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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 21 Nov 2009 03:00:03 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/21/t1258797790pchucdr3dut0rp9.htm/, Retrieved Sun, 28 Apr 2024 16:07:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58521, Retrieved Sun, 28 Apr 2024 16:07:51 +0000

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Estimated Impact

123

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [multiple regression] [2009-11-21 10:00:03] [21abcd6b6f55e53f03dbc7aec5059429] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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=58521&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=58521&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 9.74222222222222 -1.55555555555556X[t] + 0.259999999999998M1[t] -0.180000000000001M2[t] -0.560000000000001M3[t] -0.460000000000001M4[t] -0.28M5[t] -0.3M6[t] -0.500000000000001M7[t] -0.760000000000001M8[t] -1.04M9[t] -1.02M10[t] -0.200000000000000M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  9.74222222222222 -1.55555555555556X[t] +  0.259999999999998M1[t] -0.180000000000001M2[t] -0.560000000000001M3[t] -0.460000000000001M4[t] -0.28M5[t] -0.3M6[t] -0.500000000000001M7[t] -0.760000000000001M8[t] -1.04M9[t] -1.02M10[t] -0.200000000000000M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58521&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  9.74222222222222 -1.55555555555556X[t] +  0.259999999999998M1[t] -0.180000000000001M2[t] -0.560000000000001M3[t] -0.460000000000001M4[t] -0.28M5[t] -0.3M6[t] -0.500000000000001M7[t] -0.760000000000001M8[t] -1.04M9[t] -1.02M10[t] -0.200000000000000M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58521&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 9.74222222222222 -1.55555555555556X[t] + 0.259999999999998M1[t] -0.180000000000001M2[t] -0.560000000000001M3[t] -0.460000000000001M4[t] -0.28M5[t] -0.3M6[t] -0.500000000000001M7[t] -0.760000000000001M8[t] -1.04M9[t] -1.02M10[t] -0.200000000000000M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	9.74222222222222	0.214083	45.5067	0	0
X	-1.55555555555556	0.122785	-12.6689	0	0
M1	0.259999999999998	0.294684	0.8823	0.382105	0.191052
M2	-0.180000000000001	0.294684	-0.6108	0.544259	0.27213
M3	-0.560000000000001	0.294684	-1.9003	0.063532	0.031766
M4	-0.460000000000001	0.294684	-1.561	0.125234	0.062617
M5	-0.28	0.294684	-0.9502	0.346887	0.173443
M6	-0.3	0.294684	-1.018	0.313871	0.156936
M7	-0.500000000000001	0.294684	-1.6967	0.096362	0.048181
M8	-0.760000000000001	0.294684	-2.579	0.013098	0.006549
M9	-1.04	0.294684	-3.5292	0.000944	0.000472
M10	-1.02	0.294684	-3.4613	0.001155	0.000577
M11	-0.200000000000000	0.294684	-0.6787	0.500661	0.250331

\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) & 9.74222222222222 & 0.214083 & 45.5067 & 0 & 0 \tabularnewline
X & -1.55555555555556 & 0.122785 & -12.6689 & 0 & 0 \tabularnewline
M1 & 0.259999999999998 & 0.294684 & 0.8823 & 0.382105 & 0.191052 \tabularnewline
M2 & -0.180000000000001 & 0.294684 & -0.6108 & 0.544259 & 0.27213 \tabularnewline
M3 & -0.560000000000001 & 0.294684 & -1.9003 & 0.063532 & 0.031766 \tabularnewline
M4 & -0.460000000000001 & 0.294684 & -1.561 & 0.125234 & 0.062617 \tabularnewline
M5 & -0.28 & 0.294684 & -0.9502 & 0.346887 & 0.173443 \tabularnewline
M6 & -0.3 & 0.294684 & -1.018 & 0.313871 & 0.156936 \tabularnewline
M7 & -0.500000000000001 & 0.294684 & -1.6967 & 0.096362 & 0.048181 \tabularnewline
M8 & -0.760000000000001 & 0.294684 & -2.579 & 0.013098 & 0.006549 \tabularnewline
M9 & -1.04 & 0.294684 & -3.5292 & 0.000944 & 0.000472 \tabularnewline
M10 & -1.02 & 0.294684 & -3.4613 & 0.001155 & 0.000577 \tabularnewline
