FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 01:47:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258620525uiydyy9ld26l6kb.htm/, Retrieved Fri, 19 Apr 2024 23:45:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57656, Retrieved Fri, 19 Apr 2024 23:45:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184

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]
-   PD      [Multiple Regression] [model 4] [2009-11-19 08:47:36] [c60887983b0820a525cba943a935572d] [Current]
- R  D        [Multiple Regression] [] [2009-12-15 18:57:25] [3445d50c581a74ea3ff7b84cc82fcfeb]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
127	0	130	135	139	149
122	0	127	130	135	139
117	0	122	127	130	135
112	0	117	122	127	130
113	0	112	117	122	127
149	0	113	112	117	122
157	0	149	113	112	117
157	0	157	149	113	112
147	0	157	157	149	113
137	0	147	157	157	149
132	0	137	147	157	157
125	0	132	137	147	157
123	0	125	132	137	147
117	0	123	125	132	137
114	0	117	123	125	132
111	0	114	117	123	125
112	0	111	114	117	123
144	0	112	111	114	117
150	0	144	112	111	114
149	0	150	144	112	111
134	0	149	150	144	112
123	0	134	149	150	144
116	0	123	134	149	150
117	0	116	123	134	149
111	0	117	116	123	134
105	0	111	117	116	123
102	0	105	111	117	116
95	0	102	105	111	117
93	0	95	102	105	111
124	0	93	95	102	105
130	0	124	93	95	102
124	0	130	124	93	95
115	0	124	130	124	93
106	0	115	124	130	124
105	0	106	115	124	130
105	0	105	106	115	124
101	0	105	105	106	115
95	0	101	105	105	106
93	0	95	101	105	105
84	0	93	95	101	105
87	0	84	93	95	101
116	0	87	84	93	95
120	0	116	87	84	93
117	1	120	116	87	84
109	1	117	120	116	87
105	1	109	117	120	116
107	1	105	109	117	120
109	1	107	105	109	117
109	1	109	107	105	109
108	1	109	109	107	105
107	1	108	109	109	107
99	1	107	108	109	109
103	1	99	107	108	109
131	1	103	99	107	108
137	1	131	103	99	107
135	1	137	131	103	99

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=57656&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=57656&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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
WLH[t] = + 28.0537721653424 + 4.5783344490655X[t] + 0.89389373351237`Y(t-1)`[t] + 0.269258267201097`Y(t-2)`[t] -0.239285433868153`Y(t-3)`[t] -0.102477680079240`Y(t-4)`[t] -4.41387550198146M1[t] -7.48459972952515M2[t] -5.74169225100387M3[t] -9.06607666309207M4[t] -2.46464716599568M5[t] + 28.2278520152218M6[t] + 4.32563125183533M7[t] -12.8925239435589M8[t] -15.4919697862306M9[t] -9.03535197334436M10[t] -1.16080135981364M11[t] -0.182589577259004t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WLH[t] =  +  28.0537721653424 +  4.5783344490655X[t] +  0.89389373351237`Y(t-1)`[t] +  0.269258267201097`Y(t-2)`[t] -0.239285433868153`Y(t-3)`[t] -0.102477680079240`Y(t-4)`[t] -4.41387550198146M1[t] -7.48459972952515M2[t] -5.74169225100387M3[t] -9.06607666309207M4[t] -2.46464716599568M5[t] +  28.2278520152218M6[t] +  4.32563125183533M7[t] -12.8925239435589M8[t] -15.4919697862306M9[t] -9.03535197334436M10[t] -1.16080135981364M11[t] -0.182589577259004t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57656&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WLH[t] =  +  28.0537721653424 +  4.5783344490655X[t] +  0.89389373351237`Y(t-1)`[t] +  0.269258267201097`Y(t-2)`[t] -0.239285433868153`Y(t-3)`[t] -0.102477680079240`Y(t-4)`[t] -4.41387550198146M1[t] -7.48459972952515M2[t] -5.74169225100387M3[t] -9.06607666309207M4[t] -2.46464716599568M5[t] +  28.2278520152218M6[t] +  4.32563125183533M7[t] -12.8925239435589M8[t] -15.4919697862306M9[t] -9.03535197334436M10[t] -1.16080135981364M11[t] -0.182589577259004t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57656&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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
