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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 computationThu, 19 Nov 2009 13:53:48 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258664137yd0vzcgr1g7w59c.htm/, Retrieved Thu, 25 Apr 2024 01:37:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57950, Retrieved Thu, 25 Apr 2024 01:37:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

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]
-   PD      [Multiple Regression] [4 lag ] [2009-11-19 20:53:48] [244731fa3e7e6c85774b8c0902c58f85] [Current]
- R  D        [Multiple Regression] [] [2009-11-22 15:45:38] [9b30bff5dd5a100f8196daf92e735633]
-    D        [Multiple Regression] [review 7] [2009-11-23 20:50:02] [309ee52d0058ff0a6f7eec15e07b2d9f]
-   PD          [Multiple Regression] [review 7] [2009-11-24 08:31:24] [309ee52d0058ff0a6f7eec15e07b2d9f]
-   PD        [Multiple Regression] [multiple ] [2009-11-24 21:03:26] [ba905ddf7cdf9ecb063c35348c4dab2e]
-    D        [Multiple Regression] [Review WS 7 2 maa...] [2009-11-27 11:45:11] [12f02da0296cb21dc23d82ae014a8b71]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0	6.5	6.3	6.1	6.2	6.3
0	6.6	6.5	6.3	6.1	6.2
0	6.5	6.6	6.5	6.3	6.1
0	6.2	6.5	6.6	6.5	6.3
0	6.2	6.2	6.5	6.6	6.5
0	5.9	6.2	6.2	6.5	6.6
0	6.1	5.9	6.2	6.2	6.5
0	6.1	6.1	5.9	6.2	6.2
0	6.1	6.1	6.1	5.9	6.2
0	6.1	6.1	6.1	6.1	5.9
0	6.1	6.1	6.1	6.1	6.1
0	6.4	6.1	6.1	6.1	6.1
0	6.7	6.4	6.1	6.1	6.1
0	6.9	6.7	6.4	6.1	6.1
0	7	6.9	6.7	6.4	6.1
0	7	7	6.9	6.7	6.4
0	6.8	7	7	6.9	6.7
0	6.4	6.8	7	7	6.9
0	5.9	6.4	6.8	7	7
0	5.5	5.9	6.4	6.8	7
0	5.5	5.5	5.9	6.4	6.8
0	5.6	5.5	5.5	5.9	6.4
0	5.8	5.6	5.5	5.5	5.9
0	5.9	5.8	5.6	5.5	5.5
0	6.1	5.9	5.8	5.6	5.5
0	6.1	6.1	5.9	5.8	5.6
0	6	6.1	6.1	5.9	5.8
0	6	6	6.1	6.1	5.9
0	5.9	6	6	6.1	6.1
0	5.5	5.9	6	6	6.1
0	5.6	5.5	5.9	6	6
0	5.4	5.6	5.5	5.9	6
0	5.2	5.4	5.6	5.5	5.9
0	5.2	5.2	5.4	5.6	5.5
0	5.2	5.2	5.2	5.4	5.6
0	5.5	5.2	5.2	5.2	5.4
1	5.8	5.5	5.2	5.2	5.2
1	5.8	5.8	5.5	5.2	5.2
1	5.5	5.8	5.8	5.5	5.2
1	5.3	5.5	5.8	5.8	5.5
1	5.1	5.3	5.5	5.8	5.8
1	5.2	5.1	5.3	5.5	5.8
1	5.8	5.2	5.1	5.3	5.5
1	5.8	5.8	5.2	5.1	5.3
1	5.5	5.8	5.8	5.2	5.1
1	5	5.5	5.8	5.8	5.2
1	4.9	5	5.5	5.8	5.8
1	5.3	4.9	5	5.5	5.8
1	6.1	5.3	4.9	5	5.5
1	6.5	6.1	5.3	4.9	5
1	6.8	6.5	6.1	5.3	4.9
1	6.6	6.8	6.5	6.1	5.3
1	6.4	6.6	6.8	6.5	6.1
1	6.4	6.4	6.6	6.8	6.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57950&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
y[t] = -0.0346622960368248 + 0.0589758078691045x[t] + 1.50682864869239y1[t] -0.632805983146732y2[t] -0.275699725509361y3[t] + 0.431531623605503y4[t] -0.0126969934258707M1[t] -0.209114897281531M2[t] -0.142221133838311M3[t] -0.178080352483085M4[t] -0.238176192560859M5[t] -0.383383749504528M6[t] -0.0469800234484245M7[t] -0.488027705147431M8[t] -0.340348596260656M9[t] -0.213105342498909M10[t] -0.202673655015069M11[t] + 0.00164230830510336t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  -0.0346622960368248 +  0.0589758078691045x[t] +  1.50682864869239y1[t] -0.632805983146732y2[t] -0.275699725509361y3[t] +  0.431531623605503y4[t] -0.0126969934258707M1[t] -0.209114897281531M2[t] -0.142221133838311M3[t] -0.178080352483085M4[t] -0.238176192560859M5[t] -0.383383749504528M6[t] -0.0469800234484245M7[t] -0.488027705147431M8[t] -0.340348596260656M9[t] -0.213105342498909M10[t] -0.202673655015069M11[t] +  0.00164230830510336t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57950&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  -0.0346622960368248 +  0.0589758078691045x[t] +  1.50682864869239y1[t] -0.632805983146732y2[t] -0.275699725509361y3[t] +  0.431531623605503y4[t] -0.0126969934258707M1[t] -0.209114897281531M2[t] -0.142221133838311M3[t] -0.178080352483085M4[t] -0.238176192560859M5[t] -0.383383749504528M6[t] -0.0469800234484245M7[t] -0.488027705147431M8[t] -0.340348596260656M9[t] -0.213105342498909M10[t] -0.202673655015069M11[t] +  0.00164230830510336t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
