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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 04 Dec 2015 21:39:45 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/04/t144926618170fke1sh04af7dl.htm/, Retrieved Thu, 16 May 2024 12:34:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285181, Retrieved Thu, 16 May 2024 12:34:36 +0000

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Original text written by user:

The Sokal & Rohlf Table 16.1 dataset on Air Pollution (from: http://math.fau.edu/Qian/course/sta4234/airpolut.htm) missing man as explanatory

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Multiple Regression] [Sokal & Rohlf Air...] [2015-12-04 21:39:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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10	70.3	582	6	7.05	36
13	61	132	8.2	48.52	100
12	56.7	716	8.7	20.66	67
17	51.9	515	9	12.95	86
56	49.1	158	9	43.37	127
36	54	80	9	40.25	114
29	57.3	757	9.3	38.89	111
14	68.4	529	8.8	54.47	116
10	75.5	335	9	59.8	128
24	61.5	497	9.1	48.34	115
110	50.6	3369	10.4	34.44	122
28	52.3	746	9.7	38.74	121
17	49	201	11.2	30.85	103
8	56.6	277	12.7	30.58	82
30	55.6	593	8.3	43.11	123
9	68.3	361	8.4	56.77	113
47	55	905	9.6	41.31	111
35	49.9	1513	10.1	30.96	129
29	43.5	744	10.6	25.94	137
14	54.5	507	10	37	99
56	55.9	622	9.5	35.89	105
14	51.5	347	10.9	30.18	98
11	56.8	244	8.9	7.77	58
46	47.6	116	8.8	33.36	135
11	47.1	463	12.4	36.11	166
23	54	453	7.1	39.04	132
65	49.7	751	10.9	34.99	155
26	51.5	540	8.6	37.01	134
69	54.6	1950	9.6	39.93	115
61	50.4	520	9.4	36.22	147
94	50	179	10.6	42.75	125
10	61.6	624	9.2	49.1	105
18	59.4	448	7.9	46	119
9	66.2	844	10.9	35.94	78
10	68.9	1233	10.8	48.19	103
28	51	176	8.7	15.17	89
31	59.3	308	10.6	44.68	116
26	57.8	299	7.6	42.59	115
29	51.1	531	9.4	38.79	164
31	55.2	71	6.5	40.75	148
16	45.7	717	11.8	29.07	123

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	'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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	'George Udny Yule' @ yule.wessa.net

Multiple Linear Regression - Estimated Regression Equation
SO2[t] = + 147.197 -2.05305Temp[t] + 0.0207699Pop[t] -3.64948Wind[t] + 0.66966Rain[t] -0.0479529RainDays[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
SO2[t] =  +  147.197 -2.05305Temp[t] +  0.0207699Pop[t] -3.64948Wind[t] +  0.66966Rain[t] -0.0479529RainDays[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]SO2[t] =  +  147.197 -2.05305Temp[t] +  0.0207699Pop[t] -3.64948Wind[t] +  0.66966Rain[t] -0.0479529RainDays[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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
SO2[t] = + 147.197 -2.05305Temp[t] + 0.0207699Pop[t] -3.64948Wind[t] + 0.66966Rain[t] -0.0479529RainDays[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)	+147.2	56.16	+2.6210e+00	0.01289	0.006444
Temp	-2.053	0.7137	-2.8770e+00	0.006801	0.0034
Pop	+0.02077	0.00495	+4.1960e+00	0.0001764	8.821e-05
Wind	-3.65	2.187	-1.6690e+00	0.104	0.05201
Rain	+0.6697	0.4354	+1.5380e+00	0.1331	0.06653
RainDays	-0.04795	0.1956	-2.4520e-01	0.8077	0.4039

