/C][C]0.278027[/C][C]-2.5606[/C][C]0.014433[/C][C]0.007217[/C][/ROW]
[ROW][C]`Y-3`[/C][C]-0.264801000441926[/C][C]0.277183[/C][C]-0.9553[/C][C]0.345296[/C][C]0.172648[/C][/ROW]
[ROW][C]`Y-4`[/C][C]0.461488266484942[/C][C]0.153193[/C][C]3.0125[/C][C]0.004534[/C][C]0.002267[/C][/ROW]
[ROW][C]M1[/C][C]0.266355376773095[/C][C]0.138643[/C][C]1.9212[/C][C]0.062042[/C][C]0.031021[/C][/ROW]
[ROW][C]M2[/C][C]0.155434228591892[/C][C]0.146075[/C][C]1.0641[/C][C]0.293841[/C][C]0.14692[/C][/ROW]
[ROW][C]M3[/C][C]-0.0233346187909136[/C][C]0.148041[/C][C]-0.1576[/C][C]0.875568[/C][C]0.437784[/C][/ROW]
[ROW][C]M4[/C][C]0.0582735063385753[/C][C]0.146148[/C][C]0.3987[/C][C]0.692267[/C][C]0.346133[/C][/ROW]
[ROW][C]M5[/C][C]0.113138663587701[/C][C]0.145224[/C][C]0.7791[/C][C]0.440643[/C][C]0.220322[/C][/ROW]
[ROW][C]M6[/C][C]-0.0762817036946616[/C][C]0.141797[/C][C]-0.538[/C][C]0.593658[/C][C]0.296829[/C][/ROW]
[ROW][C]M7[/C][C]-0.117538108379314[/C][C]0.140423[/C][C]-0.837[/C][C]0.407677[/C][C]0.203839[/C][/ROW]
[ROW][C]M8[/C][C]0.410083083239657[/C][C]0.139288[/C][C]2.9441[/C][C]0.005433[/C][C]0.002717[/C][/ROW]
[ROW][C]M9[/C][C]-0.348315498829714[/C][C]0.159101[/C][C]-2.1893[/C][C]0.034626[/C][C]0.017313[/C][/ROW]
[ROW][C]M10[/C][C]-0.068081760433958[/C][C]0.16833[/C][C]-0.4045[/C][C]0.688088[/C][C]0.344044[/C][/ROW]
[ROW][C]M11[/C][C]0.0996209060985931[/C][C]0.157438[/C][C]0.6328[/C][C]0.530581[/C][C]0.26529[/C][/ROW]
[ROW][C]t[/C][C]0.00138288697974347[/C][C]0.003385[/C][C]0.4085[/C][C]0.685157[/C][C]0.342579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60495&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=2

As an alternative you can also use a QR Code:  
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)-0.2066188787644140.544443-0.37950.7063710.353186
X0.08358182299504860.1056950.79080.4338550.216927
`Y-1`1.528902545100510.14563810.49800
`Y-2`-0.7119243258105140.278027-2.56060.0144330.007217
`Y-3`-0.2648010004419260.277183-0.95530.3452960.172648
`Y-4`0.4614882664849420.1531933.01250.0045340.002267
M10.2663553767730950.1386431.92120.0620420.031021
M20.1554342285918920.1460751.06410.2938410.14692
M3-0.02333461879091360.148041-0.15760.8755680.437784
M40.05827350633857530.1461480.39870.6922670.346133
M50.1131386635877010.1452240.77910.4406430.220322
M6-0.07628170369466160.141797-0.5380.5936580.296829
M7-0.1175381083793140.140423-0.8370.4076770.203839
M80.4100830832396570.1392882.94410.0054330.002717
M9-0.3483154988297140.159101-2.18930.0346260.017313
M10-0.0680817604339580.16833-0.40450.6880880.344044
M110.09962090609859310.1574380.63280.5305810.26529
t0.001382886979743470.0033850.40850.6851570.342579






Multiple Linear Regression - Regression Statistics
Multiple R0.966437910189696
R-squared0.934002234251826
Adjusted R-squared0.905233977387238
F-TEST (value)32.4664173657845
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.203197265081223
Sum Squared Residuals1.61027601292307

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.966437910189696 \tabularnewline
R-squared & 0.934002234251826 \tabularnewline
Adjusted R-squared & 0.905233977387238 \tabularnewline
F-TEST (value) & 32.4664173657845 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.203197265081223 \tabularnewline
Sum Squared Residuals & 1.61027601292307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.966437910189696[/C][/ROW]
[ROW][C]R-squared[/C][C]0.934002234251826[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.905233977387238[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]32.4664173657845[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.203197265081223[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.61027601292307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60495&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.966437910189696
