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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 11:30:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258741912yxoumsxq14190rg.htm/, Retrieved Fri, 26 Apr 2024 18:45:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58397, Retrieved Fri, 26 Apr 2024 18:45:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

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] [Model 4] [2009-11-20 18:30:41] [e1f26cfd746b288ac2a466939c6f316e] [Current]
-    D        [Multiple Regression] [model 5] [2009-11-20 18:35:34] [36becc366f59efff5c3495030cea7527]
-    D          [Multiple Regression] [relatie lichten-o...] [2009-11-23 15:43:30] [74be16979710d4c4e7c6647856088456]
-    D        [Multiple Regression] [relatie lichten-o...] [2009-11-23 15:40:43] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82.4	0	82.4	111.1	105.7	105.7
60	0	60	82.4	111.1	105.7
107.3	0	107.3	60	82.4	111.1
99.3	0	99.3	107.3	60	82.4
113.5	0	113.5	99.3	107.3	60
108.9	0	108.9	113.5	99.3	107.3
100.2	0	100.2	108.9	113.5	99.3
103.9	0	103.9	100.2	108.9	113.5
138.7	0	138.7	103.9	100.2	108.9
120.2	0	120.2	138.7	103.9	100.2
100.2	0	100.2	120.2	138.7	103.9
143.2	0	143.2	100.2	120.2	138.7
70.9	0	70.9	143.2	100.2	120.2
85.2	0	85.2	70.9	143.2	100.2
133	0	133	85.2	70.9	143.2
136.6	0	136.6	133	85.2	70.9
117.9	0	117.9	136.6	133	85.2
106.3	0	106.3	117.9	136.6	133
122.3	0	122.3	106.3	117.9	136.6
125.5	0	125.5	122.3	106.3	117.9
148.4	0	148.4	125.5	122.3	106.3
126.3	0	126.3	148.4	125.5	122.3
99.6	0	99.6	126.3	148.4	125.5
140.4	0	140.4	99.6	126.3	148.4
80.3	0	80.3	140.4	99.6	126.3
92.6	0	92.6	80.3	140.4	99.6
138.5	0	138.5	92.6	80.3	140.4
110.9	0	110.9	138.5	92.6	80.3
119.6	0	119.6	110.9	138.5	92.6
105	0	105	119.6	110.9	138.5
109	0	109	105	119.6	110.9
129.4	0	129.4	109	105	119.6
148.6	0	148.6	129.4	109	105
101.4	0	101.4	148.6	129.4	109
134.8	0	134.8	101.4	148.6	129.4
143.7	0	143.7	134.8	101.4	148.6
81.6	0	81.6	143.7	134.8	101.4
90.3	0	90.3	81.6	143.7	134.8
141.5	0	141.5	90.3	81.6	143.7
140.7	0	140.7	141.5	90.3	81.6
140.2	0	140.2	140.7	141.5	90.3
100.2	0	100.2	140.2	140.7	141.5
125.7	0	125.7	100.2	140.2	140.7
119.6	0	119.6	125.7	100.2	140.2
134.7	0	134.7	119.6	125.7	100.2
109	0	109	134.7	119.6	125.7
116.3	0	116.3	109	134.7	119.6
146.9	0	146.9	116.3	109	134.7
97.4	0	97.4	146.9	116.3	109
89.4	0	89.4	97.4	146.9	116.3
132.1	0	132.1	89.4	97.4	146.9
139.8	0	139.8	132.1	89.4	97.4
129	0	129	139.8	132.1	89.4
112.5	0	112.5	129	139.8	132.1
121.9	1	121.9	112.5	129	139.8
121.7	1	121.7	121.9	112.5	129
123.1	1	123.1	121.7	121.9	112.5
131.6	1	131.6	123.1	121.7	121.9
119.3	1	119.3	131.6	123.1	121.7
132.5	1	132.5	119.3	131.6	123.1
98.3	1	98.3	132.5	119.3	131.6
85.1	1	85.1	98.3	132.5	119.3
131.7	1	131.7	85.1	98.3	132.5
129.3	1	129.3	131.7	85.1	98.3
90.7	1	90.7	129.3	131.7	85.1
78.6	1	78.6	90.7	129.3	131.7
68.9	1	68.9	78.6	90.7	129.3
79.1	1	79.1	68.9	78.6	90.7
83.5	1	83.5	79.1	68.9	78.6
74.1	1	74.1	83.5	79.1	68.9
59.7	1	59.7	74.1	83.5	79.1
93.3	1	93.3	59.7	74.1	83.5
61.3	1	61.3	93.3	59.7	74.1
56.6	1	56.6	61.3	93.3	59.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.8442376843341e-14 -7.4396786540785e-15X[t] + 1Y1[t] -4.92403503521023e-17Y2[t] + 6.07056167789887e-17Y3[t] -3.77501138888727e-17Y4[t] -1.84625207382948e-15M1[t] -6.36302511705444e-15M2[t] + 7.5234022191225e-15M3[t] + 4.62831145630463e-16M4[t] -1.87557162391614e-15M5[t] -1.93369031592616e-15M6[t] -1.50865872303823e-15M7[t] + 4.67700298634354e-16M8[t] + 3.20378295730025e-16M9[t] -1.23791639161708e-15M10[t] -2.31543472512414e-15M11[t] -4.10636822060831e-17t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  2.8442376843341e-14 -7.4396786540785e-15X[t] +  1Y1[t] -4.92403503521023e-17Y2[t] +  6.07056167789887e-17Y3[t] -3.77501138888727e-17Y4[t] -1.84625207382948e-15M1[t] -6.36302511705444e-15M2[t] +  7.5234022191225e-15M3[t] +  4.62831145630463e-16M4[t] -1.87557162391614e-15M5[t] -1.93369031592616e-15M6[t] -1.50865872303823e-15M7[t] +  4.67700298634354e-16M8[t] +  3.20378295730025e-16M9[t] -1.23791639161708e-15M10[t] -2.31543472512414e-15M11[t] -4.10636822060831e-17t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  2.8442376843341e-14 -7.4396786540785e-15X[t] +  1Y1[t] -4.92403503521023e-17Y2[t] +  6.07056167789887e-17Y3[t] -3.77501138888727e-17Y4[t] -1.84625207382948e-15M1[t] -6.36302511705444e-15M2[t] +  7.5234022191225e-15M3[t] +  4.62831145630463e-16M4[t] -1.87557162391614e-15M5[t] -1.93369031592616e-15M6[t] -1.50865872303823e-15M7[t] +  4.67700298634354e-16M8[t] +  