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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 computationTue, 29 Dec 2015 13:40:09 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/29/t1451397385ofas3m8t6sjk6n8.htm/, Retrieved Thu, 31 Oct 2024 22:49:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287159, Retrieved Thu, 31 Oct 2024 22:49:32 +0000
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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] [5] [2015-12-29 13:40:09] [f1753cbe688dba6ba3df6a7d2c11f204] [Current]
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Dataseries X:
46.4 392 0.4
45.7 118 0.61
45.3 44 0.53
38.6 158 0.53
37.2 81 0.53
35 374 0.37
34 187 0.3
28.3 993 0.19
24.7 1723 0.12
24.7 287 0.2
24.4 970 0.19
22.7 885 0.12
22.3 200 0.53
21.7 575 0.14
21.6 688 0.34
21.3 48 0.69
21.2 572 0.49
20.8 239 0.42
20.3 244 0.48
18.9 472 0.25
18.8 134 0.52
18.6 633 0.19
18 295 0.44
17.6 906 0.24
17 1045 0.16
16.7 775 0.1
15.9 619 0.15
15.3 901 0.05
15 910 0.24
14.8 556 0.22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Multiple Linear Regression - Estimated Regression Equation
HIV_Risk[t] = + 19.428 -0.00285669Per_Capita_Income[t] + 21.1227Prop_Population_on_Farms[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
HIV_Risk[t] =  +  19.428 -0.00285669Per_Capita_Income[t] +  21.1227Prop_Population_on_Farms[t]  + e[t] \tabularnewline
Warning: you did not specify the column number of the endogenous series! The first column was selected by default. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]HIV_Risk[t] =  +  19.428 -0.00285669Per_Capita_Income[t] +  21.1227Prop_Population_on_Farms[t]  + e[t][/C][/ROW]
[ROW][C]Warning: you did not specify the column number of the endogenous series! The first column was selected by default.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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
HIV_Risk[t] = + 19.428 -0.00285669Per_Capita_Income[t] + 21.1227Prop_Population_on_Farms[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)+19.43 7.867+2.4700e+00 0.02014 0.01007
Per_Capita_Income-0.002857 0.006518-4.3830e-01 0.6647 0.3323
Prop_Population_on_Farms+21.12 14.43+1.4640e+00 0.1548 0.07742

\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) & +19.43 &  7.867 & +2.4700e+00 &  0.02014 &  0.01007 \tabularnewline
Per_Capita_Income & -0.002857 &  0.006518 & -4.3830e-01 &  0.6647 &  0.3323 \tabularnewline
Prop_Population_on_Farms & +21.12 &  14.43 & +1.4640e+00 &  0.1548 &  0.07742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&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]+19.43[/C][C] 7.867[/C][C]+2.4700e+00[/C][C] 0.02014[/C][C] 0.01007[/C][/ROW]
[ROW][C]Per_Capita_Income[/C][C]-0.002857[/C][C] 0.006518[/C][C]-4.3830e-01[/C][C] 0.6647[/C][C] 0.3323[/C][/ROW]
[ROW][C]Prop_Population_on_Farms[/C][C]+21.12[/C][C] 14.43[/C][C]+1.4640e+00[/C][C] 0.1548[/C][C] 0.07742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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)+19.43 7.867+2.4700e+00 0.02014 0.01007
Per_Capita_Income-0.002857 0.006518-4.3830e-01 0.6647 0.3323
Prop_Population_on_Farms+21.12 14.43+1.4640e+00 0.1548 0.07742







Multiple Linear Regression - Regression Statistics
Multiple R 0.486
R-squared 0.2362
Adjusted R-squared 0.1797
F-TEST (value) 4.176
F-TEST (DF numerator)2
F-TEST (DF denominator)27
p-value 0.0263
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 8.675
Sum Squared Residuals 2032

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.486 \tabularnewline
R-squared &  0.2362 \tabularnewline
Adjusted R-squared &  0.1797 \tabularnewline
F-TEST (value) &  4.176 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 27 \tabularnewline
p-value &  0.0263 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  8.675 \tabularnewline
Sum Squared Residuals &  2032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.486[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.2362[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.1797[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 4.176[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]27[/C][/ROW]
[ROW][C]p-value[/C][C] 0.0263[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 8.675[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 2032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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 R 0.486
R-squared 0.2362
Adjusted R-squared 0.1797
F-TEST (value) 4.176
F-TEST (DF numerator)2
F-TEST (DF denominator)27
p-value 0.0263
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 8.675
Sum Squared Residuals 2032







