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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 10:02:43 -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/t1258736793bvm1gs0ma10e9yt.htm/, Retrieved Thu, 28 Mar 2024 12:00:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58334, Retrieved Thu, 28 Mar 2024 12:00:15 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
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] [ws 7 3] [2009-11-20 17:02:43] [84778c3520b84fd5786bccf2e25a5aef] [Current]
-   P         [Multiple Regression] [ws7verbetering] [2009-11-26 17:21:31] [7d268329e554b8694908ba13e6e6f258]
-    D          [Multiple Regression] [ws7verbetering2] [2009-11-26 17:29:10] [7d268329e554b8694908ba13e6e6f258]
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Dataseries X:
29.837	0
29.571	0
30.167	0
30.524	0
30.996	0
31.033	0
31.198	0
30.937	0
31.649	0
33.115	0
34.106	0
33.926	0
33.382	0
32.851	0
32.948	0
36.112	0
36.113	0
35.210	0
35.193	0
34.383	0
35.349	0
37.058	0
38.076	0
36.630	0
36.045	0
35.638	0
35.114	0
35.465	0
35.254	0
35.299	0
35.916	0
36.683	0
37.288	0
38.536	0
38.977	0
36.407	0
34.955	0
34.951	0
32.680	0
34.791	0
34.178	0
35.213	0
34.871	0
35.299	0
35.443	0
37.108	0
36.419	0
34.471	0
33.868	0
34.385	0
33.643	1
34.627	1
32.919	1
35.500	1
36.110	1
37.086	1
37.711	1
40.427	1
39.884	1
38.512	1
38.767	1




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=58334&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=58334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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 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
saldo_zichtrek[t] = + 35.5499652830189 + 2.19617358490566crisis[t] -1.44032754716980M1[t] -2.07076528301887M2[t] -3.07880000000001M3[t] -1.6854M4[t] -2.09720000000000M5[t] -1.53820000000000M6[t] -1.33160000000000M7[t] -1.11160000000000M8[t] -0.501200000000004M9[t] + 1.25960000000000M10[t] + 1.50320000000000M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
saldo_zichtrek[t] =  +  35.5499652830189 +  2.19617358490566crisis[t] -1.44032754716980M1[t] -2.07076528301887M2[t] -3.07880000000001M3[t] -1.6854M4[t] -2.09720000000000M5[t] -1.53820000000000M6[t] -1.33160000000000M7[t] -1.11160000000000M8[t] -0.501200000000004M9[t] +  1.25960000000000M10[t] +  1.50320000000000M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58334&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]saldo_zichtrek[t] =  +  35.5499652830189 +  2.19617358490566crisis[t] -1.44032754716980M1[t] -2.07076528301887M2[t] -3.07880000000001M3[t] -1.6854M4[t] -2.09720000000000M5[t] -1.53820000000000M6[t] -1.33160000000000M7[t] -1.11160000000000M8[t] -0.501200000000004M9[t] +  1.25960000000000M10[t] +  1.50320000000000M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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
saldo_zichtrek[t] = + 35.5499652830189 + 2.19617358490566crisis[t] -1.44032754716980M1[t] -2.07076528301887M2[t] -3.07880000000001M3[t] -1.6854M4[t] -2.09720000000000M5[t] -1.53820000000000M6[t] -1.33160000000000M7[t] -1.11160000000000M8[t] -0.501200000000004M9[t] + 1.25960000000000M10[t] + 1.50320000000000M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)35.54996528301890.95558937.202100
crisis2.196173584905660.7109393.08910.0033340.001667
M1-1.440327547169801.27969-1.12550.2659620.132981
M2-2.070765283018871.343906-1.54090.1299190.06496
M3-3.078800000000011.336363-2.30390.0256030.012802
M4-1.68541.336363-1.26120.2133380.106669
M5-2.097200000000001.336363-1.56930.123140.06157
M6-1.538200000000001.336363-1.1510.255420.12771
M7-1.331600000000001.336363-0.99640.3240350.162018
M8-1.111600000000001.336363-0.83180.4096360.204818
M9-0.5012000000000041.336363-0.3750.7092770.354639
M101.259600000000001.3363630.94260.3506270.175314
M111.503200000000001.3363631.12480.2662490.133124

\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) & 35.5499652830189 & 0.955589 & 37.2021 & 0 & 0 \tabularnewline
crisis & 2.19617358490566 & 0.710939 & 3.0891 & 0.003334 & 0.001667 \tabularnewline
M1 & -1.44032754716980 & 1.27969 & -1.1255 & 0.265962 & 0.132981 \tabularnewline
