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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 12:02:36 -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/t1258657457qnf0pxqxf56cnzy.htm/, Retrieved Tue, 23 Apr 2024 13:01:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57900, Retrieved Tue, 23 Apr 2024 13:01:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Indicator voor he...] [2009-11-19 19:02:36] [41dcf2419e4beff0486cef71832b5d35] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19	24,4	19	18	19	23
22	22,5	19	19	18	19
23	19,4	22	19	19	18
20	18,1	23	22	19	19
14	18,1	20	23	22	19
14	20,7	14	20	23	22
14	19,1	14	14	20	23
15	18,3	14	14	14	20
11	16,9	15	14	14	14
17	17,9	11	15	14	14
16	20,2	17	11	15	14
20	21,2	16	17	11	15
24	23,8	20	16	17	11
23	24	24	20	16	17
20	26,6	23	24	20	16
21	25,3	20	23	24	20
19	27,6	21	20	23	24
23	24,7	19	21	20	23
23	26,6	23	19	21	20
23	24,4	23	23	19	21
23	24,6	23	23	23	19
27	26	23	23	23	23
26	24,8	27	23	23	23
17	24	26	27	23	23
24	22,7	17	26	27	23
26	23	24	17	26	27
24	24,1	26	24	17	26
27	24	24	26	24	17
27	22,7	27	24	26	24
26	22,6	27	27	24	26
24	23,1	26	27	27	24
23	24,4	24	26	27	27
23	23	23	24	26	27
24	22	23	23	24	26
17	21,3	24	23	23	24
21	21,5	17	24	23	23
19	21,3	21	17	24	23
22	23,2	19	21	17	24
22	21,8	22	19	21	17
18	23,3	22	22	19	21
16	21	18	22	22	19
14	22,4	16	18	22	22
12	20,4	14	16	18	22
14	19,9	12	14	16	18
16	21,3	14	12	14	16
8	18,9	16	14	12	14
3	15,6	8	16	14	12
0	12,5	3	8	16	14
5	7,8	0	3	8	16
1	5,5	5	0	3	8
1	4	1	5	0	3
3	3,3	1	1	5	0
6	3,7	3	1	1	5
7	3,1	6	3	1	1
8	5	7	6	3	1
14	6,3	8	7	6	3
14	20	14	8	7	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=57900&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=57900&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&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] = + 0.62534313143448 + 0.134177451152066X[t] + 0.763994640040319`Y(t-1)`[t] + 0.0704456425436845`Y(t-2)`[t] + 0.0782248700521776`Y(t-3)`[t] -0.146998416229665`Y(t-4)`[t] + 3.86274414161116M1[t] + 2.64053282326136M2[t] + 0.873677019898664M3[t] + 1.00749157087014M4[t] + 0.226587076443826M5[t] + 1.87144092960793M6[t] + 0.964855849929924M7[t] + 3.12046893188267M8[t] + 0.988941013633353M9[t] + 2.26002196920389M10[t] -1.84545590981347M11[t] -0.0211274789115458t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.62534313143448 +  0.134177451152066X[t] +  0.763994640040319`Y(t-1)`[t] +  0.0704456425436845`Y(t-2)`[t] +  0.0782248700521776`Y(t-3)`[t] -0.146998416229665`Y(t-4)`[t] +  3.86274414161116M1[t] +  2.64053282326136M2[t] +  0.873677019898664M3[t] +  1.00749157087014M4[t] +  0.226587076443826M5[t] +  1.87144092960793M6[t] +  0.964855849929924M7[t] +  3.12046893188267M8[t] +  0.988941013633353M9[t] +  2.26002196920389M10[t] -1.84545590981347M11[t] -0.0211274789115458t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57900&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.62534313143448 +  0.134177451152066X[t] +  0.763994640040319`Y(t-1)`[t] +  0.0704456425436845`Y(t-2)`[t] +  0.0782248700521776`Y(t-3)`[t] -0.146998416229665`Y(t-4)`[t] +  3.86274414161116M1[t] +  2.64053282326136M2[t] +  0.873677019898664M3[t] +  1.00749157087014M4[t] +  0.226587076443826M5[t] +  1.87144092960793M6[t] +  0.964855849929924M7[t] +  3.12046893188267M8[t] +  0.988941013633353M9[t] +  2.26002196920389M10[t] -1.84545590981347M11[t] -0.0211274789115458t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57900&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&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] = + 0.62534313143448 + 0.134177451152066X[t] + 0.763994640040319`Y(t-1)`[t] + 0.0704456425436845`Y(t-2)`[t] + 0.0782248700521776`Y(t-3)`[t] -0.146998416229665`Y(t-4)`[t] + 3.86274414161116M1[t] + 2.64053282326136M2[t] + 0.873677019898664M3[t] + 1.00749157087014M4[t] + 0.226587076443826M5[t] + 1.87144092960793M6[t] + 0.964855849929924M7[t] + 3.12046893188267M8[t] + 0.988941013633353M9[t] + 2.26002196920389M10[t] -1.84545590981347M11[t] -0.0211274789115458t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.625343131434483.0922710.20220.840790.420395
