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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 computationSat, 21 Nov 2009 02:48:52 -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/21/t1258797014adh4355gjyb7fhc.htm/, Retrieved Sun, 28 Apr 2024 01:10:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58520, Retrieved Sun, 28 Apr 2024 01:10:13 +0000
QR Codes:

Original text written by user:WS 7 Multiple Regression analysis
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [WS 7 Multiple Reg...] [2009-11-21 09:48:52] [9b6f46453e60f88d91cef176fe926003] [Current]
-    D        [Multiple Regression] [WS 7] [2009-11-24 23:14:58] [9717cb857c153ca3061376906953b329]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13,7	15	14,4	15,3	14,3	14,5
14,2	15,5	13,7	14,4	15,3	14,3
13,5	15,1	14,2	13,7	14,4	15,3
11,9	11,7	13,5	14,2	13,7	14,4
14,6	16,3	11,9	13,5	14,2	13,7
15,6	16,7	14,6	11,9	13,5	14,2
14,1	15	15,6	14,6	11,9	13,5
14,9	14,9	14,1	15,6	14,6	11,9
14,2	14,6	14,9	14,1	15,6	14,6
14,6	15,3	14,2	14,9	14,1	15,6
17,2	17,9	14,6	14,2	14,9	14,1
15,4	16,4	17,2	14,6	14,2	14,9
14,3	15,4	15,4	17,2	14,6	14,2
17,5	17,9	14,3	15,4	17,2	14,6
14,5	15,9	17,5	14,3	15,4	17,2
14,4	13,9	14,5	17,5	14,3	15,4
16,6	17,8	14,4	14,5	17,5	14,3
16,7	17,9	16,6	14,4	14,5	17,5
16,6	17,4	16,7	16,6	14,4	14,5
16,9	16,7	16,6	16,7	16,6	14,4
15,7	16	16,9	16,6	16,7	16,6
16,4	16,6	15,7	16,9	16,6	16,7
18,4	19,1	16,4	15,7	16,9	16,6
16,9	17,8	18,4	16,4	15,7	16,9
16,5	17,2	16,9	18,4	16,4	15,7
18,3	18,6	16,5	16,9	18,4	16,4
15,1	16,3	18,3	16,5	16,9	18,4
15,7	15,1	15,1	18,3	16,5	16,9
18,1	19,2	15,7	15,1	18,3	16,5
16,8	17,7	18,1	15,7	15,1	18,3
18,9	19,1	16,8	18,1	15,7	15,1
19	18	18,9	16,8	18,1	15,7
18,1	17,5	19	18,9	16,8	18,1
17,8	17,8	18,1	19	18,9	16,8
21,5	21,1	17,8	18,1	19	18,9
17,1	17,2	21,5	17,8	18,1	19
18,7	19,4	17,1	21,5	17,8	18,1
19	19,8	18,7	17,1	21,5	17,8
16,4	17,6	19	18,7	17,1	21,5
16,9	16,2	16,4	19	18,7	17,1
18,6	19,5	16,9	16,4	19	18,7
19,3	19,9	18,6	16,9	16,4	19
19,4	20	19,3	18,6	16,9	16,4
17,6	17,3	19,4	19,3	18,6	16,9
18,6	18,9	17,6	19,4	19,3	18,6
18,1	18,6	18,6	17,6	19,4	19,3
20,4	21,4	18,1	18,6	17,6	19,4
18,1	18,6	20,4	18,1	18,6	17,6
19,6	19,8	18,1	20,4	18,1	18,6
19,9	20,8	19,6	18,1	20,4	18,1
19,2	19,6	19,9	19,6	18,1	20,4
17,8	17,7	19,2	19,9	19,6	18,1
19,2	19,8	17,8	19,2	19,9	19,6
22	22,2	19,2	17,8	19,2	19,9
21,1	20,7	22	19,2	17,8	19,2
19,5	17,9	21,1	22	19,2	17,8
22,2	20,9	19,5	21,1	22	19,2
20,9	21,2	22,2	19,5	21,1	22
22,2	21,4	20,9	22,2	19,5	21,1
23,5	23	22,2	20,9	22,2	19,5
21,5	21,3	23,5	22,2	20,9	22,2
24,3	23,9	21,5	23,5	22,2	20,9
22,8	22,4	24,3	21,5	23,5	22,2
20,3	18,3	22,8	24,3	21,5	23,5
23,7	22,8	20,3	22,8	24,3	21,5
23,3	22,3	23,7	20,3	22,8	24,3
19,6	17,8	23,3	23,7	20,3	22,8
18	16,4	19,6	23,3	23,7	20,3
17,3	16	18	19,6	23,3	23,7
16,8	16,4	17,3	18	19,6	23,3
18,2	17,7	16,8	17,3	18	19,6
16,5	16,6	18,2	16,8	17,3	18
16	16,2	16,5	18,2	16,8	17,3
18,4	18,3	16	16,5	18,2	16,8

Tables (Output of Computation)





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=58520&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=58520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = -2.89999021216690 + 0.873627997570757X[t] + 0.0245492114319014Y1[t] + 0.145315150831421Y2[t] + 0.110701724083021Y3[t] -0.0225391490188104Y4[t] -0.361337024228986M1[t] -0.0556593556308913M2[t] -0.472649033262836M3[t] + 0.625633258667187M4[t] -0.223770882850354M5[t] + 0.365365125566834M6[t] + 0.360498507612941M7[t] + 0.676362526335275M8[t] + 0.420586202713588M9[t] + 0.0485506948041424M10[t] + 0.465680688403872M11[t] + 0.00673586861246828t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -2.89999021216690 +  0.873627997570757X[t] +  0.0245492114319014Y1[t] +  0.145315150831421Y2[t] +  0.110701724083021Y3[t] -0.0225391490188104Y4[t] -0.361337024228986M1[t] -0.0556593556308913M2[t] -0.472649033262836M3[t] +  0.625633258667187M4[t] -0.223770882850354M5[t] +  0.365365125566834M6[t] +  0.360498507612941M7[t] +  0.676362526335275M8[t] +  0.420586202713588M9[t] +  0.0485506948041424M10[t] +  0.465680688403872M11[t] +  0.00673586861246828t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58520&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -2.89999021216690 +  0.873627997570757X[t] +  0.0245492114319014Y1[t] +  0.145315150831421Y2[t] +  0.110701724083021Y3[t] -0.0225391490188104Y4[t] -0.361337024228986M1[t] -0.0556593556308913M2[t] -0.472649033262836M3[t] +  0.625633258667187M4[t] -0.223770882850354M5[t] +  0.365365125566834M6[t] +  0.360498507612941M7[t] +  0.676362526335275M8[t] +  0.420586202713588M9[t] +  0.0485506948041424M10[t] +  0.465680688403872M11[t] +  0.00673586861246828t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58520&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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] = -2.89999021216690 + 0.873627997570757X[t] + 0.0245492114319014Y1[t] + 0.145315150831421Y2[t] + 0.110701724083021Y3[t] -0.0225391490188104Y4[t] -0.361337024228986M1[t] -0.0556593556308913M2[t] -0.472649033262836M3[t] + 0.625633258667187M4[t] -0.223770882850354M5[t] + 0.365365125566834M6[t] + 0.360498507612941M7[t] + 0.676362526335275M8[t] + 0.420586202713588M9[t] + 0.0485506948041424M10[t] + 0.465680688403872M11[t] + 0.00673586861246828t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-2.899990212166900.61411-4.72231.6e-058e-06