M2 & -2.07076528301887 & 1.343906 & -1.5409 & 0.129919 & 0.06496 \tabularnewline
M3 & -3.07880000000001 & 1.336363 & -2.3039 & 0.025603 & 0.012802 \tabularnewline
M4 & -1.6854 & 1.336363 & -1.2612 & 0.213338 & 0.106669 \tabularnewline
M5 & -2.09720000000000 & 1.336363 & -1.5693 & 0.12314 & 0.06157 \tabularnewline
M6 & -1.53820000000000 & 1.336363 & -1.151 & 0.25542 & 0.12771 \tabularnewline
M7 & -1.33160000000000 & 1.336363 & -0.9964 & 0.324035 & 0.162018 \tabularnewline
M8 & -1.11160000000000 & 1.336363 & -0.8318 & 0.409636 & 0.204818 \tabularnewline
M9 & -0.501200000000004 & 1.336363 & -0.375 & 0.709277 & 0.354639 \tabularnewline
M10 & 1.25960000000000 & 1.336363 & 0.9426 & 0.350627 & 0.175314 \tabularnewline
M11 & 1.50320000000000 & 1.336363 & 1.1248 & 0.266249 & 0.133124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58334&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]35.5499652830189[/C][C]0.955589[/C][C]37.2021[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]crisis[/C][C]2.19617358490566[/C][C]0.710939[/C][C]3.0891[/C][C]0.003334[/C][C]0.001667[/C][/ROW]
[ROW][C]M1[/C][C]-1.44032754716980[/C][C]1.27969[/C][C]-1.1255[/C][C]0.265962[/C][C]0.132981[/C][/ROW]
[ROW][C]M2[/C][C]-2.07076528301887[/C][C]1.343906[/C][C]-1.5409[/C][C]0.129919[/C][C]0.06496[/C][/ROW]
[ROW][C]M3[/C][C]-3.07880000000001[/C][C]1.336363[/C][C]-2.3039[/C][C]0.025603[/C][C]0.012802[/C][/ROW]
[ROW][C]M4[/C][C]-1.6854[/C][C]1.336363[/C][C]-1.2612[/C][C]0.213338[/C][C]0.106669[/C][/ROW]
[ROW][C]M5[/C][C]-2.09720000000000[/C][C]1.336363[/C][C]-1.5693[/C][C]0.12314[/C][C]0.06157[/C][/ROW]
[ROW][C]M6[/C][C]-1.53820000000000[/C][C]1.336363[/C][C]-1.151[/C][C]0.25542[/C][C]0.12771[/C][/ROW]
[ROW][C]M7[/C][C]-1.33160000000000[/C][C]1.336363[/C][C]-0.9964[/C][C]0.324035[/C][C]0.162018[/C][/ROW]
[ROW][C]M8[/C][C]-1.11160000000000[/C][C]1.336363[/C][C]-0.8318[/C][C]0.409636[/C][C]0.204818[/C][/ROW]
[ROW][C]M9[/C][C]-0.501200000000004[/C][C]1.336363[/C][C]-0.375[/C][C]0.709277[/C][C]0.354639[/C][/ROW]
[ROW][C]M10[/C][C]1.25960000000000[/C][C]1.336363[/C][C]0.9426[/C][C]0.350627[/C][C]0.175314[/C][/ROW]
[ROW][C]M11[/C][C]1.50320000000000[/C][C]1.336363[/C][C]1.1248[/C][C]0.266249[/C][C]0.133124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)35.54996528301890.95558937.202100
crisis2.196173584905660.7109393.08910.0033340.001667
M1-1.440327547169801.27969-1.12550.2659620.132981
M2-2.070765283018871.343906-1.54090.1299190.06496
M3-3.078800000000011.336363-2.30390.0256030.012802
M4-1.68541.336363-1.26120.2133380.106669
M5-2.097200000000001.336363-1.56930.123140.06157
M6-1.538200000000001.336363-1.1510.255420.12771
M7-1.331600000000001.336363-0.99640.3240350.162018
M8-1.111600000000001.336363-0.83180.4096360.204818
M9-0.5012000000000041.336363-0.3750.7092770.354639
M101.259600000000001.3363630.94260.3506270.175314
M111.503200000000001.3363631.12480.2662490.133124







Multiple Linear Regression - Regression Statistics
Multiple R0.642327038651281
R-squared0.412584024582524
Adjusted R-squared0.265730030728155
F-TEST (value)2.80948453463018
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.00549319063690001
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.11297592601036
Sum Squared Residuals214.304028667169

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.642327038651281 \tabularnewline
R-squared & 0.412584024582524 \tabularnewline
Adjusted R-squared & 0.265730030728155 \tabularnewline
F-TEST (value) & 2.80948453463018 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.00549319063690001 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.11297592601036 \tabularnewline
Sum Squared Residuals & 214.304028667169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58334&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.642327038651281[/C][/ROW]
[ROW][C]R-squared[/C][C]0.412584024582524[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.265730030728155[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.80948453463018[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.00549319063690001[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.11297592601036[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]214.304028667169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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 R0.642327038651281
