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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 computationTue, 17 Nov 2009 12:42:44 -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/17/t1258487199feun5ahojdntqdp.htm/, Retrieved Thu, 02 May 2024 07:51:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57417, Retrieved Thu, 02 May 2024 07:51:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJSSHWWS7P4
Estimated Impact171

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [Multuple regression] [2009-11-17 19:42:44] [c8fd62404619100d8e91184019148412] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,2	7,6	9,2	10	10,9	11,1
9,5	7,8	9,2	9,2	10	10,9
9,6	7,8	9,5	9,2	9,2	10
9,5	7,8	9,6	9,5	9,2	9,2
9,1	7,5	9,5	9,6	9,5	9,2
8,9	7,5	9,1	9,5	9,6	9,5
9	7,1	8,9	9,1	9,5	9,6
10,1	7,5	9	8,9	9,1	9,5
10,3	7,5	10,1	9	8,9	9,1
10,2	7,6	10,3	10,1	9	8,9
9,6	7,7	10,2	10,3	10,1	9
9,2	7,7	9,6	10,2	10,3	10,1
9,3	7,9	9,2	9,6	10,2	10,3
9,4	8,1	9,3	9,2	9,6	10,2
9,4	8,2	9,4	9,3	9,2	9,6
9,2	8,2	9,4	9,4	9,3	9,2
9	8,2	9,2	9,4	9,4	9,3
9	7,9	9	9,2	9,4	9,4
9	7,3	9	9	9,2	9,4
9,8	6,9	9	9	9	9,2
10	6,6	9,8	9	9	9
9,8	6,7	10	9,8	9	9
9,3	6,9	9,8	10	9,8	9
9	7	9,3	9,8	10	9,8
9	7,1	9	9,3	9,8	10
9,1	7,2	9	9	9,3	9,8
9,1	7,1	9,1	9	9	9,3
9,1	6,9	9,1	9,1	9	9
9,2	7	9,1	9,1	9,1	9
8,8	6,8	9,2	9,1	9,1	9,1
8,3	6,4	8,8	9,2	9,1	9,1
8,4	6,7	8,3	8,8	9,2	9,1
8,1	6,6	8,4	8,3	8,8	9,2
7,7	6,4	8,1	8,4	8,3	8,8
7,9	6,3	7,7	8,1	8,4	8,3
7,9	6,2	7,9	7,7	8,1	8,4
8	6,5	7,9	7,9	7,7	8,1
7,9	6,8	8	7,9	7,9	7,7
7,6	6,8	7,9	8	7,9	7,9
7,1	6,4	7,6	7,9	8	7,9
6,8	6,1	7,1	7,6	7,9	8
6,5	5,8	6,8	7,1	7,6	7,9
6,9	6,1	6,5	6,8	7,1	7,6
8,2	7,2	6,9	6,5	6,8	7,1
8,7	7,3	8,2	6,9	6,5	6,8
8,3	6,9	8,7	8,2	6,9	6,5
7,9	6,1	8,3	8,7	8,2	6,9
7,5	5,8	7,9	8,3	8,7	8,2
7,8	6,2	7,5	7,9	8,3	8,7
8,3	7,1	7,8	7,5	7,9	8,3
8,4	7,7	8,3	7,8	7,5	7,9
8,2	7,9	8,4	8,3	7,8	7,5
7,7	7,7	8,2	8,4	8,3	7,8
7,2	7,4	7,7	8,2	8,4	8,3
7,3	7,5	7,2	7,7	8,2	8,4
8,1	8	7,3	7,2	7,7	8,2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&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]5 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=57417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.80797132690177 + 0.0631745437846552X[t] + 1.41002342029138`Yt-1`[t] -0.566106428055065`Yt-2`[t] -0.308555685587945`Yt-3`[t] + 0.332779490804355`Yt-4`[t] + 0.201311751689259M1[t] -0.0408183587718783M2[t] -0.231707208277215M3[t] -0.134527991088984M4[t] -0.0880250719712937M5[t] -0.162099437565197M6[t] + 0.0678126634427705M7[t] + 0.66814134161663M8[t] -0.291632423961118M9[t] -0.225191440884684M10[t] + 0.191229439246727M11[t] -0.00471385316526875t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.80797132690177 +  0.0631745437846552X[t] +  1.41002342029138`Yt-1`[t] -0.566106428055065`Yt-2`[t] -0.308555685587945`Yt-3`[t] +  0.332779490804355`Yt-4`[t] +  0.201311751689259M1[t] -0.0408183587718783M2[t] -0.231707208277215M3[t] -0.134527991088984M4[t] -0.0880250719712937M5[t] -0.162099437565197M6[t] +  0.0678126634427705M7[t] +  0.66814134161663M8[t] -0.291632423961118M9[t] -0.225191440884684M10[t] +  0.191229439246727M11[t] -0.00471385316526875t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.80797132690177 +  0.0631745437846552X[t] +  1.41002342029138`Yt-1`[t] -0.566106428055065`Yt-2`[t] -0.308555685587945`Yt-3`[t] +  0.332779490804355`Yt-4`[t] +  0.201311751689259M1[t] -0.0408183587718783M2[t] -0.231707208277215M3[t] -0.134527991088984M4[t] -0.0880250719712937M5[t] -0.162099437565197M6[t] +  0.0678126634427705M7[t] +  0.66814134161663M8[t] -0.291632423961118M9[t] -0.225191440884684M10[t] +  0.191229439246727M11[t] -0.00471385316526875t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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] = + 