3.20378295730025e-16M9[t] -1.23791639161708e-15M10[t] -2.31543472512414e-15M11[t] -4.10636822060831e-17t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&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] = + 2.8442376843341e-14 -7.4396786540785e-15X[t] + 1Y1[t] -4.92403503521023e-17Y2[t] + 6.07056167789887e-17Y3[t] -3.77501138888727e-17Y4[t] -1.84625207382948e-15M1[t] -6.36302511705444e-15M2[t] + 7.5234022191225e-15M3[t] + 4.62831145630463e-16M4[t] -1.87557162391614e-15M5[t] -1.93369031592616e-15M6[t] -1.50865872303823e-15M7[t] + 4.67700298634354e-16M8[t] + 3.20378295730025e-16M9[t] -1.23791639161708e-15M10[t] -2.31543472512414e-15M11[t] -4.10636822060831e-17t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.8442376843341e-1404.44334.2e-052.1e-05
X-7.4396786540785e-150-3.10010.0030260.001513
Y1101798844243432820400
Y2-4.92403503521023e-170-0.89950.3722450.186123
Y36.07056167789887e-1701.11770.2684790.13424
Y4-3.77501138888727e-170-0.68790.4943810.24719
M1-1.84625207382948e-150-0.40580.6864350.343218
M2-6.36302511705444e-150-1.4260.1594280.079714
M37.5234022191225e-1502.17910.0335460.016773
M44.62831145630463e-1600.10530.9164940.458247
M5-1.87557162391614e-150-0.41080.6827750.341387
M6-1.93369031592616e-150-0.5070.6141240.307062
M7-1.50865872303823e-150-0.45090.653810.326905
M84.67700298634354e-1600.14740.8833780.441689
M93.20378295730025e-1600.09440.9251250.462563
M10-1.23791639161708e-150-0.32150.7490070.374504
M11-2.31543472512414e-150-0.61420.5415480.270774
t-4.10636822060831e-170-0.91190.3657560.182878

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 2.8442376843341e-14 & 0 & 4.4433 & 4.2e-05 & 2.1e-05 \tabularnewline
X & -7.4396786540785e-15 & 0 & -3.1001 & 0.003026 & 0.001513 \tabularnewline
Y1 & 1 & 0 & 17988442434328204 & 0 & 0 \tabularnewline
Y2 & -4.92403503521023e-17 & 0 & -0.8995 & 0.372245 & 0.186123 \tabularnewline
Y3 & 6.07056167789887e-17 & 0 & 1.1177 & 0.268479 & 0.13424 \tabularnewline
Y4 & -3.77501138888727e-17 & 0 & -0.6879 & 0.494381 & 0.24719 \tabularnewline
M1 & -1.84625207382948e-15 & 0 & -0.4058 & 0.686435 & 0.343218 \tabularnewline
M2 & -6.36302511705444e-15 & 0 & -1.426 & 0.159428 & 0.079714 \tabularnewline
M3 & 7.5234022191225e-15 & 0 & 2.1791 & 0.033546 & 0.016773 \tabularnewline
M4 & 4.62831145630463e-16 & 0 & 0.1053 & 0.916494 & 0.458247 \tabularnewline
M5 & -1.87557162391614e-15 & 0 & -0.4108 & 0.682775 & 0.341387 \tabularnewline
M6 & -1.93369031592616e-15 & 0 & -0.507 & 0.614124 & 0.307062 \tabularnewline
M7 & -1.50865872303823e-15 & 0 & -0.4509 & 0.65381 & 0.326905 \tabularnewline
M8 & 4.67700298634354e-16 & 0 & 0.1474 & 0.883378 & 0.441689 \tabularnewline
M9 & 3.20378295730025e-16 & 0 & 0.0944 & 0.925125 & 0.462563 \tabularnewline
M10 & -1.23791639161708e-15 & 0 & -0.3215 & 0.749007 & 0.374504 \tabularnewline
M11 & -2.31543472512414e-15 & 0 & -0.6142 & 0.541548 & 0.270774 \tabularnewline
t & -4.10636822060831e-17 & 0 & -0.9119 & 0.365756 & 0.182878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]2.8442376843341e-14[/C][C]0[/C][C]4.4433[/C][C]4.2e-05[/C][C]2.1e-05[/C][/ROW]
[ROW][C]X[/C][C]-7.4396786540785e-15[/C][C]0[/C][C]-3.1001[/C][C]0.003026[/C][C]0.001513[/C][/ROW]
[ROW][C]Y1[/C][C]1[/C][C]0[/C][C]17988442434328204[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-4.92403503521023e-17[/C][C]0[/C][C]-0.8995[/C][C]0.372245[/C][C]0.186123[/C][/ROW]
[ROW][C]Y3[/C][C]6.07056167789887e-17[/C][C]0[/C][C]1.1177[/C][C]0.268479[/C][C]0.13424[/C][/ROW]
[ROW][C]Y4[/C][C]-3.77501138888727e-17[/C][C]0[/C][C]-0.6879[/C][C]0.494381[/C][C]0.24719[/C][/ROW]
[ROW][C]M1[/C][C]-1.84625207382948e-15[/C][C]0[/C][C]-0.4058[/C][C]0.686435[/C][C]0.343218[/C][/ROW]
[ROW][C]M2[/C][C]-6.36302511705444e-15[/C][C]0[/C][C]-1.426[/C][C]0.159428[/C][C]0.079714[/C][/ROW]
[ROW][C]M3[/C][C]7.5234022191225e-15[/C][C]0[/C][C]2.1791[/C][C]0.033546[/C][C]0.016773[/C][/ROW]
[ROW][C]M4[/C][C]4.62831145630463e-16[/C][C]0[/C][C]0.1053[/C][C]0.916494[/C][C]0.458247[/C][/ROW]
[ROW][C]M5[/C][C]-1.87557162391614e-15[/C][C]0[/C][C]-0.4108[/C][C]0.682775[/C][C]0.341387[/C][/ROW]
[ROW][C]M6[/C][C]-1.93369031592616e-15[/C][C]0[/C][C]-0.507[/C][C]0.614124[/C][C]0.307062[/C][/ROW]
[ROW][C]M7[/C][C]-1.50865872303823e-15[/C][C]0[/C][C]-0.4509[/C][C]0.65381[/C][C]0.326905[/C][/ROW]
[ROW][C]M8[/C][C]4.67700298634354e-16[/C][C]0[/C][C]0.1474[/C][C]0.883378[/C][C]0.441689[/C][/ROW]
[ROW][C]M9[/C][C]3.20378295730025e-16[/C][C]0[/C][C]0.0944[/C][C]0.925125[/C][C]0.462563[/C][/ROW]
[ROW][C]M10[/C][C]-1.23791639161708e-15[/C][C]0[/C][C]-0.3215[/C][C]0.749007[/C][C]0.374504[/C][/ROW]
[ROW][C]M11[/C][C]-2.31543472512414e-15[/C][C]0[/C][C]-0.6142[/C][C]0.541548[/C][C]0.270774[/C][/ROW]
