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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 15 Dec 2009 08:08:14 -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/2009/Dec/15/t1260889790c2e5s4uudl6gn6s.htm/, Retrieved Wed, 05 Nov 2025 00:49:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67963, Retrieved Wed, 05 Nov 2025 00:49:33 +0000

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Estimated Impact

504

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] [] [2009-11-18 12:18:41] [6ba840d2473f9a55d7b3e13093db69b8]
-    D        [Multiple Regression] [] [2009-12-15 15:08:14] [830aa0f7fb5acd5849dbc0c6ad889830] [Current]
-    D          [Multiple Regression] [] [2009-12-21 09:27:51] [6ba840d2473f9a55d7b3e13093db69b8] 

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Dataseries X:

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Histogram

Boxplots

8.5	0	8.5	8.3	8.2	8.7
8.6	0	8.6	8.5	8.3	8.2
8.5	0	8.5	8.6	8.5	8.3
8.2	0	8.2	8.5	8.6	8.5
8.1	0	8.1	8.2	8.5	8.6
7.9	0	7.9	8.1	8.2	8.5
8.6	0	8.6	7.9	8.1	8.2
8.7	0	8.7	8.6	7.9	8.1
8.7	0	8.7	8.7	8.6	7.9
8.5	0	8.5	8.7	8.7	8.6
8.4	0	8.4	8.5	8.7	8.7
8.5	0	8.5	8.4	8.5	8.7
8.7	0	8.7	8.5	8.4	8.5
8.7	0	8.7	8.7	8.5	8.4
8.6	0	8.6	8.7	8.7	8.5
8.5	0	8.5	8.6	8.7	8.7
8.3	0	8.3	8.5	8.6	8.7
8	0	8	8.3	8.5	8.6
8.2	0	8.2	8	8.3	8.5
8.1	0	8.1	8.2	8	8.3
8.1	0	8.1	8.1	8.2	8
8	0	8	8.1	8.1	8.2
7.9	0	7.9	8	8.1	8.1
7.9	0	7.9	7.9	8	8.1
8	0	8	7.9	7.9	8
8	0	8	8	7.9	7.9
7.9	0	7.9	8	8	7.9
8	0	8	7.9	8	8
7.7	0	7.7	8	7.9	8
7.2	0	7.2	7.7	8	7.9
7.5	0	7.5	7.2	7.7	8
7.3	0	7.3	7.5	7.2	7.7
7	0	7	7.3	7.5	7.2
7	0	7	7	7.3	7.5
7	0	7	7	7	7.3
7.2	0	7.2	7	7	7
7.3	0	7.3	7.2	7	7
7.1	0	7.1	7.3	7.2	7
6.8	0	6.8	7.1	7.3	7.2
6.4	0	6.4	6.8	7.1	7.3
6.1	0	6.1	6.4	6.8	7.1
6.5	0	6.5	6.1	6.4	6.8
7.7	0	7.7	6.5	6.1	6.4
7.9	0	7.9	7.7	6.5	6.1
7.5	0	7.5	7.9	7.7	6.5
6.9	1	6.9	7.5	7.9	7.7
6.6	1	6.6	6.9	7.5	7.9
6.9	1	6.9	6.6	6.9	7.5
7.7	1	7.7	6.9	6.6	6.9
8	1	8	7.7	6.9	6.6
8	1	8	8	7.7	6.9
7.7	1	7.7	8	8	7.7
7.3	1	7.3	7.7	8	8
7.4	1	7.4	7.3	7.7	8
8.1	1	8.1	7.4	7.3	7.7
8.3	1	8.3	8.1	7.4	7.3
8.2	1	8.2	8.3	8.1	7.4

