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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 computationWed, 18 Nov 2009 09:49:45 -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/18/t12585630836s56gnwu01d6xvi.htm/, Retrieved Sun, 28 Apr 2024 16:33:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57532, Retrieved Sun, 28 Apr 2024 16:33:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws7autoregr4lagswmanecogr
Estimated Impact193

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 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-18 16:49:45] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
-    D        [Multiple Regression] [] [2009-11-20 13:30:42] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D          [Multiple Regression] [] [2009-11-20 13:35:13] [90f6d58d515a4caed6fb4b8be4e11eaa]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,60	101,60	7,50	7,70	8,10	8,00
7,80	94,60	7,60	7,50	7,70	8,10
7,80	95,90	7,80	7,60	7,50	7,70
7,80	104,70	7,80	7,80	7,60	7,50
7,50	102,80	7,80	7,80	7,80	7,60
7,50	98,10	7,50	7,80	7,80	7,80
7,10	113,90	7,50	7,50	7,80	7,80
7,50	80,90	7,10	7,50	7,50	7,80
7,50	95,70	7,50	7,10	7,50	7,50
7,60	113,20	7,50	7,50	7,10	7,50
7,70	105,90	7,60	7,50	7,50	7,10
7,70	108,80	7,70	7,60	7,50	7,50
7,90	102,30	7,70	7,70	7,60	7,50
8,10	99,00	7,90	7,70	7,70	7,60
8,20	100,70	8,10	7,90	7,70	7,70
8,20	115,50	8,20	8,10	7,90	7,70
8,20	100,70	8,20	8,20	8,10	7,90
7,90	109,90	8,20	8,20	8,20	8,10
7,30	114,60	7,90	8,20	8,20	8,20
6,90	85,40	7,30	7,90	8,20	8,20
6,60	100,50	6,90	7,30	7,90	8,20
6,70	114,80	6,60	6,90	7,30	7,90
6,90	116,50	6,70	6,60	6,90	7,30
7,00	112,90	6,90	6,70	6,60	6,90
7,10	102,00	7,00	6,90	6,70	6,60
7,20	106,00	7,10	7,00	6,90	6,70
7,10	105,30	7,20	7,10	7,00	6,90
6,90	118,80	7,10	7,20	7,10	7,00
7,00	106,10	6,90	7,10	7,20	7,10
6,80	109,30	7,00	6,90	7,10	7,20
6,40	117,20	6,80	7,00	6,90	7,10
6,70	92,50	6,40	6,80	7,00	6,90
6,60	104,20	6,70	6,40	6,80	7,00
6,40	112,50	6,60	6,70	6,40	6,80
6,30	122,40	6,40	6,60	6,70	6,40
6,20	113,30	6,30	6,40	6,60	6,70
6,50	100,00	6,20	6,30	6,40	6,60
6,80	110,70	6,50	6,20	6,30	6,40
6,80	112,80	6,80	6,50	6,20	6,30
6,40	109,80	6,80	6,80	6,50	6,20
6,10	117,30	6,40	6,80	6,80	6,50
5,80	109,10	6,10	6,40	6,80	6,80
6,10	115,90	5,80	6,10	6,40	6,80
7,20	96,00	6,10	5,80	6,10	6,40
7,30	99,80	7,20	6,10	5,80	6,10
6,90	116,80	7,30	7,20	6,10	5,80
6,10	115,70	6,90	7,30	7,20	6,10
5,80	99,40	6,10	6,90	7,30	7,20
6,20	94,30	5,80	6,10	6,90	7,30
7,10	91,00	6,20	5,80	6,10	6,90
7,70	93,20	7,10	6,20	5,80	6,10
7,90	103,10	7,70	7,10	6,20	5,80
7,70	94,10	7,90	7,70	7,10	6,20
7,40	91,80	7,70	7,90	7,70	7,10
7,50	102,70	7,40	7,70	7,90	7,70
8,00	82,60	7,50	7,40	7,70	7,90

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57532&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]4 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=57532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 1.79602878864052 -0.0114001793440848X[t] + 1.51143732820451Y1[t] -0.799982797357693Y2[t] -0.149890180597183Y3[t] + 0.348577798011597Y4[t] + 0.163755712329852M1[t] + 0.0840941126806134M2[t] -0.0646153641388665M3[t] + 0.113569726413263M4[t] + 0.0937133069211612M5[t] -0.0861895999292222M6[t] -0.0149736549364430M7[t] + 0.208290863164784M8[t] -0.445482542571144M9[t] + 0.0385107772688626M10[t] + 0.136504622499525M11[t] + 0.00059177892543175t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.79602878864052 -0.0114001793440848X[t] +  1.51143732820451Y1[t] -0.799982797357693Y2[t] -0.149890180597183Y3[t] +  0.348577798011597Y4[t] +  0.163755712329852M1[t] +  0.0840941126806134M2[t] -0.0646153641388665M3[t] +  0.113569726413263M4[t] +  0.0937133069211612M5[t] -0.0861895999292222M6[t] -0.0149736549364430M7[t] +  