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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 computationSun, 27 Nov 2011 11:56:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/27/t1322412987lyosa2mrqfz8120.htm/, Retrieved Thu, 09 Oct 2025 04:54:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147561, Retrieved Thu, 09 Oct 2025 04:54:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact351

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] [Multivariate regr...] [2009-11-19 09:34:31] [21324e9cdf3569788a3d630236984d87]
-    D      [Multiple Regression] [] [2010-12-07 12:59:34] [f47feae0308dca73181bb669fbad1c56]
- R  D        [Multiple Regression] [] [2011-11-26 18:29:52] [74be16979710d4c4e7c6647856088456]
- R P             [Multiple Regression] [] [2011-11-27 16:56:17] [5f9ad3d6882448a3cbf5628cc61fe2a1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112.3	0	117.2	96.8	80	126.1
117.3	0	112.3	117.2	96.8	80
111.1	1	117.3	112.3	117.2	96.8
102.2	1	111.1	117.3	112.3	117.2
104.3	1	102.2	111.1	117.3	112.3
122.9	1	104.3	102.2	111.1	117.3
107.6	1	122.9	104.3	102.2	111.1
121.3	1	107.6	122.9	104.3	102.2
131.5	1	121.3	107.6	122.9	104.3
89	1	131.5	121.3	107.6	122.9
104.4	1	89	131.5	121.3	107.6
128.9	1	104.4	89	131.5	121.3
135.9	1	128.9	104.4	89	131.5
133.3	1	135.9	128.9	104.4	89
121.3	1	133.3	135.9	128.9	104.4
120.5	0	121.3	133.3	135.9	128.9
120.4	0	120.5	121.3	133.3	135.9
137.9	0	120.4	120.5	121.3	133.3
126.1	0	137.9	120.4	120.5	121.3
133.2	0	126.1	137.9	120.4	120.5
151.1	0	133.2	126.1	137.9	120.4
105	0	151.1	133.2	126.1	137.9
119	0	105	151.1	133.2	126.1
140.4	0	119	105	151.1	133.2
156.6	0	140.4	119	105	151.1
137.1	0	156.6	140.4	119	105
122.7	0	137.1	156.6	140.4	119
125.8	0	122.7	137.1	156.6	140.4
139.3	0	125.8	122.7	137.1	156.6
134.9	0	139.3	125.8	122.7	137.1
149.2	0	134.9	139.3	125.8	122.7
132.3	0	149.2	134.9	139.3	125.8
149	0	132.3	149.2	134.9	139.3
117.2	0	149	132.3	149.2	134.9
119.6	0	117.2	149	132.3	149.2
152	0	119.6	117.2	149	132.3
149.4	0	152	119.6	117.2	149
127.3	0	149.4	152	119.6	117.2
114.1	0	127.3	149.4	152	119.6
102.1	0	114.1	127.3	149.4	152
107.7	0	102.1	114.1	127.3	149.4
104.4	0	107.7	102.1	114.1	127.3
102.1	0	104.4	107.7	102.1	114.1
96	1	102.1	104.4	107.7	102.1
109.3	0	96	102.1	104.4	107.7
90	1	109.3	96	102.1	104.4
83.9	1	90	109.3	96	102.1
112	1	83.9	90	109.3	96
114.3	1	112	83.9	90	109.3
103.6	1	114.3	112	83.9	90
91.7	1	103.6	114.3	112	83.9
80.8	1	91.7	103.6	114.3	112
87.2	1	80.8	91.7	103.6	114.3
109.2	1	87.2	80.8	91.7	103.6
102.7	1	109.2	87.2	80.8	91.7
95.1	1	102.7	109.2	87.2	80.8
117.5	1	95.1	102.7	109.2	87.2
85.1	1	117.5	95.1	102.7	109.2
92.1	1	85.1	117.5	95.1	102.7
113.5	1	92.1	85.1	117.5	95.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Multiple Linear Regression - Estimated Regression Equation
X[t] = + 24.1698363156221 + 3.12409265557002Y[t] + 0.354106572914146`y(t)`[t] + 0.386685471568013`y(t-1)`[t] + 0.316297204680136`y(t-2)`[t] -0.0792357995923459`y(t-3)`[t] + 4.29883047671237M1[t] -22.2968495935552M2[t] -39.5691693349632M3[t] -35.9297143015368M4[t] -20.3378644943873M5[t] -6.96633419726574M6[t] -15.9323504617263M7[t] -22.9939682907714M8[t] -6.55872286116879M9[t] -44.2832772039972M10[t] -31.4045454857823M11[t] -0.0983757038209558t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X[t] =  +  24.1698363156221 +  3.12409265557002Y[t] +  0.354106572914146`y(t)`[t] +  0.386685471568013`y(t-1)`[t] +  0.316297204680136`y(t-2)`[t] -0.0792357995923459`y(t-3)`[t] +  4.29883047671237M1[t] -22.2968495935552M2[t] -39.5691693349632M3[t] -35.9297143015368M4[t] -20.3378644943873M5[t] -6.96633419726574M6[t] -15.9323504617263M7[t] -22.9939682907714M8[t] -6.55872286116879M9[t] -44.2832772039972M10[t] -31.4045454857823M11[t] -0.0983757038209558t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X[t] =  +  24.1698363156221 +  3.12409265557002Y[t] +  0.354106572914146`y(t)`[t] +  0.386685471568013`y(t-1)`[t] +  0.316297204680136`y(t-2)`[t] -0.0792357995923459`y(t-3)`[t] +  4.29883047671237M1[t] -22.2968495935552M2[t] -39.5691693349632M3[t] -35.9297143015368M4[t] -20.3378644943873M5[t] -6.96633419726574M6[t] -15.9323504617263M7[t] -22.9939682907714M8[t] -6.55872286116879M9[t] -44.2832772039972M10[t] -31.4045454857823M11[t] -0.0983757038209558t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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
