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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 11:19:09 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258654987gd7mvq5uzweomyq.htm/, Retrieved Thu, 14 Aug 2025 07:48:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57876, Retrieved Thu, 14 Aug 2025 07:48:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact343

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2009-11-18 17:09:25] [96d96f181930b548ce74f8c3116c4873]
-   P         [Multiple Regression] [] [2009-11-19 18:19:09] [508aab72d879399b4187e5fcd8f7c773] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.9	1.4
8.8	1.2
8.3	1
7.5	1.7
7.2	2.4
7.4	2
8.8	2.1
9.3	2
9.3	1.8
8.7	2.7
8.2	2.3
8.3	1.9
8.5	2
8.6	2.3
8.5	2.8
8.2	2.4
8.1	2.3
7.9	2.7
8.6	2.7
8.7	2.9
8.7	3
8.5	2.2
8.4	2.3
8.5	2.8
8.7	2.8
8.7	2.8
8.6	2.2
8.5	2.6
8.3	2.8
8	2.5
8.2	2.4
8.1	2.3
8.1	1.9
8	1.7
7.9	2
7.9	2.1
8	1.7
8	1.8
7.9	1.8
8	1.8
7.7	1.3
7.2	1.3
7.5	1.3
7.3	1.2
7	1.4
7	2.2
7	2.9
7.2	3.1
7.3	3.5
7.1	3.6
6.8	4.4
6.4	4.1
6.1	5.1
6.5	5.8
7.7	5.9
7.9	5.4
7.5	5.5
6.9	4.8
6.6	3.2
6.9	2.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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=57876&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=57876&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 8.89484092155787 + 0.000137136588041943X[t] + 0.173170369354539M1[t] + 0.164695099652587M2[t] -0.0237856555128910M3[t] -0.292263667946609M4[t] -0.500766364966173M5[t] -0.54924437739989M6[t] + 0.242285838361675M7[t] + 0.373835253245565M8[t] + 0.265373697202413M9[t] -0.00309334430426069M10[t] -0.171535701225087M11[t] -0.031532958493326t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  8.89484092155787 +  0.000137136588041943X[t] +  0.173170369354539M1[t] +  0.164695099652587M2[t] -0.0237856555128910M3[t] -0.292263667946609M4[t] -0.500766364966173M5[t] -0.54924437739989M6[t] +  0.242285838361675M7[t] +  0.373835253245565M8[t] +  0.265373697202413M9[t] -0.00309334430426069M10[t] -0.171535701225087M11[t] -0.031532958493326t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57876&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  8.89484092155787 +  0.000137136588041943X[t] +  0.173170369354539M1[t] +  0.164695099652587M2[t] -0.0237856555128910M3[t] -0.292263667946609M4[t] -0.500766364966173M5[t] -0.54924437739989M6[t] +  0.242285838361675M7[t] +  0.373835253245565M8[t] +  0.265373697202413M9[t] -0.00309334430426069M10[t] -0.171535701225087M11[t] -0.031532958493326t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57876&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 8.89484092155787 + 0.000137136588041943X[t] + 0.173170369354539M1[t] + 0.164695099652587M2[t] -0.0237856555128910M3[t] -0.292263667946609M4[t] -0.500766364966173M5[t] -0.54924437739989M6[t] + 0.242285838361675M7[t] + 0.373835253245565M8[t] + 0.265373697202413M9[t] -0.00309334430426069M10[t] -0.171535701225087M11[t] -0.031532958493326t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.894840921557870.25554434.807400
X0.0001371365880419430.0637840.00220.9982940.499147
M10.1731703693545390.2977780.58150.5637150.281857
M20.1646950996525870.2973910.55380.5823980.291199
M3-0.02378565551289100.297183-0.080.9365550.468278
M4-0.2922636679466090.296986-0.98410.3302140.165107
M5-0.5007663649661730.297925-1.68080.0995710.049786
M6-0.549244377399890.297965-1.84330.071730.035865
M70.2422858383616750.2975960.81410.4197580.209879
M80.3738352532455650.296391.26130.2135620.106781
M90.2653736972024130.2958650.89690.374420.18721
M10-0.003093344304260690.295605-0.01050.9916960.495848
M11-0.1715357012250870.295041-0.58140.5638120.281906
t-0.0315329584933260.004289-7.351900

\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) & 8.89484092155787 & 0.255544 & 34.8074 & 0 & 0 \tabularnewline
X & 0.000137136588041943 & 0.063784 & 0.0022 & 0.998294 & 0.499147 \tabularnewline
M1 & 0.173170369354539 & 0.297778 & 0.5815 & 0.563715 & 0.281857 \tabularnewline
