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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 computationThu, 19 Nov 2009 14:10:36 -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/t12586652399xm6sgj7fo04qyv.htm/, Retrieved Fri, 29 Mar 2024 00:31:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57958, Retrieved Fri, 29 Mar 2024 00:31:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [Mulitple Regressi...] [2009-11-19 21:10:36] [f97f6131ca109ba89501d75ae11b45c9] [Current]
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Dataseries X:
.6	21.3	9.5	9.2	9.2	10
9.5	21.3	9.6	9.5	9.2	9.2
9.1	19.1	9.5	9.6	9.5	9.2
8.9	19.1	9.1	9.5	9.6	9.5
9	19.1	8.9	9.1	9.5	9.6
10.1	26.2	9	8.9	9.1	9.5
10.3	26.2	10.1	9	8.9	9.1
10.2	26.2	10.3	10.1	9	8.9
9.6	21.7	10.2	10.3	10.1	9
9.2	21.7	9.6	10.2	10.3	10.1
9.3	21.7	9.2	9.6	10.2	10.3
9.4	19.4	9.3	9.2	9.6	10.2
9.4	19.4	9.4	9.3	9.2	9.6
9.2	19.4	9.4	9.4	9.3	9.2
9	19.5	9.2	9.4	9.4	9.3
9	19.5	9	9.2	9.4	9.4
9	19.5	9	9	9.2	9.4
9.8	28.7	9	9	9	9.2
10	28.7	9.8	9	9	9
9.8	28.7	10	9.8	9	9
9.3	21.8	9.8	10	9.8	9
9	21.8	9.3	9.8	10	9.8
9	21.8	9	9.3	9.8	10
9.1	20	9	9	9.3	9.8
9.1	20	9.1	9	9	9.3
9.1	20	9.1	9.1	9	9
9.2	22.6	9.1	9.1	9.1	9
8.8	22.6	9.2	9.1	9.1	9.1
8.3	22.6	8.8	9.2	9.1	9.1
8.4	22.4	8.3	8.8	9.2	9.1
8.1	22.4	8.4	8.3	8.8	9.2
7.7	22.4	8.1	8.4	8.3	8.8
7.9	18.6	7.7	8.1	8.4	8.3
7.9	18.6	7.9	7.7	8.1	8.4
8	18.6	7.9	7.9	7.7	8.1
7.9	16.2	8	7.9	7.9	7.7
7.6	16.2	7.9	8	7.9	7.9
7.1	16.2	7.6	7.9	8	7.9
6.8	13.8	7.1	7.6	7.9	8
6.5	13.8	6.8	7.1	7.6	7.9
6.9	13.8	6.5	6.8	7.1	7.6
8.2	24.1	6.9	6.5	6.8	7.1
8.7	24.1	8.2	6.9	6.5	6.8
8.3	24.1	8.7	8.2	6.9	6.5
7.9	19.9	8.3	8.7	8.2	6.9
7.5	19.9	7.9	8.3	8.7	8.2
7.8	19.9	7.5	7.9	8.3	8.7
8.3	22.3	7.8	7.5	7.9	8.3
8.4	22.3	8.3	7.8	7.5	7.9
8.2	22.3	8.4	8.3	7.8	7.5
7.7	20.9	8.2	8.4	8.3	7.8
7.2	20.9	7.7	8.2	8.4	8.3
7.3	20.9	7.2	7.7	8.2	8.4
8.1	25.5	7.3	7.2	7.7	8.2
8.5	25.5	8.1	7.3	7.2	7.7
8.4	25.5	8.5	8.1	7.3	7.2




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=57958&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=57958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = -3.40051685044881 -0.134543923383781X[t] + 2.11094925623521`Y(t-1)`[t] -0.9087922772981`Y(t-2)`[t] + 0.928796384659762`Y(t-3)`[t] -0.536884959196374`Y(t-4)`[t] -1.77521792588231M1[t] -0.303259869607554M2[t] -0.398487322461913M3[t] -0.233131366754861M4[t] + 0.279722394838491M5[t] + 1.73437634941900M6[t] + 0.305099087362743M7[t] + 0.182267571428939M8[t] -0.752535129732793M9[t] -0.324731479878309M10[t] + 0.384426209322359M11[t] + 0.0369476158030248t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -3.40051685044881 -0.134543923383781X[t] +  2.11094925623521`Y(t-1)`[t] -0.9087922772981`Y(t-2)`[t] +  0.928796384659762`Y(t-3)`[t] -0.536884959196374`Y(t-4)`[t] -1.77521792588231M1[t] -0.303259869607554M2[t] -0.398487322461913M3[t] -0.233131366754861M4[t] +  0.279722394838491M5[t] +  1.73437634941900M6[t] +  0.305099087362743M7[t] +  0.182267571428939M8[t] -0.752535129732793M9[t] -0.324731479878309M10[t] +  0.384426209322359M11[t] +  0.0369476158030248t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57958&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -3.40051685044881 -0.134543923383781X[t] +  2.11094925623521`Y(t-1)`[t] -0.9087922772981`Y(t-2)`[t] +  0.928796384659762`Y(t-3)`[t] -0.536884959196374`Y(t-4)`[t] -1.77521792588231M1[t] -0.303259869607554M2[t] -0.398487322461913M3[t] -0.233131366754861M4[t] +  0.279722394838491M5[t] +  1.73437634941900M6[t] +  0.305099087362743M7[t] +  0.182267571428939M8[t] -0.752535129732793M9[t] -0.324731479878309M10[t] +  0.384426209322359M11[t] +  0.0369476158030248t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -3.40051685044881 -0.134543923383781X[t] + 2.11094925623521`Y(t-1)`[t] -0.9087922772981`Y(t-2)`[t] + 0.928796384659762`Y(t-3)`[t] -0.536884959196374`Y(t-4)`[t] -1.77521792588231M1[t] -0.303259869607554M2[t] -0.398487322461913M3[t] -0.233131366754861M4[t] + 0.279722394838491M5[t] + 1.73437634941900M6[t] + 0.305099087362743M7[t] + 0.182267571428939M8[t] -0.752535129732793M9[t] -0.324731479878309M10[t] + 0.384426209322359M11[t] + 0.0369476158030248t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-3.400516850448815.922119-0.57420.5692120.284606