X[t] = + 24.1698363156221 + 3.12409265557002Y[t] + 0.354106572914146`y(t)`[t] + 0.386685471568013`y(t-1)`[t] + 0.316297204680136`y(t-2)`[t] -0.0792357995923459`y(t-3)`[t] + 4.29883047671237M1[t] -22.2968495935552M2[t] -39.5691693349632M3[t] -35.9297143015368M4[t] -20.3378644943873M5[t] -6.96633419726574M6[t] -15.9323504617263M7[t] -22.9939682907714M8[t] -6.55872286116879M9[t] -44.2832772039972M10[t] -31.4045454857823M11[t] -0.0983757038209558t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)24.169836315622118.6389841.29670.2018010.100901
Y3.124092655570023.7730850.8280.4123540.206177
`y(t)`0.3541065729141460.1534972.30690.026060.01303
`y(t-1)`0.3866854715680130.1614542.3950.0211570.010578
`y(t-2)`0.3162972046801360.1562692.02410.0493560.024678
`y(t-3)`-0.07923579959234590.157901-0.50180.6184230.309212
M14.298830476712379.7994880.43870.6631420.331571
M2-22.296849593555210.749129-2.07430.0442180.022109
M3-39.56916933496327.999304-4.94661.3e-056e-06
M4-35.92971430153685.974976-6.013400
M5-20.33786449438736.115281-3.32570.0018380.000919
M6-6.966334197265746.522986-1.0680.2916360.145818
M7-15.93235046172637.900121-2.01670.0501480.025074
M8-22.99396829077147.837306-2.93390.0054040.002702
M9-6.558722861168796.469515-1.01380.3164880.158244
M10-44.28327720399727.364443-6.013100
M11-31.40454548578238.394784-3.7410.000550.000275
t-0.09837570382095580.065916-1.49240.1430570.071528

\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) & 24.1698363156221 & 18.638984 & 1.2967 & 0.201801 & 0.100901 \tabularnewline
Y & 3.12409265557002 & 3.773085 & 0.828 & 0.412354 & 0.206177 \tabularnewline
`y(t)` & 0.354106572914146 & 0.153497 & 2.3069 & 0.02606 & 0.01303 \tabularnewline
`y(t-1)` & 0.386685471568013 & 0.161454 & 2.395 & 0.021157 & 0.010578 \tabularnewline
`y(t-2)` & 0.316297204680136 & 0.156269 & 2.0241 & 0.049356 & 0.024678 \tabularnewline
`y(t-3)` & -0.0792357995923459 & 0.157901 & -0.5018 & 0.618423 & 0.309212 \tabularnewline
M1 & 4.29883047671237 & 9.799488 & 0.4387 & 0.663142 & 0.331571 \tabularnewline
M2 & -22.2968495935552 & 10.749129 & -2.0743 & 0.044218 & 0.022109 \tabularnewline
M3 & -39.5691693349632 & 7.999304 & -4.9466 & 1.3e-05 & 6e-06 \tabularnewline
M4 & -35.9297143015368 & 5.974976 & -6.0134 & 0 & 0 \tabularnewline
M5 & -20.3378644943873 & 6.115281 & -3.3257 & 0.001838 & 0.000919 \tabularnewline
M6 & -6.96633419726574 & 6.522986 & -1.068 & 0.291636 & 0.145818 \tabularnewline
M7 & -15.9323504617263 & 7.900121 & -2.0167 & 0.050148 & 0.025074 \tabularnewline
M8 & -22.9939682907714 & 7.837306 & -2.9339 & 0.005404 & 0.002702 \tabularnewline
M9 & -6.55872286116879 & 6.469515 & -1.0138 & 0.316488 & 0.158244 \tabularnewline
M10 & -44.2832772039972 & 7.364443 & -6.0131 & 0 & 0 \tabularnewline
M11 & -31.4045454857823 & 8.394784 & -3.741 & 0.00055 & 0.000275 \tabularnewline
t & -0.0983757038209558 & 0.065916 & -1.4924 & 0.143057 & 0.071528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&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]24.1698363156221[/C][C]18.638984[/C][C]1.2967[/C][C]0.201801[/C][C]0.100901[/C][/ROW]
[ROW][C]Y[/C][C]3.12409265557002[/C][C]3.773085[/C][C]0.828[/C][C]0.412354[/C][C]0.206177[/C][/ROW]
[ROW][C]`y(t)`[/C][C]0.354106572914146[/C][C]0.153497[/C][C]2.3069[/C][C]0.02606[/C][C]0.01303[/C][/ROW]
[ROW][C]`y(t-1)`[/C][C]0.386685471568013[/C][C]0.161454[/C][C]2.395[/C][C]0.021157[/C][C]0.010578[/C][/ROW]
[ROW][C]`y(t-2)`[/C][C]0.316297204680136[/C][C]0.156269[/C][C]2.0241[/C][C]0.049356[/C][C]0.024678[/C][/ROW]
[ROW][C]`y(t-3)`[/C][C]-0.0792357995923459[/C][C]0.157901[/C][C]-0.5018[/C][C]0.618423[/C][C]0.309212[/C][/ROW]
[ROW][C]M1[/C][C]4.29883047671237[/C][C]9.799488[/C][C]0.4387[/C][C]0.663142[/C][C]0.331571[/C][/ROW]
