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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 24 Nov 2009 13:46:35 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/24/t12590956687zhngm0la306rxq.htm/, Retrieved Thu, 25 Apr 2024 10:51:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59276, Retrieved Thu, 25 Apr 2024 10:51:20 +0000

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Estimated Impact

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [workshop 7 bereke...] [2009-11-19 15:24:52] [eaf42bcf5162b5692bb3c7f9d4636222]
-   PD      [Multiple Regression] [DSHW-WS7-Multiple...] [2009-11-20 13:19:23] [f15cfb7053d35072d573abca87df96a0]
-   P         [Multiple Regression] [DSHW-WS7-Multiple...] [2009-11-20 13:53:17] [f15cfb7053d35072d573abca87df96a0]
-    D          [Multiple Regression] [DSHW-WS7-MultRegr1] [2009-11-20 14:59:26] [f15cfb7053d35072d573abca87df96a0]
-    D            [Multiple Regression] [DSHW-WS7-MultRegr...] [2009-11-20 15:10:50] [f15cfb7053d35072d573abca87df96a0]
-   P               [Multiple Regression] [DSHW-WS7-MiltRegr.2] [2009-11-20 15:42:03] [f15cfb7053d35072d573abca87df96a0]
-    D                  [Multiple Regression] [review 7] [2009-11-24 20:46:35] [6198946fb53eb5eb18db46bb758f7fde] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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=59276&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=59276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
IndGez[t] = + 1.42438152443353 -0.167230832567180InvlMex[t] + 0.882141236165582`IndGez-1`[t] -0.982303190498912M1[t] -0.97592854981554M2[t] -0.825357250922293M3[t] -1.09592854981554M4[t] -1.13950030258242M5[t] -1.10542923062600M6[t] -0.924286632839504M7[t] -0.988304098246186M8[t] -1.03830409824619M9[t] -0.719197036437907M10[t] -0.861785876383442M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
IndGez[t] =  +  1.42438152443353 -0.167230832567180InvlMex[t] +  0.882141236165582`IndGez-1`[t] -0.982303190498912M1[t] -0.97592854981554M2[t] -0.825357250922293M3[t] -1.09592854981554M4[t] -1.13950030258242M5[t] -1.10542923062600M6[t] -0.924286632839504M7[t] -0.988304098246186M8[t] -1.03830409824619M9[t] -0.719197036437907M10[t] -0.861785876383442M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59276&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]IndGez[t] =  +  1.42438152443353 -0.167230832567180InvlMex[t] +  0.882141236165582`IndGez-1`[t] -0.982303190498912M1[t] -0.97592854981554M2[t] -0.825357250922293M3[t] -1.09592854981554M4[t] -1.13950030258242M5[t] -1.10542923062600M6[t] -0.924286632839504M7[t] -0.988304098246186M8[t] -1.03830409824619M9[t] -0.719197036437907M10[t] -0.861785876383442M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&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
IndGez[t] = + 1.42438152443353 -0.167230832567180InvlMex[t] + 0.882141236165582`IndGez-1`[t] -0.982303190498912M1[t] -0.97592854981554M2[t] -0.825357250922293M3[t] -1.09592854981554M4[t] -1.13950030258242M5[t] -1.10542923062600M6[t] -0.924286632839504M7[t] -0.988304098246186M8[t] -1.03830409824619M9[t] -0.719197036437907M10[t] -0.861785876383442M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	1.42438152443353	0.234209	6.0817	0	0
InvlMex	-0.167230832567180	0.150408	-1.1118	0.272681	0.136341
`IndGez-1`	0.882141236165582	0.042393	20.8085	0	0
M1	-0.982303190498912	0.215471	-4.5589	4.6e-05	2.3e-05
M2	-0.97592854981554	0.217225	-4.4927	5.6e-05	2.8e-05
M3	-0.825357250922293	0.217242	-3.7992	0.000473	0.000236
M4	-1.09592854981554	0.217225	-5.0451	1e-05	5e-06
M5	-1.13950030258242	0.217368	-5.2423	5e-06	3e-06
M6	-1.10542923062600	0.217907	-5.0729	9e-06	4e-06
