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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 25 Jan 2017 10:02:27 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/25/t148533499569721q14zlz6kbs.htm/, Retrieved Tue, 14 May 2024 08:06:36 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 08:06:36 +0200

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6 1 0 0 0 3.2 10.24 3.2
 10.24
 10.89 0
7 0 1 0 1 3.3 9 3
 10.89
 12.25 0
2 0 1 1 1 3 13.69 3.7
 9
 7.29 0
11 0 1 0 1 3.5 12.96 3.6
 12.25
 12.25 0
13 0 1 0 0 3.7 14.44 3.8
 13.69
 11.56 0
3 1 0 0 0 2.7 13.69 3.7
 7.29
 12.25 0
17 0 1 1 1 3.6 7.84 2.8
 12.96
 14.44 0
10 0 1 0 1 3.5 18.49 4.3
 12.25
 10.89 0
4 1 0 0 0 3.8 12.96 3.6
 14.44
 12.96 0
12 0 1 0 0 3.4 10.89 3.3
 11.56
 7.84 0

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

7 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	7 seconds
R Server	Big Analytics Cloud Computing Center

Multiple Linear Regression - Estimated Regression Equation
Score[t] = + 17.8143 -0.723777X1[t] -0.237134X2[t] + 0.15164X3[t] -0.270505X4[t] -0.733979X5[t] -0.709882X6[t] -0.57851Inter[t] + 0.0647765t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Score[t] =  +  17.8143 -0.723777X1[t] -0.237134X2[t] +  0.15164X3[t] -0.270505X4[t] -0.733979X5[t] -0.709882X6[t] -0.57851Inter[t] +  0.0647765t  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Score[t] =  +  17.8143 -0.723777X1[t] -0.237134X2[t] +  0.15164X3[t] -0.270505X4[t] -0.733979X5[t] -0.709882X6[t] -0.57851Inter[t] +  0.0647765t  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Score[t] = + 17.8143 -0.723777X1[t] -0.237134X2[t] + 0.15164X3[t] -0.270505X4[t] -0.733979X5[t] -0.709882X6[t] -0.57851Inter[t] + 0.0647765t + 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)	+17.81	3.405	+5.2320e+00	3.474e-05	1.737e-05
X1	-0.7238	0.2278	-3.1770e+00	0.004536	0.002268
X2	-0.2371	0.1819	-1.3040e+00	0.2064	0.1032
X3	+0.1516	0.158	+9.5970e-01	0.3481	0.1741
X4	-0.2705	0.1499	-1.8040e+00	0.08555	0.04278
X5	-0.734	0.2134	-3.4400e+00	0.002459	0.001229
X6	-0.7099	0.2576	-2.7560e+00	0.01184	0.005922
Inter	-0.5785	0.2073	-2.7910e+00	0.01096	0.005478
t	+0.06478	0.07871	+8.2300e-01	0.4198	0.2099

