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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 computationSat, 04 Dec 2010 14:53:18 +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/04/t1291474996ed1vc4klio79mzj.htm/, Retrieved Tue, 04 Nov 2025 13:28:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105170, Retrieved Tue, 04 Nov 2025 13:28:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact407

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [WS7_4] [2009-11-18 19:13:17] [8b1aef4e7013bd33fbc2a5833375c5f5]
-    D        [Multiple Regression] [Paper Multiple re...] [2010-12-04 14:53:18] [da925928e5a77063c5ecc7b801d712e1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,16	196,2	2,04	2,26	1,95	1,79
2,75	196,2	2,16	2,04	2,26	1,95
2,79	196,2	2,75	2,16	2,04	2,26
2,88	197	2,79	2,75	2,16	2,04
3,36	197,7	2,88	2,79	2,75	2,16
2,97	198	3,36	2,88	2,79	2,75
3,1	198,2	2,97	3,36	2,88	2,79
2,49	198,5	3,1	2,97	3,36	2,88
2,2	198,6	2,49	3,1	2,97	3,36
2,25	199,5	2,2	2,49	3,1	2,97
2,09	200	2,25	2,2	2,49	3,1
2,79	201,3	2,09	2,25	2,2	2,49
3,14	202,2	2,79	2,09	2,25	2,2
2,93	202,9	3,14	2,79	2,09	2,25
2,65	203,5	2,93	3,14	2,79	2,09
2,67	203,5	2,65	2,93	3,14	2,79
2,26	204	2,67	2,65	2,93	3,14
2,35	204,1	2,26	2,67	2,65	2,93
2,13	204,3	2,35	2,26	2,67	2,65
2,18	204,5	2,13	2,35	2,26	2,67
2,9	204,8	2,18	2,13	2,35	2,26
2,63	205,1	2,9	2,18	2,13	2,35
2,67	205,7	2,63	2,9	2,18	2,13
1,81	206,5	2,67	2,63	2,9	2,18
1,33	206,9	1,81	2,67	2,63	2,9
0,88	207,1	1,33	1,81	2,67	2,63
1,28	207,8	0,88	1,33	1,81	2,67
1,26	208	1,28	0,88	1,33	1,81
1,26	208,5	1,26	1,28	0,88	1,33
1,29	208,6	1,26	1,26	1,28	0,88
1,1	209	1,29	1,26	1,26	1,28
1,37	209,1	1,1	1,29	1,26	1,26
1,21	209,7	1,37	1,1	1,29	1,26
1,74	209,8	1,21	1,37	1,1	1,29
1,76	209,9	1,74	1,21	1,37	1,1
1,48	210	1,76	1,74	1,21	1,37
1,04	210,8	1,48	1,76	1,74	1,21
1,62	211,4	1,04	1,48	1,76	1,74
1,49	211,7	1,62	1,04	1,48	1,76
1,79	212	1,49	1,62	1,04	1,48
1,8	212,2	1,79	1,49	1,62	1,04
1,58	212,4	1,8	1,79	1,49	1,62
1,86	212,9	1,58	1,8	1,79	1,49
1,74	213,4	1,86	1,58	1,8	1,79
1,59	213,7	1,74	1,86	1,58	1,8
1,26	214	1,59	1,74	1,86	1,58
1,13	214,3	1,26	1,59	1,74	1,86
1,92	214,8	1,13	1,26	1,59	1,74
2,61	215	1,92	1,13	1,26	1,59
2,26	215,9	2,61	1,92	1,13	1,26
2,41	216,4	2,26	2,61	1,92	1,13
2,26	216,9	2,41	2,26	2,61	1,92
2,03	217,2	2,26	2,41	2,26	2,61
2,86	217,5	2,03	2,26	2,41	2,26
2,55	217,9	2,86	2,03	2,26	2,41
2,27	218,1	2,55	2,86	2,03	2,26
2,26	218,6	2,27	2,55	2,86	2,03
2,57	218,9	2,26	2,27	2,55	2,86
3,07	219,3	2,57	2,26	2,27	2,55
2,76	220,4	3,07	2,57	2,26	2,27
2,51	220,9	2,76	3,07	2,57	2,26
2,87	221	2,51	2,76	3,07	2,57
3,14	221,8	2,87	2,51	2,76	3,07
3,11	222	3,14	2,87	2,51	2,76
3,16	222,2	3,11	3,14	2,87	2,51
2,47	222,5	3,16	3,11	3,14	2,87
2,57	222,9	2,47	3,16	3,11	3,14
2,89	223,1	2,57	2,47	3,16	3,11

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 & 10 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&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]10 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=105170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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 time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 23.8465823459796 -0.120204819900504X[t] + 0.848503057329008Y1[t] -0.0494116230941216Y2[t] -0.0372156025966219Y3[t] + 0.111759361951538Y4[t] + 0.00711983032512751M1[t] + 0.090252044197324M2[t] + 0.0890447094819704M3[t] + 0.0592811754111258M4[t] + 0.0193491456647841M5[t] -0.052730500361094M6[t] -0.0528329084191568M7[t] -0.110932119089967M8[t] -0.0479723801614877M9[t] -0.0284545974149302M10[t] -0.0238767337808014M11[t] + 0.0487671735937128t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  23.8465823459796 -0.120204819900504X[t] +  0.848503057329008Y1[t] -0.0494116230941216Y2[t] -0.0372156025966219Y3[t] +  0.111759361951538Y4[t] +  0.00711983032512751M1[t] +  0.090252044197324M2[t] +  0.0890447094819704M3[t] +  0.0592811754111258M4[t] +  0.0193491456647841M5[t] -0.052730500361094M6[t] -0.0528329084191568M7[t] -0.110932119089967M8[t] -0.0479723801614877M9[t] -0.0284545974149302M10[t] -0.0238767337808014M11[t] +  0.0487671735937128t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  23.8465823459796 -0.120204819900504X[t] +  0.848503057329008Y1[t] -0.0494116230941216Y2[t] -0.0372156025966219Y3[t] +  0.111759361951538Y4[t] +  0.00711983032512751M1[t] +  0.090252044197324M2[t] +  0.0890447094819704M3[t] +  0.0592811754111258M4[t] +  0.0193491456647841M5[t] -0.052730500361094M6[t] -0.0528329084191568M7[t] -0.110932119089967M8[t] -0.0479723801614877M9[t] -0.0284545974149302M10[t] -0.0238767337808014M11[t] +  