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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 23 Nov 2009 13:50:02 -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/Nov/23/t1259009536k86ti3hm8f699ig.htm/, Retrieved Mon, 10 Nov 2025 04:03:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58905, Retrieved Mon, 10 Nov 2025 04:03:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

review 7

Estimated Impact

414

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]
-   PD    [Multiple Regression] [4 lag ] [2009-11-19 20:53:48] [ba905ddf7cdf9ecb063c35348c4dab2e]
-    D        [Multiple Regression] [review 7] [2009-11-23 20:50:02] [6198946fb53eb5eb18db46bb758f7fde] [Current]
-   PD          [Multiple Regression] [review 7] [2009-11-24 08:31:24] [309ee52d0058ff0a6f7eec15e07b2d9f] 

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Dataseries X:

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Histogram

Boxplots

6.5	0	6.3	6.1	6.2	6.3
6.6	0	6.5	6.3	6.1	6.2
6.5	0	6.6	6.5	6.3	6.1
6.2	0	6.5	6.6	6.5	6.3
6.2	0	6.2	6.5	6.6	6.5
5.9	0	6.2	6.2	6.5	6.6
6.1	0	5.9	6.2	6.2	6.5
6.1	0	6.1	5.9	6.2	6.2
6.1	0	6.1	6.1	5.9	6.2
6.1	0	6.1	6.1	6.1	5.9
6.1	0	6.1	6.1	6.1	6.1
6.4	0	6.1	6.1	6.1	6.1
6.7	0	6.4	6.1	6.1	6.1
6.9	0	6.7	6.4	6.1	6.1
7	0	6.9	6.7	6.4	6.1
7	0	7	6.9	6.7	6.4
6.8	0	7	7	6.9	6.7
6.4	0	6.8	7	7	6.9
5.9	0	6.4	6.8	7	7
5.5	0	5.9	6.4	6.8	7
5.5	0	5.5	5.9	6.4	6.8
5.6	0	5.5	5.5	5.9	6.4
5.8	0	5.6	5.5	5.5	5.9
5.9	0	5.8	5.6	5.5	5.5
6.1	0	5.9	5.8	5.6	5.5
6.1	0	6.1	5.9	5.8	5.6
6	0	6.1	6.1	5.9	5.8
6	0	6	6.1	6.1	5.9
5.9	0	6	6	6.1	6.1
5.5	0	5.9	6	6	6.1
5.6	0	5.5	5.9	6	6
5.4	0	5.6	5.5	5.9	6
5.2	0	5.4	5.6	5.5	5.9
5.2	0	5.2	5.4	5.6	5.5
5.2	0	5.2	5.2	5.4	5.6
5.5	0	5.2	5.2	5.2	5.4
5.8	1	5.5	5.2	5.2	5.2
5.8	1	5.8	5.5	5.2	5.2
5.5	1	5.8	5.8	5.5	5.2
5.3	1	5.5	5.8	5.8	5.5
5.1	1	5.3	5.5	5.8	5.8
5.2	1	5.1	5.3	5.5	5.8
5.8	1	5.2	5.1	5.3	5.5
5.8	1	5.8	5.2	5.1	5.3
5.5	1	5.8	5.8	5.2	5.1
5	1	5.5	5.8	5.8	5.2
4.9	1	5	5.5	5.8	5.8
5.3	1	4.9	5	5.5	5.8
6.1	1	5.3	4.9	5	5.5
6.5	1	6.1	5.3	4.9	5
6.8	1	6.5	6.1	5.3	4.9
6.6	1	6.8	6.5	6.1	5.3
6.4	1	6.6	6.8	6.5	6.1
6.4	1	6.4	6.6	6.8	6.5

