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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, 20 Nov 2009 06:34:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258724163x4hnvb9e1o1wvwx.htm/, Retrieved Tue, 24 Jun 2025 05:45:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58148, Retrieved Tue, 24 Jun 2025 05:45:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact318

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [model 1] [2009-11-17 14:36:29] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Multiple Regression] [multiple regression] [2009-11-19 21:38:11] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P         [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P           [Multiple Regression] [model3] [2009-11-20 08:47:44] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D            [Multiple Regression] [Workshop7] [2009-11-20 13:14:04] [34b80aeb109c116fd63bf2eb7493a276]
-    D                [Multiple Regression] [workshop7] [2009-11-20 13:34:45] [307139c5e328127f586f26d5bcc435d8] [Current]
-   P                   [Multiple Regression] [Workshop 7: verbe...] [2009-11-27 14:49:24] [7c2a5b25a196bd646844b8f5223c9b3e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.7	102.9	105.7	105.6	105.4	105.4
105.8	103.1	105.8	105.7	105.6	105.4
105.8	103	105.8	105.8	105.7	105.6
105.8	102.8	105.8	105.8	105.8	105.7
105.9	102.5	105.9	105.8	105.8	105.8
106.1	101.9	106.1	105.9	105.8	105.8
106.4	101.9	106.4	106.1	105.9	105.8
106.4	101.8	106.4	106.4	106.1	105.9
106.3	102	106.3	106.4	106.4	106.1
106.2	102.6	106.2	106.3	106.4	106.4
106.2	102.5	106.2	106.2	106.3	106.4
106.3	102.5	106.3	106.2	106.2	106.3
106.4	101.6	106.4	106.3	106.2	106.2
106.5	101.4	106.5	106.4	106.3	106.2
106.6	100.8	106.6	106.5	106.4	106.3
106.6	101.1	106.6	106.6	106.5	106.4
106.6	101.3	106.6	106.6	106.6	106.5
106.8	101.2	106.8	106.6	106.6	106.6
107	101.3	107	106.8	106.6	106.6
107.2	101.1	107.2	107	106.8	106.6
107.3	101.3	107.3	107.2	107	106.8
107.5	101.2	107.5	107.3	107.2	107
107.6	101.6	107.6	107.5	107.3	107.2
107.6	101.7	107.6	107.6	107.5	107.3
107.7	101.5	107.7	107.6	107.6	107.5
107.7	100.9	107.7	107.7	107.6	107.6
107.7	101.5	107.7	107.7	107.7	107.6
107.7	101.4	107.7	107.7	107.7	107.7
107.6	101.6	107.6	107.7	107.7	107.7
107.7	101.7	107.7	107.6	107.7	107.7
107.9	101.4	107.9	107.7	107.6	107.7
107.9	101.8	107.9	107.9	107.7	107.6
107.9	101.7	107.9	107.9	107.9	107.7
107.8	101.4	107.8	107.9	107.9	107.9
107.6	101.2	107.6	107.8	107.9	107.9
107.4	101	107.4	107.6	107.8	107.9
107	101.7	107	107.4	107.6	107.8
107	102.4	107	107	107.4	107.6
107.2	102	107.2	107	107	107.4
107.5	102.1	107.5	107.2	107	107
107.8	102	107.8	107.5	107.2	107
107.8	101.8	107.8	107.8	107.5	107.2
107.7	102.7	107.7	107.8	107.8	107.5
107.6	102.3	107.6	107.7	107.8	107.8
107.6	101.9	107.6	107.6	107.7	107.8
107.5	102	107.5	107.6	107.6	107.7
107.5	102.3	107.5	107.5	107.6	107.6
107.6	102.8	107.6	107.5	107.5	107.6
107.6	102.4	107.6	107.6	107.5	107.5
107.9	102.3	107.9	107.6	107.6	107.5
107.6	102.7	107.6	107.9	107.6	107.6
107.5	102.7	107.5	107.6	107.9	107.6
107.5	102.9	107.5	107.5	107.6	107.9
107.6	103	107.6	107.5	107.5	107.6
107.7	102.2	107.7	107.6	107.5	107.5
107.8	102.3	107.8	107.7	107.6	107.5
107.9	102.8	107.9	107.8	107.7	107.6
107.9	102.8	107.9	107.9	107.8	107.7