R-squared0.412584024582524
Adjusted R-squared0.265730030728155
F-TEST (value)2.80948453463018
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.00549319063690001
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.11297592601036
Sum Squared Residuals214.304028667169







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
129.83734.109637735849-4.272637735849
229.57133.4792-3.90819999999999
330.16732.4711652830189-2.30416528301887
430.52433.8645652830189-3.34056528301887
530.99633.4527652830189-2.45676528301886
631.03334.0117652830189-2.97876528301887
731.19834.2183652830189-3.02036528301887
830.93734.4383652830189-3.50136528301887
931.64935.0487652830189-3.39976528301887
1033.11536.8095652830189-3.69456528301887
1134.10637.0531652830189-2.94716528301887
1233.92635.5499652830189-1.62396528301887
1333.38234.1096377358491-0.72763773584907
1432.85133.4792-0.6282
1532.94832.47116528301890.476834716981132
1636.11233.86456528301892.24743471698113
1736.11333.45276528301892.66023471698113
1835.2134.01176528301891.19823471698113
1935.19334.21836528301890.97463471698113
2034.38334.4383652830189-0.0553652830188658
2135.34935.04876528301890.30023471698113
2237.05836.80956528301890.248434716981131
2338.07637.05316528301891.02283471698113
2436.6335.54996528301891.08003471698113
2536.04534.10963773584911.93536226415093
2635.63833.47922.1588
2735.11432.47116528301892.64283471698113
2835.46533.86456528301891.60043471698114
2935.25433.45276528301891.80123471698113
3035.29934.01176528301891.28723471698113
3135.91634.21836528301891.69763471698113
3236.68334.43836528301892.24463471698113
3337.28835.04876528301892.23923471698113
3438.53636.80956528301891.72643471698113
3538.97737.05316528301891.92383471698113
3636.40735.54996528301890.857034716981126
3734.95534.10963773584910.845362264150931
3834.95133.47921.4718
3932.6832.47116528301890.208834716981132
4034.79133.86456528301890.926434716981128
4134.17833.45276528301890.72523471698113
4235.21334.01176528301891.20123471698113
4334.87134.21836528301890.652634716981134
4435.29934.43836528301890.860634716981131
4535.44335.04876528301890.394234716981131
4637.10836.80956528301890.298434716981128
4736.41937.0531652830189-0.63416528301887
4834.47135.5499652830189-1.07896528301887
4933.86834.1096377358491-0.241637735849065
5034.38533.47920.905799999999998
5133.64334.6673388679245-1.02433886792453
5234.62736.0607388679245-1.43373886792453
5332.91935.6489388679245-2.72993886792453
5435.536.2079388679245-0.707938867924528
5536.1136.4145388679245-0.304538867924528
5637.08636.63453886792450.451461132075471
5737.71137.24493886792450.466061132075473
5840.42739.00573886792451.42126113207547
5939.88439.24933886792450.634661132075473
6038.51237.74613886792450.765861132075471
6138.76736.30581132075472.46118867924528

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 29.837 & 34.109637735849 & -4.272637735849 \tabularnewline
2 & 29.571 & 33.4792 & -3.90819999999999 \tabularnewline
3 & 30.167 & 32.4711652830189 & -2.30416528301887 \tabularnewline
4 & 30.524 & 33.8645652830189 & -3.34056528301887 \tabularnewline
5 & 30.996 & 33.4527652830189 & -2.45676528301886 \tabularnewline
6 & 31.033 & 34.0117652830189 & -2.97876528301887 \tabularnewline
7 & 31.198 & 34.2183652830189 & -3.02036528301887 \tabularnewline
8 & 30.937 & 34.4383652830189 & -3.50136528301887 \tabularnewline
9 & 31.649 & 35.0487652830189 & -3.39976528301887 \tabularnewline
10 & 33.115 & 36.8095652830189 & -3.69456528301887 \tabularnewline
11 & 34.106 & 37.0531652830189 & -2.94716528301887 \tabularnewline
12 & 33.926 & 35.5499652830189 & -1.62396528301887 \tabularnewline
13 & 33.382 & 34.1096377358491 & -0.72763773584907 \tabularnewline
14 & 32.851 & 33.4792 & -0.6282 \tabularnewline
15 & 32.948 & 32.4711652830189 & 0.476834716981132 \tabularnewline
16 & 36.112 & 33.8645652830189 & 2.24743471698113 \tabularnewline
17 & 36.113 & 33.4527652830189 & 2.66023471698113 \tabularnewline
