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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 06:24:51 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258723654kn7x2al4znkptuw.htm/, Retrieved Wed, 24 Apr 2024 11:25:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58138, Retrieved Wed, 24 Apr 2024 11:25:19 +0000

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Estimated Impact

100

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] [workshop 7,4] [2009-11-20 13:24:51] [2210215221105fab636491031ce54076] [Current]

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Dataseries X:

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8,3	9,2	8,3	8,6	8,9	8,9
8,3	9,5	8,3	8,3	8,6	8,9
8,4	9,6	8,3	8,3	8,3	8,6
8,5	9,5	8,4	8,3	8,3	8,3
8,4	9,1	8,5	8,4	8,3	8,3
8,6	8,9	8,4	8,5	8,4	8,3
8,5	9	8,6	8,4	8,5	8,4
8,5	10,1	8,5	8,6	8,4	8,5
8,4	10,3	8,5	8,5	8,6	8,4
8,5	10,2	8,4	8,5	8,5	8,6
8,5	9,6	8,5	8,4	8,5	8,5
8,5	9,2	8,5	8,5	8,4	8,5
8,5	9,3	8,5	8,5	8,5	8,4
8,5	9,4	8,5	8,5	8,5	8,5
8,5	9,4	8,5	8,5	8,5	8,5
8,5	9,2	8,5	8,5	8,5	8,5
8,5	9	8,5	8,5	8,5	8,5
8,6	9	8,5	8,5	8,5	8,5
8,4	9	8,6	8,5	8,5	8,5
8,1	9,8	8,4	8,6	8,5	8,5
8,0	10	8,1	8,4	8,6	8,5
8,0	9,8	8,0	8,1	8,4	8,6
8,0	9,3	8,0	8,0	8,1	8,4
8,0	9	8,0	8,0	8,0	8,1
7,9	9	8,0	8,0	8,0	8,0
7,8	9,1	7,9	8,0	8,0	8,0
7,8	9,1	7,8	7,9	8,0	8,0
7,9	9,1	7,8	7,8	7,9	8,0
8,1	9,2	7,9	7,8	7,8	7,9
8,0	8,8	8,1	7,9	7,8	7,8
7,6	8,3	8,0	8,1	7,9	7,8
7,3	8,4	7,6	8,0	8,1	7,9
7,0	8,1	7,3	7,6	8,0	8,1
6,8	7,7	7,0	7,3	7,6	8,0
7,0	7,9	6,8	7,0	7,3	7,6
7,1	7,9	7,0	6,8	7,0	7,3
7,2	8	7,1	7,0	6,8	7,0
7,1	7,9	7,2	7,1	7,0	6,8
6,9	7,6	7,1	7,2	7,1	7,0
6,7	7,1	6,9	7,1	7,2	7,1
6,7	6,8	6,7	6,9	7,1	7,2
6,6	6,5	6,7	6,7	6,9	7,1
6,9	6,9	6,6	6,7	6,7	6,9
7,3	8,2	6,9	6,6	6,7	6,7
7,5	8,7	7,3	6,9	6,6	6,7
7,3	8,3	7,5	7,3	6,9	6,6
7,1	7,9	7,3	7,5	7,3	6,9
6,9	7,5	7,1	7,3	7,5	7,3
7,1	7,8	6,9	7,1	7,3	7,5
7,5	8,3	7,1	6,9	7,1	7,3
7,7	8,4	7,5	7,1	6,9	7,1
7,8	8,2	7,7	7,5	7,1	6,9
7,8	7,7	7,8	7,7	7,5	7,1
7,7	7,2	7,8	7,8	7,7	7,5
7,8	7,3	7,7	7,8	7,8	7,7
7,8	8,1	7,8	7,7	7,8	7,8
7,9	8,5	7,8	7,8	7,7	7,8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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=58138&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=58138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.272223696302566 + 0.161944495338189X[t] + 1.20816388613964Y1[t] -0.4678267601091Y2[t] -0.193917063933410Y3[t] + 0.289842816853047Y4[t] + 0.0948685017759605M1[t] + 0.0220364659106159M2[t] + 0.0138541990473369M3[t] + 0.0880521230767941M4[t] + 0.127829043601995M5[t] + 0.146966512755292M6[t] + 0.0874807673669855M7[t] -0.0184272763256771M8[t] -0.0800409575166678M9[t] -0.104472012932639M10[t] + 0.0192887853678653M11[t] + 0.003684875625332t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.272223696302566 +  0.161944495338189X[t] +  1.20816388613964Y1[t] -0.4678267601091Y2[t] -0.193917063933410Y3[t] +  0.289842816853047Y4[t] +  0.0948685017759605M1[t] +  0.0220364659106159M2[t] +  0.0138541990473369M3[t] +  0.0880521230767941M4[t] +  0.127829043601995M5[t] +  0.146966512755292M6[t] +  0.0874807673669855M7[t] -0.0184272763256771M8[t] -0.0800409575166678M9[t] -0.104472012932639M10[t] +  0.0192887853678653M11[t] +  0.003684875625332t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58138&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.272223696302566 +  0.161944495338189X[t] +  1.20816388613964Y1[t] -0.4678267601091Y2[t] -0.193917063933410Y3[t] +  0.289842816853047Y4[t] +  0.0948685017759605M1[t] +  0.0220364659106159M2[t] +  0.0138541990473369M3[t] +  0.0880521230767941M4[t] +  0.127829043601995M5[t] +  0.146966512755292M6[t] +  0.0874807673669855M7[t] -0.0184272763256771M8[t] -0.0800409575166678M9[t] -0.104472012932639M10[t] +  0.0192887853678653M11[t] +  0.003684875625332t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.272223696302566 + 0.161944495338189X[t] + 1.20816388613964Y1[t] -0.4678267601091Y2[t] -0.193917063933410Y3[t] + 0.289842816853047Y4[t] + 0.0948685017759605M1[t] + 0.0220364659106159M2[t] + 0.0138541990473369M3[t] + 0.0880521230767941M4[t] + 0.127829043601995M5[t] + 0.146966512755292M6[t] + 0.0874807673669855M7[t] -0.0184272763256771M8[t] -0.0800409575166678M9[t] -0.104472012932639M10[t] + 0.0192887853678653M11[t] + 0.003684875625332t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	-0.272223696302566	0.530892	-0.5128	0.611007	0.305504
