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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, 17 Dec 2009 07:29:24 -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/Dec/17/t1261060251o0hapdl7fynoss1.htm/, Retrieved Tue, 30 Apr 2024 00:42:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68909, Retrieved Tue, 30 Apr 2024 00:42:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-18 16:22:43] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D      [Multiple Regression] [Multiple Regressi...] [2009-12-17 13:47:34] [90f6d58d515a4caed6fb4b8be4e11eaa]
-   PD          [Multiple Regression] [Multiple Regressi...] [2009-12-17 14:29:24] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
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Dataset

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

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=68909&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=68909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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] = -0.0550574197115133 + 0.00893293499343105X[t] + 1.58397870443630Y1[t] -0.915092663015896Y2[t] + 0.042692859676686Y3[t] + 0.279056782460857Y4[t] + 0.178003476798794M1[t] + 0.104752669320572M2[t] -0.0801731217262057M3[t] + 0.0423556268766096M4[t] + 0.0171277878745154M5[t] -0.116439585377464M6[t] + 0.00509285983473205M7[t] + 0.587598277423118M8[t] -0.414899756293283M9[t] + 0.0271031893206197M10[t] + 0.096307817332781M11[t] + 0.00124435720083027t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.0550574197115133 +  0.00893293499343105X[t] +  1.58397870443630Y1[t] -0.915092663015896Y2[t] +  0.042692859676686Y3[t] +  0.279056782460857Y4[t] +  0.178003476798794M1[t] +  0.104752669320572M2[t] -0.0801731217262057M3[t] +  0.0423556268766096M4[t] +  0.0171277878745154M5[t] -0.116439585377464M6[t] +  0.00509285983473205M7[t] +  0.587598277423118M8[t] -0.414899756293283M9[t] +  0.0271031893206197M10[t] +  0.096307817332781M11[t] +  0.00124435720083027t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68909&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.0550574197115133 +  0.00893293499343105X[t] +  1.58397870443630Y1[t] -0.915092663015896Y2[t] +  0.042692859676686Y3[t] +  0.279056782460857Y4[t] +  0.178003476798794M1[t] +  0.104752669320572M2[t] -0.0801731217262057M3[t] +  0.0423556268766096M4[t] +  0.0171277878745154M5[t] -0.116439585377464M6[t] +  0.00509285983473205M7[t] +  0.587598277423118M8[t] -0.414899756293283M9[t] +  0.0271031893206197M10[t] +  0.096307817332781M11[t] +  0.00124435720083027t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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] = -0.0550574197115133 + 0.00893293499343105X[t] + 1.58397870443630Y1[t] -0.915092663015896Y2[t] + 0.042692859676686Y3[t] + 0.279056782460857Y4[t] + 0.178003476798794M1[t] + 0.104752669320572M2[t] -0.0801731217262057M3[t] + 0.0423556268766096M4[t] + 0.0171277878745154M5[t] -0.116439585377464M6[t] + 0.00509285983473205M7[t] + 0.587598277423118M8[t] -0.414899756293283M9[t] + 0.0271031893206197M10[t] + 0.096307817332781M11[t] + 0.00124435720083027t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.05505741971151331.179969-0.04670.9630290.481514
X0.008932934993431050.0265480.33650.7383550.369177
Y11.583978704436300.1598899.906800
Y2-0.9150926630158960.30955-2.95620.0053270.002664
Y30.0426928596766860.3099870.13770.8911850.445593
Y40.2790567824608570.1890571.4760.1481710.074085
M10.1780034767987940.1172071.51870.1371120.068556