[ROW][C]t[/C][C]-4.10636822060831e-17[/C][C]0[/C][C]-0.9119[/C][C]0.365756[/C][C]0.182878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2.8442376843341e-1404.44334.2e-052.1e-05
X-7.4396786540785e-150-3.10010.0030260.001513
Y1101798844243432820400
Y2-4.92403503521023e-170-0.89950.3722450.186123
Y36.07056167789887e-1701.11770.2684790.13424
Y4-3.77501138888727e-170-0.68790.4943810.24719
M1-1.84625207382948e-150-0.40580.6864350.343218
M2-6.36302511705444e-150-1.4260.1594280.079714
M37.5234022191225e-1502.17910.0335460.016773
M44.62831145630463e-1600.10530.9164940.458247
M5-1.87557162391614e-150-0.41080.6827750.341387
M6-1.93369031592616e-150-0.5070.6141240.307062
M7-1.50865872303823e-150-0.45090.653810.326905
M84.67700298634354e-1600.14740.8833780.441689
M93.20378295730025e-1600.09440.9251250.462563
M10-1.23791639161708e-150-0.32150.7490070.374504
M11-2.31543472512414e-150-0.61420.5415480.270774
t-4.10636822060831e-170-0.91190.3657560.182878






Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)9.82035506992358e+31
F-TEST (DF numerator)17
F-TEST (DF denominator)56
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.13375220365013e-15
Sum Squared Residuals1.47590305455502e-27

\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) & 9.82035506992358e+31 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 56 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.13375220365013e-15 \tabularnewline
Sum Squared Residuals & 1.47590305455502e-27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&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]9.82035506992358e+31[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]56[/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]5.13375220365013e-15[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.47590305455502e-27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&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)9.82035506992358e+31
F-TEST (DF numerator)17
F-TEST (DF denominator)56
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.13375220365013e-15
Sum Squared Residuals1.47590305455502e-27






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
182.482.4-5.81015897247119e-15
26060-5.64979880604248e-15
3107.3107.33.06396323853187e-14
499.399.3-1.61898458377759e-15
5113.5113.5-3.04360978574679e-15
6108.9108.9-1.53908329093447e-16
7100.2100.2-2.20472601163642e-15
8103.9103.9-4.36745197119887e-15
9138.7138.7-5.38693239896647e-16
10120.2120.2-3.61928370165247e-17
11100.2100.2-2.03341034068912e-15
12143.2143.2-1.11363878931846e-15
1370.970.91.20037011595791e-15
1485.285.21.11698017927237e-17
15133133-7.94892872764188e-15
16136.6136.6-2.68876210223905e-15
17117.9117.9-1.16539654301937e-15
18106.3106.3-1.13959915960399e-15
19122.3122.39.6063986113853e-16
20125.5125.5-7.19870357131765e-16
21148.4148.45.07278621338346e-15
22126.3126.31.22076987333821e-15
2399.699.6-9.14099819321382e-16
24140.4140.4-1.89643275003684e-16
2580.380.32.61212265013684e-16
2692.692.6-1.14555112652662e-16
27138.5138.5-1.57589539552203e-15
28110.9110.9-8.61019173157567e-16
29119.6119.6-4.98545528795062e-16
301051051.42048174450055e-15
31109109-1.05616258323731e-15
32129.4129.42.16625891061006e-15
33148.6148.6-6.22737443100822e-16
34101.4101.4-1.09837307728577e-15
35134.8134.8-2.02776912047376e-15
36143.7143.73.00757891166888e-15
3781.681.6-2.37619408322888e-15
3890.390.31.95258218139232e-15
39141.5141.5-5.20155072215607e-15
40140.7140.71.68159866043144e-15
41140.2140.21.32498976073763e-15
42100.2100.21.14061945420715e-15
43125.7125.7-1.17683606476635e-16
44119.6119.62.62482551070241e-15
45134.7134.7-3.05231194075783e-15
461091091.31019040944554e-15
47116.3116.3-2.79771441118188e-16
48146.9146.91.07198883670056e-15
4997.497.46.13422539213657e-16
5089.489.42.48014215354681e-15
51132.1132.1-7.58341678924324e-15
52139.8139.82.51202373889514e-15
531291294.16971010984747e-15
54112.5112.59.59866230211697e-16
55121.9121.91.76197266456782e-15
56121.7121.79.16685472099057e-16
57123.1123.1-3.30738437591248e-16
58131.6131.62.93233825900414e-16
59119.3119.33.78007645365898e-15
60132.5132.5-1.75478733284302e-15
6198.398.33.08763057247380e-15
6285.185.14.22296036552288e-15
63131.7131.7-8.32984075075549e-15
64129.3129.39.75143459847632e-16
6590.790.7-7.87148013023872e-16
6678.678.6-2.22745994022196e-15
6768.968.96.55959675644015e-16
6879.179.1-6.204475650809e-16
6983.583.5-5.28305152036916e-16
7074.174.1-1.68962819438187e-15
7159.759.71.47497426794348e-15
7293.393.3-1.02149835120426e-15
7361.361.33.02371756304102e-15
7456.656.6-2.90250058355957e-15

