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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, 17 Dec 2010 12:34:10 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/17/t1292589221whfhpo8xpm6l38l.htm/, Retrieved Tue, 17 Jun 2025 20:15:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111431, Retrieved Tue, 17 Jun 2025 20:15:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact259

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD  [Multiple Regression] [] [2010-11-26 11:40:42] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D    [Multiple Regression] [] [2010-12-15 20:39:35] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D      [Multiple Regression] [] [2010-12-17 12:00:00] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D          [Multiple Regression] [] [2010-12-17 12:34:10] [1d094c42a82a95b45a19e32ad4bfff5f] [Current]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time19 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 & 19 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]19 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=111431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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 time19 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
HPC[t] = + 3.11176470588236 -0.176633986928106M1[t] + 0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
HPC[t] =  +  3.11176470588236 -0.176633986928106M1[t] +  0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]HPC[t] =  +  3.11176470588236 -0.176633986928106M1[t] +  0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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
HPC[t] = + 3.11176470588236 -0.176633986928106M1[t] + 0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.111764705882360.9155223.39890.001370.000685
M1-0.1766339869281061.067714-0.16540.8692990.434649
M20.02673202614378961.1206790.02390.9810680.490534
M3-0.06794117647058971.119248-0.06070.9518480.475924
M4-0.0826143790849691.117966-0.07390.9413990.4707
M5-0.1172875816993481.116834-0.1050.9167990.4584
M6-0.09196078431372691.115851-0.08240.9346610.46733
M7-0.2066339869281061.115019-0.18530.853760.42688
M8-0.08130718954248551.114338-0.0730.9421380.471069
M9-0.1159803921568641.113808-0.10410.91750.45875
M10-0.2506535947712431.113429-0.22510.8228430.411421
M11-0.1453267973856221.113202-0.13050.8966780.448339
t-0.02532679738562090.012989-1.94990.0570480.028524

\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) & 3.11176470588236 & 0.915522 & 3.3989 & 0.00137 & 0.000685 \tabularnewline
M1 & -0.176633986928106 & 1.067714 & -0.1654 & 0.869299 & 0.434649 \tabularnewline
M2 & 0.0267320261437896 & 1.120679 & 0.0239 & 0.981068 & 0.490534 \tabularnewline
M3 & -0.0679411764705897 & 1.119248 & -0.0607 & 0.951848 & 0.475924 \tabularnewline
M4 & -0.082614379084969 & 1.117966 & -0.0739 & 0.941399 & 0.4707 \tabularnewline
M5 & -0.117287581699348 & 1.116834 & -0.105 & 0.916799 & 0.4584 \tabularnewline
M6 & -0.0919607843137269 & 1.115851 & -0.0824 & 0.934661 & 0.46733 \tabularnewline
M7 & -0.206633986928106 & 1.115019 & -0.1853 & 0.85376 & 0.42688 \tabularnewline
M8 & -0.0813071895424855 & 1.114338 & -0.073 & 0.942138 & 0.471069 \tabularnewline
M9 & -0.115980392156864 & 1.113808 & -0.1041 & 0.9175 & 0.45875 \tabularnewline
M10 & -0.250653594771243 & 1.113429 & -0.2251 & 0.822843 & 0.411421 \tabularnewline
M11 & -0.145326797385622 & 1.113202 & -0.1305 & 0.896678 & 0.448339 \tabularnewline
t & -0.0253267973856209 & 0.012989 & -1.9499 & 0.057048 & 0.028524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]3.11176470588236[/C][C]0.915522[/C][C]3.3989[/C][C]0.00137[/C][C]0.000685[/C][/ROW]
[ROW][C]M1[/C][C]-0.176633986928106[/C][C]1.067714[/C][C]-0.1654[/C][C]0.869299[/C][C]0.434649[/C][/ROW]
