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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 computationTue, 28 Dec 2010 21:11:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/28/t1293570577x4pf60bogbr27d9.htm/, Retrieved Sat, 10 May 2025 00:05:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116554, Retrieved Sat, 10 May 2025 00:05:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact274

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [] [2009-11-19 08:06:13] [639dd97b6eeebe46a3c92d62cb04fb95]
-   PD      [Multiple Regression] [] [2009-11-19 08:07:59] [639dd97b6eeebe46a3c92d62cb04fb95]
-   P         [Multiple Regression] [] [2009-11-19 08:09:26] [639dd97b6eeebe46a3c92d62cb04fb95]
-    D          [Multiple Regression] [] [2009-11-19 08:16:57] [639dd97b6eeebe46a3c92d62cb04fb95]
- R  D              [Multiple Regression] [model 4] [2010-12-28 21:11:46] [e7b77eb06cdf8868fc9cf2043e42b3da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3,7	0	3,7	3,93	4,15	4,24
3,65	0	3,7	3,7	3,93	4,15
3,55	0	3,65	3,7	3,7	3,93
3,43	0	3,55	3,65	3,7	3,7
3,47	0	3,43	3,55	3,65	3,7
3,58	0	3,47	3,43	3,55	3,65
3,67	0	3,58	3,47	3,43	3,55
3,72	0	3,67	3,58	3,47	3,43
3,8	0	3,72	3,67	3,58	3,47
3,76	0	3,8	3,72	3,67	3,58
3,63	0	3,76	3,8	3,72	3,67
3,48	0	3,63	3,76	3,8	3,72
3,41	0	3,48	3,63	3,76	3,8
3,43	0	3,41	3,48	3,63	3,76
3,5	0	3,43	3,41	3,48	3,63
3,62	0	3,5	3,43	3,41	3,48
3,58	0	3,62	3,5	3,43	3,41
3,52	0	3,58	3,62	3,5	3,43
3,45	0	3,52	3,58	3,62	3,5
3,36	0	3,45	3,52	3,58	3,62
3,27	0	3,36	3,45	3,52	3,58
3,21	0	3,27	3,36	3,45	3,52
3,19	0	3,21	3,27	3,36	3,45
3,16	0	3,19	3,21	3,27	3,36
3,12	0	3,16	3,19	3,21	3,27
3,06	0	3,12	3,16	3,19	3,21
3,01	0	3,06	3,12	3,16	3,19
2,98	0	3,01	3,06	3,12	3,16
2,97	0	2,98	3,01	3,06	3,12
3,02	0	2,97	2,98	3,01	3,06
3,07	0	3,02	2,97	2,98	3,01
3,18	0	3,07	3,02	2,97	2,98
3,29	1	3,18	3,07	3,02	2,97
3,43	1	3,29	3,18	3,07	3,02
3,61	1	3,43	3,29	3,18	3,07
3,74	1	3,61	3,43	3,29	3,18
3,87	1	3,74	3,61	3,43	3,29
3,88	1	3,87	3,74	3,61	3,43
4,09	1	3,88	3,87	3,74	3,61
4,19	1	4,09	3,88	3,87	3,74
4,2	1	4,19	4,09	3,88	3,87
4,29	1	4,2	4,19	4,09	3,88
4,37	1	4,29	4,2	4,19	4,09
4,47	1	4,37	4,29	4,2	4,19
4,61	1	4,47	4,37	4,29	4,2
4,65	1	4,61	4,47	4,37	4,29
4,69	1	4,65	4,61	4,47	4,37
4,82	1	4,69	4,65	4,61	4,47
4,86	1	4,82	4,69	4,65	4,61
4,87	1	4,86	4,82	4,69	4,65
5,01	1	4,87	4,86	4,82	4,69
5,03	1	5,01	4,87	4,86	4,82
5,13	1	5,03	5,01	4,87	4,86
5,18	1	5,13	5,03	5,01	4,87
5,21	1	5,18	5,13	5,03	5,01
5,26	1	5,21	5,18	5,13	5,03
5,25	1	5,26	5,21	5,18	5,13
5,2	1	5,25	5,26	5,21	5,18
5,16	1	5,2	5,25	5,26	5,21
5,19	1	5,16	5,2	5,25	5,26
5,39	1	5,19	5,16	5,2	5,25
5,58	1	5,39	5,19	5,16	5,2
5,76	1	5,58	5,39	5,19	5,16
5,89	1	5,76	5,58	5,39	5,19
5,98	1	5,89	5,76	5,58	5,39
6,02	1	5,98	5,89	5,76	5,58
5,62	1	6,02	5,98	5,89	5,76
4,87	1	5,62	6,02	5,98	5,89

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&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 time9 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 0.161444463225237 + 0.0791592781596746X[t] + 2.06064556081534Y1[t] -1.51248435858741Y2[t] + 0.399499156624229Y3[t] + 0.00955021927819122Y4[t] + 0.0378650408289318M1[t] -0.0484576135319395M2[t] + 0.0596382358271586M3[t] -0.0446390881700724M4[t] + 0.0169784404865373M5[t] + 0.0241710147035326M6[t] -0.0756529773410106M7[t] -0.0303723197500138M8[t] -0.00954782897581095M9[t] -0.0461532281989728M10[t] -0.000389226894001394M11[t] -0.000475364960323572t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.161444463225237 +  0.0791592781596746X[t] +  2.06064556081534Y1[t] -1.51248435858741Y2[t] +  0.399499156624229Y3[t] +  0.00955021927819122Y4[t] +  0.0378650408289318M1[t] -0.0484576135319395M2[t] +  0.0596382358271586M3[t] -0.0446390881700724M4[t] +  0.0169784404865373M5[t] +  0.0241710147035326M6[t] -0.0756529773410106M7[t] -0.0303723197500138M8[t] -0.00954782897581095M9[t] -0.0461532281989728M10[t] -0.000389226894001394M11[t] -0.000475364960323572t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.161444463225237 +  0.0791592781596746X[t] +  2.06064556081534Y1[t] -1.51248435858741Y2[t] +  0.399499156624229Y3[t] +  0.00955021927819122Y4[t] +  0.0378650408289318M1[t] -0.0484576135319395M2[t] +  0.0596382358271586M3[t] -0.0446390881700724M4[t] +  0.0169784404865373M5[t] +  0.0241710147035326M6[t] -0.0756529773410106M7[t] -0.0303723197500138M8[t] -0.00954782897581095M9[t] -0.0461532281989728M10[t] -0.000389226894001394M11[t] -0.000475364960323572t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&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