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=58905&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=58905&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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
x[t] = + 0.828266455762903 + 0.181690649604083y[t] -0.231079892362897`y-1`[t] -0.113984746512807`y-2`[t] + 0.403116044771066`y-3`[t] -0.451911443142585`y-4`[t] + 0.260083204498035M1[t] + 0.282413524108473M2[t] + 0.234756218660789M3[t] + 0.224037734894681M4[t] + 0.301228778766867M5[t] + 0.340721141705765M6[t] + 0.230155837767498M7[t] + 0.226055172545054M8[t] + 0.249926434867650M9[t] + 0.0489566955683181M10[t] + 0.0928502573330396M11[t] + 0.0198666404747040t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
x[t] =  +  0.828266455762903 +  0.181690649604083y[t] -0.231079892362897`y-1`[t] -0.113984746512807`y-2`[t] +  0.403116044771066`y-3`[t] -0.451911443142585`y-4`[t] +  0.260083204498035M1[t] +  0.282413524108473M2[t] +  0.234756218660789M3[t] +  0.224037734894681M4[t] +  0.301228778766867M5[t] +  0.340721141705765M6[t] +  0.230155837767498M7[t] +  0.226055172545054M8[t] +  0.249926434867650M9[t] +  0.0489566955683181M10[t] +  0.0928502573330396M11[t] +  0.0198666404747040t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58905&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]x[t] =  +  0.828266455762903 +  0.181690649604083y[t] -0.231079892362897`y-1`[t] -0.113984746512807`y-2`[t] +  0.403116044771066`y-3`[t] -0.451911443142585`y-4`[t] +  0.260083204498035M1[t] +  0.282413524108473M2[t] +  0.234756218660789M3[t] +  0.224037734894681M4[t] +  0.301228778766867M5[t] +  0.340721141705765M6[t] +  0.230155837767498M7[t] +  0.226055172545054M8[t] +  0.249926434867650M9[t] +  0.0489566955683181M10[t] +  0.0928502573330396M11[t] +  0.0198666404747040t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58905&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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
x[t] = + 0.828266455762903 + 0.181690649604083y[t] -0.231079892362897`y-1`[t] -0.113984746512807`y-2`[t] + 0.403116044771066`y-3`[t] -0.451911443142585`y-4`[t] + 0.260083204498035M1[t] + 0.282413524108473M2[t] + 0.234756218660789M3[t] + 0.224037734894681M4[t] + 0.301228778766867M5[t] + 0.340721141705765M6[t] + 0.230155837767498M7[t] + 0.226055172545054M8[t] + 0.249926434867650M9[t] + 0.0489566955683181M10[t] + 0.0928502573330396M11[t] + 0.0198666404747040t + 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)	0.828266455762903	1.081117	0.7661	0.448599	0.2243
y	0.181690649604083	0.290964	0.6244	0.536273	0.268137
`y-1`	-0.231079892362897	0.523453	-0.4415	0.661525	0.330763
`y-2`	-0.113984746512807	0.549486	-0.2074	0.836836	0.418418
`y-3`	0.403116044771066	0.528222	0.7632	0.450342	0.225171
`y-4`	-0.451911443142585	0.342055	-1.3212	0.194783	0.097391
M1	0.260083204498035	0.213724	1.2169	0.231555	0.115777
M2	0.282413524108473	0.234449	1.2046	0.236224	0.118112
M3	0.234756218660789	0.238767	0.9832	0.332069	0.166035
M4	0.224037734894681	0.241102	0.9292	0.358962	0.179481
M5	0.301228778766867	0.240233	1.2539	0.217959	0.108979
M6	0.340721141705765	0.25505	1.3359	0.189966	0.094983
M7	0.230155837767498	0.233398	0.9861	0.330661	0.16533
M8	0.226055172545054	0.269844	0.8377	0.407712	0.203856
M9	0.249926434867650	0.268449	0.931	0.358054	0.179027
M10	0.0489566955683181	0.234486	0.2088	0.835794	0.417897
M11	0.0928502573330396	0.226469	0.41	0.684242	0.342121
t	0.0198666404747040	0.004439	4.4755	7.4e-05	3.7e-05