[ROW][C]M2[/C][C]0.0267320261437896[/C][C]1.120679[/C][C]0.0239[/C][C]0.981068[/C][C]0.490534[/C][/ROW]
[ROW][C]M3[/C][C]-0.0679411764705897[/C][C]1.119248[/C][C]-0.0607[/C][C]0.951848[/C][C]0.475924[/C][/ROW]
[ROW][C]M4[/C][C]-0.082614379084969[/C][C]1.117966[/C][C]-0.0739[/C][C]0.941399[/C][C]0.4707[/C][/ROW]
[ROW][C]M5[/C][C]-0.117287581699348[/C][C]1.116834[/C][C]-0.105[/C][C]0.916799[/C][C]0.4584[/C][/ROW]
[ROW][C]M6[/C][C]-0.0919607843137269[/C][C]1.115851[/C][C]-0.0824[/C][C]0.934661[/C][C]0.46733[/C][/ROW]
[ROW][C]M7[/C][C]-0.206633986928106[/C][C]1.115019[/C][C]-0.1853[/C][C]0.85376[/C][C]0.42688[/C][/ROW]
[ROW][C]M8[/C][C]-0.0813071895424855[/C][C]1.114338[/C][C]-0.073[/C][C]0.942138[/C][C]0.471069[/C][/ROW]
[ROW][C]M9[/C][C]-0.115980392156864[/C][C]1.113808[/C][C]-0.1041[/C][C]0.9175[/C][C]0.45875[/C][/ROW]
[ROW][C]M10[/C][C]-0.250653594771243[/C][C]1.113429[/C][C]-0.2251[/C][C]0.822843[/C][C]0.411421[/C][/ROW]
[ROW][C]M11[/C][C]-0.145326797385622[/C][C]1.113202[/C][C]-0.1305[/C][C]0.896678[/C][C]0.448339[/C][/ROW]
[ROW][C]t[/C][C]-0.0253267973856209[/C][C]0.012989[/C][C]-1.9499[/C][C]0.057048[/C][C]0.028524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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)3.111764705882360.9155223.39890.001370.000685
M1-0.1766339869281061.067714-0.16540.8692990.434649
M20.02673202614378961.1206790.02390.9810680.490534
M3-0.06794117647058971.119248-0.06070.9518480.475924
M4-0.0826143790849691.117966-0.07390.9413990.4707
M5-0.1172875816993481.116834-0.1050.9167990.4584
M6-0.09196078431372691.115851-0.08240.9346610.46733
M7-0.2066339869281061.115019-0.18530.853760.42688
M8-0.08130718954248551.114338-0.0730.9421380.471069
M9-0.1159803921568641.113808-0.10410.91750.45875
M10-0.2506535947712431.113429-0.22510.8228430.411421
M11-0.1453267973856221.113202-0.13050.8966780.448339
t-0.02532679738562090.012989-1.94990.0570480.028524






Multiple Linear Regression - Regression Statistics
Multiple R0.280701934462105
R-squared0.0787935760107679
Adjusted R-squared-0.15150802998654
F-TEST (value)0.34213211701046
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.976538597787572
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.76000733435786
Sum Squared Residuals148.686039215686

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.280701934462105 \tabularnewline
R-squared & 0.0787935760107679 \tabularnewline
Adjusted R-squared & -0.15150802998654 \tabularnewline
F-TEST (value) & 0.34213211701046 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.976538597787572 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.76000733435786 \tabularnewline
Sum Squared Residuals & 148.686039215686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.280701934462105[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0787935760107679[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.15150802998654[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.34213211701046[/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]0.976538597787572[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.76000733435786[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]148.686039215686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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 R0.280701934462105
R-squared0.0787935760107679
Adjusted R-squared-0.15150802998654
F-TEST (value)0.34213211701046
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.976538597787572
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.76000733435786
Sum Squared Residuals148.686039215686






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
122.90980392156862-0.909803921568623
22.33.0878431372549-0.787843137254901
32.82.9678431372549-0.167843137254902