X	0.161944495338189	0.069133	2.3425	0.024352	0.012176
Y1	1.20816388613964	0.173889	6.9479	0	0
Y2	-0.4678267601091	0.258642	-1.8088	0.078199	0.0391
Y3	-0.193917063933410	0.256736	-0.7553	0.454596	0.227298
Y4	0.289842816853047	0.147705	1.9623	0.05689	0.028445
M1	0.0948685017759605	0.09642	0.9839	0.331223	0.165612
M2	0.0220364659106159	0.096809	0.2276	0.821124	0.410562
M3	0.0138541990473369	0.097155	0.1426	0.887341	0.443671
M4	0.0880521230767941	0.096567	0.9118	0.367464	0.183732
M5	0.127829043601995	0.097706	1.3083	0.198427	0.099214
M6	0.146966512755292	0.102955	1.4275	0.161399	0.080699
M7	0.0874807673669855	0.102078	0.857	0.396682	0.198341
M8	-0.0184272763256771	0.101686	-0.1812	0.857135	0.428568
M9	-0.0800409575166678	0.107434	-0.745	0.460722	0.230361
M10	-0.104472012932639	0.107614	-0.9708	0.33763	0.168815
M11	0.0192887853678653	0.103038	0.1872	0.852474	0.426237
t	0.003684875625332	0.002479	1.4866	0.145159	0.072579

\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) & -0.272223696302566 & 0.530892 & -0.5128 & 0.611007 & 0.305504 \tabularnewline
X & 0.161944495338189 & 0.069133 & 2.3425 & 0.024352 & 0.012176 \tabularnewline
Y1 & 1.20816388613964 & 0.173889 & 6.9479 & 0 & 0 \tabularnewline
Y2 & -0.4678267601091 & 0.258642 & -1.8088 & 0.078199 & 0.0391 \tabularnewline
Y3 & -0.193917063933410 & 0.256736 & -0.7553 & 0.454596 & 0.227298 \tabularnewline
Y4 & 0.289842816853047 & 0.147705 & 1.9623 & 0.05689 & 0.028445 \tabularnewline
M1 & 0.0948685017759605 & 0.09642 & 0.9839 & 0.331223 & 0.165612 \tabularnewline
M2 & 0.0220364659106159 & 0.096809 & 0.2276 & 0.821124 & 0.410562 \tabularnewline
M3 & 0.0138541990473369 & 0.097155 & 0.1426 & 0.887341 & 0.443671 \tabularnewline
M4 & 0.0880521230767941 & 0.096567 & 0.9118 & 0.367464 & 0.183732 \tabularnewline
M5 & 0.127829043601995 & 0.097706 & 1.3083 & 0.198427 & 0.099214 \tabularnewline
M6 & 0.146966512755292 & 0.102955 & 1.4275 & 0.161399 & 0.080699 \tabularnewline
M7 & 0.0874807673669855 & 0.102078 & 0.857 & 0.396682 & 0.198341 \tabularnewline
M8 & -0.0184272763256771 & 0.101686 & -0.1812 & 0.857135 & 0.428568 \tabularnewline
M9 & -0.0800409575166678 & 0.107434 & -0.745 & 0.460722 & 0.230361 \tabularnewline
M10 & -0.104472012932639 & 0.107614 & -0.9708 & 0.33763 & 0.168815 \tabularnewline
M11 & 0.0192887853678653 & 0.103038 & 0.1872 & 0.852474 & 0.426237 \tabularnewline
t & 0.003684875625332 & 0.002479 & 1.4866 & 0.145159 & 0.072579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58138&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]-0.272223696302566[/C][C]0.530892[/C][C]-0.5128[/C][C]0.611007[/C][C]0.305504[/C][/ROW]
[ROW][C]X[/C][C]0.161944495338189[/C][C]0.069133[/C][C]2.3425[/C][C]0.024352[/C][C]0.012176[/C][/ROW]
[ROW][C]Y1[/C][C]1.20816388613964[/C][C]0.173889[/C][C]6.9479[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.4678267601091[/C][C]0.258642[/C][C]-1.8088[/C][C]0.078199[/C][C]0.0391[/C][/ROW]
[ROW][C]Y3[/C][C]-0.193917063933410[/C][C]0.256736[/C][C]-0.7553[/C][C]0.454596[/C][C]0.227298[/C][/ROW]
[ROW][C]Y4[/C][C]0.289842816853047[/C][C]0.147705[/C][C]1.9623[/C][C]0.05689[/C][C]0.028445[/C][/ROW]
[ROW][C]M1[/C][C]0.0948685017759605[/C][C]0.09642[/C][C]0.9839[/C][C]0.331223[/C][C]0.165612[/C][/ROW]
