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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 02:45:41 -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/t1261399921uvvrxgk2vo3ihgc.htm/, Retrieved Fri, 03 May 2024 19:05:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70137, Retrieved Fri, 03 May 2024 19:05:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188

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 14:14:11] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-19 15:42:20] [6ba840d2473f9a55d7b3e13093db69b8]
-    D      [Multiple Regression] [] [2009-12-15 15:12:35] [6ba840d2473f9a55d7b3e13093db69b8]
-    D          [Multiple Regression] [] [2009-12-21 09:45:41] [830aa0f7fb5acd5849dbc0c6ad889830] [Current]
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Dataset

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

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=70137&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=70137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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] = -0.292849249941967 + 0.0134244026370332X[t] + 1.08350167270624Y1[t] -0.133309614940154Y2[t] -0.137399955322172M1[t] -0.0238083435085413M2[t] -0.0357127578837311M3[t] -0.044701180135979M4[t] -0.0788911693856083M5[t] + 0.0109118261505348M6[t] -0.0355533832106162M7[t] -0.0810949181381833M8[t] -0.0331665972168241M9[t] + 0.103802503434295M10[t] -0.0288910987831445M11[t] + 0.00270333617091151t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.292849249941967 +  0.0134244026370332X[t] +  1.08350167270624Y1[t] -0.133309614940154Y2[t] -0.137399955322172M1[t] -0.0238083435085413M2[t] -0.0357127578837311M3[t] -0.044701180135979M4[t] -0.0788911693856083M5[t] +  0.0109118261505348M6[t] -0.0355533832106162M7[t] -0.0810949181381833M8[t] -0.0331665972168241M9[t] +  0.103802503434295M10[t] -0.0288910987831445M11[t] +  0.00270333617091151t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70137&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.292849249941967 +  0.0134244026370332X[t] +  1.08350167270624Y1[t] -0.133309614940154Y2[t] -0.137399955322172M1[t] -0.0238083435085413M2[t] -0.0357127578837311M3[t] -0.044701180135979M4[t] -0.0788911693856083M5[t] +  0.0109118261505348M6[t] -0.0355533832106162M7[t] -0.0810949181381833M8[t] -0.0331665972168241M9[t] +  0.103802503434295M10[t] -0.0288910987831445M11[t] +  0.00270333617091151t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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] = -0.292849249941967 + 0.0134244026370332X[t] + 1.08350167270624Y1[t] -0.133309614940154Y2[t] -0.137399955322172M1[t] -0.0238083435085413M2[t] -0.0357127578837311M3[t] -0.044701180135979M4[t] -0.0788911693856083M5[t] + 0.0109118261505348M6[t] -0.0355533832106162M7[t] -0.0810949181381833M8[t] -0.0331665972168241M9[t] + 0.103802503434295M10[t] -0.0288910987831445M11[t] + 0.00270333617091151t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.2928492499419670.45343-0.64590.5220630.261031
X0.01342440263703320.0080121.67560.1016220.050811
Y11.083501672706240.08123313.338200
Y2-0.1333096149401540.112632-1.18360.2435640.121782
M1-0.1373999553221720.275986-0.49790.6213150.310658
M2-0.02380834350854130.275796-0.08630.9316380.465819
M3-0.03571275788373110.275814-0.12950.8976260.448813
M4-0.0447011801359790.276692-0.16160.8724690.436235
M5-0.07889116938560830.275954-0.28590.7764410.388221
M60.01091182615053480.2764340.03950.9687090.484355
M7-0.03555338321061620.276285-0.12870.8982530.449126
M8-0.08109491813818330.276625-0.29320.7709160.385458
