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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sat, 19 Dec 2009 02:31:23 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/19/t1261215244xcr1356m3jjnqyz.htm/, Retrieved Sat, 04 May 2024 00:54:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69466, Retrieved Sat, 04 May 2024 00:54:01 +0000

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Estimated Impact

159

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

-     [Multiple Regression] [Paper - Regressie...] [2008-12-10 20:26:13] [93834488277b53a4510bfd06084ae13b]
-  M D  [Multiple Regression] [Paper Regressie a...] [2009-12-19 07:59:01] [1d635fe1113b56bab3f378c464a289bc]
-   P       [Multiple Regression] [Paper Regressie a...] [2009-12-19 09:31:23] [762da55b2e2304daaed24a7cc507d14d] [Current]
-   P         [Multiple Regression] [Paper Regressie a...] [2009-12-19 10:57:36] [1d635fe1113b56bab3f378c464a289bc] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Consumentenvertrouwen[t] = + 86.9885714285714 -38.3142857142857Dummy[t] + 0.937142857142851M1[t] -1.06285714285715M2[t] -1.06285714285713M3[t] -9.92571428571427M4[t] -4.26285714285714M5[t] -2.86285714285714M6[t] -2.46285714285714M7[t] -1.06285714285714M8[t] -1.46285714285714M9[t] + 2.8M10[t] + 1.2M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Consumentenvertrouwen[t] =  +  86.9885714285714 -38.3142857142857Dummy[t] +  0.937142857142851M1[t] -1.06285714285715M2[t] -1.06285714285713M3[t] -9.92571428571427M4[t] -4.26285714285714M5[t] -2.86285714285714M6[t] -2.46285714285714M7[t] -1.06285714285714M8[t] -1.46285714285714M9[t] +  2.8M10[t] +  1.2M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Consumentenvertrouwen[t] =  +  86.9885714285714 -38.3142857142857Dummy[t] +  0.937142857142851M1[t] -1.06285714285715M2[t] -1.06285714285713M3[t] -9.92571428571427M4[t] -4.26285714285714M5[t] -2.86285714285714M6[t] -2.46285714285714M7[t] -1.06285714285714M8[t] -1.46285714285714M9[t] +  2.8M10[t] +  1.2M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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] = + 86.9885714285714 -38.3142857142857Dummy[t] + 0.937142857142851M1[t] -1.06285714285715M2[t] -1.06285714285713M3[t] -9.92571428571427M4[t] -4.26285714285714M5[t] -2.86285714285714M6[t] -2.46285714285714M7[t] -1.06285714285714M8[t] -1.46285714285714M9[t] + 2.8M10[t] + 1.2M11[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)	86.9885714285714	5.54458	15.6889	0	0
Dummy	-38.3142857142857	3.11907	-12.2839	0	0
M1	0.937142857142851	7.407381	0.1265	0.899864	0.449932
M2	-1.06285714285715	7.407381	-0.1435	0.88652	0.44326
M3	-1.06285714285713	7.407381	-0.1435	0.88652	0.44326
M4	-9.92571428571427	7.485768	-1.3259	0.191266	0.095633
M5	-4.26285714285714	7.407381	-0.5755	0.567707	0.283853
M6	-2.86285714285714	7.407381	-0.3865	0.70088	0.35044
M7	-2.46285714285714	7.407381	-0.3325	0.741	0.3705
M8	-1.06285714285714	7.407381	-0.1435	0.88652	0.44326
M9	-1.46285714285714	7.407381	-0.1975	0.844299	0.422149
M10	2.8	7.381067	0.3793	0.706137	0.353069
M11	1.2	7.381067	0.1626	0.871548	0.435774

\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) & 86.9885714285714 & 5.54458 & 15.6889 & 0 & 0 \tabularnewline
Dummy & -38.3142857142857 & 3.11907 & -12.2839 & 0 & 0 \tabularnewline
M1 & 0.937142857142851 & 7.407381 & 0.1265 & 0.899864 & 0.449932 \tabularnewline
M2 & -1.06285714285715 & 7.407381 & -0.1435 & 0.88652 & 0.44326 \tabularnewline
M3 & -1.06285714285713 & 7.407381 & -0.1435 & 0.88652 & 0.44326 \tabularnewline
M4 & -9.92571428571427 & 7.485768 & -1.3259 & 0.191266 & 0.095633 \tabularnewline
M5 & -4.26285714285714 & 7.407381 & -0.5755 & 0.567707 & 0.283853 \tabularnewline
M6 & -2.86285714285714 & 7.407381 & -0.3865 & 0.70088 & 0.35044 \tabularnewline
M7 & -2.46285714285714 & 7.407381 & -0.3325 & 0.741 & 0.3705 \tabularnewline
M8 & -1.06285714285714 & 7.407381 & -0.1435 & 0.88652 & 0.44326 \tabularnewline
M9 & -1.46285714285714 & 7.407381 & -0.1975 & 0.844299 & 0.422149 \tabularnewline
