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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Thu, 10 Dec 2015 09:57:17 +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/2015/Dec/10/t1449742072v2q9yltqtldfw5r.htm/, Retrieved Thu, 16 May 2024 07:44:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285791, Retrieved Thu, 16 May 2024 07:44:59 +0000

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

-       [Multiple Regression] [X1 en X2 ] [2015-12-10 09:57:17] [a6adb6e41ce68c761989548559553e3d] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&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 Maurice George Kendall' @ kendall.wessa.net

Multiple Linear Regression - Estimated Regression Equation
(1-B12)(1-B)X1[t] = + 0.338144 -0.00274661`(1-B12)(1-B)X2`[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
(1-B12)(1-B)X1[t] =  +  0.338144 -0.00274661`(1-B12)(1-B)X2`[t]  + e[t] \tabularnewline
Warning: you did not specify the column number of the endogenous series! The first column was selected by default. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C](1-B12)(1-B)X1[t] =  +  0.338144 -0.00274661`(1-B12)(1-B)X2`[t]  + e[t][/C][/ROW]
[ROW][C]Warning: you did not specify the column number of the endogenous series! The first column was selected by default.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&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
(1-B12)(1-B)X1[t] = + 0.338144 -0.00274661`(1-B12)(1-B)X2`[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+0.3381	1.312	+2.5760e-01	0.7982	0.3991
`(1-B12)(1-B)X2`	-0.002747	0.003076	-8.9290e-01	0.378	0.189

\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) & +0.3381 &  1.312 & +2.5760e-01 &  0.7982 &  0.3991 \tabularnewline
`(1-B12)(1-B)X2` & -0.002747 &  0.003076 & -8.9290e-01 &  0.378 &  0.189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&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]+0.3381[/C][C] 1.312[/C][C]+2.5760e-01[/C][C] 0.7982[/C][C] 0.3991[/C][/ROW]
[ROW][C]`(1-B12)(1-B)X2`[/C][C]-0.002747[/C][C] 0.003076[/C][C]-8.9290e-01[/C][C] 0.378[/C][C] 0.189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&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)	+0.3381	1.312	+2.5760e-01	0.7982	0.3991
`(1-B12)(1-B)X2`	-0.002747	0.003076	-8.9290e-01	0.378	0.189

Multiple Linear Regression - Regression Statistics
Multiple R	0.1492
R-squared	0.02227
Adjusted R-squared	-0.005663
F-TEST (value)	0.7973
F-TEST (DF numerator)	1
F-TEST (DF denominator)	35
p-value	0.378
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.978
Sum Squared Residuals	2228

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.1492 \tabularnewline
R-squared &  0.02227 \tabularnewline
Adjusted R-squared & -0.005663 \tabularnewline
F-TEST (value) &  0.7973 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 35 \tabularnewline
p-value &  0.378 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  7.978 \tabularnewline
Sum Squared Residuals &  2228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.1492[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.02227[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.005663[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 0.7973[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]35[/C][/ROW]
[ROW][C]p-value[/C][C] 0.378[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 7.978[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 2228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&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	0.1492
R-squared	0.02227
Adjusted R-squared	-0.005663
F-TEST (value)	0.7973
F-TEST (DF numerator)	1
F-TEST (DF denominator)	35
p-value	0.378
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.978
Sum Squared Residuals	2228

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	2	0.5194	1.481
2	-6	0.6842	-6.684
3	5	-0.09857	5.099
4	4	1.288	2.712
5	-4	-0.07385	-3.926
6	4	-0.354	4.354
7	-1	0.8875	-1.887
8	13	-0.5106	13.51
9	-10	1.398	-11.4
10	2	-0.5078	2.508
11	15	1.407	13.59
12	-19	-1.098	-17.9
13	-5	0.1816	-5.182
14	9	1.39	7.61
15	0	-1.23	1.23
16	2	0.4508	1.549
17	2	1.519	0.4808
18	-7	-0.387	-6.613
19	-5	0.1074	-5.107
20	-2	1.272	-3.272
21	8	-0.722	8.722
22	-9	0.676	-9.676
23	-9	0.643	-9.643
24	14	1.217	12.78
25	4	-1.736	5.736
26	-15	0.5304	-15.53
27	6	1.975	4.025
28	5	-2.062	7.062
29	-2	1.643	-3.643
30	16	1.58	14.42
31	-3	-0.2936	-2.706
32	-8	0.1184	-8.118
33	0	0.8985	-0.8985
34	-2	0.9177	-2.918
35	0	-2.343	2.343
36	7	0.6265	6.373
37	3	3.486	-0.4858

