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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 computationMon, 21 Dec 2009 02:27:51 -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/21/t1261398786hn206ogt0cxk5r0.htm/, Retrieved Tue, 16 Sep 2025 03:05:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70132, Retrieved Tue, 16 Sep 2025 03:05:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact373

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 12:18:41] [6ba840d2473f9a55d7b3e13093db69b8]
-    D      [Multiple Regression] [] [2009-12-15 15:08:14] [6ba840d2473f9a55d7b3e13093db69b8]
-    D          [Multiple Regression] [] [2009-12-21 09:27:51] [830aa0f7fb5acd5849dbc0c6ad889830] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.2	27.6	2.7	2.5	2.4	2.6
2.8	24.9	3.2	2.7	2.5	2.4
2.8	23.8	2.8	3.2	2.7	2.5
3	24.3	2.8	2.8	3.2	2.7
3.1	23.6	3	2.8	2.8	3.2
3.1	24.2	3.1	3	2.8	2.8
3	28.1	3.1	3.1	3	2.8
2.4	30.1	3	3.1	3.1	3
2.7	31.1	2.4	3	3.1	3.1
3	32	2.7	2.4	3	3.1
2.7	32.4	3	2.7	2.4	3
2.7	34	2.7	3	2.7	2.4
2	35.1	2.7	2.7	3	2.7
2.4	37.1	2	2.7	2.7	3
2.6	37.3	2.4	2	2.7	2.7
2.4	38.1	2.6	2.4	2	2.7
2.3	39.5	2.4	2.6	2.4	2
2.4	38.3	2.3	2.4	2.6	2.4
2.5	37.3	2.4	2.3	2.4	2.6
2.6	38.7	2.5	2.4	2.3	2.4
2.6	37.5	2.6	2.5	2.4	2.3
2.6	38.7	2.6	2.6	2.5	2.4
2.7	37.9	2.6	2.6	2.6	2.5
2.8	36.6	2.7	2.6	2.6	2.6
2.6	35.5	2.8	2.7	2.6	2.6
2.6	37.6	2.6	2.8	2.7	2.6
2	38.6	2.6	2.6	2.8	2.7
2	40.3	2	2.6	2.6	2.8
2.1	39	2	2	2.6	2.6
1.9	36.8	2.1	2	2	2.6
2	36.5	1.9	2.1	2	2
2.5	34.1	2	1.9	2.1	2
2.9	34.2	2.5	2	1.9	2.1
3.3	31.9	2.9	2.5	2	1.9
3.5	33.7	3.3	2.9	2.5	2
3.8	33.5	3.5	3.3	2.9	2.5
4.6	33.8	3.8	3.5	3.3	2.9
4.4	29.9	4.6	3.8	3.5	3.3
5.3	32.3	4.4	4.6	3.8	3.5
5.8	30.5	5.3	4.4	4.6	3.8
5.9	28.5	5.8	5.3	4.4	4.6
5.6	29	5.9	5.8	5.3	4.4
5.8	23.8	5.6	5.9	5.8	5.3
5.5	17.9	5.8	5.6	5.9	5.8
4.6	9.9	5.5	5.8	5.6	5.9
4.2	3	4.6	5.5	5.8	5.6
4	4.2	4.2	4.6	5.5	5.8
3.5	0.4	4	4.2	4.6	5.5
2.3	0	3.5	4	4.2	4.6
2.2	2.4	2.3	3.5	4	4.2
1.4	4.2	2.2	2.3	3.5	4
0.6	8.2	1.4	2.2	2.3	3.5
0	9	0.6	1.4	2.2	2.3
0.5	13.6	0	0.6	1.4	2.2
0.1	14	0.5	0	0.6	1.4
0.1	17.6	0.1	0.5	0	0.6

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=70132&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=70132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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] = -0.242263576787918 + 0.0129113644924348X[t] + 1.01716594894248Y1[t] + 0.0309516297256258Y2[t] + 0.145700901873365Y3[t] -0.254856120930677Y4[t] -0.144913611898313M1[t] -0.0373589553748343M2[t] -0.0533338820604968M3[t] -0.0383076101529251M4[t] -0.0856496199108038M5[t] + 0.0022499825194379M6[t] -0.0393277493068645M7[t] -0.0827240337192012M8[t] -0.0267177690437285M9[t] + 0.0851241624145838M10[t] -0.0208085429383358M11[t] + 0.00284223045873546t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.242263576787918 +  0.0129113644924348X[t] +  1.01716594894248Y1[t] +  0.0309516297256258Y2[t] +  0.145700901873365Y3[t] -0.254856120930677Y4[t] -0.144913611898313M1[t] -0.0373589553748343M2[t] -0.0533338820604968M3[t] -0.0383076101529251M4[t] -0.0856496199108038M5[t] +  0.0022499825194379M6[t] -0.0393277493068645M7[t] -0.0827240337192012M8[t] -0.0267177690437285M9[t] +  0.0851241624145838M10[t] -0.0208085429383358M11[t] +  0.00284223045873546t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70132&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.242263576787918 +  0.0129113644924348X[t] +  1.01716594894248Y1[t] +  0.0309516297256258Y2[t] +  0.145700901873365Y3[t] -0.254856120930677Y4[t] -0.144913611898313M1[t] -0.0373589553748343M2[t] -0.0533338820604968M3[t] -0.0383076101529251M4[t] -0.0856496199108038M5[t] +  0.0022499825194379M6[t] -0.0393277493068645M7[t] -0.0827240337192012M8[t] -0.0267177690437285M9[t] +  