M10 & 2.8 & 7.381067 & 0.3793 & 0.706137 & 0.353069 \tabularnewline
M11 & 1.2 & 7.381067 & 0.1626 & 0.871548 & 0.435774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&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]86.9885714285714[/C][C]5.54458[/C][C]15.6889[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Dummy[/C][C]-38.3142857142857[/C][C]3.11907[/C][C]-12.2839[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.937142857142851[/C][C]7.407381[/C][C]0.1265[/C][C]0.899864[/C][C]0.449932[/C][/ROW]
[ROW][C]M2[/C][C]-1.06285714285715[/C][C]7.407381[/C][C]-0.1435[/C][C]0.88652[/C][C]0.44326[/C][/ROW]
[ROW][C]M3[/C][C]-1.06285714285713[/C][C]7.407381[/C][C]-0.1435[/C][C]0.88652[/C][C]0.44326[/C][/ROW]
[ROW][C]M4[/C][C]-9.92571428571427[/C][C]7.485768[/C][C]-1.3259[/C][C]0.191266[/C][C]0.095633[/C][/ROW]
[ROW][C]M5[/C][C]-4.26285714285714[/C][C]7.407381[/C][C]-0.5755[/C][C]0.567707[/C][C]0.283853[/C][/ROW]
[ROW][C]M6[/C][C]-2.86285714285714[/C][C]7.407381[/C][C]-0.3865[/C][C]0.70088[/C][C]0.35044[/C][/ROW]
[ROW][C]M7[/C][C]-2.46285714285714[/C][C]7.407381[/C][C]-0.3325[/C][C]0.741[/C][C]0.3705[/C][/ROW]
[ROW][C]M8[/C][C]-1.06285714285714[/C][C]7.407381[/C][C]-0.1435[/C][C]0.88652[/C][C]0.44326[/C][/ROW]
[ROW][C]M9[/C][C]-1.46285714285714[/C][C]7.407381[/C][C]-0.1975[/C][C]0.844299[/C][C]0.422149[/C][/ROW]
[ROW][C]M10[/C][C]2.8[/C][C]7.381067[/C][C]0.3793[/C][C]0.706137[/C][C]0.353069[/C][/ROW]
[ROW][C]M11[/C][C]1.2[/C][C]7.381067[/C][C]0.1626[/C][C]0.871548[/C][C]0.435774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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)	86.9885714285714	5.54458	15.6889	0	0
Dummy	-38.3142857142857	3.11907	-12.2839	0	0
M1	0.937142857142851	7.407381	0.1265	0.899864	0.449932
M2	-1.06285714285715	7.407381	-0.1435	0.88652	0.44326
M3	-1.06285714285713	7.407381	-0.1435	0.88652	0.44326
M4	-9.92571428571427	7.485768	-1.3259	0.191266	0.095633
M5	-4.26285714285714	7.407381	-0.5755	0.567707	0.283853
M6	-2.86285714285714	7.407381	-0.3865	0.70088	0.35044
M7	-2.46285714285714	7.407381	-0.3325	0.741	0.3705
M8	-1.06285714285714	7.407381	-0.1435	0.88652	0.44326
M9	-1.46285714285714	7.407381	-0.1975	0.844299	0.422149
M10	2.8	7.381067	0.3793	0.706137	0.353069
M11	1.2	7.381067	0.1626	0.871548	0.435774

Multiple Linear Regression - Regression Statistics
Multiple R	0.874918892822606
R-squared	0.765483069017934
Adjusted R-squared	0.705606405788471
F-TEST (value)	12.7843307848401
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	4.78992401298228e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.6704911953885
Sum Squared Residuals	6401.41714285715

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.874918892822606 \tabularnewline
R-squared & 0.765483069017934 \tabularnewline
Adjusted R-squared & 0.705606405788471 \tabularnewline
F-TEST (value) & 12.7843307848401 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 4.78992401298228e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 11.6704911953885 \tabularnewline
Sum Squared Residuals & 6401.41714285715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.874918892822606[/C][/ROW]
[ROW][C]R-squared[/C][C]0.765483069017934[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.705606405788471[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]12.7843307848401[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]4.78992401298228e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]11.6704911953885[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6401.41714285715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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	0.874918892822606
R-squared	0.765483069017934
Adjusted R-squared	0.705606405788471
F-TEST (value)	12.7843307848401
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	4.78992401298228e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.6704911953885
Sum Squared Residuals	6401.41714285715

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	84	87.9257142857143	-3.92571428571433
