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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 09:59:52 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258650105rug1ebobr6dn75p.htm/, Retrieved Fri, 29 Mar 2024 07:56:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57828, Retrieved Fri, 29 Mar 2024 07:56:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:14:11] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-19 16:59:52] [5858ea01c9bd81debbf921a11363ad90] [Current]
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Dataseries X:
54.8	0	56	56.6
52.7	0	54.8	56
50.9	0	52.7	54.8
50.6	0	50.9	52.7
52.1	0	50.6	50.9
53.3	0	52.1	50.6
53.9	0	53.3	52.1
54.3	0	53.9	53.3
54.2	0	54.3	53.9
54.2	0	54.2	54.3
53.5	0	54.2	54.2
51.4	0	53.5	54.2
50.5	0	51.4	53.5
50.3	0	50.5	51.4
49.8	0	50.3	50.5
50.7	0	49.8	50.3
52.8	0	50.7	49.8
55.3	0	52.8	50.7
57.3	0	55.3	52.8
57.5	0	57.3	55.3
56.8	0	57.5	57.3
56.4	0	56.8	57.5
56.3	0	56.4	56.8
56.4	0	56.3	56.4
57	0	56.4	56.3
57.9	0	57	56.4
58.9	0	57.9	57
58.8	0	58.9	57.9
56.5	1	58.8	58.9
51.9	1	56.5	58.8
47.4	1	51.9	56.5
44.9	1	47.4	51.9
43.9	1	44.9	47.4
43.4	1	43.9	44.9
42.9	1	43.4	43.9
42.6	1	42.9	43.4
42.2	1	42.6	42.9
41.2	1	42.2	42.6
40.2	1	41.2	42.2
39.3	1	40.2	41.2
38.5	1	39.3	40.2
38.3	1	38.5	39.3
37.9	1	38.3	38.5
37.6	1	37.9	38.3
37.3	1	37.6	37.9
36	1	37.3	37.6
34.5	1	36	37.3
33.5	1	34.5	36
32.9	1	33.5	34.5
32.9	1	32.9	33.5
32.8	1	32.9	32.9
31.9	1	32.8	32.9
30.5	1	31.9	32.8
29.2	1	30.5	31.9
28.7	1	29.2	30.5
28.4	1	28.7	29.2
28	1	28.4	28.7
27.4	1	28	28.4
26.9	1	27.4	28




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=57828&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=57828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=0

As an alternative you can also use a 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] = + 3.46094894308918 -1.35890812535706X[t] + 1.57594470852792Y1[t] -0.641364831745757Y2[t] + 0.301634497468656M1[t] + 0.112538207357399M2[t] + 0.0715051759643893M3[t] + 0.263299441206298M4[t] + 0.460167495643472M5[t] + 0.100278611311066M6[t] + 0.184482326076706M7[t] + 0.262352168000846M8[t] + 0.194356140873652M9[t] + 0.104842003651204M10[t] + 0.00988454894042862M11[t] -0.0031959243864679t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  3.46094894308918 -1.35890812535706X[t] +  1.57594470852792Y1[t] -0.641364831745757Y2[t] +  0.301634497468656M1[t] +  0.112538207357399M2[t] +  0.0715051759643893M3[t] +  0.263299441206298M4[t] +  0.460167495643472M5[t] +  0.100278611311066M6[t] +  0.184482326076706M7[t] +  0.262352168000846M8[t] +  0.194356140873652M9[t] +  0.104842003651204M10[t] +  0.00988454894042862M11[t] -0.0031959243864679t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57828&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  3.46094894308918 -1.35890812535706X[t] +  1.57594470852792Y1[t] -0.641364831745757Y2[t] +  0.301634497468656M1[t] +  0.112538207357399M2[t] +  0.0715051759643893M3[t] +  0.263299441206298M4[t] +  0.460167495643472M5[t] +  0.100278611311066M6[t] +  0.184482326076706M7[t] +  0.262352168000846M8[t] +  0.194356140873652M9[t] +  0.104842003651204M10[t] +  0.00988454894042862M11[t] -0.0031959243864679t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 3.46094894308918 -1.35890812535706X[t] + 1.57594470852792Y1[t] -0.641364831745757Y2[t] + 0.301634497468656M1[t] + 0.112538207357399M2[t] + 0.0715051759643893M3[t] + 0.263299441206298M4[t] + 0.460167495643472M5[t] + 0.100278611311066M6[t] + 0.184482326076706M7[t] + 0.262352168000846M8[t] + 0.194356140873652M9[t] + 0.104842003651204M10[t] + 0.00988454894042862M11[t] -0.0031959243864679t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.460948943089181.3934262.48380.0169750.008488
X-1.358908125357060.527899-2.57420.0135760.006788
Y11.575944708527920.10681114.754500
Y2-0.6413648317457570.104974-6.109800
M10.3016344974686560.5390820.55950.5787010.28935
