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Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 06:55:17 -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/20/t1258726471y7zvnaruaeii9nc.htm/, Retrieved Tue, 16 Apr 2024 11:05:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58183, Retrieved Tue, 16 Apr 2024 11:05:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

124

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]
-   PD      [Multiple Regression] [] [2009-11-20 13:55:17] [fc845972e0ebdb725d2fb9537c0c51aa] [Current]

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Dataseries X:

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Histogram

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111.4	91,2
111.5	92,2
111.6	93,2
111.7	94,2
111.8	95,2
111.9	96,2
111.10	97,2
111.11	98,2
111.12	99,2
111.13	100,2
111.14	101,2
111.15	102,2
111.16	103,2
111.17	104,2
111.18	105,2
111.19	106,2
111.20	107,2
111.21	108,2
111.22	109,2
111.23	110,2
111.24	111,2
111.25	112,2
111.26	113,2
111.27	114,2
111.28	115,2
111.29	116,2
111.30	117,2
111.31	118,2
111.32	119,2
111.33	120,2
111.34	121,2
111.35	122,2
111.36	123,2
111.37	124,2
111.38	125,2
111.39	126,2
111.40	127,2
111.41	128,2
111.42	129,2
111.43	130,2
111.44	131,2
111.45	132,2
111.46	133,2
111.47	134,2
111.48	135,2
111.49	136,2
111.50	137,2
111.51	138,2
111.52	139,2
111.53	140,2
111.54	141,2
111.55	142,2
111.56	143,2
111.57	144,2
111.58	145,2
111.59	146,2
111.60	147,2
111.61	148,2
111.62	149,2
111.63	150,2
111.64	151,2

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=58183&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=58183&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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
biti[t] = + 110.794104706504 + 0.00497884717080904`Bosni�`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
biti[t] =  +  110.794104706504 +  0.00497884717080904`Bosni�`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58183&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]biti[t] =  +  110.794104706504 +  0.00497884717080904`Bosni�`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58183&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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
biti[t] = + 110.794104706504 + 0.00497884717080904`Bosni�`[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)	110.794104706504	0.14278	775.9753	0	0
`Bosni�`	0.00497884717080904	0.001166	4.2707	7.2e-05	3.6e-05

\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) & 110.794104706504 & 0.14278 & 775.9753 & 0 & 0 \tabularnewline
`Bosni�` & 0.00497884717080904 & 0.001166 & 4.2707 & 7.2e-05 & 3.6e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58183&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]110.794104706504[/C][C]0.14278[/C][C]775.9753[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Bosni�`[/C][C]0.00497884717080904[/C][C]0.001166[/C][C]4.2707[/C][C]7.2e-05[/C][C]3.6e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58183&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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)	110.794104706504	0.14278	775.9753	0	0
`Bosni�`	0.00497884717080904	0.001166	4.2707	7.2e-05	3.6e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.485936988710422
R-squared	0.236134756996953
Adjusted R-squared	0.223187888471478
F-TEST (value)	18.2387545322110
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	7.18542786055654e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.160316037791106
Sum Squared Residuals	1.51637268640932

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.485936988710422 \tabularnewline
R-squared & 0.236134756996953 \tabularnewline
Adjusted R-squared & 0.223187888471478 \tabularnewline
F-TEST (value) & 18.2387545322110 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 7.18542786055654e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.160316037791106 \tabularnewline
Sum Squared Residuals & 1.51637268640932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58183&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.485936988710422[/C][/ROW]
[ROW][C]R-squared[/C][C]0.236134756996953[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.223187888471478[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]18.2387545322110[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]7.18542786055654e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.160316037791106[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1.51637268640932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58183&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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	0.485936988710422
R-squared	0.236134756996953
Adjusted R-squared	0.223187888471478
F-TEST (value)	18.2387545322110
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	7.18542786055654e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.160316037791106
Sum Squared Residuals	1.51637268640932