M20.1047526693205720.126090.83080.4112880.205644
M3-0.08017312172620570.131226-0.6110.5448660.272433
M40.04235562687660960.1279690.3310.7424750.371238
M50.01712778787451540.1223890.13990.8894420.444721
M6-0.1164395853774640.116067-1.00320.3221050.161053
M70.005092859834732050.1174480.04340.9656390.48282
M80.5875982774231180.1192714.92661.7e-058e-06
M9-0.4148997562932830.165026-2.51420.0162860.008143
M100.02710318932061970.1785970.15180.8801820.440091
M110.0963078173327810.1542630.62430.5361550.268078
t0.001244357200830270.0043360.2870.7756880.387844

\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) & -0.0550574197115133 & 1.179969 & -0.0467 & 0.963029 & 0.481514 \tabularnewline
X & 0.00893293499343105 & 0.026548 & 0.3365 & 0.738355 & 0.369177 \tabularnewline
Y1 & 1.58397870443630 & 0.159889 & 9.9068 & 0 & 0 \tabularnewline
Y2 & -0.915092663015896 & 0.30955 & -2.9562 & 0.005327 & 0.002664 \tabularnewline
Y3 & 0.042692859676686 & 0.309987 & 0.1377 & 0.891185 & 0.445593 \tabularnewline
Y4 & 0.279056782460857 & 0.189057 & 1.476 & 0.148171 & 0.074085 \tabularnewline
M1 & 0.178003476798794 & 0.117207 & 1.5187 & 0.137112 & 0.068556 \tabularnewline
M2 & 0.104752669320572 & 0.12609 & 0.8308 & 0.411288 & 0.205644 \tabularnewline
M3 & -0.0801731217262057 & 0.131226 & -0.611 & 0.544866 & 0.272433 \tabularnewline
M4 & 0.0423556268766096 & 0.127969 & 0.331 & 0.742475 & 0.371238 \tabularnewline
M5 & 0.0171277878745154 & 0.122389 & 0.1399 & 0.889442 & 0.444721 \tabularnewline
M6 & -0.116439585377464 & 0.116067 & -1.0032 & 0.322105 & 0.161053 \tabularnewline
M7 & 0.00509285983473205 & 0.117448 & 0.0434 & 0.965639 & 0.48282 \tabularnewline
M8 & 0.587598277423118 & 0.119271 & 4.9266 & 1.7e-05 & 8e-06 \tabularnewline
M9 & -0.414899756293283 & 0.165026 & -2.5142 & 0.016286 & 0.008143 \tabularnewline
M10 & 0.0271031893206197 & 0.178597 & 0.1518 & 0.880182 & 0.440091 \tabularnewline
M11 & 0.096307817332781 & 0.154263 & 0.6243 & 0.536155 & 0.268078 \tabularnewline
t & 0.00124435720083027 & 0.004336 & 0.287 & 0.775688 & 0.387844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68909&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]-0.0550574197115133[/C][C]1.179969[/C][C]-0.0467[/C][C]0.963029[/C][C]0.481514[/C][/ROW]
[ROW][C]X[/C][C]0.00893293499343105[/C][C]0.026548[/C][C]0.3365[/C][C]0.738355[/C][C]0.369177[/C][/ROW]
[ROW][C]Y1[/C][C]1.58397870443630[/C][C]0.159889[/C][C]9.9068[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.915092663015896[/C][C]0.30955[/C][C]-2.9562[/C][C]0.005327[/C][C]0.002664[/C][/ROW]
[ROW][C]Y3[/C][C]0.042692859676686[/C][C]0.309987[/C][C]0.1377[/C][C]0.891185[/C][C]0.445593[/C][/ROW]
[ROW][C]Y4[/C][C]0.279056782460857[/C][C]0.189057[/C][C]1.476[/C][C]0.148171[/C][C]0.074085[/C][/ROW]
[ROW][C]M1[/C][C]0.178003476798794[/C][C]0.117207[/C][C]1.5187[/C][C]0.137112[/C][C]0.068556[/C][/ROW]
[ROW][C]M2[/C][C]0.104752669320572[/C][C]0.12609[/C][C]0.8308[/C][C]0.411288[/C][C]0.205644[/C][/ROW]
[ROW][C]M3[/C][C]-0.0801731217262057[/C][C]0.131226[/C][C]-0.611[/C][C]0.544866[/C][C]0.272433[/C][/ROW]
[ROW][C]M4[/C][C]0.0423556268766096[/C][C]0.127969[/C][C]0.331[/C][C]0.742475[/C][C]0.371238[/C][/ROW]
[ROW][C]M5[/C][C]0.0171277878745154[/C][C]0.122389[/C][C]0.1399[/C][C]0.889442[/C][C]0.444721[/C][/ROW]
[ROW][C]M6[/C][C]-0.116439585377464[/C][C]0.116067[/C][C]-1.0032[/C][C]0.322105[/C][C]0.161053[/C][/ROW]
[ROW][C]M7[/C][C]0.00509285983473205[/C][C]0.117448[/C][C]0.0434[/C][C]0.965639[/C][C]0.48282[/C][/ROW]
