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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 09 Dec 2009 07:20:25 -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/09/t12603685510ormh8cijwzqawr.htm/, Retrieved Mon, 29 Apr 2024 12:59:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64963, Retrieved Mon, 29 Apr 2024 12:59:06 +0000

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Estimated Impact

116

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-12-09 14:20:25] [faa1ded5041cd5a0e2be04844f08502a] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&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]4 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=64963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
S.[t] = + 5.29372655439379 + 0.400869981642590E.S.[t] -0.35576928193259M1[t] -2.27843403304333M2[t] + 1.52156596695666M3[t] + 0.838782025700374M4[t] + 1.03878202570037M5[t] -0.241391970628143M6[t] -3.32243594859925M7[t] -0.71982600367148M8[t] + 0.6M9[t] -0.079304014685929M10[t] -1.36121797429962M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
S.[t] =  +  5.29372655439379 +  0.400869981642590E.S.[t] -0.35576928193259M1[t] -2.27843403304333M2[t] +  1.52156596695666M3[t] +  0.838782025700374M4[t] +  1.03878202570037M5[t] -0.241391970628143M6[t] -3.32243594859925M7[t] -0.71982600367148M8[t] +  0.6M9[t] -0.079304014685929M10[t] -1.36121797429962M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]S.[t] =  +  5.29372655439379 +  0.400869981642590E.S.[t] -0.35576928193259M1[t] -2.27843403304333M2[t] +  1.52156596695666M3[t] +  0.838782025700374M4[t] +  1.03878202570037M5[t] -0.241391970628143M6[t] -3.32243594859925M7[t] -0.71982600367148M8[t] +  0.6M9[t] -0.079304014685929M10[t] -1.36121797429962M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&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
S.[t] = + 5.29372655439379 + 0.400869981642590E.S.[t] -0.35576928193259M1[t] -2.27843403304333M2[t] + 1.52156596695666M3[t] + 0.838782025700374M4[t] + 1.03878202570037M5[t] -0.241391970628143M6[t] -3.32243594859925M7[t] -0.71982600367148M8[t] + 0.6M9[t] -0.079304014685929M10[t] -1.36121797429962M11[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)	5.29372655439379	3.325294	1.592	0.117959	0.05898
E.S.	0.400869981642590	0.076001	5.2745	3e-06	2e-06
M1	-0.35576928193259	3.264875	-0.109	0.913682	0.456841
M2	-2.27843403304333	3.405549	-0.669	0.506678	0.253339
M3	1.52156596695666	3.405549	0.4468	0.657036	0.328518
M4	0.838782025700374	3.404463	0.2464	0.806441	0.40322
M5	1.03878202570037	3.404463	0.3051	0.761591	0.380796
M6	-0.241391970628143	3.404972	-0.0709	0.943777	0.471888
M7	-3.32243594859925	3.409447	-0.9745	0.334704	0.167352
M8	-0.71982600367148	3.402834	-0.2115	0.833364	0.416682
M9	0.6	3.4028	0.1763	0.86078	0.43039
M10	-0.079304014685929	3.403343	-0.0233	0.981506	0.490753
M11	-1.36121797429962	3.404463	-0.3998	0.691053	0.345526

\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) & 5.29372655439379 & 3.325294 & 1.592 & 0.117959 & 0.05898 \tabularnewline
E.S. & 0.400869981642590 & 0.076001 & 5.2745 & 3e-06 & 2e-06 \tabularnewline
M1 & -0.35576928193259 & 3.264875 & -0.109 & 0.913682 & 0.456841 \tabularnewline
M2 & -2.27843403304333 & 3.405549 & -0.669 & 0.506678 & 0.253339 \tabularnewline
M3 & 1.52156596695666 & 3.405549 & 0.4468 & 0.657036 & 0.328518 \tabularnewline
M4 & 0.838782025700374 & 3.404463 & 0.2464 & 0.806441 & 0.40322 \tabularnewline
