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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 09:55:46 -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/t125873623590w2svhyeolwm53.htm/, Retrieved Sat, 20 Apr 2024 14:46:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58330, Retrieved Sat, 20 Apr 2024 14:46:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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] [] [2009-11-20 16:55:46] [fc845972e0ebdb725d2fb9537c0c51aa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110.3	0	114.1	96.8	87.4	111.4
103.9	0	110.3	114.1	96.8	87.4
101.6	0	103.9	110.3	114.1	96.8
94.6	0	101.6	103.9	110.3	114.1
95.9	0	94.6	101.6	103.9	110.3
104.7	0	95.9	94.6	101.6	103.9
102.8	0	104.7	95.9	94.6	101.6
98.1	0	102.8	104.7	95.9	94.6
113.9	0	98.1	102.8	104.7	95.9
80.9	0	113.9	98.1	102.8	104.7
95.7	0	80.9	113.9	98.1	102.8
113.2	0	95.7	80.9	113.9	98.1
105.9	0	113.2	95.7	80.9	113.9
108.8	0	105.9	113.2	95.7	80.9
102.3	0	108.8	105.9	113.2	95.7
99	0	102.3	108.8	105.9	113.2
100.7	0	99	102.3	108.8	105.9
115.5	0	100.7	99	102.3	108.8
100.7	0	115.5	100.7	99	102.3
109.9	0	100.7	115.5	100.7	99
114.6	0	109.9	100.7	115.5	100.7
85.4	0	114.6	109.9	100.7	115.5
100.5	0	85.4	114.6	109.9	100.7
114.8	0	100.5	85.4	114.6	109.9
116.5	0	114.8	100.5	85.4	114.6
112.9	0	116.5	114.8	100.5	85.4
102	0	112.9	116.5	114.8	100.5
106	0	102	112.9	116.5	114.8
105.3	0	106	102	112.9	116.5
118.8	0	105.3	106	102	112.9
106.1	0	118.8	105.3	106	102
109.3	0	106.1	118.8	105.3	106
117.2	0	109.3	106.1	118.8	105.3
92.5	0	117.2	109.3	106.1	118.8
104.2	0	92.5	117.2	109.3	106.1
112.5	0	104.2	92.5	117.2	109.3
122.4	0	112.5	104.2	92.5	117.2
113.3	0	122.4	112.5	104.2	92.5
100	0	113.3	122.4	112.5	104.2
110.7	0	100	113.3	122.4	112.5
112.8	0	110.7	100	113.3	122.4
109.8	0	112.8	110.7	100	113.3
117.3	0	109.8	112.8	110.7	100
109.1	0	117.3	109.8	112.8	110.7
115.9	0	109.1	117.3	109.8	112.8
96	0	115.9	109.1	117.3	109.8
99.8	0	96	115.9	109.1	117.3
116.8	1	99.8	96	115.9	109.1
115.7	1	116.8	99.8	96	115.9
99.4	1	115.7	116.8	99.8	96
94.3	1	99.4	115.7	116.8	99.8
91	1	94.3	99.4	115.7	116.8
93.2	1	91	94.3	99.4	115.7
103.1	1	93.2	91	94.3	99.4
94.1	1	103.1	93.2	91	94.3
91.8	1	94.1	103.1	93.2	91
102.7	1	91.8	94.1	103.1	93.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&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]6 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=58330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 50.2362928119604 -10.5265285686030X[t] -0.202061509463685Y1[t] + 0.236569774841816Y2[t] + 0.554834223280099Y3[t] -0.0160517215222272Y4[t] + 15.3454731041248M1[t] -1.3210319312054M2[t] -18.4272530266396M3[t] -18.0250317516137M4[t] -11.374623572876M5[t] + 1.64234957827378M6[t] -3.43736217073495M7[t] -8.17796939620031M8[t] -2.59167880781004M9[t] -24.2441038493184M10[t] -20.5106923504080M11[t] + 0.121203282376966t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  50.2362928119604 -10.5265285686030X[t] -0.202061509463685Y1[t] +  0.236569774841816Y2[t] +  0.554834223280099Y3[t] -0.0160517215222272Y4[t] +  15.3454731041248M1[t] -1.3210319312054M2[t] -18.4272530266396M3[t] -18.0250317516137M4[t] -11.374623572876M5[t] +  1.64234957827378M6[t] -3.43736217073495M7[t] -8.17796939620031M8[t] -2.59167880781004M9[t] -24.2441038493184M10[t] -20.5106923504080M11[t] +  0.121203282376966t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  50.2362928119604 -10.5265285686030X[t] -0.202061509463685Y1[t] +  0.236569774841816Y2[t] +  0.554834223280099Y3[t] -0.0160517215222272Y4[t] +  15.3454731041248M1[t] -1.3210319312054M2[t] -18.4272530266396M3[t] -18.0250317516137M4[t] -11.374623572876M5[t] +  