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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 04:59:00 -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/t1258718399kqcww4n4nbdcclp.htm/, Retrieved Tue, 23 Apr 2024 12:22:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58053, Retrieved Tue, 23 Apr 2024 12:22:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [link 4] [2009-11-20 11:59:00] [454b2df2fae01897bad5ff38ed3cc924] [Current]
-    D        [Multiple Regression] [ws7model4] [2009-11-27 12:02:57] [b5ba85a7ae9f50cb97d92cbc56161b32]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,6	0,55	1,6	1,6	1,59	1,58
1,6	0,56	1,6	1,6	1,6	1,59
1,61	0,56	1,6	1,6	1,6	1,6
1,61	0,56	1,61	1,6	1,6	1,6
1,62	0,56	1,61	1,61	1,6	1,6
1,63	0,56	1,62	1,61	1,61	1,6
1,63	0,55	1,63	1,62	1,61	1,61
1,63	0,56	1,63	1,63	1,62	1,61
1,63	0,55	1,63	1,63	1,63	1,62
1,63	0,55	1,63	1,63	1,63	1,63
1,64	0,56	1,63	1,63	1,63	1,63
1,64	0,55	1,64	1,63	1,63	1,63
1,64	0,55	1,64	1,64	1,63	1,63
1,65	0,55	1,64	1,64	1,64	1,63
1,65	0,55	1,65	1,64	1,64	1,64
1,65	0,53	1,65	1,65	1,64	1,64
1,65	0,53	1,65	1,65	1,65	1,64
1,65	0,53	1,65	1,65	1,65	1,65
1,66	0,53	1,65	1,65	1,65	1,65
1,67	0,54	1,66	1,65	1,65	1,65
1,68	0,54	1,67	1,66	1,65	1,65
1,68	0,54	1,68	1,67	1,66	1,65
1,68	0,55	1,68	1,68	1,67	1,66
1,68	0,55	1,68	1,68	1,68	1,67
1,69	0,54	1,68	1,68	1,68	1,68
1,7	0,55	1,69	1,68	1,68	1,68
1,7	0,56	1,7	1,69	1,68	1,68
1,71	0,58	1,7	1,7	1,69	1,68
1,73	0,59	1,71	1,7	1,7	1,69
1,73	0,6	1,73	1,71	1,7	1,7
1,73	0,6	1,73	1,73	1,71	1,7
1,74	0,6	1,73	1,73	1,73	1,71
1,74	0,59	1,74	1,73	1,73	1,73
1,74	0,6	1,74	1,74	1,73	1,73
1,75	0,6	1,74	1,74	1,74	1,73
1,78	0,62	1,75	1,74	1,74	1,74
1,82	0,65	1,78	1,75	1,74	1,74
1,83	0,68	1,82	1,78	1,75	1,74
1,84	0,73	1,83	1,82	1,78	1,75
1,85	0,78	1,84	1,83	1,82	1,78
1,86	0,78	1,85	1,84	1,83	1,82
1,86	0,82	1,86	1,85	1,84	1,83
1,87	0,82	1,86	1,86	1,85	1,84
1,87	0,81	1,87	1,86	1,86	1,85
1,87	0,83	1,87	1,87	1,86	1,86
1,87	0,85	1,87	1,87	1,87	1,86
1,87	0,86	1,87	1,87	1,87	1,87
1,87	0,85	1,87	1,87	1,87	1,87
1,87	0,85	1,87	1,87	1,87	1,87
1,88	0,82	1,87	1,87	1,87	1,87
1,88	0,8	1,88	1,87	1,87	1,87
1,87	0,81	1,88	1,88	1,87	1,87
1,87	0,8	1,87	1,88	1,88	1,87
1,87	0,8	1,87	1,87	1,88	1,88
1,87	0,8	1,87	1,87	1,87	1,88
1,87	0,8	1,87	1,87	1,87	1,87
1,87	0,79	1,87	1,87	1,87	1,87

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=58053&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=58053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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] = + 0.373041030730798 + 0.0731322482947126X[t] + 1.42861292764240Y1[t] -0.79401619507144Y2[t] + 0.441334049246045Y3[t] -0.334606997433555Y4[t] + 0.00358222217610623M1[t] -0.00127785491116625M2[t] -0.00305874236631328M3[t] -0.00477107569119665M4[t] + 0.00229643512668181M5[t] -0.00643096429226704M6[t] + 0.000599238113361633M7[t] -0.00360162979024544M8[t] -0.00326629003045313M9[t] -0.00469609721726716M10[t] + 0.000140090461648979M11[t] + 0.00106672568748966t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.373041030730798 +  0.0731322482947126X[t] +  1.42861292764240Y1[t] -0.79401619507144Y2[t] +  0.441334049246045Y3[t] -0.334606997433555Y4[t] +  0.00358222217610623M1[t] -0.00127785491116625M2[t] -0.00305874236631328M3[t] -0.00477107569119665M4[t] +  0.00229643512668181M5[t] -0.00643096429226704M6[t] +  0.000599238113361633M7[t] -0.00360162979024544M8[t] -0.00326629003045313M9[t] -0.00469609721726716M10[t] +  0.000140090461648979M11[t] +  0.00106672568748966t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58053&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.373041030730798 +  0.0731322482947126X[t] +  1.42861292764240Y1[t] -0.79401619507144Y2[t] +  0.441334049246045Y3[t] -0.334606997433555Y4[t] +  0.00358222217610623M1[t] -0.00127785491116625M2[t] -0.00305874236631328M3[t] -0.00477107569119665M4[t] +  0.00229643512668181M5[t] -0.00643096429226704M6[t] +  