X0.8736279975707570.04850618.010700
Y10.02454921143190140.052890.46420.6443380.322169
Y20.1453151508314210.0488012.97770.0042860.002143
Y30.1107017240830210.0504772.19310.0324690.016235
Y4-0.02253914901881040.057631-0.39110.6972120.348606
M1-0.3613370242289860.260616-1.38650.1710970.085549
M2-0.05565935563089130.27146-0.2050.8382860.419143
M3-0.4726490332628360.256836-1.84030.0710290.035514
M40.6256332586671870.2897132.15950.035110.017555
M5-0.2237708828503540.316335-0.70740.4822610.24113
M60.3653651255668340.296281.23320.2226610.111331
M70.3604985076129410.2436581.47950.1446030.072302
M80.6763625263352750.2840272.38130.0206740.010337
M90.4205862027135880.2685351.56620.122930.061465
M100.04855069480414240.2663580.18230.8560250.428012
M110.4656806884038720.2924021.59260.1168780.058439
t0.006735868612468280.0047651.41370.162990.081495

\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) & -2.89999021216690 & 0.61411 & -4.7223 & 1.6e-05 & 8e-06 \tabularnewline
X & 0.873627997570757 & 0.048506 & 18.0107 & 0 & 0 \tabularnewline
Y1 & 0.0245492114319014 & 0.05289 & 0.4642 & 0.644338 & 0.322169 \tabularnewline
Y2 & 0.145315150831421 & 0.048801 & 2.9777 & 0.004286 & 0.002143 \tabularnewline
Y3 & 0.110701724083021 & 0.050477 & 2.1931 & 0.032469 & 0.016235 \tabularnewline
Y4 & -0.0225391490188104 & 0.057631 & -0.3911 & 0.697212 & 0.348606 \tabularnewline
M1 & -0.361337024228986 & 0.260616 & -1.3865 & 0.171097 & 0.085549 \tabularnewline
M2 & -0.0556593556308913 & 0.27146 & -0.205 & 0.838286 & 0.419143 \tabularnewline
M3 & -0.472649033262836 & 0.256836 & -1.8403 & 0.071029 & 0.035514 \tabularnewline
M4 & 0.625633258667187 & 0.289713 & 2.1595 & 0.03511 & 0.017555 \tabularnewline
M5 & -0.223770882850354 & 0.316335 & -0.7074 & 0.482261 & 0.24113 \tabularnewline
M6 & 0.365365125566834 & 0.29628 & 1.2332 & 0.222661 & 0.111331 \tabularnewline
M7 & 0.360498507612941 & 0.243658 & 1.4795 & 0.144603 & 0.072302 \tabularnewline
M8 & 0.676362526335275 & 0.284027 & 2.3813 & 0.020674 & 0.010337 \tabularnewline
M9 & 0.420586202713588 & 0.268535 & 1.5662 & 0.12293 & 0.061465 \tabularnewline
M10 & 0.0485506948041424 & 0.266358 & 0.1823 & 0.856025 & 0.428012 \tabularnewline
M11 & 0.465680688403872 & 0.292402 & 1.5926 & 0.116878 & 0.058439 \tabularnewline
t & 0.00673586861246828 & 0.004765 & 1.4137 & 0.16299 & 0.081495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58520&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]-2.89999021216690[/C][C]0.61411[/C][C]-4.7223[/C][C]1.6e-05[/C][C]8e-06[/C][/ROW]
[ROW][C]X[/C][C]0.873627997570757[/C][C]0.048506[/C][C]18.0107[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y1[/C][C]0.0245492114319014[/C][C]0.05289[/C][C]0.4642[/C][C]0.644338[/C][C]0.322169[/C][/ROW]
[ROW][C]Y2[/C][C]0.145315150831421[/C][C]0.048801[/C][C]2.9777[/C][C]0.004286[/C][C]0.002143[/C][/ROW]
[ROW][C]Y3[/C][C]0.110701724083021[/C][C]0.050477[/C][C]2.1931[/C][C]0.032469[/C][C]0.016235[/C][/ROW]
[ROW][C]Y4[/C][C]-0.0225391490188104[/C][C]0.057631[/C][C]-0.3911[/C][C]0.697212[/C][C]0.348606[/C][/ROW]
[ROW][C]M1[/C][C]-0.361337024228986[/C][C]0.260616[/C][C]-1.3865[/C][C]0.171097[/C][C]0.085549[/C][/ROW]
[ROW][C]M2[/C][C]-0.0556593556308913[/C][C]0.27146[/C][C]-0.205[/C][C]0.838286[/C][C]0.419143[/C][/ROW]
[ROW][C]M3[/C][C]-0.472649033262836[/C][C]0.256836[/C][C]-1.8403[/C][C]0.071029[/C][C]0.035514[/C][/ROW]
[ROW][C]M4[/C][C]0.625633258667187[/C][C]0.289713[/C][C]2.1595[/C][C]0.03511[/C][C]0.017555[/C][/ROW]
[ROW][C]M5[/C][C]-0.223770882850354[/C][C]0.316335[/C][C]-0.7074[/C][C]0.482261[/C][C]0.24113[/C][/ROW]
[ROW][C]M6[/C][C]0.365365125566834[/C][C]0.29628[/C][C]1.2332[/C][C]0.222661[/C][C]0.111331[/C][/ROW]
[ROW][C]M7[/C][C]0.360498507612941[/C][C]0.243658[/C][C]1.4795[/C][C]0.144603[/C][C]0.072302[/C][/ROW]
[ROW][C]M8[/C][C]0.676362526335275[/C][C]0.284027[/C][C]2.3813[/C][C]0.020674[/C][C]0.010337[/C][/ROW]
[ROW][C]M9[/C][C]0.420586202713588[/C][C]0.268535[/C][C]1.5662[/C][C]0.12293[/C][C]0.061465[/C][/ROW]
[ROW][C]M10[/C][C]0.0485506948041424[/C][C]0.266358[/C][C]0.1823[/C][C]0.856025[/C][C]0.428012[/C][/ROW]
[ROW][C]M11[/C][C]0.465680688403872[/C][C]0.292402[/C][C]1.5926[/C][C]0.116878[/C][C]0.058439[/C][/ROW]
[ROW][C]t[/C][C]0.00673586861246828[/C][C]0.004765[/C][C]1.4137[/C][C]0.16299[/C][C]0.081495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58520&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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)-2.899990212166900.61411-4.72231.6e-058e-06
X0.8736279975707570.04850618.010700
Y10.02454921143190140.052890.46420.6443380.322169
Y20.1453151508314210.0488012.97770.0042860.002143
Y30.1107017240830210.0504772.19310.0324690.016235
Y4-0.02253914901881040.057631-0.39110.6972120.348606
