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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 computationFri, 20 Nov 2009 07:02:22 -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/20/t1258725844nkekb5jrworxx9n.htm/, Retrieved Thu, 25 Apr 2024 05:39:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58174, Retrieved Thu, 25 Apr 2024 05:39:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

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] [] [2009-11-20 14:02:22] [0545e25c765ce26b196961216dc11e13] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1	2	1,2	1,4
1,7	2	1	1,2
2,4	2	1,7	1
2	2	2,4	1,7
2,1	2	2	2,4
2	2	2,1	2
1,8	2	2	2,1
2,7	2	1,8	2
2,3	2	2,7	1,8
1,9	2	2,3	2,7
2	2	1,9	2,3
2,3	2	2	1,9
2,8	2	2,3	2
2,4	2	2,8	2,3
2,3	2	2,4	2,8
2,7	2	2,3	2,4
2,7	2	2,7	2,3
2,9	2	2,7	2,7
3	2	2,9	2,7
2,2	2	3	2,9
2,3	2	2,2	3
2,8	2,21	2,3	2,2
2,8	2,25	2,8	2,3
2,8	2,25	2,8	2,8
2,2	2,45	2,8	2,8
2,6	2,5	2,2	2,8
2,8	2,5	2,6	2,2
2,5	2,64	2,8	2,6
2,4	2,75	2,5	2,8
2,3	2,93	2,4	2,5
1,9	3	2,3	2,4
1,7	3,17	1,9	2,3
2	3,25	1,7	1,9
2,1	3,39	2	1,7
1,7	3,5	2,1	2
1,8	3,5	1,7	2,1
1,8	3,65	1,8	1,7
1,8	3,75	1,8	1,8
1,3	3,75	1,8	1,8
1,3	3,9	1,3	1,8
1,3	4	1,3	1,3
1,2	4	1,3	1,3
1,4	4	1,2	1,3
2,2	4	1,4	1,2
2,9	4	2,2	1,4
3,1	4	2,9	2,2
3,5	4	3,1	2,9
3,6	4	3,5	3,1
4,4	4	3,6	3,5
4,1	4	4,4	3,6
5,1	4	4,1	4,4
5,8	4	5,1	4,1
5,9	4,18	5,8	5,1
5,4	4,25	5,9	5,8
5,5	4,25	5,4	5,9
4,8	3,97	5,5	5,4
3,2	3,42	4,8	5,5
2,7	2,75	3,2	4,8

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=58174&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=58174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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] = -0.0734302746307986 + 0.240213449888453X[t] + 1.06847062139874Y1[t] -0.151877506173371Y2[t] -0.0658484772738318M1[t] -0.0807067438688125M2[t] + 0.119085905707768M3[t] -0.0704160867844202M4[t] -0.105059685311399M5[t] -0.236207021068785M6[t] -0.138233436004764M7[t] -0.0983526673209309M8[t] -0.251765154607209M9[t] -0.0539842332914323M10[t] -0.123558533753511M11[t] -0.0100825486711427t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.0734302746307986 +  0.240213449888453X[t] +  1.06847062139874Y1[t] -0.151877506173371Y2[t] -0.0658484772738318M1[t] -0.0807067438688125M2[t] +  0.119085905707768M3[t] -0.0704160867844202M4[t] -0.105059685311399M5[t] -0.236207021068785M6[t] -0.138233436004764M7[t] -0.0983526673209309M8[t] -0.251765154607209M9[t] -0.0539842332914323M10[t] -0.123558533753511M11[t] -0.0100825486711427t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58174&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.0734302746307986 +  0.240213449888453X[t] +  1.06847062139874Y1[t] -0.151877506173371Y2[t] -0.0658484772738318M1[t] -0.0807067438688125M2[t] +  0.119085905707768M3[t] -0.0704160867844202M4[t] -0.105059685311399M5[t] -0.236207021068785M6[t] -0.138233436004764M7[t] -0.0983526673209309M8[t] -0.251765154607209M9[t] -0.0539842332914323M10[t] -0.123558533753511M11[t] -0.0100825486711427t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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] = -0.0734302746307986 + 0.240213449888453X[t] + 1.06847062139874Y1[t] -0.151877506173371Y2[t] -0.0658484772738318M1[t] -0.0807067438688125M2[t] + 0.119085905707768M3[t] -0.0704160867844202M4[t] -0.105059685311399M5[t] -0.236207021068785M6[t] -0.138233436004764M7[t] -0.0983526673209309M8[t] -0.251765154607209M9[t] -0.0539842332914323M10[t] -0.123558533753511M11[t] -0.0100825486711427t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.07343027463079860.516944-0.1420.8877220.443861
X0.2402134498884530.2456190.9780.3336770.166839
Y11.068470621398740.1555866.867400
Y2-0.1518775061733710.176414-0.86090.3941730.197087
M1-0.06584847727383180.333842-0.19720.8445880.422294
M2-0.08070674386881250.333377-0.24210.809890.404945