0.000599238113361633M7[t] -0.00360162979024544M8[t] -0.00326629003045313M9[t] -0.00469609721726716M10[t] +  0.000140090461648979M11[t] +  0.00106672568748966t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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] = + 0.373041030730798 + 0.0731322482947126X[t] + 1.42861292764240Y1[t] -0.79401619507144Y2[t] + 0.441334049246045Y3[t] -0.334606997433555Y4[t] + 0.00358222217610623M1[t] -0.00127785491116625M2[t] -0.00305874236631328M3[t] -0.00477107569119665M4[t] + 0.00229643512668181M5[t] -0.00643096429226704M6[t] + 0.000599238113361633M7[t] -0.00360162979024544M8[t] -0.00326629003045313M9[t] -0.00469609721726716M10[t] + 0.000140090461648979M11[t] + 0.00106672568748966t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.3730410307307980.2481061.50360.1407520.070376
X0.07313224829471260.0708761.03180.3085060.154253
Y11.428612927642400.1562059.145800
Y2-0.794016195071440.268437-2.95790.0052390.00262
Y30.4413340492460450.2643741.66940.1030560.051528
Y4-0.3346069974335550.16104-2.07780.0443590.022179
M10.003582222176106230.0050450.71010.4818820.240941
M2-0.001277854911166250.005022-0.25440.8004980.400249
M3-0.003058742366313280.005116-0.59790.5533920.276696
M4-0.004771075691196650.005114-0.93290.3566090.178305
M50.002296435126681810.0050260.45690.6502640.325132
M6-0.006430964292267040.00496-1.29670.2023640.101182
M70.0005992381133616330.0051810.11570.9085230.454261
M8-0.003601629790245440.004982-0.72290.474050.237025
M9-0.003266290030453130.005012-0.65170.5184250.259212
M10-0.004696097217267160.005314-0.88370.3822810.191141
M110.0001400904616489790.0052780.02650.9789620.489481
t0.001066725687489660.0006451.65370.1062190.053109

\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) & 0.373041030730798 & 0.248106 & 1.5036 & 0.140752 & 0.070376 \tabularnewline
X & 0.0731322482947126 & 0.070876 & 1.0318 & 0.308506 & 0.154253 \tabularnewline
Y1 & 1.42861292764240 & 0.156205 & 9.1458 & 0 & 0 \tabularnewline
Y2 & -0.79401619507144 & 0.268437 & -2.9579 & 0.005239 & 0.00262 \tabularnewline
Y3 & 0.441334049246045 & 0.264374 & 1.6694 & 0.103056 & 0.051528 \tabularnewline
Y4 & -0.334606997433555 & 0.16104 & -2.0778 & 0.044359 & 0.022179 \tabularnewline
M1 & 0.00358222217610623 & 0.005045 & 0.7101 & 0.481882 & 0.240941 \tabularnewline
M2 & -0.00127785491116625 & 0.005022 & -0.2544 & 0.800498 & 0.400249 \tabularnewline
M3 & -0.00305874236631328 & 0.005116 & -0.5979 & 0.553392 & 0.276696 \tabularnewline
M4 & -0.00477107569119665 & 0.005114 & -0.9329 & 0.356609 & 0.178305 \tabularnewline
M5 & 0.00229643512668181 & 0.005026 & 0.4569 & 0.650264 & 0.325132 \tabularnewline
M6 & -0.00643096429226704 & 0.00496 & -1.2967 & 0.202364 & 0.101182 \tabularnewline
M7 & 0.000599238113361633 & 0.005181 & 0.1157 & 0.908523 & 0.454261 \tabularnewline
M8 & -0.00360162979024544 & 0.004982 & -0.7229 & 0.47405 & 0.237025 \tabularnewline
M9 & -0.00326629003045313 & 0.005012 & -0.6517 & 0.518425 & 0.259212 \tabularnewline
M10 & -0.00469609721726716 & 0.005314 & -0.8837 & 0.382281 & 0.191141 \tabularnewline
M11 & 0.000140090461648979 & 0.005278 & 0.0265 & 0.978962 & 0.489481 \tabularnewline
t & 0.00106672568748966 & 0.000645 & 1.6537 & 0.106219 & 0.053109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58053&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]0.373041030730798[/C][C]0.248106[/C][C]1.5036[/C][C]0.140752[/C][C]0.070376[/C][/ROW]
[ROW][C]X[/C][C]0.0731322482947126[/C][C]0.070876[/C][C]1.0318[/C][C]0.308506[/C][C]0.154253[/C][/ROW]
[ROW][C]Y1[/C][C]1.42861292764240[/C][C]0.156205[/C][C]9.1458[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.79401619507144[/C][C]0.268437[/C][C]-2.9579[/C][C]0.005239[/C][C]0.00262[/C][/ROW]
[ROW][C]Y3[/C][C]0.441334049246045[/C][C]0.264374[/C][C]1.6694[/C][C]0.103056[/C][C]0.051528[/C][/ROW]