0.0851241624145838M10[t] -0.0208085429383358M11[t] +  0.00284223045873546t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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] = -0.242263576787918 + 0.0129113644924348X[t] + 1.01716594894248Y1[t] + 0.0309516297256258Y2[t] + 0.145700901873365Y3[t] -0.254856120930677Y4[t] -0.144913611898313M1[t] -0.0373589553748343M2[t] -0.0533338820604968M3[t] -0.0383076101529251M4[t] -0.0856496199108038M5[t] + 0.0022499825194379M6[t] -0.0393277493068645M7[t] -0.0827240337192012M8[t] -0.0267177690437285M9[t] + 0.0851241624145838M10[t] -0.0208085429383358M11[t] + 0.00284223045873546t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.2422635767879180.466128-0.51970.6062620.303131
X0.01291136449243480.0081781.57880.1226760.061338
Y11.017165948942480.1534386.629200
Y20.03095162972562580.2247110.13770.8911730.445587
Y30.1457009018733650.2351180.61970.5391580.269579
Y4-0.2548561209306770.191886-1.32820.1920460.096023
M1-0.1449136118983130.281671-0.51450.6098980.304949
M2-0.03735895537483430.281109-0.13290.8949750.447488
M3-0.05333388206049680.28299-0.18850.8515150.425757
M4-0.03830761015292510.281863-0.13590.8926110.446306
M5-0.08564961991080380.281276-0.30450.7624060.381203
M60.00224998251943790.2817460.0080.993670.496835
M7-0.03932774930686450.282297-0.13930.8899380.444969
M8-0.08272403371920120.281583-0.29380.7705230.385262
M9-0.02671776904372850.296096-0.09020.9285760.464288
M100.08512416241458380.2967880.28680.775810.387905
M11-0.02080854293833580.29656-0.07020.9444290.472215
t0.002842230458735460.0043410.65470.5165950.258298

\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) & -0.242263576787918 & 0.466128 & -0.5197 & 0.606262 & 0.303131 \tabularnewline
X & 0.0129113644924348 & 0.008178 & 1.5788 & 0.122676 & 0.061338 \tabularnewline
Y1 & 1.01716594894248 & 0.153438 & 6.6292 & 0 & 0 \tabularnewline
Y2 & 0.0309516297256258 & 0.224711 & 0.1377 & 0.891173 & 0.445587 \tabularnewline
Y3 & 0.145700901873365 & 0.235118 & 0.6197 & 0.539158 & 0.269579 \tabularnewline
Y4 & -0.254856120930677 & 0.191886 & -1.3282 & 0.192046 & 0.096023 \tabularnewline
M1 & -0.144913611898313 & 0.281671 & -0.5145 & 0.609898 & 0.304949 \tabularnewline
M2 & -0.0373589553748343 & 0.281109 & -0.1329 & 0.894975 & 0.447488 \tabularnewline
M3 & -0.0533338820604968 & 0.28299 & -0.1885 & 0.851515 & 0.425757 \tabularnewline
M4 & -0.0383076101529251 & 0.281863 & -0.1359 & 0.892611 & 0.446306 \tabularnewline
M5 & -0.0856496199108038 & 0.281276 & -0.3045 & 0.762406 & 0.381203 \tabularnewline
M6 & 0.0022499825194379 & 0.281746 & 0.008 & 0.99367 & 0.496835 \tabularnewline
M7 & -0.0393277493068645 & 0.282297 & -0.1393 & 0.889938 & 0.444969 \tabularnewline
M8 & -0.0827240337192012 & 0.281583 & -0.2938 & 0.770523 & 0.385262 \tabularnewline
M9 & -0.0267177690437285 & 0.296096 & -0.0902 & 0.928576 & 0.464288 \tabularnewline
M10 & 0.0851241624145838 & 0.296788 & 0.2868 & 0.77581 & 0.387905 \tabularnewline
M11 & -0.0208085429383358 & 0.29656 & -0.0702 & 0.944429 & 0.472215 \tabularnewline
t & 0.00284223045873546 & 0.004341 & 0.6547 & 0.516595 & 0.258298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70132&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]-0.242263576787918[/C][C]0.466128[/C][C]-0.5197[/C][C]0.606262[/C][C]0.303131[/C][/ROW]
[ROW][C]X[/C][C]0.0129113644924348[/C][C]0.008178[/C][C]1.5788[/C][C]0.122676[/C][C]0.061338[/C][/ROW]
[ROW][C]Y1[/C][C]1.01716594894248[/C][C]0.153438[/C][C]6.6292[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]0.0309516297256258[/C][C]0.224711[/C][C]0.1377[/C][C]0.891173[/C][C]0.445587[/C][/ROW]