M2 & 0.164695099652587 & 0.297391 & 0.5538 & 0.582398 & 0.291199 \tabularnewline
M3 & -0.0237856555128910 & 0.297183 & -0.08 & 0.936555 & 0.468278 \tabularnewline
M4 & -0.292263667946609 & 0.296986 & -0.9841 & 0.330214 & 0.165107 \tabularnewline
M5 & -0.500766364966173 & 0.297925 & -1.6808 & 0.099571 & 0.049786 \tabularnewline
M6 & -0.54924437739989 & 0.297965 & -1.8433 & 0.07173 & 0.035865 \tabularnewline
M7 & 0.242285838361675 & 0.297596 & 0.8141 & 0.419758 & 0.209879 \tabularnewline
M8 & 0.373835253245565 & 0.29639 & 1.2613 & 0.213562 & 0.106781 \tabularnewline
M9 & 0.265373697202413 & 0.295865 & 0.8969 & 0.37442 & 0.18721 \tabularnewline
M10 & -0.00309334430426069 & 0.295605 & -0.0105 & 0.991696 & 0.495848 \tabularnewline
M11 & -0.171535701225087 & 0.295041 & -0.5814 & 0.563812 & 0.281906 \tabularnewline
t & -0.031532958493326 & 0.004289 & -7.3519 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57876&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]8.89484092155787[/C][C]0.255544[/C][C]34.8074[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.000137136588041943[/C][C]0.063784[/C][C]0.0022[/C][C]0.998294[/C][C]0.499147[/C][/ROW]
[ROW][C]M1[/C][C]0.173170369354539[/C][C]0.297778[/C][C]0.5815[/C][C]0.563715[/C][C]0.281857[/C][/ROW]
[ROW][C]M2[/C][C]0.164695099652587[/C][C]0.297391[/C][C]0.5538[/C][C]0.582398[/C][C]0.291199[/C][/ROW]
[ROW][C]M3[/C][C]-0.0237856555128910[/C][C]0.297183[/C][C]-0.08[/C][C]0.936555[/C][C]0.468278[/C][/ROW]
[ROW][C]M4[/C][C]-0.292263667946609[/C][C]0.296986[/C][C]-0.9841[/C][C]0.330214[/C][C]0.165107[/C][/ROW]
[ROW][C]M5[/C][C]-0.500766364966173[/C][C]0.297925[/C][C]-1.6808[/C][C]0.099571[/C][C]0.049786[/C][/ROW]
[ROW][C]M6[/C][C]-0.54924437739989[/C][C]0.297965[/C][C]-1.8433[/C][C]0.07173[/C][C]0.035865[/C][/ROW]
[ROW][C]M7[/C][C]0.242285838361675[/C][C]0.297596[/C][C]0.8141[/C][C]0.419758[/C][C]0.209879[/C][/ROW]
[ROW][C]M8[/C][C]0.373835253245565[/C][C]0.29639[/C][C]1.2613[/C][C]0.213562[/C][C]0.106781[/C][/ROW]
[ROW][C]M9[/C][C]0.265373697202413[/C][C]0.295865[/C][C]0.8969[/C][C]0.37442[/C][C]0.18721[/C][/ROW]
[ROW][C]M10[/C][C]-0.00309334430426069[/C][C]0.295605[/C][C]-0.0105[/C][C]0.991696[/C][C]0.495848[/C][/ROW]
[ROW][C]M11[/C][C]-0.171535701225087[/C][C]0.295041[/C][C]-0.5814[/C][C]0.563812[/C][C]0.281906[/C][/ROW]
[ROW][C]t[/C][C]-0.031532958493326[/C][C]0.004289[/C][C]-7.3519[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57876&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.894840921557870.25554434.807400
X0.0001371365880419430.0637840.00220.9982940.499147
M10.1731703693545390.2977780.58150.5637150.281857
M20.1646950996525870.2973910.55380.5823980.291199
M3-0.02378565551289100.297183-0.080.9365550.468278
M4-0.2922636679466090.296986-0.98410.3302140.165107
M5-0.5007663649661730.297925-1.68080.0995710.049786
M6-0.549244377399890.297965-1.84330.071730.035865
M70.2422858383616750.2975960.81410.4197580.209879
M80.3738352532455650.296391.26130.2135620.106781
M90.2653736972024130.2958650.89690.374420.18721
M10-0.003093344304260690.295605-0.01050.9916960.495848
M11-0.1715357012250870.295041-0.58140.5638120.281906
t-0.0315329584933260.004289-7.351900






Multiple Linear Regression - Regression Statistics
Multiple R0.832460976610311
R-squared0.692991277578994
Adjusted R-squared0.606227942981753
F-TEST (value)7.98714434842653
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value5.19511160756991e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.466431076529146
Sum Squared Residuals10.0076656609984

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.832460976610311 \tabularnewline
R-squared & 0.692991277578994 \tabularnewline
Adjusted R-squared & 0.606227942981753 \tabularnewline
F-TEST (value) & 7.98714434842653 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 5.19511160756991e-08 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.466431076529146 \tabularnewline