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	12 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 & 12 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&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]12 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=67963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&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	12 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -3.03750610467177e-17 + 1.44281539971909e-16X[t] + 1Y1[t] + 1.80407309583598e-16Y2[t] -1.34871633389605e-16Y3[t] + 1.25242085042886e-17Y4[t] -1.18735169270795e-17M1[t] -4.29542034326534e-17M2[t] + 1.71068599226658e-16M3[t] -2.53276152719436e-17M4[t] -3.45439284701359e-17M5[t] -1.26583126706111e-17M6[t] + 7.21379251138558e-17M7[t] -3.62069740559273e-17M8[t] -2.76317048100518e-17M9[t] -3.29487196717181e-17M10[t] -1.64934388509514e-17M11[t] -4.39099679542517e-18t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -3.03750610467177e-17 +  1.44281539971909e-16X[t] +  1Y1[t] +  1.80407309583598e-16Y2[t] -1.34871633389605e-16Y3[t] +  1.25242085042886e-17Y4[t] -1.18735169270795e-17M1[t] -4.29542034326534e-17M2[t] +  1.71068599226658e-16M3[t] -2.53276152719436e-17M4[t] -3.45439284701359e-17M5[t] -1.26583126706111e-17M6[t] +  7.21379251138558e-17M7[t] -3.62069740559273e-17M8[t] -2.76317048100518e-17M9[t] -3.29487196717181e-17M10[t] -1.64934388509514e-17M11[t] -4.39099679542517e-18t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -3.03750610467177e-17 +  1.44281539971909e-16X[t] +  1Y1[t] +  1.80407309583598e-16Y2[t] -1.34871633389605e-16Y3[t] +  1.25242085042886e-17Y4[t] -1.18735169270795e-17M1[t] -4.29542034326534e-17M2[t] +  1.71068599226658e-16M3[t] -2.53276152719436e-17M4[t] -3.45439284701359e-17M5[t] -1.26583126706111e-17M6[t] +  7.21379251138558e-17M7[t] -3.62069740559273e-17M8[t] -2.76317048100518e-17M9[t] -3.29487196717181e-17M10[t] -1.64934388509514e-17M11[t] -4.39099679542517e-18t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -3.03750610467177e-17 + 1.44281539971909e-16X[t] + 1Y1[t] + 1.80407309583598e-16Y2[t] -1.34871633389605e-16Y3[t] + 1.25242085042886e-17Y4[t] -1.18735169270795e-17M1[t] -4.29542034326534e-17M2[t] + 1.71068599226658e-16M3[t] -2.53276152719436e-17M4[t] -3.45439284701359e-17M5[t] -1.26583126706111e-17M6[t] + 7.21379251138558e-17M7[t] -3.62069740559273e-17M8[t] -2.76317048100518e-17M9[t] -3.29487196717181e-17M10[t] -1.64934388509514e-17M11[t] -4.39099679542517e-18t + 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)	-3.03750610467177e-17	0	-0.0513	0.95932	0.47966
X	1.44281539971909e-16	0	1.6918	0.098658	0.049329
Y1	1	0	8017416243731516	0	0
Y2	1.80407309583598e-16	0	0.7839	0.437815	0.218908
Y3	-1.34871633389605e-16	0	-0.5951	0.555196	0.277598
Y4	1.25242085042886e-17	0	0.1014	0.919765	0.459882
M1	-1.18735169270795e-17	0	-0.1279	0.898895	0.449447
M2	-4.29542034326534e-17	0	-0.4253	0.672957	0.336478
M3	1.71068599226658e-16	0	1.7027	0.096591	0.048296
M4	-2.53276152719436e-17	0	-0.2642	0.793024	0.396512
M5	-3.45439284701359e-17	0	-0.3574	0.722727	0.361363
M6	-1.26583126706111e-17	0	-0.1384	0.890627	0.445314
M7	7.21379251138558e-17	0	0.6876	0.495752	0.247876
M8	-3.62069740559273e-17	0	-0.2724	0.786738	0.393369
M9	-2.76317048100518e-17	0	-0.2365	0.814295	0.407148
M10	-3.29487196717181e-17	0	-0.3279	0.744737	0.372368
M11	-1.64934388509514e-17	0	-0.1703	0.865629	0.432815
t	-4.39099679542517e-18	0	-1.3506	0.184613	0.092306