R-squared0.934002234251826
Adjusted R-squared0.905233977387238
F-TEST (value)32.4664173657845
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.203197265081223
Sum Squared Residuals1.61027601292307






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.67.59308919280120.00691080719879664
27.87.93089527809715-0.130895278097154
37.87.85646228762755-0.0564622876275469
47.87.67829068123350.121709318766505
57.57.72772735202247-0.227727352022473
67.57.17331676148670.326683238513308
77.17.34702054152494-0.247020541524937
87.57.343903902216030.156096097783973
97.57.344772475545330.155227524454675
107.67.447539770773390.152460229226610
117.77.478999872024990.221000127975014
127.77.647054981429110.0529450185708865
137.97.81712071255670.082879287443293
148.18.033031686979650.0669683130203491
158.28.065190197083080.134809802916919
168.28.105726398451870.0942736015481242
178.28.13011946330830.0698805366917033
187.98.00789953625847-0.107899536258473
197.37.5555040816719-0.255504081671909
206.97.38074393095347-0.480743930953472
216.66.518762113442530.0812378865574694
226.76.646911825931760.0530881740682446
236.97.01149237198306-0.111492371983060
2477.04268742284186-0.0426874228418621
257.17.15600449595297-0.0560044959529722
267.27.121352683240620.0786473167593798
277.17.091482098019350.00851790198064515
286.96.97005914964179-0.0700591496417848
2976.811387844035910.188612155964093
306.86.99125441009813-0.191254410098128
316.46.58121932423196-0.181219324231957
326.76.522269496611390.177730503388607
336.66.607803322113-0.00780332211300146
346.46.53657514211508-0.136575142115077
356.36.207037012461770.0929629875382312
366.26.26322018398464-0.0632201839846451
376.56.456071999248380.043928000751624
386.86.89416120390037-0.0941612039003712
396.86.94219998268-0.142199982680004
406.46.68602457026501-0.286024570265010
416.16.18971777626658-0.0897177762665835
425.85.9662257427035-0.166225742703500
436.15.787179159388360.312820840611635
447.26.883276292798990.316723707201015
457.37.53546991976386-0.235469919763855
466.96.96897326117978-0.0689732611797782
476.16.30247074353018-0.202470743530185
485.85.747037411744380.0529625882556206
496.26.27771359944074-0.0777135994407418
507.17.02055914778220.0794408522177961
517.77.644665434590010.055334565409987
527.97.759899200407830.140100799592166
537.77.641047564366740.0589524356332608
547.47.261303549453210.138696450546792
557.57.129076893182830.370923106817168
5688.16980637742012-0.169806377420123
578.18.093192169135290.00680783086471272

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.6 & 7.5930891928012 & 0.00691080719879664 \tabularnewline
2 & 7.8 & 7.93089527809715 & -0.130895278097154 \tabularnewline
3 & 7.8 & 7.85646228762755 & -0.0564622876275469 \tabularnewline
4 & 7.8 & 7.6782906812335 & 0.121709318766505 \tabularnewline
5 & 7.5 & 7.72772735202247 & -0.227727352022473 \tabularnewline
6 & 7.5 & 7.1733167614867 & 0.326683238513308 \tabularnewline
7 & 7.1 & 7.34702054152494 & -0.247020541524937 \tabularnewline
8 & 7.5 & 7.34390390221603 & 0.156096097783973 \tabularnewline
9 & 7.5 & 7.34477247554533 & 0.155227524454675 \tabularnewline
10 & 7.6 & 7.44753977077339 & 0.152460229226610 \tabularnewline
11 & 7.7 & 7.47899987202499 & 0.221000127975014 \tabularnewline
12 & 7.7 & 7.64705498142911 & 0.0529450185708865 \tabularnewline
13 & 7.9 & 7.8171207125567 & 0.082879287443293 \tabularnewline
14 & 8.1 & 8.03303168697965 & 0.0669683130203491 \tabularnewline
15 & 8.2 & 8.06519019708308 & 0.134809802916919 \tabularnewline
16 & 8.2 & 8.10572639845187 & 0.0942736015481242 \tabularnewline
17 & 8.2 & 8.1301194633083 & 0.0698805366917033 \tabularnewline