X0.1341774511520660.1808650.74190.4626140.231307
`Y(t-1)`0.7639946400403190.1693594.51115.8e-052.9e-05
`Y(t-2)`0.07044564254368450.2067420.34070.7351270.367563
`Y(t-3)`0.07822487005217760.203440.38450.7026890.351344
`Y(t-4)`-0.1469984162296650.16191-0.90790.3695050.184753
M13.862744141611162.4425321.58150.1218520.060926
M22.640532823261362.554311.03380.3076180.153809
M30.8736770198986642.4571330.35560.724080.36204
M41.007491570870142.4439230.41220.6824180.341209
M50.2265870764438262.4232420.09350.9259810.46299
M61.871440929607932.3687990.790.4342830.217142
M70.9648558499299242.4260730.39770.6930180.346509
M83.120468931882672.3808221.31070.1976360.098818
M90.9889410136333532.4891860.39730.6933160.346658
M102.260021969203892.5052960.90210.3725430.186271
M11-1.845455909813472.554184-0.72250.4742840.237142
t-0.02112747891154580.034949-0.60450.5489970.274499

\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) & 0.62534313143448 & 3.092271 & 0.2022 & 0.84079 & 0.420395 \tabularnewline
X & 0.134177451152066 & 0.180865 & 0.7419 & 0.462614 & 0.231307 \tabularnewline
`Y(t-1)` & 0.763994640040319 & 0.169359 & 4.5111 & 5.8e-05 & 2.9e-05 \tabularnewline
`Y(t-2)` & 0.0704456425436845 & 0.206742 & 0.3407 & 0.735127 & 0.367563 \tabularnewline
`Y(t-3)` & 0.0782248700521776 & 0.20344 & 0.3845 & 0.702689 & 0.351344 \tabularnewline
`Y(t-4)` & -0.146998416229665 & 0.16191 & -0.9079 & 0.369505 & 0.184753 \tabularnewline
M1 & 3.86274414161116 & 2.442532 & 1.5815 & 0.121852 & 0.060926 \tabularnewline
M2 & 2.64053282326136 & 2.55431 & 1.0338 & 0.307618 & 0.153809 \tabularnewline
M3 & 0.873677019898664 & 2.457133 & 0.3556 & 0.72408 & 0.36204 \tabularnewline
M4 & 1.00749157087014 & 2.443923 & 0.4122 & 0.682418 & 0.341209 \tabularnewline
M5 & 0.226587076443826 & 2.423242 & 0.0935 & 0.925981 & 0.46299 \tabularnewline
M6 & 1.87144092960793 & 2.368799 & 0.79 & 0.434283 & 0.217142 \tabularnewline
M7 & 0.964855849929924 & 2.426073 & 0.3977 & 0.693018 & 0.346509 \tabularnewline
M8 & 3.12046893188267 & 2.380822 & 1.3107 & 0.197636 & 0.098818 \tabularnewline
M9 & 0.988941013633353 & 2.489186 & 0.3973 & 0.693316 & 0.346658 \tabularnewline
M10 & 2.26002196920389 & 2.505296 & 0.9021 & 0.372543 & 0.186271 \tabularnewline
M11 & -1.84545590981347 & 2.554184 & -0.7225 & 0.474284 & 0.237142 \tabularnewline
t & -0.0211274789115458 & 0.034949 & -0.6045 & 0.548997 & 0.274499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57900&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]0.62534313143448[/C][C]3.092271[/C][C]0.2022[/C][C]0.84079[/C][C]0.420395[/C][/ROW]
[ROW][C]X[/C][C]0.134177451152066[/C][C]0.180865[/C][C]0.7419[/C][C]0.462614[/C][C]0.231307[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.763994640040319[/C][C]0.169359[/C][C]4.5111[/C][C]5.8e-05[/C][C]2.9e-05[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.0704456425436845[/C][C]0.206742[/C][C]0.3407[/C][C]0.735127[/C][C]0.367563[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]0.0782248700521776[/C][C]0.20344[/C][C]0.3845[/C][C]0.702689[/C][C]0.351344[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.146998416229665[/C][C]0.16191[/C][C]-0.9079[/C][C]0.369505[/C][C]0.184753[/C][/ROW]