y[t] = -0.0346622960368248 + 0.0589758078691045x[t] + 1.50682864869239y1[t] -0.632805983146732y2[t] -0.275699725509361y3[t] + 0.431531623605503y4[t] -0.0126969934258707M1[t] -0.209114897281531M2[t] -0.142221133838311M3[t] -0.178080352483085M4[t] -0.238176192560859M5[t] -0.383383749504528M6[t] -0.0469800234484245M7[t] -0.488027705147431M8[t] -0.340348596260656M9[t] -0.213105342498909M10[t] -0.202673655015069M11[t] + 0.00164230830510336t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.03466229603682480.620921-0.05580.9557910.477895
x0.05897580786910450.0944450.62440.5362730.268137
y11.506828648692390.162339.282500
y2-0.6328059831467320.294958-2.14540.0387380.019369
y3-0.2756997255093610.299869-0.91940.3640070.182003
y40.4315316236055030.1861372.31840.0262230.013112
M1-0.01269699342587070.124226-0.10220.9191580.459579
M2-0.2091148972815310.131705-1.58770.1210890.060544
M3-0.1422211338383110.135794-1.04730.3019290.150964
M4-0.1780803524830850.135795-1.31140.198030.099015
M5-0.2381761925608590.134072-1.77650.0841060.042053
M6-0.3833837495045280.134458-2.85130.0071650.003583
M7-0.04698002344842450.13453-0.34920.7289620.364481
M8-0.4880277051474310.132214-3.69120.0007340.000367
M9-0.3403485962606560.144005-2.36350.0236240.011812
M10-0.2131053424989090.12887-1.65360.1068950.053448
M11-0.2026736550150690.124838-1.62350.113210.056605
t0.001642308305103360.0031430.52250.6045250.302263

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -0.0346622960368248 & 0.620921 & -0.0558 & 0.955791 & 0.477895 \tabularnewline
x & 0.0589758078691045 & 0.094445 & 0.6244 & 0.536273 & 0.268137 \tabularnewline
y1 & 1.50682864869239 & 0.16233 & 9.2825 & 0 & 0 \tabularnewline
y2 & -0.632805983146732 & 0.294958 & -2.1454 & 0.038738 & 0.019369 \tabularnewline
y3 & -0.275699725509361 & 0.299869 & -0.9194 & 0.364007 & 0.182003 \tabularnewline
y4 & 0.431531623605503 & 0.186137 & 2.3184 & 0.026223 & 0.013112 \tabularnewline
M1 & -0.0126969934258707 & 0.124226 & -0.1022 & 0.919158 & 0.459579 \tabularnewline
M2 & -0.209114897281531 & 0.131705 & -1.5877 & 0.121089 & 0.060544 \tabularnewline
M3 & -0.142221133838311 & 0.135794 & -1.0473 & 0.301929 & 0.150964 \tabularnewline
M4 & -0.178080352483085 & 0.135795 & -1.3114 & 0.19803 & 0.099015 \tabularnewline
M5 & -0.238176192560859 & 0.134072 & -1.7765 & 0.084106 & 0.042053 \tabularnewline
M6 & -0.383383749504528 & 0.134458 & -2.8513 & 0.007165 & 0.003583 \tabularnewline
M7 & -0.0469800234484245 & 0.13453 & -0.3492 & 0.728962 & 0.364481 \tabularnewline
M8 & -0.488027705147431 & 0.132214 & -3.6912 & 0.000734 & 0.000367 \tabularnewline
M9 & -0.340348596260656 & 0.144005 & -2.3635 & 0.023624 & 0.011812 \tabularnewline
M10 & -0.213105342498909 & 0.12887 & -1.6536 & 0.106895 & 0.053448 \tabularnewline
M11 & -0.202673655015069 & 0.124838 & -1.6235 & 0.11321 & 0.056605 \tabularnewline
t & 0.00164230830510336 & 0.003143 & 0.5225 & 0.604525 & 0.302263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57950&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-0.0346622960368248[/C][C]0.620921[/C][C]-0.0558[/C][C]0.955791[/C][C]0.477895[/C][/ROW]
