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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 computationThu, 19 Nov 2009 12:35:13 -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/19/t1258659469v2nkickzzhoqtj3.htm/, Retrieved Fri, 29 Mar 2024 12:27:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57915, Retrieved Fri, 29 Mar 2024 12:27:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Indicator voor he...] [2009-11-19 19:35:13] [41dcf2419e4beff0486cef71832b5d35] [Current]
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Dataseries X:
19	24.4	19	23
22	22.5	19	19
23	19.4	22	18
20	18.1	23	19
14	18.1	20	19
14	20.7	14	22
14	19.1	14	23
15	18.3	14	20
11	16.9	15	14
17	17.9	11	14
16	20.2	17	14
20	21.2	16	15
24	23.8	20	11
23	24	24	17
20	26.6	23	16
21	25.3	20	20
19	27.6	21	24
23	24.7	19	23
23	26.6	23	20
23	24.4	23	21
23	24.6	23	19
27	26	23	23
26	24.8	27	23
17	24	26	23
24	22.7	17	23
26	23	24	27
24	24.1	26	26
27	24	24	17
27	22.7	27	24
26	22.6	27	26
24	23.1	26	24
23	24.4	24	27
23	23	23	27
24	22	23	26
17	21.3	24	24
21	21.5	17	23
19	21.3	21	23
22	23.2	19	24
22	21.8	22	17
18	23.3	22	21
16	21	18	19
14	22.4	16	22
12	20.4	14	22
14	19.9	12	18
16	21.3	14	16
8	18.9	16	14
3	15.6	8	12
0	12.5	3	14
5	7.8	0	16
1	5.5	5	8
1	4	1	3
3	3.3	1	0
6	3.7	3	5
7	3.1	6	1
8	5	7	1
14	6.3	8	3
14	20	14	6




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=57915&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=57915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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] = + 0.633709699169343 + 0.208586394090889X[t] + 0.75975279754674`Y(t-1)`[t] -0.035428460457972`Y(t-4)`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  0.633709699169343 +  0.208586394090889X[t] +  0.75975279754674`Y(t-1)`[t] -0.035428460457972`Y(t-4)`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57915&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  0.633709699169343 +  0.208586394090889X[t] +  0.75975279754674`Y(t-1)`[t] -0.035428460457972`Y(t-4)`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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] = + 0.633709699169343 + 0.208586394090889X[t] + 0.75975279754674`Y(t-1)`[t] -0.035428460457972`Y(t-4)`[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.6337096991693431.4053330.45090.6538780.326939
X0.2085863940908890.1540121.35430.1813710.090686
`Y(t-1)`0.759752797546740.1231716.168300
`Y(t-4)`-0.0354284604579720.109207-0.32440.74690.37345

\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) & 0.633709699169343 & 1.405333 & 0.4509 & 0.653878 & 0.326939 \tabularnewline
X & 0.208586394090889 & 0.154012 & 1.3543 & 0.181371 & 0.090686 \tabularnewline
`Y(t-1)` & 0.75975279754674 & 0.123171 & 6.1683 & 0 & 0 \tabularnewline
`Y(t-4)` & -0.035428460457972 & 0.109207 & -0.3244 & 0.7469 & 0.37345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57915&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]0.633709699169343[/C][C]1.405333[/C][C]0.4509[/C][C]0.653878[/C][C]0.326939[/C][/ROW]
[ROW][C]X[/C][C]0.208586394090889[/C][C]0.154012[/C][C]1.3543[/C][C]0.181371[/C][C]0.090686[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.75975279754674[/C][C]0.123171[/C][C]6.1683[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.035428460457972[/C][C]0.109207[/C][C]-0.3244[/C][C]0.7469[/C][C]0.37345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57915&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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)0.6337096991693431.4053330.45090.6538780.326939
X0.2085863940908890.1540121.35430.1813710.090686
`Y(t-1)`0.759752797546740.1231716.168300
`Y(t-4)`-0.0354284604579720.109207-0.32440.74690.37345







Multiple Linear Regression - Regression Statistics
Multiple R0.898579324435252
R-squared0.807444802302514
Adjusted R-squared0.796545451489449
F-TEST (value)74.0819170013884
