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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 12:12:38 -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/t1258744390zsuxkbqytzv40sy.htm/, Retrieved Thu, 28 Mar 2024 09:57:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58431, Retrieved Thu, 28 Mar 2024 09:57:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Multiple Linear R...] [2009-11-20 19:12:38] [b42c0aeada8a5fa89825c81e73c10645] [Current]
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Dataseries X:
9.3	104.1
8.7	90.2
8.2	99.2
8.3	116.5
8.5	98.4
8.6	90.6
8.5	130.5
8.2	107.4
8.1	106
7.9	196.5
8.6	107.8
8.7	90.5
8.7	123.8
8.5	114.7
8.4	115.3
8.5	197
8.7	88.4
8.7	93.8
8.6	111.3
8.5	105.9
8.3	123.6
8	171
8.2	97
8.1	99.2
8.1	126.6
8	103.4
7.9	121.3
7.9	129.6
8	110.8
8	98.9
7.9	122.8
8	120.9
7.7	133.1
7.2	203.1
7.5	110.2
7.3	119.5
7	135.1
7	113.9
7	137.4
7.2	157.1
7.3	126.4
7.1	112.2
6.8	128.8
6.4	136.8
6.1	156.5
6.5	215.2
7.7	146.7
7.9	130.8
7.5	133.1
6.9	153.4
6.6	159.9
6.9	174.6
7.7	145
8	112.9
8	137.8
7.7	150.6
7.3	162.1
7.4	226.4
8.1	112.3
8.3	126.3




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=58431&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=58431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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
Y[t] = + 252.997616013072 -17.3371732026144X[t] + 12.3202303921566M1[t] -2.30092156862746M2[t] + 5.73164379084967M3[t] + 36.4988480392157M4[t] + 0.193256535947739M5[t] -11.2332565359477M6[t] + 11.2462826797386M7[t] + 5.85884803921567M8[t] + 13.2911830065359M9[t] + 77.7374656862745M10[t] + 0.846513071895421M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  252.997616013072 -17.3371732026144X[t] +  12.3202303921566M1[t] -2.30092156862746M2[t] +  5.73164379084967M3[t] +  36.4988480392157M4[t] +  0.193256535947739M5[t] -11.2332565359477M6[t] +  11.2462826797386M7[t] +  5.85884803921567M8[t] +  13.2911830065359M9[t] +  77.7374656862745M10[t] +  0.846513071895421M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58431&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  252.997616013072 -17.3371732026144X[t] +  12.3202303921566M1[t] -2.30092156862746M2[t] +  5.73164379084967M3[t] +  36.4988480392157M4[t] +  0.193256535947739M5[t] -11.2332565359477M6[t] +  11.2462826797386M7[t] +  5.85884803921567M8[t] +  13.2911830065359M9[t] +  77.7374656862745M10[t] +  0.846513071895421M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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] = + 252.997616013072 -17.3371732026144X[t] + 12.3202303921566M1[t] -2.30092156862746M2[t] + 5.73164379084967M3[t] + 36.4988480392157M4[t] + 0.193256535947739M5[t] -11.2332565359477M6[t] + 11.2462826797386M7[t] + 5.85884803921567M8[t] + 13.2911830065359M9[t] + 77.7374656862745M10[t] + 0.846513071895421M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)252.99761601307227.8606259.080800
X-17.33717320261443.333326-5.20124e-062e-06
M112.320230392156610.4326191.18090.2435710.121785
M2-2.3009215686274610.461335-0.21990.8268660.413433
M35.7316437908496710.5333110.54410.5889140.294457
M436.498848039215710.4785273.48320.0010820.000541
M50.19325653594773910.4309140.01850.9852970.492648
M6-11.233256535947710.430914-1.07690.2870130.143506
M711.246282679738610.4360261.07760.2866940.143347
M85.8588480392156710.4785270.55910.5787280.289364
M913.291183006535910.5964131.25430.2159320.107966
M1077.737465686274510.6601837.292300
M110.84651307189542110.4315540.08110.9356680.467834

\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) & 252.997616013072 & 27.860625 & 9.0808 & 0 & 0 \tabularnewline
X & -17.3371732026144 & 3.333326 & -5.2012 & 4e-06 & 2e-06 \tabularnewline
M1 & 12.3202303921566 & 10.432619 & 1.1809 & 0.243571 & 0.121785 \tabularnewline
M2 & -2.30092156862746 & 10.461335 & -0.2199 & 0.826866 & 0.413433 \tabularnewline
M3 & 5.73164379084967 & 10.533311 & 0.5441 & 0.588914 & 0.294457 \tabularnewline