WLH[t] = + 28.0537721653424 + 4.5783344490655X[t] + 0.89389373351237`Y(t-1)`[t] + 0.269258267201097`Y(t-2)`[t] -0.239285433868153`Y(t-3)`[t] -0.102477680079240`Y(t-4)`[t] -4.41387550198146M1[t] -7.48459972952515M2[t] -5.74169225100387M3[t] -9.06607666309207M4[t] -2.46464716599568M5[t] + 28.2278520152218M6[t] + 4.32563125183533M7[t] -12.8925239435589M8[t] -15.4919697862306M9[t] -9.03535197334436M10[t] -1.16080135981364M11[t] -0.182589577259004t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)28.05377216534248.9024643.15120.0031660.001583
X4.57833444906551.2778073.5830.0009520.000476
`Y(t-1)`0.893893733512370.1497155.97061e-060
`Y(t-2)`0.2692582672010970.2025921.32910.1917510.095876
`Y(t-3)`-0.2392854338681530.206193-1.16050.2530870.126543
`Y(t-4)`-0.1024776800792400.15661-0.65440.5168270.258413
M1-4.413875501981461.710078-2.58110.0138330.006917
M2-7.484599729525152.199846-3.40230.0015860.000793
M3-5.741692251003872.412995-2.37950.0224610.011231
M4-9.066076663092072.203365-4.11470.0002011e-04
M5-2.464647165995682.424432-1.01660.3157790.157889
M628.22785201522182.26301812.473500
M74.325631251835334.8752510.88730.3805190.190259
M8-12.89252394355895.422589-2.37760.0225640.011282
M9-15.49196978623066.683822-2.31780.025940.01297
M10-9.035351973344363.373712-2.67820.0108750.005437
M11-1.160801359813642.258899-0.51390.6103120.305156
t-0.1825895772590040.053886-3.38840.0016490.000825

\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) & 28.0537721653424 & 8.902464 & 3.1512 & 0.003166 & 0.001583 \tabularnewline
X & 4.5783344490655 & 1.277807 & 3.583 & 0.000952 & 0.000476 \tabularnewline
`Y(t-1)` & 0.89389373351237 & 0.149715 & 5.9706 & 1e-06 & 0 \tabularnewline
`Y(t-2)` & 0.269258267201097 & 0.202592 & 1.3291 & 0.191751 & 0.095876 \tabularnewline
`Y(t-3)` & -0.239285433868153 & 0.206193 & -1.1605 & 0.253087 & 0.126543 \tabularnewline
`Y(t-4)` & -0.102477680079240 & 0.15661 & -0.6544 & 0.516827 & 0.258413 \tabularnewline
M1 & -4.41387550198146 & 1.710078 & -2.5811 & 0.013833 & 0.006917 \tabularnewline
M2 & -7.48459972952515 & 2.199846 & -3.4023 & 0.001586 & 0.000793 \tabularnewline
M3 & -5.74169225100387 & 2.412995 & -2.3795 & 0.022461 & 0.011231 \tabularnewline
M4 & -9.06607666309207 & 2.203365 & -4.1147 & 0.000201 & 1e-04 \tabularnewline
M5 & -2.46464716599568 & 2.424432 & -1.0166 & 0.315779 & 0.157889 \tabularnewline
M6 & 28.2278520152218 & 2.263018 & 12.4735 & 0 & 0 \tabularnewline
M7 & 4.32563125183533 & 4.875251 & 0.8873 & 0.380519 & 0.190259 \tabularnewline
M8 & -12.8925239435589 & 5.422589 & -2.3776 & 0.022564 & 0.011282 \tabularnewline
M9 & -15.4919697862306 & 6.683822 & -2.3178 & 0.02594 & 0.01297 \tabularnewline
M10 & -9.03535197334436 & 3.373712 & -2.6782 & 0.010875 & 0.005437 \tabularnewline
M11 & -1.16080135981364 & 2.258899 & -0.5139 & 0.610312 & 0.305156 \tabularnewline
t & -0.182589577259004 & 0.053886 & -3.3884 & 0.001649 & 0.000825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57656&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]28.0537721653424[/C][C]8.902464[/C][C]3.1512[/C][C]0.003166[/C][C]0.001583[/C][/ROW]
[ROW][C]X[/C][C]4.5783344490655[/C][C]1.277807[/C][C]3.583[/C][C]0.000952[/C][C]0.000476[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.89389373351237[/C][C]0.149715[/C][C]5.9706[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.269258267201097[/C][C]0.202592[/C][C]1.3291[/C][C]0.191751[/C][C]0.095876[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.239285433868153[/C][C]0.206193[/C][C]-1.1605[/C][C]0.253087[/C][C]0.126543[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.102477680079240[/C][C]0.15661[/C][C]-0.6544[/C][C]0.516827[/C][C]0.258413[/C][/ROW]