42.42.9278431372549-0.527843137254901
52.32.8678431372549-0.567843137254902
62.72.8678431372549-0.167843137254902
72.72.72784313725490-0.0278431372549023
82.92.82784313725490.0721568627450983
932.76784313725490.232156862745098
102.22.60784313725490-0.407843137254902
112.32.6878431372549-0.387843137254902
122.82.80784313725490-0.00784313725490308
132.82.605882352941180.194117647058822
142.82.783921568627450.0160784313725485
152.22.66392156862745-0.463921568627451
162.62.62392156862745-0.0239215686274506
172.82.563921568627450.236078431372549
182.52.56392156862745-0.0639215686274504
192.42.42392156862745-0.0239215686274508
202.32.52392156862745-0.223921568627451
211.92.46392156862745-0.563921568627451
221.72.30392156862745-0.603921568627451
2322.38392156862745-0.383921568627451
242.12.50392156862745-0.403921568627452
251.72.30196078431373-0.601960784313726
261.82.48-0.68
271.82.36-0.56
281.82.32-0.52
291.32.26-0.96
301.32.26-0.96
311.32.12-0.82
321.22.22-1.02
331.42.16-0.76
342.220.200000000000001
352.92.080.82
363.12.20.899999999999999
373.51.998039215686271.50196078431373
383.62.176078431372551.42392156862745
394.42.056078431372552.34392156862745
404.12.016078431372552.08392156862745
415.11.956078431372553.14392156862745
425.81.956078431372553.84392156862745
435.91.816078431372554.08392156862745
445.41.916078431372553.48392156862745
455.51.856078431372553.64392156862745
464.81.696078431372553.10392156862745
473.21.776078431372551.42392156862745
482.71.896078431372550.80392156862745
492.11.694117647058820.405882352941176
501.91.87215686274510.0278431372549018
510.61.75215686274510-1.15215686274510
520.71.71215686274510-1.01215686274510
53-0.21.6521568627451-1.8521568627451
54-11.65215686274510-2.6521568627451
55-1.71.51215686274510-3.2121568627451
56-0.71.6121568627451-2.3121568627451
57-11.5521568627451-2.5521568627451
58-0.91.3921568627451-2.2921568627451
5901.4721568627451-1.4721568627451
600.31.5921568627451-1.2921568627451
610.81.39019607843137-0.590196078431373

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2 & 2.90980392156862 & -0.909803921568623 \tabularnewline
2 & 2.3 & 3.0878431372549 & -0.787843137254901 \tabularnewline
3 & 2.8 & 2.9678431372549 & -0.167843137254902 \tabularnewline
4 & 2.4 & 2.9278431372549 & -0.527843137254901 \tabularnewline
5 & 2.3 & 2.8678431372549 & -0.567843137254902 \tabularnewline
6 & 2.7 & 2.8678431372549 & -0.167843137254902 \tabularnewline
7 & 2.7 & 2.72784313725490 & -0.0278431372549023 \tabularnewline
8 & 2.9 & 2.8278431372549 & 0.0721568627450983 \tabularnewline
9 & 3 & 2.7678431372549 & 0.232156862745098 \tabularnewline
10 & 2.2 & 2.60784313725490 & -0.407843137254902 \tabularnewline
11 & 2.3 & 2.6878431372549 & -0.387843137254902 \tabularnewline
12 & 2.8 & 2.80784313725490 & -0.00784313725490308 \tabularnewline
13 & 2.8 & 2.60588235294118 & 0.194117647058822 \tabularnewline
14 & 2.8 & 2.78392156862745 & 0.0160784313725485 \tabularnewline
15 & 2.2 & 2.66392156862745 & -0.463921568627451 \tabularnewline
16 & 2.6 & 2.62392156862745 & -0.0239215686274506 \tabularnewline
17 & 2.8 & 2.56392156862745 & 0.236078431372549 \tabularnewline
18 & 2.5 & 2.56392156862745 & -0.0639215686274504 \tabularnewline
19 & 2.4 & 2.42392156862745 & -0.0239215686274508 \tabularnewline
20 & 2.3 & 2.52392156862745 & -0.223921568627451 \tabularnewline
21 & 1.9 & 2.46392156862745 & -0.563921568627451 \tabularnewline
22 & 1.7 & 2.30392156862745 & -0.603921568627451 \tabularnewline
23 & 2 & 2.38392156862745 & -0.383921568627451 \tabularnewline
24 & 2.1 & 2.50392156862745 & -0.403921568627452 \tabularnewline
25 & 1.7 & 2.30196078431373 & -0.601960784313726 \tabularnewline
26 & 1.8 & 2.48 & -0.68 \tabularnewline
27 & 1.8 & 2.36 & -0.56 \tabularnewline
28 & 1.8 & 2.32 & -0.52 \tabularnewline
