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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 12 Dec 2015 18:58:57 +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/12/t1449946780cffzu4z7oluggty.htm/, Retrieved Thu, 16 May 2024 16:02:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286123, Retrieved Thu, 16 May 2024 16:02:50 +0000

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-       [Multiple Regression] [paper 2015] [2015-12-12 18:58:57] [0bc733fc2a9ea67d386d32f0905574d4] [Current]

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-27 1.9
-29 2
-33 2
-27 1.8
-22 1.6
-23 1.4
-23 0.2
-15 0.3
-15 0.4
-24 0.7
-18 1
-14 1.1
-7 0.8
-12 0.8
-12 1
-15 1.1
-16 1
-17 0.8
-13 1.6
-8 1.5
-13 1.6
-13 1.6
-11 1.6
-16 1.9
-5 2
-3 1.9
-7 2
-10 2.1
-10 2.3
-11 2.3
-11 2.6
-19 2.6
-30 2.7
-38 2.6
-36 2.6
-40 2.4
-34 2.5
-35 2.5
-38 2.5
-32 2.4
-37 2.1
-39 2.1
-31 2.3
-30 2.3
-29 2.3
-36 2.9
-41 2.8
-42 2.9
-33 3
-43 3
-41 2.9
-34 2.6
-32 2.8
-36 2.9
-37 3.1
-30 2.8
-32 2.4
-30 1.6
-21 1.5
-19 1.7
-9 1.4
-8 1.1
-6 0.8
-4 1.2
-1 0.8
-2 0.9
-1 0.9
-4 1
-8 0.9
-6 1.1
-11 1
-11 0.7

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=286123&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=286123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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
Consumentenvertrouwen[t] = -0.821427 -11.3271Inflatie[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
Consumentenvertrouwen[t] =  -0.821427 -11.3271Inflatie[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=286123&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Consumentenvertrouwen[t] =  -0.821427 -11.3271Inflatie[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=286123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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
Consumentenvertrouwen[t] = -0.821427 -11.3271Inflatie[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)	-0.8214	2.645	-3.1050e-01	0.7571	0.3785
Inflatie	-11.33	1.35	-8.3910e+00	3.474e-12	1.737e-12

\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) & -0.8214 &  2.645 & -3.1050e-01 &  0.7571 &  0.3785 \tabularnewline
Inflatie & -11.33 &  1.35 & -8.3910e+00 &  3.474e-12 &  1.737e-12 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286123&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]-0.8214[/C][C] 2.645[/C][C]-3.1050e-01[/C][C] 0.7571[/C][C] 0.3785[/C][/ROW]
[ROW][C]Inflatie[/C][C]-11.33[/C][C] 1.35[/C][C]-8.3910e+00[/C][C] 3.474e-12[/C][C] 1.737e-12[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286123&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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)	-0.8214	2.645	-3.1050e-01	0.7571	0.3785
Inflatie	-11.33	1.35	-8.3910e+00	3.474e-12	1.737e-12

Multiple Linear Regression - Regression Statistics
Multiple R	0.7082
R-squared	0.5015
Adjusted R-squared	0.4944
F-TEST (value)	70.42
F-TEST (DF numerator)	1
F-TEST (DF denominator)	70
p-value	3.474e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	8.91
Sum Squared Residuals	5557

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.7082 \tabularnewline
R-squared &  0.5015 \tabularnewline
Adjusted R-squared &  0.4944 \tabularnewline
F-TEST (value) &  70.42 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 70 \tabularnewline
p-value &  3.474e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  8.91 \tabularnewline
Sum Squared Residuals &  5557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286123&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.7082[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.5015[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.4944[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 70.42[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]70[/C][/ROW]
[ROW][C]p-value[/C][C] 3.474e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 8.91[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 5557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286123&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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	0.7082
R-squared	0.5015
Adjusted R-squared	0.4944
F-TEST (value)	70.42
F-TEST (DF numerator)	1
F-TEST (DF denominator)	70
p-value	3.474e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	8.91
Sum Squared Residuals	5557