18 & 35.21 & 34.0117652830189 & 1.19823471698113 \tabularnewline
19 & 35.193 & 34.2183652830189 & 0.97463471698113 \tabularnewline
20 & 34.383 & 34.4383652830189 & -0.0553652830188658 \tabularnewline
21 & 35.349 & 35.0487652830189 & 0.30023471698113 \tabularnewline
22 & 37.058 & 36.8095652830189 & 0.248434716981131 \tabularnewline
23 & 38.076 & 37.0531652830189 & 1.02283471698113 \tabularnewline
24 & 36.63 & 35.5499652830189 & 1.08003471698113 \tabularnewline
25 & 36.045 & 34.1096377358491 & 1.93536226415093 \tabularnewline
26 & 35.638 & 33.4792 & 2.1588 \tabularnewline
27 & 35.114 & 32.4711652830189 & 2.64283471698113 \tabularnewline
28 & 35.465 & 33.8645652830189 & 1.60043471698114 \tabularnewline
29 & 35.254 & 33.4527652830189 & 1.80123471698113 \tabularnewline
30 & 35.299 & 34.0117652830189 & 1.28723471698113 \tabularnewline
31 & 35.916 & 34.2183652830189 & 1.69763471698113 \tabularnewline
32 & 36.683 & 34.4383652830189 & 2.24463471698113 \tabularnewline
33 & 37.288 & 35.0487652830189 & 2.23923471698113 \tabularnewline
34 & 38.536 & 36.8095652830189 & 1.72643471698113 \tabularnewline
35 & 38.977 & 37.0531652830189 & 1.92383471698113 \tabularnewline
36 & 36.407 & 35.5499652830189 & 0.857034716981126 \tabularnewline
37 & 34.955 & 34.1096377358491 & 0.845362264150931 \tabularnewline
38 & 34.951 & 33.4792 & 1.4718 \tabularnewline
39 & 32.68 & 32.4711652830189 & 0.208834716981132 \tabularnewline
40 & 34.791 & 33.8645652830189 & 0.926434716981128 \tabularnewline
41 & 34.178 & 33.4527652830189 & 0.72523471698113 \tabularnewline
42 & 35.213 & 34.0117652830189 & 1.20123471698113 \tabularnewline
43 & 34.871 & 34.2183652830189 & 0.652634716981134 \tabularnewline
44 & 35.299 & 34.4383652830189 & 0.860634716981131 \tabularnewline
45 & 35.443 & 35.0487652830189 & 0.394234716981131 \tabularnewline
46 & 37.108 & 36.8095652830189 & 0.298434716981128 \tabularnewline
47 & 36.419 & 37.0531652830189 & -0.63416528301887 \tabularnewline
48 & 34.471 & 35.5499652830189 & -1.07896528301887 \tabularnewline
49 & 33.868 & 34.1096377358491 & -0.241637735849065 \tabularnewline
50 & 34.385 & 33.4792 & 0.905799999999998 \tabularnewline
51 & 33.643 & 34.6673388679245 & -1.02433886792453 \tabularnewline
52 & 34.627 & 36.0607388679245 & -1.43373886792453 \tabularnewline
53 & 32.919 & 35.6489388679245 & -2.72993886792453 \tabularnewline
54 & 35.5 & 36.2079388679245 & -0.707938867924528 \tabularnewline
55 & 36.11 & 36.4145388679245 & -0.304538867924528 \tabularnewline
56 & 37.086 & 36.6345388679245 & 0.451461132075471 \tabularnewline
57 & 37.711 & 37.2449388679245 & 0.466061132075473 \tabularnewline
58 & 40.427 & 39.0057388679245 & 1.42126113207547 \tabularnewline
59 & 39.884 & 39.2493388679245 & 0.634661132075473 \tabularnewline
60 & 38.512 & 37.7461388679245 & 0.765861132075471 \tabularnewline
61 & 38.767 & 36.3058113207547 & 2.46118867924528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58334&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]29.837[/C][C]34.109637735849[/C][C]-4.272637735849[/C][/ROW]
[ROW][C]2[/C][C]29.571[/C][C]33.4792[/C][C]-3.90819999999999[/C][/ROW]
[ROW][C]3[/C][C]30.167[/C][C]32.4711652830189[/C][C]-2.30416528301887[/C][/ROW]
[ROW][C]4[/C][C]30.524[/C][C]33.8645652830189[/C][C]-3.34056528301887[/C][/ROW]
[ROW][C]5[/C][C]30.996[/C][C]33.4527652830189[/C][C]-2.45676528301886[/C][/ROW]
[ROW][C]6[/C][C]31.033[/C][C]34.0117652830189[/C][C]-2.97876528301887[/C][/ROW]
[ROW][C]7[/C][C]31.198[/C][C]34.2183652830189[/C][C]-3.02036528301887[/C][/ROW]
[ROW][C]8[/C][C]30.937[/C][C]34.4383652830189[/C][C]-3.50136528301887[/C][/ROW]
[ROW][C]9[/C][C]31.649[/C][C]35.0487652830189[/C][C]-3.39976528301887[/C][/ROW]
[ROW][C]10[/C][C]33.115[/C][C]36.8095652830189[/C][C]-3.69456528301887[/C][/ROW]
[ROW][C]11[/C][C]34.106[/C][C]37.0531652830189[/C][C]-2.94716528301887[/C][/ROW]
[ROW][C]12[/C][C]33.926[/C][C]35.5499652830189[/C][C]-1.62396528301887[/C][/ROW]
[ROW][C]13[/C][C]33.382[/C][C]34.1096377358491[/C][C]-0.72763773584907[/C][/ROW]
[ROW][C]14[/C][C]32.851[/C][C]33.4792[/C][C]-0.6282[/C][/ROW]
[ROW][C]15[/C][C]32.948[/C][C]32.4711652830189[/C][C]0.476834716981132[/C][/ROW]