M20.1125382073573990.5389150.20880.8355720.417786
M30.07150517596438930.5387470.13270.895030.447515
M40.2632994412062980.5388750.48860.6276010.3138
M50.4601674956434720.5464630.84210.4044010.2022
M60.1002786113110660.5457360.18370.8550740.427537
M70.1844823260767060.5404790.34130.7345170.367258
M80.2623521680008460.5390490.48670.6289470.314473
M90.1943561408736520.5389810.36060.7201650.360082
M100.1048420036512040.5388550.19460.846650.423325
M110.009884548940428620.5389310.01830.9854520.492726
t-0.00319592438646790.016433-0.19450.8467130.423356

\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) & 3.46094894308918 & 1.393426 & 2.4838 & 0.016975 & 0.008488 \tabularnewline
X & -1.35890812535706 & 0.527899 & -2.5742 & 0.013576 & 0.006788 \tabularnewline
Y1 & 1.57594470852792 & 0.106811 & 14.7545 & 0 & 0 \tabularnewline
Y2 & -0.641364831745757 & 0.104974 & -6.1098 & 0 & 0 \tabularnewline
M1 & 0.301634497468656 & 0.539082 & 0.5595 & 0.578701 & 0.28935 \tabularnewline
M2 & 0.112538207357399 & 0.538915 & 0.2088 & 0.835572 & 0.417786 \tabularnewline
M3 & 0.0715051759643893 & 0.538747 & 0.1327 & 0.89503 & 0.447515 \tabularnewline
M4 & 0.263299441206298 & 0.538875 & 0.4886 & 0.627601 & 0.3138 \tabularnewline
M5 & 0.460167495643472 & 0.546463 & 0.8421 & 0.404401 & 0.2022 \tabularnewline
M6 & 0.100278611311066 & 0.545736 & 0.1837 & 0.855074 & 0.427537 \tabularnewline
M7 & 0.184482326076706 & 0.540479 & 0.3413 & 0.734517 & 0.367258 \tabularnewline
M8 & 0.262352168000846 & 0.539049 & 0.4867 & 0.628947 & 0.314473 \tabularnewline
M9 & 0.194356140873652 & 0.538981 & 0.3606 & 0.720165 & 0.360082 \tabularnewline
M10 & 0.104842003651204 & 0.538855 & 0.1946 & 0.84665 & 0.423325 \tabularnewline
M11 & 0.00988454894042862 & 0.538931 & 0.0183 & 0.985452 & 0.492726 \tabularnewline
t & -0.0031959243864679 & 0.016433 & -0.1945 & 0.846713 & 0.423356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57828&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]3.46094894308918[/C][C]1.393426[/C][C]2.4838[/C][C]0.016975[/C][C]0.008488[/C][/ROW]
[ROW][C]X[/C][C]-1.35890812535706[/C][C]0.527899[/C][C]-2.5742[/C][C]0.013576[/C][C]0.006788[/C][/ROW]
[ROW][C]Y1[/C][C]1.57594470852792[/C][C]0.106811[/C][C]14.7545[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.641364831745757[/C][C]0.104974[/C][C]-6.1098[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.301634497468656[/C][C]0.539082[/C][C]0.5595[/C][C]0.578701[/C][C]0.28935[/C][/ROW]
[ROW][C]M2[/C][C]0.112538207357399[/C][C]0.538915[/C][C]0.2088[/C][C]0.835572[/C][C]0.417786[/C][/ROW]
[ROW][C]M3[/C][C]0.0715051759643893[/C][C]0.538747[/C][C]0.1327[/C][C]0.89503[/C][C]0.447515[/C][/ROW]
[ROW][C]M4[/C][C]0.263299441206298[/C][C]0.538875[/C][C]0.4886[/C][C]0.627601[/C][C]0.3138[/C][/ROW]
[ROW][C]M5[/C][C]0.460167495643472[/C][C]0.546463[/C][C]0.8421[/C][C]0.404401[/C][C]0.2022[/C][/ROW]
[ROW][C]M6[/C][C]0.100278611311066[/C][C]0.545736[/C][C]0.1837[/C][C]0.855074[/C][C]0.427537[/C][/ROW]
[ROW][C]M7[/C][C]0.184482326076706[/C][C]0.540479[/C][C]0.3413[/C][C]0.734517[/C][C]0.367258[/C][/ROW]
[ROW][C]M8[/C][C]0.262352168000846[/C][C]0.539049[/C][C]0.4867[/C][C]0.628947[/C][C]0.314473[/C][/ROW]
[ROW][C]M9[/C][C]0.194356140873652[/C][C]0.538981[/C][C]0.3606[/C][C]0.720165[/C][C]0.360082[/C][/ROW]
[ROW][C]M10[/C][C]0.104842003651204[/C][C]0.538855[/C][C]0.1946[/C][C]0.84665[/C][C]0.423325[/C][/ROW]
[ROW][C]M11[/C][C]0.00988454894042862[/C][C]0.538931[/C][C]0.0183[/C][C]0.985452[/C][C]0.492726[/C][/ROW]
[ROW][C]t[/C][C]-0.0031959243864679[/C][C]0.016433[/C][C]-0.1945[/C][C]0.846713[/C][C]0.423356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=2

As an alternative you can also use a 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)3.460948943089181.3934262.48380.0169750.008488
X-1.358908125357060.527899-2.57420.0135760.006788
Y11.575944708527920.10681114.754500
Y2-0.6413648317457570.104974-6.109800
