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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 27 Nov 2008 04:52:04 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/27/t1227787980ttg5wik9ao79jlk.htm/, Retrieved Mon, 20 May 2024 10:10:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25768, Retrieved Mon, 20 May 2024 10:10:55 +0000

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Estimated Impact

165

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Multiple Regression] [q3] [2008-11-27 11:52:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

1,2935	123,1
1,2811	123,08
1,2773	122,52
1,2602	119,3
1,2542	119,87
1,2634	122,07
1,2653	121,92
1,266	121,93
1,2675	122,17
1,2525	120,34
1,253	121,81
1,2747	124,77
1,2891	127,89
1,2756	124,29
1,277	124,86
1,287	127,4
1,282	127,35
1,2822	126,38

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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=25768&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=25768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25768&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
dollar[t] = + 0.682329207142466 + 0.00484602056822722yen[t] + 0.00797530448796259M1[t] + 0.00481886783646787M2[t] + 0.00461690385364145M3[t] + 0.0037368169668533M4[t] -0.00200088226087104M5[t] + 0.000741081209683945M6[t] -0.000700171980625635M7[t] + 0.000973633933706657M8[t] + 0.00233285511734688M9[t] -0.00277666112278277M10[t] -0.00837804523806218M11[t] -0.00102226612001467t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
dollar[t] =  +  0.682329207142466 +  0.00484602056822722yen[t] +  0.00797530448796259M1[t] +  0.00481886783646787M2[t] +  0.00461690385364145M3[t] +  0.0037368169668533M4[t] -0.00200088226087104M5[t] +  0.000741081209683945M6[t] -0.000700171980625635M7[t] +  0.000973633933706657M8[t] +  0.00233285511734688M9[t] -0.00277666112278277M10[t] -0.00837804523806218M11[t] -0.00102226612001467t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25768&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]dollar[t] =  +  0.682329207142466 +  0.00484602056822722yen[t] +  0.00797530448796259M1[t] +  0.00481886783646787M2[t] +  0.00461690385364145M3[t] +  0.0037368169668533M4[t] -0.00200088226087104M5[t] +  0.000741081209683945M6[t] -0.000700171980625635M7[t] +  0.000973633933706657M8[t] +  0.00233285511734688M9[t] -0.00277666112278277M10[t] -0.00837804523806218M11[t] -0.00102226612001467t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25768&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
dollar[t] = + 0.682329207142466 + 0.00484602056822722yen[t] + 0.00797530448796259M1[t] + 0.00481886783646787M2[t] + 0.00461690385364145M3[t] + 0.0037368169668533M4[t] -0.00200088226087104M5[t] + 0.000741081209683945M6[t] -0.000700171980625635M7[t] + 0.000973633933706657M8[t] + 0.00233285511734688M9[t] -0.00277666112278277M10[t] -0.00837804523806218M11[t] -0.00102226612001467t + 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)	0.682329207142466	0.185603	3.6763	0.021273	0.010637
yen	0.00484602056822722	0.001545	3.1375	0.03493	0.017465
M1	0.00797530448796259	0.009291	0.8584	0.439076	0.219538
M2	0.00481886783646787	0.008292	0.5812	0.592308	0.296154
M3	0.00461690385364145	0.008216	0.5619	0.604146	0.302073
M4	0.0037368169668533	0.008242	0.4534	0.673774	0.336887
M5	-0.00200088226087104	0.00825	-0.2425	0.820298	0.410149
M6	0.000741081209683945	0.008201	0.0904	0.932345	0.466172
M7	-0.000700171980625635	0.009654	-0.0725	0.945663	0.472831
M8	0.000973633933706657	0.009708	0.1003	0.924936	0.462468
M9	0.00233285511734688	0.009721	0.24	0.822143	0.411071
M10	-0.00277666112278277	0.010994	-0.2526	0.813048	0.406524
M11	-0.00837804523806218	0.010226	-0.8193	0.458631	0.229315
t	-0.00102226612001467	0.000685	-1.492	0.209971	0.104985