0.208290863164784M8[t] -0.445482542571144M9[t] +  0.0385107772688626M10[t] +  0.136504622499525M11[t] +  0.00059177892543175t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57532&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.79602878864052 -0.0114001793440848X[t] +  1.51143732820451Y1[t] -0.799982797357693Y2[t] -0.149890180597183Y3[t] +  0.348577798011597Y4[t] +  0.163755712329852M1[t] +  0.0840941126806134M2[t] -0.0646153641388665M3[t] +  0.113569726413263M4[t] +  0.0937133069211612M5[t] -0.0861895999292222M6[t] -0.0149736549364430M7[t] +  0.208290863164784M8[t] -0.445482542571144M9[t] +  0.0385107772688626M10[t] +  0.136504622499525M11[t] +  0.00059177892543175t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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] = + 1.79602878864052 -0.0114001793440848X[t] + 1.51143732820451Y1[t] -0.799982797357693Y2[t] -0.149890180597183Y3[t] + 0.348577798011597Y4[t] + 0.163755712329852M1[t] + 0.0840941126806134M2[t] -0.0646153641388665M3[t] + 0.113569726413263M4[t] + 0.0937133069211612M5[t] -0.0861895999292222M6[t] -0.0149736549364430M7[t] + 0.208290863164784M8[t] -0.445482542571144M9[t] + 0.0385107772688626M10[t] + 0.136504622499525M11[t] + 0.00059177892543175t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.796028788640521.0954511.63950.1093560.054678
X-0.01140017934408480.005248-2.17230.0361370.018068
Y11.511437328204510.14048810.758500
Y2-0.7999827973576930.277242-2.88550.0064080.003204
Y3-0.1498901805971830.282766-0.53010.5991360.299568
Y40.3485777980115970.1646582.1170.0408660.020433
M10.1637557123298520.1422871.15090.2569690.128485
M20.08409411268061340.1449360.58020.5651950.282597
M3-0.06461536413886650.143944-0.44890.6560590.328029
M40.1135697264132630.1413040.80370.4265540.213277
M50.09371330692116120.1399890.66940.5072660.253633
M6-0.08618959992922220.136487-0.63150.5315040.265752
M7-0.01497365493644300.141393-0.10590.9162180.458109
M80.2082908631647840.165861.25580.2168470.108423
M9-0.4454825425711440.166404-2.67710.0109030.005452
M100.03851077726886260.1695440.22710.821530.410765
M110.1365046224995250.1548020.88180.3834270.191714
t0.000591778925431750.0028240.20950.8351420.417571

\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) & 1.79602878864052 & 1.095451 & 1.6395 & 0.109356 & 0.054678 \tabularnewline
X & -0.0114001793440848 & 0.005248 & -2.1723 & 0.036137 & 0.018068 \tabularnewline
Y1 & 1.51143732820451 & 0.140488 & 10.7585 & 0 & 0 \tabularnewline
Y2 & -0.799982797357693 & 0.277242 & -2.8855 & 0.006408 & 0.003204 \tabularnewline
Y3 & -0.149890180597183 & 0.282766 & -0.5301 & 0.599136 & 0.299568 \tabularnewline
Y4 & 0.348577798011597 & 0.164658 & 2.117 & 0.040866 & 0.020433 \tabularnewline
M1 & 0.163755712329852 & 0.142287 & 1.1509 & 0.256969 & 0.128485 \tabularnewline
M2 & 0.0840941126806134 & 0.144936 & 0.5802 & 0.565195 & 0.282597 \tabularnewline
M3 & -0.0646153641388665 & 0.143944 & -0.4489 & 0.656059 & 0.328029 \tabularnewline
M4 & 0.113569726413263 & 0.141304 & 0.8037 & 0.426554 & 0.213277 \tabularnewline
M5 & 0.0937133069211612 & 0.139989 & 0.6694 & 0.507266 & 0.253633 \tabularnewline
M6 & -0.0861895999292222 & 0.136487 & -0.6315 & 0.531504 & 0.265752 \tabularnewline
M7 & -0.0149736549364430 & 0.141393 & -0.1059 & 0.916218 & 0.458109 \tabularnewline
M8 & 0.208290863164784 & 0.16586 & 1.2558 & 0.216847 & 0.108423 \tabularnewline
M9 & -0.445482542571144 & 0.166404 & -2.6771 & 0.010903 & 0.005452 \tabularnewline
M10 & 0.0385107772688626 & 0.169544 & 0.2271 & 0.82153 & 0.410765 \tabularnewline
M11 & 0.136504622499525 & 0.154802 & 0.8818 & 0.383427 & 0.191714 \tabularnewline
