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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 computationFri, 17 Dec 2010 12:30:50 +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/2010/Dec/17/t1292588995r6y6luq7dviedk5.htm/, Retrieved Wed, 19 Nov 2025 06:19:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111428, Retrieved Wed, 19 Nov 2025 06:19:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact385

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD  [Multiple Regression] [] [2010-11-26 11:40:42] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D    [Multiple Regression] [] [2010-12-15 20:39:35] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D      [Multiple Regression] [] [2010-12-17 12:00:00] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D          [Multiple Regression] [] [2010-12-17 12:30:50] [1d094c42a82a95b45a19e32ad4bfff5f] [Current]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time20 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 & 20 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&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]20 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=111428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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 time20 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
HPC[t] = + 16.5858823529412 -0.274705882352939M1[t] -0.496078431372549M2[t] + 1.45352941176471M3[t] -0.116862745098041M4[t] -0.00725490196078604M5[t] + 1.04235294117647M6[t] -0.588039215686275M7[t] -1.19843137254902M8[t] + 0.931176470588234M9[t] + 1.14078431372549M10[t] + 0.690392156862744M11[t] + 0.0103921568627451t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
HPC[t] =  +  16.5858823529412 -0.274705882352939M1[t] -0.496078431372549M2[t] +  1.45352941176471M3[t] -0.116862745098041M4[t] -0.00725490196078604M5[t] +  1.04235294117647M6[t] -0.588039215686275M7[t] -1.19843137254902M8[t] +  0.931176470588234M9[t] +  1.14078431372549M10[t] +  0.690392156862744M11[t] +  0.0103921568627451t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]HPC[t] =  +  16.5858823529412 -0.274705882352939M1[t] -0.496078431372549M2[t] +  1.45352941176471M3[t] -0.116862745098041M4[t] -0.00725490196078604M5[t] +  1.04235294117647M6[t] -0.588039215686275M7[t] -1.19843137254902M8[t] +  0.931176470588234M9[t] +  1.14078431372549M10[t] +  0.690392156862744M11[t] +  0.0103921568627451t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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
HPC[t] = + 16.5858823529412 -0.274705882352939M1[t] -0.496078431372549M2[t] + 1.45352941176471M3[t] -0.116862745098041M4[t] -0.00725490196078604M5[t] + 1.04235294117647M6[t] -0.588039215686275M7[t] -1.19843137254902M8[t] + 0.931176470588234M9[t] + 1.14078431372549M10[t] + 0.690392156862744M11[t] + 0.0103921568627451t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)16.58588235294121.07742215.39400
M1-0.2747058823529391.256527-0.21860.8278710.413935
M2-0.4960784313725491.318858-0.37610.7084690.354234
M31.453529411764711.3171741.10350.2753030.137651
M4-0.1168627450980411.315665-0.08880.9295910.464796
M5-0.007254901960786041.314333-0.00550.9956190.497809
M61.042352941176471.3131770.79380.4312390.21562
M7-0.5880392156862751.312198-0.44810.6560730.328037
M8-1.198431372549021.311396-0.91390.3653590.182679
M90.9311764705882341.3107720.71040.4808920.240446
M101.140784313725491.3103270.87060.38830.19415
M110.6903921568627441.3100590.5270.6006260.300313
t0.01039215686274510.0152860.67980.4998680.249934

\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) & 16.5858823529412 & 1.077422 & 15.394 & 0 & 0 \tabularnewline
M1 & -0.274705882352939 & 1.256527 & -0.2186 & 0.827871 & 0.413935 \tabularnewline
M2 & -0.496078431372549 & 1.318858 & -0.3761 & 0.708469 & 0.354234 \tabularnewline
M3 & 1.45352941176471 & 1.317174 & 1.1035 & 0.275303 & 0.137651 \tabularnewline
M4 & -0.116862745098041 & 1.315665 & -0.0888 & 0.929591 & 0.464796 \tabularnewline
