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Multiple Regression

Date of computation

Tue, 29 Nov 2011 17:37:55 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322606306uh8gj5wl3cvlzeu.htm/, Retrieved Thu, 06 Nov 2025 01:17:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148765, Retrieved Thu, 06 Nov 2025 01:17:24 +0000

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408

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

-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
F  MPD  [Multiple Regression] [] [2010-11-26 10:13:34] [8a9a6f7c332640af31ddca253a8ded58]
- RM        [Multiple Regression] [] [2011-11-29 22:37:55] [4be1b05f688f7fa8db5b9e9e4d3a7e33] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ yule.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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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	6 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Multiple Linear Regression - Estimated Regression Equation
vrijetijdsbesteding[t] = + 100.676931818182 -0.090488636363676M1[t] -0.0355909090909097M2[t] -0.298693181818184M3[t] -0.109795454545457M4[t] -0.394897727272729M5[t] -0.384000000000005M6[t] -0.543102272727275M7[t] -0.488204545454552M8[t] + 0.51469318181818M9[t] + 0.391590909090904M10[t] + 0.139602272727273M11[t] + 0.327102272727273t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
vrijetijdsbesteding[t] =  +  100.676931818182 -0.090488636363676M1[t] -0.0355909090909097M2[t] -0.298693181818184M3[t] -0.109795454545457M4[t] -0.394897727272729M5[t] -0.384000000000005M6[t] -0.543102272727275M7[t] -0.488204545454552M8[t] +  0.51469318181818M9[t] +  0.391590909090904M10[t] +  0.139602272727273M11[t] +  0.327102272727273t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]vrijetijdsbesteding[t] =  +  100.676931818182 -0.090488636363676M1[t] -0.0355909090909097M2[t] -0.298693181818184M3[t] -0.109795454545457M4[t] -0.394897727272729M5[t] -0.384000000000005M6[t] -0.543102272727275M7[t] -0.488204545454552M8[t] +  0.51469318181818M9[t] +  0.391590909090904M10[t] +  0.139602272727273M11[t] +  0.327102272727273t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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
vrijetijdsbesteding[t] = + 100.676931818182 -0.090488636363676M1[t] -0.0355909090909097M2[t] -0.298693181818184M3[t] -0.109795454545457M4[t] -0.394897727272729M5[t] -0.384000000000005M6[t] -0.543102272727275M7[t] -0.488204545454552M8[t] + 0.51469318181818M9[t] + 0.391590909090904M10[t] + 0.139602272727273M11[t] + 0.327102272727273t + 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)	100.676931818182	0.337006	298.7392	0	0
M1	-0.090488636363676	0.40885	-0.2213	0.825841	0.41292
M2	-0.0355909090909097	0.408592	-0.0871	0.930974	0.465487
M3	-0.298693181818184	0.408392	-0.7314	0.468334	0.234167
M4	-0.109795454545457	0.408249	-0.2689	0.789203	0.394602
M5	-0.394897727272729	0.408163	-0.9675	0.338466	0.169233
M6	-0.384000000000005	0.408135	-0.9409	0.351797	0.175899
M7	-0.543102272727275	0.408163	-1.3306	0.190024	0.095012
M8	-0.488204545454552	0.408249	-1.1958	0.238019	0.119009
M9	0.51469318181818	0.408392	1.2603	0.214061	0.10703
M10	0.391590909090904	0.408592	0.9584	0.342987	0.171494
M11	0.139602272727273	0.430239	0.3245	0.747081	0.373541
t	0.327102272727273	0.004834	67.665	0	0

\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) & 100.676931818182 & 0.337006 & 298.7392 & 0 & 0 \tabularnewline
M1 & -0.090488636363676 & 0.40885 & -0.2213 & 0.825841 & 0.41292 \tabularnewline
M2 & -0.0355909090909097 & 0.408592 & -0.0871 & 0.930974 & 0.465487 \tabularnewline
M3 & -0.298693181818184 & 0.408392 & -0.7314 & 0.468334 & 0.234167 \tabularnewline
M4 & -0.109795454545457 & 0.408249 & -0.2689 & 0.789203 & 0.394602 \tabularnewline
M5 & -0.394897727272729 & 0.408163 & -0.9675 & 0.338466 & 0.169233 \tabularnewline