[ROW][C]Y3[/C][C]0.145700901873365[/C][C]0.235118[/C][C]0.6197[/C][C]0.539158[/C][C]0.269579[/C][/ROW]
[ROW][C]Y4[/C][C]-0.254856120930677[/C][C]0.191886[/C][C]-1.3282[/C][C]0.192046[/C][C]0.096023[/C][/ROW]
[ROW][C]M1[/C][C]-0.144913611898313[/C][C]0.281671[/C][C]-0.5145[/C][C]0.609898[/C][C]0.304949[/C][/ROW]
[ROW][C]M2[/C][C]-0.0373589553748343[/C][C]0.281109[/C][C]-0.1329[/C][C]0.894975[/C][C]0.447488[/C][/ROW]
[ROW][C]M3[/C][C]-0.0533338820604968[/C][C]0.28299[/C][C]-0.1885[/C][C]0.851515[/C][C]0.425757[/C][/ROW]
[ROW][C]M4[/C][C]-0.0383076101529251[/C][C]0.281863[/C][C]-0.1359[/C][C]0.892611[/C][C]0.446306[/C][/ROW]
[ROW][C]M5[/C][C]-0.0856496199108038[/C][C]0.281276[/C][C]-0.3045[/C][C]0.762406[/C][C]0.381203[/C][/ROW]
[ROW][C]M6[/C][C]0.0022499825194379[/C][C]0.281746[/C][C]0.008[/C][C]0.99367[/C][C]0.496835[/C][/ROW]
[ROW][C]M7[/C][C]-0.0393277493068645[/C][C]0.282297[/C][C]-0.1393[/C][C]0.889938[/C][C]0.444969[/C][/ROW]
[ROW][C]M8[/C][C]-0.0827240337192012[/C][C]0.281583[/C][C]-0.2938[/C][C]0.770523[/C][C]0.385262[/C][/ROW]
[ROW][C]M9[/C][C]-0.0267177690437285[/C][C]0.296096[/C][C]-0.0902[/C][C]0.928576[/C][C]0.464288[/C][/ROW]
[ROW][C]M10[/C][C]0.0851241624145838[/C][C]0.296788[/C][C]0.2868[/C][C]0.77581[/C][C]0.387905[/C][/ROW]
[ROW][C]M11[/C][C]-0.0208085429383358[/C][C]0.29656[/C][C]-0.0702[/C][C]0.944429[/C][C]0.472215[/C][/ROW]
[ROW][C]t[/C][C]0.00284223045873546[/C][C]0.004341[/C][C]0.6547[/C][C]0.516595[/C][C]0.258298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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)-0.2422635767879180.466128-0.51970.6062620.303131
X0.01291136449243480.0081781.57880.1226760.061338
Y11.017165948942480.1534386.629200
Y20.03095162972562580.2247110.13770.8911730.445587
Y30.1457009018733650.2351180.61970.5391580.269579
Y4-0.2548561209306770.191886-1.32820.1920460.096023
M1-0.1449136118983130.281671-0.51450.6098980.304949
M2-0.03735895537483430.281109-0.13290.8949750.447488
M3-0.05333388206049680.28299-0.18850.8515150.425757
M4-0.03830761015292510.281863-0.13590.8926110.446306
M5-0.08564961991080380.281276-0.30450.7624060.381203
M60.00224998251943790.2817460.0080.993670.496835
M7-0.03932774930686450.282297-0.13930.8899380.444969
M8-0.08272403371920120.281583-0.29380.7705230.385262
M9-0.02671776904372850.296096-0.09020.9285760.464288
M100.08512416241458380.2967880.28680.775810.387905
M11-0.02080854293833580.29656-0.07020.9444290.472215
t0.002842230458735460.0043410.65470.5165950.258298






Multiple Linear Regression - Regression Statistics
Multiple R0.967681022755047
R-squared0.936406561800253
Adjusted R-squared0.907956865763524
F-TEST (value)32.9144663124464
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.417141399996893
Sum Squared Residuals6.61226400847197

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.967681022755047 \tabularnewline
R-squared & 0.936406561800253 \tabularnewline
Adjusted R-squared & 0.907956865763524 \tabularnewline
F-TEST (value) & 32.9144663124464 \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 & 0.417141399996893 \tabularnewline
Sum Squared Residuals & 6.61226400847197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70132&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.967681022755047[/C][/ROW]
[ROW][C]R-squared[/C][C]0.936406561800253[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.907956865763524[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]32.9144663124464[/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]0.417141399996893[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.61226400847197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70132&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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 R0.967681022755047