[ROW][C]16[/C][C]36.112[/C][C]33.8645652830189[/C][C]2.24743471698113[/C][/ROW]
[ROW][C]17[/C][C]36.113[/C][C]33.4527652830189[/C][C]2.66023471698113[/C][/ROW]
[ROW][C]18[/C][C]35.21[/C][C]34.0117652830189[/C][C]1.19823471698113[/C][/ROW]
[ROW][C]19[/C][C]35.193[/C][C]34.2183652830189[/C][C]0.97463471698113[/C][/ROW]
[ROW][C]20[/C][C]34.383[/C][C]34.4383652830189[/C][C]-0.0553652830188658[/C][/ROW]
[ROW][C]21[/C][C]35.349[/C][C]35.0487652830189[/C][C]0.30023471698113[/C][/ROW]
[ROW][C]22[/C][C]37.058[/C][C]36.8095652830189[/C][C]0.248434716981131[/C][/ROW]
[ROW][C]23[/C][C]38.076[/C][C]37.0531652830189[/C][C]1.02283471698113[/C][/ROW]
[ROW][C]24[/C][C]36.63[/C][C]35.5499652830189[/C][C]1.08003471698113[/C][/ROW]
[ROW][C]25[/C][C]36.045[/C][C]34.1096377358491[/C][C]1.93536226415093[/C][/ROW]
[ROW][C]26[/C][C]35.638[/C][C]33.4792[/C][C]2.1588[/C][/ROW]
[ROW][C]27[/C][C]35.114[/C][C]32.4711652830189[/C][C]2.64283471698113[/C][/ROW]
[ROW][C]28[/C][C]35.465[/C][C]33.8645652830189[/C][C]1.60043471698114[/C][/ROW]
[ROW][C]29[/C][C]35.254[/C][C]33.4527652830189[/C][C]1.80123471698113[/C][/ROW]
[ROW][C]30[/C][C]35.299[/C][C]34.0117652830189[/C][C]1.28723471698113[/C][/ROW]
[ROW][C]31[/C][C]35.916[/C][C]34.2183652830189[/C][C]1.69763471698113[/C][/ROW]
[ROW][C]32[/C][C]36.683[/C][C]34.4383652830189[/C][C]2.24463471698113[/C][/ROW]
[ROW][C]33[/C][C]37.288[/C][C]35.0487652830189[/C][C]2.23923471698113[/C][/ROW]
[ROW][C]34[/C][C]38.536[/C][C]36.8095652830189[/C][C]1.72643471698113[/C][/ROW]
[ROW][C]35[/C][C]38.977[/C][C]37.0531652830189[/C][C]1.92383471698113[/C][/ROW]
[ROW][C]36[/C][C]36.407[/C][C]35.5499652830189[/C][C]0.857034716981126[/C][/ROW]
[ROW][C]37[/C][C]34.955[/C][C]34.1096377358491[/C][C]0.845362264150931[/C][/ROW]
[ROW][C]38[/C][C]34.951[/C][C]33.4792[/C][C]1.4718[/C][/ROW]
[ROW][C]39[/C][C]32.68[/C][C]32.4711652830189[/C][C]0.208834716981132[/C][/ROW]
[ROW][C]40[/C][C]34.791[/C][C]33.8645652830189[/C][C]0.926434716981128[/C][/ROW]
[ROW][C]41[/C][C]34.178[/C][C]33.4527652830189[/C][C]0.72523471698113[/C][/ROW]
[ROW][C]42[/C][C]35.213[/C][C]34.0117652830189[/C][C]1.20123471698113[/C][/ROW]
[ROW][C]43[/C][C]34.871[/C][C]34.2183652830189[/C][C]0.652634716981134[/C][/ROW]
[ROW][C]44[/C][C]35.299[/C][C]34.4383652830189[/C][C]0.860634716981131[/C][/ROW]
[ROW][C]45[/C][C]35.443[/C][C]35.0487652830189[/C][C]0.394234716981131[/C][/ROW]
[ROW][C]46[/C][C]37.108[/C][C]36.8095652830189[/C][C]0.298434716981128[/C][/ROW]
[ROW][C]47[/C][C]36.419[/C][C]37.0531652830189[/C][C]-0.63416528301887[/C][/ROW]
[ROW][C]48[/C][C]34.471[/C][C]35.5499652830189[/C][C]-1.07896528301887[/C][/ROW]
[ROW][C]49[/C][C]33.868[/C][C]34.1096377358491[/C][C]-0.241637735849065[/C][/ROW]
[ROW][C]50[/C][C]34.385[/C][C]33.4792[/C][C]0.905799999999998[/C][/ROW]
[ROW][C]51[/C][C]33.643[/C][C]34.6673388679245[/C][C]-1.02433886792453[/C][/ROW]
[ROW][C]52[/C][C]34.627[/C][C]36.0607388679245[/C][C]-1.43373886792453[/C][/ROW]
[ROW][C]53[/C][C]32.919[/C][C]35.6489388679245[/C][C]-2.72993886792453[/C][/ROW]
[ROW][C]54[/C][C]35.5[/C][C]36.2079388679245[/C][C]-0.707938867924528[/C][/ROW]
[ROW][C]55[/C][C]36.11[/C][C]36.4145388679245[/C][C]-0.304538867924528[/C][/ROW]
[ROW][C]56[/C][C]37.086[/C][C]36.6345388679245[/C][C]0.451461132075471[/C][/ROW]
[ROW][C]57[/C][C]37.711[/C][C]37.2449388679245[/C][C]0.466061132075473[/C][/ROW]
[ROW][C]58[/C][C]40.427[/C][C]39.0057388679245[/C][C]1.42126113207547[/C][/ROW]
[ROW][C]59[/C][C]39.884[/C][C]39.2493388679245[/C][C]0.634661132075473[/C][/ROW]
[ROW][C]60[/C][C]38.512[/C][C]37.7461388679245[/C][C]0.765861132075471[/C][/ROW]
[ROW][C]61[/C][C]38.767[/C][C]36.3058113207547[/C][C]2.46118867924528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58334&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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 IndexActualsInterpolationForecastResidualsPrediction Error
129.83734.109637735849-4.272637735849
229.57133.4792-3.90819999999999
330.16732.4711652830189-2.30416528301887
430.52433.8645652830189-3.34056528301887
530.99633.4527652830189-2.45676528301886
631.03334.0117652830189-2.97876528301887
