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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 28 Dec 2010 00:49:34 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/28/t1293497257d2g5rsm3b7v5rpp.htm/, Retrieved Sun, 05 May 2024 01:52:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116207, Retrieved Sun, 05 May 2024 01:52:56 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

147

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

-       [Multiple Regression] [] [2010-12-28 00:49:34] [9c77782ba9615b1ce272b3027c583d19] [Current]

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Dataseries X:

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Histogram

Boxplots

99	94.6
106.3	95.9
128.9	104.7
111.1	102.8
102.9	98.1
130	113.9
87	80.9
87.5	95.7
117.6	113.2
103.4	105.9
110.8	108.8
112.6	102.3
102.5	99
112.4	100.7
135.6	115.5
105.1	100.7
127.7	109.9
137	114.6
91	85.4
90.5	100.5
122.4	114.8
123.3	116.5
124.3	112.9
120	102
118.1	106
119	105.3
142.7	118.8
123.6	106.1
129.6	109.3
151.6	117.2
110.4	92.5
99.2	104.2
130.5	112.5
136.2	122.4
129.7	113.3
128	100
121.6	110.7
135.8	112.8
143.8	109.8
147.5	117.3
136.2	109.1
156.6	115.9
123.3	96
104.5	99.8
139.8	116.8
136.5	115.7
112.1	99.4
118.5	94.3
94.4	91
102.3	93.2
111.4	103.1
99.2	94.1
87.8	91.8
115.8	102.7
79.7	82.6
72.7	89.1
104.5	104.5
103	105.1
95.1	95.1
104.2	88.7
78.3	86.3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation
ipi[t] = -83.6948607837712 + 2.01157944981591`tip `[t] -14.6973798833694M1[t] -8.59150522082137M2[t] -9.0930245904434M3[t] -11.9610838018231M4[t] -11.4142195211682M5[t] -8.72060225971292M6[t] + 2.29366396537288M7[t] -26.1061509349583M8[t] -23.313673168531M9[t] -27.4420937616331M10[t] -19.1181103452043M11[t] + 0.119620211242018t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
ipi[t] =  -83.6948607837712 +  2.01157944981591`tip
`[t] -14.6973798833694M1[t] -8.59150522082137M2[t] -9.0930245904434M3[t] -11.9610838018231M4[t] -11.4142195211682M5[t] -8.72060225971292M6[t] +  2.29366396537288M7[t] -26.1061509349583M8[t] -23.313673168531M9[t] -27.4420937616331M10[t] -19.1181103452043M11[t] +  0.119620211242018t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]ipi[t] =  -83.6948607837712 +  2.01157944981591`tip
`[t] -14.6973798833694M1[t] -8.59150522082137M2[t] -9.0930245904434M3[t] -11.9610838018231M4[t] -11.4142195211682M5[t] -8.72060225971292M6[t] +  2.29366396537288M7[t] -26.1061509349583M8[t] -23.313673168531M9[t] -27.4420937616331M10[t] -19.1181103452043M11[t] +  0.119620211242018t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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
ipi[t] = -83.6948607837712 + 2.01157944981591`tip `[t] -14.6973798833694M1[t] -8.59150522082137M2[t] -9.0930245904434M3[t] -11.9610838018231M4[t] -11.4142195211682M5[t] -8.72060225971292M6[t] + 2.29366396537288M7[t] -26.1061509349583M8[t] -23.313673168531M9[t] -27.4420937616331M10[t] -19.1181103452043M11[t] + 0.119620211242018t + 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)	-83.6948607837712	13.818476	-6.0567	0	0
`tip `	2.01157944981591	0.132403	15.1928	0	0
M1	-14.6973798833694	3.904156	-3.7645	0.000463	0.000232
M2	-8.59150522082137	4.117864	-2.0864	0.042394	0.021197
M3	-9.0930245904434	4.38877	-2.0719	0.043789	0.021894
M4	-11.9610838018231	4.16177	-2.874	0.006068	0.003034
M5	-11.4142195211682	4.146825	-2.7525	0.008378	0.004189
M6	-8.72060225971292	4.524442	-1.9274	0.05998	0.02999
M7	2.29366396537288	4.307948	0.5324	0.596939	0.29847
M8	-26.1061509349583	4.074633	-6.407	0	0
M9	-23.313673168531	4.507242	-5.1725	5e-06	2e-06
M10	-27.4420937616331	4.556273	-6.0229	0	0
M11	-19.1181103452043	4.217408	-4.5331	4e-05	2e-05
t	0.119620211242018	0.049506	2.4163	0.019618	0.009809