M11 & -0.200000000000000 & 0.294684 & -0.6787 & 0.500661 & 0.250331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58521&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]9.74222222222222[/C][C]0.214083[/C][C]45.5067[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-1.55555555555556[/C][C]0.122785[/C][C]-12.6689[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.259999999999998[/C][C]0.294684[/C][C]0.8823[/C][C]0.382105[/C][C]0.191052[/C][/ROW]
[ROW][C]M2[/C][C]-0.180000000000001[/C][C]0.294684[/C][C]-0.6108[/C][C]0.544259[/C][C]0.27213[/C][/ROW]
[ROW][C]M3[/C][C]-0.560000000000001[/C][C]0.294684[/C][C]-1.9003[/C][C]0.063532[/C][C]0.031766[/C][/ROW]
[ROW][C]M4[/C][C]-0.460000000000001[/C][C]0.294684[/C][C]-1.561[/C][C]0.125234[/C][C]0.062617[/C][/ROW]
[ROW][C]M5[/C][C]-0.28[/C][C]0.294684[/C][C]-0.9502[/C][C]0.346887[/C][C]0.173443[/C][/ROW]
[ROW][C]M6[/C][C]-0.3[/C][C]0.294684[/C][C]-1.018[/C][C]0.313871[/C][C]0.156936[/C][/ROW]
[ROW][C]M7[/C][C]-0.500000000000001[/C][C]0.294684[/C][C]-1.6967[/C][C]0.096362[/C][C]0.048181[/C][/ROW]
[ROW][C]M8[/C][C]-0.760000000000001[/C][C]0.294684[/C][C]-2.579[/C][C]0.013098[/C][C]0.006549[/C][/ROW]
[ROW][C]M9[/C][C]-1.04[/C][C]0.294684[/C][C]-3.5292[/C][C]0.000944[/C][C]0.000472[/C][/ROW]
[ROW][C]M10[/C][C]-1.02[/C][C]0.294684[/C][C]-3.4613[/C][C]0.001155[/C][C]0.000577[/C][/ROW]
[ROW][C]M11[/C][C]-0.200000000000000[/C][C]0.294684[/C][C]-0.6787[/C][C]0.500661[/C][C]0.250331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58521&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	9.74222222222222	0.214083	45.5067	0	0
X	-1.55555555555556	0.122785	-12.6689	0	0
M1	0.259999999999998	0.294684	0.8823	0.382105	0.191052
M2	-0.180000000000001	0.294684	-0.6108	0.544259	0.27213
M3	-0.560000000000001	0.294684	-1.9003	0.063532	0.031766
M4	-0.460000000000001	0.294684	-1.561	0.125234	0.062617
M5	-0.28	0.294684	-0.9502	0.346887	0.173443
M6	-0.3	0.294684	-1.018	0.313871	0.156936
M7	-0.500000000000001	0.294684	-1.6967	0.096362	0.048181
M8	-0.760000000000001	0.294684	-2.579	0.013098	0.006549
M9	-1.04	0.294684	-3.5292	0.000944	0.000472
M10	-1.02	0.294684	-3.4613	0.001155	0.000577
M11	-0.200000000000000	0.294684	-0.6787	0.500661	0.250331

Multiple Linear Regression - Regression Statistics
Multiple R	0.89936121167632
R-squared	0.8088505890679
Adjusted R-squared	0.760046484149065
F-TEST (value)	16.5734130441095
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	5.09037256790634e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.465936612334712
Sum Squared Residuals	10.2035555555555

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.89936121167632 \tabularnewline
R-squared & 0.8088505890679 \tabularnewline
Adjusted R-squared & 0.760046484149065 \tabularnewline
F-TEST (value) & 16.5734130441095 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 5.09037256790634e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.465936612334712 \tabularnewline
Sum Squared Residuals & 10.2035555555555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58521&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.89936121167632[/C][/ROW]
[ROW][C]R-squared[/C][C]0.8088505890679[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.760046484149065[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]16.5734130441095[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]5.09037256790634e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.465936612334712[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]10.2035555555555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58521&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.89936121167632
R-squared	0.8088505890679
Adjusted R-squared	0.760046484149065
F-TEST (value)	16.5734130441095
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	5.09037256790634e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.465936612334712
Sum Squared Residuals	10.2035555555555

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	10.9	10.0022222222222	0.897777777777774
2	10	9.56222222222222	0.437777777777779
3	9.2	9.18222222222222	0.0177777777777778
4	9.2	9.28222222222222	-0.0822222222222222