Y[t] = + 0.161444463225237 + 0.0791592781596746X[t] + 2.06064556081534Y1[t] -1.51248435858741Y2[t] + 0.399499156624229Y3[t] + 0.00955021927819122Y4[t] + 0.0378650408289318M1[t] -0.0484576135319395M2[t] + 0.0596382358271586M3[t] -0.0446390881700724M4[t] + 0.0169784404865373M5[t] + 0.0241710147035326M6[t] -0.0756529773410106M7[t] -0.0303723197500138M8[t] -0.00954782897581095M9[t] -0.0461532281989728M10[t] -0.000389226894001394M11[t] -0.000475364960323572t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.1614444632252370.0832041.94040.0579860.028993
X0.07915927815967460.0568821.39160.1701940.085097
Y12.060645560815340.1635512.599500
Y2-1.512484358587410.33353-4.53483.6e-051.8e-05
Y30.3994991566242290.3711071.07650.2868670.143434
Y40.009550219278191220.199150.0480.9619430.480972
M10.03786504082893180.0583310.64910.5192170.259609
M2-0.04845761353193950.059371-0.81620.4182660.209133
M30.05963823582715860.0605240.98540.329190.164595
M4-0.04463908817007240.059125-0.7550.4537950.226897
M50.01697844048653730.060620.28010.7805730.390287
M60.02417101470353260.0587950.41110.682750.341375
M7-0.07565297734101060.058939-1.28360.2052090.102605
M8-0.03037231975001380.059955-0.50660.6146730.307337
M9-0.009547828975810950.060623-0.15750.8754890.437744
M10-0.04615322819897280.060888-0.7580.452010.226005
M11-0.0003892268940013940.060942-0.00640.9949290.497465
t-0.0004753649603235720.001429-0.33260.7408430.370421

\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) & 0.161444463225237 & 0.083204 & 1.9404 & 0.057986 & 0.028993 \tabularnewline
X & 0.0791592781596746 & 0.056882 & 1.3916 & 0.170194 & 0.085097 \tabularnewline
Y1 & 2.06064556081534 & 0.16355 & 12.5995 & 0 & 0 \tabularnewline
Y2 & -1.51248435858741 & 0.33353 & -4.5348 & 3.6e-05 & 1.8e-05 \tabularnewline
Y3 & 0.399499156624229 & 0.371107 & 1.0765 & 0.286867 & 0.143434 \tabularnewline
Y4 & 0.00955021927819122 & 0.19915 & 0.048 & 0.961943 & 0.480972 \tabularnewline
M1 & 0.0378650408289318 & 0.058331 & 0.6491 & 0.519217 & 0.259609 \tabularnewline
M2 & -0.0484576135319395 & 0.059371 & -0.8162 & 0.418266 & 0.209133 \tabularnewline
M3 & 0.0596382358271586 & 0.060524 & 0.9854 & 0.32919 & 0.164595 \tabularnewline
M4 & -0.0446390881700724 & 0.059125 & -0.755 & 0.453795 & 0.226897 \tabularnewline
M5 & 0.0169784404865373 & 0.06062 & 0.2801 & 0.780573 & 0.390287 \tabularnewline
M6 & 0.0241710147035326 & 0.058795 & 0.4111 & 0.68275 & 0.341375 \tabularnewline
M7 & -0.0756529773410106 & 0.058939 & -1.2836 & 0.205209 & 0.102605 \tabularnewline
M8 & -0.0303723197500138 & 0.059955 & -0.5066 & 0.614673 & 0.307337 \tabularnewline
M9 & -0.00954782897581095 & 0.060623 & -0.1575 & 0.875489 & 0.437744 \tabularnewline
M10 & -0.0461532281989728 & 0.060888 & -0.758 & 0.45201 & 0.226005 \tabularnewline
M11 & -0.000389226894001394 & 0.060942 & -0.0064 & 0.994929 & 0.497465 \tabularnewline
t & -0.000475364960323572 & 0.001429 & -0.3326 & 0.740843 & 0.370421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&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]0.161444463225237[/C][C]0.083204[/C][C]1.9404[/C][C]0.057986[/C][C]0.028993[/C][/ROW]
[ROW][C]X[/C][C]0.0791592781596746[/C][C]0.056882[/C][C]1.3916[/C][C]0.170194[/C][C]0.085097[/C][/ROW]
[ROW][C]Y1[/C][C]2.06064556081534[/C][C]0.16355[/C][C]12.5995[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-1.51248435858741[/C][C]0.33353[/C][C]-4.5348[/C][C]3.6e-05[/C][C]1.8e-05[/C][/ROW]
[ROW][C]Y3[/C][C]0.399499156624229[/C][C]0.371107[/C][C]1.0765[/C][C]0.286867[/C][C]0.143434[/C][/ROW]
[ROW][C]Y4[/C][C]0.00955021927819122[/C][C]0.19915[/C][C]0.048[/C][C]0.961943[/C][C]0.480972[/C][/ROW]
[ROW][C]M1[/C][C]0.0378650408289318[/C][C]0.058331[/C][C]0.6491[/C][C]0.519217[/C][C]0.259609[/C][/ROW]
[ROW][C]M2[/C][C]-0.0484576135319395[/C][C]0.059371[/C][C]-0.8162[/C][C]0.418266[/C][C]0.209133[/C][/ROW]
[ROW][C]M3[/C][C]0.0596382358271586[/C][C]0.060524[/C][C]0.9854[/C][C]0.32919[/C][C]0.164595[/C][/ROW]
[ROW][C]M4[/C][C]-0.0446390881700724[/C][C]0.059125[/C][C]-0.755[/C][C]0.453795[/C][C]0.226897[/C][/ROW]
[ROW][C]M5[/C][C]0.0169784404865373[/C][C]0.06062[/C][C]0.2801[/C][C]0.780573[/C][C]0.390287[/C][/ROW]
[ROW][C]M6[/C][C]0.0241710147035326[/C][C]0.058795[/C][C]0.4111[/C][C]0.68275[/C][C]0.341375[/C][/ROW]
[ROW][C]M7[/C][C]-0.0756529773410106[/C][C]0.058939[/C][C]-1.2836[/C][C]0.205209[/C][C]0.102605[/C][/ROW]
[ROW][C]M8[/C][C]-0.0303723197500138[/C][C]0.059955[/C][C]-0.5066[/C][C]0.614673[/C][C]0.307337[/C][/ROW]
[ROW][C]M9[/C][C]-0.00954782897581095[/C][C]0.060623[/C][C]-0.1575[/C][C]0.875489[/C][C]0.437744[/C][/ROW]
[ROW][C]M10[/C][C]-0.0461532281989728[/C][C]0.060888[/C][C]-0.758[/C][C]0.45201[/C][C]0.226005[/C][/ROW]