Sum Squared Residuals & 10.0076656609984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57876&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.832460976610311[/C][/ROW]
[ROW][C]R-squared[/C][C]0.692991277578994[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.606227942981753[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]7.98714434842653[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]5.19511160756991e-08[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.466431076529146[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]10.0076656609984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57876&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.832460976610311
R-squared0.692991277578994
Adjusted R-squared0.606227942981753
F-TEST (value)7.98714434842653
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value5.19511160756991e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.466431076529146
Sum Squared Residuals10.0076656609984






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.99.03667032364237-0.136670323642367
28.88.99663466812946-0.196634668129456
38.38.77659352715304-0.476593527153044
47.58.47667855183763-0.97667855183763
57.28.23673889193637-1.03673889193637
67.48.1566730663741-0.756673066374107
78.88.91668403730115-0.116684037301150
89.39.016686780032910.283313219967088
99.38.876664838178830.423335161821176
108.78.576788261108060.123211738891937
118.28.3767580910587-0.176758091058695
128.38.51670597915524-0.216705979155237
138.58.65835710367526-0.158357103675255
148.68.61839001645639-0.0183900164563883
158.58.39844487109160.101555128908393
168.28.098379045529350.101620954470652
178.17.858329676357650.241670323642348
187.97.778373560065830.121626439934175
198.68.538370817334060.0616291826659352
208.78.638414701042240.0615852989577617
218.78.498433900164560.201566099835436
228.58.198324190894130.30167580910587
238.47.998362589138780.401637410861218
248.58.138433900164560.361566099835436
258.78.280071311025780.419928688974223
268.78.24006308283050.4599369171695
278.68.019967087218870.580032912781129
288.57.720010970927040.779989029072957
298.37.480002742731760.81999725726824
3087.39995063082830.600049369171695
318.28.159934174437740.0400658255622591
328.18.2599369171695-0.159936917169501
338.18.1198875479978-0.0198875479978061
3487.81986012068020.180139879319803
357.97.619925946242460.280074053757543
367.97.759942402633020.140057597366978
3787.901524958859020.0984750411409812
3887.861530444322550.138469555677454
397.97.641516730663740.258483269336259
4087.34150575973670.658494240263302
417.77.101401535929790.598598464070213
427.27.021390565002740.178609434997257
437.57.78138782227098-0.281387822270982
447.37.88139056500274-0.581390565002743
4577.74142347778387-0.741423477783873
4677.44153318705431-0.441533187054307
4777.24165386725178-0.241653867251783
487.27.38168403730115-0.181684037301152
497.37.52337630279758-0.223376302797582
507.17.48338178826111-0.383381788261109
516.87.26347778387274-0.463477783872738
526.46.96342567196928-0.563425671969282
536.16.72352715304443-0.623527153044434
546.56.64361217772902-0.143612177729019
557.77.403623148656060.296376851343938
567.97.50357103675260.396428963247394
577.57.363590235874930.136409764125068
586.97.0634942402633-0.163494240263303
596.66.86329950630828-0.263299506308284
606.97.00323368074602-0.103233680746024

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.9 & 9.03667032364237 & -0.136670323642367 \tabularnewline
2 & 8.8 & 8.99663466812946 & -0.196634668129456 \tabularnewline
3 & 8.3 & 8.77659352715304 & -0.476593527153044 \tabularnewline
4 & 7.5 & 8.47667855183763 & -0.97667855183763 \tabularnewline
5 & 7.2 & 8.23673889193637 & -1.03673889193637 \tabularnewline
6 & 7.4 & 8.1566730663741 & -0.756673066374107 \tabularnewline
7 & 8.8 & 8.91668403730115 & -0.116684037301150 \tabularnewline
8 & 9.3 & 9.01668678003291 & 0.283313219967088 \tabularnewline
9 & 9.3 & 8.87666483817883 & 0.423335161821176 \tabularnewline