\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) & -83.6948607837712 & 13.818476 & -6.0567 & 0 & 0 \tabularnewline
`tip
` & 2.01157944981591 & 0.132403 & 15.1928 & 0 & 0 \tabularnewline
M1 & -14.6973798833694 & 3.904156 & -3.7645 & 0.000463 & 0.000232 \tabularnewline
M2 & -8.59150522082137 & 4.117864 & -2.0864 & 0.042394 & 0.021197 \tabularnewline
M3 & -9.0930245904434 & 4.38877 & -2.0719 & 0.043789 & 0.021894 \tabularnewline
M4 & -11.9610838018231 & 4.16177 & -2.874 & 0.006068 & 0.003034 \tabularnewline
M5 & -11.4142195211682 & 4.146825 & -2.7525 & 0.008378 & 0.004189 \tabularnewline
M6 & -8.72060225971292 & 4.524442 & -1.9274 & 0.05998 & 0.02999 \tabularnewline
M7 & 2.29366396537288 & 4.307948 & 0.5324 & 0.596939 & 0.29847 \tabularnewline
M8 & -26.1061509349583 & 4.074633 & -6.407 & 0 & 0 \tabularnewline
M9 & -23.313673168531 & 4.507242 & -5.1725 & 5e-06 & 2e-06 \tabularnewline
M10 & -27.4420937616331 & 4.556273 & -6.0229 & 0 & 0 \tabularnewline
M11 & -19.1181103452043 & 4.217408 & -4.5331 & 4e-05 & 2e-05 \tabularnewline
t & 0.119620211242018 & 0.049506 & 2.4163 & 0.019618 & 0.009809 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&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]-83.6948607837712[/C][C]13.818476[/C][C]-6.0567[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`tip
`[/C][C]2.01157944981591[/C][C]0.132403[/C][C]15.1928[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-14.6973798833694[/C][C]3.904156[/C][C]-3.7645[/C][C]0.000463[/C][C]0.000232[/C][/ROW]
[ROW][C]M2[/C][C]-8.59150522082137[/C][C]4.117864[/C][C]-2.0864[/C][C]0.042394[/C][C]0.021197[/C][/ROW]
[ROW][C]M3[/C][C]-9.0930245904434[/C][C]4.38877[/C][C]-2.0719[/C][C]0.043789[/C][C]0.021894[/C][/ROW]
[ROW][C]M4[/C][C]-11.9610838018231[/C][C]4.16177[/C][C]-2.874[/C][C]0.006068[/C][C]0.003034[/C][/ROW]
[ROW][C]M5[/C][C]-11.4142195211682[/C][C]4.146825[/C][C]-2.7525[/C][C]0.008378[/C][C]0.004189[/C][/ROW]
[ROW][C]M6[/C][C]-8.72060225971292[/C][C]4.524442[/C][C]-1.9274[/C][C]0.05998[/C][C]0.02999[/C][/ROW]
[ROW][C]M7[/C][C]2.29366396537288[/C][C]4.307948[/C][C]0.5324[/C][C]0.596939[/C][C]0.29847[/C][/ROW]
[ROW][C]M8[/C][C]-26.1061509349583[/C][C]4.074633[/C][C]-6.407[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-23.313673168531[/C][C]4.507242[/C][C]-5.1725[/C][C]5e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M10[/C][C]-27.4420937616331[/C][C]4.556273[/C][C]-6.0229[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-19.1181103452043[/C][C]4.217408[/C][C]-4.5331[/C][C]4e-05[/C][C]2e-05[/C][/ROW]
[ROW][C]t[/C][C]0.119620211242018[/C][C]0.049506[/C][C]2.4163[/C][C]0.019618[/C][C]0.009809[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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)	-83.6948607837712	13.818476	-6.0567	0	0
`tip `	2.01157944981591	0.132403	15.1928	0	0
M1	-14.6973798833694	3.904156	-3.7645	0.000463	0.000232
M2	-8.59150522082137	4.117864	-2.0864	0.042394	0.021197
M3	-9.0930245904434	4.38877	-2.0719	0.043789	0.021894
M4	-11.9610838018231	4.16177	-2.874	0.006068	0.003034
M5	-11.4142195211682	4.146825	-2.7525	0.008378	0.004189
M6	-8.72060225971292	4.524442	-1.9274	0.05998	0.02999
M7	2.29366396537288	4.307948	0.5324	0.596939	0.29847
M8	-26.1061509349583	4.074633	-6.407	0	0
M9	-23.313673168531	4.507242	-5.1725	5e-06	2e-06
M10	-27.4420937616331	4.556273	-6.0229	0	0
M11	-19.1181103452043	4.217408	-4.5331	4e-05	2e-05
t	0.119620211242018	0.049506	2.4163	0.019618	0.009809

Multiple Linear Regression - Regression Statistics
Multiple R	0.954042074610755
R-squared	0.910196280127594
Adjusted R-squared	0.885356953354376
F-TEST (value)	36.6433554515236
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.43555143585808
Sum Squared Residuals	1946.56714732802

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.954042074610755 \tabularnewline
R-squared & 0.910196280127594 \tabularnewline
Adjusted R-squared & 0.885356953354376 \tabularnewline
F-TEST (value) & 36.6433554515236 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.43555143585808 \tabularnewline
Sum Squared Residuals & 1946.56714732802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.954042074610755[/C][/ROW]
[ROW][C]R-squared[/C][C]0.910196280127594[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.885356953354376[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]36.6433554515236[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/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]6.43555143585808[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1946.56714732802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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	0.954042074610755
R-squared	0.910196280127594
Adjusted R-squared	0.885356953354376
F-TEST (value)	36.6433554515236
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.43555143585808
Sum Squared Residuals	1946.56714732802