5	9.5	9.46222222222222	0.0377777777777778
6	9.6	9.44222222222222	0.157777777777778
7	9.5	9.24222222222222	0.257777777777778
8	9.1	8.98222222222222	0.117777777777777
9	8.9	8.70222222222222	0.197777777777778
10	9	8.72222222222222	0.277777777777778
11	10.1	9.54222222222222	0.557777777777778
12	10.3	9.74222222222222	0.557777777777778
13	10.2	10.0022222222222	0.197777777777778
14	9.6	9.56222222222222	0.0377777777777772
15	9.2	9.18222222222222	0.0177777777777771
16	9.3	9.28222222222222	0.0177777777777784
17	9.4	9.46222222222222	-0.0622222222222221
18	9.4	9.44222222222222	-0.042222222222222
19	9.2	9.24222222222222	-0.0422222222222225
20	9	8.98222222222222	0.0177777777777782
21	9	8.70222222222222	0.297777777777777
22	9	8.72222222222222	0.277777777777778
23	9.8	9.54222222222222	0.257777777777778
24	10	9.74222222222222	0.257777777777777
25	9.8	10.0022222222222	-0.202222222222221
26	9.3	9.56222222222222	-0.262222222222222
27	9	9.18222222222222	-0.182222222222222
28	9	9.28222222222222	-0.282222222222222
29	9.1	9.46222222222222	-0.362222222222223
30	9.1	9.44222222222222	-0.342222222222222
31	9.1	9.24222222222222	-0.142222222222222
32	9.2	8.98222222222222	0.217777777777777
33	8.8	8.70222222222222	0.097777777777778
34	8.3	8.72222222222222	-0.422222222222222
35	8.4	9.54222222222222	-1.14222222222222
36	8.1	9.74222222222222	-1.64222222222222
37	7.7	8.44666666666667	-0.746666666666666
38	7.9	8.00666666666667	-0.106666666666667
39	7.9	7.62666666666667	0.273333333333334
40	8	7.72666666666667	0.273333333333333
41	7.9	7.90666666666667	-0.00666666666666656
42	7.6	7.88666666666667	-0.286666666666667
43	7.1	7.68666666666667	-0.586666666666667
44	6.8	7.42666666666667	-0.626666666666666
45	6.5	7.14666666666667	-0.646666666666667
46	6.9	7.16666666666667	-0.266666666666667
47	8.2	7.98666666666667	0.213333333333332
48	8.7	8.18666666666667	0.513333333333332
49	8.3	8.44666666666667	-0.146666666666665
50	7.9	8.00666666666667	-0.106666666666667
51	7.5	7.62666666666667	-0.126666666666667
52	7.8	7.72666666666667	0.073333333333333
53	8.3	7.90666666666667	0.393333333333334
54	8.4	7.88666666666667	0.513333333333333
55	8.2	7.68666666666667	0.513333333333333
56	7.7	7.42666666666667	0.273333333333334
57	7.2	7.14666666666667	0.0533333333333332
58	7.3	7.16666666666667	0.133333333333333
59	8.1	7.98666666666667	0.113333333333333
60	8.5	8.18666666666667	0.313333333333333

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 10.9 & 10.0022222222222 & 0.897777777777774 \tabularnewline
2 & 10 & 9.56222222222222 & 0.437777777777779 \tabularnewline
3 & 9.2 & 9.18222222222222 & 0.0177777777777778 \tabularnewline
4 & 9.2 & 9.28222222222222 & -0.0822222222222222 \tabularnewline
5 & 9.5 & 9.46222222222222 & 0.0377777777777778 \tabularnewline
6 & 9.6 & 9.44222222222222 & 0.157777777777778 \tabularnewline
7 & 9.5 & 9.24222222222222 & 0.257777777777778 \tabularnewline
8 & 9.1 & 8.98222222222222 & 0.117777777777777 \tabularnewline
9 & 8.9 & 8.70222222222222 & 0.197777777777778 \tabularnewline
10 & 9 & 8.72222222222222 & 0.277777777777778 \tabularnewline
11 & 10.1 & 9.54222222222222 & 0.557777777777778 \tabularnewline
12 & 10.3 & 9.74222222222222 & 0.557777777777778 \tabularnewline
13 & 10.2 & 10.0022222222222 & 0.197777777777778 \tabularnewline
14 & 9.6 & 9.56222222222222 & 0.0377777777777772 \tabularnewline
15 & 9.2 & 9.18222222222222 & 0.0177777777777771 \tabularnewline
16 & 9.3 & 9.28222222222222 & 0.0177777777777784 \tabularnewline
17 & 9.4 & 9.46222222222222 & -0.0622222222222221 \tabularnewline
18 & 9.4 & 9.44222222222222 & -0.042222222222222 \tabularnewline
19 & 9.2 & 9.24222222222222 & -0.0422222222222225 \tabularnewline
20 & 9 & 8.98222222222222 & 0.0177777777777782 \tabularnewline
21 & 9 & 8.70222222222222 & 0.297777777777777 \tabularnewline
22 & 9 & 8.72222222222222 & 0.277777777777778 \tabularnewline
23 & 9.8 & 9.54222222222222 & 0.257777777777778 \tabularnewline
24 & 10 & 9.74222222222222 & 0.257777777777777 \tabularnewline
