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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 01:50:21 -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/20/t1258707209wb0fv06zi550fe5.htm/, Retrieved Fri, 29 Mar 2024 13:16:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57986, Retrieved Fri, 29 Mar 2024 13:16:09 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [] [2009-11-20 08:50:21] [d5175f34d1f80375edd7cbd8232724fe] [Current]
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Dataseries X:
8.2	267722
8	266003
7.9	262971
7.6	265521
7.6	264676
8.3	270223
8.4	269508
8.4	268457
8.4	265814
8.4	266680
8.6	263018
8.9	269285
8.8	269829
8.3	270911
7.5	266844
7.2	271244
7.4	269907
8.8	271296
9.3	270157
9.3	271322
8.7	267179
8.2	264101
8.3	265518
8.5	269419
8.6	268714
8.5	272482
8.2	268351
8.1	268175
7.9	270674
8.6	272764
8.7	272599
8.7	270333
8.5	270846
8.4	270491
8.5	269160
8.7	274027
8.7	273784
8.6	276663
8.5	274525
8.3	271344
8	271115
8.2	270798
8.1	273911
8.1	273985
8	271917
7.9	273338
7.9	270601
8	273547
8	275363
7.9	281229
8	277793
7.7	279913
7.2	282500
7.5	280041
7.3	282166
7	290304
7	283519
7	287816
7.2	285226
7.3	287595




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&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]4 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=57986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
wkh[t] = + 23.7242314611506 -5.62069109049765e-05los[t] -0.0275271564433608M1[t] -0.0940245016618537M2[t] -0.522924687831299M3[t] -0.698702671431273M4[t] -0.82863197409711M5[t] -0.0983733354658894M6[t] + 0.0178126737747341M7[t] + 0.0259354497915659M8[t] -0.324101697078169M9[t] -0.428680101825853M10[t] -0.408762127383254M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
wkh[t] =  +  23.7242314611506 -5.62069109049765e-05los[t] -0.0275271564433608M1[t] -0.0940245016618537M2[t] -0.522924687831299M3[t] -0.698702671431273M4[t] -0.82863197409711M5[t] -0.0983733354658894M6[t] +  0.0178126737747341M7[t] +  0.0259354497915659M8[t] -0.324101697078169M9[t] -0.428680101825853M10[t] -0.408762127383254M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]wkh[t] =  +  23.7242314611506 -5.62069109049765e-05los[t] -0.0275271564433608M1[t] -0.0940245016618537M2[t] -0.522924687831299M3[t] -0.698702671431273M4[t] -0.82863197409711M5[t] -0.0983733354658894M6[t] +  0.0178126737747341M7[t] +  0.0259354497915659M8[t] -0.324101697078169M9[t] -0.428680101825853M10[t] -0.408762127383254M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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
wkh[t] = + 23.7242314611506 -5.62069109049765e-05los[t] -0.0275271564433608M1[t] -0.0940245016618537M2[t] -0.522924687831299M3[t] -0.698702671431273M4[t] -0.82863197409711M5[t] -0.0983733354658894M6[t] + 0.0178126737747341M7[t] + 0.0259354497915659M8[t] -0.324101697078169M9[t] -0.428680101825853M10[t] -0.408762127383254M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)23.72423146115062.4506199.680900
los-5.62069109049765e-059e-06-6.320100
M1-0.02752715644336080.263103-0.10460.9171190.458559
M2-0.09402450166185370.261309-0.35980.7205920.360296
M3-0.5229246878312990.26434-1.97820.0537810.026891
M4-0.6987026714312730.262932-2.65730.0107270.005363
M5-0.828631974097110.262406-3.15780.0027760.001388
M6-0.09837333546588940.26151-0.37620.708480.35424
M70.01781267377473410.2612310.06820.9459260.472963
M80.02593544979156590.2610480.09940.9212820.460641
M9-0.3241016970781690.262334-1.23550.2228010.111401
M10-0.4286801018258530.261839-1.63720.108270.054135
M11-0.4087621273832540.263543-1.5510.1276040.063802

\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) & 23.7242314611506 & 2.450619 & 9.6809 & 0 & 0 \tabularnewline
los & -5.62069109049765e-05 & 9e-06 & -6.3201 & 0 & 0 \tabularnewline
M1 & -0.0275271564433608 & 0.263103 & -0.1046 & 0.917119 & 0.458559 \tabularnewline
M2 & -0.0940245016618537 & 0.261309 & -0.3598 & 0.720592 & 0.360296 \tabularnewline