10 & 8.7 & 8.57678826110806 & 0.123211738891937 \tabularnewline
11 & 8.2 & 8.3767580910587 & -0.176758091058695 \tabularnewline
12 & 8.3 & 8.51670597915524 & -0.216705979155237 \tabularnewline
13 & 8.5 & 8.65835710367526 & -0.158357103675255 \tabularnewline
14 & 8.6 & 8.61839001645639 & -0.0183900164563883 \tabularnewline
15 & 8.5 & 8.3984448710916 & 0.101555128908393 \tabularnewline
16 & 8.2 & 8.09837904552935 & 0.101620954470652 \tabularnewline
17 & 8.1 & 7.85832967635765 & 0.241670323642348 \tabularnewline
18 & 7.9 & 7.77837356006583 & 0.121626439934175 \tabularnewline
19 & 8.6 & 8.53837081733406 & 0.0616291826659352 \tabularnewline
20 & 8.7 & 8.63841470104224 & 0.0615852989577617 \tabularnewline
21 & 8.7 & 8.49843390016456 & 0.201566099835436 \tabularnewline
22 & 8.5 & 8.19832419089413 & 0.30167580910587 \tabularnewline
23 & 8.4 & 7.99836258913878 & 0.401637410861218 \tabularnewline
24 & 8.5 & 8.13843390016456 & 0.361566099835436 \tabularnewline
25 & 8.7 & 8.28007131102578 & 0.419928688974223 \tabularnewline
26 & 8.7 & 8.2400630828305 & 0.4599369171695 \tabularnewline
27 & 8.6 & 8.01996708721887 & 0.580032912781129 \tabularnewline
28 & 8.5 & 7.72001097092704 & 0.779989029072957 \tabularnewline
29 & 8.3 & 7.48000274273176 & 0.81999725726824 \tabularnewline
30 & 8 & 7.3999506308283 & 0.600049369171695 \tabularnewline
31 & 8.2 & 8.15993417443774 & 0.0400658255622591 \tabularnewline
32 & 8.1 & 8.2599369171695 & -0.159936917169501 \tabularnewline
33 & 8.1 & 8.1198875479978 & -0.0198875479978061 \tabularnewline
34 & 8 & 7.8198601206802 & 0.180139879319803 \tabularnewline
35 & 7.9 & 7.61992594624246 & 0.280074053757543 \tabularnewline
36 & 7.9 & 7.75994240263302 & 0.140057597366978 \tabularnewline
37 & 8 & 7.90152495885902 & 0.0984750411409812 \tabularnewline
38 & 8 & 7.86153044432255 & 0.138469555677454 \tabularnewline
39 & 7.9 & 7.64151673066374 & 0.258483269336259 \tabularnewline
40 & 8 & 7.3415057597367 & 0.658494240263302 \tabularnewline
41 & 7.7 & 7.10140153592979 & 0.598598464070213 \tabularnewline
42 & 7.2 & 7.02139056500274 & 0.178609434997257 \tabularnewline
43 & 7.5 & 7.78138782227098 & -0.281387822270982 \tabularnewline
44 & 7.3 & 7.88139056500274 & -0.581390565002743 \tabularnewline
45 & 7 & 7.74142347778387 & -0.741423477783873 \tabularnewline
46 & 7 & 7.44153318705431 & -0.441533187054307 \tabularnewline
47 & 7 & 7.24165386725178 & -0.241653867251783 \tabularnewline
48 & 7.2 & 7.38168403730115 & -0.181684037301152 \tabularnewline
49 & 7.3 & 7.52337630279758 & -0.223376302797582 \tabularnewline
50 & 7.1 & 7.48338178826111 & -0.383381788261109 \tabularnewline
51 & 6.8 & 7.26347778387274 & -0.463477783872738 \tabularnewline
52 & 6.4 & 6.96342567196928 & -0.563425671969282 \tabularnewline
53 & 6.1 & 6.72352715304443 & -0.623527153044434 \tabularnewline
54 & 6.5 & 6.64361217772902 & -0.143612177729019 \tabularnewline
55 & 7.7 & 7.40362314865606 & 0.296376851343938 \tabularnewline
56 & 7.9 & 7.5035710367526 & 0.396428963247394 \tabularnewline
57 & 7.5 & 7.36359023587493 & 0.136409764125068 \tabularnewline
58 & 6.9 & 7.0634942402633 & -0.163494240263303 \tabularnewline
59 & 6.6 & 6.86329950630828 & -0.263299506308284 \tabularnewline
60 & 6.9 & 7.00323368074602 & -0.103233680746024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57876&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]8.9[/C][C]9.03667032364237[/C][C]-0.136670323642367[/C][/ROW]
[ROW][C]2[/C][C]8.8[/C][C]8.99663466812946[/C][C]-0.196634668129456[/C][/ROW]
[ROW][C]3[/C][C]8.3[/C][C]8.77659352715304[/C][C]-0.476593527153044[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]8.47667855183763[/C][C]-0.97667855183763[/C][/ROW]
[ROW][C]5[/C][C]7.2[/C][C]8.23673889193637[/C][C]-1.03673889193637[/C][/ROW]
[ROW][C]6[/C][C]7.4[/C][C]8.1566730663741[/C][C]-0.756673066374107[/C][/ROW]
[ROW][C]7[/C][C]8.8[/C][C]8.91668403730115[/C][C]-0.116684037301150[/C][/ROW]
[ROW][C]8[/C][C]9.3[/C][C]9.01668678003291[/C][C]0.283313219967088[/C][/ROW]