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1 46.4 26.76 19.64
2 45.7 31.98 13.72
3 45.3 30.5 14.8
4 38.6 30.17 8.428
5 37.2 30.39 6.808
6 35 26.18 8.825
7 34 25.23 8.769
8 28.3 20.6 7.695
9 24.7 17.04 7.659
10 24.7 22.83 1.867
11 24.4 20.67 3.73
12 22.7 19.43 3.265
13 22.3 30.05-7.752
14 21.7 20.74 0.9574
15 21.6 24.64-3.044
16 21.3 33.87-12.57
17 21.2 28.14-6.944
18 20.8 27.62-6.817
19 20.3 28.87-8.57
20 18.9 23.36-4.46
21 18.8 30.03-11.23
22 18.6 21.63-3.033
23 18 27.88-9.879
24 17.6 21.91-4.309
25 17 19.82-2.822
26 16.7 19.33-2.626
27 15.9 20.83-4.928
28 15.3 17.91-2.61
29 15 21.9-6.898
30 14.8 22.49-7.687

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  46.4 &  26.76 &  19.64 \tabularnewline
2 &  45.7 &  31.98 &  13.72 \tabularnewline
3 &  45.3 &  30.5 &  14.8 \tabularnewline
4 &  38.6 &  30.17 &  8.428 \tabularnewline
5 &  37.2 &  30.39 &  6.808 \tabularnewline
6 &  35 &  26.18 &  8.825 \tabularnewline
7 &  34 &  25.23 &  8.769 \tabularnewline
8 &  28.3 &  20.6 &  7.695 \tabularnewline
9 &  24.7 &  17.04 &  7.659 \tabularnewline
10 &  24.7 &  22.83 &  1.867 \tabularnewline
11 &  24.4 &  20.67 &  3.73 \tabularnewline
12 &  22.7 &  19.43 &  3.265 \tabularnewline
13 &  22.3 &  30.05 & -7.752 \tabularnewline
14 &  21.7 &  20.74 &  0.9574 \tabularnewline
15 &  21.6 &  24.64 & -3.044 \tabularnewline
16 &  21.3 &  33.87 & -12.57 \tabularnewline
17 &  21.2 &  28.14 & -6.944 \tabularnewline
18 &  20.8 &  27.62 & -6.817 \tabularnewline
19 &  20.3 &  28.87 & -8.57 \tabularnewline
20 &  18.9 &  23.36 & -4.46 \tabularnewline
21 &  18.8 &  30.03 & -11.23 \tabularnewline
22 &  18.6 &  21.63 & -3.033 \tabularnewline
23 &  18 &  27.88 & -9.879 \tabularnewline
24 &  17.6 &  21.91 & -4.309 \tabularnewline
25 &  17 &  19.82 & -2.822 \tabularnewline
26 &  16.7 &  19.33 & -2.626 \tabularnewline
27 &  15.9 &  20.83 & -4.928 \tabularnewline
28 &  15.3 &  17.91 & -2.61 \tabularnewline
29 &  15 &  21.9 & -6.898 \tabularnewline
30 &  14.8 &  22.49 & -7.687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&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] 46.4[/C][C] 26.76[/C][C] 19.64[/C][/ROW]
[ROW][C]2[/C][C] 45.7[/C][C] 31.98[/C][C] 13.72[/C][/ROW]
[ROW][C]3[/C][C] 45.3[/C][C] 30.5[/C][C] 14.8[/C][/ROW]
