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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Mon, 15 Dec 2014 17:32:42 +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/2014/Dec/15/t14186649488t47xf2fujwkcu9.htm/, Retrieved Thu, 16 May 2024 11:35:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268789, Retrieved Thu, 16 May 2024 11:35:46 +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] [Paper 15] [2014-12-15 17:32:42] [3e8c20c2e60277acd0ccfb10a62c3907] [Current]

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12.9 21 1 0.5 0.67 0 0.5
12.8 22 0.89 0.4 0.67 0 1
7.4 18 0.89 0.5 0 0 0
6.7 23 0.89 0.7 0 1 1
12.6 12 0.78 0.3 0 0.5 0.5
14.8 20 0.89 0.4 0.67 0.5 0
13.3 22 1 0.4 0.67 1 1
11.1 21 0.89 0.7 0 0.5 0
8.2 19 0.78 0.6 0.67 0.5 0.5
11.4 22 1 0.6 1 0 0.5
6.4 15 0.78 0.2 0 0.5 0.5
12 19 0.89 0.4 0.67 0 1
6.3 18 0.89 0.5 0.33 0 0
11.3 15 0.89 0.3 0.67 0 0.5
11.9 20 0.89 0.4 0.33 0.5 0.5
9.3 21 0.67 0.7 0.33 0.5 1
10 15 0.78 0.2 0 0 1
13.8 23 0.89 0.6 0.33 0 1
10.8 21 0.78 0.6 0.33 0 1
11.7 25 0.89 0.7 0.67 1 0
10.9 9 0.33 0.2 0 0 0
16.1 30 1 1 0.33 1 1
9.9 23 0.89 0.4 1 0 1
11.5 16 0.67 0.2 0.67 0 0.5
8.3 16 0.56 0.4 0.33 0 1
11.7 19 0.89 0.4 0 0.5 1
9 25 0.89 0.7 0.67 0.5 0.5
10.8 23 0.78 0.6 1 0 0.5
10.4 10 0.33 0.3 0.33 0 0
12.7 14 0.78 0.2 0 0.5 0
11.8 26 0.89 0.7 0.67 0.5 1
13 24 0.89 0.6 0.33 0.5 1
10.8 24 1 0.4 1 0 1
12.3 18 0.67 0.3 0.67 0 1
11.3 23 1 0.5 0.67 0.5 0.5
11.6 23 0.89 0.4 0.67 1 0.5
10.9 19 0.78 0.2 0.67 1 1
12.1 21 1 0.5 0 0 0.5
13.3 18 0.78 0.4 0 0.5 0
10.1 27 1 0.6 0.67 1 1
14.3 13 0.67 0.4 0 0 0.5
9.3 28 1 0.8 0.67 1 0.5
12.5 23 0.78 0.8 0 0.5 1
7.6 21 0.67 0.3 1 0.5 1
9.2 19 0.89 0.4 0 0.5 1
14.5 17 0.56 0.4 1 0.5 0
12.3 25 0.89 0.8 0.33 0.5 1
12.6 14 0.78 0.3 0 0 0
13 16 1 0.4 0 0.5 0
12.6 24 1 0.6 0.67 0.5 0.5
13.2 20 0.89 0.4 0.33 0 0.5
7.7 24 0.78 0.8 0 1 1
10.5 22 0.89 0.6 0.33 1 1
10.9 22 0.78 0.5 0.67 0.5 1
4.3 20 0.78 0.4 0.33 0 1
10.3 10 0.33 0.3 0.67 0 0
11.4 22 0.89 0.4 1 0 1
5.6 20 0.67 0.4 0.33 0.5 1
8.8 22 0.78 0.5 0.33 0.5 1
9 20 0.89 0.6 0 0 1
9.6 17 0.78 0.4 0 0 0.5
6.4 18 0.89 0.3 0.67 0 1

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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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	'Gwilym Jenkins' @ jenkins.wessa.net

Multiple Linear Regression - Estimated Regression Equation
TOT[t] = + 9.09218 -0.111882NUMERACYTOT[t] + 4.02682Calculation[t] + 1.92185Algebraic_Reasoning[t] + 1.12516Proportionality_and_Ratio[t] + 0.311543Probability_and_Sampling[t] -1.36473Estimation[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TOT[t] =  +  9.09218 -0.111882NUMERACYTOT[t] +  4.02682Calculation[t] +  1.92185Algebraic_Reasoning[t] +  1.12516Proportionality_and_Ratio[t] +  0.311543Probability_and_Sampling[t] -1.36473Estimation[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TOT[t] =  +  9.09218 -0.111882NUMERACYTOT[t] +  4.02682Calculation[t] +  1.92185Algebraic_Reasoning[t] +  1.12516Proportionality_and_Ratio[t] +  0.311543Probability_and_Sampling[t] -1.36473Estimation[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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
TOT[t] = + 9.09218 -0.111882NUMERACYTOT[t] + 4.02682Calculation[t] + 1.92185Algebraic_Reasoning[t] + 1.12516Proportionality_and_Ratio[t] + 0.311543Probability_and_Sampling[t] -1.36473Estimation[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)	9.09218	1.78131	5.104	4.26801e-06	2.134e-06
NUMERACYTOT	-0.111882	0.238202	-0.4697	0.640431	0.320216
Calculation	4.02682	3.21707	1.252	0.215975	0.107987
Algebraic_Reasoning	1.92185	3.56617	0.5389	0.592123	0.296061
Proportionality_and_Ratio	1.12516	1.2642	0.89	0.377334	0.188667
Probability_and_Sampling	0.311543	1.039	0.2998	0.765423	0.382712
Estimation	-1.36473	0.995919	-1.37	0.176154	0.0880772