M5 & -0.00725490196078604 & 1.314333 & -0.0055 & 0.995619 & 0.497809 \tabularnewline
M6 & 1.04235294117647 & 1.313177 & 0.7938 & 0.431239 & 0.21562 \tabularnewline
M7 & -0.588039215686275 & 1.312198 & -0.4481 & 0.656073 & 0.328037 \tabularnewline
M8 & -1.19843137254902 & 1.311396 & -0.9139 & 0.365359 & 0.182679 \tabularnewline
M9 & 0.931176470588234 & 1.310772 & 0.7104 & 0.480892 & 0.240446 \tabularnewline
M10 & 1.14078431372549 & 1.310327 & 0.8706 & 0.3883 & 0.19415 \tabularnewline
M11 & 0.690392156862744 & 1.310059 & 0.527 & 0.600626 & 0.300313 \tabularnewline
t & 0.0103921568627451 & 0.015286 & 0.6798 & 0.499868 & 0.249934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&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]16.5858823529412[/C][C]1.077422[/C][C]15.394[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.274705882352939[/C][C]1.256527[/C][C]-0.2186[/C][C]0.827871[/C][C]0.413935[/C][/ROW]
[ROW][C]M2[/C][C]-0.496078431372549[/C][C]1.318858[/C][C]-0.3761[/C][C]0.708469[/C][C]0.354234[/C][/ROW]
[ROW][C]M3[/C][C]1.45352941176471[/C][C]1.317174[/C][C]1.1035[/C][C]0.275303[/C][C]0.137651[/C][/ROW]
[ROW][C]M4[/C][C]-0.116862745098041[/C][C]1.315665[/C][C]-0.0888[/C][C]0.929591[/C][C]0.464796[/C][/ROW]
[ROW][C]M5[/C][C]-0.00725490196078604[/C][C]1.314333[/C][C]-0.0055[/C][C]0.995619[/C][C]0.497809[/C][/ROW]
[ROW][C]M6[/C][C]1.04235294117647[/C][C]1.313177[/C][C]0.7938[/C][C]0.431239[/C][C]0.21562[/C][/ROW]
[ROW][C]M7[/C][C]-0.588039215686275[/C][C]1.312198[/C][C]-0.4481[/C][C]0.656073[/C][C]0.328037[/C][/ROW]
[ROW][C]M8[/C][C]-1.19843137254902[/C][C]1.311396[/C][C]-0.9139[/C][C]0.365359[/C][C]0.182679[/C][/ROW]
[ROW][C]M9[/C][C]0.931176470588234[/C][C]1.310772[/C][C]0.7104[/C][C]0.480892[/C][C]0.240446[/C][/ROW]
[ROW][C]M10[/C][C]1.14078431372549[/C][C]1.310327[/C][C]0.8706[/C][C]0.3883[/C][C]0.19415[/C][/ROW]
[ROW][C]M11[/C][C]0.690392156862744[/C][C]1.310059[/C][C]0.527[/C][C]0.600626[/C][C]0.300313[/C][/ROW]
[ROW][C]t[/C][C]0.0103921568627451[/C][C]0.015286[/C][C]0.6798[/C][C]0.499868[/C][C]0.249934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111428&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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)16.58588235294121.07742215.39400
M1-0.2747058823529391.256527-0.21860.8278710.413935
M2-0.4960784313725491.318858-0.37610.7084690.354234
M31.453529411764711.3171741.10350.2753030.137651
M4-0.1168627450980411.315665-0.08880.9295910.464796
M5-0.007254901960786041.314333-0.00550.9956190.497809
M61.042352941176471.3131770.79380.4312390.21562
M7-0.5880392156862751.312198-0.44810.6560730.328037
M8-1.198431372549021.311396-0.91390.3653590.182679
M90.9311764705882341.3107720.71040.4808920.240446
M101.140784313725491.3103270.87060.38830.19415
M110.6903921568627441.3100590.5270.6006260.300313
t0.01039215686274510.0152860.67980.4998680.249934






Multiple Linear Regression - Regression Statistics
Multiple R0.401668044404094
R-squared0.161337217895409
Adjusted R-squared-0.0483284776307384
F-TEST (value)0.769497449215714
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.677733752311882
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.0712441400235
Sum Squared Residuals205.922509803921

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.401668044404094 \tabularnewline
R-squared & 0.161337217895409 \tabularnewline
Adjusted R-squared & -0.0483284776307384 \tabularnewline
F-TEST (value) & 0.769497449215714 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.677733752311882 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.0712441400235 \tabularnewline
Sum Squared Residuals & 205.922509803921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.401668044404094[/C][/ROW]