[ROW][C]x[/C][C]0.0589758078691045[/C][C]0.094445[/C][C]0.6244[/C][C]0.536273[/C][C]0.268137[/C][/ROW]
[ROW][C]y1[/C][C]1.50682864869239[/C][C]0.16233[/C][C]9.2825[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]y2[/C][C]-0.632805983146732[/C][C]0.294958[/C][C]-2.1454[/C][C]0.038738[/C][C]0.019369[/C][/ROW]
[ROW][C]y3[/C][C]-0.275699725509361[/C][C]0.299869[/C][C]-0.9194[/C][C]0.364007[/C][C]0.182003[/C][/ROW]
[ROW][C]y4[/C][C]0.431531623605503[/C][C]0.186137[/C][C]2.3184[/C][C]0.026223[/C][C]0.013112[/C][/ROW]
[ROW][C]M1[/C][C]-0.0126969934258707[/C][C]0.124226[/C][C]-0.1022[/C][C]0.919158[/C][C]0.459579[/C][/ROW]
[ROW][C]M2[/C][C]-0.209114897281531[/C][C]0.131705[/C][C]-1.5877[/C][C]0.121089[/C][C]0.060544[/C][/ROW]
[ROW][C]M3[/C][C]-0.142221133838311[/C][C]0.135794[/C][C]-1.0473[/C][C]0.301929[/C][C]0.150964[/C][/ROW]
[ROW][C]M4[/C][C]-0.178080352483085[/C][C]0.135795[/C][C]-1.3114[/C][C]0.19803[/C][C]0.099015[/C][/ROW]
[ROW][C]M5[/C][C]-0.238176192560859[/C][C]0.134072[/C][C]-1.7765[/C][C]0.084106[/C][C]0.042053[/C][/ROW]
[ROW][C]M6[/C][C]-0.383383749504528[/C][C]0.134458[/C][C]-2.8513[/C][C]0.007165[/C][C]0.003583[/C][/ROW]
[ROW][C]M7[/C][C]-0.0469800234484245[/C][C]0.13453[/C][C]-0.3492[/C][C]0.728962[/C][C]0.364481[/C][/ROW]
[ROW][C]M8[/C][C]-0.488027705147431[/C][C]0.132214[/C][C]-3.6912[/C][C]0.000734[/C][C]0.000367[/C][/ROW]
[ROW][C]M9[/C][C]-0.340348596260656[/C][C]0.144005[/C][C]-2.3635[/C][C]0.023624[/C][C]0.011812[/C][/ROW]
[ROW][C]M10[/C][C]-0.213105342498909[/C][C]0.12887[/C][C]-1.6536[/C][C]0.106895[/C][C]0.053448[/C][/ROW]
[ROW][C]M11[/C][C]-0.202673655015069[/C][C]0.124838[/C][C]-1.6235[/C][C]0.11321[/C][C]0.056605[/C][/ROW]
[ROW][C]t[/C][C]0.00164230830510336[/C][C]0.003143[/C][C]0.5225[/C][C]0.604525[/C][C]0.302263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.03466229603682480.620921-0.05580.9557910.477895
x0.05897580786910450.0944450.62440.5362730.268137
y11.506828648692390.162339.282500
y2-0.6328059831467320.294958-2.14540.0387380.019369
y3-0.2756997255093610.299869-0.91940.3640070.182003
y40.4315316236055030.1861372.31840.0262230.013112
M1-0.01269699342587070.124226-0.10220.9191580.459579
M2-0.2091148972815310.131705-1.58770.1210890.060544
M3-0.1422211338383110.135794-1.04730.3019290.150964
M4-0.1780803524830850.135795-1.31140.198030.099015
M5-0.2381761925608590.134072-1.77650.0841060.042053
M6-0.3833837495045280.134458-2.85130.0071650.003583
M7-0.04698002344842450.13453-0.34920.7289620.364481
M8-0.4880277051474310.132214-3.69120.0007340.000367
M9-0.3403485962606560.144005-2.36350.0236240.011812
M10-0.2131053424989090.12887-1.65360.1068950.053448
M11-0.2026736550150690.124838-1.62350.113210.056605
t0.001642308305103360.0031430.52250.6045250.302263






Multiple Linear Regression - Regression Statistics
Multiple R0.96454395128867
R-squared0.93034503396756
Adjusted R-squared0.897452411118909
F-TEST (value)28.2843067349277
F-TEST (DF numerator)17
F-TEST (DF denominator)36
p-value7.7715611723761e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.174263106623220
Sum Squared Residuals1.09323469187913

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.96454395128867 \tabularnewline
R-squared & 0.93034503396756 \tabularnewline
Adjusted R-squared & 0.897452411118909 \tabularnewline
F-TEST (value) & 28.2843067349277 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 36 \tabularnewline
p-value & 7.7715611723761e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.174263106623220 \tabularnewline