[ROW][C]M8[/C][C]0.587598277423118[/C][C]0.119271[/C][C]4.9266[/C][C]1.7e-05[/C][C]8e-06[/C][/ROW]
[ROW][C]M9[/C][C]-0.414899756293283[/C][C]0.165026[/C][C]-2.5142[/C][C]0.016286[/C][C]0.008143[/C][/ROW]
[ROW][C]M10[/C][C]0.0271031893206197[/C][C]0.178597[/C][C]0.1518[/C][C]0.880182[/C][C]0.440091[/C][/ROW]
[ROW][C]M11[/C][C]0.096307817332781[/C][C]0.154263[/C][C]0.6243[/C][C]0.536155[/C][C]0.268078[/C][/ROW]
[ROW][C]t[/C][C]0.00124435720083027[/C][C]0.004336[/C][C]0.287[/C][C]0.775688[/C][C]0.387844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68909&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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)-0.05505741971151331.179969-0.04670.9630290.481514
X0.008932934993431050.0265480.33650.7383550.369177
Y11.583978704436300.1598899.906800
Y2-0.9150926630158960.30955-2.95620.0053270.002664
Y30.0426928596766860.3099870.13770.8911850.445593
Y40.2790567824608570.1890571.4760.1481710.074085
M10.1780034767987940.1172071.51870.1371120.068556
M20.1047526693205720.126090.83080.4112880.205644
M3-0.08017312172620570.131226-0.6110.5448660.272433
M40.04235562687660960.1279690.3310.7424750.371238
M50.01712778787451540.1223890.13990.8894420.444721
M6-0.1164395853774640.116067-1.00320.3221050.161053
M70.005092859834732050.1174480.04340.9656390.48282
M80.5875982774231180.1192714.92661.7e-058e-06
M9-0.4148997562932830.165026-2.51420.0162860.008143
M100.02710318932061970.1785970.15180.8801820.440091
M110.0963078173327810.1542630.62430.5361550.268078
t0.001244357200830270.0043360.2870.7756880.387844






Multiple Linear Regression - Regression Statistics
Multiple R0.976501869273433
R-squared0.95355590069451
Adjusted R-squared0.932778277321001
F-TEST (value)45.8934057833718
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.172455242697452
Sum Squared Residuals1.13015080788581

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.976501869273433 \tabularnewline
R-squared & 0.95355590069451 \tabularnewline
Adjusted R-squared & 0.932778277321001 \tabularnewline
F-TEST (value) & 45.8934057833718 \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 & 0.172455242697452 \tabularnewline
Sum Squared Residuals & 1.13015080788581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68909&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.976501869273433[/C][/ROW]
[ROW][C]R-squared[/C][C]0.95355590069451[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.932778277321001[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]45.8934057833718[/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]0.172455242697452[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.13015080788581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68909&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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 R0.976501869273433
R-squared0.95355590069451
Adjusted R-squared0.932778277321001
F-TEST (value)45.8934057833718
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.172455242697452
Sum Squared Residuals1.13015080788581






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.38.1786197407810.121380259219002
28.58.69783507014851-0.19783507014851
38.68.55333949207140.0466605079286011
48.58.52169929794945-0.0216992979494524
58.28.28067975558702-0.0806797555870215
68.17.823859743467070.276140256532932
77.98.08997604061702-0.189976040617023
88.68.407725804671480.192274195328521
98.78.612076020157260.0879239798427446
108.78.53760537262240.162394627377589
118.58.483472388820580.0165276111794232
128.48.272115514990980.127884485009021