M3 & -0.522924687831299 & 0.26434 & -1.9782 & 0.053781 & 0.026891 \tabularnewline
M4 & -0.698702671431273 & 0.262932 & -2.6573 & 0.010727 & 0.005363 \tabularnewline
M5 & -0.82863197409711 & 0.262406 & -3.1578 & 0.002776 & 0.001388 \tabularnewline
M6 & -0.0983733354658894 & 0.26151 & -0.3762 & 0.70848 & 0.35424 \tabularnewline
M7 & 0.0178126737747341 & 0.261231 & 0.0682 & 0.945926 & 0.472963 \tabularnewline
M8 & 0.0259354497915659 & 0.261048 & 0.0994 & 0.921282 & 0.460641 \tabularnewline
M9 & -0.324101697078169 & 0.262334 & -1.2355 & 0.222801 & 0.111401 \tabularnewline
M10 & -0.428680101825853 & 0.261839 & -1.6372 & 0.10827 & 0.054135 \tabularnewline
M11 & -0.408762127383254 & 0.263543 & -1.551 & 0.127604 & 0.063802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&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]23.7242314611506[/C][C]2.450619[/C][C]9.6809[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]los[/C][C]-5.62069109049765e-05[/C][C]9e-06[/C][C]-6.3201[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.0275271564433608[/C][C]0.263103[/C][C]-0.1046[/C][C]0.917119[/C][C]0.458559[/C][/ROW]
[ROW][C]M2[/C][C]-0.0940245016618537[/C][C]0.261309[/C][C]-0.3598[/C][C]0.720592[/C][C]0.360296[/C][/ROW]
[ROW][C]M3[/C][C]-0.522924687831299[/C][C]0.26434[/C][C]-1.9782[/C][C]0.053781[/C][C]0.026891[/C][/ROW]
[ROW][C]M4[/C][C]-0.698702671431273[/C][C]0.262932[/C][C]-2.6573[/C][C]0.010727[/C][C]0.005363[/C][/ROW]
[ROW][C]M5[/C][C]-0.82863197409711[/C][C]0.262406[/C][C]-3.1578[/C][C]0.002776[/C][C]0.001388[/C][/ROW]
[ROW][C]M6[/C][C]-0.0983733354658894[/C][C]0.26151[/C][C]-0.3762[/C][C]0.70848[/C][C]0.35424[/C][/ROW]
[ROW][C]M7[/C][C]0.0178126737747341[/C][C]0.261231[/C][C]0.0682[/C][C]0.945926[/C][C]0.472963[/C][/ROW]
[ROW][C]M8[/C][C]0.0259354497915659[/C][C]0.261048[/C][C]0.0994[/C][C]0.921282[/C][C]0.460641[/C][/ROW]
[ROW][C]M9[/C][C]-0.324101697078169[/C][C]0.262334[/C][C]-1.2355[/C][C]0.222801[/C][C]0.111401[/C][/ROW]
[ROW][C]M10[/C][C]-0.428680101825853[/C][C]0.261839[/C][C]-1.6372[/C][C]0.10827[/C][C]0.054135[/C][/ROW]
[ROW][C]M11[/C][C]-0.408762127383254[/C][C]0.263543[/C][C]-1.551[/C][C]0.127604[/C][C]0.063802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57986&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)23.72423146115062.4506199.680900
los-5.62069109049765e-059e-06-6.320100
M1-0.02752715644336080.263103-0.10460.9171190.458559
M2-0.09402450166185370.261309-0.35980.7205920.360296
M3-0.5229246878312990.26434-1.97820.0537810.026891
M4-0.6987026714312730.262932-2.65730.0107270.005363
M5-0.828631974097110.262406-3.15780.0027760.001388
M6-0.09837333546588940.26151-0.37620.708480.35424
M70.01781267377473410.2612310.06820.9459260.472963
M80.02593544979156590.2610480.09940.9212820.460641
M9-0.3241016970781690.262334-1.23550.2228010.111401
M10-0.4286801018258530.261839-1.63720.108270.054135
M11-0.4087621273832540.263543-1.5510.1276040.063802







Multiple Linear Regression - Regression Statistics
Multiple R0.747816602639393
R-squared0.559229671183124
Adjusted R-squared0.446692565953283
F-TEST (value)4.96929141762602
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value3.04602975735868e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.412749828750751
Sum Squared Residuals8.00703379328739

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.747816602639393 \tabularnewline
R-squared & 0.559229671183124 \tabularnewline
Adjusted R-squared & 0.446692565953283 \tabularnewline
F-TEST (value) & 4.96929141762602 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 3.04602975735868e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.412749828750751 \tabularnewline
Sum Squared Residuals & 8.00703379328739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.747816602639393[/C][/ROW]