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' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&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' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = -2.98556262486551e-14 0Infl[t] + 1`Yt-1`[t] + 1.81519184532925e-16`Yt-2`[t] -2.45507207353906e-16`Yt-3`[t] + 7.4137832331761e-17`Yt-4`[t] + 6.5975896112844e-17M1[t] + 9.08061661664562e-17M2[t] -2.66567376381162e-16M3[t] + 7.09161574221674e-17M4[t] + 1.63667482847923e-17M5[t] + 3.81721703518880e-17M6[t] + 2.98530572921271e-17M7[t] -2.71027271967783e-18M8[t] + 6.79620888317612e-17M9[t] + 3.47356474680704e-17M10[t] + 5.46324815218279e-17M11[t] + 6.35636611756634e-18t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  -2.98556262486551e-14 0Infl[t] +  1`Yt-1`[t] +  1.81519184532925e-16`Yt-2`[t] -2.45507207353906e-16`Yt-3`[t] +  7.4137832331761e-17`Yt-4`[t] +  6.5975896112844e-17M1[t] +  9.08061661664562e-17M2[t] -2.66567376381162e-16M3[t] +  7.09161574221674e-17M4[t] +  1.63667482847923e-17M5[t] +  3.81721703518880e-17M6[t] +  2.98530572921271e-17M7[t] -2.71027271967783e-18M8[t] +  6.79620888317612e-17M9[t] +  3.47356474680704e-17M10[t] +  5.46324815218279e-17M11[t] +  6.35636611756634e-18t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  -2.98556262486551e-14 0Infl[t] +  1`Yt-1`[t] +  1.81519184532925e-16`Yt-2`[t] -2.45507207353906e-16`Yt-3`[t] +  7.4137832331761e-17`Yt-4`[t] +  6.5975896112844e-17M1[t] +  9.08061661664562e-17M2[t] -2.66567376381162e-16M3[t] +  7.09161574221674e-17M4[t] +  1.63667482847923e-17M5[t] +  3.81721703518880e-17M6[t] +  2.98530572921271e-17M7[t] -2.71027271967783e-18M8[t] +  6.79620888317612e-17M9[t] +  3.47356474680704e-17M10[t] +  5.46324815218279e-17M11[t] +  6.35636611756634e-18t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&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
Werkl[t] = -2.98556262486551e-14 0Infl[t] + 1`Yt-1`[t] + 1.81519184532925e-16`Yt-2`[t] -2.45507207353906e-16`Yt-3`[t] + 7.4137832331761e-17`Yt-4`[t] + 6.5975896112844e-17M1[t] + 9.08061661664562e-17M2[t] -2.66567376381162e-16M3[t] + 7.09161574221674e-17M4[t] + 1.63667482847923e-17M5[t] + 3.81721703518880e-17M6[t] + 2.98530572921271e-17M7[t] -2.71027271967783e-18M8[t] + 6.79620888317612e-17M9[t] + 3.47356474680704e-17M10[t] + 5.46324815218279e-17M11[t] + 6.35636611756634e-18t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-2.98556262486551e-140-1.69460.0979240.048962
Infl00010.5
`Yt-1`10374181622579916100
`Yt-2`1.81519184532925e-1600.40350.6887340.344367
`Yt-3`-2.45507207353906e-160-0.5460.5880930.294047
`Yt-4`7.4137832331761e-1700.2810.7801910.390095
M16.5975896112844e-1700.44450.6590550.329527
M29.08061661664562e-1700.60530.5483910.274195
M3-2.66567376381162e-160-1.76880.0845440.042272
M47.09161574221674e-1700.46950.6412780.320639
M51.63667482847923e-1700.11110.9121310.456066
M63.81721703518880e-1700.25450.8004010.400201
M72.98530572921271e-1700.19690.8448710.422436
M8-2.71027271967783e-180-0.01770.9859290.492964
M96.79620888317612e-1700.4490.6558790.327939
M103.47356474680704e-1700.23620.814520.40726
M115.46324815218279e-1700.35520.7242810.36214
t6.35636611756634e-1801.33120.1906710.095335

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -2.98556262486551e-14 & 0 & -1.6946 & 0.097924 & 0.048962 \tabularnewline
Infl & 0 & 0 & 0 & 1 & 0.5 \tabularnewline
`Yt-1` & 1 & 0 & 3741816225799161 & 0 & 0 \tabularnewline
`Yt-2` & 1.81519184532925e-16 & 0 & 0.4035 & 0.688734 & 0.344367 \tabularnewline
`Yt-3` & -2.45507207353906e-16 & 0 & -0.546 & 0.588093 & 0.294047 \tabularnewline
`Yt-4` & 7.4137832331761e-17 & 0 & 0.281 & 0.780191 & 0.390095 \tabularnewline
M1 & 6.5975896112844e-17 & 0 & 0.4445 & 0.659055 & 0.329527 \tabularnewline
M2 & 9.08061661664562e-17 & 0 & 0.6053 & 0.548391 & 0.274195 \tabularnewline
M3 & -2.66567376381162e-16 & 0 & -1.7688 & 0.084544 & 0.042272 \tabularnewline
M4 & 7.09161574221674e-17 & 0 & 0.4695 & 0.641278 & 0.320639 \tabularnewline
M5 & 1.63667482847923e-17 & 0 & 0.1111 & 0.912131 & 0.456066 \tabularnewline
M6 & 3.81721703518880e-17 & 0 & 0.2545 & 0.800401 & 0.400201 \tabularnewline