29 & 1.3 & 2.26 & -0.96 \tabularnewline
30 & 1.3 & 2.26 & -0.96 \tabularnewline
31 & 1.3 & 2.12 & -0.82 \tabularnewline
32 & 1.2 & 2.22 & -1.02 \tabularnewline
33 & 1.4 & 2.16 & -0.76 \tabularnewline
34 & 2.2 & 2 & 0.200000000000001 \tabularnewline
35 & 2.9 & 2.08 & 0.82 \tabularnewline
36 & 3.1 & 2.2 & 0.899999999999999 \tabularnewline
37 & 3.5 & 1.99803921568627 & 1.50196078431373 \tabularnewline
38 & 3.6 & 2.17607843137255 & 1.42392156862745 \tabularnewline
39 & 4.4 & 2.05607843137255 & 2.34392156862745 \tabularnewline
40 & 4.1 & 2.01607843137255 & 2.08392156862745 \tabularnewline
41 & 5.1 & 1.95607843137255 & 3.14392156862745 \tabularnewline
42 & 5.8 & 1.95607843137255 & 3.84392156862745 \tabularnewline
43 & 5.9 & 1.81607843137255 & 4.08392156862745 \tabularnewline
44 & 5.4 & 1.91607843137255 & 3.48392156862745 \tabularnewline
45 & 5.5 & 1.85607843137255 & 3.64392156862745 \tabularnewline
46 & 4.8 & 1.69607843137255 & 3.10392156862745 \tabularnewline
47 & 3.2 & 1.77607843137255 & 1.42392156862745 \tabularnewline
48 & 2.7 & 1.89607843137255 & 0.80392156862745 \tabularnewline
49 & 2.1 & 1.69411764705882 & 0.405882352941176 \tabularnewline
50 & 1.9 & 1.8721568627451 & 0.0278431372549018 \tabularnewline
51 & 0.6 & 1.75215686274510 & -1.15215686274510 \tabularnewline
52 & 0.7 & 1.71215686274510 & -1.01215686274510 \tabularnewline
53 & -0.2 & 1.6521568627451 & -1.8521568627451 \tabularnewline
54 & -1 & 1.65215686274510 & -2.6521568627451 \tabularnewline
55 & -1.7 & 1.51215686274510 & -3.2121568627451 \tabularnewline
56 & -0.7 & 1.6121568627451 & -2.3121568627451 \tabularnewline
57 & -1 & 1.5521568627451 & -2.5521568627451 \tabularnewline
58 & -0.9 & 1.3921568627451 & -2.2921568627451 \tabularnewline
59 & 0 & 1.4721568627451 & -1.4721568627451 \tabularnewline
60 & 0.3 & 1.5921568627451 & -1.2921568627451 \tabularnewline
61 & 0.8 & 1.39019607843137 & -0.590196078431373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]2[/C][C]2.90980392156862[/C][C]-0.909803921568623[/C][/ROW]
[ROW][C]2[/C][C]2.3[/C][C]3.0878431372549[/C][C]-0.787843137254901[/C][/ROW]
[ROW][C]3[/C][C]2.8[/C][C]2.9678431372549[/C][C]-0.167843137254902[/C][/ROW]
[ROW][C]4[/C][C]2.4[/C][C]2.9278431372549[/C][C]-0.527843137254901[/C][/ROW]
[ROW][C]5[/C][C]2.3[/C][C]2.8678431372549[/C][C]-0.567843137254902[/C][/ROW]
[ROW][C]6[/C][C]2.7[/C][C]2.8678431372549[/C][C]-0.167843137254902[/C][/ROW]
[ROW][C]7[/C][C]2.7[/C][C]2.72784313725490[/C][C]-0.0278431372549023[/C][/ROW]
[ROW][C]8[/C][C]2.9[/C][C]2.8278431372549[/C][C]0.0721568627450983[/C][/ROW]
[ROW][C]9[/C][C]3[/C][C]2.7678431372549[/C][C]0.232156862745098[/C][/ROW]
[ROW][C]10[/C][C]2.2[/C][C]2.60784313725490[/C][C]-0.407843137254902[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]2.6878431372549[/C][C]-0.387843137254902[/C][/ROW]
[ROW][C]12[/C][C]2.8[/C][C]2.80784313725490[/C][C]-0.00784313725490308[/C][/ROW]
[ROW][C]13[/C][C]2.8[/C][C]2.60588235294118[/C][C]0.194117647058822[/C][/ROW]
[ROW][C]14[/C][C]2.8[/C][C]2.78392156862745[/C][C]0.0160784313725485[/C][/ROW]
[ROW][C]15[/C][C]2.2[/C][C]2.66392156862745[/C][C]-0.463921568627451[/C][/ROW]
[ROW][C]16[/C][C]2.6[/C][C]2.62392156862745[/C][C]-0.0239215686274506[/C][/ROW]
[ROW][C]17[/C][C]2.8[/C][C]2.56392156862745[/C][C]0.236078431372549[/C][/ROW]
[ROW][C]18[/C][C]2.5[/C][C]2.56392156862745[/C][C]-0.0639215686274504[/C][/ROW]
[ROW][C]19[/C][C]2.4[/C][C]2.42392156862745[/C][C]-0.0239215686274508[/C][/ROW]
[ROW][C]20[/C][C]2.3[/C][C]2.52392156862745[/C][C]-0.223921568627451[/C][/ROW]
[ROW][C]21[/C][C]1.9[/C][C]2.46392156862745[/C][C]-0.563921568627451[/C][/ROW]
[ROW][C]22[/C][C]1.7[/C][C]2.30392156862745[/C][C]-0.603921568627451[/C][/ROW]
[ROW][C]23[/C][C]2[/C][C]2.38392156862745[/C][C]-0.383921568627451[/C][/ROW]