M30.1190859057077680.3327210.35790.72220.3611
M4-0.07041608678442020.334438-0.21060.8342560.417128
M5-0.1050596853113990.335323-0.31330.7555970.377798
M6-0.2362070210687850.335886-0.70320.4857890.242894
M7-0.1382334360047640.335708-0.41180.6826040.341302
M8-0.09835266732093090.332598-0.29570.7689080.384454
M9-0.2517651546072090.333541-0.75480.4545660.227283
M10-0.05398423329143230.337482-0.160.8736780.436839
M11-0.1235585337535110.350141-0.35290.7259420.362971
t-0.01008254867114270.014672-0.68720.4957480.247874

\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) & -0.0734302746307986 & 0.516944 & -0.142 & 0.887722 & 0.443861 \tabularnewline
X & 0.240213449888453 & 0.245619 & 0.978 & 0.333677 & 0.166839 \tabularnewline
Y1 & 1.06847062139874 & 0.155586 & 6.8674 & 0 & 0 \tabularnewline
Y2 & -0.151877506173371 & 0.176414 & -0.8609 & 0.394173 & 0.197087 \tabularnewline
M1 & -0.0658484772738318 & 0.333842 & -0.1972 & 0.844588 & 0.422294 \tabularnewline
M2 & -0.0807067438688125 & 0.333377 & -0.2421 & 0.80989 & 0.404945 \tabularnewline
M3 & 0.119085905707768 & 0.332721 & 0.3579 & 0.7222 & 0.3611 \tabularnewline
M4 & -0.0704160867844202 & 0.334438 & -0.2106 & 0.834256 & 0.417128 \tabularnewline
M5 & -0.105059685311399 & 0.335323 & -0.3133 & 0.755597 & 0.377798 \tabularnewline
M6 & -0.236207021068785 & 0.335886 & -0.7032 & 0.485789 & 0.242894 \tabularnewline
M7 & -0.138233436004764 & 0.335708 & -0.4118 & 0.682604 & 0.341302 \tabularnewline
M8 & -0.0983526673209309 & 0.332598 & -0.2957 & 0.768908 & 0.384454 \tabularnewline
M9 & -0.251765154607209 & 0.333541 & -0.7548 & 0.454566 & 0.227283 \tabularnewline
M10 & -0.0539842332914323 & 0.337482 & -0.16 & 0.873678 & 0.436839 \tabularnewline
M11 & -0.123558533753511 & 0.350141 & -0.3529 & 0.725942 & 0.362971 \tabularnewline
t & -0.0100825486711427 & 0.014672 & -0.6872 & 0.495748 & 0.247874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58174&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]-0.0734302746307986[/C][C]0.516944[/C][C]-0.142[/C][C]0.887722[/C][C]0.443861[/C][/ROW]
[ROW][C]X[/C][C]0.240213449888453[/C][C]0.245619[/C][C]0.978[/C][C]0.333677[/C][C]0.166839[/C][/ROW]
[ROW][C]Y1[/C][C]1.06847062139874[/C][C]0.155586[/C][C]6.8674[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.151877506173371[/C][C]0.176414[/C][C]-0.8609[/C][C]0.394173[/C][C]0.197087[/C][/ROW]
[ROW][C]M1[/C][C]-0.0658484772738318[/C][C]0.333842[/C][C]-0.1972[/C][C]0.844588[/C][C]0.422294[/C][/ROW]
[ROW][C]M2[/C][C]-0.0807067438688125[/C][C]0.333377[/C][C]-0.2421[/C][C]0.80989[/C][C]0.404945[/C][/ROW]
[ROW][C]M3[/C][C]0.119085905707768[/C][C]0.332721[/C][C]0.3579[/C][C]0.7222[/C][C]0.3611[/C][/ROW]
[ROW][C]M4[/C][C]-0.0704160867844202[/C][C]0.334438[/C][C]-0.2106[/C][C]0.834256[/C][C]0.417128[/C][/ROW]
[ROW][C]M5[/C][C]-0.105059685311399[/C][C]0.335323[/C][C]-0.3133[/C][C]0.755597[/C][C]0.377798[/C][/ROW]
[ROW][C]M6[/C][C]-0.236207021068785[/C][C]0.335886[/C][C]-0.7032[/C][C]0.485789[/C][C]0.242894[/C][/ROW]
[ROW][C]M7[/C][C]-0.138233436004764[/C][C]0.335708[/C][C]-0.4118[/C][C]0.682604[/C][C]0.341302[/C][/ROW]
[ROW][C]M8[/C][C]-0.0983526673209309[/C][C]0.332598[/C][C]-0.2957[/C][C]0.768908[/C][C]0.384454[/C][/ROW]
[ROW][C]M9[/C][C]-0.251765154607209[/C][C]0.333541[/C][C]-0.7548[/C][C]0.454566[/C][C]0.227283[/C][/ROW]
[ROW][C]M10[/C][C]-0.0539842332914323[/C][C]0.337482[/C][C]-0.16[/C][C]0.873678[/C][C]0.436839[/C][/ROW]
[ROW][C]M11[/C][C]-0.123558533753511[/C][C]0.350141[/C][C]-0.3529[/C][C]0.725942[/C][C]0.362971[/C][/ROW]
[ROW][C]t[/C][C]-0.0100825486711427[/C][C]0.014672[/C][C]-0.6872[/C][C]0.495748[/C][C]0.247874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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)-0.07343027463079860.516944-0.1420.8877220.443861
X0.2402134498884530.2456190.9780.3336770.166839
Y11.068470621398740.1555866.867400