2	78	85.9257142857143	-7.92571428571435
3	74	85.9257142857143	-11.9257142857143
4	75	77.0628571428572	-2.06285714285715
5	79	82.7257142857143	-3.72571428571428
6	79	84.1257142857143	-5.12571428571429
7	82	84.5257142857143	-2.52571428571428
8	88	85.9257142857143	2.07428571428572
9	81	85.5257142857143	-4.52571428571428
10	69	51.4742857142857	17.5257142857143
11	62	49.8742857142857	12.1257142857143
12	62	48.6742857142857	13.3257142857143
13	68	49.6114285714286	18.3885714285714
14	57	47.6114285714286	9.38857142857144
15	67	47.6114285714286	19.3885714285714
16	72	77.0628571428571	-5.06285714285714
17	75	82.7257142857143	-7.72571428571428
18	81	84.1257142857143	-3.12571428571428
19	80	84.5257142857143	-4.52571428571428
20	79	85.9257142857143	-6.92571428571428
21	81	85.5257142857143	-4.52571428571428
22	83	89.7885714285714	-6.78857142857142
23	84	88.1885714285714	-4.18857142857142
24	90	86.9885714285714	3.01142857142858
25	84	87.9257142857143	-3.92571428571427
26	90	85.9257142857143	4.07428571428573
27	92	85.9257142857143	6.07428571428571
28	93	77.0628571428571	15.9371428571429
29	85	82.7257142857143	2.27428571428572
30	93	84.1257142857143	8.87428571428572
31	94	84.5257142857143	9.47428571428572
32	94	85.9257142857143	8.07428571428572
33	102	85.5257142857143	16.4742857142857
34	96	89.7885714285714	6.21142857142858
35	96	88.1885714285714	7.81142857142858
36	92	86.9885714285714	5.01142857142858
37	90	87.9257142857143	2.07428571428573
38	84	85.9257142857143	-1.92571428571427
39	86	85.9257142857143	0.0742857142857098
40	70	77.0628571428571	-7.06285714285714
41	67	44.4114285714286	22.5885714285714
42	60	45.8114285714286	14.1885714285714
43	62	46.2114285714286	15.7885714285714
44	61	47.6114285714286	13.3885714285714
45	54	47.2114285714286	6.78857142857142
46	50	51.4742857142857	-1.47428571428571
47	45	49.8742857142857	-4.87428571428572
48	34	48.6742857142857	-14.6742857142857
49	37	49.6114285714286	-12.6114285714286
50	44	47.6114285714286	-3.61142857142856
51	34	47.6114285714286	-13.6114285714286
52	37	38.7485714285714	-1.74857142857143
53	31	44.4114285714286	-13.4114285714286
54	31	45.8114285714286	-14.8114285714286
55	28	46.2114285714286	-18.2114285714286
56	31	47.6114285714286	-16.6114285714286
57	33	47.2114285714286	-14.2114285714286
58	36	51.4742857142857	-15.4742857142857
59	39	49.8742857142857	-10.8742857142857
60	42	48.6742857142857	-6.67428571428571

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 84 & 87.9257142857143 & -3.92571428571433 \tabularnewline
2 & 78 & 85.9257142857143 & -7.92571428571435 \tabularnewline
3 & 74 & 85.9257142857143 & -11.9257142857143 \tabularnewline
4 & 75 & 77.0628571428572 & -2.06285714285715 \tabularnewline
5 & 79 & 82.7257142857143 & -3.72571428571428 \tabularnewline
6 & 79 & 84.1257142857143 & -5.12571428571429 \tabularnewline
7 & 82 & 84.5257142857143 & -2.52571428571428 \tabularnewline
8 & 88 & 85.9257142857143 & 2.07428571428572 \tabularnewline
9 & 81 & 85.5257142857143 & -4.52571428571428 \tabularnewline
10 & 69 & 51.4742857142857 & 17.5257142857143 \tabularnewline
11 & 62 & 49.8742857142857 & 12.1257142857143 \tabularnewline
12 & 62 & 48.6742857142857 & 13.3257142857143 \tabularnewline
13 & 68 & 49.6114285714286 & 18.3885714285714 \tabularnewline
14 & 57 & 47.6114285714286 & 9.38857142857144 \tabularnewline
15 & 67 & 47.6114285714286 & 19.3885714285714 \tabularnewline
16 & 72 & 77.0628571428571 & -5.06285714285714 \tabularnewline
17 & 75 & 82.7257142857143 & -7.72571428571428 \tabularnewline
18 & 81 & 84.1257142857143 & -3.12571428571428 \tabularnewline
19 & 80 & 84.5257142857143 & -4.52571428571428 \tabularnewline
20 & 79 & 85.9257142857143 & -6.92571428571428 \tabularnewline
21 & 81 & 85.5257142857143 & -4.52571428571428 \tabularnewline
22 & 83 & 89.7885714285714 & -6.78857142857142 \tabularnewline
23 & 84 & 88.1885714285714 & -4.18857142857142 \tabularnewline
24 & 90 & 86.9885714285714 & 3.01142857142858 \tabularnewline
25 & 84 & 87.9257142857143 & -3.92571428571427 \tabularnewline