[ROW][C]24[/C][C]2.1[/C][C]2.50392156862745[/C][C]-0.403921568627452[/C][/ROW]
[ROW][C]25[/C][C]1.7[/C][C]2.30196078431373[/C][C]-0.601960784313726[/C][/ROW]
[ROW][C]26[/C][C]1.8[/C][C]2.48[/C][C]-0.68[/C][/ROW]
[ROW][C]27[/C][C]1.8[/C][C]2.36[/C][C]-0.56[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]2.32[/C][C]-0.52[/C][/ROW]
[ROW][C]29[/C][C]1.3[/C][C]2.26[/C][C]-0.96[/C][/ROW]
[ROW][C]30[/C][C]1.3[/C][C]2.26[/C][C]-0.96[/C][/ROW]
[ROW][C]31[/C][C]1.3[/C][C]2.12[/C][C]-0.82[/C][/ROW]
[ROW][C]32[/C][C]1.2[/C][C]2.22[/C][C]-1.02[/C][/ROW]
[ROW][C]33[/C][C]1.4[/C][C]2.16[/C][C]-0.76[/C][/ROW]
[ROW][C]34[/C][C]2.2[/C][C]2[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]35[/C][C]2.9[/C][C]2.08[/C][C]0.82[/C][/ROW]
[ROW][C]36[/C][C]3.1[/C][C]2.2[/C][C]0.899999999999999[/C][/ROW]
[ROW][C]37[/C][C]3.5[/C][C]1.99803921568627[/C][C]1.50196078431373[/C][/ROW]
[ROW][C]38[/C][C]3.6[/C][C]2.17607843137255[/C][C]1.42392156862745[/C][/ROW]
[ROW][C]39[/C][C]4.4[/C][C]2.05607843137255[/C][C]2.34392156862745[/C][/ROW]
[ROW][C]40[/C][C]4.1[/C][C]2.01607843137255[/C][C]2.08392156862745[/C][/ROW]
[ROW][C]41[/C][C]5.1[/C][C]1.95607843137255[/C][C]3.14392156862745[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]1.95607843137255[/C][C]3.84392156862745[/C][/ROW]
[ROW][C]43[/C][C]5.9[/C][C]1.81607843137255[/C][C]4.08392156862745[/C][/ROW]
[ROW][C]44[/C][C]5.4[/C][C]1.91607843137255[/C][C]3.48392156862745[/C][/ROW]
[ROW][C]45[/C][C]5.5[/C][C]1.85607843137255[/C][C]3.64392156862745[/C][/ROW]
[ROW][C]46[/C][C]4.8[/C][C]1.69607843137255[/C][C]3.10392156862745[/C][/ROW]
[ROW][C]47[/C][C]3.2[/C][C]1.77607843137255[/C][C]1.42392156862745[/C][/ROW]
[ROW][C]48[/C][C]2.7[/C][C]1.89607843137255[/C][C]0.80392156862745[/C][/ROW]
[ROW][C]49[/C][C]2.1[/C][C]1.69411764705882[/C][C]0.405882352941176[/C][/ROW]
[ROW][C]50[/C][C]1.9[/C][C]1.8721568627451[/C][C]0.0278431372549018[/C][/ROW]
[ROW][C]51[/C][C]0.6[/C][C]1.75215686274510[/C][C]-1.15215686274510[/C][/ROW]
[ROW][C]52[/C][C]0.7[/C][C]1.71215686274510[/C][C]-1.01215686274510[/C][/ROW]
[ROW][C]53[/C][C]-0.2[/C][C]1.6521568627451[/C][C]-1.8521568627451[/C][/ROW]
[ROW][C]54[/C][C]-1[/C][C]1.65215686274510[/C][C]-2.6521568627451[/C][/ROW]
[ROW][C]55[/C][C]-1.7[/C][C]1.51215686274510[/C][C]-3.2121568627451[/C][/ROW]
[ROW][C]56[/C][C]-0.7[/C][C]1.6121568627451[/C][C]-2.3121568627451[/C][/ROW]
[ROW][C]57[/C][C]-1[/C][C]1.5521568627451[/C][C]-2.5521568627451[/C][/ROW]
[ROW][C]58[/C][C]-0.9[/C][C]1.3921568627451[/C][C]-2.2921568627451[/C][/ROW]
[ROW][C]59[/C][C]0[/C][C]1.4721568627451[/C][C]-1.4721568627451[/C][/ROW]
[ROW][C]60[/C][C]0.3[/C][C]1.5921568627451[/C][C]-1.2921568627451[/C][/ROW]
[ROW][C]61[/C][C]0.8[/C][C]1.39019607843137[/C][C]-0.590196078431373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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
122.90980392156862-0.909803921568623
22.33.0878431372549-0.787843137254901
32.82.9678431372549-0.167843137254902
42.42.9278431372549-0.527843137254901
52.32.8678431372549-0.567843137254902
62.72.8678431372549-0.167843137254902
72.72.72784313725490-0.0278431372549023
82.92.82784313725490.0721568627450983
932.76784313725490.232156862745098
102.22.60784313725490-0.407843137254902
112.32.6878431372549-0.387843137254902
122.82.80784313725490-0.00784313725490308
132.82.605882352941180.194117647058822
142.82.783921568627450.0160784313725485
152.22.66392156862745-0.463921568627451
162.62.62392156862745-0.0239215686274506
172.82.563921568627450.236078431372549
182.52.56392156862745-0.0639215686274504
192.42.42392156862745-0.0239215686274508
202.32.52392156862745-0.223921568627451
211.92.46392156862745-0.563921568627451
221.72.30392156862745-0.603921568627451
2322.38392156862745-0.383921568627451
242.12.50392156862745-0.403921568627452