M5 & 1.03878202570037 & 3.404463 & 0.3051 & 0.761591 & 0.380796 \tabularnewline
M6 & -0.241391970628143 & 3.404972 & -0.0709 & 0.943777 & 0.471888 \tabularnewline
M7 & -3.32243594859925 & 3.409447 & -0.9745 & 0.334704 & 0.167352 \tabularnewline
M8 & -0.71982600367148 & 3.402834 & -0.2115 & 0.833364 & 0.416682 \tabularnewline
M9 & 0.6 & 3.4028 & 0.1763 & 0.86078 & 0.43039 \tabularnewline
M10 & -0.079304014685929 & 3.403343 & -0.0233 & 0.981506 & 0.490753 \tabularnewline
M11 & -1.36121797429962 & 3.404463 & -0.3998 & 0.691053 & 0.345526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&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]5.29372655439379[/C][C]3.325294[/C][C]1.592[/C][C]0.117959[/C][C]0.05898[/C][/ROW]
[ROW][C]E.S.[/C][C]0.400869981642590[/C][C]0.076001[/C][C]5.2745[/C][C]3e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M1[/C][C]-0.35576928193259[/C][C]3.264875[/C][C]-0.109[/C][C]0.913682[/C][C]0.456841[/C][/ROW]
[ROW][C]M2[/C][C]-2.27843403304333[/C][C]3.405549[/C][C]-0.669[/C][C]0.506678[/C][C]0.253339[/C][/ROW]
[ROW][C]M3[/C][C]1.52156596695666[/C][C]3.405549[/C][C]0.4468[/C][C]0.657036[/C][C]0.328518[/C][/ROW]
[ROW][C]M4[/C][C]0.838782025700374[/C][C]3.404463[/C][C]0.2464[/C][C]0.806441[/C][C]0.40322[/C][/ROW]
[ROW][C]M5[/C][C]1.03878202570037[/C][C]3.404463[/C][C]0.3051[/C][C]0.761591[/C][C]0.380796[/C][/ROW]
[ROW][C]M6[/C][C]-0.241391970628143[/C][C]3.404972[/C][C]-0.0709[/C][C]0.943777[/C][C]0.471888[/C][/ROW]
[ROW][C]M7[/C][C]-3.32243594859925[/C][C]3.409447[/C][C]-0.9745[/C][C]0.334704[/C][C]0.167352[/C][/ROW]
[ROW][C]M8[/C][C]-0.71982600367148[/C][C]3.402834[/C][C]-0.2115[/C][C]0.833364[/C][C]0.416682[/C][/ROW]
[ROW][C]M9[/C][C]0.6[/C][C]3.4028[/C][C]0.1763[/C][C]0.86078[/C][C]0.43039[/C][/ROW]
[ROW][C]M10[/C][C]-0.079304014685929[/C][C]3.403343[/C][C]-0.0233[/C][C]0.981506[/C][C]0.490753[/C][/ROW]
[ROW][C]M11[/C][C]-1.36121797429962[/C][C]3.404463[/C][C]-0.3998[/C][C]0.691053[/C][C]0.345526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&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)	5.29372655439379	3.325294	1.592	0.117959	0.05898
E.S.	0.400869981642590	0.076001	5.2745	3e-06	2e-06
M1	-0.35576928193259	3.264875	-0.109	0.913682	0.456841
M2	-2.27843403304333	3.405549	-0.669	0.506678	0.253339
M3	1.52156596695666	3.405549	0.4468	0.657036	0.328518
M4	0.838782025700374	3.404463	0.2464	0.806441	0.40322
M5	1.03878202570037	3.404463	0.3051	0.761591	0.380796
M6	-0.241391970628143	3.404972	-0.0709	0.943777	0.471888
M7	-3.32243594859925	3.409447	-0.9745	0.334704	0.167352
M8	-0.71982600367148	3.402834	-0.2115	0.833364	0.416682
M9	0.6	3.4028	0.1763	0.86078	0.43039
M10	-0.079304014685929	3.403343	-0.0233	0.981506	0.490753
M11	-1.36121797429962	3.404463	-0.3998	0.691053	0.345526

Multiple Linear Regression - Regression Statistics
Multiple R	0.62965823162227
R-squared	0.396469488649684
Adjusted R-squared	0.245586860812105
F-TEST (value)	2.62766823677324
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.00881546071620987
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.38029882265957
Sum Squared Residuals	1389.48554021337

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.62965823162227 \tabularnewline
R-squared & 0.396469488649684 \tabularnewline
Adjusted R-squared & 0.245586860812105 \tabularnewline
F-TEST (value) & 2.62766823677324 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.00881546071620987 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.38029882265957 \tabularnewline