M9-0.03316659721682410.290904-0.1140.9097990.454899
M100.1038025034342950.2900520.35790.7223180.361159
M11-0.02889109878314450.290153-0.09960.9211810.460591
t0.002703336170911510.0042630.63410.5296450.264823

\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) & -0.292849249941967 & 0.45343 & -0.6459 & 0.522063 & 0.261031 \tabularnewline
X & 0.0134244026370332 & 0.008012 & 1.6756 & 0.101622 & 0.050811 \tabularnewline
Y1 & 1.08350167270624 & 0.081233 & 13.3382 & 0 & 0 \tabularnewline
Y2 & -0.133309614940154 & 0.112632 & -1.1836 & 0.243564 & 0.121782 \tabularnewline
M1 & -0.137399955322172 & 0.275986 & -0.4979 & 0.621315 & 0.310658 \tabularnewline
M2 & -0.0238083435085413 & 0.275796 & -0.0863 & 0.931638 & 0.465819 \tabularnewline
M3 & -0.0357127578837311 & 0.275814 & -0.1295 & 0.897626 & 0.448813 \tabularnewline
M4 & -0.044701180135979 & 0.276692 & -0.1616 & 0.872469 & 0.436235 \tabularnewline
M5 & -0.0788911693856083 & 0.275954 & -0.2859 & 0.776441 & 0.388221 \tabularnewline
M6 & 0.0109118261505348 & 0.276434 & 0.0395 & 0.968709 & 0.484355 \tabularnewline
M7 & -0.0355533832106162 & 0.276285 & -0.1287 & 0.898253 & 0.449126 \tabularnewline
M8 & -0.0810949181381833 & 0.276625 & -0.2932 & 0.770916 & 0.385458 \tabularnewline
M9 & -0.0331665972168241 & 0.290904 & -0.114 & 0.909799 & 0.454899 \tabularnewline
M10 & 0.103802503434295 & 0.290052 & 0.3579 & 0.722318 & 0.361159 \tabularnewline
M11 & -0.0288910987831445 & 0.290153 & -0.0996 & 0.921181 & 0.460591 \tabularnewline
t & 0.00270333617091151 & 0.004263 & 0.6341 & 0.529645 & 0.264823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70137&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]-0.292849249941967[/C][C]0.45343[/C][C]-0.6459[/C][C]0.522063[/C][C]0.261031[/C][/ROW]
[ROW][C]X[/C][C]0.0134244026370332[/C][C]0.008012[/C][C]1.6756[/C][C]0.101622[/C][C]0.050811[/C][/ROW]
[ROW][C]Y1[/C][C]1.08350167270624[/C][C]0.081233[/C][C]13.3382[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.133309614940154[/C][C]0.112632[/C][C]-1.1836[/C][C]0.243564[/C][C]0.121782[/C][/ROW]
[ROW][C]M1[/C][C]-0.137399955322172[/C][C]0.275986[/C][C]-0.4979[/C][C]0.621315[/C][C]0.310658[/C][/ROW]
[ROW][C]M2[/C][C]-0.0238083435085413[/C][C]0.275796[/C][C]-0.0863[/C][C]0.931638[/C][C]0.465819[/C][/ROW]
[ROW][C]M3[/C][C]-0.0357127578837311[/C][C]0.275814[/C][C]-0.1295[/C][C]0.897626[/C][C]0.448813[/C][/ROW]
[ROW][C]M4[/C][C]-0.044701180135979[/C][C]0.276692[/C][C]-0.1616[/C][C]0.872469[/C][C]0.436235[/C][/ROW]
[ROW][C]M5[/C][C]-0.0788911693856083[/C][C]0.275954[/C][C]-0.2859[/C][C]0.776441[/C][C]0.388221[/C][/ROW]
[ROW][C]M6[/C][C]0.0109118261505348[/C][C]0.276434[/C][C]0.0395[/C][C]0.968709[/C][C]0.484355[/C][/ROW]
[ROW][C]M7[/C][C]-0.0355533832106162[/C][C]0.276285[/C][C]-0.1287[/C][C]0.898253[/C][C]0.449126[/C][/ROW]
[ROW][C]M8[/C][C]-0.0810949181381833[/C][C]0.276625[/C][C]-0.2932[/C][C]0.770916[/C][C]0.385458[/C][/ROW]
[ROW][C]M9[/C][C]-0.0331665972168241[/C][C]0.290904[/C][C]-0.114[/C][C]0.909799[/C][C]0.454899[/C][/ROW]
[ROW][C]M10[/C][C]0.103802503434295[/C][C]0.290052[/C][C]0.3579[/C][C]0.722318[/C][C]0.361159[/C][/ROW]
[ROW][C]M11[/C][C]-0.0288910987831445[/C][C]0.290153[/C][C]-0.0996[/C][C]0.921181[/C][C]0.460591[/C][/ROW]
[ROW][C]t[/C][C]0.00270333617091151[/C][C]0.004263[/C][C]0.6341[/C][C]0.529645[/C][C]0.264823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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)-0.2928492499419670.45343-0.64590.5220630.261031
X0.01342440263703320.0080121.67560.1016220.050811
Y11.083501672706240.08123313.338200
Y2-0.1333096149401540.112632-1.18360.2435640.121782