251.72.30196078431373-0.601960784313726
261.82.48-0.68
271.82.36-0.56
281.82.32-0.52
291.32.26-0.96
301.32.26-0.96
311.32.12-0.82
321.22.22-1.02
331.42.16-0.76
342.220.200000000000001
352.92.080.82
363.12.20.899999999999999
373.51.998039215686271.50196078431373
383.62.176078431372551.42392156862745
394.42.056078431372552.34392156862745
404.12.016078431372552.08392156862745
415.11.956078431372553.14392156862745
425.81.956078431372553.84392156862745
435.91.816078431372554.08392156862745
445.41.916078431372553.48392156862745
455.51.856078431372553.64392156862745
464.81.696078431372553.10392156862745
473.21.776078431372551.42392156862745
482.71.896078431372550.80392156862745
492.11.694117647058820.405882352941176
501.91.87215686274510.0278431372549018
510.61.75215686274510-1.15215686274510
520.71.71215686274510-1.01215686274510
53-0.21.6521568627451-1.8521568627451
54-11.65215686274510-2.6521568627451
55-1.71.51215686274510-3.2121568627451
56-0.71.6121568627451-2.3121568627451
57-11.5521568627451-2.5521568627451
58-0.91.3921568627451-2.2921568627451
5901.4721568627451-1.4721568627451
600.31.5921568627451-1.2921568627451
610.81.39019607843137-0.590196078431373






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.01113217501903760.02226435003807520.988867824980962
170.001976030050514370.003952060101028740.998023969949486
180.0004236225071140230.0008472450142280470.999576377492886
199.40906718038906e-050.0001881813436077810.999905909328196
203.28433449934913e-056.56866899869825e-050.999967156655007
212.90369671519759e-055.80739343039517e-050.999970963032848
226.61332579055521e-061.32266515811104e-050.99999338667421
231.22411756558044e-062.44823513116087e-060.999998775882434
243.21460393808537e-076.42920787617074e-070.999999678539606
257.9648074379939e-081.59296148759878e-070.999999920351926
261.95519261053518e-083.91038522107036e-080.999999980448074
274.20133902652341e-098.40267805304683e-090.99999999579866
288.86851316440512e-101.77370263288102e-090.999999999113149
296.60105038255032e-101.32021007651006e-090.999999999339895
305.10036308418355e-101.02007261683671e-090.999999999489964
313.30649947531936e-106.61299895063872e-100.99999999966935
324.71654399629039e-109.43308799258079e-100.999999999528346
335.63848792077113e-101.12769758415423e-090.999999999436151
343.38770359436159e-096.77540718872317e-090.999999996612296
355.57372018510203e-081.11474403702041e-070.999999944262798
366.62492956223794e-071.32498591244759e-060.999999337507044
370.0001327455212411380.0002654910424822750.999867254478759
380.000987026683187470.001974053366374940.999012973316812
390.003739149243676560.007478298487353120.996260850756323
400.00601126050819330.01202252101638660.993988739491807
410.01313096175678970.02626192351357950.98686903824321
420.03888218274808980.07776436549617950.96111781725191
430.1341934154139950.268386830827990.865806584586005
440.1647480199099350.3294960398198710.835251980090065
450.3340787878973950.668157575794790.665921212102605

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0111321750190376 & 0.0222643500380752 & 0.988867824980962 \tabularnewline
17 & 0.00197603005051437 & 0.00395206010102874 & 0.998023969949486 \tabularnewline
18 & 0.000423622507114023 & 0.000847245014228047 & 0.999576377492886 \tabularnewline
19 & 9.40906718038906e-05 & 0.000188181343607781 & 0.999905909328196 \tabularnewline
20 & 3.28433449934913e-05 & 6.56866899869825e-05 & 0.999967156655007 \tabularnewline
21 & 2.90369671519759e-05 & 5.80739343039517e-05 & 0.999970963032848 \tabularnewline
22 & 6.61332579055521e-06 & 1.32266515811104e-05 & 0.99999338667421 \tabularnewline
23 & 1.22411756558044e-06 & 2.44823513116087e-06 & 0.999998775882434 \tabularnewline
24 & 3.21460393808537e-07 & 6.42920787617074e-07 & 0.999999678539606 \tabularnewline