[ROW][C]M11[/C][C]-0.000389226894001394[/C][C]0.060942[/C][C]-0.0064[/C][C]0.994929[/C][C]0.497465[/C][/ROW]
[ROW][C]t[/C][C]-0.000475364960323572[/C][C]0.001429[/C][C]-0.3326[/C][C]0.740843[/C][C]0.370421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&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)0.1614444632252370.0832041.94040.0579860.028993
X0.07915927815967460.0568821.39160.1701940.085097
Y12.060645560815340.1635512.599500
Y2-1.512484358587410.33353-4.53483.6e-051.8e-05
Y30.3994991566242290.3711071.07650.2868670.143434
Y40.009550219278191220.199150.0480.9619430.480972
M10.03786504082893180.0583310.64910.5192170.259609
M2-0.04845761353193950.059371-0.81620.4182660.209133
M30.05963823582715860.0605240.98540.329190.164595
M4-0.04463908817007240.059125-0.7550.4537950.226897
M50.01697844048653730.060620.28010.7805730.390287
M60.02417101470353260.0587950.41110.682750.341375
M7-0.07565297734101060.058939-1.28360.2052090.102605
M8-0.03037231975001380.059955-0.50660.6146730.307337
M9-0.009547828975810950.060623-0.15750.8754890.437744
M10-0.04615322819897280.060888-0.7580.452010.226005
M11-0.0003892268940013940.060942-0.00640.9949290.497465
t-0.0004753649603235720.001429-0.33260.7408430.370421






Multiple Linear Regression - Regression Statistics
Multiple R0.99576834325729
R-squared0.99155459343337
Adjusted R-squared0.988683155200714
F-TEST (value)345.316358247658
F-TEST (DF numerator)17
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0952174421747424
Sum Squared Residuals0.45331806471502

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99576834325729 \tabularnewline
R-squared & 0.99155459343337 \tabularnewline
Adjusted R-squared & 0.988683155200714 \tabularnewline
F-TEST (value) & 345.316358247658 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0952174421747424 \tabularnewline
Sum Squared Residuals & 0.45331806471502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99576834325729[/C][/ROW]
[ROW][C]R-squared[/C][C]0.99155459343337[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.988683155200714[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]345.316358247658[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]50[/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]0.0952174421747424[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.45331806471502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.99576834325729
R-squared0.99155459343337
Adjusted R-squared0.988683155200714
F-TEST (value)345.316358247658
F-TEST (DF numerator)17
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0952174421747424
Sum Squared Residuals0.45331806471502






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13.73.577573614592180.122426385407819
23.653.74989766355371-0.0998976635537103
33.553.66050001564694-0.110500015646943
43.433.423110438103240.00688956189675844
53.473.368248612529220.101751387470783
63.583.59846234062266-0.0184623406226591
73.673.615439700241260.0545602997587431
83.723.694163753852280.0258362461477184
93.83.725748481433850.0742515185661449
103.763.81490059240301-0.0549005924030069
113.633.6775991351943-0.0475991351942975
123.483.50256589205933-0.0225658920593253
133.413.41226575169928-0.00226575169928146
143.433.355778297776850.074221702223153
153.53.54931919649325-0.0493191964932478
163.623.529164535765590.0908354642344062
173.583.73903172944161-0.159031729441614
183.523.509980938584440.0100190614155575
193.453.395150636418530.0548493635814677
203.363.37162586135579-0.0116258613557907
213.273.28803883362883-0.0180388336288255
223.213.173085607124440.0369143928755603
233.193.19423566264738-0.00423566264737936
243.163.20687123104878-0.0468712310487771
253.123.18786175813218-0.0678617581321828
263.063.055449450846820.00455054915317979
273.013.08775459685588-0.0777545968558802
282.982.954452218529490.0255477814705124
292.973.00504727516210-0.0350472751621032
303.023.015984588580340.00401541141965914
313.073.021379867539480.0486201324605214
323.183.089311722136960.09068827786304
333.293.35974637550926-0.0697463755092619
343.433.403415812365970.0265841876340307
353.613.61524396597273-0.00524396597272548
363.743.81932165000019-0.0793216500001923
373.873.90932847027706-0.0393284702770553
383.883.9670382861368-0.0870382861367992
394.093.952296189358590.137703810641412
404.194.3183306434537-0.128330643453695
414.24.27315216800057-0.073152168000568
424.294.233217722090520.0567822779094791
434.374.3452070836840.024792916315996
444.474.42369044240110.0463095575989001
454.614.565155801898480.0448441981015185
464.654.69813643263538-0.0481364326353802
474.694.654817014415080.0351829855849185