M1-0.1373999553221720.275986-0.49790.6213150.310658
M2-0.02380834350854130.275796-0.08630.9316380.465819
M3-0.03571275788373110.275814-0.12950.8976260.448813
M4-0.0447011801359790.276692-0.16160.8724690.436235
M5-0.07889116938560830.275954-0.28590.7764410.388221
M60.01091182615053480.2764340.03950.9687090.484355
M7-0.03555338321061620.276285-0.12870.8982530.449126
M8-0.08109491813818330.276625-0.29320.7709160.385458
M9-0.03316659721682410.290904-0.1140.9097990.454899
M100.1038025034342950.2900520.35790.7223180.361159
M11-0.02889109878314450.290153-0.09960.9211810.460591
t0.002703336170911510.0042630.63410.5296450.264823






Multiple Linear Regression - Regression Statistics
Multiple R0.967121489718825
R-squared0.935323975875959
Adjusted R-squared0.911070466829444
F-TEST (value)38.5644804668107
F-TEST (DF numerator)15
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.410025249215748
Sum Squared Residuals6.72482819977743

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.967121489718825 \tabularnewline
R-squared & 0.935323975875959 \tabularnewline
Adjusted R-squared & 0.911070466829444 \tabularnewline
F-TEST (value) & 38.5644804668107 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.410025249215748 \tabularnewline
Sum Squared Residuals & 6.72482819977743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70137&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.967121489718825[/C][/ROW]
[ROW][C]R-squared[/C][C]0.935323975875959[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.911070466829444[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]38.5644804668107[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/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]0.410025249215748[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.72482819977743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70137&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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 R0.967121489718825
R-squared0.935323975875959
Adjusted R-squared0.911070466829444
F-TEST (value)38.5644804668107
F-TEST (DF numerator)15
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.410025249215748
Sum Squared Residuals6.72482819977743






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13.22.521817161151340.678182838848662
22.83.17027898135704-0.370278981357045
32.82.699579429675520.100420570324478
432.673344621924670.326655378075332
53.12.78250641407120.317493585928802
63.13.044741400607160.0552585993928412
733.05333469770135-0.0533346977013491
82.42.90233321396010-0.502333213960105
92.72.302957308571650.397042691428352
1032.779762209578880.220237790421119
112.72.99352316789305-0.293523167893054
122.72.80153191421858-0.101531914218584
1322.64160925348601-0.641609253486014
142.41.986308951368210.413691048631793
152.62.453186307255880.146813692744122
162.42.67434107782542-0.274341077825417
172.32.53826498435541-0.238264984355405
182.42.45298801965133-0.0529880196513338
192.52.477489988106650.0225100118933455
202.62.58845804330050.0115419566994995
212.62.74466154599297-0.144661545992971
222.62.88711230448543-0.287112304485426
232.72.73305155483526-0.033051554835256
242.82.84221347213778-0.0422134721377779
252.62.80110017735640-0.201100177356405
262.62.72888603633747-0.128886036337468
2722.71977839927621-0.719778399276208
2822.07288283256007-0.0728828325600675
292.12.050606379041240.0493936209587626
301.92.22192919221744-0.321929192217443
3122.03742543265894-0.0374254326589376
322.52.070718834844030.429281165155973
332.92.651112807059110.248887192940894
