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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSun, 20 Dec 2009 06:25:49 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/20/t126131760022cbjtuc84wdhx7.htm/, Retrieved Sat, 27 Apr 2024 12:25:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69886, Retrieved Sat, 27 Apr 2024 12:25:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

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] [Multiple regressi...] [2009-11-17 17:36:08] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-    D        [Multiple Regression] [Multiple Regressi...] [2009-12-20 13:25:49] [8cd69d0f4298074aa572ca2f9b39b6ae] [Current]
-    D          [Multiple Regression] [Multiple Regressi...] [2009-12-20 14:49:21] [73863f7f907331e734eff34b7de6fc83]
-    D          [Multiple Regression] [Multiple Regressi...] [2009-12-20 15:10:27] [73863f7f907331e734eff34b7de6fc83]
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Dataset

Dataseries X:
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Histogram
Boxplots 
-1,2	23,6	-1,5	-0,1	0,8	-2,4	-1,2
-2,4	25,7	-4,4	-1,5	-0,1	0,8	-2,4
0,8	32,5	-4,2	-4,4	-1,5	-0,1	0,8
-0,1	33,5	3,5	-4,2	-4,4	-1,5	-0,1
-1,5	34,5	10	3,5	-4,2	-4,4	-1,5
-4,4	27,9	8,6	10	3,5	-4,2	-4,4
-4,2	45,3	9,5	8,6	10	3,5	-4,2
3,5	40,8	9,9	9,5	8,6	10	3,5
10	58,5	10,4	9,9	9,5	8,6	10
8,6	32,5	16	10,4	9,9	9,5	8,6
9,5	35,5	12,7	16	10,4	9,9	9,5
9,9	46,7	10,2	12,7	16	10,4	9,9
10,4	53,2	8,9	10,2	12,7	16	10,4
16	36,1	12,6	8,9	10,2	12,7	16
12,7	54	13,6	12,6	8,9	10,2	12,7
10,2	58,1	14,8	13,6	12,6	8,9	10,2
8,9	41,8	9,5	14,8	13,6	12,6	8,9
12,6	43,1	13,7	9,5	14,8	13,6	12,6
13,6	76	17	13,7	9,5	14,8	13,6
14,8	42,8	14,7	17	13,7	9,5	14,8
9,5	41	17,4	14,7	17	13,7	9,5
13,7	61,4	9	17,4	14,7	17	13,7
17	34,2	9,1	9	17,4	14,7	17
14,7	53,8	12,2	9,1	9	17,4	14,7
17,4	80,7	15,9	12,2	9,1	9	17,4
9	79,5	12,9	15,9	12,2	9,1	9
9,1	96,5	10,9	12,9	15,9	12,2	9,1
12,2	108,3	10,6	10,9	12,9	15,9	12,2
15,9	100,1	13,2	10,6	10,9	12,9	15,9
12,9	108,5	9,6	13,2	10,6	10,9	12,9
10,9	127,4	6,4	9,6	13,2	10,6	10,9
10,6	86,5	5,8	6,4	9,6	13,2	10,6
13,2	71,4	-1	5,8	6,4	9,6	13,2
9,6	88,2	-0,2	-1	5,8	6,4	9,6
6,4	135,6	2,7	-0,2	-1	5,8	6,4
5,8	70,5	3,6	2,7	-0,2	-1	5,8
-1	87,5	-0,9	3,6	2,7	-0,2	-1
-0,2	73,3	0,3	-0,9	3,6	2,7	-0,2
2,7	92,2	-1,1	0,3	-0,9	3,6	2,7
3,6	61,1	-2,5	-1,1	0,3	-0,9	3,6
-0,9	45,7	-3,4	-2,5	-1,1	0,3	-0,9
0,3	30,5	-3,5	-3,4	-2,5	-1,1	0,3
-1,1	34,8	-3,9	-3,5	-3,4	-2,5	-1,1
-2,5	29,2	-4,6	-3,9	-3,5	-3,4	-2,5
-3,4	56,7	-0,1	-4,6	-3,9	-3,5	-3,4
-3,5	67,1	4,3	-0,1	-4,6	-3,9	-3,5
-3,9	41,8	10,2	4,3	-0,1	-4,6	-3,9
-4,6	46,8	8,7	10,2	4,3	-0,1	-4,6
-0,1	50,1	13,3	8,7	10,2	4,3	-0,1
4,3	81,9	15	13,3	8,7	10,2	4,3
10,2	115,8	20,7	15	13,3	8,7	10,2
8,7	102,5	20,7	20,7	15	13,3	8,7
13,3	106,6	26,4	20,7	20,7	15	13,3
15	101,4	31,2	26,4	20,7	20,7	15
20,7	136,1	31,4	31,2	26,4	20,7	20,7
20,7	143,4	26,6	31,4	31,2	26,4	20,7
26,4	127,5	26,6	26,6	31,4	31,2	26,4
31,2	113,8	19,2	26,6	26,6	31,4	31,2
31,4	75,3	6,5	19,2	26,6	26,6	31,4
26,6	98,5	3,1	6,5	19,2	26,6	26,6
26,6	113,7	-0,2	3,1	6,5	19,2	26,6
19,2	103,7	-4	-0,2	3,1	6,5	19,2
6,5	73,9	-12,6	-4	-0,2	3,1	6,5
3,1	52,5	-13	-12,6	-4	-0,2	3,1
-0,2	63,9	-17,6	-13	-12,6	-4	-0,2
-4	44,9	-21,7	-17,6	-13	-12,6	-4
-12,6	31,3	-23,2	-21,7	-17,6	-13	-12,6
-13	24,9	-16,8	-23,2	-21,7	-17,6	-13

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&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]4 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=69886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = -6.7410055781125e-16 -5.51997139784975e-18X[t] + 1.64466097895753e-16Y1[t] -1.02908788633393e-16Y2[t] + 5.91709644638093e-17Y3[t] -6.48383136321993e-16Y4[t] + 1Y5[t] + 5.08900110588273e-16M1[t] + 6.13641105722188e-16M2[t] -1.92254299500813e-16M3[t] + 4.23698049502417e-16M4[t] -3.73445448798915e-16M5[t] + 5.18109028675700e-16M6[t] -2.91285122320073e-15M7[t] + 1.62774370167809e-16M8[t] + 3.05260597135593e-16M9[t] -9.53294474458686e-17M10[t] -1.79618245866484e-16M11[t] + 1.44954276012951e-17t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -6.7410055781125e-16 -5.51997139784975e-18X[t] +  1.64466097895753e-16Y1[t] -1.02908788633393e-16Y2[t] +  5.91709644638093e-17Y3[t] -6.48383136321993e-16Y4[t] +  1Y5[t] +  5.08900110588273e-16M1[t] +  6.13641105722188e-16M2[t] -1.92254299500813e-16M3[t] +  