X-0.1345439233837810.15339-0.87710.3859250.192963
`Y(t-1)`2.110949256235211.2795151.64980.1072260.053613
`Y(t-2)`-0.90879227729811.814831-0.50080.6194290.309715
`Y(t-3)`0.9287963846597621.8025820.51530.6093570.304678
`Y(t-4)`-0.5368849591963741.007742-0.53280.5973010.298651
M1-1.775217925882310.933856-1.9010.0649120.032456
M2-0.3032598696075540.981059-0.30910.7589230.379461
M3-0.3984873224619130.993127-0.40120.6904870.345244
M4-0.2331313667548610.974736-0.23920.8122560.406128
M50.2797223948384911.0099960.2770.7833170.391658
M61.734376349419001.5064491.15130.2568010.128401
M70.3050990873627431.1225020.27180.7872450.393623
M80.1822675714289391.4369230.12680.8997310.449866
M9-0.7525351297327931.304439-0.57690.5674070.283703
M10-0.3247314798783091.049079-0.30950.7586020.379301
M110.3844262093223591.0022690.38360.7034450.351723
t0.03694761580302480.0337651.09430.2807310.140366

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -3.40051685044881 & 5.922119 & -0.5742 & 0.569212 & 0.284606 \tabularnewline
X & -0.134543923383781 & 0.15339 & -0.8771 & 0.385925 & 0.192963 \tabularnewline
`Y(t-1)` & 2.11094925623521 & 1.279515 & 1.6498 & 0.107226 & 0.053613 \tabularnewline
`Y(t-2)` & -0.9087922772981 & 1.814831 & -0.5008 & 0.619429 & 0.309715 \tabularnewline
`Y(t-3)` & 0.928796384659762 & 1.802582 & 0.5153 & 0.609357 & 0.304678 \tabularnewline
`Y(t-4)` & -0.536884959196374 & 1.007742 & -0.5328 & 0.597301 & 0.298651 \tabularnewline
M1 & -1.77521792588231 & 0.933856 & -1.901 & 0.064912 & 0.032456 \tabularnewline
M2 & -0.303259869607554 & 0.981059 & -0.3091 & 0.758923 & 0.379461 \tabularnewline
M3 & -0.398487322461913 & 0.993127 & -0.4012 & 0.690487 & 0.345244 \tabularnewline
M4 & -0.233131366754861 & 0.974736 & -0.2392 & 0.812256 & 0.406128 \tabularnewline
M5 & 0.279722394838491 & 1.009996 & 0.277 & 0.783317 & 0.391658 \tabularnewline
M6 & 1.73437634941900 & 1.506449 & 1.1513 & 0.256801 & 0.128401 \tabularnewline
M7 & 0.305099087362743 & 1.122502 & 0.2718 & 0.787245 & 0.393623 \tabularnewline
M8 & 0.182267571428939 & 1.436923 & 0.1268 & 0.899731 & 0.449866 \tabularnewline
M9 & -0.752535129732793 & 1.304439 & -0.5769 & 0.567407 & 0.283703 \tabularnewline
M10 & -0.324731479878309 & 1.049079 & -0.3095 & 0.758602 & 0.379301 \tabularnewline
M11 & 0.384426209322359 & 1.002269 & 0.3836 & 0.703445 & 0.351723 \tabularnewline
t & 0.0369476158030248 & 0.033765 & 1.0943 & 0.280731 & 0.140366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57958&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-3.40051685044881[/C][C]5.922119[/C][C]-0.5742[/C][C]0.569212[/C][C]0.284606[/C][/ROW]
[ROW][C]X[/C][C]-0.134543923383781[/C][C]0.15339[/C][C]-0.8771[/C][C]0.385925[/C][C]0.192963[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]2.11094925623521[/C][C]1.279515[/C][C]1.6498[/C][C]0.107226[/C][C]0.053613[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.9087922772981[/C][C]1.814831[/C][C]-0.5008[/C][C]0.619429[/C][C]0.309715[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]0.928796384659762[/C][C]1.802582[/C][C]0.5153[/C][C]0.609357[/C][C]0.304678[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.536884959196374[/C][C]1.007742[/C][C]-0.5328[/C][C]0.597301[/C][C]0.298651[/C][/ROW]