0.0487671735937128t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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] = + 23.8465823459796 -0.120204819900504X[t] + 0.848503057329008Y1[t] -0.0494116230941216Y2[t] -0.0372156025966219Y3[t] + 0.111759361951538Y4[t] + 0.00711983032512751M1[t] + 0.090252044197324M2[t] + 0.0890447094819704M3[t] + 0.0592811754111258M4[t] + 0.0193491456647841M5[t] -0.052730500361094M6[t] -0.0528329084191568M7[t] -0.110932119089967M8[t] -0.0479723801614877M9[t] -0.0284545974149302M10[t] -0.0238767337808014M11[t] + 0.0487671735937128t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)23.846582345979618.022411.32320.19180.0959
X-0.1202048199005040.091846-1.30880.1965980.098299
Y10.8485030573290080.1408466.024300
Y2-0.04941162309412160.183996-0.26850.7893830.394691
Y3-0.03721560259662190.187414-0.19860.8434010.4217
Y40.1117593619515380.1456930.76710.4466360.223318
M10.007119830325127510.2413160.02950.976580.48829
M20.0902520441973240.2414180.37380.7101030.355052
M30.08904470948197040.241480.36870.7138740.356937
M40.05928117541112580.2410860.24590.8067720.403386
M50.01934914566478410.241280.08020.9364030.468202
M6-0.0527305003610940.241588-0.21830.828110.414055
M7-0.05283290841915680.242444-0.21790.828380.41419
M8-0.1109321190899670.244087-0.45450.6514520.325726
M9-0.04797238016148770.255583-0.18770.8518730.425937
M10-0.02845459741493020.255613-0.11130.9118090.455904
M11-0.02387673378080140.254794-0.09370.9257140.462857
t0.04876717359371280.0367261.32790.190250.095125

\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) & 23.8465823459796 & 18.02241 & 1.3232 & 0.1918 & 0.0959 \tabularnewline
X & -0.120204819900504 & 0.091846 & -1.3088 & 0.196598 & 0.098299 \tabularnewline
Y1 & 0.848503057329008 & 0.140846 & 6.0243 & 0 & 0 \tabularnewline
Y2 & -0.0494116230941216 & 0.183996 & -0.2685 & 0.789383 & 0.394691 \tabularnewline
Y3 & -0.0372156025966219 & 0.187414 & -0.1986 & 0.843401 & 0.4217 \tabularnewline
Y4 & 0.111759361951538 & 0.145693 & 0.7671 & 0.446636 & 0.223318 \tabularnewline
M1 & 0.00711983032512751 & 0.241316 & 0.0295 & 0.97658 & 0.48829 \tabularnewline
M2 & 0.090252044197324 & 0.241418 & 0.3738 & 0.710103 & 0.355052 \tabularnewline
M3 & 0.0890447094819704 & 0.24148 & 0.3687 & 0.713874 & 0.356937 \tabularnewline
M4 & 0.0592811754111258 & 0.241086 & 0.2459 & 0.806772 & 0.403386 \tabularnewline
M5 & 0.0193491456647841 & 0.24128 & 0.0802 & 0.936403 & 0.468202 \tabularnewline
M6 & -0.052730500361094 & 0.241588 & -0.2183 & 0.82811 & 0.414055 \tabularnewline
M7 & -0.0528329084191568 & 0.242444 & -0.2179 & 0.82838 & 0.41419 \tabularnewline
M8 & -0.110932119089967 & 0.244087 & -0.4545 & 0.651452 & 0.325726 \tabularnewline
M9 & -0.0479723801614877 & 0.255583 & -0.1877 & 0.851873 & 0.425937 \tabularnewline
M10 & -0.0284545974149302 & 0.255613 & -0.1113 & 0.911809 & 0.455904 \tabularnewline
M11 & -0.0238767337808014 & 0.254794 & -0.0937 & 0.925714 & 0.462857 \tabularnewline
t & 0.0487671735937128 & 0.036726 & 1.3279 & 0.19025 & 0.095125 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&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]23.8465823459796[/C][C]18.02241[/C][C]1.3232[/C][C]0.1918[/C][C]0.0959[/C][/ROW]
[ROW][C]X[/C][C]-0.120204819900504[/C][C]0.091846[/C][C]-1.3088[/C][C]0.196598[/C][C]0.098299[/C][/ROW]
[ROW][C]Y1[/C][C]0.848503057329008[/C][C]0.140846[/C][C]6.0243[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.0494116230941216[/C][C]0.183996[/C][C]-0.2685[/C][C]0.789383[/C][C]0.394691[/C][/ROW]
[ROW][C]Y3[/C][C]-0.0372156025966219[/C][C]0.187414[/C][C]-0.1986[/C][C]0.843401[/C][C]0.4217[/C][/ROW]
[ROW][C]Y4[/C][C]0.111759361951538[/C][C]0.145693[/C][C]0.7671[/C][C]0.446636[/C][C]0.223318[/C][/ROW]
[ROW][C]M1[/C][C]0.00711983032512751[/C][C]0.241316[/C][C]0.0295[/C][C]0.97658[/C][C]0.48829[/C][/ROW]
[ROW][C]M2[/C][C]0.090252044197324[/C][C]0.241418[/C][C]0.3738[/C][C]0.710103[/C][C]0.355052[/C][/ROW]
[ROW][C]M3[/C][C]0.0890447094819704[/C][C]0.24148[/C][C]0.3687[/C][C]0.713874[/C][C]0.356937[/C][/ROW]
[ROW][C]M4[/C][C]0.0592811754111258[/C][C]0.241086[/C][C]0.2459[/C][C]0.806772[/C][C]0.403386[/C][/ROW]
[ROW][C]M5[/C][C]0.0193491456647841[/C][C]0.24128[/C][C]0.0802[/C][C]0.936403[/C][C]0.468202[/C][/ROW]
[ROW][C]M6[/C][C]-0.052730500361094[/C][C]0.241588[/C][C]-0.2183[/C][C]0.82811[/C][C]0.414055[/C][/ROW]
[ROW][C]M7[/C][C]-0.0528329084191568[/C][C]0.242444[/C][C]-0.2179[/C][C]0.82838[/C][C]0.41419[/C][/ROW]