Sum Squared Residuals & 1.09323469187913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57950&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.96454395128867[/C][/ROW]
[ROW][C]R-squared[/C][C]0.93034503396756[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.897452411118909[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]28.2843067349277[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]36[/C][/ROW]
[ROW][C]p-value[/C][C]7.7715611723761e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.174263106623220[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.09323469187913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57950&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&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 R0.96454395128867
R-squared0.93034503396756
Adjusted R-squared0.897452411118909
F-TEST (value)28.2843067349277
F-TEST (DF numerator)17
F-TEST (DF denominator)36
p-value7.7715611723761e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.174263106623220
Sum Squared Residuals1.09323469187913






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.56.59649793896602-0.0964979389660187
26.66.560943686714970.0390563132850288
36.56.55530831924076-0.0553083192407632
46.26.33829432533641-0.138294325336408
56.25.949809149440860.250190850559141
65.96.0668088306578-0.166808830657799
76.15.992363025703550.107636974296451
86.15.914705689910490.185294310089509
96.16.020175828125830.0798241718741687
106.15.964461958009160.135538041990841
116.16.06284227851920.0371577214807976
126.46.267158241839370.132841758160626
136.76.70815215132632-0.00815215132632399
146.96.775583355439460.124416644560537
1576.872933444329440.127066555670564
1676.90958777165850.0904122283415
176.86.86217318355093-0.0621731835509351
186.46.47597855734406-0.0759785573440556
195.96.38100749121821-0.481007491218206
205.55.496450131838670.00354986816132527
215.55.383416646609610.116583353390393
225.65.73066181524763-0.13066181524763
235.85.78793275430680.0120672456931957
245.96.05772119960858-0.157721199608579
256.16.043218210176770.0567817898232305
266.16.074540963308690.0254590366913063
2766.07525219059784-0.075252190597835
2865.87836563264760.121634367352395
295.95.96949902391071-0.0694990239107069
305.55.70282088295384-0.202820882953839
315.65.458262893792210.141737106207786
325.45.45023275107718-0.0502327510771779
335.25.3020345680591-0.102034568059102
345.25.055932975023680.144067024976317
355.25.2928612749044-0.0928612749043944
365.55.466010858605340.0339891413946611
375.85.87967425124029-0.0796742512402913
385.85.94710545535343-0.147105455353431
395.55.74308981450493-0.243089814504926
405.35.30357387898638-0.00357387898638284
415.15.2630558995009-0.163055899500905
425.25.027396035406020.172603964593985
435.85.568366589286030.231633410713970
445.85.93861142717366-0.138611427173657
455.55.59437295720546-0.0943729572054596
4655.14894325171953-0.148943251719528
474.94.85636369226960.043636307730401
485.35.30910969994671-0.00910969994670775
496.15.97245744829060.127542551709403
506.56.54182653918344-0.0418265391834409
516.86.553416231327040.246583768672960
526.66.6701783913711-0.070178391371104
536.46.35546274359660.0445372564034061
546.46.126995693638290.273004306361709

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.5 & 6.59649793896602 & -0.0964979389660187 \tabularnewline
2 & 6.6 & 6.56094368671497 & 0.0390563132850288 \tabularnewline
3 & 6.5 & 6.55530831924076 & -0.0553083192407632 \tabularnewline
4 & 6.2 & 6.33829432533641 & -0.138294325336408 \tabularnewline
5 & 6.2 & 5.94980914944086 & 0.250190850559141 \tabularnewline