4.23698049502417e-16M4[t] -3.73445448798915e-16M5[t] +  5.18109028675700e-16M6[t] -2.91285122320073e-15M7[t] +  1.62774370167809e-16M8[t] +  3.05260597135593e-16M9[t] -9.53294474458686e-17M10[t] -1.79618245866484e-16M11[t] +  1.44954276012951e-17t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -6.7410055781125e-16 -5.51997139784975e-18X[t] +  1.64466097895753e-16Y1[t] -1.02908788633393e-16Y2[t] +  5.91709644638093e-17Y3[t] -6.48383136321993e-16Y4[t] +  1Y5[t] +  5.08900110588273e-16M1[t] +  6.13641105722188e-16M2[t] -1.92254299500813e-16M3[t] +  4.23698049502417e-16M4[t] -3.73445448798915e-16M5[t] +  5.18109028675700e-16M6[t] -2.91285122320073e-15M7[t] +  1.62774370167809e-16M8[t] +  3.05260597135593e-16M9[t] -9.53294474458686e-17M10[t] -1.79618245866484e-16M11[t] +  1.44954276012951e-17t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&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] = -6.7410055781125e-16 -5.51997139784975e-18X[t] + 1.64466097895753e-16Y1[t] -1.02908788633393e-16Y2[t] + 5.91709644638093e-17Y3[t] -6.48383136321993e-16Y4[t] + 1Y5[t] + 5.08900110588273e-16M1[t] + 6.13641105722188e-16M2[t] -1.92254299500813e-16M3[t] + 4.23698049502417e-16M4[t] -3.73445448798915e-16M5[t] + 5.18109028675700e-16M6[t] -2.91285122320073e-15M7[t] + 1.62774370167809e-16M8[t] + 3.05260597135593e-16M9[t] -9.53294474458686e-17M10[t] -1.79618245866484e-16M11[t] + 1.44954276012951e-17t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-6.7410055781125e-160-0.51950.6057670.302883
X-5.51997139784975e-180-0.36720.7150860.357543
Y11.64466097895753e-1601.99460.0516660.025833
Y2-1.02908788633393e-160-0.79890.4282310.214116
Y35.91709644638093e-1700.45120.6538020.326901
Y4-6.48383136321993e-160-4.99758e-064e-06
Y5101116840776074454600
M15.08900110588273e-1600.33720.7373730.368687
M26.13641105722188e-1600.40720.6856420.342821
M3-1.92254299500813e-160-0.12480.9012090.450604
M44.23698049502417e-1600.27920.7812730.390637
M5-3.73445448798915e-160-0.24640.8064140.403207
M65.18109028675700e-1600.34160.734090.367045
M7-2.91285122320073e-150-1.89530.0639610.03198
M81.62774370167809e-1600.10840.9141040.457052
M93.05260597135593e-1600.19530.8459970.422999
M10-9.53294474458686e-170-0.06090.9516860.475843
M11-1.79618245866484e-160-0.11450.909270.454635
t1.44954276012951e-1700.71280.4793710.239686

\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) & -6.7410055781125e-16 & 0 & -0.5195 & 0.605767 & 0.302883 \tabularnewline
X & -5.51997139784975e-18 & 0 & -0.3672 & 0.715086 & 0.357543 \tabularnewline
Y1 & 1.64466097895753e-16 & 0 & 1.9946 & 0.051666 & 0.025833 \tabularnewline
Y2 & -1.02908788633393e-16 & 0 & -0.7989 & 0.428231 & 0.214116 \tabularnewline
Y3 & 5.91709644638093e-17 & 0 & 0.4512 & 0.653802 & 0.326901 \tabularnewline
Y4 & -6.48383136321993e-16 & 0 & -4.9975 & 8e-06 & 4e-06 \tabularnewline
Y5 & 1 & 0 & 11168407760744546 & 0 & 0 \tabularnewline
M1 & 5.08900110588273e-16 & 0 & 0.3372 & 0.737373 & 0.368687 \tabularnewline
M2 & 6.13641105722188e-16 & 0 & 0.4072 & 0.685642 & 0.342821 \tabularnewline
M3 & -1.92254299500813e-16 & 0 & -0.1248 & 0.901209 & 0.450604 \tabularnewline
M4 & 4.23698049502417e-16 & 0 & 0.2792 & 0.781273 & 0.390637 \tabularnewline
M5 & -3.73445448798915e-16 & 0 & -0.2464 & 0.806414 & 0.403207 \tabularnewline
M6 & 5.18109028675700e-16 & 0 & 0.3416 & 0.73409 & 0.367045 \tabularnewline
M7 & -2.91285122320073e-15 & 0 & -1.8953 & 0.063961 & 0.03198 \tabularnewline
M8 & 1.62774370167809e-16 & 0 & 0.1084 & 0.914104 & 0.457052 \tabularnewline
M9 & 3.05260597135593e-16 & 0 & 0.1953 & 0.845997 & 0.422999 \tabularnewline
M10 & -9.53294474458686e-17 & 0 & -0.0609 & 0.951686 & 0.475843 \tabularnewline
M11 & -1.79618245866484e-16 & 0 & -0.1145 & 0.90927 & 0.454635 \tabularnewline
t & 1.44954276012951e-17 & 0 & 0.7128 & 0.479371 & 0.239686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&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]-6.7410055781125e-16[/C][C]0[/C][C]-0.5195[/C][C]0.605767[/C][C]0.302883[/C][/ROW]
[ROW][C]X[/C][C]-5.51997139784975e-18[/C][C]0[/C][C]-0.3672[/C][C]0.715086[/C][C]0.357543[/C][/ROW]
[ROW][C]Y1[/C][C]1.64466097895753e-16[/C][C]0[/C][C]1.9946[/C][C]0.051666[/C][C]0.025833[/C][/ROW]
[ROW][C]Y2[/C][C]-1.02908788633393e-16[/C][C]0[/C][C]-0.7989[/C][C]0.428231[/C][C]0.214116[/C][/ROW]