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	99	92.0227954966864	6.9772045033136
2	106.3	100.863343655237	5.4366563447628
3	128.9	118.183343655237	10.7166563447628
4	111.1	111.612903700449	-0.512903700449282
5	102.9	102.824964778211	0.0750352217886005
6	130	137.421157558	-7.42115755800011
7	87	82.1729221504029	4.82707784959712
8	87.5	83.6641033185892	3.8358966814108
9	117.6	121.778841668037	-4.17884166803694
10	103.4	103.085511302521	0.314488697479326
11	110.8	117.362695334658	-6.56269533465769
12	112.6	123.525159467301	-10.9251594673006
13	102.5	102.309187610781	0.190812389219359
14	112.4	111.954367549258	0.445632450742226
15	135.6	141.343844248153	-5.74384424815325
16	105.1	108.82402939074	-3.72402939074011
17	127.7	127.997044820943	-0.297044820943388
18	137	140.264705707775	-3.26470570777545
19	91	92.6604722094787	-1.66047220947870
20	90.5	94.7551272126098	-4.25512721260978
21	122.4	126.432811322647	-4.03281132264659
22	123.3	125.843696005474	-2.54369600547356
23	124.3	127.045613613807	-2.74561361380716
24	120	124.35712816726	-4.35712816726001
25	118.1	117.825686294396	0.274313705603763
26	119	122.643075553315	-3.64307555331518
27	142.7	149.41749896745	-6.71749896744997
28	123.6	121.122000954650	2.47799904534977
29	129.6	128.225539685958	1.37446031404194
30	151.6	146.930254812201	4.66974518779895
31	110.4	108.378128838076	2.02187116192414
32	99.2	103.633413711833	-4.43341371183287
33	130.5	123.241621122974	7.25837887702577
34	136.2	139.147457294292	-2.94745729429167
35	129.7	129.285687928638	0.414312071362261
36	128	121.769411802532	6.23058819746759
37	121.6	128.715552243435	-7.11555224343524
38	135.8	139.165363961839	-3.36536396183872
39	143.8	132.748726454011	11.0512735459890
40	147.5	145.087133327493	2.41286667250735
41	136.2	129.258666330899	6.94133366910091
42	156.6	145.750644062345	10.8493559376554
43	123.3	116.854099447336	6.44590055266422
44	104.5	96.217906667547	8.28209333245291
45	139.8	133.326855292087	6.47314470791315
46	136.5	127.105317515429	9.39468248457073
47	112.1	102.760176111101	9.33982388889919
48	118.5	111.738851473486	6.76114852651406
49	94.4	90.522879616966	3.87712038303399
50	102.3	101.173849280351	1.12615071964888
51	111.4	120.706586675149	-9.3065866751486
52	99.2	99.8539326266677	-0.653932626667735
53	87.8	95.893784383988	-8.09378438398807
54	115.8	120.633237859679	-4.83323785967879
55	79.7	91.3343773547068	-11.6343773547068
56	72.7	76.129449089421	-3.42944908942106
57	104.5	110.019870594255	-5.51987059425538
58	103	107.218017882285	-4.21801788228482
59	95.1	95.5458270117966	-0.4458270117966
60	104.2	101.909449089421	2.29055091057893
61	78.3	82.5038987377355	-4.20389873773546