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -3.03750610467177e-17 & 0 & -0.0513 & 0.95932 & 0.47966 \tabularnewline
X & 1.44281539971909e-16 & 0 & 1.6918 & 0.098658 & 0.049329 \tabularnewline
Y1 & 1 & 0 & 8017416243731516 & 0 & 0 \tabularnewline
Y2 & 1.80407309583598e-16 & 0 & 0.7839 & 0.437815 & 0.218908 \tabularnewline
Y3 & -1.34871633389605e-16 & 0 & -0.5951 & 0.555196 & 0.277598 \tabularnewline
Y4 & 1.25242085042886e-17 & 0 & 0.1014 & 0.919765 & 0.459882 \tabularnewline
M1 & -1.18735169270795e-17 & 0 & -0.1279 & 0.898895 & 0.449447 \tabularnewline
M2 & -4.29542034326534e-17 & 0 & -0.4253 & 0.672957 & 0.336478 \tabularnewline
M3 & 1.71068599226658e-16 & 0 & 1.7027 & 0.096591 & 0.048296 \tabularnewline
M4 & -2.53276152719436e-17 & 0 & -0.2642 & 0.793024 & 0.396512 \tabularnewline
M5 & -3.45439284701359e-17 & 0 & -0.3574 & 0.722727 & 0.361363 \tabularnewline
M6 & -1.26583126706111e-17 & 0 & -0.1384 & 0.890627 & 0.445314 \tabularnewline
M7 & 7.21379251138558e-17 & 0 & 0.6876 & 0.495752 & 0.247876 \tabularnewline
M8 & -3.62069740559273e-17 & 0 & -0.2724 & 0.786738 & 0.393369 \tabularnewline
M9 & -2.76317048100518e-17 & 0 & -0.2365 & 0.814295 & 0.407148 \tabularnewline
M10 & -3.29487196717181e-17 & 0 & -0.3279 & 0.744737 & 0.372368 \tabularnewline
M11 & -1.64934388509514e-17 & 0 & -0.1703 & 0.865629 & 0.432815 \tabularnewline
t & -4.39099679542517e-18 & 0 & -1.3506 & 0.184613 & 0.092306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-3.03750610467177e-17[/C][C]0[/C][C]-0.0513[/C][C]0.95932[/C][C]0.47966[/C][/ROW]
[ROW][C]X[/C][C]1.44281539971909e-16[/C][C]0[/C][C]1.6918[/C][C]0.098658[/C][C]0.049329[/C][/ROW]
[ROW][C]Y1[/C][C]1[/C][C]0[/C][C]8017416243731516[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]1.80407309583598e-16[/C][C]0[/C][C]0.7839[/C][C]0.437815[/C][C]0.218908[/C][/ROW]
[ROW][C]Y3[/C][C]-1.34871633389605e-16[/C][C]0[/C][C]-0.5951[/C][C]0.555196[/C][C]0.277598[/C][/ROW]
[ROW][C]Y4[/C][C]1.25242085042886e-17[/C][C]0[/C][C]0.1014[/C][C]0.919765[/C][C]0.459882[/C][/ROW]
[ROW][C]M1[/C][C]-1.18735169270795e-17[/C][C]0[/C][C]-0.1279[/C][C]0.898895[/C][C]0.449447[/C][/ROW]
[ROW][C]M2[/C][C]-4.29542034326534e-17[/C][C]0[/C][C]-0.4253[/C][C]0.672957[/C][C]0.336478[/C][/ROW]
[ROW][C]M3[/C][C]1.71068599226658e-16[/C][C]0[/C][C]1.7027[/C][C]0.096591[/C][C]0.048296[/C][/ROW]
[ROW][C]M4[/C][C]-2.53276152719436e-17[/C][C]0[/C][C]-0.2642[/C][C]0.793024[/C][C]0.396512[/C][/ROW]
[ROW][C]M5[/C][C]-3.45439284701359e-17[/C][C]0[/C][C]-0.3574[/C][C]0.722727[/C][C]0.361363[/C][/ROW]
[ROW][C]M6[/C][C]-1.26583126706111e-17[/C][C]0[/C][C]-0.1384[/C][C]0.890627[/C][C]0.445314[/C][/ROW]
[ROW][C]M7[/C][C]7.21379251138558e-17[/C][C]0[/C][C]0.6876[/C][C]0.495752[/C][C]0.247876[/C][/ROW]
[ROW][C]M8[/C][C]-3.62069740559273e-17[/C][C]0[/C][C]-0.2724[/C][C]0.786738[/C][C]0.393369[/C][/ROW]
[ROW][C]M9[/C][C]-2.76317048100518e-17[/C][C]0[/C][C]-0.2365[/C][C]0.814295[/C][C]0.407148[/C][/ROW]
[ROW][C]M10[/C][C]-3.29487196717181e-17[/C][C]0[/C][C]-0.3279[/C][C]0.744737[/C][C]0.372368[/C][/ROW]
[ROW][C]M11[/C][C]-1.64934388509514e-17[/C][C]0[/C][C]-0.1703[/C][C]0.865629[/C][C]0.432815[/C][/ROW]
[ROW][C]t[/C][C]-4.39099679542517e-18[/C][C]0[/C][C]-1.3506[/C][C]0.184613[/C][C]0.092306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&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)	-3.03750610467177e-17	0	-0.0513	0.95932	0.47966
X	1.44281539971909e-16	0	1.6918	0.098658	0.049329
Y1	1	0	8017416243731516	0	0
Y2	1.80407309583598e-16	0	0.7839	0.437815	0.218908
Y3	-1.34871633389605e-16	0	-0.5951	0.555196	0.277598
Y4	1.25242085042886e-17	0	0.1014	0.919765	0.459882
M1	-1.18735169270795e-17	0	-0.1279	0.898895	0.449447
M2	-4.29542034326534e-17	0	-0.4253	0.672957	0.336478
M3	1.71068599226658e-16	0	1.7027	0.096591	0.048296
M4	-2.53276152719436e-17	0	-0.2642	0.793024	0.396512
M5	-3.45439284701359e-17	0	-0.3574	0.722727	0.361363
M6	-1.26583126706111e-17	0	-0.1384	0.890627	0.445314
M7	7.21379251138558e-17	0	0.6876	0.495752	0.247876
M8	-3.62069740559273e-17	0	-0.2724	0.786738	0.393369
M9	-2.76317048100518e-17	0	-0.2365	0.814295	0.407148
M10	-3.29487196717181e-17	0	-0.3279	0.744737	0.372368
M11	-1.64934388509514e-17	0	-0.1703	0.865629	0.432815
t	-4.39099679542517e-18	0	-1.3506	0.184613	0.092306