F-TEST (DF numerator)3
F-TEST (DF denominator)53
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.34001626392747
Sum Squared Residuals591.252558094901

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.898579324435252 \tabularnewline
R-squared & 0.807444802302514 \tabularnewline
Adjusted R-squared & 0.796545451489449 \tabularnewline
F-TEST (value) & 74.0819170013884 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 53 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.34001626392747 \tabularnewline
Sum Squared Residuals & 591.252558094901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57915&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.898579324435252[/C][/ROW]
[ROW][C]R-squared[/C][C]0.807444802302514[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.796545451489449[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]74.0819170013884[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]53[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.34001626392747[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]591.252558094901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57915&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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 R0.898579324435252
R-squared0.807444802302514
Adjusted R-squared0.796545451489449
F-TEST (value)74.0819170013884
F-TEST (DF numerator)3
F-TEST (DF denominator)53
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.34001626392747
Sum Squared Residuals591.252558094901







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11919.3436662778418-0.343666277841756
22219.08906597090102.91093402909904
32320.75713500231742.24286499768262
42021.210297027088-1.21029702708800
51418.9310386344478-4.93103863444777
61414.8085610924297-0.80856109242973
71414.4393944014263-0.439394401426334
81514.37881066752750.621189332472461
91115.0591132760949-4.05911327609487
101712.22868847999884.77131152000121
111617.2669539716883-1.26695397168828
122016.68035910777453.31964089222554
132420.40340876442963.59659123557038
142323.2715664706869-0.271566470686929
152023.0895667582345-3.08956675823447
162120.39743221144420.602567788555793
171921.4952198735681-2.49521987356811
182319.4062421960693.59375780393098
192322.94785291640260.0521470835974146
202322.45353438894470.546465611055345
212322.56610858867880.433891411321222
222722.71641569857414.28358430142586
232625.50512321585200.49487678414797
241724.5785013030326-7.57850130303258
252417.46956381279386.53043618720624
262622.70869547201633.29130452798368
272424.4930745610678-0.493074561067751
282723.27156647068693.72843352931307
292725.03166332780321.96833667219681
302624.93994776747821.06005223252184
312424.3553450878928-0.355345087892805
322323.0007164237436-0.000716423743563926
332321.94894267446961.05105732553042
342421.77578474083672.22421525916334
351722.4603839834357-5.46038398343572
362117.21926013988473.78073986011531
371920.2165540512535-1.21655405125347
382219.05793414447472.94206585552529
392221.29317080859350.706829191406509
401821.4643365578979-3.46433655789794
411618.0164335822179-2.01643358221787
421416.6826635574777-2.68266355747772
431214.7459851742025-2.74598517420246
441413.26390022389540.736099776104575
451615.14628369163210.853716308367904
46816.2360388618234-8.23603886182338
4739.54053830186547-6.54053830186547
4805.02429957153407-5.02429957153407
4951.693828205750723.30617179424928
5015.29627117073916-4.29627117073916
5112.12152269170572-1.12152269170572
5232.081797597216010.918202402783987
5363.507595447655992.49240455234401
5475.803415845673571.19658415432643
5586.9594827919931.04051720800701
56147.919540980941956.08045901905805
571415.2294059838937-1.22940598389366

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 19 & 19.3436662778418 & -0.343666277841756 \tabularnewline
2 & 22 & 19.0890659709010 & 2.91093402909904 \tabularnewline