[ROW][C]M2[/C][C]0.0220364659106159[/C][C]0.096809[/C][C]0.2276[/C][C]0.821124[/C][C]0.410562[/C][/ROW]
[ROW][C]M3[/C][C]0.0138541990473369[/C][C]0.097155[/C][C]0.1426[/C][C]0.887341[/C][C]0.443671[/C][/ROW]
[ROW][C]M4[/C][C]0.0880521230767941[/C][C]0.096567[/C][C]0.9118[/C][C]0.367464[/C][C]0.183732[/C][/ROW]
[ROW][C]M5[/C][C]0.127829043601995[/C][C]0.097706[/C][C]1.3083[/C][C]0.198427[/C][C]0.099214[/C][/ROW]
[ROW][C]M6[/C][C]0.146966512755292[/C][C]0.102955[/C][C]1.4275[/C][C]0.161399[/C][C]0.080699[/C][/ROW]
[ROW][C]M7[/C][C]0.0874807673669855[/C][C]0.102078[/C][C]0.857[/C][C]0.396682[/C][C]0.198341[/C][/ROW]
[ROW][C]M8[/C][C]-0.0184272763256771[/C][C]0.101686[/C][C]-0.1812[/C][C]0.857135[/C][C]0.428568[/C][/ROW]
[ROW][C]M9[/C][C]-0.0800409575166678[/C][C]0.107434[/C][C]-0.745[/C][C]0.460722[/C][C]0.230361[/C][/ROW]
[ROW][C]M10[/C][C]-0.104472012932639[/C][C]0.107614[/C][C]-0.9708[/C][C]0.33763[/C][C]0.168815[/C][/ROW]
[ROW][C]M11[/C][C]0.0192887853678653[/C][C]0.103038[/C][C]0.1872[/C][C]0.852474[/C][C]0.426237[/C][/ROW]
[ROW][C]t[/C][C]0.003684875625332[/C][C]0.002479[/C][C]1.4866[/C][C]0.145159[/C][C]0.072579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58138&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	-0.272223696302566	0.530892	-0.5128	0.611007	0.305504
X	0.161944495338189	0.069133	2.3425	0.024352	0.012176
Y1	1.20816388613964	0.173889	6.9479	0	0
Y2	-0.4678267601091	0.258642	-1.8088	0.078199	0.0391
Y3	-0.193917063933410	0.256736	-0.7553	0.454596	0.227298
Y4	0.289842816853047	0.147705	1.9623	0.05689	0.028445
M1	0.0948685017759605	0.09642	0.9839	0.331223	0.165612
M2	0.0220364659106159	0.096809	0.2276	0.821124	0.410562
M3	0.0138541990473369	0.097155	0.1426	0.887341	0.443671
M4	0.0880521230767941	0.096567	0.9118	0.367464	0.183732
M5	0.127829043601995	0.097706	1.3083	0.198427	0.099214
M6	0.146966512755292	0.102955	1.4275	0.161399	0.080699
M7	0.0874807673669855	0.102078	0.857	0.396682	0.198341
M8	-0.0184272763256771	0.101686	-0.1812	0.857135	0.428568
M9	-0.0800409575166678	0.107434	-0.745	0.460722	0.230361
M10	-0.104472012932639	0.107614	-0.9708	0.33763	0.168815
M11	0.0192887853678653	0.103038	0.1872	0.852474	0.426237
t	0.003684875625332	0.002479	1.4866	0.145159	0.072579

Multiple Linear Regression - Regression Statistics
Multiple R	0.981039838756772
R-squared	0.962439165227914
Adjusted R-squared	0.946066493660594
F-TEST (value)	58.7832695031255
F-TEST (DF numerator)	17
F-TEST (DF denominator)	39
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.141875843766754
Sum Squared Residuals	0.785021446736605

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.981039838756772 \tabularnewline
R-squared & 0.962439165227914 \tabularnewline
Adjusted R-squared & 0.946066493660594 \tabularnewline
F-TEST (value) & 58.7832695031255 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.141875843766754 \tabularnewline
Sum Squared Residuals & 0.785021446736605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58138&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.981039838756772[/C][/ROW]
[ROW][C]R-squared[/C][C]0.962439165227914[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.946066493660594[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]58.7832695031255[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.141875843766754[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.785021446736605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58138&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.981039838756772
R-squared	0.962439165227914
Adjusted R-squared	0.946066493660594
F-TEST (value)	58.7832695031255
F-TEST (DF numerator)	17
F-TEST (DF denominator)	39
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.141875843766754
Sum Squared Residuals	0.785021446736605

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.3	8.17440835721559	0.125591642784410
