## Free Statistics

of Irreproducible Research!

Author's title
Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 10 Nov 2012 06:47:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/10/t1352548068lz1hec4l9h09wjm.htm/, Retrieved Sat, 10 Dec 2022 06:22:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187304, Retrieved Sat, 10 Dec 2022 06:22:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Classical Decomposition] [Unemployment] [2010-11-30 13:33:27] [b98453cac15ba1066b407e146608df68]
- RMPD      [Multiple Regression] [] [2012-11-10 11:47:28] [eeec99d459a890eb36d32eb90406e4cb] [Current]
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Dataseries X:
99.2	96.7	101.0
99.0	98.1	100.1
100.0	100.0	100.0
111.6	104.9	90.6
122.2	104.9	86.5
117.6	109.5	89.7
121.1	110.8	90.6
136.0	112.3	82.8
154.2	109.3	70.1
153.6	105.3	65.4
158.5	101.7	61.3
140.6	95.4	62.5
136.2	96.4	63.6
168.0	97.6	52.6
154.3	102.4	59.7
149.0	101.6	59.5
165.5	103.8	61.3

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187304&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187304&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187304&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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

 Multiple Linear Regression - Estimated Regression Equation Cons[t] = + 141.648090178319 + 0.660084237790883Inc[t] -1.13957260765924Price[t] + 1.90575805616525M1[t] + 9.46692807187031M2[t] + 4.2938865424838M3[t] + 0.0205018786537541M4[t] + 10.9336372586813M5[t] + 2.29076793304609M6[t] + 5.35801031121686M7[t] + 9.77895415519412M8[t] + 14.8863712917001M9[t] + 10.9704535272708M10[t] + 12.9742456323207M11[t] + 0.600263459594387t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Cons[t] =  +  141.648090178319 +  0.660084237790883Inc[t] -1.13957260765924Price[t] +  1.90575805616525M1[t] +  9.46692807187031M2[t] +  4.2938865424838M3[t] +  0.0205018786537541M4[t] +  10.9336372586813M5[t] +  2.29076793304609M6[t] +  5.35801031121686M7[t] +  9.77895415519412M8[t] +  14.8863712917001M9[t] +  10.9704535272708M10[t] +  12.9742456323207M11[t] +  0.600263459594387t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187304&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Cons[t] =  +  141.648090178319 +  0.660084237790883Inc[t] -1.13957260765924Price[t] +  1.90575805616525M1[t] +  9.46692807187031M2[t] +  4.2938865424838M3[t] +  0.0205018786537541M4[t] +  10.9336372586813M5[t] +  2.29076793304609M6[t] +  5.35801031121686M7[t] +  9.77895415519412M8[t] +  14.8863712917001M9[t] +  10.9704535272708M10[t] +  12.9742456323207M11[t] +  0.600263459594387t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187304&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187304&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 Cons[t] = + 141.648090178319 + 0.660084237790883Inc[t] -1.13957260765924Price[t] + 1.90575805616525M1[t] + 9.46692807187031M2[t] + 4.2938865424838M3[t] + 0.0205018786537541M4[t] + 10.9336372586813M5[t] + 2.29076793304609M6[t] + 5.35801031121686M7[t] + 9.77895415519412M8[t] + 14.8863712917001M9[t] + 10.9704535272708M10[t] + 12.9742456323207M11[t] + 0.600263459594387t + e[t]

 Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STATH0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 141.648090178319 371.220354 0.3816 0.739502 0.369751 Inc 0.660084237790883 3.401459 0.1941 0.864053 0.432027 Price -1.13957260765924 0.810546 -1.4059 0.294973 0.147486 M1 1.90575805616525 12.346393 0.1544 0.891497 0.445749 M2 9.46692807187031 13.671871 0.6924 0.560254 0.280127 M3 4.2938865424838 25.529205 0.1682 0.8819 0.44095 M4 0.0205018786537541 31.11733 7e-04 0.999534 0.499767 M5 10.9336372586813 35.637695 0.3068 0.787991 0.393996 M6 2.29076793304609 52.410089 0.0437 0.969108 0.484554 M7 5.35801031121686 58.652923 0.0914 0.935539 0.46777 M8 9.77895415519412 61.533945 0.1589 0.88833 0.444165 M9 14.8863712917001 47.856552 0.3111 0.785181 0.39259 M10 10.9704535272708 34.477717 0.3182 0.780493 0.390247 M11 12.9742456323207 23.339099 0.5559 0.634166 0.317083 t 0.600263459594387 2.571551 0.2334 0.837147 0.418574

\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) & 141.648090178319 & 371.220354 & 0.3816 & 0.739502 & 0.369751 \tabularnewline
Inc & 0.660084237790883 & 3.401459 & 0.1941 & 0.864053 & 0.432027 \tabularnewline
Price & -1.13957260765924 & 0.810546 & -1.4059 & 0.294973 & 0.147486 \tabularnewline
M1 & 1.90575805616525 & 12.346393 & 0.1544 & 0.891497 & 0.445749 \tabularnewline
M2 & 9.46692807187031 & 13.671871 & 0.6924 & 0.560254 & 0.280127 \tabularnewline
M3 & 4.2938865424838 & 25.529205 & 0.1682 & 0.8819 & 0.44095 \tabularnewline
M4 & 0.0205018786537541 & 31.11733 & 7e-04 & 0.999534 & 0.499767 \tabularnewline
M5 & 10.9336372586813 & 35.637695 & 0.3068 & 0.787991 & 0.393996 \tabularnewline
M6 & 2.29076793304609 & 52.410089 & 0.0437 & 0.969108 & 0.484554 \tabularnewline
M7 & 5.35801031121686 & 58.652923 & 0.0914 & 0.935539 & 0.46777 \tabularnewline
M8 & 9.77895415519412 & 61.533945 & 0.1589 & 0.88833 & 0.444165 \tabularnewline
M9 & 14.8863712917001 & 47.856552 & 0.3111 & 0.785181 & 0.39259 \tabularnewline
M10 & 10.9704535272708 & 34.477717 & 0.3182 & 0.780493 & 0.390247 \tabularnewline
M11 & 12.9742456323207 & 23.339099 & 0.5559 & 0.634166 & 0.317083 \tabularnewline
t & 0.600263459594387 & 2.571551 & 0.2334 & 0.837147 & 0.418574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187304&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]141.648090178319[/C][C]371.220354[/C][C]0.3816[/C][C]0.739502[/C][C]0.369751[/C][/ROW]
[ROW][C]Inc[/C][C]0.660084237790883[/C][C]3.401459[/C][C]0.1941[/C][C]0.864053[/C][C]0.432027[/C][/ROW]
[ROW][C]Price[/C][C]-1.13957260765924[/C][C]0.810546[/C][C]-1.4059[/C][C]0.294973[/C][C]0.147486[/C][/ROW]
[ROW][C]M1[/C][C]1.90575805616525[/C][C]12.346393[/C][C]0.1544[/C][C]0.891497[/C][C]0.445749[/C][/ROW]
[ROW][C]M2[/C][C]9.46692807187031[/C][C]13.671871[/C][C]0.6924[/C][C]0.560254[/C][C]0.280127[/C][/ROW]
[ROW][C]M3[/C][C]4.2938865424838[/C][C]25.529205[/C][C]0.1682[/C][C]0.8819[/C][C]0.44095[/C][/ROW]
[ROW][C]M4[/C][C]0.0205018786537541[/C][C]31.11733[/C][C]7e-04[/C][C]0.999534[/C][C]0.499767[/C][/ROW]
[ROW][C]M5[/C][C]10.9336372586813[/C][C]35.637695[/C][C]0.3068[/C][C]0.787991[/C][C]0.393996[/C][/ROW]
[ROW][C]M6[/C][C]2.29076793304609[/C][C]52.410089[/C][C]0.0437[/C][C]0.969108[/C][C]0.484554[/C][/ROW]
[ROW][C]M7[/C][C]5.35801031121686[/C][C]58.652923[/C][C]0.0914[/C][C]0.935539[/C][C]0.46777[/C][/ROW]
[ROW][C]M8[/C][C]9.77895415519412[/C][C]61.533945[/C][C]0.1589[/C][C]0.88833[/C][C]0.444165[/C][/ROW]
[ROW][C]M9[/C][C]14.8863712917001[/C][C]47.856552[/C][C]0.3111[/C][C]0.785181[/C][C]0.39259[/C][/ROW]
[ROW][C]M10[/C][C]10.9704535272708[/C][C]34.477717[/C][C]0.3182[/C][C]0.780493[/C][C]0.390247[/C][/ROW]
[ROW][C]M11[/C][C]12.9742456323207[/C][C]23.339099[/C][C]0.5559[/C][C]0.634166[/C][C]0.317083[/C][/ROW]
[ROW][C]t[/C][C]0.600263459594387[/C][C]2.571551[/C][C]0.2334[/C][C]0.837147[/C][C]0.418574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187304&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187304&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 Variable Parameter S.D. T-STATH0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 141.648090178319 371.220354 0.3816 0.739502 0.369751 Inc 0.660084237790883 3.401459 0.1941 0.864053 0.432027 Price -1.13957260765924 0.810546 -1.4059 0.294973 0.147486 M1 1.90575805616525 12.346393 0.1544 0.891497 0.445749 M2 9.46692807187031 13.671871 0.6924 0.560254 0.280127 M3 4.2938865424838 25.529205 0.1682 0.8819 0.44095 M4 0.0205018786537541 31.11733 7e-04 0.999534 0.499767 M5 10.9336372586813 35.637695 0.3068 0.787991 0.393996 M6 2.29076793304609 52.410089 0.0437 0.969108 0.484554 M7 5.35801031121686 58.652923 0.0914 0.935539 0.46777 M8 9.77895415519412 61.533945 0.1589 0.88833 0.444165 M9 14.8863712917001 47.856552 0.3111 0.785181 0.39259 M10 10.9704535272708 34.477717 0.3182 0.780493 0.390247 M11 12.9742456323207 23.339099 0.5559 0.634166 0.317083 t 0.600263459594387 2.571551 0.2334 0.837147 0.418574