25 & 9.8 & 10.0022222222222 & -0.202222222222221 \tabularnewline
26 & 9.3 & 9.56222222222222 & -0.262222222222222 \tabularnewline
27 & 9 & 9.18222222222222 & -0.182222222222222 \tabularnewline
28 & 9 & 9.28222222222222 & -0.282222222222222 \tabularnewline
29 & 9.1 & 9.46222222222222 & -0.362222222222223 \tabularnewline
30 & 9.1 & 9.44222222222222 & -0.342222222222222 \tabularnewline
31 & 9.1 & 9.24222222222222 & -0.142222222222222 \tabularnewline
32 & 9.2 & 8.98222222222222 & 0.217777777777777 \tabularnewline
33 & 8.8 & 8.70222222222222 & 0.097777777777778 \tabularnewline
34 & 8.3 & 8.72222222222222 & -0.422222222222222 \tabularnewline
35 & 8.4 & 9.54222222222222 & -1.14222222222222 \tabularnewline
36 & 8.1 & 9.74222222222222 & -1.64222222222222 \tabularnewline
37 & 7.7 & 8.44666666666667 & -0.746666666666666 \tabularnewline
38 & 7.9 & 8.00666666666667 & -0.106666666666667 \tabularnewline
39 & 7.9 & 7.62666666666667 & 0.273333333333334 \tabularnewline
40 & 8 & 7.72666666666667 & 0.273333333333333 \tabularnewline
41 & 7.9 & 7.90666666666667 & -0.00666666666666656 \tabularnewline
42 & 7.6 & 7.88666666666667 & -0.286666666666667 \tabularnewline
43 & 7.1 & 7.68666666666667 & -0.586666666666667 \tabularnewline
44 & 6.8 & 7.42666666666667 & -0.626666666666666 \tabularnewline
45 & 6.5 & 7.14666666666667 & -0.646666666666667 \tabularnewline
46 & 6.9 & 7.16666666666667 & -0.266666666666667 \tabularnewline
47 & 8.2 & 7.98666666666667 & 0.213333333333332 \tabularnewline
48 & 8.7 & 8.18666666666667 & 0.513333333333332 \tabularnewline
49 & 8.3 & 8.44666666666667 & -0.146666666666665 \tabularnewline
50 & 7.9 & 8.00666666666667 & -0.106666666666667 \tabularnewline
51 & 7.5 & 7.62666666666667 & -0.126666666666667 \tabularnewline
52 & 7.8 & 7.72666666666667 & 0.073333333333333 \tabularnewline
53 & 8.3 & 7.90666666666667 & 0.393333333333334 \tabularnewline
54 & 8.4 & 7.88666666666667 & 0.513333333333333 \tabularnewline
55 & 8.2 & 7.68666666666667 & 0.513333333333333 \tabularnewline
56 & 7.7 & 7.42666666666667 & 0.273333333333334 \tabularnewline
57 & 7.2 & 7.14666666666667 & 0.0533333333333332 \tabularnewline
58 & 7.3 & 7.16666666666667 & 0.133333333333333 \tabularnewline
59 & 8.1 & 7.98666666666667 & 0.113333333333333 \tabularnewline
60 & 8.5 & 8.18666666666667 & 0.313333333333333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58521&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]10.9[/C][C]10.0022222222222[/C][C]0.897777777777774[/C][/ROW]
[ROW][C]2[/C][C]10[/C][C]9.56222222222222[/C][C]0.437777777777779[/C][/ROW]
[ROW][C]3[/C][C]9.2[/C][C]9.18222222222222[/C][C]0.0177777777777778[/C][/ROW]
[ROW][C]4[/C][C]9.2[/C][C]9.28222222222222[/C][C]-0.0822222222222222[/C][/ROW]
[ROW][C]5[/C][C]9.5[/C][C]9.46222222222222[/C][C]0.0377777777777778[/C][/ROW]
[ROW][C]6[/C][C]9.6[/C][C]9.44222222222222[/C][C]0.157777777777778[/C][/ROW]
[ROW][C]7[/C][C]9.5[/C][C]9.24222222222222[/C][C]0.257777777777778[/C][/ROW]
[ROW][C]8[/C][C]9.1[/C][C]8.98222222222222[/C][C]0.117777777777777[/C][/ROW]
[ROW][C]9[/C][C]8.9[/C][C]8.70222222222222[/C][C]0.197777777777778[/C][/ROW]
[ROW][C]10[/C][C]9[/C][C]8.72222222222222[/C][C]0.277777777777778[/C][/ROW]
[ROW][C]11[/C][C]10.1[/C][C]9.54222222222222[/C][C]0.557777777777778[/C][/ROW]
[ROW][C]12[/C][C]10.3[/C][C]9.74222222222222[/C][C]0.557777777777778[/C][/ROW]
[ROW][C]13[/C][C]10.2[/C][C]10.0022222222222[/C][C]0.197777777777778[/C][/ROW]
[ROW][C]14[/C][C]9.6[/C][C]9.56222222222222[/C][C]0.0377777777777772[/C][/ROW]
[ROW][C]15[/C][C]9.2[/C][C]9.18222222222222[/C][C]0.0177777777777771[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]9.28222222222222[/C][C]0.0177777777777784[/C][/ROW]
[ROW][C]17[/C][C]9.4[/C][C]9.46222222222222[/C][C]-0.0622222222222221[/C][/ROW]
[ROW][C]18[/C][C]9.4[/C][C]9.44222222222222[/C][C]-0.042222222222222[/C][/ROW]