2	8.3	8.3523676927898	-0.052367692789801
3	8.4	8.33528702520978	0.06471297479022
4	8.5	8.4308389188888	0.0691610811112
5	8.4	8.48355662950711	-0.0835566295071102
6	8.6	8.28699930419989	0.313000695800113
7	8.5	8.54540091250153	-0.0454009125015326
8	8.5	8.45531093674907	0.0446890632509271
9	8.4	8.40878601178998	-0.00878601178997573
10	8.5	8.3283892636155	0.171610736384496
11	8.5	8.497283023278	0.00271697672200471
12	8.5	8.38951034578262	0.110489654217383
13	8.5	8.45588218463908	0.0441178153609167
14	8.5	8.4319137556182	0.0680862443818058
15	8.5	8.42741636438025	0.072583635619753
16	8.5	8.4729102649674	0.0270897350326019
17	8.5	8.4839831620503	0.0160168379497067
18	8.6	8.50680550682892	0.0931944931710776
19	8.4	8.57182102567991	-0.171821025679911
20	8.1	8.3107380006443	-0.210738000644296
21	8	7.99692257393286	0.00307742606713911
22	8	8.03108682896534	-0.0310868289653364
23	8	8.1245494870424	-0.124549487042402
24	8	7.99280109003584	0.00719890996416227
25	7.9	8.06237018575183	-0.162370185751825
26	7.8	7.88860108643167	-0.0886010864316686
27	7.8	7.81006998259067	-0.0100699825906667
28	7.9	7.9541271646497	-0.0541271646497065
29	8.1	8.12500722365606	-0.0250072236560602
30	8	8.24891758983112	-0.248917589831125
31	7.6	7.87837102536993	-0.278371025369932
32	7.3	7.3460602972901	-0.0460602972900963
33	7	7.14158995108868	-0.141589951088679
34	6.8	6.88254737924166	-0.0825473792416607
35	7	6.88333519547874	0.116664804521259
36	7.1	7.17415168911006	-0.0741516891100646
37	7.2	7.26798112036809	-0.0679811203680868
38	7.1	7.15992124704002	-0.0599212470400195
39	6.9	6.97781829955301	-0.0778182995530084
40	6.7	6.78947132561365	-0.0894713256136493
41	6.7	6.68465833603526	0.0153416639647373
42	6.6	6.76226181533563	-0.162261815335632
43	6.9	6.63123720451004	0.268762795489959
44	7.3	7.09080515886455	0.209194841135449
45	7.5	7.47615783378445	0.0238421662155463
46	7.3	7.3579765281775	-0.0579765281774995
47	7.1	7.09483229420086	0.00516770579913756
48	6.9	6.94353687507148	-0.0435368750714809
49	7.1	7.03935815202541	0.0606418479745848
50	7.5	7.36719621812032	0.132803781879683
51	7.7	7.7494083282663	-0.0494083282662976
52	7.8	7.75265232588045	0.0473476741195537
53	7.8	7.72279464875127	0.0772053512487265
54	7.7	7.69501578380443	0.00498421619556606
55	7.8	7.57316983193858	0.226830168061416
56	7.8	7.79708560645198	0.00291439354801666
57	7.9	7.77654362940403	0.123456370595969

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.3 & 8.17440835721559 & 0.125591642784410 \tabularnewline
2 & 8.3 & 8.3523676927898 & -0.052367692789801 \tabularnewline
3 & 8.4 & 8.33528702520978 & 0.06471297479022 \tabularnewline
4 & 8.5 & 8.4308389188888 & 0.0691610811112 \tabularnewline
5 & 8.4 & 8.48355662950711 & -0.0835566295071102 \tabularnewline
6 & 8.6 & 8.28699930419989 & 0.313000695800113 \tabularnewline
7 & 8.5 & 8.54540091250153 & -0.0454009125015326 \tabularnewline
8 & 8.5 & 8.45531093674907 & 0.0446890632509271 \tabularnewline
9 & 8.4 & 8.40878601178998 & -0.00878601178997573 \tabularnewline
10 & 8.5 & 8.3283892636155 & 0.171610736384496 \tabularnewline
11 & 8.5 & 8.497283023278 & 0.00271697672200471 \tabularnewline
12 & 8.5 & 8.38951034578262 & 0.110489654217383 \tabularnewline
13 & 8.5 & 8.45588218463908 & 0.0441178153609167 \tabularnewline
14 & 8.5 & 8.4319137556182 & 0.0680862443818058 \tabularnewline
15 & 8.5 & 8.42741636438025 & 0.072583635619753 \tabularnewline
16 & 8.5 & 8.4729102649674 & 0.0270897350326019 \tabularnewline
17 & 8.5 & 8.4839831620503 & 0.0160168379497067 \tabularnewline
18 & 8.6 & 8.50680550682892 & 0.0931944931710776 \tabularnewline
19 & 8.4 & 8.57182102567991 & -0.171821025679911 \tabularnewline
20 & 8.1 & 8.3107380006443 & -0.210738000644296 \tabularnewline
21 & 8 & 7.99692257393286 & 0.00307742606713911 \tabularnewline