[ROW][C]R-squared[/C][C]0.161337217895409[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.0483284776307384[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.769497449215714[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.677733752311882[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.0712441400235[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]205.922509803921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111428&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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 R0.401668044404094
R-squared0.161337217895409
Adjusted R-squared-0.0483284776307384
F-TEST (value)0.769497449215714
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.677733752311882
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.0712441400235
Sum Squared Residuals205.922509803921






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
114.116.3215686274510-2.22156862745096
214.816.1105882352941-1.31058823529412
316.818.0705882352941-1.27058823529412
415.416.5105882352941-1.11058823529412
515.216.6305882352941-1.43058823529412
616.917.6905882352941-0.79058823529412
714.116.0705882352941-1.97058823529412
814.715.4705882352941-0.770588235294119
916.517.6105882352941-1.11058823529412
1015.217.8305882352941-2.63058823529412
1117.617.39058823529410.209411764705882
121816.71058823529411.28941176470588
1316.916.44627450980390.453725490196074
1416.716.23529411764710.464705882352941
1519.718.19529411764711.50470588235294
1615.916.6352941176471-0.735294117647057
1717.416.75529411764710.644705882352941
1817.717.8152941176471-0.115294117647059
1915.216.1952941176471-0.99529411764706
2015.715.59529411764710.104705882352941
2117.217.7352941176471-0.53529411764706
2217.717.9552941176471-0.255294117647060
2317.917.51529411764710.384705882352940
2416.216.8352941176471-0.63529411764706
2517.516.57098039215690.929019607843134
2616.816.360.440000000000001
2719.118.320.780000000000002
2816.716.76-0.0599999999999994
2918.216.881.32
3018.517.940.560000000000001
3117.816.321.48
3216.415.720.68
331817.860.140000000000000
3420.318.082.22
3519.517.641.86
361816.961.04
3720.216.69568627450983.50431372549019
381916.48470588235292.51529411764706
3920.218.44470588235291.75529411764706
4021.516.88470588235294.61529411764706
4119.717.00470588235292.69529411764706
4221.118.06470588235293.03529411764706
4320.216.44470588235293.75529411764706
4418.215.84470588235292.35529411764706
4521.317.98470588235293.31529411764706
4620.418.20470588235292.19529411764706
4717.217.7647058823529-0.564705882352941
4815.817.0847058823529-1.28470588235294
4915.116.8203921568627-1.72039215686275
5014.516.6094117647059-2.10941176470588
5115.818.5694117647059-2.76941176470588
5214.317.0094117647059-2.70941176470588
5313.917.1294117647059-3.22941176470588
5415.518.1894117647059-2.68941176470588
5514.316.5694117647059-2.26941176470588
5613.615.9694117647059-2.36941176470588
5716.318.1094117647059-1.80941176470588
5816.818.3294117647059-1.52941176470588
591617.8894117647059-1.88941176470588
6016.817.2094117647059-0.409411764705882
611616.9450980392157-0.945098039215689

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 14.1 & 16.3215686274510 & -2.22156862745096 \tabularnewline
2 & 14.8 & 16.1105882352941 & -1.31058823529412 \tabularnewline
3 & 16.8 & 18.0705882352941 & -1.27058823529412 \tabularnewline
4 & 15.4 & 16.5105882352941 & -1.11058823529412 \tabularnewline
5 & 15.2 & 16.6305882352941 & -1.43058823529412 \tabularnewline
6 & 16.9 & 17.6905882352941 & -0.79058823529412 \tabularnewline
7 & 14.1 & 16.0705882352941 & -1.97058823529412 \tabularnewline
8 & 14.7 & 15.4705882352941 & -0.770588235294119 \tabularnewline
9 & 16.5 & 17.6105882352941 & -1.11058823529412 \tabularnewline
10 & 15.2 & 17.8305882352941 & -2.63058823529412 \tabularnewline
11 & 17.6 & 17.3905882352941 & 0.209411764705882 \tabularnewline
12 & 18 & 16.7105882352941 & 1.28941176470588 \tabularnewline
13 & 16.9 & 16.4462745098039 & 0.453725490196074 \tabularnewline
14 & 16.7 & 16.2352941176471 & 0.464705882352941 \tabularnewline
15 & 19.7 & 18.1952941176471 & 1.50470588235294 \tabularnewline
16 & 15.9 & 16.6352941176471 & -0.735294117647057 \tabularnewline