R-squared0.936406561800253
Adjusted R-squared0.907956865763524
F-TEST (value)32.9144663124464
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.417141399996893
Sum Squared Residuals6.61226400847197






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13.22.482802088298780.717197911701219
22.83.13865290594126-0.338652905941261
32.82.723581712340090.0764182876599137
432.757404471812900.242595528187096
53.12.721591505942870.378408494057132
63.13.029929526738950.0700704732610494
733.07378369023911-0.073783690239115
82.42.92093463637734-0.520934636377336
92.72.353814151572860.346185848427139
1032.752127258193130.247872741806868
112.72.9067016736654-0.206701673665402
122.72.85177027760573-0.151770277605728
1322.68186934247295-0.681869342472948
142.41.985905687339080.414094312660918
152.62.43701233905890.162987660941101
162.42.57903314338655-0.179033143386545
172.32.59204605593426-0.292046055934260
182.42.48658506259534-0.0865850625953439
192.52.453448224096220.0465517759037808
202.62.572182972297640.0278170277023637
212.62.76040529018814-0.160405290188138
222.62.88276273056294-0.282762730562939
232.72.75842764216908-0.0584276421690752
242.82.84152462452716-0.0415246245271623
252.62.79006250001272-0.190062500012717
262.62.74180531580045-0.141805315800447
2722.7244781362151-0.724478136215098
2822.09937059638532-0.0993705963853155
292.12.070486289596770.0295137104032333
301.92.14711917437262-0.247119174372616
3122.05708590939979-0.0570859093997912
322.52.095640939800810.404359060199194
332.92.612832916360320.28716708363968
343.33.185704448758040.114295551241955
353.53.5724663002611-0.0724663002611008
363.83.740200942722440.0597990572775602
374.63.869680993635540.730319006364462
384.44.67993953917133-0.27993953917133
395.34.511861278094130.788138721905873
405.85.455852237696650.344147762303352
415.95.688944093517720.211055906482277
425.66.08543605428214-0.485436054282144
435.85.520986777942810.279013222057192
445.55.485545404076650.0144545959233521
454.65.07294764187868-0.472947641878682
464.24.27940556248588-0.0794055624858843
4743.662404383904420.337595616095578
483.53.366504155144670.133495844855331
492.32.87558507558001-0.575585075580015
502.21.853696551747880.346303448252121
511.41.70306653429179-0.303066534291789
520.60.908339550718588-0.308339550718588
5300.326932055008382-0.326932055008382
540.5-0.2490698179890550.749069817989055
550.10.294695398322066-0.194695398322066
560.10.02569604744757320.0743039525524268

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.2 & 2.48280208829878 & 0.717197911701219 \tabularnewline
2 & 2.8 & 3.13865290594126 & -0.338652905941261 \tabularnewline
3 & 2.8 & 2.72358171234009 & 0.0764182876599137 \tabularnewline
4 & 3 & 2.75740447181290 & 0.242595528187096 \tabularnewline
5 & 3.1 & 2.72159150594287 & 0.378408494057132 \tabularnewline
6 & 3.1 & 3.02992952673895 & 0.0700704732610494 \tabularnewline
7 & 3 & 3.07378369023911 & -0.073783690239115 \tabularnewline
8 & 2.4 & 2.92093463637734 & -0.520934636377336 \tabularnewline
9 & 2.7 & 2.35381415157286 & 0.346185848427139 \tabularnewline
10 & 3 & 2.75212725819313 & 0.247872741806868 \tabularnewline
11 & 2.7 & 2.9067016736654 & -0.206701673665402 \tabularnewline
12 & 2.7 & 2.85177027760573 & -0.151770277605728 \tabularnewline
13 & 2 & 2.68186934247295 & -0.681869342472948 \tabularnewline
14 & 2.4 & 1.98590568733908 & 0.414094312660918 \tabularnewline
15 & 2.6 & 2.4370123390589 & 0.162987660941101 \tabularnewline
16 & 2.4 & 2.57903314338655 & -0.179033143386545 \tabularnewline
17 & 2.3 & 2.59204605593426 & -0.292046055934260 \tabularnewline
18 & 2.4 & 2.48658506259534 & -0.0865850625953439 \tabularnewline
