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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 04 Dec 2015 21:51:40 +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/t14492660306ygbxmf458h504x.htm/, Retrieved Thu, 16 May 2024 03:33:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285180, Retrieved Thu, 16 May 2024 03:33:24 +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) with Wind, Rain, RainDays as explanatory

IsPrivate?

No (this computation is public)

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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 21:51:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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10	6	7.05	36
13	8.2	48.52	100
12	8.7	20.66	67
17	9	12.95	86
56	9	43.37	127
36	9	40.25	114
29	9.3	38.89	111
14	8.8	54.47	116
10	9	59.8	128
24	9.1	48.34	115
110	10.4	34.44	122
28	9.7	38.74	121
17	11.2	30.85	103
8	12.7	30.58	82
30	8.3	43.11	123
9	8.4	56.77	113
47	9.6	41.31	111
35	10.1	30.96	129
29	10.6	25.94	137
14	10	37	99
56	9.5	35.89	105
14	10.9	30.18	98
11	8.9	7.77	58
46	8.8	33.36	135
11	12.4	36.11	166
23	7.1	39.04	132
65	10.9	34.99	155
26	8.6	37.01	134
69	9.6	39.93	115
61	9.4	36.22	147
94	10.6	42.75	125
10	9.2	49.1	105
18	7.9	46	119
9	10.9	35.94	78
10	10.8	48.19	103
28	8.7	15.17	89
31	10.6	44.68	116
26	7.6	42.59	115
29	9.4	38.79	164
31	6.5	40.75	148
16	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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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' @ fisher.wessa.net

Multiple Linear Regression - Estimated Regression Equation
SO2[t] = -5.87526 + 0.305661Wind[t] -0.33667Rain[t] + 0.398731RainDays[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
SO2[t] =  -5.87526 +  0.305661Wind[t] -0.33667Rain[t] +  0.398731RainDays[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]SO2[t] =  -5.87526 +  0.305661Wind[t] -0.33667Rain[t] +  0.398731RainDays[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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] = -5.87526 + 0.305661Wind[t] -0.33667Rain[t] + 0.398731RainDays[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)	-5.875	27.08	-2.1690e-01	0.8294	0.4147
Wind	+0.3057	2.526	+1.2100e-01	0.9044	0.4522
Rain	-0.3367	0.3483	-9.6650e-01	0.3401	0.17
RainDays	+0.3987	0.1568	+2.5430e+00	0.01532	0.007659

\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) & -5.875 &  27.08 & -2.1690e-01 &  0.8294 &  0.4147 \tabularnewline
Wind & +0.3057 &  2.526 & +1.2100e-01 &  0.9044 &  0.4522 \tabularnewline
Rain & -0.3367 &  0.3483 & -9.6650e-01 &  0.3401 &  0.17 \tabularnewline
RainDays & +0.3987 &  0.1568 & +2.5430e+00 &  0.01532 &  0.007659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&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]-5.875[/C][C] 27.08[/C][C]-2.1690e-01[/C][C] 0.8294[/C][C] 0.4147[/C][/ROW]
[ROW][C]Wind[/C][C]+0.3057[/C][C] 2.526[/C][C]+1.2100e-01[/C][C] 0.9044[/C][C] 0.4522[/C][/ROW]
[ROW][C]Rain[/C][C]-0.3367[/C][C] 0.3483[/C][C]-9.6650e-01[/C][C] 0.3401[/C][C] 0.17[/C][/ROW]
[ROW][C]RainDays[/C][C]+0.3987[/C][C] 0.1568[/C][C]+2.5430e+00[/C][C] 0.01532[/C][C] 0.007659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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)	-5.875	27.08	-2.1690e-01	0.8294	0.4147
Wind	+0.3057	2.526	+1.2100e-01	0.9044	0.4522
Rain	-0.3367	0.3483	-9.6650e-01	0.3401	0.17
RainDays	+0.3987	0.1568	+2.5430e+00	0.01532	0.007659