[ROW][C]M8[/C][C]-0.110932119089967[/C][C]0.244087[/C][C]-0.4545[/C][C]0.651452[/C][C]0.325726[/C][/ROW]
[ROW][C]M9[/C][C]-0.0479723801614877[/C][C]0.255583[/C][C]-0.1877[/C][C]0.851873[/C][C]0.425937[/C][/ROW]
[ROW][C]M10[/C][C]-0.0284545974149302[/C][C]0.255613[/C][C]-0.1113[/C][C]0.911809[/C][C]0.455904[/C][/ROW]
[ROW][C]M11[/C][C]-0.0238767337808014[/C][C]0.254794[/C][C]-0.0937[/C][C]0.925714[/C][C]0.462857[/C][/ROW]
[ROW][C]t[/C][C]0.0487671735937128[/C][C]0.036726[/C][C]1.3279[/C][C]0.19025[/C][C]0.095125[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105170&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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)23.846582345979618.022411.32320.19180.0959
X-0.1202048199005040.091846-1.30880.1965980.098299
Y10.8485030573290080.1408466.024300
Y2-0.04941162309412160.183996-0.26850.7893830.394691
Y3-0.03721560259662190.187414-0.19860.8434010.4217
Y40.1117593619515380.1456930.76710.4466360.223318
M10.007119830325127510.2413160.02950.976580.48829
M20.0902520441973240.2414180.37380.7101030.355052
M30.08904470948197040.241480.36870.7138740.356937
M40.05928117541112580.2410860.24590.8067720.403386
M50.01934914566478410.241280.08020.9364030.468202
M6-0.0527305003610940.241588-0.21830.828110.414055
M7-0.05283290841915680.242444-0.21790.828380.41419
M8-0.1109321190899670.244087-0.45450.6514520.325726
M9-0.04797238016148770.255583-0.18770.8518730.425937
M10-0.02845459741493020.255613-0.11130.9118090.455904
M11-0.02387673378080140.254794-0.09370.9257140.462857
t0.04876717359371280.0367261.32790.190250.095125






Multiple Linear Regression - Regression Statistics
Multiple R0.850761679392294
R-squared0.723795435122397
Adjusted R-squared0.629885883064012
F-TEST (value)7.70736756014342
F-TEST (DF numerator)17
F-TEST (DF denominator)50
p-value7.36950378499301e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.397227911713991
Sum Squared Residuals7.88950069223292

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.850761679392294 \tabularnewline
R-squared & 0.723795435122397 \tabularnewline
Adjusted R-squared & 0.629885883064012 \tabularnewline
F-TEST (value) & 7.70736756014342 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 7.36950378499301e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.397227911713991 \tabularnewline
Sum Squared Residuals & 7.88950069223292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.850761679392294[/C][/ROW]
[ROW][C]R-squared[/C][C]0.723795435122397[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.629885883064012[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]7.70736756014342[/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]7.36950378499301e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.397227911713991[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7.88950069223292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105170&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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 R0.850761679392294
R-squared0.723795435122397
Adjusted R-squared0.629885883064012
F-TEST (value)7.70736756014342
F-TEST (DF numerator)17
F-TEST (DF denominator)50
p-value7.36950378499301e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.397227911713991
Sum Squared Residuals7.88950069223292






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.162.065038487007810.0949615129921882
22.752.315973459541200.434026540458797
32.792.90105354224862-0.111053542248617
42.882.799627658577770.0803723414222256
53.362.790162156632820.569837843367182
62.973.19807205911749-0.228072059117494
73.12.869183059473920.230816940526081
82.492.94556036021541-0.455560360215408
92.22.58941499352404-0.389414993524039
102.252.28516663591720-0.0351666359171965
112.092.37239402139617-0.282394021396171
122.792.093159906535260.696840093464738
133.142.608449577273240.53155042272676
142.932.9301359892211-0.000135989221098943
152.652.66616080630724-0.0161608063072401
162.672.523166123085010.146833876914990
172.262.54963522582339-0.289635225823392
182.352.152378688151630.197621311848368
192.132.24158959693702-0.111589596937017
202.182.034592461492610.145407538507387
212.92.114382895357980.785617104642017
222.632.77330380099718-0.143303800997180
232.672.463405912418950.20659408758105
241.812.46595995862964-0.655959958629642
251.331.83259089366776-0.502590893667762
260.881.54399819366581-0.663998193665813
271.281.185781654612100.0942183453879027
281.261.46413122144688-0.204131221446880
291.261.33923177239151-0.0792317723915122
301.291.239709096514340.0502909034856609
311.11.31119508264220-0.211195082642204