1.64234957827378M6[t] -3.43736217073495M7[t] -8.17796939620031M8[t] -2.59167880781004M9[t] -24.2441038493184M10[t] -20.5106923504080M11[t] +  0.121203282376966t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&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] = + 50.2362928119604 -10.5265285686030X[t] -0.202061509463685Y1[t] + 0.236569774841816Y2[t] + 0.554834223280099Y3[t] -0.0160517215222272Y4[t] + 15.3454731041248M1[t] -1.3210319312054M2[t] -18.4272530266396M3[t] -18.0250317516137M4[t] -11.374623572876M5[t] + 1.64234957827378M6[t] -3.43736217073495M7[t] -8.17796939620031M8[t] -2.59167880781004M9[t] -24.2441038493184M10[t] -20.5106923504080M11[t] + 0.121203282376966t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)50.236292811960417.6138642.85210.0069120.003456
X-10.52652856860302.790755-3.77190.0005380.000269
Y1-0.2020615094636850.156023-1.29510.2029080.101454
Y20.2365697748418160.1206811.96030.0571340.028567
Y30.5548342232800990.1217994.55535e-052.5e-05
Y4-0.01605172152222720.149372-0.10750.9149740.457487
M115.34547310412485.054743.03590.0042590.00213
M2-1.32103193120547.150494-0.18470.8543850.427192
M3-18.42725302663964.747283-3.88160.0003890.000195
M4-18.02503175161373.206325-5.62172e-061e-06
M5-11.3746235728762.91686-3.89960.0003690.000185
M61.642349578273783.4322360.47850.6349610.31748
M7-3.437362170734954.611566-0.74540.4605120.230256
M8-8.177969396200314.622097-1.76930.084660.04233
M9-2.591678807810043.509868-0.73840.4646930.232347
M10-24.24410384931844.060683-5.97041e-060
M11-20.51069235040804.351302-4.71373.1e-051.5e-05
t0.1212032823769660.0580582.08760.0434130.021707

\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) & 50.2362928119604 & 17.613864 & 2.8521 & 0.006912 & 0.003456 \tabularnewline
X & -10.5265285686030 & 2.790755 & -3.7719 & 0.000538 & 0.000269 \tabularnewline
Y1 & -0.202061509463685 & 0.156023 & -1.2951 & 0.202908 & 0.101454 \tabularnewline
Y2 & 0.236569774841816 & 0.120681 & 1.9603 & 0.057134 & 0.028567 \tabularnewline
Y3 & 0.554834223280099 & 0.121799 & 4.5553 & 5e-05 & 2.5e-05 \tabularnewline
Y4 & -0.0160517215222272 & 0.149372 & -0.1075 & 0.914974 & 0.457487 \tabularnewline
M1 & 15.3454731041248 & 5.05474 & 3.0359 & 0.004259 & 0.00213 \tabularnewline
M2 & -1.3210319312054 & 7.150494 & -0.1847 & 0.854385 & 0.427192 \tabularnewline
M3 & -18.4272530266396 & 4.747283 & -3.8816 & 0.000389 & 0.000195 \tabularnewline
M4 & -18.0250317516137 & 3.206325 & -5.6217 & 2e-06 & 1e-06 \tabularnewline
M5 & -11.374623572876 & 2.91686 & -3.8996 & 0.000369 & 0.000185 \tabularnewline
M6 & 1.64234957827378 & 3.432236 & 0.4785 & 0.634961 & 0.31748 \tabularnewline
M7 & -3.43736217073495 & 4.611566 & -0.7454 & 0.460512 & 0.230256 \tabularnewline
M8 & -8.17796939620031 & 4.622097 & -1.7693 & 0.08466 & 0.04233 \tabularnewline
M9 & -2.59167880781004 & 3.509868 & -0.7384 & 0.464693 & 0.232347 \tabularnewline
M10 & -24.2441038493184 & 4.060683 & -5.9704 & 1e-06 & 0 \tabularnewline
M11 & -20.5106923504080 & 4.351302 & -4.7137 & 3.1e-05 & 1.5e-05 \tabularnewline
t & 0.121203282376966 & 0.058058 & 2.0876 & 0.043413 & 0.021707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&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]50.2362928119604[/C][C]17.613864[/C][C]2.8521[/C][C]0.006912[/C][C]0.003456[/C][/ROW]
[ROW][C]X[/C][C]-10.5265285686030[/C][C]2.790755[/C][C]-3.7719[/C][C]0.000538[/C][C]0.000269[/C][/ROW]
[ROW][C]Y1[/C][C]-0.202061509463685[/C][C]0.156023[/C][C]-1.2951[/C][C]0.202908[/C][C]0.101454[/C][/ROW]
[ROW][C]Y2[/C][C]0.236569774841816[/C][C]0.120681[/C][C]1.9603[/C][C]0.057134[/C][C]0.028567[/C][/ROW]
[ROW][C]Y3[/C][C]0.554834223280099[/C][C]0.121799[/C][C]4.5553[/C][C]5e-05[/C][C]2.5e-05[/C][/ROW]