138.58.50835615689295-0.0083561568929538
148.78.677718271425440.0222817285745550
158.78.659242669705320.0407573302946741
168.68.571001089631320.0289989103686828
178.58.428637161565220.0713628384347812
188.38.287023484862890.0129765151371135
1988.17756464622455-0.177564646224547
208.28.43607108457295-0.236071084572955
218.17.988803404168650.111196595831355
228.18.018441915544020.081558084455979
2388.103435117257-0.103435117256995
247.97.90419573770395-0.00419573770394694
257.97.98954258281479-0.0895425828147887
2688.00120293887395-0.00120293887394611
2787.944637704757220.0553622952427837
287.97.94899586601319-0.0489958660131867
2987.770883799735960.229116200264037
307.77.9119071311794-0.211907131179402
317.27.46371176999228-0.263711769992281
327.57.5063635991897-0.00636359918970111
337.37.4520543923567-0.152054392356704
3477.20070127780149-0.200701277801494
3576.85940099895410.140599001045902
3677.12029685502524-0.120296855025238
377.27.23271206162837-0.0327120616283708
387.37.39735749149736-0.0973574914973551
397.17.1899486889912-0.0899486889912003
406.86.92110170753608-0.121101707536079
416.46.66234390896892-0.262343908968915
426.16.1992572513522-0.0992572513521968
436.56.150511347740910.349488652259086
447.77.542479518099830.157520481900168
457.97.9470661833174-0.0470661833173954
467.57.54325143403207-0.0432514340320731
476.96.95369149496833-0.0536914949683296
486.66.60339189227984-0.00339189227983658
496.96.890769457882890.00923054211711141
507.77.425886228054740.274113771945256
5188.05283144447486-0.0528314444748587
5287.837202038869960.162797961130035
537.77.657455374142880.0425446258571185
547.37.277952389138450.0220476108615526
557.47.118236195425230.281763804574765
568.18.20735999346603-0.107359993466033

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.3 & 8.178619740781 & 0.121380259219002 \tabularnewline
2 & 8.5 & 8.69783507014851 & -0.19783507014851 \tabularnewline
3 & 8.6 & 8.5533394920714 & 0.0466605079286011 \tabularnewline
4 & 8.5 & 8.52169929794945 & -0.0216992979494524 \tabularnewline
5 & 8.2 & 8.28067975558702 & -0.0806797555870215 \tabularnewline
6 & 8.1 & 7.82385974346707 & 0.276140256532932 \tabularnewline
7 & 7.9 & 8.08997604061702 & -0.189976040617023 \tabularnewline
8 & 8.6 & 8.40772580467148 & 0.192274195328521 \tabularnewline
9 & 8.7 & 8.61207602015726 & 0.0879239798427446 \tabularnewline
10 & 8.7 & 8.5376053726224 & 0.162394627377589 \tabularnewline
11 & 8.5 & 8.48347238882058 & 0.0165276111794232 \tabularnewline
12 & 8.4 & 8.27211551499098 & 0.127884485009021 \tabularnewline
13 & 8.5 & 8.50835615689295 & -0.0083561568929538 \tabularnewline
14 & 8.7 & 8.67771827142544 & 0.0222817285745550 \tabularnewline
15 & 8.7 & 8.65924266970532 & 0.0407573302946741 \tabularnewline
16 & 8.6 & 8.57100108963132 & 0.0289989103686828 \tabularnewline
17 & 8.5 & 8.42863716156522 & 0.0713628384347812 \tabularnewline
18 & 8.3 & 8.28702348486289 & 0.0129765151371135 \tabularnewline
19 & 8 & 8.17756464622455 & -0.177564646224547 \tabularnewline
20 & 8.2 & 8.43607108457295 & -0.236071084572955 \tabularnewline
21 & 8.1 & 7.98880340416865 & 0.111196595831355 \tabularnewline
22 & 8.1 & 8.01844191554402 & 0.081558084455979 \tabularnewline
23 & 8 & 8.103435117257 & -0.103435117256995 \tabularnewline
24 & 7.9 & 7.90419573770395 & -0.00419573770394694 \tabularnewline
25 & 7.9 & 7.98954258281479 & -0.0895425828147887 \tabularnewline
26 & 8 & 8.00120293887395 & -0.00120293887394611 \tabularnewline
27 & 8 & 7.94463770475722 & 0.0553622952427837 \tabularnewline