M4 & 36.4988480392157 & 10.478527 & 3.4832 & 0.001082 & 0.000541 \tabularnewline
M5 & 0.193256535947739 & 10.430914 & 0.0185 & 0.985297 & 0.492648 \tabularnewline
M6 & -11.2332565359477 & 10.430914 & -1.0769 & 0.287013 & 0.143506 \tabularnewline
M7 & 11.2462826797386 & 10.436026 & 1.0776 & 0.286694 & 0.143347 \tabularnewline
M8 & 5.85884803921567 & 10.478527 & 0.5591 & 0.578728 & 0.289364 \tabularnewline
M9 & 13.2911830065359 & 10.596413 & 1.2543 & 0.215932 & 0.107966 \tabularnewline
M10 & 77.7374656862745 & 10.660183 & 7.2923 & 0 & 0 \tabularnewline
M11 & 0.846513071895421 & 10.431554 & 0.0811 & 0.935668 & 0.467834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58431&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]252.997616013072[/C][C]27.860625[/C][C]9.0808[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-17.3371732026144[/C][C]3.333326[/C][C]-5.2012[/C][C]4e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M1[/C][C]12.3202303921566[/C][C]10.432619[/C][C]1.1809[/C][C]0.243571[/C][C]0.121785[/C][/ROW]
[ROW][C]M2[/C][C]-2.30092156862746[/C][C]10.461335[/C][C]-0.2199[/C][C]0.826866[/C][C]0.413433[/C][/ROW]
[ROW][C]M3[/C][C]5.73164379084967[/C][C]10.533311[/C][C]0.5441[/C][C]0.588914[/C][C]0.294457[/C][/ROW]
[ROW][C]M4[/C][C]36.4988480392157[/C][C]10.478527[/C][C]3.4832[/C][C]0.001082[/C][C]0.000541[/C][/ROW]
[ROW][C]M5[/C][C]0.193256535947739[/C][C]10.430914[/C][C]0.0185[/C][C]0.985297[/C][C]0.492648[/C][/ROW]
[ROW][C]M6[/C][C]-11.2332565359477[/C][C]10.430914[/C][C]-1.0769[/C][C]0.287013[/C][C]0.143506[/C][/ROW]
[ROW][C]M7[/C][C]11.2462826797386[/C][C]10.436026[/C][C]1.0776[/C][C]0.286694[/C][C]0.143347[/C][/ROW]
[ROW][C]M8[/C][C]5.85884803921567[/C][C]10.478527[/C][C]0.5591[/C][C]0.578728[/C][C]0.289364[/C][/ROW]
[ROW][C]M9[/C][C]13.2911830065359[/C][C]10.596413[/C][C]1.2543[/C][C]0.215932[/C][C]0.107966[/C][/ROW]
[ROW][C]M10[/C][C]77.7374656862745[/C][C]10.660183[/C][C]7.2923[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]0.846513071895421[/C][C]10.431554[/C][C]0.0811[/C][C]0.935668[/C][C]0.467834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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)252.99761601307227.8606259.080800
X-17.33717320261443.333326-5.20124e-062e-06
M112.320230392156610.4326191.18090.2435710.121785
M2-2.3009215686274610.461335-0.21990.8268660.413433
M35.7316437908496710.5333110.54410.5889140.294457
M436.498848039215710.4785273.48320.0010820.000541
M50.19325653594773910.4309140.01850.9852970.492648
M6-11.233256535947710.430914-1.07690.2870130.143506
M711.246282679738610.4360261.07760.2866940.143347
M85.8588480392156710.4785270.55910.5787280.289364
M913.291183006535910.5964131.25430.2159320.107966
M1077.737465686274510.6601837.292300
M110.84651307189542110.4315540.08110.9356680.467834







Multiple Linear Regression - Regression Statistics
Multiple R0.885262235683724
R-squared0.783689225927746
Adjusted R-squared0.728460943185894
F-TEST (value)14.18999807745
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value8.0138118363493e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation16.4923870073344
Sum Squared Residuals12783.9449723856

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.885262235683724 \tabularnewline
R-squared & 0.783689225927746 \tabularnewline
Adjusted R-squared & 0.728460943185894 \tabularnewline
F-TEST (value) & 14.18999807745 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 8.0138118363493e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 16.4923870073344 \tabularnewline
Sum Squared Residuals & 12783.9449723856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58431&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.885262235683724[/C][/ROW]
[ROW][C]R-squared[/C][C]0.783689225927746[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.728460943185894[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]14.18999807745[/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]8.0138118363493e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]16.4923870073344[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]12783.9449723856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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 R0.885262235683724