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 82.4 & 82.4 & -5.81015897247119e-15 \tabularnewline
2 & 60 & 60 & -5.64979880604248e-15 \tabularnewline
3 & 107.3 & 107.3 & 3.06396323853187e-14 \tabularnewline
4 & 99.3 & 99.3 & -1.61898458377759e-15 \tabularnewline
5 & 113.5 & 113.5 & -3.04360978574679e-15 \tabularnewline
6 & 108.9 & 108.9 & -1.53908329093447e-16 \tabularnewline
7 & 100.2 & 100.2 & -2.20472601163642e-15 \tabularnewline
8 & 103.9 & 103.9 & -4.36745197119887e-15 \tabularnewline
9 & 138.7 & 138.7 & -5.38693239896647e-16 \tabularnewline
10 & 120.2 & 120.2 & -3.61928370165247e-17 \tabularnewline
11 & 100.2 & 100.2 & -2.03341034068912e-15 \tabularnewline
12 & 143.2 & 143.2 & -1.11363878931846e-15 \tabularnewline
13 & 70.9 & 70.9 & 1.20037011595791e-15 \tabularnewline
14 & 85.2 & 85.2 & 1.11698017927237e-17 \tabularnewline
15 & 133 & 133 & -7.94892872764188e-15 \tabularnewline
16 & 136.6 & 136.6 & -2.68876210223905e-15 \tabularnewline
17 & 117.9 & 117.9 & -1.16539654301937e-15 \tabularnewline
18 & 106.3 & 106.3 & -1.13959915960399e-15 \tabularnewline
19 & 122.3 & 122.3 & 9.6063986113853e-16 \tabularnewline
20 & 125.5 & 125.5 & -7.19870357131765e-16 \tabularnewline
21 & 148.4 & 148.4 & 5.07278621338346e-15 \tabularnewline
22 & 126.3 & 126.3 & 1.22076987333821e-15 \tabularnewline
23 & 99.6 & 99.6 & -9.14099819321382e-16 \tabularnewline
24 & 140.4 & 140.4 & -1.89643275003684e-16 \tabularnewline
25 & 80.3 & 80.3 & 2.61212265013684e-16 \tabularnewline
26 & 92.6 & 92.6 & -1.14555112652662e-16 \tabularnewline
27 & 138.5 & 138.5 & -1.57589539552203e-15 \tabularnewline
28 & 110.9 & 110.9 & -8.61019173157567e-16 \tabularnewline
29 & 119.6 & 119.6 & -4.98545528795062e-16 \tabularnewline
30 & 105 & 105 & 1.42048174450055e-15 \tabularnewline
31 & 109 & 109 & -1.05616258323731e-15 \tabularnewline
32 & 129.4 & 129.4 & 2.16625891061006e-15 \tabularnewline
33 & 148.6 & 148.6 & -6.22737443100822e-16 \tabularnewline
34 & 101.4 & 101.4 & -1.09837307728577e-15 \tabularnewline
35 & 134.8 & 134.8 & -2.02776912047376e-15 \tabularnewline
36 & 143.7 & 143.7 & 3.00757891166888e-15 \tabularnewline
37 & 81.6 & 81.6 & -2.37619408322888e-15 \tabularnewline
38 & 90.3 & 90.3 & 1.95258218139232e-15 \tabularnewline
39 & 141.5 & 141.5 & -5.20155072215607e-15 \tabularnewline
40 & 140.7 & 140.7 & 1.68159866043144e-15 \tabularnewline
41 & 140.2 & 140.2 & 1.32498976073763e-15 \tabularnewline
42 & 100.2 & 100.2 & 1.14061945420715e-15 \tabularnewline
43 & 125.7 & 125.7 & -1.17683606476635e-16 \tabularnewline
44 & 119.6 & 119.6 & 2.62482551070241e-15 \tabularnewline
45 & 134.7 & 134.7 & -3.05231194075783e-15 \tabularnewline
46 & 109 & 109 & 1.31019040944554e-15 \tabularnewline
47 & 116.3 & 116.3 & -2.79771441118188e-16 \tabularnewline
48 & 146.9 & 146.9 & 1.07198883670056e-15 \tabularnewline
49 & 97.4 & 97.4 & 6.13422539213657e-16 \tabularnewline
50 & 89.4 & 89.4 & 2.48014215354681e-15 \tabularnewline
51 & 132.1 & 132.1 & -7.58341678924324e-15 \tabularnewline
52 & 139.8 & 139.8 & 2.51202373889514e-15 \tabularnewline
53 & 129 & 129 & 4.16971010984747e-15 \tabularnewline
54 & 112.5 & 112.5 & 9.59866230211697e-16 \tabularnewline
55 & 121.9 & 121.9 & 1.76197266456782e-15 \tabularnewline
56 & 121.7 & 121.7 & 9.16685472099057e-16 \tabularnewline
57 & 123.1 & 123.1 & -3.30738437591248e-16 \tabularnewline
58 & 131.6 & 131.6 & 2.93233825900414e-16 \tabularnewline
59 & 119.3 & 119.3 & 3.78007645365898e-15 \tabularnewline
60 & 132.5 & 132.5 & -1.75478733284302e-15 \tabularnewline
61 & 98.3 & 98.3 & 3.08763057247380e-15 \tabularnewline
62 & 85.1 & 85.1 & 4.22296036552288e-15 \tabularnewline
63 & 131.7 & 131.7 & -8.32984075075549e-15 \tabularnewline
64 & 129.3 & 129.3 & 9.75143459847632e-16 \tabularnewline
65 & 90.7 & 90.7 & -7.87148013023872e-16 \tabularnewline
66 & 78.6 & 78.6 & -2.22745994022196e-15 \tabularnewline
67 & 68.9 & 68.9 & 6.55959675644015e-16 \tabularnewline
68 & 79.1 & 79.1 & -6.204475650809e-16 \tabularnewline
69 & 83.5 & 83.5 & -5.28305152036916e-16 \tabularnewline
70 & 74.1 & 74.1 & -1.68962819438187e-15 \tabularnewline
71 & 59.7 & 59.7 & 1.47497426794348e-15 \tabularnewline
72 & 93.3 & 93.3 & -1.02149835120426e-15 \tabularnewline
73 & 61.3 & 61.3 & 3.02371756304102e-15 \tabularnewline
74 & 56.6 & 56.6 & -2.90250058355957e-15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&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]82.4[/C][C]82.4[/C][C]-5.81015897247119e-15[/C][/ROW]
[ROW][C]2[/C][C]60[/C][C]60[/C][C]-5.64979880604248e-15[/C][/ROW]
[ROW][C]3[/C][C]107.3[/C][C]107.3[/C][C]3.06396323853187e-14[/C][/ROW]