28 & 7.9 & 7.94899586601319 & -0.0489958660131867 \tabularnewline
29 & 8 & 7.77088379973596 & 0.229116200264037 \tabularnewline
30 & 7.7 & 7.9119071311794 & -0.211907131179402 \tabularnewline
31 & 7.2 & 7.46371176999228 & -0.263711769992281 \tabularnewline
32 & 7.5 & 7.5063635991897 & -0.00636359918970111 \tabularnewline
33 & 7.3 & 7.4520543923567 & -0.152054392356704 \tabularnewline
34 & 7 & 7.20070127780149 & -0.200701277801494 \tabularnewline
35 & 7 & 6.8594009989541 & 0.140599001045902 \tabularnewline
36 & 7 & 7.12029685502524 & -0.120296855025238 \tabularnewline
37 & 7.2 & 7.23271206162837 & -0.0327120616283708 \tabularnewline
38 & 7.3 & 7.39735749149736 & -0.0973574914973551 \tabularnewline
39 & 7.1 & 7.1899486889912 & -0.0899486889912003 \tabularnewline
40 & 6.8 & 6.92110170753608 & -0.121101707536079 \tabularnewline
41 & 6.4 & 6.66234390896892 & -0.262343908968915 \tabularnewline
42 & 6.1 & 6.1992572513522 & -0.0992572513521968 \tabularnewline
43 & 6.5 & 6.15051134774091 & 0.349488652259086 \tabularnewline
44 & 7.7 & 7.54247951809983 & 0.157520481900168 \tabularnewline
45 & 7.9 & 7.9470661833174 & -0.0470661833173954 \tabularnewline
46 & 7.5 & 7.54325143403207 & -0.0432514340320731 \tabularnewline
47 & 6.9 & 6.95369149496833 & -0.0536914949683296 \tabularnewline
48 & 6.6 & 6.60339189227984 & -0.00339189227983658 \tabularnewline
49 & 6.9 & 6.89076945788289 & 0.00923054211711141 \tabularnewline
50 & 7.7 & 7.42588622805474 & 0.274113771945256 \tabularnewline
51 & 8 & 8.05283144447486 & -0.0528314444748587 \tabularnewline
52 & 8 & 7.83720203886996 & 0.162797961130035 \tabularnewline
53 & 7.7 & 7.65745537414288 & 0.0425446258571185 \tabularnewline
54 & 7.3 & 7.27795238913845 & 0.0220476108615526 \tabularnewline
55 & 7.4 & 7.11823619542523 & 0.281763804574765 \tabularnewline
56 & 8.1 & 8.20735999346603 & -0.107359993466033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68909&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]8.3[/C][C]8.178619740781[/C][C]0.121380259219002[/C][/ROW]
[ROW][C]2[/C][C]8.5[/C][C]8.69783507014851[/C][C]-0.19783507014851[/C][/ROW]
[ROW][C]3[/C][C]8.6[/C][C]8.5533394920714[/C][C]0.0466605079286011[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.52169929794945[/C][C]-0.0216992979494524[/C][/ROW]
[ROW][C]5[/C][C]8.2[/C][C]8.28067975558702[/C][C]-0.0806797555870215[/C][/ROW]
[ROW][C]6[/C][C]8.1[/C][C]7.82385974346707[/C][C]0.276140256532932[/C][/ROW]
[ROW][C]7[/C][C]7.9[/C][C]8.08997604061702[/C][C]-0.189976040617023[/C][/ROW]
[ROW][C]8[/C][C]8.6[/C][C]8.40772580467148[/C][C]0.192274195328521[/C][/ROW]
[ROW][C]9[/C][C]8.7[/C][C]8.61207602015726[/C][C]0.0879239798427446[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]8.5376053726224[/C][C]0.162394627377589[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.48347238882058[/C][C]0.0165276111794232[/C][/ROW]
[ROW][C]12[/C][C]8.4[/C][C]8.27211551499098[/C][C]0.127884485009021[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.50835615689295[/C][C]-0.0083561568929538[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.67771827142544[/C][C]0.0222817285745550[/C][/ROW]
[ROW][C]15[/C][C]8.7[/C][C]8.65924266970532[/C][C]0.0407573302946741[/C][/ROW]
[ROW][C]16[/C][C]8.6[/C][C]8.57100108963132[/C][C]0.0289989103686828[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.42863716156522[/C][C]0.0713628384347812[/C][/ROW]