M1-0.3613370242289860.260616-1.38650.1710970.085549
M2-0.05565935563089130.27146-0.2050.8382860.419143
M3-0.4726490332628360.256836-1.84030.0710290.035514
M40.6256332586671870.2897132.15950.035110.017555
M5-0.2237708828503540.316335-0.70740.4822610.24113
M60.3653651255668340.296281.23320.2226610.111331
M70.3604985076129410.2436581.47950.1446030.072302
M80.6763625263352750.2840272.38130.0206740.010337
M90.4205862027135880.2685351.56620.122930.061465
M100.04855069480414240.2663580.18230.8560250.428012
M110.4656806884038720.2924021.59260.1168780.058439
t0.006735868612468280.0047651.41370.162990.081495






Multiple Linear Regression - Regression Statistics
Multiple R0.992141366913702
R-squared0.98434449194139
Adjusted R-squared0.979591926995026
F-TEST (value)207.118577662895
F-TEST (DF numerator)17
F-TEST (DF denominator)56
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.385429189322686
Sum Squared Residuals8.31911695898883

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.992141366913702 \tabularnewline
R-squared & 0.98434449194139 \tabularnewline
Adjusted R-squared & 0.979591926995026 \tabularnewline
F-TEST (value) & 207.118577662895 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 56 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.385429189322686 \tabularnewline
Sum Squared Residuals & 8.31911695898883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58520&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.992141366913702[/C][/ROW]
[ROW][C]R-squared[/C][C]0.98434449194139[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.979591926995026[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]207.118577662895[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]56[/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]0.385429189322686[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8.31911695898883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58520&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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 R0.992141366913702
R-squared0.98434449194139
Adjusted R-squared0.979591926995026
F-TEST (value)207.118577662895
F-TEST (DF numerator)17
F-TEST (DF denominator)56
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.385429189322686
Sum Squared Residuals8.31911695898883






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
113.713.68287604173250.0171239582674963
214.214.3993450478646-0.199345047864642
313.513.42802333925730.0719766607427173
411.911.56097346273140.339026537268607
514.614.6671229011334-0.0671229011334472
615.615.35746382535970.242536174640255
714.114.1297202446051-0.0297202446051058
814.914.80840595932070.0915940406793455
914.214.14878976967080.0512102303291676
1014.614.30550566619280.294494333807151
1117.217.03127350387440.168726496125587
1215.415.28831817170920.111681828290779
1314.314.4537779240526-0.153777924052595
1417.516.94049887412670.559501125873268
1514.514.44383498983490.0561650101650815
1614.414.11175657534330.288243424656726
1716.616.6168757003131-0.0168757003130596
1816.716.9353566780576-0.235356678057576
1916.616.8791074575512-0.279107457551217
2016.916.84804204841100.0519579515890279
2115.715.9417792880156-0.241779288015571
2216.416.1014678514820.298532148517988
2318.418.5876744067525-0.187674406752515
2416.917.0042284049597-0.104228404959656
2516.516.48379512099640.0162048790036415
2618.317.99712148783900.302878512161034
2715.115.3524549204894-0.252454920489449
2815.715.58165731275650.118342687243487
2918.118.07886363704710.0211363629529026
3016.817.1155847303565-0.315584730356508
3118.918.79592187605810.104078123941907
321918.27233526237920.72766473762083
3318.117.69609134752070.403908652479327
3417.817.8470918465882-0.0470918465881536
3521.520.97951966107480.520480338925197
3617.117.05877772122950.0412222787705488
3718.719.0428824049365-0.342882404936517
381919.520997339621-0.520997339620994
3916.416.8581485033708-0.458148503370805
4016.916.9961490770563-0.0961490770563166
4118.618.6680562884838-0.068056288483806
4219.319.4331843720702-0.133184372070209
4319.419.9005892763920-0.50058927639203
4417.618.1454924534427-0.5454924534427
4518.619.3037743825785-0.703774382578548
4618.118.4346610520408-0.334661052040824
4720.421.2362088343153-0.836208834315295
4818.118.4661834245203-0.366183424520313
4919.619.35980751554730.240192484452722
5019.920.5143315604645-0.614331560464538
5119.218.97460763590260.225392364097358
5217.818.6640353271756-0.864035327175582
5319.219.5192981412791-0.319298141279137
542221.95855194575550.0414480542444776
5521.120.78295319382820.317046806171787
5619.519.23072004234670.269279957653273
5722.221.71091122481660.489088775183414
5820.921.2787374453993-0.378737445399308
5922.222.08092831509310.119071684906883
6023.523.19774986364980.302250136350196
6121.521.37403683944660.125963160553397
6224.324.27090757859060.0290924214094412
6322.822.44293061114490.357069388855098
6420.320.08542824493690.214571755063078
6523.723.24978333174350.450216668256547
6623.322.89985844840040.400141551599560
6719.619.21170795156530.388292048434659