Y2-0.1518775061733710.176414-0.86090.3941730.197087
M1-0.06584847727383180.333842-0.19720.8445880.422294
M2-0.08070674386881250.333377-0.24210.809890.404945
M30.1190859057077680.3327210.35790.72220.3611
M4-0.07041608678442020.334438-0.21060.8342560.417128
M5-0.1050596853113990.335323-0.31330.7555970.377798
M6-0.2362070210687850.335886-0.70320.4857890.242894
M7-0.1382334360047640.335708-0.41180.6826040.341302
M8-0.09835266732093090.332598-0.29570.7689080.384454
M9-0.2517651546072090.333541-0.75480.4545660.227283
M10-0.05398423329143230.337482-0.160.8736780.436839
M11-0.1235585337535110.350141-0.35290.7259420.362971
t-0.01008254867114270.014672-0.68720.4957480.247874






Multiple Linear Regression - Regression Statistics
Multiple R0.93060263788341
R-squared0.866021269635562
Adjusted R-squared0.818171723076834
F-TEST (value)18.0988396321093
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value1.14797060746241e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.494837629499835
Sum Squared Residuals10.2842997418987

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.93060263788341 \tabularnewline
R-squared & 0.866021269635562 \tabularnewline
Adjusted R-squared & 0.818171723076834 \tabularnewline
F-TEST (value) & 18.0988396321093 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 1.14797060746241e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.494837629499835 \tabularnewline
Sum Squared Residuals & 10.2842997418987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58174&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.93060263788341[/C][/ROW]
[ROW][C]R-squared[/C][C]0.866021269635562[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.818171723076834[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]18.0988396321093[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]1.14797060746241e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.494837629499835[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]10.2842997418987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58174&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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 R0.93060263788341
R-squared0.866021269635562
Adjusted R-squared0.818171723076834
F-TEST (value)18.0988396321093
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value1.14797060746241e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.494837629499835
Sum Squared Residuals10.2842997418987






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
111.40060183623691-0.400601836236909
21.71.192342397925700.507657602074297
32.42.160357435044930.239642564955067
422.60238807453935-0.602388074539354
52.12.023959424460380.0760405755396217
622.05032760464107-0.0503276046410725
71.82.01618382827674-0.216183828276739
82.71.847475674627020.85252432537298
92.32.67597969916314-0.375979699163136
101.92.29960006769224-0.399600067692242
1121.853305972468870.146694027531126
122.32.134380022160460.165619977839535
132.82.363802432017770.436197567982226
142.42.82753367559901-0.427533675599007
152.32.51391677485826-0.213916774858265
162.72.268236174024410.431763825975592
172.72.666086026003120.0339139739968816
182.92.464105139105240.435894860894758
1932.765690299777870.234309700222133
202.22.87196008069576-0.671960080695757
212.31.838500797002010.461499202997989
222.82.304993061201790.495006938798211
232.82.753992310146140.0460076898538632
242.82.791529542141820.00847045785817974
252.22.76364120617454-0.563641206174536
262.62.109628690563590.490371309436406
272.82.81785354373255-0.0178535437325490
282.52.804842007364-0.304842007364
292.42.43562265199931-0.035622651999313
302.32.276347378262840.0236526217371558
311.92.28939404462538-0.389394044625376
321.71.94782805317695-0.247828053176947
3321.650606971400200.349393028599796
342.12.22285191468352-0.122851914683516