484.824.733542228293090.0864577717069119
494.864.99563344968811-0.135633449688110
504.874.811000261219260.0589997387807372
515.014.931044726014970.0789552739850286
525.035.11687906675682-0.0868790667568239
535.135.011863331804550.118136668195449
545.185.25042079409118-0.0704207940911813
555.215.111232293099770.0987677069002278
565.265.182373654673520.0776263453264774
575.255.28131050752958-0.0313105075295761
585.25.16046155547120.0395384445287960
595.165.138104221770520.021895778229484
605.195.127698998598620.0623010014013826
615.395.267336955611190.122663044388810
625.585.530836040466560.0491639595334396
635.765.739085275630370.0209147243696306
645.895.798063097391160.091936902608842
655.985.932656883061950.0473431169380536
666.026.001933616030850.0180663839691445
675.625.90159041901696-0.281590419016956
684.875.09883456558035-0.228834565580345

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3.7 & 3.57757361459218 & 0.122426385407819 \tabularnewline
2 & 3.65 & 3.74989766355371 & -0.0998976635537103 \tabularnewline
3 & 3.55 & 3.66050001564694 & -0.110500015646943 \tabularnewline
4 & 3.43 & 3.42311043810324 & 0.00688956189675844 \tabularnewline
5 & 3.47 & 3.36824861252922 & 0.101751387470783 \tabularnewline
6 & 3.58 & 3.59846234062266 & -0.0184623406226591 \tabularnewline
7 & 3.67 & 3.61543970024126 & 0.0545602997587431 \tabularnewline
8 & 3.72 & 3.69416375385228 & 0.0258362461477184 \tabularnewline
9 & 3.8 & 3.72574848143385 & 0.0742515185661449 \tabularnewline
10 & 3.76 & 3.81490059240301 & -0.0549005924030069 \tabularnewline
11 & 3.63 & 3.6775991351943 & -0.0475991351942975 \tabularnewline
12 & 3.48 & 3.50256589205933 & -0.0225658920593253 \tabularnewline
13 & 3.41 & 3.41226575169928 & -0.00226575169928146 \tabularnewline
14 & 3.43 & 3.35577829777685 & 0.074221702223153 \tabularnewline
15 & 3.5 & 3.54931919649325 & -0.0493191964932478 \tabularnewline
16 & 3.62 & 3.52916453576559 & 0.0908354642344062 \tabularnewline
17 & 3.58 & 3.73903172944161 & -0.159031729441614 \tabularnewline
18 & 3.52 & 3.50998093858444 & 0.0100190614155575 \tabularnewline
19 & 3.45 & 3.39515063641853 & 0.0548493635814677 \tabularnewline
20 & 3.36 & 3.37162586135579 & -0.0116258613557907 \tabularnewline
21 & 3.27 & 3.28803883362883 & -0.0180388336288255 \tabularnewline
22 & 3.21 & 3.17308560712444 & 0.0369143928755603 \tabularnewline
23 & 3.19 & 3.19423566264738 & -0.00423566264737936 \tabularnewline
24 & 3.16 & 3.20687123104878 & -0.0468712310487771 \tabularnewline
25 & 3.12 & 3.18786175813218 & -0.0678617581321828 \tabularnewline
26 & 3.06 & 3.05544945084682 & 0.00455054915317979 \tabularnewline
27 & 3.01 & 3.08775459685588 & -0.0777545968558802 \tabularnewline
28 & 2.98 & 2.95445221852949 & 0.0255477814705124 \tabularnewline
29 & 2.97 & 3.00504727516210 & -0.0350472751621032 \tabularnewline
30 & 3.02 & 3.01598458858034 & 0.00401541141965914 \tabularnewline
31 & 3.07 & 3.02137986753948 & 0.0486201324605214 \tabularnewline
32 & 3.18 & 3.08931172213696 & 0.09068827786304 \tabularnewline
33 & 3.29 & 3.35974637550926 & -0.0697463755092619 \tabularnewline
34 & 3.43 & 3.40341581236597 & 0.0265841876340307 \tabularnewline
35 & 3.61 & 3.61524396597273 & -0.00524396597272548 \tabularnewline
36 & 3.74 & 3.81932165000019 & -0.0793216500001923 \tabularnewline
37 & 3.87 & 3.90932847027706 & -0.0393284702770553 \tabularnewline
38 & 3.88 & 3.9670382861368 & -0.0870382861367992 \tabularnewline
39 & 4.09 & 3.95229618935859 & 0.137703810641412 \tabularnewline
40 & 4.19 & 4.3183306434537 & -0.128330643453695 \tabularnewline
41 & 4.2 & 4.27315216800057 & -0.073152168000568 \tabularnewline
42 & 4.29 & 4.23321772209052 & 0.0567822779094791 \tabularnewline
43 & 4.37 & 4.345207083684 & 0.024792916315996 \tabularnewline
44 & 4.47 & 4.4236904424011 & 0.0463095575989001 \tabularnewline
45 & 4.61 & 4.56515580189848 & 0.0448441981015185 \tabularnewline
46 & 4.65 & 4.69813643263538 & -0.0481364326353802 \tabularnewline
47 & 4.69 & 4.65481701441508 & 0.0351829855849185 \tabularnewline
48 & 4.82 & 4.73354222829309 & 0.0864577717069119 \tabularnewline
49 & 4.86 & 4.99563344968811 & -0.135633449688110 \tabularnewline
50 & 4.87 & 4.81100026121926 & 0.0589997387807372 \tabularnewline
51 & 5.01 & 4.93104472601497 & 0.0789552739850286 \tabularnewline
52 & 5.03 & 5.11687906675682 & -0.0868790667568239 \tabularnewline
53 & 5.13 & 5.01186333180455 & 0.118136668195449 \tabularnewline
54 & 5.18 & 5.25042079409118 & -0.0704207940911813 \tabularnewline
55 & 5.21 & 5.11123229309977 & 0.0987677069002278 \tabularnewline
56 & 5.26 & 5.18237365467352 & 0.0776263453264774 \tabularnewline