681818.5950042340998-0.595004234099776
6917.317.29865398739780.00134601260221030
7016.816.63253613829690.167463861703146
7118.217.98439527888990.215604721110143
7216.516.48474241393160.0152575860684450
731615.90282415328810.0971758467118542
7418.417.95679811149360.44320188850643

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 13.7 & 13.6828760417325 & 0.0171239582674963 \tabularnewline
2 & 14.2 & 14.3993450478646 & -0.199345047864642 \tabularnewline
3 & 13.5 & 13.4280233392573 & 0.0719766607427173 \tabularnewline
4 & 11.9 & 11.5609734627314 & 0.339026537268607 \tabularnewline
5 & 14.6 & 14.6671229011334 & -0.0671229011334472 \tabularnewline
6 & 15.6 & 15.3574638253597 & 0.242536174640255 \tabularnewline
7 & 14.1 & 14.1297202446051 & -0.0297202446051058 \tabularnewline
8 & 14.9 & 14.8084059593207 & 0.0915940406793455 \tabularnewline
9 & 14.2 & 14.1487897696708 & 0.0512102303291676 \tabularnewline
10 & 14.6 & 14.3055056661928 & 0.294494333807151 \tabularnewline
11 & 17.2 & 17.0312735038744 & 0.168726496125587 \tabularnewline
12 & 15.4 & 15.2883181717092 & 0.111681828290779 \tabularnewline
13 & 14.3 & 14.4537779240526 & -0.153777924052595 \tabularnewline
14 & 17.5 & 16.9404988741267 & 0.559501125873268 \tabularnewline
15 & 14.5 & 14.4438349898349 & 0.0561650101650815 \tabularnewline
16 & 14.4 & 14.1117565753433 & 0.288243424656726 \tabularnewline
17 & 16.6 & 16.6168757003131 & -0.0168757003130596 \tabularnewline
18 & 16.7 & 16.9353566780576 & -0.235356678057576 \tabularnewline
19 & 16.6 & 16.8791074575512 & -0.279107457551217 \tabularnewline
20 & 16.9 & 16.8480420484110 & 0.0519579515890279 \tabularnewline
21 & 15.7 & 15.9417792880156 & -0.241779288015571 \tabularnewline
22 & 16.4 & 16.101467851482 & 0.298532148517988 \tabularnewline
23 & 18.4 & 18.5876744067525 & -0.187674406752515 \tabularnewline
24 & 16.9 & 17.0042284049597 & -0.104228404959656 \tabularnewline
25 & 16.5 & 16.4837951209964 & 0.0162048790036415 \tabularnewline
26 & 18.3 & 17.9971214878390 & 0.302878512161034 \tabularnewline
27 & 15.1 & 15.3524549204894 & -0.252454920489449 \tabularnewline
28 & 15.7 & 15.5816573127565 & 0.118342687243487 \tabularnewline
29 & 18.1 & 18.0788636370471 & 0.0211363629529026 \tabularnewline
30 & 16.8 & 17.1155847303565 & -0.315584730356508 \tabularnewline
31 & 18.9 & 18.7959218760581 & 0.104078123941907 \tabularnewline
32 & 19 & 18.2723352623792 & 0.72766473762083 \tabularnewline
33 & 18.1 & 17.6960913475207 & 0.403908652479327 \tabularnewline
34 & 17.8 & 17.8470918465882 & -0.0470918465881536 \tabularnewline
35 & 21.5 & 20.9795196610748 & 0.520480338925197 \tabularnewline
36 & 17.1 & 17.0587777212295 & 0.0412222787705488 \tabularnewline
37 & 18.7 & 19.0428824049365 & -0.342882404936517 \tabularnewline
38 & 19 & 19.520997339621 & -0.520997339620994 \tabularnewline
39 & 16.4 & 16.8581485033708 & -0.458148503370805 \tabularnewline
40 & 16.9 & 16.9961490770563 & -0.0961490770563166 \tabularnewline
41 & 18.6 & 18.6680562884838 & -0.068056288483806 \tabularnewline
42 & 19.3 & 19.4331843720702 & -0.133184372070209 \tabularnewline
43 & 19.4 & 19.9005892763920 & -0.50058927639203 \tabularnewline
44 & 17.6 & 18.1454924534427 & -0.5454924534427 \tabularnewline
45 & 18.6 & 19.3037743825785 & -0.703774382578548 \tabularnewline
46 & 18.1 & 18.4346610520408 & -0.334661052040824 \tabularnewline
47 & 20.4 & 21.2362088343153 & -0.836208834315295 \tabularnewline
48 & 18.1 & 18.4661834245203 & -0.366183424520313 \tabularnewline
49 & 19.6 & 19.3598075155473 & 0.240192484452722 \tabularnewline
50 & 19.9 & 20.5143315604645 & -0.614331560464538 \tabularnewline
51 & 19.2 & 18.9746076359026 & 0.225392364097358 \tabularnewline
52 & 17.8 & 18.6640353271756 & -0.864035327175582 \tabularnewline
53 & 19.2 & 19.5192981412791 & -0.319298141279137 \tabularnewline
54 & 22 & 21.9585519457555 & 0.0414480542444776 \tabularnewline
55 & 21.1 & 20.7829531938282 & 0.317046806171787 \tabularnewline
56 & 19.5 & 19.2307200423467 & 0.269279957653273 \tabularnewline
57 & 22.2 & 21.7109112248166 & 0.489088775183414 \tabularnewline
58 & 20.9 & 21.2787374453993 & -0.378737445399308 \tabularnewline
59 & 22.2 & 22.0809283150931 & 0.119071684906883 \tabularnewline
60 & 23.5 & 23.1977498636498 & 0.302250136350196 \tabularnewline
61 & 21.5 & 21.3740368394466 & 0.125963160553397 \tabularnewline
62 & 24.3 & 24.2709075785906 & 0.0290924214094412 \tabularnewline
63 & 22.8 & 22.4429306111449 & 0.357069388855098 \tabularnewline
64 & 20.3 & 20.0854282449369 & 0.214571755063078 \tabularnewline
65 & 23.7 & 23.2497833317435 & 0.450216668256547 \tabularnewline
66 & 23.3 & 22.8998584484004 & 0.400141551599560 \tabularnewline
67 & 19.6 & 19.2117079515653 & 0.388292048434659 \tabularnewline
68 & 18 & 18.5950042340998 & -0.595004234099776 \tabularnewline
69 & 17.3 & 17.2986539873978 & 0.00134601260221030 \tabularnewline
70 & 16.8 & 16.6325361382969 & 0.167463861703146 \tabularnewline
71 & 18.2 & 17.9843952788899 & 0.215604721110143 \tabularnewline
72 & 16.5 & 16.4847424139316 & 0.0152575860684450 \tabularnewline