M6 & -0.384000000000005 & 0.408135 & -0.9409 & 0.351797 & 0.175899 \tabularnewline
M7 & -0.543102272727275 & 0.408163 & -1.3306 & 0.190024 & 0.095012 \tabularnewline
M8 & -0.488204545454552 & 0.408249 & -1.1958 & 0.238019 & 0.119009 \tabularnewline
M9 & 0.51469318181818 & 0.408392 & 1.2603 & 0.214061 & 0.10703 \tabularnewline
M10 & 0.391590909090904 & 0.408592 & 0.9584 & 0.342987 & 0.171494 \tabularnewline
M11 & 0.139602272727273 & 0.430239 & 0.3245 & 0.747081 & 0.373541 \tabularnewline
t & 0.327102272727273 & 0.004834 & 67.665 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&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]100.676931818182[/C][C]0.337006[/C][C]298.7392[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.090488636363676[/C][C]0.40885[/C][C]-0.2213[/C][C]0.825841[/C][C]0.41292[/C][/ROW]
[ROW][C]M2[/C][C]-0.0355909090909097[/C][C]0.408592[/C][C]-0.0871[/C][C]0.930974[/C][C]0.465487[/C][/ROW]
[ROW][C]M3[/C][C]-0.298693181818184[/C][C]0.408392[/C][C]-0.7314[/C][C]0.468334[/C][C]0.234167[/C][/ROW]
[ROW][C]M4[/C][C]-0.109795454545457[/C][C]0.408249[/C][C]-0.2689[/C][C]0.789203[/C][C]0.394602[/C][/ROW]
[ROW][C]M5[/C][C]-0.394897727272729[/C][C]0.408163[/C][C]-0.9675[/C][C]0.338466[/C][C]0.169233[/C][/ROW]
[ROW][C]M6[/C][C]-0.384000000000005[/C][C]0.408135[/C][C]-0.9409[/C][C]0.351797[/C][C]0.175899[/C][/ROW]
[ROW][C]M7[/C][C]-0.543102272727275[/C][C]0.408163[/C][C]-1.3306[/C][C]0.190024[/C][C]0.095012[/C][/ROW]
[ROW][C]M8[/C][C]-0.488204545454552[/C][C]0.408249[/C][C]-1.1958[/C][C]0.238019[/C][C]0.119009[/C][/ROW]
[ROW][C]M9[/C][C]0.51469318181818[/C][C]0.408392[/C][C]1.2603[/C][C]0.214061[/C][C]0.10703[/C][/ROW]
[ROW][C]M10[/C][C]0.391590909090904[/C][C]0.408592[/C][C]0.9584[/C][C]0.342987[/C][C]0.171494[/C][/ROW]
[ROW][C]M11[/C][C]0.139602272727273[/C][C]0.430239[/C][C]0.3245[/C][C]0.747081[/C][C]0.373541[/C][/ROW]
[ROW][C]t[/C][C]0.327102272727273[/C][C]0.004834[/C][C]67.665[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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)	100.676931818182	0.337006	298.7392	0	0
M1	-0.090488636363676	0.40885	-0.2213	0.825841	0.41292
M2	-0.0355909090909097	0.408592	-0.0871	0.930974	0.465487
M3	-0.298693181818184	0.408392	-0.7314	0.468334	0.234167
M4	-0.109795454545457	0.408249	-0.2689	0.789203	0.394602
M5	-0.394897727272729	0.408163	-0.9675	0.338466	0.169233
M6	-0.384000000000005	0.408135	-0.9409	0.351797	0.175899
M7	-0.543102272727275	0.408163	-1.3306	0.190024	0.095012
M8	-0.488204545454552	0.408249	-1.1958	0.238019	0.119009
M9	0.51469318181818	0.408392	1.2603	0.214061	0.10703
M10	0.391590909090904	0.408592	0.9584	0.342987	0.171494
M11	0.139602272727273	0.430239	0.3245	0.747081	0.373541
t	0.327102272727273	0.004834	67.665	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.995287469888219
R-squared	0.990597147716492
Adjusted R-squared	0.98808972044089
F-TEST (value)	395.065155968917
F-TEST (DF numerator)	12
F-TEST (DF denominator)	45
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.608411215437963
Sum Squared Residuals	16.6573893181815

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.995287469888219 \tabularnewline
R-squared & 0.990597147716492 \tabularnewline
Adjusted R-squared & 0.98808972044089 \tabularnewline
F-TEST (value) & 395.065155968917 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 45 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.608411215437963 \tabularnewline
Sum Squared Residuals & 16.6573893181815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.995287469888219[/C][/ROW]
[ROW][C]R-squared[/C][C]0.990597147716492[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.98808972044089[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]395.065155968917[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]45[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.608411215437963[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]16.6573893181815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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	0.995287469888219