[ROW][C]18[/C][C]8.3[/C][C]8.28702348486289[/C][C]0.0129765151371135[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]8.17756464622455[/C][C]-0.177564646224547[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.43607108457295[/C][C]-0.236071084572955[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.98880340416865[/C][C]0.111196595831355[/C][/ROW]
[ROW][C]22[/C][C]8.1[/C][C]8.01844191554402[/C][C]0.081558084455979[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.103435117257[/C][C]-0.103435117256995[/C][/ROW]
[ROW][C]24[/C][C]7.9[/C][C]7.90419573770395[/C][C]-0.00419573770394694[/C][/ROW]
[ROW][C]25[/C][C]7.9[/C][C]7.98954258281479[/C][C]-0.0895425828147887[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.00120293887395[/C][C]-0.00120293887394611[/C][/ROW]
[ROW][C]27[/C][C]8[/C][C]7.94463770475722[/C][C]0.0553622952427837[/C][/ROW]
[ROW][C]28[/C][C]7.9[/C][C]7.94899586601319[/C][C]-0.0489958660131867[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]7.77088379973596[/C][C]0.229116200264037[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.9119071311794[/C][C]-0.211907131179402[/C][/ROW]
[ROW][C]31[/C][C]7.2[/C][C]7.46371176999228[/C][C]-0.263711769992281[/C][/ROW]
[ROW][C]32[/C][C]7.5[/C][C]7.5063635991897[/C][C]-0.00636359918970111[/C][/ROW]
[ROW][C]33[/C][C]7.3[/C][C]7.4520543923567[/C][C]-0.152054392356704[/C][/ROW]
[ROW][C]34[/C][C]7[/C][C]7.20070127780149[/C][C]-0.200701277801494[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]6.8594009989541[/C][C]0.140599001045902[/C][/ROW]
[ROW][C]36[/C][C]7[/C][C]7.12029685502524[/C][C]-0.120296855025238[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.23271206162837[/C][C]-0.0327120616283708[/C][/ROW]
[ROW][C]38[/C][C]7.3[/C][C]7.39735749149736[/C][C]-0.0973574914973551[/C][/ROW]
[ROW][C]39[/C][C]7.1[/C][C]7.1899486889912[/C][C]-0.0899486889912003[/C][/ROW]
[ROW][C]40[/C][C]6.8[/C][C]6.92110170753608[/C][C]-0.121101707536079[/C][/ROW]
[ROW][C]41[/C][C]6.4[/C][C]6.66234390896892[/C][C]-0.262343908968915[/C][/ROW]
[ROW][C]42[/C][C]6.1[/C][C]6.1992572513522[/C][C]-0.0992572513521968[/C][/ROW]
[ROW][C]43[/C][C]6.5[/C][C]6.15051134774091[/C][C]0.349488652259086[/C][/ROW]
[ROW][C]44[/C][C]7.7[/C][C]7.54247951809983[/C][C]0.157520481900168[/C][/ROW]
[ROW][C]45[/C][C]7.9[/C][C]7.9470661833174[/C][C]-0.0470661833173954[/C][/ROW]
[ROW][C]46[/C][C]7.5[/C][C]7.54325143403207[/C][C]-0.0432514340320731[/C][/ROW]
[ROW][C]47[/C][C]6.9[/C][C]6.95369149496833[/C][C]-0.0536914949683296[/C][/ROW]
[ROW][C]48[/C][C]6.6[/C][C]6.60339189227984[/C][C]-0.00339189227983658[/C][/ROW]
[ROW][C]49[/C][C]6.9[/C][C]6.89076945788289[/C][C]0.00923054211711141[/C][/ROW]
[ROW][C]50[/C][C]7.7[/C][C]7.42588622805474[/C][C]0.274113771945256[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.05283144447486[/C][C]-0.0528314444748587[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]7.83720203886996[/C][C]0.162797961130035[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.65745537414288[/C][C]0.0425446258571185[/C][/ROW]
[ROW][C]54[/C][C]7.3[/C][C]7.27795238913845[/C][C]0.0220476108615526[/C][/ROW]
[ROW][C]55[/C][C]7.4[/C][C]7.11823619542523[/C][C]0.281763804574765[/C][/ROW]
[ROW][C]56[/C][C]8.1[/C][C]8.20735999346603[/C][C]-0.107359993466033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68909&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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
18.38.1786197407810.121380259219002
28.58.69783507014851-0.19783507014851
38.68.55333949207140.0466605079286011
48.58.52169929794945-0.0216992979494524
58.28.28067975558702-0.0806797555870215
68.17.823859743467070.276140256532932