[ROW][C]19[/C][C]9.2[/C][C]9.24222222222222[/C][C]-0.0422222222222225[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]8.98222222222222[/C][C]0.0177777777777782[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]8.70222222222222[/C][C]0.297777777777777[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]8.72222222222222[/C][C]0.277777777777778[/C][/ROW]
[ROW][C]23[/C][C]9.8[/C][C]9.54222222222222[/C][C]0.257777777777778[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]9.74222222222222[/C][C]0.257777777777777[/C][/ROW]
[ROW][C]25[/C][C]9.8[/C][C]10.0022222222222[/C][C]-0.202222222222221[/C][/ROW]
[ROW][C]26[/C][C]9.3[/C][C]9.56222222222222[/C][C]-0.262222222222222[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]9.18222222222222[/C][C]-0.182222222222222[/C][/ROW]
[ROW][C]28[/C][C]9[/C][C]9.28222222222222[/C][C]-0.282222222222222[/C][/ROW]
[ROW][C]29[/C][C]9.1[/C][C]9.46222222222222[/C][C]-0.362222222222223[/C][/ROW]
[ROW][C]30[/C][C]9.1[/C][C]9.44222222222222[/C][C]-0.342222222222222[/C][/ROW]
[ROW][C]31[/C][C]9.1[/C][C]9.24222222222222[/C][C]-0.142222222222222[/C][/ROW]
[ROW][C]32[/C][C]9.2[/C][C]8.98222222222222[/C][C]0.217777777777777[/C][/ROW]
[ROW][C]33[/C][C]8.8[/C][C]8.70222222222222[/C][C]0.097777777777778[/C][/ROW]
[ROW][C]34[/C][C]8.3[/C][C]8.72222222222222[/C][C]-0.422222222222222[/C][/ROW]
[ROW][C]35[/C][C]8.4[/C][C]9.54222222222222[/C][C]-1.14222222222222[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]9.74222222222222[/C][C]-1.64222222222222[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]8.44666666666667[/C][C]-0.746666666666666[/C][/ROW]
[ROW][C]38[/C][C]7.9[/C][C]8.00666666666667[/C][C]-0.106666666666667[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.62666666666667[/C][C]0.273333333333334[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.72666666666667[/C][C]0.273333333333333[/C][/ROW]
[ROW][C]41[/C][C]7.9[/C][C]7.90666666666667[/C][C]-0.00666666666666656[/C][/ROW]
[ROW][C]42[/C][C]7.6[/C][C]7.88666666666667[/C][C]-0.286666666666667[/C][/ROW]
[ROW][C]43[/C][C]7.1[/C][C]7.68666666666667[/C][C]-0.586666666666667[/C][/ROW]
[ROW][C]44[/C][C]6.8[/C][C]7.42666666666667[/C][C]-0.626666666666666[/C][/ROW]
[ROW][C]45[/C][C]6.5[/C][C]7.14666666666667[/C][C]-0.646666666666667[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]7.16666666666667[/C][C]-0.266666666666667[/C][/ROW]
[ROW][C]47[/C][C]8.2[/C][C]7.98666666666667[/C][C]0.213333333333332[/C][/ROW]
[ROW][C]48[/C][C]8.7[/C][C]8.18666666666667[/C][C]0.513333333333332[/C][/ROW]
[ROW][C]49[/C][C]8.3[/C][C]8.44666666666667[/C][C]-0.146666666666665[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]8.00666666666667[/C][C]-0.106666666666667[/C][/ROW]
[ROW][C]51[/C][C]7.5[/C][C]7.62666666666667[/C][C]-0.126666666666667[/C][/ROW]
[ROW][C]52[/C][C]7.8[/C][C]7.72666666666667[/C][C]0.073333333333333[/C][/ROW]
[ROW][C]53[/C][C]8.3[/C][C]7.90666666666667[/C][C]0.393333333333334[/C][/ROW]
[ROW][C]54[/C][C]8.4[/C][C]7.88666666666667[/C][C]0.513333333333333[/C][/ROW]
[ROW][C]55[/C][C]8.2[/C][C]7.68666666666667[/C][C]0.513333333333333[/C][/ROW]
[ROW][C]56[/C][C]7.7[/C][C]7.42666666666667[/C][C]0.273333333333334[/C][/ROW]
[ROW][C]57[/C][C]7.2[/C][C]7.14666666666667[/C][C]0.0533333333333332[/C][/ROW]
[ROW][C]58[/C][C]7.3[/C][C]7.16666666666667[/C][C]0.133333333333333[/C][/ROW]
[ROW][C]59[/C][C]8.1[/C][C]7.98666666666667[/C][C]0.113333333333333[/C][/ROW]
[ROW][C]60[/C][C]8.5[/C][C]8.18666666666667[/C][C]0.313333333333333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58521&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	10.9	10.0022222222222	0.897777777777774
2	10	9.56222222222222	0.437777777777779
3	9.2	9.18222222222222	0.0177777777777778
4	9.2	9.28222222222222	-0.0822222222222222
5	9.5	9.46222222222222	0.0377777777777778
6	9.6	9.44222222222222	0.157777777777778
7	9.5	9.24222222222222	0.257777777777778
8	9.1	8.98222222222222	0.117777777777777
9	8.9	8.70222222222222	0.197777777777778
10	9	8.72222222222222	0.277777777777778
11	10.1	9.54222222222222	0.557777777777778