[ROW][C]M1[/C][C]-1.77521792588231[/C][C]0.933856[/C][C]-1.901[/C][C]0.064912[/C][C]0.032456[/C][/ROW]
[ROW][C]M2[/C][C]-0.303259869607554[/C][C]0.981059[/C][C]-0.3091[/C][C]0.758923[/C][C]0.379461[/C][/ROW]
[ROW][C]M3[/C][C]-0.398487322461913[/C][C]0.993127[/C][C]-0.4012[/C][C]0.690487[/C][C]0.345244[/C][/ROW]
[ROW][C]M4[/C][C]-0.233131366754861[/C][C]0.974736[/C][C]-0.2392[/C][C]0.812256[/C][C]0.406128[/C][/ROW]
[ROW][C]M5[/C][C]0.279722394838491[/C][C]1.009996[/C][C]0.277[/C][C]0.783317[/C][C]0.391658[/C][/ROW]
[ROW][C]M6[/C][C]1.73437634941900[/C][C]1.506449[/C][C]1.1513[/C][C]0.256801[/C][C]0.128401[/C][/ROW]
[ROW][C]M7[/C][C]0.305099087362743[/C][C]1.122502[/C][C]0.2718[/C][C]0.787245[/C][C]0.393623[/C][/ROW]
[ROW][C]M8[/C][C]0.182267571428939[/C][C]1.436923[/C][C]0.1268[/C][C]0.899731[/C][C]0.449866[/C][/ROW]
[ROW][C]M9[/C][C]-0.752535129732793[/C][C]1.304439[/C][C]-0.5769[/C][C]0.567407[/C][C]0.283703[/C][/ROW]
[ROW][C]M10[/C][C]-0.324731479878309[/C][C]1.049079[/C][C]-0.3095[/C][C]0.758602[/C][C]0.379301[/C][/ROW]
[ROW][C]M11[/C][C]0.384426209322359[/C][C]1.002269[/C][C]0.3836[/C][C]0.703445[/C][C]0.351723[/C][/ROW]
[ROW][C]t[/C][C]0.0369476158030248[/C][C]0.033765[/C][C]1.0943[/C][C]0.280731[/C][C]0.140366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&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)-3.400516850448815.922119-0.57420.5692120.284606
X-0.1345439233837810.15339-0.87710.3859250.192963
`Y(t-1)`2.110949256235211.2795151.64980.1072260.053613
`Y(t-2)`-0.90879227729811.814831-0.50080.6194290.309715
`Y(t-3)`0.9287963846597621.8025820.51530.6093570.304678
`Y(t-4)`-0.5368849591963741.007742-0.53280.5973010.298651
M1-1.775217925882310.933856-1.9010.0649120.032456
M2-0.3032598696075540.981059-0.30910.7589230.379461
M3-0.3984873224619130.993127-0.40120.6904870.345244
M4-0.2331313667548610.974736-0.23920.8122560.406128
M50.2797223948384911.0099960.2770.7833170.391658
M61.734376349419001.5064491.15130.2568010.128401
M70.3050990873627431.1225020.27180.7872450.393623
M80.1822675714289391.4369230.12680.8997310.449866
M9-0.7525351297327931.304439-0.57690.5674070.283703
M10-0.3247314798783091.049079-0.30950.7586020.379301
M110.3844262093223591.0022690.38360.7034450.351723
t0.03694761580302480.0337651.09430.2807310.140366







Multiple Linear Regression - Regression Statistics
Multiple R0.6652577704075
R-squared0.442567901087558
Adjusted R-squared0.193190383153044
F-TEST (value)1.77469045627351
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0.0704654438906093
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.25163224664294
Sum Squared Residuals59.5301646717848

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.6652577704075 \tabularnewline
R-squared & 0.442567901087558 \tabularnewline
Adjusted R-squared & 0.193190383153044 \tabularnewline
F-TEST (value) & 1.77469045627351 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0.0704654438906093 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.25163224664294 \tabularnewline
Sum Squared Residuals & 59.5301646717848 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57958&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.6652577704075[/C][/ROW]
[ROW][C]R-squared[/C][C]0.442567901087558[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.193190383153044[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.77469045627351[/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]0.0704654438906093[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.25163224664294[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]59.5301646717848[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&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 R0.6652577704075
R-squared0.442567901087558
Adjusted R-squared0.193190383153044