18 & 7.9 & 8.00789953625847 & -0.107899536258473 \tabularnewline
19 & 7.3 & 7.5555040816719 & -0.255504081671909 \tabularnewline
20 & 6.9 & 7.38074393095347 & -0.480743930953472 \tabularnewline
21 & 6.6 & 6.51876211344253 & 0.0812378865574694 \tabularnewline
22 & 6.7 & 6.64691182593176 & 0.0530881740682446 \tabularnewline
23 & 6.9 & 7.01149237198306 & -0.111492371983060 \tabularnewline
24 & 7 & 7.04268742284186 & -0.0426874228418621 \tabularnewline
25 & 7.1 & 7.15600449595297 & -0.0560044959529722 \tabularnewline
26 & 7.2 & 7.12135268324062 & 0.0786473167593798 \tabularnewline
27 & 7.1 & 7.09148209801935 & 0.00851790198064515 \tabularnewline
28 & 6.9 & 6.97005914964179 & -0.0700591496417848 \tabularnewline
29 & 7 & 6.81138784403591 & 0.188612155964093 \tabularnewline
30 & 6.8 & 6.99125441009813 & -0.191254410098128 \tabularnewline
31 & 6.4 & 6.58121932423196 & -0.181219324231957 \tabularnewline
32 & 6.7 & 6.52226949661139 & 0.177730503388607 \tabularnewline
33 & 6.6 & 6.607803322113 & -0.00780332211300146 \tabularnewline
34 & 6.4 & 6.53657514211508 & -0.136575142115077 \tabularnewline
35 & 6.3 & 6.20703701246177 & 0.0929629875382312 \tabularnewline
36 & 6.2 & 6.26322018398464 & -0.0632201839846451 \tabularnewline
37 & 6.5 & 6.45607199924838 & 0.043928000751624 \tabularnewline
38 & 6.8 & 6.89416120390037 & -0.0941612039003712 \tabularnewline
39 & 6.8 & 6.94219998268 & -0.142199982680004 \tabularnewline
40 & 6.4 & 6.68602457026501 & -0.286024570265010 \tabularnewline
41 & 6.1 & 6.18971777626658 & -0.0897177762665835 \tabularnewline
42 & 5.8 & 5.9662257427035 & -0.166225742703500 \tabularnewline
43 & 6.1 & 5.78717915938836 & 0.312820840611635 \tabularnewline
44 & 7.2 & 6.88327629279899 & 0.316723707201015 \tabularnewline
45 & 7.3 & 7.53546991976386 & -0.235469919763855 \tabularnewline
46 & 6.9 & 6.96897326117978 & -0.0689732611797782 \tabularnewline
47 & 6.1 & 6.30247074353018 & -0.202470743530185 \tabularnewline
48 & 5.8 & 5.74703741174438 & 0.0529625882556206 \tabularnewline
49 & 6.2 & 6.27771359944074 & -0.0777135994407418 \tabularnewline
50 & 7.1 & 7.0205591477822 & 0.0794408522177961 \tabularnewline
51 & 7.7 & 7.64466543459001 & 0.055334565409987 \tabularnewline
52 & 7.9 & 7.75989920040783 & 0.140100799592166 \tabularnewline
53 & 7.7 & 7.64104756436674 & 0.0589524356332608 \tabularnewline
54 & 7.4 & 7.26130354945321 & 0.138696450546792 \tabularnewline
55 & 7.5 & 7.12907689318283 & 0.370923106817168 \tabularnewline
56 & 8 & 8.16980637742012 & -0.169806377420123 \tabularnewline
57 & 8.1 & 8.09319216913529 & 0.00680783086471272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&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]7.6[/C][C]7.5930891928012[/C][C]0.00691080719879664[/C][/ROW]
[ROW][C]2[/C][C]7.8[/C][C]7.93089527809715[/C][C]-0.130895278097154[/C][/ROW]
[ROW][C]3[/C][C]7.8[/C][C]7.85646228762755[/C][C]-0.0564622876275469[/C][/ROW]
[ROW][C]4[/C][C]7.8[/C][C]7.6782906812335[/C][C]0.121709318766505[/C][/ROW]
[ROW][C]5[/C][C]7.5[/C][C]7.72772735202247[/C][C]-0.227727352022473[/C][/ROW]
[ROW][C]6[/C][C]7.5[/C][C]7.1733167614867[/C][C]0.326683238513308[/C][/ROW]
[ROW][C]7[/C][C]7.1[/C][C]7.34702054152494[/C][C]-0.247020541524937[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]7.34390390221603[/C][C]0.156096097783973[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.34477247554533[/C][C]0.155227524454675[/C][/ROW]
[ROW][C]10[/C][C]7.6[/C][C]7.44753977077339[/C][C]0.152460229226610[/C][/ROW]
[ROW][C]11[/C][C]7.7[/C][C]7.47899987202499[/C][C]0.221000127975014[/C][/ROW]
[ROW][C]12[/C][C]7.7[/C][C]7.64705498142911[/C][C]0.0529450185708865[/C][/ROW]
[ROW][C]13[/C][C]7.9[/C][C]7.8171207125567[/C][C]0.082879287443293[/C][/ROW]