731.19834.2183652830189-3.02036528301887
830.93734.4383652830189-3.50136528301887
931.64935.0487652830189-3.39976528301887
1033.11536.8095652830189-3.69456528301887
1134.10637.0531652830189-2.94716528301887
1233.92635.5499652830189-1.62396528301887
1333.38234.1096377358491-0.72763773584907
1432.85133.4792-0.6282
1532.94832.47116528301890.476834716981132
1636.11233.86456528301892.24743471698113
1736.11333.45276528301892.66023471698113
1835.2134.01176528301891.19823471698113
1935.19334.21836528301890.97463471698113
2034.38334.4383652830189-0.0553652830188658
2135.34935.04876528301890.30023471698113
2237.05836.80956528301890.248434716981131
2338.07637.05316528301891.02283471698113
2436.6335.54996528301891.08003471698113
2536.04534.10963773584911.93536226415093
2635.63833.47922.1588
2735.11432.47116528301892.64283471698113
2835.46533.86456528301891.60043471698114
2935.25433.45276528301891.80123471698113
3035.29934.01176528301891.28723471698113
3135.91634.21836528301891.69763471698113
3236.68334.43836528301892.24463471698113
3337.28835.04876528301892.23923471698113
3438.53636.80956528301891.72643471698113
3538.97737.05316528301891.92383471698113
3636.40735.54996528301890.857034716981126
3734.95534.10963773584910.845362264150931
3834.95133.47921.4718
3932.6832.47116528301890.208834716981132
4034.79133.86456528301890.926434716981128
4134.17833.45276528301890.72523471698113
4235.21334.01176528301891.20123471698113
4334.87134.21836528301890.652634716981134
4435.29934.43836528301890.860634716981131
4535.44335.04876528301890.394234716981131
4637.10836.80956528301890.298434716981128
4736.41937.0531652830189-0.63416528301887
4834.47135.5499652830189-1.07896528301887
4933.86834.1096377358491-0.241637735849065
5034.38533.47920.905799999999998
5133.64334.6673388679245-1.02433886792453
5234.62736.0607388679245-1.43373886792453
5332.91935.6489388679245-2.72993886792453
5435.536.2079388679245-0.707938867924528
5536.1136.4145388679245-0.304538867924528
5637.08636.63453886792450.451461132075471
5737.71137.24493886792450.466061132075473
5840.42739.00573886792451.42126113207547
5939.88439.24933886792450.634661132075473
6038.51237.74613886792450.765861132075471
6138.76736.30581132075472.46118867924528







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.9993850944775270.001229811044945150.000614905522472573
170.999912356141240.0001752877175208898.76438587604445e-05
180.9999288790616040.0001422418767918677.11209383959335e-05
190.9999266929927860.0001466140144280937.33070072140467e-05
200.9999281771728280.0001436456543445587.18228271722788e-05
210.9999205264241780.0001589471516432437.94735758216217e-05
220.9999219879887020.0001560240225961657.80120112980823e-05
230.9998964029570530.0002071940858931250.000103597042946562
240.9998072220835540.0003855558328913310.000192777916445665
250.9998237008868710.0003525982262581240.000176299113129062
260.9998308044087220.0003383911825569150.000169195591278458
270.999901153406750.0001976931865018289.8846593250914e-05
280.9998406105799570.0003187788400867760.000159389420043388
290.9998615205584340.000276958883131430.000138479441565715
300.9997147997441060.0005704005117875550.000285200255893778
310.999548898411110.0009022031777791860.000451101588889593
320.99945668732650.001086625346999250.000543312673499626
330.9993687636886490.001262472622702410.000631236311351203
340.9988579759227510.002284048154497170.00114202407724858
350.998560583652030.002878832695941680.00143941634797084
360.9969409022036820.006118195592636250.00305909779631813
370.9934032651306330.01319346973873460.00659673486936732
380.9867991735134550.02640165297309080.0132008264865454
390.9741783501886980.05164329962260370.0258216498113018
400.9670064180291660.0659871639416680.032993581970834
410.9869935880240520.02601282395189590.0130064119759480
420.9909403823034290.01811923539314230.00905961769657117
430.9902003565679980.01959928686400370.00979964343200183
440.9883464094319960.02330718113600830.0116535905680041
450.987402351948170.02519529610365990.0125976480518300

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.999385094477527 & 0.00122981104494515 & 0.000614905522472573 \tabularnewline