M10.3016344974686560.5390820.55950.5787010.28935
M20.1125382073573990.5389150.20880.8355720.417786
M30.07150517596438930.5387470.13270.895030.447515
M40.2632994412062980.5388750.48860.6276010.3138
M50.4601674956434720.5464630.84210.4044010.2022
M60.1002786113110660.5457360.18370.8550740.427537
M70.1844823260767060.5404790.34130.7345170.367258
M80.2623521680008460.5390490.48670.6289470.314473
M90.1943561408736520.5389810.36060.7201650.360082
M100.1048420036512040.5388550.19460.846650.423325
M110.009884548940428620.5389310.01830.9854520.492726
t-0.00319592438646790.016433-0.19450.8467130.423356







Multiple Linear Regression - Regression Statistics
Multiple R0.997691270248974
R-squared0.995387870731012
Adjusted R-squared0.993778988427876
F-TEST (value)618.682838882126
F-TEST (DF numerator)15
F-TEST (DF denominator)43
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.801038532138557
Sum Squared Residuals27.5914973887398

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.997691270248974 \tabularnewline
R-squared & 0.995387870731012 \tabularnewline
Adjusted R-squared & 0.993778988427876 \tabularnewline
F-TEST (value) & 618.682838882126 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 43 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.801038532138557 \tabularnewline
Sum Squared Residuals & 27.5914973887398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57828&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.997691270248974[/C][/ROW]
[ROW][C]R-squared[/C][C]0.995387870731012[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.993778988427876[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]618.682838882126[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]43[/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]0.801038532138557[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]27.5914973887398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57828&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.997691270248974
R-squared0.995387870731012
Adjusted R-squared0.993778988427876
F-TEST (value)618.682838882126
F-TEST (DF numerator)15
F-TEST (DF denominator)43
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.801038532138557
Sum Squared Residuals27.5914973887398







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
154.855.7110417169253-0.911041716925267
252.754.0124347512415-1.31243475124146
350.951.4283597056483-0.528359705648272
450.650.12712371781950.472876282180463
552.151.00246913245421.09753086754576
653.353.1957108360510.104289163949020
753.954.205805029045-0.305805029045017
854.354.4564079736045-0.156407973604542
954.254.6307750064546-0.430775006454585
1054.254.12392454129460.076075458705416
1153.554.0899076453719-0.589907645371917
1251.452.9736658760755-1.57366587607547
1350.550.4115759434710.0884240565289558
1450.350.14779963796430.152200362035715
1549.850.3656100890504-0.565610089050398
1650.749.8945090419910.805490958008976
1752.851.82721382558980.972786174410244
1855.354.19638455620831.10361544379167
1957.356.87038797124120.429612028758775
2057.558.4935392264703-0.99353922647035
2156.857.4548065531708-0.654806553170764
2256.456.13066222924310.269337770756858
2356.355.85108634895680.448913651043235
2456.455.93695733747540.463042662524625
255756.45712686458490.542873135415067
2657.957.14626499202940.75373500797061
2758.958.13556737487760.764432625122414
2858.859.3228820756898-0.522882075689771
2956.557.3586867777849-0.858686777784864
3051.953.4350656226264-1.53506562262635
3147.447.7418668667923-0.341866866792309
3244.943.67506782198481.22493217801519
3343.942.55015584200721.34984415799276
3443.442.48491315123480.915086848765203
3542.942.24015224961930.65984775038065
3642.641.75978183790140.840218162098634
3742.241.90611941429810.293880585701941
3841.241.2758587659129-0.0758587659128922
3940.239.91223103430380.287768965696208