73 & 16 & 15.9028241532881 & 0.0971758467118542 \tabularnewline
74 & 18.4 & 17.9567981114936 & 0.44320188850643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58520&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]13.7[/C][C]13.6828760417325[/C][C]0.0171239582674963[/C][/ROW]
[ROW][C]2[/C][C]14.2[/C][C]14.3993450478646[/C][C]-0.199345047864642[/C][/ROW]
[ROW][C]3[/C][C]13.5[/C][C]13.4280233392573[/C][C]0.0719766607427173[/C][/ROW]
[ROW][C]4[/C][C]11.9[/C][C]11.5609734627314[/C][C]0.339026537268607[/C][/ROW]
[ROW][C]5[/C][C]14.6[/C][C]14.6671229011334[/C][C]-0.0671229011334472[/C][/ROW]
[ROW][C]6[/C][C]15.6[/C][C]15.3574638253597[/C][C]0.242536174640255[/C][/ROW]
[ROW][C]7[/C][C]14.1[/C][C]14.1297202446051[/C][C]-0.0297202446051058[/C][/ROW]
[ROW][C]8[/C][C]14.9[/C][C]14.8084059593207[/C][C]0.0915940406793455[/C][/ROW]
[ROW][C]9[/C][C]14.2[/C][C]14.1487897696708[/C][C]0.0512102303291676[/C][/ROW]
[ROW][C]10[/C][C]14.6[/C][C]14.3055056661928[/C][C]0.294494333807151[/C][/ROW]
[ROW][C]11[/C][C]17.2[/C][C]17.0312735038744[/C][C]0.168726496125587[/C][/ROW]
[ROW][C]12[/C][C]15.4[/C][C]15.2883181717092[/C][C]0.111681828290779[/C][/ROW]
[ROW][C]13[/C][C]14.3[/C][C]14.4537779240526[/C][C]-0.153777924052595[/C][/ROW]
[ROW][C]14[/C][C]17.5[/C][C]16.9404988741267[/C][C]0.559501125873268[/C][/ROW]
[ROW][C]15[/C][C]14.5[/C][C]14.4438349898349[/C][C]0.0561650101650815[/C][/ROW]
[ROW][C]16[/C][C]14.4[/C][C]14.1117565753433[/C][C]0.288243424656726[/C][/ROW]
[ROW][C]17[/C][C]16.6[/C][C]16.6168757003131[/C][C]-0.0168757003130596[/C][/ROW]
[ROW][C]18[/C][C]16.7[/C][C]16.9353566780576[/C][C]-0.235356678057576[/C][/ROW]
[ROW][C]19[/C][C]16.6[/C][C]16.8791074575512[/C][C]-0.279107457551217[/C][/ROW]
[ROW][C]20[/C][C]16.9[/C][C]16.8480420484110[/C][C]0.0519579515890279[/C][/ROW]
[ROW][C]21[/C][C]15.7[/C][C]15.9417792880156[/C][C]-0.241779288015571[/C][/ROW]
[ROW][C]22[/C][C]16.4[/C][C]16.101467851482[/C][C]0.298532148517988[/C][/ROW]
[ROW][C]23[/C][C]18.4[/C][C]18.5876744067525[/C][C]-0.187674406752515[/C][/ROW]
[ROW][C]24[/C][C]16.9[/C][C]17.0042284049597[/C][C]-0.104228404959656[/C][/ROW]
[ROW][C]25[/C][C]16.5[/C][C]16.4837951209964[/C][C]0.0162048790036415[/C][/ROW]
[ROW][C]26[/C][C]18.3[/C][C]17.9971214878390[/C][C]0.302878512161034[/C][/ROW]
[ROW][C]27[/C][C]15.1[/C][C]15.3524549204894[/C][C]-0.252454920489449[/C][/ROW]
[ROW][C]28[/C][C]15.7[/C][C]15.5816573127565[/C][C]0.118342687243487[/C][/ROW]
[ROW][C]29[/C][C]18.1[/C][C]18.0788636370471[/C][C]0.0211363629529026[/C][/ROW]
[ROW][C]30[/C][C]16.8[/C][C]17.1155847303565[/C][C]-0.315584730356508[/C][/ROW]
[ROW][C]31[/C][C]18.9[/C][C]18.7959218760581[/C][C]0.104078123941907[/C][/ROW]
[ROW][C]32[/C][C]19[/C][C]18.2723352623792[/C][C]0.72766473762083[/C][/ROW]
[ROW][C]33[/C][C]18.1[/C][C]17.6960913475207[/C][C]0.403908652479327[/C][/ROW]
[ROW][C]34[/C][C]17.8[/C][C]17.8470918465882[/C][C]-0.0470918465881536[/C][/ROW]
[ROW][C]35[/C][C]21.5[/C][C]20.9795196610748[/C][C]0.520480338925197[/C][/ROW]
[ROW][C]36[/C][C]17.1[/C][C]17.0587777212295[/C][C]0.0412222787705488[/C][/ROW]
[ROW][C]37[/C][C]18.7[/C][C]19.0428824049365[/C][C]-0.342882404936517[/C][/ROW]
[ROW][C]38[/C][C]19[/C][C]19.520997339621[/C][C]-0.520997339620994[/C][/ROW]
[ROW][C]39[/C][C]16.4[/C][C]16.8581485033708[/C][C]-0.458148503370805[/C][/ROW]
[ROW][C]40[/C][C]16.9[/C][C]16.9961490770563[/C][C]-0.0961490770563166[/C][/ROW]
[ROW][C]41[/C][C]18.6[/C][C]18.6680562884838[/C][C]-0.068056288483806[/C][/ROW]
[ROW][C]42[/C][C]19.3[/C][C]19.4331843720702[/C][C]-0.133184372070209[/C][/ROW]
[ROW][C]43[/C][C]19.4[/C][C]19.9005892763920[/C][C]-0.50058927639203[/C][/ROW]
[ROW][C]44[/C][C]17.6[/C][C]18.1454924534427[/C][C]-0.5454924534427[/C][/ROW]
[ROW][C]45[/C][C]18.6[/C][C]19.3037743825785[/C][C]-0.703774382578548[/C][/ROW]
[ROW][C]46[/C][C]18.1[/C][C]18.4346610520408[/C][C]-0.334661052040824[/C][/ROW]
[ROW][C]47[/C][C]20.4[/C][C]21.2362088343153[/C][C]-0.836208834315295[/C][/ROW]
[ROW][C]48[/C][C]18.1[/C][C]18.4661834245203[/C][C]-0.366183424520313[/C][/ROW]
[ROW][C]49[/C][C]19.6[/C][C]19.3598075155473[/C][C]0.240192484452722[/C][/ROW]
[ROW][C]50[/C][C]19.9[/C][C]20.5143315604645[/C][C]-0.614331560464538[/C][/ROW]
[ROW][C]51[/C][C]19.2[/C][C]18.9746076359026[/C][C]0.225392364097358[/C][/ROW]
[ROW][C]52[/C][C]17.8[/C][C]18.6640353271756[/C][C]-0.864035327175582[/C][/ROW]
[ROW][C]53[/C][C]19.2[/C][C]19.5192981412791[/C][C]-0.319298141279137[/C][/ROW]
[ROW][C]54[/C][C]22[/C][C]21.9585519457555[/C][C]0.0414480542444776[/C][/ROW]
[ROW][C]55[/C][C]21.1[/C][C]20.7829531938282[/C][C]0.317046806171787[/C][/ROW]
[ROW][C]56[/C][C]19.5[/C][C]19.2307200423467[/C][C]0.269279957653273[/C][/ROW]
[ROW][C]57[/C][C]22.2[/C][C]21.7109112248166[/C][C]0.489088775183414[/C][/ROW]
[ROW][C]58[/C][C]20.9[/C][C]21.2787374453993[/C][C]-0.378737445399308[/C][/ROW]
[ROW][C]59[/C][C]22.2[/C][C]22.0809283150931[/C][C]0.119071684906883[/C][/ROW]
[ROW][C]60[/C][C]23.5[/C][C]23.1977498636498[/C][C]0.302250136350196[/C][/ROW]
[ROW][C]61[/C][C]21.5[/C][C]21.3740368394466[/C][C]0.125963160553397[/C][/ROW]