R-squared	0.990597147716492
Adjusted R-squared	0.98808972044089
F-TEST (value)	395.065155968917
F-TEST (DF numerator)	12
F-TEST (DF denominator)	45
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.608411215437963
Sum Squared Residuals	16.6573893181815

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	101.76	100.913545454546	0.8464545454544
2	102.37	101.295545454545	1.07445454545456
3	102.38	101.359545454545	1.02045454545455
4	102.86	101.875545454545	0.984454545454555
5	102.87	101.917545454545	0.952454545454554
6	102.92	102.255545454545	0.664454545454556
7	102.95	102.423545454545	0.526454545454553
8	103.02	102.805545454545	0.21445454545455
9	104.08	104.135545454545	-0.0555454545454503
10	104.16	104.339545454545	-0.179545454545449
11	104.24	104.414659090909	-0.174659090909094
12	104.33	104.602159090909	-0.27215909090909
13	104.73	104.838772727273	-0.108772727272687
14	104.86	105.220772727273	-0.360772727272727
15	105.03	105.284772727273	-0.254772727272722
16	105.62	105.800772727273	-0.18077272727272
17	105.63	105.842772727273	-0.212772727272729
18	105.63	106.180772727273	-0.550772727272726
19	105.94	106.348772727273	-0.408772727272728
20	106.61	106.730772727273	-0.120772727272722
21	107.69	108.060772727273	-0.370772727272728
22	107.78	108.264772727273	-0.484772727272721
23	107.93	108.339886363636	-0.409886363636358
24	108.48	108.527386363636	-0.0473863636363602
25	108.14	108.764	-0.623999999999961
26	108.48	109.146	-0.665999999999996
27	108.48	109.21	-0.729999999999996
28	108.89	109.726	-0.835999999999999
29	108.93	109.768	-0.837999999999993
30	109.21	110.106	-0.896000000000003
31	109.47	110.274	-0.804000000000001
32	109.8	110.656	-0.856
33	111.73	111.986	-0.255999999999998
34	111.85	112.19	-0.340000000000004
35	112.12	112.265113636364	-0.145113636363635
36	112.15	112.452613636364	-0.302613636363634
37	112.17	112.689227272727	-0.519227272727236
38	112.67	113.071227272727	-0.401227272727275
39	112.8	113.135227272727	-0.335227272727278
40	113.44	113.651227272727	-0.211227272727276
41	113.53	113.693227272727	-0.163227272727275
42	114.53	114.031227272727	0.498772727272728
43	114.51	114.199227272727	0.310772727272729
44	115.05	114.581227272727	0.468772727272723
45	116.67	115.911227272727	0.758772727272724
46	117.07	116.115227272727	0.95477272727272
47	116.92	116.190340909091	0.729659090909087
48	117	116.377840909091	0.622159090909082
49	117.02	116.614454545455	0.405545454545484
50	117.35	116.996454545455	0.353545454545441
51	117.36	117.060454545455	0.299545454545449
52	117.82	117.576454545455	0.24354545454544
53	117.88	117.618454545455	0.261545454545442
54	118.24	117.956454545455	0.283545454545444
55	118.5	118.124454545455	0.375545454545447
56	118.8	118.506454545455	0.293545454545449
57	119.76	119.836454545455	-0.0764545454545484
58	120.09	120.040454545455	0.0495454545454541

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 101.76 & 100.913545454546 & 0.8464545454544 \tabularnewline
2 & 102.37 & 101.295545454545 & 1.07445454545456 \tabularnewline
3 & 102.38 & 101.359545454545 & 1.02045454545455 \tabularnewline
4 & 102.86 & 101.875545454545 & 0.984454545454555 \tabularnewline
5 & 102.87 & 101.917545454545 & 0.952454545454554 \tabularnewline
6 & 102.92 & 102.255545454545 & 0.664454545454556 \tabularnewline
7 & 102.95 & 102.423545454545 & 0.526454545454553 \tabularnewline
8 & 103.02 & 102.805545454545 & 0.21445454545455 \tabularnewline
9 & 104.08 & 104.135545454545 & -0.0555454545454503 \tabularnewline
10 & 104.16 & 104.339545454545 & -0.179545454545449 \tabularnewline
11 & 104.24 & 104.414659090909 & -0.174659090909094 \tabularnewline
12 & 104.33 & 104.602159090909 & -0.27215909090909 \tabularnewline
13 & 104.73 & 104.838772727273 & -0.108772727272687 \tabularnewline
14 & 104.86 & 105.220772727273 & -0.360772727272727 \tabularnewline