M7	-0.924286632839504	0.218548	-4.2292	0.000128	6.4e-05
M8	-0.988304098246186	0.227301	-4.348	8.9e-05	4.4e-05
M9	-1.03830409824619	0.227301	-4.568	4.4e-05	2.2e-05
M10	-0.719197036437907	0.227439	-3.1621	0.002945	0.001472
M11	-0.861785876383442	0.226923	-3.7977	0.000475	0.000237

\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) & 1.42438152443353 & 0.234209 & 6.0817 & 0 & 0 \tabularnewline
InvlMex & -0.167230832567180 & 0.150408 & -1.1118 & 0.272681 & 0.136341 \tabularnewline
`IndGez-1` & 0.882141236165582 & 0.042393 & 20.8085 & 0 & 0 \tabularnewline
M1 & -0.982303190498912 & 0.215471 & -4.5589 & 4.6e-05 & 2.3e-05 \tabularnewline
M2 & -0.97592854981554 & 0.217225 & -4.4927 & 5.6e-05 & 2.8e-05 \tabularnewline
M3 & -0.825357250922293 & 0.217242 & -3.7992 & 0.000473 & 0.000236 \tabularnewline
M4 & -1.09592854981554 & 0.217225 & -5.0451 & 1e-05 & 5e-06 \tabularnewline
M5 & -1.13950030258242 & 0.217368 & -5.2423 & 5e-06 & 3e-06 \tabularnewline
M6 & -1.10542923062600 & 0.217907 & -5.0729 & 9e-06 & 4e-06 \tabularnewline
M7 & -0.924286632839504 & 0.218548 & -4.2292 & 0.000128 & 6.4e-05 \tabularnewline
M8 & -0.988304098246186 & 0.227301 & -4.348 & 8.9e-05 & 4.4e-05 \tabularnewline
M9 & -1.03830409824619 & 0.227301 & -4.568 & 4.4e-05 & 2.2e-05 \tabularnewline
M10 & -0.719197036437907 & 0.227439 & -3.1621 & 0.002945 & 0.001472 \tabularnewline
M11 & -0.861785876383442 & 0.226923 & -3.7977 & 0.000475 & 0.000237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59276&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]1.42438152443353[/C][C]0.234209[/C][C]6.0817[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]InvlMex[/C][C]-0.167230832567180[/C][C]0.150408[/C][C]-1.1118[/C][C]0.272681[/C][C]0.136341[/C][/ROW]
[ROW][C]`IndGez-1`[/C][C]0.882141236165582[/C][C]0.042393[/C][C]20.8085[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.982303190498912[/C][C]0.215471[/C][C]-4.5589[/C][C]4.6e-05[/C][C]2.3e-05[/C][/ROW]
[ROW][C]M2[/C][C]-0.97592854981554[/C][C]0.217225[/C][C]-4.4927[/C][C]5.6e-05[/C][C]2.8e-05[/C][/ROW]
[ROW][C]M3[/C][C]-0.825357250922293[/C][C]0.217242[/C][C]-3.7992[/C][C]0.000473[/C][C]0.000236[/C][/ROW]
[ROW][C]M4[/C][C]-1.09592854981554[/C][C]0.217225[/C][C]-5.0451[/C][C]1e-05[/C][C]5e-06[/C][/ROW]
[ROW][C]M5[/C][C]-1.13950030258242[/C][C]0.217368[/C][C]-5.2423[/C][C]5e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]M6[/C][C]-1.10542923062600[/C][C]0.217907[/C][C]-5.0729[/C][C]9e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]M7[/C][C]-0.924286632839504[/C][C]0.218548[/C][C]-4.2292[/C][C]0.000128[/C][C]6.4e-05[/C][/ROW]
[ROW][C]M8[/C][C]-0.988304098246186[/C][C]0.227301[/C][C]-4.348[/C][C]8.9e-05[/C][C]4.4e-05[/C][/ROW]
[ROW][C]M9[/C][C]-1.03830409824619[/C][C]0.227301[/C][C]-4.568[/C][C]4.4e-05[/C][C]2.2e-05[/C][/ROW]
[ROW][C]M10[/C][C]-0.719197036437907[/C][C]0.227439[/C][C]-3.1621[/C][C]0.002945[/C][C]0.001472[/C][/ROW]
[ROW][C]M11[/C][C]-0.861785876383442[/C][C]0.226923[/C][C]-3.7977[/C][C]0.000475[/C][C]0.000237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59276&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	1.42438152443353	0.234209	6.0817	0	0
InvlMex	-0.167230832567180	0.150408	-1.1118	0.272681	0.136341
`IndGez-1`	0.882141236165582	0.042393	20.8085	0	0
M1	-0.982303190498912	0.215471	-4.5589	4.6e-05	2.3e-05
M2	-0.97592854981554	0.217225	-4.4927	5.6e-05	2.8e-05
M3	-0.825357250922293	0.217242	-3.7992	0.000473	0.000236
M4	-1.09592854981554	0.217225	-5.0451	1e-05	5e-06
M5	-1.13950030258242	0.217368	-5.2423	5e-06	3e-06
M6	-1.10542923062600	0.217907	-5.0729	9e-06	4e-06
M7	-0.924286632839504	0.218548	-4.2292	0.000128	6.4e-05
M8	-0.988304098246186	0.227301	-4.348	8.9e-05	4.4e-05
M9	-1.03830409824619	0.227301	-4.568	4.4e-05	2.2e-05