Multiple Linear Regression - Regression Statistics
Multiple R	0.3987
R-squared	0.159
Adjusted R-squared	0.09081
F-TEST (value)	2.332
F-TEST (DF numerator)	3
F-TEST (DF denominator)	37
p-value	0.09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	22.38
Sum Squared Residuals	1.853e+04

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.3987 \tabularnewline
R-squared &  0.159 \tabularnewline
Adjusted R-squared &  0.09081 \tabularnewline
F-TEST (value) &  2.332 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 37 \tabularnewline
p-value &  0.09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  22.38 \tabularnewline
Sum Squared Residuals &  1.853e+04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.3987[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.159[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.09081[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 2.332[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]37[/C][/ROW]
[ROW][C]p-value[/C][C] 0.09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 22.38[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 1.853e+04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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	0.3987
R-squared	0.159
Adjusted R-squared	0.09081
F-TEST (value)	2.332
F-TEST (DF numerator)	3
F-TEST (DF denominator)	37
p-value	0.09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	22.38
Sum Squared Residuals	1.853e+04

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	10	7.939	2.061
2	13	20.17	-7.169
3	12	16.54	-4.543
4	17	26.81	-9.807
5	56	32.91	23.09
6	36	28.78	7.22
7	29	28.13	0.8666
8	14	24.73	-10.73
9	10	27.78	-17.78
10	24	26.49	-2.486
11	110	34.35	75.65
12	28	32.29	-4.294
13	17	28.23	-11.23
14	8	20.41	-12.41
15	30	31.19	-1.192
16	9	22.64	-13.64
17	47	27.41	19.59
18	35	38.22	-3.225
19	29	43.26	-14.26
20	14	24.2	-10.2
21	56	26.81	29.19
22	14	26.37	-12.37
23	11	17.36	-6.356
24	46	39.41	6.588
25	11	51.95	-40.95
26	23	35.78	-12.78
27	65	47.48	17.52
28	26	37.72	-11.72
29	69	29.47	39.53
30	61	43.42	17.58
31	94	32.81	61.19
32	10	22.27	-12.27
33	18	28.5	-10.5
34	9	16.46	-7.458
35	10	22.27	-12.27
36	28	27.16	0.8362
37	31	28.58	2.425
38	26	27.96	-1.963
39	29	49.33	-20.33
40	31	41.4	-10.4
41	16	36.99	-20.99