 Multiple Linear Regression - Regression Statistics Multiple R 0.991570863798807 R-squared 0.983212777934713 Adjusted R-squared 0.865702223477705 F-TEST (value) 8.36701675417961 F-TEST (DF numerator) 14 F-TEST (DF denominator) 2 p-value 0.111755354104154 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.64030497087169 Sum Squared Residuals 149.30973997934

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.991570863798807 \tabularnewline
R-squared & 0.983212777934713 \tabularnewline
F-TEST (value) & 8.36701675417961 \tabularnewline
F-TEST (DF numerator) & 14 \tabularnewline
F-TEST (DF denominator) & 2 \tabularnewline
p-value & 0.111755354104154 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 8.64030497087169 \tabularnewline
Sum Squared Residuals & 149.30973997934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187304&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.991570863798807[/C][/ROW]
[ROW][C]R-squared[/C][C]0.983212777934713[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.36701675417961[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]14[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]2[/C][/ROW]
[ROW][C]p-value[/C][C]0.111755354104154[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]8.64030497087169[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]149.30973997934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187304&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187304&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 R 0.991570863798807 R-squared 0.983212777934713 Adjusted R-squared 0.865702223477705 F-TEST (value) 8.36701675417961 F-TEST (DF numerator) 14 F-TEST (DF denominator) 2 p-value 0.111755354104154 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.64030497087169 Sum Squared Residuals 149.30973997934