[ROW][C]Y3[/C][C]5.91709644638093e-17[/C][C]0[/C][C]0.4512[/C][C]0.653802[/C][C]0.326901[/C][/ROW]
[ROW][C]Y4[/C][C]-6.48383136321993e-16[/C][C]0[/C][C]-4.9975[/C][C]8e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]Y5[/C][C]1[/C][C]0[/C][C]11168407760744546[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]5.08900110588273e-16[/C][C]0[/C][C]0.3372[/C][C]0.737373[/C][C]0.368687[/C][/ROW]
[ROW][C]M2[/C][C]6.13641105722188e-16[/C][C]0[/C][C]0.4072[/C][C]0.685642[/C][C]0.342821[/C][/ROW]
[ROW][C]M3[/C][C]-1.92254299500813e-16[/C][C]0[/C][C]-0.1248[/C][C]0.901209[/C][C]0.450604[/C][/ROW]
[ROW][C]M4[/C][C]4.23698049502417e-16[/C][C]0[/C][C]0.2792[/C][C]0.781273[/C][C]0.390637[/C][/ROW]
[ROW][C]M5[/C][C]-3.73445448798915e-16[/C][C]0[/C][C]-0.2464[/C][C]0.806414[/C][C]0.403207[/C][/ROW]
[ROW][C]M6[/C][C]5.18109028675700e-16[/C][C]0[/C][C]0.3416[/C][C]0.73409[/C][C]0.367045[/C][/ROW]
[ROW][C]M7[/C][C]-2.91285122320073e-15[/C][C]0[/C][C]-1.8953[/C][C]0.063961[/C][C]0.03198[/C][/ROW]
[ROW][C]M8[/C][C]1.62774370167809e-16[/C][C]0[/C][C]0.1084[/C][C]0.914104[/C][C]0.457052[/C][/ROW]
[ROW][C]M9[/C][C]3.05260597135593e-16[/C][C]0[/C][C]0.1953[/C][C]0.845997[/C][C]0.422999[/C][/ROW]
[ROW][C]M10[/C][C]-9.53294474458686e-17[/C][C]0[/C][C]-0.0609[/C][C]0.951686[/C][C]0.475843[/C][/ROW]
[ROW][C]M11[/C][C]-1.79618245866484e-16[/C][C]0[/C][C]-0.1145[/C][C]0.90927[/C][C]0.454635[/C][/ROW]
[ROW][C]t[/C][C]1.44954276012951e-17[/C][C]0[/C][C]0.7128[/C][C]0.479371[/C][C]0.239686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69886&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&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)-6.7410055781125e-160-0.51950.6057670.302883
X-5.51997139784975e-180-0.36720.7150860.357543
Y11.64466097895753e-1601.99460.0516660.025833
Y2-1.02908788633393e-160-0.79890.4282310.214116
Y35.91709644638093e-1700.45120.6538020.326901
Y4-6.48383136321993e-160-4.99758e-064e-06
Y5101116840776074454600
M15.08900110588273e-1600.33720.7373730.368687
M26.13641105722188e-1600.40720.6856420.342821
M3-1.92254299500813e-160-0.12480.9012090.450604
M44.23698049502417e-1600.27920.7812730.390637
M5-3.73445448798915e-160-0.24640.8064140.403207
M65.18109028675700e-1600.34160.734090.367045
M7-2.91285122320073e-150-1.89530.0639610.03198
M81.62774370167809e-1600.10840.9141040.457052
M93.05260597135593e-1600.19530.8459970.422999
M10-9.53294474458686e-170-0.06090.9516860.475843
M11-1.79618245866484e-160-0.11450.909270.454635
t1.44954276012951e-1700.71280.4793710.239686






Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)5.75706249266541e+31
F-TEST (DF numerator)18
F-TEST (DF denominator)49
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.45680206245715e-15
Sum Squared Residuals2.95757942330591e-28

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 1 \tabularnewline
R-squared & 1 \tabularnewline
Adjusted R-squared & 1 \tabularnewline
F-TEST (value) & 5.75706249266541e+31 \tabularnewline
F-TEST (DF numerator) & 18 \tabularnewline
F-TEST (DF denominator) & 49 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.45680206245715e-15 \tabularnewline
Sum Squared Residuals & 2.95757942330591e-28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]1[/C][/ROW]
[ROW][C]R-squared[/C][C]1[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]5.75706249266541e+31[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]18[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]49[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.45680206245715e-15[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.95757942330591e-28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69886&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)5.75706249266541e+31
F-TEST (DF numerator)18
F-TEST (DF denominator)49
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.45680206245715e-15
Sum Squared Residuals2.95757942330591e-28






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1-1.2-1.200000000000001.8304966328995e-15
2-2.4-2.41.95063474786787e-15
30.80.8-4.88781045850116e-16
4-0.1-0.1000000000000016.49831818578219e-16
5-1.5-1.50000000000000-1.59176103319823e-15
6-4.4-4.43.0853539815945e-15
7-4.2-4.19999999999999-1.43370677776675e-14
83.53.57.58261115252052e-16