57 & 5.25 & 5.28131050752958 & -0.0313105075295761 \tabularnewline
58 & 5.2 & 5.1604615554712 & 0.0395384445287960 \tabularnewline
59 & 5.16 & 5.13810422177052 & 0.021895778229484 \tabularnewline
60 & 5.19 & 5.12769899859862 & 0.0623010014013826 \tabularnewline
61 & 5.39 & 5.26733695561119 & 0.122663044388810 \tabularnewline
62 & 5.58 & 5.53083604046656 & 0.0491639595334396 \tabularnewline
63 & 5.76 & 5.73908527563037 & 0.0209147243696306 \tabularnewline
64 & 5.89 & 5.79806309739116 & 0.091936902608842 \tabularnewline
65 & 5.98 & 5.93265688306195 & 0.0473431169380536 \tabularnewline
66 & 6.02 & 6.00193361603085 & 0.0180663839691445 \tabularnewline
67 & 5.62 & 5.90159041901696 & -0.281590419016956 \tabularnewline
68 & 4.87 & 5.09883456558035 & -0.228834565580345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&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]3.7[/C][C]3.57757361459218[/C][C]0.122426385407819[/C][/ROW]
[ROW][C]2[/C][C]3.65[/C][C]3.74989766355371[/C][C]-0.0998976635537103[/C][/ROW]
[ROW][C]3[/C][C]3.55[/C][C]3.66050001564694[/C][C]-0.110500015646943[/C][/ROW]
[ROW][C]4[/C][C]3.43[/C][C]3.42311043810324[/C][C]0.00688956189675844[/C][/ROW]
[ROW][C]5[/C][C]3.47[/C][C]3.36824861252922[/C][C]0.101751387470783[/C][/ROW]
[ROW][C]6[/C][C]3.58[/C][C]3.59846234062266[/C][C]-0.0184623406226591[/C][/ROW]
[ROW][C]7[/C][C]3.67[/C][C]3.61543970024126[/C][C]0.0545602997587431[/C][/ROW]
[ROW][C]8[/C][C]3.72[/C][C]3.69416375385228[/C][C]0.0258362461477184[/C][/ROW]
[ROW][C]9[/C][C]3.8[/C][C]3.72574848143385[/C][C]0.0742515185661449[/C][/ROW]
[ROW][C]10[/C][C]3.76[/C][C]3.81490059240301[/C][C]-0.0549005924030069[/C][/ROW]
[ROW][C]11[/C][C]3.63[/C][C]3.6775991351943[/C][C]-0.0475991351942975[/C][/ROW]
[ROW][C]12[/C][C]3.48[/C][C]3.50256589205933[/C][C]-0.0225658920593253[/C][/ROW]
[ROW][C]13[/C][C]3.41[/C][C]3.41226575169928[/C][C]-0.00226575169928146[/C][/ROW]
[ROW][C]14[/C][C]3.43[/C][C]3.35577829777685[/C][C]0.074221702223153[/C][/ROW]
[ROW][C]15[/C][C]3.5[/C][C]3.54931919649325[/C][C]-0.0493191964932478[/C][/ROW]
[ROW][C]16[/C][C]3.62[/C][C]3.52916453576559[/C][C]0.0908354642344062[/C][/ROW]
[ROW][C]17[/C][C]3.58[/C][C]3.73903172944161[/C][C]-0.159031729441614[/C][/ROW]
[ROW][C]18[/C][C]3.52[/C][C]3.50998093858444[/C][C]0.0100190614155575[/C][/ROW]
[ROW][C]19[/C][C]3.45[/C][C]3.39515063641853[/C][C]0.0548493635814677[/C][/ROW]
[ROW][C]20[/C][C]3.36[/C][C]3.37162586135579[/C][C]-0.0116258613557907[/C][/ROW]
[ROW][C]21[/C][C]3.27[/C][C]3.28803883362883[/C][C]-0.0180388336288255[/C][/ROW]
[ROW][C]22[/C][C]3.21[/C][C]3.17308560712444[/C][C]0.0369143928755603[/C][/ROW]
[ROW][C]23[/C][C]3.19[/C][C]3.19423566264738[/C][C]-0.00423566264737936[/C][/ROW]
[ROW][C]24[/C][C]3.16[/C][C]3.20687123104878[/C][C]-0.0468712310487771[/C][/ROW]
[ROW][C]25[/C][C]3.12[/C][C]3.18786175813218[/C][C]-0.0678617581321828[/C][/ROW]
[ROW][C]26[/C][C]3.06[/C][C]3.05544945084682[/C][C]0.00455054915317979[/C][/ROW]
[ROW][C]27[/C][C]3.01[/C][C]3.08775459685588[/C][C]-0.0777545968558802[/C][/ROW]
[ROW][C]28[/C][C]2.98[/C][C]2.95445221852949[/C][C]0.0255477814705124[/C][/ROW]
[ROW][C]29[/C][C]2.97[/C][C]3.00504727516210[/C][C]-0.0350472751621032[/C][/ROW]
[ROW][C]30[/C][C]3.02[/C][C]3.01598458858034[/C][C]0.00401541141965914[/C][/ROW]
[ROW][C]31[/C][C]3.07[/C][C]3.02137986753948[/C][C]0.0486201324605214[/C][/ROW]
[ROW][C]32[/C][C]3.18[/C][C]3.08931172213696[/C][C]0.09068827786304[/C][/ROW]
[ROW][C]33[/C][C]3.29[/C][C]3.35974637550926[/C][C]-0.0697463755092619[/C][/ROW]
[ROW][C]34[/C][C]3.43[/C][C]3.40341581236597[/C][C]0.0265841876340307[/C][/ROW]
[ROW][C]35[/C][C]3.61[/C][C]3.61524396597273[/C][C]-0.00524396597272548[/C][/ROW]
[ROW][C]36[/C][C]3.74[/C][C]3.81932165000019[/C][C]-0.0793216500001923[/C][/ROW]
[ROW][C]37[/C][C]3.87[/C][C]3.90932847027706[/C][C]-0.0393284702770553[/C][/ROW]
[ROW][C]38[/C][C]3.88[/C][C]3.9670382861368[/C][C]-0.0870382861367992[/C][/ROW]
[ROW][C]39[/C][C]4.09[/C][C]3.95229618935859[/C][C]0.137703810641412[/C][/ROW]
[ROW][C]40[/C][C]4.19[/C][C]4.3183306434537[/C][C]-0.128330643453695[/C][/ROW]
[ROW][C]41[/C][C]4.2[/C][C]4.27315216800057[/C][C]-0.073152168000568[/C][/ROW]
[ROW][C]42[/C][C]4.29[/C][C]4.23321772209052[/C][C]0.0567822779094791[/C][/ROW]
[ROW][C]43[/C][C]4.37[/C][C]4.345207083684[/C][C]0.024792916315996[/C][/ROW]
[ROW][C]44[/C][C]4.47[/C][C]4.4236904424011[/C][C]0.0463095575989001[/C][/ROW]
[ROW][C]45[/C][C]4.61[/C][C]4.56515580189848[/C][C]0.0448441981015185[/C][/ROW]
[ROW][C]46[/C][C]4.65[/C][C]4.69813643263538[/C][C]-0.0481364326353802[/C][/ROW]
[ROW][C]47[/C][C]4.69[/C][C]4.65481701441508[/C][C]0.0351829855849185[/C][/ROW]