12	10.3	9.74222222222222	0.557777777777778
13	10.2	10.0022222222222	0.197777777777778
14	9.6	9.56222222222222	0.0377777777777772
15	9.2	9.18222222222222	0.0177777777777771
16	9.3	9.28222222222222	0.0177777777777784
17	9.4	9.46222222222222	-0.0622222222222221
18	9.4	9.44222222222222	-0.042222222222222
19	9.2	9.24222222222222	-0.0422222222222225
20	9	8.98222222222222	0.0177777777777782
21	9	8.70222222222222	0.297777777777777
22	9	8.72222222222222	0.277777777777778
23	9.8	9.54222222222222	0.257777777777778
24	10	9.74222222222222	0.257777777777777
25	9.8	10.0022222222222	-0.202222222222221
26	9.3	9.56222222222222	-0.262222222222222
27	9	9.18222222222222	-0.182222222222222
28	9	9.28222222222222	-0.282222222222222
29	9.1	9.46222222222222	-0.362222222222223
30	9.1	9.44222222222222	-0.342222222222222
31	9.1	9.24222222222222	-0.142222222222222
32	9.2	8.98222222222222	0.217777777777777
33	8.8	8.70222222222222	0.097777777777778
34	8.3	8.72222222222222	-0.422222222222222
35	8.4	9.54222222222222	-1.14222222222222
36	8.1	9.74222222222222	-1.64222222222222
37	7.7	8.44666666666667	-0.746666666666666
38	7.9	8.00666666666667	-0.106666666666667
39	7.9	7.62666666666667	0.273333333333334
40	8	7.72666666666667	0.273333333333333
41	7.9	7.90666666666667	-0.00666666666666656
42	7.6	7.88666666666667	-0.286666666666667
43	7.1	7.68666666666667	-0.586666666666667
44	6.8	7.42666666666667	-0.626666666666666
45	6.5	7.14666666666667	-0.646666666666667
46	6.9	7.16666666666667	-0.266666666666667
47	8.2	7.98666666666667	0.213333333333332
48	8.7	8.18666666666667	0.513333333333332
49	8.3	8.44666666666667	-0.146666666666665
50	7.9	8.00666666666667	-0.106666666666667
51	7.5	7.62666666666667	-0.126666666666667
52	7.8	7.72666666666667	0.073333333333333
53	8.3	7.90666666666667	0.393333333333334
54	8.4	7.88666666666667	0.513333333333333
55	8.2	7.68666666666667	0.513333333333333
56	7.7	7.42666666666667	0.273333333333334
57	7.2	7.14666666666667	0.0533333333333332
58	7.3	7.16666666666667	0.133333333333333
59	8.1	7.98666666666667	0.113333333333333
60	8.5	8.18666666666667	0.313333333333333

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.296795934498721	0.593591868997443	0.703204065501279
17	0.157223714595178	0.314447429190356	0.842776285404822
18	0.0832762897115845	0.166552579423169	0.916723710288415
19	0.0493058207308733	0.0986116414617466	0.950694179269127
20	0.0223113841723108	0.0446227683446216	0.97768861582769
21	0.0107371767169032	0.0214743534338064	0.989262823283097
22	0.00492995525732523	0.00985991051465047	0.995070044742675
23	0.00364665574174569	0.00729331148349138	0.996353344258254
24	0.00291428712782469	0.00582857425564938	0.997085712872175
25	0.0171368642807347	0.0342737285614693	0.982863135719265
26	0.0185023627501214	0.0370047255002428	0.981497637249879
27	0.0106660351132213	0.0213320702264426	0.989333964886779
28	0.00617719985943318	0.0123543997188664	0.993822800140567
29	0.00416471086765328	0.00832942173530657	0.995835289132347
30	0.00304849331772107	0.00609698663544213	0.99695150668228
31	0.00188902697749817	0.00377805395499633	0.998110973022502
32	0.00245889535961065	0.0049177907192213	0.99754110464039
33	0.00988674278497403	0.0197734855699481	0.990113257215026
34	0.0605196399718852	0.121039279943770	0.939480360028115
35	0.383818706174033	0.767637412348067	0.616181293825967
36	0.726581286625815	0.546837426748371	0.273418713374185
37	0.688176748787356	0.623646502425288	0.311823251212644
38	0.611986587153915	0.776026825692171	0.388013412846086
39	0.569965753270924	0.860068493458153	0.430034246729076
40	0.480333018036403	0.960666036072806	0.519666981963597
41	0.386507786179606	0.773015572359211	0.613492213820394
42	0.378783406159027	0.757566812318053	0.621216593840973
43	0.54977526315652	0.90044947368696	0.45022473684348
44	0.69769186437076	0.604616271258481	0.302308135629240

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.296795934498721 & 0.593591868997443 & 0.703204065501279 \tabularnewline