[ROW][C]4[/C][C] 38.6[/C][C] 30.17[/C][C] 8.428[/C][/ROW]
[ROW][C]5[/C][C] 37.2[/C][C] 30.39[/C][C] 6.808[/C][/ROW]
[ROW][C]6[/C][C] 35[/C][C] 26.18[/C][C] 8.825[/C][/ROW]
[ROW][C]7[/C][C] 34[/C][C] 25.23[/C][C] 8.769[/C][/ROW]
[ROW][C]8[/C][C] 28.3[/C][C] 20.6[/C][C] 7.695[/C][/ROW]
[ROW][C]9[/C][C] 24.7[/C][C] 17.04[/C][C] 7.659[/C][/ROW]
[ROW][C]10[/C][C] 24.7[/C][C] 22.83[/C][C] 1.867[/C][/ROW]
[ROW][C]11[/C][C] 24.4[/C][C] 20.67[/C][C] 3.73[/C][/ROW]
[ROW][C]12[/C][C] 22.7[/C][C] 19.43[/C][C] 3.265[/C][/ROW]
[ROW][C]13[/C][C] 22.3[/C][C] 30.05[/C][C]-7.752[/C][/ROW]
[ROW][C]14[/C][C] 21.7[/C][C] 20.74[/C][C] 0.9574[/C][/ROW]
[ROW][C]15[/C][C] 21.6[/C][C] 24.64[/C][C]-3.044[/C][/ROW]
[ROW][C]16[/C][C] 21.3[/C][C] 33.87[/C][C]-12.57[/C][/ROW]
[ROW][C]17[/C][C] 21.2[/C][C] 28.14[/C][C]-6.944[/C][/ROW]
[ROW][C]18[/C][C] 20.8[/C][C] 27.62[/C][C]-6.817[/C][/ROW]
[ROW][C]19[/C][C] 20.3[/C][C] 28.87[/C][C]-8.57[/C][/ROW]
[ROW][C]20[/C][C] 18.9[/C][C] 23.36[/C][C]-4.46[/C][/ROW]
[ROW][C]21[/C][C] 18.8[/C][C] 30.03[/C][C]-11.23[/C][/ROW]
[ROW][C]22[/C][C] 18.6[/C][C] 21.63[/C][C]-3.033[/C][/ROW]
[ROW][C]23[/C][C] 18[/C][C] 27.88[/C][C]-9.879[/C][/ROW]
[ROW][C]24[/C][C] 17.6[/C][C] 21.91[/C][C]-4.309[/C][/ROW]
[ROW][C]25[/C][C] 17[/C][C] 19.82[/C][C]-2.822[/C][/ROW]
[ROW][C]26[/C][C] 16.7[/C][C] 19.33[/C][C]-2.626[/C][/ROW]
[ROW][C]27[/C][C] 15.9[/C][C] 20.83[/C][C]-4.928[/C][/ROW]
[ROW][C]28[/C][C] 15.3[/C][C] 17.91[/C][C]-2.61[/C][/ROW]
[ROW][C]29[/C][C] 15[/C][C] 21.9[/C][C]-6.898[/C][/ROW]
[ROW][C]30[/C][C] 14.8[/C][C] 22.49[/C][C]-7.687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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
1 46.4 26.76 19.64
2 45.7 31.98 13.72
3 45.3 30.5 14.8
4 38.6 30.17 8.428
5 37.2 30.39 6.808
6 35 26.18 8.825
7 34 25.23 8.769
8 28.3 20.6 7.695
9 24.7 17.04 7.659
10 24.7 22.83 1.867
11 24.4 20.67 3.73
12 22.7 19.43 3.265
13 22.3 30.05-7.752
14 21.7 20.74 0.9574
15 21.6 24.64-3.044
16 21.3 33.87-12.57
17 21.2 28.14-6.944
18 20.8 27.62-6.817
19 20.3 28.87-8.57
20 18.9 23.36-4.46
21 18.8 30.03-11.23
22 18.6 21.63-3.033
23 18 27.88-9.879
24 17.6 21.91-4.309
25 17 19.82-2.822
26 16.7 19.33-2.626
27 15.9 20.83-4.928
28 15.3 17.91-2.61
29 15 21.9-6.898
30 14.8 22.49-7.687