\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) & +17.81 &  3.405 & +5.2320e+00 &  3.474e-05 &  1.737e-05 \tabularnewline
X1 & -0.7238 &  0.2278 & -3.1770e+00 &  0.004536 &  0.002268 \tabularnewline
X2 & -0.2371 &  0.1819 & -1.3040e+00 &  0.2064 &  0.1032 \tabularnewline
X3 & +0.1516 &  0.158 & +9.5970e-01 &  0.3481 &  0.1741 \tabularnewline
X4 & -0.2705 &  0.1499 & -1.8040e+00 &  0.08555 &  0.04278 \tabularnewline
X5 & -0.734 &  0.2134 & -3.4400e+00 &  0.002459 &  0.001229 \tabularnewline
X6 & -0.7099 &  0.2576 & -2.7560e+00 &  0.01184 &  0.005922 \tabularnewline
Inter & -0.5785 &  0.2073 & -2.7910e+00 &  0.01096 &  0.005478 \tabularnewline
t & +0.06478 &  0.07871 & +8.2300e-01 &  0.4198 &  0.2099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]+17.81[/C][C] 3.405[/C][C]+5.2320e+00[/C][C] 3.474e-05[/C][C] 1.737e-05[/C][/ROW]
[ROW][C]X1[/C][C]-0.7238[/C][C] 0.2278[/C][C]-3.1770e+00[/C][C] 0.004536[/C][C] 0.002268[/C][/ROW]
[ROW][C]X2[/C][C]-0.2371[/C][C] 0.1819[/C][C]-1.3040e+00[/C][C] 0.2064[/C][C] 0.1032[/C][/ROW]
[ROW][C]X3[/C][C]+0.1516[/C][C] 0.158[/C][C]+9.5970e-01[/C][C] 0.3481[/C][C] 0.1741[/C][/ROW]
[ROW][C]X4[/C][C]-0.2705[/C][C] 0.1499[/C][C]-1.8040e+00[/C][C] 0.08555[/C][C] 0.04278[/C][/ROW]
[ROW][C]X5[/C][C]-0.734[/C][C] 0.2134[/C][C]-3.4400e+00[/C][C] 0.002459[/C][C] 0.001229[/C][/ROW]
[ROW][C]X6[/C][C]-0.7099[/C][C] 0.2576[/C][C]-2.7560e+00[/C][C] 0.01184[/C][C] 0.005922[/C][/ROW]
[ROW][C]Inter[/C][C]-0.5785[/C][C] 0.2073[/C][C]-2.7910e+00[/C][C] 0.01096[/C][C] 0.005478[/C][/ROW]
[ROW][C]t[/C][C]+0.06478[/C][C] 0.07871[/C][C]+8.2300e-01[/C][C] 0.4198[/C][C] 0.2099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)	+17.81	3.405	+5.2320e+00	3.474e-05	1.737e-05
X1	-0.7238	0.2278	-3.1770e+00	0.004536	0.002268
X2	-0.2371	0.1819	-1.3040e+00	0.2064	0.1032
X3	+0.1516	0.158	+9.5970e-01	0.3481	0.1741
X4	-0.2705	0.1499	-1.8040e+00	0.08555	0.04278
X5	-0.734	0.2134	-3.4400e+00	0.002459	0.001229
X6	-0.7099	0.2576	-2.7560e+00	0.01184	0.005922
Inter	-0.5785	0.2073	-2.7910e+00	0.01096	0.005478
t	+0.06478	0.07871	+8.2300e-01	0.4198	0.2099

Multiple Linear Regression - Regression Statistics
Multiple R	0.8313
R-squared	0.6911
Adjusted R-squared	0.5734
F-TEST (value)	5.873
F-TEST (DF numerator)	8
F-TEST (DF denominator)	21
p-value	0.0005283
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.556
Sum Squared Residuals	265.6

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.8313 \tabularnewline
R-squared &  0.6911 \tabularnewline
Adjusted R-squared &  0.5734 \tabularnewline
F-TEST (value) &  5.873 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 21 \tabularnewline
p-value &  0.0005283 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  3.556 \tabularnewline
Sum Squared Residuals &  265.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.8313[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.6911[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.5734[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 5.873[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]21[/C][/ROW]
[ROW][C]p-value[/C][C] 0.0005283[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 3.556[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 265.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.8313
R-squared	0.6911
Adjusted R-squared	0.5734
F-TEST (value)	5.873
F-TEST (DF numerator)	8
F-TEST (DF denominator)	21
p-value	0.0005283
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.556
Sum Squared Residuals	265.6

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	6	5.686	0.3138
2	10.24	9.811	0.4291
3	3.3	7.701	-4.401
4	1	0.5422	0.4578
5	0	-0.3878	0.3878
6	3.6	2.205	1.395
7	0	-1.182	1.182
8	1	0.7101	0.2899
9	12.25	10.57	1.681
10	7.84	7.634	0.2064
11	0	1.892	-1.892
12	4	3.796	0.204
13	14.44	10.36	4.078
14	3.4	4.851	-1.451
15	0	0.5834	-0.5834
16	0	5.653	-5.653
17	3	6.299	-3.299
18	1	-0.02519	1.025
19	0	-1.629	1.629
20	12.25	13.62	-1.366
21	14.44	12.02	2.421
22	0	5.627	-5.627
23	17	9.121	7.879
24	12.96	9.122	3.838
25	3.5	0.5252	2.975
26	0	-3.821	3.821
27	0	2.316	-2.316
28	3.3	7.045	-3.745
29	0	0.6212	-0.6212
30	0	3.257	-3.257