[ROW][C]R-squared[/C][C]0.559229671183124[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.446692565953283[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.96929141762602[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]3.04602975735868e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.412749828750751[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8.00703379328739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57986&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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 R0.747816602639393
R-squared0.559229671183124
Adjusted R-squared0.446692565953283
F-TEST (value)4.96929141762602
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value3.04602975735868e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.412749828750751
Sum Squared Residuals8.00703379328739







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
18.28.6488777034051-0.448877703405109
288.67900003803224-0.679000038032239
37.98.42051920572668-0.520519205726682
47.68.10141359931902-0.501413599319018
57.68.01897913636789-0.418979136367885
68.38.4374580402092-0.137458040209200
78.48.59383199074688-0.193831990746883
88.48.66102823012485-0.261028230124845
98.48.45954594877696-0.0595459487769628
108.48.306292359185570.0937076408144305
118.68.53204004136220.0679599586378067
128.98.588553458103960.311446541896041
138.88.530449742128290.269550257871709
148.38.40313651931061-0.103136519310613
157.58.2028298397917-0.702829839791707
167.27.77974144820984-0.579741448209837
177.47.72496078542395-0.324960785423953
188.88.377148024808160.422851975191839
199.38.557353705569550.742646294430447
209.38.499995430382090.800004569617913
218.78.382823515391670.317176484608329
228.28.4512499824095-0.251249982409505
238.38.39152276409975-0.0915227640997506
248.58.5810217320427-0.0810217320426921
258.68.593120447787340.00687955221266002
268.58.31483546227890.185164537721105
278.28.118126025057910.0818739749420914
288.17.952240457777210.147759542222789
297.97.681850084759840.218149915240164
308.68.294636279599660.305363720400343
318.78.42009642913960.279903570860399
328.78.555584065267110.14441593473289
338.58.176712773103120.323287226896879
348.48.09208782172670.307912178273296
358.58.186817194583830.313182805416173
368.78.322020286592560.377979713407439
378.78.308151409499110.391848590500891
388.68.079834367785190.520165632214811
398.57.771104557130580.728895442869417
408.37.774120757119340.525879242880661
4187.657062837050740.342937162949258
428.28.40513906643884-0.205139066438841
438.18.34635296203227-0.246352962032272
448.18.35031642664213-0.250316426642135
4588.1165151715239-0.116515171523891
467.97.93206674638024-0.0320667463802358
477.98.10582303596976-0.205823035969755
4888.34899960382695-0.348999603826949
4988.21940069718015-0.219400697180151
507.97.823193612593070.0768063874069349
5187.587420372293120.412579627706881
527.77.29248373757460.407516262425405
537.27.017147156397580.182852843602416
547.57.88561858894414-0.385618588944142
557.37.88236491251169-0.58236491251169
5677.43307584758382-0.433075847583823
5777.46440259120435-0.464402591204354
5877.11830309029799-0.118303090297986
597.27.28379696398447-0.0837969639844735
607.37.55940491943384-0.259404919433839

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.2 & 8.6488777034051 & -0.448877703405109 \tabularnewline
2 & 8 & 8.67900003803224 & -0.679000038032239 \tabularnewline
3 & 7.9 & 8.42051920572668 & -0.520519205726682 \tabularnewline
4 & 7.6 & 8.10141359931902 & -0.501413599319018 \tabularnewline
5 & 7.6 & 8.01897913636789 & -0.418979136367885 \tabularnewline
6 & 8.3 & 8.4374580402092 & -0.137458040209200 \tabularnewline
7 & 8.4 & 8.59383199074688 & -0.193831990746883 \tabularnewline
8 & 8.4 & 8.66102823012485 & -0.261028230124845 \tabularnewline
9 & 8.4 & 8.45954594877696 & -0.0595459487769628 \tabularnewline
10 & 8.4 & 8.30629235918557 & 0.0937076408144305 \tabularnewline
11 & 8.6 & 8.5320400413622 & 0.0679599586378067 \tabularnewline
12 & 8.9 & 8.58855345810396 & 0.311446541896041 \tabularnewline
13 & 8.8 & 8.53044974212829 & 0.269550257871709 \tabularnewline