351.72.23090235532589-0.530902355325887
361.81.90180234123142-0.101802341231424
371.82.02950139737894-0.229501397378939
381.82.01339417648432-0.213394176484324
391.32.20310427738976-0.903104277389762
401.31.50531644301033-0.205316443010331
411.31.56055039388774-0.260550393887739
421.21.41932050945921-0.219320509459211
431.41.40036448371222-0.000364483712215286
442.21.659044578621990.54095542137801
452.92.319950538548880.580049461451115
463.13.13407634123394-0.0340763412339369
473.53.16179936205910.338200637940897
483.63.67228809446629-0.0722880944662918
494.43.642453128191840.757546871808157
504.14.45710105942737-0.357101059427372
515.14.204767968974490.895232031025509
525.85.119217301061910.680782698938093
535.95.713781503649450.186218496350549
545.45.58989936853163-0.189899368531630
555.55.12836734360780.371632656392198
564.85.27369161287829-0.473691612878285
573.24.21496199388576-1.01496199388576
582.72.638478615188520.0615213848114844

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1 & 1.40060183623691 & -0.400601836236909 \tabularnewline
2 & 1.7 & 1.19234239792570 & 0.507657602074297 \tabularnewline
3 & 2.4 & 2.16035743504493 & 0.239642564955067 \tabularnewline
4 & 2 & 2.60238807453935 & -0.602388074539354 \tabularnewline
5 & 2.1 & 2.02395942446038 & 0.0760405755396217 \tabularnewline
6 & 2 & 2.05032760464107 & -0.0503276046410725 \tabularnewline
7 & 1.8 & 2.01618382827674 & -0.216183828276739 \tabularnewline
8 & 2.7 & 1.84747567462702 & 0.85252432537298 \tabularnewline
9 & 2.3 & 2.67597969916314 & -0.375979699163136 \tabularnewline
10 & 1.9 & 2.29960006769224 & -0.399600067692242 \tabularnewline
11 & 2 & 1.85330597246887 & 0.146694027531126 \tabularnewline
12 & 2.3 & 2.13438002216046 & 0.165619977839535 \tabularnewline
13 & 2.8 & 2.36380243201777 & 0.436197567982226 \tabularnewline
14 & 2.4 & 2.82753367559901 & -0.427533675599007 \tabularnewline
15 & 2.3 & 2.51391677485826 & -0.213916774858265 \tabularnewline
16 & 2.7 & 2.26823617402441 & 0.431763825975592 \tabularnewline
17 & 2.7 & 2.66608602600312 & 0.0339139739968816 \tabularnewline
18 & 2.9 & 2.46410513910524 & 0.435894860894758 \tabularnewline
19 & 3 & 2.76569029977787 & 0.234309700222133 \tabularnewline
20 & 2.2 & 2.87196008069576 & -0.671960080695757 \tabularnewline
21 & 2.3 & 1.83850079700201 & 0.461499202997989 \tabularnewline
22 & 2.8 & 2.30499306120179 & 0.495006938798211 \tabularnewline
23 & 2.8 & 2.75399231014614 & 0.0460076898538632 \tabularnewline
24 & 2.8 & 2.79152954214182 & 0.00847045785817974 \tabularnewline
25 & 2.2 & 2.76364120617454 & -0.563641206174536 \tabularnewline
26 & 2.6 & 2.10962869056359 & 0.490371309436406 \tabularnewline
27 & 2.8 & 2.81785354373255 & -0.0178535437325490 \tabularnewline
28 & 2.5 & 2.804842007364 & -0.304842007364 \tabularnewline
29 & 2.4 & 2.43562265199931 & -0.035622651999313 \tabularnewline
30 & 2.3 & 2.27634737826284 & 0.0236526217371558 \tabularnewline
31 & 1.9 & 2.28939404462538 & -0.389394044625376 \tabularnewline
32 & 1.7 & 1.94782805317695 & -0.247828053176947 \tabularnewline
33 & 2 & 1.65060697140020 & 0.349393028599796 \tabularnewline
34 & 2.1 & 2.22285191468352 & -0.122851914683516 \tabularnewline
35 & 1.7 & 2.23090235532589 & -0.530902355325887 \tabularnewline
36 & 1.8 & 1.90180234123142 & -0.101802341231424 \tabularnewline
37 & 1.8 & 2.02950139737894 & -0.229501397378939 \tabularnewline
38 & 1.8 & 2.01339417648432 & -0.213394176484324 \tabularnewline
39 & 1.3 & 2.20310427738976 & -0.903104277389762 \tabularnewline
40 & 1.3 & 1.50531644301033 & -0.205316443010331 \tabularnewline
41 & 1.3 & 1.56055039388774 & -0.260550393887739 \tabularnewline
42 & 1.2 & 1.41932050945921 & -0.219320509459211 \tabularnewline
43 & 1.4 & 1.40036448371222 & -0.000364483712215286 \tabularnewline
44 & 2.2 & 1.65904457862199 & 0.54095542137801 \tabularnewline