[ROW][C]M1[/C][C]3.86274414161116[/C][C]2.442532[/C][C]1.5815[/C][C]0.121852[/C][C]0.060926[/C][/ROW]
[ROW][C]M2[/C][C]2.64053282326136[/C][C]2.55431[/C][C]1.0338[/C][C]0.307618[/C][C]0.153809[/C][/ROW]
[ROW][C]M3[/C][C]0.873677019898664[/C][C]2.457133[/C][C]0.3556[/C][C]0.72408[/C][C]0.36204[/C][/ROW]
[ROW][C]M4[/C][C]1.00749157087014[/C][C]2.443923[/C][C]0.4122[/C][C]0.682418[/C][C]0.341209[/C][/ROW]
[ROW][C]M5[/C][C]0.226587076443826[/C][C]2.423242[/C][C]0.0935[/C][C]0.925981[/C][C]0.46299[/C][/ROW]
[ROW][C]M6[/C][C]1.87144092960793[/C][C]2.368799[/C][C]0.79[/C][C]0.434283[/C][C]0.217142[/C][/ROW]
[ROW][C]M7[/C][C]0.964855849929924[/C][C]2.426073[/C][C]0.3977[/C][C]0.693018[/C][C]0.346509[/C][/ROW]
[ROW][C]M8[/C][C]3.12046893188267[/C][C]2.380822[/C][C]1.3107[/C][C]0.197636[/C][C]0.098818[/C][/ROW]
[ROW][C]M9[/C][C]0.988941013633353[/C][C]2.489186[/C][C]0.3973[/C][C]0.693316[/C][C]0.346658[/C][/ROW]
[ROW][C]M10[/C][C]2.26002196920389[/C][C]2.505296[/C][C]0.9021[/C][C]0.372543[/C][C]0.186271[/C][/ROW]
[ROW][C]M11[/C][C]-1.84545590981347[/C][C]2.554184[/C][C]-0.7225[/C][C]0.474284[/C][C]0.237142[/C][/ROW]
[ROW][C]t[/C][C]-0.0211274789115458[/C][C]0.034949[/C][C]-0.6045[/C][C]0.548997[/C][C]0.274499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57900&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&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)0.625343131434483.0922710.20220.840790.420395
X0.1341774511520660.1808650.74190.4626140.231307
`Y(t-1)`0.7639946400403190.1693594.51115.8e-052.9e-05
`Y(t-2)`0.07044564254368450.2067420.34070.7351270.367563
`Y(t-3)`0.07822487005217760.203440.38450.7026890.351344
`Y(t-4)`-0.1469984162296650.16191-0.90790.3695050.184753
M13.862744141611162.4425321.58150.1218520.060926
M22.640532823261362.554311.03380.3076180.153809
M30.8736770198986642.4571330.35560.724080.36204
M41.007491570870142.4439230.41220.6824180.341209
M50.2265870764438262.4232420.09350.9259810.46299
M61.871440929607932.3687990.790.4342830.217142
M70.9648558499299242.4260730.39770.6930180.346509
M83.120468931882672.3808221.31070.1976360.098818
M90.9889410136333532.4891860.39730.6933160.346658
M102.260021969203892.5052960.90210.3725430.186271
M11-1.845455909813472.554184-0.72250.4742840.237142
t-0.02112747891154580.034949-0.60450.5489970.274499






Multiple Linear Regression - Regression Statistics
Multiple R0.919899890899325
R-squared0.84621580927659
Adjusted R-squared0.779181674858694
F-TEST (value)12.6236553455171
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value6.12756512197166e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.47962494480970
Sum Squared Residuals472.203800505133

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.919899890899325 \tabularnewline
R-squared & 0.84621580927659 \tabularnewline
Adjusted R-squared & 0.779181674858694 \tabularnewline
F-TEST (value) & 12.6236553455171 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 6.12756512197166e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.47962494480970 \tabularnewline
Sum Squared Residuals & 472.203800505133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57900&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.919899890899325[/C][/ROW]
[ROW][C]R-squared[/C][C]0.84621580927659[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.779181674858694[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]12.6236553455171[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]6.12756512197166e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.47962494480970[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]472.203800505133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57900&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&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 R0.919899890899325