[ROW][C]14[/C][C]8.1[/C][C]8.03303168697965[/C][C]0.0669683130203491[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.06519019708308[/C][C]0.134809802916919[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]8.10572639845187[/C][C]0.0942736015481242[/C][/ROW]
[ROW][C]17[/C][C]8.2[/C][C]8.1301194633083[/C][C]0.0698805366917033[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]8.00789953625847[/C][C]-0.107899536258473[/C][/ROW]
[ROW][C]19[/C][C]7.3[/C][C]7.5555040816719[/C][C]-0.255504081671909[/C][/ROW]
[ROW][C]20[/C][C]6.9[/C][C]7.38074393095347[/C][C]-0.480743930953472[/C][/ROW]
[ROW][C]21[/C][C]6.6[/C][C]6.51876211344253[/C][C]0.0812378865574694[/C][/ROW]
[ROW][C]22[/C][C]6.7[/C][C]6.64691182593176[/C][C]0.0530881740682446[/C][/ROW]
[ROW][C]23[/C][C]6.9[/C][C]7.01149237198306[/C][C]-0.111492371983060[/C][/ROW]
[ROW][C]24[/C][C]7[/C][C]7.04268742284186[/C][C]-0.0426874228418621[/C][/ROW]
[ROW][C]25[/C][C]7.1[/C][C]7.15600449595297[/C][C]-0.0560044959529722[/C][/ROW]
[ROW][C]26[/C][C]7.2[/C][C]7.12135268324062[/C][C]0.0786473167593798[/C][/ROW]
[ROW][C]27[/C][C]7.1[/C][C]7.09148209801935[/C][C]0.00851790198064515[/C][/ROW]
[ROW][C]28[/C][C]6.9[/C][C]6.97005914964179[/C][C]-0.0700591496417848[/C][/ROW]
[ROW][C]29[/C][C]7[/C][C]6.81138784403591[/C][C]0.188612155964093[/C][/ROW]
[ROW][C]30[/C][C]6.8[/C][C]6.99125441009813[/C][C]-0.191254410098128[/C][/ROW]
[ROW][C]31[/C][C]6.4[/C][C]6.58121932423196[/C][C]-0.181219324231957[/C][/ROW]
[ROW][C]32[/C][C]6.7[/C][C]6.52226949661139[/C][C]0.177730503388607[/C][/ROW]
[ROW][C]33[/C][C]6.6[/C][C]6.607803322113[/C][C]-0.00780332211300146[/C][/ROW]
[ROW][C]34[/C][C]6.4[/C][C]6.53657514211508[/C][C]-0.136575142115077[/C][/ROW]
[ROW][C]35[/C][C]6.3[/C][C]6.20703701246177[/C][C]0.0929629875382312[/C][/ROW]
[ROW][C]36[/C][C]6.2[/C][C]6.26322018398464[/C][C]-0.0632201839846451[/C][/ROW]
[ROW][C]37[/C][C]6.5[/C][C]6.45607199924838[/C][C]0.043928000751624[/C][/ROW]
[ROW][C]38[/C][C]6.8[/C][C]6.89416120390037[/C][C]-0.0941612039003712[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.94219998268[/C][C]-0.142199982680004[/C][/ROW]
[ROW][C]40[/C][C]6.4[/C][C]6.68602457026501[/C][C]-0.286024570265010[/C][/ROW]
[ROW][C]41[/C][C]6.1[/C][C]6.18971777626658[/C][C]-0.0897177762665835[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]5.9662257427035[/C][C]-0.166225742703500[/C][/ROW]
[ROW][C]43[/C][C]6.1[/C][C]5.78717915938836[/C][C]0.312820840611635[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]6.88327629279899[/C][C]0.316723707201015[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.53546991976386[/C][C]-0.235469919763855[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]6.96897326117978[/C][C]-0.0689732611797782[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]6.30247074353018[/C][C]-0.202470743530185[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.74703741174438[/C][C]0.0529625882556206[/C][/ROW]
[ROW][C]49[/C][C]6.2[/C][C]6.27771359944074[/C][C]-0.0777135994407418[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.0205591477822[/C][C]0.0794408522177961[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.64466543459001[/C][C]0.055334565409987[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.75989920040783[/C][C]0.140100799592166[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.64104756436674[/C][C]0.0589524356332608[/C][/ROW]
[ROW][C]54[/C][C]7.4[/C][C]7.26130354945321[/C][C]0.138696450546792[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.12907689318283[/C][C]0.370923106817168[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]8.16980637742012[/C][C]-0.169806377420123[/C][/ROW]
[ROW][C]57[/C][C]8.1[/C][C]8.09319216913529[/C][C]0.00680783086471272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60495&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.67.59308919280120.00691080719879664