0.80797132690177 + 0.0631745437846552X[t] + 1.41002342029138`Yt-1`[t] -0.566106428055065`Yt-2`[t] -0.308555685587945`Yt-3`[t] + 0.332779490804355`Yt-4`[t] + 0.201311751689259M1[t] -0.0408183587718783M2[t] -0.231707208277215M3[t] -0.134527991088984M4[t] -0.0880250719712937M5[t] -0.162099437565197M6[t] + 0.0678126634427705M7[t] + 0.66814134161663M8[t] -0.291632423961118M9[t] -0.225191440884684M10[t] + 0.191229439246727M11[t] -0.00471385316526875t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.807971326901770.705681.1450.2593890.129694
X0.06317454378465520.0544471.16030.2531710.126585
`Yt-1`1.410023420291380.1581278.91700
`Yt-2`-0.5661064280550650.280564-2.01770.050720.02536
`Yt-3`-0.3085556855879450.272636-1.13180.2648310.132415
`Yt-4`0.3327794908043550.1463862.27330.0287460.014373
M10.2013117516892590.1358671.48170.1466690.073335
M2-0.04081835877187830.149189-0.27360.7858730.392936
M3-0.2317072082772150.162334-1.42740.1616450.080822
M4-0.1345279910889840.145241-0.92620.3601660.180083
M5-0.08802507197129370.136447-0.64510.5227240.261362
M6-0.1620994375651970.133765-1.21180.2330620.116531
M70.06781266344277050.1384580.48980.6271120.313556
M80.668141341616630.144024.63924.1e-052e-05
M9-0.2916324239611180.186162-1.56650.1255110.062755
M10-0.2251914408846840.203813-1.10490.2761540.138077
M110.1912294392467270.153261.24770.2197590.10988
t-0.004713853165268750.003499-1.3470.1859520.092976

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 0.80797132690177 & 0.70568 & 1.145 & 0.259389 & 0.129694 \tabularnewline
X & 0.0631745437846552 & 0.054447 & 1.1603 & 0.253171 & 0.126585 \tabularnewline
`Yt-1` & 1.41002342029138 & 0.158127 & 8.917 & 0 & 0 \tabularnewline
`Yt-2` & -0.566106428055065 & 0.280564 & -2.0177 & 0.05072 & 0.02536 \tabularnewline
`Yt-3` & -0.308555685587945 & 0.272636 & -1.1318 & 0.264831 & 0.132415 \tabularnewline
`Yt-4` & 0.332779490804355 & 0.146386 & 2.2733 & 0.028746 & 0.014373 \tabularnewline
M1 & 0.201311751689259 & 0.135867 & 1.4817 & 0.146669 & 0.073335 \tabularnewline
M2 & -0.0408183587718783 & 0.149189 & -0.2736 & 0.785873 & 0.392936 \tabularnewline
M3 & -0.231707208277215 & 0.162334 & -1.4274 & 0.161645 & 0.080822 \tabularnewline
M4 & -0.134527991088984 & 0.145241 & -0.9262 & 0.360166 & 0.180083 \tabularnewline
M5 & -0.0880250719712937 & 0.136447 & -0.6451 & 0.522724 & 0.261362 \tabularnewline
M6 & -0.162099437565197 & 0.133765 & -1.2118 & 0.233062 & 0.116531 \tabularnewline
M7 & 0.0678126634427705 & 0.138458 & 0.4898 & 0.627112 & 0.313556 \tabularnewline
M8 & 0.66814134161663 & 0.14402 & 4.6392 & 4.1e-05 & 2e-05 \tabularnewline
M9 & -0.291632423961118 & 0.186162 & -1.5665 & 0.125511 & 0.062755 \tabularnewline
M10 & -0.225191440884684 & 0.203813 & -1.1049 & 0.276154 & 0.138077 \tabularnewline
M11 & 0.191229439246727 & 0.15326 & 1.2477 & 0.219759 & 0.10988 \tabularnewline
t & -0.00471385316526875 & 0.003499 & -1.347 & 0.185952 & 0.092976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]0.80797132690177[/C][C]0.70568[/C][C]1.145[/C][C]0.259389[/C][C]0.129694[/C][/ROW]
[ROW][C]X[/C][C]0.0631745437846552[/C][C]0.054447[/C][C]1.1603[/C][C]0.253171[/C][C]0.126585[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]1.41002342029138[/C][C]0.158127[/C][C]8.917[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]-0.566106428055065[/C][C]0.280564[/C][C]-2.0177[/C][C]0.05072[/C][C]0.02536[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]-0.308555685587945[/C][C]0.272636[/C][C]-1.1318[/C][C]0.264831[/C][C]0.132415[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]0.332779490804355[/C][C]0.146386[/C][C]2.2733[/C][C]0.028746[/C][C]0.014373[/C][/ROW]