4039.339.16624949837710.133750501622929
4138.538.5829362224984-0.0829362224983919
4238.337.53632399552840.763676004471629
4337.937.81523470959860.0847652904014438
4437.637.38780371007420.212196289925788
4537.337.10037427870050.199625721299517
463636.7272902540569-0.727290254056906
4734.534.7728182033971-0.272818203397096
4833.533.22959494854780.270405051452204
4932.932.9141360607207-0.0141360607206959
5032.932.41764185285200.482358147148027
5132.832.75823179612000.0417682038800483
5231.932.7892356661226-0.889235666122597
5330.531.6286940416727-1.12869404167275
5429.229.636514989586-0.436514989585965
5528.728.56670542332290.133294576677107
5628.428.6871812678661-0.287181267866087
572828.4638883196669-0.463888319666924
5827.427.9332098241706-0.533209824170572
5926.927.1460355526549-0.246035552654873

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 54.8 & 55.7110417169253 & -0.911041716925267 \tabularnewline
2 & 52.7 & 54.0124347512415 & -1.31243475124146 \tabularnewline
3 & 50.9 & 51.4283597056483 & -0.528359705648272 \tabularnewline
4 & 50.6 & 50.1271237178195 & 0.472876282180463 \tabularnewline
5 & 52.1 & 51.0024691324542 & 1.09753086754576 \tabularnewline
6 & 53.3 & 53.195710836051 & 0.104289163949020 \tabularnewline
7 & 53.9 & 54.205805029045 & -0.305805029045017 \tabularnewline
8 & 54.3 & 54.4564079736045 & -0.156407973604542 \tabularnewline
9 & 54.2 & 54.6307750064546 & -0.430775006454585 \tabularnewline
10 & 54.2 & 54.1239245412946 & 0.076075458705416 \tabularnewline
11 & 53.5 & 54.0899076453719 & -0.589907645371917 \tabularnewline
12 & 51.4 & 52.9736658760755 & -1.57366587607547 \tabularnewline
13 & 50.5 & 50.411575943471 & 0.0884240565289558 \tabularnewline
14 & 50.3 & 50.1477996379643 & 0.152200362035715 \tabularnewline
15 & 49.8 & 50.3656100890504 & -0.565610089050398 \tabularnewline
16 & 50.7 & 49.894509041991 & 0.805490958008976 \tabularnewline
17 & 52.8 & 51.8272138255898 & 0.972786174410244 \tabularnewline
18 & 55.3 & 54.1963845562083 & 1.10361544379167 \tabularnewline
19 & 57.3 & 56.8703879712412 & 0.429612028758775 \tabularnewline
20 & 57.5 & 58.4935392264703 & -0.99353922647035 \tabularnewline
21 & 56.8 & 57.4548065531708 & -0.654806553170764 \tabularnewline
22 & 56.4 & 56.1306622292431 & 0.269337770756858 \tabularnewline
23 & 56.3 & 55.8510863489568 & 0.448913651043235 \tabularnewline
24 & 56.4 & 55.9369573374754 & 0.463042662524625 \tabularnewline
25 & 57 & 56.4571268645849 & 0.542873135415067 \tabularnewline
26 & 57.9 & 57.1462649920294 & 0.75373500797061 \tabularnewline
27 & 58.9 & 58.1355673748776 & 0.764432625122414 \tabularnewline
28 & 58.8 & 59.3228820756898 & -0.522882075689771 \tabularnewline
29 & 56.5 & 57.3586867777849 & -0.858686777784864 \tabularnewline
30 & 51.9 & 53.4350656226264 & -1.53506562262635 \tabularnewline
31 & 47.4 & 47.7418668667923 & -0.341866866792309 \tabularnewline
32 & 44.9 & 43.6750678219848 & 1.22493217801519 \tabularnewline
33 & 43.9 & 42.5501558420072 & 1.34984415799276 \tabularnewline
34 & 43.4 & 42.4849131512348 & 0.915086848765203 \tabularnewline
35 & 42.9 & 42.2401522496193 & 0.65984775038065 \tabularnewline
36 & 42.6 & 41.7597818379014 & 0.840218162098634 \tabularnewline
37 & 42.2 & 41.9061194142981 & 0.293880585701941 \tabularnewline
38 & 41.2 & 41.2758587659129 & -0.0758587659128922 \tabularnewline
39 & 40.2 & 39.9122310343038 & 0.287768965696208 \tabularnewline
40 & 39.3 & 39.1662494983771 & 0.133750501622929 \tabularnewline
41 & 38.5 & 38.5829362224984 & -0.0829362224983919 \tabularnewline
42 & 38.3 & 37.5363239955284 & 0.763676004471629 \tabularnewline
43 & 37.9 & 37.8152347095986 & 0.0847652904014438 \tabularnewline
44 & 37.6 & 37.3878037100742 & 0.212196289925788 \tabularnewline
45 & 37.3 & 37.1003742787005 & 0.199625721299517 \tabularnewline
46 & 36 & 36.7272902540569 & -0.727290254056906 \tabularnewline
47 & 34.5 & 34.7728182033971 & -0.272818203397096 \tabularnewline