\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) & 0.828266455762903 & 1.081117 & 0.7661 & 0.448599 & 0.2243 \tabularnewline
y & 0.181690649604083 & 0.290964 & 0.6244 & 0.536273 & 0.268137 \tabularnewline
`y-1` & -0.231079892362897 & 0.523453 & -0.4415 & 0.661525 & 0.330763 \tabularnewline
`y-2` & -0.113984746512807 & 0.549486 & -0.2074 & 0.836836 & 0.418418 \tabularnewline
`y-3` & 0.403116044771066 & 0.528222 & 0.7632 & 0.450342 & 0.225171 \tabularnewline
`y-4` & -0.451911443142585 & 0.342055 & -1.3212 & 0.194783 & 0.097391 \tabularnewline
M1 & 0.260083204498035 & 0.213724 & 1.2169 & 0.231555 & 0.115777 \tabularnewline
M2 & 0.282413524108473 & 0.234449 & 1.2046 & 0.236224 & 0.118112 \tabularnewline
M3 & 0.234756218660789 & 0.238767 & 0.9832 & 0.332069 & 0.166035 \tabularnewline
M4 & 0.224037734894681 & 0.241102 & 0.9292 & 0.358962 & 0.179481 \tabularnewline
M5 & 0.301228778766867 & 0.240233 & 1.2539 & 0.217959 & 0.108979 \tabularnewline
M6 & 0.340721141705765 & 0.25505 & 1.3359 & 0.189966 & 0.094983 \tabularnewline
M7 & 0.230155837767498 & 0.233398 & 0.9861 & 0.330661 & 0.16533 \tabularnewline
M8 & 0.226055172545054 & 0.269844 & 0.8377 & 0.407712 & 0.203856 \tabularnewline
M9 & 0.249926434867650 & 0.268449 & 0.931 & 0.358054 & 0.179027 \tabularnewline
M10 & 0.0489566955683181 & 0.234486 & 0.2088 & 0.835794 & 0.417897 \tabularnewline
M11 & 0.0928502573330396 & 0.226469 & 0.41 & 0.684242 & 0.342121 \tabularnewline
t & 0.0198666404747040 & 0.004439 & 4.4755 & 7.4e-05 & 3.7e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58905&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]0.828266455762903[/C][C]1.081117[/C][C]0.7661[/C][C]0.448599[/C][C]0.2243[/C][/ROW]
[ROW][C]y[/C][C]0.181690649604083[/C][C]0.290964[/C][C]0.6244[/C][C]0.536273[/C][C]0.268137[/C][/ROW]
[ROW][C]`y-1`[/C][C]-0.231079892362897[/C][C]0.523453[/C][C]-0.4415[/C][C]0.661525[/C][C]0.330763[/C][/ROW]
[ROW][C]`y-2`[/C][C]-0.113984746512807[/C][C]0.549486[/C][C]-0.2074[/C][C]0.836836[/C][C]0.418418[/C][/ROW]
[ROW][C]`y-3`[/C][C]0.403116044771066[/C][C]0.528222[/C][C]0.7632[/C][C]0.450342[/C][C]0.225171[/C][/ROW]
[ROW][C]`y-4`[/C][C]-0.451911443142585[/C][C]0.342055[/C][C]-1.3212[/C][C]0.194783[/C][C]0.097391[/C][/ROW]
[ROW][C]M1[/C][C]0.260083204498035[/C][C]0.213724[/C][C]1.2169[/C][C]0.231555[/C][C]0.115777[/C][/ROW]
[ROW][C]M2[/C][C]0.282413524108473[/C][C]0.234449[/C][C]1.2046[/C][C]0.236224[/C][C]0.118112[/C][/ROW]
[ROW][C]M3[/C][C]0.234756218660789[/C][C]0.238767[/C][C]0.9832[/C][C]0.332069[/C][C]0.166035[/C][/ROW]
[ROW][C]M4[/C][C]0.224037734894681[/C][C]0.241102[/C][C]0.9292[/C][C]0.358962[/C][C]0.179481[/C][/ROW]
[ROW][C]M5[/C][C]0.301228778766867[/C][C]0.240233[/C][C]1.2539[/C][C]0.217959[/C][C]0.108979[/C][/ROW]
[ROW][C]M6[/C][C]0.340721141705765[/C][C]0.25505[/C][C]1.3359[/C][C]0.189966[/C][C]0.094983[/C][/ROW]
[ROW][C]M7[/C][C]0.230155837767498[/C][C]0.233398[/C][C]0.9861[/C][C]0.330661[/C][C]0.16533[/C][/ROW]
[ROW][C]M8[/C][C]0.226055172545054[/C][C]0.269844[/C][C]0.8377[/C][C]0.407712[/C][C]0.203856[/C][/ROW]
[ROW][C]M9[/C][C]0.249926434867650[/C][C]0.268449[/C][C]0.931[/C][C]0.358054[/C][C]0.179027[/C][/ROW]
[ROW][C]M10[/C][C]0.0489566955683181[/C][C]0.234486[/C][C]0.2088[/C][C]0.835794[/C][C]0.417897[/C][/ROW]
[ROW][C]M11[/C][C]0.0928502573330396[/C][C]0.226469[/C][C]0.41[/C][C]0.684242[/C][C]0.342121[/C][/ROW]
[ROW][C]t[/C][C]0.0198666404747040[/C][C]0.004439[/C][C]4.4755[/C][C]7.4e-05[/C][C]3.7e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58905&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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)	0.828266455762903	1.081117	0.7661	0.448599	0.2243
y	0.181690649604083	0.290964	0.6244	0.536273	0.268137
`y-1`	-0.231079892362897	0.523453	-0.4415	0.661525	0.330763
`y-2`	-0.113984746512807	0.549486	-0.2074	0.836836	0.418418
`y-3`	0.403116044771066	0.528222	0.7632	0.450342	0.225171
`y-4`	-0.451911443142585	0.342055	-1.3212	0.194783	0.097391
M1	0.260083204498035	0.213724	1.2169	0.231555	0.115777
M2	0.282413524108473	0.234449	1.2046	0.236224	0.118112
M3	0.234756218660789	0.238767	0.9832	0.332069	0.166035
M4	0.224037734894681	0.241102	0.9292	0.358962	0.179481
M5	0.301228778766867	0.240233	1.2539	0.217959	0.108979
M6	0.340721141705765	0.25505	1.3359	0.189966	0.094983
M7	0.230155837767498	0.233398	0.9861	0.330661	0.16533
M8	0.226055172545054	0.269844	0.8377	0.407712	0.203856
M9	0.249926434867650	0.268449	0.931	0.358054	0.179027
M10	0.0489566955683181	0.234486	0.2088	0.835794	0.417897
M11	0.0928502573330396	0.226469	0.41	0.684242	0.342121
t	0.0198666404747040	0.004439	4.4755	7.4e-05	3.7e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.848135208984957
R-squared	0.719333332719956
Adjusted R-squared	0.586796295393269
F-TEST (value)	5.42741370434356
F-TEST (DF numerator)	17
F-TEST (DF denominator)	36
p-value	1.01676818082819e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.305868526919679
Sum Squared Residuals	3.36800000736053