Sum Squared Residuals & 1389.48554021337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.62965823162227[/C][/ROW]
[ROW][C]R-squared[/C][C]0.396469488649684[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.245586860812105[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.62766823677324[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.00881546071620987[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.38029882265957[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1389.48554021337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64963&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&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	0.62965823162227
R-squared	0.396469488649684
Adjusted R-squared	0.245586860812105
F-TEST (value)	2.62766823677324
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.00881546071620987
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.38029882265957
Sum Squared Residuals	1389.48554021337

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	24	18.1666666666667	5.83333333333329
2	22	16.6448718971985	5.35512810280152
3	25	21.2466118604837	3.75338813951632
4	24	20.5638279192274	3.43617208077261
5	29	21.5655678825126	7.43443211748743
6	26	21.8888738127544	4.11112618724559
7	26	16.0017399632852	9.99826003671482
8	21	14.5956500917870	6.40434990821295
9	23	15.5146061138159	7.48539388618406
10	22	14.0335621358448	7.96643786415516
11	21	14.7559980844441	6.24400191555591
12	16	12.1085162423178	3.89148375768218
13	19	16.9640567217389	2.03594327826111
14	16	15.0413919706281	0.958608029371852
15	25	20.4448718971985	4.5551281028015
16	27	20.96469790087	6.03530209913002
17	23	20.7638279192274	2.23617208077261
18	22	18.2810439779711	3.71895602202889
19	23	15.2	7.8
20	20	17.8026099449278	2.19739005507223
21	24	20.7259158751696	3.27408412483039
22	23	21.2492218054114	1.75077819458855
23	20	17.9629579375848	2.03704206241520
24	21	20.1259158751696	0.874084124830393
25	22	22.1753664830925	-0.175366483092550
26	17	19.8518317503392	-2.85183175033922
27	21	20.0440019155559	0.95599808444409
28	19	21.7664378641552	-2.76643786415516
29	23	22.3673078457978	0.63269215420225
30	22	19.8845239045415	2.11547609545854
31	15	19.6095697980685	-4.60956979806848
32	23	21.4104397797111	1.58956022028893
33	21	23.1311357650251	-2.13113576502514
34	18	21.2492218054114	-3.24922180541145
35	18	15.9586080293719	2.04139197062814
36	18	17.3198260036715	0.680173996328518
37	18	17.3649267033815	0.635073296618521
38	10	10.2309521909171	-0.230952190917076
39	13	16.4361720807726	-3.43617208077261
40	10	14.9516481762311	-4.95164817623114
41	9	16.7551281028015	-7.7551281028015
42	9	16.2766940697582	-7.27669406975816
43	6	11.1913001835741	-5.19130018357411
44	11	11.3886902386463	-0.388690238646338
45	9	10.7041663341049	-1.70416633410488
46	10	8.82225237449118	1.17774762550882
47	9	11.5490382313034	-2.54903823130338
48	16	13.7119961688882	2.28800383111182
49	10	12.1536169420278	-2.15361694202782
50	7	10.2309521909171	-3.23095219091708
51	7	12.8283422459893	-5.8283422459893
52	14	15.7533881395163	-1.75338813951632
53	11	13.5481682496608	-2.54816824966079
54	10	12.6688642349749	-2.66886423497486
55	6	13.9973900550722	-7.99739005507223
56	8	17.8026099449278	-9.80260994492777
57	13	19.9241759118844	-6.92417591188443
58	12	19.6457418788411	-7.64574187884109
59	15	22.7733977172959	-7.77339771729588
60	16	23.7337457099529	-7.73374570995291