\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) & +147.2 &  56.16 & +2.6210e+00 &  0.01289 &  0.006444 \tabularnewline
Temp & -2.053 &  0.7137 & -2.8770e+00 &  0.006801 &  0.0034 \tabularnewline
Pop & +0.02077 &  0.00495 & +4.1960e+00 &  0.0001764 &  8.821e-05 \tabularnewline
Wind & -3.65 &  2.187 & -1.6690e+00 &  0.104 &  0.05201 \tabularnewline
Rain & +0.6697 &  0.4354 & +1.5380e+00 &  0.1331 &  0.06653 \tabularnewline
RainDays & -0.04795 &  0.1956 & -2.4520e-01 &  0.8077 &  0.4039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&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]+147.2[/C][C] 56.16[/C][C]+2.6210e+00[/C][C] 0.01289[/C][C] 0.006444[/C][/ROW]
[ROW][C]Temp[/C][C]-2.053[/C][C] 0.7137[/C][C]-2.8770e+00[/C][C] 0.006801[/C][C] 0.0034[/C][/ROW]
[ROW][C]Pop[/C][C]+0.02077[/C][C] 0.00495[/C][C]+4.1960e+00[/C][C] 0.0001764[/C][C] 8.821e-05[/C][/ROW]
[ROW][C]Wind[/C][C]-3.65[/C][C] 2.187[/C][C]-1.6690e+00[/C][C] 0.104[/C][C] 0.05201[/C][/ROW]
[ROW][C]Rain[/C][C]+0.6697[/C][C] 0.4354[/C][C]+1.5380e+00[/C][C] 0.1331[/C][C] 0.06653[/C][/ROW]
[ROW][C]RainDays[/C][C]-0.04795[/C][C] 0.1956[/C][C]-2.4520e-01[/C][C] 0.8077[/C][C] 0.4039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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)	+147.2	56.16	+2.6210e+00	0.01289	0.006444
Temp	-2.053	0.7137	-2.8770e+00	0.006801	0.0034
Pop	+0.02077	0.00495	+4.1960e+00	0.0001764	8.821e-05
Wind	-3.65	2.187	-1.6690e+00	0.104	0.05201
Rain	+0.6697	0.4354	+1.5380e+00	0.1331	0.06653
RainDays	-0.04795	0.1956	-2.4520e-01	0.8077	0.4039

Multiple Linear Regression - Regression Statistics
Multiple R	0.7102
R-squared	0.5043
Adjusted R-squared	0.4335
F-TEST (value)	7.122
F-TEST (DF numerator)	5
F-TEST (DF denominator)	35
p-value	0.0001096
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.67
Sum Squared Residuals	1.092e+04

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.7102 \tabularnewline
R-squared &  0.5043 \tabularnewline
Adjusted R-squared &  0.4335 \tabularnewline
F-TEST (value) &  7.122 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 35 \tabularnewline
p-value &  0.0001096 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  17.67 \tabularnewline
Sum Squared Residuals &  1.092e+04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.7102[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.5043[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.4335[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 7.122[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]35[/C][/ROW]
[ROW][C]p-value[/C][C] 0.0001096[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 17.67[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 1.092e+04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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	0.7102
R-squared	0.5043
Adjusted R-squared	0.4335
F-TEST (value)	7.122
F-TEST (DF numerator)	5
F-TEST (DF denominator)	35
p-value	0.0001096
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.67
Sum Squared Residuals	1.092e+04

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	10	-3.946	13.95
2	13	22.47	-9.474
3	12	24.53	-12.53
4	17	23.04	-6.044
5	56	39.78	16.22
6	36	26.64	9.364
7	29	32.06	-3.061
8	14	16.55	-2.555
9	10	0.2127	9.787
10	24	24.9	-0.9042
11	110	92.55	17.45
12	28	40.06	-12.06
13	17	25.62	-8.619
14	8	6.946	1.054
15	30	38.04	-8.045
16	9	16.41	-7.415
17	47	40.38	6.617
18	35	53.86	-18.86
19	29	45.46	-16.46
20	14	29.37	-15.37
21	56	29.68	26.32
22	14	24.4	-10.4
23	11	5.594	5.406
24	46	35.63	10.37
25	11	31.08	-20.08
26	23	39.64	-16.64
27	65	36.98	28.02
28	26	39.65	-13.65
29	69	61.79	7.208
30	61	37.43	23.57
31	94	32.21	61.79
32	10	27.96	-17.96
33	18	30.82	-12.82
34	9	9.363	-0.3635
35	10	19.27	-9.269
36	28	20.29	7.712
37	31	17.52	13.48
38	26	30.01	-4.012
39	29	37.12	-8.122
40	31	31.81	-0.8139
41	16	38.77	-22.77