[ROW][C]M1[/C][C]-4.41387550198146[/C][C]1.710078[/C][C]-2.5811[/C][C]0.013833[/C][C]0.006917[/C][/ROW]
[ROW][C]M2[/C][C]-7.48459972952515[/C][C]2.199846[/C][C]-3.4023[/C][C]0.001586[/C][C]0.000793[/C][/ROW]
[ROW][C]M3[/C][C]-5.74169225100387[/C][C]2.412995[/C][C]-2.3795[/C][C]0.022461[/C][C]0.011231[/C][/ROW]
[ROW][C]M4[/C][C]-9.06607666309207[/C][C]2.203365[/C][C]-4.1147[/C][C]0.000201[/C][C]1e-04[/C][/ROW]
[ROW][C]M5[/C][C]-2.46464716599568[/C][C]2.424432[/C][C]-1.0166[/C][C]0.315779[/C][C]0.157889[/C][/ROW]
[ROW][C]M6[/C][C]28.2278520152218[/C][C]2.263018[/C][C]12.4735[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]4.32563125183533[/C][C]4.875251[/C][C]0.8873[/C][C]0.380519[/C][C]0.190259[/C][/ROW]
[ROW][C]M8[/C][C]-12.8925239435589[/C][C]5.422589[/C][C]-2.3776[/C][C]0.022564[/C][C]0.011282[/C][/ROW]
[ROW][C]M9[/C][C]-15.4919697862306[/C][C]6.683822[/C][C]-2.3178[/C][C]0.02594[/C][C]0.01297[/C][/ROW]
[ROW][C]M10[/C][C]-9.03535197334436[/C][C]3.373712[/C][C]-2.6782[/C][C]0.010875[/C][C]0.005437[/C][/ROW]
[ROW][C]M11[/C][C]-1.16080135981364[/C][C]2.258899[/C][C]-0.5139[/C][C]0.610312[/C][C]0.305156[/C][/ROW]
[ROW][C]t[/C][C]-0.182589577259004[/C][C]0.053886[/C][C]-3.3884[/C][C]0.001649[/C][C]0.000825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57656&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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)28.05377216534248.9024643.15120.0031660.001583
X4.57833444906551.2778073.5830.0009520.000476
`Y(t-1)`0.893893733512370.1497155.97061e-060
`Y(t-2)`0.2692582672010970.2025921.32910.1917510.095876
`Y(t-3)`-0.2392854338681530.206193-1.16050.2530870.126543
`Y(t-4)`-0.1024776800792400.15661-0.65440.5168270.258413
M1-4.413875501981461.710078-2.58110.0138330.006917
M2-7.484599729525152.199846-3.40230.0015860.000793
M3-5.741692251003872.412995-2.37950.0224610.011231
M4-9.066076663092072.203365-4.11470.0002011e-04
M5-2.464647165995682.424432-1.01660.3157790.157889
M628.22785201522182.26301812.473500
M74.325631251835334.8752510.88730.3805190.190259
M8-12.89252394355895.422589-2.37760.0225640.011282
M9-15.49196978623066.683822-2.31780.025940.01297
M10-9.035351973344363.373712-2.67820.0108750.005437
M11-1.160801359813642.258899-0.51390.6103120.305156
t-0.1825895772590040.053886-3.38840.0016490.000825






Multiple Linear Regression - Regression Statistics
Multiple R0.99431080101004
R-squared0.988653969005226
Adjusted R-squared0.98357811303388
F-TEST (value)194.775812116472
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.23576648500679
Sum Squared Residuals189.948767468226

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99431080101004 \tabularnewline
R-squared & 0.988653969005226 \tabularnewline
Adjusted R-squared & 0.98357811303388 \tabularnewline
F-TEST (value) & 194.775812116472 \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 & 2.23576648500679 \tabularnewline
Sum Squared Residuals & 189.948767468226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57656&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99431080101004[/C][/ROW]
[ROW][C]R-squared[/C][C]0.988653969005226[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.98357811303388[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]194.775812116472[/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]2.23576648500679[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]189.948767468226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57656&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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 R0.99431080101004