48 & 33.5 & 33.2295949485478 & 0.270405051452204 \tabularnewline
49 & 32.9 & 32.9141360607207 & -0.0141360607206959 \tabularnewline
50 & 32.9 & 32.4176418528520 & 0.482358147148027 \tabularnewline
51 & 32.8 & 32.7582317961200 & 0.0417682038800483 \tabularnewline
52 & 31.9 & 32.7892356661226 & -0.889235666122597 \tabularnewline
53 & 30.5 & 31.6286940416727 & -1.12869404167275 \tabularnewline
54 & 29.2 & 29.636514989586 & -0.436514989585965 \tabularnewline
55 & 28.7 & 28.5667054233229 & 0.133294576677107 \tabularnewline
56 & 28.4 & 28.6871812678661 & -0.287181267866087 \tabularnewline
57 & 28 & 28.4638883196669 & -0.463888319666924 \tabularnewline
58 & 27.4 & 27.9332098241706 & -0.533209824170572 \tabularnewline
59 & 26.9 & 27.1460355526549 & -0.246035552654873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57828&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]54.8[/C][C]55.7110417169253[/C][C]-0.911041716925267[/C][/ROW]
[ROW][C]2[/C][C]52.7[/C][C]54.0124347512415[/C][C]-1.31243475124146[/C][/ROW]
[ROW][C]3[/C][C]50.9[/C][C]51.4283597056483[/C][C]-0.528359705648272[/C][/ROW]
[ROW][C]4[/C][C]50.6[/C][C]50.1271237178195[/C][C]0.472876282180463[/C][/ROW]
[ROW][C]5[/C][C]52.1[/C][C]51.0024691324542[/C][C]1.09753086754576[/C][/ROW]
[ROW][C]6[/C][C]53.3[/C][C]53.195710836051[/C][C]0.104289163949020[/C][/ROW]
[ROW][C]7[/C][C]53.9[/C][C]54.205805029045[/C][C]-0.305805029045017[/C][/ROW]
[ROW][C]8[/C][C]54.3[/C][C]54.4564079736045[/C][C]-0.156407973604542[/C][/ROW]
[ROW][C]9[/C][C]54.2[/C][C]54.6307750064546[/C][C]-0.430775006454585[/C][/ROW]
[ROW][C]10[/C][C]54.2[/C][C]54.1239245412946[/C][C]0.076075458705416[/C][/ROW]
[ROW][C]11[/C][C]53.5[/C][C]54.0899076453719[/C][C]-0.589907645371917[/C][/ROW]
[ROW][C]12[/C][C]51.4[/C][C]52.9736658760755[/C][C]-1.57366587607547[/C][/ROW]
[ROW][C]13[/C][C]50.5[/C][C]50.411575943471[/C][C]0.0884240565289558[/C][/ROW]
[ROW][C]14[/C][C]50.3[/C][C]50.1477996379643[/C][C]0.152200362035715[/C][/ROW]
[ROW][C]15[/C][C]49.8[/C][C]50.3656100890504[/C][C]-0.565610089050398[/C][/ROW]
[ROW][C]16[/C][C]50.7[/C][C]49.894509041991[/C][C]0.805490958008976[/C][/ROW]
[ROW][C]17[/C][C]52.8[/C][C]51.8272138255898[/C][C]0.972786174410244[/C][/ROW]
[ROW][C]18[/C][C]55.3[/C][C]54.1963845562083[/C][C]1.10361544379167[/C][/ROW]
[ROW][C]19[/C][C]57.3[/C][C]56.8703879712412[/C][C]0.429612028758775[/C][/ROW]
[ROW][C]20[/C][C]57.5[/C][C]58.4935392264703[/C][C]-0.99353922647035[/C][/ROW]
[ROW][C]21[/C][C]56.8[/C][C]57.4548065531708[/C][C]-0.654806553170764[/C][/ROW]
[ROW][C]22[/C][C]56.4[/C][C]56.1306622292431[/C][C]0.269337770756858[/C][/ROW]
[ROW][C]23[/C][C]56.3[/C][C]55.8510863489568[/C][C]0.448913651043235[/C][/ROW]
[ROW][C]24[/C][C]56.4[/C][C]55.9369573374754[/C][C]0.463042662524625[/C][/ROW]
[ROW][C]25[/C][C]57[/C][C]56.4571268645849[/C][C]0.542873135415067[/C][/ROW]
[ROW][C]26[/C][C]57.9[/C][C]57.1462649920294[/C][C]0.75373500797061[/C][/ROW]
[ROW][C]27[/C][C]58.9[/C][C]58.1355673748776[/C][C]0.764432625122414[/C][/ROW]
[ROW][C]28[/C][C]58.8[/C][C]59.3228820756898[/C][C]-0.522882075689771[/C][/ROW]
[ROW][C]29[/C][C]56.5[/C][C]57.3586867777849[/C][C]-0.858686777784864[/C][/ROW]
[ROW][C]30[/C][C]51.9[/C][C]53.4350656226264[/C][C]-1.53506562262635[/C][/ROW]
[ROW][C]31[/C][C]47.4[/C][C]47.7418668667923[/C][C]-0.341866866792309[/C][/ROW]
[ROW][C]32[/C][C]44.9[/C][C]43.6750678219848[/C][C]1.22493217801519[/C][/ROW]
[ROW][C]33[/C][C]43.9[/C][C]42.5501558420072[/C][C]1.34984415799276[/C][/ROW]
[ROW][C]34[/C][C]43.4[/C][C]42.4849131512348[/C][C]0.915086848765203[/C][/ROW]
[ROW][C]35[/C][C]42.9[/C][C]42.2401522496193[/C][C]0.65984775038065[/C][/ROW]
[ROW][C]36[/C][C]42.6[/C][C]41.7597818379014[/C][C]0.840218162098634[/C][/ROW]
[ROW][C]37[/C][C]42.2[/C][C]41.9061194142981[/C][C]0.293880585701941[/C][/ROW]
[ROW][C]38[/C][C]41.2[/C][C]41.2758587659129[/C][C]-0.0758587659128922[/C][/ROW]