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  10 & -3.946 &  13.95 \tabularnewline
2 &  13 &  22.47 & -9.474 \tabularnewline
3 &  12 &  24.53 & -12.53 \tabularnewline
4 &  17 &  23.04 & -6.044 \tabularnewline
5 &  56 &  39.78 &  16.22 \tabularnewline
6 &  36 &  26.64 &  9.364 \tabularnewline
7 &  29 &  32.06 & -3.061 \tabularnewline
8 &  14 &  16.55 & -2.555 \tabularnewline
9 &  10 &  0.2127 &  9.787 \tabularnewline
10 &  24 &  24.9 & -0.9042 \tabularnewline
11 &  110 &  92.55 &  17.45 \tabularnewline
12 &  28 &  40.06 & -12.06 \tabularnewline
13 &  17 &  25.62 & -8.619 \tabularnewline
14 &  8 &  6.946 &  1.054 \tabularnewline
15 &  30 &  38.04 & -8.045 \tabularnewline
16 &  9 &  16.41 & -7.415 \tabularnewline
17 &  47 &  40.38 &  6.617 \tabularnewline
18 &  35 &  53.86 & -18.86 \tabularnewline
19 &  29 &  45.46 & -16.46 \tabularnewline
20 &  14 &  29.37 & -15.37 \tabularnewline
21 &  56 &  29.68 &  26.32 \tabularnewline
22 &  14 &  24.4 & -10.4 \tabularnewline
23 &  11 &  5.594 &  5.406 \tabularnewline
24 &  46 &  35.63 &  10.37 \tabularnewline
25 &  11 &  31.08 & -20.08 \tabularnewline
26 &  23 &  39.64 & -16.64 \tabularnewline
27 &  65 &  36.98 &  28.02 \tabularnewline
28 &  26 &  39.65 & -13.65 \tabularnewline
29 &  69 &  61.79 &  7.208 \tabularnewline
30 &  61 &  37.43 &  23.57 \tabularnewline
31 &  94 &  32.21 &  61.79 \tabularnewline
32 &  10 &  27.96 & -17.96 \tabularnewline
33 &  18 &  30.82 & -12.82 \tabularnewline
34 &  9 &  9.363 & -0.3635 \tabularnewline
35 &  10 &  19.27 & -9.269 \tabularnewline
36 &  28 &  20.29 &  7.712 \tabularnewline
37 &  31 &  17.52 &  13.48 \tabularnewline
38 &  26 &  30.01 & -4.012 \tabularnewline
39 &  29 &  37.12 & -8.122 \tabularnewline
40 &  31 &  31.81 & -0.8139 \tabularnewline
41 &  16 &  38.77 & -22.77 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&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] 10[/C][C]-3.946[/C][C] 13.95[/C][/ROW]
[ROW][C]2[/C][C] 13[/C][C] 22.47[/C][C]-9.474[/C][/ROW]
[ROW][C]3[/C][C] 12[/C][C] 24.53[/C][C]-12.53[/C][/ROW]
[ROW][C]4[/C][C] 17[/C][C] 23.04[/C][C]-6.044[/C][/ROW]
[ROW][C]5[/C][C] 56[/C][C] 39.78[/C][C] 16.22[/C][/ROW]
[ROW][C]6[/C][C] 36[/C][C] 26.64[/C][C] 9.364[/C][/ROW]
[ROW][C]7[/C][C] 29[/C][C] 32.06[/C][C]-3.061[/C][/ROW]
[ROW][C]8[/C][C] 14[/C][C] 16.55[/C][C]-2.555[/C][/ROW]
[ROW][C]9[/C][C] 10[/C][C] 0.2127[/C][C] 9.787[/C][/ROW]
[ROW][C]10[/C][C] 24[/C][C] 24.9[/C][C]-0.9042[/C][/ROW]
[ROW][C]11[/C][C] 110[/C][C] 92.55[/C][C] 17.45[/C][/ROW]
[ROW][C]12[/C][C] 28[/C][C] 40.06[/C][C]-12.06[/C][/ROW]