26 & 90 & 85.9257142857143 & 4.07428571428573 \tabularnewline
27 & 92 & 85.9257142857143 & 6.07428571428571 \tabularnewline
28 & 93 & 77.0628571428571 & 15.9371428571429 \tabularnewline
29 & 85 & 82.7257142857143 & 2.27428571428572 \tabularnewline
30 & 93 & 84.1257142857143 & 8.87428571428572 \tabularnewline
31 & 94 & 84.5257142857143 & 9.47428571428572 \tabularnewline
32 & 94 & 85.9257142857143 & 8.07428571428572 \tabularnewline
33 & 102 & 85.5257142857143 & 16.4742857142857 \tabularnewline
34 & 96 & 89.7885714285714 & 6.21142857142858 \tabularnewline
35 & 96 & 88.1885714285714 & 7.81142857142858 \tabularnewline
36 & 92 & 86.9885714285714 & 5.01142857142858 \tabularnewline
37 & 90 & 87.9257142857143 & 2.07428571428573 \tabularnewline
38 & 84 & 85.9257142857143 & -1.92571428571427 \tabularnewline
39 & 86 & 85.9257142857143 & 0.0742857142857098 \tabularnewline
40 & 70 & 77.0628571428571 & -7.06285714285714 \tabularnewline
41 & 67 & 44.4114285714286 & 22.5885714285714 \tabularnewline
42 & 60 & 45.8114285714286 & 14.1885714285714 \tabularnewline
43 & 62 & 46.2114285714286 & 15.7885714285714 \tabularnewline
44 & 61 & 47.6114285714286 & 13.3885714285714 \tabularnewline
45 & 54 & 47.2114285714286 & 6.78857142857142 \tabularnewline
46 & 50 & 51.4742857142857 & -1.47428571428571 \tabularnewline
47 & 45 & 49.8742857142857 & -4.87428571428572 \tabularnewline
48 & 34 & 48.6742857142857 & -14.6742857142857 \tabularnewline
49 & 37 & 49.6114285714286 & -12.6114285714286 \tabularnewline
50 & 44 & 47.6114285714286 & -3.61142857142856 \tabularnewline
51 & 34 & 47.6114285714286 & -13.6114285714286 \tabularnewline
52 & 37 & 38.7485714285714 & -1.74857142857143 \tabularnewline
53 & 31 & 44.4114285714286 & -13.4114285714286 \tabularnewline
54 & 31 & 45.8114285714286 & -14.8114285714286 \tabularnewline
55 & 28 & 46.2114285714286 & -18.2114285714286 \tabularnewline
56 & 31 & 47.6114285714286 & -16.6114285714286 \tabularnewline
57 & 33 & 47.2114285714286 & -14.2114285714286 \tabularnewline
58 & 36 & 51.4742857142857 & -15.4742857142857 \tabularnewline
59 & 39 & 49.8742857142857 & -10.8742857142857 \tabularnewline
60 & 42 & 48.6742857142857 & -6.67428571428571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&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]84[/C][C]87.9257142857143[/C][C]-3.92571428571433[/C][/ROW]
[ROW][C]2[/C][C]78[/C][C]85.9257142857143[/C][C]-7.92571428571435[/C][/ROW]
[ROW][C]3[/C][C]74[/C][C]85.9257142857143[/C][C]-11.9257142857143[/C][/ROW]
[ROW][C]4[/C][C]75[/C][C]77.0628571428572[/C][C]-2.06285714285715[/C][/ROW]
[ROW][C]5[/C][C]79[/C][C]82.7257142857143[/C][C]-3.72571428571428[/C][/ROW]
[ROW][C]6[/C][C]79[/C][C]84.1257142857143[/C][C]-5.12571428571429[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]84.5257142857143[/C][C]-2.52571428571428[/C][/ROW]
[ROW][C]8[/C][C]88[/C][C]85.9257142857143[/C][C]2.07428571428572[/C][/ROW]
[ROW][C]9[/C][C]81[/C][C]85.5257142857143[/C][C]-4.52571428571428[/C][/ROW]
[ROW][C]10[/C][C]69[/C][C]51.4742857142857[/C][C]17.5257142857143[/C][/ROW]
[ROW][C]11[/C][C]62[/C][C]49.8742857142857[/C][C]12.1257142857143[/C][/ROW]
[ROW][C]12[/C][C]62[/C][C]48.6742857142857[/C][C]13.3257142857143[/C][/ROW]
[ROW][C]13[/C][C]68[/C][C]49.6114285714286[/C][C]18.3885714285714[/C][/ROW]
[ROW][C]14[/C][C]57[/C][C]47.6114285714286[/C][C]9.38857142857144[/C][/ROW]
[ROW][C]15[/C][C]67[/C][C]47.6114285714286[/C][C]19.3885714285714[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]77.0628571428571[/C][C]-5.06285714285714[/C][/ROW]
[ROW][C]17[/C][C]75[/C][C]82.7257142857143[/C][C]-7.72571428571428[/C][/ROW]
[ROW][C]18[/C][C]81[/C][C]84.1257142857143[/C][C]-3.12571428571428[/C][/ROW]
[ROW][C]19[/C][C]80[/C][C]84.5257142857143[/C][C]-4.52571428571428[/C][/ROW]
[ROW][C]20[/C][C]79[/C][C]85.9257142857143[/C][C]-6.92571428571428[/C][/ROW]
[ROW][C]21[/C][C]81[/C][C]85.5257142857143[/C][C]-4.52571428571428[/C][/ROW]
[ROW][C]22[/C][C]83[/C][C]89.7885714285714[/C][C]-6.78857142857142[/C][/ROW]