22 & 8 & 8.03108682896534 & -0.0310868289653364 \tabularnewline
23 & 8 & 8.1245494870424 & -0.124549487042402 \tabularnewline
24 & 8 & 7.99280109003584 & 0.00719890996416227 \tabularnewline
25 & 7.9 & 8.06237018575183 & -0.162370185751825 \tabularnewline
26 & 7.8 & 7.88860108643167 & -0.0886010864316686 \tabularnewline
27 & 7.8 & 7.81006998259067 & -0.0100699825906667 \tabularnewline
28 & 7.9 & 7.9541271646497 & -0.0541271646497065 \tabularnewline
29 & 8.1 & 8.12500722365606 & -0.0250072236560602 \tabularnewline
30 & 8 & 8.24891758983112 & -0.248917589831125 \tabularnewline
31 & 7.6 & 7.87837102536993 & -0.278371025369932 \tabularnewline
32 & 7.3 & 7.3460602972901 & -0.0460602972900963 \tabularnewline
33 & 7 & 7.14158995108868 & -0.141589951088679 \tabularnewline
34 & 6.8 & 6.88254737924166 & -0.0825473792416607 \tabularnewline
35 & 7 & 6.88333519547874 & 0.116664804521259 \tabularnewline
36 & 7.1 & 7.17415168911006 & -0.0741516891100646 \tabularnewline
37 & 7.2 & 7.26798112036809 & -0.0679811203680868 \tabularnewline
38 & 7.1 & 7.15992124704002 & -0.0599212470400195 \tabularnewline
39 & 6.9 & 6.97781829955301 & -0.0778182995530084 \tabularnewline
40 & 6.7 & 6.78947132561365 & -0.0894713256136493 \tabularnewline
41 & 6.7 & 6.68465833603526 & 0.0153416639647373 \tabularnewline
42 & 6.6 & 6.76226181533563 & -0.162261815335632 \tabularnewline
43 & 6.9 & 6.63123720451004 & 0.268762795489959 \tabularnewline
44 & 7.3 & 7.09080515886455 & 0.209194841135449 \tabularnewline
45 & 7.5 & 7.47615783378445 & 0.0238421662155463 \tabularnewline
46 & 7.3 & 7.3579765281775 & -0.0579765281774995 \tabularnewline
47 & 7.1 & 7.09483229420086 & 0.00516770579913756 \tabularnewline
48 & 6.9 & 6.94353687507148 & -0.0435368750714809 \tabularnewline
49 & 7.1 & 7.03935815202541 & 0.0606418479745848 \tabularnewline
50 & 7.5 & 7.36719621812032 & 0.132803781879683 \tabularnewline
51 & 7.7 & 7.7494083282663 & -0.0494083282662976 \tabularnewline
52 & 7.8 & 7.75265232588045 & 0.0473476741195537 \tabularnewline
53 & 7.8 & 7.72279464875127 & 0.0772053512487265 \tabularnewline
54 & 7.7 & 7.69501578380443 & 0.00498421619556606 \tabularnewline
55 & 7.8 & 7.57316983193858 & 0.226830168061416 \tabularnewline
56 & 7.8 & 7.79708560645198 & 0.00291439354801666 \tabularnewline
57 & 7.9 & 7.77654362940403 & 0.123456370595969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58138&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]8.3[/C][C]8.17440835721559[/C][C]0.125591642784410[/C][/ROW]
[ROW][C]2[/C][C]8.3[/C][C]8.3523676927898[/C][C]-0.052367692789801[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.33528702520978[/C][C]0.06471297479022[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.4308389188888[/C][C]0.0691610811112[/C][/ROW]
[ROW][C]5[/C][C]8.4[/C][C]8.48355662950711[/C][C]-0.0835566295071102[/C][/ROW]
[ROW][C]6[/C][C]8.6[/C][C]8.28699930419989[/C][C]0.313000695800113[/C][/ROW]
[ROW][C]7[/C][C]8.5[/C][C]8.54540091250153[/C][C]-0.0454009125015326[/C][/ROW]
[ROW][C]8[/C][C]8.5[/C][C]8.45531093674907[/C][C]0.0446890632509271[/C][/ROW]
[ROW][C]9[/C][C]8.4[/C][C]8.40878601178998[/C][C]-0.00878601178997573[/C][/ROW]
[ROW][C]10[/C][C]8.5[/C][C]8.3283892636155[/C][C]0.171610736384496[/C][/ROW]
[ROW][C]11[/C][C]8.5[/C][C]8.497283023278[/C][C]0.00271697672200471[/C][/ROW]
[ROW][C]12[/C][C]8.5[/C][C]8.38951034578262[/C][C]0.110489654217383[/C][/ROW]
[ROW][C]13[/C][C]8.5[/C][C]8.45588218463908[/C][C]0.0441178153609167[/C][/ROW]
[ROW][C]14[/C][C]8.5[/C][C]8.4319137556182[/C][C]0.0680862443818058[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]8.42741636438025[/C][C]0.072583635619753[/C][/ROW]
[ROW][C]16[/C][C]8.5[/C][C]8.4729102649674[/C][C]0.0270897350326019[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.4839831620503[/C][C]0.0160168379497067[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.50680550682892[/C][C]0.0931944931710776[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.57182102567991[/C][C]-0.171821025679911[/C][/ROW]