[ROW][C]Y4[/C][C]-0.0160517215222272[/C][C]0.149372[/C][C]-0.1075[/C][C]0.914974[/C][C]0.457487[/C][/ROW]
[ROW][C]M1[/C][C]15.3454731041248[/C][C]5.05474[/C][C]3.0359[/C][C]0.004259[/C][C]0.00213[/C][/ROW]
[ROW][C]M2[/C][C]-1.3210319312054[/C][C]7.150494[/C][C]-0.1847[/C][C]0.854385[/C][C]0.427192[/C][/ROW]
[ROW][C]M3[/C][C]-18.4272530266396[/C][C]4.747283[/C][C]-3.8816[/C][C]0.000389[/C][C]0.000195[/C][/ROW]
[ROW][C]M4[/C][C]-18.0250317516137[/C][C]3.206325[/C][C]-5.6217[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M5[/C][C]-11.374623572876[/C][C]2.91686[/C][C]-3.8996[/C][C]0.000369[/C][C]0.000185[/C][/ROW]
[ROW][C]M6[/C][C]1.64234957827378[/C][C]3.432236[/C][C]0.4785[/C][C]0.634961[/C][C]0.31748[/C][/ROW]
[ROW][C]M7[/C][C]-3.43736217073495[/C][C]4.611566[/C][C]-0.7454[/C][C]0.460512[/C][C]0.230256[/C][/ROW]
[ROW][C]M8[/C][C]-8.17796939620031[/C][C]4.622097[/C][C]-1.7693[/C][C]0.08466[/C][C]0.04233[/C][/ROW]
[ROW][C]M9[/C][C]-2.59167880781004[/C][C]3.509868[/C][C]-0.7384[/C][C]0.464693[/C][C]0.232347[/C][/ROW]
[ROW][C]M10[/C][C]-24.2441038493184[/C][C]4.060683[/C][C]-5.9704[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-20.5106923504080[/C][C]4.351302[/C][C]-4.7137[/C][C]3.1e-05[/C][C]1.5e-05[/C][/ROW]
[ROW][C]t[/C][C]0.121203282376966[/C][C]0.058058[/C][C]2.0876[/C][C]0.043413[/C][C]0.021707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58330&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&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)50.236292811960417.6138642.85210.0069120.003456
X-10.52652856860302.790755-3.77190.0005380.000269
Y1-0.2020615094636850.156023-1.29510.2029080.101454
Y20.2365697748418160.1206811.96030.0571340.028567
Y30.5548342232800990.1217994.55535e-052.5e-05
Y4-0.01605172152222720.149372-0.10750.9149740.457487
M115.34547310412485.054743.03590.0042590.00213
M2-1.32103193120547.150494-0.18470.8543850.427192
M3-18.42725302663964.747283-3.88160.0003890.000195
M4-18.02503175161373.206325-5.62172e-061e-06
M5-11.3746235728762.91686-3.89960.0003690.000185
M61.642349578273783.4322360.47850.6349610.31748
M7-3.437362170734954.611566-0.74540.4605120.230256
M8-8.177969396200314.622097-1.76930.084660.04233
M9-2.591678807810043.509868-0.73840.4646930.232347
M10-24.24410384931844.060683-5.97041e-060
M11-20.51069235040804.351302-4.71373.1e-051.5e-05
t0.1212032823769660.0580582.08760.0434130.021707






Multiple Linear Regression - Regression Statistics
Multiple R0.947256615280796
R-squared0.89729509519323
Adjusted R-squared0.852526290533869
F-TEST (value)20.0428647139588
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value3.530509218308e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.49639337270593
Sum Squared Residuals476.765898051377

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.947256615280796 \tabularnewline
R-squared & 0.89729509519323 \tabularnewline
Adjusted R-squared & 0.852526290533869 \tabularnewline
F-TEST (value) & 20.0428647139588 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 3.530509218308e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.49639337270593 \tabularnewline
Sum Squared Residuals & 476.765898051377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.947256615280796[/C][/ROW]
[ROW][C]R-squared[/C][C]0.89729509519323[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.852526290533869[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]20.0428647139588[/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]3.530509218308e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.49639337270593[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]476.765898051377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58330&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&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 R0.947256615280796