R-squared0.988653969005226
Adjusted R-squared0.98357811303388
F-TEST (value)194.775812116472
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.23576648500679
Sum Squared Residuals189.948767468226






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1127127.483508875378-0.483508875378087
2122122.184141070298-0.184141070297849
3117120.073553392053-3.07355339205266
4112111.9810641011390.0189358988611628
5113114.088004226987-1.08800422698736
6149145.8543317981903.14566820181027
7157155.9277697009281.07223029907242
8157155.6445753821411.35542461785918
9147146.2998528004860.70014719951383
10137138.031463747192-1.03146374719181
11132133.272083335695-1.27208333569496
12125129.481098117358-4.4810981173583
13123120.6987167070002.30128329300029
14117115.9940115348981.00598846510224
15114113.8398369381570.160163061843093
16111107.2315467733573.768453226643
17112111.8015986544210.198401345578616
18144143.7303495723690.269650427631110
19150149.5446863131620.455313686837538
20149146.1917160983882.80828390161191
21134136.371724984291-2.37172498429149
22123124.253090584287-1.25309058428748
23116117.697765897299-1.69776589729938
24117113.1486397941573.85136020584309
25111111.730565551759-0.730565551759419
26105106.185400131032-1.18540013103232
27102101.2448643547000.755135645299677
289594.77389448473910.226105515260888
299396.178282152071-3.17828215207097
30124124.348318800677-0.348318800676983
31130129.4181287418280.581871258172482
32124126.923667281773-2.92366728177347
33115113.1809259742211.81907402577911
34106105.1818403193650.818159680635145
35105103.2262798719491.77372012805115
36105103.655708501471.34429149852994
37101101.865853180555-0.865853180555036
389596.1985489962842-1.19854899628418
399391.4209491077471.57905089225291
408485.4677797836412-1.46777978364118
418785.1486828909911.85131710900907
42116117.010386238888-1.01038623888843
43120122.014793236677-2.01479323667678
44117120.780890415079-3.780890415079
45109109.147496241001-0.147496241001446
46105103.5336053491561.46639465084415
47107105.8038708950571.19612910494319
48109109.714553587015-0.714553587014742
49109109.221355685308-0.221355685307748
50108106.4378982674881.5621017325121
51107106.4207962073430.579203792656976
5299101.545714857124-2.54571485712387
53103100.7834320755292.21656792447064
54131133.056613589876-2.05661358987597
55137137.094622007406-0.0946220074056544
56135132.4591508226192.54084917738138

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 127 & 127.483508875378 & -0.483508875378087 \tabularnewline
2 & 122 & 122.184141070298 & -0.184141070297849 \tabularnewline
3 & 117 & 120.073553392053 & -3.07355339205266 \tabularnewline
4 & 112 & 111.981064101139 & 0.0189358988611628 \tabularnewline
5 & 113 & 114.088004226987 & -1.08800422698736 \tabularnewline
6 & 149 & 145.854331798190 & 3.14566820181027 \tabularnewline
7 & 157 & 155.927769700928 & 1.07223029907242 \tabularnewline
8 & 157 & 155.644575382141 & 1.35542461785918 \tabularnewline
9 & 147 & 146.299852800486 & 0.70014719951383 \tabularnewline
10 & 137 & 138.031463747192 & -1.03146374719181 \tabularnewline
11 & 132 & 133.272083335695 & -1.27208333569496 \tabularnewline
12 & 125 & 129.481098117358 & -4.4810981173583 \tabularnewline
13 & 123 & 120.698716707000 & 2.30128329300029 \tabularnewline
14 & 117 & 115.994011534898 & 1.00598846510224 \tabularnewline
15 & 114 & 113.839836938157 & 0.160163061843093 \tabularnewline
16 & 111 & 107.231546773357 & 3.768453226643 \tabularnewline
17 & 112 & 111.801598654421 & 0.198401345578616 \tabularnewline
18 & 144 & 143.730349572369 & 0.269650427631110 \tabularnewline