[ROW][C]M1[/C][C]0.201311751689259[/C][C]0.135867[/C][C]1.4817[/C][C]0.146669[/C][C]0.073335[/C][/ROW]
[ROW][C]M2[/C][C]-0.0408183587718783[/C][C]0.149189[/C][C]-0.2736[/C][C]0.785873[/C][C]0.392936[/C][/ROW]
[ROW][C]M3[/C][C]-0.231707208277215[/C][C]0.162334[/C][C]-1.4274[/C][C]0.161645[/C][C]0.080822[/C][/ROW]
[ROW][C]M4[/C][C]-0.134527991088984[/C][C]0.145241[/C][C]-0.9262[/C][C]0.360166[/C][C]0.180083[/C][/ROW]
[ROW][C]M5[/C][C]-0.0880250719712937[/C][C]0.136447[/C][C]-0.6451[/C][C]0.522724[/C][C]0.261362[/C][/ROW]
[ROW][C]M6[/C][C]-0.162099437565197[/C][C]0.133765[/C][C]-1.2118[/C][C]0.233062[/C][C]0.116531[/C][/ROW]
[ROW][C]M7[/C][C]0.0678126634427705[/C][C]0.138458[/C][C]0.4898[/C][C]0.627112[/C][C]0.313556[/C][/ROW]
[ROW][C]M8[/C][C]0.66814134161663[/C][C]0.14402[/C][C]4.6392[/C][C]4.1e-05[/C][C]2e-05[/C][/ROW]
[ROW][C]M9[/C][C]-0.291632423961118[/C][C]0.186162[/C][C]-1.5665[/C][C]0.125511[/C][C]0.062755[/C][/ROW]
[ROW][C]M10[/C][C]-0.225191440884684[/C][C]0.203813[/C][C]-1.1049[/C][C]0.276154[/C][C]0.138077[/C][/ROW]
[ROW][C]M11[/C][C]0.191229439246727[/C][C]0.15326[/C][C]1.2477[/C][C]0.219759[/C][C]0.10988[/C][/ROW]
[ROW][C]t[/C][C]-0.00471385316526875[/C][C]0.003499[/C][C]-1.347[/C][C]0.185952[/C][C]0.092976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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)0.807971326901770.705681.1450.2593890.129694
X0.06317454378465520.0544471.16030.2531710.126585
`Yt-1`1.410023420291380.1581278.91700
`Yt-2`-0.5661064280550650.280564-2.01770.050720.02536
`Yt-3`-0.3085556855879450.272636-1.13180.2648310.132415
`Yt-4`0.3327794908043550.1463862.27330.0287460.014373
M10.2013117516892590.1358671.48170.1466690.073335
M2-0.04081835877187830.149189-0.27360.7858730.392936
M3-0.2317072082772150.162334-1.42740.1616450.080822
M4-0.1345279910889840.145241-0.92620.3601660.180083
M5-0.08802507197129370.136447-0.64510.5227240.261362
M6-0.1620994375651970.133765-1.21180.2330620.116531
M70.06781266344277050.1384580.48980.6271120.313556
M80.668141341616630.144024.63924.1e-052e-05
M9-0.2916324239611180.186162-1.56650.1255110.062755
M10-0.2251914408846840.203813-1.10490.2761540.138077
M110.1912294392467270.153261.24770.2197590.10988
t-0.004713853165268750.003499-1.3470.1859520.092976






Multiple Linear Regression - Regression Statistics
Multiple R0.985384503603201
R-squared0.970982619941328
Adjusted R-squared0.958001160441395
F-TEST (value)74.7976465933113
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.188034632645485
Sum Squared Residuals1.34356687681666

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.985384503603201 \tabularnewline
R-squared & 0.970982619941328 \tabularnewline
Adjusted R-squared & 0.958001160441395 \tabularnewline
F-TEST (value) & 74.7976465933113 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.188034632645485 \tabularnewline
Sum Squared Residuals & 1.34356687681666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.985384503603201[/C][/ROW]
[ROW][C]R-squared[/C][C]0.970982619941328[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.958001160441395[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]74.7976465933113[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.188034632645485[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.34356687681666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57417&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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 R0.985384503603201
R-squared0.970982619941328
Adjusted R-squared0.958001160441395
F-TEST (value)74.7976465933113
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.188034632645485
Sum Squared Residuals1.34356687681666