t & 0.00059177892543175 & 0.002824 & 0.2095 & 0.835142 & 0.417571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57532&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]1.79602878864052[/C][C]1.095451[/C][C]1.6395[/C][C]0.109356[/C][C]0.054678[/C][/ROW]
[ROW][C]X[/C][C]-0.0114001793440848[/C][C]0.005248[/C][C]-2.1723[/C][C]0.036137[/C][C]0.018068[/C][/ROW]
[ROW][C]Y1[/C][C]1.51143732820451[/C][C]0.140488[/C][C]10.7585[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.799982797357693[/C][C]0.277242[/C][C]-2.8855[/C][C]0.006408[/C][C]0.003204[/C][/ROW]
[ROW][C]Y3[/C][C]-0.149890180597183[/C][C]0.282766[/C][C]-0.5301[/C][C]0.599136[/C][C]0.299568[/C][/ROW]
[ROW][C]Y4[/C][C]0.348577798011597[/C][C]0.164658[/C][C]2.117[/C][C]0.040866[/C][C]0.020433[/C][/ROW]
[ROW][C]M1[/C][C]0.163755712329852[/C][C]0.142287[/C][C]1.1509[/C][C]0.256969[/C][C]0.128485[/C][/ROW]
[ROW][C]M2[/C][C]0.0840941126806134[/C][C]0.144936[/C][C]0.5802[/C][C]0.565195[/C][C]0.282597[/C][/ROW]
[ROW][C]M3[/C][C]-0.0646153641388665[/C][C]0.143944[/C][C]-0.4489[/C][C]0.656059[/C][C]0.328029[/C][/ROW]
[ROW][C]M4[/C][C]0.113569726413263[/C][C]0.141304[/C][C]0.8037[/C][C]0.426554[/C][C]0.213277[/C][/ROW]
[ROW][C]M5[/C][C]0.0937133069211612[/C][C]0.139989[/C][C]0.6694[/C][C]0.507266[/C][C]0.253633[/C][/ROW]
[ROW][C]M6[/C][C]-0.0861895999292222[/C][C]0.136487[/C][C]-0.6315[/C][C]0.531504[/C][C]0.265752[/C][/ROW]
[ROW][C]M7[/C][C]-0.0149736549364430[/C][C]0.141393[/C][C]-0.1059[/C][C]0.916218[/C][C]0.458109[/C][/ROW]
[ROW][C]M8[/C][C]0.208290863164784[/C][C]0.16586[/C][C]1.2558[/C][C]0.216847[/C][C]0.108423[/C][/ROW]
[ROW][C]M9[/C][C]-0.445482542571144[/C][C]0.166404[/C][C]-2.6771[/C][C]0.010903[/C][C]0.005452[/C][/ROW]
[ROW][C]M10[/C][C]0.0385107772688626[/C][C]0.169544[/C][C]0.2271[/C][C]0.82153[/C][C]0.410765[/C][/ROW]
[ROW][C]M11[/C][C]0.136504622499525[/C][C]0.154802[/C][C]0.8818[/C][C]0.383427[/C][C]0.191714[/C][/ROW]
[ROW][C]t[/C][C]0.00059177892543175[/C][C]0.002824[/C][C]0.2095[/C][C]0.835142[/C][C]0.417571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57532&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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)1.796028788640521.0954511.63950.1093560.054678
X-0.01140017934408480.005248-2.17230.0361370.018068
Y11.511437328204510.14048810.758500
Y2-0.7999827973576930.277242-2.88550.0064080.003204
Y3-0.1498901805971830.282766-0.53010.5991360.299568
Y40.3485777980115970.1646582.1170.0408660.020433
M10.1637557123298520.1422871.15090.2569690.128485
M20.08409411268061340.1449360.58020.5651950.282597
M3-0.06461536413886650.143944-0.44890.6560590.328029
M40.1135697264132630.1413040.80370.4265540.213277
M50.09371330692116120.1399890.66940.5072660.253633
M6-0.08618959992922220.136487-0.63150.5315040.265752
M7-0.01497365493644300.141393-0.10590.9162180.458109
M80.2082908631647840.165861.25580.2168470.108423
M9-0.4454825425711440.166404-2.67710.0109030.005452
M100.03851077726886260.1695440.22710.821530.410765
M110.1365046224995250.1548020.88180.3834270.191714
t0.000591778925431750.0028240.20950.8351420.417571






Multiple Linear Regression - Regression Statistics
Multiple R0.96849898486634
R-squared0.937990283687128
Adjusted R-squared0.910249094810317
F-TEST (value)33.812187640999
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.195680862179208
Sum Squared Residuals1.45505799328153

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.96849898486634 \tabularnewline
R-squared & 0.937990283687128 \tabularnewline
Adjusted R-squared & 0.910249094810317 \tabularnewline
F-TEST (value) & 33.812187640999 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.195680862179208 \tabularnewline
Sum Squared Residuals & 1.45505799328153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57532&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.96849898486634[/C][/ROW]