14 & 8.3 & 8.40313651931061 & -0.103136519310613 \tabularnewline
15 & 7.5 & 8.2028298397917 & -0.702829839791707 \tabularnewline
16 & 7.2 & 7.77974144820984 & -0.579741448209837 \tabularnewline
17 & 7.4 & 7.72496078542395 & -0.324960785423953 \tabularnewline
18 & 8.8 & 8.37714802480816 & 0.422851975191839 \tabularnewline
19 & 9.3 & 8.55735370556955 & 0.742646294430447 \tabularnewline
20 & 9.3 & 8.49999543038209 & 0.800004569617913 \tabularnewline
21 & 8.7 & 8.38282351539167 & 0.317176484608329 \tabularnewline
22 & 8.2 & 8.4512499824095 & -0.251249982409505 \tabularnewline
23 & 8.3 & 8.39152276409975 & -0.0915227640997506 \tabularnewline
24 & 8.5 & 8.5810217320427 & -0.0810217320426921 \tabularnewline
25 & 8.6 & 8.59312044778734 & 0.00687955221266002 \tabularnewline
26 & 8.5 & 8.3148354622789 & 0.185164537721105 \tabularnewline
27 & 8.2 & 8.11812602505791 & 0.0818739749420914 \tabularnewline
28 & 8.1 & 7.95224045777721 & 0.147759542222789 \tabularnewline
29 & 7.9 & 7.68185008475984 & 0.218149915240164 \tabularnewline
30 & 8.6 & 8.29463627959966 & 0.305363720400343 \tabularnewline
31 & 8.7 & 8.4200964291396 & 0.279903570860399 \tabularnewline
32 & 8.7 & 8.55558406526711 & 0.14441593473289 \tabularnewline
33 & 8.5 & 8.17671277310312 & 0.323287226896879 \tabularnewline
34 & 8.4 & 8.0920878217267 & 0.307912178273296 \tabularnewline
35 & 8.5 & 8.18681719458383 & 0.313182805416173 \tabularnewline
36 & 8.7 & 8.32202028659256 & 0.377979713407439 \tabularnewline
37 & 8.7 & 8.30815140949911 & 0.391848590500891 \tabularnewline
38 & 8.6 & 8.07983436778519 & 0.520165632214811 \tabularnewline
39 & 8.5 & 7.77110455713058 & 0.728895442869417 \tabularnewline
40 & 8.3 & 7.77412075711934 & 0.525879242880661 \tabularnewline
41 & 8 & 7.65706283705074 & 0.342937162949258 \tabularnewline
42 & 8.2 & 8.40513906643884 & -0.205139066438841 \tabularnewline
43 & 8.1 & 8.34635296203227 & -0.246352962032272 \tabularnewline
44 & 8.1 & 8.35031642664213 & -0.250316426642135 \tabularnewline
45 & 8 & 8.1165151715239 & -0.116515171523891 \tabularnewline
46 & 7.9 & 7.93206674638024 & -0.0320667463802358 \tabularnewline
47 & 7.9 & 8.10582303596976 & -0.205823035969755 \tabularnewline
48 & 8 & 8.34899960382695 & -0.348999603826949 \tabularnewline
49 & 8 & 8.21940069718015 & -0.219400697180151 \tabularnewline
50 & 7.9 & 7.82319361259307 & 0.0768063874069349 \tabularnewline
51 & 8 & 7.58742037229312 & 0.412579627706881 \tabularnewline
52 & 7.7 & 7.2924837375746 & 0.407516262425405 \tabularnewline
53 & 7.2 & 7.01714715639758 & 0.182852843602416 \tabularnewline
54 & 7.5 & 7.88561858894414 & -0.385618588944142 \tabularnewline
55 & 7.3 & 7.88236491251169 & -0.58236491251169 \tabularnewline
56 & 7 & 7.43307584758382 & -0.433075847583823 \tabularnewline
57 & 7 & 7.46440259120435 & -0.464402591204354 \tabularnewline
58 & 7 & 7.11830309029799 & -0.118303090297986 \tabularnewline
59 & 7.2 & 7.28379696398447 & -0.0837969639844735 \tabularnewline
60 & 7.3 & 7.55940491943384 & -0.259404919433839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&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]8.2[/C][C]8.6488777034051[/C][C]-0.448877703405109[/C][/ROW]
[ROW][C]2[/C][C]8[/C][C]8.67900003803224[/C][C]-0.679000038032239[/C][/ROW]
[ROW][C]3[/C][C]7.9[/C][C]8.42051920572668[/C][C]-0.520519205726682[/C][/ROW]
[ROW][C]4[/C][C]7.6[/C][C]8.10141359931902[/C][C]-0.501413599319018[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]8.01897913636789[/C][C]-0.418979136367885[/C][/ROW]
[ROW][C]6[/C][C]8.3[/C][C]8.4374580402092[/C][C]-0.137458040209200[/C][/ROW]
[ROW][C]7[/C][C]8.4[/C][C]8.59383199074688[/C][C]-0.193831990746883[/C][/ROW]
[ROW][C]8[/C][C]8.4[/C][C]8.66102823012485[/C][C]-0.261028230124845[/C][/ROW]
[ROW][C]9[/C][C]8.4[/C][C]8.45954594877696[/C][C]-0.0595459487769628[/C][/ROW]
[ROW][C]10[/C][C]8.4[/C][C]8.30629235918557[/C][C]0.0937076408144305[/C][/ROW]
[ROW][C]11[/C][C]8.6[/C][C]8.5320400413622[/C][C]0.0679599586378067[/C][/ROW]