15 & 105.03 & 105.284772727273 & -0.254772727272722 \tabularnewline
16 & 105.62 & 105.800772727273 & -0.18077272727272 \tabularnewline
17 & 105.63 & 105.842772727273 & -0.212772727272729 \tabularnewline
18 & 105.63 & 106.180772727273 & -0.550772727272726 \tabularnewline
19 & 105.94 & 106.348772727273 & -0.408772727272728 \tabularnewline
20 & 106.61 & 106.730772727273 & -0.120772727272722 \tabularnewline
21 & 107.69 & 108.060772727273 & -0.370772727272728 \tabularnewline
22 & 107.78 & 108.264772727273 & -0.484772727272721 \tabularnewline
23 & 107.93 & 108.339886363636 & -0.409886363636358 \tabularnewline
24 & 108.48 & 108.527386363636 & -0.0473863636363602 \tabularnewline
25 & 108.14 & 108.764 & -0.623999999999961 \tabularnewline
26 & 108.48 & 109.146 & -0.665999999999996 \tabularnewline
27 & 108.48 & 109.21 & -0.729999999999996 \tabularnewline
28 & 108.89 & 109.726 & -0.835999999999999 \tabularnewline
29 & 108.93 & 109.768 & -0.837999999999993 \tabularnewline
30 & 109.21 & 110.106 & -0.896000000000003 \tabularnewline
31 & 109.47 & 110.274 & -0.804000000000001 \tabularnewline
32 & 109.8 & 110.656 & -0.856 \tabularnewline
33 & 111.73 & 111.986 & -0.255999999999998 \tabularnewline
34 & 111.85 & 112.19 & -0.340000000000004 \tabularnewline
35 & 112.12 & 112.265113636364 & -0.145113636363635 \tabularnewline
36 & 112.15 & 112.452613636364 & -0.302613636363634 \tabularnewline
37 & 112.17 & 112.689227272727 & -0.519227272727236 \tabularnewline
38 & 112.67 & 113.071227272727 & -0.401227272727275 \tabularnewline
39 & 112.8 & 113.135227272727 & -0.335227272727278 \tabularnewline
40 & 113.44 & 113.651227272727 & -0.211227272727276 \tabularnewline
41 & 113.53 & 113.693227272727 & -0.163227272727275 \tabularnewline
42 & 114.53 & 114.031227272727 & 0.498772727272728 \tabularnewline
43 & 114.51 & 114.199227272727 & 0.310772727272729 \tabularnewline
44 & 115.05 & 114.581227272727 & 0.468772727272723 \tabularnewline
45 & 116.67 & 115.911227272727 & 0.758772727272724 \tabularnewline
46 & 117.07 & 116.115227272727 & 0.95477272727272 \tabularnewline
47 & 116.92 & 116.190340909091 & 0.729659090909087 \tabularnewline
48 & 117 & 116.377840909091 & 0.622159090909082 \tabularnewline
49 & 117.02 & 116.614454545455 & 0.405545454545484 \tabularnewline
50 & 117.35 & 116.996454545455 & 0.353545454545441 \tabularnewline
51 & 117.36 & 117.060454545455 & 0.299545454545449 \tabularnewline
52 & 117.82 & 117.576454545455 & 0.24354545454544 \tabularnewline
53 & 117.88 & 117.618454545455 & 0.261545454545442 \tabularnewline
54 & 118.24 & 117.956454545455 & 0.283545454545444 \tabularnewline
55 & 118.5 & 118.124454545455 & 0.375545454545447 \tabularnewline
56 & 118.8 & 118.506454545455 & 0.293545454545449 \tabularnewline
57 & 119.76 & 119.836454545455 & -0.0764545454545484 \tabularnewline
58 & 120.09 & 120.040454545455 & 0.0495454545454541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&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]101.76[/C][C]100.913545454546[/C][C]0.8464545454544[/C][/ROW]
[ROW][C]2[/C][C]102.37[/C][C]101.295545454545[/C][C]1.07445454545456[/C][/ROW]
[ROW][C]3[/C][C]102.38[/C][C]101.359545454545[/C][C]1.02045454545455[/C][/ROW]
[ROW][C]4[/C][C]102.86[/C][C]101.875545454545[/C][C]0.984454545454555[/C][/ROW]
[ROW][C]5[/C][C]102.87[/C][C]101.917545454545[/C][C]0.952454545454554[/C][/ROW]
[ROW][C]6[/C][C]102.92[/C][C]102.255545454545[/C][C]0.664454545454556[/C][/ROW]
[ROW][C]7[/C][C]102.95[/C][C]102.423545454545[/C][C]0.526454545454553[/C][/ROW]
[ROW][C]8[/C][C]103.02[/C][C]102.805545454545[/C][C]0.21445454545455[/C][/ROW]
[ROW][C]9[/C][C]104.08[/C][C]104.135545454545[/C][C]-0.0555454545454503[/C][/ROW]
[ROW][C]10[/C][C]104.16[/C][C]104.339545454545[/C][C]-0.179545454545449[/C][/ROW]
[ROW][C]11[/C][C]104.24[/C][C]104.414659090909[/C][C]-0.174659090909094[/C][/ROW]
[ROW][C]12[/C][C]104.33[/C][C]104.602159090909[/C][C]-0.27215909090909[/C][/ROW]