[ROW][C]13[/C][C] 17[/C][C] 25.62[/C][C]-8.619[/C][/ROW]
[ROW][C]14[/C][C] 8[/C][C] 6.946[/C][C] 1.054[/C][/ROW]
[ROW][C]15[/C][C] 30[/C][C] 38.04[/C][C]-8.045[/C][/ROW]
[ROW][C]16[/C][C] 9[/C][C] 16.41[/C][C]-7.415[/C][/ROW]
[ROW][C]17[/C][C] 47[/C][C] 40.38[/C][C] 6.617[/C][/ROW]
[ROW][C]18[/C][C] 35[/C][C] 53.86[/C][C]-18.86[/C][/ROW]
[ROW][C]19[/C][C] 29[/C][C] 45.46[/C][C]-16.46[/C][/ROW]
[ROW][C]20[/C][C] 14[/C][C] 29.37[/C][C]-15.37[/C][/ROW]
[ROW][C]21[/C][C] 56[/C][C] 29.68[/C][C] 26.32[/C][/ROW]
[ROW][C]22[/C][C] 14[/C][C] 24.4[/C][C]-10.4[/C][/ROW]
[ROW][C]23[/C][C] 11[/C][C] 5.594[/C][C] 5.406[/C][/ROW]
[ROW][C]24[/C][C] 46[/C][C] 35.63[/C][C] 10.37[/C][/ROW]
[ROW][C]25[/C][C] 11[/C][C] 31.08[/C][C]-20.08[/C][/ROW]
[ROW][C]26[/C][C] 23[/C][C] 39.64[/C][C]-16.64[/C][/ROW]
[ROW][C]27[/C][C] 65[/C][C] 36.98[/C][C] 28.02[/C][/ROW]
[ROW][C]28[/C][C] 26[/C][C] 39.65[/C][C]-13.65[/C][/ROW]
[ROW][C]29[/C][C] 69[/C][C] 61.79[/C][C] 7.208[/C][/ROW]
[ROW][C]30[/C][C] 61[/C][C] 37.43[/C][C] 23.57[/C][/ROW]
[ROW][C]31[/C][C] 94[/C][C] 32.21[/C][C] 61.79[/C][/ROW]
[ROW][C]32[/C][C] 10[/C][C] 27.96[/C][C]-17.96[/C][/ROW]
[ROW][C]33[/C][C] 18[/C][C] 30.82[/C][C]-12.82[/C][/ROW]
[ROW][C]34[/C][C] 9[/C][C] 9.363[/C][C]-0.3635[/C][/ROW]
[ROW][C]35[/C][C] 10[/C][C] 19.27[/C][C]-9.269[/C][/ROW]
[ROW][C]36[/C][C] 28[/C][C] 20.29[/C][C] 7.712[/C][/ROW]
[ROW][C]37[/C][C] 31[/C][C] 17.52[/C][C] 13.48[/C][/ROW]
[ROW][C]38[/C][C] 26[/C][C] 30.01[/C][C]-4.012[/C][/ROW]
[ROW][C]39[/C][C] 29[/C][C] 37.12[/C][C]-8.122[/C][/ROW]
[ROW][C]40[/C][C] 31[/C][C] 31.81[/C][C]-0.8139[/C][/ROW]
[ROW][C]41[/C][C] 16[/C][C] 38.77[/C][C]-22.77[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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	10	-3.946	13.95
2	13	22.47	-9.474
3	12	24.53	-12.53
4	17	23.04	-6.044
5	56	39.78	16.22
6	36	26.64	9.364
7	29	32.06	-3.061
8	14	16.55	-2.555
9	10	0.2127	9.787
10	24	24.9	-0.9042
11	110	92.55	17.45
12	28	40.06	-12.06
13	17	25.62	-8.619
14	8	6.946	1.054
15	30	38.04	-8.045
16	9	16.41	-7.415
17	47	40.38	6.617
18	35	53.86	-18.86
19	29	45.46	-16.46
20	14	29.37	-15.37
21	56	29.68	26.32
22	14	24.4	-10.4
23	11	5.594	5.406
24	46	35.63	10.37
25	11	31.08	-20.08
26	23	39.64	-16.64
27	65	36.98	28.02
28	26	39.65	-13.65
29	69	61.79	7.208
30	61	37.43	23.57
31	94	32.21	61.79
32	10	27.96	-17.96
33	18	30.82	-12.82
34	9	9.363	-0.3635
35	10	19.27	-9.269
36	28	20.29	7.712
37	31	17.52	13.48
38	26	30.01	-4.012
39	29	37.12	-8.122
40	31	31.81	-0.8139
41	16	38.77	-22.77