Multiple Linear Regression - Regression Statistics
Multiple R	1
R-squared	1
Adjusted R-squared	1
F-TEST (value)	8.20700486715373e+31
F-TEST (DF numerator)	17
F-TEST (DF denominator)	39
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.32513466822904e-16
Sum Squared Residuals	6.84832936687566e-31

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 1 \tabularnewline
R-squared & 1 \tabularnewline
Adjusted R-squared & 1 \tabularnewline
F-TEST (value) & 8.20700486715373e+31 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.32513466822904e-16 \tabularnewline
Sum Squared Residuals & 6.84832936687566e-31 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]1[/C][/ROW]
[ROW][C]R-squared[/C][C]1[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.20700486715373e+31[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.32513466822904e-16[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6.84832936687566e-31[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67963&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&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	1
R-squared	1
Adjusted R-squared	1
F-TEST (value)	8.20700486715373e+31
F-TEST (DF numerator)	17
F-TEST (DF denominator)	39
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.32513466822904e-16
Sum Squared Residuals	6.84832936687566e-31

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.5	8.5	-7.6991384674347e-17
2	8.6	8.6	-6.43709360977525e-17
3	8.5	8.5	6.5756488250235e-16
4	8.2	8.2	-5.67866034633681e-17
5	8.1	8.1	-6.34876583350881e-18
6	7.9	7.9	-6.39936729524118e-17
7	8.6	8.6	-3.07938464271981e-17
8	8.7	8.7	-1.50779618795439e-16
9	8.7	8.7	-7.60896371306682e-17
10	8.5	8.5	-1.12544189552567e-17
11	8.4	8.4	-1.87973185793847e-17
12	8.5	8.5	-9.52569968939496e-18
13	8.7	8.7	-7.26912276957142e-17
14	8.7	8.7	-5.85614221220454e-17
15	8.6	8.6	-1.61756676361002e-16
16	8.5	8.5	2.42587675254507e-17
17	8.3	8.3	3.73154830395712e-17
18	8	8	1.31687079577835e-18
19	8.2	8.2	-3.86450271428722e-17
20	8.1	8.1	-2.49932245985543e-18
21	8.1	8.1	4.20887252772615e-17
22	8	8	2.63137569411794e-17
23	7.9	7.9	2.40516497712711e-17
24	7.9	7.9	1.65027753351442e-17
25	8	8	3.00235215224727e-17
26	8	8	4.87068947155409e-17
27	7.9	7.9	-1.56928722762741e-16
28	8	8	7.01377735925727e-17
29	7.7	7.7	2.37442644288036e-17
30	7.2	7.2	-2.09157096049553e-17
31	7.5	7.5	3.80917633257233e-17
32	7.3	7.3	8.34339014046975e-17
33	7	7	-3.98905873177544e-17
34	7	7	-6.79197201479108e-18
35	7	7	-5.68129043561564e-17
36	7.2	7.2	-4.54277053024157e-18
37	7.3	7.3	1.16970240403136e-16
38	7.1	7.1	1.00760206093542e-16
39	6.8	6.8	-1.52730786210754e-16
40	6.4	6.4	-4.72787562303053e-17
41	6.1	6.1	-9.03881407145042e-17
42	6.5	6.5	1.72786690122292e-17
43	7.7	7.7	2.64171238617347e-17
44	7.9	7.9	-6.47885859535384e-19
45	7.5	7.5	9.18365444334975e-17
46	6.9	6.9	-8.2673659711316e-18
47	6.6	6.6	5.15585731642701e-17
48	6.9	6.9	-2.43430511550802e-18
49	7.7	7.7	2.68885044445246e-18
50	8	8	-2.65347425892852e-17
51	8	8	-1.86148697167854e-16
52	7.7	7.7	9.6688185756501e-18
53	7.3	7.3	3.56771590796384e-17
54	7.4	7.4	6.63138427493595e-17
55	8.1	8.1	4.92998638261233e-18
56	8.3	8.3	7.04929257101326e-17
57	8.2	8.2	-1.79450452623363e-17