[ROW][C]39[/C][C]40.2[/C][C]39.9122310343038[/C][C]0.287768965696208[/C][/ROW]
[ROW][C]40[/C][C]39.3[/C][C]39.1662494983771[/C][C]0.133750501622929[/C][/ROW]
[ROW][C]41[/C][C]38.5[/C][C]38.5829362224984[/C][C]-0.0829362224983919[/C][/ROW]
[ROW][C]42[/C][C]38.3[/C][C]37.5363239955284[/C][C]0.763676004471629[/C][/ROW]
[ROW][C]43[/C][C]37.9[/C][C]37.8152347095986[/C][C]0.0847652904014438[/C][/ROW]
[ROW][C]44[/C][C]37.6[/C][C]37.3878037100742[/C][C]0.212196289925788[/C][/ROW]
[ROW][C]45[/C][C]37.3[/C][C]37.1003742787005[/C][C]0.199625721299517[/C][/ROW]
[ROW][C]46[/C][C]36[/C][C]36.7272902540569[/C][C]-0.727290254056906[/C][/ROW]
[ROW][C]47[/C][C]34.5[/C][C]34.7728182033971[/C][C]-0.272818203397096[/C][/ROW]
[ROW][C]48[/C][C]33.5[/C][C]33.2295949485478[/C][C]0.270405051452204[/C][/ROW]
[ROW][C]49[/C][C]32.9[/C][C]32.9141360607207[/C][C]-0.0141360607206959[/C][/ROW]
[ROW][C]50[/C][C]32.9[/C][C]32.4176418528520[/C][C]0.482358147148027[/C][/ROW]
[ROW][C]51[/C][C]32.8[/C][C]32.7582317961200[/C][C]0.0417682038800483[/C][/ROW]
[ROW][C]52[/C][C]31.9[/C][C]32.7892356661226[/C][C]-0.889235666122597[/C][/ROW]
[ROW][C]53[/C][C]30.5[/C][C]31.6286940416727[/C][C]-1.12869404167275[/C][/ROW]
[ROW][C]54[/C][C]29.2[/C][C]29.636514989586[/C][C]-0.436514989585965[/C][/ROW]
[ROW][C]55[/C][C]28.7[/C][C]28.5667054233229[/C][C]0.133294576677107[/C][/ROW]
[ROW][C]56[/C][C]28.4[/C][C]28.6871812678661[/C][C]-0.287181267866087[/C][/ROW]
[ROW][C]57[/C][C]28[/C][C]28.4638883196669[/C][C]-0.463888319666924[/C][/ROW]
[ROW][C]58[/C][C]27.4[/C][C]27.9332098241706[/C][C]-0.533209824170572[/C][/ROW]
[ROW][C]59[/C][C]26.9[/C][C]27.1460355526549[/C][C]-0.246035552654873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57828&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
154.855.7110417169253-0.911041716925267
252.754.0124347512415-1.31243475124146
350.951.4283597056483-0.528359705648272
450.650.12712371781950.472876282180463
552.151.00246913245421.09753086754576
653.353.1957108360510.104289163949020
753.954.205805029045-0.305805029045017
854.354.4564079736045-0.156407973604542
954.254.6307750064546-0.430775006454585
1054.254.12392454129460.076075458705416
1153.554.0899076453719-0.589907645371917
1251.452.9736658760755-1.57366587607547
1350.550.4115759434710.0884240565289558
1450.350.14779963796430.152200362035715
1549.850.3656100890504-0.565610089050398
1650.749.8945090419910.805490958008976
1752.851.82721382558980.972786174410244
1855.354.19638455620831.10361544379167
1957.356.87038797124120.429612028758775
2057.558.4935392264703-0.99353922647035
2156.857.4548065531708-0.654806553170764
2256.456.13066222924310.269337770756858
2356.355.85108634895680.448913651043235
2456.455.93695733747540.463042662524625
255756.45712686458490.542873135415067
2657.957.14626499202940.75373500797061
2758.958.13556737487760.764432625122414
2858.859.3228820756898-0.522882075689771
2956.557.3586867777849-0.858686777784864
3051.953.4350656226264-1.53506562262635
3147.447.7418668667923-0.341866866792309
3244.943.67506782198481.22493217801519
3343.942.55015584200721.34984415799276
3443.442.48491315123480.915086848765203
3542.942.24015224961930.65984775038065
3642.641.75978183790140.840218162098634
3742.241.90611941429810.293880585701941
3841.241.2758587659129-0.0758587659128922
3940.239.91223103430380.287768965696208
4039.339.16624949837710.133750501622929
4138.538.5829362224984-0.0829362224983919
4238.337.53632399552840.763676004471629
4337.937.81523470959860.0847652904014438
4437.637.38780371007420.212196289925788
4537.337.10037427870050.199625721299517
463636.7272902540569-0.727290254056906
4734.534.7728182033971-0.272818203397096
4833.533.22959494854780.270405051452204
4932.932.9141360607207-0.0141360607206959
5032.932.41764185285200.482358147148027
5132.832.75823179612000.0417682038800483
5231.932.7892356661226-0.889235666122597
5330.531.6286940416727-1.12869404167275