910104.61550733010356e-17
108.68.66.8438722597674e-16
119.59.5-9.29611414495739e-17
129.99.91.13643955481513e-15
1310.410.48.55800401417946e-16
141616-5.70197197942546e-16
1512.712.7-9.7400482169366e-17
1610.210.21.64422924547185e-17
178.98.91.11660543620842e-15
1812.612.64.80550877191365e-16
1913.613.62.55667123881589e-15
2014.814.8-9.8321044135619e-16
219.59.57.73771102857058e-16
2213.713.72.66370871789208e-16
2317179.77997771997552e-16
2414.714.7-1.8551974684157e-16
2517.417.4-9.81567522463475e-16
2699-6.53270521720141e-16
279.19.11.16067965488100e-15
2812.212.23.41672287054848e-16
2915.915.9-1.02977603013466e-16
3012.912.9-9.87337603058453e-16
3110.910.93.65640360742578e-15
3210.610.64.85520556284682e-16
3313.213.2-7.29099146388262e-16
349.69.63.57293433026125e-16
356.46.4-2.84404972837730e-16
365.85.8-8.79770346414387e-16
37-1-16.78214774078345e-17
38-0.2-0.2000000000000019.82113012800742e-16
392.72.7-2.24997932450973e-16
403.63.6-5.13089664517223e-16
41-0.9-0.96.84793660245499e-16
420.30.300000000000001-5.309716353361e-16
43-1.1-1.100000000000002.85789140612151e-15
44-2.5-2.5-8.88536752333538e-17
45-3.4-3.41.24754287261528e-17
46-3.5-3.5-1.84245569126804e-16
47-3.9-3.92.14877584449574e-16
48-4.6-4.6-1.41226576552465e-16
49-0.1-0.1000000000000004.42922370695556e-16
504.34.3-3.42074210981781e-16
5110.210.29.5084701948019e-17
528.78.7-1.17553837503853e-16
5313.313.37.0064584577974e-16
541515-1.05294677715092e-15
5520.720.72.45763880883434e-15
5620.720.73.79748886020396e-16
5726.426.4-1.03302458495984e-16
5831.231.2-1.12380596166527e-15
5931.431.4-8.15509242159822e-16
6026.626.67.00771149932925e-17
6126.626.6-2.21547335995736e-15
6219.219.2-1.36720583002414e-15
636.56.5-4.44584896358559e-16
643.13.1-3.77302896066711e-16
65-0.2-0.199999999999999-8.07306306021965e-16
66-4-4-9.94648843240393e-16
67-12.6-12.62.80846271647001e-15
68-13-13-5.5146644096759e-16

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -1.2 & -1.20000000000000 & 1.8304966328995e-15 \tabularnewline
2 & -2.4 & -2.4 & 1.95063474786787e-15 \tabularnewline
3 & 0.8 & 0.8 & -4.88781045850116e-16 \tabularnewline
4 & -0.1 & -0.100000000000001 & 6.49831818578219e-16 \tabularnewline
5 & -1.5 & -1.50000000000000 & -1.59176103319823e-15 \tabularnewline
6 & -4.4 & -4.4 & 3.0853539815945e-15 \tabularnewline
7 & -4.2 & -4.19999999999999 & -1.43370677776675e-14 \tabularnewline
8 & 3.5 & 3.5 & 7.58261115252052e-16 \tabularnewline
9 & 10 & 10 & 4.61550733010356e-17 \tabularnewline
10 & 8.6 & 8.6 & 6.8438722597674e-16 \tabularnewline
11 & 9.5 & 9.5 & -9.29611414495739e-17 \tabularnewline
12 & 9.9 & 9.9 & 1.13643955481513e-15 \tabularnewline
13 & 10.4 & 10.4 & 8.55800401417946e-16 \tabularnewline
14 & 16 & 16 & -5.70197197942546e-16 \tabularnewline
15 & 12.7 & 12.7 & -9.7400482169366e-17 \tabularnewline
16 & 10.2 & 10.2 & 1.64422924547185e-17 \tabularnewline
17 & 8.9 & 8.9 & 1.11660543620842e-15 \tabularnewline
18 & 12.6 & 12.6 & 4.80550877191365e-16 \tabularnewline
19 & 13.6 & 13.6 & 2.55667123881589e-15 \tabularnewline
20 & 14.8 & 14.8 & -9.8321044135619e-16 \tabularnewline
21 & 9.5 & 9.5 & 7.73771102857058e-16 \tabularnewline
22 & 13.7 & 13.7 & 2.66370871789208e-16 \tabularnewline
23 & 17 & 17 & 9.77997771997552e-16 \tabularnewline
24 & 14.7 & 14.7 & -1.8551974684157e-16 \tabularnewline
25 & 17.4 & 17.4 & -9.81567522463475e-16 \tabularnewline
26 & 9 & 9 & -6.53270521720141e-16 \tabularnewline
27 & 9.1 & 9.1 & 1.16067965488100e-15 \tabularnewline
28 & 12.2 & 12.2 & 3.41672287054848e-16 \tabularnewline
29 & 15.9 & 15.9 & -1.02977603013466e-16 \tabularnewline
30 & 12.9 & 12.9 & -9.87337603058453e-16 \tabularnewline
31 & 10.9 & 10.9 & 3.65640360742578e-15 \tabularnewline
32 & 10.6 & 10.6 & 4.85520556284682e-16 \tabularnewline
33 & 13.2 & 13.2 & -7.29099146388262e-16 \tabularnewline
34 & 9.6 & 9.6 & 3.57293433026125e-16 \tabularnewline
35 & 6.4 & 6.4 & -2.84404972837730e-16 \tabularnewline
36 & 5.8 & 5.8 & -8.79770346414387e-16 \tabularnewline
37 & -1 & -1 & 6.78214774078345e-17 \tabularnewline
38 & -0.2 & -0.200000000000001 & 9.82113012800742e-16 \tabularnewline
39 & 2.7 & 2.7 & -2.24997932450973e-16 \tabularnewline
40 & 3.6 & 3.6 & -5.13089664517223e-16 \tabularnewline
41 & -0.9 & -0.9 & 6.84793660245499e-16 \tabularnewline