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  6 &  5.686 &  0.3138 \tabularnewline
2 &  10.24 &  9.811 &  0.4291 \tabularnewline
3 &  3.3 &  7.701 & -4.401 \tabularnewline
4 &  1 &  0.5422 &  0.4578 \tabularnewline
5 &  0 & -0.3878 &  0.3878 \tabularnewline
6 &  3.6 &  2.205 &  1.395 \tabularnewline
7 &  0 & -1.182 &  1.182 \tabularnewline
8 &  1 &  0.7101 &  0.2899 \tabularnewline
9 &  12.25 &  10.57 &  1.681 \tabularnewline
10 &  7.84 &  7.634 &  0.2064 \tabularnewline
11 &  0 &  1.892 & -1.892 \tabularnewline
12 &  4 &  3.796 &  0.204 \tabularnewline
13 &  14.44 &  10.36 &  4.078 \tabularnewline
14 &  3.4 &  4.851 & -1.451 \tabularnewline
15 &  0 &  0.5834 & -0.5834 \tabularnewline
16 &  0 &  5.653 & -5.653 \tabularnewline
17 &  3 &  6.299 & -3.299 \tabularnewline
18 &  1 & -0.02519 &  1.025 \tabularnewline
19 &  0 & -1.629 &  1.629 \tabularnewline
20 &  12.25 &  13.62 & -1.366 \tabularnewline
21 &  14.44 &  12.02 &  2.421 \tabularnewline
22 &  0 &  5.627 & -5.627 \tabularnewline
23 &  17 &  9.121 &  7.879 \tabularnewline
24 &  12.96 &  9.122 &  3.838 \tabularnewline
25 &  3.5 &  0.5252 &  2.975 \tabularnewline
26 &  0 & -3.821 &  3.821 \tabularnewline
27 &  0 &  2.316 & -2.316 \tabularnewline
28 &  3.3 &  7.045 & -3.745 \tabularnewline
29 &  0 &  0.6212 & -0.6212 \tabularnewline
30 &  0 &  3.257 & -3.257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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] 6[/C][C] 5.686[/C][C] 0.3138[/C][/ROW]
[ROW][C]2[/C][C] 10.24[/C][C] 9.811[/C][C] 0.4291[/C][/ROW]
[ROW][C]3[/C][C] 3.3[/C][C] 7.701[/C][C]-4.401[/C][/ROW]
[ROW][C]4[/C][C] 1[/C][C] 0.5422[/C][C] 0.4578[/C][/ROW]
[ROW][C]5[/C][C] 0[/C][C]-0.3878[/C][C] 0.3878[/C][/ROW]
[ROW][C]6[/C][C] 3.6[/C][C] 2.205[/C][C] 1.395[/C][/ROW]
[ROW][C]7[/C][C] 0[/C][C]-1.182[/C][C] 1.182[/C][/ROW]
[ROW][C]8[/C][C] 1[/C][C] 0.7101[/C][C] 0.2899[/C][/ROW]
[ROW][C]9[/C][C] 12.25[/C][C] 10.57[/C][C] 1.681[/C][/ROW]
[ROW][C]10[/C][C] 7.84[/C][C] 7.634[/C][C] 0.2064[/C][/ROW]
[ROW][C]11[/C][C] 0[/C][C] 1.892[/C][C]-1.892[/C][/ROW]
[ROW][C]12[/C][C] 4[/C][C] 3.796[/C][C] 0.204[/C][/ROW]
[ROW][C]13[/C][C] 14.44[/C][C] 10.36[/C][C] 4.078[/C][/ROW]
[ROW][C]14[/C][C] 3.4[/C][C] 4.851[/C][C]-1.451[/C][/ROW]
[ROW][C]15[/C][C] 0[/C][C] 0.5834[/C][C]-0.5834[/C][/ROW]
[ROW][C]16[/C][C] 0[/C][C] 5.653[/C][C]-5.653[/C][/ROW]
[ROW][C]17[/C][C] 3[/C][C] 6.299[/C][C]-3.299[/C][/ROW]
[ROW][C]18[/C][C] 1[/C][C]-0.02519[/C][C] 1.025[/C][/ROW]
[ROW][C]19[/C][C] 0[/C][C]-1.629[/C][C] 1.629[/C][/ROW]
[ROW][C]20[/C][C] 12.25[/C][C] 13.62[/C][C]-1.366[/C][/ROW]
[ROW][C]21[/C][C] 14.44[/C][C] 12.02[/C][C] 2.421[/C][/ROW]
[ROW][C]22[/C][C] 0[/C][C] 5.627[/C][C]-5.627[/C][/ROW]
[ROW][C]23[/C][C] 17[/C][C] 9.121[/C][C] 7.879[/C][/ROW]
[ROW][C]24[/C][C] 12.96[/C][C] 9.122[/C][C] 3.838[/C][/ROW]
[ROW][C]25[/C][C] 3.5[/C][C] 0.5252[/C][C] 2.975[/C][/ROW]
[ROW][C]26[/C][C] 0[/C][C]-3.821[/C][C] 3.821[/C][/ROW]
[ROW][C]27[/C][C] 0[/C][C] 2.316[/C][C]-2.316[/C][/ROW]
[ROW][C]28[/C][C] 3.3[/C][C] 7.045[/C][C]-3.745[/C][/ROW]
[ROW][C]29[/C][C] 0[/C][C] 0.6212[/C][C]-0.6212[/C][/ROW]
[ROW][C]30[/C][C] 0[/C][C] 3.257[/C][C]-3.257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	6	5.686	0.3138
2	10.24	9.811	0.4291
3	3.3	7.701	-4.401
4	1	0.5422	0.4578
5	0	-0.3878	0.3878
6	3.6	2.205	1.395
7	0	-1.182	1.182
8	1	0.7101	0.2899
9	12.25	10.57	1.681
10	7.84	7.634	0.2064
11	0	1.892	-1.892
12	4	3.796	0.204
13	14.44	10.36	4.078
14	3.4	4.851	-1.451
15	0	0.5834	-0.5834
16	0	5.653	-5.653
17	3	6.299	-3.299
18	1	-0.02519	1.025
19	0	-1.629	1.629
20	12.25	13.62	-1.366
21	14.44	12.02	2.421
22	0	5.627	-5.627
23	17	9.121	7.879
24	12.96	9.122	3.838
25	3.5	0.5252	2.975
26	0	-3.821	3.821
27	0	2.316	-2.316
28	3.3	7.045	-3.745
29	0	0.6212	-0.6212
30	0	3.257	-3.257