\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) & 9.09218 & 1.78131 & 5.104 & 4.26801e-06 & 2.134e-06 \tabularnewline
NUMERACYTOT & -0.111882 & 0.238202 & -0.4697 & 0.640431 & 0.320216 \tabularnewline
Calculation & 4.02682 & 3.21707 & 1.252 & 0.215975 & 0.107987 \tabularnewline
Algebraic_Reasoning & 1.92185 & 3.56617 & 0.5389 & 0.592123 & 0.296061 \tabularnewline
Proportionality_and_Ratio & 1.12516 & 1.2642 & 0.89 & 0.377334 & 0.188667 \tabularnewline
Probability_and_Sampling & 0.311543 & 1.039 & 0.2998 & 0.765423 & 0.382712 \tabularnewline
Estimation & -1.36473 & 0.995919 & -1.37 & 0.176154 & 0.0880772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&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]9.09218[/C][C]1.78131[/C][C]5.104[/C][C]4.26801e-06[/C][C]2.134e-06[/C][/ROW]
[ROW][C]NUMERACYTOT[/C][C]-0.111882[/C][C]0.238202[/C][C]-0.4697[/C][C]0.640431[/C][C]0.320216[/C][/ROW]
[ROW][C]Calculation[/C][C]4.02682[/C][C]3.21707[/C][C]1.252[/C][C]0.215975[/C][C]0.107987[/C][/ROW]
[ROW][C]Algebraic_Reasoning[/C][C]1.92185[/C][C]3.56617[/C][C]0.5389[/C][C]0.592123[/C][C]0.296061[/C][/ROW]
[ROW][C]Proportionality_and_Ratio[/C][C]1.12516[/C][C]1.2642[/C][C]0.89[/C][C]0.377334[/C][C]0.188667[/C][/ROW]
[ROW][C]Probability_and_Sampling[/C][C]0.311543[/C][C]1.039[/C][C]0.2998[/C][C]0.765423[/C][C]0.382712[/C][/ROW]
[ROW][C]Estimation[/C][C]-1.36473[/C][C]0.995919[/C][C]-1.37[/C][C]0.176154[/C][C]0.0880772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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)	9.09218	1.78131	5.104	4.26801e-06	2.134e-06
NUMERACYTOT	-0.111882	0.238202	-0.4697	0.640431	0.320216
Calculation	4.02682	3.21707	1.252	0.215975	0.107987
Algebraic_Reasoning	1.92185	3.56617	0.5389	0.592123	0.296061
Proportionality_and_Ratio	1.12516	1.2642	0.89	0.377334	0.188667
Probability_and_Sampling	0.311543	1.039	0.2998	0.765423	0.382712
Estimation	-1.36473	0.995919	-1.37	0.176154	0.0880772

Multiple Linear Regression - Regression Statistics
Multiple R	0.314829
R-squared	0.0991173
Adjusted R-squared	0.000839189
F-TEST (value)	1.00854
F-TEST (DF numerator)	6
F-TEST (DF denominator)	55
p-value	0.429333
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.41624
Sum Squared Residuals	321.101

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.314829 \tabularnewline
R-squared & 0.0991173 \tabularnewline
Adjusted R-squared & 0.000839189 \tabularnewline
F-TEST (value) & 1.00854 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 55 \tabularnewline
p-value & 0.429333 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.41624 \tabularnewline
Sum Squared Residuals & 321.101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.314829[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0991173[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.000839189[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.00854[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]55[/C][/ROW]
[ROW][C]p-value[/C][C]0.429333[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.41624[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]321.101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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	0.314829
R-squared	0.0991173
Adjusted R-squared	0.000839189
F-TEST (value)	1.00854
F-TEST (DF numerator)	6
F-TEST (DF denominator)	55
p-value	0.429333
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.41624
Sum Squared Residuals	321.101