R-squared0.783689225927746
Adjusted R-squared0.728460943185894
F-TEST (value)14.18999807745
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value8.0138118363493e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation16.4923870073344
Sum Squared Residuals12783.9449723856







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1104.1104.0821356209160.0178643790841724
290.299.8632875816993-9.6632875816993
399.2116.564439542484-17.3644395424836
4116.5145.597926470588-29.0979264705882
598.4105.824900326797-7.42490032679736
690.692.6646699346405-2.06466993464051
7130.5116.87792647058813.6220735294117
8107.4116.691643790850-9.29164379084967
9106125.857696078431-19.8576960784313
10196.5193.7714133986932.72858660130724
11107.8104.7444395424843.05556045751636
1290.5102.164209150327-11.6642091503267
13123.8114.4844395424839.31556045751657
14114.7103.33072222222211.3692777777778
15115.3113.0970049019612.20299509803925
16197142.13049183006554.8695081699347
1788.4102.357465686274-13.9574656862745
1893.890.9309526143792.86904738562093
19111.3115.144209150327-3.84420915032678
20105.9111.490491830065-5.59049183006532
21123.6122.3902614379081.20973856209155
22171192.037696078431-21.0376960784314
2397111.679308823529-14.6793088235294
2499.2112.566513071895-13.3665130718954
25126.6124.8867434640521.71325653594792
26103.4111.999308823529-8.59930882352942
27121.3121.765591503268-0.465591503267971
28129.6152.532795751634-22.932795751634
29110.8114.493486928105-3.69348692810458
3098.9103.066973856209-4.16697385620915
31122.8127.280230392157-4.48023039215686
32120.9120.1590784313730.740921568627468
33133.1132.7925653594770.307434640522879
34203.1205.907434640523-2.80743464052288
35110.2123.815330065359-13.6153300653595
36119.5126.436251633987-6.93625163398695
37135.1143.957633986928-8.85763398692795
38113.9129.336482026144-15.4364820261438
39137.4137.3690473856210.0309526143790445
40157.1164.668816993464-7.5688169934641
41126.4126.629508169935-0.229508169934665
42112.2118.670429738562-6.47042973856214
43128.8146.351120915033-17.5511209150327
44136.8147.898555555556-11.0985555555556
45156.5160.532042483660-4.03204248366019
46215.2218.043455882353-2.843455882353
47146.7120.34789542483726.3521045751634
48130.8116.03394771241814.7660522875817
49133.1135.289047385621-2.18904738562073
50153.4131.07019934640522.3298006535947
51159.9144.30391666666715.5960833333333
52174.6169.8699689542484.73003104575157
53145119.69463888888925.3053611111111
54112.9103.0669738562099.83302614379085
55137.8125.54651307189512.2534869281046
56150.6125.36023039215725.2397696078431
57162.1139.72743464052322.3725653594771
58226.4202.4423.96
59112.3113.413026143791-1.11302614379084
60126.3109.09907843137317.2009215686275

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 104.1 & 104.082135620916 & 0.0178643790841724 \tabularnewline
2 & 90.2 & 99.8632875816993 & -9.6632875816993 \tabularnewline
3 & 99.2 & 116.564439542484 & -17.3644395424836 \tabularnewline
4 & 116.5 & 145.597926470588 & -29.0979264705882 \tabularnewline
5 & 98.4 & 105.824900326797 & -7.42490032679736 \tabularnewline
6 & 90.6 & 92.6646699346405 & -2.06466993464051 \tabularnewline
7 & 130.5 & 116.877926470588 & 13.6220735294117 \tabularnewline
8 & 107.4 & 116.691643790850 & -9.29164379084967 \tabularnewline
9 & 106 & 125.857696078431 & -19.8576960784313 \tabularnewline
10 & 196.5 & 193.771413398693 & 2.72858660130724 \tabularnewline
11 & 107.8 & 104.744439542484 & 3.05556045751636 \tabularnewline
12 & 90.5 & 102.164209150327 & -11.6642091503267 \tabularnewline
13 & 123.8 & 114.484439542483 & 9.31556045751657 \tabularnewline
14 & 114.7 & 103.330722222222 & 11.3692777777778 \tabularnewline
15 & 115.3 & 113.097004901961 & 2.20299509803925 \tabularnewline