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	111.4	111.248175568482	0.151824431517746
2	111.5	111.253154415653	0.246845584346904
3	111.6	111.258133262824	0.341866737176090
4	111.7	111.263112109995	0.436887890005289
5	111.8	111.268090957166	0.531909042834474
6	111.9	111.273069804336	0.626930195663674
7	111.1	111.278048651507	-0.178048651507147
8	111.11	111.283027498678	-0.173027498677951
9	111.12	111.288006345849	-0.168006345848754
10	111.13	111.292985193020	-0.162985193019573
11	111.14	111.297964040190	-0.157964040190376
12	111.15	111.302942887361	-0.152942887361180
13	111.16	111.307921734532	-0.147921734531999
14	111.17	111.312900581703	-0.142900581702802
15	111.18	111.317879428874	-0.137879428873606
16	111.19	111.322858276044	-0.132858276044425
17	111.2	111.327837123215	-0.127837123215228
18	111.21	111.332815970386	-0.122815970386047
19	111.22	111.337794817557	-0.117794817556851
20	111.23	111.342773664728	-0.112773664727654
21	111.24	111.347752511898	-0.107752511898473
22	111.25	111.352731359069	-0.102731359069276
23	111.26	111.35771020624	-0.0977102062400804
24	111.27	111.362689053411	-0.0926890534108986
25	111.28	111.367667900582	-0.0876679005817025
26	111.29	111.372646747753	-0.0826467477525064
27	111.3	111.377625594923	-0.0776255949233245
28	111.31	111.382604442094	-0.0726044420941285
29	111.32	111.387583289265	-0.0675832892649466
30	111.33	111.392562136436	-0.0625621364357505
31	111.34	111.397540983607	-0.0575409836065544
32	111.35	111.402519830777	-0.0525198307773726
33	111.36	111.407498677948	-0.0474986779481765
34	111.37	111.412477525119	-0.0424775251189804
35	111.38	111.417456372290	-0.0374563722897986
36	111.39	111.422435219461	-0.0324352194606025
37	111.4	111.427414066631	-0.0274140666314064
38	111.41	111.432392913802	-0.0223929138022245
39	111.42	111.437371760973	-0.0173717609730284
40	111.43	111.442350608144	-0.0123506081438323
41	111.44	111.447329455315	-0.00732945531465045
42	111.45	111.452308302485	-0.00230830248545437
43	111.46	111.457287149656	0.00271285034372749
44	111.47	111.462265996827	0.00773400317292357
45	111.48	111.467244843998	0.0127551560021196
46	111.49	111.472223691169	0.0177763088313015
47	111.5	111.477202538339	0.0227974616604976
48	111.51	111.482181385510	0.0278186144896937
49	111.52	111.487160232681	0.0328397673188755
50	111.53	111.492139079852	0.0378609201480716
51	111.54	111.497117927023	0.0428820729772677
52	111.55	111.502096774194	0.0479032258064496
53	111.56	111.507075621364	0.0529243786356456
54	111.57	111.512054468535	0.0579455314648275
55	111.58	111.517033315706	0.0629666842940236
56	111.59	111.522012162877	0.0679878371232197
57	111.6	111.526991010048	0.0730089899524015
58	111.61	111.531969857218	0.0780301427815976
59	111.62	111.536948704389	0.0830512956107937
60	111.63	111.54192755156	0.0880724484399755
61	111.64	111.546906398731	0.0930936012691716