[ROW][C]48[/C][C]4.82[/C][C]4.73354222829309[/C][C]0.0864577717069119[/C][/ROW]
[ROW][C]49[/C][C]4.86[/C][C]4.99563344968811[/C][C]-0.135633449688110[/C][/ROW]
[ROW][C]50[/C][C]4.87[/C][C]4.81100026121926[/C][C]0.0589997387807372[/C][/ROW]
[ROW][C]51[/C][C]5.01[/C][C]4.93104472601497[/C][C]0.0789552739850286[/C][/ROW]
[ROW][C]52[/C][C]5.03[/C][C]5.11687906675682[/C][C]-0.0868790667568239[/C][/ROW]
[ROW][C]53[/C][C]5.13[/C][C]5.01186333180455[/C][C]0.118136668195449[/C][/ROW]
[ROW][C]54[/C][C]5.18[/C][C]5.25042079409118[/C][C]-0.0704207940911813[/C][/ROW]
[ROW][C]55[/C][C]5.21[/C][C]5.11123229309977[/C][C]0.0987677069002278[/C][/ROW]
[ROW][C]56[/C][C]5.26[/C][C]5.18237365467352[/C][C]0.0776263453264774[/C][/ROW]
[ROW][C]57[/C][C]5.25[/C][C]5.28131050752958[/C][C]-0.0313105075295761[/C][/ROW]
[ROW][C]58[/C][C]5.2[/C][C]5.1604615554712[/C][C]0.0395384445287960[/C][/ROW]
[ROW][C]59[/C][C]5.16[/C][C]5.13810422177052[/C][C]0.021895778229484[/C][/ROW]
[ROW][C]60[/C][C]5.19[/C][C]5.12769899859862[/C][C]0.0623010014013826[/C][/ROW]
[ROW][C]61[/C][C]5.39[/C][C]5.26733695561119[/C][C]0.122663044388810[/C][/ROW]
[ROW][C]62[/C][C]5.58[/C][C]5.53083604046656[/C][C]0.0491639595334396[/C][/ROW]
[ROW][C]63[/C][C]5.76[/C][C]5.73908527563037[/C][C]0.0209147243696306[/C][/ROW]
[ROW][C]64[/C][C]5.89[/C][C]5.79806309739116[/C][C]0.091936902608842[/C][/ROW]
[ROW][C]65[/C][C]5.98[/C][C]5.93265688306195[/C][C]0.0473431169380536[/C][/ROW]
[ROW][C]66[/C][C]6.02[/C][C]6.00193361603085[/C][C]0.0180663839691445[/C][/ROW]
[ROW][C]67[/C][C]5.62[/C][C]5.90159041901696[/C][C]-0.281590419016956[/C][/ROW]
[ROW][C]68[/C][C]4.87[/C][C]5.09883456558035[/C][C]-0.228834565580345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&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
13.73.577573614592180.122426385407819
23.653.74989766355371-0.0998976635537103
33.553.66050001564694-0.110500015646943
43.433.423110438103240.00688956189675844
53.473.368248612529220.101751387470783
63.583.59846234062266-0.0184623406226591
73.673.615439700241260.0545602997587431
83.723.694163753852280.0258362461477184
93.83.725748481433850.0742515185661449
103.763.81490059240301-0.0549005924030069
113.633.6775991351943-0.0475991351942975
123.483.50256589205933-0.0225658920593253
133.413.41226575169928-0.00226575169928146
143.433.355778297776850.074221702223153
153.53.54931919649325-0.0493191964932478
163.623.529164535765590.0908354642344062
173.583.73903172944161-0.159031729441614
183.523.509980938584440.0100190614155575
193.453.395150636418530.0548493635814677
203.363.37162586135579-0.0116258613557907
213.273.28803883362883-0.0180388336288255
223.213.173085607124440.0369143928755603
233.193.19423566264738-0.00423566264737936
243.163.20687123104878-0.0468712310487771
253.123.18786175813218-0.0678617581321828
263.063.055449450846820.00455054915317979
273.013.08775459685588-0.0777545968558802
282.982.954452218529490.0255477814705124
292.973.00504727516210-0.0350472751621032
303.023.015984588580340.00401541141965914
313.073.021379867539480.0486201324605214
323.183.089311722136960.09068827786304
333.293.35974637550926-0.0697463755092619
343.433.403415812365970.0265841876340307
353.613.61524396597273-0.00524396597272548
363.743.81932165000019-0.0793216500001923
373.873.90932847027706-0.0393284702770553
383.883.9670382861368-0.0870382861367992
394.093.952296189358590.137703810641412
404.194.3183306434537-0.128330643453695
414.24.27315216800057-0.073152168000568
424.294.233217722090520.0567822779094791
434.374.3452070836840.024792916315996
444.474.42369044240110.0463095575989001
454.614.565155801898480.0448441981015185
464.654.69813643263538-0.0481364326353802
474.694.654817014415080.0351829855849185
484.824.733542228293090.0864577717069119
494.864.99563344968811-0.135633449688110
504.874.811000261219260.0589997387807372
515.014.931044726014970.0789552739850286
525.035.11687906675682-0.0868790667568239
535.135.011863331804550.118136668195449
545.185.25042079409118-0.0704207940911813
555.215.111232293099770.0987677069002278
565.265.182373654673520.0776263453264774
575.255.28131050752958-0.0313105075295761
585.25.16046155547120.0395384445287960
595.165.138104221770520.021895778229484
605.195.127698998598620.0623010014013826
615.395.267336955611190.122663044388810
625.585.530836040466560.0491639595334396
635.765.739085275630370.0209147243696306
645.895.798063097391160.091936902608842
655.985.932656883061950.0473431169380536
666.026.001933616030850.0180663839691445
675.625.90159041901696-0.281590419016956
684.875.09883456558035-0.228834565580345






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.741664293847760.5166714123044790.258335706152240