45 & 2.9 & 2.31995053854888 & 0.580049461451115 \tabularnewline
46 & 3.1 & 3.13407634123394 & -0.0340763412339369 \tabularnewline
47 & 3.5 & 3.1617993620591 & 0.338200637940897 \tabularnewline
48 & 3.6 & 3.67228809446629 & -0.0722880944662918 \tabularnewline
49 & 4.4 & 3.64245312819184 & 0.757546871808157 \tabularnewline
50 & 4.1 & 4.45710105942737 & -0.357101059427372 \tabularnewline
51 & 5.1 & 4.20476796897449 & 0.895232031025509 \tabularnewline
52 & 5.8 & 5.11921730106191 & 0.680782698938093 \tabularnewline
53 & 5.9 & 5.71378150364945 & 0.186218496350549 \tabularnewline
54 & 5.4 & 5.58989936853163 & -0.189899368531630 \tabularnewline
55 & 5.5 & 5.1283673436078 & 0.371632656392198 \tabularnewline
56 & 4.8 & 5.27369161287829 & -0.473691612878285 \tabularnewline
57 & 3.2 & 4.21496199388576 & -1.01496199388576 \tabularnewline
58 & 2.7 & 2.63847861518852 & 0.0615213848114844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58174&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]1[/C][C]1.40060183623691[/C][C]-0.400601836236909[/C][/ROW]
[ROW][C]2[/C][C]1.7[/C][C]1.19234239792570[/C][C]0.507657602074297[/C][/ROW]
[ROW][C]3[/C][C]2.4[/C][C]2.16035743504493[/C][C]0.239642564955067[/C][/ROW]
[ROW][C]4[/C][C]2[/C][C]2.60238807453935[/C][C]-0.602388074539354[/C][/ROW]
[ROW][C]5[/C][C]2.1[/C][C]2.02395942446038[/C][C]0.0760405755396217[/C][/ROW]
[ROW][C]6[/C][C]2[/C][C]2.05032760464107[/C][C]-0.0503276046410725[/C][/ROW]
[ROW][C]7[/C][C]1.8[/C][C]2.01618382827674[/C][C]-0.216183828276739[/C][/ROW]
[ROW][C]8[/C][C]2.7[/C][C]1.84747567462702[/C][C]0.85252432537298[/C][/ROW]
[ROW][C]9[/C][C]2.3[/C][C]2.67597969916314[/C][C]-0.375979699163136[/C][/ROW]
[ROW][C]10[/C][C]1.9[/C][C]2.29960006769224[/C][C]-0.399600067692242[/C][/ROW]
[ROW][C]11[/C][C]2[/C][C]1.85330597246887[/C][C]0.146694027531126[/C][/ROW]
[ROW][C]12[/C][C]2.3[/C][C]2.13438002216046[/C][C]0.165619977839535[/C][/ROW]
[ROW][C]13[/C][C]2.8[/C][C]2.36380243201777[/C][C]0.436197567982226[/C][/ROW]
[ROW][C]14[/C][C]2.4[/C][C]2.82753367559901[/C][C]-0.427533675599007[/C][/ROW]
[ROW][C]15[/C][C]2.3[/C][C]2.51391677485826[/C][C]-0.213916774858265[/C][/ROW]
[ROW][C]16[/C][C]2.7[/C][C]2.26823617402441[/C][C]0.431763825975592[/C][/ROW]
[ROW][C]17[/C][C]2.7[/C][C]2.66608602600312[/C][C]0.0339139739968816[/C][/ROW]
[ROW][C]18[/C][C]2.9[/C][C]2.46410513910524[/C][C]0.435894860894758[/C][/ROW]
[ROW][C]19[/C][C]3[/C][C]2.76569029977787[/C][C]0.234309700222133[/C][/ROW]
[ROW][C]20[/C][C]2.2[/C][C]2.87196008069576[/C][C]-0.671960080695757[/C][/ROW]
[ROW][C]21[/C][C]2.3[/C][C]1.83850079700201[/C][C]0.461499202997989[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]2.30499306120179[/C][C]0.495006938798211[/C][/ROW]
[ROW][C]23[/C][C]2.8[/C][C]2.75399231014614[/C][C]0.0460076898538632[/C][/ROW]
[ROW][C]24[/C][C]2.8[/C][C]2.79152954214182[/C][C]0.00847045785817974[/C][/ROW]
[ROW][C]25[/C][C]2.2[/C][C]2.76364120617454[/C][C]-0.563641206174536[/C][/ROW]
[ROW][C]26[/C][C]2.6[/C][C]2.10962869056359[/C][C]0.490371309436406[/C][/ROW]
[ROW][C]27[/C][C]2.8[/C][C]2.81785354373255[/C][C]-0.0178535437325490[/C][/ROW]
[ROW][C]28[/C][C]2.5[/C][C]2.804842007364[/C][C]-0.304842007364[/C][/ROW]
[ROW][C]29[/C][C]2.4[/C][C]2.43562265199931[/C][C]-0.035622651999313[/C][/ROW]
[ROW][C]30[/C][C]2.3[/C][C]2.27634737826284[/C][C]0.0236526217371558[/C][/ROW]
[ROW][C]31[/C][C]1.9[/C][C]2.28939404462538[/C][C]-0.389394044625376[/C][/ROW]
[ROW][C]32[/C][C]1.7[/C][C]1.94782805317695[/C][C]-0.247828053176947[/C][/ROW]
[ROW][C]33[/C][C]2[/C][C]1.65060697140020[/C][C]0.349393028599796[/C][/ROW]
[ROW][C]34[/C][C]2.1[/C][C]2.22285191468352[/C][C]-0.122851914683516[/C][/ROW]
[ROW][C]35[/C][C]1.7[/C][C]2.23090235532589[/C][C]-0.530902355325887[/C][/ROW]
[ROW][C]36[/C][C]1.8[/C][C]1.90180234123142[/C][C]-0.101802341231424[/C][/ROW]