 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals InterpolationForecast ResidualsPrediction Error 1 99.2 92.8874241148746 6.31257588512536 2 99 102.998590869975 -3.99859086997455 3 100 99.793930112751 0.206069887248988 4 111.6 110.067204185688 1.53279581431248 5 122.2 126.252850716712 -4.05285071671228 6 117.6 117.6 -5.12610787151146e-16 7 121.1 121.1 -2.90566182226115e-16 8 136 136 1.53523027623947e-16 9 154.2 154.2 3.75567632548979e-16 10 153.6 153.6 1.04170144732407e-15 11 158.5 158.5 -6.85215773010839e-17 12 140.6 140.6 -6.85215773010839e-17 13 136.2 142.512575885125 -6.31257588512536 14 168 164.001409130025 3.99859086997455 15 154.3 154.506069887249 -0.206069887248988 16 149 150.532795814312 -1.53279581431248 17 165.5 161.447149283288 4.05285071671228

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 99.2 & 92.8874241148746 & 6.31257588512536 \tabularnewline
2 & 99 & 102.998590869975 & -3.99859086997455 \tabularnewline
3 & 100 & 99.793930112751 & 0.206069887248988 \tabularnewline
4 & 111.6 & 110.067204185688 & 1.53279581431248 \tabularnewline
5 & 122.2 & 126.252850716712 & -4.05285071671228 \tabularnewline
6 & 117.6 & 117.6 & -5.12610787151146e-16 \tabularnewline
7 & 121.1 & 121.1 & -2.90566182226115e-16 \tabularnewline
8 & 136 & 136 & 1.53523027623947e-16 \tabularnewline
9 & 154.2 & 154.2 & 3.75567632548979e-16 \tabularnewline
10 & 153.6 & 153.6 & 1.04170144732407e-15 \tabularnewline
11 & 158.5 & 158.5 & -6.85215773010839e-17 \tabularnewline
12 & 140.6 & 140.6 & -6.85215773010839e-17 \tabularnewline
13 & 136.2 & 142.512575885125 & -6.31257588512536 \tabularnewline
14 & 168 & 164.001409130025 & 3.99859086997455 \tabularnewline
15 & 154.3 & 154.506069887249 & -0.206069887248988 \tabularnewline
16 & 149 & 150.532795814312 & -1.53279581431248 \tabularnewline
17 & 165.5 & 161.447149283288 & 4.05285071671228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187304&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]99.2[/C][C]92.8874241148746[/C][C]6.31257588512536[/C][/ROW]
[ROW][C]2[/C][C]99[/C][C]102.998590869975[/C][C]-3.99859086997455[/C][/ROW]
[ROW][C]3[/C][C]100[/C][C]99.793930112751[/C][C]0.206069887248988[/C][/ROW]
[ROW][C]4[/C][C]111.6[/C][C]110.067204185688[/C][C]1.53279581431248[/C][/ROW]
[ROW][C]5[/C][C]122.2[/C][C]126.252850716712[/C][C]-4.05285071671228[/C][/ROW]
[ROW][C]6[/C][C]117.6[/C][C]117.6[/C][C]-5.12610787151146e-16[/C][/ROW]
[ROW][C]7[/C][C]121.1[/C][C]121.1[/C][C]-2.90566182226115e-16[/C][/ROW]
[ROW][C]8[/C][C]136[/C][C]136[/C][C]1.53523027623947e-16[/C][/ROW]
[ROW][C]9[/C][C]154.2[/C][C]154.2[/C][C]3.75567632548979e-16[/C][/ROW]
[ROW][C]10[/C][C]153.6[/C][C]153.6[/C][C]1.04170144732407e-15[/C][/ROW]
[ROW][C]11[/C][C]158.5[/C][C]158.5[/C][C]-6.85215773010839e-17[/C][/ROW]
[ROW][C]12[/C][C]140.6[/C][C]140.6[/C][C]-6.85215773010839e-17[/C][/ROW]
[ROW][C]13[/C][C]136.2[/C][C]142.512575885125[/C][C]-6.31257588512536[/C][/ROW]
[ROW][C]14[/C][C]168[/C][C]164.001409130025[/C][C]3.99859086997455[/C][/ROW]
[ROW][C]15[/C][C]154.3[/C][C]154.506069887249[/C][C]-0.206069887248988[/C][/ROW]
[ROW][C]16[/C][C]149[/C][C]150.532795814312[/C][C]-1.53279581431248[/C][/ROW]
[ROW][C]17[/C][C]165.5[/C][C]161.447149283288[/C][C]4.05285071671228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187304&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187304&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 Index Actuals InterpolationForecast ResidualsPrediction Error 1 99.2 92.8874241148746 6.31257588512536 2 99 102.998590869975 -3.99859086997455 3 100 99.793930112751 0.206069887248988 4 111.6 110.067204185688 1.53279581431248 5 122.2 126.252850716712 -4.05285071671228 6 117.6 117.6 -5.12610787151146e-16 7 121.1 121.1 -2.90566182226115e-16 8 136 136 1.53523027623947e-16 9 154.2 154.2 3.75567632548979e-16 10 153.6 153.6 1.04170144732407e-15 11 158.5 158.5 -6.85215773010839e-17 12 140.6 140.6 -6.85215773010839e-17 13 136.2 142.512575885125 -6.31257588512536 14 168 164.001409130025 3.99859086997455 15 154.3 154.506069887249 -0.206069887248988 16 149 150.532795814312 -1.53279581431248 17 165.5 161.447149283288 4.05285071671228