[ROW][C]12[/C][C]8.9[/C][C]8.58855345810396[/C][C]0.311446541896041[/C][/ROW]
[ROW][C]13[/C][C]8.8[/C][C]8.53044974212829[/C][C]0.269550257871709[/C][/ROW]
[ROW][C]14[/C][C]8.3[/C][C]8.40313651931061[/C][C]-0.103136519310613[/C][/ROW]
[ROW][C]15[/C][C]7.5[/C][C]8.2028298397917[/C][C]-0.702829839791707[/C][/ROW]
[ROW][C]16[/C][C]7.2[/C][C]7.77974144820984[/C][C]-0.579741448209837[/C][/ROW]
[ROW][C]17[/C][C]7.4[/C][C]7.72496078542395[/C][C]-0.324960785423953[/C][/ROW]
[ROW][C]18[/C][C]8.8[/C][C]8.37714802480816[/C][C]0.422851975191839[/C][/ROW]
[ROW][C]19[/C][C]9.3[/C][C]8.55735370556955[/C][C]0.742646294430447[/C][/ROW]
[ROW][C]20[/C][C]9.3[/C][C]8.49999543038209[/C][C]0.800004569617913[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.38282351539167[/C][C]0.317176484608329[/C][/ROW]
[ROW][C]22[/C][C]8.2[/C][C]8.4512499824095[/C][C]-0.251249982409505[/C][/ROW]
[ROW][C]23[/C][C]8.3[/C][C]8.39152276409975[/C][C]-0.0915227640997506[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.5810217320427[/C][C]-0.0810217320426921[/C][/ROW]
[ROW][C]25[/C][C]8.6[/C][C]8.59312044778734[/C][C]0.00687955221266002[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.3148354622789[/C][C]0.185164537721105[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.11812602505791[/C][C]0.0818739749420914[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]7.95224045777721[/C][C]0.147759542222789[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]7.68185008475984[/C][C]0.218149915240164[/C][/ROW]
[ROW][C]30[/C][C]8.6[/C][C]8.29463627959966[/C][C]0.305363720400343[/C][/ROW]
[ROW][C]31[/C][C]8.7[/C][C]8.4200964291396[/C][C]0.279903570860399[/C][/ROW]
[ROW][C]32[/C][C]8.7[/C][C]8.55558406526711[/C][C]0.14441593473289[/C][/ROW]
[ROW][C]33[/C][C]8.5[/C][C]8.17671277310312[/C][C]0.323287226896879[/C][/ROW]
[ROW][C]34[/C][C]8.4[/C][C]8.0920878217267[/C][C]0.307912178273296[/C][/ROW]
[ROW][C]35[/C][C]8.5[/C][C]8.18681719458383[/C][C]0.313182805416173[/C][/ROW]
[ROW][C]36[/C][C]8.7[/C][C]8.32202028659256[/C][C]0.377979713407439[/C][/ROW]
[ROW][C]37[/C][C]8.7[/C][C]8.30815140949911[/C][C]0.391848590500891[/C][/ROW]
[ROW][C]38[/C][C]8.6[/C][C]8.07983436778519[/C][C]0.520165632214811[/C][/ROW]
[ROW][C]39[/C][C]8.5[/C][C]7.77110455713058[/C][C]0.728895442869417[/C][/ROW]
[ROW][C]40[/C][C]8.3[/C][C]7.77412075711934[/C][C]0.525879242880661[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]7.65706283705074[/C][C]0.342937162949258[/C][/ROW]
[ROW][C]42[/C][C]8.2[/C][C]8.40513906643884[/C][C]-0.205139066438841[/C][/ROW]
[ROW][C]43[/C][C]8.1[/C][C]8.34635296203227[/C][C]-0.246352962032272[/C][/ROW]
[ROW][C]44[/C][C]8.1[/C][C]8.35031642664213[/C][C]-0.250316426642135[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]8.1165151715239[/C][C]-0.116515171523891[/C][/ROW]
[ROW][C]46[/C][C]7.9[/C][C]7.93206674638024[/C][C]-0.0320667463802358[/C][/ROW]
[ROW][C]47[/C][C]7.9[/C][C]8.10582303596976[/C][C]-0.205823035969755[/C][/ROW]
[ROW][C]48[/C][C]8[/C][C]8.34899960382695[/C][C]-0.348999603826949[/C][/ROW]
[ROW][C]49[/C][C]8[/C][C]8.21940069718015[/C][C]-0.219400697180151[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.82319361259307[/C][C]0.0768063874069349[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]7.58742037229312[/C][C]0.412579627706881[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]7.2924837375746[/C][C]0.407516262425405[/C][/ROW]
[ROW][C]53[/C][C]7.2[/C][C]7.01714715639758[/C][C]0.182852843602416[/C][/ROW]
[ROW][C]54[/C][C]7.5[/C][C]7.88561858894414[/C][C]-0.385618588944142[/C][/ROW]
[ROW][C]55[/C][C]7.3[/C][C]7.88236491251169[/C][C]-0.58236491251169[/C][/ROW]
[ROW][C]56[/C][C]7[/C][C]7.43307584758382[/C][C]-0.433075847583823[/C][/ROW]
[ROW][C]57[/C][C]7[/C][C]7.46440259120435[/C][C]-0.464402591204354[/C][/ROW]
[ROW][C]58[/C][C]7[/C][C]7.11830309029799[/C][C]-0.118303090297986[/C][/ROW]
[ROW][C]59[/C][C]7.2[/C][C]7.28379696398447[/C][C]-0.0837969639844735[/C][/ROW]