343.33.219971709886490.0800282901135123
353.53.5342150761751-0.0342150761751004
363.83.713170157672920.0868298423270787
374.63.854227515148580.745772484851418
384.44.73164478503763-0.331644785037625
395.34.511300015632950.788699984367051
405.85.416009625758520.383990374241477
415.95.792777311806740.107222688193265
425.66.02700793509096-0.427007935090962
435.85.468410012930140.331589987069861
445.55.496413365686160.00358663431384228
454.65.10126833837627-0.501268338376275
464.24.21315377604920-0.0131537760492046
4743.639210201096590.36078979890341
483.53.443084455970720.0569155440292828
492.32.88124589285766-0.581245892857662
502.21.782881245899660.417118754100345
511.41.71615584815944-0.316155848159444
520.60.963421841931324-0.363421841931324
5300.235844910725424-0.235844910725424
540.5-0.2466665475668980.746666547566898
550.10.36333986860292-0.26333986860292
560.10.04207654220921070.0579234577907893

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.2 & 2.52181716115134 & 0.678182838848662 \tabularnewline
2 & 2.8 & 3.17027898135704 & -0.370278981357045 \tabularnewline
3 & 2.8 & 2.69957942967552 & 0.100420570324478 \tabularnewline
4 & 3 & 2.67334462192467 & 0.326655378075332 \tabularnewline
5 & 3.1 & 2.7825064140712 & 0.317493585928802 \tabularnewline
6 & 3.1 & 3.04474140060716 & 0.0552585993928412 \tabularnewline
7 & 3 & 3.05333469770135 & -0.0533346977013491 \tabularnewline
8 & 2.4 & 2.90233321396010 & -0.502333213960105 \tabularnewline
9 & 2.7 & 2.30295730857165 & 0.397042691428352 \tabularnewline
10 & 3 & 2.77976220957888 & 0.220237790421119 \tabularnewline
11 & 2.7 & 2.99352316789305 & -0.293523167893054 \tabularnewline
12 & 2.7 & 2.80153191421858 & -0.101531914218584 \tabularnewline
13 & 2 & 2.64160925348601 & -0.641609253486014 \tabularnewline
14 & 2.4 & 1.98630895136821 & 0.413691048631793 \tabularnewline
15 & 2.6 & 2.45318630725588 & 0.146813692744122 \tabularnewline
16 & 2.4 & 2.67434107782542 & -0.274341077825417 \tabularnewline
17 & 2.3 & 2.53826498435541 & -0.238264984355405 \tabularnewline
18 & 2.4 & 2.45298801965133 & -0.0529880196513338 \tabularnewline
19 & 2.5 & 2.47748998810665 & 0.0225100118933455 \tabularnewline
20 & 2.6 & 2.5884580433005 & 0.0115419566994995 \tabularnewline
21 & 2.6 & 2.74466154599297 & -0.144661545992971 \tabularnewline
22 & 2.6 & 2.88711230448543 & -0.287112304485426 \tabularnewline
23 & 2.7 & 2.73305155483526 & -0.033051554835256 \tabularnewline
24 & 2.8 & 2.84221347213778 & -0.0422134721377779 \tabularnewline
25 & 2.6 & 2.80110017735640 & -0.201100177356405 \tabularnewline
26 & 2.6 & 2.72888603633747 & -0.128886036337468 \tabularnewline
27 & 2 & 2.71977839927621 & -0.719778399276208 \tabularnewline
28 & 2 & 2.07288283256007 & -0.0728828325600675 \tabularnewline
29 & 2.1 & 2.05060637904124 & 0.0493936209587626 \tabularnewline
30 & 1.9 & 2.22192919221744 & -0.321929192217443 \tabularnewline
31 & 2 & 2.03742543265894 & -0.0374254326589376 \tabularnewline
32 & 2.5 & 2.07071883484403 & 0.429281165155973 \tabularnewline
33 & 2.9 & 2.65111280705911 & 0.248887192940894 \tabularnewline
34 & 3.3 & 3.21997170988649 & 0.0800282901135123 \tabularnewline
35 & 3.5 & 3.5342150761751 & -0.0342150761751004 \tabularnewline
36 & 3.8 & 3.71317015767292 & 0.0868298423270787 \tabularnewline
37 & 4.6 & 3.85422751514858 & 0.745772484851418 \tabularnewline
38 & 4.4 & 4.73164478503763 & -0.331644785037625 \tabularnewline
39 & 5.3 & 4.51130001563295 & 0.788699984367051 \tabularnewline
40 & 5.8 & 5.41600962575852 & 0.383990374241477 \tabularnewline
41 & 5.9 & 5.79277731180674 & 0.107222688193265 \tabularnewline