[ROW][C]Y4[/C][C]-0.334606997433555[/C][C]0.16104[/C][C]-2.0778[/C][C]0.044359[/C][C]0.022179[/C][/ROW]
[ROW][C]M1[/C][C]0.00358222217610623[/C][C]0.005045[/C][C]0.7101[/C][C]0.481882[/C][C]0.240941[/C][/ROW]
[ROW][C]M2[/C][C]-0.00127785491116625[/C][C]0.005022[/C][C]-0.2544[/C][C]0.800498[/C][C]0.400249[/C][/ROW]
[ROW][C]M3[/C][C]-0.00305874236631328[/C][C]0.005116[/C][C]-0.5979[/C][C]0.553392[/C][C]0.276696[/C][/ROW]
[ROW][C]M4[/C][C]-0.00477107569119665[/C][C]0.005114[/C][C]-0.9329[/C][C]0.356609[/C][C]0.178305[/C][/ROW]
[ROW][C]M5[/C][C]0.00229643512668181[/C][C]0.005026[/C][C]0.4569[/C][C]0.650264[/C][C]0.325132[/C][/ROW]
[ROW][C]M6[/C][C]-0.00643096429226704[/C][C]0.00496[/C][C]-1.2967[/C][C]0.202364[/C][C]0.101182[/C][/ROW]
[ROW][C]M7[/C][C]0.000599238113361633[/C][C]0.005181[/C][C]0.1157[/C][C]0.908523[/C][C]0.454261[/C][/ROW]
[ROW][C]M8[/C][C]-0.00360162979024544[/C][C]0.004982[/C][C]-0.7229[/C][C]0.47405[/C][C]0.237025[/C][/ROW]
[ROW][C]M9[/C][C]-0.00326629003045313[/C][C]0.005012[/C][C]-0.6517[/C][C]0.518425[/C][C]0.259212[/C][/ROW]
[ROW][C]M10[/C][C]-0.00469609721726716[/C][C]0.005314[/C][C]-0.8837[/C][C]0.382281[/C][C]0.191141[/C][/ROW]
[ROW][C]M11[/C][C]0.000140090461648979[/C][C]0.005278[/C][C]0.0265[/C][C]0.978962[/C][C]0.489481[/C][/ROW]
[ROW][C]t[/C][C]0.00106672568748966[/C][C]0.000645[/C][C]1.6537[/C][C]0.106219[/C][C]0.053109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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)0.3730410307307980.2481061.50360.1407520.070376
X0.07313224829471260.0708761.03180.3085060.154253
Y11.428612927642400.1562059.145800
Y2-0.794016195071440.268437-2.95790.0052390.00262
Y30.4413340492460450.2643741.66940.1030560.051528
Y4-0.3346069974335550.16104-2.07780.0443590.022179
M10.003582222176106230.0050450.71010.4818820.240941
M2-0.001277854911166250.005022-0.25440.8004980.400249
M3-0.003058742366313280.005116-0.59790.5533920.276696
M4-0.004771075691196650.005114-0.93290.3566090.178305
M50.002296435126681810.0050260.45690.6502640.325132
M6-0.006430964292267040.00496-1.29670.2023640.101182
M70.0005992381133616330.0051810.11570.9085230.454261
M8-0.003601629790245440.004982-0.72290.474050.237025
M9-0.003266290030453130.005012-0.65170.5184250.259212
M10-0.004696097217267160.005314-0.88370.3822810.191141
M110.0001400904616489790.0052780.02650.9789620.489481
t0.001066725687489660.0006451.65370.1062190.053109






Multiple Linear Regression - Regression Statistics
Multiple R0.998175276796487
R-squared0.996353883207744
Adjusted R-squared0.994764550247017
F-TEST (value)626.900660735122
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.00734352971707821
Sum Squared Residuals0.00210316971951882

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.998175276796487 \tabularnewline
R-squared & 0.996353883207744 \tabularnewline
Adjusted R-squared & 0.994764550247017 \tabularnewline
F-TEST (value) & 626.900660735122 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.00734352971707821 \tabularnewline
Sum Squared Residuals & 0.00210316971951882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58053&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.998175276796487[/C][/ROW]
[ROW][C]R-squared[/C][C]0.996353883207744[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.994764550247017[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]626.900660735122[/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]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.00734352971707821[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.00210316971951882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58053&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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 R0.998175276796487
R-squared0.996353883207744
Adjusted R-squared0.994764550247017
F-TEST (value)626.900660735122
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.00734352971707821