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.5 & 8.5 & -7.6991384674347e-17 \tabularnewline
2 & 8.6 & 8.6 & -6.43709360977525e-17 \tabularnewline
3 & 8.5 & 8.5 & 6.5756488250235e-16 \tabularnewline
4 & 8.2 & 8.2 & -5.67866034633681e-17 \tabularnewline
5 & 8.1 & 8.1 & -6.34876583350881e-18 \tabularnewline
6 & 7.9 & 7.9 & -6.39936729524118e-17 \tabularnewline
7 & 8.6 & 8.6 & -3.07938464271981e-17 \tabularnewline
8 & 8.7 & 8.7 & -1.50779618795439e-16 \tabularnewline
9 & 8.7 & 8.7 & -7.60896371306682e-17 \tabularnewline
10 & 8.5 & 8.5 & -1.12544189552567e-17 \tabularnewline
11 & 8.4 & 8.4 & -1.87973185793847e-17 \tabularnewline
12 & 8.5 & 8.5 & -9.52569968939496e-18 \tabularnewline
13 & 8.7 & 8.7 & -7.26912276957142e-17 \tabularnewline
14 & 8.7 & 8.7 & -5.85614221220454e-17 \tabularnewline
15 & 8.6 & 8.6 & -1.61756676361002e-16 \tabularnewline
16 & 8.5 & 8.5 & 2.42587675254507e-17 \tabularnewline
17 & 8.3 & 8.3 & 3.73154830395712e-17 \tabularnewline
18 & 8 & 8 & 1.31687079577835e-18 \tabularnewline
19 & 8.2 & 8.2 & -3.86450271428722e-17 \tabularnewline
20 & 8.1 & 8.1 & -2.49932245985543e-18 \tabularnewline
21 & 8.1 & 8.1 & 4.20887252772615e-17 \tabularnewline
22 & 8 & 8 & 2.63137569411794e-17 \tabularnewline
23 & 7.9 & 7.9 & 2.40516497712711e-17 \tabularnewline
24 & 7.9 & 7.9 & 1.65027753351442e-17 \tabularnewline
25 & 8 & 8 & 3.00235215224727e-17 \tabularnewline
26 & 8 & 8 & 4.87068947155409e-17 \tabularnewline
27 & 7.9 & 7.9 & -1.56928722762741e-16 \tabularnewline
28 & 8 & 8 & 7.01377735925727e-17 \tabularnewline
29 & 7.7 & 7.7 & 2.37442644288036e-17 \tabularnewline
30 & 7.2 & 7.2 & -2.09157096049553e-17 \tabularnewline
31 & 7.5 & 7.5 & 3.80917633257233e-17 \tabularnewline
32 & 7.3 & 7.3 & 8.34339014046975e-17 \tabularnewline
33 & 7 & 7 & -3.98905873177544e-17 \tabularnewline
34 & 7 & 7 & -6.79197201479108e-18 \tabularnewline
35 & 7 & 7 & -5.68129043561564e-17 \tabularnewline
36 & 7.2 & 7.2 & -4.54277053024157e-18 \tabularnewline
37 & 7.3 & 7.3 & 1.16970240403136e-16 \tabularnewline
38 & 7.1 & 7.1 & 1.00760206093542e-16 \tabularnewline
39 & 6.8 & 6.8 & -1.52730786210754e-16 \tabularnewline
40 & 6.4 & 6.4 & -4.72787562303053e-17 \tabularnewline
41 & 6.1 & 6.1 & -9.03881407145042e-17 \tabularnewline
42 & 6.5 & 6.5 & 1.72786690122292e-17 \tabularnewline
43 & 7.7 & 7.7 & 2.64171238617347e-17 \tabularnewline
44 & 7.9 & 7.9 & -6.47885859535384e-19 \tabularnewline
45 & 7.5 & 7.5 & 9.18365444334975e-17 \tabularnewline
46 & 6.9 & 6.9 & -8.2673659711316e-18 \tabularnewline
47 & 6.6 & 6.6 & 5.15585731642701e-17 \tabularnewline
48 & 6.9 & 6.9 & -2.43430511550802e-18 \tabularnewline
49 & 7.7 & 7.7 & 2.68885044445246e-18 \tabularnewline
50 & 8 & 8 & -2.65347425892852e-17 \tabularnewline
51 & 8 & 8 & -1.86148697167854e-16 \tabularnewline
52 & 7.7 & 7.7 & 9.6688185756501e-18 \tabularnewline
53 & 7.3 & 7.3 & 3.56771590796384e-17 \tabularnewline
54 & 7.4 & 7.4 & 6.63138427493595e-17 \tabularnewline
55 & 8.1 & 8.1 & 4.92998638261233e-18 \tabularnewline
56 & 8.3 & 8.3 & 7.04929257101326e-17 \tabularnewline