42 & 5.6 & 6.02700793509096 & -0.427007935090962 \tabularnewline
43 & 5.8 & 5.46841001293014 & 0.331589987069861 \tabularnewline
44 & 5.5 & 5.49641336568616 & 0.00358663431384228 \tabularnewline
45 & 4.6 & 5.10126833837627 & -0.501268338376275 \tabularnewline
46 & 4.2 & 4.21315377604920 & -0.0131537760492046 \tabularnewline
47 & 4 & 3.63921020109659 & 0.36078979890341 \tabularnewline
48 & 3.5 & 3.44308445597072 & 0.0569155440292828 \tabularnewline
49 & 2.3 & 2.88124589285766 & -0.581245892857662 \tabularnewline
50 & 2.2 & 1.78288124589966 & 0.417118754100345 \tabularnewline
51 & 1.4 & 1.71615584815944 & -0.316155848159444 \tabularnewline
52 & 0.6 & 0.963421841931324 & -0.363421841931324 \tabularnewline
53 & 0 & 0.235844910725424 & -0.235844910725424 \tabularnewline
54 & 0.5 & -0.246666547566898 & 0.746666547566898 \tabularnewline
55 & 0.1 & 0.36333986860292 & -0.26333986860292 \tabularnewline
56 & 0.1 & 0.0420765422092107 & 0.0579234577907893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70137&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]2.52181716115134[/C][C]0.678182838848662[/C][/ROW]
[ROW][C]2[/C][C]2.8[/C][C]3.17027898135704[/C][C]-0.370278981357045[/C][/ROW]
[ROW][C]3[/C][C]2.8[/C][C]2.69957942967552[/C][C]0.100420570324478[/C][/ROW]
[ROW][C]4[/C][C]3[/C][C]2.67334462192467[/C][C]0.326655378075332[/C][/ROW]
[ROW][C]5[/C][C]3.1[/C][C]2.7825064140712[/C][C]0.317493585928802[/C][/ROW]
[ROW][C]6[/C][C]3.1[/C][C]3.04474140060716[/C][C]0.0552585993928412[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]3.05333469770135[/C][C]-0.0533346977013491[/C][/ROW]
[ROW][C]8[/C][C]2.4[/C][C]2.90233321396010[/C][C]-0.502333213960105[/C][/ROW]
[ROW][C]9[/C][C]2.7[/C][C]2.30295730857165[/C][C]0.397042691428352[/C][/ROW]
[ROW][C]10[/C][C]3[/C][C]2.77976220957888[/C][C]0.220237790421119[/C][/ROW]
[ROW][C]11[/C][C]2.7[/C][C]2.99352316789305[/C][C]-0.293523167893054[/C][/ROW]
[ROW][C]12[/C][C]2.7[/C][C]2.80153191421858[/C][C]-0.101531914218584[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]2.64160925348601[/C][C]-0.641609253486014[/C][/ROW]
[ROW][C]14[/C][C]2.4[/C][C]1.98630895136821[/C][C]0.413691048631793[/C][/ROW]
[ROW][C]15[/C][C]2.6[/C][C]2.45318630725588[/C][C]0.146813692744122[/C][/ROW]
[ROW][C]16[/C][C]2.4[/C][C]2.67434107782542[/C][C]-0.274341077825417[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.53826498435541[/C][C]-0.238264984355405[/C][/ROW]
[ROW][C]18[/C][C]2.4[/C][C]2.45298801965133[/C][C]-0.0529880196513338[/C][/ROW]
[ROW][C]19[/C][C]2.5[/C][C]2.47748998810665[/C][C]0.0225100118933455[/C][/ROW]
[ROW][C]20[/C][C]2.6[/C][C]2.5884580433005[/C][C]0.0115419566994995[/C][/ROW]
[ROW][C]21[/C][C]2.6[/C][C]2.74466154599297[/C][C]-0.144661545992971[/C][/ROW]
[ROW][C]22[/C][C]2.6[/C][C]2.88711230448543[/C][C]-0.287112304485426[/C][/ROW]
[ROW][C]23[/C][C]2.7[/C][C]2.73305155483526[/C][C]-0.033051554835256[/C][/ROW]
[ROW][C]24[/C][C]2.8[/C][C]2.84221347213778[/C][C]-0.0422134721377779[/C][/ROW]
[ROW][C]25[/C][C]2.6[/C][C]2.80110017735640[/C][C]-0.201100177356405[/C][/ROW]
[ROW][C]26[/C][C]2.6[/C][C]2.72888603633747[/C][C]-0.128886036337468[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]2.71977839927621[/C][C]-0.719778399276208[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]2.07288283256007[/C][C]-0.0728828325600675[/C][/ROW]
[ROW][C]29[/C][C]2.1[/C][C]2.05060637904124[/C][C]0.0493936209587626[/C][/ROW]
[ROW][C]30[/C][C]1.9[/C][C]2.22192919221744[/C][C]-0.321929192217443[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]2.03742543265894[/C][C]-0.0374254326589376[/C][/ROW]
[ROW][C]32[/C][C]2.5[/C][C]2.07071883484403[/C][C]0.429281165155973[/C][/ROW]