[ROW][C]13[/C][C]104.73[/C][C]104.838772727273[/C][C]-0.108772727272687[/C][/ROW]
[ROW][C]14[/C][C]104.86[/C][C]105.220772727273[/C][C]-0.360772727272727[/C][/ROW]
[ROW][C]15[/C][C]105.03[/C][C]105.284772727273[/C][C]-0.254772727272722[/C][/ROW]
[ROW][C]16[/C][C]105.62[/C][C]105.800772727273[/C][C]-0.18077272727272[/C][/ROW]
[ROW][C]17[/C][C]105.63[/C][C]105.842772727273[/C][C]-0.212772727272729[/C][/ROW]
[ROW][C]18[/C][C]105.63[/C][C]106.180772727273[/C][C]-0.550772727272726[/C][/ROW]
[ROW][C]19[/C][C]105.94[/C][C]106.348772727273[/C][C]-0.408772727272728[/C][/ROW]
[ROW][C]20[/C][C]106.61[/C][C]106.730772727273[/C][C]-0.120772727272722[/C][/ROW]
[ROW][C]21[/C][C]107.69[/C][C]108.060772727273[/C][C]-0.370772727272728[/C][/ROW]
[ROW][C]22[/C][C]107.78[/C][C]108.264772727273[/C][C]-0.484772727272721[/C][/ROW]
[ROW][C]23[/C][C]107.93[/C][C]108.339886363636[/C][C]-0.409886363636358[/C][/ROW]
[ROW][C]24[/C][C]108.48[/C][C]108.527386363636[/C][C]-0.0473863636363602[/C][/ROW]
[ROW][C]25[/C][C]108.14[/C][C]108.764[/C][C]-0.623999999999961[/C][/ROW]
[ROW][C]26[/C][C]108.48[/C][C]109.146[/C][C]-0.665999999999996[/C][/ROW]
[ROW][C]27[/C][C]108.48[/C][C]109.21[/C][C]-0.729999999999996[/C][/ROW]
[ROW][C]28[/C][C]108.89[/C][C]109.726[/C][C]-0.835999999999999[/C][/ROW]
[ROW][C]29[/C][C]108.93[/C][C]109.768[/C][C]-0.837999999999993[/C][/ROW]
[ROW][C]30[/C][C]109.21[/C][C]110.106[/C][C]-0.896000000000003[/C][/ROW]
[ROW][C]31[/C][C]109.47[/C][C]110.274[/C][C]-0.804000000000001[/C][/ROW]
[ROW][C]32[/C][C]109.8[/C][C]110.656[/C][C]-0.856[/C][/ROW]
[ROW][C]33[/C][C]111.73[/C][C]111.986[/C][C]-0.255999999999998[/C][/ROW]
[ROW][C]34[/C][C]111.85[/C][C]112.19[/C][C]-0.340000000000004[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]112.265113636364[/C][C]-0.145113636363635[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]112.452613636364[/C][C]-0.302613636363634[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]112.689227272727[/C][C]-0.519227272727236[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]113.071227272727[/C][C]-0.401227272727275[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]113.135227272727[/C][C]-0.335227272727278[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]113.651227272727[/C][C]-0.211227272727276[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]113.693227272727[/C][C]-0.163227272727275[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]114.031227272727[/C][C]0.498772727272728[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]114.199227272727[/C][C]0.310772727272729[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]114.581227272727[/C][C]0.468772727272723[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]115.911227272727[/C][C]0.758772727272724[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]116.115227272727[/C][C]0.95477272727272[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]116.190340909091[/C][C]0.729659090909087[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]116.377840909091[/C][C]0.622159090909082[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]116.614454545455[/C][C]0.405545454545484[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]116.996454545455[/C][C]0.353545454545441[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]117.060454545455[/C][C]0.299545454545449[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]117.576454545455[/C][C]0.24354545454544[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]117.618454545455[/C][C]0.261545454545442[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]117.956454545455[/C][C]0.283545454545444[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]118.124454545455[/C][C]0.375545454545447[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]118.506454545455[/C][C]0.293545454545449[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]119.836454545455[/C][C]-0.0764545454545484[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]120.040454545455[/C][C]0.0495454545454541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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	101.76	100.913545454546	0.8464545454544