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  10 &  7.939 &  2.061 \tabularnewline
2 &  13 &  20.17 & -7.169 \tabularnewline
3 &  12 &  16.54 & -4.543 \tabularnewline
4 &  17 &  26.81 & -9.807 \tabularnewline
5 &  56 &  32.91 &  23.09 \tabularnewline
6 &  36 &  28.78 &  7.22 \tabularnewline
7 &  29 &  28.13 &  0.8666 \tabularnewline
8 &  14 &  24.73 & -10.73 \tabularnewline
9 &  10 &  27.78 & -17.78 \tabularnewline
10 &  24 &  26.49 & -2.486 \tabularnewline
11 &  110 &  34.35 &  75.65 \tabularnewline
12 &  28 &  32.29 & -4.294 \tabularnewline
13 &  17 &  28.23 & -11.23 \tabularnewline
14 &  8 &  20.41 & -12.41 \tabularnewline
15 &  30 &  31.19 & -1.192 \tabularnewline
16 &  9 &  22.64 & -13.64 \tabularnewline
17 &  47 &  27.41 &  19.59 \tabularnewline
18 &  35 &  38.22 & -3.225 \tabularnewline
19 &  29 &  43.26 & -14.26 \tabularnewline
20 &  14 &  24.2 & -10.2 \tabularnewline
21 &  56 &  26.81 &  29.19 \tabularnewline
22 &  14 &  26.37 & -12.37 \tabularnewline
23 &  11 &  17.36 & -6.356 \tabularnewline
24 &  46 &  39.41 &  6.588 \tabularnewline
25 &  11 &  51.95 & -40.95 \tabularnewline
26 &  23 &  35.78 & -12.78 \tabularnewline
27 &  65 &  47.48 &  17.52 \tabularnewline
28 &  26 &  37.72 & -11.72 \tabularnewline
29 &  69 &  29.47 &  39.53 \tabularnewline
30 &  61 &  43.42 &  17.58 \tabularnewline
31 &  94 &  32.81 &  61.19 \tabularnewline
32 &  10 &  22.27 & -12.27 \tabularnewline
33 &  18 &  28.5 & -10.5 \tabularnewline
34 &  9 &  16.46 & -7.458 \tabularnewline
35 &  10 &  22.27 & -12.27 \tabularnewline
36 &  28 &  27.16 &  0.8362 \tabularnewline
37 &  31 &  28.58 &  2.425 \tabularnewline
38 &  26 &  27.96 & -1.963 \tabularnewline
39 &  29 &  49.33 & -20.33 \tabularnewline
40 &  31 &  41.4 & -10.4 \tabularnewline
41 &  16 &  36.99 & -20.99 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&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] 7.939[/C][C] 2.061[/C][/ROW]
[ROW][C]2[/C][C] 13[/C][C] 20.17[/C][C]-7.169[/C][/ROW]
[ROW][C]3[/C][C] 12[/C][C] 16.54[/C][C]-4.543[/C][/ROW]
[ROW][C]4[/C][C] 17[/C][C] 26.81[/C][C]-9.807[/C][/ROW]
[ROW][C]5[/C][C] 56[/C][C] 32.91[/C][C] 23.09[/C][/ROW]
[ROW][C]6[/C][C] 36[/C][C] 28.78[/C][C] 7.22[/C][/ROW]
[ROW][C]7[/C][C] 29[/C][C] 28.13[/C][C] 0.8666[/C][/ROW]
[ROW][C]8[/C][C] 14[/C][C] 24.73[/C][C]-10.73[/C][/ROW]
[ROW][C]9[/C][C] 10[/C][C] 27.78[/C][C]-17.78[/C][/ROW]
[ROW][C]10[/C][C] 24[/C][C] 26.49[/C][C]-2.486[/C][/ROW]
[ROW][C]11[/C][C] 110[/C][C] 34.35[/C][C] 75.65[/C][/ROW]
[ROW][C]12[/C][C] 28[/C][C] 32.29[/C][C]-4.294[/C][/ROW]