19 & 2.5 & 2.45344822409622 & 0.0465517759037808 \tabularnewline
20 & 2.6 & 2.57218297229764 & 0.0278170277023637 \tabularnewline
21 & 2.6 & 2.76040529018814 & -0.160405290188138 \tabularnewline
22 & 2.6 & 2.88276273056294 & -0.282762730562939 \tabularnewline
23 & 2.7 & 2.75842764216908 & -0.0584276421690752 \tabularnewline
24 & 2.8 & 2.84152462452716 & -0.0415246245271623 \tabularnewline
25 & 2.6 & 2.79006250001272 & -0.190062500012717 \tabularnewline
26 & 2.6 & 2.74180531580045 & -0.141805315800447 \tabularnewline
27 & 2 & 2.7244781362151 & -0.724478136215098 \tabularnewline
28 & 2 & 2.09937059638532 & -0.0993705963853155 \tabularnewline
29 & 2.1 & 2.07048628959677 & 0.0295137104032333 \tabularnewline
30 & 1.9 & 2.14711917437262 & -0.247119174372616 \tabularnewline
31 & 2 & 2.05708590939979 & -0.0570859093997912 \tabularnewline
32 & 2.5 & 2.09564093980081 & 0.404359060199194 \tabularnewline
33 & 2.9 & 2.61283291636032 & 0.28716708363968 \tabularnewline
34 & 3.3 & 3.18570444875804 & 0.114295551241955 \tabularnewline
35 & 3.5 & 3.5724663002611 & -0.0724663002611008 \tabularnewline
36 & 3.8 & 3.74020094272244 & 0.0597990572775602 \tabularnewline
37 & 4.6 & 3.86968099363554 & 0.730319006364462 \tabularnewline
38 & 4.4 & 4.67993953917133 & -0.27993953917133 \tabularnewline
39 & 5.3 & 4.51186127809413 & 0.788138721905873 \tabularnewline
40 & 5.8 & 5.45585223769665 & 0.344147762303352 \tabularnewline
41 & 5.9 & 5.68894409351772 & 0.211055906482277 \tabularnewline
42 & 5.6 & 6.08543605428214 & -0.485436054282144 \tabularnewline
43 & 5.8 & 5.52098677794281 & 0.279013222057192 \tabularnewline
44 & 5.5 & 5.48554540407665 & 0.0144545959233521 \tabularnewline
45 & 4.6 & 5.07294764187868 & -0.472947641878682 \tabularnewline
46 & 4.2 & 4.27940556248588 & -0.0794055624858843 \tabularnewline
47 & 4 & 3.66240438390442 & 0.337595616095578 \tabularnewline
48 & 3.5 & 3.36650415514467 & 0.133495844855331 \tabularnewline
49 & 2.3 & 2.87558507558001 & -0.575585075580015 \tabularnewline
50 & 2.2 & 1.85369655174788 & 0.346303448252121 \tabularnewline
51 & 1.4 & 1.70306653429179 & -0.303066534291789 \tabularnewline
52 & 0.6 & 0.908339550718588 & -0.308339550718588 \tabularnewline
53 & 0 & 0.326932055008382 & -0.326932055008382 \tabularnewline
54 & 0.5 & -0.249069817989055 & 0.749069817989055 \tabularnewline
55 & 0.1 & 0.294695398322066 & -0.194695398322066 \tabularnewline
56 & 0.1 & 0.0256960474475732 & 0.0743039525524268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70132&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]3.2[/C][C]2.48280208829878[/C][C]0.717197911701219[/C][/ROW]
[ROW][C]2[/C][C]2.8[/C][C]3.13865290594126[/C][C]-0.338652905941261[/C][/ROW]
[ROW][C]3[/C][C]2.8[/C][C]2.72358171234009[/C][C]0.0764182876599137[/C][/ROW]
[ROW][C]4[/C][C]3[/C][C]2.75740447181290[/C][C]0.242595528187096[/C][/ROW]
[ROW][C]5[/C][C]3.1[/C][C]2.72159150594287[/C][C]0.378408494057132[/C][/ROW]
[ROW][C]6[/C][C]3.1[/C][C]3.02992952673895[/C][C]0.0700704732610494[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]3.07378369023911[/C][C]-0.073783690239115[/C][/ROW]
[ROW][C]8[/C][C]2.4[/C][C]2.92093463637734[/C][C]-0.520934636377336[/C][/ROW]
[ROW][C]9[/C][C]2.7[/C][C]2.35381415157286[/C][C]0.346185848427139[/C][/ROW]
[ROW][C]10[/C][C]3[/C][C]2.75212725819313[/C][C]0.247872741806868[/C][/ROW]
[ROW][C]11[/C][C]2.7[/C][C]2.9067016736654[/C][C]-0.206701673665402[/C][/ROW]
[ROW][C]12[/C][C]2.7[/C][C]2.85177027760573[/C][C]-0.151770277605728[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]2.68186934247295[/C][C]-0.681869342472948[/C][/ROW]
[ROW][C]14[/C][C]2.4[/C][C]1.98590568733908[/C][C]0.414094312660918[/C][/ROW]