[ROW][C]33[/C][C]2.9[/C][C]2.65111280705911[/C][C]0.248887192940894[/C][/ROW]
[ROW][C]34[/C][C]3.3[/C][C]3.21997170988649[/C][C]0.0800282901135123[/C][/ROW]
[ROW][C]35[/C][C]3.5[/C][C]3.5342150761751[/C][C]-0.0342150761751004[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.71317015767292[/C][C]0.0868298423270787[/C][/ROW]
[ROW][C]37[/C][C]4.6[/C][C]3.85422751514858[/C][C]0.745772484851418[/C][/ROW]
[ROW][C]38[/C][C]4.4[/C][C]4.73164478503763[/C][C]-0.331644785037625[/C][/ROW]
[ROW][C]39[/C][C]5.3[/C][C]4.51130001563295[/C][C]0.788699984367051[/C][/ROW]
[ROW][C]40[/C][C]5.8[/C][C]5.41600962575852[/C][C]0.383990374241477[/C][/ROW]
[ROW][C]41[/C][C]5.9[/C][C]5.79277731180674[/C][C]0.107222688193265[/C][/ROW]
[ROW][C]42[/C][C]5.6[/C][C]6.02700793509096[/C][C]-0.427007935090962[/C][/ROW]
[ROW][C]43[/C][C]5.8[/C][C]5.46841001293014[/C][C]0.331589987069861[/C][/ROW]
[ROW][C]44[/C][C]5.5[/C][C]5.49641336568616[/C][C]0.00358663431384228[/C][/ROW]
[ROW][C]45[/C][C]4.6[/C][C]5.10126833837627[/C][C]-0.501268338376275[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.21315377604920[/C][C]-0.0131537760492046[/C][/ROW]
[ROW][C]47[/C][C]4[/C][C]3.63921020109659[/C][C]0.36078979890341[/C][/ROW]
[ROW][C]48[/C][C]3.5[/C][C]3.44308445597072[/C][C]0.0569155440292828[/C][/ROW]
[ROW][C]49[/C][C]2.3[/C][C]2.88124589285766[/C][C]-0.581245892857662[/C][/ROW]
[ROW][C]50[/C][C]2.2[/C][C]1.78288124589966[/C][C]0.417118754100345[/C][/ROW]
[ROW][C]51[/C][C]1.4[/C][C]1.71615584815944[/C][C]-0.316155848159444[/C][/ROW]
[ROW][C]52[/C][C]0.6[/C][C]0.963421841931324[/C][C]-0.363421841931324[/C][/ROW]
[ROW][C]53[/C][C]0[/C][C]0.235844910725424[/C][C]-0.235844910725424[/C][/ROW]
[ROW][C]54[/C][C]0.5[/C][C]-0.246666547566898[/C][C]0.746666547566898[/C][/ROW]
[ROW][C]55[/C][C]0.1[/C][C]0.36333986860292[/C][C]-0.26333986860292[/C][/ROW]
[ROW][C]56[/C][C]0.1[/C][C]0.0420765422092107[/C][C]0.0579234577907893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70137&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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
13.22.521817161151340.678182838848662
22.83.17027898135704-0.370278981357045
32.82.699579429675520.100420570324478
432.673344621924670.326655378075332
53.12.78250641407120.317493585928802
63.13.044741400607160.0552585993928412
733.05333469770135-0.0533346977013491
82.42.90233321396010-0.502333213960105
92.72.302957308571650.397042691428352
1032.779762209578880.220237790421119
112.72.99352316789305-0.293523167893054
122.72.80153191421858-0.101531914218584
1322.64160925348601-0.641609253486014
142.41.986308951368210.413691048631793
152.62.453186307255880.146813692744122
162.42.67434107782542-0.274341077825417
172.32.53826498435541-0.238264984355405
182.42.45298801965133-0.0529880196513338
192.52.477489988106650.0225100118933455
202.62.58845804330050.0115419566994995
212.62.74466154599297-0.144661545992971
222.62.88711230448543-0.287112304485426
232.72.73305155483526-0.033051554835256
242.82.84221347213778-0.0422134721377779
252.62.80110017735640-0.201100177356405
262.62.72888603633747-0.128886036337468
2722.71977839927621-0.719778399276208
2822.07288283256007-0.0728828325600675
292.12.050606379041240.0493936209587626
301.92.22192919221744-0.321929192217443
3122.03742543265894-0.0374254326589376
322.52.070718834844030.429281165155973
332.92.651112807059110.248887192940894
343.33.219971709886490.0800282901135123
353.53.5342150761751-0.0342150761751004
363.83.713170157672920.0868298423270787
374.63.854227515148580.745772484851418
384.44.73164478503763-0.331644785037625