[ROW][C]13[/C][C] 17[/C][C] 28.23[/C][C]-11.23[/C][/ROW]
[ROW][C]14[/C][C] 8[/C][C] 20.41[/C][C]-12.41[/C][/ROW]
[ROW][C]15[/C][C] 30[/C][C] 31.19[/C][C]-1.192[/C][/ROW]
[ROW][C]16[/C][C] 9[/C][C] 22.64[/C][C]-13.64[/C][/ROW]
[ROW][C]17[/C][C] 47[/C][C] 27.41[/C][C] 19.59[/C][/ROW]
[ROW][C]18[/C][C] 35[/C][C] 38.22[/C][C]-3.225[/C][/ROW]
[ROW][C]19[/C][C] 29[/C][C] 43.26[/C][C]-14.26[/C][/ROW]
[ROW][C]20[/C][C] 14[/C][C] 24.2[/C][C]-10.2[/C][/ROW]
[ROW][C]21[/C][C] 56[/C][C] 26.81[/C][C] 29.19[/C][/ROW]
[ROW][C]22[/C][C] 14[/C][C] 26.37[/C][C]-12.37[/C][/ROW]
[ROW][C]23[/C][C] 11[/C][C] 17.36[/C][C]-6.356[/C][/ROW]
[ROW][C]24[/C][C] 46[/C][C] 39.41[/C][C] 6.588[/C][/ROW]
[ROW][C]25[/C][C] 11[/C][C] 51.95[/C][C]-40.95[/C][/ROW]
[ROW][C]26[/C][C] 23[/C][C] 35.78[/C][C]-12.78[/C][/ROW]
[ROW][C]27[/C][C] 65[/C][C] 47.48[/C][C] 17.52[/C][/ROW]
[ROW][C]28[/C][C] 26[/C][C] 37.72[/C][C]-11.72[/C][/ROW]
[ROW][C]29[/C][C] 69[/C][C] 29.47[/C][C] 39.53[/C][/ROW]
[ROW][C]30[/C][C] 61[/C][C] 43.42[/C][C] 17.58[/C][/ROW]
[ROW][C]31[/C][C] 94[/C][C] 32.81[/C][C] 61.19[/C][/ROW]
[ROW][C]32[/C][C] 10[/C][C] 22.27[/C][C]-12.27[/C][/ROW]
[ROW][C]33[/C][C] 18[/C][C] 28.5[/C][C]-10.5[/C][/ROW]
[ROW][C]34[/C][C] 9[/C][C] 16.46[/C][C]-7.458[/C][/ROW]
[ROW][C]35[/C][C] 10[/C][C] 22.27[/C][C]-12.27[/C][/ROW]
[ROW][C]36[/C][C] 28[/C][C] 27.16[/C][C] 0.8362[/C][/ROW]
[ROW][C]37[/C][C] 31[/C][C] 28.58[/C][C] 2.425[/C][/ROW]
[ROW][C]38[/C][C] 26[/C][C] 27.96[/C][C]-1.963[/C][/ROW]
[ROW][C]39[/C][C] 29[/C][C] 49.33[/C][C]-20.33[/C][/ROW]
[ROW][C]40[/C][C] 31[/C][C] 41.4[/C][C]-10.4[/C][/ROW]
[ROW][C]41[/C][C] 16[/C][C] 36.99[/C][C]-20.99[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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	7.939	2.061
2	13	20.17	-7.169
3	12	16.54	-4.543
4	17	26.81	-9.807
5	56	32.91	23.09
6	36	28.78	7.22
7	29	28.13	0.8666
8	14	24.73	-10.73
9	10	27.78	-17.78
10	24	26.49	-2.486
11	110	34.35	75.65
12	28	32.29	-4.294
13	17	28.23	-11.23
14	8	20.41	-12.41
15	30	31.19	-1.192
16	9	22.64	-13.64
17	47	27.41	19.59
18	35	38.22	-3.225
19	29	43.26	-14.26
20	14	24.2	-10.2
21	56	26.81	29.19
22	14	26.37	-12.37
23	11	17.36	-6.356
24	46	39.41	6.588
25	11	51.95	-40.95
26	23	35.78	-12.78
27	65	47.48	17.52
28	26	37.72	-11.72
29	69	29.47	39.53
30	61	43.42	17.58
31	94	32.81	61.19
32	10	22.27	-12.27
33	18	28.5	-10.5
34	9	16.46	-7.458
35	10	22.27	-12.27
36	28	27.16	0.8362
37	31	28.58	2.425
38	26	27.96	-1.963
39	29	49.33	-20.33
40	31	41.4	-10.4
41	16	36.99	-20.99