[ROW][C]9[/C][C]9.3[/C][C]8.87666483817883[/C][C]0.423335161821176[/C][/ROW]
[ROW][C]10[/C][C]8.7[/C][C]8.57678826110806[/C][C]0.123211738891937[/C][/ROW]
[ROW][C]11[/C][C]8.2[/C][C]8.3767580910587[/C][C]-0.176758091058695[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.51670597915524[/C][C]-0.216705979155237[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.65835710367526[/C][C]-0.158357103675255[/C][/ROW]
[ROW][C]14[/C][C]8.6[/C][C]8.61839001645639[/C][C]-0.0183900164563883[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]8.3984448710916[/C][C]0.101555128908393[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]8.09837904552935[/C][C]0.101620954470652[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]7.85832967635765[/C][C]0.241670323642348[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.77837356006583[/C][C]0.121626439934175[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]8.53837081733406[/C][C]0.0616291826659352[/C][/ROW]
[ROW][C]20[/C][C]8.7[/C][C]8.63841470104224[/C][C]0.0615852989577617[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.49843390016456[/C][C]0.201566099835436[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.19832419089413[/C][C]0.30167580910587[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]7.99836258913878[/C][C]0.401637410861218[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.13843390016456[/C][C]0.361566099835436[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.28007131102578[/C][C]0.419928688974223[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.2400630828305[/C][C]0.4599369171695[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.01996708721887[/C][C]0.580032912781129[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]7.72001097092704[/C][C]0.779989029072957[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]7.48000274273176[/C][C]0.81999725726824[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.3999506308283[/C][C]0.600049369171695[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.15993417443774[/C][C]0.0400658255622591[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.2599369171695[/C][C]-0.159936917169501[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.1198875479978[/C][C]-0.0198875479978061[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.8198601206802[/C][C]0.180139879319803[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.61992594624246[/C][C]0.280074053757543[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.75994240263302[/C][C]0.140057597366978[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]7.90152495885902[/C][C]0.0984750411409812[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.86153044432255[/C][C]0.138469555677454[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.64151673066374[/C][C]0.258483269336259[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.3415057597367[/C][C]0.658494240263302[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]7.10140153592979[/C][C]0.598598464070213[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]7.02139056500274[/C][C]0.178609434997257[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.78138782227098[/C][C]-0.281387822270982[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]7.88139056500274[/C][C]-0.581390565002743[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.74142347778387[/C][C]-0.741423477783873[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]7.44153318705431[/C][C]-0.441533187054307[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]7.24165386725178[/C][C]-0.241653867251783[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.38168403730115[/C][C]-0.181684037301152[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.52337630279758[/C][C]-0.223376302797582[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.48338178826111[/C][C]-0.383381788261109[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]7.26347778387274[/C][C]-0.463477783872738[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]6.96342567196928[/C][C]-0.563425671969282[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]6.72352715304443[/C][C]-0.623527153044434[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.64361217772902[/C][C]-0.143612177729019[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.40362314865606[/C][C]0.296376851343938[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]7.5035710367526[/C][C]0.396428963247394[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]7.36359023587493[/C][C]0.136409764125068[/C][/ROW]