25 & 7.9648074379939e-08 & 1.59296148759878e-07 & 0.999999920351926 \tabularnewline
26 & 1.95519261053518e-08 & 3.91038522107036e-08 & 0.999999980448074 \tabularnewline
27 & 4.20133902652341e-09 & 8.40267805304683e-09 & 0.99999999579866 \tabularnewline
28 & 8.86851316440512e-10 & 1.77370263288102e-09 & 0.999999999113149 \tabularnewline
29 & 6.60105038255032e-10 & 1.32021007651006e-09 & 0.999999999339895 \tabularnewline
30 & 5.10036308418355e-10 & 1.02007261683671e-09 & 0.999999999489964 \tabularnewline
31 & 3.30649947531936e-10 & 6.61299895063872e-10 & 0.99999999966935 \tabularnewline
32 & 4.71654399629039e-10 & 9.43308799258079e-10 & 0.999999999528346 \tabularnewline
33 & 5.63848792077113e-10 & 1.12769758415423e-09 & 0.999999999436151 \tabularnewline
34 & 3.38770359436159e-09 & 6.77540718872317e-09 & 0.999999996612296 \tabularnewline
35 & 5.57372018510203e-08 & 1.11474403702041e-07 & 0.999999944262798 \tabularnewline
36 & 6.62492956223794e-07 & 1.32498591244759e-06 & 0.999999337507044 \tabularnewline
37 & 0.000132745521241138 & 0.000265491042482275 & 0.999867254478759 \tabularnewline
38 & 0.00098702668318747 & 0.00197405336637494 & 0.999012973316812 \tabularnewline
39 & 0.00373914924367656 & 0.00747829848735312 & 0.996260850756323 \tabularnewline
40 & 0.0060112605081933 & 0.0120225210163866 & 0.993988739491807 \tabularnewline
41 & 0.0131309617567897 & 0.0262619235135795 & 0.98686903824321 \tabularnewline
42 & 0.0388821827480898 & 0.0777643654961795 & 0.96111781725191 \tabularnewline
43 & 0.134193415413995 & 0.26838683082799 & 0.865806584586005 \tabularnewline
44 & 0.164748019909935 & 0.329496039819871 & 0.835251980090065 \tabularnewline
45 & 0.334078787897395 & 0.66815757579479 & 0.665921212102605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]0.0111321750190376[/C][C]0.0222643500380752[/C][C]0.988867824980962[/C][/ROW]
[ROW][C]17[/C][C]0.00197603005051437[/C][C]0.00395206010102874[/C][C]0.998023969949486[/C][/ROW]
[ROW][C]18[/C][C]0.000423622507114023[/C][C]0.000847245014228047[/C][C]0.999576377492886[/C][/ROW]
[ROW][C]19[/C][C]9.40906718038906e-05[/C][C]0.000188181343607781[/C][C]0.999905909328196[/C][/ROW]
[ROW][C]20[/C][C]3.28433449934913e-05[/C][C]6.56866899869825e-05[/C][C]0.999967156655007[/C][/ROW]
[ROW][C]21[/C][C]2.90369671519759e-05[/C][C]5.80739343039517e-05[/C][C]0.999970963032848[/C][/ROW]
[ROW][C]22[/C][C]6.61332579055521e-06[/C][C]1.32266515811104e-05[/C][C]0.99999338667421[/C][/ROW]
[ROW][C]23[/C][C]1.22411756558044e-06[/C][C]2.44823513116087e-06[/C][C]0.999998775882434[/C][/ROW]
[ROW][C]24[/C][C]3.21460393808537e-07[/C][C]6.42920787617074e-07[/C][C]0.999999678539606[/C][/ROW]
[ROW][C]25[/C][C]7.9648074379939e-08[/C][C]1.59296148759878e-07[/C][C]0.999999920351926[/C][/ROW]
[ROW][C]26[/C][C]1.95519261053518e-08[/C][C]3.91038522107036e-08[/C][C]0.999999980448074[/C][/ROW]
[ROW][C]27[/C][C]4.20133902652341e-09[/C][C]8.40267805304683e-09[/C][C]0.99999999579866[/C][/ROW]
[ROW][C]28[/C][C]8.86851316440512e-10[/C][C]1.77370263288102e-09[/C][C]0.999999999113149[/C][/ROW]
[ROW][C]29[/C][C]6.60105038255032e-10[/C][C]1.32021007651006e-09[/C][C]0.999999999339895[/C][/ROW]
[ROW][C]30[/C][C]5.10036308418355e-10[/C][C]1.02007261683671e-09[/C][C]0.999999999489964[/C][/ROW]
[ROW][C]31[/C][C]3.30649947531936e-10[/C][C]6.61299895063872e-10[/C][C]0.99999999966935[/C][/ROW]
[ROW][C]32[/C][C]4.71654399629039e-10[/C][C]9.43308799258079e-10[/C][C]0.999999999528346[/C][/ROW]
[ROW][C]33[/C][C]5.63848792077113e-10[/C][C]1.12769758415423e-09[/C][C]0.999999999436151[/C][/ROW]
[ROW][C]34[/C][C]3.38770359436159e-09[/C][C]6.77540718872317e-09[/C][C]0.999999996612296[/C][/ROW]
[ROW][C]35[/C][C]5.57372018510203e-08[/C][C]1.11474403702041e-07[/C][C]0.999999944262798[/C][/ROW]