16 & 197 & 142.130491830065 & 54.8695081699347 \tabularnewline
17 & 88.4 & 102.357465686274 & -13.9574656862745 \tabularnewline
18 & 93.8 & 90.930952614379 & 2.86904738562093 \tabularnewline
19 & 111.3 & 115.144209150327 & -3.84420915032678 \tabularnewline
20 & 105.9 & 111.490491830065 & -5.59049183006532 \tabularnewline
21 & 123.6 & 122.390261437908 & 1.20973856209155 \tabularnewline
22 & 171 & 192.037696078431 & -21.0376960784314 \tabularnewline
23 & 97 & 111.679308823529 & -14.6793088235294 \tabularnewline
24 & 99.2 & 112.566513071895 & -13.3665130718954 \tabularnewline
25 & 126.6 & 124.886743464052 & 1.71325653594792 \tabularnewline
26 & 103.4 & 111.999308823529 & -8.59930882352942 \tabularnewline
27 & 121.3 & 121.765591503268 & -0.465591503267971 \tabularnewline
28 & 129.6 & 152.532795751634 & -22.932795751634 \tabularnewline
29 & 110.8 & 114.493486928105 & -3.69348692810458 \tabularnewline
30 & 98.9 & 103.066973856209 & -4.16697385620915 \tabularnewline
31 & 122.8 & 127.280230392157 & -4.48023039215686 \tabularnewline
32 & 120.9 & 120.159078431373 & 0.740921568627468 \tabularnewline
33 & 133.1 & 132.792565359477 & 0.307434640522879 \tabularnewline
34 & 203.1 & 205.907434640523 & -2.80743464052288 \tabularnewline
35 & 110.2 & 123.815330065359 & -13.6153300653595 \tabularnewline
36 & 119.5 & 126.436251633987 & -6.93625163398695 \tabularnewline
37 & 135.1 & 143.957633986928 & -8.85763398692795 \tabularnewline
38 & 113.9 & 129.336482026144 & -15.4364820261438 \tabularnewline
39 & 137.4 & 137.369047385621 & 0.0309526143790445 \tabularnewline
40 & 157.1 & 164.668816993464 & -7.5688169934641 \tabularnewline
41 & 126.4 & 126.629508169935 & -0.229508169934665 \tabularnewline
42 & 112.2 & 118.670429738562 & -6.47042973856214 \tabularnewline
43 & 128.8 & 146.351120915033 & -17.5511209150327 \tabularnewline
44 & 136.8 & 147.898555555556 & -11.0985555555556 \tabularnewline
45 & 156.5 & 160.532042483660 & -4.03204248366019 \tabularnewline
46 & 215.2 & 218.043455882353 & -2.843455882353 \tabularnewline
47 & 146.7 & 120.347895424837 & 26.3521045751634 \tabularnewline
48 & 130.8 & 116.033947712418 & 14.7660522875817 \tabularnewline
49 & 133.1 & 135.289047385621 & -2.18904738562073 \tabularnewline
50 & 153.4 & 131.070199346405 & 22.3298006535947 \tabularnewline
51 & 159.9 & 144.303916666667 & 15.5960833333333 \tabularnewline
52 & 174.6 & 169.869968954248 & 4.73003104575157 \tabularnewline
53 & 145 & 119.694638888889 & 25.3053611111111 \tabularnewline
54 & 112.9 & 103.066973856209 & 9.83302614379085 \tabularnewline
55 & 137.8 & 125.546513071895 & 12.2534869281046 \tabularnewline
56 & 150.6 & 125.360230392157 & 25.2397696078431 \tabularnewline
57 & 162.1 & 139.727434640523 & 22.3725653594771 \tabularnewline
58 & 226.4 & 202.44 & 23.96 \tabularnewline
59 & 112.3 & 113.413026143791 & -1.11302614379084 \tabularnewline
60 & 126.3 & 109.099078431373 & 17.2009215686275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58431&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]104.1[/C][C]104.082135620916[/C][C]0.0178643790841724[/C][/ROW]
[ROW][C]2[/C][C]90.2[/C][C]99.8632875816993[/C][C]-9.6632875816993[/C][/ROW]
[ROW][C]3[/C][C]99.2[/C][C]116.564439542484[/C][C]-17.3644395424836[/C][/ROW]
[ROW][C]4[/C][C]116.5[/C][C]145.597926470588[/C][C]-29.0979264705882[/C][/ROW]
[ROW][C]5[/C][C]98.4[/C][C]105.824900326797[/C][C]-7.42490032679736[/C][/ROW]
[ROW][C]6[/C][C]90.6[/C][C]92.6646699346405[/C][C]-2.06466993464051[/C][/ROW]
[ROW][C]7[/C][C]130.5[/C][C]116.877926470588[/C][C]13.6220735294117[/C][/ROW]
[ROW][C]8[/C][C]107.4[/C][C]116.691643790850[/C][C]-9.29164379084967[/C][/ROW]
[ROW][C]9[/C][C]106[/C][C]125.857696078431[/C][C]-19.8576960784313[/C][/ROW]
[ROW][C]10[/C][C]196.5[/C][C]193.771413398693[/C][C]2.72858660130724[/C][/ROW]
[ROW][C]11[/C][C]107.8[/C][C]104.744439542484[/C][C]3.05556045751636[/C][/ROW]
[ROW][C]12[/C][C]90.5[/C][C]102.164209150327[/C][C]-11.6642091503267[/C][/ROW]