3 & 23 & 20.7571350023174 & 2.24286499768262 \tabularnewline
4 & 20 & 21.210297027088 & -1.21029702708800 \tabularnewline
5 & 14 & 18.9310386344478 & -4.93103863444777 \tabularnewline
6 & 14 & 14.8085610924297 & -0.80856109242973 \tabularnewline
7 & 14 & 14.4393944014263 & -0.439394401426334 \tabularnewline
8 & 15 & 14.3788106675275 & 0.621189332472461 \tabularnewline
9 & 11 & 15.0591132760949 & -4.05911327609487 \tabularnewline
10 & 17 & 12.2286884799988 & 4.77131152000121 \tabularnewline
11 & 16 & 17.2669539716883 & -1.26695397168828 \tabularnewline
12 & 20 & 16.6803591077745 & 3.31964089222554 \tabularnewline
13 & 24 & 20.4034087644296 & 3.59659123557038 \tabularnewline
14 & 23 & 23.2715664706869 & -0.271566470686929 \tabularnewline
15 & 20 & 23.0895667582345 & -3.08956675823447 \tabularnewline
16 & 21 & 20.3974322114442 & 0.602567788555793 \tabularnewline
17 & 19 & 21.4952198735681 & -2.49521987356811 \tabularnewline
18 & 23 & 19.406242196069 & 3.59375780393098 \tabularnewline
19 & 23 & 22.9478529164026 & 0.0521470835974146 \tabularnewline
20 & 23 & 22.4535343889447 & 0.546465611055345 \tabularnewline
21 & 23 & 22.5661085886788 & 0.433891411321222 \tabularnewline
22 & 27 & 22.7164156985741 & 4.28358430142586 \tabularnewline
23 & 26 & 25.5051232158520 & 0.49487678414797 \tabularnewline
24 & 17 & 24.5785013030326 & -7.57850130303258 \tabularnewline
25 & 24 & 17.4695638127938 & 6.53043618720624 \tabularnewline
26 & 26 & 22.7086954720163 & 3.29130452798368 \tabularnewline
27 & 24 & 24.4930745610678 & -0.493074561067751 \tabularnewline
28 & 27 & 23.2715664706869 & 3.72843352931307 \tabularnewline
29 & 27 & 25.0316633278032 & 1.96833667219681 \tabularnewline
30 & 26 & 24.9399477674782 & 1.06005223252184 \tabularnewline
31 & 24 & 24.3553450878928 & -0.355345087892805 \tabularnewline
32 & 23 & 23.0007164237436 & -0.000716423743563926 \tabularnewline
33 & 23 & 21.9489426744696 & 1.05105732553042 \tabularnewline
34 & 24 & 21.7757847408367 & 2.22421525916334 \tabularnewline
35 & 17 & 22.4603839834357 & -5.46038398343572 \tabularnewline
36 & 21 & 17.2192601398847 & 3.78073986011531 \tabularnewline
37 & 19 & 20.2165540512535 & -1.21655405125347 \tabularnewline
38 & 22 & 19.0579341444747 & 2.94206585552529 \tabularnewline
39 & 22 & 21.2931708085935 & 0.706829191406509 \tabularnewline
40 & 18 & 21.4643365578979 & -3.46433655789794 \tabularnewline
41 & 16 & 18.0164335822179 & -2.01643358221787 \tabularnewline
42 & 14 & 16.6826635574777 & -2.68266355747772 \tabularnewline
43 & 12 & 14.7459851742025 & -2.74598517420246 \tabularnewline
44 & 14 & 13.2639002238954 & 0.736099776104575 \tabularnewline
45 & 16 & 15.1462836916321 & 0.853716308367904 \tabularnewline
46 & 8 & 16.2360388618234 & -8.23603886182338 \tabularnewline
47 & 3 & 9.54053830186547 & -6.54053830186547 \tabularnewline
48 & 0 & 5.02429957153407 & -5.02429957153407 \tabularnewline
49 & 5 & 1.69382820575072 & 3.30617179424928 \tabularnewline
50 & 1 & 5.29627117073916 & -4.29627117073916 \tabularnewline
51 & 1 & 2.12152269170572 & -1.12152269170572 \tabularnewline
52 & 3 & 2.08179759721601 & 0.918202402783987 \tabularnewline
53 & 6 & 3.50759544765599 & 2.49240455234401 \tabularnewline
54 & 7 & 5.80341584567357 & 1.19658415432643 \tabularnewline
55 & 8 & 6.959482791993 & 1.04051720800701 \tabularnewline
56 & 14 & 7.91954098094195 & 6.08045901905805 \tabularnewline
57 & 14 & 15.2294059838937 & -1.22940598389366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57915&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]19[/C][C]19.3436662778418[/C][C]-0.343666277841756[/C][/ROW]
[ROW][C]2[/C][C]22[/C][C]19.0890659709010[/C][C]2.91093402909904[/C][/ROW]
[ROW][C]3[/C][C]23[/C][C]20.7571350023174[/C][C]2.24286499768262[/C][/ROW]
[ROW][C]4[/C][C]20[/C][C]21.210297027088[/C][C]-1.21029702708800[/C][/ROW]
[ROW][C]5[/C][C]14[/C][C]18.9310386344478[/C][C]-4.93103863444777[/C][/ROW]