17 & 17.4 & 16.7552941176471 & 0.644705882352941 \tabularnewline
18 & 17.7 & 17.8152941176471 & -0.115294117647059 \tabularnewline
19 & 15.2 & 16.1952941176471 & -0.99529411764706 \tabularnewline
20 & 15.7 & 15.5952941176471 & 0.104705882352941 \tabularnewline
21 & 17.2 & 17.7352941176471 & -0.53529411764706 \tabularnewline
22 & 17.7 & 17.9552941176471 & -0.255294117647060 \tabularnewline
23 & 17.9 & 17.5152941176471 & 0.384705882352940 \tabularnewline
24 & 16.2 & 16.8352941176471 & -0.63529411764706 \tabularnewline
25 & 17.5 & 16.5709803921569 & 0.929019607843134 \tabularnewline
26 & 16.8 & 16.36 & 0.440000000000001 \tabularnewline
27 & 19.1 & 18.32 & 0.780000000000002 \tabularnewline
28 & 16.7 & 16.76 & -0.0599999999999994 \tabularnewline
29 & 18.2 & 16.88 & 1.32 \tabularnewline
30 & 18.5 & 17.94 & 0.560000000000001 \tabularnewline
31 & 17.8 & 16.32 & 1.48 \tabularnewline
32 & 16.4 & 15.72 & 0.68 \tabularnewline
33 & 18 & 17.86 & 0.140000000000000 \tabularnewline
34 & 20.3 & 18.08 & 2.22 \tabularnewline
35 & 19.5 & 17.64 & 1.86 \tabularnewline
36 & 18 & 16.96 & 1.04 \tabularnewline
37 & 20.2 & 16.6956862745098 & 3.50431372549019 \tabularnewline
38 & 19 & 16.4847058823529 & 2.51529411764706 \tabularnewline
39 & 20.2 & 18.4447058823529 & 1.75529411764706 \tabularnewline
40 & 21.5 & 16.8847058823529 & 4.61529411764706 \tabularnewline
41 & 19.7 & 17.0047058823529 & 2.69529411764706 \tabularnewline
42 & 21.1 & 18.0647058823529 & 3.03529411764706 \tabularnewline
43 & 20.2 & 16.4447058823529 & 3.75529411764706 \tabularnewline
44 & 18.2 & 15.8447058823529 & 2.35529411764706 \tabularnewline
45 & 21.3 & 17.9847058823529 & 3.31529411764706 \tabularnewline
46 & 20.4 & 18.2047058823529 & 2.19529411764706 \tabularnewline
47 & 17.2 & 17.7647058823529 & -0.564705882352941 \tabularnewline
48 & 15.8 & 17.0847058823529 & -1.28470588235294 \tabularnewline
49 & 15.1 & 16.8203921568627 & -1.72039215686275 \tabularnewline
50 & 14.5 & 16.6094117647059 & -2.10941176470588 \tabularnewline
51 & 15.8 & 18.5694117647059 & -2.76941176470588 \tabularnewline
52 & 14.3 & 17.0094117647059 & -2.70941176470588 \tabularnewline
53 & 13.9 & 17.1294117647059 & -3.22941176470588 \tabularnewline
54 & 15.5 & 18.1894117647059 & -2.68941176470588 \tabularnewline
55 & 14.3 & 16.5694117647059 & -2.26941176470588 \tabularnewline
56 & 13.6 & 15.9694117647059 & -2.36941176470588 \tabularnewline
57 & 16.3 & 18.1094117647059 & -1.80941176470588 \tabularnewline
58 & 16.8 & 18.3294117647059 & -1.52941176470588 \tabularnewline
59 & 16 & 17.8894117647059 & -1.88941176470588 \tabularnewline
60 & 16.8 & 17.2094117647059 & -0.409411764705882 \tabularnewline
61 & 16 & 16.9450980392157 & -0.945098039215689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&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]14.1[/C][C]16.3215686274510[/C][C]-2.22156862745096[/C][/ROW]
[ROW][C]2[/C][C]14.8[/C][C]16.1105882352941[/C][C]-1.31058823529412[/C][/ROW]
[ROW][C]3[/C][C]16.8[/C][C]18.0705882352941[/C][C]-1.27058823529412[/C][/ROW]
[ROW][C]4[/C][C]15.4[/C][C]16.5105882352941[/C][C]-1.11058823529412[/C][/ROW]
[ROW][C]5[/C][C]15.2[/C][C]16.6305882352941[/C][C]-1.43058823529412[/C][/ROW]
[ROW][C]6[/C][C]16.9[/C][C]17.6905882352941[/C][C]-0.79058823529412[/C][/ROW]
[ROW][C]7[/C][C]14.1[/C][C]16.0705882352941[/C][C]-1.97058823529412[/C][/ROW]
[ROW][C]8[/C][C]14.7[/C][C]15.4705882352941[/C][C]-0.770588235294119[/C][/ROW]
[ROW][C]9[/C][C]16.5[/C][C]17.6105882352941[/C][C]-1.11058823529412[/C][/ROW]
[ROW][C]10[/C][C]15.2[/C][C]17.8305882352941[/C][C]-2.63058823529412[/C][/ROW]
[ROW][C]11[/C][C]17.6[/C][C]17.3905882352941[/C][C]0.209411764705882[/C][/ROW]
[ROW][C]12[/C][C]18[/C][C]16.7105882352941[/C][C]1.28941176470588[/C][/ROW]
[ROW][C]13[/C][C]16.9[/C][C]16.4462745098039[/C][C]0.453725490196074[/C][/ROW]
[ROW][C]14[/C][C]16.7[/C][C]16.2352941176471[/C][C]0.464705882352941[/C][/ROW]
[ROW][C]15[/C][C]19.7[/C][C]18.1952941176471[/C][C]1.50470588235294[/C][/ROW]