R-squared0.84621580927659
Adjusted R-squared0.779181674858694
F-TEST (value)12.6236553455171
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value6.12756512197166e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.47962494480970
Sum Squared Residuals472.203800505133






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11921.630118286506-2.63011828650599
22220.71205676946591.28794323053411
32321.02533059502301.97466940497697
42021.791920132027-1.79192013202699
51419.0030244912684-5.00302449126839
61415.8175370920065-1.81753709200653
71413.87079372992540.129206270074637
81515.8695834004208-0.869583400420844
91115.1750647090654-4.17506470906540
101713.57366271925893.42633728074114
111614.13607563909911.86392436090094
122015.29336283993654.70663716006354
132423.52671667848080.473283321519236
142324.6877591343557-1.68775913435569
152023.2263230516496-3.22632305164961
162120.52705568983730.472944310162739
171919.9200710315876-0.920071031587584
182319.60946296603533.39053703396467
192322.37099495844980.629005041550219
202324.1886245827972-1.18862458279716
212322.66970098853470.330299011465254
222723.51950923188803.48049076811203
232622.28786949273793.71213050726213
241723.5226438928525-6.52264389285255
252420.55633194635663.44366805364337
262623.40097954685912.59902045314085
272423.22467482449870.775325175501328
282723.80740599288243.19259400711764
292724.10949679457712.89050320542290
302625.48069577878180.519304221218178
312424.3847487483438-0.384748748343841
322324.6542348665694-1.65423486656941
332321.33062024261581.66937975738421
342422.36649930170431.63350069829566
351719.1257363304165-2.12573633041646
362115.84638183003995.15361816996009
371922.3022469349168-3.30224693491677
382219.37306607834352.62693392165645
392220.89021539330641.10978460669364
401820.6710621647024-2.67106216470244
411617.0331149361694-1.03311493616941
421416.5939226430905-2.59392264309049
431213.4160751368201-1.41607513682008
441414.2461353739316-0.246135373931552
451613.80597349573182.19402650426818
46816.5403287471488-8.54032874714883
4736.45031853774661-3.45031853774661
4803.33761143717108-3.33761143717108
4952.984586153739852.01541384626015
5015.82613847097573-4.82613847097573
5111.63345613552232-0.633456135522325
5232.202556020550960.797443979449044
5361.934292746397534.06570725360247
5476.498381520085840.501618479914164
5586.957387426460931.04261257353907
561410.04142177628103.95857822371897
571414.0186405640523-0.0186405640522542

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 19 & 21.630118286506 & -2.63011828650599 \tabularnewline
2 & 22 & 20.7120567694659 & 1.28794323053411 \tabularnewline
3 & 23 & 21.0253305950230 & 1.97466940497697 \tabularnewline
4 & 20 & 21.791920132027 & -1.79192013202699 \tabularnewline
5 & 14 & 19.0030244912684 & -5.00302449126839 \tabularnewline
6 & 14 & 15.8175370920065 & -1.81753709200653 \tabularnewline
7 & 14 & 13.8707937299254 & 0.129206270074637 \tabularnewline
8 & 15 & 15.8695834004208 & -0.869583400420844 \tabularnewline
9 & 11 & 15.1750647090654 & -4.17506470906540 \tabularnewline
10 & 17 & 13.5736627192589 & 3.42633728074114 \tabularnewline
11 & 16 & 14.1360756390991 & 1.86392436090094 \tabularnewline
12 & 20 & 15.2933628399365 & 4.70663716006354 \tabularnewline
13 & 24 & 23.5267166784808 & 0.473283321519236 \tabularnewline
14 & 23 & 24.6877591343557 & -1.68775913435569 \tabularnewline
15 & 20 & 23.2263230516496 & -3.22632305164961 \tabularnewline