R-squared0.89729509519323
Adjusted R-squared0.852526290533869
F-TEST (value)20.0428647139588
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value3.530509218308e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.49639337270593
Sum Squared Residuals476.765898051377






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1110.3112.252054510448-1.95205451044806
2103.9106.167926613587-2.26792661358659
3101.699.02488319713482.57511680286515
494.696.1129378365177-1.51293783651767
595.9100.264926894534-4.36492689453374
6104.7110.311047246063-5.61104724606301
7102.8100.0350175999862.7649824000144
898.198.714991084406-0.614991084405923
9113.9109.7843654043394.11563459566102
1080.982.753253680297-1.853253680297
1195.794.43647813786251.26352186213746
12113.2113.1128846797850.0871153202149736
13105.9109.981570750037-4.08157075003667
14108.8107.7925423906791.00745760932087
15102.397.96662027270484.33337972729524
169996.15830203207912.84169796792085
17100.7103.785209752577-3.08520975257667
18115.5112.1462289193023.35377108069795
19100.7102.872761982909-2.17276198290899
20109.9105.7412899081424.15871009185848
21114.6114.2728438021420.327156197858334
2285.485.5192628940012-0.119262894001209
23100.5101.727992026091-1.22799202609066
24114.8114.860966452005-0.0609664520048876
25116.5114.7337644423541.76623555764602
26112.9110.0746129435292.82538705647099
27102101.9109335796920.0890664203080536
28106104.4988559626271.50114403737323
29105.3105.858919709715-0.558919709714725
30118.8114.0949114629604.70508853703975
31106.1108.637274433892-2.53727443389214
32109.3109.325152778972-0.0251527789720770
33117.2118.883111898311-1.68311189831134
3492.589.24953461770333.25046538229669
35104.2101.9432962818232.25670371817728
36112.5118.699623670331-6.19962367033133
37122.4121.4258419788900.97415802111033
38113.3111.7316983474091.56830165259076
39100103.344799952820-3.34479995282032
40110.7109.7624871568680.937512843131833
41112.8106.0177589864066.78224101359374
42109.8114.029678337094-4.22967833709365
43117.3116.3243650113630.975634988636562
44109.1110.473188871372-1.37318887137233
45115.9117.913649146018-2.01364914601842
469697.2779488079985-1.27794880799848
4799.8102.092233554224-2.29223355422409
48116.8110.6265251978796.17347480212124
49115.7112.4067683182723.29323168172839
5099.4102.533219704796-3.13321970479604
5194.397.9527629976481-3.65276299764814
529194.7674170119082-3.76741701190823
5393.291.97318465676861.22681534323140
54103.1101.3181340345811.78186596541895
5594.193.13058097184980.969419028150166
5691.893.9453773571081-2.14537735710815
57102.7103.446029749190-0.746029749189583

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 110.3 & 112.252054510448 & -1.95205451044806 \tabularnewline
2 & 103.9 & 106.167926613587 & -2.26792661358659 \tabularnewline
3 & 101.6 & 99.0248831971348 & 2.57511680286515 \tabularnewline
4 & 94.6 & 96.1129378365177 & -1.51293783651767 \tabularnewline
5 & 95.9 & 100.264926894534 & -4.36492689453374 \tabularnewline
6 & 104.7 & 110.311047246063 & -5.61104724606301 \tabularnewline
7 & 102.8 & 100.035017599986 & 2.7649824000144 \tabularnewline
8 & 98.1 & 98.714991084406 & -0.614991084405923 \tabularnewline
9 & 113.9 & 109.784365404339 & 4.11563459566102 \tabularnewline
10 & 80.9 & 82.753253680297 & -1.853253680297 \tabularnewline
11 & 95.7 & 94.4364781378625 & 1.26352186213746 \tabularnewline
12 & 113.2 & 113.112884679785 & 0.0871153202149736 \tabularnewline
13 & 105.9 & 109.981570750037 & -4.08157075003667 \tabularnewline
14 & 108.8 & 107.792542390679 & 1.00745760932087 \tabularnewline
15 & 102.3 & 97.9666202727048 & 4.33337972729524 \tabularnewline