17 & 0.157223714595178 & 0.314447429190356 & 0.842776285404822 \tabularnewline
18 & 0.0832762897115845 & 0.166552579423169 & 0.916723710288415 \tabularnewline
19 & 0.0493058207308733 & 0.0986116414617466 & 0.950694179269127 \tabularnewline
20 & 0.0223113841723108 & 0.0446227683446216 & 0.97768861582769 \tabularnewline
21 & 0.0107371767169032 & 0.0214743534338064 & 0.989262823283097 \tabularnewline
22 & 0.00492995525732523 & 0.00985991051465047 & 0.995070044742675 \tabularnewline
23 & 0.00364665574174569 & 0.00729331148349138 & 0.996353344258254 \tabularnewline
24 & 0.00291428712782469 & 0.00582857425564938 & 0.997085712872175 \tabularnewline
25 & 0.0171368642807347 & 0.0342737285614693 & 0.982863135719265 \tabularnewline
26 & 0.0185023627501214 & 0.0370047255002428 & 0.981497637249879 \tabularnewline
27 & 0.0106660351132213 & 0.0213320702264426 & 0.989333964886779 \tabularnewline
28 & 0.00617719985943318 & 0.0123543997188664 & 0.993822800140567 \tabularnewline
29 & 0.00416471086765328 & 0.00832942173530657 & 0.995835289132347 \tabularnewline
30 & 0.00304849331772107 & 0.00609698663544213 & 0.99695150668228 \tabularnewline
31 & 0.00188902697749817 & 0.00377805395499633 & 0.998110973022502 \tabularnewline
32 & 0.00245889535961065 & 0.0049177907192213 & 0.99754110464039 \tabularnewline
33 & 0.00988674278497403 & 0.0197734855699481 & 0.990113257215026 \tabularnewline
34 & 0.0605196399718852 & 0.121039279943770 & 0.939480360028115 \tabularnewline
35 & 0.383818706174033 & 0.767637412348067 & 0.616181293825967 \tabularnewline
36 & 0.726581286625815 & 0.546837426748371 & 0.273418713374185 \tabularnewline
37 & 0.688176748787356 & 0.623646502425288 & 0.311823251212644 \tabularnewline
38 & 0.611986587153915 & 0.776026825692171 & 0.388013412846086 \tabularnewline
39 & 0.569965753270924 & 0.860068493458153 & 0.430034246729076 \tabularnewline
40 & 0.480333018036403 & 0.960666036072806 & 0.519666981963597 \tabularnewline
41 & 0.386507786179606 & 0.773015572359211 & 0.613492213820394 \tabularnewline
42 & 0.378783406159027 & 0.757566812318053 & 0.621216593840973 \tabularnewline
43 & 0.54977526315652 & 0.90044947368696 & 0.45022473684348 \tabularnewline
44 & 0.69769186437076 & 0.604616271258481 & 0.302308135629240 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58521&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]16[/C][C]0.296795934498721[/C][C]0.593591868997443[/C][C]0.703204065501279[/C][/ROW]
[ROW][C]17[/C][C]0.157223714595178[/C][C]0.314447429190356[/C][C]0.842776285404822[/C][/ROW]
[ROW][C]18[/C][C]0.0832762897115845[/C][C]0.166552579423169[/C][C]0.916723710288415[/C][/ROW]
[ROW][C]19[/C][C]0.0493058207308733[/C][C]0.0986116414617466[/C][C]0.950694179269127[/C][/ROW]
[ROW][C]20[/C][C]0.0223113841723108[/C][C]0.0446227683446216[/C][C]0.97768861582769[/C][/ROW]
[ROW][C]21[/C][C]0.0107371767169032[/C][C]0.0214743534338064[/C][C]0.989262823283097[/C][/ROW]
[ROW][C]22[/C][C]0.00492995525732523[/C][C]0.00985991051465047[/C][C]0.995070044742675[/C][/ROW]
[ROW][C]23[/C][C]0.00364665574174569[/C][C]0.00729331148349138[/C][C]0.996353344258254[/C][/ROW]
[ROW][C]24[/C][C]0.00291428712782469[/C][C]0.00582857425564938[/C][C]0.997085712872175[/C][/ROW]
[ROW][C]25[/C][C]0.0171368642807347[/C][C]0.0342737285614693[/C][C]0.982863135719265[/C][/ROW]
[ROW][C]26[/C][C]0.0185023627501214[/C][C]0.0370047255002428[/C][C]0.981497637249879[/C][/ROW]
[ROW][C]27[/C][C]0.0106660351132213[/C][C]0.0213320702264426[/C][C]0.989333964886779[/C][/ROW]
[ROW][C]28[/C][C]0.00617719985943318[/C][C]0.0123543997188664[/C][C]0.993822800140567[/C][/ROW]
[ROW][C]29[/C][C]0.00416471086765328[/C][C]0.00832942173530657[/C][C]0.995835289132347[/C][/ROW]
[ROW][C]30[/C][C]0.00304849331772107[/C][C]0.00609698663544213[/C][C]0.99695150668228[/C][/ROW]
[ROW][C]31[/C][C]0.00188902697749817[/C][C]0.00377805395499633[/C][C]0.998110973022502[/C][/ROW]
[ROW][C]32[/C][C]0.00245889535961065[/C][C]0.0049177907192213[/C][C]0.99754110464039[/C][/ROW]