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	-27	-22.34	-4.657
2	-29	-23.48	-5.524
3	-33	-23.48	-9.524
4	-27	-21.21	-5.79
5	-22	-18.94	-3.055
6	-23	-16.68	-6.321
7	-23	-3.087	-19.91
8	-15	-4.22	-10.78
9	-15	-5.352	-9.648
10	-24	-8.75	-15.25
11	-18	-12.15	-5.851
12	-14	-13.28	-0.7188
13	-7	-9.883	2.883
14	-12	-9.883	-2.117
15	-12	-12.15	0.1485
16	-15	-13.28	-1.719
17	-16	-12.15	-3.851
18	-17	-9.883	-7.117
19	-13	-18.94	5.945
20	-8	-17.81	9.812
21	-13	-18.94	5.945
22	-13	-18.94	5.945
23	-11	-18.94	7.945
24	-16	-22.34	6.343
25	-5	-23.48	18.48
26	-3	-22.34	19.34
27	-7	-23.48	16.48
28	-10	-24.61	14.61
29	-10	-26.87	16.87
30	-11	-26.87	15.87
31	-11	-30.27	19.27
32	-19	-30.27	11.27
33	-30	-31.4	1.405
34	-38	-30.27	-7.728
35	-36	-30.27	-5.728
36	-40	-28.01	-11.99
37	-34	-29.14	-4.861
38	-35	-29.14	-5.861
39	-38	-29.14	-8.861
40	-32	-28.01	-3.994
41	-37	-24.61	-12.39
42	-39	-24.61	-14.39
43	-31	-26.87	-4.126
44	-30	-26.87	-3.126
45	-29	-26.87	-2.126
46	-36	-33.67	-2.33
47	-41	-32.54	-8.463
48	-42	-33.67	-8.33
49	-33	-34.8	1.803
50	-43	-34.8	-8.197
51	-41	-33.67	-7.33
52	-34	-30.27	-3.728
53	-32	-32.54	0.5373
54	-36	-33.67	-2.33
55	-37	-35.94	-1.065
56	-30	-32.54	2.537
57	-32	-28.01	-3.994
58	-30	-18.94	-11.06
59	-21	-17.81	-3.188
60	-19	-20.08	1.077
61	-9	-16.68	7.679
62	-8	-13.28	5.281
63	-6	-9.883	3.883
64	-4	-14.41	10.41
65	-1	-9.883	8.883
66	-2	-11.02	9.016
67	-1	-11.02	10.02
68	-4	-12.15	8.149
69	-8	-11.02	3.016
70	-6	-13.28	7.281
71	-11	-12.15	1.149
72	-11	-8.75	-2.25