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	12.9	11.8019	1.09811
2	12.8	10.3725	2.42749
3	7.4	11.6231	-4.2231
4	6.7	10.3949	-3.69487
5	12.6	10.9405	1.65953
6	14.8	12.1168	2.68323
7	13.3	11.127	2.173
8	11.1	11.8276	-0.727591
9	8.2	11.4877	-3.28771
10	11.4	12.2535	-0.853498
11	6.4	10.4126	-4.01264
12	12	10.7082	1.29184
13	6.3	11.9944	-5.6944
14	11.3	11.6459	-0.345864
15	11.9	11.0519	0.848143
16	9.3	9.94827	-0.648266
17	10	9.57451	0.425492
18	13.8	10.2624	3.53755
19	10.8	10.0433	0.75674
20	11.7	12.2897	-0.589692
21	10.9	9.79846	1.10154
22	16.1	11.0025	5.0975
23	9.9	10.6319	-0.731933
24	11.5	10.4559	1.0441
25	8.3	9.3324	-1.0324
26	11.7	10.1101	1.58993
27	9	11.4516	-2.45156
28	10.8	11.2557	-0.455717
29	10.4	10.2501	0.149935
30	12.7	11.2069	1.49311
31	11.8	10.6573	1.14269
32	13	10.3063	2.69366
33	10.8	10.963	-0.163001
34	12.3	9.74195	2.55805
35	11.3	11.7339	-0.4339
36	11.6	11.2545	0.345464
37	10.9	10.1924	0.70762
38	12.1	11.048	1.05196
39	13.3	11.1437	2.15627
40	10.1	10.952	-0.851965
41	14.3	10.4221	3.87794
42	9.3	11.9068	-2.60682
43	12.5	9.98833	2.51167
44	7.6	9.93338	-2.33338
45	9.2	10.1101	-0.910072
46	14.5	11.4949	3.00513
47	12.3	10.5788	1.72118
48	12.6	11.2433	1.3567
49	13	12.2534	0.746605
50	12.6	11.8142	0.785797
51	13.2	10.8961	2.30391
52	7.7	10.0322	-2.33222
53	10.5	10.6859	-0.18587
54	10.9	10.2775	0.622482
55	4.3	9.77077	-5.47077
56	10.3	10.6326	-0.33262
57	11.4	10.7438	0.656186
58	5.6	9.48359	-3.88359
59	8.8	9.89496	-1.09496
60	9	10.2268	-1.22679
61	9.6	10.4175	-0.817478
62	6.4	10.6279	-4.22785