[ROW][C]60[/C][C]7.3[/C][C]7.55940491943384[/C][C]-0.259404919433839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57986&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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 IndexActualsInterpolationForecastResidualsPrediction Error
18.28.6488777034051-0.448877703405109
288.67900003803224-0.679000038032239
37.98.42051920572668-0.520519205726682
47.68.10141359931902-0.501413599319018
57.68.01897913636789-0.418979136367885
68.38.4374580402092-0.137458040209200
78.48.59383199074688-0.193831990746883
88.48.66102823012485-0.261028230124845
98.48.45954594877696-0.0595459487769628
108.48.306292359185570.0937076408144305
118.68.53204004136220.0679599586378067
128.98.588553458103960.311446541896041
138.88.530449742128290.269550257871709
148.38.40313651931061-0.103136519310613
157.58.2028298397917-0.702829839791707
167.27.77974144820984-0.579741448209837
177.47.72496078542395-0.324960785423953
188.88.377148024808160.422851975191839
199.38.557353705569550.742646294430447
209.38.499995430382090.800004569617913
218.78.382823515391670.317176484608329
228.28.4512499824095-0.251249982409505
238.38.39152276409975-0.0915227640997506
248.58.5810217320427-0.0810217320426921
258.68.593120447787340.00687955221266002
268.58.31483546227890.185164537721105
278.28.118126025057910.0818739749420914
288.17.952240457777210.147759542222789
297.97.681850084759840.218149915240164
308.68.294636279599660.305363720400343
318.78.42009642913960.279903570860399
328.78.555584065267110.14441593473289
338.58.176712773103120.323287226896879
348.48.09208782172670.307912178273296
358.58.186817194583830.313182805416173
368.78.322020286592560.377979713407439
378.78.308151409499110.391848590500891
388.68.079834367785190.520165632214811
398.57.771104557130580.728895442869417
408.37.774120757119340.525879242880661
4187.657062837050740.342937162949258
428.28.40513906643884-0.205139066438841
438.18.34635296203227-0.246352962032272
448.18.35031642664213-0.250316426642135
4588.1165151715239-0.116515171523891
467.97.93206674638024-0.0320667463802358
477.98.10582303596976-0.205823035969755
4888.34899960382695-0.348999603826949
4988.21940069718015-0.219400697180151
507.97.823193612593070.0768063874069349
5187.587420372293120.412579627706881
527.77.29248373757460.407516262425405
537.27.017147156397580.182852843602416
547.57.88561858894414-0.385618588944142
557.37.88236491251169-0.58236491251169
5677.43307584758382-0.433075847583823
5777.46440259120435-0.464402591204354
5877.11830309029799-0.118303090297986
597.27.28379696398447-0.0837969639844735
607.37.55940491943384-0.259404919433839







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.6105700810410990.7788598379178030.389429918958901
170.4888527096920110.9777054193840210.511147290307989
180.5175609056910020.9648781886179960.482439094308998
190.8067555604828810.3864888790342370.193244439517119
200.9468830332666640.1062339334666730.0531169667333364
210.925320111374930.1493597772501410.0746798886250707
220.9122384519726450.1755230960547110.0877615480273554
230.888695721419760.2226085571604820.111304278580241
240.8615639641461740.2768720717076530.138436035853826
250.8062245758036170.3875508483927660.193775424196383
260.7633680542583090.4732638914833820.236631945741691
270.828601572266160.342796855467680.17139842773384
280.9035529277132680.1928941445734650.0964470722867324
290.873694143070540.2526117138589190.126305856929459
300.8850981135752070.2298037728495870.114901886424793
310.9176394703156070.1647210593687860.082360529684393
320.8884935378291440.2230129243417120.111506462170856
330.9076088008693990.1847823982612030.0923911991306014
340.8707869440780940.2584261118438130.129213055921907
350.8508906887118850.298218622576230.149109311288115
360.9376450180719440.1247099638561130.0623549819280564
370.9813143828150440.03737123436991290.0186856171849565
380.9895506031408140.02089879371837190.0104493968591860
390.9912148852570980.01757022948580410.00878511474290203