[ROW][C]13[/C][C]123.8[/C][C]114.484439542483[/C][C]9.31556045751657[/C][/ROW]
[ROW][C]14[/C][C]114.7[/C][C]103.330722222222[/C][C]11.3692777777778[/C][/ROW]
[ROW][C]15[/C][C]115.3[/C][C]113.097004901961[/C][C]2.20299509803925[/C][/ROW]
[ROW][C]16[/C][C]197[/C][C]142.130491830065[/C][C]54.8695081699347[/C][/ROW]
[ROW][C]17[/C][C]88.4[/C][C]102.357465686274[/C][C]-13.9574656862745[/C][/ROW]
[ROW][C]18[/C][C]93.8[/C][C]90.930952614379[/C][C]2.86904738562093[/C][/ROW]
[ROW][C]19[/C][C]111.3[/C][C]115.144209150327[/C][C]-3.84420915032678[/C][/ROW]
[ROW][C]20[/C][C]105.9[/C][C]111.490491830065[/C][C]-5.59049183006532[/C][/ROW]
[ROW][C]21[/C][C]123.6[/C][C]122.390261437908[/C][C]1.20973856209155[/C][/ROW]
[ROW][C]22[/C][C]171[/C][C]192.037696078431[/C][C]-21.0376960784314[/C][/ROW]
[ROW][C]23[/C][C]97[/C][C]111.679308823529[/C][C]-14.6793088235294[/C][/ROW]
[ROW][C]24[/C][C]99.2[/C][C]112.566513071895[/C][C]-13.3665130718954[/C][/ROW]
[ROW][C]25[/C][C]126.6[/C][C]124.886743464052[/C][C]1.71325653594792[/C][/ROW]
[ROW][C]26[/C][C]103.4[/C][C]111.999308823529[/C][C]-8.59930882352942[/C][/ROW]
[ROW][C]27[/C][C]121.3[/C][C]121.765591503268[/C][C]-0.465591503267971[/C][/ROW]
[ROW][C]28[/C][C]129.6[/C][C]152.532795751634[/C][C]-22.932795751634[/C][/ROW]
[ROW][C]29[/C][C]110.8[/C][C]114.493486928105[/C][C]-3.69348692810458[/C][/ROW]
[ROW][C]30[/C][C]98.9[/C][C]103.066973856209[/C][C]-4.16697385620915[/C][/ROW]
[ROW][C]31[/C][C]122.8[/C][C]127.280230392157[/C][C]-4.48023039215686[/C][/ROW]
[ROW][C]32[/C][C]120.9[/C][C]120.159078431373[/C][C]0.740921568627468[/C][/ROW]
[ROW][C]33[/C][C]133.1[/C][C]132.792565359477[/C][C]0.307434640522879[/C][/ROW]
[ROW][C]34[/C][C]203.1[/C][C]205.907434640523[/C][C]-2.80743464052288[/C][/ROW]
[ROW][C]35[/C][C]110.2[/C][C]123.815330065359[/C][C]-13.6153300653595[/C][/ROW]
[ROW][C]36[/C][C]119.5[/C][C]126.436251633987[/C][C]-6.93625163398695[/C][/ROW]
[ROW][C]37[/C][C]135.1[/C][C]143.957633986928[/C][C]-8.85763398692795[/C][/ROW]
[ROW][C]38[/C][C]113.9[/C][C]129.336482026144[/C][C]-15.4364820261438[/C][/ROW]
[ROW][C]39[/C][C]137.4[/C][C]137.369047385621[/C][C]0.0309526143790445[/C][/ROW]
[ROW][C]40[/C][C]157.1[/C][C]164.668816993464[/C][C]-7.5688169934641[/C][/ROW]
[ROW][C]41[/C][C]126.4[/C][C]126.629508169935[/C][C]-0.229508169934665[/C][/ROW]
[ROW][C]42[/C][C]112.2[/C][C]118.670429738562[/C][C]-6.47042973856214[/C][/ROW]
[ROW][C]43[/C][C]128.8[/C][C]146.351120915033[/C][C]-17.5511209150327[/C][/ROW]
[ROW][C]44[/C][C]136.8[/C][C]147.898555555556[/C][C]-11.0985555555556[/C][/ROW]
[ROW][C]45[/C][C]156.5[/C][C]160.532042483660[/C][C]-4.03204248366019[/C][/ROW]
[ROW][C]46[/C][C]215.2[/C][C]218.043455882353[/C][C]-2.843455882353[/C][/ROW]
[ROW][C]47[/C][C]146.7[/C][C]120.347895424837[/C][C]26.3521045751634[/C][/ROW]
[ROW][C]48[/C][C]130.8[/C][C]116.033947712418[/C][C]14.7660522875817[/C][/ROW]
[ROW][C]49[/C][C]133.1[/C][C]135.289047385621[/C][C]-2.18904738562073[/C][/ROW]
[ROW][C]50[/C][C]153.4[/C][C]131.070199346405[/C][C]22.3298006535947[/C][/ROW]
[ROW][C]51[/C][C]159.9[/C][C]144.303916666667[/C][C]15.5960833333333[/C][/ROW]
[ROW][C]52[/C][C]174.6[/C][C]169.869968954248[/C][C]4.73003104575157[/C][/ROW]
[ROW][C]53[/C][C]145[/C][C]119.694638888889[/C][C]25.3053611111111[/C][/ROW]
[ROW][C]54[/C][C]112.9[/C][C]103.066973856209[/C][C]9.83302614379085[/C][/ROW]
[ROW][C]55[/C][C]137.8[/C][C]125.546513071895[/C][C]12.2534869281046[/C][/ROW]
[ROW][C]56[/C][C]150.6[/C][C]125.360230392157[/C][C]25.2397696078431[/C][/ROW]
[ROW][C]57[/C][C]162.1[/C][C]139.727434640523[/C][C]22.3725653594771[/C][/ROW]
[ROW][C]58[/C][C]226.4[/C][C]202.44[/C][C]23.96[/C][/ROW]
[ROW][C]59[/C][C]112.3[/C][C]113.413026143791[/C][C]-1.11302614379084[/C][/ROW]
[ROW][C]60[/C][C]126.3[/C][C]109.099078431373[/C][C]17.2009215686275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58431&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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
1104.1104.0821356209160.0178643790841724