42 & 0.3 & 0.300000000000001 & -5.309716353361e-16 \tabularnewline
43 & -1.1 & -1.10000000000000 & 2.85789140612151e-15 \tabularnewline
44 & -2.5 & -2.5 & -8.88536752333538e-17 \tabularnewline
45 & -3.4 & -3.4 & 1.24754287261528e-17 \tabularnewline
46 & -3.5 & -3.5 & -1.84245569126804e-16 \tabularnewline
47 & -3.9 & -3.9 & 2.14877584449574e-16 \tabularnewline
48 & -4.6 & -4.6 & -1.41226576552465e-16 \tabularnewline
49 & -0.1 & -0.100000000000000 & 4.42922370695556e-16 \tabularnewline
50 & 4.3 & 4.3 & -3.42074210981781e-16 \tabularnewline
51 & 10.2 & 10.2 & 9.5084701948019e-17 \tabularnewline
52 & 8.7 & 8.7 & -1.17553837503853e-16 \tabularnewline
53 & 13.3 & 13.3 & 7.0064584577974e-16 \tabularnewline
54 & 15 & 15 & -1.05294677715092e-15 \tabularnewline
55 & 20.7 & 20.7 & 2.45763880883434e-15 \tabularnewline
56 & 20.7 & 20.7 & 3.79748886020396e-16 \tabularnewline
57 & 26.4 & 26.4 & -1.03302458495984e-16 \tabularnewline
58 & 31.2 & 31.2 & -1.12380596166527e-15 \tabularnewline
59 & 31.4 & 31.4 & -8.15509242159822e-16 \tabularnewline
60 & 26.6 & 26.6 & 7.00771149932925e-17 \tabularnewline
61 & 26.6 & 26.6 & -2.21547335995736e-15 \tabularnewline
62 & 19.2 & 19.2 & -1.36720583002414e-15 \tabularnewline
63 & 6.5 & 6.5 & -4.44584896358559e-16 \tabularnewline
64 & 3.1 & 3.1 & -3.77302896066711e-16 \tabularnewline
65 & -0.2 & -0.199999999999999 & -8.07306306021965e-16 \tabularnewline
66 & -4 & -4 & -9.94648843240393e-16 \tabularnewline
67 & -12.6 & -12.6 & 2.80846271647001e-15 \tabularnewline
68 & -13 & -13 & -5.5146644096759e-16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&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]-1.2[/C][C]-1.20000000000000[/C][C]1.8304966328995e-15[/C][/ROW]
[ROW][C]2[/C][C]-2.4[/C][C]-2.4[/C][C]1.95063474786787e-15[/C][/ROW]
[ROW][C]3[/C][C]0.8[/C][C]0.8[/C][C]-4.88781045850116e-16[/C][/ROW]
[ROW][C]4[/C][C]-0.1[/C][C]-0.100000000000001[/C][C]6.49831818578219e-16[/C][/ROW]
[ROW][C]5[/C][C]-1.5[/C][C]-1.50000000000000[/C][C]-1.59176103319823e-15[/C][/ROW]
[ROW][C]6[/C][C]-4.4[/C][C]-4.4[/C][C]3.0853539815945e-15[/C][/ROW]
[ROW][C]7[/C][C]-4.2[/C][C]-4.19999999999999[/C][C]-1.43370677776675e-14[/C][/ROW]
[ROW][C]8[/C][C]3.5[/C][C]3.5[/C][C]7.58261115252052e-16[/C][/ROW]
[ROW][C]9[/C][C]10[/C][C]10[/C][C]4.61550733010356e-17[/C][/ROW]
[ROW][C]10[/C][C]8.6[/C][C]8.6[/C][C]6.8438722597674e-16[/C][/ROW]
[ROW][C]11[/C][C]9.5[/C][C]9.5[/C][C]-9.29611414495739e-17[/C][/ROW]
[ROW][C]12[/C][C]9.9[/C][C]9.9[/C][C]1.13643955481513e-15[/C][/ROW]
[ROW][C]13[/C][C]10.4[/C][C]10.4[/C][C]8.55800401417946e-16[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]16[/C][C]-5.70197197942546e-16[/C][/ROW]
[ROW][C]15[/C][C]12.7[/C][C]12.7[/C][C]-9.7400482169366e-17[/C][/ROW]
[ROW][C]16[/C][C]10.2[/C][C]10.2[/C][C]1.64422924547185e-17[/C][/ROW]
[ROW][C]17[/C][C]8.9[/C][C]8.9[/C][C]1.11660543620842e-15[/C][/ROW]
[ROW][C]18[/C][C]12.6[/C][C]12.6[/C][C]4.80550877191365e-16[/C][/ROW]
[ROW][C]19[/C][C]13.6[/C][C]13.6[/C][C]2.55667123881589e-15[/C][/ROW]
[ROW][C]20[/C][C]14.8[/C][C]14.8[/C][C]-9.8321044135619e-16[/C][/ROW]
[ROW][C]21[/C][C]9.5[/C][C]9.5[/C][C]7.73771102857058e-16[/C][/ROW]
[ROW][C]22[/C][C]13.7[/C][C]13.7[/C][C]2.66370871789208e-16[/C][/ROW]
[ROW][C]23[/C][C]17[/C][C]17[/C][C]9.77997771997552e-16[/C][/ROW]
[ROW][C]24[/C][C]14.7[/C][C]14.7[/C][C]-1.8551974684157e-16[/C][/ROW]
[ROW][C]25[/C][C]17.4[/C][C]17.4[/C][C]-9.81567522463475e-16[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]9[/C][C]-6.53270521720141e-16[/C][/ROW]
[ROW][C]27[/C][C]9.1[/C][C]9.1[/C][C]1.16067965488100e-15[/C][/ROW]
[ROW][C]28[/C][C]12.2[/C][C]12.2[/C][C]3.41672287054848e-16[/C][/ROW]
[ROW][C]29[/C][C]15.9[/C][C]15.9[/C][C]-1.02977603013466e-16[/C][/ROW]
[ROW][C]30[/C][C]12.9[/C][C]12.9[/C][C]-9.87337603058453e-16[/C][/ROW]
[ROW][C]31[/C][C]10.9[/C][C]10.9[/C][C]3.65640360742578e-15[/C][/ROW]
[ROW][C]32[/C][C]10.6[/C][C]10.6[/C][C]4.85520556284682e-16[/C][/ROW]
[ROW][C]33[/C][C]13.2[/C][C]13.2[/C][C]-7.29099146388262e-16[/C][/ROW]
[ROW][C]34[/C][C]9.6[/C][C]9.6[/C][C]3.57293433026125e-16[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]6.4[/C][C]-2.84404972837730e-16[/C][/ROW]
[ROW][C]36[/C][C]5.8[/C][C]5.8[/C][C]-8.79770346414387e-16[/C][/ROW]
[ROW][C]37[/C][C]-1[/C][C]-1[/C][C]6.78214774078345e-17[/C][/ROW]