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  2 &  0.5194 &  1.481 \tabularnewline
2 & -6 &  0.6842 & -6.684 \tabularnewline
3 &  5 & -0.09857 &  5.099 \tabularnewline
4 &  4 &  1.288 &  2.712 \tabularnewline
5 & -4 & -0.07385 & -3.926 \tabularnewline
6 &  4 & -0.354 &  4.354 \tabularnewline
7 & -1 &  0.8875 & -1.887 \tabularnewline
8 &  13 & -0.5106 &  13.51 \tabularnewline
9 & -10 &  1.398 & -11.4 \tabularnewline
10 &  2 & -0.5078 &  2.508 \tabularnewline
11 &  15 &  1.407 &  13.59 \tabularnewline
12 & -19 & -1.098 & -17.9 \tabularnewline
13 & -5 &  0.1816 & -5.182 \tabularnewline
14 &  9 &  1.39 &  7.61 \tabularnewline
15 &  0 & -1.23 &  1.23 \tabularnewline
16 &  2 &  0.4508 &  1.549 \tabularnewline
17 &  2 &  1.519 &  0.4808 \tabularnewline
18 & -7 & -0.387 & -6.613 \tabularnewline
19 & -5 &  0.1074 & -5.107 \tabularnewline
20 & -2 &  1.272 & -3.272 \tabularnewline
21 &  8 & -0.722 &  8.722 \tabularnewline
22 & -9 &  0.676 & -9.676 \tabularnewline
23 & -9 &  0.643 & -9.643 \tabularnewline
24 &  14 &  1.217 &  12.78 \tabularnewline
25 &  4 & -1.736 &  5.736 \tabularnewline
26 & -15 &  0.5304 & -15.53 \tabularnewline
27 &  6 &  1.975 &  4.025 \tabularnewline
28 &  5 & -2.062 &  7.062 \tabularnewline
29 & -2 &  1.643 & -3.643 \tabularnewline
30 &  16 &  1.58 &  14.42 \tabularnewline
31 & -3 & -0.2936 & -2.706 \tabularnewline
32 & -8 &  0.1184 & -8.118 \tabularnewline
33 &  0 &  0.8985 & -0.8985 \tabularnewline
34 & -2 &  0.9177 & -2.918 \tabularnewline
35 &  0 & -2.343 &  2.343 \tabularnewline
36 &  7 &  0.6265 &  6.373 \tabularnewline
37 &  3 &  3.486 & -0.4858 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&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] 2[/C][C] 0.5194[/C][C] 1.481[/C][/ROW]
[ROW][C]2[/C][C]-6[/C][C] 0.6842[/C][C]-6.684[/C][/ROW]
[ROW][C]3[/C][C] 5[/C][C]-0.09857[/C][C] 5.099[/C][/ROW]
[ROW][C]4[/C][C] 4[/C][C] 1.288[/C][C] 2.712[/C][/ROW]
[ROW][C]5[/C][C]-4[/C][C]-0.07385[/C][C]-3.926[/C][/ROW]
[ROW][C]6[/C][C] 4[/C][C]-0.354[/C][C] 4.354[/C][/ROW]
[ROW][C]7[/C][C]-1[/C][C] 0.8875[/C][C]-1.887[/C][/ROW]
[ROW][C]8[/C][C] 13[/C][C]-0.5106[/C][C] 13.51[/C][/ROW]
[ROW][C]9[/C][C]-10[/C][C] 1.398[/C][C]-11.4[/C][/ROW]
[ROW][C]10[/C][C] 2[/C][C]-0.5078[/C][C] 2.508[/C][/ROW]
[ROW][C]11[/C][C] 15[/C][C] 1.407[/C][C] 13.59[/C][/ROW]