[ROW][C]M2[/C][C]-22.2968495935552[/C][C]10.749129[/C][C]-2.0743[/C][C]0.044218[/C][C]0.022109[/C][/ROW]
[ROW][C]M3[/C][C]-39.5691693349632[/C][C]7.999304[/C][C]-4.9466[/C][C]1.3e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]M4[/C][C]-35.9297143015368[/C][C]5.974976[/C][C]-6.0134[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-20.3378644943873[/C][C]6.115281[/C][C]-3.3257[/C][C]0.001838[/C][C]0.000919[/C][/ROW]
[ROW][C]M6[/C][C]-6.96633419726574[/C][C]6.522986[/C][C]-1.068[/C][C]0.291636[/C][C]0.145818[/C][/ROW]
[ROW][C]M7[/C][C]-15.9323504617263[/C][C]7.900121[/C][C]-2.0167[/C][C]0.050148[/C][C]0.025074[/C][/ROW]
[ROW][C]M8[/C][C]-22.9939682907714[/C][C]7.837306[/C][C]-2.9339[/C][C]0.005404[/C][C]0.002702[/C][/ROW]
[ROW][C]M9[/C][C]-6.55872286116879[/C][C]6.469515[/C][C]-1.0138[/C][C]0.316488[/C][C]0.158244[/C][/ROW]
[ROW][C]M10[/C][C]-44.2832772039972[/C][C]7.364443[/C][C]-6.0131[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-31.4045454857823[/C][C]8.394784[/C][C]-3.741[/C][C]0.00055[/C][C]0.000275[/C][/ROW]
[ROW][C]t[/C][C]-0.0983757038209558[/C][C]0.065916[/C][C]-1.4924[/C][C]0.143057[/C][C]0.071528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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)24.169836315622118.6389841.29670.2018010.100901
Y3.124092655570023.7730850.8280.4123540.206177
`y(t)`0.3541065729141460.1534972.30690.026060.01303
`y(t-1)`0.3866854715680130.1614542.3950.0211570.010578
`y(t-2)`0.3162972046801360.1562692.02410.0493560.024678
`y(t-3)`-0.07923579959234590.157901-0.50180.6184230.309212
M14.298830476712379.7994880.43870.6631420.331571
M2-22.296849593555210.749129-2.07430.0442180.022109
M3-39.56916933496327.999304-4.94661.3e-056e-06
M4-35.92971430153685.974976-6.013400
M5-20.33786449438736.115281-3.32570.0018380.000919
M6-6.966334197265746.522986-1.0680.2916360.145818
M7-15.93235046172637.900121-2.01670.0501480.025074
M8-22.99396829077147.837306-2.93390.0054040.002702
M9-6.558722861168796.469515-1.01380.3164880.158244
M10-44.28327720399727.364443-6.013100
M11-31.40454548578238.394784-3.7410.000550.000275
t-0.09837570382095580.065916-1.49240.1430570.071528






Multiple Linear Regression - Regression Statistics
Multiple R0.938958363418636
R-squared0.881642808233803
Adjusted R-squared0.833736325852247
F-TEST (value)18.4034135758888
F-TEST (DF numerator)17
F-TEST (DF denominator)42
p-value3.19744231092045e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.73467319800471
Sum Squared Residuals2512.65711815716

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.938958363418636 \tabularnewline
R-squared & 0.881642808233803 \tabularnewline
Adjusted R-squared & 0.833736325852247 \tabularnewline
F-TEST (value) & 18.4034135758888 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 3.19744231092045e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 7.73467319800471 \tabularnewline
Sum Squared Residuals & 2512.65711815716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.938958363418636[/C][/ROW]
[ROW][C]R-squared[/C][C]0.881642808233803[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.833736325852247[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]18.4034135758888[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]3.19744231092045e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]7.73467319800471[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2512.65711815716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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 R0.938958363418636
R-squared0.881642808233803
Adjusted R-squared0.833736325852247
F-TEST (value)18.4034135758888
F-TEST (DF numerator)17
F-TEST (DF denominator)42
p-value3.19744231092045e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.73467319800471
Sum Squared Residuals2512.65711815716






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1112.3122.614877127651-10.3148771276511
2117.3111.0406461661046.25935383389574
3111.1101.7911189726569.30888102734388
4102.2101.9038982934170.296101706582642
5104.3113.818115415492-9.51811541549151
6122.9122.0361714479780.863828552022047