[ROW][C]36[/C][C]6.62492956223794e-07[/C][C]1.32498591244759e-06[/C][C]0.999999337507044[/C][/ROW]
[ROW][C]37[/C][C]0.000132745521241138[/C][C]0.000265491042482275[/C][C]0.999867254478759[/C][/ROW]
[ROW][C]38[/C][C]0.00098702668318747[/C][C]0.00197405336637494[/C][C]0.999012973316812[/C][/ROW]
[ROW][C]39[/C][C]0.00373914924367656[/C][C]0.00747829848735312[/C][C]0.996260850756323[/C][/ROW]
[ROW][C]40[/C][C]0.0060112605081933[/C][C]0.0120225210163866[/C][C]0.993988739491807[/C][/ROW]
[ROW][C]41[/C][C]0.0131309617567897[/C][C]0.0262619235135795[/C][C]0.98686903824321[/C][/ROW]
[ROW][C]42[/C][C]0.0388821827480898[/C][C]0.0777643654961795[/C][C]0.96111781725191[/C][/ROW]
[ROW][C]43[/C][C]0.134193415413995[/C][C]0.26838683082799[/C][C]0.865806584586005[/C][/ROW]
[ROW][C]44[/C][C]0.164748019909935[/C][C]0.329496039819871[/C][C]0.835251980090065[/C][/ROW]
[ROW][C]45[/C][C]0.334078787897395[/C][C]0.66815757579479[/C][C]0.665921212102605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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
160.01113217501903760.02226435003807520.988867824980962
170.001976030050514370.003952060101028740.998023969949486
180.0004236225071140230.0008472450142280470.999576377492886
199.40906718038906e-050.0001881813436077810.999905909328196
203.28433449934913e-056.56866899869825e-050.999967156655007
212.90369671519759e-055.80739343039517e-050.999970963032848
226.61332579055521e-061.32266515811104e-050.99999338667421
231.22411756558044e-062.44823513116087e-060.999998775882434
243.21460393808537e-076.42920787617074e-070.999999678539606
257.9648074379939e-081.59296148759878e-070.999999920351926
261.95519261053518e-083.91038522107036e-080.999999980448074
274.20133902652341e-098.40267805304683e-090.99999999579866
288.86851316440512e-101.77370263288102e-090.999999999113149
296.60105038255032e-101.32021007651006e-090.999999999339895
305.10036308418355e-101.02007261683671e-090.999999999489964
313.30649947531936e-106.61299895063872e-100.99999999966935
324.71654399629039e-109.43308799258079e-100.999999999528346
335.63848792077113e-101.12769758415423e-090.999999999436151
343.38770359436159e-096.77540718872317e-090.999999996612296
355.57372018510203e-081.11474403702041e-070.999999944262798
366.62492956223794e-071.32498591244759e-060.999999337507044
370.0001327455212411380.0002654910424822750.999867254478759
380.000987026683187470.001974053366374940.999012973316812
390.003739149243676560.007478298487353120.996260850756323
400.00601126050819330.01202252101638660.993988739491807
410.01313096175678970.02626192351357950.98686903824321
420.03888218274808980.07776436549617950.96111781725191
430.1341934154139950.268386830827990.865806584586005
440.1647480199099350.3294960398198710.835251980090065
450.3340787878973950.668157575794790.665921212102605






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level230.766666666666667NOK
5% type I error level260.866666666666667NOK
10% type I error level270.9NOK

\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 & 23 & 0.766666666666667 & NOK \tabularnewline
5% type I error level & 26 & 0.866666666666667 & NOK \tabularnewline
10% type I error level & 27 & 0.9 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]23[/C][C]0.766666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]26[/C][C]0.866666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]27[/C][C]0.9[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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 level230.766666666666667NOK
5% type I error level260.866666666666667NOK
10% type I error level270.9NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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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')
}