[ROW][C]16[/C][C]15.9[/C][C]16.6352941176471[/C][C]-0.735294117647057[/C][/ROW]
[ROW][C]17[/C][C]17.4[/C][C]16.7552941176471[/C][C]0.644705882352941[/C][/ROW]
[ROW][C]18[/C][C]17.7[/C][C]17.8152941176471[/C][C]-0.115294117647059[/C][/ROW]
[ROW][C]19[/C][C]15.2[/C][C]16.1952941176471[/C][C]-0.99529411764706[/C][/ROW]
[ROW][C]20[/C][C]15.7[/C][C]15.5952941176471[/C][C]0.104705882352941[/C][/ROW]
[ROW][C]21[/C][C]17.2[/C][C]17.7352941176471[/C][C]-0.53529411764706[/C][/ROW]
[ROW][C]22[/C][C]17.7[/C][C]17.9552941176471[/C][C]-0.255294117647060[/C][/ROW]
[ROW][C]23[/C][C]17.9[/C][C]17.5152941176471[/C][C]0.384705882352940[/C][/ROW]
[ROW][C]24[/C][C]16.2[/C][C]16.8352941176471[/C][C]-0.63529411764706[/C][/ROW]
[ROW][C]25[/C][C]17.5[/C][C]16.5709803921569[/C][C]0.929019607843134[/C][/ROW]
[ROW][C]26[/C][C]16.8[/C][C]16.36[/C][C]0.440000000000001[/C][/ROW]
[ROW][C]27[/C][C]19.1[/C][C]18.32[/C][C]0.780000000000002[/C][/ROW]
[ROW][C]28[/C][C]16.7[/C][C]16.76[/C][C]-0.0599999999999994[/C][/ROW]
[ROW][C]29[/C][C]18.2[/C][C]16.88[/C][C]1.32[/C][/ROW]
[ROW][C]30[/C][C]18.5[/C][C]17.94[/C][C]0.560000000000001[/C][/ROW]
[ROW][C]31[/C][C]17.8[/C][C]16.32[/C][C]1.48[/C][/ROW]
[ROW][C]32[/C][C]16.4[/C][C]15.72[/C][C]0.68[/C][/ROW]
[ROW][C]33[/C][C]18[/C][C]17.86[/C][C]0.140000000000000[/C][/ROW]
[ROW][C]34[/C][C]20.3[/C][C]18.08[/C][C]2.22[/C][/ROW]
[ROW][C]35[/C][C]19.5[/C][C]17.64[/C][C]1.86[/C][/ROW]
[ROW][C]36[/C][C]18[/C][C]16.96[/C][C]1.04[/C][/ROW]
[ROW][C]37[/C][C]20.2[/C][C]16.6956862745098[/C][C]3.50431372549019[/C][/ROW]
[ROW][C]38[/C][C]19[/C][C]16.4847058823529[/C][C]2.51529411764706[/C][/ROW]
[ROW][C]39[/C][C]20.2[/C][C]18.4447058823529[/C][C]1.75529411764706[/C][/ROW]
[ROW][C]40[/C][C]21.5[/C][C]16.8847058823529[/C][C]4.61529411764706[/C][/ROW]
[ROW][C]41[/C][C]19.7[/C][C]17.0047058823529[/C][C]2.69529411764706[/C][/ROW]
[ROW][C]42[/C][C]21.1[/C][C]18.0647058823529[/C][C]3.03529411764706[/C][/ROW]
[ROW][C]43[/C][C]20.2[/C][C]16.4447058823529[/C][C]3.75529411764706[/C][/ROW]
[ROW][C]44[/C][C]18.2[/C][C]15.8447058823529[/C][C]2.35529411764706[/C][/ROW]
[ROW][C]45[/C][C]21.3[/C][C]17.9847058823529[/C][C]3.31529411764706[/C][/ROW]
[ROW][C]46[/C][C]20.4[/C][C]18.2047058823529[/C][C]2.19529411764706[/C][/ROW]
[ROW][C]47[/C][C]17.2[/C][C]17.7647058823529[/C][C]-0.564705882352941[/C][/ROW]
[ROW][C]48[/C][C]15.8[/C][C]17.0847058823529[/C][C]-1.28470588235294[/C][/ROW]
[ROW][C]49[/C][C]15.1[/C][C]16.8203921568627[/C][C]-1.72039215686275[/C][/ROW]
[ROW][C]50[/C][C]14.5[/C][C]16.6094117647059[/C][C]-2.10941176470588[/C][/ROW]
[ROW][C]51[/C][C]15.8[/C][C]18.5694117647059[/C][C]-2.76941176470588[/C][/ROW]
[ROW][C]52[/C][C]14.3[/C][C]17.0094117647059[/C][C]-2.70941176470588[/C][/ROW]
[ROW][C]53[/C][C]13.9[/C][C]17.1294117647059[/C][C]-3.22941176470588[/C][/ROW]
[ROW][C]54[/C][C]15.5[/C][C]18.1894117647059[/C][C]-2.68941176470588[/C][/ROW]
[ROW][C]55[/C][C]14.3[/C][C]16.5694117647059[/C][C]-2.26941176470588[/C][/ROW]
[ROW][C]56[/C][C]13.6[/C][C]15.9694117647059[/C][C]-2.36941176470588[/C][/ROW]
[ROW][C]57[/C][C]16.3[/C][C]18.1094117647059[/C][C]-1.80941176470588[/C][/ROW]
[ROW][C]58[/C][C]16.8[/C][C]18.3294117647059[/C][C]-1.52941176470588[/C][/ROW]
[ROW][C]59[/C][C]16[/C][C]17.8894117647059[/C][C]-1.88941176470588[/C][/ROW]
[ROW][C]60[/C][C]16.8[/C][C]17.2094117647059[/C][C]-0.409411764705882[/C][/ROW]
[ROW][C]61[/C][C]16[/C][C]16.9450980392157[/C][C]-0.945098039215689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111428&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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
114.116.3215686274510-2.22156862745096
214.816.1105882352941-1.31058823529412
316.818.0705882352941-1.27058823529412
415.416.5105882352941-1.11058823529412
515.216.6305882352941-1.43058823529412
616.917.6905882352941-0.79058823529412
714.116.0705882352941-1.97058823529412
814.715.4705882352941-0.770588235294119
916.517.6105882352941-1.11058823529412
1015.217.8305882352941-2.63058823529412
1117.617.39058823529410.209411764705882