2	102.37	101.295545454545	1.07445454545456
3	102.38	101.359545454545	1.02045454545455
4	102.86	101.875545454545	0.984454545454555
5	102.87	101.917545454545	0.952454545454554
6	102.92	102.255545454545	0.664454545454556
7	102.95	102.423545454545	0.526454545454553
8	103.02	102.805545454545	0.21445454545455
9	104.08	104.135545454545	-0.0555454545454503
10	104.16	104.339545454545	-0.179545454545449
11	104.24	104.414659090909	-0.174659090909094
12	104.33	104.602159090909	-0.27215909090909
13	104.73	104.838772727273	-0.108772727272687
14	104.86	105.220772727273	-0.360772727272727
15	105.03	105.284772727273	-0.254772727272722
16	105.62	105.800772727273	-0.18077272727272
17	105.63	105.842772727273	-0.212772727272729
18	105.63	106.180772727273	-0.550772727272726
19	105.94	106.348772727273	-0.408772727272728
20	106.61	106.730772727273	-0.120772727272722
21	107.69	108.060772727273	-0.370772727272728
22	107.78	108.264772727273	-0.484772727272721
23	107.93	108.339886363636	-0.409886363636358
24	108.48	108.527386363636	-0.0473863636363602
25	108.14	108.764	-0.623999999999961
26	108.48	109.146	-0.665999999999996
27	108.48	109.21	-0.729999999999996
28	108.89	109.726	-0.835999999999999
29	108.93	109.768	-0.837999999999993
30	109.21	110.106	-0.896000000000003
31	109.47	110.274	-0.804000000000001
32	109.8	110.656	-0.856
33	111.73	111.986	-0.255999999999998
34	111.85	112.19	-0.340000000000004
35	112.12	112.265113636364	-0.145113636363635
36	112.15	112.452613636364	-0.302613636363634
37	112.17	112.689227272727	-0.519227272727236
38	112.67	113.071227272727	-0.401227272727275
39	112.8	113.135227272727	-0.335227272727278
40	113.44	113.651227272727	-0.211227272727276
41	113.53	113.693227272727	-0.163227272727275
42	114.53	114.031227272727	0.498772727272728
43	114.51	114.199227272727	0.310772727272729
44	115.05	114.581227272727	0.468772727272723
45	116.67	115.911227272727	0.758772727272724
46	117.07	116.115227272727	0.95477272727272
47	116.92	116.190340909091	0.729659090909087
48	117	116.377840909091	0.622159090909082
49	117.02	116.614454545455	0.405545454545484
50	117.35	116.996454545455	0.353545454545441
51	117.36	117.060454545455	0.299545454545449
52	117.82	117.576454545455	0.24354545454544
53	117.88	117.618454545455	0.261545454545442
54	118.24	117.956454545455	0.283545454545444
55	118.5	118.124454545455	0.375545454545447
56	118.8	118.506454545455	0.293545454545449
57	119.76	119.836454545455	-0.0764545454545484
58	120.09	120.040454545455	0.0495454545454541

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0577063209451328	0.115412641890266	0.942293679054867
17	0.019739302720929	0.039478605441858	0.980260697279071
18	0.00535063146476823	0.0107012629295365	0.994649368535232
19	0.00426899606102449	0.00853799212204898	0.995731003938976
20	0.101377248225139	0.202754496450277	0.898622751774861
21	0.193496468950704	0.386992937901407	0.806503531049296
22	0.235644735312614	0.471289470625229	0.764355264687386
23	0.26002738288873	0.520054765777461	0.73997261711127
24	0.459618447571994	0.919236895143988	0.540381552428006
25	0.364204097994082	0.728408195988165	0.635795902005918
26	0.272759828499015	0.545519656998031	0.727240171500985
27	0.192915890128643	0.385831780257286	0.807084109871357
28	0.133282101613714	0.266564203227428	0.866717898386286
29	0.0875443865868321	0.175088773173664	0.912455613413168
30	0.0735845586927304	0.147169117385461	0.92641544130727
31	0.0612717359939966	0.122543471987993	0.938728264006003
32	0.061846277454788	0.123692554909576	0.938153722545212
33	0.124886854057839	0.249773708115678	0.87511314594216
34	0.191697033206665	0.383394066413331	0.808302966793335
35	0.29323642813062	0.58647285626124	0.70676357186938
36	0.347076714499711	0.694153428999422	0.652923285500289