[ROW][C]4[/C][C]99.3[/C][C]99.3[/C][C]-1.61898458377759e-15[/C][/ROW]
[ROW][C]5[/C][C]113.5[/C][C]113.5[/C][C]-3.04360978574679e-15[/C][/ROW]
[ROW][C]6[/C][C]108.9[/C][C]108.9[/C][C]-1.53908329093447e-16[/C][/ROW]
[ROW][C]7[/C][C]100.2[/C][C]100.2[/C][C]-2.20472601163642e-15[/C][/ROW]
[ROW][C]8[/C][C]103.9[/C][C]103.9[/C][C]-4.36745197119887e-15[/C][/ROW]
[ROW][C]9[/C][C]138.7[/C][C]138.7[/C][C]-5.38693239896647e-16[/C][/ROW]
[ROW][C]10[/C][C]120.2[/C][C]120.2[/C][C]-3.61928370165247e-17[/C][/ROW]
[ROW][C]11[/C][C]100.2[/C][C]100.2[/C][C]-2.03341034068912e-15[/C][/ROW]
[ROW][C]12[/C][C]143.2[/C][C]143.2[/C][C]-1.11363878931846e-15[/C][/ROW]
[ROW][C]13[/C][C]70.9[/C][C]70.9[/C][C]1.20037011595791e-15[/C][/ROW]
[ROW][C]14[/C][C]85.2[/C][C]85.2[/C][C]1.11698017927237e-17[/C][/ROW]
[ROW][C]15[/C][C]133[/C][C]133[/C][C]-7.94892872764188e-15[/C][/ROW]
[ROW][C]16[/C][C]136.6[/C][C]136.6[/C][C]-2.68876210223905e-15[/C][/ROW]
[ROW][C]17[/C][C]117.9[/C][C]117.9[/C][C]-1.16539654301937e-15[/C][/ROW]
[ROW][C]18[/C][C]106.3[/C][C]106.3[/C][C]-1.13959915960399e-15[/C][/ROW]
[ROW][C]19[/C][C]122.3[/C][C]122.3[/C][C]9.6063986113853e-16[/C][/ROW]
[ROW][C]20[/C][C]125.5[/C][C]125.5[/C][C]-7.19870357131765e-16[/C][/ROW]
[ROW][C]21[/C][C]148.4[/C][C]148.4[/C][C]5.07278621338346e-15[/C][/ROW]
[ROW][C]22[/C][C]126.3[/C][C]126.3[/C][C]1.22076987333821e-15[/C][/ROW]
[ROW][C]23[/C][C]99.6[/C][C]99.6[/C][C]-9.14099819321382e-16[/C][/ROW]
[ROW][C]24[/C][C]140.4[/C][C]140.4[/C][C]-1.89643275003684e-16[/C][/ROW]
[ROW][C]25[/C][C]80.3[/C][C]80.3[/C][C]2.61212265013684e-16[/C][/ROW]
[ROW][C]26[/C][C]92.6[/C][C]92.6[/C][C]-1.14555112652662e-16[/C][/ROW]
[ROW][C]27[/C][C]138.5[/C][C]138.5[/C][C]-1.57589539552203e-15[/C][/ROW]
[ROW][C]28[/C][C]110.9[/C][C]110.9[/C][C]-8.61019173157567e-16[/C][/ROW]
[ROW][C]29[/C][C]119.6[/C][C]119.6[/C][C]-4.98545528795062e-16[/C][/ROW]
[ROW][C]30[/C][C]105[/C][C]105[/C][C]1.42048174450055e-15[/C][/ROW]
[ROW][C]31[/C][C]109[/C][C]109[/C][C]-1.05616258323731e-15[/C][/ROW]
[ROW][C]32[/C][C]129.4[/C][C]129.4[/C][C]2.16625891061006e-15[/C][/ROW]
[ROW][C]33[/C][C]148.6[/C][C]148.6[/C][C]-6.22737443100822e-16[/C][/ROW]
[ROW][C]34[/C][C]101.4[/C][C]101.4[/C][C]-1.09837307728577e-15[/C][/ROW]
[ROW][C]35[/C][C]134.8[/C][C]134.8[/C][C]-2.02776912047376e-15[/C][/ROW]
[ROW][C]36[/C][C]143.7[/C][C]143.7[/C][C]3.00757891166888e-15[/C][/ROW]
[ROW][C]37[/C][C]81.6[/C][C]81.6[/C][C]-2.37619408322888e-15[/C][/ROW]
[ROW][C]38[/C][C]90.3[/C][C]90.3[/C][C]1.95258218139232e-15[/C][/ROW]
[ROW][C]39[/C][C]141.5[/C][C]141.5[/C][C]-5.20155072215607e-15[/C][/ROW]
[ROW][C]40[/C][C]140.7[/C][C]140.7[/C][C]1.68159866043144e-15[/C][/ROW]
[ROW][C]41[/C][C]140.2[/C][C]140.2[/C][C]1.32498976073763e-15[/C][/ROW]
[ROW][C]42[/C][C]100.2[/C][C]100.2[/C][C]1.14061945420715e-15[/C][/ROW]
[ROW][C]43[/C][C]125.7[/C][C]125.7[/C][C]-1.17683606476635e-16[/C][/ROW]
[ROW][C]44[/C][C]119.6[/C][C]119.6[/C][C]2.62482551070241e-15[/C][/ROW]
[ROW][C]45[/C][C]134.7[/C][C]134.7[/C][C]-3.05231194075783e-15[/C][/ROW]
[ROW][C]46[/C][C]109[/C][C]109[/C][C]1.31019040944554e-15[/C][/ROW]
[ROW][C]47[/C][C]116.3[/C][C]116.3[/C][C]-2.79771441118188e-16[/C][/ROW]
[ROW][C]48[/C][C]146.9[/C][C]146.9[/C][C]1.07198883670056e-15[/C][/ROW]
[ROW][C]49[/C][C]97.4[/C][C]97.4[/C][C]6.13422539213657e-16[/C][/ROW]
[ROW][C]50[/C][C]89.4[/C][C]89.4[/C][C]2.48014215354681e-15[/C][/ROW]
[ROW][C]51[/C][C]132.1[/C][C]132.1[/C][C]-7.58341678924324e-15[/C][/ROW]
[ROW][C]52[/C][C]139.8[/C][C]139.8[/C][C]2.51202373889514e-15[/C][/ROW]
[ROW][C]53[/C][C]129[/C][C]129[/C][C]4.16971010984747e-15[/C][/ROW]
[ROW][C]54[/C][C]112.5[/C][C]112.5[/C][C]9.59866230211697e-16[/C][/ROW]
[ROW][C]55[/C][C]121.9[/C][C]121.9[/C][C]1.76197266456782e-15[/C][/ROW]
[ROW][C]56[/C][C]121.7[/C][C]121.7[/C][C]9.16685472099057e-16[/C][/ROW]
[ROW][C]57[/C][C]123.1[/C][C]123.1[/C][C]-3.30738437591248e-16[/C][/ROW]
[ROW][C]58[/C][C]131.6[/C][C]131.6[/C][C]2.93233825900414e-16[/C][/ROW]
[ROW][C]59[/C][C]119.3[/C][C]119.3[/C][C]3.78007645365898e-15[/C][/ROW]
[ROW][C]60[/C][C]132.5[/C][C]132.5[/C][C]-1.75478733284302e-15[/C][/ROW]
[ROW][C]61[/C][C]98.3[/C][C]98.3[/C][C]3.08763057247380e-15[/C][/ROW]
[ROW][C]62[/C][C]85.1[/C][C]85.1[/C][C]4.22296036552288e-15[/C][/ROW]
[ROW][C]63[/C][C]131.7[/C][C]131.7[/C][C]-8.32984075075549e-15[/C][/ROW]
[ROW][C]64[/C][C]129.3[/C][C]129.3[/C][C]9.75143459847632e-16[/C][/ROW]
[ROW][C]65[/C][C]90.7[/C][C]90.7[/C][C]-7.87148013023872e-16[/C][/ROW]
[ROW][C]66[/C][C]78.6[/C][C]78.6[/C][C]-2.22745994022196e-15[/C][/ROW]
[ROW][C]67[/C][C]68.9[/C][C]68.9[/C][C]6.55959675644015e-16[/C][/ROW]