5429.229.636514989586-0.436514989585965
5528.728.56670542332290.133294576677107
5628.428.6871812678661-0.287181267866087
572828.4638883196669-0.463888319666924
5827.427.9332098241706-0.533209824170572
5926.927.1460355526549-0.246035552654873







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.3837977048946200.7675954097892410.61620229510538
200.5680139897458880.8639720205082240.431986010254112
210.68157814113010.63684371773980.3184218588699
220.5862692512411310.8274614975177380.413730748758869
230.638525697685490.7229486046290190.361474302314510
240.947946809830370.1041063803392590.0520531901696295
250.926808318727810.146383362544380.07319168127219
260.9115659738191780.1768680523616440.0884340261808222
270.8879158984992980.2241682030014030.112084101500702
280.9462478258012610.1075043483974770.0537521741987387
290.9968806168045020.006238766390995150.00311938319549758
300.9962502614134070.007499477173185050.00374973858659253
310.9922029236610930.01559415267781410.00779707633890706
320.9968096116156540.006380776768692910.00319038838434646
330.9956745687739170.008650862452165010.00432543122608251
340.991440854360570.01711829127886130.00855914563943065
350.9867012739142090.02659745217158260.0132987260857913
360.970416152094340.05916769581132130.0295838479056607
370.946540854667740.1069182906645190.0534591453322594
380.9486931436223740.1026137127552520.0513068563776259
390.89537865985970.2092426802806000.104621340140300
400.7982171314032750.4035657371934490.201782868596725

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.383797704894620 & 0.767595409789241 & 0.61620229510538 \tabularnewline
20 & 0.568013989745888 & 0.863972020508224 & 0.431986010254112 \tabularnewline
21 & 0.6815781411301 & 0.6368437177398 & 0.3184218588699 \tabularnewline
22 & 0.586269251241131 & 0.827461497517738 & 0.413730748758869 \tabularnewline
23 & 0.63852569768549 & 0.722948604629019 & 0.361474302314510 \tabularnewline
24 & 0.94794680983037 & 0.104106380339259 & 0.0520531901696295 \tabularnewline
25 & 0.92680831872781 & 0.14638336254438 & 0.07319168127219 \tabularnewline
26 & 0.911565973819178 & 0.176868052361644 & 0.0884340261808222 \tabularnewline
27 & 0.887915898499298 & 0.224168203001403 & 0.112084101500702 \tabularnewline
28 & 0.946247825801261 & 0.107504348397477 & 0.0537521741987387 \tabularnewline
29 & 0.996880616804502 & 0.00623876639099515 & 0.00311938319549758 \tabularnewline
30 & 0.996250261413407 & 0.00749947717318505 & 0.00374973858659253 \tabularnewline
31 & 0.992202923661093 & 0.0155941526778141 & 0.00779707633890706 \tabularnewline
32 & 0.996809611615654 & 0.00638077676869291 & 0.00319038838434646 \tabularnewline
33 & 0.995674568773917 & 0.00865086245216501 & 0.00432543122608251 \tabularnewline
34 & 0.99144085436057 & 0.0171182912788613 & 0.00855914563943065 \tabularnewline
35 & 0.986701273914209 & 0.0265974521715826 & 0.0132987260857913 \tabularnewline
36 & 0.97041615209434 & 0.0591676958113213 & 0.0295838479056607 \tabularnewline
37 & 0.94654085466774 & 0.106918290664519 & 0.0534591453322594 \tabularnewline
38 & 0.948693143622374 & 0.102613712755252 & 0.0513068563776259 \tabularnewline
39 & 0.8953786598597 & 0.209242680280600 & 0.104621340140300 \tabularnewline
40 & 0.798217131403275 & 0.403565737193449 & 0.201782868596725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57828&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]0.383797704894620[/C][C]0.767595409789241[/C][C]0.61620229510538[/C][/ROW]
[ROW][C]20[/C][C]0.568013989745888[/C][C]0.863972020508224[/C][C]0.431986010254112[/C][/ROW]
[ROW][C]21[/C][C]0.6815781411301[/C][C]0.6368437177398[/C][C]0.3184218588699[/C][/ROW]
[ROW][C]22[/C][C]0.586269251241131[/C][C]0.827461497517738[/C][C]0.413730748758869[/C][/ROW]
[ROW][C]23[/C][C]0.63852569768549[/C][C]0.722948604629019[/C][C]0.361474302314510[/C][/ROW]
[ROW][C]24[/C][C]0.94794680983037[/C][C]0.104106380339259[/C][C]0.0520531901696295[/C][/ROW]