[ROW][C]R-squared[/C][C]0.937990283687128[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.910249094810317[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]33.812187640999[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/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]0.195680862179208[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.45505799328153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57532&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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 R0.96849898486634
R-squared0.937990283687128
Adjusted R-squared0.910249094810317
F-TEST (value)33.812187640999
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.195680862179208
Sum Squared Residuals1.45505799328153






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.67.552542401671970.0474575983280287
27.87.9592279806888-0.159227980688793
37.87.90912615246737-0.109126152467365
47.87.74288030658340.057119693416598
57.57.75015575045222-0.250155750452216
67.57.240709826585430.259290173414571
77.17.37238955607441-0.272389556074408
87.57.412843894353220.0871561056467839
97.57.410934324071670.089065675928332
107.67.435979237611420.164020762388583
117.77.569542712356270.130457287643732
127.77.611145920973650.0888540790263492
137.97.754607280170.145392719830002
148.18.035314278664020.0646857213359837
158.28.044964961855540.155035038144454
168.28.016188314270130.183811685729872
178.28.125385571743030.0746144282569725
187.97.89591933539510.00408066460490439
197.37.49557279773592-0.195572797735916
206.97.38544677389445-0.485446773894451
216.66.480504240300240.119495759699759
226.76.653989463881820.0460105361181818
236.96.97514274861264-0.0751427486126431
2477.0080956715569-0.0080956715569044
257.17.16828993354843-0.0682899335484273
267.27.119644592214690.0803554077853144
277.17.10537901448878-0.00537901448878178
286.96.91898021200642-0.0189802120064168
2976.842077424945930.157922575054066
306.86.98727281327278-0.187272813272778
316.46.58185363131432-0.181853631314323
326.76.558011408667580.141988591332424
336.66.60970781685631-0.00970781685631363
346.46.59877336767464-0.19877336767464
356.36.177809857035370.122190142964630
366.26.27405382960673-0.0740538296067317
376.56.51399850937194-0.0139985093719392
386.86.791649706320950.00835029367905362
396.86.81315922931692-0.0131592293169240
406.46.70631696363912-0.306316963639117
416.16.056582331934330.0434176680656684
425.85.94188793451608-0.141887934516077
436.15.782694151879340.317305848120661
447.26.832375990496460.367624009503536
457.37.49885361877178-0.198853618771777
466.96.91125793083213-0.0112579308321255
476.16.27750468199572-0.177504681995719
485.85.80670457786271-0.00670457786271334
496.26.31056187523766-0.110561875237664
507.17.094163442111560.00583655788844133
517.77.72737064187138-0.0273706418713827
527.97.815634203500940.0843657964990638
537.77.72579892092449-0.0257989209244906
547.47.334210090230620.0657899097693797
557.57.167489862996010.332510137003986
5688.1113219325883-0.111321932588294

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.6 & 7.55254240167197 & 0.0474575983280287 \tabularnewline
2 & 7.8 & 7.9592279806888 & -0.159227980688793 \tabularnewline
3 & 7.8 & 7.90912615246737 & -0.109126152467365 \tabularnewline
4 & 7.8 & 7.7428803065834 & 0.057119693416598 \tabularnewline
5 & 7.5 & 7.75015575045222 & -0.250155750452216 \tabularnewline
6 & 7.5 & 7.24070982658543 & 0.259290173414571 \tabularnewline
7 & 7.1 & 7.37238955607441 & -0.272389556074408 \tabularnewline
8 & 7.5 & 7.41284389435322 & 0.0871561056467839 \tabularnewline
9 & 7.5 & 7.41093432407167 & 0.089065675928332 \tabularnewline
10 & 7.6 & 7.43597923761142 & 0.164020762388583 \tabularnewline