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12.9 & 11.8019 & 1.09811 \tabularnewline
2 & 12.8 & 10.3725 & 2.42749 \tabularnewline
3 & 7.4 & 11.6231 & -4.2231 \tabularnewline
4 & 6.7 & 10.3949 & -3.69487 \tabularnewline
5 & 12.6 & 10.9405 & 1.65953 \tabularnewline
6 & 14.8 & 12.1168 & 2.68323 \tabularnewline
7 & 13.3 & 11.127 & 2.173 \tabularnewline
8 & 11.1 & 11.8276 & -0.727591 \tabularnewline
9 & 8.2 & 11.4877 & -3.28771 \tabularnewline
10 & 11.4 & 12.2535 & -0.853498 \tabularnewline
11 & 6.4 & 10.4126 & -4.01264 \tabularnewline
12 & 12 & 10.7082 & 1.29184 \tabularnewline
13 & 6.3 & 11.9944 & -5.6944 \tabularnewline
14 & 11.3 & 11.6459 & -0.345864 \tabularnewline
15 & 11.9 & 11.0519 & 0.848143 \tabularnewline
16 & 9.3 & 9.94827 & -0.648266 \tabularnewline
17 & 10 & 9.57451 & 0.425492 \tabularnewline
18 & 13.8 & 10.2624 & 3.53755 \tabularnewline
19 & 10.8 & 10.0433 & 0.75674 \tabularnewline
20 & 11.7 & 12.2897 & -0.589692 \tabularnewline
21 & 10.9 & 9.79846 & 1.10154 \tabularnewline
22 & 16.1 & 11.0025 & 5.0975 \tabularnewline
23 & 9.9 & 10.6319 & -0.731933 \tabularnewline
24 & 11.5 & 10.4559 & 1.0441 \tabularnewline
25 & 8.3 & 9.3324 & -1.0324 \tabularnewline
26 & 11.7 & 10.1101 & 1.58993 \tabularnewline
27 & 9 & 11.4516 & -2.45156 \tabularnewline
28 & 10.8 & 11.2557 & -0.455717 \tabularnewline
29 & 10.4 & 10.2501 & 0.149935 \tabularnewline
30 & 12.7 & 11.2069 & 1.49311 \tabularnewline
31 & 11.8 & 10.6573 & 1.14269 \tabularnewline
32 & 13 & 10.3063 & 2.69366 \tabularnewline
33 & 10.8 & 10.963 & -0.163001 \tabularnewline
34 & 12.3 & 9.74195 & 2.55805 \tabularnewline
35 & 11.3 & 11.7339 & -0.4339 \tabularnewline
36 & 11.6 & 11.2545 & 0.345464 \tabularnewline
37 & 10.9 & 10.1924 & 0.70762 \tabularnewline
38 & 12.1 & 11.048 & 1.05196 \tabularnewline
39 & 13.3 & 11.1437 & 2.15627 \tabularnewline
40 & 10.1 & 10.952 & -0.851965 \tabularnewline
41 & 14.3 & 10.4221 & 3.87794 \tabularnewline
42 & 9.3 & 11.9068 & -2.60682 \tabularnewline
43 & 12.5 & 9.98833 & 2.51167 \tabularnewline
44 & 7.6 & 9.93338 & -2.33338 \tabularnewline
45 & 9.2 & 10.1101 & -0.910072 \tabularnewline
46 & 14.5 & 11.4949 & 3.00513 \tabularnewline
47 & 12.3 & 10.5788 & 1.72118 \tabularnewline
48 & 12.6 & 11.2433 & 1.3567 \tabularnewline
49 & 13 & 12.2534 & 0.746605 \tabularnewline
50 & 12.6 & 11.8142 & 0.785797 \tabularnewline
51 & 13.2 & 10.8961 & 2.30391 \tabularnewline
52 & 7.7 & 10.0322 & -2.33222 \tabularnewline
53 & 10.5 & 10.6859 & -0.18587 \tabularnewline
54 & 10.9 & 10.2775 & 0.622482 \tabularnewline
55 & 4.3 & 9.77077 & -5.47077 \tabularnewline
56 & 10.3 & 10.6326 & -0.33262 \tabularnewline
57 & 11.4 & 10.7438 & 0.656186 \tabularnewline
58 & 5.6 & 9.48359 & -3.88359 \tabularnewline
59 & 8.8 & 9.89496 & -1.09496 \tabularnewline
60 & 9 & 10.2268 & -1.22679 \tabularnewline
61 & 9.6 & 10.4175 & -0.817478 \tabularnewline
62 & 6.4 & 10.6279 & -4.22785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&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]12.9[/C][C]11.8019[/C][C]1.09811[/C][/ROW]
[ROW][C]2[/C][C]12.8[/C][C]10.3725[/C][C]2.42749[/C][/ROW]
[ROW][C]3[/C][C]7.4[/C][C]11.6231[/C][C]-4.2231[/C][/ROW]
[ROW][C]4[/C][C]6.7[/C][C]10.3949[/C][C]-3.69487[/C][/ROW]
[ROW][C]5[/C][C]12.6[/C][C]10.9405[/C][C]1.65953[/C][/ROW]
[ROW][C]6[/C][C]14.8[/C][C]12.1168[/C][C]2.68323[/C][/ROW]
[ROW][C]7[/C][C]13.3[/C][C]11.127[/C][C]2.173[/C][/ROW]
[ROW][C]8[/C][C]11.1[/C][C]11.8276[/C][C]-0.727591[/C][/ROW]
[ROW][C]9[/C][C]8.2[/C][C]11.4877[/C][C]-3.28771[/C][/ROW]
[ROW][C]10[/C][C]11.4[/C][C]12.2535[/C][C]-0.853498[/C][/ROW]
[ROW][C]11[/C][C]6.4[/C][C]10.4126[/C][C]-4.01264[/C][/ROW]
[ROW][C]12[/C][C]12[/C][C]10.7082[/C][C]1.29184[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]11.9944[/C][C]-5.6944[/C][/ROW]
[ROW][C]14[/C][C]11.3[/C][C]11.6459[/C][C]-0.345864[/C][/ROW]
[ROW][C]15[/C][C]11.9[/C][C]11.0519[/C][C]0.848143[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]9.94827[/C][C]-0.648266[/C][/ROW]
[ROW][C]17[/C][C]10[/C][C]9.57451[/C][C]0.425492[/C][/ROW]
[ROW][C]18[/C][C]13.8[/C][C]10.2624[/C][C]3.53755[/C][/ROW]
[ROW][C]19[/C][C]10.8[/C][C]10.0433[/C][C]0.75674[/C][/ROW]
[ROW][C]20[/C][C]11.7[/C][C]12.2897[/C][C]-0.589692[/C][/ROW]