[ROW][C]20[/C][C]8.1[/C][C]8.3107380006443[/C][C]-0.210738000644296[/C][/ROW]
[ROW][C]21[/C][C]8[/C][C]7.99692257393286[/C][C]0.00307742606713911[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]8.03108682896534[/C][C]-0.0310868289653364[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.1245494870424[/C][C]-0.124549487042402[/C][/ROW]
[ROW][C]24[/C][C]8[/C][C]7.99280109003584[/C][C]0.00719890996416227[/C][/ROW]
[ROW][C]25[/C][C]7.9[/C][C]8.06237018575183[/C][C]-0.162370185751825[/C][/ROW]
[ROW][C]26[/C][C]7.8[/C][C]7.88860108643167[/C][C]-0.0886010864316686[/C][/ROW]
[ROW][C]27[/C][C]7.8[/C][C]7.81006998259067[/C][C]-0.0100699825906667[/C][/ROW]
[ROW][C]28[/C][C]7.9[/C][C]7.9541271646497[/C][C]-0.0541271646497065[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.12500722365606[/C][C]-0.0250072236560602[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.24891758983112[/C][C]-0.248917589831125[/C][/ROW]
[ROW][C]31[/C][C]7.6[/C][C]7.87837102536993[/C][C]-0.278371025369932[/C][/ROW]
[ROW][C]32[/C][C]7.3[/C][C]7.3460602972901[/C][C]-0.0460602972900963[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]7.14158995108868[/C][C]-0.141589951088679[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]6.88254737924166[/C][C]-0.0825473792416607[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]6.88333519547874[/C][C]0.116664804521259[/C][/ROW]
[ROW][C]36[/C][C]7.1[/C][C]7.17415168911006[/C][C]-0.0741516891100646[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.26798112036809[/C][C]-0.0679811203680868[/C][/ROW]
[ROW][C]38[/C][C]7.1[/C][C]7.15992124704002[/C][C]-0.0599212470400195[/C][/ROW]
[ROW][C]39[/C][C]6.9[/C][C]6.97781829955301[/C][C]-0.0778182995530084[/C][/ROW]
[ROW][C]40[/C][C]6.7[/C][C]6.78947132561365[/C][C]-0.0894713256136493[/C][/ROW]
[ROW][C]41[/C][C]6.7[/C][C]6.68465833603526[/C][C]0.0153416639647373[/C][/ROW]
[ROW][C]42[/C][C]6.6[/C][C]6.76226181533563[/C][C]-0.162261815335632[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]6.63123720451004[/C][C]0.268762795489959[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]7.09080515886455[/C][C]0.209194841135449[/C][/ROW]
[ROW][C]45[/C][C]7.5[/C][C]7.47615783378445[/C][C]0.0238421662155463[/C][/ROW]
[ROW][C]46[/C][C]7.3[/C][C]7.3579765281775[/C][C]-0.0579765281774995[/C][/ROW]
[ROW][C]47[/C][C]7.1[/C][C]7.09483229420086[/C][C]0.00516770579913756[/C][/ROW]
[ROW][C]48[/C][C]6.9[/C][C]6.94353687507148[/C][C]-0.0435368750714809[/C][/ROW]
[ROW][C]49[/C][C]7.1[/C][C]7.03935815202541[/C][C]0.0606418479745848[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]7.36719621812032[/C][C]0.132803781879683[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.7494083282663[/C][C]-0.0494083282662976[/C][/ROW]
[ROW][C]52[/C][C]7.8[/C][C]7.75265232588045[/C][C]0.0473476741195537[/C][/ROW]
[ROW][C]53[/C][C]7.8[/C][C]7.72279464875127[/C][C]0.0772053512487265[/C][/ROW]
[ROW][C]54[/C][C]7.7[/C][C]7.69501578380443[/C][C]0.00498421619556606[/C][/ROW]
[ROW][C]55[/C][C]7.8[/C][C]7.57316983193858[/C][C]0.226830168061416[/C][/ROW]
[ROW][C]56[/C][C]7.8[/C][C]7.79708560645198[/C][C]0.00291439354801666[/C][/ROW]
[ROW][C]57[/C][C]7.9[/C][C]7.77654362940403[/C][C]0.123456370595969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58138&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.3	8.17440835721559	0.125591642784410
2	8.3	8.3523676927898	-0.052367692789801
3	8.4	8.33528702520978	0.06471297479022
4	8.5	8.4308389188888	0.0691610811112
5	8.4	8.48355662950711	-0.0835566295071102
6	8.6	8.28699930419989	0.313000695800113
7	8.5	8.54540091250153	-0.0454009125015326
8	8.5	8.45531093674907	0.0446890632509271
9	8.4	8.40878601178998	-0.00878601178997573