395.34.511300015632950.788699984367051
405.85.416009625758520.383990374241477
415.95.792777311806740.107222688193265
425.66.02700793509096-0.427007935090962
435.85.468410012930140.331589987069861
445.55.496413365686160.00358663431384228
454.65.10126833837627-0.501268338376275
464.24.21315377604920-0.0131537760492046
4743.639210201096590.36078979890341
483.53.443084455970720.0569155440292828
492.32.88124589285766-0.581245892857662
502.21.782881245899660.417118754100345
511.41.71615584815944-0.316155848159444
520.60.963421841931324-0.363421841931324
5300.235844910725424-0.235844910725424
540.5-0.2466665475668980.746666547566898
550.10.36333986860292-0.26333986860292
560.10.04207654220921070.0579234577907893






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.1597260648738170.3194521297476340.840273935126183
200.4663948525194980.9327897050389950.533605147480502
210.4045510977188050.8091021954376090.595448902281196
220.2785774703497280.5571549406994550.721422529650272
230.1818844356910120.3637688713820240.818115564308988
240.1197963194905270.2395926389810550.880203680509473
250.06785988877178620.1357197775435720.932140111228214
260.03919445546403450.0783889109280690.960805544535966
270.0607651659052670.1215303318105340.939234834094733
280.07265874298409250.1453174859681850.927341257015908
290.0627390856725660.1254781713451320.937260914327434
300.1031098446107810.2062196892215620.896890155389219
310.08481801438846710.1696360287769340.915181985611533
320.06042139671204360.1208427934240870.939578603287956
330.05801516153523570.1160303230704710.941984838464764
340.03581855857598480.07163711715196960.964181441424015
350.02975516388148110.05951032776296210.97024483611852
360.02397398362686350.0479479672537270.976026016373136
370.03773676016473210.07547352032946420.962263239835268

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.159726064873817 & 0.319452129747634 & 0.840273935126183 \tabularnewline
20 & 0.466394852519498 & 0.932789705038995 & 0.533605147480502 \tabularnewline
21 & 0.404551097718805 & 0.809102195437609 & 0.595448902281196 \tabularnewline
22 & 0.278577470349728 & 0.557154940699455 & 0.721422529650272 \tabularnewline
23 & 0.181884435691012 & 0.363768871382024 & 0.818115564308988 \tabularnewline
24 & 0.119796319490527 & 0.239592638981055 & 0.880203680509473 \tabularnewline
25 & 0.0678598887717862 & 0.135719777543572 & 0.932140111228214 \tabularnewline
26 & 0.0391944554640345 & 0.078388910928069 & 0.960805544535966 \tabularnewline
27 & 0.060765165905267 & 0.121530331810534 & 0.939234834094733 \tabularnewline
28 & 0.0726587429840925 & 0.145317485968185 & 0.927341257015908 \tabularnewline
29 & 0.062739085672566 & 0.125478171345132 & 0.937260914327434 \tabularnewline
30 & 0.103109844610781 & 0.206219689221562 & 0.896890155389219 \tabularnewline
31 & 0.0848180143884671 & 0.169636028776934 & 0.915181985611533 \tabularnewline
32 & 0.0604213967120436 & 0.120842793424087 & 0.939578603287956 \tabularnewline
33 & 0.0580151615352357 & 0.116030323070471 & 0.941984838464764 \tabularnewline
34 & 0.0358185585759848 & 0.0716371171519696 & 0.964181441424015 \tabularnewline
35 & 0.0297551638814811 & 0.0595103277629621 & 0.97024483611852 \tabularnewline
36 & 0.0239739836268635 & 0.047947967253727 & 0.976026016373136 \tabularnewline
37 & 0.0377367601647321 & 0.0754735203294642 & 0.962263239835268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70137&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]19[/C][C]0.159726064873817[/C][C]0.319452129747634[/C][C]0.840273935126183[/C][/ROW]
[ROW][C]20[/C][C]0.466394852519498[/C][C]0.932789705038995[/C][C]0.533605147480502[/C][/ROW]