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.848135208984957 \tabularnewline
R-squared & 0.719333332719956 \tabularnewline
Adjusted R-squared & 0.586796295393269 \tabularnewline
F-TEST (value) & 5.42741370434356 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 36 \tabularnewline
p-value & 1.01676818082819e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.305868526919679 \tabularnewline
Sum Squared Residuals & 3.36800000736053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58905&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.848135208984957[/C][/ROW]
[ROW][C]R-squared[/C][C]0.719333332719956[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.586796295393269[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]5.42741370434356[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]36[/C][/ROW]
[ROW][C]p-value[/C][C]1.01676818082819e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.305868526919679[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3.36800000736053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58905&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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	0.848135208984957
R-squared	0.719333332719956
Adjusted R-squared	0.586796295393269
F-TEST (value)	5.42741370434356
F-TEST (DF numerator)	17
F-TEST (DF denominator)	36
p-value	1.01676818082819e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.305868526919679
Sum Squared Residuals	3.36800000736053

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0	-0.209627366669886	0.209627366669886
2	0	-0.21339472956232	0.21339472956232
3	0	-0.179445044766085	0.179445044766085
4	0	-0.22285364802801	0.22285364802801
5	0	-0.0951442054723797	0.0951442054723797
6	0	-0.141599721777526	0.141599721777526
7	0	-0.202379956728465	0.202379956728465
8	0	-0.0630611030521655	0.0630611030521655
9	0	-0.163054962988747	0.163054962988747
10	0	-0.127961419916386	0.127961419916386
11	0	-0.154583506305478	0.154583506305478
12	0	-0.173059928282589	0.173059928282589
13	0	0.092073143862506	-0.092073143862506
14	0	0.0670888422057528	-0.0670888422057528
15	0	0.0979906531980796	-0.0979906531980796
16	0	0.0465952518563678	-0.0465952518563678
17	0	0.0409661076425993	-0.0409661076425993
18	0	0.0237941455357358	-0.0237941455357358
19	0	-0.0877120807964054	0.0877120807964054
20	0	-0.0641117295534201	0.0641117295534201
21	0	0.0581863741655331	-0.0581863741655331
22	0	-0.0799472062220622	0.0799472062220622
23	0	0.0617524403647565	-0.0617524403647565
24	0	0.130088012600003	-0.130088012600003
25	0	0.440782653431814	-0.440782653431814
26	0	0.46079722503305	-0.46079722503305
27	0	0.341969861645691	-0.341969861645691
28	0	0.40965807223053	-0.40965807223053
29	0	0.409562877639777	-0.409562877639777
30	0	0.379042005970928	-0.379042005970928
31	0	0.455533983378472	-0.455533983378472
32	0	0.417136133601642	-0.417136133601642
33	0	0.343298136705256	-0.343298136705256
34	0	0.45228414738991	-0.45228414738991
35	0	0.413026945663426	-0.413026945663426
36	0	0.404309603360619	-0.404309603360619
37	1	0.75982496413423	0.24017503586577
38	1	0.69850253255666	0.301497467443339
39	1	0.702944062179934	0.297055937820066
40	1	0.730439437165126	0.269560562834874
41	1	0.735996961074847	0.264003038925153
42	1	0.761603143792678	0.238396856207322
43	1	0.834558054146398	0.165441945853602
44	1	0.710036699003943	0.289963300996057
45	1	0.761570452117958	0.238429547882042
46	1	0.755624478748539	0.244375521251461
47	1	0.679804120277295	0.320195879722705
48	1	0.638662312321966	0.361337687678034
49	1	0.916946605241336	0.0830533947586643
50	1	0.987006129766856	0.0129938702331438
51	1	1.03654046774238	-0.0365404677423810
52	1	1.03616088677599	-0.0361608867759864
53	1	0.908618259115157	0.0913817408848432
54	1	0.977160426478184	0.0228395735218164