F-TEST (value)1.77469045627351
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0.0704654438906093
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.25163224664294
Sum Squared Residuals59.5301646717848







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
10.66.86463340139552-6.26463340139552
29.58.74150428326440.758495716735606
39.18.955885839701970.144114160298025
48.98.336503087154840.563496912845157
598.68106338983780.318936610162192
610.19.292426427335360.807573572664635
710.310.16025644195760.139743558042351
810.29.697147518351250.502852481648744
99.69.97987423434252-0.37987423434252
109.28.864120995804660.335879004195342
119.39.110865334387870.189134665612129
129.49.143860266317780.256139733682221
139.47.476418075786121.92358192421388
149.29.20207814227862-0.00207814227862302
1598.74734520418820.252654795811797
1698.655528883991220.344471116008777
1799.20132943991526-0.201329439915265
189.89.376744630075340.423255369924664
19109.780551380649550.219448619350453
209.89.389823509927330.410176490072674
219.39.55941029693786-0.25941029693786
2298.906696699512240.0933033004877626
2399.18077709752319-0.180777097523188
249.18.991094048793490.108905951206515
259.17.453722228537981.64627777146202
269.19.032814160644860.0671858393551382
279.28.717599761261670.482400238738328
288.89.07730976247563-0.277309762475630
298.38.69185220964812-0.391852209648117
308.49.61128448597602-1.21128448597602
318.18.45923885421182-0.359238854211815
327.77.399546740829330.300453259170672
337.96.80253866308851.0974613369115
347.97.720669279594730.179330720405275
3588.0745630630338-0.0745630630338049
367.98.66159807186957-0.76159807186957
377.66.513976616597681.08602338340232
387.17.57335637800068-0.473356378000682
396.86.90857687775663-0.108576877756635
406.56.7070413915669-0.207041391566907
416.96.592862970711180.307137029288818
428.27.805483080125540.394516919874456
438.78.676297128419820.0237028715801756
448.38.99704193754194-0.697041937541937
457.98.35817680563112-0.458176805631121
467.58.10851302508838-0.60851302508838
477.87.733794505055140.0662054949448635
488.37.903447613019170.396552386980827
498.46.791249677682711.60875032231729
508.28.55024703581144-0.35024703581144
517.78.47059231709152-0.770592317091515
527.27.6236168748114-0.423616874811398
537.37.33289198988763-0.0328919898876289
548.18.51406137648774-0.414061376487735
558.58.52365619476116-0.0236561947611641
568.48.91644029335015-0.516440293350152

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 0.6 & 6.86463340139552 & -6.26463340139552 \tabularnewline
2 & 9.5 & 8.7415042832644 & 0.758495716735606 \tabularnewline
3 & 9.1 & 8.95588583970197 & 0.144114160298025 \tabularnewline
4 & 8.9 & 8.33650308715484 & 0.563496912845157 \tabularnewline
5 & 9 & 8.6810633898378 & 0.318936610162192 \tabularnewline
6 & 10.1 & 9.29242642733536 & 0.807573572664635 \tabularnewline
7 & 10.3 & 10.1602564419576 & 0.139743558042351 \tabularnewline
8 & 10.2 & 9.69714751835125 & 0.502852481648744 \tabularnewline
9 & 9.6 & 9.97987423434252 & -0.37987423434252 \tabularnewline
10 & 9.2 & 8.86412099580466 & 0.335879004195342 \tabularnewline
11 & 9.3 & 9.11086533438787 & 0.189134665612129 \tabularnewline
12 & 9.4 & 9.14386026631778 & 0.256139733682221 \tabularnewline
13 & 9.4 & 7.47641807578612 & 1.92358192421388 \tabularnewline
14 & 9.2 & 9.20207814227862 & -0.00207814227862302 \tabularnewline
15 & 9 & 8.7473452041882 & 0.252654795811797 \tabularnewline
16 & 9 & 8.65552888399122 & 0.344471116008777 \tabularnewline
17 & 9 & 9.20132943991526 & -0.201329439915265 \tabularnewline
18 & 9.8 & 9.37674463007534 & 0.423255369924664 \tabularnewline
19 & 10 & 9.78055138064955 & 0.219448619350453 \tabularnewline
20 & 9.8 & 9.38982350992733 & 0.410176490072674 \tabularnewline