77.98.08997604061702-0.189976040617023
88.68.407725804671480.192274195328521
98.78.612076020157260.0879239798427446
108.78.53760537262240.162394627377589
118.58.483472388820580.0165276111794232
128.48.272115514990980.127884485009021
138.58.50835615689295-0.0083561568929538
148.78.677718271425440.0222817285745550
158.78.659242669705320.0407573302946741
168.68.571001089631320.0289989103686828
178.58.428637161565220.0713628384347812
188.38.287023484862890.0129765151371135
1988.17756464622455-0.177564646224547
208.28.43607108457295-0.236071084572955
218.17.988803404168650.111196595831355
228.18.018441915544020.081558084455979
2388.103435117257-0.103435117256995
247.97.90419573770395-0.00419573770394694
257.97.98954258281479-0.0895425828147887
2688.00120293887395-0.00120293887394611
2787.944637704757220.0553622952427837
287.97.94899586601319-0.0489958660131867
2987.770883799735960.229116200264037
307.77.9119071311794-0.211907131179402
317.27.46371176999228-0.263711769992281
327.57.5063635991897-0.00636359918970111
337.37.4520543923567-0.152054392356704
3477.20070127780149-0.200701277801494
3576.85940099895410.140599001045902
3677.12029685502524-0.120296855025238
377.27.23271206162837-0.0327120616283708
387.37.39735749149736-0.0973574914973551
397.17.1899486889912-0.0899486889912003
406.86.92110170753608-0.121101707536079
416.46.66234390896892-0.262343908968915
426.16.1992572513522-0.0992572513521968
436.56.150511347740910.349488652259086
447.77.542479518099830.157520481900168
457.97.9470661833174-0.0470661833173954
467.57.54325143403207-0.0432514340320731
476.96.95369149496833-0.0536914949683296
486.66.60339189227984-0.00339189227983658
496.96.890769457882890.00923054211711141
507.77.425886228054740.274113771945256
5188.05283144447486-0.0528314444748587
5287.837202038869960.162797961130035
537.77.657455374142880.0425446258571185
547.37.277952389138450.0220476108615526
557.47.118236195425230.281763804574765
568.18.20735999346603-0.107359993466033






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.6016513629576230.7966972740847540.398348637042377
220.512205224388310.975589551223380.48779477561169
230.3632720127863490.7265440255726970.636727987213651
240.2407731248502600.4815462497005210.75922687514974
250.1422128249803250.2844256499606500.857787175019675
260.08503959794282330.1700791958856470.914960402057177
270.05793121440909370.1158624288181870.942068785590906
280.02856584520784760.05713169041569530.971434154792152
290.3001159935473080.6002319870946150.699884006452692
300.3167224318933360.6334448637866710.683277568106664
310.2174131951312900.4348263902625810.78258680486871
320.2621498384488160.5242996768976320.737850161551184
330.2187964544257990.4375929088515990.7812035455742
340.2102114341075670.4204228682151330.789788565892433
350.2966237212040770.5932474424081530.703376278795923

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.601651362957623 & 0.796697274084754 & 0.398348637042377 \tabularnewline
22 & 0.51220522438831 & 0.97558955122338 & 0.48779477561169 \tabularnewline
23 & 0.363272012786349 & 0.726544025572697 & 0.636727987213651 \tabularnewline
24 & 0.240773124850260 & 0.481546249700521 & 0.75922687514974 \tabularnewline
25 & 0.142212824980325 & 0.284425649960650 & 0.857787175019675 \tabularnewline
26 & 0.0850395979428233 & 0.170079195885647 & 0.914960402057177 \tabularnewline
27 & 0.0579312144090937 & 0.115862428818187 & 0.942068785590906 \tabularnewline
28 & 0.0285658452078476 & 0.0571316904156953 & 0.971434154792152 \tabularnewline