57 & 8.2 & 8.2 & -1.79450452623363e-17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&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]8.5[/C][C]8.5[/C][C]-7.6991384674347e-17[/C][/ROW]
[ROW][C]2[/C][C]8.6[/C][C]8.6[/C][C]-6.43709360977525e-17[/C][/ROW]
[ROW][C]3[/C][C]8.5[/C][C]8.5[/C][C]6.5756488250235e-16[/C][/ROW]
[ROW][C]4[/C][C]8.2[/C][C]8.2[/C][C]-5.67866034633681e-17[/C][/ROW]
[ROW][C]5[/C][C]8.1[/C][C]8.1[/C][C]-6.34876583350881e-18[/C][/ROW]
[ROW][C]6[/C][C]7.9[/C][C]7.9[/C][C]-6.39936729524118e-17[/C][/ROW]
[ROW][C]7[/C][C]8.6[/C][C]8.6[/C][C]-3.07938464271981e-17[/C][/ROW]
[ROW][C]8[/C][C]8.7[/C][C]8.7[/C][C]-1.50779618795439e-16[/C][/ROW]
[ROW][C]9[/C][C]8.7[/C][C]8.7[/C][C]-7.60896371306682e-17[/C][/ROW]
[ROW][C]10[/C][C]8.5[/C][C]8.5[/C][C]-1.12544189552567e-17[/C][/ROW]
[ROW][C]11[/C][C]8.4[/C][C]8.4[/C][C]-1.87973185793847e-17[/C][/ROW]
[ROW][C]12[/C][C]8.5[/C][C]8.5[/C][C]-9.52569968939496e-18[/C][/ROW]
[ROW][C]13[/C][C]8.7[/C][C]8.7[/C][C]-7.26912276957142e-17[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.7[/C][C]-5.85614221220454e-17[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.6[/C][C]-1.61756676361002e-16[/C][/ROW]
[ROW][C]16[/C][C]8.5[/C][C]8.5[/C][C]2.42587675254507e-17[/C][/ROW]
[ROW][C]17[/C][C]8.3[/C][C]8.3[/C][C]3.73154830395712e-17[/C][/ROW]
[ROW][C]18[/C][C]8[/C][C]8[/C][C]1.31687079577835e-18[/C][/ROW]
[ROW][C]19[/C][C]8.2[/C][C]8.2[/C][C]-3.86450271428722e-17[/C][/ROW]
[ROW][C]20[/C][C]8.1[/C][C]8.1[/C][C]-2.49932245985543e-18[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]8.1[/C][C]4.20887252772615e-17[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]8[/C][C]2.63137569411794e-17[/C][/ROW]
[ROW][C]23[/C][C]7.9[/C][C]7.9[/C][C]2.40516497712711e-17[/C][/ROW]
[ROW][C]24[/C][C]7.9[/C][C]7.9[/C][C]1.65027753351442e-17[/C][/ROW]
[ROW][C]25[/C][C]8[/C][C]8[/C][C]3.00235215224727e-17[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8[/C][C]4.87068947155409e-17[/C][/ROW]
[ROW][C]27[/C][C]7.9[/C][C]7.9[/C][C]-1.56928722762741e-16[/C][/ROW]
[ROW][C]28[/C][C]8[/C][C]8[/C][C]7.01377735925727e-17[/C][/ROW]
[ROW][C]29[/C][C]7.7[/C][C]7.7[/C][C]2.37442644288036e-17[/C][/ROW]
[ROW][C]30[/C][C]7.2[/C][C]7.2[/C][C]-2.09157096049553e-17[/C][/ROW]
[ROW][C]31[/C][C]7.5[/C][C]7.5[/C][C]3.80917633257233e-17[/C][/ROW]
[ROW][C]32[/C][C]7.3[/C][C]7.3[/C][C]8.34339014046975e-17[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]7[/C][C]-3.98905873177544e-17[/C][/ROW]
[ROW][C]34[/C][C]7[/C][C]7[/C][C]-6.79197201479108e-18[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]7[/C][C]-5.68129043561564e-17[/C][/ROW]
[ROW][C]36[/C][C]7.2[/C][C]7.2[/C][C]-4.54277053024157e-18[/C][/ROW]
[ROW][C]37[/C][C]7.3[/C][C]7.3[/C][C]1.16970240403136e-16[/C][/ROW]
[ROW][C]38[/C][C]7.1[/C][C]7.1[/C][C]1.00760206093542e-16[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.8[/C][C]-1.52730786210754e-16[/C][/ROW]
[ROW][C]40[/C][C]6.4[/C][C]6.4[/C][C]-4.72787562303053e-17[/C][/ROW]
[ROW][C]41[/C][C]6.1[/C][C]6.1[/C][C]-9.03881407145042e-17[/C][/ROW]
[ROW][C]42[/C][C]6.5[/C][C]6.5[/C][C]1.72786690122292e-17[/C][/ROW]