16 & 99 & 96.1583020320791 & 2.84169796792085 \tabularnewline
17 & 100.7 & 103.785209752577 & -3.08520975257667 \tabularnewline
18 & 115.5 & 112.146228919302 & 3.35377108069795 \tabularnewline
19 & 100.7 & 102.872761982909 & -2.17276198290899 \tabularnewline
20 & 109.9 & 105.741289908142 & 4.15871009185848 \tabularnewline
21 & 114.6 & 114.272843802142 & 0.327156197858334 \tabularnewline
22 & 85.4 & 85.5192628940012 & -0.119262894001209 \tabularnewline
23 & 100.5 & 101.727992026091 & -1.22799202609066 \tabularnewline
24 & 114.8 & 114.860966452005 & -0.0609664520048876 \tabularnewline
25 & 116.5 & 114.733764442354 & 1.76623555764602 \tabularnewline
26 & 112.9 & 110.074612943529 & 2.82538705647099 \tabularnewline
27 & 102 & 101.910933579692 & 0.0890664203080536 \tabularnewline
28 & 106 & 104.498855962627 & 1.50114403737323 \tabularnewline
29 & 105.3 & 105.858919709715 & -0.558919709714725 \tabularnewline
30 & 118.8 & 114.094911462960 & 4.70508853703975 \tabularnewline
31 & 106.1 & 108.637274433892 & -2.53727443389214 \tabularnewline
32 & 109.3 & 109.325152778972 & -0.0251527789720770 \tabularnewline
33 & 117.2 & 118.883111898311 & -1.68311189831134 \tabularnewline
34 & 92.5 & 89.2495346177033 & 3.25046538229669 \tabularnewline
35 & 104.2 & 101.943296281823 & 2.25670371817728 \tabularnewline
36 & 112.5 & 118.699623670331 & -6.19962367033133 \tabularnewline
37 & 122.4 & 121.425841978890 & 0.97415802111033 \tabularnewline
38 & 113.3 & 111.731698347409 & 1.56830165259076 \tabularnewline
39 & 100 & 103.344799952820 & -3.34479995282032 \tabularnewline
40 & 110.7 & 109.762487156868 & 0.937512843131833 \tabularnewline
41 & 112.8 & 106.017758986406 & 6.78224101359374 \tabularnewline
42 & 109.8 & 114.029678337094 & -4.22967833709365 \tabularnewline
43 & 117.3 & 116.324365011363 & 0.975634988636562 \tabularnewline
44 & 109.1 & 110.473188871372 & -1.37318887137233 \tabularnewline
45 & 115.9 & 117.913649146018 & -2.01364914601842 \tabularnewline
46 & 96 & 97.2779488079985 & -1.27794880799848 \tabularnewline
47 & 99.8 & 102.092233554224 & -2.29223355422409 \tabularnewline
48 & 116.8 & 110.626525197879 & 6.17347480212124 \tabularnewline
49 & 115.7 & 112.406768318272 & 3.29323168172839 \tabularnewline
50 & 99.4 & 102.533219704796 & -3.13321970479604 \tabularnewline
51 & 94.3 & 97.9527629976481 & -3.65276299764814 \tabularnewline
52 & 91 & 94.7674170119082 & -3.76741701190823 \tabularnewline
53 & 93.2 & 91.9731846567686 & 1.22681534323140 \tabularnewline
54 & 103.1 & 101.318134034581 & 1.78186596541895 \tabularnewline
55 & 94.1 & 93.1305809718498 & 0.969419028150166 \tabularnewline
56 & 91.8 & 93.9453773571081 & -2.14537735710815 \tabularnewline
57 & 102.7 & 103.446029749190 & -0.746029749189583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&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]110.3[/C][C]112.252054510448[/C][C]-1.95205451044806[/C][/ROW]
[ROW][C]2[/C][C]103.9[/C][C]106.167926613587[/C][C]-2.26792661358659[/C][/ROW]
[ROW][C]3[/C][C]101.6[/C][C]99.0248831971348[/C][C]2.57511680286515[/C][/ROW]
[ROW][C]4[/C][C]94.6[/C][C]96.1129378365177[/C][C]-1.51293783651767[/C][/ROW]
[ROW][C]5[/C][C]95.9[/C][C]100.264926894534[/C][C]-4.36492689453374[/C][/ROW]
[ROW][C]6[/C][C]104.7[/C][C]110.311047246063[/C][C]-5.61104724606301[/C][/ROW]
[ROW][C]7[/C][C]102.8[/C][C]100.035017599986[/C][C]2.7649824000144[/C][/ROW]
[ROW][C]8[/C][C]98.1[/C][C]98.714991084406[/C][C]-0.614991084405923[/C][/ROW]
[ROW][C]9[/C][C]113.9[/C][C]109.784365404339[/C][C]4.11563459566102[/C][/ROW]
[ROW][C]10[/C][C]80.9[/C][C]82.753253680297[/C][C]-1.853253680297[/C][/ROW]
[ROW][C]11[/C][C]95.7[/C][C]94.4364781378625[/C][C]1.26352186213746[/C][/ROW]