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 111.4 & 111.248175568482 & 0.151824431517746 \tabularnewline
2 & 111.5 & 111.253154415653 & 0.246845584346904 \tabularnewline
3 & 111.6 & 111.258133262824 & 0.341866737176090 \tabularnewline
4 & 111.7 & 111.263112109995 & 0.436887890005289 \tabularnewline
5 & 111.8 & 111.268090957166 & 0.531909042834474 \tabularnewline
6 & 111.9 & 111.273069804336 & 0.626930195663674 \tabularnewline
7 & 111.1 & 111.278048651507 & -0.178048651507147 \tabularnewline
8 & 111.11 & 111.283027498678 & -0.173027498677951 \tabularnewline
9 & 111.12 & 111.288006345849 & -0.168006345848754 \tabularnewline
10 & 111.13 & 111.292985193020 & -0.162985193019573 \tabularnewline
11 & 111.14 & 111.297964040190 & -0.157964040190376 \tabularnewline
12 & 111.15 & 111.302942887361 & -0.152942887361180 \tabularnewline
13 & 111.16 & 111.307921734532 & -0.147921734531999 \tabularnewline
14 & 111.17 & 111.312900581703 & -0.142900581702802 \tabularnewline
15 & 111.18 & 111.317879428874 & -0.137879428873606 \tabularnewline
16 & 111.19 & 111.322858276044 & -0.132858276044425 \tabularnewline
17 & 111.2 & 111.327837123215 & -0.127837123215228 \tabularnewline
18 & 111.21 & 111.332815970386 & -0.122815970386047 \tabularnewline
19 & 111.22 & 111.337794817557 & -0.117794817556851 \tabularnewline
20 & 111.23 & 111.342773664728 & -0.112773664727654 \tabularnewline
21 & 111.24 & 111.347752511898 & -0.107752511898473 \tabularnewline
22 & 111.25 & 111.352731359069 & -0.102731359069276 \tabularnewline
23 & 111.26 & 111.35771020624 & -0.0977102062400804 \tabularnewline
24 & 111.27 & 111.362689053411 & -0.0926890534108986 \tabularnewline
25 & 111.28 & 111.367667900582 & -0.0876679005817025 \tabularnewline
26 & 111.29 & 111.372646747753 & -0.0826467477525064 \tabularnewline
27 & 111.3 & 111.377625594923 & -0.0776255949233245 \tabularnewline
28 & 111.31 & 111.382604442094 & -0.0726044420941285 \tabularnewline
29 & 111.32 & 111.387583289265 & -0.0675832892649466 \tabularnewline
30 & 111.33 & 111.392562136436 & -0.0625621364357505 \tabularnewline
31 & 111.34 & 111.397540983607 & -0.0575409836065544 \tabularnewline
32 & 111.35 & 111.402519830777 & -0.0525198307773726 \tabularnewline
33 & 111.36 & 111.407498677948 & -0.0474986779481765 \tabularnewline
34 & 111.37 & 111.412477525119 & -0.0424775251189804 \tabularnewline
35 & 111.38 & 111.417456372290 & -0.0374563722897986 \tabularnewline
36 & 111.39 & 111.422435219461 & -0.0324352194606025 \tabularnewline
37 & 111.4 & 111.427414066631 & -0.0274140666314064 \tabularnewline
38 & 111.41 & 111.432392913802 & -0.0223929138022245 \tabularnewline
39 & 111.42 & 111.437371760973 & -0.0173717609730284 \tabularnewline
40 & 111.43 & 111.442350608144 & -0.0123506081438323 \tabularnewline
41 & 111.44 & 111.447329455315 & -0.00732945531465045 \tabularnewline
42 & 111.45 & 111.452308302485 & -0.00230830248545437 \tabularnewline
43 & 111.46 & 111.457287149656 & 0.00271285034372749 \tabularnewline
44 & 111.47 & 111.462265996827 & 0.00773400317292357 \tabularnewline
45 & 111.48 & 111.467244843998 & 0.0127551560021196 \tabularnewline
46 & 111.49 & 111.472223691169 & 0.0177763088313015 \tabularnewline
47 & 111.5 & 111.477202538339 & 0.0227974616604976 \tabularnewline
48 & 111.51 & 111.482181385510 & 0.0278186144896937 \tabularnewline
49 & 111.52 & 111.487160232681 & 0.0328397673188755 \tabularnewline
50 & 111.53 & 111.492139079852 & 0.0378609201480716 \tabularnewline
51 & 111.54 & 111.497117927023 & 0.0428820729772677 \tabularnewline
52 & 111.55 & 111.502096774194 & 0.0479032258064496 \tabularnewline
53 & 111.56 & 111.507075621364 & 0.0529243786356456 \tabularnewline
54 & 111.57 & 111.512054468535 & 0.0579455314648275 \tabularnewline
55 & 111.58 & 111.517033315706 & 0.0629666842940236 \tabularnewline
56 & 111.59 & 111.522012162877 & 0.0679878371232197 \tabularnewline
57 & 111.6 & 111.526991010048 & 0.0730089899524015 \tabularnewline
58 & 111.61 & 111.531969857218 & 0.0780301427815976 \tabularnewline
59 & 111.62 & 111.536948704389 & 0.0830512956107937 \tabularnewline