37	0.415023206029049	0.830046412058098	0.584976793970951
38	0.481716329291993	0.963432658583987	0.518283670708007
39	0.554444443730993	0.891111112538013	0.445555556269007
40	0.61259315499723	0.774813690005539	0.38740684500277
41	0.743354509673894	0.513290980652211	0.256645490326106
42	0.698178696460078	0.603642607079844	0.301821303539922

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0577063209451328 & 0.115412641890266 & 0.942293679054867 \tabularnewline
17 & 0.019739302720929 & 0.039478605441858 & 0.980260697279071 \tabularnewline
18 & 0.00535063146476823 & 0.0107012629295365 & 0.994649368535232 \tabularnewline
19 & 0.00426899606102449 & 0.00853799212204898 & 0.995731003938976 \tabularnewline
20 & 0.101377248225139 & 0.202754496450277 & 0.898622751774861 \tabularnewline
21 & 0.193496468950704 & 0.386992937901407 & 0.806503531049296 \tabularnewline
22 & 0.235644735312614 & 0.471289470625229 & 0.764355264687386 \tabularnewline
23 & 0.26002738288873 & 0.520054765777461 & 0.73997261711127 \tabularnewline
24 & 0.459618447571994 & 0.919236895143988 & 0.540381552428006 \tabularnewline
25 & 0.364204097994082 & 0.728408195988165 & 0.635795902005918 \tabularnewline
26 & 0.272759828499015 & 0.545519656998031 & 0.727240171500985 \tabularnewline
27 & 0.192915890128643 & 0.385831780257286 & 0.807084109871357 \tabularnewline
28 & 0.133282101613714 & 0.266564203227428 & 0.866717898386286 \tabularnewline
29 & 0.0875443865868321 & 0.175088773173664 & 0.912455613413168 \tabularnewline
30 & 0.0735845586927304 & 0.147169117385461 & 0.92641544130727 \tabularnewline
31 & 0.0612717359939966 & 0.122543471987993 & 0.938728264006003 \tabularnewline
32 & 0.061846277454788 & 0.123692554909576 & 0.938153722545212 \tabularnewline
33 & 0.124886854057839 & 0.249773708115678 & 0.87511314594216 \tabularnewline
34 & 0.191697033206665 & 0.383394066413331 & 0.808302966793335 \tabularnewline
35 & 0.29323642813062 & 0.58647285626124 & 0.70676357186938 \tabularnewline
36 & 0.347076714499711 & 0.694153428999422 & 0.652923285500289 \tabularnewline
37 & 0.415023206029049 & 0.830046412058098 & 0.584976793970951 \tabularnewline
38 & 0.481716329291993 & 0.963432658583987 & 0.518283670708007 \tabularnewline
39 & 0.554444443730993 & 0.891111112538013 & 0.445555556269007 \tabularnewline
40 & 0.61259315499723 & 0.774813690005539 & 0.38740684500277 \tabularnewline
41 & 0.743354509673894 & 0.513290980652211 & 0.256645490326106 \tabularnewline
42 & 0.698178696460078 & 0.603642607079844 & 0.301821303539922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&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]0.0577063209451328[/C][C]0.115412641890266[/C][C]0.942293679054867[/C][/ROW]
[ROW][C]17[/C][C]0.019739302720929[/C][C]0.039478605441858[/C][C]0.980260697279071[/C][/ROW]
[ROW][C]18[/C][C]0.00535063146476823[/C][C]0.0107012629295365[/C][C]0.994649368535232[/C][/ROW]
[ROW][C]19[/C][C]0.00426899606102449[/C][C]0.00853799212204898[/C][C]0.995731003938976[/C][/ROW]
[ROW][C]20[/C][C]0.101377248225139[/C][C]0.202754496450277[/C][C]0.898622751774861[/C][/ROW]
[ROW][C]21[/C][C]0.193496468950704[/C][C]0.386992937901407[/C][C]0.806503531049296[/C][/ROW]
[ROW][C]22[/C][C]0.235644735312614[/C][C]0.471289470625229[/C][C]0.764355264687386[/C][/ROW]
[ROW][C]23[/C][C]0.26002738288873[/C][C]0.520054765777461[/C][C]0.73997261711127[/C][/ROW]
[ROW][C]24[/C][C]0.459618447571994[/C][C]0.919236895143988[/C][C]0.540381552428006[/C][/ROW]
[ROW][C]25[/C][C]0.364204097994082[/C][C]0.728408195988165[/C][C]0.635795902005918[/C][/ROW]
[ROW][C]26[/C][C]0.272759828499015[/C][C]0.545519656998031[/C][C]0.727240171500985[/C][/ROW]
[ROW][C]27[/C][C]0.192915890128643[/C][C]0.385831780257286[/C][C]0.807084109871357[/C][/ROW]
[ROW][C]28[/C][C]0.133282101613714[/C][C]0.266564203227428[/C][C]0.866717898386286[/C][/ROW]
[ROW][C]29[/C][C]0.0875443865868321[/C][C]0.175088773173664[/C][C]0.912455613413168[/C][/ROW]