[ROW][C]58[/C][C]6.9[/C][C]7.0634942402633[/C][C]-0.163494240263303[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]6.86329950630828[/C][C]-0.263299506308284[/C][/ROW]
[ROW][C]60[/C][C]6.9[/C][C]7.00323368074602[/C][C]-0.103233680746024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57876&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.99.03667032364237-0.136670323642367
28.88.99663466812946-0.196634668129456
38.38.77659352715304-0.476593527153044
47.58.47667855183763-0.97667855183763
57.28.23673889193637-1.03673889193637
67.48.1566730663741-0.756673066374107
78.88.91668403730115-0.116684037301150
89.39.016686780032910.283313219967088
99.38.876664838178830.423335161821176
108.78.576788261108060.123211738891937
118.28.3767580910587-0.176758091058695
128.38.51670597915524-0.216705979155237
138.58.65835710367526-0.158357103675255
148.68.61839001645639-0.0183900164563883
158.58.39844487109160.101555128908393
168.28.098379045529350.101620954470652
178.17.858329676357650.241670323642348
187.97.778373560065830.121626439934175
198.68.538370817334060.0616291826659352
208.78.638414701042240.0615852989577617
218.78.498433900164560.201566099835436
228.58.198324190894130.30167580910587
238.47.998362589138780.401637410861218
248.58.138433900164560.361566099835436
258.78.280071311025780.419928688974223
268.78.24006308283050.4599369171695
278.68.019967087218870.580032912781129
288.57.720010970927040.779989029072957
298.37.480002742731760.81999725726824
3087.39995063082830.600049369171695
318.28.159934174437740.0400658255622591
328.18.2599369171695-0.159936917169501
338.18.1198875479978-0.0198875479978061
3487.81986012068020.180139879319803
357.97.619925946242460.280074053757543
367.97.759942402633020.140057597366978
3787.901524958859020.0984750411409812
3887.861530444322550.138469555677454
397.97.641516730663740.258483269336259
4087.34150575973670.658494240263302
417.77.101401535929790.598598464070213
427.27.021390565002740.178609434997257
437.57.78138782227098-0.281387822270982
447.37.88139056500274-0.581390565002743
4577.74142347778387-0.741423477783873
4677.44153318705431-0.441533187054307
4777.24165386725178-0.241653867251783
487.27.38168403730115-0.181684037301152
497.37.52337630279758-0.223376302797582
507.17.48338178826111-0.383381788261109
516.87.26347778387274-0.463477783872738
526.46.96342567196928-0.563425671969282
536.16.72352715304443-0.623527153044434
546.56.64361217772902-0.143612177729019
557.77.403623148656060.296376851343938
567.97.50357103675260.396428963247394
577.57.363590235874930.136409764125068
586.97.0634942402633-0.163494240263303
596.66.86329950630828-0.263299506308284
606.97.00323368074602-0.103233680746024






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.6880701334701620.6238597330596760.311929866529838
180.5724059224699460.8551881550601080.427594077530054
190.5624950984049880.8750098031900230.437504901595012
200.6411042693020080.7177914613959850.358895730697992
210.6072778889916880.7854442220166230.392722111008312
220.596503064436830.8069938711263390.403496935563170
230.4844231816351390.9688463632702770.515576818364861
240.3984875355536920.7969750711073850.601512464446308
250.2972679573902870.5945359147805740.702732042609713
260.2105298158000160.4210596316000310.789470184199984
270.1459060892050610.2918121784101220.854093910794939
280.1392108895187380.2784217790374770.860789110481262