321.371.124909446750690.245090553249308
331.211.40188103312140-0.191881033121398
341.741.319467625415470.420532374584535
351.761.78712216926081-0.0271221692608111
361.481.87465701969435-0.394657019694346
371.041.55820531189032-0.518205311890321
381.621.316963866439900.303036133560099
391.491.85499070272643-0.364990702726434
401.791.684051001227870.105948998772129
411.81.85906044053136-0.059060440531364
421.581.87502700603360-0.295027006033602
431.861.650731174942990.20926882505701
441.741.86290379360797-0.122903793607965
451.591.83221866500494-0.242218665004945
461.261.70808868319061-0.448088683190613
471.131.48853650265187-0.358536502651873
481.921.399249655199730.520750344800267
492.612.103353865994780.506646134005219
502.262.64145828175645-0.381458281756449
512.412.253916577579430.156083422420573
522.262.41999846398438-0.159998463984383
532.032.34822438045351-0.318224380453514
542.862.056408385257110.80359161474289
552.552.79495967840951-0.244959678409507
562.272.44933476671669-0.179334766716689
572.262.222102412991630.0378975870083654
582.572.363973254479550.206026745520455
593.072.608541394272200.461458605727804
602.762.92697345994102-0.166973459941018
612.512.62236186416608-0.112361864166084
622.872.561470209375540.308529790624465
633.142.898096716526180.241903283473816
643.113.079025531678080.0309744683219196
653.162.98368602416740.1763139758326
662.472.99840476492582-0.528404764925823
672.572.442341407594360.127658592405638
682.892.522699171216630.367300828783367

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.16 & 2.06503848700781 & 0.0949615129921882 \tabularnewline
2 & 2.75 & 2.31597345954120 & 0.434026540458797 \tabularnewline
3 & 2.79 & 2.90105354224862 & -0.111053542248617 \tabularnewline
4 & 2.88 & 2.79962765857777 & 0.0803723414222256 \tabularnewline
5 & 3.36 & 2.79016215663282 & 0.569837843367182 \tabularnewline
6 & 2.97 & 3.19807205911749 & -0.228072059117494 \tabularnewline
7 & 3.1 & 2.86918305947392 & 0.230816940526081 \tabularnewline
8 & 2.49 & 2.94556036021541 & -0.455560360215408 \tabularnewline
9 & 2.2 & 2.58941499352404 & -0.389414993524039 \tabularnewline
10 & 2.25 & 2.28516663591720 & -0.0351666359171965 \tabularnewline
11 & 2.09 & 2.37239402139617 & -0.282394021396171 \tabularnewline
12 & 2.79 & 2.09315990653526 & 0.696840093464738 \tabularnewline
13 & 3.14 & 2.60844957727324 & 0.53155042272676 \tabularnewline
14 & 2.93 & 2.9301359892211 & -0.000135989221098943 \tabularnewline
15 & 2.65 & 2.66616080630724 & -0.0161608063072401 \tabularnewline
16 & 2.67 & 2.52316612308501 & 0.146833876914990 \tabularnewline
17 & 2.26 & 2.54963522582339 & -0.289635225823392 \tabularnewline
18 & 2.35 & 2.15237868815163 & 0.197621311848368 \tabularnewline
19 & 2.13 & 2.24158959693702 & -0.111589596937017 \tabularnewline
20 & 2.18 & 2.03459246149261 & 0.145407538507387 \tabularnewline
21 & 2.9 & 2.11438289535798 & 0.785617104642017 \tabularnewline
22 & 2.63 & 2.77330380099718 & -0.143303800997180 \tabularnewline
23 & 2.67 & 2.46340591241895 & 0.20659408758105 \tabularnewline
24 & 1.81 & 2.46595995862964 & -0.655959958629642 \tabularnewline
25 & 1.33 & 1.83259089366776 & -0.502590893667762 \tabularnewline
26 & 0.88 & 1.54399819366581 & -0.663998193665813 \tabularnewline
27 & 1.28 & 1.18578165461210 & 0.0942183453879027 \tabularnewline
28 & 1.26 & 1.46413122144688 & -0.204131221446880 \tabularnewline
29 & 1.26 & 1.33923177239151 & -0.0792317723915122 \tabularnewline
30 & 1.29 & 1.23970909651434 & 0.0502909034856609 \tabularnewline
31 & 1.1 & 1.31119508264220 & -0.211195082642204 \tabularnewline
32 & 1.37 & 1.12490944675069 & 0.245090553249308 \tabularnewline
33 & 1.21 & 1.40188103312140 & -0.191881033121398 \tabularnewline
34 & 1.74 & 1.31946762541547 & 0.420532374584535 \tabularnewline
35 & 1.76 & 1.78712216926081 & -0.0271221692608111 \tabularnewline
36 & 1.48 & 1.87465701969435 & -0.394657019694346 \tabularnewline
37 & 1.04 & 1.55820531189032 & -0.518205311890321 \tabularnewline
38 & 1.62 & 1.31696386643990 & 0.303036133560099 \tabularnewline
39 & 1.49 & 1.85499070272643 & -0.364990702726434 \tabularnewline
40 & 1.79 & 1.68405100122787 & 0.105948998772129 \tabularnewline
41 & 1.8 & 1.85906044053136 & -0.059060440531364 \tabularnewline
42 & 1.58 & 1.87502700603360 & -0.295027006033602 \tabularnewline
43 & 1.86 & 1.65073117494299 & 0.20926882505701 \tabularnewline
44 & 1.74 & 1.86290379360797 & -0.122903793607965 \tabularnewline
45 & 1.59 & 1.83221866500494 & -0.242218665004945 \tabularnewline
46 & 1.26 & 1.70808868319061 & -0.448088683190613 \tabularnewline