290.299.8632875816993-9.6632875816993
399.2116.564439542484-17.3644395424836
4116.5145.597926470588-29.0979264705882
598.4105.824900326797-7.42490032679736
690.692.6646699346405-2.06466993464051
7130.5116.87792647058813.6220735294117
8107.4116.691643790850-9.29164379084967
9106125.857696078431-19.8576960784313
10196.5193.7714133986932.72858660130724
11107.8104.7444395424843.05556045751636
1290.5102.164209150327-11.6642091503267
13123.8114.4844395424839.31556045751657
14114.7103.33072222222211.3692777777778
15115.3113.0970049019612.20299509803925
16197142.13049183006554.8695081699347
1788.4102.357465686274-13.9574656862745
1893.890.9309526143792.86904738562093
19111.3115.144209150327-3.84420915032678
20105.9111.490491830065-5.59049183006532
21123.6122.3902614379081.20973856209155
22171192.037696078431-21.0376960784314
2397111.679308823529-14.6793088235294
2499.2112.566513071895-13.3665130718954
25126.6124.8867434640521.71325653594792
26103.4111.999308823529-8.59930882352942
27121.3121.765591503268-0.465591503267971
28129.6152.532795751634-22.932795751634
29110.8114.493486928105-3.69348692810458
3098.9103.066973856209-4.16697385620915
31122.8127.280230392157-4.48023039215686
32120.9120.1590784313730.740921568627468
33133.1132.7925653594770.307434640522879
34203.1205.907434640523-2.80743464052288
35110.2123.815330065359-13.6153300653595
36119.5126.436251633987-6.93625163398695
37135.1143.957633986928-8.85763398692795
38113.9129.336482026144-15.4364820261438
39137.4137.3690473856210.0309526143790445
40157.1164.668816993464-7.5688169934641
41126.4126.629508169935-0.229508169934665
42112.2118.670429738562-6.47042973856214
43128.8146.351120915033-17.5511209150327
44136.8147.898555555556-11.0985555555556
45156.5160.532042483660-4.03204248366019
46215.2218.043455882353-2.843455882353
47146.7120.34789542483726.3521045751634
48130.8116.03394771241814.7660522875817
49133.1135.289047385621-2.18904738562073
50153.4131.07019934640522.3298006535947
51159.9144.30391666666715.5960833333333
52174.6169.8699689542484.73003104575157
53145119.69463888888925.3053611111111
54112.9103.0669738562099.83302614379085
55137.8125.54651307189512.2534869281046
56150.6125.36023039215725.2397696078431
57162.1139.72743464052322.3725653594771
58226.4202.4423.96
59112.3113.413026143791-1.11302614379084
60126.3109.09907843137317.2009215686275







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.9971112999026970.005777400194605910.00288870009730295
170.9941387670303920.01172246593921670.00586123296960834
180.9860347336804140.02793053263917140.0139652663195857
190.9758759135367220.0482481729265560.024124086463278
200.95633645326050.08732709347900170.0436635467395008
210.9340487888469490.1319024223061020.065951211153051
220.944736871798160.1105262564036800.0552631282018399
230.9284266042081340.1431467915837320.0715733957918659
240.9158040048619580.1683919902760830.0841959951380417
250.8733327774547050.253334445090590.126667222545295
260.8385778430764290.3228443138471430.161422156923571
270.8048826899700420.3902346200599160.195117310029958
280.8727848352038340.2544303295923320.127215164796166
290.8704525160002650.2590949679994710.129547483999735
300.8252055723302240.3495888553395510.174794427669776
310.7632801015714420.4734397968571150.236719898428558
320.752422223023680.4951555539526390.247577776976319
330.7964662310852010.4070675378295970.203533768914799
340.782546554393610.4349068912127810.217453445606391
350.7542241496420980.4915517007158050.245775850357902
360.681675225659870.636649548680260.31832477434013
370.5814806950945370.8370386098109260.418519304905463
380.7648441375753930.4703117248492140.235155862424607
390.7974201327101720.4051597345796560.202579867289828
400.7860291006482420.4279417987035160.213970899351758
410.7626353934211140.4747292131577720.237364606578886
420.6406514876470360.7186970247059290.359348512352964
430.4982882622742470.9965765245484940.501711737725753
440.3636110943566320.7272221887132630.636388905643368