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 0 & -0.209627366669886 & 0.209627366669886 \tabularnewline
2 & 0 & -0.21339472956232 & 0.21339472956232 \tabularnewline
3 & 0 & -0.179445044766085 & 0.179445044766085 \tabularnewline
4 & 0 & -0.22285364802801 & 0.22285364802801 \tabularnewline
5 & 0 & -0.0951442054723797 & 0.0951442054723797 \tabularnewline
6 & 0 & -0.141599721777526 & 0.141599721777526 \tabularnewline
7 & 0 & -0.202379956728465 & 0.202379956728465 \tabularnewline
8 & 0 & -0.0630611030521655 & 0.0630611030521655 \tabularnewline
9 & 0 & -0.163054962988747 & 0.163054962988747 \tabularnewline
10 & 0 & -0.127961419916386 & 0.127961419916386 \tabularnewline
11 & 0 & -0.154583506305478 & 0.154583506305478 \tabularnewline
12 & 0 & -0.173059928282589 & 0.173059928282589 \tabularnewline
13 & 0 & 0.092073143862506 & -0.092073143862506 \tabularnewline
14 & 0 & 0.0670888422057528 & -0.0670888422057528 \tabularnewline
15 & 0 & 0.0979906531980796 & -0.0979906531980796 \tabularnewline
16 & 0 & 0.0465952518563678 & -0.0465952518563678 \tabularnewline
17 & 0 & 0.0409661076425993 & -0.0409661076425993 \tabularnewline
18 & 0 & 0.0237941455357358 & -0.0237941455357358 \tabularnewline
19 & 0 & -0.0877120807964054 & 0.0877120807964054 \tabularnewline
20 & 0 & -0.0641117295534201 & 0.0641117295534201 \tabularnewline
21 & 0 & 0.0581863741655331 & -0.0581863741655331 \tabularnewline
22 & 0 & -0.0799472062220622 & 0.0799472062220622 \tabularnewline
23 & 0 & 0.0617524403647565 & -0.0617524403647565 \tabularnewline
24 & 0 & 0.130088012600003 & -0.130088012600003 \tabularnewline
25 & 0 & 0.440782653431814 & -0.440782653431814 \tabularnewline
26 & 0 & 0.46079722503305 & -0.46079722503305 \tabularnewline
27 & 0 & 0.341969861645691 & -0.341969861645691 \tabularnewline
28 & 0 & 0.40965807223053 & -0.40965807223053 \tabularnewline
29 & 0 & 0.409562877639777 & -0.409562877639777 \tabularnewline
30 & 0 & 0.379042005970928 & -0.379042005970928 \tabularnewline
31 & 0 & 0.455533983378472 & -0.455533983378472 \tabularnewline
32 & 0 & 0.417136133601642 & -0.417136133601642 \tabularnewline
33 & 0 & 0.343298136705256 & -0.343298136705256 \tabularnewline
34 & 0 & 0.45228414738991 & -0.45228414738991 \tabularnewline
35 & 0 & 0.413026945663426 & -0.413026945663426 \tabularnewline
36 & 0 & 0.404309603360619 & -0.404309603360619 \tabularnewline
37 & 1 & 0.75982496413423 & 0.24017503586577 \tabularnewline
38 & 1 & 0.69850253255666 & 0.301497467443339 \tabularnewline
39 & 1 & 0.702944062179934 & 0.297055937820066 \tabularnewline
40 & 1 & 0.730439437165126 & 0.269560562834874 \tabularnewline
41 & 1 & 0.735996961074847 & 0.264003038925153 \tabularnewline
42 & 1 & 0.761603143792678 & 0.238396856207322 \tabularnewline
43 & 1 & 0.834558054146398 & 0.165441945853602 \tabularnewline
44 & 1 & 0.710036699003943 & 0.289963300996057 \tabularnewline
45 & 1 & 0.761570452117958 & 0.238429547882042 \tabularnewline
46 & 1 & 0.755624478748539 & 0.244375521251461 \tabularnewline
47 & 1 & 0.679804120277295 & 0.320195879722705 \tabularnewline
48 & 1 & 0.638662312321966 & 0.361337687678034 \tabularnewline
49 & 1 & 0.916946605241336 & 0.0830533947586643 \tabularnewline
50 & 1 & 0.987006129766856 & 0.0129938702331438 \tabularnewline
51 & 1 & 1.03654046774238 & -0.0365404677423810 \tabularnewline
52 & 1 & 1.03616088677599 & -0.0361608867759864 \tabularnewline
53 & 1 & 0.908618259115157 & 0.0913817408848432 \tabularnewline