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -27 & -22.34 & -4.657 \tabularnewline
2 & -29 & -23.48 & -5.524 \tabularnewline
3 & -33 & -23.48 & -9.524 \tabularnewline
4 & -27 & -21.21 & -5.79 \tabularnewline
5 & -22 & -18.94 & -3.055 \tabularnewline
6 & -23 & -16.68 & -6.321 \tabularnewline
7 & -23 & -3.087 & -19.91 \tabularnewline
8 & -15 & -4.22 & -10.78 \tabularnewline
9 & -15 & -5.352 & -9.648 \tabularnewline
10 & -24 & -8.75 & -15.25 \tabularnewline
11 & -18 & -12.15 & -5.851 \tabularnewline
12 & -14 & -13.28 & -0.7188 \tabularnewline
13 & -7 & -9.883 &  2.883 \tabularnewline
14 & -12 & -9.883 & -2.117 \tabularnewline
15 & -12 & -12.15 &  0.1485 \tabularnewline
16 & -15 & -13.28 & -1.719 \tabularnewline
17 & -16 & -12.15 & -3.851 \tabularnewline
18 & -17 & -9.883 & -7.117 \tabularnewline
19 & -13 & -18.94 &  5.945 \tabularnewline
20 & -8 & -17.81 &  9.812 \tabularnewline
21 & -13 & -18.94 &  5.945 \tabularnewline
22 & -13 & -18.94 &  5.945 \tabularnewline
23 & -11 & -18.94 &  7.945 \tabularnewline
24 & -16 & -22.34 &  6.343 \tabularnewline
25 & -5 & -23.48 &  18.48 \tabularnewline
26 & -3 & -22.34 &  19.34 \tabularnewline
27 & -7 & -23.48 &  16.48 \tabularnewline
28 & -10 & -24.61 &  14.61 \tabularnewline
29 & -10 & -26.87 &  16.87 \tabularnewline
30 & -11 & -26.87 &  15.87 \tabularnewline
31 & -11 & -30.27 &  19.27 \tabularnewline
32 & -19 & -30.27 &  11.27 \tabularnewline
33 & -30 & -31.4 &  1.405 \tabularnewline
34 & -38 & -30.27 & -7.728 \tabularnewline
35 & -36 & -30.27 & -5.728 \tabularnewline
36 & -40 & -28.01 & -11.99 \tabularnewline
37 & -34 & -29.14 & -4.861 \tabularnewline
38 & -35 & -29.14 & -5.861 \tabularnewline
39 & -38 & -29.14 & -8.861 \tabularnewline
40 & -32 & -28.01 & -3.994 \tabularnewline
41 & -37 & -24.61 & -12.39 \tabularnewline
42 & -39 & -24.61 & -14.39 \tabularnewline
43 & -31 & -26.87 & -4.126 \tabularnewline
44 & -30 & -26.87 & -3.126 \tabularnewline
45 & -29 & -26.87 & -2.126 \tabularnewline
46 & -36 & -33.67 & -2.33 \tabularnewline
47 & -41 & -32.54 & -8.463 \tabularnewline
48 & -42 & -33.67 & -8.33 \tabularnewline
49 & -33 & -34.8 &  1.803 \tabularnewline
50 & -43 & -34.8 & -8.197 \tabularnewline
51 & -41 & -33.67 & -7.33 \tabularnewline
52 & -34 & -30.27 & -3.728 \tabularnewline
53 & -32 & -32.54 &  0.5373 \tabularnewline
54 & -36 & -33.67 & -2.33 \tabularnewline
55 & -37 & -35.94 & -1.065 \tabularnewline
56 & -30 & -32.54 &  2.537 \tabularnewline
57 & -32 & -28.01 & -3.994 \tabularnewline
58 & -30 & -18.94 & -11.06 \tabularnewline
59 & -21 & -17.81 & -3.188 \tabularnewline
60 & -19 & -20.08 &  1.077 \tabularnewline
61 & -9 & -16.68 &  7.679 \tabularnewline
62 & -8 & -13.28 &  5.281 \tabularnewline
63 & -6 & -9.883 &  3.883 \tabularnewline
64 & -4 & -14.41 &  10.41 \tabularnewline
65 & -1 & -9.883 &  8.883 \tabularnewline
66 & -2 & -11.02 &  9.016 \tabularnewline
67 & -1 & -11.02 &  10.02 \tabularnewline
68 & -4 & -12.15 &  8.149 \tabularnewline
69 & -8 & -11.02 &  3.016 \tabularnewline
70 & -6 & -13.28 &  7.281 \tabularnewline
71 & -11 & -12.15 &  1.149 \tabularnewline
72 & -11 & -8.75 & -2.25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286123&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]-27[/C][C]-22.34[/C][C]-4.657[/C][/ROW]
[ROW][C]2[/C][C]-29[/C][C]-23.48[/C][C]-5.524[/C][/ROW]
[ROW][C]3[/C][C]-33[/C][C]-23.48[/C][C]-9.524[/C][/ROW]
[ROW][C]4[/C][C]-27[/C][C]-21.21[/C][C]-5.79[/C][/ROW]
[ROW][C]5[/C][C]-22[/C][C]-18.94[/C][C]-3.055[/C][/ROW]
[ROW][C]6[/C][C]-23[/C][C]-16.68[/C][C]-6.321[/C][/ROW]
[ROW][C]7[/C][C]-23[/C][C]-3.087[/C][C]-19.91[/C][/ROW]
[ROW][C]8[/C][C]-15[/C][C]-4.22[/C][C]-10.78[/C][/ROW]
[ROW][C]9[/C][C]-15[/C][C]-5.352[/C][C]-9.648[/C][/ROW]
[ROW][C]10[/C][C]-24[/C][C]-8.75[/C][C]-15.25[/C][/ROW]
[ROW][C]11[/C][C]-18[/C][C]-12.15[/C][C]-5.851[/C][/ROW]
[ROW][C]12[/C][C]-14[/C][C]-13.28[/C][C]-0.7188[/C][/ROW]
[ROW][C]13[/C][C]-7[/C][C]-9.883[/C][C] 2.883[/C][/ROW]
[ROW][C]14[/C][C]-12[/C][C]-9.883[/C][C]-2.117[/C][/ROW]
[ROW][C]15[/C][C]-12[/C][C]-12.15[/C][C] 0.1485[/C][/ROW]
[ROW][C]16[/C][C]-15[/C][C]-13.28[/C][C]-1.719[/C][/ROW]
[ROW][C]17[/C][C]-16[/C][C]-12.15[/C][C]-3.851[/C][/ROW]
[ROW][C]18[/C][C]-17[/C][C]-9.883[/C][C]-7.117[/C][/ROW]
[ROW][C]19[/C][C]-13[/C][C]-18.94[/C][C] 5.945[/C][/ROW]
[ROW][C]20[/C][C]-8[/C][C]-17.81[/C][C] 9.812[/C][/ROW]
[ROW][C]21[/C][C]-13[/C][C]-18.94[/C][C] 5.945[/C][/ROW]
[ROW][C]22[/C][C]-13[/C][C]-18.94[/C][C] 5.945[/C][/ROW]