11 & 7.7 & 7.56954271235627 & 0.130457287643732 \tabularnewline
12 & 7.7 & 7.61114592097365 & 0.0888540790263492 \tabularnewline
13 & 7.9 & 7.75460728017 & 0.145392719830002 \tabularnewline
14 & 8.1 & 8.03531427866402 & 0.0646857213359837 \tabularnewline
15 & 8.2 & 8.04496496185554 & 0.155035038144454 \tabularnewline
16 & 8.2 & 8.01618831427013 & 0.183811685729872 \tabularnewline
17 & 8.2 & 8.12538557174303 & 0.0746144282569725 \tabularnewline
18 & 7.9 & 7.8959193353951 & 0.00408066460490439 \tabularnewline
19 & 7.3 & 7.49557279773592 & -0.195572797735916 \tabularnewline
20 & 6.9 & 7.38544677389445 & -0.485446773894451 \tabularnewline
21 & 6.6 & 6.48050424030024 & 0.119495759699759 \tabularnewline
22 & 6.7 & 6.65398946388182 & 0.0460105361181818 \tabularnewline
23 & 6.9 & 6.97514274861264 & -0.0751427486126431 \tabularnewline
24 & 7 & 7.0080956715569 & -0.0080956715569044 \tabularnewline
25 & 7.1 & 7.16828993354843 & -0.0682899335484273 \tabularnewline
26 & 7.2 & 7.11964459221469 & 0.0803554077853144 \tabularnewline
27 & 7.1 & 7.10537901448878 & -0.00537901448878178 \tabularnewline
28 & 6.9 & 6.91898021200642 & -0.0189802120064168 \tabularnewline
29 & 7 & 6.84207742494593 & 0.157922575054066 \tabularnewline
30 & 6.8 & 6.98727281327278 & -0.187272813272778 \tabularnewline
31 & 6.4 & 6.58185363131432 & -0.181853631314323 \tabularnewline
32 & 6.7 & 6.55801140866758 & 0.141988591332424 \tabularnewline
33 & 6.6 & 6.60970781685631 & -0.00970781685631363 \tabularnewline
34 & 6.4 & 6.59877336767464 & -0.19877336767464 \tabularnewline
35 & 6.3 & 6.17780985703537 & 0.122190142964630 \tabularnewline
36 & 6.2 & 6.27405382960673 & -0.0740538296067317 \tabularnewline
37 & 6.5 & 6.51399850937194 & -0.0139985093719392 \tabularnewline
38 & 6.8 & 6.79164970632095 & 0.00835029367905362 \tabularnewline
39 & 6.8 & 6.81315922931692 & -0.0131592293169240 \tabularnewline
40 & 6.4 & 6.70631696363912 & -0.306316963639117 \tabularnewline
41 & 6.1 & 6.05658233193433 & 0.0434176680656684 \tabularnewline
42 & 5.8 & 5.94188793451608 & -0.141887934516077 \tabularnewline
43 & 6.1 & 5.78269415187934 & 0.317305848120661 \tabularnewline
44 & 7.2 & 6.83237599049646 & 0.367624009503536 \tabularnewline
45 & 7.3 & 7.49885361877178 & -0.198853618771777 \tabularnewline
46 & 6.9 & 6.91125793083213 & -0.0112579308321255 \tabularnewline
47 & 6.1 & 6.27750468199572 & -0.177504681995719 \tabularnewline
48 & 5.8 & 5.80670457786271 & -0.00670457786271334 \tabularnewline
49 & 6.2 & 6.31056187523766 & -0.110561875237664 \tabularnewline
50 & 7.1 & 7.09416344211156 & 0.00583655788844133 \tabularnewline
51 & 7.7 & 7.72737064187138 & -0.0273706418713827 \tabularnewline
52 & 7.9 & 7.81563420350094 & 0.0843657964990638 \tabularnewline
53 & 7.7 & 7.72579892092449 & -0.0257989209244906 \tabularnewline
54 & 7.4 & 7.33421009023062 & 0.0657899097693797 \tabularnewline
55 & 7.5 & 7.16748986299601 & 0.332510137003986 \tabularnewline
56 & 8 & 8.1113219325883 & -0.111321932588294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57532&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]7.55254240167197[/C][C]0.0474575983280287[/C][/ROW]
[ROW][C]2[/C][C]7.8[/C][C]7.9592279806888[/C][C]-0.159227980688793[/C][/ROW]
[ROW][C]3[/C][C]7.8[/C][C]7.90912615246737[/C][C]-0.109126152467365[/C][/ROW]
[ROW][C]4[/C][C]7.8[/C][C]7.7428803065834[/C][C]0.057119693416598[/C][/ROW]
[ROW][C]5[/C][C]7.5[/C][C]7.75015575045222[/C][C]-0.250155750452216[/C][/ROW]
[ROW][C]6[/C][C]7.5[/C][C]7.24070982658543[/C][C]0.259290173414571[/C][/ROW]
[ROW][C]7[/C][C]7.1[/C][C]7.37238955607441[/C][C]-0.272389556074408[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]7.41284389435322[/C][C]0.0871561056467839[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.41093432407167[/C][C]0.089065675928332[/C][/ROW]