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.09225	0.1845	0.9077
10	0.0307	0.0614	0.9693
11	0.01304	0.02607	0.987
12	0.01985	0.03971	0.9801
13	0.04161	0.08322	0.9584
14	0.05571	0.1114	0.9443
15	0.03685	0.07371	0.9631
16	0.02073	0.04145	0.9793
17	0.01139	0.02278	0.9886
18	0.0178	0.03561	0.9822
19	0.01121	0.02242	0.9888
20	0.01012	0.02024	0.9899
21	0.03076	0.06152	0.9692
22	0.02276	0.04551	0.9772
23	0.01307	0.02614	0.9869
24	0.009566	0.01913	0.9904
25	0.01408	0.02815	0.9859
26	0.01107	0.02214	0.9889
27	0.02949	0.05899	0.9705
28	0.02185	0.04371	0.9781
29	0.06133	0.1227	0.9387
30	0.1409	0.2817	0.8591
31	0.9941	0.0118	0.005899
32	0.9821	0.03573	0.01786

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 &  0.09225 &  0.1845 &  0.9077 \tabularnewline
10 &  0.0307 &  0.0614 &  0.9693 \tabularnewline
11 &  0.01304 &  0.02607 &  0.987 \tabularnewline
12 &  0.01985 &  0.03971 &  0.9801 \tabularnewline
13 &  0.04161 &  0.08322 &  0.9584 \tabularnewline
14 &  0.05571 &  0.1114 &  0.9443 \tabularnewline
15 &  0.03685 &  0.07371 &  0.9631 \tabularnewline
16 &  0.02073 &  0.04145 &  0.9793 \tabularnewline
17 &  0.01139 &  0.02278 &  0.9886 \tabularnewline
18 &  0.0178 &  0.03561 &  0.9822 \tabularnewline
19 &  0.01121 &  0.02242 &  0.9888 \tabularnewline
20 &  0.01012 &  0.02024 &  0.9899 \tabularnewline
21 &  0.03076 &  0.06152 &  0.9692 \tabularnewline
22 &  0.02276 &  0.04551 &  0.9772 \tabularnewline
23 &  0.01307 &  0.02614 &  0.9869 \tabularnewline
24 &  0.009566 &  0.01913 &  0.9904 \tabularnewline
25 &  0.01408 &  0.02815 &  0.9859 \tabularnewline
26 &  0.01107 &  0.02214 &  0.9889 \tabularnewline
27 &  0.02949 &  0.05899 &  0.9705 \tabularnewline
28 &  0.02185 &  0.04371 &  0.9781 \tabularnewline
29 &  0.06133 &  0.1227 &  0.9387 \tabularnewline
30 &  0.1409 &  0.2817 &  0.8591 \tabularnewline
31 &  0.9941 &  0.0118 &  0.005899 \tabularnewline
32 &  0.9821 &  0.03573 &  0.01786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&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]9[/C][C] 0.09225[/C][C] 0.1845[/C][C] 0.9077[/C][/ROW]
[ROW][C]10[/C][C] 0.0307[/C][C] 0.0614[/C][C] 0.9693[/C][/ROW]
[ROW][C]11[/C][C] 0.01304[/C][C] 0.02607[/C][C] 0.987[/C][/ROW]
[ROW][C]12[/C][C] 0.01985[/C][C] 0.03971[/C][C] 0.9801[/C][/ROW]
[ROW][C]13[/C][C] 0.04161[/C][C] 0.08322[/C][C] 0.9584[/C][/ROW]
[ROW][C]14[/C][C] 0.05571[/C][C] 0.1114[/C][C] 0.9443[/C][/ROW]
[ROW][C]15[/C][C] 0.03685[/C][C] 0.07371[/C][C] 0.9631[/C][/ROW]
[ROW][C]16[/C][C] 0.02073[/C][C] 0.04145[/C][C] 0.9793[/C][/ROW]
[ROW][C]17[/C][C] 0.01139[/C][C] 0.02278[/C][C] 0.9886[/C][/ROW]
[ROW][C]18[/C][C] 0.0178[/C][C] 0.03561[/C][C] 0.9822[/C][/ROW]
[ROW][C]19[/C][C] 0.01121[/C][C] 0.02242[/C][C] 0.9888[/C][/ROW]
[ROW][C]20[/C][C] 0.01012[/C][C] 0.02024[/C][C] 0.9899[/C][/ROW]
[ROW][C]21[/C][C] 0.03076[/C][C] 0.06152[/C][C] 0.9692[/C][/ROW]
[ROW][C]22[/C][C] 0.02276[/C][C] 0.04551[/C][C] 0.9772[/C][/ROW]