400.983539431708690.032921136582620.01646056829131
410.963329906982070.07334018603586020.0366700930179301
420.9292974721761280.1414050556477440.070702527823872
430.9426649843134620.1146700313730750.0573350156865377
440.8930105947717310.2139788104565390.106989405228269

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.610570081041099 & 0.778859837917803 & 0.389429918958901 \tabularnewline
17 & 0.488852709692011 & 0.977705419384021 & 0.511147290307989 \tabularnewline
18 & 0.517560905691002 & 0.964878188617996 & 0.482439094308998 \tabularnewline
19 & 0.806755560482881 & 0.386488879034237 & 0.193244439517119 \tabularnewline
20 & 0.946883033266664 & 0.106233933466673 & 0.0531169667333364 \tabularnewline
21 & 0.92532011137493 & 0.149359777250141 & 0.0746798886250707 \tabularnewline
22 & 0.912238451972645 & 0.175523096054711 & 0.0877615480273554 \tabularnewline
23 & 0.88869572141976 & 0.222608557160482 & 0.111304278580241 \tabularnewline
24 & 0.861563964146174 & 0.276872071707653 & 0.138436035853826 \tabularnewline
25 & 0.806224575803617 & 0.387550848392766 & 0.193775424196383 \tabularnewline
26 & 0.763368054258309 & 0.473263891483382 & 0.236631945741691 \tabularnewline
27 & 0.82860157226616 & 0.34279685546768 & 0.17139842773384 \tabularnewline
28 & 0.903552927713268 & 0.192894144573465 & 0.0964470722867324 \tabularnewline
29 & 0.87369414307054 & 0.252611713858919 & 0.126305856929459 \tabularnewline
30 & 0.885098113575207 & 0.229803772849587 & 0.114901886424793 \tabularnewline
31 & 0.917639470315607 & 0.164721059368786 & 0.082360529684393 \tabularnewline
32 & 0.888493537829144 & 0.223012924341712 & 0.111506462170856 \tabularnewline
33 & 0.907608800869399 & 0.184782398261203 & 0.0923911991306014 \tabularnewline
34 & 0.870786944078094 & 0.258426111843813 & 0.129213055921907 \tabularnewline
35 & 0.850890688711885 & 0.29821862257623 & 0.149109311288115 \tabularnewline
36 & 0.937645018071944 & 0.124709963856113 & 0.0623549819280564 \tabularnewline
37 & 0.981314382815044 & 0.0373712343699129 & 0.0186856171849565 \tabularnewline
38 & 0.989550603140814 & 0.0208987937183719 & 0.0104493968591860 \tabularnewline
39 & 0.991214885257098 & 0.0175702294858041 & 0.00878511474290203 \tabularnewline
40 & 0.98353943170869 & 0.03292113658262 & 0.01646056829131 \tabularnewline
41 & 0.96332990698207 & 0.0733401860358602 & 0.0366700930179301 \tabularnewline
42 & 0.929297472176128 & 0.141405055647744 & 0.070702527823872 \tabularnewline
43 & 0.942664984313462 & 0.114670031373075 & 0.0573350156865377 \tabularnewline
44 & 0.893010594771731 & 0.213978810456539 & 0.106989405228269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&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]16[/C][C]0.610570081041099[/C][C]0.778859837917803[/C][C]0.389429918958901[/C][/ROW]
[ROW][C]17[/C][C]0.488852709692011[/C][C]0.977705419384021[/C][C]0.511147290307989[/C][/ROW]
[ROW][C]18[/C][C]0.517560905691002[/C][C]0.964878188617996[/C][C]0.482439094308998[/C][/ROW]
[ROW][C]19[/C][C]0.806755560482881[/C][C]0.386488879034237[/C][C]0.193244439517119[/C][/ROW]
[ROW][C]20[/C][C]0.946883033266664[/C][C]0.106233933466673[/C][C]0.0531169667333364[/C][/ROW]
[ROW][C]21[/C][C]0.92532011137493[/C][C]0.149359777250141[/C][C]0.0746798886250707[/C][/ROW]
[ROW][C]22[/C][C]0.912238451972645[/C][C]0.175523096054711[/C][C]0.0877615480273554[/C][/ROW]
[ROW][C]23[/C][C]0.88869572141976[/C][C]0.222608557160482[/C][C]0.111304278580241[/C][/ROW]
[ROW][C]24[/C][C]0.861563964146174[/C][C]0.276872071707653[/C][C]0.138436035853826[/C][/ROW]
[ROW][C]25[/C][C]0.806224575803617[/C][C]0.387550848392766[/C][C]0.193775424196383[/C][/ROW]
[ROW][C]26[/C][C]0.763368054258309[/C][C]0.473263891483382[/C][C]0.236631945741691[/C][/ROW]
[ROW][C]27[/C][C]0.82860157226616[/C][C]0.34279685546768[/C][C]0.17139842773384[/C][/ROW]
[ROW][C]28[/C][C]0.903552927713268[/C][C]0.192894144573465[/C][C]0.0964470722867324[/C][/ROW]