Sum Squared Residuals0.00210316971951882






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.61.60630956962621-0.00630956962621468
21.61.6043148112275-0.00431481122750106
31.611.600254579485510.0097454205144918
41.611.61389510112454-0.00389510112453837
51.621.614089175679190.00591082432080794
61.631.625127971716620.00487202828338250
71.631.63549347467816-0.00549347467816241
81.631.629563833486740.000436166513261634
91.631.63130184696920-0.00130184696919800
101.631.627592695495540.00240730450446184
111.641.634226931344890.00577306865510891
121.641.64870837336421-0.00870837336420861
131.641.64541715927709-0.0054171592770901
141.651.646037148369770.00396285163023228
151.651.6562630459042-0.00626304590419878
161.651.646214631350200.00378536864980361
171.651.65876220834802-0.00876220834802496
181.651.647755464642230.00224453535776977
191.661.655852392735350.00414760726465145
201.671.667735702278600.00226429772139774
211.681.675483735051590.00451626494840622
221.681.68587996137044-0.00587996137043944
231.681.68564130578720-0.00564130578720288
241.681.68763521153117-0.00763521153116847
251.691.688206766937480.00179323306251834
261.71.699430867297070.000569132702930058
271.71.70579399533807-0.00579399533806928
281.711.703084211208320.00691578879168415
291.731.727303169991180.00269683000882003
301.731.73765984537047-0.0076598453704659
311.731.73428979005462-0.00428979005461587
321.741.736636258849080.00336374115091619
331.741.74490099114117-0.00490099114117154
341.741.737329070174080.00267092982592012
351.751.747645324032950.00235467596705387
361.781.760974663526770.0190253364732305
371.821.802735804717760.0172641952822358
381.831.83887379251284-0.00887379251283594
391.841.834235676136530.00576432386347366
401.851.85120780028641-0.00120780028641301
411.861.856717064712610.00328293528739105
421.861.859394918756770.000605081243227267
431.871.86061895541730.00938104458269844
441.871.87210689051279-0.00210689051278590
451.871.863685369000910.00631463099908783
461.871.869198272959940.000801727040057486
471.871.87248643883496-0.00248643883495991
481.871.87268175157785-0.00268175157785346
491.871.87733069944145-0.00733069944144935
501.881.871343380592830.00865661940717465
511.881.88345270313570-0.00345270313569739
521.871.87559825603054-0.00559825603053637
531.871.87312838126899-0.00312838126899405
541.871.87006179951391-6.17995139136242e-05
551.871.87374538711457-0.00374538711457161
561.871.87395731487279-0.00395731487278968
571.871.87462805783712-0.00462805783712452

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.6 & 1.60630956962621 & -0.00630956962621468 \tabularnewline
2 & 1.6 & 1.6043148112275 & -0.00431481122750106 \tabularnewline
3 & 1.61 & 1.60025457948551 & 0.0097454205144918 \tabularnewline
4 & 1.61 & 1.61389510112454 & -0.00389510112453837 \tabularnewline
5 & 1.62 & 1.61408917567919 & 0.00591082432080794 \tabularnewline
6 & 1.63 & 1.62512797171662 & 0.00487202828338250 \tabularnewline
7 & 1.63 & 1.63549347467816 & -0.00549347467816241 \tabularnewline
8 & 1.63 & 1.62956383348674 & 0.000436166513261634 \tabularnewline
9 & 1.63 & 1.63130184696920 & -0.00130184696919800 \tabularnewline
10 & 1.63 & 1.62759269549554 & 0.00240730450446184 \tabularnewline
11 & 1.64 & 1.63422693134489 & 0.00577306865510891 \tabularnewline
12 & 1.64 & 1.64870837336421 & -0.00870837336420861 \tabularnewline
13 & 1.64 & 1.64541715927709 & -0.0054171592770901 \tabularnewline
14 & 1.65 & 1.64603714836977 & 0.00396285163023228 \tabularnewline
15 & 1.65 & 1.6562630459042 & -0.00626304590419878 \tabularnewline
16 & 1.65 & 1.64621463135020 & 0.00378536864980361 \tabularnewline
17 & 1.65 & 1.65876220834802 & -0.00876220834802496 \tabularnewline
18 & 1.65 & 1.64775546464223 & 0.00224453535776977 \tabularnewline
19 & 1.66 & 1.65585239273535 & 0.00414760726465145 \tabularnewline
20 & 1.67 & 1.66773570227860 & 0.00226429772139774 \tabularnewline