M7 & 2.98530572921271e-17 & 0 & 0.1969 & 0.844871 & 0.422436 \tabularnewline
M8 & -2.71027271967783e-18 & 0 & -0.0177 & 0.985929 & 0.492964 \tabularnewline
M9 & 6.79620888317612e-17 & 0 & 0.449 & 0.655879 & 0.327939 \tabularnewline
M10 & 3.47356474680704e-17 & 0 & 0.2362 & 0.81452 & 0.40726 \tabularnewline
M11 & 5.46324815218279e-17 & 0 & 0.3552 & 0.724281 & 0.36214 \tabularnewline
t & 6.35636611756634e-18 & 0 & 1.3312 & 0.190671 & 0.095335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-2.98556262486551e-14[/C][C]0[/C][C]-1.6946[/C][C]0.097924[/C][C]0.048962[/C][/ROW]
[ROW][C]Infl[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]0.5[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]1[/C][C]0[/C][C]3741816225799161[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]1.81519184532925e-16[/C][C]0[/C][C]0.4035[/C][C]0.688734[/C][C]0.344367[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]-2.45507207353906e-16[/C][C]0[/C][C]-0.546[/C][C]0.588093[/C][C]0.294047[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]7.4137832331761e-17[/C][C]0[/C][C]0.281[/C][C]0.780191[/C][C]0.390095[/C][/ROW]
[ROW][C]M1[/C][C]6.5975896112844e-17[/C][C]0[/C][C]0.4445[/C][C]0.659055[/C][C]0.329527[/C][/ROW]
[ROW][C]M2[/C][C]9.08061661664562e-17[/C][C]0[/C][C]0.6053[/C][C]0.548391[/C][C]0.274195[/C][/ROW]
[ROW][C]M3[/C][C]-2.66567376381162e-16[/C][C]0[/C][C]-1.7688[/C][C]0.084544[/C][C]0.042272[/C][/ROW]
[ROW][C]M4[/C][C]7.09161574221674e-17[/C][C]0[/C][C]0.4695[/C][C]0.641278[/C][C]0.320639[/C][/ROW]
[ROW][C]M5[/C][C]1.63667482847923e-17[/C][C]0[/C][C]0.1111[/C][C]0.912131[/C][C]0.456066[/C][/ROW]
[ROW][C]M6[/C][C]3.81721703518880e-17[/C][C]0[/C][C]0.2545[/C][C]0.800401[/C][C]0.400201[/C][/ROW]
[ROW][C]M7[/C][C]2.98530572921271e-17[/C][C]0[/C][C]0.1969[/C][C]0.844871[/C][C]0.422436[/C][/ROW]
[ROW][C]M8[/C][C]-2.71027271967783e-18[/C][C]0[/C][C]-0.0177[/C][C]0.985929[/C][C]0.492964[/C][/ROW]
[ROW][C]M9[/C][C]6.79620888317612e-17[/C][C]0[/C][C]0.449[/C][C]0.655879[/C][C]0.327939[/C][/ROW]
[ROW][C]M10[/C][C]3.47356474680704e-17[/C][C]0[/C][C]0.2362[/C][C]0.81452[/C][C]0.40726[/C][/ROW]
[ROW][C]M11[/C][C]5.46324815218279e-17[/C][C]0[/C][C]0.3552[/C][C]0.724281[/C][C]0.36214[/C][/ROW]
[ROW][C]t[/C][C]6.35636611756634e-18[/C][C]0[/C][C]1.3312[/C][C]0.190671[/C][C]0.095335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-2.98556262486551e-140-1.69460.0979240.048962
Infl00010.5
`Yt-1`10374181622579916100
`Yt-2`1.81519184532925e-1600.40350.6887340.344367
`Yt-3`-2.45507207353906e-160-0.5460.5880930.294047
`Yt-4`7.4137832331761e-1700.2810.7801910.390095
M16.5975896112844e-1700.44450.6590550.329527
M29.08061661664562e-1700.60530.5483910.274195
M3-2.66567376381162e-160-1.76880.0845440.042272
M47.09161574221674e-1700.46950.6412780.320639
M51.63667482847923e-1700.11110.9121310.456066
M63.81721703518880e-1700.25450.8004010.400201
M72.98530572921271e-1700.19690.8448710.422436
M8-2.71027271967783e-180-0.01770.9859290.492964
M96.79620888317612e-1700.4490.6558790.327939
M103.47356474680704e-1700.23620.814520.40726
M115.46324815218279e-1700.35520.7242810.36214
t6.35636611756634e-1801.33120.1906710.095335






Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)3.33185245735595e+31
F-TEST (DF numerator)17
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.17097405565436e-16
Sum Squared Residuals1.88525134012973e-30

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 1 \tabularnewline
R-squared & 1 \tabularnewline
Adjusted R-squared & 1 \tabularnewline
F-TEST (value) & 3.33185245735595e+31 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.17097405565436e-16 \tabularnewline
Sum Squared Residuals & 1.88525134012973e-30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]1[/C][/ROW]