M10	-0.719197036437907	0.227439	-3.1621	0.002945	0.001472
M11	-0.861785876383442	0.226923	-3.7977	0.000475	0.000237

Multiple Linear Regression - Regression Statistics
Multiple R	0.962194952626626
R-squared	0.925819126860156
Adjusted R-squared	0.902298362206059
F-TEST (value)	39.3617784317609
F-TEST (DF numerator)	13
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.320861133855173
Sum Squared Residuals	4.22102655597193

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.962194952626626 \tabularnewline
R-squared & 0.925819126860156 \tabularnewline
Adjusted R-squared & 0.902298362206059 \tabularnewline
F-TEST (value) & 39.3617784317609 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.320861133855173 \tabularnewline
Sum Squared Residuals & 4.22102655597193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59276&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.962194952626626[/C][/ROW]
[ROW][C]R-squared[/C][C]0.925819126860156[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.902298362206059[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]39.3617784317609[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/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]0.320861133855173[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4.22102655597193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59276&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.962194952626626
R-squared	0.925819126860156
Adjusted R-squared	0.902298362206059
F-TEST (value)	39.3617784317609
F-TEST (DF numerator)	13
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.320861133855173
Sum Squared Residuals	4.22102655597193

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.6	1.67707606456644	-0.0770760645664356
2	1.7	1.85987895248292	-0.15987895248292
3	2	2.09866437499272	-0.0986643749927234
4	2	2.09273544694915	-0.0927354469491545
5	2.1	2.04916369418227	0.0508363058177288
6	2.5	2.17144888975526	0.328551110244742
7	2.5	2.70544798200798	-0.205447982007984
8	2.6	2.64143051660130	-0.0414305166013019
9	2.7	2.67964464021786	0.0203553597821408
10	3.7	3.0869658256427	0.613034174357303
11	4	3.82651822186274	0.173481778137255
12	5	4.95294646909586	0.0470535309041391
13	5.1	4.85278451476253	0.247215485237469
14	5.1	4.94737327906246	0.15262672093754
15	5	5.09794457795571	-0.0979445779557072
16	5.1	4.7391591554459	0.360840844554098
17	4.7	4.78380152629558	-0.0838015262955758
18	4.5	4.46501610378577	0.0349838962142288
19	4.5	4.46973045433915	0.0302695456608515
20	4.6	4.40571298893247	0.194287011067534
21	4.6	4.44392711254902	0.156072887450976
22	4.6	4.7630341743573	-0.163034174357303
23	4.6	4.62044533441177	-0.0204453344117677
24	5.3	5.48223121079521	-0.18223121079521
25	5.4	5.1174268856122	0.282573114387795
26	5.3	5.21201564991213	0.0879843500878647
27	5.2	5.27437282518882	-0.0743728251888235
28	5	4.91558740267902	0.084412597320982
29	4.2	4.69558740267902	-0.495587402679018
30	4.3	4.02394548570298	0.276054514297019
31	4.3	4.29330220710603	0.00669779289396837
32	4.3	4.22928474169935	0.070715258300651
33	4	4.17928474169935	-0.179284741699349
34	4	4.23374943265795	-0.233749432657954
35	4.1	4.09116059271242	0.0088394072875814
36	4.4	5.04116059271242	-0.641160592712419
37	3.6	4.32349977306318	-0.723499773063182
38	3.7	3.62416142481409	0.0758385751859131
39	3.8	3.86294684732389	-0.0629468473238928
40	3.3	3.68058967204720	-0.380589672047203
41	3.3	3.19594730119753	0.104052698802471
42	3.3	3.23001837315396	0.0699816268460437
43	3.5	3.41116097094045	0.0888390290595506
44	3.3	3.52357175276688	-0.223571752766883
45	3.3	3.29714350553377	0.00285649446623263
46	3.4	3.61625056734205	-0.216250567342046
47	3.4	3.56187585101307	-0.161875851013069