54 & 1 & 0.977160426478184 & 0.0228395735218164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58905&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]0[/C][C]-0.209627366669886[/C][C]0.209627366669886[/C][/ROW]
[ROW][C]2[/C][C]0[/C][C]-0.21339472956232[/C][C]0.21339472956232[/C][/ROW]
[ROW][C]3[/C][C]0[/C][C]-0.179445044766085[/C][C]0.179445044766085[/C][/ROW]
[ROW][C]4[/C][C]0[/C][C]-0.22285364802801[/C][C]0.22285364802801[/C][/ROW]
[ROW][C]5[/C][C]0[/C][C]-0.0951442054723797[/C][C]0.0951442054723797[/C][/ROW]
[ROW][C]6[/C][C]0[/C][C]-0.141599721777526[/C][C]0.141599721777526[/C][/ROW]
[ROW][C]7[/C][C]0[/C][C]-0.202379956728465[/C][C]0.202379956728465[/C][/ROW]
[ROW][C]8[/C][C]0[/C][C]-0.0630611030521655[/C][C]0.0630611030521655[/C][/ROW]
[ROW][C]9[/C][C]0[/C][C]-0.163054962988747[/C][C]0.163054962988747[/C][/ROW]
[ROW][C]10[/C][C]0[/C][C]-0.127961419916386[/C][C]0.127961419916386[/C][/ROW]
[ROW][C]11[/C][C]0[/C][C]-0.154583506305478[/C][C]0.154583506305478[/C][/ROW]
[ROW][C]12[/C][C]0[/C][C]-0.173059928282589[/C][C]0.173059928282589[/C][/ROW]
[ROW][C]13[/C][C]0[/C][C]0.092073143862506[/C][C]-0.092073143862506[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]0.0670888422057528[/C][C]-0.0670888422057528[/C][/ROW]
[ROW][C]15[/C][C]0[/C][C]0.0979906531980796[/C][C]-0.0979906531980796[/C][/ROW]
[ROW][C]16[/C][C]0[/C][C]0.0465952518563678[/C][C]-0.0465952518563678[/C][/ROW]
[ROW][C]17[/C][C]0[/C][C]0.0409661076425993[/C][C]-0.0409661076425993[/C][/ROW]
[ROW][C]18[/C][C]0[/C][C]0.0237941455357358[/C][C]-0.0237941455357358[/C][/ROW]
[ROW][C]19[/C][C]0[/C][C]-0.0877120807964054[/C][C]0.0877120807964054[/C][/ROW]
[ROW][C]20[/C][C]0[/C][C]-0.0641117295534201[/C][C]0.0641117295534201[/C][/ROW]
[ROW][C]21[/C][C]0[/C][C]0.0581863741655331[/C][C]-0.0581863741655331[/C][/ROW]
[ROW][C]22[/C][C]0[/C][C]-0.0799472062220622[/C][C]0.0799472062220622[/C][/ROW]
[ROW][C]23[/C][C]0[/C][C]0.0617524403647565[/C][C]-0.0617524403647565[/C][/ROW]
[ROW][C]24[/C][C]0[/C][C]0.130088012600003[/C][C]-0.130088012600003[/C][/ROW]
[ROW][C]25[/C][C]0[/C][C]0.440782653431814[/C][C]-0.440782653431814[/C][/ROW]
[ROW][C]26[/C][C]0[/C][C]0.46079722503305[/C][C]-0.46079722503305[/C][/ROW]
[ROW][C]27[/C][C]0[/C][C]0.341969861645691[/C][C]-0.341969861645691[/C][/ROW]
[ROW][C]28[/C][C]0[/C][C]0.40965807223053[/C][C]-0.40965807223053[/C][/ROW]
[ROW][C]29[/C][C]0[/C][C]0.409562877639777[/C][C]-0.409562877639777[/C][/ROW]
[ROW][C]30[/C][C]0[/C][C]0.379042005970928[/C][C]-0.379042005970928[/C][/ROW]
[ROW][C]31[/C][C]0[/C][C]0.455533983378472[/C][C]-0.455533983378472[/C][/ROW]
[ROW][C]32[/C][C]0[/C][C]0.417136133601642[/C][C]-0.417136133601642[/C][/ROW]
[ROW][C]33[/C][C]0[/C][C]0.343298136705256[/C][C]-0.343298136705256[/C][/ROW]
[ROW][C]34[/C][C]0[/C][C]0.45228414738991[/C][C]-0.45228414738991[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]0.413026945663426[/C][C]-0.413026945663426[/C][/ROW]
[ROW][C]36[/C][C]0[/C][C]0.404309603360619[/C][C]-0.404309603360619[/C][/ROW]
[ROW][C]37[/C][C]1[/C][C]0.75982496413423[/C][C]0.24017503586577[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]0.69850253255666[/C][C]0.301497467443339[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]0.702944062179934[/C][C]0.297055937820066[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]0.730439437165126[/C][C]0.269560562834874[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]0.735996961074847[/C][C]0.264003038925153[/C][/ROW]