[ROW][C]37[/C][C]1.8[/C][C]2.02950139737894[/C][C]-0.229501397378939[/C][/ROW]
[ROW][C]38[/C][C]1.8[/C][C]2.01339417648432[/C][C]-0.213394176484324[/C][/ROW]
[ROW][C]39[/C][C]1.3[/C][C]2.20310427738976[/C][C]-0.903104277389762[/C][/ROW]
[ROW][C]40[/C][C]1.3[/C][C]1.50531644301033[/C][C]-0.205316443010331[/C][/ROW]
[ROW][C]41[/C][C]1.3[/C][C]1.56055039388774[/C][C]-0.260550393887739[/C][/ROW]
[ROW][C]42[/C][C]1.2[/C][C]1.41932050945921[/C][C]-0.219320509459211[/C][/ROW]
[ROW][C]43[/C][C]1.4[/C][C]1.40036448371222[/C][C]-0.000364483712215286[/C][/ROW]
[ROW][C]44[/C][C]2.2[/C][C]1.65904457862199[/C][C]0.54095542137801[/C][/ROW]
[ROW][C]45[/C][C]2.9[/C][C]2.31995053854888[/C][C]0.580049461451115[/C][/ROW]
[ROW][C]46[/C][C]3.1[/C][C]3.13407634123394[/C][C]-0.0340763412339369[/C][/ROW]
[ROW][C]47[/C][C]3.5[/C][C]3.1617993620591[/C][C]0.338200637940897[/C][/ROW]
[ROW][C]48[/C][C]3.6[/C][C]3.67228809446629[/C][C]-0.0722880944662918[/C][/ROW]
[ROW][C]49[/C][C]4.4[/C][C]3.64245312819184[/C][C]0.757546871808157[/C][/ROW]
[ROW][C]50[/C][C]4.1[/C][C]4.45710105942737[/C][C]-0.357101059427372[/C][/ROW]
[ROW][C]51[/C][C]5.1[/C][C]4.20476796897449[/C][C]0.895232031025509[/C][/ROW]
[ROW][C]52[/C][C]5.8[/C][C]5.11921730106191[/C][C]0.680782698938093[/C][/ROW]
[ROW][C]53[/C][C]5.9[/C][C]5.71378150364945[/C][C]0.186218496350549[/C][/ROW]
[ROW][C]54[/C][C]5.4[/C][C]5.58989936853163[/C][C]-0.189899368531630[/C][/ROW]
[ROW][C]55[/C][C]5.5[/C][C]5.1283673436078[/C][C]0.371632656392198[/C][/ROW]
[ROW][C]56[/C][C]4.8[/C][C]5.27369161287829[/C][C]-0.473691612878285[/C][/ROW]
[ROW][C]57[/C][C]3.2[/C][C]4.21496199388576[/C][C]-1.01496199388576[/C][/ROW]
[ROW][C]58[/C][C]2.7[/C][C]2.63847861518852[/C][C]0.0615213848114844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58174&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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
111.40060183623691-0.400601836236909
21.71.192342397925700.507657602074297
32.42.160357435044930.239642564955067
422.60238807453935-0.602388074539354
52.12.023959424460380.0760405755396217
622.05032760464107-0.0503276046410725
71.82.01618382827674-0.216183828276739
82.71.847475674627020.85252432537298
92.32.67597969916314-0.375979699163136
101.92.29960006769224-0.399600067692242
1121.853305972468870.146694027531126
122.32.134380022160460.165619977839535
132.82.363802432017770.436197567982226
142.42.82753367559901-0.427533675599007
152.32.51391677485826-0.213916774858265
162.72.268236174024410.431763825975592
172.72.666086026003120.0339139739968816
182.92.464105139105240.435894860894758
1932.765690299777870.234309700222133
202.22.87196008069576-0.671960080695757
212.31.838500797002010.461499202997989
222.82.304993061201790.495006938798211
232.82.753992310146140.0460076898538632
242.82.791529542141820.00847045785817974
252.22.76364120617454-0.563641206174536
262.62.109628690563590.490371309436406
272.82.81785354373255-0.0178535437325490
282.52.804842007364-0.304842007364
292.42.43562265199931-0.035622651999313
302.32.276347378262840.0236526217371558
311.92.28939404462538-0.389394044625376
321.71.94782805317695-0.247828053176947
3321.650606971400200.349393028599796
342.12.22285191468352-0.122851914683516
351.72.23090235532589-0.530902355325887
361.81.90180234123142-0.101802341231424
371.82.02950139737894-0.229501397378939
381.82.01339417648432-0.213394176484324
391.32.20310427738976-0.903104277389762
401.31.50531644301033-0.205316443010331
411.31.56055039388774-0.260550393887739
421.21.41932050945921-0.219320509459211
431.41.40036448371222-0.000364483712215286
442.21.659044578621990.54095542137801
452.92.319950538548880.580049461451115
463.13.13407634123394-0.0340763412339369
473.53.16179936205910.338200637940897
483.63.67228809446629-0.0722880944662918
494.43.642453128191840.757546871808157
504.14.45710105942737-0.357101059427372