19 & 150 & 149.544686313162 & 0.455313686837538 \tabularnewline
20 & 149 & 146.191716098388 & 2.80828390161191 \tabularnewline
21 & 134 & 136.371724984291 & -2.37172498429149 \tabularnewline
22 & 123 & 124.253090584287 & -1.25309058428748 \tabularnewline
23 & 116 & 117.697765897299 & -1.69776589729938 \tabularnewline
24 & 117 & 113.148639794157 & 3.85136020584309 \tabularnewline
25 & 111 & 111.730565551759 & -0.730565551759419 \tabularnewline
26 & 105 & 106.185400131032 & -1.18540013103232 \tabularnewline
27 & 102 & 101.244864354700 & 0.755135645299677 \tabularnewline
28 & 95 & 94.7738944847391 & 0.226105515260888 \tabularnewline
29 & 93 & 96.178282152071 & -3.17828215207097 \tabularnewline
30 & 124 & 124.348318800677 & -0.348318800676983 \tabularnewline
31 & 130 & 129.418128741828 & 0.581871258172482 \tabularnewline
32 & 124 & 126.923667281773 & -2.92366728177347 \tabularnewline
33 & 115 & 113.180925974221 & 1.81907402577911 \tabularnewline
34 & 106 & 105.181840319365 & 0.818159680635145 \tabularnewline
35 & 105 & 103.226279871949 & 1.77372012805115 \tabularnewline
36 & 105 & 103.65570850147 & 1.34429149852994 \tabularnewline
37 & 101 & 101.865853180555 & -0.865853180555036 \tabularnewline
38 & 95 & 96.1985489962842 & -1.19854899628418 \tabularnewline
39 & 93 & 91.420949107747 & 1.57905089225291 \tabularnewline
40 & 84 & 85.4677797836412 & -1.46777978364118 \tabularnewline
41 & 87 & 85.148682890991 & 1.85131710900907 \tabularnewline
42 & 116 & 117.010386238888 & -1.01038623888843 \tabularnewline
43 & 120 & 122.014793236677 & -2.01479323667678 \tabularnewline
44 & 117 & 120.780890415079 & -3.780890415079 \tabularnewline
45 & 109 & 109.147496241001 & -0.147496241001446 \tabularnewline
46 & 105 & 103.533605349156 & 1.46639465084415 \tabularnewline
47 & 107 & 105.803870895057 & 1.19612910494319 \tabularnewline
48 & 109 & 109.714553587015 & -0.714553587014742 \tabularnewline
49 & 109 & 109.221355685308 & -0.221355685307748 \tabularnewline
50 & 108 & 106.437898267488 & 1.5621017325121 \tabularnewline
51 & 107 & 106.420796207343 & 0.579203792656976 \tabularnewline
52 & 99 & 101.545714857124 & -2.54571485712387 \tabularnewline
53 & 103 & 100.783432075529 & 2.21656792447064 \tabularnewline
54 & 131 & 133.056613589876 & -2.05661358987597 \tabularnewline
55 & 137 & 137.094622007406 & -0.0946220074056544 \tabularnewline
56 & 135 & 132.459150822619 & 2.54084917738138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57656&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]127[/C][C]127.483508875378[/C][C]-0.483508875378087[/C][/ROW]
[ROW][C]2[/C][C]122[/C][C]122.184141070298[/C][C]-0.184141070297849[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]120.073553392053[/C][C]-3.07355339205266[/C][/ROW]
[ROW][C]4[/C][C]112[/C][C]111.981064101139[/C][C]0.0189358988611628[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]114.088004226987[/C][C]-1.08800422698736[/C][/ROW]
[ROW][C]6[/C][C]149[/C][C]145.854331798190[/C][C]3.14566820181027[/C][/ROW]
[ROW][C]7[/C][C]157[/C][C]155.927769700928[/C][C]1.07223029907242[/C][/ROW]
[ROW][C]8[/C][C]157[/C][C]155.644575382141[/C][C]1.35542461785918[/C][/ROW]
[ROW][C]9[/C][C]147[/C][C]146.299852800486[/C][C]0.70014719951383[/C][/ROW]
[ROW][C]10[/C][C]137[/C][C]138.031463747192[/C][C]-1.03146374719181[/C][/ROW]
[ROW][C]11[/C][C]132[/C][C]133.272083335695[/C][C]-1.27208333569496[/C][/ROW]
[ROW][C]12[/C][C]125[/C][C]129.481098117358[/C][C]-4.4810981173583[/C][/ROW]
[ROW][C]13[/C][C]123[/C][C]120.698716707000[/C][C]2.30128329300029[/C][/ROW]
[ROW][C]14[/C][C]117[/C][C]115.994011534898[/C][C]1.00598846510224[/C][/ROW]
[ROW][C]15[/C][C]114[/C][C]113.839836938157[/C][C]0.160163061843093[/C][/ROW]