[ROW][C]R-squared[/C][C]1[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3.33185245735595e+31[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.17097405565436e-16[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.88525134012973e-30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&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 R1
R-squared1
Adjusted R-squared1
F-TEST (value)3.33185245735595e+31
F-TEST (DF numerator)17
F-TEST (DF denominator)40
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.17097405565436e-16
Sum Squared Residuals1.88525134012973e-30






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1105.7105.71.49552512497658e-16
2105.8105.83.33937539667287e-16
3105.8105.8-1.08719992884711e-15
4105.8105.81.39426622871516e-16
5105.9105.91.55265102064878e-16
6106.1106.1-5.19524682221481e-17
7106.4106.46.00412829751428e-17
8106.4106.45.16349872797564e-17
9106.3106.33.65264734765019e-17
10106.2106.23.87610830091879e-17
11106.2106.29.52862205509342e-17
12106.3106.35.59978027992261e-17
13106.4106.43.89602548763855e-17
14106.5106.5-9.99454996011432e-17
15106.6106.62.70602730345035e-16
16106.6106.6-8.71666312490517e-18
17106.6106.6-1.07186601307071e-17
18106.8106.81.30500196016333e-17
19107107-2.92787967404063e-17
20107.2107.2-8.28629083039791e-18
21107.3107.3-5.90047807583614e-17
22107.5107.51.60096074424447e-17
23107.6107.6-4.76267967664343e-17
24107.6107.64.60302208894893e-17
25107.7107.73.58366460334465e-17
26107.7107.7-9.6475515397015e-17
27107.7107.73.54652205341242e-16
28107.7107.7-7.39577915114317e-17
29107.6107.6-2.26691303656988e-17
30107.7107.7-2.57502820522133e-17
31107.9107.9-5.08362480832184e-17
32107.9107.9-5.26102697201318e-17
33107.9107.91.22580084363961e-18
34107.8107.8-9.28618845873883e-17
35107.6107.6-5.93094511638587e-17
36107.4107.4-6.5179359957401e-17
37107107-1.28072004818785e-16
38107107-2.35198561410580e-17
39107.2107.22.10175191946292e-16
40107.5107.5-5.21952802861169e-17
41107.8107.8-1.31462198121498e-16
42107.8107.82.30991340641218e-17
43107.7107.71.21462146447795e-16
44107.6107.61.26626624880166e-16
45107.6107.6-4.41815549403141e-17
46107.5107.5-5.31979615378214e-17
47107.5107.51.16500273793586e-17
48107.6107.6-3.68486637313149e-17
49107.6107.6-9.6277408588705e-17
50107.9107.9-1.13996668528071e-16
51107.6107.62.51769801214538e-16
52107.5107.5-4.55688794906218e-18
53107.5107.59.58488655302598e-18
54107.6107.64.15535966086062e-17
55107.7107.7-1.01388384599313e-16
56107.8107.8-1.17365051609393e-16
57107.9107.96.54340613785344e-17
58107.9107.99.1289155673577e-17

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 105.7 & 105.7 & 1.49552512497658e-16 \tabularnewline
2 & 105.8 & 105.8 & 3.33937539667287e-16 \tabularnewline
3 & 105.8 & 105.8 & -1.08719992884711e-15 \tabularnewline
4 & 105.8 & 105.8 & 1.39426622871516e-16 \tabularnewline
5 & 105.9 & 105.9 & 1.55265102064878e-16 \tabularnewline
6 & 106.1 & 106.1 & -5.19524682221481e-17 \tabularnewline
7 & 106.4 & 106.4 & 6.00412829751428e-17 \tabularnewline
8 & 106.4 & 106.4 & 5.16349872797564e-17 \tabularnewline
9 & 106.3 & 106.3 & 3.65264734765019e-17 \tabularnewline
10 & 106.2 & 106.2 & 3.87610830091879e-17 \tabularnewline
11 & 106.2 & 106.2 & 9.52862205509342e-17 \tabularnewline
12 & 106.3 & 106.3 & 5.59978027992261e-17 \tabularnewline
13 & 106.4 & 106.4 & 3.89602548763855e-17 \tabularnewline
14 & 106.5 & 106.5 & -9.99454996011432e-17 \tabularnewline
15 & 106.6 & 106.6 & 2.70602730345035e-16 \tabularnewline
16 & 106.6 & 106.6 & -8.71666312490517e-18 \tabularnewline
17 & 106.6 & 106.6 & -1.07186601307071e-17 \tabularnewline
18 & 106.8 & 106.8 & 1.30500196016333e-17 \tabularnewline
19 & 107 & 107 & -2.92787967404063e-17 \tabularnewline