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
19.29.126442319338970.0735576806610257
29.59.55626262578181-0.0562626257818134
39.69.73100995594506-0.131009955945064
49.59.52842214093716-0.0284221409371571
59.19.26107915324316-0.161079153243157
68.98.743870487855450.156129512144552
798.952370322987270.0476296770127346
810.19.91762291830460.182377081695388
910.310.3761497598725-0.0761497598724539
1010.210.00607049064010.193929509359871
119.69.86373803927828-0.263738039278278
129.29.182737640264160.0172623597358371
139.39.265036402981230.0349635970187668
149.49.55012772363526-0.150127723635256
159.49.368988754319310.0310112456806879
169.29.24087611065623-0.0408761106562316
1799.00308287307202-0.00308287307201619
1898.769836841810620.230163158189379
1999.13206278611113-0.132062786111129
209.89.697563032562580.102436967437426
21109.77558588875640.224414111243603
229.89.672750014660250.127249985339748
239.39.45502143224368-0.155021432243681
2498.878117625201370.121882374798632
2599.0693462013224-0.0693462013223991
269.19.086373565124080.0136264348759192
279.18.951632710378350.148367289621646
289.18.875018675597570.224981324402428
299.28.892269627369660.307730372630335
308.88.97512679096313-0.175126790963134
318.38.55443521036992-0.254435210369914
328.48.65957769103144-0.25957769103144
338.18.26952839728224-0.169528397282241
347.77.86016899601578-0.160168996015784
357.97.674135814942460.225864185057544
367.98.10616697818912-0.206166978189116
3788.23208438123136-0.232084381231361
387.97.95037218933016-0.0503721893301582
397.67.62371239998578-0.0237123999857807
407.17.29365599465418-0.193655994654177
416.86.84544643338126-0.0454464333812602
426.56.66704079602276-0.167040796022757
436.96.712460304882620.187539695117377
448.28.037585384861610.162414615138386
458.78.67873595408890.0212640459110920
468.38.46101049868384-0.161010498683835
477.97.707104713535580.192895286464416
487.57.432977756345350.0670222436546477
497.87.607090695126030.192909304873968
508.38.05686389612870.243136103871308
518.48.42465617937149-0.0246561793714894
528.28.162027078154860.0379729218451374
537.77.7981219129339-0.098121912933902
547.27.24412508334804-0.0441250833480401
557.37.148671375649070.151328624350930
568.18.28765097323976-0.187650973239759

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9.2 & 9.12644231933897 & 0.0735576806610257 \tabularnewline
2 & 9.5 & 9.55626262578181 & -0.0562626257818134 \tabularnewline
3 & 9.6 & 9.73100995594506 & -0.131009955945064 \tabularnewline
4 & 9.5 & 9.52842214093716 & -0.0284221409371571 \tabularnewline
5 & 9.1 & 9.26107915324316 & -0.161079153243157 \tabularnewline
6 & 8.9 & 8.74387048785545 & 0.156129512144552 \tabularnewline
7 & 9 & 8.95237032298727 & 0.0476296770127346 \tabularnewline
8 & 10.1 & 9.9176229183046 & 0.182377081695388 \tabularnewline
9 & 10.3 & 10.3761497598725 & -0.0761497598724539 \tabularnewline
10 & 10.2 & 10.0060704906401 & 0.193929509359871 \tabularnewline
11 & 9.6 & 9.86373803927828 & -0.263738039278278 \tabularnewline
12 & 9.2 & 9.18273764026416 & 0.0172623597358371 \tabularnewline
13 & 9.3 & 9.26503640298123 & 0.0349635970187668 \tabularnewline
14 & 9.4 & 9.55012772363526 & -0.150127723635256 \tabularnewline
15 & 9.4 & 9.36898875431931 & 0.0310112456806879 \tabularnewline
16 & 9.2 & 9.24087611065623 & -0.0408761106562316 \tabularnewline
17 & 9 & 9.00308287307202 & -0.00308287307201619 \tabularnewline
18 & 9 & 8.76983684181062 & 0.230163158189379 \tabularnewline
19 & 9 & 9.13206278611113 & -0.132062786111129 \tabularnewline
20 & 9.8 & 9.69756303256258 & 0.102436967437426 \tabularnewline
21 & 10 & 9.7755858887564 & 0.224414111243603 \tabularnewline