[ROW][C]10[/C][C]7.6[/C][C]7.43597923761142[/C][C]0.164020762388583[/C][/ROW]
[ROW][C]11[/C][C]7.7[/C][C]7.56954271235627[/C][C]0.130457287643732[/C][/ROW]
[ROW][C]12[/C][C]7.7[/C][C]7.61114592097365[/C][C]0.0888540790263492[/C][/ROW]
[ROW][C]13[/C][C]7.9[/C][C]7.75460728017[/C][C]0.145392719830002[/C][/ROW]
[ROW][C]14[/C][C]8.1[/C][C]8.03531427866402[/C][C]0.0646857213359837[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.04496496185554[/C][C]0.155035038144454[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]8.01618831427013[/C][C]0.183811685729872[/C][/ROW]
[ROW][C]17[/C][C]8.2[/C][C]8.12538557174303[/C][C]0.0746144282569725[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.8959193353951[/C][C]0.00408066460490439[/C][/ROW]
[ROW][C]19[/C][C]7.3[/C][C]7.49557279773592[/C][C]-0.195572797735916[/C][/ROW]
[ROW][C]20[/C][C]6.9[/C][C]7.38544677389445[/C][C]-0.485446773894451[/C][/ROW]
[ROW][C]21[/C][C]6.6[/C][C]6.48050424030024[/C][C]0.119495759699759[/C][/ROW]
[ROW][C]22[/C][C]6.7[/C][C]6.65398946388182[/C][C]0.0460105361181818[/C][/ROW]
[ROW][C]23[/C][C]6.9[/C][C]6.97514274861264[/C][C]-0.0751427486126431[/C][/ROW]
[ROW][C]24[/C][C]7[/C][C]7.0080956715569[/C][C]-0.0080956715569044[/C][/ROW]
[ROW][C]25[/C][C]7.1[/C][C]7.16828993354843[/C][C]-0.0682899335484273[/C][/ROW]
[ROW][C]26[/C][C]7.2[/C][C]7.11964459221469[/C][C]0.0803554077853144[/C][/ROW]
[ROW][C]27[/C][C]7.1[/C][C]7.10537901448878[/C][C]-0.00537901448878178[/C][/ROW]
[ROW][C]28[/C][C]6.9[/C][C]6.91898021200642[/C][C]-0.0189802120064168[/C][/ROW]
[ROW][C]29[/C][C]7[/C][C]6.84207742494593[/C][C]0.157922575054066[/C][/ROW]
[ROW][C]30[/C][C]6.8[/C][C]6.98727281327278[/C][C]-0.187272813272778[/C][/ROW]
[ROW][C]31[/C][C]6.4[/C][C]6.58185363131432[/C][C]-0.181853631314323[/C][/ROW]
[ROW][C]32[/C][C]6.7[/C][C]6.55801140866758[/C][C]0.141988591332424[/C][/ROW]
[ROW][C]33[/C][C]6.6[/C][C]6.60970781685631[/C][C]-0.00970781685631363[/C][/ROW]
[ROW][C]34[/C][C]6.4[/C][C]6.59877336767464[/C][C]-0.19877336767464[/C][/ROW]
[ROW][C]35[/C][C]6.3[/C][C]6.17780985703537[/C][C]0.122190142964630[/C][/ROW]
[ROW][C]36[/C][C]6.2[/C][C]6.27405382960673[/C][C]-0.0740538296067317[/C][/ROW]
[ROW][C]37[/C][C]6.5[/C][C]6.51399850937194[/C][C]-0.0139985093719392[/C][/ROW]
[ROW][C]38[/C][C]6.8[/C][C]6.79164970632095[/C][C]0.00835029367905362[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.81315922931692[/C][C]-0.0131592293169240[/C][/ROW]
[ROW][C]40[/C][C]6.4[/C][C]6.70631696363912[/C][C]-0.306316963639117[/C][/ROW]
[ROW][C]41[/C][C]6.1[/C][C]6.05658233193433[/C][C]0.0434176680656684[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]5.94188793451608[/C][C]-0.141887934516077[/C][/ROW]
[ROW][C]43[/C][C]6.1[/C][C]5.78269415187934[/C][C]0.317305848120661[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]6.83237599049646[/C][C]0.367624009503536[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.49885361877178[/C][C]-0.198853618771777[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]6.91125793083213[/C][C]-0.0112579308321255[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]6.27750468199572[/C][C]-0.177504681995719[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.80670457786271[/C][C]-0.00670457786271334[/C][/ROW]
[ROW][C]49[/C][C]6.2[/C][C]6.31056187523766[/C][C]-0.110561875237664[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.09416344211156[/C][C]0.00583655788844133[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.72737064187138[/C][C]-0.0273706418713827[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.81563420350094[/C][C]0.0843657964990638[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.72579892092449[/C][C]-0.0257989209244906[/C][/ROW]