[ROW][C]12[/C][C]-19[/C][C]-1.098[/C][C]-17.9[/C][/ROW]
[ROW][C]13[/C][C]-5[/C][C] 0.1816[/C][C]-5.182[/C][/ROW]
[ROW][C]14[/C][C] 9[/C][C] 1.39[/C][C] 7.61[/C][/ROW]
[ROW][C]15[/C][C] 0[/C][C]-1.23[/C][C] 1.23[/C][/ROW]
[ROW][C]16[/C][C] 2[/C][C] 0.4508[/C][C] 1.549[/C][/ROW]
[ROW][C]17[/C][C] 2[/C][C] 1.519[/C][C] 0.4808[/C][/ROW]
[ROW][C]18[/C][C]-7[/C][C]-0.387[/C][C]-6.613[/C][/ROW]
[ROW][C]19[/C][C]-5[/C][C] 0.1074[/C][C]-5.107[/C][/ROW]
[ROW][C]20[/C][C]-2[/C][C] 1.272[/C][C]-3.272[/C][/ROW]
[ROW][C]21[/C][C] 8[/C][C]-0.722[/C][C] 8.722[/C][/ROW]
[ROW][C]22[/C][C]-9[/C][C] 0.676[/C][C]-9.676[/C][/ROW]
[ROW][C]23[/C][C]-9[/C][C] 0.643[/C][C]-9.643[/C][/ROW]
[ROW][C]24[/C][C] 14[/C][C] 1.217[/C][C] 12.78[/C][/ROW]
[ROW][C]25[/C][C] 4[/C][C]-1.736[/C][C] 5.736[/C][/ROW]
[ROW][C]26[/C][C]-15[/C][C] 0.5304[/C][C]-15.53[/C][/ROW]
[ROW][C]27[/C][C] 6[/C][C] 1.975[/C][C] 4.025[/C][/ROW]
[ROW][C]28[/C][C] 5[/C][C]-2.062[/C][C] 7.062[/C][/ROW]
[ROW][C]29[/C][C]-2[/C][C] 1.643[/C][C]-3.643[/C][/ROW]
[ROW][C]30[/C][C] 16[/C][C] 1.58[/C][C] 14.42[/C][/ROW]
[ROW][C]31[/C][C]-3[/C][C]-0.2936[/C][C]-2.706[/C][/ROW]
[ROW][C]32[/C][C]-8[/C][C] 0.1184[/C][C]-8.118[/C][/ROW]
[ROW][C]33[/C][C] 0[/C][C] 0.8985[/C][C]-0.8985[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C] 0.9177[/C][C]-2.918[/C][/ROW]
[ROW][C]35[/C][C] 0[/C][C]-2.343[/C][C] 2.343[/C][/ROW]
[ROW][C]36[/C][C] 7[/C][C] 0.6265[/C][C] 6.373[/C][/ROW]
[ROW][C]37[/C][C] 3[/C][C] 3.486[/C][C]-0.4858[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&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	2	0.5194	1.481
2	-6	0.6842	-6.684
3	5	-0.09857	5.099
4	4	1.288	2.712
5	-4	-0.07385	-3.926
6	4	-0.354	4.354
7	-1	0.8875	-1.887
8	13	-0.5106	13.51
9	-10	1.398	-11.4
10	2	-0.5078	2.508
11	15	1.407	13.59
12	-19	-1.098	-17.9
13	-5	0.1816	-5.182
14	9	1.39	7.61
15	0	-1.23	1.23
16	2	0.4508	1.549
17	2	1.519	0.4808
18	-7	-0.387	-6.613
19	-5	0.1074	-5.107
20	-2	1.272	-3.272
21	8	-0.722	8.722
22	-9	0.676	-9.676
23	-9	0.643	-9.643
24	14	1.217	12.78
25	4	-1.736	5.736
26	-15	0.5304	-15.53
27	6	1.975	4.025
28	5	-2.062	7.062
29	-2	1.643	-3.643
30	16	1.58	14.42
31	-3	-0.2936	-2.706
32	-8	0.1184	-8.118
33	0	0.8985	-0.8985
34	-2	0.9177	-2.918
35	0	-2.343	2.343
36	7	0.6265	6.373
37	3	3.486	-0.4858