48	5.2	4.42366172739651	0.77633827260349
49	5.3	5.02921276199565	0.270787238004353
50	4.8	4.9565706937284	-0.156570693728398
51	5	4.66607137453885	0.333928625461147
52	4.6	4.57192832287872	0.0280716771212774
53	4.6	4.17550007564561	0.424499924354394
54	3.5	4.20957114760203	-0.709571147602033
55	3.5	3.42035838560639	0.0796416143936131

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.6 & 1.67707606456644 & -0.0770760645664356 \tabularnewline
2 & 1.7 & 1.85987895248292 & -0.15987895248292 \tabularnewline
3 & 2 & 2.09866437499272 & -0.0986643749927234 \tabularnewline
4 & 2 & 2.09273544694915 & -0.0927354469491545 \tabularnewline
5 & 2.1 & 2.04916369418227 & 0.0508363058177288 \tabularnewline
6 & 2.5 & 2.17144888975526 & 0.328551110244742 \tabularnewline
7 & 2.5 & 2.70544798200798 & -0.205447982007984 \tabularnewline
8 & 2.6 & 2.64143051660130 & -0.0414305166013019 \tabularnewline
9 & 2.7 & 2.67964464021786 & 0.0203553597821408 \tabularnewline
10 & 3.7 & 3.0869658256427 & 0.613034174357303 \tabularnewline
11 & 4 & 3.82651822186274 & 0.173481778137255 \tabularnewline
12 & 5 & 4.95294646909586 & 0.0470535309041391 \tabularnewline
13 & 5.1 & 4.85278451476253 & 0.247215485237469 \tabularnewline
14 & 5.1 & 4.94737327906246 & 0.15262672093754 \tabularnewline
15 & 5 & 5.09794457795571 & -0.0979445779557072 \tabularnewline
16 & 5.1 & 4.7391591554459 & 0.360840844554098 \tabularnewline
17 & 4.7 & 4.78380152629558 & -0.0838015262955758 \tabularnewline
18 & 4.5 & 4.46501610378577 & 0.0349838962142288 \tabularnewline
19 & 4.5 & 4.46973045433915 & 0.0302695456608515 \tabularnewline
20 & 4.6 & 4.40571298893247 & 0.194287011067534 \tabularnewline
21 & 4.6 & 4.44392711254902 & 0.156072887450976 \tabularnewline
22 & 4.6 & 4.7630341743573 & -0.163034174357303 \tabularnewline
23 & 4.6 & 4.62044533441177 & -0.0204453344117677 \tabularnewline
24 & 5.3 & 5.48223121079521 & -0.18223121079521 \tabularnewline
25 & 5.4 & 5.1174268856122 & 0.282573114387795 \tabularnewline
26 & 5.3 & 5.21201564991213 & 0.0879843500878647 \tabularnewline
27 & 5.2 & 5.27437282518882 & -0.0743728251888235 \tabularnewline
28 & 5 & 4.91558740267902 & 0.084412597320982 \tabularnewline
29 & 4.2 & 4.69558740267902 & -0.495587402679018 \tabularnewline
30 & 4.3 & 4.02394548570298 & 0.276054514297019 \tabularnewline
31 & 4.3 & 4.29330220710603 & 0.00669779289396837 \tabularnewline
32 & 4.3 & 4.22928474169935 & 0.070715258300651 \tabularnewline
33 & 4 & 4.17928474169935 & -0.179284741699349 \tabularnewline
34 & 4 & 4.23374943265795 & -0.233749432657954 \tabularnewline
35 & 4.1 & 4.09116059271242 & 0.0088394072875814 \tabularnewline
36 & 4.4 & 5.04116059271242 & -0.641160592712419 \tabularnewline
37 & 3.6 & 4.32349977306318 & -0.723499773063182 \tabularnewline
38 & 3.7 & 3.62416142481409 & 0.0758385751859131 \tabularnewline
39 & 3.8 & 3.86294684732389 & -0.0629468473238928 \tabularnewline
40 & 3.3 & 3.68058967204720 & -0.380589672047203 \tabularnewline
41 & 3.3 & 3.19594730119753 & 0.104052698802471 \tabularnewline
42 & 3.3 & 3.23001837315396 & 0.0699816268460437 \tabularnewline
43 & 3.5 & 3.41116097094045 & 0.0888390290595506 \tabularnewline
44 & 3.3 & 3.52357175276688 & -0.223571752766883 \tabularnewline
45 & 3.3 & 3.29714350553377 & 0.00285649446623263 \tabularnewline
46 & 3.4 & 3.61625056734205 & -0.216250567342046 \tabularnewline
47 & 3.4 & 3.56187585101307 & -0.161875851013069 \tabularnewline
48 & 5.2 & 4.42366172739651 & 0.77633827260349 \tabularnewline
49 & 5.3 & 5.02921276199565 & 0.270787238004353 \tabularnewline
50 & 4.8 & 4.9565706937284 & -0.156570693728398 \tabularnewline
51 & 5 & 4.66607137453885 & 0.333928625461147 \tabularnewline