[ROW][C]6[/C][C]14[/C][C]14.8085610924297[/C][C]-0.80856109242973[/C][/ROW]
[ROW][C]7[/C][C]14[/C][C]14.4393944014263[/C][C]-0.439394401426334[/C][/ROW]
[ROW][C]8[/C][C]15[/C][C]14.3788106675275[/C][C]0.621189332472461[/C][/ROW]
[ROW][C]9[/C][C]11[/C][C]15.0591132760949[/C][C]-4.05911327609487[/C][/ROW]
[ROW][C]10[/C][C]17[/C][C]12.2286884799988[/C][C]4.77131152000121[/C][/ROW]
[ROW][C]11[/C][C]16[/C][C]17.2669539716883[/C][C]-1.26695397168828[/C][/ROW]
[ROW][C]12[/C][C]20[/C][C]16.6803591077745[/C][C]3.31964089222554[/C][/ROW]
[ROW][C]13[/C][C]24[/C][C]20.4034087644296[/C][C]3.59659123557038[/C][/ROW]
[ROW][C]14[/C][C]23[/C][C]23.2715664706869[/C][C]-0.271566470686929[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]23.0895667582345[/C][C]-3.08956675823447[/C][/ROW]
[ROW][C]16[/C][C]21[/C][C]20.3974322114442[/C][C]0.602567788555793[/C][/ROW]
[ROW][C]17[/C][C]19[/C][C]21.4952198735681[/C][C]-2.49521987356811[/C][/ROW]
[ROW][C]18[/C][C]23[/C][C]19.406242196069[/C][C]3.59375780393098[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]22.9478529164026[/C][C]0.0521470835974146[/C][/ROW]
[ROW][C]20[/C][C]23[/C][C]22.4535343889447[/C][C]0.546465611055345[/C][/ROW]
[ROW][C]21[/C][C]23[/C][C]22.5661085886788[/C][C]0.433891411321222[/C][/ROW]
[ROW][C]22[/C][C]27[/C][C]22.7164156985741[/C][C]4.28358430142586[/C][/ROW]
[ROW][C]23[/C][C]26[/C][C]25.5051232158520[/C][C]0.49487678414797[/C][/ROW]
[ROW][C]24[/C][C]17[/C][C]24.5785013030326[/C][C]-7.57850130303258[/C][/ROW]
[ROW][C]25[/C][C]24[/C][C]17.4695638127938[/C][C]6.53043618720624[/C][/ROW]
[ROW][C]26[/C][C]26[/C][C]22.7086954720163[/C][C]3.29130452798368[/C][/ROW]
[ROW][C]27[/C][C]24[/C][C]24.4930745610678[/C][C]-0.493074561067751[/C][/ROW]
[ROW][C]28[/C][C]27[/C][C]23.2715664706869[/C][C]3.72843352931307[/C][/ROW]
[ROW][C]29[/C][C]27[/C][C]25.0316633278032[/C][C]1.96833667219681[/C][/ROW]
[ROW][C]30[/C][C]26[/C][C]24.9399477674782[/C][C]1.06005223252184[/C][/ROW]
[ROW][C]31[/C][C]24[/C][C]24.3553450878928[/C][C]-0.355345087892805[/C][/ROW]
[ROW][C]32[/C][C]23[/C][C]23.0007164237436[/C][C]-0.000716423743563926[/C][/ROW]
[ROW][C]33[/C][C]23[/C][C]21.9489426744696[/C][C]1.05105732553042[/C][/ROW]
[ROW][C]34[/C][C]24[/C][C]21.7757847408367[/C][C]2.22421525916334[/C][/ROW]
[ROW][C]35[/C][C]17[/C][C]22.4603839834357[/C][C]-5.46038398343572[/C][/ROW]
[ROW][C]36[/C][C]21[/C][C]17.2192601398847[/C][C]3.78073986011531[/C][/ROW]
[ROW][C]37[/C][C]19[/C][C]20.2165540512535[/C][C]-1.21655405125347[/C][/ROW]
[ROW][C]38[/C][C]22[/C][C]19.0579341444747[/C][C]2.94206585552529[/C][/ROW]
[ROW][C]39[/C][C]22[/C][C]21.2931708085935[/C][C]0.706829191406509[/C][/ROW]
[ROW][C]40[/C][C]18[/C][C]21.4643365578979[/C][C]-3.46433655789794[/C][/ROW]
[ROW][C]41[/C][C]16[/C][C]18.0164335822179[/C][C]-2.01643358221787[/C][/ROW]
[ROW][C]42[/C][C]14[/C][C]16.6826635574777[/C][C]-2.68266355747772[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]14.7459851742025[/C][C]-2.74598517420246[/C][/ROW]
[ROW][C]44[/C][C]14[/C][C]13.2639002238954[/C][C]0.736099776104575[/C][/ROW]
[ROW][C]45[/C][C]16[/C][C]15.1462836916321[/C][C]0.853716308367904[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]16.2360388618234[/C][C]-8.23603886182338[/C][/ROW]
[ROW][C]47[/C][C]3[/C][C]9.54053830186547[/C][C]-6.54053830186547[/C][/ROW]
[ROW][C]48[/C][C]0[/C][C]5.02429957153407[/C][C]-5.02429957153407[/C][/ROW]
[ROW][C]49[/C][C]5[/C][C]1.69382820575072[/C][C]3.30617179424928[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]5.29627117073916[/C][C]-4.29627117073916[/C][/ROW]
[ROW][C]51[/C][C]1[/C][C]2.12152269170572[/C][C]-1.12152269170572[/C][/ROW]
[ROW][C]52[/C][C]3[/C][C]2.08179759721601[/C][C]0.918202402783987[/C][/ROW]
[ROW][C]53[/C][C]6[/C][C]3.50759544765599[/C][C]2.49240455234401[/C][/ROW]
[ROW][C]54[/C][C]7[/C][C]5.80341584567357[/C][C]1.19658415432643[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]6.959482791993[/C][C]1.04051720800701[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]7.91954098094195[/C][C]6.08045901905805[/C][/ROW]