[ROW][C]15[/C][C]2.6[/C][C]2.4370123390589[/C][C]0.162987660941101[/C][/ROW]
[ROW][C]16[/C][C]2.4[/C][C]2.57903314338655[/C][C]-0.179033143386545[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.59204605593426[/C][C]-0.292046055934260[/C][/ROW]
[ROW][C]18[/C][C]2.4[/C][C]2.48658506259534[/C][C]-0.0865850625953439[/C][/ROW]
[ROW][C]19[/C][C]2.5[/C][C]2.45344822409622[/C][C]0.0465517759037808[/C][/ROW]
[ROW][C]20[/C][C]2.6[/C][C]2.57218297229764[/C][C]0.0278170277023637[/C][/ROW]
[ROW][C]21[/C][C]2.6[/C][C]2.76040529018814[/C][C]-0.160405290188138[/C][/ROW]
[ROW][C]22[/C][C]2.6[/C][C]2.88276273056294[/C][C]-0.282762730562939[/C][/ROW]
[ROW][C]23[/C][C]2.7[/C][C]2.75842764216908[/C][C]-0.0584276421690752[/C][/ROW]
[ROW][C]24[/C][C]2.8[/C][C]2.84152462452716[/C][C]-0.0415246245271623[/C][/ROW]
[ROW][C]25[/C][C]2.6[/C][C]2.79006250001272[/C][C]-0.190062500012717[/C][/ROW]
[ROW][C]26[/C][C]2.6[/C][C]2.74180531580045[/C][C]-0.141805315800447[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]2.7244781362151[/C][C]-0.724478136215098[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]2.09937059638532[/C][C]-0.0993705963853155[/C][/ROW]
[ROW][C]29[/C][C]2.1[/C][C]2.07048628959677[/C][C]0.0295137104032333[/C][/ROW]
[ROW][C]30[/C][C]1.9[/C][C]2.14711917437262[/C][C]-0.247119174372616[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]2.05708590939979[/C][C]-0.0570859093997912[/C][/ROW]
[ROW][C]32[/C][C]2.5[/C][C]2.09564093980081[/C][C]0.404359060199194[/C][/ROW]
[ROW][C]33[/C][C]2.9[/C][C]2.61283291636032[/C][C]0.28716708363968[/C][/ROW]
[ROW][C]34[/C][C]3.3[/C][C]3.18570444875804[/C][C]0.114295551241955[/C][/ROW]
[ROW][C]35[/C][C]3.5[/C][C]3.5724663002611[/C][C]-0.0724663002611008[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.74020094272244[/C][C]0.0597990572775602[/C][/ROW]
[ROW][C]37[/C][C]4.6[/C][C]3.86968099363554[/C][C]0.730319006364462[/C][/ROW]
[ROW][C]38[/C][C]4.4[/C][C]4.67993953917133[/C][C]-0.27993953917133[/C][/ROW]
[ROW][C]39[/C][C]5.3[/C][C]4.51186127809413[/C][C]0.788138721905873[/C][/ROW]
[ROW][C]40[/C][C]5.8[/C][C]5.45585223769665[/C][C]0.344147762303352[/C][/ROW]
[ROW][C]41[/C][C]5.9[/C][C]5.68894409351772[/C][C]0.211055906482277[/C][/ROW]
[ROW][C]42[/C][C]5.6[/C][C]6.08543605428214[/C][C]-0.485436054282144[/C][/ROW]
[ROW][C]43[/C][C]5.8[/C][C]5.52098677794281[/C][C]0.279013222057192[/C][/ROW]
[ROW][C]44[/C][C]5.5[/C][C]5.48554540407665[/C][C]0.0144545959233521[/C][/ROW]
[ROW][C]45[/C][C]4.6[/C][C]5.07294764187868[/C][C]-0.472947641878682[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.27940556248588[/C][C]-0.0794055624858843[/C][/ROW]
[ROW][C]47[/C][C]4[/C][C]3.66240438390442[/C][C]0.337595616095578[/C][/ROW]
[ROW][C]48[/C][C]3.5[/C][C]3.36650415514467[/C][C]0.133495844855331[/C][/ROW]
[ROW][C]49[/C][C]2.3[/C][C]2.87558507558001[/C][C]-0.575585075580015[/C][/ROW]
[ROW][C]50[/C][C]2.2[/C][C]1.85369655174788[/C][C]0.346303448252121[/C][/ROW]
[ROW][C]51[/C][C]1.4[/C][C]1.70306653429179[/C][C]-0.303066534291789[/C][/ROW]
[ROW][C]52[/C][C]0.6[/C][C]0.908339550718588[/C][C]-0.308339550718588[/C][/ROW]
[ROW][C]53[/C][C]0[/C][C]0.326932055008382[/C][C]-0.326932055008382[/C][/ROW]
[ROW][C]54[/C][C]0.5[/C][C]-0.249069817989055[/C][C]0.749069817989055[/C][/ROW]
[ROW][C]55[/C][C]0.1[/C][C]0.294695398322066[/C][C]-0.194695398322066[/C][/ROW]
[ROW][C]56[/C][C]0.1[/C][C]0.0256960474475732[/C][C]0.0743039525524268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70132&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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
13.22.482802088298780.717197911701219
22.83.13865290594126-0.338652905941261
32.82.723581712340090.0764182876599137