[ROW][C]33[/C][C]0.00988674278497403[/C][C]0.0197734855699481[/C][C]0.990113257215026[/C][/ROW]
[ROW][C]34[/C][C]0.0605196399718852[/C][C]0.121039279943770[/C][C]0.939480360028115[/C][/ROW]
[ROW][C]35[/C][C]0.383818706174033[/C][C]0.767637412348067[/C][C]0.616181293825967[/C][/ROW]
[ROW][C]36[/C][C]0.726581286625815[/C][C]0.546837426748371[/C][C]0.273418713374185[/C][/ROW]
[ROW][C]37[/C][C]0.688176748787356[/C][C]0.623646502425288[/C][C]0.311823251212644[/C][/ROW]
[ROW][C]38[/C][C]0.611986587153915[/C][C]0.776026825692171[/C][C]0.388013412846086[/C][/ROW]
[ROW][C]39[/C][C]0.569965753270924[/C][C]0.860068493458153[/C][C]0.430034246729076[/C][/ROW]
[ROW][C]40[/C][C]0.480333018036403[/C][C]0.960666036072806[/C][C]0.519666981963597[/C][/ROW]
[ROW][C]41[/C][C]0.386507786179606[/C][C]0.773015572359211[/C][C]0.613492213820394[/C][/ROW]
[ROW][C]42[/C][C]0.378783406159027[/C][C]0.757566812318053[/C][C]0.621216593840973[/C][/ROW]
[ROW][C]43[/C][C]0.54977526315652[/C][C]0.90044947368696[/C][C]0.45022473684348[/C][/ROW]
[ROW][C]44[/C][C]0.69769186437076[/C][C]0.604616271258481[/C][C]0.302308135629240[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58521&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.296795934498721	0.593591868997443	0.703204065501279
17	0.157223714595178	0.314447429190356	0.842776285404822
18	0.0832762897115845	0.166552579423169	0.916723710288415
19	0.0493058207308733	0.0986116414617466	0.950694179269127
20	0.0223113841723108	0.0446227683446216	0.97768861582769
21	0.0107371767169032	0.0214743534338064	0.989262823283097
22	0.00492995525732523	0.00985991051465047	0.995070044742675
23	0.00364665574174569	0.00729331148349138	0.996353344258254
24	0.00291428712782469	0.00582857425564938	0.997085712872175
25	0.0171368642807347	0.0342737285614693	0.982863135719265
26	0.0185023627501214	0.0370047255002428	0.981497637249879
27	0.0106660351132213	0.0213320702264426	0.989333964886779
28	0.00617719985943318	0.0123543997188664	0.993822800140567
29	0.00416471086765328	0.00832942173530657	0.995835289132347
30	0.00304849331772107	0.00609698663544213	0.99695150668228
31	0.00188902697749817	0.00377805395499633	0.998110973022502
32	0.00245889535961065	0.0049177907192213	0.99754110464039
33	0.00988674278497403	0.0197734855699481	0.990113257215026
34	0.0605196399718852	0.121039279943770	0.939480360028115
35	0.383818706174033	0.767637412348067	0.616181293825967
36	0.726581286625815	0.546837426748371	0.273418713374185
37	0.688176748787356	0.623646502425288	0.311823251212644
38	0.611986587153915	0.776026825692171	0.388013412846086
39	0.569965753270924	0.860068493458153	0.430034246729076
40	0.480333018036403	0.960666036072806	0.519666981963597
41	0.386507786179606	0.773015572359211	0.613492213820394
42	0.378783406159027	0.757566812318053	0.621216593840973
43	0.54977526315652	0.90044947368696	0.45022473684348
44	0.69769186437076	0.604616271258481	0.302308135629240

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.241379310344828	NOK
5% type I error level	14	0.482758620689655	NOK
10% type I error level	15	0.517241379310345	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 7 & 0.241379310344828 & NOK \tabularnewline
5% type I error level & 14 & 0.482758620689655 & NOK \tabularnewline
10% type I error level & 15 & 0.517241379310345 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58521&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]7[/C][C]0.241379310344828[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.482758620689655[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]0.517241379310345[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58521&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58521&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.241379310344828	NOK
5% type I error level	14	0.482758620689655	NOK
10% type I error level	15	0.517241379310345	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code