6 & 5.9 & 6.0668088306578 & -0.166808830657799 \tabularnewline
7 & 6.1 & 5.99236302570355 & 0.107636974296451 \tabularnewline
8 & 6.1 & 5.91470568991049 & 0.185294310089509 \tabularnewline
9 & 6.1 & 6.02017582812583 & 0.0798241718741687 \tabularnewline
10 & 6.1 & 5.96446195800916 & 0.135538041990841 \tabularnewline
11 & 6.1 & 6.0628422785192 & 0.0371577214807976 \tabularnewline
12 & 6.4 & 6.26715824183937 & 0.132841758160626 \tabularnewline
13 & 6.7 & 6.70815215132632 & -0.00815215132632399 \tabularnewline
14 & 6.9 & 6.77558335543946 & 0.124416644560537 \tabularnewline
15 & 7 & 6.87293344432944 & 0.127066555670564 \tabularnewline
16 & 7 & 6.9095877716585 & 0.0904122283415 \tabularnewline
17 & 6.8 & 6.86217318355093 & -0.0621731835509351 \tabularnewline
18 & 6.4 & 6.47597855734406 & -0.0759785573440556 \tabularnewline
19 & 5.9 & 6.38100749121821 & -0.481007491218206 \tabularnewline
20 & 5.5 & 5.49645013183867 & 0.00354986816132527 \tabularnewline
21 & 5.5 & 5.38341664660961 & 0.116583353390393 \tabularnewline
22 & 5.6 & 5.73066181524763 & -0.13066181524763 \tabularnewline
23 & 5.8 & 5.7879327543068 & 0.0120672456931957 \tabularnewline
24 & 5.9 & 6.05772119960858 & -0.157721199608579 \tabularnewline
25 & 6.1 & 6.04321821017677 & 0.0567817898232305 \tabularnewline
26 & 6.1 & 6.07454096330869 & 0.0254590366913063 \tabularnewline
27 & 6 & 6.07525219059784 & -0.075252190597835 \tabularnewline
28 & 6 & 5.8783656326476 & 0.121634367352395 \tabularnewline
29 & 5.9 & 5.96949902391071 & -0.0694990239107069 \tabularnewline
30 & 5.5 & 5.70282088295384 & -0.202820882953839 \tabularnewline
31 & 5.6 & 5.45826289379221 & 0.141737106207786 \tabularnewline
32 & 5.4 & 5.45023275107718 & -0.0502327510771779 \tabularnewline
33 & 5.2 & 5.3020345680591 & -0.102034568059102 \tabularnewline
34 & 5.2 & 5.05593297502368 & 0.144067024976317 \tabularnewline
35 & 5.2 & 5.2928612749044 & -0.0928612749043944 \tabularnewline
36 & 5.5 & 5.46601085860534 & 0.0339891413946611 \tabularnewline
37 & 5.8 & 5.87967425124029 & -0.0796742512402913 \tabularnewline
38 & 5.8 & 5.94710545535343 & -0.147105455353431 \tabularnewline
39 & 5.5 & 5.74308981450493 & -0.243089814504926 \tabularnewline
40 & 5.3 & 5.30357387898638 & -0.00357387898638284 \tabularnewline
41 & 5.1 & 5.2630558995009 & -0.163055899500905 \tabularnewline
42 & 5.2 & 5.02739603540602 & 0.172603964593985 \tabularnewline
43 & 5.8 & 5.56836658928603 & 0.231633410713970 \tabularnewline
44 & 5.8 & 5.93861142717366 & -0.138611427173657 \tabularnewline
45 & 5.5 & 5.59437295720546 & -0.0943729572054596 \tabularnewline
46 & 5 & 5.14894325171953 & -0.148943251719528 \tabularnewline
47 & 4.9 & 4.8563636922696 & 0.043636307730401 \tabularnewline
48 & 5.3 & 5.30910969994671 & -0.00910969994670775 \tabularnewline
49 & 6.1 & 5.9724574482906 & 0.127542551709403 \tabularnewline
50 & 6.5 & 6.54182653918344 & -0.0418265391834409 \tabularnewline
51 & 6.8 & 6.55341623132704 & 0.246583768672960 \tabularnewline
52 & 6.6 & 6.6701783913711 & -0.070178391371104 \tabularnewline
53 & 6.4 & 6.3554627435966 & 0.0445372564034061 \tabularnewline
54 & 6.4 & 6.12699569363829 & 0.273004306361709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57950&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]6.5[/C][C]6.59649793896602[/C][C]-0.0964979389660187[/C][/ROW]
[ROW][C]2[/C][C]6.6[/C][C]6.56094368671497[/C][C]0.0390563132850288[/C][/ROW]
[ROW][C]3[/C][C]6.5[/C][C]6.55530831924076[/C][C]-0.0553083192407632[/C][/ROW]
[ROW][C]4[/C][C]6.2[/C][C]6.33829432533641[/C][C]-0.138294325336408[/C][/ROW]