47 & 1.13 & 1.48853650265187 & -0.358536502651873 \tabularnewline
48 & 1.92 & 1.39924965519973 & 0.520750344800267 \tabularnewline
49 & 2.61 & 2.10335386599478 & 0.506646134005219 \tabularnewline
50 & 2.26 & 2.64145828175645 & -0.381458281756449 \tabularnewline
51 & 2.41 & 2.25391657757943 & 0.156083422420573 \tabularnewline
52 & 2.26 & 2.41999846398438 & -0.159998463984383 \tabularnewline
53 & 2.03 & 2.34822438045351 & -0.318224380453514 \tabularnewline
54 & 2.86 & 2.05640838525711 & 0.80359161474289 \tabularnewline
55 & 2.55 & 2.79495967840951 & -0.244959678409507 \tabularnewline
56 & 2.27 & 2.44933476671669 & -0.179334766716689 \tabularnewline
57 & 2.26 & 2.22210241299163 & 0.0378975870083654 \tabularnewline
58 & 2.57 & 2.36397325447955 & 0.206026745520455 \tabularnewline
59 & 3.07 & 2.60854139427220 & 0.461458605727804 \tabularnewline
60 & 2.76 & 2.92697345994102 & -0.166973459941018 \tabularnewline
61 & 2.51 & 2.62236186416608 & -0.112361864166084 \tabularnewline
62 & 2.87 & 2.56147020937554 & 0.308529790624465 \tabularnewline
63 & 3.14 & 2.89809671652618 & 0.241903283473816 \tabularnewline
64 & 3.11 & 3.07902553167808 & 0.0309744683219196 \tabularnewline
65 & 3.16 & 2.9836860241674 & 0.1763139758326 \tabularnewline
66 & 2.47 & 2.99840476492582 & -0.528404764925823 \tabularnewline
67 & 2.57 & 2.44234140759436 & 0.127658592405638 \tabularnewline
68 & 2.89 & 2.52269917121663 & 0.367300828783367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&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]2.16[/C][C]2.06503848700781[/C][C]0.0949615129921882[/C][/ROW]
[ROW][C]2[/C][C]2.75[/C][C]2.31597345954120[/C][C]0.434026540458797[/C][/ROW]
[ROW][C]3[/C][C]2.79[/C][C]2.90105354224862[/C][C]-0.111053542248617[/C][/ROW]
[ROW][C]4[/C][C]2.88[/C][C]2.79962765857777[/C][C]0.0803723414222256[/C][/ROW]
[ROW][C]5[/C][C]3.36[/C][C]2.79016215663282[/C][C]0.569837843367182[/C][/ROW]
[ROW][C]6[/C][C]2.97[/C][C]3.19807205911749[/C][C]-0.228072059117494[/C][/ROW]
[ROW][C]7[/C][C]3.1[/C][C]2.86918305947392[/C][C]0.230816940526081[/C][/ROW]
[ROW][C]8[/C][C]2.49[/C][C]2.94556036021541[/C][C]-0.455560360215408[/C][/ROW]
[ROW][C]9[/C][C]2.2[/C][C]2.58941499352404[/C][C]-0.389414993524039[/C][/ROW]
[ROW][C]10[/C][C]2.25[/C][C]2.28516663591720[/C][C]-0.0351666359171965[/C][/ROW]
[ROW][C]11[/C][C]2.09[/C][C]2.37239402139617[/C][C]-0.282394021396171[/C][/ROW]
[ROW][C]12[/C][C]2.79[/C][C]2.09315990653526[/C][C]0.696840093464738[/C][/ROW]
[ROW][C]13[/C][C]3.14[/C][C]2.60844957727324[/C][C]0.53155042272676[/C][/ROW]
[ROW][C]14[/C][C]2.93[/C][C]2.9301359892211[/C][C]-0.000135989221098943[/C][/ROW]
[ROW][C]15[/C][C]2.65[/C][C]2.66616080630724[/C][C]-0.0161608063072401[/C][/ROW]
[ROW][C]16[/C][C]2.67[/C][C]2.52316612308501[/C][C]0.146833876914990[/C][/ROW]
[ROW][C]17[/C][C]2.26[/C][C]2.54963522582339[/C][C]-0.289635225823392[/C][/ROW]
[ROW][C]18[/C][C]2.35[/C][C]2.15237868815163[/C][C]0.197621311848368[/C][/ROW]
[ROW][C]19[/C][C]2.13[/C][C]2.24158959693702[/C][C]-0.111589596937017[/C][/ROW]
[ROW][C]20[/C][C]2.18[/C][C]2.03459246149261[/C][C]0.145407538507387[/C][/ROW]
[ROW][C]21[/C][C]2.9[/C][C]2.11438289535798[/C][C]0.785617104642017[/C][/ROW]
[ROW][C]22[/C][C]2.63[/C][C]2.77330380099718[/C][C]-0.143303800997180[/C][/ROW]
[ROW][C]23[/C][C]2.67[/C][C]2.46340591241895[/C][C]0.20659408758105[/C][/ROW]
[ROW][C]24[/C][C]1.81[/C][C]2.46595995862964[/C][C]-0.655959958629642[/C][/ROW]
[ROW][C]25[/C][C]1.33[/C][C]1.83259089366776[/C][C]-0.502590893667762[/C][/ROW]
[ROW][C]26[/C][C]0.88[/C][C]1.54399819366581[/C][C]-0.663998193665813[/C][/ROW]
[ROW][C]27[/C][C]1.28[/C][C]1.18578165461210[/C][C]0.0942183453879027[/C][/ROW]
[ROW][C]28[/C][C]1.26[/C][C]1.46413122144688[/C][C]-0.204131221446880[/C][/ROW]
[ROW][C]29[/C][C]1.26[/C][C]1.33923177239151[/C][C]-0.0792317723915122[/C][/ROW]
[ROW][C]30[/C][C]1.29[/C][C]1.23970909651434[/C][C]0.0502909034856609[/C][/ROW]
[ROW][C]31[/C][C]1.1[/C][C]1.31119508264220[/C][C]-0.211195082642204[/C][/ROW]
[ROW][C]32[/C][C]1.37[/C][C]1.12490944675069[/C][C]0.245090553249308[/C][/ROW]
[ROW][C]33[/C][C]1.21[/C][C]1.40188103312140[/C][C]-0.191881033121398[/C][/ROW]
[ROW][C]34[/C][C]1.74[/C][C]1.31946762541547[/C][C]0.420532374584535[/C][/ROW]
[ROW][C]35[/C][C]1.76[/C][C]1.78712216926081[/C][C]-0.0271221692608111[/C][/ROW]
[ROW][C]36[/C][C]1.48[/C][C]1.87465701969435[/C][C]-0.394657019694346[/C][/ROW]
[ROW][C]37[/C][C]1.04[/C][C]1.55820531189032[/C][C]-0.518205311890321[/C][/ROW]
[ROW][C]38[/C][C]1.62[/C][C]1.31696386643990[/C][C]0.303036133560099[/C][/ROW]