17 & 0.99991235614124 & 0.000175287717520889 & 8.76438587604445e-05 \tabularnewline
18 & 0.999928879061604 & 0.000142241876791867 & 7.11209383959335e-05 \tabularnewline
19 & 0.999926692992786 & 0.000146614014428093 & 7.33070072140467e-05 \tabularnewline
20 & 0.999928177172828 & 0.000143645654344558 & 7.18228271722788e-05 \tabularnewline
21 & 0.999920526424178 & 0.000158947151643243 & 7.94735758216217e-05 \tabularnewline
22 & 0.999921987988702 & 0.000156024022596165 & 7.80120112980823e-05 \tabularnewline
23 & 0.999896402957053 & 0.000207194085893125 & 0.000103597042946562 \tabularnewline
24 & 0.999807222083554 & 0.000385555832891331 & 0.000192777916445665 \tabularnewline
25 & 0.999823700886871 & 0.000352598226258124 & 0.000176299113129062 \tabularnewline
26 & 0.999830804408722 & 0.000338391182556915 & 0.000169195591278458 \tabularnewline
27 & 0.99990115340675 & 0.000197693186501828 & 9.8846593250914e-05 \tabularnewline
28 & 0.999840610579957 & 0.000318778840086776 & 0.000159389420043388 \tabularnewline
29 & 0.999861520558434 & 0.00027695888313143 & 0.000138479441565715 \tabularnewline
30 & 0.999714799744106 & 0.000570400511787555 & 0.000285200255893778 \tabularnewline
31 & 0.99954889841111 & 0.000902203177779186 & 0.000451101588889593 \tabularnewline
32 & 0.9994566873265 & 0.00108662534699925 & 0.000543312673499626 \tabularnewline
33 & 0.999368763688649 & 0.00126247262270241 & 0.000631236311351203 \tabularnewline
34 & 0.998857975922751 & 0.00228404815449717 & 0.00114202407724858 \tabularnewline
35 & 0.99856058365203 & 0.00287883269594168 & 0.00143941634797084 \tabularnewline
36 & 0.996940902203682 & 0.00611819559263625 & 0.00305909779631813 \tabularnewline
37 & 0.993403265130633 & 0.0131934697387346 & 0.00659673486936732 \tabularnewline
38 & 0.986799173513455 & 0.0264016529730908 & 0.0132008264865454 \tabularnewline
39 & 0.974178350188698 & 0.0516432996226037 & 0.0258216498113018 \tabularnewline
40 & 0.967006418029166 & 0.065987163941668 & 0.032993581970834 \tabularnewline
41 & 0.986993588024052 & 0.0260128239518959 & 0.0130064119759480 \tabularnewline
42 & 0.990940382303429 & 0.0181192353931423 & 0.00905961769657117 \tabularnewline
43 & 0.990200356567998 & 0.0195992868640037 & 0.00979964343200183 \tabularnewline
44 & 0.988346409431996 & 0.0233071811360083 & 0.0116535905680041 \tabularnewline
45 & 0.98740235194817 & 0.0251952961036599 & 0.0125976480518300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58334&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]0.999385094477527[/C][C]0.00122981104494515[/C][C]0.000614905522472573[/C][/ROW]
[ROW][C]17[/C][C]0.99991235614124[/C][C]0.000175287717520889[/C][C]8.76438587604445e-05[/C][/ROW]
[ROW][C]18[/C][C]0.999928879061604[/C][C]0.000142241876791867[/C][C]7.11209383959335e-05[/C][/ROW]
[ROW][C]19[/C][C]0.999926692992786[/C][C]0.000146614014428093[/C][C]7.33070072140467e-05[/C][/ROW]
[ROW][C]20[/C][C]0.999928177172828[/C][C]0.000143645654344558[/C][C]7.18228271722788e-05[/C][/ROW]
[ROW][C]21[/C][C]0.999920526424178[/C][C]0.000158947151643243[/C][C]7.94735758216217e-05[/C][/ROW]
[ROW][C]22[/C][C]0.999921987988702[/C][C]0.000156024022596165[/C][C]7.80120112980823e-05[/C][/ROW]
[ROW][C]23[/C][C]0.999896402957053[/C][C]0.000207194085893125[/C][C]0.000103597042946562[/C][/ROW]
[ROW][C]24[/C][C]0.999807222083554[/C][C]0.000385555832891331[/C][C]0.000192777916445665[/C][/ROW]
[ROW][C]25[/C][C]0.999823700886871[/C][C]0.000352598226258124[/C][C]0.000176299113129062[/C][/ROW]
[ROW][C]26[/C][C]0.999830804408722[/C][C]0.000338391182556915[/C][C]0.000169195591278458[/C][/ROW]
[ROW][C]27[/C][C]0.99990115340675[/C][C]0.000197693186501828[/C][C]9.8846593250914e-05[/C][/ROW]
[ROW][C]28[/C][C]0.999840610579957[/C][C]0.000318778840086776[/C][C]0.000159389420043388[/C][/ROW]
[ROW][C]29[/C][C]0.999861520558434[/C][C]0.00027695888313143[/C][C]0.000138479441565715[/C][/ROW]
[ROW][C]30[/C][C]0.999714799744106[/C][C]0.000570400511787555[/C][C]0.000285200255893778[/C][/ROW]
[ROW][C]31[/C][C]0.99954889841111[/C][C]0.000902203177779186[/C][C]0.000451101588889593[/C][/ROW]