61	16	22.1753664830926	-6.17536648309255

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 24 & 18.1666666666667 & 5.83333333333329 \tabularnewline
2 & 22 & 16.6448718971985 & 5.35512810280152 \tabularnewline
3 & 25 & 21.2466118604837 & 3.75338813951632 \tabularnewline
4 & 24 & 20.5638279192274 & 3.43617208077261 \tabularnewline
5 & 29 & 21.5655678825126 & 7.43443211748743 \tabularnewline
6 & 26 & 21.8888738127544 & 4.11112618724559 \tabularnewline
7 & 26 & 16.0017399632852 & 9.99826003671482 \tabularnewline
8 & 21 & 14.5956500917870 & 6.40434990821295 \tabularnewline
9 & 23 & 15.5146061138159 & 7.48539388618406 \tabularnewline
10 & 22 & 14.0335621358448 & 7.96643786415516 \tabularnewline
11 & 21 & 14.7559980844441 & 6.24400191555591 \tabularnewline
12 & 16 & 12.1085162423178 & 3.89148375768218 \tabularnewline
13 & 19 & 16.9640567217389 & 2.03594327826111 \tabularnewline
14 & 16 & 15.0413919706281 & 0.958608029371852 \tabularnewline
15 & 25 & 20.4448718971985 & 4.5551281028015 \tabularnewline
16 & 27 & 20.96469790087 & 6.03530209913002 \tabularnewline
17 & 23 & 20.7638279192274 & 2.23617208077261 \tabularnewline
18 & 22 & 18.2810439779711 & 3.71895602202889 \tabularnewline
19 & 23 & 15.2 & 7.8 \tabularnewline
20 & 20 & 17.8026099449278 & 2.19739005507223 \tabularnewline
21 & 24 & 20.7259158751696 & 3.27408412483039 \tabularnewline
22 & 23 & 21.2492218054114 & 1.75077819458855 \tabularnewline
23 & 20 & 17.9629579375848 & 2.03704206241520 \tabularnewline
24 & 21 & 20.1259158751696 & 0.874084124830393 \tabularnewline
25 & 22 & 22.1753664830925 & -0.175366483092550 \tabularnewline
26 & 17 & 19.8518317503392 & -2.85183175033922 \tabularnewline
27 & 21 & 20.0440019155559 & 0.95599808444409 \tabularnewline
28 & 19 & 21.7664378641552 & -2.76643786415516 \tabularnewline
29 & 23 & 22.3673078457978 & 0.63269215420225 \tabularnewline
30 & 22 & 19.8845239045415 & 2.11547609545854 \tabularnewline
31 & 15 & 19.6095697980685 & -4.60956979806848 \tabularnewline
32 & 23 & 21.4104397797111 & 1.58956022028893 \tabularnewline
33 & 21 & 23.1311357650251 & -2.13113576502514 \tabularnewline
34 & 18 & 21.2492218054114 & -3.24922180541145 \tabularnewline
35 & 18 & 15.9586080293719 & 2.04139197062814 \tabularnewline
36 & 18 & 17.3198260036715 & 0.680173996328518 \tabularnewline
37 & 18 & 17.3649267033815 & 0.635073296618521 \tabularnewline
38 & 10 & 10.2309521909171 & -0.230952190917076 \tabularnewline
39 & 13 & 16.4361720807726 & -3.43617208077261 \tabularnewline
40 & 10 & 14.9516481762311 & -4.95164817623114 \tabularnewline
41 & 9 & 16.7551281028015 & -7.7551281028015 \tabularnewline
42 & 9 & 16.2766940697582 & -7.27669406975816 \tabularnewline
43 & 6 & 11.1913001835741 & -5.19130018357411 \tabularnewline
44 & 11 & 11.3886902386463 & -0.388690238646338 \tabularnewline
45 & 9 & 10.7041663341049 & -1.70416633410488 \tabularnewline
46 & 10 & 8.82225237449118 & 1.17774762550882 \tabularnewline
47 & 9 & 11.5490382313034 & -2.54903823130338 \tabularnewline
48 & 16 & 13.7119961688882 & 2.28800383111182 \tabularnewline
49 & 10 & 12.1536169420278 & -2.15361694202782 \tabularnewline
50 & 7 & 10.2309521909171 & -3.23095219091708 \tabularnewline
51 & 7 & 12.8283422459893 & -5.8283422459893 \tabularnewline
52 & 14 & 15.7533881395163 & -1.75338813951632 \tabularnewline
53 & 11 & 13.5481682496608 & -2.54816824966079 \tabularnewline
54 & 10 & 12.6688642349749 & -2.66886423497486 \tabularnewline