[ROW][C]39[/C][C]1.49[/C][C]1.85499070272643[/C][C]-0.364990702726434[/C][/ROW]
[ROW][C]40[/C][C]1.79[/C][C]1.68405100122787[/C][C]0.105948998772129[/C][/ROW]
[ROW][C]41[/C][C]1.8[/C][C]1.85906044053136[/C][C]-0.059060440531364[/C][/ROW]
[ROW][C]42[/C][C]1.58[/C][C]1.87502700603360[/C][C]-0.295027006033602[/C][/ROW]
[ROW][C]43[/C][C]1.86[/C][C]1.65073117494299[/C][C]0.20926882505701[/C][/ROW]
[ROW][C]44[/C][C]1.74[/C][C]1.86290379360797[/C][C]-0.122903793607965[/C][/ROW]
[ROW][C]45[/C][C]1.59[/C][C]1.83221866500494[/C][C]-0.242218665004945[/C][/ROW]
[ROW][C]46[/C][C]1.26[/C][C]1.70808868319061[/C][C]-0.448088683190613[/C][/ROW]
[ROW][C]47[/C][C]1.13[/C][C]1.48853650265187[/C][C]-0.358536502651873[/C][/ROW]
[ROW][C]48[/C][C]1.92[/C][C]1.39924965519973[/C][C]0.520750344800267[/C][/ROW]
[ROW][C]49[/C][C]2.61[/C][C]2.10335386599478[/C][C]0.506646134005219[/C][/ROW]
[ROW][C]50[/C][C]2.26[/C][C]2.64145828175645[/C][C]-0.381458281756449[/C][/ROW]
[ROW][C]51[/C][C]2.41[/C][C]2.25391657757943[/C][C]0.156083422420573[/C][/ROW]
[ROW][C]52[/C][C]2.26[/C][C]2.41999846398438[/C][C]-0.159998463984383[/C][/ROW]
[ROW][C]53[/C][C]2.03[/C][C]2.34822438045351[/C][C]-0.318224380453514[/C][/ROW]
[ROW][C]54[/C][C]2.86[/C][C]2.05640838525711[/C][C]0.80359161474289[/C][/ROW]
[ROW][C]55[/C][C]2.55[/C][C]2.79495967840951[/C][C]-0.244959678409507[/C][/ROW]
[ROW][C]56[/C][C]2.27[/C][C]2.44933476671669[/C][C]-0.179334766716689[/C][/ROW]
[ROW][C]57[/C][C]2.26[/C][C]2.22210241299163[/C][C]0.0378975870083654[/C][/ROW]
[ROW][C]58[/C][C]2.57[/C][C]2.36397325447955[/C][C]0.206026745520455[/C][/ROW]
[ROW][C]59[/C][C]3.07[/C][C]2.60854139427220[/C][C]0.461458605727804[/C][/ROW]
[ROW][C]60[/C][C]2.76[/C][C]2.92697345994102[/C][C]-0.166973459941018[/C][/ROW]
[ROW][C]61[/C][C]2.51[/C][C]2.62236186416608[/C][C]-0.112361864166084[/C][/ROW]
[ROW][C]62[/C][C]2.87[/C][C]2.56147020937554[/C][C]0.308529790624465[/C][/ROW]
[ROW][C]63[/C][C]3.14[/C][C]2.89809671652618[/C][C]0.241903283473816[/C][/ROW]
[ROW][C]64[/C][C]3.11[/C][C]3.07902553167808[/C][C]0.0309744683219196[/C][/ROW]
[ROW][C]65[/C][C]3.16[/C][C]2.9836860241674[/C][C]0.1763139758326[/C][/ROW]
[ROW][C]66[/C][C]2.47[/C][C]2.99840476492582[/C][C]-0.528404764925823[/C][/ROW]
[ROW][C]67[/C][C]2.57[/C][C]2.44234140759436[/C][C]0.127658592405638[/C][/ROW]
[ROW][C]68[/C][C]2.89[/C][C]2.52269917121663[/C][C]0.367300828783367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105170&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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
12.162.065038487007810.0949615129921882
22.752.315973459541200.434026540458797
32.792.90105354224862-0.111053542248617
42.882.799627658577770.0803723414222256
53.362.790162156632820.569837843367182
62.973.19807205911749-0.228072059117494
73.12.869183059473920.230816940526081
82.492.94556036021541-0.455560360215408
92.22.58941499352404-0.389414993524039
102.252.28516663591720-0.0351666359171965
112.092.37239402139617-0.282394021396171
122.792.093159906535260.696840093464738
133.142.608449577273240.53155042272676
142.932.9301359892211-0.000135989221098943
152.652.66616080630724-0.0161608063072401
162.672.523166123085010.146833876914990
172.262.54963522582339-0.289635225823392
182.352.152378688151630.197621311848368
192.132.24158959693702-0.111589596937017
202.182.034592461492610.145407538507387
212.92.114382895357980.785617104642017
222.632.77330380099718-0.143303800997180
232.672.463405912418950.20659408758105
241.812.46595995862964-0.655959958629642
251.331.83259089366776-0.502590893667762
260.881.54399819366581-0.663998193665813
271.281.185781654612100.0942183453879027
281.261.46413122144688-0.204131221446880
291.261.33923177239151-0.0792317723915122
301.291.239709096514340.0502909034856609
311.11.31119508264220-0.211195082642204
321.371.124909446750690.245090553249308
331.211.40188103312140-0.191881033121398
341.741.319467625415470.420532374584535
351.761.78712216926081-0.0271221692608111
361.481.87465701969435-0.394657019694346
371.041.55820531189032-0.518205311890321
381.621.316963866439900.303036133560099
391.491.85499070272643-0.364990702726434
401.791.684051001227870.105948998772129
411.81.85906044053136-0.059060440531364
421.581.87502700603360-0.295027006033602
431.861.650731174942990.20926882505701
441.741.86290379360797-0.122903793607965
451.591.83221866500494-0.242218665004945
461.261.70808868319061-0.448088683190613
471.131.48853650265187-0.358536502651873
481.921.399249655199730.520750344800267
492.612.103353865994780.506646134005219
502.262.64145828175645-0.381458281756449