[ROW][C]5[/C][C]6.2[/C][C]5.94980914944086[/C][C]0.250190850559141[/C][/ROW]
[ROW][C]6[/C][C]5.9[/C][C]6.0668088306578[/C][C]-0.166808830657799[/C][/ROW]
[ROW][C]7[/C][C]6.1[/C][C]5.99236302570355[/C][C]0.107636974296451[/C][/ROW]
[ROW][C]8[/C][C]6.1[/C][C]5.91470568991049[/C][C]0.185294310089509[/C][/ROW]
[ROW][C]9[/C][C]6.1[/C][C]6.02017582812583[/C][C]0.0798241718741687[/C][/ROW]
[ROW][C]10[/C][C]6.1[/C][C]5.96446195800916[/C][C]0.135538041990841[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.0628422785192[/C][C]0.0371577214807976[/C][/ROW]
[ROW][C]12[/C][C]6.4[/C][C]6.26715824183937[/C][C]0.132841758160626[/C][/ROW]
[ROW][C]13[/C][C]6.7[/C][C]6.70815215132632[/C][C]-0.00815215132632399[/C][/ROW]
[ROW][C]14[/C][C]6.9[/C][C]6.77558335543946[/C][C]0.124416644560537[/C][/ROW]
[ROW][C]15[/C][C]7[/C][C]6.87293344432944[/C][C]0.127066555670564[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]6.9095877716585[/C][C]0.0904122283415[/C][/ROW]
[ROW][C]17[/C][C]6.8[/C][C]6.86217318355093[/C][C]-0.0621731835509351[/C][/ROW]
[ROW][C]18[/C][C]6.4[/C][C]6.47597855734406[/C][C]-0.0759785573440556[/C][/ROW]
[ROW][C]19[/C][C]5.9[/C][C]6.38100749121821[/C][C]-0.481007491218206[/C][/ROW]
[ROW][C]20[/C][C]5.5[/C][C]5.49645013183867[/C][C]0.00354986816132527[/C][/ROW]
[ROW][C]21[/C][C]5.5[/C][C]5.38341664660961[/C][C]0.116583353390393[/C][/ROW]
[ROW][C]22[/C][C]5.6[/C][C]5.73066181524763[/C][C]-0.13066181524763[/C][/ROW]
[ROW][C]23[/C][C]5.8[/C][C]5.7879327543068[/C][C]0.0120672456931957[/C][/ROW]
[ROW][C]24[/C][C]5.9[/C][C]6.05772119960858[/C][C]-0.157721199608579[/C][/ROW]
[ROW][C]25[/C][C]6.1[/C][C]6.04321821017677[/C][C]0.0567817898232305[/C][/ROW]
[ROW][C]26[/C][C]6.1[/C][C]6.07454096330869[/C][C]0.0254590366913063[/C][/ROW]
[ROW][C]27[/C][C]6[/C][C]6.07525219059784[/C][C]-0.075252190597835[/C][/ROW]
[ROW][C]28[/C][C]6[/C][C]5.8783656326476[/C][C]0.121634367352395[/C][/ROW]
[ROW][C]29[/C][C]5.9[/C][C]5.96949902391071[/C][C]-0.0694990239107069[/C][/ROW]
[ROW][C]30[/C][C]5.5[/C][C]5.70282088295384[/C][C]-0.202820882953839[/C][/ROW]
[ROW][C]31[/C][C]5.6[/C][C]5.45826289379221[/C][C]0.141737106207786[/C][/ROW]
[ROW][C]32[/C][C]5.4[/C][C]5.45023275107718[/C][C]-0.0502327510771779[/C][/ROW]
[ROW][C]33[/C][C]5.2[/C][C]5.3020345680591[/C][C]-0.102034568059102[/C][/ROW]
[ROW][C]34[/C][C]5.2[/C][C]5.05593297502368[/C][C]0.144067024976317[/C][/ROW]
[ROW][C]35[/C][C]5.2[/C][C]5.2928612749044[/C][C]-0.0928612749043944[/C][/ROW]
[ROW][C]36[/C][C]5.5[/C][C]5.46601085860534[/C][C]0.0339891413946611[/C][/ROW]
[ROW][C]37[/C][C]5.8[/C][C]5.87967425124029[/C][C]-0.0796742512402913[/C][/ROW]
[ROW][C]38[/C][C]5.8[/C][C]5.94710545535343[/C][C]-0.147105455353431[/C][/ROW]
[ROW][C]39[/C][C]5.5[/C][C]5.74308981450493[/C][C]-0.243089814504926[/C][/ROW]
[ROW][C]40[/C][C]5.3[/C][C]5.30357387898638[/C][C]-0.00357387898638284[/C][/ROW]
[ROW][C]41[/C][C]5.1[/C][C]5.2630558995009[/C][C]-0.163055899500905[/C][/ROW]
[ROW][C]42[/C][C]5.2[/C][C]5.02739603540602[/C][C]0.172603964593985[/C][/ROW]
[ROW][C]43[/C][C]5.8[/C][C]5.56836658928603[/C][C]0.231633410713970[/C][/ROW]
[ROW][C]44[/C][C]5.8[/C][C]5.93861142717366[/C][C]-0.138611427173657[/C][/ROW]
[ROW][C]45[/C][C]5.5[/C][C]5.59437295720546[/C][C]-0.0943729572054596[/C][/ROW]
[ROW][C]46[/C][C]5[/C][C]5.14894325171953[/C][C]-0.148943251719528[/C][/ROW]
[ROW][C]47[/C][C]4.9[/C][C]4.8563636922696[/C][C]0.043636307730401[/C][/ROW]