[ROW][C]23[/C][C]-11[/C][C]-18.94[/C][C] 7.945[/C][/ROW]
[ROW][C]24[/C][C]-16[/C][C]-22.34[/C][C] 6.343[/C][/ROW]
[ROW][C]25[/C][C]-5[/C][C]-23.48[/C][C] 18.48[/C][/ROW]
[ROW][C]26[/C][C]-3[/C][C]-22.34[/C][C] 19.34[/C][/ROW]
[ROW][C]27[/C][C]-7[/C][C]-23.48[/C][C] 16.48[/C][/ROW]
[ROW][C]28[/C][C]-10[/C][C]-24.61[/C][C] 14.61[/C][/ROW]
[ROW][C]29[/C][C]-10[/C][C]-26.87[/C][C] 16.87[/C][/ROW]
[ROW][C]30[/C][C]-11[/C][C]-26.87[/C][C] 15.87[/C][/ROW]
[ROW][C]31[/C][C]-11[/C][C]-30.27[/C][C] 19.27[/C][/ROW]
[ROW][C]32[/C][C]-19[/C][C]-30.27[/C][C] 11.27[/C][/ROW]
[ROW][C]33[/C][C]-30[/C][C]-31.4[/C][C] 1.405[/C][/ROW]
[ROW][C]34[/C][C]-38[/C][C]-30.27[/C][C]-7.728[/C][/ROW]
[ROW][C]35[/C][C]-36[/C][C]-30.27[/C][C]-5.728[/C][/ROW]
[ROW][C]36[/C][C]-40[/C][C]-28.01[/C][C]-11.99[/C][/ROW]
[ROW][C]37[/C][C]-34[/C][C]-29.14[/C][C]-4.861[/C][/ROW]
[ROW][C]38[/C][C]-35[/C][C]-29.14[/C][C]-5.861[/C][/ROW]
[ROW][C]39[/C][C]-38[/C][C]-29.14[/C][C]-8.861[/C][/ROW]
[ROW][C]40[/C][C]-32[/C][C]-28.01[/C][C]-3.994[/C][/ROW]
[ROW][C]41[/C][C]-37[/C][C]-24.61[/C][C]-12.39[/C][/ROW]
[ROW][C]42[/C][C]-39[/C][C]-24.61[/C][C]-14.39[/C][/ROW]
[ROW][C]43[/C][C]-31[/C][C]-26.87[/C][C]-4.126[/C][/ROW]
[ROW][C]44[/C][C]-30[/C][C]-26.87[/C][C]-3.126[/C][/ROW]
[ROW][C]45[/C][C]-29[/C][C]-26.87[/C][C]-2.126[/C][/ROW]
[ROW][C]46[/C][C]-36[/C][C]-33.67[/C][C]-2.33[/C][/ROW]
[ROW][C]47[/C][C]-41[/C][C]-32.54[/C][C]-8.463[/C][/ROW]
[ROW][C]48[/C][C]-42[/C][C]-33.67[/C][C]-8.33[/C][/ROW]
[ROW][C]49[/C][C]-33[/C][C]-34.8[/C][C] 1.803[/C][/ROW]
[ROW][C]50[/C][C]-43[/C][C]-34.8[/C][C]-8.197[/C][/ROW]
[ROW][C]51[/C][C]-41[/C][C]-33.67[/C][C]-7.33[/C][/ROW]
[ROW][C]52[/C][C]-34[/C][C]-30.27[/C][C]-3.728[/C][/ROW]
[ROW][C]53[/C][C]-32[/C][C]-32.54[/C][C] 0.5373[/C][/ROW]
[ROW][C]54[/C][C]-36[/C][C]-33.67[/C][C]-2.33[/C][/ROW]
[ROW][C]55[/C][C]-37[/C][C]-35.94[/C][C]-1.065[/C][/ROW]
[ROW][C]56[/C][C]-30[/C][C]-32.54[/C][C] 2.537[/C][/ROW]
[ROW][C]57[/C][C]-32[/C][C]-28.01[/C][C]-3.994[/C][/ROW]
[ROW][C]58[/C][C]-30[/C][C]-18.94[/C][C]-11.06[/C][/ROW]
[ROW][C]59[/C][C]-21[/C][C]-17.81[/C][C]-3.188[/C][/ROW]
[ROW][C]60[/C][C]-19[/C][C]-20.08[/C][C] 1.077[/C][/ROW]
[ROW][C]61[/C][C]-9[/C][C]-16.68[/C][C] 7.679[/C][/ROW]
[ROW][C]62[/C][C]-8[/C][C]-13.28[/C][C] 5.281[/C][/ROW]
[ROW][C]63[/C][C]-6[/C][C]-9.883[/C][C] 3.883[/C][/ROW]
[ROW][C]64[/C][C]-4[/C][C]-14.41[/C][C] 10.41[/C][/ROW]
[ROW][C]65[/C][C]-1[/C][C]-9.883[/C][C] 8.883[/C][/ROW]
[ROW][C]66[/C][C]-2[/C][C]-11.02[/C][C] 9.016[/C][/ROW]
[ROW][C]67[/C][C]-1[/C][C]-11.02[/C][C] 10.02[/C][/ROW]
[ROW][C]68[/C][C]-4[/C][C]-12.15[/C][C] 8.149[/C][/ROW]
[ROW][C]69[/C][C]-8[/C][C]-11.02[/C][C] 3.016[/C][/ROW]
[ROW][C]70[/C][C]-6[/C][C]-13.28[/C][C] 7.281[/C][/ROW]
[ROW][C]71[/C][C]-11[/C][C]-12.15[/C][C] 1.149[/C][/ROW]
[ROW][C]72[/C][C]-11[/C][C]-8.75[/C][C]-2.25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286123&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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	-27	-22.34	-4.657
2	-29	-23.48	-5.524
3	-33	-23.48	-9.524
4	-27	-21.21	-5.79
5	-22	-18.94	-3.055
6	-23	-16.68	-6.321
7	-23	-3.087	-19.91
8	-15	-4.22	-10.78
9	-15	-5.352	-9.648
10	-24	-8.75	-15.25
11	-18	-12.15	-5.851
12	-14	-13.28	-0.7188
13	-7	-9.883	2.883
14	-12	-9.883	-2.117
15	-12	-12.15	0.1485
16	-15	-13.28	-1.719
17	-16	-12.15	-3.851
18	-17	-9.883	-7.117
19	-13	-18.94	5.945
20	-8	-17.81	9.812
21	-13	-18.94	5.945
22	-13	-18.94	5.945
23	-11	-18.94	7.945
24	-16	-22.34	6.343
25	-5	-23.48	18.48
26	-3	-22.34	19.34
27	-7	-23.48	16.48
28	-10	-24.61	14.61
29	-10	-26.87	16.87
30	-11	-26.87	15.87
31	-11	-30.27	19.27
32	-19	-30.27	11.27
33	-30	-31.4	1.405
34	-38	-30.27	-7.728
35	-36	-30.27	-5.728
36	-40	-28.01	-11.99
37	-34	-29.14	-4.861
38	-35	-29.14	-5.861
39	-38	-29.14	-8.861
40	-32	-28.01	-3.994
41	-37	-24.61	-12.39
42	-39	-24.61	-14.39
43	-31	-26.87	-4.126
44	-30	-26.87	-3.126
45	-29	-26.87	-2.126
46	-36	-33.67	-2.33
47	-41	-32.54	-8.463
48	-42	-33.67	-8.33
49	-33	-34.8	1.803
50	-43	-34.8	-8.197
51	-41	-33.67	-7.33
52	-34	-30.27	-3.728
53	-32	-32.54	0.5373
54	-36	-33.67	-2.33
55	-37	-35.94	-1.065
56	-30	-32.54	2.537
57	-32	-28.01	-3.994
58	-30	-18.94	-11.06
59	-21	-17.81	-3.188
60	-19	-20.08	1.077
61	-9	-16.68	7.679
62	-8	-13.28	5.281
63	-6	-9.883	3.883
64	-4	-14.41	10.41
65	-1	-9.883	8.883
66	-2	-11.02	9.016
67	-1	-11.02	10.02
68	-4	-12.15	8.149
69	-8	-11.02	3.016
70	-6	-13.28	7.281
71	-11	-12.15	1.149
72	-11	-8.75	-2.25