512.412.253916577579430.156083422420573
522.262.41999846398438-0.159998463984383
532.032.34822438045351-0.318224380453514
542.862.056408385257110.80359161474289
552.552.79495967840951-0.244959678409507
562.272.44933476671669-0.179334766716689
572.262.222102412991630.0378975870083654
582.572.363973254479550.206026745520455
593.072.608541394272200.461458605727804
602.762.92697345994102-0.166973459941018
612.512.62236186416608-0.112361864166084
622.872.561470209375540.308529790624465
633.142.898096716526180.241903283473816
643.113.079025531678080.0309744683219196
653.162.98368602416740.1763139758326
662.472.99840476492582-0.528404764925823
672.572.442341407594360.127658592405638
682.892.522699171216630.367300828783367






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.2393055153105140.4786110306210280.760694484689486
220.7099959421854390.5800081156291230.290004057814561
230.7457085664721040.5085828670557930.254291433527896
240.9053632943288740.1892734113422510.0946367056711256
250.884329286177430.2313414276451390.115670713822570
260.8249487688095420.3501024623809160.175051231190458
270.7674857984289460.4650284031421070.232514201571054
280.7612791457973940.4774417084052120.238720854202606
290.7416091046775220.5167817906449560.258390895322478
300.651895987598170.6962080248036610.348104012401830
310.5922527420416630.8154945159166740.407747257958337
320.5318495393663520.9363009212672960.468150460633648
330.4882768709290980.9765537418581960.511723129070902
340.5474910604787860.9050178790424280.452508939521214
350.5658145822748510.8683708354502980.434185417725149
360.4858763869455270.9717527738910540.514123613054473
370.4090189493944460.8180378987888920.590981050605554
380.5291527645695110.9416944708609780.470847235430489
390.4818619367273570.9637238734547130.518138063272643
400.4214238839158460.842847767831690.578576116084154
410.3315217175016410.6630434350032820.668478282498359
420.2424260370822590.4848520741645190.75757396291774
430.2389840836087540.4779681672175070.761015916391246
440.1763231907386590.3526463814773190.82367680926134
450.1048748541079230.2097497082158460.895125145892077
460.06589685204630980.1317937040926200.93410314795369
470.1605261656459660.3210523312919310.839473834354034

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.239305515310514 & 0.478611030621028 & 0.760694484689486 \tabularnewline
22 & 0.709995942185439 & 0.580008115629123 & 0.290004057814561 \tabularnewline
23 & 0.745708566472104 & 0.508582867055793 & 0.254291433527896 \tabularnewline
24 & 0.905363294328874 & 0.189273411342251 & 0.0946367056711256 \tabularnewline
25 & 0.88432928617743 & 0.231341427645139 & 0.115670713822570 \tabularnewline
26 & 0.824948768809542 & 0.350102462380916 & 0.175051231190458 \tabularnewline
27 & 0.767485798428946 & 0.465028403142107 & 0.232514201571054 \tabularnewline
28 & 0.761279145797394 & 0.477441708405212 & 0.238720854202606 \tabularnewline
29 & 0.741609104677522 & 0.516781790644956 & 0.258390895322478 \tabularnewline
30 & 0.65189598759817 & 0.696208024803661 & 0.348104012401830 \tabularnewline
31 & 0.592252742041663 & 0.815494515916674 & 0.407747257958337 \tabularnewline
32 & 0.531849539366352 & 0.936300921267296 & 0.468150460633648 \tabularnewline
33 & 0.488276870929098 & 0.976553741858196 & 0.511723129070902 \tabularnewline
34 & 0.547491060478786 & 0.905017879042428 & 0.452508939521214 \tabularnewline
35 & 0.565814582274851 & 0.868370835450298 & 0.434185417725149 \tabularnewline
36 & 0.485876386945527 & 0.971752773891054 & 0.514123613054473 \tabularnewline
37 & 0.409018949394446 & 0.818037898788892 & 0.590981050605554 \tabularnewline
38 & 0.529152764569511 & 0.941694470860978 & 0.470847235430489 \tabularnewline
39 & 0.481861936727357 & 0.963723873454713 & 0.518138063272643 \tabularnewline
40 & 0.421423883915846 & 0.84284776783169 & 0.578576116084154 \tabularnewline
41 & 0.331521717501641 & 0.663043435003282 & 0.668478282498359 \tabularnewline
42 & 0.242426037082259 & 0.484852074164519 & 0.75757396291774 \tabularnewline
43 & 0.238984083608754 & 0.477968167217507 & 0.761015916391246 \tabularnewline
44 & 0.176323190738659 & 0.352646381477319 & 0.82367680926134 \tabularnewline
45 & 0.104874854107923 & 0.209749708215846 & 0.895125145892077 \tabularnewline
46 & 0.0658968520463098 & 0.131793704092620 & 0.93410314795369 \tabularnewline
47 & 0.160526165645966 & 0.321052331291931 & 0.839473834354034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&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]0.239305515310514[/C][C]0.478611030621028[/C][C]0.760694484689486[/C][/ROW]