[ROW][C]12[/C][C]113.2[/C][C]113.112884679785[/C][C]0.0871153202149736[/C][/ROW]
[ROW][C]13[/C][C]105.9[/C][C]109.981570750037[/C][C]-4.08157075003667[/C][/ROW]
[ROW][C]14[/C][C]108.8[/C][C]107.792542390679[/C][C]1.00745760932087[/C][/ROW]
[ROW][C]15[/C][C]102.3[/C][C]97.9666202727048[/C][C]4.33337972729524[/C][/ROW]
[ROW][C]16[/C][C]99[/C][C]96.1583020320791[/C][C]2.84169796792085[/C][/ROW]
[ROW][C]17[/C][C]100.7[/C][C]103.785209752577[/C][C]-3.08520975257667[/C][/ROW]
[ROW][C]18[/C][C]115.5[/C][C]112.146228919302[/C][C]3.35377108069795[/C][/ROW]
[ROW][C]19[/C][C]100.7[/C][C]102.872761982909[/C][C]-2.17276198290899[/C][/ROW]
[ROW][C]20[/C][C]109.9[/C][C]105.741289908142[/C][C]4.15871009185848[/C][/ROW]
[ROW][C]21[/C][C]114.6[/C][C]114.272843802142[/C][C]0.327156197858334[/C][/ROW]
[ROW][C]22[/C][C]85.4[/C][C]85.5192628940012[/C][C]-0.119262894001209[/C][/ROW]
[ROW][C]23[/C][C]100.5[/C][C]101.727992026091[/C][C]-1.22799202609066[/C][/ROW]
[ROW][C]24[/C][C]114.8[/C][C]114.860966452005[/C][C]-0.0609664520048876[/C][/ROW]
[ROW][C]25[/C][C]116.5[/C][C]114.733764442354[/C][C]1.76623555764602[/C][/ROW]
[ROW][C]26[/C][C]112.9[/C][C]110.074612943529[/C][C]2.82538705647099[/C][/ROW]
[ROW][C]27[/C][C]102[/C][C]101.910933579692[/C][C]0.0890664203080536[/C][/ROW]
[ROW][C]28[/C][C]106[/C][C]104.498855962627[/C][C]1.50114403737323[/C][/ROW]
[ROW][C]29[/C][C]105.3[/C][C]105.858919709715[/C][C]-0.558919709714725[/C][/ROW]
[ROW][C]30[/C][C]118.8[/C][C]114.094911462960[/C][C]4.70508853703975[/C][/ROW]
[ROW][C]31[/C][C]106.1[/C][C]108.637274433892[/C][C]-2.53727443389214[/C][/ROW]
[ROW][C]32[/C][C]109.3[/C][C]109.325152778972[/C][C]-0.0251527789720770[/C][/ROW]
[ROW][C]33[/C][C]117.2[/C][C]118.883111898311[/C][C]-1.68311189831134[/C][/ROW]
[ROW][C]34[/C][C]92.5[/C][C]89.2495346177033[/C][C]3.25046538229669[/C][/ROW]
[ROW][C]35[/C][C]104.2[/C][C]101.943296281823[/C][C]2.25670371817728[/C][/ROW]
[ROW][C]36[/C][C]112.5[/C][C]118.699623670331[/C][C]-6.19962367033133[/C][/ROW]
[ROW][C]37[/C][C]122.4[/C][C]121.425841978890[/C][C]0.97415802111033[/C][/ROW]
[ROW][C]38[/C][C]113.3[/C][C]111.731698347409[/C][C]1.56830165259076[/C][/ROW]
[ROW][C]39[/C][C]100[/C][C]103.344799952820[/C][C]-3.34479995282032[/C][/ROW]
[ROW][C]40[/C][C]110.7[/C][C]109.762487156868[/C][C]0.937512843131833[/C][/ROW]
[ROW][C]41[/C][C]112.8[/C][C]106.017758986406[/C][C]6.78224101359374[/C][/ROW]
[ROW][C]42[/C][C]109.8[/C][C]114.029678337094[/C][C]-4.22967833709365[/C][/ROW]
[ROW][C]43[/C][C]117.3[/C][C]116.324365011363[/C][C]0.975634988636562[/C][/ROW]
[ROW][C]44[/C][C]109.1[/C][C]110.473188871372[/C][C]-1.37318887137233[/C][/ROW]
[ROW][C]45[/C][C]115.9[/C][C]117.913649146018[/C][C]-2.01364914601842[/C][/ROW]
[ROW][C]46[/C][C]96[/C][C]97.2779488079985[/C][C]-1.27794880799848[/C][/ROW]
[ROW][C]47[/C][C]99.8[/C][C]102.092233554224[/C][C]-2.29223355422409[/C][/ROW]
[ROW][C]48[/C][C]116.8[/C][C]110.626525197879[/C][C]6.17347480212124[/C][/ROW]
[ROW][C]49[/C][C]115.7[/C][C]112.406768318272[/C][C]3.29323168172839[/C][/ROW]
[ROW][C]50[/C][C]99.4[/C][C]102.533219704796[/C][C]-3.13321970479604[/C][/ROW]
[ROW][C]51[/C][C]94.3[/C][C]97.9527629976481[/C][C]-3.65276299764814[/C][/ROW]
[ROW][C]52[/C][C]91[/C][C]94.7674170119082[/C][C]-3.76741701190823[/C][/ROW]
[ROW][C]53[/C][C]93.2[/C][C]91.9731846567686[/C][C]1.22681534323140[/C][/ROW]
[ROW][C]54[/C][C]103.1[/C][C]101.318134034581[/C][C]1.78186596541895[/C][/ROW]
[ROW][C]55[/C][C]94.1[/C][C]93.1305809718498[/C][C]0.969419028150166[/C][/ROW]
[ROW][C]56[/C][C]91.8[/C][C]93.9453773571081[/C][C]-2.14537735710815[/C][/ROW]
[ROW][C]57[/C][C]102.7[/C][C]103.446029749190[/C][C]-0.746029749189583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58330&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&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