220.5960348914119910.8079302171760180.403965108588009
230.4440571050830520.8881142101661040.555942894916948
240.3205676376936010.6411352753872020.679432362306399
250.3104978708899490.6209957417798990.68950212911005
260.2101151020652150.4202302041304310.789884897934785
270.1640278793710930.3280557587421850.835972120628907
280.1049880315770550.209976063154110.895011968422945
290.06739064167092730.1347812833418550.932609358329073
300.04166309413629660.08332618827259320.958336905863703
310.02225688902661070.04451377805322140.97774311097339
320.01761159513224450.0352231902644890.982388404867755
330.00923420528251040.01846841056502080.99076579471749
340.007090213441321310.01418042688264260.992909786558679
350.00479421241700520.00958842483401040.995205787582995
360.003982689612111760.007965379224223520.996017310387888
370.001929650107608820.003859300215217650.998070349892391
380.001293849575052660.002587699150105320.998706150424947
390.004513711668768990.009027423337537980.99548628833123
400.005434366663099910.01086873332619980.9945656333369
410.01085429050097070.02170858100194130.98914570949903
420.005680198915412940.01136039783082590.994319801084587
430.002524713515072570.005049427030145140.997475286484927
440.001153937961778710.002307875923557420.998846062038221
450.0006462638821952670.001292527764390530.999353736117805
460.001014507761079830.002029015522159660.99898549223892
470.0006017256104417410.001203451220883480.999398274389558

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.74166429384776 & 0.516671412304479 & 0.258335706152240 \tabularnewline
22 & 0.596034891411991 & 0.807930217176018 & 0.403965108588009 \tabularnewline
23 & 0.444057105083052 & 0.888114210166104 & 0.555942894916948 \tabularnewline
24 & 0.320567637693601 & 0.641135275387202 & 0.679432362306399 \tabularnewline
25 & 0.310497870889949 & 0.620995741779899 & 0.68950212911005 \tabularnewline
26 & 0.210115102065215 & 0.420230204130431 & 0.789884897934785 \tabularnewline
27 & 0.164027879371093 & 0.328055758742185 & 0.835972120628907 \tabularnewline
28 & 0.104988031577055 & 0.20997606315411 & 0.895011968422945 \tabularnewline
29 & 0.0673906416709273 & 0.134781283341855 & 0.932609358329073 \tabularnewline
30 & 0.0416630941362966 & 0.0833261882725932 & 0.958336905863703 \tabularnewline
31 & 0.0222568890266107 & 0.0445137780532214 & 0.97774311097339 \tabularnewline
32 & 0.0176115951322445 & 0.035223190264489 & 0.982388404867755 \tabularnewline
33 & 0.0092342052825104 & 0.0184684105650208 & 0.99076579471749 \tabularnewline
34 & 0.00709021344132131 & 0.0141804268826426 & 0.992909786558679 \tabularnewline
35 & 0.0047942124170052 & 0.0095884248340104 & 0.995205787582995 \tabularnewline
36 & 0.00398268961211176 & 0.00796537922422352 & 0.996017310387888 \tabularnewline
37 & 0.00192965010760882 & 0.00385930021521765 & 0.998070349892391 \tabularnewline
38 & 0.00129384957505266 & 0.00258769915010532 & 0.998706150424947 \tabularnewline
39 & 0.00451371166876899 & 0.00902742333753798 & 0.99548628833123 \tabularnewline
40 & 0.00543436666309991 & 0.0108687333261998 & 0.9945656333369 \tabularnewline
41 & 0.0108542905009707 & 0.0217085810019413 & 0.98914570949903 \tabularnewline
42 & 0.00568019891541294 & 0.0113603978308259 & 0.994319801084587 \tabularnewline
43 & 0.00252471351507257 & 0.00504942703014514 & 0.997475286484927 \tabularnewline
44 & 0.00115393796177871 & 0.00230787592355742 & 0.998846062038221 \tabularnewline
45 & 0.000646263882195267 & 0.00129252776439053 & 0.999353736117805 \tabularnewline
46 & 0.00101450776107983 & 0.00202901552215966 & 0.99898549223892 \tabularnewline
47 & 0.000601725610441741 & 0.00120345122088348 & 0.999398274389558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&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]0.74166429384776[/C][C]0.516671412304479[/C][C]0.258335706152240[/C][/ROW]
[ROW][C]22[/C][C]0.596034891411991[/C][C]0.807930217176018[/C][C]0.403965108588009[/C][/ROW]
[ROW][C]23[/C][C]0.444057105083052[/C][C]0.888114210166104[/C][C]0.555942894916948[/C][/ROW]
[ROW][C]24[/C][C]0.320567637693601[/C][C]0.641135275387202[/C][C]0.679432362306399[/C][/ROW]
[ROW][C]25[/C][C]0.310497870889949[/C][C]0.620995741779899[/C][C]0.68950212911005[/C][/ROW]
[ROW][C]26[/C][C]0.210115102065215[/C][C]0.420230204130431[/C][C]0.789884897934785[/C][/ROW]
[ROW][C]27[/C][C]0.164027879371093[/C][C]0.328055758742185[/C][C]0.835972120628907[/C][/ROW]
[ROW][C]28[/C][C]0.104988031577055[/C][C]0.20997606315411[/C][C]0.895011968422945[/C][/ROW]
[ROW][C]29[/C][C]0.0673906416709273[/C][C]0.134781283341855[/C][C]0.932609358329073[/C][/ROW]