16 & 21 & 20.5270556898373 & 0.472944310162739 \tabularnewline
17 & 19 & 19.9200710315876 & -0.920071031587584 \tabularnewline
18 & 23 & 19.6094629660353 & 3.39053703396467 \tabularnewline
19 & 23 & 22.3709949584498 & 0.629005041550219 \tabularnewline
20 & 23 & 24.1886245827972 & -1.18862458279716 \tabularnewline
21 & 23 & 22.6697009885347 & 0.330299011465254 \tabularnewline
22 & 27 & 23.5195092318880 & 3.48049076811203 \tabularnewline
23 & 26 & 22.2878694927379 & 3.71213050726213 \tabularnewline
24 & 17 & 23.5226438928525 & -6.52264389285255 \tabularnewline
25 & 24 & 20.5563319463566 & 3.44366805364337 \tabularnewline
26 & 26 & 23.4009795468591 & 2.59902045314085 \tabularnewline
27 & 24 & 23.2246748244987 & 0.775325175501328 \tabularnewline
28 & 27 & 23.8074059928824 & 3.19259400711764 \tabularnewline
29 & 27 & 24.1094967945771 & 2.89050320542290 \tabularnewline
30 & 26 & 25.4806957787818 & 0.519304221218178 \tabularnewline
31 & 24 & 24.3847487483438 & -0.384748748343841 \tabularnewline
32 & 23 & 24.6542348665694 & -1.65423486656941 \tabularnewline
33 & 23 & 21.3306202426158 & 1.66937975738421 \tabularnewline
34 & 24 & 22.3664993017043 & 1.63350069829566 \tabularnewline
35 & 17 & 19.1257363304165 & -2.12573633041646 \tabularnewline
36 & 21 & 15.8463818300399 & 5.15361816996009 \tabularnewline
37 & 19 & 22.3022469349168 & -3.30224693491677 \tabularnewline
38 & 22 & 19.3730660783435 & 2.62693392165645 \tabularnewline
39 & 22 & 20.8902153933064 & 1.10978460669364 \tabularnewline
40 & 18 & 20.6710621647024 & -2.67106216470244 \tabularnewline
41 & 16 & 17.0331149361694 & -1.03311493616941 \tabularnewline
42 & 14 & 16.5939226430905 & -2.59392264309049 \tabularnewline
43 & 12 & 13.4160751368201 & -1.41607513682008 \tabularnewline
44 & 14 & 14.2461353739316 & -0.246135373931552 \tabularnewline
45 & 16 & 13.8059734957318 & 2.19402650426818 \tabularnewline
46 & 8 & 16.5403287471488 & -8.54032874714883 \tabularnewline
47 & 3 & 6.45031853774661 & -3.45031853774661 \tabularnewline
48 & 0 & 3.33761143717108 & -3.33761143717108 \tabularnewline
49 & 5 & 2.98458615373985 & 2.01541384626015 \tabularnewline
50 & 1 & 5.82613847097573 & -4.82613847097573 \tabularnewline
51 & 1 & 1.63345613552232 & -0.633456135522325 \tabularnewline
52 & 3 & 2.20255602055096 & 0.797443979449044 \tabularnewline
53 & 6 & 1.93429274639753 & 4.06570725360247 \tabularnewline
54 & 7 & 6.49838152008584 & 0.501618479914164 \tabularnewline
55 & 8 & 6.95738742646093 & 1.04261257353907 \tabularnewline
56 & 14 & 10.0414217762810 & 3.95857822371897 \tabularnewline
57 & 14 & 14.0186405640523 & -0.0186405640522542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57900&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]19[/C][C]21.630118286506[/C][C]-2.63011828650599[/C][/ROW]
[ROW][C]2[/C][C]22[/C][C]20.7120567694659[/C][C]1.28794323053411[/C][/ROW]
[ROW][C]3[/C][C]23[/C][C]21.0253305950230[/C][C]1.97466940497697[/C][/ROW]
[ROW][C]4[/C][C]20[/C][C]21.791920132027[/C][C]-1.79192013202699[/C][/ROW]
[ROW][C]5[/C][C]14[/C][C]19.0030244912684[/C][C]-5.00302449126839[/C][/ROW]
[ROW][C]6[/C][C]14[/C][C]15.8175370920065[/C][C]-1.81753709200653[/C][/ROW]
[ROW][C]7[/C][C]14[/C][C]13.8707937299254[/C][C]0.129206270074637[/C][/ROW]
[ROW][C]8[/C][C]15[/C][C]15.8695834004208[/C][C]-0.869583400420844[/C][/ROW]
[ROW][C]9[/C][C]11[/C][C]15.1750647090654[/C][C]-4.17506470906540[/C][/ROW]
[ROW][C]10[/C][C]17[/C][C]13.5736627192589[/C][C]3.42633728074114[/C][/ROW]
[ROW][C]11[/C][C]16[/C][C]14.1360756390991[/C][C]1.86392436090094[/C][/ROW]
[ROW][C]12[/C][C]20[/C][C]15.2933628399365[/C][C]4.70663716006354[/C][/ROW]
[ROW][C]13[/C][C]24[/C][C]23.5267166784808[/C][C]0.473283321519236[/C][/ROW]