20 & 107.2 & 107.2 & -8.28629083039791e-18 \tabularnewline
21 & 107.3 & 107.3 & -5.90047807583614e-17 \tabularnewline
22 & 107.5 & 107.5 & 1.60096074424447e-17 \tabularnewline
23 & 107.6 & 107.6 & -4.76267967664343e-17 \tabularnewline
24 & 107.6 & 107.6 & 4.60302208894893e-17 \tabularnewline
25 & 107.7 & 107.7 & 3.58366460334465e-17 \tabularnewline
26 & 107.7 & 107.7 & -9.6475515397015e-17 \tabularnewline
27 & 107.7 & 107.7 & 3.54652205341242e-16 \tabularnewline
28 & 107.7 & 107.7 & -7.39577915114317e-17 \tabularnewline
29 & 107.6 & 107.6 & -2.26691303656988e-17 \tabularnewline
30 & 107.7 & 107.7 & -2.57502820522133e-17 \tabularnewline
31 & 107.9 & 107.9 & -5.08362480832184e-17 \tabularnewline
32 & 107.9 & 107.9 & -5.26102697201318e-17 \tabularnewline
33 & 107.9 & 107.9 & 1.22580084363961e-18 \tabularnewline
34 & 107.8 & 107.8 & -9.28618845873883e-17 \tabularnewline
35 & 107.6 & 107.6 & -5.93094511638587e-17 \tabularnewline
36 & 107.4 & 107.4 & -6.5179359957401e-17 \tabularnewline
37 & 107 & 107 & -1.28072004818785e-16 \tabularnewline
38 & 107 & 107 & -2.35198561410580e-17 \tabularnewline
39 & 107.2 & 107.2 & 2.10175191946292e-16 \tabularnewline
40 & 107.5 & 107.5 & -5.21952802861169e-17 \tabularnewline
41 & 107.8 & 107.8 & -1.31462198121498e-16 \tabularnewline
42 & 107.8 & 107.8 & 2.30991340641218e-17 \tabularnewline
43 & 107.7 & 107.7 & 1.21462146447795e-16 \tabularnewline
44 & 107.6 & 107.6 & 1.26626624880166e-16 \tabularnewline
45 & 107.6 & 107.6 & -4.41815549403141e-17 \tabularnewline
46 & 107.5 & 107.5 & -5.31979615378214e-17 \tabularnewline
47 & 107.5 & 107.5 & 1.16500273793586e-17 \tabularnewline
48 & 107.6 & 107.6 & -3.68486637313149e-17 \tabularnewline
49 & 107.6 & 107.6 & -9.6277408588705e-17 \tabularnewline
50 & 107.9 & 107.9 & -1.13996668528071e-16 \tabularnewline
51 & 107.6 & 107.6 & 2.51769801214538e-16 \tabularnewline
52 & 107.5 & 107.5 & -4.55688794906218e-18 \tabularnewline
53 & 107.5 & 107.5 & 9.58488655302598e-18 \tabularnewline
54 & 107.6 & 107.6 & 4.15535966086062e-17 \tabularnewline
55 & 107.7 & 107.7 & -1.01388384599313e-16 \tabularnewline
56 & 107.8 & 107.8 & -1.17365051609393e-16 \tabularnewline
57 & 107.9 & 107.9 & 6.54340613785344e-17 \tabularnewline
58 & 107.9 & 107.9 & 9.1289155673577e-17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&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]105.7[/C][C]105.7[/C][C]1.49552512497658e-16[/C][/ROW]
[ROW][C]2[/C][C]105.8[/C][C]105.8[/C][C]3.33937539667287e-16[/C][/ROW]
[ROW][C]3[/C][C]105.8[/C][C]105.8[/C][C]-1.08719992884711e-15[/C][/ROW]
[ROW][C]4[/C][C]105.8[/C][C]105.8[/C][C]1.39426622871516e-16[/C][/ROW]
[ROW][C]5[/C][C]105.9[/C][C]105.9[/C][C]1.55265102064878e-16[/C][/ROW]
[ROW][C]6[/C][C]106.1[/C][C]106.1[/C][C]-5.19524682221481e-17[/C][/ROW]
[ROW][C]7[/C][C]106.4[/C][C]106.4[/C][C]6.00412829751428e-17[/C][/ROW]
[ROW][C]8[/C][C]106.4[/C][C]106.4[/C][C]5.16349872797564e-17[/C][/ROW]
[ROW][C]9[/C][C]106.3[/C][C]106.3[/C][C]3.65264734765019e-17[/C][/ROW]
[ROW][C]10[/C][C]106.2[/C][C]106.2[/C][C]3.87610830091879e-17[/C][/ROW]
[ROW][C]11[/C][C]106.2[/C][C]106.2[/C][C]9.52862205509342e-17[/C][/ROW]
[ROW][C]12[/C][C]106.3[/C][C]106.3[/C][C]5.59978027992261e-17[/C][/ROW]
[ROW][C]13[/C][C]106.4[/C][C]106.4[/C][C]3.89602548763855e-17[/C][/ROW]
[ROW][C]14[/C][C]106.5[/C][C]106.5[/C][C]-9.99454996011432e-17[/C][/ROW]
[ROW][C]15[/C][C]106.6[/C][C]106.6[/C][C]2.70602730345035e-16[/C][/ROW]
[ROW][C]16[/C][C]106.6[/C][C]106.6[/C][C]-8.71666312490517e-18[/C][/ROW]
[ROW][C]17[/C][C]106.6[/C][C]106.6[/C][C]-1.07186601307071e-17[/C][/ROW]
[ROW][C]18[/C][C]106.8[/C][C]106.8[/C][C]1.30500196016333e-17[/C][/ROW]
[ROW][C]19[/C][C]107[/C][C]107[/C][C]-2.92787967404063e-17[/C][/ROW]