22 & 9.8 & 9.67275001466025 & 0.127249985339748 \tabularnewline
23 & 9.3 & 9.45502143224368 & -0.155021432243681 \tabularnewline
24 & 9 & 8.87811762520137 & 0.121882374798632 \tabularnewline
25 & 9 & 9.0693462013224 & -0.0693462013223991 \tabularnewline
26 & 9.1 & 9.08637356512408 & 0.0136264348759192 \tabularnewline
27 & 9.1 & 8.95163271037835 & 0.148367289621646 \tabularnewline
28 & 9.1 & 8.87501867559757 & 0.224981324402428 \tabularnewline
29 & 9.2 & 8.89226962736966 & 0.307730372630335 \tabularnewline
30 & 8.8 & 8.97512679096313 & -0.175126790963134 \tabularnewline
31 & 8.3 & 8.55443521036992 & -0.254435210369914 \tabularnewline
32 & 8.4 & 8.65957769103144 & -0.25957769103144 \tabularnewline
33 & 8.1 & 8.26952839728224 & -0.169528397282241 \tabularnewline
34 & 7.7 & 7.86016899601578 & -0.160168996015784 \tabularnewline
35 & 7.9 & 7.67413581494246 & 0.225864185057544 \tabularnewline
36 & 7.9 & 8.10616697818912 & -0.206166978189116 \tabularnewline
37 & 8 & 8.23208438123136 & -0.232084381231361 \tabularnewline
38 & 7.9 & 7.95037218933016 & -0.0503721893301582 \tabularnewline
39 & 7.6 & 7.62371239998578 & -0.0237123999857807 \tabularnewline
40 & 7.1 & 7.29365599465418 & -0.193655994654177 \tabularnewline
41 & 6.8 & 6.84544643338126 & -0.0454464333812602 \tabularnewline
42 & 6.5 & 6.66704079602276 & -0.167040796022757 \tabularnewline
43 & 6.9 & 6.71246030488262 & 0.187539695117377 \tabularnewline
44 & 8.2 & 8.03758538486161 & 0.162414615138386 \tabularnewline
45 & 8.7 & 8.6787359540889 & 0.0212640459110920 \tabularnewline
46 & 8.3 & 8.46101049868384 & -0.161010498683835 \tabularnewline
47 & 7.9 & 7.70710471353558 & 0.192895286464416 \tabularnewline
48 & 7.5 & 7.43297775634535 & 0.0670222436546477 \tabularnewline
49 & 7.8 & 7.60709069512603 & 0.192909304873968 \tabularnewline
50 & 8.3 & 8.0568638961287 & 0.243136103871308 \tabularnewline
51 & 8.4 & 8.42465617937149 & -0.0246561793714894 \tabularnewline
52 & 8.2 & 8.16202707815486 & 0.0379729218451374 \tabularnewline
53 & 7.7 & 7.7981219129339 & -0.098121912933902 \tabularnewline
54 & 7.2 & 7.24412508334804 & -0.0441250833480401 \tabularnewline
55 & 7.3 & 7.14867137564907 & 0.151328624350930 \tabularnewline
56 & 8.1 & 8.28765097323976 & -0.187650973239759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&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]9.2[/C][C]9.12644231933897[/C][C]0.0735576806610257[/C][/ROW]
[ROW][C]2[/C][C]9.5[/C][C]9.55626262578181[/C][C]-0.0562626257818134[/C][/ROW]
[ROW][C]3[/C][C]9.6[/C][C]9.73100995594506[/C][C]-0.131009955945064[/C][/ROW]
[ROW][C]4[/C][C]9.5[/C][C]9.52842214093716[/C][C]-0.0284221409371571[/C][/ROW]
[ROW][C]5[/C][C]9.1[/C][C]9.26107915324316[/C][C]-0.161079153243157[/C][/ROW]
[ROW][C]6[/C][C]8.9[/C][C]8.74387048785545[/C][C]0.156129512144552[/C][/ROW]
[ROW][C]7[/C][C]9[/C][C]8.95237032298727[/C][C]0.0476296770127346[/C][/ROW]
[ROW][C]8[/C][C]10.1[/C][C]9.9176229183046[/C][C]0.182377081695388[/C][/ROW]
[ROW][C]9[/C][C]10.3[/C][C]10.3761497598725[/C][C]-0.0761497598724539[/C][/ROW]
[ROW][C]10[/C][C]10.2[/C][C]10.0060704906401[/C][C]0.193929509359871[/C][/ROW]
[ROW][C]11[/C][C]9.6[/C][C]9.86373803927828[/C][C]-0.263738039278278[/C][/ROW]
[ROW][C]12[/C][C]9.2[/C][C]9.18273764026416[/C][C]0.0172623597358371[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]9.26503640298123[/C][C]0.0349635970187668[/C][/ROW]
[ROW][C]14[/C][C]9.4[/C][C]9.55012772363526[/C][C]-0.150127723635256[/C][/ROW]
[ROW][C]15[/C][C]9.4[/C][C]9.36898875431931[/C][C]0.0310112456806879[/C][/ROW]
[ROW][C]16[/C][C]9.2[/C][C]9.24087611065623[/C][C]-0.0408761106562316[/C][/ROW]