library(lattice)library(lmtest)n25 <- 25 #minimum number of obs. for Goldfeld-Quandt testpar1 <- 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 <- x1if (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'}xk <- length(x[1,])df <- as.data.frame(x)(mylm <- lm(df))(mysum <- summary(mylm))if (n > n25) {kp3 <- k + 3nmkm3 <- n - k - 3gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))numgqtests <- 0numsignificant1 <- 0numsignificant5 <- 0numsignificant10 <- 0for (mypoint in kp3:nmkm3) {j <- 0numgqtests <- numgqtests + 1for (myalt in c('greater', 'two.sided', 'less')) {j <- j + 1gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value}if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1}gqarr}bitmap(file='test0.png')plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')points(x[,1]-mysum$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)dumdum1 <- dum[2:length(myerror),]dum1z <- as.data.frame(dum1)zplot(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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')}}myeq <- paste(myeq, ' + e[t]')a<-table.row.start(a)a<-table.element(a, myeq)a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable1.tab')a<-table.start()a<-table.row.start(a)a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Variable',header=TRUE)a<-table.element(a,'Parameter',header=TRUE)a<-table.element(a,'S.D.',header=TRUE)a<-table.element(a,'T-STATH0: parameter = 0',header=TRUE)a<-table.element(a,'2-tail p-value',header=TRUE)a<-table.element(a,'1-tail p-value',header=TRUE)a<-table.row.end(a)for (i in 1:k){a<-table.row.start(a)a<-table.element(a,rownames(mysum$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$sigma)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a, 'Sum Squared Residuals',1,TRUE)a<-table.element(a, sum(myerror*myerror))a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable3.tab')a<-table.start()a<-table.row.start(a)a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a, 'Time or Index', 1, TRUE)a<-table.element(a, 'Actuals', 1, TRUE)a<-table.element(a, 'InterpolationForecast', 1, TRUE)a<-table.element(a, 'ResidualsPrediction Error', 1, TRUE)a<-table.row.end(a)for (i in 1:n) {a<-table.row.start(a)a<-table.element(a,i, 1, TRUE)a<-table.element(a,x[i])a<-table.element(a,x[i]-mysum$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')}