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.09831	0.1966	0.9017
8	0.05893	0.1179	0.9411
9	0.05376	0.1075	0.9462
10	0.02215	0.04429	0.9779
11	0.7328	0.5344	0.2672
12	0.7075	0.585	0.2925
13	0.6564	0.6872	0.3436
14	0.5698	0.8604	0.4302
15	0.4895	0.979	0.5105
16	0.4121	0.8243	0.5879
17	0.3722	0.7443	0.6278
18	0.3697	0.7394	0.6303
19	0.4016	0.8031	0.5984
20	0.3233	0.6465	0.6767
21	0.3661	0.7321	0.6339
22	0.2968	0.5936	0.7032
23	0.2202	0.4404	0.7798
24	0.1593	0.3186	0.8407
25	0.3493	0.6987	0.6507
26	0.2816	0.5633	0.7184
27	0.2265	0.4531	0.7735
28	0.1688	0.3376	0.8312
29	0.2942	0.5884	0.7058
30	0.2493	0.4986	0.7507
31	0.9974	0.005222	0.002611
32	0.993	0.01393	0.006965
33	0.9809	0.03812	0.01906
34	0.947	0.106	0.05298

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
7 &  0.09831 &  0.1966 &  0.9017 \tabularnewline
8 &  0.05893 &  0.1179 &  0.9411 \tabularnewline
9 &  0.05376 &  0.1075 &  0.9462 \tabularnewline
10 &  0.02215 &  0.04429 &  0.9779 \tabularnewline
11 &  0.7328 &  0.5344 &  0.2672 \tabularnewline
12 &  0.7075 &  0.585 &  0.2925 \tabularnewline
13 &  0.6564 &  0.6872 &  0.3436 \tabularnewline
14 &  0.5698 &  0.8604 &  0.4302 \tabularnewline
15 &  0.4895 &  0.979 &  0.5105 \tabularnewline
16 &  0.4121 &  0.8243 &  0.5879 \tabularnewline
17 &  0.3722 &  0.7443 &  0.6278 \tabularnewline
18 &  0.3697 &  0.7394 &  0.6303 \tabularnewline
19 &  0.4016 &  0.8031 &  0.5984 \tabularnewline
20 &  0.3233 &  0.6465 &  0.6767 \tabularnewline
21 &  0.3661 &  0.7321 &  0.6339 \tabularnewline
22 &  0.2968 &  0.5936 &  0.7032 \tabularnewline
23 &  0.2202 &  0.4404 &  0.7798 \tabularnewline
24 &  0.1593 &  0.3186 &  0.8407 \tabularnewline
25 &  0.3493 &  0.6987 &  0.6507 \tabularnewline
26 &  0.2816 &  0.5633 &  0.7184 \tabularnewline
27 &  0.2265 &  0.4531 &  0.7735 \tabularnewline
28 &  0.1688 &  0.3376 &  0.8312 \tabularnewline
29 &  0.2942 &  0.5884 &  0.7058 \tabularnewline
30 &  0.2493 &  0.4986 &  0.7507 \tabularnewline
31 &  0.9974 &  0.005222 &  0.002611 \tabularnewline
32 &  0.993 &  0.01393 &  0.006965 \tabularnewline
33 &  0.9809 &  0.03812 &  0.01906 \tabularnewline
34 &  0.947 &  0.106 &  0.05298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]7[/C][C] 0.09831[/C][C] 0.1966[/C][C] 0.9017[/C][/ROW]
[ROW][C]8[/C][C] 0.05893[/C][C] 0.1179[/C][C] 0.9411[/C][/ROW]
[ROW][C]9[/C][C] 0.05376[/C][C] 0.1075[/C][C] 0.9462[/C][/ROW]
[ROW][C]10[/C][C] 0.02215[/C][C] 0.04429[/C][C] 0.9779[/C][/ROW]
[ROW][C]11[/C][C] 0.7328[/C][C] 0.5344[/C][C] 0.2672[/C][/ROW]
[ROW][C]12[/C][C] 0.7075[/C][C] 0.585[/C][C] 0.2925[/C][/ROW]
[ROW][C]13[/C][C] 0.6564[/C][C] 0.6872[/C][C] 0.3436[/C][/ROW]
[ROW][C]14[/C][C] 0.5698[/C][C] 0.8604[/C][C] 0.4302[/C][/ROW]
[ROW][C]15[/C][C] 0.4895[/C][C] 0.979[/C][C] 0.5105[/C][/ROW]
[ROW][C]16[/C][C] 0.4121[/C][C] 0.8243[/C][C] 0.5879[/C][/ROW]