[ROW][C]48[/C][C]5.3[/C][C]5.30910969994671[/C][C]-0.00910969994670775[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]5.9724574482906[/C][C]0.127542551709403[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]6.54182653918344[/C][C]-0.0418265391834409[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]6.55341623132704[/C][C]0.246583768672960[/C][/ROW]
[ROW][C]52[/C][C]6.6[/C][C]6.6701783913711[/C][C]-0.070178391371104[/C][/ROW]
[ROW][C]53[/C][C]6.4[/C][C]6.3554627435966[/C][C]0.0445372564034061[/C][/ROW]
[ROW][C]54[/C][C]6.4[/C][C]6.12699569363829[/C][C]0.273004306361709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57950&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&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
16.56.59649793896602-0.0964979389660187
26.66.560943686714970.0390563132850288
36.56.55530831924076-0.0553083192407632
46.26.33829432533641-0.138294325336408
56.25.949809149440860.250190850559141
65.96.0668088306578-0.166808830657799
76.15.992363025703550.107636974296451
86.15.914705689910490.185294310089509
96.16.020175828125830.0798241718741687
106.15.964461958009160.135538041990841
116.16.06284227851920.0371577214807976
126.46.267158241839370.132841758160626
136.76.70815215132632-0.00815215132632399
146.96.775583355439460.124416644560537
1576.872933444329440.127066555670564
1676.90958777165850.0904122283415
176.86.86217318355093-0.0621731835509351
186.46.47597855734406-0.0759785573440556
195.96.38100749121821-0.481007491218206
205.55.496450131838670.00354986816132527
215.55.383416646609610.116583353390393
225.65.73066181524763-0.13066181524763
235.85.78793275430680.0120672456931957
245.96.05772119960858-0.157721199608579
256.16.043218210176770.0567817898232305
266.16.074540963308690.0254590366913063
2766.07525219059784-0.075252190597835
2865.87836563264760.121634367352395
295.95.96949902391071-0.0694990239107069
305.55.70282088295384-0.202820882953839
315.65.458262893792210.141737106207786
325.45.45023275107718-0.0502327510771779
335.25.3020345680591-0.102034568059102
345.25.055932975023680.144067024976317
355.25.2928612749044-0.0928612749043944
365.55.466010858605340.0339891413946611
375.85.87967425124029-0.0796742512402913
385.85.94710545535343-0.147105455353431
395.55.74308981450493-0.243089814504926
405.35.30357387898638-0.00357387898638284
415.15.2630558995009-0.163055899500905
425.25.027396035406020.172603964593985
435.85.568366589286030.231633410713970
445.85.93861142717366-0.138611427173657
455.55.59437295720546-0.0943729572054596
4655.14894325171953-0.148943251719528
474.94.85636369226960.043636307730401
485.35.30910969994671-0.00910969994670775
496.15.97245744829060.127542551709403
506.56.54182653918344-0.0418265391834409
516.86.553416231327040.246583768672960
526.66.6701783913711-0.070178391371104
536.46.35546274359660.0445372564034061
546.46.126995693638290.273004306361709






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.860797249946650.2784055001067010.139202750053350
220.8163992087215220.3672015825569550.183600791278478
230.8138208340297290.3723583319405420.186179165970271
240.8955297521673740.2089404956652510.104470247832626
250.8315191008129050.336961798374190.168480899187095
260.8044171829771510.3911656340456980.195582817022849
270.7039221116336230.5921557767327550.296077888366378
280.6983656391993750.603268721601250.301634360800625
290.6915250260639760.6169499478720480.308474973936024
300.7216489947567230.5567020104865540.278351005243277
310.730197692617140.539604614765720.26980230738286
320.5908923944288520.8182152111422950.409107605571148
330.4674125921369790.9348251842739570.532587407863021