[ROW][C]21[/C][C]10.9[/C][C]9.79846[/C][C]1.10154[/C][/ROW]
[ROW][C]22[/C][C]16.1[/C][C]11.0025[/C][C]5.0975[/C][/ROW]
[ROW][C]23[/C][C]9.9[/C][C]10.6319[/C][C]-0.731933[/C][/ROW]
[ROW][C]24[/C][C]11.5[/C][C]10.4559[/C][C]1.0441[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]9.3324[/C][C]-1.0324[/C][/ROW]
[ROW][C]26[/C][C]11.7[/C][C]10.1101[/C][C]1.58993[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]11.4516[/C][C]-2.45156[/C][/ROW]
[ROW][C]28[/C][C]10.8[/C][C]11.2557[/C][C]-0.455717[/C][/ROW]
[ROW][C]29[/C][C]10.4[/C][C]10.2501[/C][C]0.149935[/C][/ROW]
[ROW][C]30[/C][C]12.7[/C][C]11.2069[/C][C]1.49311[/C][/ROW]
[ROW][C]31[/C][C]11.8[/C][C]10.6573[/C][C]1.14269[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]10.3063[/C][C]2.69366[/C][/ROW]
[ROW][C]33[/C][C]10.8[/C][C]10.963[/C][C]-0.163001[/C][/ROW]
[ROW][C]34[/C][C]12.3[/C][C]9.74195[/C][C]2.55805[/C][/ROW]
[ROW][C]35[/C][C]11.3[/C][C]11.7339[/C][C]-0.4339[/C][/ROW]
[ROW][C]36[/C][C]11.6[/C][C]11.2545[/C][C]0.345464[/C][/ROW]
[ROW][C]37[/C][C]10.9[/C][C]10.1924[/C][C]0.70762[/C][/ROW]
[ROW][C]38[/C][C]12.1[/C][C]11.048[/C][C]1.05196[/C][/ROW]
[ROW][C]39[/C][C]13.3[/C][C]11.1437[/C][C]2.15627[/C][/ROW]
[ROW][C]40[/C][C]10.1[/C][C]10.952[/C][C]-0.851965[/C][/ROW]
[ROW][C]41[/C][C]14.3[/C][C]10.4221[/C][C]3.87794[/C][/ROW]
[ROW][C]42[/C][C]9.3[/C][C]11.9068[/C][C]-2.60682[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]9.98833[/C][C]2.51167[/C][/ROW]
[ROW][C]44[/C][C]7.6[/C][C]9.93338[/C][C]-2.33338[/C][/ROW]
[ROW][C]45[/C][C]9.2[/C][C]10.1101[/C][C]-0.910072[/C][/ROW]
[ROW][C]46[/C][C]14.5[/C][C]11.4949[/C][C]3.00513[/C][/ROW]
[ROW][C]47[/C][C]12.3[/C][C]10.5788[/C][C]1.72118[/C][/ROW]
[ROW][C]48[/C][C]12.6[/C][C]11.2433[/C][C]1.3567[/C][/ROW]
[ROW][C]49[/C][C]13[/C][C]12.2534[/C][C]0.746605[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]11.8142[/C][C]0.785797[/C][/ROW]
[ROW][C]51[/C][C]13.2[/C][C]10.8961[/C][C]2.30391[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]10.0322[/C][C]-2.33222[/C][/ROW]
[ROW][C]53[/C][C]10.5[/C][C]10.6859[/C][C]-0.18587[/C][/ROW]
[ROW][C]54[/C][C]10.9[/C][C]10.2775[/C][C]0.622482[/C][/ROW]
[ROW][C]55[/C][C]4.3[/C][C]9.77077[/C][C]-5.47077[/C][/ROW]
[ROW][C]56[/C][C]10.3[/C][C]10.6326[/C][C]-0.33262[/C][/ROW]
[ROW][C]57[/C][C]11.4[/C][C]10.7438[/C][C]0.656186[/C][/ROW]
[ROW][C]58[/C][C]5.6[/C][C]9.48359[/C][C]-3.88359[/C][/ROW]
[ROW][C]59[/C][C]8.8[/C][C]9.89496[/C][C]-1.09496[/C][/ROW]
[ROW][C]60[/C][C]9[/C][C]10.2268[/C][C]-1.22679[/C][/ROW]
[ROW][C]61[/C][C]9.6[/C][C]10.4175[/C][C]-0.817478[/C][/ROW]
[ROW][C]62[/C][C]6.4[/C][C]10.6279[/C][C]-4.22785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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	12.9	11.8019	1.09811
2	12.8	10.3725	2.42749
3	7.4	11.6231	-4.2231
4	6.7	10.3949	-3.69487
5	12.6	10.9405	1.65953
6	14.8	12.1168	2.68323
7	13.3	11.127	2.173
8	11.1	11.8276	-0.727591
9	8.2	11.4877	-3.28771
10	11.4	12.2535	-0.853498
11	6.4	10.4126	-4.01264
12	12	10.7082	1.29184
13	6.3	11.9944	-5.6944
14	11.3	11.6459	-0.345864
15	11.9	11.0519	0.848143
16	9.3	9.94827	-0.648266
17	10	9.57451	0.425492
18	13.8	10.2624	3.53755
19	10.8	10.0433	0.75674
20	11.7	12.2897	-0.589692
21	10.9	9.79846	1.10154
22	16.1	11.0025	5.0975
23	9.9	10.6319	-0.731933
24	11.5	10.4559	1.0441
25	8.3	9.3324	-1.0324
26	11.7	10.1101	1.58993
27	9	11.4516	-2.45156
28	10.8	11.2557	-0.455717
29	10.4	10.2501	0.149935
30	12.7	11.2069	1.49311
31	11.8	10.6573	1.14269
32	13	10.3063	2.69366
33	10.8	10.963	-0.163001
34	12.3	9.74195	2.55805
35	11.3	11.7339	-0.4339
36	11.6	11.2545	0.345464
37	10.9	10.1924	0.70762
38	12.1	11.048	1.05196
39	13.3	11.1437	2.15627
40	10.1	10.952	-0.851965
41	14.3	10.4221	3.87794
42	9.3	11.9068	-2.60682
43	12.5	9.98833	2.51167
44	7.6	9.93338	-2.33338
45	9.2	10.1101	-0.910072
46	14.5	11.4949	3.00513
47	12.3	10.5788	1.72118
48	12.6	11.2433	1.3567
49	13	12.2534	0.746605
50	12.6	11.8142	0.785797
51	13.2	10.8961	2.30391
52	7.7	10.0322	-2.33222
53	10.5	10.6859	-0.18587
54	10.9	10.2775	0.622482
55	4.3	9.77077	-5.47077
56	10.3	10.6326	-0.33262
57	11.4	10.7438	0.656186
58	5.6	9.48359	-3.88359
59	8.8	9.89496	-1.09496
60	9	10.2268	-1.22679
61	9.6	10.4175	-0.817478
62	6.4	10.6279	-4.22785