1110.3112.252054510448-1.95205451044806
2103.9106.167926613587-2.26792661358659
3101.699.02488319713482.57511680286515
494.696.1129378365177-1.51293783651767
595.9100.264926894534-4.36492689453374
6104.7110.311047246063-5.61104724606301
7102.8100.0350175999862.7649824000144
898.198.714991084406-0.614991084405923
9113.9109.7843654043394.11563459566102
1080.982.753253680297-1.853253680297
1195.794.43647813786251.26352186213746
12113.2113.1128846797850.0871153202149736
13105.9109.981570750037-4.08157075003667
14108.8107.7925423906791.00745760932087
15102.397.96662027270484.33337972729524
169996.15830203207912.84169796792085
17100.7103.785209752577-3.08520975257667
18115.5112.1462289193023.35377108069795
19100.7102.872761982909-2.17276198290899
20109.9105.7412899081424.15871009185848
21114.6114.2728438021420.327156197858334
2285.485.5192628940012-0.119262894001209
23100.5101.727992026091-1.22799202609066
24114.8114.860966452005-0.0609664520048876
25116.5114.7337644423541.76623555764602
26112.9110.0746129435292.82538705647099
27102101.9109335796920.0890664203080536
28106104.4988559626271.50114403737323
29105.3105.858919709715-0.558919709714725
30118.8114.0949114629604.70508853703975
31106.1108.637274433892-2.53727443389214
32109.3109.325152778972-0.0251527789720770
33117.2118.883111898311-1.68311189831134
3492.589.24953461770333.25046538229669
35104.2101.9432962818232.25670371817728
36112.5118.699623670331-6.19962367033133
37122.4121.4258419788900.97415802111033
38113.3111.7316983474091.56830165259076
39100103.344799952820-3.34479995282032
40110.7109.7624871568680.937512843131833
41112.8106.0177589864066.78224101359374
42109.8114.029678337094-4.22967833709365
43117.3116.3243650113630.975634988636562
44109.1110.473188871372-1.37318887137233
45115.9117.913649146018-2.01364914601842
469697.2779488079985-1.27794880799848
4799.8102.092233554224-2.29223355422409
48116.8110.6265251978796.17347480212124
49115.7112.4067683182723.29323168172839
5099.4102.533219704796-3.13321970479604
5194.397.9527629976481-3.65276299764814
529194.7674170119082-3.76741701190823
5393.291.97318465676861.22681534323140
54103.1101.3181340345811.78186596541895
5594.193.13058097184980.969419028150166
5691.893.9453773571081-2.14537735710815
57102.7103.446029749190-0.746029749189583






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.7291108495587810.5417783008824370.270889150441219
220.6100231031584550.779953793683090.389976896841545
230.5062694081396980.9874611837206050.493730591860302
240.3609190855997110.7218381711994210.63908091440029
250.2511553994777510.5023107989555010.74884460052225
260.1894628301208480.3789256602416970.810537169879152
270.2102221418341290.4204442836682590.78977785816587
280.1451817029666810.2903634059333610.85481829703332
290.1491848362001640.2983696724003270.850815163799836
300.1609054716593610.3218109433187220.839094528340639
310.1565973692570740.3131947385141480.843402630742926
320.1102334458382660.2204668916765320.889766554161734
330.1130418743424260.2260837486848520.886958125657574
340.1055865265408990.2111730530817980.894413473459101
350.05571121590480240.1114224318096050.944288784095198
360.599685947429870.800628105140260.40031405257013

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.729110849558781 & 0.541778300882437 & 0.270889150441219 \tabularnewline
22 & 0.610023103158455 & 0.77995379368309 & 0.389976896841545 \tabularnewline
23 & 0.506269408139698 & 0.987461183720605 & 0.493730591860302 \tabularnewline
24 & 0.360919085599711 & 0.721838171199421 & 0.63908091440029 \tabularnewline
25 & 0.251155399477751 & 0.502310798955501 & 0.74884460052225 \tabularnewline