52 & 4.6 & 4.57192832287872 & 0.0280716771212774 \tabularnewline
53 & 4.6 & 4.17550007564561 & 0.424499924354394 \tabularnewline
54 & 3.5 & 4.20957114760203 & -0.709571147602033 \tabularnewline
55 & 3.5 & 3.42035838560639 & 0.0796416143936131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59276&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]1.6[/C][C]1.67707606456644[/C][C]-0.0770760645664356[/C][/ROW]
[ROW][C]2[/C][C]1.7[/C][C]1.85987895248292[/C][C]-0.15987895248292[/C][/ROW]
[ROW][C]3[/C][C]2[/C][C]2.09866437499272[/C][C]-0.0986643749927234[/C][/ROW]
[ROW][C]4[/C][C]2[/C][C]2.09273544694915[/C][C]-0.0927354469491545[/C][/ROW]
[ROW][C]5[/C][C]2.1[/C][C]2.04916369418227[/C][C]0.0508363058177288[/C][/ROW]
[ROW][C]6[/C][C]2.5[/C][C]2.17144888975526[/C][C]0.328551110244742[/C][/ROW]
[ROW][C]7[/C][C]2.5[/C][C]2.70544798200798[/C][C]-0.205447982007984[/C][/ROW]
[ROW][C]8[/C][C]2.6[/C][C]2.64143051660130[/C][C]-0.0414305166013019[/C][/ROW]
[ROW][C]9[/C][C]2.7[/C][C]2.67964464021786[/C][C]0.0203553597821408[/C][/ROW]
[ROW][C]10[/C][C]3.7[/C][C]3.0869658256427[/C][C]0.613034174357303[/C][/ROW]
[ROW][C]11[/C][C]4[/C][C]3.82651822186274[/C][C]0.173481778137255[/C][/ROW]
[ROW][C]12[/C][C]5[/C][C]4.95294646909586[/C][C]0.0470535309041391[/C][/ROW]
[ROW][C]13[/C][C]5.1[/C][C]4.85278451476253[/C][C]0.247215485237469[/C][/ROW]
[ROW][C]14[/C][C]5.1[/C][C]4.94737327906246[/C][C]0.15262672093754[/C][/ROW]
[ROW][C]15[/C][C]5[/C][C]5.09794457795571[/C][C]-0.0979445779557072[/C][/ROW]
[ROW][C]16[/C][C]5.1[/C][C]4.7391591554459[/C][C]0.360840844554098[/C][/ROW]
[ROW][C]17[/C][C]4.7[/C][C]4.78380152629558[/C][C]-0.0838015262955758[/C][/ROW]
[ROW][C]18[/C][C]4.5[/C][C]4.46501610378577[/C][C]0.0349838962142288[/C][/ROW]
[ROW][C]19[/C][C]4.5[/C][C]4.46973045433915[/C][C]0.0302695456608515[/C][/ROW]
[ROW][C]20[/C][C]4.6[/C][C]4.40571298893247[/C][C]0.194287011067534[/C][/ROW]
[ROW][C]21[/C][C]4.6[/C][C]4.44392711254902[/C][C]0.156072887450976[/C][/ROW]
[ROW][C]22[/C][C]4.6[/C][C]4.7630341743573[/C][C]-0.163034174357303[/C][/ROW]
[ROW][C]23[/C][C]4.6[/C][C]4.62044533441177[/C][C]-0.0204453344117677[/C][/ROW]
[ROW][C]24[/C][C]5.3[/C][C]5.48223121079521[/C][C]-0.18223121079521[/C][/ROW]
[ROW][C]25[/C][C]5.4[/C][C]5.1174268856122[/C][C]0.282573114387795[/C][/ROW]
[ROW][C]26[/C][C]5.3[/C][C]5.21201564991213[/C][C]0.0879843500878647[/C][/ROW]
[ROW][C]27[/C][C]5.2[/C][C]5.27437282518882[/C][C]-0.0743728251888235[/C][/ROW]
[ROW][C]28[/C][C]5[/C][C]4.91558740267902[/C][C]0.084412597320982[/C][/ROW]
[ROW][C]29[/C][C]4.2[/C][C]4.69558740267902[/C][C]-0.495587402679018[/C][/ROW]
[ROW][C]30[/C][C]4.3[/C][C]4.02394548570298[/C][C]0.276054514297019[/C][/ROW]
[ROW][C]31[/C][C]4.3[/C][C]4.29330220710603[/C][C]0.00669779289396837[/C][/ROW]
[ROW][C]32[/C][C]4.3[/C][C]4.22928474169935[/C][C]0.070715258300651[/C][/ROW]
[ROW][C]33[/C][C]4[/C][C]4.17928474169935[/C][C]-0.179284741699349[/C][/ROW]
[ROW][C]34[/C][C]4[/C][C]4.23374943265795[/C][C]-0.233749432657954[/C][/ROW]
[ROW][C]35[/C][C]4.1[/C][C]4.09116059271242[/C][C]0.0088394072875814[/C][/ROW]
[ROW][C]36[/C][C]4.4[/C][C]5.04116059271242[/C][C]-0.641160592712419[/C][/ROW]
[ROW][C]37[/C][C]3.6[/C][C]4.32349977306318[/C][C]-0.723499773063182[/C][/ROW]
[ROW][C]38[/C][C]3.7[/C][C]3.62416142481409[/C][C]0.0758385751859131[/C][/ROW]
[ROW][C]39[/C][C]3.8[/C][C]3.86294684732389[/C][C]-0.0629468473238928[/C][/ROW]
[ROW][C]40[/C][C]3.3[/C][C]3.68058967204720[/C][C]-0.380589672047203[/C][/ROW]
[ROW][C]41[/C][C]3.3[/C][C]3.19594730119753[/C][C]0.104052698802471[/C][/ROW]
[ROW][C]42[/C][C]3.3[/C][C]3.23001837315396[/C][C]0.0699816268460437[/C][/ROW]
[ROW][C]43[/C][C]3.5[/C][C]3.41116097094045[/C][C]0.0888390290595506[/C][/ROW]