[ROW][C]38[/C][C]-0.2[/C][C]-0.200000000000001[/C][C]9.82113012800742e-16[/C][/ROW]
[ROW][C]39[/C][C]2.7[/C][C]2.7[/C][C]-2.24997932450973e-16[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]3.6[/C][C]-5.13089664517223e-16[/C][/ROW]
[ROW][C]41[/C][C]-0.9[/C][C]-0.9[/C][C]6.84793660245499e-16[/C][/ROW]
[ROW][C]42[/C][C]0.3[/C][C]0.300000000000001[/C][C]-5.309716353361e-16[/C][/ROW]
[ROW][C]43[/C][C]-1.1[/C][C]-1.10000000000000[/C][C]2.85789140612151e-15[/C][/ROW]
[ROW][C]44[/C][C]-2.5[/C][C]-2.5[/C][C]-8.88536752333538e-17[/C][/ROW]
[ROW][C]45[/C][C]-3.4[/C][C]-3.4[/C][C]1.24754287261528e-17[/C][/ROW]
[ROW][C]46[/C][C]-3.5[/C][C]-3.5[/C][C]-1.84245569126804e-16[/C][/ROW]
[ROW][C]47[/C][C]-3.9[/C][C]-3.9[/C][C]2.14877584449574e-16[/C][/ROW]
[ROW][C]48[/C][C]-4.6[/C][C]-4.6[/C][C]-1.41226576552465e-16[/C][/ROW]
[ROW][C]49[/C][C]-0.1[/C][C]-0.100000000000000[/C][C]4.42922370695556e-16[/C][/ROW]
[ROW][C]50[/C][C]4.3[/C][C]4.3[/C][C]-3.42074210981781e-16[/C][/ROW]
[ROW][C]51[/C][C]10.2[/C][C]10.2[/C][C]9.5084701948019e-17[/C][/ROW]
[ROW][C]52[/C][C]8.7[/C][C]8.7[/C][C]-1.17553837503853e-16[/C][/ROW]
[ROW][C]53[/C][C]13.3[/C][C]13.3[/C][C]7.0064584577974e-16[/C][/ROW]
[ROW][C]54[/C][C]15[/C][C]15[/C][C]-1.05294677715092e-15[/C][/ROW]
[ROW][C]55[/C][C]20.7[/C][C]20.7[/C][C]2.45763880883434e-15[/C][/ROW]
[ROW][C]56[/C][C]20.7[/C][C]20.7[/C][C]3.79748886020396e-16[/C][/ROW]
[ROW][C]57[/C][C]26.4[/C][C]26.4[/C][C]-1.03302458495984e-16[/C][/ROW]
[ROW][C]58[/C][C]31.2[/C][C]31.2[/C][C]-1.12380596166527e-15[/C][/ROW]
[ROW][C]59[/C][C]31.4[/C][C]31.4[/C][C]-8.15509242159822e-16[/C][/ROW]
[ROW][C]60[/C][C]26.6[/C][C]26.6[/C][C]7.00771149932925e-17[/C][/ROW]
[ROW][C]61[/C][C]26.6[/C][C]26.6[/C][C]-2.21547335995736e-15[/C][/ROW]
[ROW][C]62[/C][C]19.2[/C][C]19.2[/C][C]-1.36720583002414e-15[/C][/ROW]
[ROW][C]63[/C][C]6.5[/C][C]6.5[/C][C]-4.44584896358559e-16[/C][/ROW]
[ROW][C]64[/C][C]3.1[/C][C]3.1[/C][C]-3.77302896066711e-16[/C][/ROW]
[ROW][C]65[/C][C]-0.2[/C][C]-0.199999999999999[/C][C]-8.07306306021965e-16[/C][/ROW]
[ROW][C]66[/C][C]-4[/C][C]-4[/C][C]-9.94648843240393e-16[/C][/ROW]
[ROW][C]67[/C][C]-12.6[/C][C]-12.6[/C][C]2.80846271647001e-15[/C][/ROW]
[ROW][C]68[/C][C]-13[/C][C]-13[/C][C]-5.5146644096759e-16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69886&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&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
1-1.2-1.200000000000001.8304966328995e-15
2-2.4-2.41.95063474786787e-15
30.80.8-4.88781045850116e-16
4-0.1-0.1000000000000016.49831818578219e-16
5-1.5-1.50000000000000-1.59176103319823e-15
6-4.4-4.43.0853539815945e-15
7-4.2-4.19999999999999-1.43370677776675e-14
83.53.57.58261115252052e-16
910104.61550733010356e-17
108.68.66.8438722597674e-16
119.59.5-9.29611414495739e-17
129.99.91.13643955481513e-15
1310.410.48.55800401417946e-16
141616-5.70197197942546e-16
1512.712.7-9.7400482169366e-17
1610.210.21.64422924547185e-17
178.98.91.11660543620842e-15
1812.612.64.80550877191365e-16
1913.613.62.55667123881589e-15
2014.814.8-9.8321044135619e-16
219.59.57.73771102857058e-16
2213.713.72.66370871789208e-16
2317179.77997771997552e-16
2414.714.7-1.8551974684157e-16
2517.417.4-9.81567522463475e-16
2699-6.53270521720141e-16
279.19.11.16067965488100e-15
2812.212.23.41672287054848e-16
2915.915.9-1.02977603013466e-16
3012.912.9-9.87337603058453e-16
3110.910.93.65640360742578e-15
3210.610.64.85520556284682e-16
3313.213.2-7.29099146388262e-16
349.69.63.57293433026125e-16
356.46.4-2.84404972837730e-16
365.85.8-8.79770346414387e-16
37-1-16.78214774078345e-17
38-0.2-0.2000000000000019.82113012800742e-16
392.72.7-2.24997932450973e-16
403.63.6-5.13089664517223e-16
41-0.9-0.96.84793660245499e-16
420.30.300000000000001-5.309716353361e-16
43-1.1-1.100000000000002.85789140612151e-15
44-2.5-2.5-8.88536752333538e-17
45-3.4-3.41.24754287261528e-17
46-3.5-3.5-1.84245569126804e-16
47-3.9-3.92.14877584449574e-16
48-4.6-4.6-1.41226576552465e-16
49-0.1-0.1000000000000004.42922370695556e-16
504.34.3-3.42074210981781e-16
5110.210.29.5084701948019e-17
528.78.7-1.17553837503853e-16
5313.313.37.0064584577974e-16
541515-1.05294677715092e-15
5520.720.72.45763880883434e-15
5620.720.73.79748886020396e-16
5726.426.4-1.03302458495984e-16
5831.231.2-1.12380596166527e-15