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 99 & 92.0227954966864 & 6.9772045033136 \tabularnewline
2 & 106.3 & 100.863343655237 & 5.4366563447628 \tabularnewline
3 & 128.9 & 118.183343655237 & 10.7166563447628 \tabularnewline
4 & 111.1 & 111.612903700449 & -0.512903700449282 \tabularnewline
5 & 102.9 & 102.824964778211 & 0.0750352217886005 \tabularnewline
6 & 130 & 137.421157558 & -7.42115755800011 \tabularnewline
7 & 87 & 82.1729221504029 & 4.82707784959712 \tabularnewline
8 & 87.5 & 83.6641033185892 & 3.8358966814108 \tabularnewline
9 & 117.6 & 121.778841668037 & -4.17884166803694 \tabularnewline
10 & 103.4 & 103.085511302521 & 0.314488697479326 \tabularnewline
11 & 110.8 & 117.362695334658 & -6.56269533465769 \tabularnewline
12 & 112.6 & 123.525159467301 & -10.9251594673006 \tabularnewline
13 & 102.5 & 102.309187610781 & 0.190812389219359 \tabularnewline
14 & 112.4 & 111.954367549258 & 0.445632450742226 \tabularnewline
15 & 135.6 & 141.343844248153 & -5.74384424815325 \tabularnewline
16 & 105.1 & 108.82402939074 & -3.72402939074011 \tabularnewline
17 & 127.7 & 127.997044820943 & -0.297044820943388 \tabularnewline
18 & 137 & 140.264705707775 & -3.26470570777545 \tabularnewline
19 & 91 & 92.6604722094787 & -1.66047220947870 \tabularnewline
20 & 90.5 & 94.7551272126098 & -4.25512721260978 \tabularnewline
21 & 122.4 & 126.432811322647 & -4.03281132264659 \tabularnewline
22 & 123.3 & 125.843696005474 & -2.54369600547356 \tabularnewline
23 & 124.3 & 127.045613613807 & -2.74561361380716 \tabularnewline
24 & 120 & 124.35712816726 & -4.35712816726001 \tabularnewline
25 & 118.1 & 117.825686294396 & 0.274313705603763 \tabularnewline
26 & 119 & 122.643075553315 & -3.64307555331518 \tabularnewline
27 & 142.7 & 149.41749896745 & -6.71749896744997 \tabularnewline
28 & 123.6 & 121.122000954650 & 2.47799904534977 \tabularnewline
29 & 129.6 & 128.225539685958 & 1.37446031404194 \tabularnewline
30 & 151.6 & 146.930254812201 & 4.66974518779895 \tabularnewline
31 & 110.4 & 108.378128838076 & 2.02187116192414 \tabularnewline
32 & 99.2 & 103.633413711833 & -4.43341371183287 \tabularnewline
33 & 130.5 & 123.241621122974 & 7.25837887702577 \tabularnewline
34 & 136.2 & 139.147457294292 & -2.94745729429167 \tabularnewline
35 & 129.7 & 129.285687928638 & 0.414312071362261 \tabularnewline
36 & 128 & 121.769411802532 & 6.23058819746759 \tabularnewline
37 & 121.6 & 128.715552243435 & -7.11555224343524 \tabularnewline
38 & 135.8 & 139.165363961839 & -3.36536396183872 \tabularnewline
39 & 143.8 & 132.748726454011 & 11.0512735459890 \tabularnewline
40 & 147.5 & 145.087133327493 & 2.41286667250735 \tabularnewline
41 & 136.2 & 129.258666330899 & 6.94133366910091 \tabularnewline
42 & 156.6 & 145.750644062345 & 10.8493559376554 \tabularnewline
43 & 123.3 & 116.854099447336 & 6.44590055266422 \tabularnewline
44 & 104.5 & 96.217906667547 & 8.28209333245291 \tabularnewline
45 & 139.8 & 133.326855292087 & 6.47314470791315 \tabularnewline
46 & 136.5 & 127.105317515429 & 9.39468248457073 \tabularnewline
47 & 112.1 & 102.760176111101 & 9.33982388889919 \tabularnewline
48 & 118.5 & 111.738851473486 & 6.76114852651406 \tabularnewline
49 & 94.4 & 90.522879616966 & 3.87712038303399 \tabularnewline
50 & 102.3 & 101.173849280351 & 1.12615071964888 \tabularnewline
51 & 111.4 & 120.706586675149 & -9.3065866751486 \tabularnewline
52 & 99.2 & 99.8539326266677 & -0.653932626667735 \tabularnewline
53 & 87.8 & 95.893784383988 & -8.09378438398807 \tabularnewline
54 & 115.8 & 120.633237859679 & -4.83323785967879 \tabularnewline
55 & 79.7 & 91.3343773547068 & -11.6343773547068 \tabularnewline
56 & 72.7 & 76.129449089421 & -3.42944908942106 \tabularnewline
57 & 104.5 & 110.019870594255 & -5.51987059425538 \tabularnewline
58 & 103 & 107.218017882285 & -4.21801788228482 \tabularnewline
59 & 95.1 & 95.5458270117966 & -0.4458270117966 \tabularnewline