[ROW][C]16[/C][C]111[/C][C]107.231546773357[/C][C]3.768453226643[/C][/ROW]
[ROW][C]17[/C][C]112[/C][C]111.801598654421[/C][C]0.198401345578616[/C][/ROW]
[ROW][C]18[/C][C]144[/C][C]143.730349572369[/C][C]0.269650427631110[/C][/ROW]
[ROW][C]19[/C][C]150[/C][C]149.544686313162[/C][C]0.455313686837538[/C][/ROW]
[ROW][C]20[/C][C]149[/C][C]146.191716098388[/C][C]2.80828390161191[/C][/ROW]
[ROW][C]21[/C][C]134[/C][C]136.371724984291[/C][C]-2.37172498429149[/C][/ROW]
[ROW][C]22[/C][C]123[/C][C]124.253090584287[/C][C]-1.25309058428748[/C][/ROW]
[ROW][C]23[/C][C]116[/C][C]117.697765897299[/C][C]-1.69776589729938[/C][/ROW]
[ROW][C]24[/C][C]117[/C][C]113.148639794157[/C][C]3.85136020584309[/C][/ROW]
[ROW][C]25[/C][C]111[/C][C]111.730565551759[/C][C]-0.730565551759419[/C][/ROW]
[ROW][C]26[/C][C]105[/C][C]106.185400131032[/C][C]-1.18540013103232[/C][/ROW]
[ROW][C]27[/C][C]102[/C][C]101.244864354700[/C][C]0.755135645299677[/C][/ROW]
[ROW][C]28[/C][C]95[/C][C]94.7738944847391[/C][C]0.226105515260888[/C][/ROW]
[ROW][C]29[/C][C]93[/C][C]96.178282152071[/C][C]-3.17828215207097[/C][/ROW]
[ROW][C]30[/C][C]124[/C][C]124.348318800677[/C][C]-0.348318800676983[/C][/ROW]
[ROW][C]31[/C][C]130[/C][C]129.418128741828[/C][C]0.581871258172482[/C][/ROW]
[ROW][C]32[/C][C]124[/C][C]126.923667281773[/C][C]-2.92366728177347[/C][/ROW]
[ROW][C]33[/C][C]115[/C][C]113.180925974221[/C][C]1.81907402577911[/C][/ROW]
[ROW][C]34[/C][C]106[/C][C]105.181840319365[/C][C]0.818159680635145[/C][/ROW]
[ROW][C]35[/C][C]105[/C][C]103.226279871949[/C][C]1.77372012805115[/C][/ROW]
[ROW][C]36[/C][C]105[/C][C]103.65570850147[/C][C]1.34429149852994[/C][/ROW]
[ROW][C]37[/C][C]101[/C][C]101.865853180555[/C][C]-0.865853180555036[/C][/ROW]
[ROW][C]38[/C][C]95[/C][C]96.1985489962842[/C][C]-1.19854899628418[/C][/ROW]
[ROW][C]39[/C][C]93[/C][C]91.420949107747[/C][C]1.57905089225291[/C][/ROW]
[ROW][C]40[/C][C]84[/C][C]85.4677797836412[/C][C]-1.46777978364118[/C][/ROW]
[ROW][C]41[/C][C]87[/C][C]85.148682890991[/C][C]1.85131710900907[/C][/ROW]
[ROW][C]42[/C][C]116[/C][C]117.010386238888[/C][C]-1.01038623888843[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]122.014793236677[/C][C]-2.01479323667678[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]120.780890415079[/C][C]-3.780890415079[/C][/ROW]
[ROW][C]45[/C][C]109[/C][C]109.147496241001[/C][C]-0.147496241001446[/C][/ROW]
[ROW][C]46[/C][C]105[/C][C]103.533605349156[/C][C]1.46639465084415[/C][/ROW]
[ROW][C]47[/C][C]107[/C][C]105.803870895057[/C][C]1.19612910494319[/C][/ROW]
[ROW][C]48[/C][C]109[/C][C]109.714553587015[/C][C]-0.714553587014742[/C][/ROW]
[ROW][C]49[/C][C]109[/C][C]109.221355685308[/C][C]-0.221355685307748[/C][/ROW]
[ROW][C]50[/C][C]108[/C][C]106.437898267488[/C][C]1.5621017325121[/C][/ROW]
[ROW][C]51[/C][C]107[/C][C]106.420796207343[/C][C]0.579203792656976[/C][/ROW]
[ROW][C]52[/C][C]99[/C][C]101.545714857124[/C][C]-2.54571485712387[/C][/ROW]
[ROW][C]53[/C][C]103[/C][C]100.783432075529[/C][C]2.21656792447064[/C][/ROW]
[ROW][C]54[/C][C]131[/C][C]133.056613589876[/C][C]-2.05661358987597[/C][/ROW]
[ROW][C]55[/C][C]137[/C][C]137.094622007406[/C][C]-0.0946220074056544[/C][/ROW]
[ROW][C]56[/C][C]135[/C][C]132.459150822619[/C][C]2.54084917738138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57656&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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
1127127.483508875378-0.483508875378087
2122122.184141070298-0.184141070297849
3117120.073553392053-3.07355339205266
4112111.9810641011390.0189358988611628
5113114.088004226987-1.08800422698736
6149145.8543317981903.14566820181027
7157155.9277697009281.07223029907242