[ROW][C]68[/C][C]79.1[/C][C]79.1[/C][C]-6.204475650809e-16[/C][/ROW]
[ROW][C]69[/C][C]83.5[/C][C]83.5[/C][C]-5.28305152036916e-16[/C][/ROW]
[ROW][C]70[/C][C]74.1[/C][C]74.1[/C][C]-1.68962819438187e-15[/C][/ROW]
[ROW][C]71[/C][C]59.7[/C][C]59.7[/C][C]1.47497426794348e-15[/C][/ROW]
[ROW][C]72[/C][C]93.3[/C][C]93.3[/C][C]-1.02149835120426e-15[/C][/ROW]
[ROW][C]73[/C][C]61.3[/C][C]61.3[/C][C]3.02371756304102e-15[/C][/ROW]
[ROW][C]74[/C][C]56.6[/C][C]56.6[/C][C]-2.90250058355957e-15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&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
182.482.4-5.81015897247119e-15
26060-5.64979880604248e-15
3107.3107.33.06396323853187e-14
499.399.3-1.61898458377759e-15
5113.5113.5-3.04360978574679e-15
6108.9108.9-1.53908329093447e-16
7100.2100.2-2.20472601163642e-15
8103.9103.9-4.36745197119887e-15
9138.7138.7-5.38693239896647e-16
10120.2120.2-3.61928370165247e-17
11100.2100.2-2.03341034068912e-15
12143.2143.2-1.11363878931846e-15
1370.970.91.20037011595791e-15
1485.285.21.11698017927237e-17
15133133-7.94892872764188e-15
16136.6136.6-2.68876210223905e-15
17117.9117.9-1.16539654301937e-15
18106.3106.3-1.13959915960399e-15
19122.3122.39.6063986113853e-16
20125.5125.5-7.19870357131765e-16
21148.4148.45.07278621338346e-15
22126.3126.31.22076987333821e-15
2399.699.6-9.14099819321382e-16
24140.4140.4-1.89643275003684e-16
2580.380.32.61212265013684e-16
2692.692.6-1.14555112652662e-16
27138.5138.5-1.57589539552203e-15
28110.9110.9-8.61019173157567e-16
29119.6119.6-4.98545528795062e-16
301051051.42048174450055e-15
31109109-1.05616258323731e-15
32129.4129.42.16625891061006e-15
33148.6148.6-6.22737443100822e-16
34101.4101.4-1.09837307728577e-15
35134.8134.8-2.02776912047376e-15
36143.7143.73.00757891166888e-15
3781.681.6-2.37619408322888e-15
3890.390.31.95258218139232e-15
39141.5141.5-5.20155072215607e-15
40140.7140.71.68159866043144e-15
41140.2140.21.32498976073763e-15
42100.2100.21.14061945420715e-15
43125.7125.7-1.17683606476635e-16
44119.6119.62.62482551070241e-15
45134.7134.7-3.05231194075783e-15
461091091.31019040944554e-15
47116.3116.3-2.79771441118188e-16
48146.9146.91.07198883670056e-15
4997.497.46.13422539213657e-16
5089.489.42.48014215354681e-15
51132.1132.1-7.58341678924324e-15
52139.8139.82.51202373889514e-15
531291294.16971010984747e-15
54112.5112.59.59866230211697e-16
55121.9121.91.76197266456782e-15
56121.7121.79.16685472099057e-16
57123.1123.1-3.30738437591248e-16
58131.6131.62.93233825900414e-16
59119.3119.33.78007645365898e-15
60132.5132.5-1.75478733284302e-15
6198.398.33.08763057247380e-15
6285.185.14.22296036552288e-15
63131.7131.7-8.32984075075549e-15
64129.3129.39.75143459847632e-16
6590.790.7-7.87148013023872e-16
6678.678.6-2.22745994022196e-15
6768.968.96.55959675644015e-16
6879.179.1-6.204475650809e-16
6983.583.5-5.28305152036916e-16
7074.174.1-1.68962819438187e-15
7159.759.71.47497426794348e-15
7293.393.3-1.02149835120426e-15
7361.361.33.02371756304102e-15
7456.656.6-2.90250058355957e-15






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.1182821799225390.2365643598450790.881717820077461
220.999990415399181.91692016417594e-059.5846008208797e-06
230.8450877920689520.3098244158620950.154912207931048
240.0007670527390020670.001534105478004130.999232947260998
254.54658076410444e-059.09316152820889e-050.999954534192359
260.4238012496582530.8476024993165060.576198750341747
270.9986346821264510.002730635747097740.00136531787354887
280.3624388687238350.7248777374476710.637561131276165
290.1812213836303310.3624427672606620.81877861636967
300.647596905083320.7048061898333590.352403094916679
310.9999997629762454.74047510399384e-072.37023755199692e-07
320.9976833599178120.004633280164375310.00231664008218765
337.0418425629825e-050.000140836851259650.99992958157437
340.7304702735533720.5390594528932560.269529726446628
350.9999999687923236.24153542604947e-083.12076771302473e-08
360.9997177637438270.0005644725123456040.000282236256172802
370.999982505972313.49880553789977e-051.74940276894989e-05
380.9998884813417070.0002230373165851180.000111518658292559
390.9999999999997415.17123783487239e-132.58561891743619e-13
400.999993754210641.24915787187875e-056.24578935939374e-06
410.1941334513798870.3882669027597740.805866548620113
421.60727044647992e-053.21454089295984e-050.999983927295535
430.2088048792134560.4176097584269120.791195120786544
443.51478292819305e-127.02956585638609e-120.999999999996485
451.07004725441348e-162.14009450882696e-161
460.0920604573222260.1841209146444520.907939542677774
470.2311675303913380.4623350607826770.768832469608662
48100
490.9886432218109220.02271355637815620.0113567781890781