7107.6118.046418062012-10.4464180620117
8121.3114.0303664809247.26963351907558
9131.5135.018941368546-3.51894136854591
108999.7923562220788-10.7923562220788
11104.4107.012954135496-2.61295413549615
12128.9129.478933632017-0.578933632017005
13135.9134.0591193487051.84088065129534
14133.3127.556102073185.74389792681968
15121.3118.5005780402922.79942195970813
16120.5113.9357069560296.56429304397084
17120.4123.128646812895-2.72864681289545
18137.9132.4674889944295.43251100557129
19126.1130.259085336352-4.15908533635199
20133.2125.7193889147457.48061108525489
21151.1145.5506514055765.54934859442373
22105111.692762354131-6.6927623541313
23119118.2511678866690.748832113330722
24140.4141.787775236812-1.38777523681202
25156.6142.98008532356113.6199146764389
26137.1138.378556348966-1.27855634896627
27122.7126.026546357175-3.32654635717531
28125.8120.3564929457835.44350705421722
29139.3123.92801118990715.3719888100929
30134.9140.170747824066-5.27074782406636
31149.2136.89005764976912.309942350231
32132.3137.116753319121-4.81675331912149
33149150.537433210987-1.53743321098743
34117.2116.9647860076370.235213992362893
35119.6118.4637056852821.13629431471773
36152144.9443815776447.05561842235638
37149.4150.164445482696-0.764445482696071
38127.3138.357133616103-11.0571336161034
39114.1122.21316419601-8.1131641960097
40102.1109.144675202535-7.04467520253495
41107.7108.500467061705-0.800467061705034
42104.4116.692380873722-12.2923808737218
43102.1105.875221954062-3.77522195406176
4496102.470907844206-6.47090784420566
45109.3111.146756981873-1.84675698187302
469078.332750201877311.6672497981227
4783.987.6745955213965-3.77459552139645
48112114.047776807078-2.04777680707795
49114.3118.681472717387-4.38147271738715
50103.6103.2675617956460.332438204354196
5191.792.368592433867-0.668592433867004
5280.886.0592266022357-5.25922660223575
5387.289.5247595200009-2.32475952000089
54109.297.933210859805211.2667891401948
55102.796.62921699780566.07078300219442
5695.198.5625834410033-3.46258344100332
57117.5116.1462170330171.35378296698262
5885.179.51734521427545.58265478572455
5992.187.59757677115584.50242322884416
60113.5116.541132746449-3.04113274644944

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 112.3 & 122.614877127651 & -10.3148771276511 \tabularnewline
2 & 117.3 & 111.040646166104 & 6.25935383389574 \tabularnewline
3 & 111.1 & 101.791118972656 & 9.30888102734388 \tabularnewline
4 & 102.2 & 101.903898293417 & 0.296101706582642 \tabularnewline
5 & 104.3 & 113.818115415492 & -9.51811541549151 \tabularnewline
6 & 122.9 & 122.036171447978 & 0.863828552022047 \tabularnewline
7 & 107.6 & 118.046418062012 & -10.4464180620117 \tabularnewline
8 & 121.3 & 114.030366480924 & 7.26963351907558 \tabularnewline
9 & 131.5 & 135.018941368546 & -3.51894136854591 \tabularnewline
10 & 89 & 99.7923562220788 & -10.7923562220788 \tabularnewline
11 & 104.4 & 107.012954135496 & -2.61295413549615 \tabularnewline
12 & 128.9 & 129.478933632017 & -0.578933632017005 \tabularnewline
13 & 135.9 & 134.059119348705 & 1.84088065129534 \tabularnewline
14 & 133.3 & 127.55610207318 & 5.74389792681968 \tabularnewline
15 & 121.3 & 118.500578040292 & 2.79942195970813 \tabularnewline
16 & 120.5 & 113.935706956029 & 6.56429304397084 \tabularnewline
17 & 120.4 & 123.128646812895 & -2.72864681289545 \tabularnewline
18 & 137.9 & 132.467488994429 & 5.43251100557129 \tabularnewline
19 & 126.1 & 130.259085336352 & -4.15908533635199 \tabularnewline
20 & 133.2 & 125.719388914745 & 7.48061108525489 \tabularnewline
21 & 151.1 & 145.550651405576 & 5.54934859442373 \tabularnewline
22 & 105 & 111.692762354131 & -6.6927623541313 \tabularnewline
23 & 119 & 118.251167886669 & 0.748832113330722 \tabularnewline
24 & 140.4 & 141.787775236812 & -1.38777523681202 \tabularnewline
25 & 156.6 & 142.980085323561 & 13.6199146764389 \tabularnewline
26 & 137.1 & 138.378556348966 & -1.27855634896627 \tabularnewline
27 & 122.7 & 126.026546357175 & -3.32654635717531 \tabularnewline
28 & 125.8 & 120.356492945783 & 5.44350705421722 \tabularnewline