[ROW][C]54[/C][C]7.4[/C][C]7.33421009023062[/C][C]0.0657899097693797[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.16748986299601[/C][C]0.332510137003986[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]8.1113219325883[/C][C]-0.111321932588294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57532&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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
17.67.552542401671970.0474575983280287
27.87.9592279806888-0.159227980688793
37.87.90912615246737-0.109126152467365
47.87.74288030658340.057119693416598
57.57.75015575045222-0.250155750452216
67.57.240709826585430.259290173414571
77.17.37238955607441-0.272389556074408
87.57.412843894353220.0871561056467839
97.57.410934324071670.089065675928332
107.67.435979237611420.164020762388583
117.77.569542712356270.130457287643732
127.77.611145920973650.0888540790263492
137.97.754607280170.145392719830002
148.18.035314278664020.0646857213359837
158.28.044964961855540.155035038144454
168.28.016188314270130.183811685729872
178.28.125385571743030.0746144282569725
187.97.89591933539510.00408066460490439
197.37.49557279773592-0.195572797735916
206.97.38544677389445-0.485446773894451
216.66.480504240300240.119495759699759
226.76.653989463881820.0460105361181818
236.96.97514274861264-0.0751427486126431
2477.0080956715569-0.0080956715569044
257.17.16828993354843-0.0682899335484273
267.27.119644592214690.0803554077853144
277.17.10537901448878-0.00537901448878178
286.96.91898021200642-0.0189802120064168
2976.842077424945930.157922575054066
306.86.98727281327278-0.187272813272778
316.46.58185363131432-0.181853631314323
326.76.558011408667580.141988591332424
336.66.60970781685631-0.00970781685631363
346.46.59877336767464-0.19877336767464
356.36.177809857035370.122190142964630
366.26.27405382960673-0.0740538296067317
376.56.51399850937194-0.0139985093719392
386.86.791649706320950.00835029367905362
396.86.81315922931692-0.0131592293169240
406.46.70631696363912-0.306316963639117
416.16.056582331934330.0434176680656684
425.85.94188793451608-0.141887934516077
436.15.782694151879340.317305848120661
447.26.832375990496460.367624009503536
457.37.49885361877178-0.198853618771777
466.96.91125793083213-0.0112579308321255
476.16.27750468199572-0.177504681995719
485.85.80670457786271-0.00670457786271334
496.26.31056187523766-0.110561875237664
507.17.094163442111560.00583655788844133
517.77.72737064187138-0.0273706418713827
527.97.815634203500940.0843657964990638
537.77.72579892092449-0.0257989209244906
547.47.334210090230620.0657899097693797
557.57.167489862996010.332510137003986
5688.1113219325883-0.111321932588294






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.8749236944662180.2501526110675630.125076305533782
220.7804596236989990.4390807526020020.219540376301001
230.6859607758943910.6280784482112180.314039224105609
240.5896358305332320.8207283389335360.410364169466768
250.5479785484781040.9040429030437920.452021451521896
260.4588270607495770.9176541214991540.541172939250423
270.3338755916521370.6677511833042740.666124408347863
280.2544728542263830.5089457084527660.745527145773617
290.3131130568342200.6262261136684390.68688694316578
300.2259172420008880.4518344840017770.774082757999112
310.3322960732169980.6645921464339960.667703926783002
320.3317363250833590.6634726501667180.668263674916641
330.3885776248363260.7771552496726510.611422375163674
340.3349215615021850.669843123004370.665078438497815
350.62490296612220.75019406775560.3750970338778

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.874923694466218 & 0.250152611067563 & 0.125076305533782 \tabularnewline
22 & 0.780459623698999 & 0.439080752602002 & 0.219540376301001 \tabularnewline