502.63907835480083e-085.27815670960165e-080.999999973609216
510.07844806855220160.1568961371044030.921551931447798
520.002569830298106880.005139660596213760.997430169701893
530.9780778151681730.04384436966365380.0219221848318269

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.118282179922539 & 0.236564359845079 & 0.881717820077461 \tabularnewline
22 & 0.99999041539918 & 1.91692016417594e-05 & 9.5846008208797e-06 \tabularnewline
23 & 0.845087792068952 & 0.309824415862095 & 0.154912207931048 \tabularnewline
24 & 0.000767052739002067 & 0.00153410547800413 & 0.999232947260998 \tabularnewline
25 & 4.54658076410444e-05 & 9.09316152820889e-05 & 0.999954534192359 \tabularnewline
26 & 0.423801249658253 & 0.847602499316506 & 0.576198750341747 \tabularnewline
27 & 0.998634682126451 & 0.00273063574709774 & 0.00136531787354887 \tabularnewline
28 & 0.362438868723835 & 0.724877737447671 & 0.637561131276165 \tabularnewline
29 & 0.181221383630331 & 0.362442767260662 & 0.81877861636967 \tabularnewline
30 & 0.64759690508332 & 0.704806189833359 & 0.352403094916679 \tabularnewline
31 & 0.999999762976245 & 4.74047510399384e-07 & 2.37023755199692e-07 \tabularnewline
32 & 0.997683359917812 & 0.00463328016437531 & 0.00231664008218765 \tabularnewline
33 & 7.0418425629825e-05 & 0.00014083685125965 & 0.99992958157437 \tabularnewline
34 & 0.730470273553372 & 0.539059452893256 & 0.269529726446628 \tabularnewline
35 & 0.999999968792323 & 6.24153542604947e-08 & 3.12076771302473e-08 \tabularnewline
36 & 0.999717763743827 & 0.000564472512345604 & 0.000282236256172802 \tabularnewline
37 & 0.99998250597231 & 3.49880553789977e-05 & 1.74940276894989e-05 \tabularnewline
38 & 0.999888481341707 & 0.000223037316585118 & 0.000111518658292559 \tabularnewline
39 & 0.999999999999741 & 5.17123783487239e-13 & 2.58561891743619e-13 \tabularnewline
40 & 0.99999375421064 & 1.24915787187875e-05 & 6.24578935939374e-06 \tabularnewline
41 & 0.194133451379887 & 0.388266902759774 & 0.805866548620113 \tabularnewline
42 & 1.60727044647992e-05 & 3.21454089295984e-05 & 0.999983927295535 \tabularnewline
43 & 0.208804879213456 & 0.417609758426912 & 0.791195120786544 \tabularnewline
44 & 3.51478292819305e-12 & 7.02956585638609e-12 & 0.999999999996485 \tabularnewline
45 & 1.07004725441348e-16 & 2.14009450882696e-16 & 1 \tabularnewline
46 & 0.092060457322226 & 0.184120914644452 & 0.907939542677774 \tabularnewline
47 & 0.231167530391338 & 0.462335060782677 & 0.768832469608662 \tabularnewline
48 & 1 & 0 & 0 \tabularnewline
49 & 0.988643221810922 & 0.0227135563781562 & 0.0113567781890781 \tabularnewline
50 & 2.63907835480083e-08 & 5.27815670960165e-08 & 0.999999973609216 \tabularnewline
51 & 0.0784480685522016 & 0.156896137104403 & 0.921551931447798 \tabularnewline
52 & 0.00256983029810688 & 0.00513966059621376 & 0.997430169701893 \tabularnewline
53 & 0.978077815168173 & 0.0438443696636538 & 0.0219221848318269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&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]0.118282179922539[/C][C]0.236564359845079[/C][C]0.881717820077461[/C][/ROW]
[ROW][C]22[/C][C]0.99999041539918[/C][C]1.91692016417594e-05[/C][C]9.5846008208797e-06[/C][/ROW]
[ROW][C]23[/C][C]0.845087792068952[/C][C]0.309824415862095[/C][C]0.154912207931048[/C][/ROW]
[ROW][C]24[/C][C]0.000767052739002067[/C][C]0.00153410547800413[/C][C]0.999232947260998[/C][/ROW]
[ROW][C]25[/C][C]4.54658076410444e-05[/C][C]9.09316152820889e-05[/C][C]0.999954534192359[/C][/ROW]
[ROW][C]26[/C][C]0.423801249658253[/C][C]0.847602499316506[/C][C]0.576198750341747[/C][/ROW]
[ROW][C]27[/C][C]0.998634682126451[/C][C]0.00273063574709774[/C][C]0.00136531787354887[/C][/ROW]
[ROW][C]28[/C][C]0.362438868723835[/C][C]0.724877737447671[/C][C]0.637561131276165[/C][/ROW]
[ROW][C]29[/C][C]0.181221383630331[/C][C]0.362442767260662[/C][C]0.81877861636967[/C][/ROW]
[ROW][C]30[/C][C]0.64759690508332[/C][C]0.704806189833359[/C][C]0.352403094916679[/C][/ROW]
[ROW][C]31[/C][C]0.999999762976245[/C][C]4.74047510399384e-07[/C][C]2.37023755199692e-07[/C][/ROW]
[ROW][C]32[/C][C]0.997683359917812[/C][C]0.00463328016437531[/C][C]0.00231664008218765[/C][/ROW]
[ROW][C]33[/C][C]7.0418425629825e-05[/C][C]0.00014083685125965[/C][C]0.99992958157437[/C][/ROW]
[ROW][C]34[/C][C]0.730470273553372[/C][C]0.539059452893256[/C][C]0.269529726446628[/C][/ROW]
[ROW][C]35[/C][C]0.999999968792323[/C][C]6.24153542604947e-08[/C][C]3.12076771302473e-08[/C][/ROW]
[ROW][C]36[/C][C]0.999717763743827[/C][C]0.000564472512345604[/C][C]0.000282236256172802[/C][/ROW]