[ROW][C]14[/C][C]23[/C][C]24.6877591343557[/C][C]-1.68775913435569[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]23.2263230516496[/C][C]-3.22632305164961[/C][/ROW]
[ROW][C]16[/C][C]21[/C][C]20.5270556898373[/C][C]0.472944310162739[/C][/ROW]
[ROW][C]17[/C][C]19[/C][C]19.9200710315876[/C][C]-0.920071031587584[/C][/ROW]
[ROW][C]18[/C][C]23[/C][C]19.6094629660353[/C][C]3.39053703396467[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]22.3709949584498[/C][C]0.629005041550219[/C][/ROW]
[ROW][C]20[/C][C]23[/C][C]24.1886245827972[/C][C]-1.18862458279716[/C][/ROW]
[ROW][C]21[/C][C]23[/C][C]22.6697009885347[/C][C]0.330299011465254[/C][/ROW]
[ROW][C]22[/C][C]27[/C][C]23.5195092318880[/C][C]3.48049076811203[/C][/ROW]
[ROW][C]23[/C][C]26[/C][C]22.2878694927379[/C][C]3.71213050726213[/C][/ROW]
[ROW][C]24[/C][C]17[/C][C]23.5226438928525[/C][C]-6.52264389285255[/C][/ROW]
[ROW][C]25[/C][C]24[/C][C]20.5563319463566[/C][C]3.44366805364337[/C][/ROW]
[ROW][C]26[/C][C]26[/C][C]23.4009795468591[/C][C]2.59902045314085[/C][/ROW]
[ROW][C]27[/C][C]24[/C][C]23.2246748244987[/C][C]0.775325175501328[/C][/ROW]
[ROW][C]28[/C][C]27[/C][C]23.8074059928824[/C][C]3.19259400711764[/C][/ROW]
[ROW][C]29[/C][C]27[/C][C]24.1094967945771[/C][C]2.89050320542290[/C][/ROW]
[ROW][C]30[/C][C]26[/C][C]25.4806957787818[/C][C]0.519304221218178[/C][/ROW]
[ROW][C]31[/C][C]24[/C][C]24.3847487483438[/C][C]-0.384748748343841[/C][/ROW]
[ROW][C]32[/C][C]23[/C][C]24.6542348665694[/C][C]-1.65423486656941[/C][/ROW]
[ROW][C]33[/C][C]23[/C][C]21.3306202426158[/C][C]1.66937975738421[/C][/ROW]
[ROW][C]34[/C][C]24[/C][C]22.3664993017043[/C][C]1.63350069829566[/C][/ROW]
[ROW][C]35[/C][C]17[/C][C]19.1257363304165[/C][C]-2.12573633041646[/C][/ROW]
[ROW][C]36[/C][C]21[/C][C]15.8463818300399[/C][C]5.15361816996009[/C][/ROW]
[ROW][C]37[/C][C]19[/C][C]22.3022469349168[/C][C]-3.30224693491677[/C][/ROW]
[ROW][C]38[/C][C]22[/C][C]19.3730660783435[/C][C]2.62693392165645[/C][/ROW]
[ROW][C]39[/C][C]22[/C][C]20.8902153933064[/C][C]1.10978460669364[/C][/ROW]
[ROW][C]40[/C][C]18[/C][C]20.6710621647024[/C][C]-2.67106216470244[/C][/ROW]
[ROW][C]41[/C][C]16[/C][C]17.0331149361694[/C][C]-1.03311493616941[/C][/ROW]
[ROW][C]42[/C][C]14[/C][C]16.5939226430905[/C][C]-2.59392264309049[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]13.4160751368201[/C][C]-1.41607513682008[/C][/ROW]
[ROW][C]44[/C][C]14[/C][C]14.2461353739316[/C][C]-0.246135373931552[/C][/ROW]
[ROW][C]45[/C][C]16[/C][C]13.8059734957318[/C][C]2.19402650426818[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]16.5403287471488[/C][C]-8.54032874714883[/C][/ROW]
[ROW][C]47[/C][C]3[/C][C]6.45031853774661[/C][C]-3.45031853774661[/C][/ROW]
[ROW][C]48[/C][C]0[/C][C]3.33761143717108[/C][C]-3.33761143717108[/C][/ROW]
[ROW][C]49[/C][C]5[/C][C]2.98458615373985[/C][C]2.01541384626015[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]5.82613847097573[/C][C]-4.82613847097573[/C][/ROW]
[ROW][C]51[/C][C]1[/C][C]1.63345613552232[/C][C]-0.633456135522325[/C][/ROW]
[ROW][C]52[/C][C]3[/C][C]2.20255602055096[/C][C]0.797443979449044[/C][/ROW]
[ROW][C]53[/C][C]6[/C][C]1.93429274639753[/C][C]4.06570725360247[/C][/ROW]
[ROW][C]54[/C][C]7[/C][C]6.49838152008584[/C][C]0.501618479914164[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]6.95738742646093[/C][C]1.04261257353907[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]10.0414217762810[/C][C]3.95857822371897[/C][/ROW]
[ROW][C]57[/C][C]14[/C][C]14.0186405640523[/C][C]-0.0186405640522542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57900&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&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