[ROW][C]42[/C][C]1[/C][C]0.761603143792678[/C][C]0.238396856207322[/C][/ROW]
[ROW][C]43[/C][C]1[/C][C]0.834558054146398[/C][C]0.165441945853602[/C][/ROW]
[ROW][C]44[/C][C]1[/C][C]0.710036699003943[/C][C]0.289963300996057[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]0.761570452117958[/C][C]0.238429547882042[/C][/ROW]
[ROW][C]46[/C][C]1[/C][C]0.755624478748539[/C][C]0.244375521251461[/C][/ROW]
[ROW][C]47[/C][C]1[/C][C]0.679804120277295[/C][C]0.320195879722705[/C][/ROW]
[ROW][C]48[/C][C]1[/C][C]0.638662312321966[/C][C]0.361337687678034[/C][/ROW]
[ROW][C]49[/C][C]1[/C][C]0.916946605241336[/C][C]0.0830533947586643[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]0.987006129766856[/C][C]0.0129938702331438[/C][/ROW]
[ROW][C]51[/C][C]1[/C][C]1.03654046774238[/C][C]-0.0365404677423810[/C][/ROW]
[ROW][C]52[/C][C]1[/C][C]1.03616088677599[/C][C]-0.0361608867759864[/C][/ROW]
[ROW][C]53[/C][C]1[/C][C]0.908618259115157[/C][C]0.0913817408848432[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]0.977160426478184[/C][C]0.0228395735218164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58905&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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	0	-0.209627366669886	0.209627366669886
2	0	-0.21339472956232	0.21339472956232
3	0	-0.179445044766085	0.179445044766085
4	0	-0.22285364802801	0.22285364802801
5	0	-0.0951442054723797	0.0951442054723797
6	0	-0.141599721777526	0.141599721777526
7	0	-0.202379956728465	0.202379956728465
8	0	-0.0630611030521655	0.0630611030521655
9	0	-0.163054962988747	0.163054962988747
10	0	-0.127961419916386	0.127961419916386
11	0	-0.154583506305478	0.154583506305478
12	0	-0.173059928282589	0.173059928282589
13	0	0.092073143862506	-0.092073143862506
14	0	0.0670888422057528	-0.0670888422057528
15	0	0.0979906531980796	-0.0979906531980796
16	0	0.0465952518563678	-0.0465952518563678
17	0	0.0409661076425993	-0.0409661076425993
18	0	0.0237941455357358	-0.0237941455357358
19	0	-0.0877120807964054	0.0877120807964054
20	0	-0.0641117295534201	0.0641117295534201
21	0	0.0581863741655331	-0.0581863741655331
22	0	-0.0799472062220622	0.0799472062220622
23	0	0.0617524403647565	-0.0617524403647565
24	0	0.130088012600003	-0.130088012600003
25	0	0.440782653431814	-0.440782653431814
26	0	0.46079722503305	-0.46079722503305
27	0	0.341969861645691	-0.341969861645691
28	0	0.40965807223053	-0.40965807223053
29	0	0.409562877639777	-0.409562877639777
30	0	0.379042005970928	-0.379042005970928
31	0	0.455533983378472	-0.455533983378472
32	0	0.417136133601642	-0.417136133601642
33	0	0.343298136705256	-0.343298136705256
34	0	0.45228414738991	-0.45228414738991
35	0	0.413026945663426	-0.413026945663426
36	0	0.404309603360619	-0.404309603360619
37	1	0.75982496413423	0.24017503586577
38	1	0.69850253255666	0.301497467443339
39	1	0.702944062179934	0.297055937820066
40	1	0.730439437165126	0.269560562834874
41	1	0.735996961074847	0.264003038925153
42	1	0.761603143792678	0.238396856207322
43	1	0.834558054146398	0.165441945853602
44	1	0.710036699003943	0.289963300996057
45	1	0.761570452117958	0.238429547882042
46	1	0.755624478748539	0.244375521251461
47	1	0.679804120277295	0.320195879722705
48	1	0.638662312321966	0.361337687678034
49	1	0.916946605241336	0.0830533947586643
50	1	0.987006129766856	0.0129938702331438
51	1	1.03654046774238	-0.0365404677423810
52	1	1.03616088677599	-0.0361608867759864
53	1	0.908618259115157	0.0913817408848432
54	1	0.977160426478184	0.0228395735218164