[ROW][C]23[/C][C]84[/C][C]88.1885714285714[/C][C]-4.18857142857142[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]86.9885714285714[/C][C]3.01142857142858[/C][/ROW]
[ROW][C]25[/C][C]84[/C][C]87.9257142857143[/C][C]-3.92571428571427[/C][/ROW]
[ROW][C]26[/C][C]90[/C][C]85.9257142857143[/C][C]4.07428571428573[/C][/ROW]
[ROW][C]27[/C][C]92[/C][C]85.9257142857143[/C][C]6.07428571428571[/C][/ROW]
[ROW][C]28[/C][C]93[/C][C]77.0628571428571[/C][C]15.9371428571429[/C][/ROW]
[ROW][C]29[/C][C]85[/C][C]82.7257142857143[/C][C]2.27428571428572[/C][/ROW]
[ROW][C]30[/C][C]93[/C][C]84.1257142857143[/C][C]8.87428571428572[/C][/ROW]
[ROW][C]31[/C][C]94[/C][C]84.5257142857143[/C][C]9.47428571428572[/C][/ROW]
[ROW][C]32[/C][C]94[/C][C]85.9257142857143[/C][C]8.07428571428572[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]85.5257142857143[/C][C]16.4742857142857[/C][/ROW]
[ROW][C]34[/C][C]96[/C][C]89.7885714285714[/C][C]6.21142857142858[/C][/ROW]
[ROW][C]35[/C][C]96[/C][C]88.1885714285714[/C][C]7.81142857142858[/C][/ROW]
[ROW][C]36[/C][C]92[/C][C]86.9885714285714[/C][C]5.01142857142858[/C][/ROW]
[ROW][C]37[/C][C]90[/C][C]87.9257142857143[/C][C]2.07428571428573[/C][/ROW]
[ROW][C]38[/C][C]84[/C][C]85.9257142857143[/C][C]-1.92571428571427[/C][/ROW]
[ROW][C]39[/C][C]86[/C][C]85.9257142857143[/C][C]0.0742857142857098[/C][/ROW]
[ROW][C]40[/C][C]70[/C][C]77.0628571428571[/C][C]-7.06285714285714[/C][/ROW]
[ROW][C]41[/C][C]67[/C][C]44.4114285714286[/C][C]22.5885714285714[/C][/ROW]
[ROW][C]42[/C][C]60[/C][C]45.8114285714286[/C][C]14.1885714285714[/C][/ROW]
[ROW][C]43[/C][C]62[/C][C]46.2114285714286[/C][C]15.7885714285714[/C][/ROW]
[ROW][C]44[/C][C]61[/C][C]47.6114285714286[/C][C]13.3885714285714[/C][/ROW]
[ROW][C]45[/C][C]54[/C][C]47.2114285714286[/C][C]6.78857142857142[/C][/ROW]
[ROW][C]46[/C][C]50[/C][C]51.4742857142857[/C][C]-1.47428571428571[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]49.8742857142857[/C][C]-4.87428571428572[/C][/ROW]
[ROW][C]48[/C][C]34[/C][C]48.6742857142857[/C][C]-14.6742857142857[/C][/ROW]
[ROW][C]49[/C][C]37[/C][C]49.6114285714286[/C][C]-12.6114285714286[/C][/ROW]
[ROW][C]50[/C][C]44[/C][C]47.6114285714286[/C][C]-3.61142857142856[/C][/ROW]
[ROW][C]51[/C][C]34[/C][C]47.6114285714286[/C][C]-13.6114285714286[/C][/ROW]
[ROW][C]52[/C][C]37[/C][C]38.7485714285714[/C][C]-1.74857142857143[/C][/ROW]
[ROW][C]53[/C][C]31[/C][C]44.4114285714286[/C][C]-13.4114285714286[/C][/ROW]
[ROW][C]54[/C][C]31[/C][C]45.8114285714286[/C][C]-14.8114285714286[/C][/ROW]
[ROW][C]55[/C][C]28[/C][C]46.2114285714286[/C][C]-18.2114285714286[/C][/ROW]
[ROW][C]56[/C][C]31[/C][C]47.6114285714286[/C][C]-16.6114285714286[/C][/ROW]
[ROW][C]57[/C][C]33[/C][C]47.2114285714286[/C][C]-14.2114285714286[/C][/ROW]
[ROW][C]58[/C][C]36[/C][C]51.4742857142857[/C][C]-15.4742857142857[/C][/ROW]
[ROW][C]59[/C][C]39[/C][C]49.8742857142857[/C][C]-10.8742857142857[/C][/ROW]
[ROW][C]60[/C][C]42[/C][C]48.6742857142857[/C][C]-6.67428571428571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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	84	87.9257142857143	-3.92571428571433
2	78	85.9257142857143	-7.92571428571435
3	74	85.9257142857143	-11.9257142857143
4	75	77.0628571428572	-2.06285714285715
5	79	82.7257142857143	-3.72571428571428
6	79	84.1257142857143	-5.12571428571429
7	82	84.5257142857143	-2.52571428571428
8	88	85.9257142857143	2.07428571428572
9	81	85.5257142857143	-4.52571428571428
10	69	51.4742857142857	17.5257142857143
11	62	49.8742857142857	12.1257142857143
12	62	48.6742857142857	13.3257142857143
13	68	49.6114285714286	18.3885714285714
14	57	47.6114285714286	9.38857142857144
15	67	47.6114285714286	19.3885714285714
16	72	77.0628571428571	-5.06285714285714
17	75	82.7257142857143	-7.72571428571428
18	81	84.1257142857143	-3.12571428571428
19	80	84.5257142857143	-4.52571428571428
20	79	85.9257142857143	-6.92571428571428
21	81	85.5257142857143	-4.52571428571428
22	83	89.7885714285714	-6.78857142857142
23	84	88.1885714285714	-4.18857142857142
24	90	86.9885714285714	3.01142857142858
25	84	87.9257142857143	-3.92571428571427