121816.71058823529411.28941176470588
1316.916.44627450980390.453725490196074
1416.716.23529411764710.464705882352941
1519.718.19529411764711.50470588235294
1615.916.6352941176471-0.735294117647057
1717.416.75529411764710.644705882352941
1817.717.8152941176471-0.115294117647059
1915.216.1952941176471-0.99529411764706
2015.715.59529411764710.104705882352941
2117.217.7352941176471-0.53529411764706
2217.717.9552941176471-0.255294117647060
2317.917.51529411764710.384705882352940
2416.216.8352941176471-0.63529411764706
2517.516.57098039215690.929019607843134
2616.816.360.440000000000001
2719.118.320.780000000000002
2816.716.76-0.0599999999999994
2918.216.881.32
3018.517.940.560000000000001
3117.816.321.48
3216.415.720.68
331817.860.140000000000000
3420.318.082.22
3519.517.641.86
361816.961.04
3720.216.69568627450983.50431372549019
381916.48470588235292.51529411764706
3920.218.44470588235291.75529411764706
4021.516.88470588235294.61529411764706
4119.717.00470588235292.69529411764706
4221.118.06470588235293.03529411764706
4320.216.44470588235293.75529411764706
4418.215.84470588235292.35529411764706
4521.317.98470588235293.31529411764706
4620.418.20470588235292.19529411764706
4717.217.7647058823529-0.564705882352941
4815.817.0847058823529-1.28470588235294
4915.116.8203921568627-1.72039215686275
5014.516.6094117647059-2.10941176470588
5115.818.5694117647059-2.76941176470588
5214.317.0094117647059-2.70941176470588
5313.917.1294117647059-3.22941176470588
5415.518.1894117647059-2.68941176470588
5514.316.5694117647059-2.26941176470588
5613.615.9694117647059-2.36941176470588
5716.318.1094117647059-1.80941176470588
5816.818.3294117647059-1.52941176470588
591617.8894117647059-1.88941176470588
6016.817.2094117647059-0.409411764705882
611616.9450980392157-0.945098039215689






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.06064082984484510.1212816596896900.939359170155155
170.01771742033000130.03543484066000260.982282579669999
180.00959064670563710.01918129341127420.990409353294363
190.004073683268820220.008147366537640440.99592631673118
200.001542863847201550.003085727694403100.998457136152799
210.0007865850403931740.001573170080786350.999213414959607
220.0004559584592783120.0009119169185566230.999544041540722
230.0003324386990327670.0006648773980655340.999667561300967
240.003998828132111510.007997656264223020.996001171867889
250.001957546018073040.003915092036146090.998042453981927
260.001096302255810040.002192604511620070.99890369774419
270.0005638541553078320.001127708310615660.999436145844692
280.0004252640423797030.0008505280847594070.99957473595762
290.0001786357134326280.0003572714268652560.999821364286567
300.0001001243451766110.0002002486903532220.999899875654823
310.0001328828553463310.0002657657106926620.999867117144654
329.37031650326252e-050.0001874063300652500.999906296834967
330.0002123103598878020.0004246207197756030.999787689640112
340.0007281577300854390.001456315460170880.999271842269915
350.0004148291618400040.0008296583236800070.99958517083816
360.0007737585133638710.001547517026727740.999226241486636
370.0008169341333535550.001633868266707110.999183065866647
380.0003661267984815730.0007322535969631450.999633873201518
390.0001801621251920980.0003603242503841950.999819837874808
400.002191287102460360.004382574204920720.99780871289754
410.001945537839512100.003891075679024190.998054462160488
420.002173966197247060.004347932394494130.997826033802753
430.007510175595032520.01502035119006500.992489824404967
440.0100155268172450.020031053634490.989984473182755
450.06911075294969770.1382215058993950.930889247050302

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0606408298448451 & 0.121281659689690 & 0.939359170155155 \tabularnewline
17 & 0.0177174203300013 & 0.0354348406600026 & 0.982282579669999 \tabularnewline
18 & 0.0095906467056371 & 0.0191812934112742 & 0.990409353294363 \tabularnewline
19 & 0.00407368326882022 & 0.00814736653764044 & 0.99592631673118 \tabularnewline