60 & 111.63 & 111.54192755156 & 0.0880724484399755 \tabularnewline
61 & 111.64 & 111.546906398731 & 0.0930936012691716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58183&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]111.4[/C][C]111.248175568482[/C][C]0.151824431517746[/C][/ROW]
[ROW][C]2[/C][C]111.5[/C][C]111.253154415653[/C][C]0.246845584346904[/C][/ROW]
[ROW][C]3[/C][C]111.6[/C][C]111.258133262824[/C][C]0.341866737176090[/C][/ROW]
[ROW][C]4[/C][C]111.7[/C][C]111.263112109995[/C][C]0.436887890005289[/C][/ROW]
[ROW][C]5[/C][C]111.8[/C][C]111.268090957166[/C][C]0.531909042834474[/C][/ROW]
[ROW][C]6[/C][C]111.9[/C][C]111.273069804336[/C][C]0.626930195663674[/C][/ROW]
[ROW][C]7[/C][C]111.1[/C][C]111.278048651507[/C][C]-0.178048651507147[/C][/ROW]
[ROW][C]8[/C][C]111.11[/C][C]111.283027498678[/C][C]-0.173027498677951[/C][/ROW]
[ROW][C]9[/C][C]111.12[/C][C]111.288006345849[/C][C]-0.168006345848754[/C][/ROW]
[ROW][C]10[/C][C]111.13[/C][C]111.292985193020[/C][C]-0.162985193019573[/C][/ROW]
[ROW][C]11[/C][C]111.14[/C][C]111.297964040190[/C][C]-0.157964040190376[/C][/ROW]
[ROW][C]12[/C][C]111.15[/C][C]111.302942887361[/C][C]-0.152942887361180[/C][/ROW]
[ROW][C]13[/C][C]111.16[/C][C]111.307921734532[/C][C]-0.147921734531999[/C][/ROW]
[ROW][C]14[/C][C]111.17[/C][C]111.312900581703[/C][C]-0.142900581702802[/C][/ROW]
[ROW][C]15[/C][C]111.18[/C][C]111.317879428874[/C][C]-0.137879428873606[/C][/ROW]
[ROW][C]16[/C][C]111.19[/C][C]111.322858276044[/C][C]-0.132858276044425[/C][/ROW]
[ROW][C]17[/C][C]111.2[/C][C]111.327837123215[/C][C]-0.127837123215228[/C][/ROW]
[ROW][C]18[/C][C]111.21[/C][C]111.332815970386[/C][C]-0.122815970386047[/C][/ROW]
[ROW][C]19[/C][C]111.22[/C][C]111.337794817557[/C][C]-0.117794817556851[/C][/ROW]
[ROW][C]20[/C][C]111.23[/C][C]111.342773664728[/C][C]-0.112773664727654[/C][/ROW]
[ROW][C]21[/C][C]111.24[/C][C]111.347752511898[/C][C]-0.107752511898473[/C][/ROW]
[ROW][C]22[/C][C]111.25[/C][C]111.352731359069[/C][C]-0.102731359069276[/C][/ROW]
[ROW][C]23[/C][C]111.26[/C][C]111.35771020624[/C][C]-0.0977102062400804[/C][/ROW]
[ROW][C]24[/C][C]111.27[/C][C]111.362689053411[/C][C]-0.0926890534108986[/C][/ROW]
[ROW][C]25[/C][C]111.28[/C][C]111.367667900582[/C][C]-0.0876679005817025[/C][/ROW]
[ROW][C]26[/C][C]111.29[/C][C]111.372646747753[/C][C]-0.0826467477525064[/C][/ROW]
[ROW][C]27[/C][C]111.3[/C][C]111.377625594923[/C][C]-0.0776255949233245[/C][/ROW]
[ROW][C]28[/C][C]111.31[/C][C]111.382604442094[/C][C]-0.0726044420941285[/C][/ROW]
[ROW][C]29[/C][C]111.32[/C][C]111.387583289265[/C][C]-0.0675832892649466[/C][/ROW]
[ROW][C]30[/C][C]111.33[/C][C]111.392562136436[/C][C]-0.0625621364357505[/C][/ROW]
[ROW][C]31[/C][C]111.34[/C][C]111.397540983607[/C][C]-0.0575409836065544[/C][/ROW]
[ROW][C]32[/C][C]111.35[/C][C]111.402519830777[/C][C]-0.0525198307773726[/C][/ROW]
[ROW][C]33[/C][C]111.36[/C][C]111.407498677948[/C][C]-0.0474986779481765[/C][/ROW]
[ROW][C]34[/C][C]111.37[/C][C]111.412477525119[/C][C]-0.0424775251189804[/C][/ROW]
[ROW][C]35[/C][C]111.38[/C][C]111.417456372290[/C][C]-0.0374563722897986[/C][/ROW]
[ROW][C]36[/C][C]111.39[/C][C]111.422435219461[/C][C]-0.0324352194606025[/C][/ROW]
[ROW][C]37[/C][C]111.4[/C][C]111.427414066631[/C][C]-0.0274140666314064[/C][/ROW]
[ROW][C]38[/C][C]111.41[/C][C]111.432392913802[/C][C]-0.0223929138022245[/C][/ROW]
[ROW][C]39[/C][C]111.42[/C][C]111.437371760973[/C][C]-0.0173717609730284[/C][/ROW]
[ROW][C]40[/C][C]111.43[/C][C]111.442350608144[/C][C]-0.0123506081438323[/C][/ROW]
[ROW][C]41[/C][C]111.44[/C][C]111.447329455315[/C][C]-0.00732945531465045[/C][/ROW]
[ROW][C]42[/C][C]111.45[/C][C]111.452308302485[/C][C]-0.00230830248545437[/C][/ROW]
[ROW][C]43[/C][C]111.46[/C][C]111.457287149656[/C][C]0.00271285034372749[/C][/ROW]
[ROW][C]44[/C][C]111.47[/C][C]111.462265996827[/C][C]0.00773400317292357[/C][/ROW]
[ROW][C]45[/C][C]111.48[/C][C]111.467244843998[/C][C]0.0127551560021196[/C][/ROW]
[ROW][C]46[/C][C]111.49[/C][C]111.472223691169[/C][C]0.0177763088313015[/C][/ROW]
[ROW][C]47[/C][C]111.5[/C][C]111.477202538339[/C][C]0.0227974616604976[/C][/ROW]