26	90	85.9257142857143	4.07428571428573
27	92	85.9257142857143	6.07428571428571
28	93	77.0628571428571	15.9371428571429
29	85	82.7257142857143	2.27428571428572
30	93	84.1257142857143	8.87428571428572
31	94	84.5257142857143	9.47428571428572
32	94	85.9257142857143	8.07428571428572
33	102	85.5257142857143	16.4742857142857
34	96	89.7885714285714	6.21142857142858
35	96	88.1885714285714	7.81142857142858
36	92	86.9885714285714	5.01142857142858
37	90	87.9257142857143	2.07428571428573
38	84	85.9257142857143	-1.92571428571427
39	86	85.9257142857143	0.0742857142857098
40	70	77.0628571428571	-7.06285714285714
41	67	44.4114285714286	22.5885714285714
42	60	45.8114285714286	14.1885714285714
43	62	46.2114285714286	15.7885714285714
44	61	47.6114285714286	13.3885714285714
45	54	47.2114285714286	6.78857142857142
46	50	51.4742857142857	-1.47428571428571
47	45	49.8742857142857	-4.87428571428572
48	34	48.6742857142857	-14.6742857142857
49	37	49.6114285714286	-12.6114285714286
50	44	47.6114285714286	-3.61142857142856
51	34	47.6114285714286	-13.6114285714286
52	37	38.7485714285714	-1.74857142857143
53	31	44.4114285714286	-13.4114285714286
54	31	45.8114285714286	-14.8114285714286
55	28	46.2114285714286	-18.2114285714286
56	31	47.6114285714286	-16.6114285714286
57	33	47.2114285714286	-14.2114285714286
58	36	51.4742857142857	-15.4742857142857
59	39	49.8742857142857	-10.8742857142857
60	42	48.6742857142857	-6.67428571428571

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0680090233851259	0.136018046770252	0.931990976614874
17	0.0285585574093204	0.0571171148186407	0.97144144259068
18	0.009470871682521	0.018941743365042	0.990529128317479
19	0.00306281149525672	0.00612562299051345	0.996937188504743
20	0.00411222615813483	0.00822445231626965	0.995887773841865
21	0.00147751092654899	0.00295502185309797	0.998522489073451
22	0.000476889716191045	0.00095377943238209	0.999523110283809
23	0.000334268896945277	0.000668537793890555	0.999665731103055
24	0.000590785252297	0.001181570504594	0.999409214747703
25	0.000197799288300039	0.000395598576600078	0.9998022007117
26	0.000799624852329818	0.00159924970465964	0.99920037514767
27	0.00125828008506035	0.00251656017012069	0.99874171991494
28	0.00893013446513733	0.0178602689302747	0.991069865534863
29	0.0072915042357765	0.014583008471553	0.992708495764223
30	0.00775851148646276	0.0155170229729255	0.992241488513537
31	0.0076124374115742	0.0152248748231484	0.992387562588426
32	0.00571252351748148	0.0114250470349630	0.994287476482518
33	0.0126885531447921	0.0253771062895842	0.987311446855208
34	0.0085392803314788	0.0170785606629576	0.991460719668521
35	0.00662093976206782	0.0132418795241356	0.993379060237932
36	0.00372371539125918	0.00744743078251835	0.99627628460874
37	0.00198138819291043	0.00396277638582087	0.99801861180709
38	0.000851847652512999	0.00170369530502600	0.999148152347487
39	0.000434628516133646	0.000869257032267293	0.999565371483866
40	0.000231578056050741	0.000463156112101483	0.99976842194395
41	0.000989616465318267	0.00197923293063653	0.999010383534682
42	0.00201450004714807	0.00402900009429613	0.997985499952852
43	0.0131467576062889	0.0262935152125779	0.986853242393711
44	0.0933231650504135	0.186646330100827	0.906676834949586

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0680090233851259 & 0.136018046770252 & 0.931990976614874 \tabularnewline
17 & 0.0285585574093204 & 0.0571171148186407 & 0.97144144259068 \tabularnewline
18 & 0.009470871682521 & 0.018941743365042 & 0.990529128317479 \tabularnewline
19 & 0.00306281149525672 & 0.00612562299051345 & 0.996937188504743 \tabularnewline
20 & 0.00411222615813483 & 0.00822445231626965 & 0.995887773841865 \tabularnewline
21 & 0.00147751092654899 & 0.00295502185309797 & 0.998522489073451 \tabularnewline
22 & 0.000476889716191045 & 0.00095377943238209 & 0.999523110283809 \tabularnewline
23 & 0.000334268896945277 & 0.000668537793890555 & 0.999665731103055 \tabularnewline
24 & 0.000590785252297 & 0.001181570504594 & 0.999409214747703 \tabularnewline
25 & 0.000197799288300039 & 0.000395598576600078 & 0.9998022007117 \tabularnewline