29 & 0.300115993547308 & 0.600231987094615 & 0.699884006452692 \tabularnewline
30 & 0.316722431893336 & 0.633444863786671 & 0.683277568106664 \tabularnewline
31 & 0.217413195131290 & 0.434826390262581 & 0.78258680486871 \tabularnewline
32 & 0.262149838448816 & 0.524299676897632 & 0.737850161551184 \tabularnewline
33 & 0.218796454425799 & 0.437592908851599 & 0.7812035455742 \tabularnewline
34 & 0.210211434107567 & 0.420422868215133 & 0.789788565892433 \tabularnewline
35 & 0.296623721204077 & 0.593247442408153 & 0.703376278795923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68909&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]0.601651362957623[/C][C]0.796697274084754[/C][C]0.398348637042377[/C][/ROW]
[ROW][C]22[/C][C]0.51220522438831[/C][C]0.97558955122338[/C][C]0.48779477561169[/C][/ROW]
[ROW][C]23[/C][C]0.363272012786349[/C][C]0.726544025572697[/C][C]0.636727987213651[/C][/ROW]
[ROW][C]24[/C][C]0.240773124850260[/C][C]0.481546249700521[/C][C]0.75922687514974[/C][/ROW]
[ROW][C]25[/C][C]0.142212824980325[/C][C]0.284425649960650[/C][C]0.857787175019675[/C][/ROW]
[ROW][C]26[/C][C]0.0850395979428233[/C][C]0.170079195885647[/C][C]0.914960402057177[/C][/ROW]
[ROW][C]27[/C][C]0.0579312144090937[/C][C]0.115862428818187[/C][C]0.942068785590906[/C][/ROW]
[ROW][C]28[/C][C]0.0285658452078476[/C][C]0.0571316904156953[/C][C]0.971434154792152[/C][/ROW]
[ROW][C]29[/C][C]0.300115993547308[/C][C]0.600231987094615[/C][C]0.699884006452692[/C][/ROW]
[ROW][C]30[/C][C]0.316722431893336[/C][C]0.633444863786671[/C][C]0.683277568106664[/C][/ROW]
[ROW][C]31[/C][C]0.217413195131290[/C][C]0.434826390262581[/C][C]0.78258680486871[/C][/ROW]
[ROW][C]32[/C][C]0.262149838448816[/C][C]0.524299676897632[/C][C]0.737850161551184[/C][/ROW]
[ROW][C]33[/C][C]0.218796454425799[/C][C]0.437592908851599[/C][C]0.7812035455742[/C][/ROW]
[ROW][C]34[/C][C]0.210211434107567[/C][C]0.420422868215133[/C][C]0.789788565892433[/C][/ROW]
[ROW][C]35[/C][C]0.296623721204077[/C][C]0.593247442408153[/C][C]0.703376278795923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68909&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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
210.6016513629576230.7966972740847540.398348637042377
220.512205224388310.975589551223380.48779477561169
230.3632720127863490.7265440255726970.636727987213651
240.2407731248502600.4815462497005210.75922687514974
250.1422128249803250.2844256499606500.857787175019675
260.08503959794282330.1700791958856470.914960402057177
270.05793121440909370.1158624288181870.942068785590906
280.02856584520784760.05713169041569530.971434154792152
290.3001159935473080.6002319870946150.699884006452692
300.3167224318933360.6334448637866710.683277568106664
310.2174131951312900.4348263902625810.78258680486871
320.2621498384488160.5242996768976320.737850161551184
330.2187964544257990.4375929088515990.7812035455742
340.2102114341075670.4204228682151330.789788565892433
350.2966237212040770.5932474424081530.703376278795923






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 level10.0666666666666667OK

\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 & 1 & 0.0666666666666667 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68909&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]1[/C][C]0.0666666666666667[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68909&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68909&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 level10.0666666666666667OK


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')
}