10	8.5	8.3283892636155	0.171610736384496
11	8.5	8.497283023278	0.00271697672200471
12	8.5	8.38951034578262	0.110489654217383
13	8.5	8.45588218463908	0.0441178153609167
14	8.5	8.4319137556182	0.0680862443818058
15	8.5	8.42741636438025	0.072583635619753
16	8.5	8.4729102649674	0.0270897350326019
17	8.5	8.4839831620503	0.0160168379497067
18	8.6	8.50680550682892	0.0931944931710776
19	8.4	8.57182102567991	-0.171821025679911
20	8.1	8.3107380006443	-0.210738000644296
21	8	7.99692257393286	0.00307742606713911
22	8	8.03108682896534	-0.0310868289653364
23	8	8.1245494870424	-0.124549487042402
24	8	7.99280109003584	0.00719890996416227
25	7.9	8.06237018575183	-0.162370185751825
26	7.8	7.88860108643167	-0.0886010864316686
27	7.8	7.81006998259067	-0.0100699825906667
28	7.9	7.9541271646497	-0.0541271646497065
29	8.1	8.12500722365606	-0.0250072236560602
30	8	8.24891758983112	-0.248917589831125
31	7.6	7.87837102536993	-0.278371025369932
32	7.3	7.3460602972901	-0.0460602972900963
33	7	7.14158995108868	-0.141589951088679
34	6.8	6.88254737924166	-0.0825473792416607
35	7	6.88333519547874	0.116664804521259
36	7.1	7.17415168911006	-0.0741516891100646
37	7.2	7.26798112036809	-0.0679811203680868
38	7.1	7.15992124704002	-0.0599212470400195
39	6.9	6.97781829955301	-0.0778182995530084
40	6.7	6.78947132561365	-0.0894713256136493
41	6.7	6.68465833603526	0.0153416639647373
42	6.6	6.76226181533563	-0.162261815335632
43	6.9	6.63123720451004	0.268762795489959
44	7.3	7.09080515886455	0.209194841135449
45	7.5	7.47615783378445	0.0238421662155463
46	7.3	7.3579765281775	-0.0579765281774995
47	7.1	7.09483229420086	0.00516770579913756
48	6.9	6.94353687507148	-0.0435368750714809
49	7.1	7.03935815202541	0.0606418479745848
50	7.5	7.36719621812032	0.132803781879683
51	7.7	7.7494083282663	-0.0494083282662976
52	7.8	7.75265232588045	0.0473476741195537
53	7.8	7.72279464875127	0.0772053512487265
54	7.7	7.69501578380443	0.00498421619556606
55	7.8	7.57316983193858	0.226830168061416
56	7.8	7.79708560645198	0.00291439354801666
57	7.9	7.77654362940403	0.123456370595969

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.643757673305873	0.712484653388254	0.356242326694127
22	0.518421467965326	0.963157064069347	0.481578532034674
23	0.362979864301384	0.725959728602769	0.637020135698616
24	0.355569402950905	0.71113880590181	0.644430597049095
25	0.277627438212345	0.55525487642469	0.722372561787655
26	0.205758330188626	0.411516660377252	0.794241669811374
27	0.196173657676711	0.392347315353422	0.803826342323289
28	0.161081526607222	0.322163053214444	0.838918473392778
29	0.117738835647324	0.235477671294647	0.882261164352676
30	0.158409619724040	0.316819239448079	0.84159038027596
31	0.521636104133476	0.956727791733049	0.478363895866524
32	0.841324047940721	0.317351904118558	0.158675952059279
33	0.977407684972091	0.0451846300558172	0.0225923150279086
34	0.988250556280508	0.0234988874389842	0.0117494437194921
35	0.978504159912164	0.0429916801756727	0.0214958400878364
36	0.936721026339766	0.126557947320467	0.0632789736602336

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.643757673305873 & 0.712484653388254 & 0.356242326694127 \tabularnewline
22 & 0.518421467965326 & 0.963157064069347 & 0.481578532034674 \tabularnewline
23 & 0.362979864301384 & 0.725959728602769 & 0.637020135698616 \tabularnewline
24 & 0.355569402950905 & 0.71113880590181 & 0.644430597049095 \tabularnewline
25 & 0.277627438212345 & 0.55525487642469 & 0.722372561787655 \tabularnewline
26 & 0.205758330188626 & 0.411516660377252 & 0.794241669811374 \tabularnewline
27 & 0.196173657676711 & 0.392347315353422 & 0.803826342323289 \tabularnewline
28 & 0.161081526607222 & 0.322163053214444 & 0.838918473392778 \tabularnewline
29 & 0.117738835647324 & 0.235477671294647 & 0.882261164352676 \tabularnewline