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.682329207142466 & 0.185603 & 3.6763 & 0.021273 & 0.010637 \tabularnewline
yen & 0.00484602056822722 & 0.001545 & 3.1375 & 0.03493 & 0.017465 \tabularnewline
M1 & 0.00797530448796259 & 0.009291 & 0.8584 & 0.439076 & 0.219538 \tabularnewline
M2 & 0.00481886783646787 & 0.008292 & 0.5812 & 0.592308 & 0.296154 \tabularnewline
M3 & 0.00461690385364145 & 0.008216 & 0.5619 & 0.604146 & 0.302073 \tabularnewline
M4 & 0.0037368169668533 & 0.008242 & 0.4534 & 0.673774 & 0.336887 \tabularnewline
M5 & -0.00200088226087104 & 0.00825 & -0.2425 & 0.820298 & 0.410149 \tabularnewline
M6 & 0.000741081209683945 & 0.008201 & 0.0904 & 0.932345 & 0.466172 \tabularnewline
M7 & -0.000700171980625635 & 0.009654 & -0.0725 & 0.945663 & 0.472831 \tabularnewline
M8 & 0.000973633933706657 & 0.009708 & 0.1003 & 0.924936 & 0.462468 \tabularnewline
M9 & 0.00233285511734688 & 0.009721 & 0.24 & 0.822143 & 0.411071 \tabularnewline
M10 & -0.00277666112278277 & 0.010994 & -0.2526 & 0.813048 & 0.406524 \tabularnewline
M11 & -0.00837804523806218 & 0.010226 & -0.8193 & 0.458631 & 0.229315 \tabularnewline
t & -0.00102226612001467 & 0.000685 & -1.492 & 0.209971 & 0.104985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25768&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]0.682329207142466[/C][C]0.185603[/C][C]3.6763[/C][C]0.021273[/C][C]0.010637[/C][/ROW]
[ROW][C]yen[/C][C]0.00484602056822722[/C][C]0.001545[/C][C]3.1375[/C][C]0.03493[/C][C]0.017465[/C][/ROW]
[ROW][C]M1[/C][C]0.00797530448796259[/C][C]0.009291[/C][C]0.8584[/C][C]0.439076[/C][C]0.219538[/C][/ROW]
[ROW][C]M2[/C][C]0.00481886783646787[/C][C]0.008292[/C][C]0.5812[/C][C]0.592308[/C][C]0.296154[/C][/ROW]
[ROW][C]M3[/C][C]0.00461690385364145[/C][C]0.008216[/C][C]0.5619[/C][C]0.604146[/C][C]0.302073[/C][/ROW]
[ROW][C]M4[/C][C]0.0037368169668533[/C][C]0.008242[/C][C]0.4534[/C][C]0.673774[/C][C]0.336887[/C][/ROW]
[ROW][C]M5[/C][C]-0.00200088226087104[/C][C]0.00825[/C][C]-0.2425[/C][C]0.820298[/C][C]0.410149[/C][/ROW]
[ROW][C]M6[/C][C]0.000741081209683945[/C][C]0.008201[/C][C]0.0904[/C][C]0.932345[/C][C]0.466172[/C][/ROW]
[ROW][C]M7[/C][C]-0.000700171980625635[/C][C]0.009654[/C][C]-0.0725[/C][C]0.945663[/C][C]0.472831[/C][/ROW]
[ROW][C]M8[/C][C]0.000973633933706657[/C][C]0.009708[/C][C]0.1003[/C][C]0.924936[/C][C]0.462468[/C][/ROW]
[ROW][C]M9[/C][C]0.00233285511734688[/C][C]0.009721[/C][C]0.24[/C][C]0.822143[/C][C]0.411071[/C][/ROW]
[ROW][C]M10[/C][C]-0.00277666112278277[/C][C]0.010994[/C][C]-0.2526[/C][C]0.813048[/C][C]0.406524[/C][/ROW]
[ROW][C]M11[/C][C]-0.00837804523806218[/C][C]0.010226[/C][C]-0.8193[/C][C]0.458631[/C][C]0.229315[/C][/ROW]
[ROW][C]t[/C][C]-0.00102226612001467[/C][C]0.000685[/C][C]-1.492[/C][C]0.209971[/C][C]0.104985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25768&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25768&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)	0.682329207142466	0.185603	3.6763	0.021273	0.010637
yen	0.00484602056822722	0.001545	3.1375	0.03493	0.017465
M1	0.00797530448796259	0.009291	0.8584	0.439076	0.219538
M2	0.00481886783646787	0.008292	0.5812	0.592308	0.296154
M3	0.00461690385364145	0.008216	0.5619	0.604146	0.302073
M4	0.0037368169668533	0.008242	0.4534	0.673774	0.336887
M5	-0.00200088226087104	0.00825	-0.2425	0.820298	0.410149
M6	0.000741081209683945	0.008201	0.0904	0.932345	0.466172
M7	-0.000700171980625635	0.009654	-0.0725	0.945663	0.472831
M8	0.000973633933706657	0.009708	0.1003	0.924936	0.462468
M9	0.00233285511734688	0.009721	0.24	0.822143	0.411071
M10	-0.00277666112278277	0.010994	-0.2526	0.813048	0.406524
M11	-0.00837804523806218	0.010226	-0.8193	0.458631	0.229315
t	-0.00102226612001467	0.000685	-1.492	0.209971	0.104985