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.997111299902697 & 0.00577740019460591 & 0.00288870009730295 \tabularnewline
17 & 0.994138767030392 & 0.0117224659392167 & 0.00586123296960834 \tabularnewline
18 & 0.986034733680414 & 0.0279305326391714 & 0.0139652663195857 \tabularnewline
19 & 0.975875913536722 & 0.048248172926556 & 0.024124086463278 \tabularnewline
20 & 0.9563364532605 & 0.0873270934790017 & 0.0436635467395008 \tabularnewline
21 & 0.934048788846949 & 0.131902422306102 & 0.065951211153051 \tabularnewline
22 & 0.94473687179816 & 0.110526256403680 & 0.0552631282018399 \tabularnewline
23 & 0.928426604208134 & 0.143146791583732 & 0.0715733957918659 \tabularnewline
24 & 0.915804004861958 & 0.168391990276083 & 0.0841959951380417 \tabularnewline
25 & 0.873332777454705 & 0.25333444509059 & 0.126667222545295 \tabularnewline
26 & 0.838577843076429 & 0.322844313847143 & 0.161422156923571 \tabularnewline
27 & 0.804882689970042 & 0.390234620059916 & 0.195117310029958 \tabularnewline
28 & 0.872784835203834 & 0.254430329592332 & 0.127215164796166 \tabularnewline
29 & 0.870452516000265 & 0.259094967999471 & 0.129547483999735 \tabularnewline
30 & 0.825205572330224 & 0.349588855339551 & 0.174794427669776 \tabularnewline
31 & 0.763280101571442 & 0.473439796857115 & 0.236719898428558 \tabularnewline
32 & 0.75242222302368 & 0.495155553952639 & 0.247577776976319 \tabularnewline
33 & 0.796466231085201 & 0.407067537829597 & 0.203533768914799 \tabularnewline
34 & 0.78254655439361 & 0.434906891212781 & 0.217453445606391 \tabularnewline
35 & 0.754224149642098 & 0.491551700715805 & 0.245775850357902 \tabularnewline
36 & 0.68167522565987 & 0.63664954868026 & 0.31832477434013 \tabularnewline
37 & 0.581480695094537 & 0.837038609810926 & 0.418519304905463 \tabularnewline
38 & 0.764844137575393 & 0.470311724849214 & 0.235155862424607 \tabularnewline
39 & 0.797420132710172 & 0.405159734579656 & 0.202579867289828 \tabularnewline
40 & 0.786029100648242 & 0.427941798703516 & 0.213970899351758 \tabularnewline
41 & 0.762635393421114 & 0.474729213157772 & 0.237364606578886 \tabularnewline
42 & 0.640651487647036 & 0.718697024705929 & 0.359348512352964 \tabularnewline
43 & 0.498288262274247 & 0.996576524548494 & 0.501711737725753 \tabularnewline
44 & 0.363611094356632 & 0.727222188713263 & 0.636388905643368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58431&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]0.997111299902697[/C][C]0.00577740019460591[/C][C]0.00288870009730295[/C][/ROW]
[ROW][C]17[/C][C]0.994138767030392[/C][C]0.0117224659392167[/C][C]0.00586123296960834[/C][/ROW]
[ROW][C]18[/C][C]0.986034733680414[/C][C]0.0279305326391714[/C][C]0.0139652663195857[/C][/ROW]
[ROW][C]19[/C][C]0.975875913536722[/C][C]0.048248172926556[/C][C]0.024124086463278[/C][/ROW]
[ROW][C]20[/C][C]0.9563364532605[/C][C]0.0873270934790017[/C][C]0.0436635467395008[/C][/ROW]
[ROW][C]21[/C][C]0.934048788846949[/C][C]0.131902422306102[/C][C]0.065951211153051[/C][/ROW]
[ROW][C]22[/C][C]0.94473687179816[/C][C]0.110526256403680[/C][C]0.0552631282018399[/C][/ROW]
[ROW][C]23[/C][C]0.928426604208134[/C][C]0.143146791583732[/C][C]0.0715733957918659[/C][/ROW]
[ROW][C]24[/C][C]0.915804004861958[/C][C]0.168391990276083[/C][C]0.0841959951380417[/C][/ROW]
[ROW][C]25[/C][C]0.873332777454705[/C][C]0.25333444509059[/C][C]0.126667222545295[/C][/ROW]
[ROW][C]26[/C][C]0.838577843076429[/C][C]0.322844313847143[/C][C]0.161422156923571[/C][/ROW]
[ROW][C]27[/C][C]0.804882689970042[/C][C]0.390234620059916[/C][C]0.195117310029958[/C][/ROW]
[ROW][C]28[/C][C]0.872784835203834[/C][C]0.254430329592332[/C][C]0.127215164796166[/C][/ROW]
[ROW][C]29[/C][C]0.870452516000265[/C][C]0.259094967999471[/C][C]0.129547483999735[/C][/ROW]
[ROW][C]30[/C][C]0.825205572330224[/C][C]0.349588855339551[/C][C]0.174794427669776[/C][/ROW]
[ROW][C]31[/C][C]0.763280101571442[/C][C]0.473439796857115[/C][C]0.236719898428558[/C][/ROW]