8157155.6445753821411.35542461785918
9147146.2998528004860.70014719951383
10137138.031463747192-1.03146374719181
11132133.272083335695-1.27208333569496
12125129.481098117358-4.4810981173583
13123120.6987167070002.30128329300029
14117115.9940115348981.00598846510224
15114113.8398369381570.160163061843093
16111107.2315467733573.768453226643
17112111.8015986544210.198401345578616
18144143.7303495723690.269650427631110
19150149.5446863131620.455313686837538
20149146.1917160983882.80828390161191
21134136.371724984291-2.37172498429149
22123124.253090584287-1.25309058428748
23116117.697765897299-1.69776589729938
24117113.1486397941573.85136020584309
25111111.730565551759-0.730565551759419
26105106.185400131032-1.18540013103232
27102101.2448643547000.755135645299677
289594.77389448473910.226105515260888
299396.178282152071-3.17828215207097
30124124.348318800677-0.348318800676983
31130129.4181287418280.581871258172482
32124126.923667281773-2.92366728177347
33115113.1809259742211.81907402577911
34106105.1818403193650.818159680635145
35105103.2262798719491.77372012805115
36105103.655708501471.34429149852994
37101101.865853180555-0.865853180555036
389596.1985489962842-1.19854899628418
399391.4209491077471.57905089225291
408485.4677797836412-1.46777978364118
418785.1486828909911.85131710900907
42116117.010386238888-1.01038623888843
43120122.014793236677-2.01479323667678
44117120.780890415079-3.780890415079
45109109.147496241001-0.147496241001446
46105103.5336053491561.46639465084415
47107105.8038708950571.19612910494319
48109109.714553587015-0.714553587014742
49109109.221355685308-0.221355685307748
50108106.4378982674881.5621017325121
51107106.4207962073430.579203792656976
5299101.545714857124-2.54571485712387
53103100.7834320755292.21656792447064
54131133.056613589876-2.05661358987597
55137137.094622007406-0.0946220074056544
56135132.4591508226192.54084917738138






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.8589785670740720.2820428658518560.141021432925928
220.7489106007343880.5021787985312240.251089399265612
230.7950264933598630.4099470132802730.204973506640137
240.9054659668124110.1890680663751780.094534033187589
250.903244334439060.1935113311218790.0967556655609394
260.8723999809060380.2552000381879240.127600019093962
270.8340753102733110.3318493794533780.165924689726689
280.8557840049721930.2884319900556130.144215995027807
290.9103074412432770.1793851175134470.0896925587567233
300.9465570477450360.1068859045099280.0534429522549638
310.9545349624402940.09093007511941150.0454650375597057
320.941613119485810.1167737610283790.0583868805141893
330.9480207366816560.1039585266366880.0519792633183439
340.8964840291895950.207031941620810.103515970810405
350.8547373496773250.2905253006453500.145262650322675

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.858978567074072 & 0.282042865851856 & 0.141021432925928 \tabularnewline
22 & 0.748910600734388 & 0.502178798531224 & 0.251089399265612 \tabularnewline
23 & 0.795026493359863 & 0.409947013280273 & 0.204973506640137 \tabularnewline
24 & 0.905465966812411 & 0.189068066375178 & 0.094534033187589 \tabularnewline
25 & 0.90324433443906 & 0.193511331121879 & 0.0967556655609394 \tabularnewline
26 & 0.872399980906038 & 0.255200038187924 & 0.127600019093962 \tabularnewline
27 & 0.834075310273311 & 0.331849379453378 & 0.165924689726689 \tabularnewline
28 & 0.855784004972193 & 0.288431990055613 & 0.144215995027807 \tabularnewline
29 & 0.910307441243277 & 0.179385117513447 & 0.0896925587567233 \tabularnewline
30 & 0.946557047745036 & 0.106885904509928 & 0.0534429522549638 \tabularnewline
31 & 0.954534962440294 & 0.0909300751194115 & 0.0454650375597057 \tabularnewline