26 & 0.000799624852329818 & 0.00159924970465964 & 0.99920037514767 \tabularnewline
27 & 0.00125828008506035 & 0.00251656017012069 & 0.99874171991494 \tabularnewline
28 & 0.00893013446513733 & 0.0178602689302747 & 0.991069865534863 \tabularnewline
29 & 0.0072915042357765 & 0.014583008471553 & 0.992708495764223 \tabularnewline
30 & 0.00775851148646276 & 0.0155170229729255 & 0.992241488513537 \tabularnewline
31 & 0.0076124374115742 & 0.0152248748231484 & 0.992387562588426 \tabularnewline
32 & 0.00571252351748148 & 0.0114250470349630 & 0.994287476482518 \tabularnewline
33 & 0.0126885531447921 & 0.0253771062895842 & 0.987311446855208 \tabularnewline
34 & 0.0085392803314788 & 0.0170785606629576 & 0.991460719668521 \tabularnewline
35 & 0.00662093976206782 & 0.0132418795241356 & 0.993379060237932 \tabularnewline
36 & 0.00372371539125918 & 0.00744743078251835 & 0.99627628460874 \tabularnewline
37 & 0.00198138819291043 & 0.00396277638582087 & 0.99801861180709 \tabularnewline
38 & 0.000851847652512999 & 0.00170369530502600 & 0.999148152347487 \tabularnewline
39 & 0.000434628516133646 & 0.000869257032267293 & 0.999565371483866 \tabularnewline
40 & 0.000231578056050741 & 0.000463156112101483 & 0.99976842194395 \tabularnewline
41 & 0.000989616465318267 & 0.00197923293063653 & 0.999010383534682 \tabularnewline
42 & 0.00201450004714807 & 0.00402900009429613 & 0.997985499952852 \tabularnewline
43 & 0.0131467576062889 & 0.0262935152125779 & 0.986853242393711 \tabularnewline
44 & 0.0933231650504135 & 0.186646330100827 & 0.906676834949586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&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]16[/C][C]0.0680090233851259[/C][C]0.136018046770252[/C][C]0.931990976614874[/C][/ROW]
[ROW][C]17[/C][C]0.0285585574093204[/C][C]0.0571171148186407[/C][C]0.97144144259068[/C][/ROW]
[ROW][C]18[/C][C]0.009470871682521[/C][C]0.018941743365042[/C][C]0.990529128317479[/C][/ROW]
[ROW][C]19[/C][C]0.00306281149525672[/C][C]0.00612562299051345[/C][C]0.996937188504743[/C][/ROW]
[ROW][C]20[/C][C]0.00411222615813483[/C][C]0.00822445231626965[/C][C]0.995887773841865[/C][/ROW]
[ROW][C]21[/C][C]0.00147751092654899[/C][C]0.00295502185309797[/C][C]0.998522489073451[/C][/ROW]
[ROW][C]22[/C][C]0.000476889716191045[/C][C]0.00095377943238209[/C][C]0.999523110283809[/C][/ROW]
[ROW][C]23[/C][C]0.000334268896945277[/C][C]0.000668537793890555[/C][C]0.999665731103055[/C][/ROW]
[ROW][C]24[/C][C]0.000590785252297[/C][C]0.001181570504594[/C][C]0.999409214747703[/C][/ROW]
[ROW][C]25[/C][C]0.000197799288300039[/C][C]0.000395598576600078[/C][C]0.9998022007117[/C][/ROW]
[ROW][C]26[/C][C]0.000799624852329818[/C][C]0.00159924970465964[/C][C]0.99920037514767[/C][/ROW]
[ROW][C]27[/C][C]0.00125828008506035[/C][C]0.00251656017012069[/C][C]0.99874171991494[/C][/ROW]
[ROW][C]28[/C][C]0.00893013446513733[/C][C]0.0178602689302747[/C][C]0.991069865534863[/C][/ROW]
[ROW][C]29[/C][C]0.0072915042357765[/C][C]0.014583008471553[/C][C]0.992708495764223[/C][/ROW]
[ROW][C]30[/C][C]0.00775851148646276[/C][C]0.0155170229729255[/C][C]0.992241488513537[/C][/ROW]
[ROW][C]31[/C][C]0.0076124374115742[/C][C]0.0152248748231484[/C][C]0.992387562588426[/C][/ROW]
[ROW][C]32[/C][C]0.00571252351748148[/C][C]0.0114250470349630[/C][C]0.994287476482518[/C][/ROW]
[ROW][C]33[/C][C]0.0126885531447921[/C][C]0.0253771062895842[/C][C]0.987311446855208[/C][/ROW]
[ROW][C]34[/C][C]0.0085392803314788[/C][C]0.0170785606629576[/C][C]0.991460719668521[/C][/ROW]
[ROW][C]35[/C][C]0.00662093976206782[/C][C]0.0132418795241356[/C][C]0.993379060237932[/C][/ROW]
[ROW][C]36[/C][C]0.00372371539125918[/C][C]0.00744743078251835[/C][C]0.99627628460874[/C][/ROW]
[ROW][C]37[/C][C]0.00198138819291043[/C][C]0.00396277638582087[/C][C]0.99801861180709[/C][/ROW]
[ROW][C]38[/C][C]0.000851847652512999[/C][C]0.00170369530502600[/C][C]0.999148152347487[/C][/ROW]
[ROW][C]39[/C][C]0.000434628516133646[/C][C]0.000869257032267293[/C][C]0.999565371483866[/C][/ROW]