[ROW][C]20[/C][C]107.2[/C][C]107.2[/C][C]-8.28629083039791e-18[/C][/ROW]
[ROW][C]21[/C][C]107.3[/C][C]107.3[/C][C]-5.90047807583614e-17[/C][/ROW]
[ROW][C]22[/C][C]107.5[/C][C]107.5[/C][C]1.60096074424447e-17[/C][/ROW]
[ROW][C]23[/C][C]107.6[/C][C]107.6[/C][C]-4.76267967664343e-17[/C][/ROW]
[ROW][C]24[/C][C]107.6[/C][C]107.6[/C][C]4.60302208894893e-17[/C][/ROW]
[ROW][C]25[/C][C]107.7[/C][C]107.7[/C][C]3.58366460334465e-17[/C][/ROW]
[ROW][C]26[/C][C]107.7[/C][C]107.7[/C][C]-9.6475515397015e-17[/C][/ROW]
[ROW][C]27[/C][C]107.7[/C][C]107.7[/C][C]3.54652205341242e-16[/C][/ROW]
[ROW][C]28[/C][C]107.7[/C][C]107.7[/C][C]-7.39577915114317e-17[/C][/ROW]
[ROW][C]29[/C][C]107.6[/C][C]107.6[/C][C]-2.26691303656988e-17[/C][/ROW]
[ROW][C]30[/C][C]107.7[/C][C]107.7[/C][C]-2.57502820522133e-17[/C][/ROW]
[ROW][C]31[/C][C]107.9[/C][C]107.9[/C][C]-5.08362480832184e-17[/C][/ROW]
[ROW][C]32[/C][C]107.9[/C][C]107.9[/C][C]-5.26102697201318e-17[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]107.9[/C][C]1.22580084363961e-18[/C][/ROW]
[ROW][C]34[/C][C]107.8[/C][C]107.8[/C][C]-9.28618845873883e-17[/C][/ROW]
[ROW][C]35[/C][C]107.6[/C][C]107.6[/C][C]-5.93094511638587e-17[/C][/ROW]
[ROW][C]36[/C][C]107.4[/C][C]107.4[/C][C]-6.5179359957401e-17[/C][/ROW]
[ROW][C]37[/C][C]107[/C][C]107[/C][C]-1.28072004818785e-16[/C][/ROW]
[ROW][C]38[/C][C]107[/C][C]107[/C][C]-2.35198561410580e-17[/C][/ROW]
[ROW][C]39[/C][C]107.2[/C][C]107.2[/C][C]2.10175191946292e-16[/C][/ROW]
[ROW][C]40[/C][C]107.5[/C][C]107.5[/C][C]-5.21952802861169e-17[/C][/ROW]
[ROW][C]41[/C][C]107.8[/C][C]107.8[/C][C]-1.31462198121498e-16[/C][/ROW]
[ROW][C]42[/C][C]107.8[/C][C]107.8[/C][C]2.30991340641218e-17[/C][/ROW]
[ROW][C]43[/C][C]107.7[/C][C]107.7[/C][C]1.21462146447795e-16[/C][/ROW]
[ROW][C]44[/C][C]107.6[/C][C]107.6[/C][C]1.26626624880166e-16[/C][/ROW]
[ROW][C]45[/C][C]107.6[/C][C]107.6[/C][C]-4.41815549403141e-17[/C][/ROW]
[ROW][C]46[/C][C]107.5[/C][C]107.5[/C][C]-5.31979615378214e-17[/C][/ROW]
[ROW][C]47[/C][C]107.5[/C][C]107.5[/C][C]1.16500273793586e-17[/C][/ROW]
[ROW][C]48[/C][C]107.6[/C][C]107.6[/C][C]-3.68486637313149e-17[/C][/ROW]
[ROW][C]49[/C][C]107.6[/C][C]107.6[/C][C]-9.6277408588705e-17[/C][/ROW]
[ROW][C]50[/C][C]107.9[/C][C]107.9[/C][C]-1.13996668528071e-16[/C][/ROW]
[ROW][C]51[/C][C]107.6[/C][C]107.6[/C][C]2.51769801214538e-16[/C][/ROW]
[ROW][C]52[/C][C]107.5[/C][C]107.5[/C][C]-4.55688794906218e-18[/C][/ROW]
[ROW][C]53[/C][C]107.5[/C][C]107.5[/C][C]9.58488655302598e-18[/C][/ROW]
[ROW][C]54[/C][C]107.6[/C][C]107.6[/C][C]4.15535966086062e-17[/C][/ROW]
[ROW][C]55[/C][C]107.7[/C][C]107.7[/C][C]-1.01388384599313e-16[/C][/ROW]
[ROW][C]56[/C][C]107.8[/C][C]107.8[/C][C]-1.17365051609393e-16[/C][/ROW]
[ROW][C]57[/C][C]107.9[/C][C]107.9[/C][C]6.54340613785344e-17[/C][/ROW]
[ROW][C]58[/C][C]107.9[/C][C]107.9[/C][C]9.1289155673577e-17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&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
1105.7105.71.49552512497658e-16
2105.8105.83.33937539667287e-16
3105.8105.8-1.08719992884711e-15
4105.8105.81.39426622871516e-16
5105.9105.91.55265102064878e-16
6106.1106.1-5.19524682221481e-17
7106.4106.46.00412829751428e-17
8106.4106.45.16349872797564e-17
9106.3106.33.65264734765019e-17
10106.2106.23.87610830091879e-17
11106.2106.29.52862205509342e-17
12106.3106.35.59978027992261e-17
13106.4106.43.89602548763855e-17
14106.5106.5-9.99454996011432e-17
15106.6106.62.70602730345035e-16
16106.6106.6-8.71666312490517e-18
17106.6106.6-1.07186601307071e-17
18106.8106.81.30500196016333e-17
19107107-2.92787967404063e-17
20107.2107.2-8.28629083039791e-18
21107.3107.3-5.90047807583614e-17
22107.5107.51.60096074424447e-17
23107.6107.6-4.76267967664343e-17
24107.6107.64.60302208894893e-17