29 & 139.3 & 123.928011189907 & 15.3719888100929 \tabularnewline
30 & 134.9 & 140.170747824066 & -5.27074782406636 \tabularnewline
31 & 149.2 & 136.890057649769 & 12.309942350231 \tabularnewline
32 & 132.3 & 137.116753319121 & -4.81675331912149 \tabularnewline
33 & 149 & 150.537433210987 & -1.53743321098743 \tabularnewline
34 & 117.2 & 116.964786007637 & 0.235213992362893 \tabularnewline
35 & 119.6 & 118.463705685282 & 1.13629431471773 \tabularnewline
36 & 152 & 144.944381577644 & 7.05561842235638 \tabularnewline
37 & 149.4 & 150.164445482696 & -0.764445482696071 \tabularnewline
38 & 127.3 & 138.357133616103 & -11.0571336161034 \tabularnewline
39 & 114.1 & 122.21316419601 & -8.1131641960097 \tabularnewline
40 & 102.1 & 109.144675202535 & -7.04467520253495 \tabularnewline
41 & 107.7 & 108.500467061705 & -0.800467061705034 \tabularnewline
42 & 104.4 & 116.692380873722 & -12.2923808737218 \tabularnewline
43 & 102.1 & 105.875221954062 & -3.77522195406176 \tabularnewline
44 & 96 & 102.470907844206 & -6.47090784420566 \tabularnewline
45 & 109.3 & 111.146756981873 & -1.84675698187302 \tabularnewline
46 & 90 & 78.3327502018773 & 11.6672497981227 \tabularnewline
47 & 83.9 & 87.6745955213965 & -3.77459552139645 \tabularnewline
48 & 112 & 114.047776807078 & -2.04777680707795 \tabularnewline
49 & 114.3 & 118.681472717387 & -4.38147271738715 \tabularnewline
50 & 103.6 & 103.267561795646 & 0.332438204354196 \tabularnewline
51 & 91.7 & 92.368592433867 & -0.668592433867004 \tabularnewline
52 & 80.8 & 86.0592266022357 & -5.25922660223575 \tabularnewline
53 & 87.2 & 89.5247595200009 & -2.32475952000089 \tabularnewline
54 & 109.2 & 97.9332108598052 & 11.2667891401948 \tabularnewline
55 & 102.7 & 96.6292169978056 & 6.07078300219442 \tabularnewline
56 & 95.1 & 98.5625834410033 & -3.46258344100332 \tabularnewline
57 & 117.5 & 116.146217033017 & 1.35378296698262 \tabularnewline
58 & 85.1 & 79.5173452142754 & 5.58265478572455 \tabularnewline
59 & 92.1 & 87.5975767711558 & 4.50242322884416 \tabularnewline
60 & 113.5 & 116.541132746449 & -3.04113274644944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&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]112.3[/C][C]122.614877127651[/C][C]-10.3148771276511[/C][/ROW]
[ROW][C]2[/C][C]117.3[/C][C]111.040646166104[/C][C]6.25935383389574[/C][/ROW]
[ROW][C]3[/C][C]111.1[/C][C]101.791118972656[/C][C]9.30888102734388[/C][/ROW]
[ROW][C]4[/C][C]102.2[/C][C]101.903898293417[/C][C]0.296101706582642[/C][/ROW]
[ROW][C]5[/C][C]104.3[/C][C]113.818115415492[/C][C]-9.51811541549151[/C][/ROW]
[ROW][C]6[/C][C]122.9[/C][C]122.036171447978[/C][C]0.863828552022047[/C][/ROW]
[ROW][C]7[/C][C]107.6[/C][C]118.046418062012[/C][C]-10.4464180620117[/C][/ROW]
[ROW][C]8[/C][C]121.3[/C][C]114.030366480924[/C][C]7.26963351907558[/C][/ROW]
[ROW][C]9[/C][C]131.5[/C][C]135.018941368546[/C][C]-3.51894136854591[/C][/ROW]
[ROW][C]10[/C][C]89[/C][C]99.7923562220788[/C][C]-10.7923562220788[/C][/ROW]
[ROW][C]11[/C][C]104.4[/C][C]107.012954135496[/C][C]-2.61295413549615[/C][/ROW]
[ROW][C]12[/C][C]128.9[/C][C]129.478933632017[/C][C]-0.578933632017005[/C][/ROW]
[ROW][C]13[/C][C]135.9[/C][C]134.059119348705[/C][C]1.84088065129534[/C][/ROW]
[ROW][C]14[/C][C]133.3[/C][C]127.55610207318[/C][C]5.74389792681968[/C][/ROW]
[ROW][C]15[/C][C]121.3[/C][C]118.500578040292[/C][C]2.79942195970813[/C][/ROW]
[ROW][C]16[/C][C]120.5[/C][C]113.935706956029[/C][C]6.56429304397084[/C][/ROW]
[ROW][C]17[/C][C]120.4[/C][C]123.128646812895[/C][C]-2.72864681289545[/C][/ROW]
[ROW][C]18[/C][C]137.9[/C][C]132.467488994429[/C][C]5.43251100557129[/C][/ROW]
[ROW][C]19[/C][C]126.1[/C][C]130.259085336352[/C][C]-4.15908533635199[/C][/ROW]
[ROW][C]20[/C][C]133.2[/C][C]125.719388914745[/C][C]7.48061108525489[/C][/ROW]
[ROW][C]21[/C][C]151.1[/C][C]145.550651405576[/C][C]5.54934859442373[/C][/ROW]
[ROW][C]22[/C][C]105[/C][C]111.692762354131[/C][C]-6.6927623541313[/C][/ROW]
[ROW][C]23[/C][C]119[/C][C]118.251167886669[/C][C]0.748832113330722[/C][/ROW]
[ROW][C]24[/C][C]140.4[/C][C]141.787775236812[/C][C]-1.38777523681202[/C][/ROW]