[ROW][C]62[/C][C]24.3[/C][C]24.2709075785906[/C][C]0.0290924214094412[/C][/ROW]
[ROW][C]63[/C][C]22.8[/C][C]22.4429306111449[/C][C]0.357069388855098[/C][/ROW]
[ROW][C]64[/C][C]20.3[/C][C]20.0854282449369[/C][C]0.214571755063078[/C][/ROW]
[ROW][C]65[/C][C]23.7[/C][C]23.2497833317435[/C][C]0.450216668256547[/C][/ROW]
[ROW][C]66[/C][C]23.3[/C][C]22.8998584484004[/C][C]0.400141551599560[/C][/ROW]
[ROW][C]67[/C][C]19.6[/C][C]19.2117079515653[/C][C]0.388292048434659[/C][/ROW]
[ROW][C]68[/C][C]18[/C][C]18.5950042340998[/C][C]-0.595004234099776[/C][/ROW]
[ROW][C]69[/C][C]17.3[/C][C]17.2986539873978[/C][C]0.00134601260221030[/C][/ROW]
[ROW][C]70[/C][C]16.8[/C][C]16.6325361382969[/C][C]0.167463861703146[/C][/ROW]
[ROW][C]71[/C][C]18.2[/C][C]17.9843952788899[/C][C]0.215604721110143[/C][/ROW]
[ROW][C]72[/C][C]16.5[/C][C]16.4847424139316[/C][C]0.0152575860684450[/C][/ROW]
[ROW][C]73[/C][C]16[/C][C]15.9028241532881[/C][C]0.0971758467118542[/C][/ROW]
[ROW][C]74[/C][C]18.4[/C][C]17.9567981114936[/C][C]0.44320188850643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58520&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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
113.713.68287604173250.0171239582674963
214.214.3993450478646-0.199345047864642
313.513.42802333925730.0719766607427173
411.911.56097346273140.339026537268607
514.614.6671229011334-0.0671229011334472
615.615.35746382535970.242536174640255
714.114.1297202446051-0.0297202446051058
814.914.80840595932070.0915940406793455
914.214.14878976967080.0512102303291676
1014.614.30550566619280.294494333807151
1117.217.03127350387440.168726496125587
1215.415.28831817170920.111681828290779
1314.314.4537779240526-0.153777924052595
1417.516.94049887412670.559501125873268
1514.514.44383498983490.0561650101650815
1614.414.11175657534330.288243424656726
1716.616.6168757003131-0.0168757003130596
1816.716.9353566780576-0.235356678057576
1916.616.8791074575512-0.279107457551217
2016.916.84804204841100.0519579515890279
2115.715.9417792880156-0.241779288015571
2216.416.1014678514820.298532148517988
2318.418.5876744067525-0.187674406752515
2416.917.0042284049597-0.104228404959656
2516.516.48379512099640.0162048790036415
2618.317.99712148783900.302878512161034
2715.115.3524549204894-0.252454920489449
2815.715.58165731275650.118342687243487
2918.118.07886363704710.0211363629529026
3016.817.1155847303565-0.315584730356508
3118.918.79592187605810.104078123941907
321918.27233526237920.72766473762083
3318.117.69609134752070.403908652479327
3417.817.8470918465882-0.0470918465881536
3521.520.97951966107480.520480338925197
3617.117.05877772122950.0412222787705488
3718.719.0428824049365-0.342882404936517
381919.520997339621-0.520997339620994
3916.416.8581485033708-0.458148503370805
4016.916.9961490770563-0.0961490770563166
4118.618.6680562884838-0.068056288483806
4219.319.4331843720702-0.133184372070209
4319.419.9005892763920-0.50058927639203
4417.618.1454924534427-0.5454924534427
4518.619.3037743825785-0.703774382578548
4618.118.4346610520408-0.334661052040824
4720.421.2362088343153-0.836208834315295
4818.118.4661834245203-0.366183424520313
4919.619.35980751554730.240192484452722
5019.920.5143315604645-0.614331560464538
5119.218.97460763590260.225392364097358
5217.818.6640353271756-0.864035327175582
5319.219.5192981412791-0.319298141279137
542221.95855194575550.0414480542444776
5521.120.78295319382820.317046806171787
5619.519.23072004234670.269279957653273
5722.221.71091122481660.489088775183414
5820.921.2787374453993-0.378737445399308
5922.222.08092831509310.119071684906883
6023.523.19774986364980.302250136350196
6121.521.37403683944660.125963160553397
6224.324.27090757859060.0290924214094412
6322.822.44293061114490.357069388855098
6420.320.08542824493690.214571755063078
6523.723.24978333174350.450216668256547
6623.322.89985844840040.400141551599560
6719.619.21170795156530.388292048434659
681818.5950042340998-0.595004234099776
6917.317.29865398739780.00134601260221030
7016.816.63253613829690.167463861703146
7118.217.98439527888990.215604721110143
7216.516.48474241393160.0152575860684450
731615.90282415328810.0971758467118542
7418.417.95679811149360.44320188850643






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.06419711590493760.1283942318098750.935802884095062
220.04085153648639140.08170307297278280.959148463513609
230.01572856502223860.03145713004447720.984271434977761
240.00501951951934980.01003903903869960.99498048048065
250.001447172784733160.002894345569466310.998552827215267
260.000576060342238970.001152120684477940.99942393965776
270.0001694149788093410.0003388299576186820.99983058502119
280.0001027829982688910.0002055659965377820.99989721700173
293.32736923598257e-056.65473847196515e-050.99996672630764
301.10792150882343e-052.21584301764686e-050.999988920784912
313.28694967846295e-066.5738993569259e-060.999996713050322
322.22459011017784e-054.44918022035568e-050.999977754098898
330.0001529911735493700.0003059823470987410.99984700882645
347.3674708443508e-050.0001473494168870160.999926325291556