432.757404471812900.242595528187096
53.12.721591505942870.378408494057132
63.13.029929526738950.0700704732610494
733.07378369023911-0.073783690239115
82.42.92093463637734-0.520934636377336
92.72.353814151572860.346185848427139
1032.752127258193130.247872741806868
112.72.9067016736654-0.206701673665402
122.72.85177027760573-0.151770277605728
1322.68186934247295-0.681869342472948
142.41.985905687339080.414094312660918
152.62.43701233905890.162987660941101
162.42.57903314338655-0.179033143386545
172.32.59204605593426-0.292046055934260
182.42.48658506259534-0.0865850625953439
192.52.453448224096220.0465517759037808
202.62.572182972297640.0278170277023637
212.62.76040529018814-0.160405290188138
222.62.88276273056294-0.282762730562939
232.72.75842764216908-0.0584276421690752
242.82.84152462452716-0.0415246245271623
252.62.79006250001272-0.190062500012717
262.62.74180531580045-0.141805315800447
2722.7244781362151-0.724478136215098
2822.09937059638532-0.0993705963853155
292.12.070486289596770.0295137104032333
301.92.14711917437262-0.247119174372616
3122.05708590939979-0.0570859093997912
322.52.095640939800810.404359060199194
332.92.612832916360320.28716708363968
343.33.185704448758040.114295551241955
353.53.5724663002611-0.0724663002611008
363.83.740200942722440.0597990572775602
374.63.869680993635540.730319006364462
384.44.67993953917133-0.27993953917133
395.34.511861278094130.788138721905873
405.85.455852237696650.344147762303352
415.95.688944093517720.211055906482277
425.66.08543605428214-0.485436054282144
435.85.520986777942810.279013222057192
445.55.485545404076650.0144545959233521
454.65.07294764187868-0.472947641878682
464.24.27940556248588-0.0794055624858843
4743.662404383904420.337595616095578
483.53.366504155144670.133495844855331
492.32.87558507558001-0.575585075580015
502.21.853696551747880.346303448252121
511.41.70306653429179-0.303066534291789
520.60.908339550718588-0.308339550718588
5300.326932055008382-0.326932055008382
540.5-0.2490698179890550.749069817989055
550.10.294695398322066-0.194695398322066
560.10.02569604744757320.0743039525524268






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.3120806678999290.6241613357998580.687919332100071
220.1788838547804770.3577677095609540.821116145219523
230.1207618697098320.2415237394196650.879238130290168
240.05897851248445120.1179570249689020.941021487515549
250.03370939053550470.06741878107100940.966290609464495
260.02458151418661750.0491630283732350.975418485813383
270.03045152002736810.06090304005473620.969548479972632
280.03401418669770410.06802837339540820.965985813302296
290.05397529388666340.1079505877733270.946024706113337
300.1076607502479760.2153215004959520.892339249752024
310.08122114824412470.1624422964882490.918778851755875
320.04994187950013420.09988375900026840.950058120499866
330.03993276592227040.07986553184454080.96006723407773
340.02861821676488640.05723643352977280.971381783235114
350.05531624646181270.1106324929236250.944683753538187

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.312080667899929 & 0.624161335799858 & 0.687919332100071 \tabularnewline
22 & 0.178883854780477 & 0.357767709560954 & 0.821116145219523 \tabularnewline
23 & 0.120761869709832 & 0.241523739419665 & 0.879238130290168 \tabularnewline
24 & 0.0589785124844512 & 0.117957024968902 & 0.941021487515549 \tabularnewline
25 & 0.0337093905355047 & 0.0674187810710094 & 0.966290609464495 \tabularnewline
26 & 0.0245815141866175 & 0.049163028373235 & 0.975418485813383 \tabularnewline
27 & 0.0304515200273681 & 0.0609030400547362 & 0.969548479972632 \tabularnewline
28 & 0.0340141866977041 & 0.0680283733954082 & 0.965985813302296 \tabularnewline