5931.431.4-8.15509242159822e-16
6026.626.67.00771149932925e-17
6126.626.6-2.21547335995736e-15
6219.219.2-1.36720583002414e-15
636.56.5-4.44584896358559e-16
643.13.1-3.77302896066711e-16
65-0.2-0.199999999999999-8.07306306021965e-16
66-4-4-9.94648843240393e-16
67-12.6-12.62.80846271647001e-15
68-13-13-5.5146644096759e-16






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
220.8052647531035130.3894704937929730.194735246896487
230.7105883477472710.5788233045054570.289411652252729
240.2221743093747100.4443486187494210.77782569062529
25001
260.8193679255115250.3612641489769510.180632074488475
270.7368246117468130.5263507765063750.263175388253187
280.5498401857039450.900319628592110.450159814296055
290.97728218366240.04543563267519860.0227178163375993
300.9999999999999984.46412881003123e-152.23206440501561e-15
310.9342488272152310.1315023455695380.0657511727847688
320.006000267924758660.01200053584951730.993999732075241
330.7807575901091890.4384848197816220.219242409890811
340.9996713197084430.000657360583114770.000328680291557385
350.8310393473775180.3379213052449650.168960652622482
360.9999205835052180.0001588329895640457.94164947820225e-05
370.0006023449824213110.001204689964842620.999397655017579
380.9994211057257010.001157788548597760.000578894274298881
394.63744596238110e-079.27489192476219e-070.999999536255404
400.9745101438744970.05097971225100670.0254898561255034
410.01163637013915510.02327274027831010.988363629860845
420.9666500929619560.06669981407608810.0333499070380441
430.709300649904160.5813987001916820.290699350095841
440.08520996574628530.1704199314925710.914790034253715
456.6781823187364e-091.33563646374728e-080.999999993321818
460.3005456732428870.6010913464857740.699454326757113

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
22 & 0.805264753103513 & 0.389470493792973 & 0.194735246896487 \tabularnewline
23 & 0.710588347747271 & 0.578823304505457 & 0.289411652252729 \tabularnewline
24 & 0.222174309374710 & 0.444348618749421 & 0.77782569062529 \tabularnewline
25 & 0 & 0 & 1 \tabularnewline
26 & 0.819367925511525 & 0.361264148976951 & 0.180632074488475 \tabularnewline
27 & 0.736824611746813 & 0.526350776506375 & 0.263175388253187 \tabularnewline
28 & 0.549840185703945 & 0.90031962859211 & 0.450159814296055 \tabularnewline
29 & 0.9772821836624 & 0.0454356326751986 & 0.0227178163375993 \tabularnewline
30 & 0.999999999999998 & 4.46412881003123e-15 & 2.23206440501561e-15 \tabularnewline
31 & 0.934248827215231 & 0.131502345569538 & 0.0657511727847688 \tabularnewline
32 & 0.00600026792475866 & 0.0120005358495173 & 0.993999732075241 \tabularnewline
33 & 0.780757590109189 & 0.438484819781622 & 0.219242409890811 \tabularnewline
34 & 0.999671319708443 & 0.00065736058311477 & 0.000328680291557385 \tabularnewline
35 & 0.831039347377518 & 0.337921305244965 & 0.168960652622482 \tabularnewline
36 & 0.999920583505218 & 0.000158832989564045 & 7.94164947820225e-05 \tabularnewline
37 & 0.000602344982421311 & 0.00120468996484262 & 0.999397655017579 \tabularnewline
38 & 0.999421105725701 & 0.00115778854859776 & 0.000578894274298881 \tabularnewline
39 & 4.63744596238110e-07 & 9.27489192476219e-07 & 0.999999536255404 \tabularnewline
40 & 0.974510143874497 & 0.0509797122510067 & 0.0254898561255034 \tabularnewline
41 & 0.0116363701391551 & 0.0232727402783101 & 0.988363629860845 \tabularnewline
42 & 0.966650092961956 & 0.0666998140760881 & 0.0333499070380441 \tabularnewline
43 & 0.70930064990416 & 0.581398700191682 & 0.290699350095841 \tabularnewline
44 & 0.0852099657462853 & 0.170419931492571 & 0.914790034253715 \tabularnewline
45 & 6.6781823187364e-09 & 1.33563646374728e-08 & 0.999999993321818 \tabularnewline
46 & 0.300545673242887 & 0.601091346485774 & 0.699454326757113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&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]22[/C][C]0.805264753103513[/C][C]0.389470493792973[/C][C]0.194735246896487[/C][/ROW]
[ROW][C]23[/C][C]0.710588347747271[/C][C]0.578823304505457[/C][C]0.289411652252729[/C][/ROW]
[ROW][C]24[/C][C]0.222174309374710[/C][C]0.444348618749421[/C][C]0.77782569062529[/C][/ROW]
[ROW][C]25[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]26[/C][C]0.819367925511525[/C][C]0.361264148976951[/C][C]0.180632074488475[/C][/ROW]