21 & 1.68 & 1.67548373505159 & 0.00451626494840622 \tabularnewline
22 & 1.68 & 1.68587996137044 & -0.00587996137043944 \tabularnewline
23 & 1.68 & 1.68564130578720 & -0.00564130578720288 \tabularnewline
24 & 1.68 & 1.68763521153117 & -0.00763521153116847 \tabularnewline
25 & 1.69 & 1.68820676693748 & 0.00179323306251834 \tabularnewline
26 & 1.7 & 1.69943086729707 & 0.000569132702930058 \tabularnewline
27 & 1.7 & 1.70579399533807 & -0.00579399533806928 \tabularnewline
28 & 1.71 & 1.70308421120832 & 0.00691578879168415 \tabularnewline
29 & 1.73 & 1.72730316999118 & 0.00269683000882003 \tabularnewline
30 & 1.73 & 1.73765984537047 & -0.0076598453704659 \tabularnewline
31 & 1.73 & 1.73428979005462 & -0.00428979005461587 \tabularnewline
32 & 1.74 & 1.73663625884908 & 0.00336374115091619 \tabularnewline
33 & 1.74 & 1.74490099114117 & -0.00490099114117154 \tabularnewline
34 & 1.74 & 1.73732907017408 & 0.00267092982592012 \tabularnewline
35 & 1.75 & 1.74764532403295 & 0.00235467596705387 \tabularnewline
36 & 1.78 & 1.76097466352677 & 0.0190253364732305 \tabularnewline
37 & 1.82 & 1.80273580471776 & 0.0172641952822358 \tabularnewline
38 & 1.83 & 1.83887379251284 & -0.00887379251283594 \tabularnewline
39 & 1.84 & 1.83423567613653 & 0.00576432386347366 \tabularnewline
40 & 1.85 & 1.85120780028641 & -0.00120780028641301 \tabularnewline
41 & 1.86 & 1.85671706471261 & 0.00328293528739105 \tabularnewline
42 & 1.86 & 1.85939491875677 & 0.000605081243227267 \tabularnewline
43 & 1.87 & 1.8606189554173 & 0.00938104458269844 \tabularnewline
44 & 1.87 & 1.87210689051279 & -0.00210689051278590 \tabularnewline
45 & 1.87 & 1.86368536900091 & 0.00631463099908783 \tabularnewline
46 & 1.87 & 1.86919827295994 & 0.000801727040057486 \tabularnewline
47 & 1.87 & 1.87248643883496 & -0.00248643883495991 \tabularnewline
48 & 1.87 & 1.87268175157785 & -0.00268175157785346 \tabularnewline
49 & 1.87 & 1.87733069944145 & -0.00733069944144935 \tabularnewline
50 & 1.88 & 1.87134338059283 & 0.00865661940717465 \tabularnewline
51 & 1.88 & 1.88345270313570 & -0.00345270313569739 \tabularnewline
52 & 1.87 & 1.87559825603054 & -0.00559825603053637 \tabularnewline
53 & 1.87 & 1.87312838126899 & -0.00312838126899405 \tabularnewline
54 & 1.87 & 1.87006179951391 & -6.17995139136242e-05 \tabularnewline
55 & 1.87 & 1.87374538711457 & -0.00374538711457161 \tabularnewline
56 & 1.87 & 1.87395731487279 & -0.00395731487278968 \tabularnewline
57 & 1.87 & 1.87462805783712 & -0.00462805783712452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58053&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]1.6[/C][C]1.60630956962621[/C][C]-0.00630956962621468[/C][/ROW]
[ROW][C]2[/C][C]1.6[/C][C]1.6043148112275[/C][C]-0.00431481122750106[/C][/ROW]
[ROW][C]3[/C][C]1.61[/C][C]1.60025457948551[/C][C]0.0097454205144918[/C][/ROW]
[ROW][C]4[/C][C]1.61[/C][C]1.61389510112454[/C][C]-0.00389510112453837[/C][/ROW]
[ROW][C]5[/C][C]1.62[/C][C]1.61408917567919[/C][C]0.00591082432080794[/C][/ROW]
[ROW][C]6[/C][C]1.63[/C][C]1.62512797171662[/C][C]0.00487202828338250[/C][/ROW]
[ROW][C]7[/C][C]1.63[/C][C]1.63549347467816[/C][C]-0.00549347467816241[/C][/ROW]
[ROW][C]8[/C][C]1.63[/C][C]1.62956383348674[/C][C]0.000436166513261634[/C][/ROW]
[ROW][C]9[/C][C]1.63[/C][C]1.63130184696920[/C][C]-0.00130184696919800[/C][/ROW]
[ROW][C]10[/C][C]1.63[/C][C]1.62759269549554[/C][C]0.00240730450446184[/C][/ROW]
[ROW][C]11[/C][C]1.64[/C][C]1.63422693134489[/C][C]0.00577306865510891[/C][/ROW]
[ROW][C]12[/C][C]1.64[/C][C]1.64870837336421[/C][C]-0.00870837336420861[/C][/ROW]
[ROW][C]13[/C][C]1.64[/C][C]1.64541715927709[/C][C]-0.0054171592770901[/C][/ROW]
[ROW][C]14[/C][C]1.65[/C][C]1.64603714836977[/C][C]0.00396285163023228[/C][/ROW]
[ROW][C]15[/C][C]1.65[/C][C]1.6562630459042[/C][C]-0.00626304590419878[/C][/ROW]
[ROW][C]16[/C][C]1.65[/C][C]1.64621463135020[/C][C]0.00378536864980361[/C][/ROW]