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.01243	0.02485	0.9876
6	0.006966	0.01393	0.993
7	0.0202	0.04041	0.9798
8	0.01802	0.03604	0.982
9	0.01141	0.02282	0.9886
10	0.009093	0.01819	0.9909
11	0.006851	0.0137	0.9931
12	0.01583	0.03166	0.9842
13	0.06881	0.1376	0.9312
14	0.06397	0.1279	0.936
15	0.06483	0.1297	0.9352
16	0.05061	0.1012	0.9494
17	0.03618	0.07236	0.9638
18	0.02775	0.05551	0.9722
19	0.04194	0.08388	0.9581
20	0.09427	0.1885	0.9057
21	0.09338	0.1868	0.9066
22	0.08715	0.1743	0.9129
23	0.09186	0.1837	0.9081
24	0.07292	0.1458	0.9271
25	0.1862	0.3723	0.8138
26	0.3705	0.741	0.6295
27	0.4682	0.9364	0.5318
28	0.5167	0.9665	0.4833
29	0.6239	0.7522	0.3761
30	0.7263	0.5473	0.2737
31	0.9167	0.1666	0.08328
32	0.9646	0.07072	0.03536
33	0.9816	0.03672	0.01836
34	0.9942	0.01166	0.00583
35	0.9962	0.007513	0.003757
36	0.999	0.001985	0.0009925
37	0.9989	0.002256	0.001128
38	0.9987	0.002523	0.001261
39	0.999	0.002003	0.001001
40	0.9985	0.00302	0.00151
41	0.9995	0.00096	0.00048
42	1	9.176e-05	4.588e-05
43	0.9999	0.0001608	8.041e-05
44	0.9998	0.0003067	0.0001533
45	0.9997	0.0006098	0.0003049
46	0.9994	0.0011	0.00055
47	0.9994	0.001207	0.0006033
48	0.9993	0.001387	0.0006937
49	0.9991	0.001869	0.0009344
50	0.9988	0.002425	0.001213
51	0.9984	0.003235	0.001618
52	0.9972	0.005695	0.002847
53	0.9948	0.01039	0.005194
54	0.9904	0.01926	0.009629
55	0.9837	0.03267	0.01634
56	0.9844	0.03117	0.01558
57	0.9734	0.05313	0.02657
58	0.9943	0.01141	0.005706
59	0.9963	0.007304	0.003652
60	0.9978	0.004425	0.002212
61	0.9957	0.008524	0.004262
62	0.9917	0.01662	0.008308
63	0.9803	0.03947	0.01973
64	0.9584	0.08322	0.04161
65	0.9498	0.1004	0.05022
66	0.9298	0.1404	0.07018
67	0.96	0.07993	0.03997