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.709739	0.580523	0.290261
11	0.905148	0.189704	0.094852
12	0.848471	0.303058	0.151529
13	0.951209	0.097583	0.0487915
14	0.920003	0.159995	0.0799974
15	0.878059	0.243882	0.121941
16	0.851101	0.297797	0.148899
17	0.792279	0.415441	0.207721
18	0.862051	0.275897	0.137949
19	0.809119	0.381763	0.190881
20	0.75494	0.49012	0.24506
21	0.716641	0.566717	0.283359
22	0.904341	0.191318	0.0956592
23	0.910604	0.178793	0.0893964
24	0.875068	0.249863	0.124932
25	0.84221	0.31558	0.15779
26	0.808149	0.383703	0.191851
27	0.829819	0.340362	0.170181
28	0.780528	0.438944	0.219472
29	0.740823	0.518354	0.259177
30	0.701879	0.596242	0.298121
31	0.639262	0.721476	0.360738
32	0.662067	0.675866	0.337933
33	0.603812	0.792375	0.396188
34	0.657506	0.684989	0.342494
35	0.585238	0.829524	0.414762
36	0.512035	0.97593	0.487965
37	0.545692	0.908617	0.454308
38	0.470947	0.941894	0.529053
39	0.44638	0.892759	0.55362
40	0.398858	0.797717	0.601142
41	0.515271	0.969458	0.484729
42	0.803642	0.392716	0.196358
43	0.827011	0.345978	0.172989
44	0.785444	0.429112	0.214556
45	0.809506	0.380989	0.190494
46	0.762209	0.475582	0.237791
47	0.69035	0.619301	0.30965
48	0.609216	0.781569	0.390784
49	0.496228	0.992456	0.503772
50	0.753953	0.492095	0.246047
51	0.621777	0.756446	0.378223
52	0.844356	0.311289	0.155644