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0	0	1
22	0	0	1
23	0	0	1
24	0	0	1
25	0	0	1
26	0	0	1
27	0	0	1
28	0	0	1
29	0	0	1
30	0	0	1
31	0	0	1
32	0	0	1
33	0	0	1

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0 & 0 & 1 \tabularnewline
22 & 0 & 0 & 1 \tabularnewline
23 & 0 & 0 & 1 \tabularnewline
24 & 0 & 0 & 1 \tabularnewline
25 & 0 & 0 & 1 \tabularnewline
26 & 0 & 0 & 1 \tabularnewline
27 & 0 & 0 & 1 \tabularnewline
28 & 0 & 0 & 1 \tabularnewline
29 & 0 & 0 & 1 \tabularnewline
30 & 0 & 0 & 1 \tabularnewline
31 & 0 & 0 & 1 \tabularnewline
32 & 0 & 0 & 1 \tabularnewline
33 & 0 & 0 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58905&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[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]22[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]23[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]24[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]25[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]26[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]27[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]28[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]29[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]30[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]31[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]32[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]33[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58905&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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	0	1
22	0	0	1
23	0	0	1
24	0	0	1
25	0	0	1
26	0	0	1
27	0	0	1
28	0	0	1
29	0	0	1
30	0	0	1
31	0	0	1
32	0	0	1
33	0	0	1

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	13	1	NOK
5% type I error level	13	1	NOK
10% type I error level	13	1	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 & 13 & 1 & NOK \tabularnewline
5% type I error level & 13 & 1 & NOK \tabularnewline
10% type I error level & 13 & 1 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58905&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]13[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]13[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]1[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58905&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58905&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	13	1	NOK
5% type I error level	13	1	NOK
10% type I error level	13	1	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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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