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 &  0.01243 &  0.02485 &  0.9876 \tabularnewline
6 &  0.006966 &  0.01393 &  0.993 \tabularnewline
7 &  0.0202 &  0.04041 &  0.9798 \tabularnewline
8 &  0.01802 &  0.03604 &  0.982 \tabularnewline
9 &  0.01141 &  0.02282 &  0.9886 \tabularnewline
10 &  0.009093 &  0.01819 &  0.9909 \tabularnewline
11 &  0.006851 &  0.0137 &  0.9931 \tabularnewline
12 &  0.01583 &  0.03166 &  0.9842 \tabularnewline
13 &  0.06881 &  0.1376 &  0.9312 \tabularnewline
14 &  0.06397 &  0.1279 &  0.936 \tabularnewline
15 &  0.06483 &  0.1297 &  0.9352 \tabularnewline
16 &  0.05061 &  0.1012 &  0.9494 \tabularnewline
17 &  0.03618 &  0.07236 &  0.9638 \tabularnewline
18 &  0.02775 &  0.05551 &  0.9722 \tabularnewline
19 &  0.04194 &  0.08388 &  0.9581 \tabularnewline
20 &  0.09427 &  0.1885 &  0.9057 \tabularnewline
21 &  0.09338 &  0.1868 &  0.9066 \tabularnewline
22 &  0.08715 &  0.1743 &  0.9129 \tabularnewline
23 &  0.09186 &  0.1837 &  0.9081 \tabularnewline
24 &  0.07292 &  0.1458 &  0.9271 \tabularnewline
25 &  0.1862 &  0.3723 &  0.8138 \tabularnewline
26 &  0.3705 &  0.741 &  0.6295 \tabularnewline
27 &  0.4682 &  0.9364 &  0.5318 \tabularnewline
28 &  0.5167 &  0.9665 &  0.4833 \tabularnewline
29 &  0.6239 &  0.7522 &  0.3761 \tabularnewline
30 &  0.7263 &  0.5473 &  0.2737 \tabularnewline
31 &  0.9167 &  0.1666 &  0.08328 \tabularnewline
32 &  0.9646 &  0.07072 &  0.03536 \tabularnewline
33 &  0.9816 &  0.03672 &  0.01836 \tabularnewline
34 &  0.9942 &  0.01166 &  0.00583 \tabularnewline
35 &  0.9962 &  0.007513 &  0.003757 \tabularnewline
36 &  0.999 &  0.001985 &  0.0009925 \tabularnewline
37 &  0.9989 &  0.002256 &  0.001128 \tabularnewline
38 &  0.9987 &  0.002523 &  0.001261 \tabularnewline
39 &  0.999 &  0.002003 &  0.001001 \tabularnewline
40 &  0.9985 &  0.00302 &  0.00151 \tabularnewline
41 &  0.9995 &  0.00096 &  0.00048 \tabularnewline
42 &  1 &  9.176e-05 &  4.588e-05 \tabularnewline
43 &  0.9999 &  0.0001608 &  8.041e-05 \tabularnewline
44 &  0.9998 &  0.0003067 &  0.0001533 \tabularnewline
45 &  0.9997 &  0.0006098 &  0.0003049 \tabularnewline
46 &  0.9994 &  0.0011 &  0.00055 \tabularnewline
47 &  0.9994 &  0.001207 &  0.0006033 \tabularnewline
48 &  0.9993 &  0.001387 &  0.0006937 \tabularnewline
49 &  0.9991 &  0.001869 &  0.0009344 \tabularnewline
50 &  0.9988 &  0.002425 &  0.001213 \tabularnewline
51 &  0.9984 &  0.003235 &  0.001618 \tabularnewline
52 &  0.9972 &  0.005695 &  0.002847 \tabularnewline
53 &  0.9948 &  0.01039 &  0.005194 \tabularnewline
54 &  0.9904 &  0.01926 &  0.009629 \tabularnewline
55 &  0.9837 &  0.03267 &  0.01634 \tabularnewline
56 &  0.9844 &  0.03117 &  0.01558 \tabularnewline
57 &  0.9734 &  0.05313 &  0.02657 \tabularnewline
58 &  0.9943 &  0.01141 &  0.005706 \tabularnewline
59 &  0.9963 &  0.007304 &  0.003652 \tabularnewline
60 &  0.9978 &  0.004425 &  0.002212 \tabularnewline
61 &  0.9957 &  0.008524 &  0.004262 \tabularnewline
62 &  0.9917 &  0.01662 &  0.008308 \tabularnewline
63 &  0.9803 &  0.03947 &  0.01973 \tabularnewline
64 &  0.9584 &  0.08322 &  0.04161 \tabularnewline
65 &  0.9498 &  0.1004 &  0.05022 \tabularnewline
66 &  0.9298 &  0.1404 &  0.07018 \tabularnewline
67 &  0.96 &  0.07993 &  0.03997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286123&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] 0.01243[/C][C] 0.02485[/C][C] 0.9876[/C][/ROW]
[ROW][C]6[/C][C] 0.006966[/C][C] 0.01393[/C][C] 0.993[/C][/ROW]