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.709739 & 0.580523 & 0.290261 \tabularnewline
11 & 0.905148 & 0.189704 & 0.094852 \tabularnewline
12 & 0.848471 & 0.303058 & 0.151529 \tabularnewline
13 & 0.951209 & 0.097583 & 0.0487915 \tabularnewline
14 & 0.920003 & 0.159995 & 0.0799974 \tabularnewline
15 & 0.878059 & 0.243882 & 0.121941 \tabularnewline
16 & 0.851101 & 0.297797 & 0.148899 \tabularnewline
17 & 0.792279 & 0.415441 & 0.207721 \tabularnewline
18 & 0.862051 & 0.275897 & 0.137949 \tabularnewline
19 & 0.809119 & 0.381763 & 0.190881 \tabularnewline
20 & 0.75494 & 0.49012 & 0.24506 \tabularnewline
21 & 0.716641 & 0.566717 & 0.283359 \tabularnewline
22 & 0.904341 & 0.191318 & 0.0956592 \tabularnewline
23 & 0.910604 & 0.178793 & 0.0893964 \tabularnewline
24 & 0.875068 & 0.249863 & 0.124932 \tabularnewline
25 & 0.84221 & 0.31558 & 0.15779 \tabularnewline
26 & 0.808149 & 0.383703 & 0.191851 \tabularnewline
27 & 0.829819 & 0.340362 & 0.170181 \tabularnewline
28 & 0.780528 & 0.438944 & 0.219472 \tabularnewline
29 & 0.740823 & 0.518354 & 0.259177 \tabularnewline
30 & 0.701879 & 0.596242 & 0.298121 \tabularnewline
31 & 0.639262 & 0.721476 & 0.360738 \tabularnewline
32 & 0.662067 & 0.675866 & 0.337933 \tabularnewline
33 & 0.603812 & 0.792375 & 0.396188 \tabularnewline
34 & 0.657506 & 0.684989 & 0.342494 \tabularnewline
35 & 0.585238 & 0.829524 & 0.414762 \tabularnewline
36 & 0.512035 & 0.97593 & 0.487965 \tabularnewline
37 & 0.545692 & 0.908617 & 0.454308 \tabularnewline
38 & 0.470947 & 0.941894 & 0.529053 \tabularnewline
39 & 0.44638 & 0.892759 & 0.55362 \tabularnewline
40 & 0.398858 & 0.797717 & 0.601142 \tabularnewline
41 & 0.515271 & 0.969458 & 0.484729 \tabularnewline
42 & 0.803642 & 0.392716 & 0.196358 \tabularnewline
43 & 0.827011 & 0.345978 & 0.172989 \tabularnewline
44 & 0.785444 & 0.429112 & 0.214556 \tabularnewline
45 & 0.809506 & 0.380989 & 0.190494 \tabularnewline
46 & 0.762209 & 0.475582 & 0.237791 \tabularnewline
47 & 0.69035 & 0.619301 & 0.30965 \tabularnewline
48 & 0.609216 & 0.781569 & 0.390784 \tabularnewline
49 & 0.496228 & 0.992456 & 0.503772 \tabularnewline
50 & 0.753953 & 0.492095 & 0.246047 \tabularnewline
51 & 0.621777 & 0.756446 & 0.378223 \tabularnewline
52 & 0.844356 & 0.311289 & 0.155644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&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]10[/C][C]0.709739[/C][C]0.580523[/C][C]0.290261[/C][/ROW]
[ROW][C]11[/C][C]0.905148[/C][C]0.189704[/C][C]0.094852[/C][/ROW]
[ROW][C]12[/C][C]0.848471[/C][C]0.303058[/C][C]0.151529[/C][/ROW]
[ROW][C]13[/C][C]0.951209[/C][C]0.097583[/C][C]0.0487915[/C][/ROW]
[ROW][C]14[/C][C]0.920003[/C][C]0.159995[/C][C]0.0799974[/C][/ROW]
[ROW][C]15[/C][C]0.878059[/C][C]0.243882[/C][C]0.121941[/C][/ROW]
[ROW][C]16[/C][C]0.851101[/C][C]0.297797[/C][C]0.148899[/C][/ROW]
[ROW][C]17[/C][C]0.792279[/C][C]0.415441[/C][C]0.207721[/C][/ROW]
[ROW][C]18[/C][C]0.862051[/C][C]0.275897[/C][C]0.137949[/C][/ROW]
[ROW][C]19[/C][C]0.809119[/C][C]0.381763[/C][C]0.190881[/C][/ROW]
[ROW][C]20[/C][C]0.75494[/C][C]0.49012[/C][C]0.24506[/C][/ROW]
[ROW][C]21[/C][C]0.716641[/C][C]0.566717[/C][C]0.283359[/C][/ROW]
[ROW][C]22[/C][C]0.904341[/C][C]0.191318[/C][C]0.0956592[/C][/ROW]
[ROW][C]23[/C][C]0.910604[/C][C]0.178793[/C][C]0.0893964[/C][/ROW]
[ROW][C]24[/C][C]0.875068[/C][C]0.249863[/C][C]0.124932[/C][/ROW]
[ROW][C]25[/C][C]0.84221[/C][C]0.31558[/C][C]0.15779[/C][/ROW]
[ROW][C]26[/C][C]0.808149[/C][C]0.383703[/C][C]0.191851[/C][/ROW]
[ROW][C]27[/C][C]0.829819[/C][C]0.340362[/C][C]0.170181[/C][/ROW]
[ROW][C]28[/C][C]0.780528[/C][C]0.438944[/C][C]0.219472[/C][/ROW]
[ROW][C]29[/C][C]0.740823[/C][C]0.518354[/C][C]0.259177[/C][/ROW]
[ROW][C]30[/C][C]0.701879[/C][C]0.596242[/C][C]0.298121[/C][/ROW]
[ROW][C]31[/C][C]0.639262[/C][C]0.721476[/C][C]0.360738[/C][/ROW]
[ROW][C]32[/C][C]0.662067[/C][C]0.675866[/C][C]0.337933[/C][/ROW]
[ROW][C]33[/C][C]0.603812[/C][C]0.792375[/C][C]0.396188[/C][/ROW]