[ROW][C]21[/C][C]0.404551097718805[/C][C]0.809102195437609[/C][C]0.595448902281196[/C][/ROW]
[ROW][C]22[/C][C]0.278577470349728[/C][C]0.557154940699455[/C][C]0.721422529650272[/C][/ROW]
[ROW][C]23[/C][C]0.181884435691012[/C][C]0.363768871382024[/C][C]0.818115564308988[/C][/ROW]
[ROW][C]24[/C][C]0.119796319490527[/C][C]0.239592638981055[/C][C]0.880203680509473[/C][/ROW]
[ROW][C]25[/C][C]0.0678598887717862[/C][C]0.135719777543572[/C][C]0.932140111228214[/C][/ROW]
[ROW][C]26[/C][C]0.0391944554640345[/C][C]0.078388910928069[/C][C]0.960805544535966[/C][/ROW]
[ROW][C]27[/C][C]0.060765165905267[/C][C]0.121530331810534[/C][C]0.939234834094733[/C][/ROW]
[ROW][C]28[/C][C]0.0726587429840925[/C][C]0.145317485968185[/C][C]0.927341257015908[/C][/ROW]
[ROW][C]29[/C][C]0.062739085672566[/C][C]0.125478171345132[/C][C]0.937260914327434[/C][/ROW]
[ROW][C]30[/C][C]0.103109844610781[/C][C]0.206219689221562[/C][C]0.896890155389219[/C][/ROW]
[ROW][C]31[/C][C]0.0848180143884671[/C][C]0.169636028776934[/C][C]0.915181985611533[/C][/ROW]
[ROW][C]32[/C][C]0.0604213967120436[/C][C]0.120842793424087[/C][C]0.939578603287956[/C][/ROW]
[ROW][C]33[/C][C]0.0580151615352357[/C][C]0.116030323070471[/C][C]0.941984838464764[/C][/ROW]
[ROW][C]34[/C][C]0.0358185585759848[/C][C]0.0716371171519696[/C][C]0.964181441424015[/C][/ROW]
[ROW][C]35[/C][C]0.0297551638814811[/C][C]0.0595103277629621[/C][C]0.97024483611852[/C][/ROW]
[ROW][C]36[/C][C]0.0239739836268635[/C][C]0.047947967253727[/C][C]0.976026016373136[/C][/ROW]
[ROW][C]37[/C][C]0.0377367601647321[/C][C]0.0754735203294642[/C][C]0.962263239835268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70137&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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
190.1597260648738170.3194521297476340.840273935126183
200.4663948525194980.9327897050389950.533605147480502
210.4045510977188050.8091021954376090.595448902281196
220.2785774703497280.5571549406994550.721422529650272
230.1818844356910120.3637688713820240.818115564308988
240.1197963194905270.2395926389810550.880203680509473
250.06785988877178620.1357197775435720.932140111228214
260.03919445546403450.0783889109280690.960805544535966
270.0607651659052670.1215303318105340.939234834094733
280.07265874298409250.1453174859681850.927341257015908
290.0627390856725660.1254781713451320.937260914327434
300.1031098446107810.2062196892215620.896890155389219
310.08481801438846710.1696360287769340.915181985611533
320.06042139671204360.1208427934240870.939578603287956
330.05801516153523570.1160303230704710.941984838464764
340.03581855857598480.07163711715196960.964181441424015
350.02975516388148110.05951032776296210.97024483611852
360.02397398362686350.0479479672537270.976026016373136
370.03773676016473210.07547352032946420.962263239835268






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0526315789473684NOK
10% type I error level50.263157894736842NOK

\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 & 0.0526315789473684 & NOK \tabularnewline
10% type I error level & 5 & 0.263157894736842 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70137&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]0.0526315789473684[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.263157894736842[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70137&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70137&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 level10.0526315789473684NOK
10% type I error level50.263157894736842NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}