[ROW][C]25[/C][C]156.6[/C][C]142.980085323561[/C][C]13.6199146764389[/C][/ROW]
[ROW][C]26[/C][C]137.1[/C][C]138.378556348966[/C][C]-1.27855634896627[/C][/ROW]
[ROW][C]27[/C][C]122.7[/C][C]126.026546357175[/C][C]-3.32654635717531[/C][/ROW]
[ROW][C]28[/C][C]125.8[/C][C]120.356492945783[/C][C]5.44350705421722[/C][/ROW]
[ROW][C]29[/C][C]139.3[/C][C]123.928011189907[/C][C]15.3719888100929[/C][/ROW]
[ROW][C]30[/C][C]134.9[/C][C]140.170747824066[/C][C]-5.27074782406636[/C][/ROW]
[ROW][C]31[/C][C]149.2[/C][C]136.890057649769[/C][C]12.309942350231[/C][/ROW]
[ROW][C]32[/C][C]132.3[/C][C]137.116753319121[/C][C]-4.81675331912149[/C][/ROW]
[ROW][C]33[/C][C]149[/C][C]150.537433210987[/C][C]-1.53743321098743[/C][/ROW]
[ROW][C]34[/C][C]117.2[/C][C]116.964786007637[/C][C]0.235213992362893[/C][/ROW]
[ROW][C]35[/C][C]119.6[/C][C]118.463705685282[/C][C]1.13629431471773[/C][/ROW]
[ROW][C]36[/C][C]152[/C][C]144.944381577644[/C][C]7.05561842235638[/C][/ROW]
[ROW][C]37[/C][C]149.4[/C][C]150.164445482696[/C][C]-0.764445482696071[/C][/ROW]
[ROW][C]38[/C][C]127.3[/C][C]138.357133616103[/C][C]-11.0571336161034[/C][/ROW]
[ROW][C]39[/C][C]114.1[/C][C]122.21316419601[/C][C]-8.1131641960097[/C][/ROW]
[ROW][C]40[/C][C]102.1[/C][C]109.144675202535[/C][C]-7.04467520253495[/C][/ROW]
[ROW][C]41[/C][C]107.7[/C][C]108.500467061705[/C][C]-0.800467061705034[/C][/ROW]
[ROW][C]42[/C][C]104.4[/C][C]116.692380873722[/C][C]-12.2923808737218[/C][/ROW]
[ROW][C]43[/C][C]102.1[/C][C]105.875221954062[/C][C]-3.77522195406176[/C][/ROW]
[ROW][C]44[/C][C]96[/C][C]102.470907844206[/C][C]-6.47090784420566[/C][/ROW]
[ROW][C]45[/C][C]109.3[/C][C]111.146756981873[/C][C]-1.84675698187302[/C][/ROW]
[ROW][C]46[/C][C]90[/C][C]78.3327502018773[/C][C]11.6672497981227[/C][/ROW]
[ROW][C]47[/C][C]83.9[/C][C]87.6745955213965[/C][C]-3.77459552139645[/C][/ROW]
[ROW][C]48[/C][C]112[/C][C]114.047776807078[/C][C]-2.04777680707795[/C][/ROW]
[ROW][C]49[/C][C]114.3[/C][C]118.681472717387[/C][C]-4.38147271738715[/C][/ROW]
[ROW][C]50[/C][C]103.6[/C][C]103.267561795646[/C][C]0.332438204354196[/C][/ROW]
[ROW][C]51[/C][C]91.7[/C][C]92.368592433867[/C][C]-0.668592433867004[/C][/ROW]
[ROW][C]52[/C][C]80.8[/C][C]86.0592266022357[/C][C]-5.25922660223575[/C][/ROW]
[ROW][C]53[/C][C]87.2[/C][C]89.5247595200009[/C][C]-2.32475952000089[/C][/ROW]
[ROW][C]54[/C][C]109.2[/C][C]97.9332108598052[/C][C]11.2667891401948[/C][/ROW]
[ROW][C]55[/C][C]102.7[/C][C]96.6292169978056[/C][C]6.07078300219442[/C][/ROW]
[ROW][C]56[/C][C]95.1[/C][C]98.5625834410033[/C][C]-3.46258344100332[/C][/ROW]
[ROW][C]57[/C][C]117.5[/C][C]116.146217033017[/C][C]1.35378296698262[/C][/ROW]
[ROW][C]58[/C][C]85.1[/C][C]79.5173452142754[/C][C]5.58265478572455[/C][/ROW]
[ROW][C]59[/C][C]92.1[/C][C]87.5975767711558[/C][C]4.50242322884416[/C][/ROW]
[ROW][C]60[/C][C]113.5[/C][C]116.541132746449[/C][C]-3.04113274644944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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
1112.3122.614877127651-10.3148771276511
2117.3111.0406461661046.25935383389574
3111.1101.7911189726569.30888102734388
4102.2101.9038982934170.296101706582642
5104.3113.818115415492-9.51811541549151
6122.9122.0361714479780.863828552022047
7107.6118.046418062012-10.4464180620117
8121.3114.0303664809247.26963351907558
9131.5135.018941368546-3.51894136854591
108999.7923562220788-10.7923562220788
11104.4107.012954135496-2.61295413549615
12128.9129.478933632017-0.578933632017005
13135.9134.0591193487051.84088065129534
14133.3127.556102073185.74389792681968
15121.3118.5005780402922.79942195970813
16120.5113.9357069560296.56429304397084
17120.4123.128646812895-2.72864681289545
18137.9132.4674889944295.43251100557129
19126.1130.259085336352-4.15908533635199
20133.2125.7193889147457.48061108525489
21151.1145.5506514055765.54934859442373
22105111.692762354131-6.6927623541313
23119118.2511678866690.748832113330722
24140.4141.787775236812-1.38777523681202
25156.6142.98008532356113.6199146764389
26137.1138.378556348966-1.27855634896627
27122.7126.026546357175-3.32654635717531
28125.8120.3564929457835.44350705421722