Multiple Linear Regression - Regression Statistics
Multiple R	0.966707358725284
R-squared	0.934523117413615
Adjusted R-squared	0.721723249007862
F-TEST (value)	4.39155871859717
F-TEST (DF numerator)	13
F-TEST (DF denominator)	4
p-value	0.0820206215292726
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.00666103527654522
Sum Squared Residuals	0.000177477563821520

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.966707358725284 \tabularnewline
R-squared & 0.934523117413615 \tabularnewline
Adjusted R-squared & 0.721723249007862 \tabularnewline
F-TEST (value) & 4.39155871859717 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 4 \tabularnewline
p-value & 0.0820206215292726 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.00666103527654522 \tabularnewline
Sum Squared Residuals & 0.000177477563821520 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25768&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.966707358725284[/C][/ROW]
[ROW][C]R-squared[/C][C]0.934523117413615[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.721723249007862[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.39155871859717[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]4[/C][/ROW]
[ROW][C]p-value[/C][C]0.0820206215292726[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.00666103527654522[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.000177477563821520[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25768&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25768&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	0.966707358725284
R-squared	0.934523117413615
Adjusted R-squared	0.721723249007862
F-TEST (value)	4.39155871859717
F-TEST (DF numerator)	13
F-TEST (DF denominator)	4
p-value	0.0820206215292726
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.00666103527654522
Sum Squared Residuals	0.000177477563821520

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.2935	1.28582737745918	0.0076726225408169
2	1.2811	1.28155175427631	-0.000451754276310604
3	1.2773	1.27761375265526	-0.000313752655262051
4	1.2602	1.26010721341877	9.27865812322944e-05
5	1.2542	1.25610947979492	-0.00190947979491824
6	1.2634	1.26849042239556	-0.0050904223955583
7	1.2653	1.2653	-6.50521303491303e-19
8	1.266	1.266	2.16840434497101e-19
9	1.2675	1.2675	-4.33680868994202e-19
10	1.2525	1.2525	2.16840434497101e-19
11	1.253	1.253	-1.51788304147971e-18
12	1.2747	1.2747	4.33680868994202e-18
13	1.2891	1.29677262254082	-0.0076726225408169
14	1.2756	1.27514824572369	0.000451754276310605
15	1.277	1.27668624734474	0.00031375265526205
16	1.287	1.28709278658123	-9.27865812322952e-05
17	1.282	1.28009052020508	0.00190947979491824
18	1.2822	1.27710957760444	0.0050904223955583