[ROW][C]43[/C][C]7.7[/C][C]7.7[/C][C]2.64171238617347e-17[/C][/ROW]
[ROW][C]44[/C][C]7.9[/C][C]7.9[/C][C]-6.47885859535384e-19[/C][/ROW]
[ROW][C]45[/C][C]7.5[/C][C]7.5[/C][C]9.18365444334975e-17[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]6.9[/C][C]-8.2673659711316e-18[/C][/ROW]
[ROW][C]47[/C][C]6.6[/C][C]6.6[/C][C]5.15585731642701e-17[/C][/ROW]
[ROW][C]48[/C][C]6.9[/C][C]6.9[/C][C]-2.43430511550802e-18[/C][/ROW]
[ROW][C]49[/C][C]7.7[/C][C]7.7[/C][C]2.68885044445246e-18[/C][/ROW]
[ROW][C]50[/C][C]8[/C][C]8[/C][C]-2.65347425892852e-17[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8[/C][C]-1.86148697167854e-16[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]7.7[/C][C]9.6688185756501e-18[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.3[/C][C]3.56771590796384e-17[/C][/ROW]
[ROW][C]54[/C][C]7.4[/C][C]7.4[/C][C]6.63138427493595e-17[/C][/ROW]
[ROW][C]55[/C][C]8.1[/C][C]8.1[/C][C]4.92998638261233e-18[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]8.3[/C][C]7.04929257101326e-17[/C][/ROW]
[ROW][C]57[/C][C]8.2[/C][C]8.2[/C][C]-1.79450452623363e-17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67963&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&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	8.5	8.5	-7.6991384674347e-17
2	8.6	8.6	-6.43709360977525e-17
3	8.5	8.5	6.5756488250235e-16
4	8.2	8.2	-5.67866034633681e-17
5	8.1	8.1	-6.34876583350881e-18
6	7.9	7.9	-6.39936729524118e-17
7	8.6	8.6	-3.07938464271981e-17
8	8.7	8.7	-1.50779618795439e-16
9	8.7	8.7	-7.60896371306682e-17
10	8.5	8.5	-1.12544189552567e-17
11	8.4	8.4	-1.87973185793847e-17
12	8.5	8.5	-9.52569968939496e-18
13	8.7	8.7	-7.26912276957142e-17
14	8.7	8.7	-5.85614221220454e-17
15	8.6	8.6	-1.61756676361002e-16
16	8.5	8.5	2.42587675254507e-17
17	8.3	8.3	3.73154830395712e-17
18	8	8	1.31687079577835e-18
19	8.2	8.2	-3.86450271428722e-17
20	8.1	8.1	-2.49932245985543e-18
21	8.1	8.1	4.20887252772615e-17
22	8	8	2.63137569411794e-17
23	7.9	7.9	2.40516497712711e-17
24	7.9	7.9	1.65027753351442e-17
25	8	8	3.00235215224727e-17
26	8	8	4.87068947155409e-17
27	7.9	7.9	-1.56928722762741e-16
28	8	8	7.01377735925727e-17
29	7.7	7.7	2.37442644288036e-17
30	7.2	7.2	-2.09157096049553e-17
31	7.5	7.5	3.80917633257233e-17
32	7.3	7.3	8.34339014046975e-17
33	7	7	-3.98905873177544e-17
34	7	7	-6.79197201479108e-18
35	7	7	-5.68129043561564e-17
36	7.2	7.2	-4.54277053024157e-18
37	7.3	7.3	1.16970240403136e-16
38	7.1	7.1	1.00760206093542e-16
39	6.8	6.8	-1.52730786210754e-16
40	6.4	6.4	-4.72787562303053e-17
41	6.1	6.1	-9.03881407145042e-17
42	6.5	6.5	1.72786690122292e-17
43	7.7	7.7	2.64171238617347e-17
44	7.9	7.9	-6.47885859535384e-19
45	7.5	7.5	9.18365444334975e-17
46	6.9	6.9	-8.2673659711316e-18
47	6.6	6.6	5.15585731642701e-17
48	6.9	6.9	-2.43430511550802e-18
49	7.7	7.7	2.68885044445246e-18
50	8	8	-2.65347425892852e-17
51	8	8	-1.86148697167854e-16
52	7.7	7.7	9.6688185756501e-18
53	7.3	7.3	3.56771590796384e-17
54	7.4	7.4	6.63138427493595e-17
55	8.1	8.1	4.92998638261233e-18
56	8.3	8.3	7.04929257101326e-17
57	8.2	8.2	-1.79450452623363e-17