21 & 9.3 & 9.55941029693786 & -0.25941029693786 \tabularnewline
22 & 9 & 8.90669669951224 & 0.0933033004877626 \tabularnewline
23 & 9 & 9.18077709752319 & -0.180777097523188 \tabularnewline
24 & 9.1 & 8.99109404879349 & 0.108905951206515 \tabularnewline
25 & 9.1 & 7.45372222853798 & 1.64627777146202 \tabularnewline
26 & 9.1 & 9.03281416064486 & 0.0671858393551382 \tabularnewline
27 & 9.2 & 8.71759976126167 & 0.482400238738328 \tabularnewline
28 & 8.8 & 9.07730976247563 & -0.277309762475630 \tabularnewline
29 & 8.3 & 8.69185220964812 & -0.391852209648117 \tabularnewline
30 & 8.4 & 9.61128448597602 & -1.21128448597602 \tabularnewline
31 & 8.1 & 8.45923885421182 & -0.359238854211815 \tabularnewline
32 & 7.7 & 7.39954674082933 & 0.300453259170672 \tabularnewline
33 & 7.9 & 6.8025386630885 & 1.0974613369115 \tabularnewline
34 & 7.9 & 7.72066927959473 & 0.179330720405275 \tabularnewline
35 & 8 & 8.0745630630338 & -0.0745630630338049 \tabularnewline
36 & 7.9 & 8.66159807186957 & -0.76159807186957 \tabularnewline
37 & 7.6 & 6.51397661659768 & 1.08602338340232 \tabularnewline
38 & 7.1 & 7.57335637800068 & -0.473356378000682 \tabularnewline
39 & 6.8 & 6.90857687775663 & -0.108576877756635 \tabularnewline
40 & 6.5 & 6.7070413915669 & -0.207041391566907 \tabularnewline
41 & 6.9 & 6.59286297071118 & 0.307137029288818 \tabularnewline
42 & 8.2 & 7.80548308012554 & 0.394516919874456 \tabularnewline
43 & 8.7 & 8.67629712841982 & 0.0237028715801756 \tabularnewline
44 & 8.3 & 8.99704193754194 & -0.697041937541937 \tabularnewline
45 & 7.9 & 8.35817680563112 & -0.458176805631121 \tabularnewline
46 & 7.5 & 8.10851302508838 & -0.60851302508838 \tabularnewline
47 & 7.8 & 7.73379450505514 & 0.0662054949448635 \tabularnewline
48 & 8.3 & 7.90344761301917 & 0.396552386980827 \tabularnewline
49 & 8.4 & 6.79124967768271 & 1.60875032231729 \tabularnewline
50 & 8.2 & 8.55024703581144 & -0.35024703581144 \tabularnewline
51 & 7.7 & 8.47059231709152 & -0.770592317091515 \tabularnewline
52 & 7.2 & 7.6236168748114 & -0.423616874811398 \tabularnewline
53 & 7.3 & 7.33289198988763 & -0.0328919898876289 \tabularnewline
54 & 8.1 & 8.51406137648774 & -0.414061376487735 \tabularnewline
55 & 8.5 & 8.52365619476116 & -0.0236561947611641 \tabularnewline
56 & 8.4 & 8.91644029335015 & -0.516440293350152 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57958&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]0.6[/C][C]6.86463340139552[/C][C]-6.26463340139552[/C][/ROW]
[ROW][C]2[/C][C]9.5[/C][C]8.7415042832644[/C][C]0.758495716735606[/C][/ROW]
[ROW][C]3[/C][C]9.1[/C][C]8.95588583970197[/C][C]0.144114160298025[/C][/ROW]
[ROW][C]4[/C][C]8.9[/C][C]8.33650308715484[/C][C]0.563496912845157[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]8.6810633898378[/C][C]0.318936610162192[/C][/ROW]
[ROW][C]6[/C][C]10.1[/C][C]9.29242642733536[/C][C]0.807573572664635[/C][/ROW]
[ROW][C]7[/C][C]10.3[/C][C]10.1602564419576[/C][C]0.139743558042351[/C][/ROW]
[ROW][C]8[/C][C]10.2[/C][C]9.69714751835125[/C][C]0.502852481648744[/C][/ROW]
[ROW][C]9[/C][C]9.6[/C][C]9.97987423434252[/C][C]-0.37987423434252[/C][/ROW]
[ROW][C]10[/C][C]9.2[/C][C]8.86412099580466[/C][C]0.335879004195342[/C][/ROW]
[ROW][C]11[/C][C]9.3[/C][C]9.11086533438787[/C][C]0.189134665612129[/C][/ROW]
[ROW][C]12[/C][C]9.4[/C][C]9.14386026631778[/C][C]0.256139733682221[/C][/ROW]
[ROW][C]13[/C][C]9.4[/C][C]7.47641807578612[/C][C]1.92358192421388[/C][/ROW]
[ROW][C]14[/C][C]9.2[/C][C]9.20207814227862[/C][C]-0.00207814227862302[/C][/ROW]
[ROW][C]15[/C][C]9[/C][C]8.7473452041882[/C][C]0.252654795811797[/C][/ROW]
[ROW][C]16[/C][C]9[/C][C]8.65552888399122[/C][C]0.344471116008777[/C][/ROW]
[ROW][C]17[/C][C]9[/C][C]9.20132943991526[/C][C]-0.201329439915265[/C][/ROW]