[ROW][C]57[/C][C]14[/C][C]15.2294059838937[/C][C]-1.22940598389366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57915&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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
11919.3436662778418-0.343666277841756
22219.08906597090102.91093402909904
32320.75713500231742.24286499768262
42021.210297027088-1.21029702708800
51418.9310386344478-4.93103863444777
61414.8085610924297-0.80856109242973
71414.4393944014263-0.439394401426334
81514.37881066752750.621189332472461
91115.0591132760949-4.05911327609487
101712.22868847999884.77131152000121
111617.2669539716883-1.26695397168828
122016.68035910777453.31964089222554
132420.40340876442963.59659123557038
142323.2715664706869-0.271566470686929
152023.0895667582345-3.08956675823447
162120.39743221144420.602567788555793
171921.4952198735681-2.49521987356811
182319.4062421960693.59375780393098
192322.94785291640260.0521470835974146
202322.45353438894470.546465611055345
212322.56610858867880.433891411321222
222722.71641569857414.28358430142586
232625.50512321585200.49487678414797
241724.5785013030326-7.57850130303258
252417.46956381279386.53043618720624
262622.70869547201633.29130452798368
272424.4930745610678-0.493074561067751
282723.27156647068693.72843352931307
292725.03166332780321.96833667219681
302624.93994776747821.06005223252184
312424.3553450878928-0.355345087892805
322323.0007164237436-0.000716423743563926
332321.94894267446961.05105732553042
342421.77578474083672.22421525916334
351722.4603839834357-5.46038398343572
362117.21926013988473.78073986011531
371920.2165540512535-1.21655405125347
382219.05793414447472.94206585552529
392221.29317080859350.706829191406509
401821.4643365578979-3.46433655789794
411618.0164335822179-2.01643358221787
421416.6826635574777-2.68266355747772
431214.7459851742025-2.74598517420246
441413.26390022389540.736099776104575
451615.14628369163210.853716308367904
46816.2360388618234-8.23603886182338
4739.54053830186547-6.54053830186547
4805.02429957153407-5.02429957153407
4951.693828205750723.30617179424928
5015.29627117073916-4.29627117073916
5112.12152269170572-1.12152269170572
5232.081797597216010.918202402783987
5363.507595447655992.49240455234401
5475.803415845673571.19658415432643
5586.9594827919931.04051720800701
56147.919540980941956.08045901905805
571415.2294059838937-1.22940598389366







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.4187229333531650.837445866706330.581277066646835
80.2583081430702120.5166162861404240.741691856929788
90.3271208613179720.6542417226359430.672879138682028
100.4291775397778280.8583550795556570.570822460222172
110.3918157988349220.7836315976698440.608184201165078
120.3146313655195660.6292627310391330.685368634480434
130.2417482536773650.4834965073547290.758251746322635
140.1770136460926920.3540272921853840.822986353907308
150.2545547318219630.5091094636439270.745445268178037
160.1817584396719710.3635168793439410.81824156032803
170.1455974330628190.2911948661256370.854402566937181
180.1758079697223880.3516159394447760.824192030277612
190.1223153682677910.2446307365355810.87768463173221
200.08732418187791860.1746483637558370.912675818122081
210.05807942770834860.1161588554166970.941920572291651
220.0923763393940810.1847526787881620.907623660605919
230.06572121027498240.1314424205499650.934278789725018
240.2060418273055190.4120836546110380.79395817269448
250.4121725498127470.8243450996254940.587827450187253
260.447562180613290.895124361226580.55243781938671
270.3702996669643940.7405993339287880.629700333035606
280.4270985514202830.8541971028405670.572901448579717
290.3945338102843220.7890676205686440.605466189715678
300.3305277798094530.6610555596189060.669472220190547
310.2598610304954490.5197220609908980.740138969504551