60 & 104.2 & 101.909449089421 & 2.29055091057893 \tabularnewline
61 & 78.3 & 82.5038987377355 & -4.20389873773546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&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]99[/C][C]92.0227954966864[/C][C]6.9772045033136[/C][/ROW]
[ROW][C]2[/C][C]106.3[/C][C]100.863343655237[/C][C]5.4366563447628[/C][/ROW]
[ROW][C]3[/C][C]128.9[/C][C]118.183343655237[/C][C]10.7166563447628[/C][/ROW]
[ROW][C]4[/C][C]111.1[/C][C]111.612903700449[/C][C]-0.512903700449282[/C][/ROW]
[ROW][C]5[/C][C]102.9[/C][C]102.824964778211[/C][C]0.0750352217886005[/C][/ROW]
[ROW][C]6[/C][C]130[/C][C]137.421157558[/C][C]-7.42115755800011[/C][/ROW]
[ROW][C]7[/C][C]87[/C][C]82.1729221504029[/C][C]4.82707784959712[/C][/ROW]
[ROW][C]8[/C][C]87.5[/C][C]83.6641033185892[/C][C]3.8358966814108[/C][/ROW]
[ROW][C]9[/C][C]117.6[/C][C]121.778841668037[/C][C]-4.17884166803694[/C][/ROW]
[ROW][C]10[/C][C]103.4[/C][C]103.085511302521[/C][C]0.314488697479326[/C][/ROW]
[ROW][C]11[/C][C]110.8[/C][C]117.362695334658[/C][C]-6.56269533465769[/C][/ROW]
[ROW][C]12[/C][C]112.6[/C][C]123.525159467301[/C][C]-10.9251594673006[/C][/ROW]
[ROW][C]13[/C][C]102.5[/C][C]102.309187610781[/C][C]0.190812389219359[/C][/ROW]
[ROW][C]14[/C][C]112.4[/C][C]111.954367549258[/C][C]0.445632450742226[/C][/ROW]
[ROW][C]15[/C][C]135.6[/C][C]141.343844248153[/C][C]-5.74384424815325[/C][/ROW]
[ROW][C]16[/C][C]105.1[/C][C]108.82402939074[/C][C]-3.72402939074011[/C][/ROW]
[ROW][C]17[/C][C]127.7[/C][C]127.997044820943[/C][C]-0.297044820943388[/C][/ROW]
[ROW][C]18[/C][C]137[/C][C]140.264705707775[/C][C]-3.26470570777545[/C][/ROW]
[ROW][C]19[/C][C]91[/C][C]92.6604722094787[/C][C]-1.66047220947870[/C][/ROW]
[ROW][C]20[/C][C]90.5[/C][C]94.7551272126098[/C][C]-4.25512721260978[/C][/ROW]
[ROW][C]21[/C][C]122.4[/C][C]126.432811322647[/C][C]-4.03281132264659[/C][/ROW]
[ROW][C]22[/C][C]123.3[/C][C]125.843696005474[/C][C]-2.54369600547356[/C][/ROW]
[ROW][C]23[/C][C]124.3[/C][C]127.045613613807[/C][C]-2.74561361380716[/C][/ROW]
[ROW][C]24[/C][C]120[/C][C]124.35712816726[/C][C]-4.35712816726001[/C][/ROW]
[ROW][C]25[/C][C]118.1[/C][C]117.825686294396[/C][C]0.274313705603763[/C][/ROW]
[ROW][C]26[/C][C]119[/C][C]122.643075553315[/C][C]-3.64307555331518[/C][/ROW]
[ROW][C]27[/C][C]142.7[/C][C]149.41749896745[/C][C]-6.71749896744997[/C][/ROW]
[ROW][C]28[/C][C]123.6[/C][C]121.122000954650[/C][C]2.47799904534977[/C][/ROW]
[ROW][C]29[/C][C]129.6[/C][C]128.225539685958[/C][C]1.37446031404194[/C][/ROW]
[ROW][C]30[/C][C]151.6[/C][C]146.930254812201[/C][C]4.66974518779895[/C][/ROW]
[ROW][C]31[/C][C]110.4[/C][C]108.378128838076[/C][C]2.02187116192414[/C][/ROW]
[ROW][C]32[/C][C]99.2[/C][C]103.633413711833[/C][C]-4.43341371183287[/C][/ROW]
[ROW][C]33[/C][C]130.5[/C][C]123.241621122974[/C][C]7.25837887702577[/C][/ROW]
[ROW][C]34[/C][C]136.2[/C][C]139.147457294292[/C][C]-2.94745729429167[/C][/ROW]
[ROW][C]35[/C][C]129.7[/C][C]129.285687928638[/C][C]0.414312071362261[/C][/ROW]
[ROW][C]36[/C][C]128[/C][C]121.769411802532[/C][C]6.23058819746759[/C][/ROW]
[ROW][C]37[/C][C]121.6[/C][C]128.715552243435[/C][C]-7.11555224343524[/C][/ROW]
[ROW][C]38[/C][C]135.8[/C][C]139.165363961839[/C][C]-3.36536396183872[/C][/ROW]
[ROW][C]39[/C][C]143.8[/C][C]132.748726454011[/C][C]11.0512735459890[/C][/ROW]
[ROW][C]40[/C][C]147.5[/C][C]145.087133327493[/C][C]2.41286667250735[/C][/ROW]
[ROW][C]41[/C][C]136.2[/C][C]129.258666330899[/C][C]6.94133366910091[/C][/ROW]
[ROW][C]42[/C][C]156.6[/C][C]145.750644062345[/C][C]10.8493559376554[/C][/ROW]
[ROW][C]43[/C][C]123.3[/C][C]116.854099447336[/C][C]6.44590055266422[/C][/ROW]
[ROW][C]44[/C][C]104.5[/C][C]96.217906667547[/C][C]8.28209333245291[/C][/ROW]
[ROW][C]45[/C][C]139.8[/C][C]133.326855292087[/C][C]6.47314470791315[/C][/ROW]
[ROW][C]46[/C][C]136.5[/C][C]127.105317515429[/C][C]9.39468248457073[/C][/ROW]