515.14.204767968974490.895232031025509
525.85.119217301061910.680782698938093
535.95.713781503649450.186218496350549
545.45.58989936853163-0.189899368531630
555.55.12836734360780.371632656392198
564.85.27369161287829-0.473691612878285
573.24.21496199388576-1.01496199388576
582.72.638478615188520.0615213848114844






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4594417951185450.918883590237090.540558204881455
200.6551180938456680.6897638123086640.344881906154332
210.5318025812820740.9363948374358520.468197418717926
220.4105583770050220.8211167540100430.589441622994978
230.2889023708384560.5778047416769120.711097629161544
240.198229878056660.396459756113320.80177012194334
250.1394487522029320.2788975044058650.860551247797068
260.1320489839076340.2640979678152690.867951016092366
270.08920956064443160.1784191212888630.910790439355568
280.05432323484490990.1086464696898200.94567676515509
290.03219695834261670.06439391668523340.967803041657383
300.02210948722791760.04421897445583510.977890512772082
310.01259187193604590.02518374387209170.987408128063954
320.006524949755619530.01304989951123910.99347505024438
330.01079594238396360.02159188476792720.989204057616036
340.006705601192090430.01341120238418090.99329439880791
350.002868791472667950.00573758294533590.997131208527332
360.004807719408228820.009615438816457630.995192280591771
370.002372675144473760.004745350288947510.997627324855526
380.08143614826483490.1628722965296700.918563851735165
390.1972179678250720.3944359356501440.802782032174928

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.459441795118545 & 0.91888359023709 & 0.540558204881455 \tabularnewline
20 & 0.655118093845668 & 0.689763812308664 & 0.344881906154332 \tabularnewline
21 & 0.531802581282074 & 0.936394837435852 & 0.468197418717926 \tabularnewline
22 & 0.410558377005022 & 0.821116754010043 & 0.589441622994978 \tabularnewline
23 & 0.288902370838456 & 0.577804741676912 & 0.711097629161544 \tabularnewline
24 & 0.19822987805666 & 0.39645975611332 & 0.80177012194334 \tabularnewline
25 & 0.139448752202932 & 0.278897504405865 & 0.860551247797068 \tabularnewline
26 & 0.132048983907634 & 0.264097967815269 & 0.867951016092366 \tabularnewline
27 & 0.0892095606444316 & 0.178419121288863 & 0.910790439355568 \tabularnewline
28 & 0.0543232348449099 & 0.108646469689820 & 0.94567676515509 \tabularnewline
29 & 0.0321969583426167 & 0.0643939166852334 & 0.967803041657383 \tabularnewline
30 & 0.0221094872279176 & 0.0442189744558351 & 0.977890512772082 \tabularnewline
31 & 0.0125918719360459 & 0.0251837438720917 & 0.987408128063954 \tabularnewline
32 & 0.00652494975561953 & 0.0130498995112391 & 0.99347505024438 \tabularnewline
33 & 0.0107959423839636 & 0.0215918847679272 & 0.989204057616036 \tabularnewline
34 & 0.00670560119209043 & 0.0134112023841809 & 0.99329439880791 \tabularnewline
35 & 0.00286879147266795 & 0.0057375829453359 & 0.997131208527332 \tabularnewline
36 & 0.00480771940822882 & 0.00961543881645763 & 0.995192280591771 \tabularnewline
37 & 0.00237267514447376 & 0.00474535028894751 & 0.997627324855526 \tabularnewline
38 & 0.0814361482648349 & 0.162872296529670 & 0.918563851735165 \tabularnewline
39 & 0.197217967825072 & 0.394435935650144 & 0.802782032174928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58174&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]0.459441795118545[/C][C]0.91888359023709[/C][C]0.540558204881455[/C][/ROW]
[ROW][C]20[/C][C]0.655118093845668[/C][C]0.689763812308664[/C][C]0.344881906154332[/C][/ROW]
[ROW][C]21[/C][C]0.531802581282074[/C][C]0.936394837435852[/C][C]0.468197418717926[/C][/ROW]
[ROW][C]22[/C][C]0.410558377005022[/C][C]0.821116754010043[/C][C]0.589441622994978[/C][/ROW]
[ROW][C]23[/C][C]0.288902370838456[/C][C]0.577804741676912[/C][C]0.711097629161544[/C][/ROW]