320.1990512801228520.3981025602457040.800948719877148
330.1520738841659780.3041477683319560.847926115834022
340.1316629671485920.2633259342971830.868337032851408
350.2107165171556430.4214330343112870.789283482844357
360.2437165316242120.4874330632484230.756283468375789
370.1881215780958510.3762431561917030.811878421904149
380.2150257724359940.4300515448719880.784974227564006
390.1808893916481850.3617787832963690.819110608351815
400.1552629191229950.3105258382459900.844737080877005
410.1169210037775380.2338420075550760.883078996222462
420.09679292438520320.1935858487704060.903207075614797
430.07370674062268810.1474134812453760.926293259377312
440.07310114001427060.1462022800285410.92689885998573
450.1351355958440010.2702711916880020.864864404156
460.2109265341237020.4218530682474040.789073465876298
470.2559829788918980.5119659577837950.744017021108102
480.2719717851675150.5439435703350310.728028214832485
490.4563112981851380.9126225963702770.543688701814862
500.6258615626191320.7482768747617370.374138437380868

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
7 & 0.418722933353165 & 0.83744586670633 & 0.581277066646835 \tabularnewline
8 & 0.258308143070212 & 0.516616286140424 & 0.741691856929788 \tabularnewline
9 & 0.327120861317972 & 0.654241722635943 & 0.672879138682028 \tabularnewline
10 & 0.429177539777828 & 0.858355079555657 & 0.570822460222172 \tabularnewline
11 & 0.391815798834922 & 0.783631597669844 & 0.608184201165078 \tabularnewline
12 & 0.314631365519566 & 0.629262731039133 & 0.685368634480434 \tabularnewline
13 & 0.241748253677365 & 0.483496507354729 & 0.758251746322635 \tabularnewline
14 & 0.177013646092692 & 0.354027292185384 & 0.822986353907308 \tabularnewline
15 & 0.254554731821963 & 0.509109463643927 & 0.745445268178037 \tabularnewline
16 & 0.181758439671971 & 0.363516879343941 & 0.81824156032803 \tabularnewline
17 & 0.145597433062819 & 0.291194866125637 & 0.854402566937181 \tabularnewline
18 & 0.175807969722388 & 0.351615939444776 & 0.824192030277612 \tabularnewline
19 & 0.122315368267791 & 0.244630736535581 & 0.87768463173221 \tabularnewline
20 & 0.0873241818779186 & 0.174648363755837 & 0.912675818122081 \tabularnewline
21 & 0.0580794277083486 & 0.116158855416697 & 0.941920572291651 \tabularnewline
22 & 0.092376339394081 & 0.184752678788162 & 0.907623660605919 \tabularnewline
23 & 0.0657212102749824 & 0.131442420549965 & 0.934278789725018 \tabularnewline
24 & 0.206041827305519 & 0.412083654611038 & 0.79395817269448 \tabularnewline
25 & 0.412172549812747 & 0.824345099625494 & 0.587827450187253 \tabularnewline
26 & 0.44756218061329 & 0.89512436122658 & 0.55243781938671 \tabularnewline
27 & 0.370299666964394 & 0.740599333928788 & 0.629700333035606 \tabularnewline
28 & 0.427098551420283 & 0.854197102840567 & 0.572901448579717 \tabularnewline
29 & 0.394533810284322 & 0.789067620568644 & 0.605466189715678 \tabularnewline
30 & 0.330527779809453 & 0.661055559618906 & 0.669472220190547 \tabularnewline
31 & 0.259861030495449 & 0.519722060990898 & 0.740138969504551 \tabularnewline
32 & 0.199051280122852 & 0.398102560245704 & 0.800948719877148 \tabularnewline
33 & 0.152073884165978 & 0.304147768331956 & 0.847926115834022 \tabularnewline
34 & 0.131662967148592 & 0.263325934297183 & 0.868337032851408 \tabularnewline
35 & 0.210716517155643 & 0.421433034311287 & 0.789283482844357 \tabularnewline
36 & 0.243716531624212 & 0.487433063248423 & 0.756283468375789 \tabularnewline
37 & 0.188121578095851 & 0.376243156191703 & 0.811878421904149 \tabularnewline
38 & 0.215025772435994 & 0.430051544871988 & 0.784974227564006 \tabularnewline
39 & 0.180889391648185 & 0.361778783296369 & 0.819110608351815 \tabularnewline
40 & 0.155262919122995 & 0.310525838245990 & 0.844737080877005 \tabularnewline
41 & 0.116921003777538 & 0.233842007555076 & 0.883078996222462 \tabularnewline
42 & 0.0967929243852032 & 0.193585848770406 & 0.903207075614797 \tabularnewline