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.2935 & 1.28582737745918 & 0.0076726225408169 \tabularnewline
2 & 1.2811 & 1.28155175427631 & -0.000451754276310604 \tabularnewline
3 & 1.2773 & 1.27761375265526 & -0.000313752655262051 \tabularnewline
4 & 1.2602 & 1.26010721341877 & 9.27865812322944e-05 \tabularnewline
5 & 1.2542 & 1.25610947979492 & -0.00190947979491824 \tabularnewline
6 & 1.2634 & 1.26849042239556 & -0.0050904223955583 \tabularnewline
7 & 1.2653 & 1.2653 & -6.50521303491303e-19 \tabularnewline
8 & 1.266 & 1.266 & 2.16840434497101e-19 \tabularnewline
9 & 1.2675 & 1.2675 & -4.33680868994202e-19 \tabularnewline
10 & 1.2525 & 1.2525 & 2.16840434497101e-19 \tabularnewline
11 & 1.253 & 1.253 & -1.51788304147971e-18 \tabularnewline
12 & 1.2747 & 1.2747 & 4.33680868994202e-18 \tabularnewline
13 & 1.2891 & 1.29677262254082 & -0.0076726225408169 \tabularnewline
14 & 1.2756 & 1.27514824572369 & 0.000451754276310605 \tabularnewline
15 & 1.277 & 1.27668624734474 & 0.00031375265526205 \tabularnewline
16 & 1.287 & 1.28709278658123 & -9.27865812322952e-05 \tabularnewline
17 & 1.282 & 1.28009052020508 & 0.00190947979491824 \tabularnewline
18 & 1.2822 & 1.27710957760444 & 0.0050904223955583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25768&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]1.2935[/C][C]1.28582737745918[/C][C]0.0076726225408169[/C][/ROW]
[ROW][C]2[/C][C]1.2811[/C][C]1.28155175427631[/C][C]-0.000451754276310604[/C][/ROW]
[ROW][C]3[/C][C]1.2773[/C][C]1.27761375265526[/C][C]-0.000313752655262051[/C][/ROW]
[ROW][C]4[/C][C]1.2602[/C][C]1.26010721341877[/C][C]9.27865812322944e-05[/C][/ROW]
[ROW][C]5[/C][C]1.2542[/C][C]1.25610947979492[/C][C]-0.00190947979491824[/C][/ROW]
[ROW][C]6[/C][C]1.2634[/C][C]1.26849042239556[/C][C]-0.0050904223955583[/C][/ROW]
[ROW][C]7[/C][C]1.2653[/C][C]1.2653[/C][C]-6.50521303491303e-19[/C][/ROW]
[ROW][C]8[/C][C]1.266[/C][C]1.266[/C][C]2.16840434497101e-19[/C][/ROW]
[ROW][C]9[/C][C]1.2675[/C][C]1.2675[/C][C]-4.33680868994202e-19[/C][/ROW]
[ROW][C]10[/C][C]1.2525[/C][C]1.2525[/C][C]2.16840434497101e-19[/C][/ROW]
[ROW][C]11[/C][C]1.253[/C][C]1.253[/C][C]-1.51788304147971e-18[/C][/ROW]
[ROW][C]12[/C][C]1.2747[/C][C]1.2747[/C][C]4.33680868994202e-18[/C][/ROW]
[ROW][C]13[/C][C]1.2891[/C][C]1.29677262254082[/C][C]-0.0076726225408169[/C][/ROW]
[ROW][C]14[/C][C]1.2756[/C][C]1.27514824572369[/C][C]0.000451754276310605[/C][/ROW]
[ROW][C]15[/C][C]1.277[/C][C]1.27668624734474[/C][C]0.00031375265526205[/C][/ROW]
[ROW][C]16[/C][C]1.287[/C][C]1.28709278658123[/C][C]-9.27865812322952e-05[/C][/ROW]
[ROW][C]17[/C][C]1.282[/C][C]1.28009052020508[/C][C]0.00190947979491824[/C][/ROW]
[ROW][C]18[/C][C]1.2822[/C][C]1.27710957760444[/C][C]0.0050904223955583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25768&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25768&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	1.2935	1.28582737745918	0.0076726225408169
2	1.2811	1.28155175427631	-0.000451754276310604
3	1.2773	1.27761375265526	-0.000313752655262051
4	1.2602	1.26010721341877	9.27865812322944e-05
5	1.2542	1.25610947979492	-0.00190947979491824
6	1.2634	1.26849042239556	-0.0050904223955583
7	1.2653	1.2653	-6.50521303491303e-19
8	1.266	1.266	2.16840434497101e-19
9	1.2675	1.2675	-4.33680868994202e-19
10	1.2525	1.2525	2.16840434497101e-19
11	1.253	1.253	-1.51788304147971e-18
12	1.2747	1.2747	4.33680868994202e-18
13	1.2891	1.29677262254082	-0.0076726225408169
14	1.2756	1.27514824572369	0.000451754276310605
15	1.277	1.27668624734474	0.00031375265526205
16	1.287	1.28709278658123	-9.27865812322952e-05
17	1.282	1.28009052020508	0.00190947979491824
18	1.2822	1.27710957760444	0.0050904223955583

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code