32 & 0.94161311948581 & 0.116773761028379 & 0.0583868805141893 \tabularnewline
33 & 0.948020736681656 & 0.103958526636688 & 0.0519792633183439 \tabularnewline
34 & 0.896484029189595 & 0.20703194162081 & 0.103515970810405 \tabularnewline
35 & 0.854737349677325 & 0.290525300645350 & 0.145262650322675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57656&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]0.858978567074072[/C][C]0.282042865851856[/C][C]0.141021432925928[/C][/ROW]
[ROW][C]22[/C][C]0.748910600734388[/C][C]0.502178798531224[/C][C]0.251089399265612[/C][/ROW]
[ROW][C]23[/C][C]0.795026493359863[/C][C]0.409947013280273[/C][C]0.204973506640137[/C][/ROW]
[ROW][C]24[/C][C]0.905465966812411[/C][C]0.189068066375178[/C][C]0.094534033187589[/C][/ROW]
[ROW][C]25[/C][C]0.90324433443906[/C][C]0.193511331121879[/C][C]0.0967556655609394[/C][/ROW]
[ROW][C]26[/C][C]0.872399980906038[/C][C]0.255200038187924[/C][C]0.127600019093962[/C][/ROW]
[ROW][C]27[/C][C]0.834075310273311[/C][C]0.331849379453378[/C][C]0.165924689726689[/C][/ROW]
[ROW][C]28[/C][C]0.855784004972193[/C][C]0.288431990055613[/C][C]0.144215995027807[/C][/ROW]
[ROW][C]29[/C][C]0.910307441243277[/C][C]0.179385117513447[/C][C]0.0896925587567233[/C][/ROW]
[ROW][C]30[/C][C]0.946557047745036[/C][C]0.106885904509928[/C][C]0.0534429522549638[/C][/ROW]
[ROW][C]31[/C][C]0.954534962440294[/C][C]0.0909300751194115[/C][C]0.0454650375597057[/C][/ROW]
[ROW][C]32[/C][C]0.94161311948581[/C][C]0.116773761028379[/C][C]0.0583868805141893[/C][/ROW]
[ROW][C]33[/C][C]0.948020736681656[/C][C]0.103958526636688[/C][C]0.0519792633183439[/C][/ROW]
[ROW][C]34[/C][C]0.896484029189595[/C][C]0.20703194162081[/C][C]0.103515970810405[/C][/ROW]
[ROW][C]35[/C][C]0.854737349677325[/C][C]0.290525300645350[/C][C]0.145262650322675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57656&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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
210.8589785670740720.2820428658518560.141021432925928
220.7489106007343880.5021787985312240.251089399265612
230.7950264933598630.4099470132802730.204973506640137
240.9054659668124110.1890680663751780.094534033187589
250.903244334439060.1935113311218790.0967556655609394
260.8723999809060380.2552000381879240.127600019093962
270.8340753102733110.3318493794533780.165924689726689
280.8557840049721930.2884319900556130.144215995027807
290.9103074412432770.1793851175134470.0896925587567233
300.9465570477450360.1068859045099280.0534429522549638
310.9545349624402940.09093007511941150.0454650375597057
320.941613119485810.1167737610283790.0583868805141893
330.9480207366816560.1039585266366880.0519792633183439
340.8964840291895950.207031941620810.103515970810405
350.8547373496773250.2905253006453500.145262650322675






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=57656&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=57656&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57656&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
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 2
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 3
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 4
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 5
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 6
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 7
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 8
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 9
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


Figure 10
PNG link  
QR Code
Postscript link  
QR Code
PDF link  
QR Code


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')
}