27.87.93089527809715-0.130895278097154
37.87.85646228762755-0.0564622876275469
47.87.67829068123350.121709318766505
57.57.72772735202247-0.227727352022473
67.57.17331676148670.326683238513308
77.17.34702054152494-0.247020541524937
87.57.343903902216030.156096097783973
97.57.344772475545330.155227524454675
107.67.447539770773390.152460229226610
117.77.478999872024990.221000127975014
127.77.647054981429110.0529450185708865
137.97.81712071255670.082879287443293
148.18.033031686979650.0669683130203491
158.28.065190197083080.134809802916919
168.28.105726398451870.0942736015481242
178.28.13011946330830.0698805366917033
187.98.00789953625847-0.107899536258473
197.37.5555040816719-0.255504081671909
206.97.38074393095347-0.480743930953472
216.66.518762113442530.0812378865574694
226.76.646911825931760.0530881740682446
236.97.01149237198306-0.111492371983060
2477.04268742284186-0.0426874228418621
257.17.15600449595297-0.0560044959529722
267.27.121352683240620.0786473167593798
277.17.091482098019350.00851790198064515
286.96.97005914964179-0.0700591496417848
2976.811387844035910.188612155964093
306.86.99125441009813-0.191254410098128
316.46.58121932423196-0.181219324231957
326.76.522269496611390.177730503388607
336.66.607803322113-0.00780332211300146
346.46.53657514211508-0.136575142115077
356.36.207037012461770.0929629875382312
366.26.26322018398464-0.0632201839846451
376.56.456071999248380.043928000751624
386.86.89416120390037-0.0941612039003712
396.86.94219998268-0.142199982680004
406.46.68602457026501-0.286024570265010
416.16.18971777626658-0.0897177762665835
425.85.9662257427035-0.166225742703500
436.15.787179159388360.312820840611635
447.26.883276292798990.316723707201015
457.37.53546991976386-0.235469919763855
466.96.96897326117978-0.0689732611797782
476.16.30247074353018-0.202470743530185
485.85.747037411744380.0529625882556206
496.26.27771359944074-0.0777135994407418
507.17.02055914778220.0794408522177961
517.77.644665434590010.055334565409987
527.97.759899200407830.140100799592166
537.77.641047564366740.0589524356332608
547.47.261303549453210.138696450546792
557.57.129076893182830.370923106817168
5688.16980637742012-0.169806377420123
578.18.093192169135290.00680783086471272






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.866931609589830.2661367808203410.133068390410171
220.8110531174395730.3778937651208540.188946882560427
230.7814104942902390.4371790114195220.218589505709761
240.721630675460980.556738649078040.27836932453902
250.7002027753762970.5995944492474060.299797224623703
260.5998214217260360.8003571565479290.400178578273964
270.4891021439835050.978204287967010.510897856016495
280.3959256981105090.7918513962210170.604074301889491
290.637385447118020.725229105763960.36261455288198
300.6183185118977110.7633629762045770.381681488102289
310.6407856674182450.718428665163510.359214332581755
320.6397946594829820.7204106810340370.360205340517018
330.5184838242786090.9630323514427830.481516175721391
340.4468549211652110.8937098423304220.553145078834789
350.687998608634880.6240027827302390.312001391365119
360.8665832847515260.2668334304969470.133416715248474

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.86693160958983 & 0.266136780820341 & 0.133068390410171 \tabularnewline
22 & 0.811053117439573 & 0.377893765120854 & 0.188946882560427 \tabularnewline
23 & 0.781410494290239 & 0.437179011419522 & 0.218589505709761 \tabularnewline
24 & 0.72163067546098 & 0.55673864907804 & 0.27836932453902 \tabularnewline
25 & 0.700202775376297 & 0.599594449247406 & 0.299797224623703 \tabularnewline
26 & 0.599821421726036 & 0.800357156547929 & 0.400178578273964 \tabularnewline