[ROW][C]34[/C][C]0.657506[/C][C]0.684989[/C][C]0.342494[/C][/ROW]
[ROW][C]35[/C][C]0.585238[/C][C]0.829524[/C][C]0.414762[/C][/ROW]
[ROW][C]36[/C][C]0.512035[/C][C]0.97593[/C][C]0.487965[/C][/ROW]
[ROW][C]37[/C][C]0.545692[/C][C]0.908617[/C][C]0.454308[/C][/ROW]
[ROW][C]38[/C][C]0.470947[/C][C]0.941894[/C][C]0.529053[/C][/ROW]
[ROW][C]39[/C][C]0.44638[/C][C]0.892759[/C][C]0.55362[/C][/ROW]
[ROW][C]40[/C][C]0.398858[/C][C]0.797717[/C][C]0.601142[/C][/ROW]
[ROW][C]41[/C][C]0.515271[/C][C]0.969458[/C][C]0.484729[/C][/ROW]
[ROW][C]42[/C][C]0.803642[/C][C]0.392716[/C][C]0.196358[/C][/ROW]
[ROW][C]43[/C][C]0.827011[/C][C]0.345978[/C][C]0.172989[/C][/ROW]
[ROW][C]44[/C][C]0.785444[/C][C]0.429112[/C][C]0.214556[/C][/ROW]
[ROW][C]45[/C][C]0.809506[/C][C]0.380989[/C][C]0.190494[/C][/ROW]
[ROW][C]46[/C][C]0.762209[/C][C]0.475582[/C][C]0.237791[/C][/ROW]
[ROW][C]47[/C][C]0.69035[/C][C]0.619301[/C][C]0.30965[/C][/ROW]
[ROW][C]48[/C][C]0.609216[/C][C]0.781569[/C][C]0.390784[/C][/ROW]
[ROW][C]49[/C][C]0.496228[/C][C]0.992456[/C][C]0.503772[/C][/ROW]
[ROW][C]50[/C][C]0.753953[/C][C]0.492095[/C][C]0.246047[/C][/ROW]
[ROW][C]51[/C][C]0.621777[/C][C]0.756446[/C][C]0.378223[/C][/ROW]
[ROW][C]52[/C][C]0.844356[/C][C]0.311289[/C][C]0.155644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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
10	0.709739	0.580523	0.290261
11	0.905148	0.189704	0.094852
12	0.848471	0.303058	0.151529
13	0.951209	0.097583	0.0487915
14	0.920003	0.159995	0.0799974
15	0.878059	0.243882	0.121941
16	0.851101	0.297797	0.148899
17	0.792279	0.415441	0.207721
18	0.862051	0.275897	0.137949
19	0.809119	0.381763	0.190881
20	0.75494	0.49012	0.24506
21	0.716641	0.566717	0.283359
22	0.904341	0.191318	0.0956592
23	0.910604	0.178793	0.0893964
24	0.875068	0.249863	0.124932
25	0.84221	0.31558	0.15779
26	0.808149	0.383703	0.191851
27	0.829819	0.340362	0.170181
28	0.780528	0.438944	0.219472
29	0.740823	0.518354	0.259177
30	0.701879	0.596242	0.298121
31	0.639262	0.721476	0.360738
32	0.662067	0.675866	0.337933
33	0.603812	0.792375	0.396188
34	0.657506	0.684989	0.342494
35	0.585238	0.829524	0.414762
36	0.512035	0.97593	0.487965
37	0.545692	0.908617	0.454308
38	0.470947	0.941894	0.529053
39	0.44638	0.892759	0.55362
40	0.398858	0.797717	0.601142
41	0.515271	0.969458	0.484729
42	0.803642	0.392716	0.196358
43	0.827011	0.345978	0.172989
44	0.785444	0.429112	0.214556
45	0.809506	0.380989	0.190494
46	0.762209	0.475582	0.237791
47	0.69035	0.619301	0.30965
48	0.609216	0.781569	0.390784
49	0.496228	0.992456	0.503772
50	0.753953	0.492095	0.246047
51	0.621777	0.756446	0.378223
52	0.844356	0.311289	0.155644

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	1	0.0232558	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 & 1 & 0.0232558 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268789&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]1[/C][C]0.0232558[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268789&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268789&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	1	0.0232558	OK

Figure 1

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Figure 3

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Figure 4

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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 ;

Parameters (R input):

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

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

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$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$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
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, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
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,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
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,signif(numsignificant1/numgqtests,6))
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