[ROW][C]40[/C][C]0.000231578056050741[/C][C]0.000463156112101483[/C][C]0.99976842194395[/C][/ROW]
[ROW][C]41[/C][C]0.000989616465318267[/C][C]0.00197923293063653[/C][C]0.999010383534682[/C][/ROW]
[ROW][C]42[/C][C]0.00201450004714807[/C][C]0.00402900009429613[/C][C]0.997985499952852[/C][/ROW]
[ROW][C]43[/C][C]0.0131467576062889[/C][C]0.0262935152125779[/C][C]0.986853242393711[/C][/ROW]
[ROW][C]44[/C][C]0.0933231650504135[/C][C]0.186646330100827[/C][C]0.906676834949586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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
16	0.0680090233851259	0.136018046770252	0.931990976614874
17	0.0285585574093204	0.0571171148186407	0.97144144259068
18	0.009470871682521	0.018941743365042	0.990529128317479
19	0.00306281149525672	0.00612562299051345	0.996937188504743
20	0.00411222615813483	0.00822445231626965	0.995887773841865
21	0.00147751092654899	0.00295502185309797	0.998522489073451
22	0.000476889716191045	0.00095377943238209	0.999523110283809
23	0.000334268896945277	0.000668537793890555	0.999665731103055
24	0.000590785252297	0.001181570504594	0.999409214747703
25	0.000197799288300039	0.000395598576600078	0.9998022007117
26	0.000799624852329818	0.00159924970465964	0.99920037514767
27	0.00125828008506035	0.00251656017012069	0.99874171991494
28	0.00893013446513733	0.0178602689302747	0.991069865534863
29	0.0072915042357765	0.014583008471553	0.992708495764223
30	0.00775851148646276	0.0155170229729255	0.992241488513537
31	0.0076124374115742	0.0152248748231484	0.992387562588426
32	0.00571252351748148	0.0114250470349630	0.994287476482518
33	0.0126885531447921	0.0253771062895842	0.987311446855208
34	0.0085392803314788	0.0170785606629576	0.991460719668521
35	0.00662093976206782	0.0132418795241356	0.993379060237932
36	0.00372371539125918	0.00744743078251835	0.99627628460874
37	0.00198138819291043	0.00396277638582087	0.99801861180709
38	0.000851847652512999	0.00170369530502600	0.999148152347487
39	0.000434628516133646	0.000869257032267293	0.999565371483866
40	0.000231578056050741	0.000463156112101483	0.99976842194395
41	0.000989616465318267	0.00197923293063653	0.999010383534682
42	0.00201450004714807	0.00402900009429613	0.997985499952852
43	0.0131467576062889	0.0262935152125779	0.986853242393711
44	0.0933231650504135	0.186646330100827	0.906676834949586

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	16	0.551724137931034	NOK
5% type I error level	26	0.896551724137931	NOK
10% type I error level	27	0.93103448275862	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 & 16 & 0.551724137931034 & NOK \tabularnewline
5% type I error level & 26 & 0.896551724137931 & NOK \tabularnewline
10% type I error level & 27 & 0.93103448275862 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69466&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]16[/C][C]0.551724137931034[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]26[/C][C]0.896551724137931[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]27[/C][C]0.93103448275862[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69466&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69466&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	16	0.551724137931034	NOK
5% type I error level	26	0.896551724137931	NOK
10% type I error level	27	0.93103448275862	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], 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,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
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, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
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,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
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,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
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,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
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,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
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