27 & 0.489102143983505 & 0.97820428796701 & 0.510897856016495 \tabularnewline
28 & 0.395925698110509 & 0.791851396221017 & 0.604074301889491 \tabularnewline
29 & 0.63738544711802 & 0.72522910576396 & 0.36261455288198 \tabularnewline
30 & 0.618318511897711 & 0.763362976204577 & 0.381681488102289 \tabularnewline
31 & 0.640785667418245 & 0.71842866516351 & 0.359214332581755 \tabularnewline
32 & 0.639794659482982 & 0.720410681034037 & 0.360205340517018 \tabularnewline
33 & 0.518483824278609 & 0.963032351442783 & 0.481516175721391 \tabularnewline
34 & 0.446854921165211 & 0.893709842330422 & 0.553145078834789 \tabularnewline
35 & 0.68799860863488 & 0.624002782730239 & 0.312001391365119 \tabularnewline
36 & 0.866583284751526 & 0.266833430496947 & 0.133416715248474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&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]21[/C][C]0.86693160958983[/C][C]0.266136780820341[/C][C]0.133068390410171[/C][/ROW]
[ROW][C]22[/C][C]0.811053117439573[/C][C]0.377893765120854[/C][C]0.188946882560427[/C][/ROW]
[ROW][C]23[/C][C]0.781410494290239[/C][C]0.437179011419522[/C][C]0.218589505709761[/C][/ROW]
[ROW][C]24[/C][C]0.72163067546098[/C][C]0.55673864907804[/C][C]0.27836932453902[/C][/ROW]
[ROW][C]25[/C][C]0.700202775376297[/C][C]0.599594449247406[/C][C]0.299797224623703[/C][/ROW]
[ROW][C]26[/C][C]0.599821421726036[/C][C]0.800357156547929[/C][C]0.400178578273964[/C][/ROW]
[ROW][C]27[/C][C]0.489102143983505[/C][C]0.97820428796701[/C][C]0.510897856016495[/C][/ROW]
[ROW][C]28[/C][C]0.395925698110509[/C][C]0.791851396221017[/C][C]0.604074301889491[/C][/ROW]
[ROW][C]29[/C][C]0.63738544711802[/C][C]0.72522910576396[/C][C]0.36261455288198[/C][/ROW]
[ROW][C]30[/C][C]0.618318511897711[/C][C]0.763362976204577[/C][C]0.381681488102289[/C][/ROW]
[ROW][C]31[/C][C]0.640785667418245[/C][C]0.71842866516351[/C][C]0.359214332581755[/C][/ROW]
[ROW][C]32[/C][C]0.639794659482982[/C][C]0.720410681034037[/C][C]0.360205340517018[/C][/ROW]
[ROW][C]33[/C][C]0.518483824278609[/C][C]0.963032351442783[/C][C]0.481516175721391[/C][/ROW]
[ROW][C]34[/C][C]0.446854921165211[/C][C]0.893709842330422[/C][C]0.553145078834789[/C][/ROW]
[ROW][C]35[/C][C]0.68799860863488[/C][C]0.624002782730239[/C][C]0.312001391365119[/C][/ROW]
[ROW][C]36[/C][C]0.866583284751526[/C][C]0.266833430496947[/C][C]0.133416715248474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60495&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.866931609589830.2661367808203410.133068390410171
220.8110531174395730.3778937651208540.188946882560427
230.7814104942902390.4371790114195220.218589505709761
240.721630675460980.556738649078040.27836932453902
250.7002027753762970.5995944492474060.299797224623703
260.5998214217260360.8003571565479290.400178578273964
270.4891021439835050.978204287967010.510897856016495
280.3959256981105090.7918513962210170.604074301889491
290.637385447118020.725229105763960.36261455288198
300.6183185118977110.7633629762045770.381681488102289
310.6407856674182450.718428665163510.359214332581755
320.6397946594829820.7204106810340370.360205340517018
330.5184838242786090.9630323514427830.481516175721391
340.4468549211652110.8937098423304220.553145078834789
350.687998608634880.6240027827302390.312001391365119
360.8665832847515260.2668334304969470.133416715248474






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60495&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60495&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60495&T=6

As an alternative you can also use a QR Code:  
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 level00OK
5% type I error level00OK
10% type I error level00OK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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')
}