[ROW][C]48[/C][C]111.51[/C][C]111.482181385510[/C][C]0.0278186144896937[/C][/ROW]
[ROW][C]49[/C][C]111.52[/C][C]111.487160232681[/C][C]0.0328397673188755[/C][/ROW]
[ROW][C]50[/C][C]111.53[/C][C]111.492139079852[/C][C]0.0378609201480716[/C][/ROW]
[ROW][C]51[/C][C]111.54[/C][C]111.497117927023[/C][C]0.0428820729772677[/C][/ROW]
[ROW][C]52[/C][C]111.55[/C][C]111.502096774194[/C][C]0.0479032258064496[/C][/ROW]
[ROW][C]53[/C][C]111.56[/C][C]111.507075621364[/C][C]0.0529243786356456[/C][/ROW]
[ROW][C]54[/C][C]111.57[/C][C]111.512054468535[/C][C]0.0579455314648275[/C][/ROW]
[ROW][C]55[/C][C]111.58[/C][C]111.517033315706[/C][C]0.0629666842940236[/C][/ROW]
[ROW][C]56[/C][C]111.59[/C][C]111.522012162877[/C][C]0.0679878371232197[/C][/ROW]
[ROW][C]57[/C][C]111.6[/C][C]111.526991010048[/C][C]0.0730089899524015[/C][/ROW]
[ROW][C]58[/C][C]111.61[/C][C]111.531969857218[/C][C]0.0780301427815976[/C][/ROW]
[ROW][C]59[/C][C]111.62[/C][C]111.536948704389[/C][C]0.0830512956107937[/C][/ROW]
[ROW][C]60[/C][C]111.63[/C][C]111.54192755156[/C][C]0.0880724484399755[/C][/ROW]
[ROW][C]61[/C][C]111.64[/C][C]111.546906398731[/C][C]0.0930936012691716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58183&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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	111.4	111.248175568482	0.151824431517746
2	111.5	111.253154415653	0.246845584346904
3	111.6	111.258133262824	0.341866737176090
4	111.7	111.263112109995	0.436887890005289
5	111.8	111.268090957166	0.531909042834474
6	111.9	111.273069804336	0.626930195663674
7	111.1	111.278048651507	-0.178048651507147
8	111.11	111.283027498678	-0.173027498677951
9	111.12	111.288006345849	-0.168006345848754
10	111.13	111.292985193020	-0.162985193019573
11	111.14	111.297964040190	-0.157964040190376
12	111.15	111.302942887361	-0.152942887361180
13	111.16	111.307921734532	-0.147921734531999
14	111.17	111.312900581703	-0.142900581702802
15	111.18	111.317879428874	-0.137879428873606
16	111.19	111.322858276044	-0.132858276044425
17	111.2	111.327837123215	-0.127837123215228
18	111.21	111.332815970386	-0.122815970386047
19	111.22	111.337794817557	-0.117794817556851
20	111.23	111.342773664728	-0.112773664727654
21	111.24	111.347752511898	-0.107752511898473
22	111.25	111.352731359069	-0.102731359069276
23	111.26	111.35771020624	-0.0977102062400804
24	111.27	111.362689053411	-0.0926890534108986
25	111.28	111.367667900582	-0.0876679005817025
26	111.29	111.372646747753	-0.0826467477525064
27	111.3	111.377625594923	-0.0776255949233245
28	111.31	111.382604442094	-0.0726044420941285
29	111.32	111.387583289265	-0.0675832892649466
30	111.33	111.392562136436	-0.0625621364357505
31	111.34	111.397540983607	-0.0575409836065544
32	111.35	111.402519830777	-0.0525198307773726
33	111.36	111.407498677948	-0.0474986779481765
34	111.37	111.412477525119	-0.0424775251189804
35	111.38	111.417456372290	-0.0374563722897986
36	111.39	111.422435219461	-0.0324352194606025
37	111.4	111.427414066631	-0.0274140666314064
38	111.41	111.432392913802	-0.0223929138022245
39	111.42	111.437371760973	-0.0173717609730284
40	111.43	111.442350608144	-0.0123506081438323
41	111.44	111.447329455315	-0.00732945531465045
42	111.45	111.452308302485	-0.00230830248545437
43	111.46	111.457287149656	0.00271285034372749
44	111.47	111.462265996827	0.00773400317292357
45	111.48	111.467244843998	0.0127551560021196
46	111.49	111.472223691169	0.0177763088313015
47	111.5	111.477202538339	0.0227974616604976
48	111.51	111.482181385510	0.0278186144896937
49	111.52	111.487160232681	0.0328397673188755
50	111.53	111.492139079852	0.0378609201480716
51	111.54	111.497117927023	0.0428820729772677
52	111.55	111.502096774194	0.0479032258064496
53	111.56	111.507075621364	0.0529243786356456
54	111.57	111.512054468535	0.0579455314648275
55	111.58	111.517033315706	0.0629666842940236
56	111.59	111.522012162877	0.0679878371232197
57	111.6	111.526991010048	0.0730089899524015
58	111.61	111.531969857218	0.0780301427815976
59	111.62	111.536948704389	0.0830512956107937
60	111.63	111.54192755156	0.0880724484399755
61	111.64	111.546906398731	0.0930936012691716