[ROW][C]24[/C][C]0.19822987805666[/C][C]0.39645975611332[/C][C]0.80177012194334[/C][/ROW]
[ROW][C]25[/C][C]0.139448752202932[/C][C]0.278897504405865[/C][C]0.860551247797068[/C][/ROW]
[ROW][C]26[/C][C]0.132048983907634[/C][C]0.264097967815269[/C][C]0.867951016092366[/C][/ROW]
[ROW][C]27[/C][C]0.0892095606444316[/C][C]0.178419121288863[/C][C]0.910790439355568[/C][/ROW]
[ROW][C]28[/C][C]0.0543232348449099[/C][C]0.108646469689820[/C][C]0.94567676515509[/C][/ROW]
[ROW][C]29[/C][C]0.0321969583426167[/C][C]0.0643939166852334[/C][C]0.967803041657383[/C][/ROW]
[ROW][C]30[/C][C]0.0221094872279176[/C][C]0.0442189744558351[/C][C]0.977890512772082[/C][/ROW]
[ROW][C]31[/C][C]0.0125918719360459[/C][C]0.0251837438720917[/C][C]0.987408128063954[/C][/ROW]
[ROW][C]32[/C][C]0.00652494975561953[/C][C]0.0130498995112391[/C][C]0.99347505024438[/C][/ROW]
[ROW][C]33[/C][C]0.0107959423839636[/C][C]0.0215918847679272[/C][C]0.989204057616036[/C][/ROW]
[ROW][C]34[/C][C]0.00670560119209043[/C][C]0.0134112023841809[/C][C]0.99329439880791[/C][/ROW]
[ROW][C]35[/C][C]0.00286879147266795[/C][C]0.0057375829453359[/C][C]0.997131208527332[/C][/ROW]
[ROW][C]36[/C][C]0.00480771940822882[/C][C]0.00961543881645763[/C][C]0.995192280591771[/C][/ROW]
[ROW][C]37[/C][C]0.00237267514447376[/C][C]0.00474535028894751[/C][C]0.997627324855526[/C][/ROW]
[ROW][C]38[/C][C]0.0814361482648349[/C][C]0.162872296529670[/C][C]0.918563851735165[/C][/ROW]
[ROW][C]39[/C][C]0.197217967825072[/C][C]0.394435935650144[/C][C]0.802782032174928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58174&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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
190.4594417951185450.918883590237090.540558204881455
200.6551180938456680.6897638123086640.344881906154332
210.5318025812820740.9363948374358520.468197418717926
220.4105583770050220.8211167540100430.589441622994978
230.2889023708384560.5778047416769120.711097629161544
240.198229878056660.396459756113320.80177012194334
250.1394487522029320.2788975044058650.860551247797068
260.1320489839076340.2640979678152690.867951016092366
270.08920956064443160.1784191212888630.910790439355568
280.05432323484490990.1086464696898200.94567676515509
290.03219695834261670.06439391668523340.967803041657383
300.02210948722791760.04421897445583510.977890512772082
310.01259187193604590.02518374387209170.987408128063954
320.006524949755619530.01304989951123910.99347505024438
330.01079594238396360.02159188476792720.989204057616036
340.006705601192090430.01341120238418090.99329439880791
350.002868791472667950.00573758294533590.997131208527332
360.004807719408228820.009615438816457630.995192280591771
370.002372675144473760.004745350288947510.997627324855526
380.08143614826483490.1628722965296700.918563851735165
390.1972179678250720.3944359356501440.802782032174928






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.142857142857143NOK
5% type I error level80.380952380952381NOK
10% type I error level90.428571428571429NOK

\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 & 3 & 0.142857142857143 & NOK \tabularnewline
5% type I error level & 8 & 0.380952380952381 & NOK \tabularnewline
10% type I error level & 9 & 0.428571428571429 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58174&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]3[/C][C]0.142857142857143[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]8[/C][C]0.380952380952381[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]9[/C][C]0.428571428571429[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58174&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58174&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 level30.142857142857143NOK
5% type I error level80.380952380952381NOK
10% type I error level90.428571428571429NOK


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')
}