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.2787	0.5573	0.7213
6	0.1727	0.3453	0.8273
7	0.08634	0.1727	0.9137
8	0.1707	0.3414	0.8293
9	0.1653	0.3305	0.8347
10	0.1131	0.2261	0.8869
11	0.4637	0.9275	0.5363
12	0.8492	0.3016	0.1508
13	0.8053	0.3894	0.1947
14	0.7788	0.4425	0.2212
15	0.7048	0.5904	0.2952
16	0.6139	0.7721	0.3861
17	0.5176	0.9648	0.4824
18	0.4746	0.9492	0.5254
19	0.4122	0.8244	0.5878
20	0.3374	0.6749	0.6626
21	0.3534	0.7068	0.6466
22	0.3886	0.7772	0.6114
23	0.4319	0.8638	0.5681
24	0.5599	0.8802	0.4401
25	0.4998	0.9996	0.5002
26	0.7988	0.4025	0.2012
27	0.7222	0.5555	0.2778
28	0.6835	0.633	0.3165
29	0.5995	0.801	0.4005
30	0.8927	0.2146	0.1073
31	0.8033	0.3934	0.1967
32	0.8869	0.2261	0.1131

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 &  0.2787 &  0.5573 &  0.7213 \tabularnewline
6 &  0.1727 &  0.3453 &  0.8273 \tabularnewline
7 &  0.08634 &  0.1727 &  0.9137 \tabularnewline
8 &  0.1707 &  0.3414 &  0.8293 \tabularnewline
9 &  0.1653 &  0.3305 &  0.8347 \tabularnewline
10 &  0.1131 &  0.2261 &  0.8869 \tabularnewline
11 &  0.4637 &  0.9275 &  0.5363 \tabularnewline
12 &  0.8492 &  0.3016 &  0.1508 \tabularnewline
13 &  0.8053 &  0.3894 &  0.1947 \tabularnewline
14 &  0.7788 &  0.4425 &  0.2212 \tabularnewline
15 &  0.7048 &  0.5904 &  0.2952 \tabularnewline
16 &  0.6139 &  0.7721 &  0.3861 \tabularnewline
17 &  0.5176 &  0.9648 &  0.4824 \tabularnewline
18 &  0.4746 &  0.9492 &  0.5254 \tabularnewline
19 &  0.4122 &  0.8244 &  0.5878 \tabularnewline
20 &  0.3374 &  0.6749 &  0.6626 \tabularnewline
21 &  0.3534 &  0.7068 &  0.6466 \tabularnewline
22 &  0.3886 &  0.7772 &  0.6114 \tabularnewline
23 &  0.4319 &  0.8638 &  0.5681 \tabularnewline
24 &  0.5599 &  0.8802 &  0.4401 \tabularnewline
25 &  0.4998 &  0.9996 &  0.5002 \tabularnewline
26 &  0.7988 &  0.4025 &  0.2012 \tabularnewline
27 &  0.7222 &  0.5555 &  0.2778 \tabularnewline
28 &  0.6835 &  0.633 &  0.3165 \tabularnewline
29 &  0.5995 &  0.801 &  0.4005 \tabularnewline
30 &  0.8927 &  0.2146 &  0.1073 \tabularnewline
31 &  0.8033 &  0.3934 &  0.1967 \tabularnewline
32 &  0.8869 &  0.2261 &  0.1131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]5[/C][C] 0.2787[/C][C] 0.5573[/C][C] 0.7213[/C][/ROW]
[ROW][C]6[/C][C] 0.1727[/C][C] 0.3453[/C][C] 0.8273[/C][/ROW]
[ROW][C]7[/C][C] 0.08634[/C][C] 0.1727[/C][C] 0.9137[/C][/ROW]
[ROW][C]8[/C][C] 0.1707[/C][C] 0.3414[/C][C] 0.8293[/C][/ROW]
[ROW][C]9[/C][C] 0.1653[/C][C] 0.3305[/C][C] 0.8347[/C][/ROW]
[ROW][C]10[/C][C] 0.1131[/C][C] 0.2261[/C][C] 0.8869[/C][/ROW]
[ROW][C]11[/C][C] 0.4637[/C][C] 0.9275[/C][C] 0.5363[/C][/ROW]
[ROW][C]12[/C][C] 0.8492[/C][C] 0.3016[/C][C] 0.1508[/C][/ROW]
[ROW][C]13[/C][C] 0.8053[/C][C] 0.3894[/C][C] 0.1947[/C][/ROW]
[ROW][C]14[/C][C] 0.7788[/C][C] 0.4425[/C][C] 0.2212[/C][/ROW]
[ROW][C]15[/C][C] 0.7048[/C][C] 0.5904[/C][C] 0.2952[/C][/ROW]
[ROW][C]16[/C][C] 0.6139[/C][C] 0.7721[/C][C] 0.3861[/C][/ROW]
[ROW][C]17[/C][C] 0.5176[/C][C] 0.9648[/C][C] 0.4824[/C][/ROW]
[ROW][C]18[/C][C] 0.4746[/C][C] 0.9492[/C][C] 0.5254[/C][/ROW]
[ROW][C]19[/C][C] 0.4122[/C][C] 0.8244[/C][C] 0.5878[/C][/ROW]