[ROW][C]25[/C][C]0.92680831872781[/C][C]0.14638336254438[/C][C]0.07319168127219[/C][/ROW]
[ROW][C]26[/C][C]0.911565973819178[/C][C]0.176868052361644[/C][C]0.0884340261808222[/C][/ROW]
[ROW][C]27[/C][C]0.887915898499298[/C][C]0.224168203001403[/C][C]0.112084101500702[/C][/ROW]
[ROW][C]28[/C][C]0.946247825801261[/C][C]0.107504348397477[/C][C]0.0537521741987387[/C][/ROW]
[ROW][C]29[/C][C]0.996880616804502[/C][C]0.00623876639099515[/C][C]0.00311938319549758[/C][/ROW]
[ROW][C]30[/C][C]0.996250261413407[/C][C]0.00749947717318505[/C][C]0.00374973858659253[/C][/ROW]
[ROW][C]31[/C][C]0.992202923661093[/C][C]0.0155941526778141[/C][C]0.00779707633890706[/C][/ROW]
[ROW][C]32[/C][C]0.996809611615654[/C][C]0.00638077676869291[/C][C]0.00319038838434646[/C][/ROW]
[ROW][C]33[/C][C]0.995674568773917[/C][C]0.00865086245216501[/C][C]0.00432543122608251[/C][/ROW]
[ROW][C]34[/C][C]0.99144085436057[/C][C]0.0171182912788613[/C][C]0.00855914563943065[/C][/ROW]
[ROW][C]35[/C][C]0.986701273914209[/C][C]0.0265974521715826[/C][C]0.0132987260857913[/C][/ROW]
[ROW][C]36[/C][C]0.97041615209434[/C][C]0.0591676958113213[/C][C]0.0295838479056607[/C][/ROW]
[ROW][C]37[/C][C]0.94654085466774[/C][C]0.106918290664519[/C][C]0.0534591453322594[/C][/ROW]
[ROW][C]38[/C][C]0.948693143622374[/C][C]0.102613712755252[/C][C]0.0513068563776259[/C][/ROW]
[ROW][C]39[/C][C]0.8953786598597[/C][C]0.209242680280600[/C][C]0.104621340140300[/C][/ROW]
[ROW][C]40[/C][C]0.798217131403275[/C][C]0.403565737193449[/C][C]0.201782868596725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57828&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.3837977048946200.7675954097892410.61620229510538
200.5680139897458880.8639720205082240.431986010254112
210.68157814113010.63684371773980.3184218588699
220.5862692512411310.8274614975177380.413730748758869
230.638525697685490.7229486046290190.361474302314510
240.947946809830370.1041063803392590.0520531901696295
250.926808318727810.146383362544380.07319168127219
260.9115659738191780.1768680523616440.0884340261808222
270.8879158984992980.2241682030014030.112084101500702
280.9462478258012610.1075043483974770.0537521741987387
290.9968806168045020.006238766390995150.00311938319549758
300.9962502614134070.007499477173185050.00374973858659253
310.9922029236610930.01559415267781410.00779707633890706
320.9968096116156540.006380776768692910.00319038838434646
330.9956745687739170.008650862452165010.00432543122608251
340.991440854360570.01711829127886130.00855914563943065
350.9867012739142090.02659745217158260.0132987260857913
360.970416152094340.05916769581132130.0295838479056607
370.946540854667740.1069182906645190.0534591453322594
380.9486931436223740.1026137127552520.0513068563776259
390.89537865985970.2092426802806000.104621340140300
400.7982171314032750.4035657371934490.201782868596725







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.181818181818182NOK
5% type I error level70.318181818181818NOK
10% type I error level80.363636363636364NOK

\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 & 4 & 0.181818181818182 & NOK \tabularnewline
5% type I error level & 7 & 0.318181818181818 & NOK \tabularnewline
10% type I error level & 8 & 0.363636363636364 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57828&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]4[/C][C]0.181818181818182[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.318181818181818[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.363636363636364[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57828&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57828&T=6

As an alternative you can also use a 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 level40.181818181818182NOK
5% type I error level70.318181818181818NOK
10% type I error level80.363636363636364NOK



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')
}