11921.630118286506-2.63011828650599
22220.71205676946591.28794323053411
32321.02533059502301.97466940497697
42021.791920132027-1.79192013202699
51419.0030244912684-5.00302449126839
61415.8175370920065-1.81753709200653
71413.87079372992540.129206270074637
81515.8695834004208-0.869583400420844
91115.1750647090654-4.17506470906540
101713.57366271925893.42633728074114
111614.13607563909911.86392436090094
122015.29336283993654.70663716006354
132423.52671667848080.473283321519236
142324.6877591343557-1.68775913435569
152023.2263230516496-3.22632305164961
162120.52705568983730.472944310162739
171919.9200710315876-0.920071031587584
182319.60946296603533.39053703396467
192322.37099495844980.629005041550219
202324.1886245827972-1.18862458279716
212322.66970098853470.330299011465254
222723.51950923188803.48049076811203
232622.28786949273793.71213050726213
241723.5226438928525-6.52264389285255
252420.55633194635663.44366805364337
262623.40097954685912.59902045314085
272423.22467482449870.775325175501328
282723.80740599288243.19259400711764
292724.10949679457712.89050320542290
302625.48069577878180.519304221218178
312424.3847487483438-0.384748748343841
322324.6542348665694-1.65423486656941
332321.33062024261581.66937975738421
342422.36649930170431.63350069829566
351719.1257363304165-2.12573633041646
362115.84638183003995.15361816996009
371922.3022469349168-3.30224693491677
382219.37306607834352.62693392165645
392220.89021539330641.10978460669364
401820.6710621647024-2.67106216470244
411617.0331149361694-1.03311493616941
421416.5939226430905-2.59392264309049
431213.4160751368201-1.41607513682008
441414.2461353739316-0.246135373931552
451613.80597349573182.19402650426818
46816.5403287471488-8.54032874714883
4736.45031853774661-3.45031853774661
4803.33761143717108-3.33761143717108
4952.984586153739852.01541384626015
5015.82613847097573-4.82613847097573
5111.63345613552232-0.633456135522325
5232.202556020550960.797443979449044
5361.934292746397534.06570725360247
5476.498381520085840.501618479914164
5586.957387426460931.04261257353907
561410.04142177628103.95857822371897
571414.0186405640523-0.0186405640522542






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.3730705498448110.7461410996896220.626929450155189
220.3494746747906750.6989493495813510.650525325209325
230.2720163638306970.5440327276613940.727983636169303
240.7293196655396290.5413606689207430.270680334460371
250.6953982245886540.6092035508226930.304601775411346
260.6217226702113970.7565546595772050.378277329788603
270.5299546549091370.9400906901817250.470045345090863
280.4390547558486340.8781095116972680.560945244151366
290.3830310023120290.7660620046240580.616968997687971
300.2726053909449690.5452107818899390.72739460905503
310.1789071544292730.3578143088585460.821092845570727
320.1515896935334770.3031793870669540.848410306466523
330.1985084836216000.3970169672431990.8014915163784
340.1928819839114040.3857639678228080.807118016088596
350.1589036220512040.3178072441024070.841096377948797
360.1211535364035800.2423070728071590.87884646359642

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.373070549844811 & 0.746141099689622 & 0.626929450155189 \tabularnewline
22 & 0.349474674790675 & 0.698949349581351 & 0.650525325209325 \tabularnewline
23 & 0.272016363830697 & 0.544032727661394 & 0.727983636169303 \tabularnewline
24 & 0.729319665539629 & 0.541360668920743 & 0.270680334460371 \tabularnewline
25 & 0.695398224588654 & 0.609203550822693 & 0.304601775411346 \tabularnewline
26 & 0.621722670211397 & 0.756554659577205 & 0.378277329788603 \tabularnewline