[ROW][C]22[/C][C]0.709995942185439[/C][C]0.580008115629123[/C][C]0.290004057814561[/C][/ROW]
[ROW][C]23[/C][C]0.745708566472104[/C][C]0.508582867055793[/C][C]0.254291433527896[/C][/ROW]
[ROW][C]24[/C][C]0.905363294328874[/C][C]0.189273411342251[/C][C]0.0946367056711256[/C][/ROW]
[ROW][C]25[/C][C]0.88432928617743[/C][C]0.231341427645139[/C][C]0.115670713822570[/C][/ROW]
[ROW][C]26[/C][C]0.824948768809542[/C][C]0.350102462380916[/C][C]0.175051231190458[/C][/ROW]
[ROW][C]27[/C][C]0.767485798428946[/C][C]0.465028403142107[/C][C]0.232514201571054[/C][/ROW]
[ROW][C]28[/C][C]0.761279145797394[/C][C]0.477441708405212[/C][C]0.238720854202606[/C][/ROW]
[ROW][C]29[/C][C]0.741609104677522[/C][C]0.516781790644956[/C][C]0.258390895322478[/C][/ROW]
[ROW][C]30[/C][C]0.65189598759817[/C][C]0.696208024803661[/C][C]0.348104012401830[/C][/ROW]
[ROW][C]31[/C][C]0.592252742041663[/C][C]0.815494515916674[/C][C]0.407747257958337[/C][/ROW]
[ROW][C]32[/C][C]0.531849539366352[/C][C]0.936300921267296[/C][C]0.468150460633648[/C][/ROW]
[ROW][C]33[/C][C]0.488276870929098[/C][C]0.976553741858196[/C][C]0.511723129070902[/C][/ROW]
[ROW][C]34[/C][C]0.547491060478786[/C][C]0.905017879042428[/C][C]0.452508939521214[/C][/ROW]
[ROW][C]35[/C][C]0.565814582274851[/C][C]0.868370835450298[/C][C]0.434185417725149[/C][/ROW]
[ROW][C]36[/C][C]0.485876386945527[/C][C]0.971752773891054[/C][C]0.514123613054473[/C][/ROW]
[ROW][C]37[/C][C]0.409018949394446[/C][C]0.818037898788892[/C][C]0.590981050605554[/C][/ROW]
[ROW][C]38[/C][C]0.529152764569511[/C][C]0.941694470860978[/C][C]0.470847235430489[/C][/ROW]
[ROW][C]39[/C][C]0.481861936727357[/C][C]0.963723873454713[/C][C]0.518138063272643[/C][/ROW]
[ROW][C]40[/C][C]0.421423883915846[/C][C]0.84284776783169[/C][C]0.578576116084154[/C][/ROW]
[ROW][C]41[/C][C]0.331521717501641[/C][C]0.663043435003282[/C][C]0.668478282498359[/C][/ROW]
[ROW][C]42[/C][C]0.242426037082259[/C][C]0.484852074164519[/C][C]0.75757396291774[/C][/ROW]
[ROW][C]43[/C][C]0.238984083608754[/C][C]0.477968167217507[/C][C]0.761015916391246[/C][/ROW]
[ROW][C]44[/C][C]0.176323190738659[/C][C]0.352646381477319[/C][C]0.82367680926134[/C][/ROW]
[ROW][C]45[/C][C]0.104874854107923[/C][C]0.209749708215846[/C][C]0.895125145892077[/C][/ROW]
[ROW][C]46[/C][C]0.0658968520463098[/C][C]0.131793704092620[/C][C]0.93410314795369[/C][/ROW]
[ROW][C]47[/C][C]0.160526165645966[/C][C]0.321052331291931[/C][C]0.839473834354034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105170&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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
210.2393055153105140.4786110306210280.760694484689486
220.7099959421854390.5800081156291230.290004057814561
230.7457085664721040.5085828670557930.254291433527896
240.9053632943288740.1892734113422510.0946367056711256
250.884329286177430.2313414276451390.115670713822570
260.8249487688095420.3501024623809160.175051231190458
270.7674857984289460.4650284031421070.232514201571054
280.7612791457973940.4774417084052120.238720854202606
290.7416091046775220.5167817906449560.258390895322478
300.651895987598170.6962080248036610.348104012401830
310.5922527420416630.8154945159166740.407747257958337
320.5318495393663520.9363009212672960.468150460633648
330.4882768709290980.9765537418581960.511723129070902
340.5474910604787860.9050178790424280.452508939521214
350.5658145822748510.8683708354502980.434185417725149
360.4858763869455270.9717527738910540.514123613054473
370.4090189493944460.8180378987888920.590981050605554
380.5291527645695110.9416944708609780.470847235430489
390.4818619367273570.9637238734547130.518138063272643
400.4214238839158460.842847767831690.578576116084154
410.3315217175016410.6630434350032820.668478282498359
420.2424260370822590.4848520741645190.75757396291774
430.2389840836087540.4779681672175070.761015916391246
440.1763231907386590.3526463814773190.82367680926134
450.1048748541079230.2097497082158460.895125145892077
460.06589685204630980.1317937040926200.93410314795369
470.1605261656459660.3210523312919310.839473834354034






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\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 & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105170&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105170&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105170&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 level00OK
5% type I error level00OK
10% type I error level00OK


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')
}