[ROW][C]17[/C][C]9[/C][C]9.00308287307202[/C][C]-0.00308287307201619[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]8.76983684181062[/C][C]0.230163158189379[/C][/ROW]
[ROW][C]19[/C][C]9[/C][C]9.13206278611113[/C][C]-0.132062786111129[/C][/ROW]
[ROW][C]20[/C][C]9.8[/C][C]9.69756303256258[/C][C]0.102436967437426[/C][/ROW]
[ROW][C]21[/C][C]10[/C][C]9.7755858887564[/C][C]0.224414111243603[/C][/ROW]
[ROW][C]22[/C][C]9.8[/C][C]9.67275001466025[/C][C]0.127249985339748[/C][/ROW]
[ROW][C]23[/C][C]9.3[/C][C]9.45502143224368[/C][C]-0.155021432243681[/C][/ROW]
[ROW][C]24[/C][C]9[/C][C]8.87811762520137[/C][C]0.121882374798632[/C][/ROW]
[ROW][C]25[/C][C]9[/C][C]9.0693462013224[/C][C]-0.0693462013223991[/C][/ROW]
[ROW][C]26[/C][C]9.1[/C][C]9.08637356512408[/C][C]0.0136264348759192[/C][/ROW]
[ROW][C]27[/C][C]9.1[/C][C]8.95163271037835[/C][C]0.148367289621646[/C][/ROW]
[ROW][C]28[/C][C]9.1[/C][C]8.87501867559757[/C][C]0.224981324402428[/C][/ROW]
[ROW][C]29[/C][C]9.2[/C][C]8.89226962736966[/C][C]0.307730372630335[/C][/ROW]
[ROW][C]30[/C][C]8.8[/C][C]8.97512679096313[/C][C]-0.175126790963134[/C][/ROW]
[ROW][C]31[/C][C]8.3[/C][C]8.55443521036992[/C][C]-0.254435210369914[/C][/ROW]
[ROW][C]32[/C][C]8.4[/C][C]8.65957769103144[/C][C]-0.25957769103144[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.26952839728224[/C][C]-0.169528397282241[/C][/ROW]
[ROW][C]34[/C][C]7.7[/C][C]7.86016899601578[/C][C]-0.160168996015784[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.67413581494246[/C][C]0.225864185057544[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8.10616697818912[/C][C]-0.206166978189116[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]8.23208438123136[/C][C]-0.232084381231361[/C][/ROW]
[ROW][C]38[/C][C]7.9[/C][C]7.95037218933016[/C][C]-0.0503721893301582[/C][/ROW]
[ROW][C]39[/C][C]7.6[/C][C]7.62371239998578[/C][C]-0.0237123999857807[/C][/ROW]
[ROW][C]40[/C][C]7.1[/C][C]7.29365599465418[/C][C]-0.193655994654177[/C][/ROW]
[ROW][C]41[/C][C]6.8[/C][C]6.84544643338126[/C][C]-0.0454464333812602[/C][/ROW]
[ROW][C]42[/C][C]6.5[/C][C]6.66704079602276[/C][C]-0.167040796022757[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]6.71246030488262[/C][C]0.187539695117377[/C][/ROW]
[ROW][C]44[/C][C]8.2[/C][C]8.03758538486161[/C][C]0.162414615138386[/C][/ROW]
[ROW][C]45[/C][C]8.7[/C][C]8.6787359540889[/C][C]0.0212640459110920[/C][/ROW]
[ROW][C]46[/C][C]8.3[/C][C]8.46101049868384[/C][C]-0.161010498683835[/C][/ROW]
[ROW][C]47[/C][C]7.9[/C][C]7.70710471353558[/C][C]0.192895286464416[/C][/ROW]
[ROW][C]48[/C][C]7.5[/C][C]7.43297775634535[/C][C]0.0670222436546477[/C][/ROW]
[ROW][C]49[/C][C]7.8[/C][C]7.60709069512603[/C][C]0.192909304873968[/C][/ROW]
[ROW][C]50[/C][C]8.3[/C][C]8.0568638961287[/C][C]0.243136103871308[/C][/ROW]
[ROW][C]51[/C][C]8.4[/C][C]8.42465617937149[/C][C]-0.0246561793714894[/C][/ROW]
[ROW][C]52[/C][C]8.2[/C][C]8.16202707815486[/C][C]0.0379729218451374[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.7981219129339[/C][C]-0.098121912933902[/C][/ROW]
[ROW][C]54[/C][C]7.2[/C][C]7.24412508334804[/C][C]-0.0441250833480401[/C][/ROW]
[ROW][C]55[/C][C]7.3[/C][C]7.14867137564907[/C][C]0.151328624350930[/C][/ROW]
[ROW][C]56[/C][C]8.1[/C][C]8.28765097323976[/C][C]-0.187650973239759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57417&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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
19.29.126442319338970.0735576806610257
29.59.55626262578181-0.0562626257818134
39.69.73100995594506-0.131009955945064
49.59.52842214093716-0.0284221409371571
59.19.26107915324316-0.161079153243157
68.98.743870487855450.156129512144552
798.952370322987270.0476296770127346
810.19.91762291830460.182377081695388
910.310.3761497598725-0.0761497598724539