30 & 0.158409619724040 & 0.316819239448079 & 0.84159038027596 \tabularnewline
31 & 0.521636104133476 & 0.956727791733049 & 0.478363895866524 \tabularnewline
32 & 0.841324047940721 & 0.317351904118558 & 0.158675952059279 \tabularnewline
33 & 0.977407684972091 & 0.0451846300558172 & 0.0225923150279086 \tabularnewline
34 & 0.988250556280508 & 0.0234988874389842 & 0.0117494437194921 \tabularnewline
35 & 0.978504159912164 & 0.0429916801756727 & 0.0214958400878364 \tabularnewline
36 & 0.936721026339766 & 0.126557947320467 & 0.0632789736602336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58138&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]0.643757673305873[/C][C]0.712484653388254[/C][C]0.356242326694127[/C][/ROW]
[ROW][C]22[/C][C]0.518421467965326[/C][C]0.963157064069347[/C][C]0.481578532034674[/C][/ROW]
[ROW][C]23[/C][C]0.362979864301384[/C][C]0.725959728602769[/C][C]0.637020135698616[/C][/ROW]
[ROW][C]24[/C][C]0.355569402950905[/C][C]0.71113880590181[/C][C]0.644430597049095[/C][/ROW]
[ROW][C]25[/C][C]0.277627438212345[/C][C]0.55525487642469[/C][C]0.722372561787655[/C][/ROW]
[ROW][C]26[/C][C]0.205758330188626[/C][C]0.411516660377252[/C][C]0.794241669811374[/C][/ROW]
[ROW][C]27[/C][C]0.196173657676711[/C][C]0.392347315353422[/C][C]0.803826342323289[/C][/ROW]
[ROW][C]28[/C][C]0.161081526607222[/C][C]0.322163053214444[/C][C]0.838918473392778[/C][/ROW]
[ROW][C]29[/C][C]0.117738835647324[/C][C]0.235477671294647[/C][C]0.882261164352676[/C][/ROW]
[ROW][C]30[/C][C]0.158409619724040[/C][C]0.316819239448079[/C][C]0.84159038027596[/C][/ROW]
[ROW][C]31[/C][C]0.521636104133476[/C][C]0.956727791733049[/C][C]0.478363895866524[/C][/ROW]
[ROW][C]32[/C][C]0.841324047940721[/C][C]0.317351904118558[/C][C]0.158675952059279[/C][/ROW]
[ROW][C]33[/C][C]0.977407684972091[/C][C]0.0451846300558172[/C][C]0.0225923150279086[/C][/ROW]
[ROW][C]34[/C][C]0.988250556280508[/C][C]0.0234988874389842[/C][C]0.0117494437194921[/C][/ROW]
[ROW][C]35[/C][C]0.978504159912164[/C][C]0.0429916801756727[/C][C]0.0214958400878364[/C][/ROW]
[ROW][C]36[/C][C]0.936721026339766[/C][C]0.126557947320467[/C][C]0.0632789736602336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58138&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.643757673305873	0.712484653388254	0.356242326694127
22	0.518421467965326	0.963157064069347	0.481578532034674
23	0.362979864301384	0.725959728602769	0.637020135698616
24	0.355569402950905	0.71113880590181	0.644430597049095
25	0.277627438212345	0.55525487642469	0.722372561787655
26	0.205758330188626	0.411516660377252	0.794241669811374
27	0.196173657676711	0.392347315353422	0.803826342323289
28	0.161081526607222	0.322163053214444	0.838918473392778
29	0.117738835647324	0.235477671294647	0.882261164352676
30	0.158409619724040	0.316819239448079	0.84159038027596
31	0.521636104133476	0.956727791733049	0.478363895866524
32	0.841324047940721	0.317351904118558	0.158675952059279
33	0.977407684972091	0.0451846300558172	0.0225923150279086
34	0.988250556280508	0.0234988874389842	0.0117494437194921
35	0.978504159912164	0.0429916801756727	0.0214958400878364
36	0.936721026339766	0.126557947320467	0.0632789736602336

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	3	0.1875	NOK
10% type I error level	3	0.1875	NOK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 3 & 0.1875 & NOK \tabularnewline
10% type I error level & 3 & 0.1875 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58138&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]3[/C][C]0.1875[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.1875[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58138&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58138&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	3	0.1875	NOK
10% type I error level	3	0.1875	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code