[ROW][C]44[/C][C]3.3[/C][C]3.52357175276688[/C][C]-0.223571752766883[/C][/ROW]
[ROW][C]45[/C][C]3.3[/C][C]3.29714350553377[/C][C]0.00285649446623263[/C][/ROW]
[ROW][C]46[/C][C]3.4[/C][C]3.61625056734205[/C][C]-0.216250567342046[/C][/ROW]
[ROW][C]47[/C][C]3.4[/C][C]3.56187585101307[/C][C]-0.161875851013069[/C][/ROW]
[ROW][C]48[/C][C]5.2[/C][C]4.42366172739651[/C][C]0.77633827260349[/C][/ROW]
[ROW][C]49[/C][C]5.3[/C][C]5.02921276199565[/C][C]0.270787238004353[/C][/ROW]
[ROW][C]50[/C][C]4.8[/C][C]4.9565706937284[/C][C]-0.156570693728398[/C][/ROW]
[ROW][C]51[/C][C]5[/C][C]4.66607137453885[/C][C]0.333928625461147[/C][/ROW]
[ROW][C]52[/C][C]4.6[/C][C]4.57192832287872[/C][C]0.0280716771212774[/C][/ROW]
[ROW][C]53[/C][C]4.6[/C][C]4.17550007564561[/C][C]0.424499924354394[/C][/ROW]
[ROW][C]54[/C][C]3.5[/C][C]4.20957114760203[/C][C]-0.709571147602033[/C][/ROW]
[ROW][C]55[/C][C]3.5[/C][C]3.42035838560639[/C][C]0.0796416143936131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59276&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1.6	1.67707606456644	-0.0770760645664356
2	1.7	1.85987895248292	-0.15987895248292
3	2	2.09866437499272	-0.0986643749927234
4	2	2.09273544694915	-0.0927354469491545
5	2.1	2.04916369418227	0.0508363058177288
6	2.5	2.17144888975526	0.328551110244742
7	2.5	2.70544798200798	-0.205447982007984
8	2.6	2.64143051660130	-0.0414305166013019
9	2.7	2.67964464021786	0.0203553597821408
10	3.7	3.0869658256427	0.613034174357303
11	4	3.82651822186274	0.173481778137255
12	5	4.95294646909586	0.0470535309041391
13	5.1	4.85278451476253	0.247215485237469
14	5.1	4.94737327906246	0.15262672093754
15	5	5.09794457795571	-0.0979445779557072
16	5.1	4.7391591554459	0.360840844554098
17	4.7	4.78380152629558	-0.0838015262955758
18	4.5	4.46501610378577	0.0349838962142288
19	4.5	4.46973045433915	0.0302695456608515
20	4.6	4.40571298893247	0.194287011067534
21	4.6	4.44392711254902	0.156072887450976
22	4.6	4.7630341743573	-0.163034174357303
23	4.6	4.62044533441177	-0.0204453344117677
24	5.3	5.48223121079521	-0.18223121079521
25	5.4	5.1174268856122	0.282573114387795
26	5.3	5.21201564991213	0.0879843500878647
27	5.2	5.27437282518882	-0.0743728251888235
28	5	4.91558740267902	0.084412597320982
29	4.2	4.69558740267902	-0.495587402679018
30	4.3	4.02394548570298	0.276054514297019
31	4.3	4.29330220710603	0.00669779289396837
32	4.3	4.22928474169935	0.070715258300651
33	4	4.17928474169935	-0.179284741699349
34	4	4.23374943265795	-0.233749432657954
35	4.1	4.09116059271242	0.0088394072875814
36	4.4	5.04116059271242	-0.641160592712419
37	3.6	4.32349977306318	-0.723499773063182
38	3.7	3.62416142481409	0.0758385751859131
39	3.8	3.86294684732389	-0.0629468473238928
40	3.3	3.68058967204720	-0.380589672047203
41	3.3	3.19594730119753	0.104052698802471
42	3.3	3.23001837315396	0.0699816268460437
43	3.5	3.41116097094045	0.0888390290595506
44	3.3	3.52357175276688	-0.223571752766883
45	3.3	3.29714350553377	0.00285649446623263
46	3.4	3.61625056734205	-0.216250567342046
47	3.4	3.56187585101307	-0.161875851013069
48	5.2	4.42366172739651	0.77633827260349
49	5.3	5.02921276199565	0.270787238004353
50	4.8	4.9565706937284	-0.156570693728398
51	5	4.66607137453885	0.333928625461147
52	4.6	4.57192832287872	0.0280716771212774
53	4.6	4.17550007564561	0.424499924354394
54	3.5	4.20957114760203	-0.709571147602033
55	3.5	3.42035838560639	0.0796416143936131

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.178880341166081	0.357760682332162	0.821119658833919
18	0.181103307737641	0.362206615475283	0.818896692262359
19	0.0977050454092338	0.195410090818468	0.902294954590766
20	0.0513025329271525	0.102605065854305	0.948697467072848
21	0.0231229580446458	0.0462459160892916	0.976877041955354