[ROW][C]47[/C][C]112.1[/C][C]102.760176111101[/C][C]9.33982388889919[/C][/ROW]
[ROW][C]48[/C][C]118.5[/C][C]111.738851473486[/C][C]6.76114852651406[/C][/ROW]
[ROW][C]49[/C][C]94.4[/C][C]90.522879616966[/C][C]3.87712038303399[/C][/ROW]
[ROW][C]50[/C][C]102.3[/C][C]101.173849280351[/C][C]1.12615071964888[/C][/ROW]
[ROW][C]51[/C][C]111.4[/C][C]120.706586675149[/C][C]-9.3065866751486[/C][/ROW]
[ROW][C]52[/C][C]99.2[/C][C]99.8539326266677[/C][C]-0.653932626667735[/C][/ROW]
[ROW][C]53[/C][C]87.8[/C][C]95.893784383988[/C][C]-8.09378438398807[/C][/ROW]
[ROW][C]54[/C][C]115.8[/C][C]120.633237859679[/C][C]-4.83323785967879[/C][/ROW]
[ROW][C]55[/C][C]79.7[/C][C]91.3343773547068[/C][C]-11.6343773547068[/C][/ROW]
[ROW][C]56[/C][C]72.7[/C][C]76.129449089421[/C][C]-3.42944908942106[/C][/ROW]
[ROW][C]57[/C][C]104.5[/C][C]110.019870594255[/C][C]-5.51987059425538[/C][/ROW]
[ROW][C]58[/C][C]103[/C][C]107.218017882285[/C][C]-4.21801788228482[/C][/ROW]
[ROW][C]59[/C][C]95.1[/C][C]95.5458270117966[/C][C]-0.4458270117966[/C][/ROW]
[ROW][C]60[/C][C]104.2[/C][C]101.909449089421[/C][C]2.29055091057893[/C][/ROW]
[ROW][C]61[/C][C]78.3[/C][C]82.5038987377355[/C][C]-4.20389873773546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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	99	92.0227954966864	6.9772045033136
2	106.3	100.863343655237	5.4366563447628
3	128.9	118.183343655237	10.7166563447628
4	111.1	111.612903700449	-0.512903700449282
5	102.9	102.824964778211	0.0750352217886005
6	130	137.421157558	-7.42115755800011
7	87	82.1729221504029	4.82707784959712
8	87.5	83.6641033185892	3.8358966814108
9	117.6	121.778841668037	-4.17884166803694
10	103.4	103.085511302521	0.314488697479326
11	110.8	117.362695334658	-6.56269533465769
12	112.6	123.525159467301	-10.9251594673006
13	102.5	102.309187610781	0.190812389219359
14	112.4	111.954367549258	0.445632450742226
15	135.6	141.343844248153	-5.74384424815325
16	105.1	108.82402939074	-3.72402939074011
17	127.7	127.997044820943	-0.297044820943388
18	137	140.264705707775	-3.26470570777545
19	91	92.6604722094787	-1.66047220947870
20	90.5	94.7551272126098	-4.25512721260978
21	122.4	126.432811322647	-4.03281132264659
22	123.3	125.843696005474	-2.54369600547356
23	124.3	127.045613613807	-2.74561361380716
24	120	124.35712816726	-4.35712816726001
25	118.1	117.825686294396	0.274313705603763
26	119	122.643075553315	-3.64307555331518
27	142.7	149.41749896745	-6.71749896744997
28	123.6	121.122000954650	2.47799904534977
29	129.6	128.225539685958	1.37446031404194
30	151.6	146.930254812201	4.66974518779895
31	110.4	108.378128838076	2.02187116192414
32	99.2	103.633413711833	-4.43341371183287
33	130.5	123.241621122974	7.25837887702577
34	136.2	139.147457294292	-2.94745729429167
35	129.7	129.285687928638	0.414312071362261
36	128	121.769411802532	6.23058819746759
37	121.6	128.715552243435	-7.11555224343524
38	135.8	139.165363961839	-3.36536396183872
39	143.8	132.748726454011	11.0512735459890
40	147.5	145.087133327493	2.41286667250735
41	136.2	129.258666330899	6.94133366910091
42	156.6	145.750644062345	10.8493559376554
43	123.3	116.854099447336	6.44590055266422
44	104.5	96.217906667547	8.28209333245291
45	139.8	133.326855292087	6.47314470791315
46	136.5	127.105317515429	9.39468248457073
47	112.1	102.760176111101	9.33982388889919
48	118.5	111.738851473486	6.76114852651406
49	94.4	90.522879616966	3.87712038303399
50	102.3	101.173849280351	1.12615071964888
51	111.4	120.706586675149	-9.3065866751486
52	99.2	99.8539326266677	-0.653932626667735
53	87.8	95.893784383988	-8.09378438398807
54	115.8	120.633237859679	-4.83323785967879
55	79.7	91.3343773547068	-11.6343773547068
56	72.7	76.129449089421	-3.42944908942106
57	104.5	110.019870594255	-5.51987059425538
58	103	107.218017882285	-4.21801788228482
59	95.1	95.5458270117966	-0.4458270117966
60	104.2	101.909449089421	2.29055091057893
61	78.3	82.5038987377355	-4.20389873773546