[ROW][C]17[/C][C]1.65[/C][C]1.65876220834802[/C][C]-0.00876220834802496[/C][/ROW]
[ROW][C]18[/C][C]1.65[/C][C]1.64775546464223[/C][C]0.00224453535776977[/C][/ROW]
[ROW][C]19[/C][C]1.66[/C][C]1.65585239273535[/C][C]0.00414760726465145[/C][/ROW]
[ROW][C]20[/C][C]1.67[/C][C]1.66773570227860[/C][C]0.00226429772139774[/C][/ROW]
[ROW][C]21[/C][C]1.68[/C][C]1.67548373505159[/C][C]0.00451626494840622[/C][/ROW]
[ROW][C]22[/C][C]1.68[/C][C]1.68587996137044[/C][C]-0.00587996137043944[/C][/ROW]
[ROW][C]23[/C][C]1.68[/C][C]1.68564130578720[/C][C]-0.00564130578720288[/C][/ROW]
[ROW][C]24[/C][C]1.68[/C][C]1.68763521153117[/C][C]-0.00763521153116847[/C][/ROW]
[ROW][C]25[/C][C]1.69[/C][C]1.68820676693748[/C][C]0.00179323306251834[/C][/ROW]
[ROW][C]26[/C][C]1.7[/C][C]1.69943086729707[/C][C]0.000569132702930058[/C][/ROW]
[ROW][C]27[/C][C]1.7[/C][C]1.70579399533807[/C][C]-0.00579399533806928[/C][/ROW]
[ROW][C]28[/C][C]1.71[/C][C]1.70308421120832[/C][C]0.00691578879168415[/C][/ROW]
[ROW][C]29[/C][C]1.73[/C][C]1.72730316999118[/C][C]0.00269683000882003[/C][/ROW]
[ROW][C]30[/C][C]1.73[/C][C]1.73765984537047[/C][C]-0.0076598453704659[/C][/ROW]
[ROW][C]31[/C][C]1.73[/C][C]1.73428979005462[/C][C]-0.00428979005461587[/C][/ROW]
[ROW][C]32[/C][C]1.74[/C][C]1.73663625884908[/C][C]0.00336374115091619[/C][/ROW]
[ROW][C]33[/C][C]1.74[/C][C]1.74490099114117[/C][C]-0.00490099114117154[/C][/ROW]
[ROW][C]34[/C][C]1.74[/C][C]1.73732907017408[/C][C]0.00267092982592012[/C][/ROW]
[ROW][C]35[/C][C]1.75[/C][C]1.74764532403295[/C][C]0.00235467596705387[/C][/ROW]
[ROW][C]36[/C][C]1.78[/C][C]1.76097466352677[/C][C]0.0190253364732305[/C][/ROW]
[ROW][C]37[/C][C]1.82[/C][C]1.80273580471776[/C][C]0.0172641952822358[/C][/ROW]
[ROW][C]38[/C][C]1.83[/C][C]1.83887379251284[/C][C]-0.00887379251283594[/C][/ROW]
[ROW][C]39[/C][C]1.84[/C][C]1.83423567613653[/C][C]0.00576432386347366[/C][/ROW]
[ROW][C]40[/C][C]1.85[/C][C]1.85120780028641[/C][C]-0.00120780028641301[/C][/ROW]
[ROW][C]41[/C][C]1.86[/C][C]1.85671706471261[/C][C]0.00328293528739105[/C][/ROW]
[ROW][C]42[/C][C]1.86[/C][C]1.85939491875677[/C][C]0.000605081243227267[/C][/ROW]
[ROW][C]43[/C][C]1.87[/C][C]1.8606189554173[/C][C]0.00938104458269844[/C][/ROW]
[ROW][C]44[/C][C]1.87[/C][C]1.87210689051279[/C][C]-0.00210689051278590[/C][/ROW]
[ROW][C]45[/C][C]1.87[/C][C]1.86368536900091[/C][C]0.00631463099908783[/C][/ROW]
[ROW][C]46[/C][C]1.87[/C][C]1.86919827295994[/C][C]0.000801727040057486[/C][/ROW]
[ROW][C]47[/C][C]1.87[/C][C]1.87248643883496[/C][C]-0.00248643883495991[/C][/ROW]
[ROW][C]48[/C][C]1.87[/C][C]1.87268175157785[/C][C]-0.00268175157785346[/C][/ROW]
[ROW][C]49[/C][C]1.87[/C][C]1.87733069944145[/C][C]-0.00733069944144935[/C][/ROW]
[ROW][C]50[/C][C]1.88[/C][C]1.87134338059283[/C][C]0.00865661940717465[/C][/ROW]
[ROW][C]51[/C][C]1.88[/C][C]1.88345270313570[/C][C]-0.00345270313569739[/C][/ROW]
[ROW][C]52[/C][C]1.87[/C][C]1.87559825603054[/C][C]-0.00559825603053637[/C][/ROW]
[ROW][C]53[/C][C]1.87[/C][C]1.87312838126899[/C][C]-0.00312838126899405[/C][/ROW]
[ROW][C]54[/C][C]1.87[/C][C]1.87006179951391[/C][C]-6.17995139136242e-05[/C][/ROW]
[ROW][C]55[/C][C]1.87[/C][C]1.87374538711457[/C][C]-0.00374538711457161[/C][/ROW]
[ROW][C]56[/C][C]1.87[/C][C]1.87395731487279[/C][C]-0.00395731487278968[/C][/ROW]
[ROW][C]57[/C][C]1.87[/C][C]1.87462805783712[/C][C]-0.00462805783712452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58053&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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
11.61.60630956962621-0.00630956962621468
21.61.6043148112275-0.00431481122750106
31.611.600254579485510.0097454205144918
41.611.61389510112454-0.00389510112453837
51.621.614089175679190.00591082432080794
61.631.625127971716620.00487202828338250
71.631.63549347467816-0.00549347467816241
81.631.629563833486740.000436166513261634
91.631.63130184696920-0.00130184696919800