1010.210.00607049064010.193929509359871
119.69.86373803927828-0.263738039278278
129.29.182737640264160.0172623597358371
139.39.265036402981230.0349635970187668
149.49.55012772363526-0.150127723635256
159.49.368988754319310.0310112456806879
169.29.24087611065623-0.0408761106562316
1799.00308287307202-0.00308287307201619
1898.769836841810620.230163158189379
1999.13206278611113-0.132062786111129
209.89.697563032562580.102436967437426
21109.77558588875640.224414111243603
229.89.672750014660250.127249985339748
239.39.45502143224368-0.155021432243681
2498.878117625201370.121882374798632
2599.0693462013224-0.0693462013223991
269.19.086373565124080.0136264348759192
279.18.951632710378350.148367289621646
289.18.875018675597570.224981324402428
299.28.892269627369660.307730372630335
308.88.97512679096313-0.175126790963134
318.38.55443521036992-0.254435210369914
328.48.65957769103144-0.25957769103144
338.18.26952839728224-0.169528397282241
347.77.86016899601578-0.160168996015784
357.97.674135814942460.225864185057544
367.98.10616697818912-0.206166978189116
3788.23208438123136-0.232084381231361
387.97.95037218933016-0.0503721893301582
397.67.62371239998578-0.0237123999857807
407.17.29365599465418-0.193655994654177
416.86.84544643338126-0.0454464333812602
426.56.66704079602276-0.167040796022757
436.96.712460304882620.187539695117377
448.28.037585384861610.162414615138386
458.78.67873595408890.0212640459110920
468.38.46101049868384-0.161010498683835
477.97.707104713535580.192895286464416
487.57.432977756345350.0670222436546477
497.87.607090695126030.192909304873968
508.38.05686389612870.243136103871308
518.48.42465617937149-0.0246561793714894
528.28.162027078154860.0379729218451374
537.77.7981219129339-0.098121912933902
547.27.24412508334804-0.0441250833480401
557.37.148671375649070.151328624350930
568.18.28765097323976-0.187650973239759






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.055082493266530.110164986533060.94491750673347
220.04916758245456990.09833516490913970.95083241754543
230.02578342651747180.05156685303494360.974216573482528
240.01510302741687660.03020605483375310.984896972583123
250.009744222487652280.01948844497530460.990255777512348
260.003643482514901510.007286965029803020.996356517485099
270.001324785639443050.002649571278886110.998675214360557
280.003107590930763950.006215181861527910.996892409069236
290.1637444552523670.3274889105047330.836255544747633
300.1620118899637430.3240237799274860.837988110036257
310.1288002056592180.2576004113184370.871199794340782
320.6636272570774550.6727454858450910.336372742922545
330.7855622950183560.4288754099632870.214437704981644
340.9947524228593020.01049515428139580.00524757714069789
350.9823515998065510.03529680038689760.0176484001934488

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.05508249326653 & 0.11016498653306 & 0.94491750673347 \tabularnewline
22 & 0.0491675824545699 & 0.0983351649091397 & 0.95083241754543 \tabularnewline
23 & 0.0257834265174718 & 0.0515668530349436 & 0.974216573482528 \tabularnewline
24 & 0.0151030274168766 & 0.0302060548337531 & 0.984896972583123 \tabularnewline
25 & 0.00974422248765228 & 0.0194884449753046 & 0.990255777512348 \tabularnewline
26 & 0.00364348251490151 & 0.00728696502980302 & 0.996356517485099 \tabularnewline
27 & 0.00132478563944305 & 0.00264957127888611 & 0.998675214360557 \tabularnewline
28 & 0.00310759093076395 & 0.00621518186152791 & 0.996892409069236 \tabularnewline
29 & 0.163744455252367 & 0.327488910504733 & 0.836255544747633 \tabularnewline
30 & 0.162011889963743 & 0.324023779927486 & 0.837988110036257 \tabularnewline
31 & 0.128800205659218 & 0.257600411318437 & 0.871199794340782 \tabularnewline