290.1248167486305880.2496334972611750.875183251369412
300.08321247385903640.1664249477180730.916787526140964
310.1355221976186330.2710443952372660.864477802381367
320.2607004273978510.5214008547957010.73929957260215
330.2763330782253250.552666156450650.723666921774675
340.2097550438771910.4195100877543830.790244956122809
350.1460456700865400.2920913401730810.85395432991346
360.1002676450050110.2005352900100230.899732354994989
370.06626165516632780.1325233103326560.933738344833672
380.04373035595489410.08746071190978820.956269644045106
390.03369012807265720.06738025614531430.966309871927343
400.08244185248668060.1648837049733610.91755814751332
410.540532153495160.918935693009680.45946784650484
420.9444404996043160.1111190007913680.0555595003956839
430.9341425398431720.1317149203136570.0658574601568284

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.688070133470162 & 0.623859733059676 & 0.311929866529838 \tabularnewline
18 & 0.572405922469946 & 0.855188155060108 & 0.427594077530054 \tabularnewline
19 & 0.562495098404988 & 0.875009803190023 & 0.437504901595012 \tabularnewline
20 & 0.641104269302008 & 0.717791461395985 & 0.358895730697992 \tabularnewline
21 & 0.607277888991688 & 0.785444222016623 & 0.392722111008312 \tabularnewline
22 & 0.59650306443683 & 0.806993871126339 & 0.403496935563170 \tabularnewline
23 & 0.484423181635139 & 0.968846363270277 & 0.515576818364861 \tabularnewline
24 & 0.398487535553692 & 0.796975071107385 & 0.601512464446308 \tabularnewline
25 & 0.297267957390287 & 0.594535914780574 & 0.702732042609713 \tabularnewline
26 & 0.210529815800016 & 0.421059631600031 & 0.789470184199984 \tabularnewline
27 & 0.145906089205061 & 0.291812178410122 & 0.854093910794939 \tabularnewline
28 & 0.139210889518738 & 0.278421779037477 & 0.860789110481262 \tabularnewline
29 & 0.124816748630588 & 0.249633497261175 & 0.875183251369412 \tabularnewline
30 & 0.0832124738590364 & 0.166424947718073 & 0.916787526140964 \tabularnewline
31 & 0.135522197618633 & 0.271044395237266 & 0.864477802381367 \tabularnewline
32 & 0.260700427397851 & 0.521400854795701 & 0.73929957260215 \tabularnewline
33 & 0.276333078225325 & 0.55266615645065 & 0.723666921774675 \tabularnewline
34 & 0.209755043877191 & 0.419510087754383 & 0.790244956122809 \tabularnewline
35 & 0.146045670086540 & 0.292091340173081 & 0.85395432991346 \tabularnewline
36 & 0.100267645005011 & 0.200535290010023 & 0.899732354994989 \tabularnewline
37 & 0.0662616551663278 & 0.132523310332656 & 0.933738344833672 \tabularnewline
38 & 0.0437303559548941 & 0.0874607119097882 & 0.956269644045106 \tabularnewline
39 & 0.0336901280726572 & 0.0673802561453143 & 0.966309871927343 \tabularnewline
40 & 0.0824418524866806 & 0.164883704973361 & 0.91755814751332 \tabularnewline
41 & 0.54053215349516 & 0.91893569300968 & 0.45946784650484 \tabularnewline
42 & 0.944440499604316 & 0.111119000791368 & 0.0555595003956839 \tabularnewline
43 & 0.934142539843172 & 0.131714920313657 & 0.0658574601568284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57876&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]17[/C][C]0.688070133470162[/C][C]0.623859733059676[/C][C]0.311929866529838[/C][/ROW]
[ROW][C]18[/C][C]0.572405922469946[/C][C]0.855188155060108[/C][C]0.427594077530054[/C][/ROW]
[ROW][C]19[/C][C]0.562495098404988[/C][C]0.875009803190023[/C][C]0.437504901595012[/C][/ROW]
[ROW][C]20[/C][C]0.641104269302008[/C][C]0.717791461395985[/C][C]0.358895730697992[/C][/ROW]
[ROW][C]21[/C][C]0.607277888991688[/C][C]0.785444222016623[/C][C]0.392722111008312[/C][/ROW]
[ROW][C]22[/C][C]0.59650306443683[/C][C]0.806993871126339[/C][C]0.403496935563170[/C][/ROW]
[ROW][C]23[/C][C]0.484423181635139[/C][C]0.968846363270277[/C][C]0.515576818364861[/C][/ROW]
[ROW][C]24[/C][C]0.398487535553692[/C][C]0.796975071107385[/C][C]0.601512464446308[/C][/ROW]
[ROW][C]25[/C][C]0.297267957390287[/C][C]0.594535914780574[/C][C]0.702732042609713[/C][/ROW]
[ROW][C]26[/C][C]0.210529815800016[/C][C]0.421059631600031[/C][C]0.789470184199984[/C][/ROW]