101.631.627592695495540.00240730450446184
111.641.634226931344890.00577306865510891
121.641.64870837336421-0.00870837336420861
131.641.64541715927709-0.0054171592770901
141.651.646037148369770.00396285163023228
151.651.6562630459042-0.00626304590419878
161.651.646214631350200.00378536864980361
171.651.65876220834802-0.00876220834802496
181.651.647755464642230.00224453535776977
191.661.655852392735350.00414760726465145
201.671.667735702278600.00226429772139774
211.681.675483735051590.00451626494840622
221.681.68587996137044-0.00587996137043944
231.681.68564130578720-0.00564130578720288
241.681.68763521153117-0.00763521153116847
251.691.688206766937480.00179323306251834
261.71.699430867297070.000569132702930058
271.71.70579399533807-0.00579399533806928
281.711.703084211208320.00691578879168415
291.731.727303169991180.00269683000882003
301.731.73765984537047-0.0076598453704659
311.731.73428979005462-0.00428979005461587
321.741.736636258849080.00336374115091619
331.741.74490099114117-0.00490099114117154
341.741.737329070174080.00267092982592012
351.751.747645324032950.00235467596705387
361.781.760974663526770.0190253364732305
371.821.802735804717760.0172641952822358
381.831.83887379251284-0.00887379251283594
391.841.834235676136530.00576432386347366
401.851.85120780028641-0.00120780028641301
411.861.856717064712610.00328293528739105
421.861.859394918756770.000605081243227267
431.871.86061895541730.00938104458269844
441.871.87210689051279-0.00210689051278590
451.871.863685369000910.00631463099908783
461.871.869198272959940.000801727040057486
471.871.87248643883496-0.00248643883495991
481.871.87268175157785-0.00268175157785346
491.871.87733069944145-0.00733069944144935
501.881.871343380592830.00865661940717465
511.881.88345270313570-0.00345270313569739
521.871.87559825603054-0.00559825603053637
531.871.87312838126899-0.00312838126899405
541.871.87006179951391-6.17995139136242e-05
551.871.87374538711457-0.00374538711457161
561.871.87395731487279-0.00395731487278968
571.871.87462805783712-0.00462805783712452






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.205748964488810.411497928977620.79425103551119
220.1550100201938660.3100200403877320.844989979806134
230.1038055046139150.2076110092278290.896194495386085
240.0721496062601110.1442992125202220.927850393739889
250.1053391421275600.2106782842551200.89466085787244
260.05658819760784210.1131763952156840.943411802392158
270.04301535984532380.08603071969064750.956984640154676
280.02442766970204660.04885533940409330.975572330297953
290.01352338435551400.02704676871102790.986476615644486
300.01114226636462050.02228453272924100.98885773363538
310.008419710551357360.01683942110271470.991580289448643
320.004538124220040670.009076248440081340.99546187577996
330.01391354083812840.02782708167625680.986086459161872
340.02282055561492230.04564111122984470.977179444385078
350.07076881550572760.1415376310114550.929231184494272
360.8777242327314310.2445515345371380.122275767268569

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.20574896448881 & 0.41149792897762 & 0.79425103551119 \tabularnewline
22 & 0.155010020193866 & 0.310020040387732 & 0.844989979806134 \tabularnewline
23 & 0.103805504613915 & 0.207611009227829 & 0.896194495386085 \tabularnewline
24 & 0.072149606260111 & 0.144299212520222 & 0.927850393739889 \tabularnewline
25 & 0.105339142127560 & 0.210678284255120 & 0.89466085787244 \tabularnewline
26 & 0.0565881976078421 & 0.113176395215684 & 0.943411802392158 \tabularnewline
27 & 0.0430153598453238 & 0.0860307196906475 & 0.956984640154676 \tabularnewline
28 & 0.0244276697020466 & 0.0488553394040933 & 0.975572330297953 \tabularnewline
29 & 0.0135233843555140 & 0.0270467687110279 & 0.986476615644486 \tabularnewline
30 & 0.0111422663646205 & 0.0222845327292410 & 0.98885773363538 \tabularnewline
31 & 0.00841971055135736 & 0.0168394211027147 & 0.991580289448643 \tabularnewline