29139.3123.92801118990715.3719888100929
30134.9140.170747824066-5.27074782406636
31149.2136.89005764976912.309942350231
32132.3137.116753319121-4.81675331912149
33149150.537433210987-1.53743321098743
34117.2116.9647860076370.235213992362893
35119.6118.4637056852821.13629431471773
36152144.9443815776447.05561842235638
37149.4150.164445482696-0.764445482696071
38127.3138.357133616103-11.0571336161034
39114.1122.21316419601-8.1131641960097
40102.1109.144675202535-7.04467520253495
41107.7108.500467061705-0.800467061705034
42104.4116.692380873722-12.2923808737218
43102.1105.875221954062-3.77522195406176
4496102.470907844206-6.47090784420566
45109.3111.146756981873-1.84675698187302
469078.332750201877311.6672497981227
4783.987.6745955213965-3.77459552139645
48112114.047776807078-2.04777680707795
49114.3118.681472717387-4.38147271738715
50103.6103.2675617956460.332438204354196
5191.792.368592433867-0.668592433867004
5280.886.0592266022357-5.25922660223575
5387.289.5247595200009-2.32475952000089
54109.297.933210859805211.2667891401948
55102.796.62921699780566.07078300219442
5695.198.5625834410033-3.46258344100332
57117.5116.1462170330171.35378296698262
5885.179.51734521427545.58265478572455
5992.187.59757677115584.50242322884416
60113.5116.541132746449-3.04113274644944






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.02599734881168950.0519946976233790.974002651188311
220.00808627798476310.01617255596952620.991913722015237
230.001803603887778530.003607207775557070.998196396112221
240.002275122198873770.004550244397747530.997724877801126
250.0008654850374799720.001730970074959940.99913451496252
260.004872591171290060.009745182342580130.99512740882871
270.1140087418931570.2280174837863140.885991258106843
280.3078054434329430.6156108868658870.692194556567057
290.3323833128300790.6647666256601580.667616687169921
300.2911401810720030.5822803621440070.708859818927997
310.5939275480010240.8121449039979520.406072451998976
320.5175188770473270.9649622459053470.482481122952673
330.7043062810377710.5913874379244570.295693718962229
340.5997720583350150.800455883329970.400227941664985
350.5120295903143810.9759408193712380.487970409685619
360.7449612387327650.5100775225344710.255038761267235
370.6389562866082750.722087426783450.361043713391725
380.6344583207135010.7310833585729980.365541679286499
390.5276491356894520.9447017286210950.472350864310548

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0259973488116895 & 0.051994697623379 & 0.974002651188311 \tabularnewline
22 & 0.0080862779847631 & 0.0161725559695262 & 0.991913722015237 \tabularnewline
23 & 0.00180360388777853 & 0.00360720777555707 & 0.998196396112221 \tabularnewline
24 & 0.00227512219887377 & 0.00455024439774753 & 0.997724877801126 \tabularnewline
25 & 0.000865485037479972 & 0.00173097007495994 & 0.99913451496252 \tabularnewline
26 & 0.00487259117129006 & 0.00974518234258013 & 0.99512740882871 \tabularnewline
27 & 0.114008741893157 & 0.228017483786314 & 0.885991258106843 \tabularnewline
28 & 0.307805443432943 & 0.615610886865887 & 0.692194556567057 \tabularnewline
29 & 0.332383312830079 & 0.664766625660158 & 0.667616687169921 \tabularnewline
30 & 0.291140181072003 & 0.582280362144007 & 0.708859818927997 \tabularnewline
31 & 0.593927548001024 & 0.812144903997952 & 0.406072451998976 \tabularnewline
32 & 0.517518877047327 & 0.964962245905347 & 0.482481122952673 \tabularnewline
33 & 0.704306281037771 & 0.591387437924457 & 0.295693718962229 \tabularnewline
34 & 0.599772058335015 & 0.80045588332997 & 0.400227941664985 \tabularnewline
35 & 0.512029590314381 & 0.975940819371238 & 0.487970409685619 \tabularnewline
36 & 0.744961238732765 & 0.510077522534471 & 0.255038761267235 \tabularnewline
37 & 0.638956286608275 & 0.72208742678345 & 0.361043713391725 \tabularnewline
38 & 0.634458320713501 & 0.731083358572998 & 0.365541679286499 \tabularnewline
39 & 0.527649135689452 & 0.944701728621095 & 0.472350864310548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&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]0.0259973488116895[/C][C]0.051994697623379[/C][C]0.974002651188311[/C][/ROW]