[ROW][C]17[/C][C] 0.3722[/C][C] 0.7443[/C][C] 0.6278[/C][/ROW]
[ROW][C]18[/C][C] 0.3697[/C][C] 0.7394[/C][C] 0.6303[/C][/ROW]
[ROW][C]19[/C][C] 0.4016[/C][C] 0.8031[/C][C] 0.5984[/C][/ROW]
[ROW][C]20[/C][C] 0.3233[/C][C] 0.6465[/C][C] 0.6767[/C][/ROW]
[ROW][C]21[/C][C] 0.3661[/C][C] 0.7321[/C][C] 0.6339[/C][/ROW]
[ROW][C]22[/C][C] 0.2968[/C][C] 0.5936[/C][C] 0.7032[/C][/ROW]
[ROW][C]23[/C][C] 0.2202[/C][C] 0.4404[/C][C] 0.7798[/C][/ROW]
[ROW][C]24[/C][C] 0.1593[/C][C] 0.3186[/C][C] 0.8407[/C][/ROW]
[ROW][C]25[/C][C] 0.3493[/C][C] 0.6987[/C][C] 0.6507[/C][/ROW]
[ROW][C]26[/C][C] 0.2816[/C][C] 0.5633[/C][C] 0.7184[/C][/ROW]
[ROW][C]27[/C][C] 0.2265[/C][C] 0.4531[/C][C] 0.7735[/C][/ROW]
[ROW][C]28[/C][C] 0.1688[/C][C] 0.3376[/C][C] 0.8312[/C][/ROW]
[ROW][C]29[/C][C] 0.2942[/C][C] 0.5884[/C][C] 0.7058[/C][/ROW]
[ROW][C]30[/C][C] 0.2493[/C][C] 0.4986[/C][C] 0.7507[/C][/ROW]
[ROW][C]31[/C][C] 0.9974[/C][C] 0.005222[/C][C] 0.002611[/C][/ROW]
[ROW][C]32[/C][C] 0.993[/C][C] 0.01393[/C][C] 0.006965[/C][/ROW]
[ROW][C]33[/C][C] 0.9809[/C][C] 0.03812[/C][C] 0.01906[/C][/ROW]
[ROW][C]34[/C][C] 0.947[/C][C] 0.106[/C][C] 0.05298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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
7	0.09831	0.1966	0.9017
8	0.05893	0.1179	0.9411
9	0.05376	0.1075	0.9462
10	0.02215	0.04429	0.9779
11	0.7328	0.5344	0.2672
12	0.7075	0.585	0.2925
13	0.6564	0.6872	0.3436
14	0.5698	0.8604	0.4302
15	0.4895	0.979	0.5105
16	0.4121	0.8243	0.5879
17	0.3722	0.7443	0.6278
18	0.3697	0.7394	0.6303
19	0.4016	0.8031	0.5984
20	0.3233	0.6465	0.6767
21	0.3661	0.7321	0.6339
22	0.2968	0.5936	0.7032
23	0.2202	0.4404	0.7798
24	0.1593	0.3186	0.8407
25	0.3493	0.6987	0.6507
26	0.2816	0.5633	0.7184
27	0.2265	0.4531	0.7735
28	0.1688	0.3376	0.8312
29	0.2942	0.5884	0.7058
30	0.2493	0.4986	0.7507
31	0.9974	0.005222	0.002611
32	0.993	0.01393	0.006965
33	0.9809	0.03812	0.01906
34	0.947	0.106	0.05298

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.03571	NOK
5% type I error level	4	0.142857	NOK
10% type I error level	4	0.142857	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 & 1 &  0.03571 & NOK \tabularnewline
5% type I error level & 4 & 0.142857 & NOK \tabularnewline
10% type I error level & 4 & 0.142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285180&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]1[/C][C] 0.03571[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]4[/C][C]0.142857[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285180&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285180&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	1	0.03571	NOK
5% type I error level	4	0.142857	NOK
10% type I error level	4	0.142857	NOK

Figure 1

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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