[ROW][C]27[/C][C]0.145906089205061[/C][C]0.291812178410122[/C][C]0.854093910794939[/C][/ROW]
[ROW][C]28[/C][C]0.139210889518738[/C][C]0.278421779037477[/C][C]0.860789110481262[/C][/ROW]
[ROW][C]29[/C][C]0.124816748630588[/C][C]0.249633497261175[/C][C]0.875183251369412[/C][/ROW]
[ROW][C]30[/C][C]0.0832124738590364[/C][C]0.166424947718073[/C][C]0.916787526140964[/C][/ROW]
[ROW][C]31[/C][C]0.135522197618633[/C][C]0.271044395237266[/C][C]0.864477802381367[/C][/ROW]
[ROW][C]32[/C][C]0.260700427397851[/C][C]0.521400854795701[/C][C]0.73929957260215[/C][/ROW]
[ROW][C]33[/C][C]0.276333078225325[/C][C]0.55266615645065[/C][C]0.723666921774675[/C][/ROW]
[ROW][C]34[/C][C]0.209755043877191[/C][C]0.419510087754383[/C][C]0.790244956122809[/C][/ROW]
[ROW][C]35[/C][C]0.146045670086540[/C][C]0.292091340173081[/C][C]0.85395432991346[/C][/ROW]
[ROW][C]36[/C][C]0.100267645005011[/C][C]0.200535290010023[/C][C]0.899732354994989[/C][/ROW]
[ROW][C]37[/C][C]0.0662616551663278[/C][C]0.132523310332656[/C][C]0.933738344833672[/C][/ROW]
[ROW][C]38[/C][C]0.0437303559548941[/C][C]0.0874607119097882[/C][C]0.956269644045106[/C][/ROW]
[ROW][C]39[/C][C]0.0336901280726572[/C][C]0.0673802561453143[/C][C]0.966309871927343[/C][/ROW]
[ROW][C]40[/C][C]0.0824418524866806[/C][C]0.164883704973361[/C][C]0.91755814751332[/C][/ROW]
[ROW][C]41[/C][C]0.54053215349516[/C][C]0.91893569300968[/C][C]0.45946784650484[/C][/ROW]
[ROW][C]42[/C][C]0.944440499604316[/C][C]0.111119000791368[/C][C]0.0555595003956839[/C][/ROW]
[ROW][C]43[/C][C]0.934142539843172[/C][C]0.131714920313657[/C][C]0.0658574601568284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57876&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.6880701334701620.6238597330596760.311929866529838
180.5724059224699460.8551881550601080.427594077530054
190.5624950984049880.8750098031900230.437504901595012
200.6411042693020080.7177914613959850.358895730697992
210.6072778889916880.7854442220166230.392722111008312
220.596503064436830.8069938711263390.403496935563170
230.4844231816351390.9688463632702770.515576818364861
240.3984875355536920.7969750711073850.601512464446308
250.2972679573902870.5945359147805740.702732042609713
260.2105298158000160.4210596316000310.789470184199984
270.1459060892050610.2918121784101220.854093910794939
280.1392108895187380.2784217790374770.860789110481262
290.1248167486305880.2496334972611750.875183251369412
300.08321247385903640.1664249477180730.916787526140964
310.1355221976186330.2710443952372660.864477802381367
320.2607004273978510.5214008547957010.73929957260215
330.2763330782253250.552666156450650.723666921774675
340.2097550438771910.4195100877543830.790244956122809
350.1460456700865400.2920913401730810.85395432991346
360.1002676450050110.2005352900100230.899732354994989
370.06626165516632780.1325233103326560.933738344833672
380.04373035595489410.08746071190978820.956269644045106
390.03369012807265720.06738025614531430.966309871927343
400.08244185248668060.1648837049733610.91755814751332
410.540532153495160.918935693009680.45946784650484
420.9444404996043160.1111190007913680.0555595003956839
430.9341425398431720.1317149203136570.0658574601568284






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level20.0740740740740741OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 2 & 0.0740740740740741 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57876&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]2[/C][C]0.0740740740740741[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57876&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57876&T=6

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


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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level20.0740740740740741OK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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Input Parameters & R Code

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