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.05486	0.1097	0.9451
13	0.07872	0.1574	0.9213
14	0.03882	0.07764	0.9612
15	0.01422	0.02845	0.9858
16	0.1338	0.2676	0.8662
17	0.08841	0.1768	0.9116
18	0.03917	0.07834	0.9608

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 &  0.05486 &  0.1097 &  0.9451 \tabularnewline
13 &  0.07872 &  0.1574 &  0.9213 \tabularnewline
14 &  0.03882 &  0.07764 &  0.9612 \tabularnewline
15 &  0.01422 &  0.02845 &  0.9858 \tabularnewline
16 &  0.1338 &  0.2676 &  0.8662 \tabularnewline
17 &  0.08841 &  0.1768 &  0.9116 \tabularnewline
18 &  0.03917 &  0.07834 &  0.9608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]12[/C][C] 0.05486[/C][C] 0.1097[/C][C] 0.9451[/C][/ROW]
[ROW][C]13[/C][C] 0.07872[/C][C] 0.1574[/C][C] 0.9213[/C][/ROW]
[ROW][C]14[/C][C] 0.03882[/C][C] 0.07764[/C][C] 0.9612[/C][/ROW]
[ROW][C]15[/C][C] 0.01422[/C][C] 0.02845[/C][C] 0.9858[/C][/ROW]
[ROW][C]16[/C][C] 0.1338[/C][C] 0.2676[/C][C] 0.8662[/C][/ROW]
[ROW][C]17[/C][C] 0.08841[/C][C] 0.1768[/C][C] 0.9116[/C][/ROW]
[ROW][C]18[/C][C] 0.03917[/C][C] 0.07834[/C][C] 0.9608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
12	0.05486	0.1097	0.9451
13	0.07872	0.1574	0.9213
14	0.03882	0.07764	0.9612
15	0.01422	0.02845	0.9858
16	0.1338	0.2676	0.8662
17	0.08841	0.1768	0.9116
18	0.03917	0.07834	0.9608