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
6 0.7667 0.4667 0.2333
7 0.8667 0.2666 0.1333
8 0.9412 0.1177 0.05885
9 0.9335 0.133 0.0665
10 0.9674 0.06522 0.03261
11 0.9862 0.02757 0.01378
12 0.9951 0.009866 0.004933
13 1 5.651e-05 2.825e-05
14 1 1.131e-05 5.657e-06
15 1 3.143e-06 1.571e-06
16 1 1.357e-06 6.783e-07
17 1 2.577e-06 1.289e-06
18 1 4.68e-06 2.34e-06
19 1 1.242e-05 6.212e-06
20 1 3.293e-05 1.646e-05
21 0.9999 0.000163 8.151e-05
22 0.9999 0.0002887 0.0001444
23 0.9995 0.001037 0.0005185
24 0.9982 0.0036 0.0018

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
6 &  0.7667 &  0.4667 &  0.2333 \tabularnewline
7 &  0.8667 &  0.2666 &  0.1333 \tabularnewline
8 &  0.9412 &  0.1177 &  0.05885 \tabularnewline
9 &  0.9335 &  0.133 &  0.0665 \tabularnewline
10 &  0.9674 &  0.06522 &  0.03261 \tabularnewline
11 &  0.9862 &  0.02757 &  0.01378 \tabularnewline
12 &  0.9951 &  0.009866 &  0.004933 \tabularnewline
13 &  1 &  5.651e-05 &  2.825e-05 \tabularnewline
14 &  1 &  1.131e-05 &  5.657e-06 \tabularnewline
15 &  1 &  3.143e-06 &  1.571e-06 \tabularnewline
16 &  1 &  1.357e-06 &  6.783e-07 \tabularnewline
17 &  1 &  2.577e-06 &  1.289e-06 \tabularnewline
18 &  1 &  4.68e-06 &  2.34e-06 \tabularnewline
19 &  1 &  1.242e-05 &  6.212e-06 \tabularnewline
20 &  1 &  3.293e-05 &  1.646e-05 \tabularnewline
21 &  0.9999 &  0.000163 &  8.151e-05 \tabularnewline
22 &  0.9999 &  0.0002887 &  0.0001444 \tabularnewline
23 &  0.9995 &  0.001037 &  0.0005185 \tabularnewline
24 &  0.9982 &  0.0036 &  0.0018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&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]6[/C][C] 0.7667[/C][C] 0.4667[/C][C] 0.2333[/C][/ROW]
[ROW][C]7[/C][C] 0.8667[/C][C] 0.2666[/C][C] 0.1333[/C][/ROW]
[ROW][C]8[/C][C] 0.9412[/C][C] 0.1177[/C][C] 0.05885[/C][/ROW]
[ROW][C]9[/C][C] 0.9335[/C][C] 0.133[/C][C] 0.0665[/C][/ROW]
[ROW][C]10[/C][C] 0.9674[/C][C] 0.06522[/C][C] 0.03261[/C][/ROW]
[ROW][C]11[/C][C] 0.9862[/C][C] 0.02757[/C][C] 0.01378[/C][/ROW]
[ROW][C]12[/C][C] 0.9951[/C][C] 0.009866[/C][C] 0.004933[/C][/ROW]
[ROW][C]13[/C][C] 1[/C][C] 5.651e-05[/C][C] 2.825e-05[/C][/ROW]
[ROW][C]14[/C][C] 1[/C][C] 1.131e-05[/C][C] 5.657e-06[/C][/ROW]
[ROW][C]15[/C][C] 1[/C][C] 3.143e-06[/C][C] 1.571e-06[/C][/ROW]
[ROW][C]16[/C][C] 1[/C][C] 1.357e-06[/C][C] 6.783e-07[/C][/ROW]
[ROW][C]17[/C][C] 1[/C][C] 2.577e-06[/C][C] 1.289e-06[/C][/ROW]
[ROW][C]18[/C][C] 1[/C][C] 4.68e-06[/C][C] 2.34e-06[/C][/ROW]
[ROW][C]19[/C][C] 1[/C][C] 1.242e-05[/C][C] 6.212e-06[/C][/ROW]
[ROW][C]20[/C][C] 1[/C][C] 3.293e-05[/C][C] 1.646e-05[/C][/ROW]
[ROW][C]21[/C][C] 0.9999[/C][C] 0.000163[/C][C] 8.151e-05[/C][/ROW]
[ROW][C]22[/C][C] 0.9999[/C][C] 0.0002887[/C][C] 0.0001444[/C][/ROW]
[ROW][C]23[/C][C] 0.9995[/C][C] 0.001037[/C][C] 0.0005185[/C][/ROW]
[ROW][C]24[/C][C] 0.9982[/C][C] 0.0036[/C][C] 0.0018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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
6 0.7667 0.4667 0.2333
7 0.8667 0.2666 0.1333
8 0.9412 0.1177 0.05885
9 0.9335 0.133 0.0665
10 0.9674 0.06522 0.03261
11 0.9862 0.02757 0.01378
12 0.9951 0.009866 0.004933
13 1 5.651e-05 2.825e-05
14 1 1.131e-05 5.657e-06
15 1 3.143e-06 1.571e-06
16 1 1.357e-06 6.783e-07
17 1 2.577e-06 1.289e-06
18 1 4.68e-06 2.34e-06
19 1 1.242e-05 6.212e-06
20 1 3.293e-05 1.646e-05
21 0.9999 0.000163 8.151e-05
22 0.9999 0.0002887 0.0001444
23 0.9995 0.001037 0.0005185
24 0.9982 0.0036 0.0018







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level13 0.6842NOK
5% type I error level140.736842NOK
10% type I error level150.789474NOK

\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 & 13 &  0.6842 & NOK \tabularnewline
5% type I error level & 14 & 0.736842 & NOK \tabularnewline
10% type I error level & 15 & 0.789474 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287159&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]13[/C][C] 0.6842[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.736842[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]0.789474[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287159&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287159&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 level13 0.6842NOK
5% type I error level140.736842NOK
10% type I error level150.789474NOK



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 99 ; par4 = two.sided ; par5 = paired ; par6 = 0 ;
Parameters (R input):
par1 = ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = ; par5 = ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
x <- na.omit(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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s=12)'){
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s=12)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
if(par5 > 0) {
x2 <- array(0, dim=c(n-par5*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*12)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*12-j*12,par1]
}
}
x <- cbind(x[(par5*12+1):n,], x2)
n <- n - par5*12
}
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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
(k <- length(x[n,]))
head(x)
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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, mywarning)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
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,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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')
}
}