[ROW][C]37[/C][C]0.99998250597231[/C][C]3.49880553789977e-05[/C][C]1.74940276894989e-05[/C][/ROW]
[ROW][C]38[/C][C]0.999888481341707[/C][C]0.000223037316585118[/C][C]0.000111518658292559[/C][/ROW]
[ROW][C]39[/C][C]0.999999999999741[/C][C]5.17123783487239e-13[/C][C]2.58561891743619e-13[/C][/ROW]
[ROW][C]40[/C][C]0.99999375421064[/C][C]1.24915787187875e-05[/C][C]6.24578935939374e-06[/C][/ROW]
[ROW][C]41[/C][C]0.194133451379887[/C][C]0.388266902759774[/C][C]0.805866548620113[/C][/ROW]
[ROW][C]42[/C][C]1.60727044647992e-05[/C][C]3.21454089295984e-05[/C][C]0.999983927295535[/C][/ROW]
[ROW][C]43[/C][C]0.208804879213456[/C][C]0.417609758426912[/C][C]0.791195120786544[/C][/ROW]
[ROW][C]44[/C][C]3.51478292819305e-12[/C][C]7.02956585638609e-12[/C][C]0.999999999996485[/C][/ROW]
[ROW][C]45[/C][C]1.07004725441348e-16[/C][C]2.14009450882696e-16[/C][C]1[/C][/ROW]
[ROW][C]46[/C][C]0.092060457322226[/C][C]0.184120914644452[/C][C]0.907939542677774[/C][/ROW]
[ROW][C]47[/C][C]0.231167530391338[/C][C]0.462335060782677[/C][C]0.768832469608662[/C][/ROW]
[ROW][C]48[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]0.988643221810922[/C][C]0.0227135563781562[/C][C]0.0113567781890781[/C][/ROW]
[ROW][C]50[/C][C]2.63907835480083e-08[/C][C]5.27815670960165e-08[/C][C]0.999999973609216[/C][/ROW]
[ROW][C]51[/C][C]0.0784480685522016[/C][C]0.156896137104403[/C][C]0.921551931447798[/C][/ROW]
[ROW][C]52[/C][C]0.00256983029810688[/C][C]0.00513966059621376[/C][C]0.997430169701893[/C][/ROW]
[ROW][C]53[/C][C]0.978077815168173[/C][C]0.0438443696636538[/C][C]0.0219221848318269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&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
210.1182821799225390.2365643598450790.881717820077461
220.999990415399181.91692016417594e-059.5846008208797e-06
230.8450877920689520.3098244158620950.154912207931048
240.0007670527390020670.001534105478004130.999232947260998
254.54658076410444e-059.09316152820889e-050.999954534192359
260.4238012496582530.8476024993165060.576198750341747
270.9986346821264510.002730635747097740.00136531787354887
280.3624388687238350.7248777374476710.637561131276165
290.1812213836303310.3624427672606620.81877861636967
300.647596905083320.7048061898333590.352403094916679
310.9999997629762454.74047510399384e-072.37023755199692e-07
320.9976833599178120.004633280164375310.00231664008218765
337.0418425629825e-050.000140836851259650.99992958157437
340.7304702735533720.5390594528932560.269529726446628
350.9999999687923236.24153542604947e-083.12076771302473e-08
360.9997177637438270.0005644725123456040.000282236256172802
370.999982505972313.49880553789977e-051.74940276894989e-05
380.9998884813417070.0002230373165851180.000111518658292559
390.9999999999997415.17123783487239e-132.58561891743619e-13
400.999993754210641.24915787187875e-056.24578935939374e-06
410.1941334513798870.3882669027597740.805866548620113
421.60727044647992e-053.21454089295984e-050.999983927295535
430.2088048792134560.4176097584269120.791195120786544
443.51478292819305e-127.02956585638609e-120.999999999996485
451.07004725441348e-162.14009450882696e-161
460.0920604573222260.1841209146444520.907939542677774
470.2311675303913380.4623350607826770.768832469608662
48100
490.9886432218109220.02271355637815620.0113567781890781
502.63907835480083e-085.27815670960165e-080.999999973609216
510.07844806855220160.1568961371044030.921551931447798
520.002569830298106880.005139660596213760.997430169701893
530.9780778151681730.04384436966365380.0219221848318269






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.575757575757576NOK
5% type I error level210.636363636363636NOK
10% type I error level210.636363636363636NOK

\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 & 19 & 0.575757575757576 & NOK \tabularnewline
5% type I error level & 21 & 0.636363636363636 & NOK \tabularnewline
10% type I error level & 21 & 0.636363636363636 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58397&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]19[/C][C]0.575757575757576[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]21[/C][C]0.636363636363636[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]21[/C][C]0.636363636363636[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58397&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58397&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 level190.575757575757576NOK
5% type I error level210.636363636363636NOK
10% type I error level210.636363636363636NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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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')
}