20 & 0.00154286384720155 & 0.00308572769440310 & 0.998457136152799 \tabularnewline
21 & 0.000786585040393174 & 0.00157317008078635 & 0.999213414959607 \tabularnewline
22 & 0.000455958459278312 & 0.000911916918556623 & 0.999544041540722 \tabularnewline
23 & 0.000332438699032767 & 0.000664877398065534 & 0.999667561300967 \tabularnewline
24 & 0.00399882813211151 & 0.00799765626422302 & 0.996001171867889 \tabularnewline
25 & 0.00195754601807304 & 0.00391509203614609 & 0.998042453981927 \tabularnewline
26 & 0.00109630225581004 & 0.00219260451162007 & 0.99890369774419 \tabularnewline
27 & 0.000563854155307832 & 0.00112770831061566 & 0.999436145844692 \tabularnewline
28 & 0.000425264042379703 & 0.000850528084759407 & 0.99957473595762 \tabularnewline
29 & 0.000178635713432628 & 0.000357271426865256 & 0.999821364286567 \tabularnewline
30 & 0.000100124345176611 & 0.000200248690353222 & 0.999899875654823 \tabularnewline
31 & 0.000132882855346331 & 0.000265765710692662 & 0.999867117144654 \tabularnewline
32 & 9.37031650326252e-05 & 0.000187406330065250 & 0.999906296834967 \tabularnewline
33 & 0.000212310359887802 & 0.000424620719775603 & 0.999787689640112 \tabularnewline
34 & 0.000728157730085439 & 0.00145631546017088 & 0.999271842269915 \tabularnewline
35 & 0.000414829161840004 & 0.000829658323680007 & 0.99958517083816 \tabularnewline
36 & 0.000773758513363871 & 0.00154751702672774 & 0.999226241486636 \tabularnewline
37 & 0.000816934133353555 & 0.00163386826670711 & 0.999183065866647 \tabularnewline
38 & 0.000366126798481573 & 0.000732253596963145 & 0.999633873201518 \tabularnewline
39 & 0.000180162125192098 & 0.000360324250384195 & 0.999819837874808 \tabularnewline
40 & 0.00219128710246036 & 0.00438257420492072 & 0.99780871289754 \tabularnewline
41 & 0.00194553783951210 & 0.00389107567902419 & 0.998054462160488 \tabularnewline
42 & 0.00217396619724706 & 0.00434793239449413 & 0.997826033802753 \tabularnewline
43 & 0.00751017559503252 & 0.0150203511900650 & 0.992489824404967 \tabularnewline
44 & 0.010015526817245 & 0.02003105363449 & 0.989984473182755 \tabularnewline
45 & 0.0691107529496977 & 0.138221505899395 & 0.930889247050302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]16[/C][C]0.0606408298448451[/C][C]0.121281659689690[/C][C]0.939359170155155[/C][/ROW]
[ROW][C]17[/C][C]0.0177174203300013[/C][C]0.0354348406600026[/C][C]0.982282579669999[/C][/ROW]
[ROW][C]18[/C][C]0.0095906467056371[/C][C]0.0191812934112742[/C][C]0.990409353294363[/C][/ROW]
[ROW][C]19[/C][C]0.00407368326882022[/C][C]0.00814736653764044[/C][C]0.99592631673118[/C][/ROW]
[ROW][C]20[/C][C]0.00154286384720155[/C][C]0.00308572769440310[/C][C]0.998457136152799[/C][/ROW]
[ROW][C]21[/C][C]0.000786585040393174[/C][C]0.00157317008078635[/C][C]0.999213414959607[/C][/ROW]
[ROW][C]22[/C][C]0.000455958459278312[/C][C]0.000911916918556623[/C][C]0.999544041540722[/C][/ROW]
[ROW][C]23[/C][C]0.000332438699032767[/C][C]0.000664877398065534[/C][C]0.999667561300967[/C][/ROW]
[ROW][C]24[/C][C]0.00399882813211151[/C][C]0.00799765626422302[/C][C]0.996001171867889[/C][/ROW]
[ROW][C]25[/C][C]0.00195754601807304[/C][C]0.00391509203614609[/C][C]0.998042453981927[/C][/ROW]
[ROW][C]26[/C][C]0.00109630225581004[/C][C]0.00219260451162007[/C][C]0.99890369774419[/C][/ROW]
[ROW][C]27[/C][C]0.000563854155307832[/C][C]0.00112770831061566[/C][C]0.999436145844692[/C][/ROW]
[ROW][C]28[/C][C]0.000425264042379703[/C][C]0.000850528084759407[/C][C]0.99957473595762[/C][/ROW]
[ROW][C]29[/C][C]0.000178635713432628[/C][C]0.000357271426865256[/C][C]0.999821364286567[/C][/ROW]
[ROW][C]30[/C][C]0.000100124345176611[/C][C]0.000200248690353222[/C][C]0.999899875654823[/C][/ROW]
[ROW][C]31[/C][C]0.000132882855346331[/C][C]0.000265765710692662[/C][C]0.999867117144654[/C][/ROW]
[ROW][C]32[/C][C]9.37031650326252e-05[/C][C]0.000187406330065250[/C][C]0.999906296834967[/C][/ROW]
[ROW][C]33[/C][C]0.000212310359887802[/C][C]0.000424620719775603[/C][C]0.999787689640112[/C][/ROW]