[ROW][C]7[/C][C] 0.0202[/C][C] 0.04041[/C][C] 0.9798[/C][/ROW]
[ROW][C]8[/C][C] 0.01802[/C][C] 0.03604[/C][C] 0.982[/C][/ROW]
[ROW][C]9[/C][C] 0.01141[/C][C] 0.02282[/C][C] 0.9886[/C][/ROW]
[ROW][C]10[/C][C] 0.009093[/C][C] 0.01819[/C][C] 0.9909[/C][/ROW]
[ROW][C]11[/C][C] 0.006851[/C][C] 0.0137[/C][C] 0.9931[/C][/ROW]
[ROW][C]12[/C][C] 0.01583[/C][C] 0.03166[/C][C] 0.9842[/C][/ROW]
[ROW][C]13[/C][C] 0.06881[/C][C] 0.1376[/C][C] 0.9312[/C][/ROW]
[ROW][C]14[/C][C] 0.06397[/C][C] 0.1279[/C][C] 0.936[/C][/ROW]
[ROW][C]15[/C][C] 0.06483[/C][C] 0.1297[/C][C] 0.9352[/C][/ROW]
[ROW][C]16[/C][C] 0.05061[/C][C] 0.1012[/C][C] 0.9494[/C][/ROW]
[ROW][C]17[/C][C] 0.03618[/C][C] 0.07236[/C][C] 0.9638[/C][/ROW]
[ROW][C]18[/C][C] 0.02775[/C][C] 0.05551[/C][C] 0.9722[/C][/ROW]
[ROW][C]19[/C][C] 0.04194[/C][C] 0.08388[/C][C] 0.9581[/C][/ROW]
[ROW][C]20[/C][C] 0.09427[/C][C] 0.1885[/C][C] 0.9057[/C][/ROW]
[ROW][C]21[/C][C] 0.09338[/C][C] 0.1868[/C][C] 0.9066[/C][/ROW]
[ROW][C]22[/C][C] 0.08715[/C][C] 0.1743[/C][C] 0.9129[/C][/ROW]
[ROW][C]23[/C][C] 0.09186[/C][C] 0.1837[/C][C] 0.9081[/C][/ROW]
[ROW][C]24[/C][C] 0.07292[/C][C] 0.1458[/C][C] 0.9271[/C][/ROW]
[ROW][C]25[/C][C] 0.1862[/C][C] 0.3723[/C][C] 0.8138[/C][/ROW]
[ROW][C]26[/C][C] 0.3705[/C][C] 0.741[/C][C] 0.6295[/C][/ROW]
[ROW][C]27[/C][C] 0.4682[/C][C] 0.9364[/C][C] 0.5318[/C][/ROW]
[ROW][C]28[/C][C] 0.5167[/C][C] 0.9665[/C][C] 0.4833[/C][/ROW]
[ROW][C]29[/C][C] 0.6239[/C][C] 0.7522[/C][C] 0.3761[/C][/ROW]
[ROW][C]30[/C][C] 0.7263[/C][C] 0.5473[/C][C] 0.2737[/C][/ROW]
[ROW][C]31[/C][C] 0.9167[/C][C] 0.1666[/C][C] 0.08328[/C][/ROW]
[ROW][C]32[/C][C] 0.9646[/C][C] 0.07072[/C][C] 0.03536[/C][/ROW]
[ROW][C]33[/C][C] 0.9816[/C][C] 0.03672[/C][C] 0.01836[/C][/ROW]
[ROW][C]34[/C][C] 0.9942[/C][C] 0.01166[/C][C] 0.00583[/C][/ROW]
[ROW][C]35[/C][C] 0.9962[/C][C] 0.007513[/C][C] 0.003757[/C][/ROW]
[ROW][C]36[/C][C] 0.999[/C][C] 0.001985[/C][C] 0.0009925[/C][/ROW]
[ROW][C]37[/C][C] 0.9989[/C][C] 0.002256[/C][C] 0.001128[/C][/ROW]
[ROW][C]38[/C][C] 0.9987[/C][C] 0.002523[/C][C] 0.001261[/C][/ROW]
[ROW][C]39[/C][C] 0.999[/C][C] 0.002003[/C][C] 0.001001[/C][/ROW]
[ROW][C]40[/C][C] 0.9985[/C][C] 0.00302[/C][C] 0.00151[/C][/ROW]
[ROW][C]41[/C][C] 0.9995[/C][C] 0.00096[/C][C] 0.00048[/C][/ROW]
[ROW][C]42[/C][C] 1[/C][C] 9.176e-05[/C][C] 4.588e-05[/C][/ROW]
[ROW][C]43[/C][C] 0.9999[/C][C] 0.0001608[/C][C] 8.041e-05[/C][/ROW]
[ROW][C]44[/C][C] 0.9998[/C][C] 0.0003067[/C][C] 0.0001533[/C][/ROW]
[ROW][C]45[/C][C] 0.9997[/C][C] 0.0006098[/C][C] 0.0003049[/C][/ROW]
[ROW][C]46[/C][C] 0.9994[/C][C] 0.0011[/C][C] 0.00055[/C][/ROW]
[ROW][C]47[/C][C] 0.9994[/C][C] 0.001207[/C][C] 0.0006033[/C][/ROW]
[ROW][C]48[/C][C] 0.9993[/C][C] 0.001387[/C][C] 0.0006937[/C][/ROW]
[ROW][C]49[/C][C] 0.9991[/C][C] 0.001869[/C][C] 0.0009344[/C][/ROW]
[ROW][C]50[/C][C] 0.9988[/C][C] 0.002425[/C][C] 0.001213[/C][/ROW]
[ROW][C]51[/C][C] 0.9984[/C][C] 0.003235[/C][C] 0.001618[/C][/ROW]
[ROW][C]52[/C][C] 0.9972[/C][C] 0.005695[/C][C] 0.002847[/C][/ROW]
[ROW][C]53[/C][C] 0.9948[/C][C] 0.01039[/C][C] 0.005194[/C][/ROW]
[ROW][C]54[/C][C] 0.9904[/C][C] 0.01926[/C][C] 0.009629[/C][/ROW]
[ROW][C]55[/C][C] 0.9837[/C][C] 0.03267[/C][C] 0.01634[/C][/ROW]
[ROW][C]56[/C][C] 0.9844[/C][C] 0.03117[/C][C] 0.01558[/C][/ROW]
[ROW][C]57[/C][C] 0.9734[/C][C] 0.05313[/C][C] 0.02657[/C][/ROW]
[ROW][C]58[/C][C] 0.9943[/C][C] 0.01141[/C][C] 0.005706[/C][/ROW]
[ROW][C]59[/C][C] 0.9963[/C][C] 0.007304[/C][C] 0.003652[/C][/ROW]