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	5.74174410334181e-41	1.14834882066836e-40	1
6	0.66891206270431	0.66217587459138	0.33108793729569
7	1	0	0
8	1	0	0
9	1	0	0
10	1	0	0
11	1	0	0
12	1	0	0
13	1	0	0
14	1	0	0
15	1	0	0
16	1	0	0
17	1	0	0
18	1	0	0
19	1	0	0
20	1	0	0
21	1	0	0
22	1	0	0
23	1	0	0
24	1	0	0
25	1	0	0
26	1	0	0
27	1	0	0
28	1	0	0
29	1	0	0
30	1	0	0
31	1	0	0
32	1	0	0
33	1	6.91691904177745e-322	3.45845952088873e-322
34	1	2.71821852281784e-315	1.35910926140892e-315
35	1	3.75371227743421e-313	1.87685613871710e-313
36	1	3.05674766522315e-309	1.52837383261157e-309
37	1	1.98484004503375e-276	9.92420022516877e-277
38	1	7.03931875902687e-275	3.51965937951344e-275
39	1	1.58155063731923e-252	7.90775318659615e-253
40	1	5.7884942588019e-244	2.89424712940095e-244
41	1	2.83615019628197e-225	1.41807509814098e-225
42	1	5.28442217127445e-215	2.64221108563722e-215
43	1	7.88947414431829e-205	3.94473707215914e-205
44	1	1.23957622093428e-200	6.19788110467141e-201
45	1	3.61618661672094e-180	1.80809330836047e-180
46	1	2.62996980084302e-173	1.31498490042151e-173
47	1	6.30056044728085e-153	3.15028022364042e-153
48	1	9.86266938694187e-146	4.93133469347094e-146
49	1	5.92107724989251e-126	2.96053862494625e-126
50	1	1.88498303179141e-117	9.42491515895704e-118
51	1	3.40285618524393e-103	1.70142809262197e-103
52	1	7.07212172074543e-90	3.53606086037271e-90
53	1	9.84622237139753e-79	4.92311118569876e-79
54	1	4.33427280348829e-65	2.16713640174415e-65
55	1	2.13440006054049e-51	1.06720003027024e-51
56	1	8.26119226757836e-41	4.13059613378918e-41