[ROW][C]30[/C][C]0.0416630941362966[/C][C]0.0833261882725932[/C][C]0.958336905863703[/C][/ROW]
[ROW][C]31[/C][C]0.0222568890266107[/C][C]0.0445137780532214[/C][C]0.97774311097339[/C][/ROW]
[ROW][C]32[/C][C]0.0176115951322445[/C][C]0.035223190264489[/C][C]0.982388404867755[/C][/ROW]
[ROW][C]33[/C][C]0.0092342052825104[/C][C]0.0184684105650208[/C][C]0.99076579471749[/C][/ROW]
[ROW][C]34[/C][C]0.00709021344132131[/C][C]0.0141804268826426[/C][C]0.992909786558679[/C][/ROW]
[ROW][C]35[/C][C]0.0047942124170052[/C][C]0.0095884248340104[/C][C]0.995205787582995[/C][/ROW]
[ROW][C]36[/C][C]0.00398268961211176[/C][C]0.00796537922422352[/C][C]0.996017310387888[/C][/ROW]
[ROW][C]37[/C][C]0.00192965010760882[/C][C]0.00385930021521765[/C][C]0.998070349892391[/C][/ROW]
[ROW][C]38[/C][C]0.00129384957505266[/C][C]0.00258769915010532[/C][C]0.998706150424947[/C][/ROW]
[ROW][C]39[/C][C]0.00451371166876899[/C][C]0.00902742333753798[/C][C]0.99548628833123[/C][/ROW]
[ROW][C]40[/C][C]0.00543436666309991[/C][C]0.0108687333261998[/C][C]0.9945656333369[/C][/ROW]
[ROW][C]41[/C][C]0.0108542905009707[/C][C]0.0217085810019413[/C][C]0.98914570949903[/C][/ROW]
[ROW][C]42[/C][C]0.00568019891541294[/C][C]0.0113603978308259[/C][C]0.994319801084587[/C][/ROW]
[ROW][C]43[/C][C]0.00252471351507257[/C][C]0.00504942703014514[/C][C]0.997475286484927[/C][/ROW]
[ROW][C]44[/C][C]0.00115393796177871[/C][C]0.00230787592355742[/C][C]0.998846062038221[/C][/ROW]
[ROW][C]45[/C][C]0.000646263882195267[/C][C]0.00129252776439053[/C][C]0.999353736117805[/C][/ROW]
[ROW][C]46[/C][C]0.00101450776107983[/C][C]0.00202901552215966[/C][C]0.99898549223892[/C][/ROW]
[ROW][C]47[/C][C]0.000601725610441741[/C][C]0.00120345122088348[/C][C]0.999398274389558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&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
210.741664293847760.5166714123044790.258335706152240
220.5960348914119910.8079302171760180.403965108588009
230.4440571050830520.8881142101661040.555942894916948
240.3205676376936010.6411352753872020.679432362306399
250.3104978708899490.6209957417798990.68950212911005
260.2101151020652150.4202302041304310.789884897934785
270.1640278793710930.3280557587421850.835972120628907
280.1049880315770550.209976063154110.895011968422945
290.06739064167092730.1347812833418550.932609358329073
300.04166309413629660.08332618827259320.958336905863703
310.02225688902661070.04451377805322140.97774311097339
320.01761159513224450.0352231902644890.982388404867755
330.00923420528251040.01846841056502080.99076579471749
340.007090213441321310.01418042688264260.992909786558679
350.00479421241700520.00958842483401040.995205787582995
360.003982689612111760.007965379224223520.996017310387888
370.001929650107608820.003859300215217650.998070349892391
380.001293849575052660.002587699150105320.998706150424947
390.004513711668768990.009027423337537980.99548628833123
400.005434366663099910.01086873332619980.9945656333369
410.01085429050097070.02170858100194130.98914570949903
420.005680198915412940.01136039783082590.994319801084587
430.002524713515072570.005049427030145140.997475286484927
440.001153937961778710.002307875923557420.998846062038221
450.0006462638821952670.001292527764390530.999353736117805
460.001014507761079830.002029015522159660.99898549223892
470.0006017256104417410.001203451220883480.999398274389558






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level100.370370370370370NOK
5% type I error level170.62962962962963NOK
10% type I error level180.666666666666667NOK

\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 & 10 & 0.370370370370370 & NOK \tabularnewline
5% type I error level & 17 & 0.62962962962963 & NOK \tabularnewline
10% type I error level & 18 & 0.666666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116554&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]10[/C][C]0.370370370370370[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]17[/C][C]0.62962962962963[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]18[/C][C]0.666666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116554&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116554&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 level100.370370370370370NOK
5% type I error level170.62962962962963NOK
10% type I error level180.666666666666667NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 6
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Figure 7
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Figure 9
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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')
}