32 & 0.00453812422004067 & 0.00907624844008134 & 0.99546187577996 \tabularnewline
33 & 0.0139135408381284 & 0.0278270816762568 & 0.986086459161872 \tabularnewline
34 & 0.0228205556149223 & 0.0456411112298447 & 0.977179444385078 \tabularnewline
35 & 0.0707688155057276 & 0.141537631011455 & 0.929231184494272 \tabularnewline
36 & 0.877724232731431 & 0.244551534537138 & 0.122275767268569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58053&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]0.20574896448881[/C][C]0.41149792897762[/C][C]0.79425103551119[/C][/ROW]
[ROW][C]22[/C][C]0.155010020193866[/C][C]0.310020040387732[/C][C]0.844989979806134[/C][/ROW]
[ROW][C]23[/C][C]0.103805504613915[/C][C]0.207611009227829[/C][C]0.896194495386085[/C][/ROW]
[ROW][C]24[/C][C]0.072149606260111[/C][C]0.144299212520222[/C][C]0.927850393739889[/C][/ROW]
[ROW][C]25[/C][C]0.105339142127560[/C][C]0.210678284255120[/C][C]0.89466085787244[/C][/ROW]
[ROW][C]26[/C][C]0.0565881976078421[/C][C]0.113176395215684[/C][C]0.943411802392158[/C][/ROW]
[ROW][C]27[/C][C]0.0430153598453238[/C][C]0.0860307196906475[/C][C]0.956984640154676[/C][/ROW]
[ROW][C]28[/C][C]0.0244276697020466[/C][C]0.0488553394040933[/C][C]0.975572330297953[/C][/ROW]
[ROW][C]29[/C][C]0.0135233843555140[/C][C]0.0270467687110279[/C][C]0.986476615644486[/C][/ROW]
[ROW][C]30[/C][C]0.0111422663646205[/C][C]0.0222845327292410[/C][C]0.98885773363538[/C][/ROW]
[ROW][C]31[/C][C]0.00841971055135736[/C][C]0.0168394211027147[/C][C]0.991580289448643[/C][/ROW]
[ROW][C]32[/C][C]0.00453812422004067[/C][C]0.00907624844008134[/C][C]0.99546187577996[/C][/ROW]
[ROW][C]33[/C][C]0.0139135408381284[/C][C]0.0278270816762568[/C][C]0.986086459161872[/C][/ROW]
[ROW][C]34[/C][C]0.0228205556149223[/C][C]0.0456411112298447[/C][C]0.977179444385078[/C][/ROW]
[ROW][C]35[/C][C]0.0707688155057276[/C][C]0.141537631011455[/C][C]0.929231184494272[/C][/ROW]
[ROW][C]36[/C][C]0.877724232731431[/C][C]0.244551534537138[/C][C]0.122275767268569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58053&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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
210.205748964488810.411497928977620.79425103551119
220.1550100201938660.3100200403877320.844989979806134
230.1038055046139150.2076110092278290.896194495386085
240.0721496062601110.1442992125202220.927850393739889
250.1053391421275600.2106782842551200.89466085787244
260.05658819760784210.1131763952156840.943411802392158
270.04301535984532380.08603071969064750.956984640154676
280.02442766970204660.04885533940409330.975572330297953
290.01352338435551400.02704676871102790.986476615644486
300.01114226636462050.02228453272924100.98885773363538
310.008419710551357360.01683942110271470.991580289448643
320.004538124220040670.009076248440081340.99546187577996
330.01391354083812840.02782708167625680.986086459161872
340.02282055561492230.04564111122984470.977179444385078
350.07076881550572760.1415376310114550.929231184494272
360.8777242327314310.2445515345371380.122275767268569






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0625NOK
5% type I error level70.4375NOK
10% type I error level80.5NOK

\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 & 1 & 0.0625 & NOK \tabularnewline
5% type I error level & 7 & 0.4375 & NOK \tabularnewline
10% type I error level & 8 & 0.5 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58053&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]1[/C][C]0.0625[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.4375[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.5[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58053&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58053&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 level10.0625NOK
5% type I error level70.4375NOK
10% type I error level80.5NOK


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')
}