350.01094426718756130.02188853437512260.989055732812439
360.02981430172757020.05962860345514030.97018569827243
370.02060381281629470.04120762563258930.979396187183705
380.08129365073261050.1625873014652210.91870634926739
390.0575723034407490.1151446068814980.942427696559251
400.1081167883952170.2162335767904340.891883211604783
410.1132633667313810.2265267334627630.886736633268619
420.07624662625046440.1524932525009290.923753373749536
430.0815990918403010.1631981836806020.9184009081597
440.0650643377278020.1301286754556040.934935662272198
450.1145110837561970.2290221675123930.885488916243803
460.1103438093249460.2206876186498920.889656190675054
470.2515579766368250.503115953273650.748442023363175
480.2253758559349510.4507517118699020.77462414406505
490.4555392552144780.9110785104289570.544460744785522
500.539007908026380.9219841839472390.460992091973620
510.4575037238047770.9150074476095540.542496276195223
520.413832347299440.827664694598880.58616765270056
530.2677727669801620.5355455339603240.732227233019838

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0641971159049376 & 0.128394231809875 & 0.935802884095062 \tabularnewline
22 & 0.0408515364863914 & 0.0817030729727828 & 0.959148463513609 \tabularnewline
23 & 0.0157285650222386 & 0.0314571300444772 & 0.984271434977761 \tabularnewline
24 & 0.0050195195193498 & 0.0100390390386996 & 0.99498048048065 \tabularnewline
25 & 0.00144717278473316 & 0.00289434556946631 & 0.998552827215267 \tabularnewline
26 & 0.00057606034223897 & 0.00115212068447794 & 0.99942393965776 \tabularnewline
27 & 0.000169414978809341 & 0.000338829957618682 & 0.99983058502119 \tabularnewline
28 & 0.000102782998268891 & 0.000205565996537782 & 0.99989721700173 \tabularnewline
29 & 3.32736923598257e-05 & 6.65473847196515e-05 & 0.99996672630764 \tabularnewline
30 & 1.10792150882343e-05 & 2.21584301764686e-05 & 0.999988920784912 \tabularnewline
31 & 3.28694967846295e-06 & 6.5738993569259e-06 & 0.999996713050322 \tabularnewline
32 & 2.22459011017784e-05 & 4.44918022035568e-05 & 0.999977754098898 \tabularnewline
33 & 0.000152991173549370 & 0.000305982347098741 & 0.99984700882645 \tabularnewline
34 & 7.3674708443508e-05 & 0.000147349416887016 & 0.999926325291556 \tabularnewline
35 & 0.0109442671875613 & 0.0218885343751226 & 0.989055732812439 \tabularnewline
36 & 0.0298143017275702 & 0.0596286034551403 & 0.97018569827243 \tabularnewline
37 & 0.0206038128162947 & 0.0412076256325893 & 0.979396187183705 \tabularnewline
38 & 0.0812936507326105 & 0.162587301465221 & 0.91870634926739 \tabularnewline
39 & 0.057572303440749 & 0.115144606881498 & 0.942427696559251 \tabularnewline
40 & 0.108116788395217 & 0.216233576790434 & 0.891883211604783 \tabularnewline
41 & 0.113263366731381 & 0.226526733462763 & 0.886736633268619 \tabularnewline
42 & 0.0762466262504644 & 0.152493252500929 & 0.923753373749536 \tabularnewline
43 & 0.081599091840301 & 0.163198183680602 & 0.9184009081597 \tabularnewline
44 & 0.065064337727802 & 0.130128675455604 & 0.934935662272198 \tabularnewline
45 & 0.114511083756197 & 0.229022167512393 & 0.885488916243803 \tabularnewline
46 & 0.110343809324946 & 0.220687618649892 & 0.889656190675054 \tabularnewline
47 & 0.251557976636825 & 0.50311595327365 & 0.748442023363175 \tabularnewline
48 & 0.225375855934951 & 0.450751711869902 & 0.77462414406505 \tabularnewline
49 & 0.455539255214478 & 0.911078510428957 & 0.544460744785522 \tabularnewline
50 & 0.53900790802638 & 0.921984183947239 & 0.460992091973620 \tabularnewline
51 & 0.457503723804777 & 0.915007447609554 & 0.542496276195223 \tabularnewline
52 & 0.41383234729944 & 0.82766469459888 & 0.58616765270056 \tabularnewline
53 & 0.267772766980162 & 0.535545533960324 & 0.732227233019838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58520&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]0.0641971159049376[/C][C]0.128394231809875[/C][C]0.935802884095062[/C][/ROW]
[ROW][C]22[/C][C]0.0408515364863914[/C][C]0.0817030729727828[/C][C]0.959148463513609[/C][/ROW]
[ROW][C]23[/C][C]0.0157285650222386[/C][C]0.0314571300444772[/C][C]0.984271434977761[/C][/ROW]
[ROW][C]24[/C][C]0.0050195195193498[/C][C]0.0100390390386996[/C][C]0.99498048048065[/C][/ROW]
[ROW][C]25[/C][C]0.00144717278473316[/C][C]0.00289434556946631[/C][C]0.998552827215267[/C][/ROW]
[ROW][C]26[/C][C]0.00057606034223897[/C][C]0.00115212068447794[/C][C]0.99942393965776[/C][/ROW]
[ROW][C]27[/C][C]0.000169414978809341[/C][C]0.000338829957618682[/C][C]0.99983058502119[/C][/ROW]
[ROW][C]28[/C][C]0.000102782998268891[/C][C]0.000205565996537782[/C][C]0.99989721700173[/C][/ROW]
[ROW][C]29[/C][C]3.32736923598257e-05[/C][C]6.65473847196515e-05[/C][C]0.99996672630764[/C][/ROW]
[ROW][C]30[/C][C]1.10792150882343e-05[/C][C]2.21584301764686e-05[/C][C]0.999988920784912[/C][/ROW]
[ROW][C]31[/C][C]3.28694967846295e-06[/C][C]6.5738993569259e-06[/C][C]0.999996713050322[/C][/ROW]
[ROW][C]32[/C][C]2.22459011017784e-05[/C][C]4.44918022035568e-05[/C][C]0.999977754098898[/C][/ROW]
[ROW][C]33[/C][C]0.000152991173549370[/C][C]0.000305982347098741[/C][C]0.99984700882645[/C][/ROW]