[ROW][C]20[/C][C] 0.3374[/C][C] 0.6749[/C][C] 0.6626[/C][/ROW]
[ROW][C]21[/C][C] 0.3534[/C][C] 0.7068[/C][C] 0.6466[/C][/ROW]
[ROW][C]22[/C][C] 0.3886[/C][C] 0.7772[/C][C] 0.6114[/C][/ROW]
[ROW][C]23[/C][C] 0.4319[/C][C] 0.8638[/C][C] 0.5681[/C][/ROW]
[ROW][C]24[/C][C] 0.5599[/C][C] 0.8802[/C][C] 0.4401[/C][/ROW]
[ROW][C]25[/C][C] 0.4998[/C][C] 0.9996[/C][C] 0.5002[/C][/ROW]
[ROW][C]26[/C][C] 0.7988[/C][C] 0.4025[/C][C] 0.2012[/C][/ROW]
[ROW][C]27[/C][C] 0.7222[/C][C] 0.5555[/C][C] 0.2778[/C][/ROW]
[ROW][C]28[/C][C] 0.6835[/C][C] 0.633[/C][C] 0.3165[/C][/ROW]
[ROW][C]29[/C][C] 0.5995[/C][C] 0.801[/C][C] 0.4005[/C][/ROW]
[ROW][C]30[/C][C] 0.8927[/C][C] 0.2146[/C][C] 0.1073[/C][/ROW]
[ROW][C]31[/C][C] 0.8033[/C][C] 0.3934[/C][C] 0.1967[/C][/ROW]
[ROW][C]32[/C][C] 0.8869[/C][C] 0.2261[/C][C] 0.1131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.2787	0.5573	0.7213
6	0.1727	0.3453	0.8273
7	0.08634	0.1727	0.9137
8	0.1707	0.3414	0.8293
9	0.1653	0.3305	0.8347
10	0.1131	0.2261	0.8869
11	0.4637	0.9275	0.5363
12	0.8492	0.3016	0.1508
13	0.8053	0.3894	0.1947
14	0.7788	0.4425	0.2212
15	0.7048	0.5904	0.2952
16	0.6139	0.7721	0.3861
17	0.5176	0.9648	0.4824
18	0.4746	0.9492	0.5254
19	0.4122	0.8244	0.5878
20	0.3374	0.6749	0.6626
21	0.3534	0.7068	0.6466
22	0.3886	0.7772	0.6114
23	0.4319	0.8638	0.5681
24	0.5599	0.8802	0.4401
25	0.4998	0.9996	0.5002
26	0.7988	0.4025	0.2012
27	0.7222	0.5555	0.2778
28	0.6835	0.633	0.3165
29	0.5995	0.801	0.4005
30	0.8927	0.2146	0.1073
31	0.8033	0.3934	0.1967
32	0.8869	0.2261	0.1131

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	0	0	OK
10% type I error level	0	0	OK

\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 & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285791&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285791&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285791&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	0	0	OK
10% type I error level	0	0	OK

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):

par2 = Do not include Seasonal Dummies ; par3 = First and Seasonal Differences (s=12) ;

Parameters (R input):

par1 = ; par2 = Do not include Seasonal Dummies ; par3 = First and Seasonal Differences (s=12) ; par4 = ; par5 = ;

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

par5 <- ''
par4 <- ''
par3 <- 'First and Seasonal Differences (s=12)'
par2 <- 'Do not include Seasonal Dummies'
par1 <- ''
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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s=12)'){
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s=12)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,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(par5 > 0) {
x2 <- array(0, dim=c(n-par5*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*12)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*12-j*12,par1]
}
}
x <- cbind(x[(par5*12+1):n,], x2)
n <- n - par5*12
}
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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
(k <- length(x[n,]))
head(x)
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