[ROW][C]29[/C][C]0.87369414307054[/C][C]0.252611713858919[/C][C]0.126305856929459[/C][/ROW]
[ROW][C]30[/C][C]0.885098113575207[/C][C]0.229803772849587[/C][C]0.114901886424793[/C][/ROW]
[ROW][C]31[/C][C]0.917639470315607[/C][C]0.164721059368786[/C][C]0.082360529684393[/C][/ROW]
[ROW][C]32[/C][C]0.888493537829144[/C][C]0.223012924341712[/C][C]0.111506462170856[/C][/ROW]
[ROW][C]33[/C][C]0.907608800869399[/C][C]0.184782398261203[/C][C]0.0923911991306014[/C][/ROW]
[ROW][C]34[/C][C]0.870786944078094[/C][C]0.258426111843813[/C][C]0.129213055921907[/C][/ROW]
[ROW][C]35[/C][C]0.850890688711885[/C][C]0.29821862257623[/C][C]0.149109311288115[/C][/ROW]
[ROW][C]36[/C][C]0.937645018071944[/C][C]0.124709963856113[/C][C]0.0623549819280564[/C][/ROW]
[ROW][C]37[/C][C]0.981314382815044[/C][C]0.0373712343699129[/C][C]0.0186856171849565[/C][/ROW]
[ROW][C]38[/C][C]0.989550603140814[/C][C]0.0208987937183719[/C][C]0.0104493968591860[/C][/ROW]
[ROW][C]39[/C][C]0.991214885257098[/C][C]0.0175702294858041[/C][C]0.00878511474290203[/C][/ROW]
[ROW][C]40[/C][C]0.98353943170869[/C][C]0.03292113658262[/C][C]0.01646056829131[/C][/ROW]
[ROW][C]41[/C][C]0.96332990698207[/C][C]0.0733401860358602[/C][C]0.0366700930179301[/C][/ROW]
[ROW][C]42[/C][C]0.929297472176128[/C][C]0.141405055647744[/C][C]0.070702527823872[/C][/ROW]
[ROW][C]43[/C][C]0.942664984313462[/C][C]0.114670031373075[/C][C]0.0573350156865377[/C][/ROW]
[ROW][C]44[/C][C]0.893010594771731[/C][C]0.213978810456539[/C][C]0.106989405228269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57986&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.6105700810410990.7788598379178030.389429918958901
170.4888527096920110.9777054193840210.511147290307989
180.5175609056910020.9648781886179960.482439094308998
190.8067555604828810.3864888790342370.193244439517119
200.9468830332666640.1062339334666730.0531169667333364
210.925320111374930.1493597772501410.0746798886250707
220.9122384519726450.1755230960547110.0877615480273554
230.888695721419760.2226085571604820.111304278580241
240.8615639641461740.2768720717076530.138436035853826
250.8062245758036170.3875508483927660.193775424196383
260.7633680542583090.4732638914833820.236631945741691
270.828601572266160.342796855467680.17139842773384
280.9035529277132680.1928941445734650.0964470722867324
290.873694143070540.2526117138589190.126305856929459
300.8850981135752070.2298037728495870.114901886424793
310.9176394703156070.1647210593687860.082360529684393
320.8884935378291440.2230129243417120.111506462170856
330.9076088008693990.1847823982612030.0923911991306014
340.8707869440780940.2584261118438130.129213055921907
350.8508906887118850.298218622576230.149109311288115
360.9376450180719440.1247099638561130.0623549819280564
370.9813143828150440.03737123436991290.0186856171849565
380.9895506031408140.02089879371837190.0104493968591860
390.9912148852570980.01757022948580410.00878511474290203
400.983539431708690.032921136582620.01646056829131
410.963329906982070.07334018603586020.0366700930179301
420.9292974721761280.1414050556477440.070702527823872
430.9426649843134620.1146700313730750.0573350156865377
440.8930105947717310.2139788104565390.106989405228269







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.137931034482759NOK
10% type I error level50.172413793103448NOK

\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 & 4 & 0.137931034482759 & NOK \tabularnewline
10% type I error level & 5 & 0.172413793103448 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57986&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]4[/C][C]0.137931034482759[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.172413793103448[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57986&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57986&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 testsOK/NOK
1% type I error level00OK
5% type I error level40.137931034482759NOK
10% type I error level50.172413793103448NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}