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.350705546926428	0.701411093852856	0.649294453073572
18	0.315356652003748	0.630713304007496	0.684643347996252
19	0.193911504748982	0.387823009497964	0.806088495251018
20	0.117899730709766	0.235799461419532	0.882100269290234
21	0.0723104433869092	0.144620886773818	0.92768955661309
22	0.0488036576448555	0.097607315289711	0.951196342355144
23	0.0508296289876381	0.101659257975276	0.949170371012362
24	0.0572240356388942	0.114448071277788	0.942775964361106
25	0.0328110219184523	0.0656220438369047	0.967188978081548
26	0.0195470257336247	0.0390940514672495	0.980452974266375
27	0.0170149422603178	0.0340298845206355	0.982985057739682
28	0.0173783347151543	0.0347566694303086	0.982621665284846
29	0.0108035581028501	0.0216071162057002	0.98919644189715
30	0.0158955917171871	0.0317911834343742	0.984104408282813
31	0.0107090896129871	0.0214181792259743	0.989290910387013
32	0.0110174183631066	0.0220348367262133	0.988982581636893
33	0.00708325732107652	0.0141665146421530	0.992916742678923
34	0.00996502651086717	0.0199300530217343	0.990034973489133
35	0.0131732453467699	0.0263464906935397	0.98682675465323
36	0.0248521414605858	0.0497042829211716	0.975147858539414
37	0.217157684447213	0.434315368894426	0.782842315552787
38	0.460941861253163	0.921883722506326	0.539058138746837
39	0.557276361544705	0.88544727691059	0.442723638455295
40	0.984645938845046	0.0307081223099071	0.0153540611549535
41	0.978938433520451	0.0421231329590978	0.0210615664795489
42	0.950935195904115	0.09812960819177	0.049064804095885
43	0.94648119613933	0.107037607721339	0.0535188038606695
44	0.861130064584313	0.277739870831374	0.138869935415687