32 & 0.663627257077455 & 0.672745485845091 & 0.336372742922545 \tabularnewline
33 & 0.785562295018356 & 0.428875409963287 & 0.214437704981644 \tabularnewline
34 & 0.994752422859302 & 0.0104951542813958 & 0.00524757714069789 \tabularnewline
35 & 0.982351599806551 & 0.0352968003868976 & 0.0176484001934488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.05508249326653[/C][C]0.11016498653306[/C][C]0.94491750673347[/C][/ROW]
[ROW][C]22[/C][C]0.0491675824545699[/C][C]0.0983351649091397[/C][C]0.95083241754543[/C][/ROW]
[ROW][C]23[/C][C]0.0257834265174718[/C][C]0.0515668530349436[/C][C]0.974216573482528[/C][/ROW]
[ROW][C]24[/C][C]0.0151030274168766[/C][C]0.0302060548337531[/C][C]0.984896972583123[/C][/ROW]
[ROW][C]25[/C][C]0.00974422248765228[/C][C]0.0194884449753046[/C][C]0.990255777512348[/C][/ROW]
[ROW][C]26[/C][C]0.00364348251490151[/C][C]0.00728696502980302[/C][C]0.996356517485099[/C][/ROW]
[ROW][C]27[/C][C]0.00132478563944305[/C][C]0.00264957127888611[/C][C]0.998675214360557[/C][/ROW]
[ROW][C]28[/C][C]0.00310759093076395[/C][C]0.00621518186152791[/C][C]0.996892409069236[/C][/ROW]
[ROW][C]29[/C][C]0.163744455252367[/C][C]0.327488910504733[/C][C]0.836255544747633[/C][/ROW]
[ROW][C]30[/C][C]0.162011889963743[/C][C]0.324023779927486[/C][C]0.837988110036257[/C][/ROW]
[ROW][C]31[/C][C]0.128800205659218[/C][C]0.257600411318437[/C][C]0.871199794340782[/C][/ROW]
[ROW][C]32[/C][C]0.663627257077455[/C][C]0.672745485845091[/C][C]0.336372742922545[/C][/ROW]
[ROW][C]33[/C][C]0.785562295018356[/C][C]0.428875409963287[/C][C]0.214437704981644[/C][/ROW]
[ROW][C]34[/C][C]0.994752422859302[/C][C]0.0104951542813958[/C][C]0.00524757714069789[/C][/ROW]
[ROW][C]35[/C][C]0.982351599806551[/C][C]0.0352968003868976[/C][C]0.0176484001934488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57417&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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
210.055082493266530.110164986533060.94491750673347
220.04916758245456990.09833516490913970.95083241754543
230.02578342651747180.05156685303494360.974216573482528
240.01510302741687660.03020605483375310.984896972583123
250.009744222487652280.01948844497530460.990255777512348
260.003643482514901510.007286965029803020.996356517485099
270.001324785639443050.002649571278886110.998675214360557
280.003107590930763950.006215181861527910.996892409069236
290.1637444552523670.3274889105047330.836255544747633
300.1620118899637430.3240237799274860.837988110036257
310.1288002056592180.2576004113184370.871199794340782
320.6636272570774550.6727454858450910.336372742922545
330.7855622950183560.4288754099632870.214437704981644
340.9947524228593020.01049515428139580.00524757714069789
350.9823515998065510.03529680038689760.0176484001934488






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.2NOK
5% type I error level70.466666666666667NOK
10% type I error level90.6NOK

\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 & 3 & 0.2 & NOK \tabularnewline
5% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
10% type I error level & 9 & 0.6 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57417&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]3[/C][C]0.2[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]9[/C][C]0.6[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57417&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57417&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 level30.2NOK
5% type I error level70.466666666666667NOK
10% type I error level90.6NOK


Figures (Output of Computation)

Figure 1
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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')
}