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.86079724994665 & 0.278405500106701 & 0.139202750053350 \tabularnewline
22 & 0.816399208721522 & 0.367201582556955 & 0.183600791278478 \tabularnewline
23 & 0.813820834029729 & 0.372358331940542 & 0.186179165970271 \tabularnewline
24 & 0.895529752167374 & 0.208940495665251 & 0.104470247832626 \tabularnewline
25 & 0.831519100812905 & 0.33696179837419 & 0.168480899187095 \tabularnewline
26 & 0.804417182977151 & 0.391165634045698 & 0.195582817022849 \tabularnewline
27 & 0.703922111633623 & 0.592155776732755 & 0.296077888366378 \tabularnewline
28 & 0.698365639199375 & 0.60326872160125 & 0.301634360800625 \tabularnewline
29 & 0.691525026063976 & 0.616949947872048 & 0.308474973936024 \tabularnewline
30 & 0.721648994756723 & 0.556702010486554 & 0.278351005243277 \tabularnewline
31 & 0.73019769261714 & 0.53960461476572 & 0.26980230738286 \tabularnewline
32 & 0.590892394428852 & 0.818215211142295 & 0.409107605571148 \tabularnewline
33 & 0.467412592136979 & 0.934825184273957 & 0.532587407863021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57950&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]0.86079724994665[/C][C]0.278405500106701[/C][C]0.139202750053350[/C][/ROW]
[ROW][C]22[/C][C]0.816399208721522[/C][C]0.367201582556955[/C][C]0.183600791278478[/C][/ROW]
[ROW][C]23[/C][C]0.813820834029729[/C][C]0.372358331940542[/C][C]0.186179165970271[/C][/ROW]
[ROW][C]24[/C][C]0.895529752167374[/C][C]0.208940495665251[/C][C]0.104470247832626[/C][/ROW]
[ROW][C]25[/C][C]0.831519100812905[/C][C]0.33696179837419[/C][C]0.168480899187095[/C][/ROW]
[ROW][C]26[/C][C]0.804417182977151[/C][C]0.391165634045698[/C][C]0.195582817022849[/C][/ROW]
[ROW][C]27[/C][C]0.703922111633623[/C][C]0.592155776732755[/C][C]0.296077888366378[/C][/ROW]
[ROW][C]28[/C][C]0.698365639199375[/C][C]0.60326872160125[/C][C]0.301634360800625[/C][/ROW]
[ROW][C]29[/C][C]0.691525026063976[/C][C]0.616949947872048[/C][C]0.308474973936024[/C][/ROW]
[ROW][C]30[/C][C]0.721648994756723[/C][C]0.556702010486554[/C][C]0.278351005243277[/C][/ROW]
[ROW][C]31[/C][C]0.73019769261714[/C][C]0.53960461476572[/C][C]0.26980230738286[/C][/ROW]
[ROW][C]32[/C][C]0.590892394428852[/C][C]0.818215211142295[/C][C]0.409107605571148[/C][/ROW]
[ROW][C]33[/C][C]0.467412592136979[/C][C]0.934825184273957[/C][C]0.532587407863021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57950&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&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
210.860797249946650.2784055001067010.139202750053350
220.8163992087215220.3672015825569550.183600791278478
230.8138208340297290.3723583319405420.186179165970271
240.8955297521673740.2089404956652510.104470247832626
250.8315191008129050.336961798374190.168480899187095
260.8044171829771510.3911656340456980.195582817022849
270.7039221116336230.5921557767327550.296077888366378
280.6983656391993750.603268721601250.301634360800625
290.6915250260639760.6169499478720480.308474973936024
300.7216489947567230.5567020104865540.278351005243277
310.730197692617140.539604614765720.26980230738286
320.5908923944288520.8182152111422950.409107605571148
330.4674125921369790.9348251842739570.532587407863021






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=57950&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=57950&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57950&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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 2 ; 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')
}