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 5.74174410334181e-41 & 1.14834882066836e-40 & 1 \tabularnewline
6 & 0.66891206270431 & 0.66217587459138 & 0.33108793729569 \tabularnewline
7 & 1 & 0 & 0 \tabularnewline
8 & 1 & 0 & 0 \tabularnewline
9 & 1 & 0 & 0 \tabularnewline
10 & 1 & 0 & 0 \tabularnewline
11 & 1 & 0 & 0 \tabularnewline
12 & 1 & 0 & 0 \tabularnewline
13 & 1 & 0 & 0 \tabularnewline
14 & 1 & 0 & 0 \tabularnewline
15 & 1 & 0 & 0 \tabularnewline
16 & 1 & 0 & 0 \tabularnewline
17 & 1 & 0 & 0 \tabularnewline
18 & 1 & 0 & 0 \tabularnewline
19 & 1 & 0 & 0 \tabularnewline
20 & 1 & 0 & 0 \tabularnewline
21 & 1 & 0 & 0 \tabularnewline
22 & 1 & 0 & 0 \tabularnewline
23 & 1 & 0 & 0 \tabularnewline
24 & 1 & 0 & 0 \tabularnewline
25 & 1 & 0 & 0 \tabularnewline
26 & 1 & 0 & 0 \tabularnewline
27 & 1 & 0 & 0 \tabularnewline
28 & 1 & 0 & 0 \tabularnewline
29 & 1 & 0 & 0 \tabularnewline
30 & 1 & 0 & 0 \tabularnewline
31 & 1 & 0 & 0 \tabularnewline
32 & 1 & 0 & 0 \tabularnewline
33 & 1 & 6.91691904177745e-322 & 3.45845952088873e-322 \tabularnewline
34 & 1 & 2.71821852281784e-315 & 1.35910926140892e-315 \tabularnewline
35 & 1 & 3.75371227743421e-313 & 1.87685613871710e-313 \tabularnewline
36 & 1 & 3.05674766522315e-309 & 1.52837383261157e-309 \tabularnewline
37 & 1 & 1.98484004503375e-276 & 9.92420022516877e-277 \tabularnewline
38 & 1 & 7.03931875902687e-275 & 3.51965937951344e-275 \tabularnewline
39 & 1 & 1.58155063731923e-252 & 7.90775318659615e-253 \tabularnewline
40 & 1 & 5.7884942588019e-244 & 2.89424712940095e-244 \tabularnewline
41 & 1 & 2.83615019628197e-225 & 1.41807509814098e-225 \tabularnewline
42 & 1 & 5.28442217127445e-215 & 2.64221108563722e-215 \tabularnewline
43 & 1 & 7.88947414431829e-205 & 3.94473707215914e-205 \tabularnewline
44 & 1 & 1.23957622093428e-200 & 6.19788110467141e-201 \tabularnewline
45 & 1 & 3.61618661672094e-180 & 1.80809330836047e-180 \tabularnewline
46 & 1 & 2.62996980084302e-173 & 1.31498490042151e-173 \tabularnewline
47 & 1 & 6.30056044728085e-153 & 3.15028022364042e-153 \tabularnewline
48 & 1 & 9.86266938694187e-146 & 4.93133469347094e-146 \tabularnewline
49 & 1 & 5.92107724989251e-126 & 2.96053862494625e-126 \tabularnewline
50 & 1 & 1.88498303179141e-117 & 9.42491515895704e-118 \tabularnewline
51 & 1 & 3.40285618524393e-103 & 1.70142809262197e-103 \tabularnewline
52 & 1 & 7.07212172074543e-90 & 3.53606086037271e-90 \tabularnewline
53 & 1 & 9.84622237139753e-79 & 4.92311118569876e-79 \tabularnewline
54 & 1 & 4.33427280348829e-65 & 2.16713640174415e-65 \tabularnewline
55 & 1 & 2.13440006054049e-51 & 1.06720003027024e-51 \tabularnewline
56 & 1 & 8.26119226757836e-41 & 4.13059613378918e-41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58183&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]5[/C][C]5.74174410334181e-41[/C][C]1.14834882066836e-40[/C][C]1[/C][/ROW]
[ROW][C]6[/C][C]0.66891206270431[/C][C]0.66217587459138[/C][C]0.33108793729569[/C][/ROW]
[ROW][C]7[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]1[/C][C]6.91691904177745e-322[/C][C]3.45845952088873e-322[/C][/ROW]
[ROW][C]34[/C][C]1[/C][C]2.71821852281784e-315[/C][C]1.35910926140892e-315[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]3.75371227743421e-313[/C][C]1.87685613871710e-313[/C][/ROW]
[ROW][C]36[/C][C]1[/C][C]3.05674766522315e-309[/C][C]1.52837383261157e-309[/C][/ROW]
[ROW][C]37[/C][C]1[/C][C]1.98484004503375e-276[/C][C]9.92420022516877e-277[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]7.03931875902687e-275[/C][C]3.51965937951344e-275[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]1.58155063731923e-252[/C][C]7.90775318659615e-253[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]5.7884942588019e-244[/C][C]2.89424712940095e-244[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]2.83615019628197e-225[/C][C]1.41807509814098e-225[/C][/ROW]
[ROW][C]42[/C][C]1[/C][C]5.28442217127445e-215[/C][C]2.64221108563722e-215[/C][/ROW]
[ROW][C]43[/C][C]1[/C][C]7.88947414431829e-205[/C][C]3.94473707215914e-205[/C][/ROW]