23 & 0.685960775894391 & 0.628078448211218 & 0.314039224105609 \tabularnewline
24 & 0.589635830533232 & 0.820728338933536 & 0.410364169466768 \tabularnewline
25 & 0.547978548478104 & 0.904042903043792 & 0.452021451521896 \tabularnewline
26 & 0.458827060749577 & 0.917654121499154 & 0.541172939250423 \tabularnewline
27 & 0.333875591652137 & 0.667751183304274 & 0.666124408347863 \tabularnewline
28 & 0.254472854226383 & 0.508945708452766 & 0.745527145773617 \tabularnewline
29 & 0.313113056834220 & 0.626226113668439 & 0.68688694316578 \tabularnewline
30 & 0.225917242000888 & 0.451834484001777 & 0.774082757999112 \tabularnewline
31 & 0.332296073216998 & 0.664592146433996 & 0.667703926783002 \tabularnewline
32 & 0.331736325083359 & 0.663472650166718 & 0.668263674916641 \tabularnewline
33 & 0.388577624836326 & 0.777155249672651 & 0.611422375163674 \tabularnewline
34 & 0.334921561502185 & 0.66984312300437 & 0.665078438497815 \tabularnewline
35 & 0.6249029661222 & 0.7501940677556 & 0.3750970338778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57532&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]0.874923694466218[/C][C]0.250152611067563[/C][C]0.125076305533782[/C][/ROW]
[ROW][C]22[/C][C]0.780459623698999[/C][C]0.439080752602002[/C][C]0.219540376301001[/C][/ROW]
[ROW][C]23[/C][C]0.685960775894391[/C][C]0.628078448211218[/C][C]0.314039224105609[/C][/ROW]
[ROW][C]24[/C][C]0.589635830533232[/C][C]0.820728338933536[/C][C]0.410364169466768[/C][/ROW]
[ROW][C]25[/C][C]0.547978548478104[/C][C]0.904042903043792[/C][C]0.452021451521896[/C][/ROW]
[ROW][C]26[/C][C]0.458827060749577[/C][C]0.917654121499154[/C][C]0.541172939250423[/C][/ROW]
[ROW][C]27[/C][C]0.333875591652137[/C][C]0.667751183304274[/C][C]0.666124408347863[/C][/ROW]
[ROW][C]28[/C][C]0.254472854226383[/C][C]0.508945708452766[/C][C]0.745527145773617[/C][/ROW]
[ROW][C]29[/C][C]0.313113056834220[/C][C]0.626226113668439[/C][C]0.68688694316578[/C][/ROW]
[ROW][C]30[/C][C]0.225917242000888[/C][C]0.451834484001777[/C][C]0.774082757999112[/C][/ROW]
[ROW][C]31[/C][C]0.332296073216998[/C][C]0.664592146433996[/C][C]0.667703926783002[/C][/ROW]
[ROW][C]32[/C][C]0.331736325083359[/C][C]0.663472650166718[/C][C]0.668263674916641[/C][/ROW]
[ROW][C]33[/C][C]0.388577624836326[/C][C]0.777155249672651[/C][C]0.611422375163674[/C][/ROW]
[ROW][C]34[/C][C]0.334921561502185[/C][C]0.66984312300437[/C][C]0.665078438497815[/C][/ROW]
[ROW][C]35[/C][C]0.6249029661222[/C][C]0.7501940677556[/C][C]0.3750970338778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57532&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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
210.8749236944662180.2501526110675630.125076305533782
220.7804596236989990.4390807526020020.219540376301001
230.6859607758943910.6280784482112180.314039224105609
240.5896358305332320.8207283389335360.410364169466768
250.5479785484781040.9040429030437920.452021451521896
260.4588270607495770.9176541214991540.541172939250423
270.3338755916521370.6677511833042740.666124408347863
280.2544728542263830.5089457084527660.745527145773617
290.3131130568342200.6262261136684390.68688694316578
300.2259172420008880.4518344840017770.774082757999112
310.3322960732169980.6645921464339960.667703926783002
320.3317363250833590.6634726501667180.668263674916641
330.3885776248363260.7771552496726510.611422375163674
340.3349215615021850.669843123004370.665078438497815
350.62490296612220.75019406775560.3750970338778






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=57532&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=57532&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57532&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')
}