26 & 0.189462830120848 & 0.378925660241697 & 0.810537169879152 \tabularnewline
27 & 0.210222141834129 & 0.420444283668259 & 0.78977785816587 \tabularnewline
28 & 0.145181702966681 & 0.290363405933361 & 0.85481829703332 \tabularnewline
29 & 0.149184836200164 & 0.298369672400327 & 0.850815163799836 \tabularnewline
30 & 0.160905471659361 & 0.321810943318722 & 0.839094528340639 \tabularnewline
31 & 0.156597369257074 & 0.313194738514148 & 0.843402630742926 \tabularnewline
32 & 0.110233445838266 & 0.220466891676532 & 0.889766554161734 \tabularnewline
33 & 0.113041874342426 & 0.226083748684852 & 0.886958125657574 \tabularnewline
34 & 0.105586526540899 & 0.211173053081798 & 0.894413473459101 \tabularnewline
35 & 0.0557112159048024 & 0.111422431809605 & 0.944288784095198 \tabularnewline
36 & 0.59968594742987 & 0.80062810514026 & 0.40031405257013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&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]0.729110849558781[/C][C]0.541778300882437[/C][C]0.270889150441219[/C][/ROW]
[ROW][C]22[/C][C]0.610023103158455[/C][C]0.77995379368309[/C][C]0.389976896841545[/C][/ROW]
[ROW][C]23[/C][C]0.506269408139698[/C][C]0.987461183720605[/C][C]0.493730591860302[/C][/ROW]
[ROW][C]24[/C][C]0.360919085599711[/C][C]0.721838171199421[/C][C]0.63908091440029[/C][/ROW]
[ROW][C]25[/C][C]0.251155399477751[/C][C]0.502310798955501[/C][C]0.74884460052225[/C][/ROW]
[ROW][C]26[/C][C]0.189462830120848[/C][C]0.378925660241697[/C][C]0.810537169879152[/C][/ROW]
[ROW][C]27[/C][C]0.210222141834129[/C][C]0.420444283668259[/C][C]0.78977785816587[/C][/ROW]
[ROW][C]28[/C][C]0.145181702966681[/C][C]0.290363405933361[/C][C]0.85481829703332[/C][/ROW]
[ROW][C]29[/C][C]0.149184836200164[/C][C]0.298369672400327[/C][C]0.850815163799836[/C][/ROW]
[ROW][C]30[/C][C]0.160905471659361[/C][C]0.321810943318722[/C][C]0.839094528340639[/C][/ROW]
[ROW][C]31[/C][C]0.156597369257074[/C][C]0.313194738514148[/C][C]0.843402630742926[/C][/ROW]
[ROW][C]32[/C][C]0.110233445838266[/C][C]0.220466891676532[/C][C]0.889766554161734[/C][/ROW]
[ROW][C]33[/C][C]0.113041874342426[/C][C]0.226083748684852[/C][C]0.886958125657574[/C][/ROW]
[ROW][C]34[/C][C]0.105586526540899[/C][C]0.211173053081798[/C][C]0.894413473459101[/C][/ROW]
[ROW][C]35[/C][C]0.0557112159048024[/C][C]0.111422431809605[/C][C]0.944288784095198[/C][/ROW]
[ROW][C]36[/C][C]0.59968594742987[/C][C]0.80062810514026[/C][C]0.40031405257013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58330&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&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
210.7291108495587810.5417783008824370.270889150441219
220.6100231031584550.779953793683090.389976896841545
230.5062694081396980.9874611837206050.493730591860302
240.3609190855997110.7218381711994210.63908091440029
250.2511553994777510.5023107989555010.74884460052225
260.1894628301208480.3789256602416970.810537169879152
270.2102221418341290.4204442836682590.78977785816587
280.1451817029666810.2903634059333610.85481829703332
290.1491848362001640.2983696724003270.850815163799836
300.1609054716593610.3218109433187220.839094528340639
310.1565973692570740.3131947385141480.843402630742926
320.1102334458382660.2204668916765320.889766554161734
330.1130418743424260.2260837486848520.886958125657574
340.1055865265408990.2111730530817980.894413473459101
350.05571121590480240.1114224318096050.944288784095198
360.599685947429870.800628105140260.40031405257013






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58330&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58330&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58330&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}