22	0.13412888835865	0.2682577767173	0.86587111164135
23	0.0854344386100902	0.170868877220180	0.91456556138991
24	0.0551698135868272	0.110339627173654	0.944830186413173
25	0.038480659361674	0.076961318723348	0.961519340638326
26	0.0203123529982687	0.0406247059965375	0.979687647001731
27	0.00972970359330364	0.0194594071866073	0.990270296406696
28	0.00528936708339018	0.0105787341667804	0.99471063291661
29	0.0123146804252546	0.0246293608505092	0.987685319574745
30	0.00973279333350235	0.0194655866670047	0.990267206666498
31	0.00449762448957547	0.00899524897915093	0.995502375510425
32	0.00222755636149520	0.00445511272299039	0.997772443638505
33	0.00123948015100782	0.00247896030201563	0.998760519848992
34	0.00111384365177268	0.00222768730354536	0.998886156348227
35	0.000439794117558488	0.000879588235116976	0.999560205882442
36	0.0233682983587977	0.0467365967175955	0.976631701641202
37	0.195703567348831	0.391407134697662	0.804296432651169
38	0.115294210592324	0.230588421184649	0.884705789407676

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.178880341166081 & 0.357760682332162 & 0.821119658833919 \tabularnewline
18 & 0.181103307737641 & 0.362206615475283 & 0.818896692262359 \tabularnewline
19 & 0.0977050454092338 & 0.195410090818468 & 0.902294954590766 \tabularnewline
20 & 0.0513025329271525 & 0.102605065854305 & 0.948697467072848 \tabularnewline
21 & 0.0231229580446458 & 0.0462459160892916 & 0.976877041955354 \tabularnewline
22 & 0.13412888835865 & 0.2682577767173 & 0.86587111164135 \tabularnewline
23 & 0.0854344386100902 & 0.170868877220180 & 0.91456556138991 \tabularnewline
24 & 0.0551698135868272 & 0.110339627173654 & 0.944830186413173 \tabularnewline
25 & 0.038480659361674 & 0.076961318723348 & 0.961519340638326 \tabularnewline
26 & 0.0203123529982687 & 0.0406247059965375 & 0.979687647001731 \tabularnewline
27 & 0.00972970359330364 & 0.0194594071866073 & 0.990270296406696 \tabularnewline
28 & 0.00528936708339018 & 0.0105787341667804 & 0.99471063291661 \tabularnewline
29 & 0.0123146804252546 & 0.0246293608505092 & 0.987685319574745 \tabularnewline
30 & 0.00973279333350235 & 0.0194655866670047 & 0.990267206666498 \tabularnewline
31 & 0.00449762448957547 & 0.00899524897915093 & 0.995502375510425 \tabularnewline
32 & 0.00222755636149520 & 0.00445511272299039 & 0.997772443638505 \tabularnewline
33 & 0.00123948015100782 & 0.00247896030201563 & 0.998760519848992 \tabularnewline
34 & 0.00111384365177268 & 0.00222768730354536 & 0.998886156348227 \tabularnewline
35 & 0.000439794117558488 & 0.000879588235116976 & 0.999560205882442 \tabularnewline
36 & 0.0233682983587977 & 0.0467365967175955 & 0.976631701641202 \tabularnewline
37 & 0.195703567348831 & 0.391407134697662 & 0.804296432651169 \tabularnewline
38 & 0.115294210592324 & 0.230588421184649 & 0.884705789407676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59276&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]17[/C][C]0.178880341166081[/C][C]0.357760682332162[/C][C]0.821119658833919[/C][/ROW]
[ROW][C]18[/C][C]0.181103307737641[/C][C]0.362206615475283[/C][C]0.818896692262359[/C][/ROW]
[ROW][C]19[/C][C]0.0977050454092338[/C][C]0.195410090818468[/C][C]0.902294954590766[/C][/ROW]
[ROW][C]20[/C][C]0.0513025329271525[/C][C]0.102605065854305[/C][C]0.948697467072848[/C][/ROW]
[ROW][C]21[/C][C]0.0231229580446458[/C][C]0.0462459160892916[/C][C]0.976877041955354[/C][/ROW]
[ROW][C]22[/C][C]0.13412888835865[/C][C]0.2682577767173[/C][C]0.86587111164135[/C][/ROW]
[ROW][C]23[/C][C]0.0854344386100902[/C][C]0.170868877220180[/C][C]0.91456556138991[/C][/ROW]
[ROW][C]24[/C][C]0.0551698135868272[/C][C]0.110339627173654[/C][C]0.944830186413173[/C][/ROW]
[ROW][C]25[/C][C]0.038480659361674[/C][C]0.076961318723348[/C][C]0.961519340638326[/C][/ROW]