[ROW][C]18[/C][C]9.8[/C][C]9.37674463007534[/C][C]0.423255369924664[/C][/ROW]
[ROW][C]19[/C][C]10[/C][C]9.78055138064955[/C][C]0.219448619350453[/C][/ROW]
[ROW][C]20[/C][C]9.8[/C][C]9.38982350992733[/C][C]0.410176490072674[/C][/ROW]
[ROW][C]21[/C][C]9.3[/C][C]9.55941029693786[/C][C]-0.25941029693786[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]8.90669669951224[/C][C]0.0933033004877626[/C][/ROW]
[ROW][C]23[/C][C]9[/C][C]9.18077709752319[/C][C]-0.180777097523188[/C][/ROW]
[ROW][C]24[/C][C]9.1[/C][C]8.99109404879349[/C][C]0.108905951206515[/C][/ROW]
[ROW][C]25[/C][C]9.1[/C][C]7.45372222853798[/C][C]1.64627777146202[/C][/ROW]
[ROW][C]26[/C][C]9.1[/C][C]9.03281416064486[/C][C]0.0671858393551382[/C][/ROW]
[ROW][C]27[/C][C]9.2[/C][C]8.71759976126167[/C][C]0.482400238738328[/C][/ROW]
[ROW][C]28[/C][C]8.8[/C][C]9.07730976247563[/C][C]-0.277309762475630[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]8.69185220964812[/C][C]-0.391852209648117[/C][/ROW]
[ROW][C]30[/C][C]8.4[/C][C]9.61128448597602[/C][C]-1.21128448597602[/C][/ROW]
[ROW][C]31[/C][C]8.1[/C][C]8.45923885421182[/C][C]-0.359238854211815[/C][/ROW]
[ROW][C]32[/C][C]7.7[/C][C]7.39954674082933[/C][C]0.300453259170672[/C][/ROW]
[ROW][C]33[/C][C]7.9[/C][C]6.8025386630885[/C][C]1.0974613369115[/C][/ROW]
[ROW][C]34[/C][C]7.9[/C][C]7.72066927959473[/C][C]0.179330720405275[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]8.0745630630338[/C][C]-0.0745630630338049[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]8.66159807186957[/C][C]-0.76159807186957[/C][/ROW]
[ROW][C]37[/C][C]7.6[/C][C]6.51397661659768[/C][C]1.08602338340232[/C][/ROW]
[ROW][C]38[/C][C]7.1[/C][C]7.57335637800068[/C][C]-0.473356378000682[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.90857687775663[/C][C]-0.108576877756635[/C][/ROW]
[ROW][C]40[/C][C]6.5[/C][C]6.7070413915669[/C][C]-0.207041391566907[/C][/ROW]
[ROW][C]41[/C][C]6.9[/C][C]6.59286297071118[/C][C]0.307137029288818[/C][/ROW]
[ROW][C]42[/C][C]8.2[/C][C]7.80548308012554[/C][C]0.394516919874456[/C][/ROW]
[ROW][C]43[/C][C]8.7[/C][C]8.67629712841982[/C][C]0.0237028715801756[/C][/ROW]
[ROW][C]44[/C][C]8.3[/C][C]8.99704193754194[/C][C]-0.697041937541937[/C][/ROW]
[ROW][C]45[/C][C]7.9[/C][C]8.35817680563112[/C][C]-0.458176805631121[/C][/ROW]
[ROW][C]46[/C][C]7.5[/C][C]8.10851302508838[/C][C]-0.60851302508838[/C][/ROW]
[ROW][C]47[/C][C]7.8[/C][C]7.73379450505514[/C][C]0.0662054949448635[/C][/ROW]
[ROW][C]48[/C][C]8.3[/C][C]7.90344761301917[/C][C]0.396552386980827[/C][/ROW]
[ROW][C]49[/C][C]8.4[/C][C]6.79124967768271[/C][C]1.60875032231729[/C][/ROW]
[ROW][C]50[/C][C]8.2[/C][C]8.55024703581144[/C][C]-0.35024703581144[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]8.47059231709152[/C][C]-0.770592317091515[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.6236168748114[/C][C]-0.423616874811398[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.33289198988763[/C][C]-0.0328919898876289[/C][/ROW]
[ROW][C]54[/C][C]8.1[/C][C]8.51406137648774[/C][C]-0.414061376487735[/C][/ROW]
[ROW][C]55[/C][C]8.5[/C][C]8.52365619476116[/C][C]-0.0236561947611641[/C][/ROW]
[ROW][C]56[/C][C]8.4[/C][C]8.91644029335015[/C][C]-0.516440293350152[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57958&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&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
10.66.86463340139552-6.26463340139552
29.58.74150428326440.758495716735606
39.18.955885839701970.144114160298025
48.98.336503087154840.563496912845157
598.68106338983780.318936610162192
610.19.292426427335360.807573572664635
710.310.16025644195760.139743558042351
810.29.697147518351250.502852481648744
99.69.97987423434252-0.37987423434252
109.28.864120995804660.335879004195342
119.39.110865334387870.189134665612129