[ROW][C]22[/C][C]0.0080862779847631[/C][C]0.0161725559695262[/C][C]0.991913722015237[/C][/ROW]
[ROW][C]23[/C][C]0.00180360388777853[/C][C]0.00360720777555707[/C][C]0.998196396112221[/C][/ROW]
[ROW][C]24[/C][C]0.00227512219887377[/C][C]0.00455024439774753[/C][C]0.997724877801126[/C][/ROW]
[ROW][C]25[/C][C]0.000865485037479972[/C][C]0.00173097007495994[/C][C]0.99913451496252[/C][/ROW]
[ROW][C]26[/C][C]0.00487259117129006[/C][C]0.00974518234258013[/C][C]0.99512740882871[/C][/ROW]
[ROW][C]27[/C][C]0.114008741893157[/C][C]0.228017483786314[/C][C]0.885991258106843[/C][/ROW]
[ROW][C]28[/C][C]0.307805443432943[/C][C]0.615610886865887[/C][C]0.692194556567057[/C][/ROW]
[ROW][C]29[/C][C]0.332383312830079[/C][C]0.664766625660158[/C][C]0.667616687169921[/C][/ROW]
[ROW][C]30[/C][C]0.291140181072003[/C][C]0.582280362144007[/C][C]0.708859818927997[/C][/ROW]
[ROW][C]31[/C][C]0.593927548001024[/C][C]0.812144903997952[/C][C]0.406072451998976[/C][/ROW]
[ROW][C]32[/C][C]0.517518877047327[/C][C]0.964962245905347[/C][C]0.482481122952673[/C][/ROW]
[ROW][C]33[/C][C]0.704306281037771[/C][C]0.591387437924457[/C][C]0.295693718962229[/C][/ROW]
[ROW][C]34[/C][C]0.599772058335015[/C][C]0.80045588332997[/C][C]0.400227941664985[/C][/ROW]
[ROW][C]35[/C][C]0.512029590314381[/C][C]0.975940819371238[/C][C]0.487970409685619[/C][/ROW]
[ROW][C]36[/C][C]0.744961238732765[/C][C]0.510077522534471[/C][C]0.255038761267235[/C][/ROW]
[ROW][C]37[/C][C]0.638956286608275[/C][C]0.72208742678345[/C][C]0.361043713391725[/C][/ROW]
[ROW][C]38[/C][C]0.634458320713501[/C][C]0.731083358572998[/C][C]0.365541679286499[/C][/ROW]
[ROW][C]39[/C][C]0.527649135689452[/C][C]0.944701728621095[/C][C]0.472350864310548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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
210.02599734881168950.0519946976233790.974002651188311
220.00808627798476310.01617255596952620.991913722015237
230.001803603887778530.003607207775557070.998196396112221
240.002275122198873770.004550244397747530.997724877801126
250.0008654850374799720.001730970074959940.99913451496252
260.004872591171290060.009745182342580130.99512740882871
270.1140087418931570.2280174837863140.885991258106843
280.3078054434329430.6156108868658870.692194556567057
290.3323833128300790.6647666256601580.667616687169921
300.2911401810720030.5822803621440070.708859818927997
310.5939275480010240.8121449039979520.406072451998976
320.5175188770473270.9649622459053470.482481122952673
330.7043062810377710.5913874379244570.295693718962229
340.5997720583350150.800455883329970.400227941664985
350.5120295903143810.9759408193712380.487970409685619
360.7449612387327650.5100775225344710.255038761267235
370.6389562866082750.722087426783450.361043713391725
380.6344583207135010.7310833585729980.365541679286499
390.5276491356894520.9447017286210950.472350864310548






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.210526315789474NOK
5% type I error level50.263157894736842NOK
10% type I error level60.315789473684211NOK

\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 & 4 & 0.210526315789474 & NOK \tabularnewline
5% type I error level & 5 & 0.263157894736842 & NOK \tabularnewline
10% type I error level & 6 & 0.315789473684211 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147561&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]4[/C][C]0.210526315789474[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]5[/C][C]0.263157894736842[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]6[/C][C]0.315789473684211[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147561&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147561&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 level40.210526315789474NOK
5% type I error level50.263157894736842NOK
10% type I error level60.315789473684211NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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Input Parameters & R Code

Parameters (Session):
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')
}