[ROW][C]44[/C][C]1[/C][C]1.23957622093428e-200[/C][C]6.19788110467141e-201[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]3.61618661672094e-180[/C][C]1.80809330836047e-180[/C][/ROW]
[ROW][C]46[/C][C]1[/C][C]2.62996980084302e-173[/C][C]1.31498490042151e-173[/C][/ROW]
[ROW][C]47[/C][C]1[/C][C]6.30056044728085e-153[/C][C]3.15028022364042e-153[/C][/ROW]
[ROW][C]48[/C][C]1[/C][C]9.86266938694187e-146[/C][C]4.93133469347094e-146[/C][/ROW]
[ROW][C]49[/C][C]1[/C][C]5.92107724989251e-126[/C][C]2.96053862494625e-126[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]1.88498303179141e-117[/C][C]9.42491515895704e-118[/C][/ROW]
[ROW][C]51[/C][C]1[/C][C]3.40285618524393e-103[/C][C]1.70142809262197e-103[/C][/ROW]
[ROW][C]52[/C][C]1[/C][C]7.07212172074543e-90[/C][C]3.53606086037271e-90[/C][/ROW]
[ROW][C]53[/C][C]1[/C][C]9.84622237139753e-79[/C][C]4.92311118569876e-79[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]4.33427280348829e-65[/C][C]2.16713640174415e-65[/C][/ROW]
[ROW][C]55[/C][C]1[/C][C]2.13440006054049e-51[/C][C]1.06720003027024e-51[/C][/ROW]
[ROW][C]56[/C][C]1[/C][C]8.26119226757836e-41[/C][C]4.13059613378918e-41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58183&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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
5	5.74174410334181e-41	1.14834882066836e-40	1
6	0.66891206270431	0.66217587459138	0.33108793729569
7	1	0	0
8	1	0	0
9	1	0	0
10	1	0	0
11	1	0	0
12	1	0	0
13	1	0	0
14	1	0	0
15	1	0	0
16	1	0	0
17	1	0	0
18	1	0	0
19	1	0	0
20	1	0	0
21	1	0	0
22	1	0	0
23	1	0	0
24	1	0	0
25	1	0	0
26	1	0	0
27	1	0	0
28	1	0	0
29	1	0	0
30	1	0	0
31	1	0	0
32	1	0	0
33	1	6.91691904177745e-322	3.45845952088873e-322
34	1	2.71821852281784e-315	1.35910926140892e-315
35	1	3.75371227743421e-313	1.87685613871710e-313
36	1	3.05674766522315e-309	1.52837383261157e-309
37	1	1.98484004503375e-276	9.92420022516877e-277
38	1	7.03931875902687e-275	3.51965937951344e-275
39	1	1.58155063731923e-252	7.90775318659615e-253
40	1	5.7884942588019e-244	2.89424712940095e-244
41	1	2.83615019628197e-225	1.41807509814098e-225
42	1	5.28442217127445e-215	2.64221108563722e-215
43	1	7.88947414431829e-205	3.94473707215914e-205
44	1	1.23957622093428e-200	6.19788110467141e-201
45	1	3.61618661672094e-180	1.80809330836047e-180
46	1	2.62996980084302e-173	1.31498490042151e-173
47	1	6.30056044728085e-153	3.15028022364042e-153
48	1	9.86266938694187e-146	4.93133469347094e-146
49	1	5.92107724989251e-126	2.96053862494625e-126
50	1	1.88498303179141e-117	9.42491515895704e-118
51	1	3.40285618524393e-103	1.70142809262197e-103
52	1	7.07212172074543e-90	3.53606086037271e-90
53	1	9.84622237139753e-79	4.92311118569876e-79
54	1	4.33427280348829e-65	2.16713640174415e-65
55	1	2.13440006054049e-51	1.06720003027024e-51
56	1	8.26119226757836e-41	4.13059613378918e-41

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	51	0.98076923076923	NOK
5% type I error level	51	0.98076923076923	NOK
10% type I error level	51	0.98076923076923	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 & 51 & 0.98076923076923 & NOK \tabularnewline
5% type I error level & 51 & 0.98076923076923 & NOK \tabularnewline
10% type I error level & 51 & 0.98076923076923 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58183&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]51[/C][C]0.98076923076923[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]51[/C][C]0.98076923076923[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]51[/C][C]0.98076923076923[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58183&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58183&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	51	0.98076923076923	NOK
5% type I error level	51	0.98076923076923	NOK
10% type I error level	51	0.98076923076923	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 = Omvatten niet seizoensgebonden Dummies ; par3 = Geen lineaire trend ;

Parameters (R input):

par1 = 1 ; par2 = Omvatten niet seizoensgebonden Dummies ; par3 = Geen lineaire 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