[ROW][C]27[/C][C]0.736824611746813[/C][C]0.526350776506375[/C][C]0.263175388253187[/C][/ROW]
[ROW][C]28[/C][C]0.549840185703945[/C][C]0.90031962859211[/C][C]0.450159814296055[/C][/ROW]
[ROW][C]29[/C][C]0.9772821836624[/C][C]0.0454356326751986[/C][C]0.0227178163375993[/C][/ROW]
[ROW][C]30[/C][C]0.999999999999998[/C][C]4.46412881003123e-15[/C][C]2.23206440501561e-15[/C][/ROW]
[ROW][C]31[/C][C]0.934248827215231[/C][C]0.131502345569538[/C][C]0.0657511727847688[/C][/ROW]
[ROW][C]32[/C][C]0.00600026792475866[/C][C]0.0120005358495173[/C][C]0.993999732075241[/C][/ROW]
[ROW][C]33[/C][C]0.780757590109189[/C][C]0.438484819781622[/C][C]0.219242409890811[/C][/ROW]
[ROW][C]34[/C][C]0.999671319708443[/C][C]0.00065736058311477[/C][C]0.000328680291557385[/C][/ROW]
[ROW][C]35[/C][C]0.831039347377518[/C][C]0.337921305244965[/C][C]0.168960652622482[/C][/ROW]
[ROW][C]36[/C][C]0.999920583505218[/C][C]0.000158832989564045[/C][C]7.94164947820225e-05[/C][/ROW]
[ROW][C]37[/C][C]0.000602344982421311[/C][C]0.00120468996484262[/C][C]0.999397655017579[/C][/ROW]
[ROW][C]38[/C][C]0.999421105725701[/C][C]0.00115778854859776[/C][C]0.000578894274298881[/C][/ROW]
[ROW][C]39[/C][C]4.63744596238110e-07[/C][C]9.27489192476219e-07[/C][C]0.999999536255404[/C][/ROW]
[ROW][C]40[/C][C]0.974510143874497[/C][C]0.0509797122510067[/C][C]0.0254898561255034[/C][/ROW]
[ROW][C]41[/C][C]0.0116363701391551[/C][C]0.0232727402783101[/C][C]0.988363629860845[/C][/ROW]
[ROW][C]42[/C][C]0.966650092961956[/C][C]0.0666998140760881[/C][C]0.0333499070380441[/C][/ROW]
[ROW][C]43[/C][C]0.70930064990416[/C][C]0.581398700191682[/C][C]0.290699350095841[/C][/ROW]
[ROW][C]44[/C][C]0.0852099657462853[/C][C]0.170419931492571[/C][C]0.914790034253715[/C][/ROW]
[ROW][C]45[/C][C]6.6781823187364e-09[/C][C]1.33563646374728e-08[/C][C]0.999999993321818[/C][/ROW]
[ROW][C]46[/C][C]0.300545673242887[/C][C]0.601091346485774[/C][C]0.699454326757113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69886&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&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
220.8052647531035130.3894704937929730.194735246896487
230.7105883477472710.5788233045054570.289411652252729
240.2221743093747100.4443486187494210.77782569062529
25001
260.8193679255115250.3612641489769510.180632074488475
270.7368246117468130.5263507765063750.263175388253187
280.5498401857039450.900319628592110.450159814296055
290.97728218366240.04543563267519860.0227178163375993
300.9999999999999984.46412881003123e-152.23206440501561e-15
310.9342488272152310.1315023455695380.0657511727847688
320.006000267924758660.01200053584951730.993999732075241
330.7807575901091890.4384848197816220.219242409890811
340.9996713197084430.000657360583114770.000328680291557385
350.8310393473775180.3379213052449650.168960652622482
360.9999205835052180.0001588329895640457.94164947820225e-05
370.0006023449824213110.001204689964842620.999397655017579
380.9994211057257010.001157788548597760.000578894274298881
394.63744596238110e-079.27489192476219e-070.999999536255404
400.9745101438744970.05097971225100670.0254898561255034
410.01163637013915510.02327274027831010.988363629860845
420.9666500929619560.06669981407608810.0333499070380441
430.709300649904160.5813987001916820.290699350095841
440.08520996574628530.1704199314925710.914790034253715
456.6781823187364e-091.33563646374728e-080.999999993321818
460.3005456732428870.6010913464857740.699454326757113






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level80.32NOK
5% type I error level110.44NOK
10% type I error level130.52NOK

\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 & 8 & 0.32 & NOK \tabularnewline
5% type I error level & 11 & 0.44 & NOK \tabularnewline
10% type I error level & 13 & 0.52 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69886&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]8[/C][C]0.32[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]11[/C][C]0.44[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]0.52[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69886&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69886&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 level80.32NOK
5% type I error level110.44NOK
10% type I error level130.52NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}