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	1	0.142857	NOK
10% type I error level	3	0.428571	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 &  0 & OK \tabularnewline
5% type I error level & 1 & 0.142857 & NOK \tabularnewline
10% type I error level & 3 & 0.428571 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1[/C][C]0.142857[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.428571[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1	0.142857	NOK
10% type I error level	3	0.428571	NOK

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 4.6131, df1 = 2, df2 = 19, p-value = 0.02328
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 2.4436, df1 = 16, df2 = 5, p-value = 0.1646
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 0.37319, df1 = 2, df2 = 19, p-value = 0.6935

\begin{tabular}{lllllllll}
\hline
Ramsey RESET F-Test for powers (2 and 3) of fitted values \tabularnewline
> reset_test_fitted
	RESET test
data:  mylm
RESET = 4.6131, df1 = 2, df2 = 19, p-value = 0.02328
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 2.4436, df1 = 16, df2 = 5, p-value = 0.1646
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.37319, df1 = 2, df2 = 19, p-value = 0.6935
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=7

[TABLE]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of fitted values[/C][/ROW]
[ROW][C]> reset_test_fitted
	RESET test
data:  mylm
RESET = 4.6131, df1 = 2, df2 = 19, p-value = 0.02328
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of regressors[/C][/ROW]
[ROW][C]> reset_test_regressors
	RESET test
data:  mylm
RESET = 2.4436, df1 = 16, df2 = 5, p-value = 0.1646
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of principal components[/C][/ROW]
[ROW][C]> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.37319, df1 = 2, df2 = 19, p-value = 0.6935
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=7

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=7

As an alternative you can also use a QR Code:

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

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 4.6131, df1 = 2, df2 = 19, p-value = 0.02328
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 2.4436, df1 = 16, df2 = 5, p-value = 0.1646
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 0.37319, df1 = 2, df2 = 19, p-value = 0.6935

Variance Inflation Factors (Multicollinearity)
> vif X1 X2 X3 X4 X5 X6 Inter t 3.770139 2.677418 1.794140 1.356450 2.181962 3.211522 2.154097 1.100910

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
      X1       X2       X3       X4       X5       X6    Inter        t 
3.770139 2.677418 1.794140 1.356450 2.181962 3.211522 2.154097 1.100910 
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=8

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]> vif
      X1       X2       X3       X4       X5       X6    Inter        t 
3.770139 2.677418 1.794140 1.356450 2.181962 3.211522 2.154097 1.100910 
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=8

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=8

As an alternative you can also use a QR Code:

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

Variance Inflation Factors (Multicollinearity)
> vif X1 X2 X3 X4 X5 X6 Inter t 3.770139 2.677418 1.794140 1.356450 2.181962 3.211522 2.154097 1.100910

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Parameters (Session):

par1 = pearson111111111 ; par2 = 22Do not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal Dummies ; par3 = 0.993Linear TrendLinear TrendLinear TrendLinear TrendLinear TrendLinear TrendLinear Trend ; par4 = two.sidedTRUE ; par5 = unpaired ; par6 = 0 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; par4 = ; par5 = ;

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

library(lattice)
library(lmtest)
library(car)
library(MASS)
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'
}
print(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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
sresid <- studres(mylm)
hist(sresid, freq=FALSE, main='Distribution of Studentized Residuals')
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqPlot(mylm, main='QQ Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
print(z)
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$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,'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')
myr <- as.numeric(mysum$resid)
myr
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$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')
}
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of fitted values',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_fitted <- resettest(mylm,power=2:3,type='fitted')
a<-table.element(a,paste('',RC.texteval('reset_test_fitted'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of regressors',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_regressors <- resettest(mylm,power=2:3,type='regressor')
a<-table.element(a,paste('',RC.texteval('reset_test_regressors'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of principal components',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_principal_components <- resettest(mylm,power=2:3,type='princomp')
a<-table.element(a,paste('',RC.texteval('reset_test_principal_components'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable8.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Inflation Factors (Multicollinearity)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
vif <- vif(mylm)
a<-table.element(a,paste('',RC.texteval('vif'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable9.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code