27 & 0.529954654909137 & 0.940090690181725 & 0.470045345090863 \tabularnewline
28 & 0.439054755848634 & 0.878109511697268 & 0.560945244151366 \tabularnewline
29 & 0.383031002312029 & 0.766062004624058 & 0.616968997687971 \tabularnewline
30 & 0.272605390944969 & 0.545210781889939 & 0.72739460905503 \tabularnewline
31 & 0.178907154429273 & 0.357814308858546 & 0.821092845570727 \tabularnewline
32 & 0.151589693533477 & 0.303179387066954 & 0.848410306466523 \tabularnewline
33 & 0.198508483621600 & 0.397016967243199 & 0.8014915163784 \tabularnewline
34 & 0.192881983911404 & 0.385763967822808 & 0.807118016088596 \tabularnewline
35 & 0.158903622051204 & 0.317807244102407 & 0.841096377948797 \tabularnewline
36 & 0.121153536403580 & 0.242307072807159 & 0.87884646359642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57900&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]0.373070549844811[/C][C]0.746141099689622[/C][C]0.626929450155189[/C][/ROW]
[ROW][C]22[/C][C]0.349474674790675[/C][C]0.698949349581351[/C][C]0.650525325209325[/C][/ROW]
[ROW][C]23[/C][C]0.272016363830697[/C][C]0.544032727661394[/C][C]0.727983636169303[/C][/ROW]
[ROW][C]24[/C][C]0.729319665539629[/C][C]0.541360668920743[/C][C]0.270680334460371[/C][/ROW]
[ROW][C]25[/C][C]0.695398224588654[/C][C]0.609203550822693[/C][C]0.304601775411346[/C][/ROW]
[ROW][C]26[/C][C]0.621722670211397[/C][C]0.756554659577205[/C][C]0.378277329788603[/C][/ROW]
[ROW][C]27[/C][C]0.529954654909137[/C][C]0.940090690181725[/C][C]0.470045345090863[/C][/ROW]
[ROW][C]28[/C][C]0.439054755848634[/C][C]0.878109511697268[/C][C]0.560945244151366[/C][/ROW]
[ROW][C]29[/C][C]0.383031002312029[/C][C]0.766062004624058[/C][C]0.616968997687971[/C][/ROW]
[ROW][C]30[/C][C]0.272605390944969[/C][C]0.545210781889939[/C][C]0.72739460905503[/C][/ROW]
[ROW][C]31[/C][C]0.178907154429273[/C][C]0.357814308858546[/C][C]0.821092845570727[/C][/ROW]
[ROW][C]32[/C][C]0.151589693533477[/C][C]0.303179387066954[/C][C]0.848410306466523[/C][/ROW]
[ROW][C]33[/C][C]0.198508483621600[/C][C]0.397016967243199[/C][C]0.8014915163784[/C][/ROW]
[ROW][C]34[/C][C]0.192881983911404[/C][C]0.385763967822808[/C][C]0.807118016088596[/C][/ROW]
[ROW][C]35[/C][C]0.158903622051204[/C][C]0.317807244102407[/C][C]0.841096377948797[/C][/ROW]
[ROW][C]36[/C][C]0.121153536403580[/C][C]0.242307072807159[/C][C]0.87884646359642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57900&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&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
210.3730705498448110.7461410996896220.626929450155189
220.3494746747906750.6989493495813510.650525325209325
230.2720163638306970.5440327276613940.727983636169303
240.7293196655396290.5413606689207430.270680334460371
250.6953982245886540.6092035508226930.304601775411346
260.6217226702113970.7565546595772050.378277329788603
270.5299546549091370.9400906901817250.470045345090863
280.4390547558486340.8781095116972680.560945244151366
290.3830310023120290.7660620046240580.616968997687971
300.2726053909449690.5452107818899390.72739460905503
310.1789071544292730.3578143088585460.821092845570727
320.1515896935334770.3031793870669540.848410306466523
330.1985084836216000.3970169672431990.8014915163784
340.1928819839114040.3857639678228080.807118016088596
350.1589036220512040.3178072441024070.841096377948797
360.1211535364035800.2423070728071590.87884646359642






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57900&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57900&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57900&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 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')
}