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.350705546926428 & 0.701411093852856 & 0.649294453073572 \tabularnewline
18 & 0.315356652003748 & 0.630713304007496 & 0.684643347996252 \tabularnewline
19 & 0.193911504748982 & 0.387823009497964 & 0.806088495251018 \tabularnewline
20 & 0.117899730709766 & 0.235799461419532 & 0.882100269290234 \tabularnewline
21 & 0.0723104433869092 & 0.144620886773818 & 0.92768955661309 \tabularnewline
22 & 0.0488036576448555 & 0.097607315289711 & 0.951196342355144 \tabularnewline
23 & 0.0508296289876381 & 0.101659257975276 & 0.949170371012362 \tabularnewline
24 & 0.0572240356388942 & 0.114448071277788 & 0.942775964361106 \tabularnewline
25 & 0.0328110219184523 & 0.0656220438369047 & 0.967188978081548 \tabularnewline
26 & 0.0195470257336247 & 0.0390940514672495 & 0.980452974266375 \tabularnewline
27 & 0.0170149422603178 & 0.0340298845206355 & 0.982985057739682 \tabularnewline
28 & 0.0173783347151543 & 0.0347566694303086 & 0.982621665284846 \tabularnewline
29 & 0.0108035581028501 & 0.0216071162057002 & 0.98919644189715 \tabularnewline
30 & 0.0158955917171871 & 0.0317911834343742 & 0.984104408282813 \tabularnewline
31 & 0.0107090896129871 & 0.0214181792259743 & 0.989290910387013 \tabularnewline
32 & 0.0110174183631066 & 0.0220348367262133 & 0.988982581636893 \tabularnewline
33 & 0.00708325732107652 & 0.0141665146421530 & 0.992916742678923 \tabularnewline
34 & 0.00996502651086717 & 0.0199300530217343 & 0.990034973489133 \tabularnewline
35 & 0.0131732453467699 & 0.0263464906935397 & 0.98682675465323 \tabularnewline
36 & 0.0248521414605858 & 0.0497042829211716 & 0.975147858539414 \tabularnewline
37 & 0.217157684447213 & 0.434315368894426 & 0.782842315552787 \tabularnewline
38 & 0.460941861253163 & 0.921883722506326 & 0.539058138746837 \tabularnewline
39 & 0.557276361544705 & 0.88544727691059 & 0.442723638455295 \tabularnewline
40 & 0.984645938845046 & 0.0307081223099071 & 0.0153540611549535 \tabularnewline
41 & 0.978938433520451 & 0.0421231329590978 & 0.0210615664795489 \tabularnewline
42 & 0.950935195904115 & 0.09812960819177 & 0.049064804095885 \tabularnewline
43 & 0.94648119613933 & 0.107037607721339 & 0.0535188038606695 \tabularnewline
44 & 0.861130064584313 & 0.277739870831374 & 0.138869935415687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&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]0.350705546926428[/C][C]0.701411093852856[/C][C]0.649294453073572[/C][/ROW]
[ROW][C]18[/C][C]0.315356652003748[/C][C]0.630713304007496[/C][C]0.684643347996252[/C][/ROW]
[ROW][C]19[/C][C]0.193911504748982[/C][C]0.387823009497964[/C][C]0.806088495251018[/C][/ROW]
[ROW][C]20[/C][C]0.117899730709766[/C][C]0.235799461419532[/C][C]0.882100269290234[/C][/ROW]
[ROW][C]21[/C][C]0.0723104433869092[/C][C]0.144620886773818[/C][C]0.92768955661309[/C][/ROW]
[ROW][C]22[/C][C]0.0488036576448555[/C][C]0.097607315289711[/C][C]0.951196342355144[/C][/ROW]
[ROW][C]23[/C][C]0.0508296289876381[/C][C]0.101659257975276[/C][C]0.949170371012362[/C][/ROW]
[ROW][C]24[/C][C]0.0572240356388942[/C][C]0.114448071277788[/C][C]0.942775964361106[/C][/ROW]
[ROW][C]25[/C][C]0.0328110219184523[/C][C]0.0656220438369047[/C][C]0.967188978081548[/C][/ROW]
[ROW][C]26[/C][C]0.0195470257336247[/C][C]0.0390940514672495[/C][C]0.980452974266375[/C][/ROW]
[ROW][C]27[/C][C]0.0170149422603178[/C][C]0.0340298845206355[/C][C]0.982985057739682[/C][/ROW]
[ROW][C]28[/C][C]0.0173783347151543[/C][C]0.0347566694303086[/C][C]0.982621665284846[/C][/ROW]
[ROW][C]29[/C][C]0.0108035581028501[/C][C]0.0216071162057002[/C][C]0.98919644189715[/C][/ROW]
[ROW][C]30[/C][C]0.0158955917171871[/C][C]0.0317911834343742[/C][C]0.984104408282813[/C][/ROW]
[ROW][C]31[/C][C]0.0107090896129871[/C][C]0.0214181792259743[/C][C]0.989290910387013[/C][/ROW]
[ROW][C]32[/C][C]0.0110174183631066[/C][C]0.0220348367262133[/C][C]0.988982581636893[/C][/ROW]
[ROW][C]33[/C][C]0.00708325732107652[/C][C]0.0141665146421530[/C][C]0.992916742678923[/C][/ROW]
[ROW][C]34[/C][C]0.00996502651086717[/C][C]0.0199300530217343[/C][C]0.990034973489133[/C][/ROW]
[ROW][C]35[/C][C]0.0131732453467699[/C][C]0.0263464906935397[/C][C]0.98682675465323[/C][/ROW]
[ROW][C]36[/C][C]0.0248521414605858[/C][C]0.0497042829211716[/C][C]0.975147858539414[/C][/ROW]
[ROW][C]37[/C][C]0.217157684447213[/C][C]0.434315368894426[/C][C]0.782842315552787[/C][/ROW]
[ROW][C]38[/C][C]0.460941861253163[/C][C]0.921883722506326[/C][C]0.539058138746837[/C][/ROW]
[ROW][C]39[/C][C]0.557276361544705[/C][C]0.88544727691059[/C][C]0.442723638455295[/C][/ROW]
[ROW][C]40[/C][C]0.984645938845046[/C][C]0.0307081223099071[/C][C]0.0153540611549535[/C][/ROW]
[ROW][C]41[/C][C]0.978938433520451[/C][C]0.0421231329590978[/C][C]0.0210615664795489[/C][/ROW]
[ROW][C]42[/C][C]0.950935195904115[/C][C]0.09812960819177[/C][C]0.049064804095885[/C][/ROW]
[ROW][C]43[/C][C]0.94648119613933[/C][C]0.107037607721339[/C][C]0.0535188038606695[/C][/ROW]
[ROW][C]44[/C][C]0.861130064584313[/C][C]0.277739870831374[/C][C]0.138869935415687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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	0.350705546926428	0.701411093852856	0.649294453073572
18	0.315356652003748	0.630713304007496	0.684643347996252
19	0.193911504748982	0.387823009497964	0.806088495251018
20	0.117899730709766	0.235799461419532	0.882100269290234
21	0.0723104433869092	0.144620886773818	0.92768955661309
22	0.0488036576448555	0.097607315289711	0.951196342355144
23	0.0508296289876381	0.101659257975276	0.949170371012362
24	0.0572240356388942	0.114448071277788	0.942775964361106
25	0.0328110219184523	0.0656220438369047	0.967188978081548
26	0.0195470257336247	0.0390940514672495	0.980452974266375
27	0.0170149422603178	0.0340298845206355	0.982985057739682
28	0.0173783347151543	0.0347566694303086	0.982621665284846
29	0.0108035581028501	0.0216071162057002	0.98919644189715
30	0.0158955917171871	0.0317911834343742	0.984104408282813
31	0.0107090896129871	0.0214181792259743	0.989290910387013
32	0.0110174183631066	0.0220348367262133	0.988982581636893
33	0.00708325732107652	0.0141665146421530	0.992916742678923
34	0.00996502651086717	0.0199300530217343	0.990034973489133
35	0.0131732453467699	0.0263464906935397	0.98682675465323
36	0.0248521414605858	0.0497042829211716	0.975147858539414
37	0.217157684447213	0.434315368894426	0.782842315552787
38	0.460941861253163	0.921883722506326	0.539058138746837
39	0.557276361544705	0.88544727691059	0.442723638455295
40	0.984645938845046	0.0307081223099071	0.0153540611549535
41	0.978938433520451	0.0421231329590978	0.0210615664795489
42	0.950935195904115	0.09812960819177	0.049064804095885
43	0.94648119613933	0.107037607721339	0.0535188038606695
44	0.861130064584313	0.277739870831374	0.138869935415687

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	13	0.464285714285714	NOK
10% type I error level	16	0.571428571428571	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 & 0 & 0 & OK \tabularnewline
5% type I error level & 13 & 0.464285714285714 & NOK \tabularnewline
10% type I error level & 16 & 0.571428571428571 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116207&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]13[/C][C]0.464285714285714[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]16[/C][C]0.571428571428571[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116207&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116207&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	0	0	OK
5% type I error level	13	0.464285714285714	NOK
10% type I error level	16	0.571428571428571	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 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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