43 & 0.0737067406226881 & 0.147413481245376 & 0.926293259377312 \tabularnewline
44 & 0.0731011400142706 & 0.146202280028541 & 0.92689885998573 \tabularnewline
45 & 0.135135595844001 & 0.270271191688002 & 0.864864404156 \tabularnewline
46 & 0.210926534123702 & 0.421853068247404 & 0.789073465876298 \tabularnewline
47 & 0.255982978891898 & 0.511965957783795 & 0.744017021108102 \tabularnewline
48 & 0.271971785167515 & 0.543943570335031 & 0.728028214832485 \tabularnewline
49 & 0.456311298185138 & 0.912622596370277 & 0.543688701814862 \tabularnewline
50 & 0.625861562619132 & 0.748276874761737 & 0.374138437380868 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57915&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]7[/C][C]0.418722933353165[/C][C]0.83744586670633[/C][C]0.581277066646835[/C][/ROW]
[ROW][C]8[/C][C]0.258308143070212[/C][C]0.516616286140424[/C][C]0.741691856929788[/C][/ROW]
[ROW][C]9[/C][C]0.327120861317972[/C][C]0.654241722635943[/C][C]0.672879138682028[/C][/ROW]
[ROW][C]10[/C][C]0.429177539777828[/C][C]0.858355079555657[/C][C]0.570822460222172[/C][/ROW]
[ROW][C]11[/C][C]0.391815798834922[/C][C]0.783631597669844[/C][C]0.608184201165078[/C][/ROW]
[ROW][C]12[/C][C]0.314631365519566[/C][C]0.629262731039133[/C][C]0.685368634480434[/C][/ROW]
[ROW][C]13[/C][C]0.241748253677365[/C][C]0.483496507354729[/C][C]0.758251746322635[/C][/ROW]
[ROW][C]14[/C][C]0.177013646092692[/C][C]0.354027292185384[/C][C]0.822986353907308[/C][/ROW]
[ROW][C]15[/C][C]0.254554731821963[/C][C]0.509109463643927[/C][C]0.745445268178037[/C][/ROW]
[ROW][C]16[/C][C]0.181758439671971[/C][C]0.363516879343941[/C][C]0.81824156032803[/C][/ROW]
[ROW][C]17[/C][C]0.145597433062819[/C][C]0.291194866125637[/C][C]0.854402566937181[/C][/ROW]
[ROW][C]18[/C][C]0.175807969722388[/C][C]0.351615939444776[/C][C]0.824192030277612[/C][/ROW]
[ROW][C]19[/C][C]0.122315368267791[/C][C]0.244630736535581[/C][C]0.87768463173221[/C][/ROW]
[ROW][C]20[/C][C]0.0873241818779186[/C][C]0.174648363755837[/C][C]0.912675818122081[/C][/ROW]
[ROW][C]21[/C][C]0.0580794277083486[/C][C]0.116158855416697[/C][C]0.941920572291651[/C][/ROW]
[ROW][C]22[/C][C]0.092376339394081[/C][C]0.184752678788162[/C][C]0.907623660605919[/C][/ROW]
[ROW][C]23[/C][C]0.0657212102749824[/C][C]0.131442420549965[/C][C]0.934278789725018[/C][/ROW]
[ROW][C]24[/C][C]0.206041827305519[/C][C]0.412083654611038[/C][C]0.79395817269448[/C][/ROW]
[ROW][C]25[/C][C]0.412172549812747[/C][C]0.824345099625494[/C][C]0.587827450187253[/C][/ROW]
[ROW][C]26[/C][C]0.44756218061329[/C][C]0.89512436122658[/C][C]0.55243781938671[/C][/ROW]
[ROW][C]27[/C][C]0.370299666964394[/C][C]0.740599333928788[/C][C]0.629700333035606[/C][/ROW]
[ROW][C]28[/C][C]0.427098551420283[/C][C]0.854197102840567[/C][C]0.572901448579717[/C][/ROW]
[ROW][C]29[/C][C]0.394533810284322[/C][C]0.789067620568644[/C][C]0.605466189715678[/C][/ROW]
[ROW][C]30[/C][C]0.330527779809453[/C][C]0.661055559618906[/C][C]0.669472220190547[/C][/ROW]
[ROW][C]31[/C][C]0.259861030495449[/C][C]0.519722060990898[/C][C]0.740138969504551[/C][/ROW]
[ROW][C]32[/C][C]0.199051280122852[/C][C]0.398102560245704[/C][C]0.800948719877148[/C][/ROW]
[ROW][C]33[/C][C]0.152073884165978[/C][C]0.304147768331956[/C][C]0.847926115834022[/C][/ROW]
[ROW][C]34[/C][C]0.131662967148592[/C][C]0.263325934297183[/C][C]0.868337032851408[/C][/ROW]
[ROW][C]35[/C][C]0.210716517155643[/C][C]0.421433034311287[/C][C]0.789283482844357[/C][/ROW]
[ROW][C]36[/C][C]0.243716531624212[/C][C]0.487433063248423[/C][C]0.756283468375789[/C][/ROW]
[ROW][C]37[/C][C]0.188121578095851[/C][C]0.376243156191703[/C][C]0.811878421904149[/C][/ROW]
[ROW][C]38[/C][C]0.215025772435994[/C][C]0.430051544871988[/C][C]0.784974227564006[/C][/ROW]
[ROW][C]39[/C][C]0.180889391648185[/C][C]0.361778783296369[/C][C]0.819110608351815[/C][/ROW]
[ROW][C]40[/C][C]0.155262919122995[/C][C]0.310525838245990[/C][C]0.844737080877005[/C][/ROW]