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.158294841147041	0.316589682294082	0.841705158852959
22	0.472545462453909	0.945090924907818	0.527454537546091
23	0.0113339049571471	0.0226678099142943	0.988666095042853
24	0.00327250994365368	0.00654501988730735	0.996727490056346
25	3.15455655968536e-05	6.30911311937072e-05	0.999968454434403
26	0.800661376100752	0.398677247798496	0.199338623899248
27	4.1744642165599e-13	8.3489284331198e-13	0.999999999999583
28	8.48769212319241e-06	1.69753842463848e-05	0.999991512307877
29	0.000103362618003300	0.000206725236006601	0.999896637381997
30	0	0	1
31	3.04215469987899e-20	6.08430939975798e-20	1
32	0.887069516552428	0.225860966895143	0.112930483447572
33	3.59512425445158e-05	7.19024850890317e-05	0.999964048757455
34	0.980176438260019	0.0396471234799623	0.0198235617399812
35	0.0192602136189009	0.0385204272378017	0.9807397863811
36	0.000106107607578102	0.000212215215156204	0.999893892392422

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.158294841147041 & 0.316589682294082 & 0.841705158852959 \tabularnewline
22 & 0.472545462453909 & 0.945090924907818 & 0.527454537546091 \tabularnewline
23 & 0.0113339049571471 & 0.0226678099142943 & 0.988666095042853 \tabularnewline
24 & 0.00327250994365368 & 0.00654501988730735 & 0.996727490056346 \tabularnewline
25 & 3.15455655968536e-05 & 6.30911311937072e-05 & 0.999968454434403 \tabularnewline
26 & 0.800661376100752 & 0.398677247798496 & 0.199338623899248 \tabularnewline
27 & 4.1744642165599e-13 & 8.3489284331198e-13 & 0.999999999999583 \tabularnewline
28 & 8.48769212319241e-06 & 1.69753842463848e-05 & 0.999991512307877 \tabularnewline
29 & 0.000103362618003300 & 0.000206725236006601 & 0.999896637381997 \tabularnewline
30 & 0 & 0 & 1 \tabularnewline
31 & 3.04215469987899e-20 & 6.08430939975798e-20 & 1 \tabularnewline
32 & 0.887069516552428 & 0.225860966895143 & 0.112930483447572 \tabularnewline
33 & 3.59512425445158e-05 & 7.19024850890317e-05 & 0.999964048757455 \tabularnewline
34 & 0.980176438260019 & 0.0396471234799623 & 0.0198235617399812 \tabularnewline
35 & 0.0192602136189009 & 0.0385204272378017 & 0.9807397863811 \tabularnewline
36 & 0.000106107607578102 & 0.000212215215156204 & 0.999893892392422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&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]0.158294841147041[/C][C]0.316589682294082[/C][C]0.841705158852959[/C][/ROW]
[ROW][C]22[/C][C]0.472545462453909[/C][C]0.945090924907818[/C][C]0.527454537546091[/C][/ROW]
[ROW][C]23[/C][C]0.0113339049571471[/C][C]0.0226678099142943[/C][C]0.988666095042853[/C][/ROW]
[ROW][C]24[/C][C]0.00327250994365368[/C][C]0.00654501988730735[/C][C]0.996727490056346[/C][/ROW]
[ROW][C]25[/C][C]3.15455655968536e-05[/C][C]6.30911311937072e-05[/C][C]0.999968454434403[/C][/ROW]
[ROW][C]26[/C][C]0.800661376100752[/C][C]0.398677247798496[/C][C]0.199338623899248[/C][/ROW]
[ROW][C]27[/C][C]4.1744642165599e-13[/C][C]8.3489284331198e-13[/C][C]0.999999999999583[/C][/ROW]
[ROW][C]28[/C][C]8.48769212319241e-06[/C][C]1.69753842463848e-05[/C][C]0.999991512307877[/C][/ROW]
[ROW][C]29[/C][C]0.000103362618003300[/C][C]0.000206725236006601[/C][C]0.999896637381997[/C][/ROW]
[ROW][C]30[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]31[/C][C]3.04215469987899e-20[/C][C]6.08430939975798e-20[/C][C]1[/C][/ROW]
[ROW][C]32[/C][C]0.887069516552428[/C][C]0.225860966895143[/C][C]0.112930483447572[/C][/ROW]
[ROW][C]33[/C][C]3.59512425445158e-05[/C][C]7.19024850890317e-05[/C][C]0.999964048757455[/C][/ROW]
[ROW][C]34[/C][C]0.980176438260019[/C][C]0.0396471234799623[/C][C]0.0198235617399812[/C][/ROW]
[ROW][C]35[/C][C]0.0192602136189009[/C][C]0.0385204272378017[/C][C]0.9807397863811[/C][/ROW]
[ROW][C]36[/C][C]0.000106107607578102[/C][C]0.000212215215156204[/C][C]0.999893892392422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67963&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.158294841147041	0.316589682294082	0.841705158852959
22	0.472545462453909	0.945090924907818	0.527454537546091
23	0.0113339049571471	0.0226678099142943	0.988666095042853
24	0.00327250994365368	0.00654501988730735	0.996727490056346
25	3.15455655968536e-05	6.30911311937072e-05	0.999968454434403
26	0.800661376100752	0.398677247798496	0.199338623899248
27	4.1744642165599e-13	8.3489284331198e-13	0.999999999999583
28	8.48769212319241e-06	1.69753842463848e-05	0.999991512307877
29	0.000103362618003300	0.000206725236006601	0.999896637381997
30	0	0	1
31	3.04215469987899e-20	6.08430939975798e-20	1
32	0.887069516552428	0.225860966895143	0.112930483447572
33	3.59512425445158e-05	7.19024850890317e-05	0.999964048757455
34	0.980176438260019	0.0396471234799623	0.0198235617399812
35	0.0192602136189009	0.0385204272378017	0.9807397863811
36	0.000106107607578102	0.000212215215156204	0.999893892392422

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.5625	NOK
5% type I error level	12	0.75	NOK
10% type I error level	12	0.75	NOK

\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 & 9 & 0.5625 & NOK \tabularnewline
5% type I error level & 12 & 0.75 & NOK \tabularnewline
10% type I error level & 12 & 0.75 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67963&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]9[/C][C]0.5625[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]12[/C][C]0.75[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.75[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67963&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67963&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.5625	NOK
5% type I error level	12	0.75	NOK
10% type I error level	12	0.75	NOK

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