[ROW][C]32[/C][C]0.9994566873265[/C][C]0.00108662534699925[/C][C]0.000543312673499626[/C][/ROW]
[ROW][C]33[/C][C]0.999368763688649[/C][C]0.00126247262270241[/C][C]0.000631236311351203[/C][/ROW]
[ROW][C]34[/C][C]0.998857975922751[/C][C]0.00228404815449717[/C][C]0.00114202407724858[/C][/ROW]
[ROW][C]35[/C][C]0.99856058365203[/C][C]0.00287883269594168[/C][C]0.00143941634797084[/C][/ROW]
[ROW][C]36[/C][C]0.996940902203682[/C][C]0.00611819559263625[/C][C]0.00305909779631813[/C][/ROW]
[ROW][C]37[/C][C]0.993403265130633[/C][C]0.0131934697387346[/C][C]0.00659673486936732[/C][/ROW]
[ROW][C]38[/C][C]0.986799173513455[/C][C]0.0264016529730908[/C][C]0.0132008264865454[/C][/ROW]
[ROW][C]39[/C][C]0.974178350188698[/C][C]0.0516432996226037[/C][C]0.0258216498113018[/C][/ROW]
[ROW][C]40[/C][C]0.967006418029166[/C][C]0.065987163941668[/C][C]0.032993581970834[/C][/ROW]
[ROW][C]41[/C][C]0.986993588024052[/C][C]0.0260128239518959[/C][C]0.0130064119759480[/C][/ROW]
[ROW][C]42[/C][C]0.990940382303429[/C][C]0.0181192353931423[/C][C]0.00905961769657117[/C][/ROW]
[ROW][C]43[/C][C]0.990200356567998[/C][C]0.0195992868640037[/C][C]0.00979964343200183[/C][/ROW]
[ROW][C]44[/C][C]0.988346409431996[/C][C]0.0233071811360083[/C][C]0.0116535905680041[/C][/ROW]
[ROW][C]45[/C][C]0.98740235194817[/C][C]0.0251952961036599[/C][C]0.0125976480518300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58334&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.9993850944775270.001229811044945150.000614905522472573
170.999912356141240.0001752877175208898.76438587604445e-05
180.9999288790616040.0001422418767918677.11209383959335e-05
190.9999266929927860.0001466140144280937.33070072140467e-05
200.9999281771728280.0001436456543445587.18228271722788e-05
210.9999205264241780.0001589471516432437.94735758216217e-05
220.9999219879887020.0001560240225961657.80120112980823e-05
230.9998964029570530.0002071940858931250.000103597042946562
240.9998072220835540.0003855558328913310.000192777916445665
250.9998237008868710.0003525982262581240.000176299113129062
260.9998308044087220.0003383911825569150.000169195591278458
270.999901153406750.0001976931865018289.8846593250914e-05
280.9998406105799570.0003187788400867760.000159389420043388
290.9998615205584340.000276958883131430.000138479441565715
300.9997147997441060.0005704005117875550.000285200255893778
310.999548898411110.0009022031777791860.000451101588889593
320.99945668732650.001086625346999250.000543312673499626
330.9993687636886490.001262472622702410.000631236311351203
340.9988579759227510.002284048154497170.00114202407724858
350.998560583652030.002878832695941680.00143941634797084
360.9969409022036820.006118195592636250.00305909779631813
370.9934032651306330.01319346973873460.00659673486936732
380.9867991735134550.02640165297309080.0132008264865454
390.9741783501886980.05164329962260370.0258216498113018
400.9670064180291660.0659871639416680.032993581970834
410.9869935880240520.02601282395189590.0130064119759480
420.9909403823034290.01811923539314230.00905961769657117
430.9902003565679980.01959928686400370.00979964343200183
440.9883464094319960.02330718113600830.0116535905680041
450.987402351948170.02519529610365990.0125976480518300







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level210.7NOK
5% type I error level280.933333333333333NOK
10% type I error level301NOK

\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 & 21 & 0.7 & NOK \tabularnewline
5% type I error level & 28 & 0.933333333333333 & NOK \tabularnewline
10% type I error level & 30 & 1 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58334&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]21[/C][C]0.7[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]28[/C][C]0.933333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]30[/C][C]1[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58334&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58334&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 testsOK/NOK
1% type I error level210.7NOK
5% type I error level280.933333333333333NOK
10% type I error level301NOK



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')
}