[ROW][C]41[/C][C]0.116921003777538[/C][C]0.233842007555076[/C][C]0.883078996222462[/C][/ROW]
[ROW][C]42[/C][C]0.0967929243852032[/C][C]0.193585848770406[/C][C]0.903207075614797[/C][/ROW]
[ROW][C]43[/C][C]0.0737067406226881[/C][C]0.147413481245376[/C][C]0.926293259377312[/C][/ROW]
[ROW][C]44[/C][C]0.0731011400142706[/C][C]0.146202280028541[/C][C]0.92689885998573[/C][/ROW]
[ROW][C]45[/C][C]0.135135595844001[/C][C]0.270271191688002[/C][C]0.864864404156[/C][/ROW]
[ROW][C]46[/C][C]0.210926534123702[/C][C]0.421853068247404[/C][C]0.789073465876298[/C][/ROW]
[ROW][C]47[/C][C]0.255982978891898[/C][C]0.511965957783795[/C][C]0.744017021108102[/C][/ROW]
[ROW][C]48[/C][C]0.271971785167515[/C][C]0.543943570335031[/C][C]0.728028214832485[/C][/ROW]
[ROW][C]49[/C][C]0.456311298185138[/C][C]0.912622596370277[/C][C]0.543688701814862[/C][/ROW]
[ROW][C]50[/C][C]0.625861562619132[/C][C]0.748276874761737[/C][C]0.374138437380868[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57915&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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
70.4187229333531650.837445866706330.581277066646835
80.2583081430702120.5166162861404240.741691856929788
90.3271208613179720.6542417226359430.672879138682028
100.4291775397778280.8583550795556570.570822460222172
110.3918157988349220.7836315976698440.608184201165078
120.3146313655195660.6292627310391330.685368634480434
130.2417482536773650.4834965073547290.758251746322635
140.1770136460926920.3540272921853840.822986353907308
150.2545547318219630.5091094636439270.745445268178037
160.1817584396719710.3635168793439410.81824156032803
170.1455974330628190.2911948661256370.854402566937181
180.1758079697223880.3516159394447760.824192030277612
190.1223153682677910.2446307365355810.87768463173221
200.08732418187791860.1746483637558370.912675818122081
210.05807942770834860.1161588554166970.941920572291651
220.0923763393940810.1847526787881620.907623660605919
230.06572121027498240.1314424205499650.934278789725018
240.2060418273055190.4120836546110380.79395817269448
250.4121725498127470.8243450996254940.587827450187253
260.447562180613290.895124361226580.55243781938671
270.3702996669643940.7405993339287880.629700333035606
280.4270985514202830.8541971028405670.572901448579717
290.3945338102843220.7890676205686440.605466189715678
300.3305277798094530.6610555596189060.669472220190547
310.2598610304954490.5197220609908980.740138969504551
320.1990512801228520.3981025602457040.800948719877148
330.1520738841659780.3041477683319560.847926115834022
340.1316629671485920.2633259342971830.868337032851408
350.2107165171556430.4214330343112870.789283482844357
360.2437165316242120.4874330632484230.756283468375789
370.1881215780958510.3762431561917030.811878421904149
380.2150257724359940.4300515448719880.784974227564006
390.1808893916481850.3617787832963690.819110608351815
400.1552629191229950.3105258382459900.844737080877005
410.1169210037775380.2338420075550760.883078996222462
420.09679292438520320.1935858487704060.903207075614797
430.07370674062268810.1474134812453760.926293259377312
440.07310114001427060.1462022800285410.92689885998573
450.1351355958440010.2702711916880020.864864404156
460.2109265341237020.4218530682474040.789073465876298
470.2559829788918980.5119659577837950.744017021108102
480.2719717851675150.5439435703350310.728028214832485
490.4563112981851380.9126225963702770.543688701814862
500.6258615626191320.7482768747617370.374138437380868







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57915&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57915&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57915&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 level00OK
5% type I error level00OK
10% type I error level00OK



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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')
}