[ROW][C]34[/C][C]7.3674708443508e-05[/C][C]0.000147349416887016[/C][C]0.999926325291556[/C][/ROW]
[ROW][C]35[/C][C]0.0109442671875613[/C][C]0.0218885343751226[/C][C]0.989055732812439[/C][/ROW]
[ROW][C]36[/C][C]0.0298143017275702[/C][C]0.0596286034551403[/C][C]0.97018569827243[/C][/ROW]
[ROW][C]37[/C][C]0.0206038128162947[/C][C]0.0412076256325893[/C][C]0.979396187183705[/C][/ROW]
[ROW][C]38[/C][C]0.0812936507326105[/C][C]0.162587301465221[/C][C]0.91870634926739[/C][/ROW]
[ROW][C]39[/C][C]0.057572303440749[/C][C]0.115144606881498[/C][C]0.942427696559251[/C][/ROW]
[ROW][C]40[/C][C]0.108116788395217[/C][C]0.216233576790434[/C][C]0.891883211604783[/C][/ROW]
[ROW][C]41[/C][C]0.113263366731381[/C][C]0.226526733462763[/C][C]0.886736633268619[/C][/ROW]
[ROW][C]42[/C][C]0.0762466262504644[/C][C]0.152493252500929[/C][C]0.923753373749536[/C][/ROW]
[ROW][C]43[/C][C]0.081599091840301[/C][C]0.163198183680602[/C][C]0.9184009081597[/C][/ROW]
[ROW][C]44[/C][C]0.065064337727802[/C][C]0.130128675455604[/C][C]0.934935662272198[/C][/ROW]
[ROW][C]45[/C][C]0.114511083756197[/C][C]0.229022167512393[/C][C]0.885488916243803[/C][/ROW]
[ROW][C]46[/C][C]0.110343809324946[/C][C]0.220687618649892[/C][C]0.889656190675054[/C][/ROW]
[ROW][C]47[/C][C]0.251557976636825[/C][C]0.50311595327365[/C][C]0.748442023363175[/C][/ROW]
[ROW][C]48[/C][C]0.225375855934951[/C][C]0.450751711869902[/C][C]0.77462414406505[/C][/ROW]
[ROW][C]49[/C][C]0.455539255214478[/C][C]0.911078510428957[/C][C]0.544460744785522[/C][/ROW]
[ROW][C]50[/C][C]0.53900790802638[/C][C]0.921984183947239[/C][C]0.460992091973620[/C][/ROW]
[ROW][C]51[/C][C]0.457503723804777[/C][C]0.915007447609554[/C][C]0.542496276195223[/C][/ROW]
[ROW][C]52[/C][C]0.41383234729944[/C][C]0.82766469459888[/C][C]0.58616765270056[/C][/ROW]
[ROW][C]53[/C][C]0.267772766980162[/C][C]0.535545533960324[/C][C]0.732227233019838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58520&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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
210.06419711590493760.1283942318098750.935802884095062
220.04085153648639140.08170307297278280.959148463513609
230.01572856502223860.03145713004447720.984271434977761
240.00501951951934980.01003903903869960.99498048048065
250.001447172784733160.002894345569466310.998552827215267
260.000576060342238970.001152120684477940.99942393965776
270.0001694149788093410.0003388299576186820.99983058502119
280.0001027829982688910.0002055659965377820.99989721700173
293.32736923598257e-056.65473847196515e-050.99996672630764
301.10792150882343e-052.21584301764686e-050.999988920784912
313.28694967846295e-066.5738993569259e-060.999996713050322
322.22459011017784e-054.44918022035568e-050.999977754098898
330.0001529911735493700.0003059823470987410.99984700882645
347.3674708443508e-050.0001473494168870160.999926325291556
350.01094426718756130.02188853437512260.989055732812439
360.02981430172757020.05962860345514030.97018569827243
370.02060381281629470.04120762563258930.979396187183705
380.08129365073261050.1625873014652210.91870634926739
390.0575723034407490.1151446068814980.942427696559251
400.1081167883952170.2162335767904340.891883211604783
410.1132633667313810.2265267334627630.886736633268619
420.07624662625046440.1524932525009290.923753373749536
430.0815990918403010.1631981836806020.9184009081597
440.0650643377278020.1301286754556040.934935662272198
450.1145110837561970.2290221675123930.885488916243803
460.1103438093249460.2206876186498920.889656190675054
470.2515579766368250.503115953273650.748442023363175
480.2253758559349510.4507517118699020.77462414406505
490.4555392552144780.9110785104289570.544460744785522
500.539007908026380.9219841839472390.460992091973620
510.4575037238047770.9150074476095540.542496276195223
520.413832347299440.827664694598880.58616765270056
530.2677727669801620.5355455339603240.732227233019838






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level100.303030303030303NOK
5% type I error level140.424242424242424NOK
10% type I error level160.484848484848485NOK

\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 & 10 & 0.303030303030303 & NOK \tabularnewline
5% type I error level & 14 & 0.424242424242424 & NOK \tabularnewline
10% type I error level & 16 & 0.484848484848485 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58520&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]10[/C][C]0.303030303030303[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.424242424242424[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]16[/C][C]0.484848484848485[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58520&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58520&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 level100.303030303030303NOK
5% type I error level140.424242424242424NOK
10% type I error level160.484848484848485NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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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')
}