[ROW][C]32[/C][C]0.75242222302368[/C][C]0.495155553952639[/C][C]0.247577776976319[/C][/ROW]
[ROW][C]33[/C][C]0.796466231085201[/C][C]0.407067537829597[/C][C]0.203533768914799[/C][/ROW]
[ROW][C]34[/C][C]0.78254655439361[/C][C]0.434906891212781[/C][C]0.217453445606391[/C][/ROW]
[ROW][C]35[/C][C]0.754224149642098[/C][C]0.491551700715805[/C][C]0.245775850357902[/C][/ROW]
[ROW][C]36[/C][C]0.68167522565987[/C][C]0.63664954868026[/C][C]0.31832477434013[/C][/ROW]
[ROW][C]37[/C][C]0.581480695094537[/C][C]0.837038609810926[/C][C]0.418519304905463[/C][/ROW]
[ROW][C]38[/C][C]0.764844137575393[/C][C]0.470311724849214[/C][C]0.235155862424607[/C][/ROW]
[ROW][C]39[/C][C]0.797420132710172[/C][C]0.405159734579656[/C][C]0.202579867289828[/C][/ROW]
[ROW][C]40[/C][C]0.786029100648242[/C][C]0.427941798703516[/C][C]0.213970899351758[/C][/ROW]
[ROW][C]41[/C][C]0.762635393421114[/C][C]0.474729213157772[/C][C]0.237364606578886[/C][/ROW]
[ROW][C]42[/C][C]0.640651487647036[/C][C]0.718697024705929[/C][C]0.359348512352964[/C][/ROW]
[ROW][C]43[/C][C]0.498288262274247[/C][C]0.996576524548494[/C][C]0.501711737725753[/C][/ROW]
[ROW][C]44[/C][C]0.363611094356632[/C][C]0.727222188713263[/C][C]0.636388905643368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58431&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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
160.9971112999026970.005777400194605910.00288870009730295
170.9941387670303920.01172246593921670.00586123296960834
180.9860347336804140.02793053263917140.0139652663195857
190.9758759135367220.0482481729265560.024124086463278
200.95633645326050.08732709347900170.0436635467395008
210.9340487888469490.1319024223061020.065951211153051
220.944736871798160.1105262564036800.0552631282018399
230.9284266042081340.1431467915837320.0715733957918659
240.9158040048619580.1683919902760830.0841959951380417
250.8733327774547050.253334445090590.126667222545295
260.8385778430764290.3228443138471430.161422156923571
270.8048826899700420.3902346200599160.195117310029958
280.8727848352038340.2544303295923320.127215164796166
290.8704525160002650.2590949679994710.129547483999735
300.8252055723302240.3495888553395510.174794427669776
310.7632801015714420.4734397968571150.236719898428558
320.752422223023680.4951555539526390.247577776976319
330.7964662310852010.4070675378295970.203533768914799
340.782546554393610.4349068912127810.217453445606391
350.7542241496420980.4915517007158050.245775850357902
360.681675225659870.636649548680260.31832477434013
370.5814806950945370.8370386098109260.418519304905463
380.7648441375753930.4703117248492140.235155862424607
390.7974201327101720.4051597345796560.202579867289828
400.7860291006482420.4279417987035160.213970899351758
410.7626353934211140.4747292131577720.237364606578886
420.6406514876470360.7186970247059290.359348512352964
430.4982882622742470.9965765245484940.501711737725753
440.3636110943566320.7272221887132630.636388905643368







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0344827586206897NOK
5% type I error level40.137931034482759NOK
10% type I error level50.172413793103448NOK

\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 & 1 & 0.0344827586206897 & NOK \tabularnewline
5% type I error level & 4 & 0.137931034482759 & NOK \tabularnewline
10% type I error level & 5 & 0.172413793103448 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58431&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]1[/C][C]0.0344827586206897[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]4[/C][C]0.137931034482759[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.172413793103448[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58431&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58431&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 level10.0344827586206897NOK
5% type I error level40.137931034482759NOK
10% type I error level50.172413793103448NOK



Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 2 ; 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')
}