29 & 0.0539752938866634 & 0.107950587773327 & 0.946024706113337 \tabularnewline
30 & 0.107660750247976 & 0.215321500495952 & 0.892339249752024 \tabularnewline
31 & 0.0812211482441247 & 0.162442296488249 & 0.918778851755875 \tabularnewline
32 & 0.0499418795001342 & 0.0998837590002684 & 0.950058120499866 \tabularnewline
33 & 0.0399327659222704 & 0.0798655318445408 & 0.96006723407773 \tabularnewline
34 & 0.0286182167648864 & 0.0572364335297728 & 0.971381783235114 \tabularnewline
35 & 0.0553162464618127 & 0.110632492923625 & 0.944683753538187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70132&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]0.312080667899929[/C][C]0.624161335799858[/C][C]0.687919332100071[/C][/ROW]
[ROW][C]22[/C][C]0.178883854780477[/C][C]0.357767709560954[/C][C]0.821116145219523[/C][/ROW]
[ROW][C]23[/C][C]0.120761869709832[/C][C]0.241523739419665[/C][C]0.879238130290168[/C][/ROW]
[ROW][C]24[/C][C]0.0589785124844512[/C][C]0.117957024968902[/C][C]0.941021487515549[/C][/ROW]
[ROW][C]25[/C][C]0.0337093905355047[/C][C]0.0674187810710094[/C][C]0.966290609464495[/C][/ROW]
[ROW][C]26[/C][C]0.0245815141866175[/C][C]0.049163028373235[/C][C]0.975418485813383[/C][/ROW]
[ROW][C]27[/C][C]0.0304515200273681[/C][C]0.0609030400547362[/C][C]0.969548479972632[/C][/ROW]
[ROW][C]28[/C][C]0.0340141866977041[/C][C]0.0680283733954082[/C][C]0.965985813302296[/C][/ROW]
[ROW][C]29[/C][C]0.0539752938866634[/C][C]0.107950587773327[/C][C]0.946024706113337[/C][/ROW]
[ROW][C]30[/C][C]0.107660750247976[/C][C]0.215321500495952[/C][C]0.892339249752024[/C][/ROW]
[ROW][C]31[/C][C]0.0812211482441247[/C][C]0.162442296488249[/C][C]0.918778851755875[/C][/ROW]
[ROW][C]32[/C][C]0.0499418795001342[/C][C]0.0998837590002684[/C][C]0.950058120499866[/C][/ROW]
[ROW][C]33[/C][C]0.0399327659222704[/C][C]0.0798655318445408[/C][C]0.96006723407773[/C][/ROW]
[ROW][C]34[/C][C]0.0286182167648864[/C][C]0.0572364335297728[/C][C]0.971381783235114[/C][/ROW]
[ROW][C]35[/C][C]0.0553162464618127[/C][C]0.110632492923625[/C][C]0.944683753538187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70132&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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
210.3120806678999290.6241613357998580.687919332100071
220.1788838547804770.3577677095609540.821116145219523
230.1207618697098320.2415237394196650.879238130290168
240.05897851248445120.1179570249689020.941021487515549
250.03370939053550470.06741878107100940.966290609464495
260.02458151418661750.0491630283732350.975418485813383
270.03045152002736810.06090304005473620.969548479972632
280.03401418669770410.06802837339540820.965985813302296
290.05397529388666340.1079505877733270.946024706113337
300.1076607502479760.2153215004959520.892339249752024
310.08122114824412470.1624422964882490.918778851755875
320.04994187950013420.09988375900026840.950058120499866
330.03993276592227040.07986553184454080.96006723407773
340.02861821676488640.05723643352977280.971381783235114
350.05531624646181270.1106324929236250.944683753538187






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0666666666666667NOK
10% type I error level70.466666666666667NOK

\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 & 1 & 0.0666666666666667 & NOK \tabularnewline
10% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70132&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]1[/C][C]0.0666666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70132&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70132&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 level10.0666666666666667NOK
10% type I error level70.466666666666667NOK


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')
}