[ROW][C]23[/C][C] 0.01307[/C][C] 0.02614[/C][C] 0.9869[/C][/ROW]
[ROW][C]24[/C][C] 0.009566[/C][C] 0.01913[/C][C] 0.9904[/C][/ROW]
[ROW][C]25[/C][C] 0.01408[/C][C] 0.02815[/C][C] 0.9859[/C][/ROW]
[ROW][C]26[/C][C] 0.01107[/C][C] 0.02214[/C][C] 0.9889[/C][/ROW]
[ROW][C]27[/C][C] 0.02949[/C][C] 0.05899[/C][C] 0.9705[/C][/ROW]
[ROW][C]28[/C][C] 0.02185[/C][C] 0.04371[/C][C] 0.9781[/C][/ROW]
[ROW][C]29[/C][C] 0.06133[/C][C] 0.1227[/C][C] 0.9387[/C][/ROW]
[ROW][C]30[/C][C] 0.1409[/C][C] 0.2817[/C][C] 0.8591[/C][/ROW]
[ROW][C]31[/C][C] 0.9941[/C][C] 0.0118[/C][C] 0.005899[/C][/ROW]
[ROW][C]32[/C][C] 0.9821[/C][C] 0.03573[/C][C] 0.01786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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
9	0.09225	0.1845	0.9077
10	0.0307	0.0614	0.9693
11	0.01304	0.02607	0.987
12	0.01985	0.03971	0.9801
13	0.04161	0.08322	0.9584
14	0.05571	0.1114	0.9443
15	0.03685	0.07371	0.9631
16	0.02073	0.04145	0.9793
17	0.01139	0.02278	0.9886
18	0.0178	0.03561	0.9822
19	0.01121	0.02242	0.9888
20	0.01012	0.02024	0.9899
21	0.03076	0.06152	0.9692
22	0.02276	0.04551	0.9772
23	0.01307	0.02614	0.9869
24	0.009566	0.01913	0.9904
25	0.01408	0.02815	0.9859
26	0.01107	0.02214	0.9889
27	0.02949	0.05899	0.9705
28	0.02185	0.04371	0.9781
29	0.06133	0.1227	0.9387
30	0.1409	0.2817	0.8591
31	0.9941	0.0118	0.005899
32	0.9821	0.03573	0.01786

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	15	0.625	NOK
10% type I error level	20	0.833333	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 & 15 & 0.625 & NOK \tabularnewline
10% type I error level & 20 & 0.833333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285181&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]15[/C][C]0.625[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]20[/C][C]0.833333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285181&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285181&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	15	0.625	NOK
10% type I error level	20	0.833333	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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;

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

par5 <- '0'
par4 <- '0'
par3 <- 'No Linear Trend'
par2 <- 'Do not include Seasonal Dummies'
par1 <- '1'
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
x <- na.omit(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(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
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+par4,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1+par4,])
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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, mywarning)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
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,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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