[ROW][C]34[/C][C]0.000728157730085439[/C][C]0.00145631546017088[/C][C]0.999271842269915[/C][/ROW]
[ROW][C]35[/C][C]0.000414829161840004[/C][C]0.000829658323680007[/C][C]0.99958517083816[/C][/ROW]
[ROW][C]36[/C][C]0.000773758513363871[/C][C]0.00154751702672774[/C][C]0.999226241486636[/C][/ROW]
[ROW][C]37[/C][C]0.000816934133353555[/C][C]0.00163386826670711[/C][C]0.999183065866647[/C][/ROW]
[ROW][C]38[/C][C]0.000366126798481573[/C][C]0.000732253596963145[/C][C]0.999633873201518[/C][/ROW]
[ROW][C]39[/C][C]0.000180162125192098[/C][C]0.000360324250384195[/C][C]0.999819837874808[/C][/ROW]
[ROW][C]40[/C][C]0.00219128710246036[/C][C]0.00438257420492072[/C][C]0.99780871289754[/C][/ROW]
[ROW][C]41[/C][C]0.00194553783951210[/C][C]0.00389107567902419[/C][C]0.998054462160488[/C][/ROW]
[ROW][C]42[/C][C]0.00217396619724706[/C][C]0.00434793239449413[/C][C]0.997826033802753[/C][/ROW]
[ROW][C]43[/C][C]0.00751017559503252[/C][C]0.0150203511900650[/C][C]0.992489824404967[/C][/ROW]
[ROW][C]44[/C][C]0.010015526817245[/C][C]0.02003105363449[/C][C]0.989984473182755[/C][/ROW]
[ROW][C]45[/C][C]0.0691107529496977[/C][C]0.138221505899395[/C][C]0.930889247050302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111428&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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
160.06064082984484510.1212816596896900.939359170155155
170.01771742033000130.03543484066000260.982282579669999
180.00959064670563710.01918129341127420.990409353294363
190.004073683268820220.008147366537640440.99592631673118
200.001542863847201550.003085727694403100.998457136152799
210.0007865850403931740.001573170080786350.999213414959607
220.0004559584592783120.0009119169185566230.999544041540722
230.0003324386990327670.0006648773980655340.999667561300967
240.003998828132111510.007997656264223020.996001171867889
250.001957546018073040.003915092036146090.998042453981927
260.001096302255810040.002192604511620070.99890369774419
270.0005638541553078320.001127708310615660.999436145844692
280.0004252640423797030.0008505280847594070.99957473595762
290.0001786357134326280.0003572714268652560.999821364286567
300.0001001243451766110.0002002486903532220.999899875654823
310.0001328828553463310.0002657657106926620.999867117144654
329.37031650326252e-050.0001874063300652500.999906296834967
330.0002123103598878020.0004246207197756030.999787689640112
340.0007281577300854390.001456315460170880.999271842269915
350.0004148291618400040.0008296583236800070.99958517083816
360.0007737585133638710.001547517026727740.999226241486636
370.0008169341333535550.001633868266707110.999183065866647
380.0003661267984815730.0007322535969631450.999633873201518
390.0001801621251920980.0003603242503841950.999819837874808
400.002191287102460360.004382574204920720.99780871289754
410.001945537839512100.003891075679024190.998054462160488
420.002173966197247060.004347932394494130.997826033802753
430.007510175595032520.01502035119006500.992489824404967
440.0100155268172450.020031053634490.989984473182755
450.06911075294969770.1382215058993950.930889247050302






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level240.8NOK
5% type I error level280.933333333333333NOK
10% type I error level280.933333333333333NOK

\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 & 24 & 0.8 & NOK \tabularnewline
5% type I error level & 28 & 0.933333333333333 & NOK \tabularnewline
10% type I error level & 28 & 0.933333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111428&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]24[/C][C]0.8[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]28[/C][C]0.933333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]28[/C][C]0.933333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111428&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111428&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 level240.8NOK
5% type I error level280.933333333333333NOK
10% type I error level280.933333333333333NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}