129.49.143860266317780.256139733682221
139.47.476418075786121.92358192421388
149.29.20207814227862-0.00207814227862302
1598.74734520418820.252654795811797
1698.655528883991220.344471116008777
1799.20132943991526-0.201329439915265
189.89.376744630075340.423255369924664
19109.780551380649550.219448619350453
209.89.389823509927330.410176490072674
219.39.55941029693786-0.25941029693786
2298.906696699512240.0933033004877626
2399.18077709752319-0.180777097523188
249.18.991094048793490.108905951206515
259.17.453722228537981.64627777146202
269.19.032814160644860.0671858393551382
279.28.717599761261670.482400238738328
288.89.07730976247563-0.277309762475630
298.38.69185220964812-0.391852209648117
308.49.61128448597602-1.21128448597602
318.18.45923885421182-0.359238854211815
327.77.399546740829330.300453259170672
337.96.80253866308851.0974613369115
347.97.720669279594730.179330720405275
3588.0745630630338-0.0745630630338049
367.98.66159807186957-0.76159807186957
377.66.513976616597681.08602338340232
387.17.57335637800068-0.473356378000682
396.86.90857687775663-0.108576877756635
406.56.7070413915669-0.207041391566907
416.96.592862970711180.307137029288818
428.27.805483080125540.394516919874456
438.78.676297128419820.0237028715801756
448.38.99704193754194-0.697041937541937
457.98.35817680563112-0.458176805631121
467.58.10851302508838-0.60851302508838
477.87.733794505055140.0662054949448635
488.37.903447613019170.396552386980827
498.46.791249677682711.60875032231729
508.28.55024703581144-0.35024703581144
517.78.47059231709152-0.770592317091515
527.27.6236168748114-0.423616874811398
537.37.33289198988763-0.0328919898876289
548.18.51406137648774-0.414061376487735
558.58.52365619476116-0.0236561947611641
568.48.91644029335015-0.516440293350152







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.9999999994222321.15553604809741e-095.77768024048704e-10
220.9999999999818613.62780054313983e-111.81390027156991e-11
230.99999999988692.26200309557485e-101.13100154778743e-10
240.999999999551248.97521821857054e-104.48760910928527e-10
250.9999999972872875.42542516826538e-092.71271258413269e-09
260.9999999967772576.44548500741335e-093.22274250370667e-09
270.9999999991230111.75397767101586e-098.76988835507932e-10
280.999999997727354.54530199453031e-092.27265099726515e-09
290.999999978016684.39666388834681e-082.19833194417340e-08
300.9999999946023131.07953731860369e-085.39768659301845e-09
310.9999999377906851.24418630365924e-076.22093151829618e-08
320.9999990046107971.99077840599051e-069.95389202995255e-07
330.999992999551111.40008977822431e-057.00044889112154e-06
340.9999903512262431.92975475137934e-059.6487737568967e-06
350.9998454585519980.0003090828960030760.000154541448001538

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.999999999422232 & 1.15553604809741e-09 & 5.77768024048704e-10 \tabularnewline
22 & 0.999999999981861 & 3.62780054313983e-11 & 1.81390027156991e-11 \tabularnewline
23 & 0.9999999998869 & 2.26200309557485e-10 & 1.13100154778743e-10 \tabularnewline
24 & 0.99999999955124 & 8.97521821857054e-10 & 4.48760910928527e-10 \tabularnewline
25 & 0.999999997287287 & 5.42542516826538e-09 & 2.71271258413269e-09 \tabularnewline
26 & 0.999999996777257 & 6.44548500741335e-09 & 3.22274250370667e-09 \tabularnewline
27 & 0.999999999123011 & 1.75397767101586e-09 & 8.76988835507932e-10 \tabularnewline
28 & 0.99999999772735 & 4.54530199453031e-09 & 2.27265099726515e-09 \tabularnewline
29 & 0.99999997801668 & 4.39666388834681e-08 & 2.19833194417340e-08 \tabularnewline
30 & 0.999999994602313 & 1.07953731860369e-08 & 5.39768659301845e-09 \tabularnewline
31 & 0.999999937790685 & 1.24418630365924e-07 & 6.22093151829618e-08 \tabularnewline