25107.7107.73.58366460334465e-17
26107.7107.7-9.6475515397015e-17
27107.7107.73.54652205341242e-16
28107.7107.7-7.39577915114317e-17
29107.6107.6-2.26691303656988e-17
30107.7107.7-2.57502820522133e-17
31107.9107.9-5.08362480832184e-17
32107.9107.9-5.26102697201318e-17
33107.9107.91.22580084363961e-18
34107.8107.8-9.28618845873883e-17
35107.6107.6-5.93094511638587e-17
36107.4107.4-6.5179359957401e-17
37107107-1.28072004818785e-16
38107107-2.35198561410580e-17
39107.2107.22.10175191946292e-16
40107.5107.5-5.21952802861169e-17
41107.8107.8-1.31462198121498e-16
42107.8107.82.30991340641218e-17
43107.7107.71.21462146447795e-16
44107.6107.61.26626624880166e-16
45107.6107.6-4.41815549403141e-17
46107.5107.5-5.31979615378214e-17
47107.5107.51.16500273793586e-17
48107.6107.6-3.68486637313149e-17
49107.6107.6-9.6277408588705e-17
50107.9107.9-1.13996668528071e-16
51107.6107.62.51769801214538e-16
52107.5107.5-4.55688794906218e-18
53107.5107.59.58488655302598e-18
54107.6107.64.15535966086062e-17
55107.7107.7-1.01388384599313e-16
56107.8107.8-1.17365051609393e-16
57107.9107.96.54340613785344e-17
58107.9107.99.1289155673577e-17






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.5910697855094820.8178604289810370.408930214490519
220.9999999969638876.07222536272485e-093.03611268136242e-09
230.001022210089033940.002044420178067870.998977789910966
240.9999975504034974.89919300658841e-062.44959650329421e-06
250.6235077849101550.752984430179690.376492215089845
260.0006504263677426550.001300852735485310.999349573632257
270.8599394637118080.2801210725763840.140060536288192
280.0009543922296260920.001908784459252180.999045607770374
290.9999999999878142.43719023926068e-111.21859511963034e-11
300.824556444000380.3508871119992410.175443555999620
310.005465394394637160.01093078878927430.994534605605363
320.9304293699494850.1391412601010300.0695706300505151
330.9997316964792760.0005366070414476330.000268303520723816
340.9999995283089569.43382087935302e-074.71691043967651e-07
350.9541822988185550.09163540236288970.0458177011814448
360.8695621603688460.2608756792623080.130437839631154
370.9999238612486330.0001522775027330417.61387513665206e-05

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.591069785509482 & 0.817860428981037 & 0.408930214490519 \tabularnewline
22 & 0.999999996963887 & 6.07222536272485e-09 & 3.03611268136242e-09 \tabularnewline
23 & 0.00102221008903394 & 0.00204442017806787 & 0.998977789910966 \tabularnewline
24 & 0.999997550403497 & 4.89919300658841e-06 & 2.44959650329421e-06 \tabularnewline
25 & 0.623507784910155 & 0.75298443017969 & 0.376492215089845 \tabularnewline
26 & 0.000650426367742655 & 0.00130085273548531 & 0.999349573632257 \tabularnewline
27 & 0.859939463711808 & 0.280121072576384 & 0.140060536288192 \tabularnewline
28 & 0.000954392229626092 & 0.00190878445925218 & 0.999045607770374 \tabularnewline
29 & 0.999999999987814 & 2.43719023926068e-11 & 1.21859511963034e-11 \tabularnewline
30 & 0.82455644400038 & 0.350887111999241 & 0.175443555999620 \tabularnewline
31 & 0.00546539439463716 & 0.0109307887892743 & 0.994534605605363 \tabularnewline
32 & 0.930429369949485 & 0.139141260101030 & 0.0695706300505151 \tabularnewline
33 & 0.999731696479276 & 0.000536607041447633 & 0.000268303520723816 \tabularnewline
34 & 0.999999528308956 & 9.43382087935302e-07 & 4.71691043967651e-07 \tabularnewline
35 & 0.954182298818555 & 0.0916354023628897 & 0.0458177011814448 \tabularnewline
36 & 0.869562160368846 & 0.260875679262308 & 0.130437839631154 \tabularnewline
37 & 0.999923861248633 & 0.000152277502733041 & 7.61387513665206e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&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]0.591069785509482[/C][C]0.817860428981037[/C][C]0.408930214490519[/C][/ROW]