[ROW][C]30[/C][C]0.0735845586927304[/C][C]0.147169117385461[/C][C]0.92641544130727[/C][/ROW]
[ROW][C]31[/C][C]0.0612717359939966[/C][C]0.122543471987993[/C][C]0.938728264006003[/C][/ROW]
[ROW][C]32[/C][C]0.061846277454788[/C][C]0.123692554909576[/C][C]0.938153722545212[/C][/ROW]
[ROW][C]33[/C][C]0.124886854057839[/C][C]0.249773708115678[/C][C]0.87511314594216[/C][/ROW]
[ROW][C]34[/C][C]0.191697033206665[/C][C]0.383394066413331[/C][C]0.808302966793335[/C][/ROW]
[ROW][C]35[/C][C]0.29323642813062[/C][C]0.58647285626124[/C][C]0.70676357186938[/C][/ROW]
[ROW][C]36[/C][C]0.347076714499711[/C][C]0.694153428999422[/C][C]0.652923285500289[/C][/ROW]
[ROW][C]37[/C][C]0.415023206029049[/C][C]0.830046412058098[/C][C]0.584976793970951[/C][/ROW]
[ROW][C]38[/C][C]0.481716329291993[/C][C]0.963432658583987[/C][C]0.518283670708007[/C][/ROW]
[ROW][C]39[/C][C]0.554444443730993[/C][C]0.891111112538013[/C][C]0.445555556269007[/C][/ROW]
[ROW][C]40[/C][C]0.61259315499723[/C][C]0.774813690005539[/C][C]0.38740684500277[/C][/ROW]
[ROW][C]41[/C][C]0.743354509673894[/C][C]0.513290980652211[/C][C]0.256645490326106[/C][/ROW]
[ROW][C]42[/C][C]0.698178696460078[/C][C]0.603642607079844[/C][C]0.301821303539922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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	0.0577063209451328	0.115412641890266	0.942293679054867
17	0.019739302720929	0.039478605441858	0.980260697279071
18	0.00535063146476823	0.0107012629295365	0.994649368535232
19	0.00426899606102449	0.00853799212204898	0.995731003938976
20	0.101377248225139	0.202754496450277	0.898622751774861
21	0.193496468950704	0.386992937901407	0.806503531049296
22	0.235644735312614	0.471289470625229	0.764355264687386
23	0.26002738288873	0.520054765777461	0.73997261711127
24	0.459618447571994	0.919236895143988	0.540381552428006
25	0.364204097994082	0.728408195988165	0.635795902005918
26	0.272759828499015	0.545519656998031	0.727240171500985
27	0.192915890128643	0.385831780257286	0.807084109871357
28	0.133282101613714	0.266564203227428	0.866717898386286
29	0.0875443865868321	0.175088773173664	0.912455613413168
30	0.0735845586927304	0.147169117385461	0.92641544130727
31	0.0612717359939966	0.122543471987993	0.938728264006003
32	0.061846277454788	0.123692554909576	0.938153722545212
33	0.124886854057839	0.249773708115678	0.87511314594216
34	0.191697033206665	0.383394066413331	0.808302966793335
35	0.29323642813062	0.58647285626124	0.70676357186938
36	0.347076714499711	0.694153428999422	0.652923285500289
37	0.415023206029049	0.830046412058098	0.584976793970951
38	0.481716329291993	0.963432658583987	0.518283670708007
39	0.554444443730993	0.891111112538013	0.445555556269007
40	0.61259315499723	0.774813690005539	0.38740684500277
41	0.743354509673894	0.513290980652211	0.256645490326106
42	0.698178696460078	0.603642607079844	0.301821303539922

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.037037037037037	NOK
5% type I error level	3	0.111111111111111	NOK
10% type I error level	3	0.111111111111111	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 & 1 & 0.037037037037037 & NOK \tabularnewline
5% type I error level & 3 & 0.111111111111111 & NOK \tabularnewline
10% type I error level & 3 & 0.111111111111111 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148765&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]1[/C][C]0.037037037037037[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]3[/C][C]0.111111111111111[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.111111111111111[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148765&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148765&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	1	0.037037037037037	NOK
5% type I error level	3	0.111111111111111	NOK
10% type I error level	3	0.111111111111111	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 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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