[ROW][C]26[/C][C]0.0203123529982687[/C][C]0.0406247059965375[/C][C]0.979687647001731[/C][/ROW]
[ROW][C]27[/C][C]0.00972970359330364[/C][C]0.0194594071866073[/C][C]0.990270296406696[/C][/ROW]
[ROW][C]28[/C][C]0.00528936708339018[/C][C]0.0105787341667804[/C][C]0.99471063291661[/C][/ROW]
[ROW][C]29[/C][C]0.0123146804252546[/C][C]0.0246293608505092[/C][C]0.987685319574745[/C][/ROW]
[ROW][C]30[/C][C]0.00973279333350235[/C][C]0.0194655866670047[/C][C]0.990267206666498[/C][/ROW]
[ROW][C]31[/C][C]0.00449762448957547[/C][C]0.00899524897915093[/C][C]0.995502375510425[/C][/ROW]
[ROW][C]32[/C][C]0.00222755636149520[/C][C]0.00445511272299039[/C][C]0.997772443638505[/C][/ROW]
[ROW][C]33[/C][C]0.00123948015100782[/C][C]0.00247896030201563[/C][C]0.998760519848992[/C][/ROW]
[ROW][C]34[/C][C]0.00111384365177268[/C][C]0.00222768730354536[/C][C]0.998886156348227[/C][/ROW]
[ROW][C]35[/C][C]0.000439794117558488[/C][C]0.000879588235116976[/C][C]0.999560205882442[/C][/ROW]
[ROW][C]36[/C][C]0.0233682983587977[/C][C]0.0467365967175955[/C][C]0.976631701641202[/C][/ROW]
[ROW][C]37[/C][C]0.195703567348831[/C][C]0.391407134697662[/C][C]0.804296432651169[/C][/ROW]
[ROW][C]38[/C][C]0.115294210592324[/C][C]0.230588421184649[/C][C]0.884705789407676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59276&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.178880341166081	0.357760682332162	0.821119658833919
18	0.181103307737641	0.362206615475283	0.818896692262359
19	0.0977050454092338	0.195410090818468	0.902294954590766
20	0.0513025329271525	0.102605065854305	0.948697467072848
21	0.0231229580446458	0.0462459160892916	0.976877041955354
22	0.13412888835865	0.2682577767173	0.86587111164135
23	0.0854344386100902	0.170868877220180	0.91456556138991
24	0.0551698135868272	0.110339627173654	0.944830186413173
25	0.038480659361674	0.076961318723348	0.961519340638326
26	0.0203123529982687	0.0406247059965375	0.979687647001731
27	0.00972970359330364	0.0194594071866073	0.990270296406696
28	0.00528936708339018	0.0105787341667804	0.99471063291661
29	0.0123146804252546	0.0246293608505092	0.987685319574745
30	0.00973279333350235	0.0194655866670047	0.990267206666498
31	0.00449762448957547	0.00899524897915093	0.995502375510425
32	0.00222755636149520	0.00445511272299039	0.997772443638505
33	0.00123948015100782	0.00247896030201563	0.998760519848992
34	0.00111384365177268	0.00222768730354536	0.998886156348227
35	0.000439794117558488	0.000879588235116976	0.999560205882442
36	0.0233682983587977	0.0467365967175955	0.976631701641202
37	0.195703567348831	0.391407134697662	0.804296432651169
38	0.115294210592324	0.230588421184649	0.884705789407676

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	5	0.227272727272727	NOK
5% type I error level	12	0.545454545454545	NOK
10% type I error level	13	0.590909090909091	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 5 & 0.227272727272727 & NOK \tabularnewline
5% type I error level & 12 & 0.545454545454545 & NOK \tabularnewline
10% type I error level & 13 & 0.590909090909091 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59276&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]5[/C][C]0.227272727272727[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]12[/C][C]0.545454545454545[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]0.590909090909091[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59276&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59276&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	5	0.227272727272727	NOK
5% type I error level	12	0.545454545454545	NOK
10% type I error level	13	0.590909090909091	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code