[ROW][C]22[/C][C]0.999999996963887[/C][C]6.07222536272485e-09[/C][C]3.03611268136242e-09[/C][/ROW]
[ROW][C]23[/C][C]0.00102221008903394[/C][C]0.00204442017806787[/C][C]0.998977789910966[/C][/ROW]
[ROW][C]24[/C][C]0.999997550403497[/C][C]4.89919300658841e-06[/C][C]2.44959650329421e-06[/C][/ROW]
[ROW][C]25[/C][C]0.623507784910155[/C][C]0.75298443017969[/C][C]0.376492215089845[/C][/ROW]
[ROW][C]26[/C][C]0.000650426367742655[/C][C]0.00130085273548531[/C][C]0.999349573632257[/C][/ROW]
[ROW][C]27[/C][C]0.859939463711808[/C][C]0.280121072576384[/C][C]0.140060536288192[/C][/ROW]
[ROW][C]28[/C][C]0.000954392229626092[/C][C]0.00190878445925218[/C][C]0.999045607770374[/C][/ROW]
[ROW][C]29[/C][C]0.999999999987814[/C][C]2.43719023926068e-11[/C][C]1.21859511963034e-11[/C][/ROW]
[ROW][C]30[/C][C]0.82455644400038[/C][C]0.350887111999241[/C][C]0.175443555999620[/C][/ROW]
[ROW][C]31[/C][C]0.00546539439463716[/C][C]0.0109307887892743[/C][C]0.994534605605363[/C][/ROW]
[ROW][C]32[/C][C]0.930429369949485[/C][C]0.139141260101030[/C][C]0.0695706300505151[/C][/ROW]
[ROW][C]33[/C][C]0.999731696479276[/C][C]0.000536607041447633[/C][C]0.000268303520723816[/C][/ROW]
[ROW][C]34[/C][C]0.999999528308956[/C][C]9.43382087935302e-07[/C][C]4.71691043967651e-07[/C][/ROW]
[ROW][C]35[/C][C]0.954182298818555[/C][C]0.0916354023628897[/C][C]0.0458177011814448[/C][/ROW]
[ROW][C]36[/C][C]0.869562160368846[/C][C]0.260875679262308[/C][C]0.130437839631154[/C][/ROW]
[ROW][C]37[/C][C]0.999923861248633[/C][C]0.000152277502733041[/C][C]7.61387513665206e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&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
210.5910697855094820.8178604289810370.408930214490519
220.9999999969638876.07222536272485e-093.03611268136242e-09
230.001022210089033940.002044420178067870.998977789910966
240.9999975504034974.89919300658841e-062.44959650329421e-06
250.6235077849101550.752984430179690.376492215089845
260.0006504263677426550.001300852735485310.999349573632257
270.8599394637118080.2801210725763840.140060536288192
280.0009543922296260920.001908784459252180.999045607770374
290.9999999999878142.43719023926068e-111.21859511963034e-11
300.824556444000380.3508871119992410.175443555999620
310.005465394394637160.01093078878927430.994534605605363
320.9304293699494850.1391412601010300.0695706300505151
330.9997316964792760.0005366070414476330.000268303520723816
340.9999995283089569.43382087935302e-074.71691043967651e-07
350.9541822988185550.09163540236288970.0458177011814448
360.8695621603688460.2608756792623080.130437839631154
370.9999238612486330.0001522775027330417.61387513665206e-05






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level90.529411764705882NOK
5% type I error level100.588235294117647NOK
10% type I error level110.647058823529412NOK

\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 & 9 & 0.529411764705882 & NOK \tabularnewline
5% type I error level & 10 & 0.588235294117647 & NOK \tabularnewline
10% type I error level & 11 & 0.647058823529412 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58148&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]9[/C][C]0.529411764705882[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]10[/C][C]0.588235294117647[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]11[/C][C]0.647058823529412[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58148&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58148&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 level90.529411764705882NOK
5% type I error level100.588235294117647NOK
10% type I error level110.647058823529412NOK


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')
}