32 & 0.999999004610797 & 1.99077840599051e-06 & 9.95389202995255e-07 \tabularnewline
33 & 0.99999299955111 & 1.40008977822431e-05 & 7.00044889112154e-06 \tabularnewline
34 & 0.999990351226243 & 1.92975475137934e-05 & 9.6487737568967e-06 \tabularnewline
35 & 0.999845458551998 & 0.000309082896003076 & 0.000154541448001538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57958&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]0.999999999422232[/C][C]1.15553604809741e-09[/C][C]5.77768024048704e-10[/C][/ROW]
[ROW][C]22[/C][C]0.999999999981861[/C][C]3.62780054313983e-11[/C][C]1.81390027156991e-11[/C][/ROW]
[ROW][C]23[/C][C]0.9999999998869[/C][C]2.26200309557485e-10[/C][C]1.13100154778743e-10[/C][/ROW]
[ROW][C]24[/C][C]0.99999999955124[/C][C]8.97521821857054e-10[/C][C]4.48760910928527e-10[/C][/ROW]
[ROW][C]25[/C][C]0.999999997287287[/C][C]5.42542516826538e-09[/C][C]2.71271258413269e-09[/C][/ROW]
[ROW][C]26[/C][C]0.999999996777257[/C][C]6.44548500741335e-09[/C][C]3.22274250370667e-09[/C][/ROW]
[ROW][C]27[/C][C]0.999999999123011[/C][C]1.75397767101586e-09[/C][C]8.76988835507932e-10[/C][/ROW]
[ROW][C]28[/C][C]0.99999999772735[/C][C]4.54530199453031e-09[/C][C]2.27265099726515e-09[/C][/ROW]
[ROW][C]29[/C][C]0.99999997801668[/C][C]4.39666388834681e-08[/C][C]2.19833194417340e-08[/C][/ROW]
[ROW][C]30[/C][C]0.999999994602313[/C][C]1.07953731860369e-08[/C][C]5.39768659301845e-09[/C][/ROW]
[ROW][C]31[/C][C]0.999999937790685[/C][C]1.24418630365924e-07[/C][C]6.22093151829618e-08[/C][/ROW]
[ROW][C]32[/C][C]0.999999004610797[/C][C]1.99077840599051e-06[/C][C]9.95389202995255e-07[/C][/ROW]
[ROW][C]33[/C][C]0.99999299955111[/C][C]1.40008977822431e-05[/C][C]7.00044889112154e-06[/C][/ROW]
[ROW][C]34[/C][C]0.999990351226243[/C][C]1.92975475137934e-05[/C][C]9.6487737568967e-06[/C][/ROW]
[ROW][C]35[/C][C]0.999845458551998[/C][C]0.000309082896003076[/C][C]0.000154541448001538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57958&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&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
210.9999999994222321.15553604809741e-095.77768024048704e-10
220.9999999999818613.62780054313983e-111.81390027156991e-11
230.99999999988692.26200309557485e-101.13100154778743e-10
240.999999999551248.97521821857054e-104.48760910928527e-10
250.9999999972872875.42542516826538e-092.71271258413269e-09
260.9999999967772576.44548500741335e-093.22274250370667e-09
270.9999999991230111.75397767101586e-098.76988835507932e-10
280.999999997727354.54530199453031e-092.27265099726515e-09
290.999999978016684.39666388834681e-082.19833194417340e-08
300.9999999946023131.07953731860369e-085.39768659301845e-09
310.9999999377906851.24418630365924e-076.22093151829618e-08
320.9999990046107971.99077840599051e-069.95389202995255e-07
330.999992999551111.40008977822431e-057.00044889112154e-06
340.9999903512262431.92975475137934e-059.6487737568967e-06
350.9998454585519980.0003090828960030760.000154541448001538







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level151NOK
5% type I error level151NOK
10% type I error level151NOK

\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 & 15 & 1 & NOK \tabularnewline
5% type I error level & 15 & 1 & NOK \tabularnewline
10% type I error level & 15 & 1 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57958&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]15[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]15[/C][C]1[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]1[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57958&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57958&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 level151NOK
5% type I error level151NOK
10% type I error level151NOK



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')
}