[ROW][C]60[/C][C] 0.9978[/C][C] 0.004425[/C][C] 0.002212[/C][/ROW]
[ROW][C]61[/C][C] 0.9957[/C][C] 0.008524[/C][C] 0.004262[/C][/ROW]
[ROW][C]62[/C][C] 0.9917[/C][C] 0.01662[/C][C] 0.008308[/C][/ROW]
[ROW][C]63[/C][C] 0.9803[/C][C] 0.03947[/C][C] 0.01973[/C][/ROW]
[ROW][C]64[/C][C] 0.9584[/C][C] 0.08322[/C][C] 0.04161[/C][/ROW]
[ROW][C]65[/C][C] 0.9498[/C][C] 0.1004[/C][C] 0.05022[/C][/ROW]
[ROW][C]66[/C][C] 0.9298[/C][C] 0.1404[/C][C] 0.07018[/C][/ROW]
[ROW][C]67[/C][C] 0.96[/C][C] 0.07993[/C][C] 0.03997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286123&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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	0.01243	0.02485	0.9876
6	0.006966	0.01393	0.993
7	0.0202	0.04041	0.9798
8	0.01802	0.03604	0.982
9	0.01141	0.02282	0.9886
10	0.009093	0.01819	0.9909
11	0.006851	0.0137	0.9931
12	0.01583	0.03166	0.9842
13	0.06881	0.1376	0.9312
14	0.06397	0.1279	0.936
15	0.06483	0.1297	0.9352
16	0.05061	0.1012	0.9494
17	0.03618	0.07236	0.9638
18	0.02775	0.05551	0.9722
19	0.04194	0.08388	0.9581
20	0.09427	0.1885	0.9057
21	0.09338	0.1868	0.9066
22	0.08715	0.1743	0.9129
23	0.09186	0.1837	0.9081
24	0.07292	0.1458	0.9271
25	0.1862	0.3723	0.8138
26	0.3705	0.741	0.6295
27	0.4682	0.9364	0.5318
28	0.5167	0.9665	0.4833
29	0.6239	0.7522	0.3761
30	0.7263	0.5473	0.2737
31	0.9167	0.1666	0.08328
32	0.9646	0.07072	0.03536
33	0.9816	0.03672	0.01836
34	0.9942	0.01166	0.00583
35	0.9962	0.007513	0.003757
36	0.999	0.001985	0.0009925
37	0.9989	0.002256	0.001128
38	0.9987	0.002523	0.001261
39	0.999	0.002003	0.001001
40	0.9985	0.00302	0.00151
41	0.9995	0.00096	0.00048
42	1	9.176e-05	4.588e-05
43	0.9999	0.0001608	8.041e-05
44	0.9998	0.0003067	0.0001533
45	0.9997	0.0006098	0.0003049
46	0.9994	0.0011	0.00055
47	0.9994	0.001207	0.0006033
48	0.9993	0.001387	0.0006937
49	0.9991	0.001869	0.0009344
50	0.9988	0.002425	0.001213
51	0.9984	0.003235	0.001618
52	0.9972	0.005695	0.002847
53	0.9948	0.01039	0.005194
54	0.9904	0.01926	0.009629
55	0.9837	0.03267	0.01634
56	0.9844	0.03117	0.01558
57	0.9734	0.05313	0.02657
58	0.9943	0.01141	0.005706
59	0.9963	0.007304	0.003652
60	0.9978	0.004425	0.002212
61	0.9957	0.008524	0.004262
62	0.9917	0.01662	0.008308
63	0.9803	0.03947	0.01973
64	0.9584	0.08322	0.04161
65	0.9498	0.1004	0.05022
66	0.9298	0.1404	0.07018
67	0.96	0.07993	0.03997

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	21	0.3333	NOK
5% type I error level	38	0.603175	NOK
10% type I error level	45	0.714286	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 & 21 &  0.3333 & NOK \tabularnewline
5% type I error level & 38 & 0.603175 & NOK \tabularnewline
10% type I error level & 45 & 0.714286 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286123&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]21[/C][C] 0.3333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]38[/C][C]0.603175[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]45[/C][C]0.714286[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286123&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286123&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	21	0.3333	NOK
5% type I error level	38	0.603175	NOK
10% type I error level	45	0.714286	NOK

Figure 1

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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 = No Linear Trend ;

Parameters (R input):

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

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

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