55 & 6 & 13.9973900550722 & -7.99739005507223 \tabularnewline
56 & 8 & 17.8026099449278 & -9.80260994492777 \tabularnewline
57 & 13 & 19.9241759118844 & -6.92417591188443 \tabularnewline
58 & 12 & 19.6457418788411 & -7.64574187884109 \tabularnewline
59 & 15 & 22.7733977172959 & -7.77339771729588 \tabularnewline
60 & 16 & 23.7337457099529 & -7.73374570995291 \tabularnewline
61 & 16 & 22.1753664830926 & -6.17536648309255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&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]24[/C][C]18.1666666666667[/C][C]5.83333333333329[/C][/ROW]
[ROW][C]2[/C][C]22[/C][C]16.6448718971985[/C][C]5.35512810280152[/C][/ROW]
[ROW][C]3[/C][C]25[/C][C]21.2466118604837[/C][C]3.75338813951632[/C][/ROW]
[ROW][C]4[/C][C]24[/C][C]20.5638279192274[/C][C]3.43617208077261[/C][/ROW]
[ROW][C]5[/C][C]29[/C][C]21.5655678825126[/C][C]7.43443211748743[/C][/ROW]
[ROW][C]6[/C][C]26[/C][C]21.8888738127544[/C][C]4.11112618724559[/C][/ROW]
[ROW][C]7[/C][C]26[/C][C]16.0017399632852[/C][C]9.99826003671482[/C][/ROW]
[ROW][C]8[/C][C]21[/C][C]14.5956500917870[/C][C]6.40434990821295[/C][/ROW]
[ROW][C]9[/C][C]23[/C][C]15.5146061138159[/C][C]7.48539388618406[/C][/ROW]
[ROW][C]10[/C][C]22[/C][C]14.0335621358448[/C][C]7.96643786415516[/C][/ROW]
[ROW][C]11[/C][C]21[/C][C]14.7559980844441[/C][C]6.24400191555591[/C][/ROW]
[ROW][C]12[/C][C]16[/C][C]12.1085162423178[/C][C]3.89148375768218[/C][/ROW]
[ROW][C]13[/C][C]19[/C][C]16.9640567217389[/C][C]2.03594327826111[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]15.0413919706281[/C][C]0.958608029371852[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]20.4448718971985[/C][C]4.5551281028015[/C][/ROW]
[ROW][C]16[/C][C]27[/C][C]20.96469790087[/C][C]6.03530209913002[/C][/ROW]
[ROW][C]17[/C][C]23[/C][C]20.7638279192274[/C][C]2.23617208077261[/C][/ROW]
[ROW][C]18[/C][C]22[/C][C]18.2810439779711[/C][C]3.71895602202889[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]15.2[/C][C]7.8[/C][/ROW]
[ROW][C]20[/C][C]20[/C][C]17.8026099449278[/C][C]2.19739005507223[/C][/ROW]
[ROW][C]21[/C][C]24[/C][C]20.7259158751696[/C][C]3.27408412483039[/C][/ROW]
[ROW][C]22[/C][C]23[/C][C]21.2492218054114[/C][C]1.75077819458855[/C][/ROW]
[ROW][C]23[/C][C]20[/C][C]17.9629579375848[/C][C]2.03704206241520[/C][/ROW]
[ROW][C]24[/C][C]21[/C][C]20.1259158751696[/C][C]0.874084124830393[/C][/ROW]
[ROW][C]25[/C][C]22[/C][C]22.1753664830925[/C][C]-0.175366483092550[/C][/ROW]
[ROW][C]26[/C][C]17[/C][C]19.8518317503392[/C][C]-2.85183175033922[/C][/ROW]
[ROW][C]27[/C][C]21[/C][C]20.0440019155559[/C][C]0.95599808444409[/C][/ROW]
[ROW][C]28[/C][C]19[/C][C]21.7664378641552[/C][C]-2.76643786415516[/C][/ROW]
[ROW][C]29[/C][C]23[/C][C]22.3673078457978[/C][C]0.63269215420225[/C][/ROW]
[ROW][C]30[/C][C]22[/C][C]19.8845239045415[/C][C]2.11547609545854[/C][/ROW]
[ROW][C]31[/C][C]15[/C][C]19.6095697980685[/C][C]-4.60956979806848[/C][/ROW]
[ROW][C]32[/C][C]23[/C][C]21.4104397797111[/C][C]1.58956022028893[/C][/ROW]
[ROW][C]33[/C][C]21[/C][C]23.1311357650251[/C][C]-2.13113576502514[/C][/ROW]
[ROW][C]34[/C][C]18[/C][C]21.2492218054114[/C][C]-3.24922180541145[/C][/ROW]
[ROW][C]35[/C][C]18[/C][C]15.9586080293719[/C][C]2.04139197062814[/C][/ROW]
[ROW][C]36[/C][C]18[/C][C]17.3198260036715[/C][C]0.680173996328518[/C][/ROW]
[ROW][C]37[/C][C]18[/C][C]17.3649267033815[/C][C]0.635073296618521[/C][/ROW]
[ROW][C]38[/C][C]10[/C][C]10.2309521909171[/C][C]-0.230952190917076[/C][/ROW]
[ROW][C]39[/C][C]13[/C][C]16.4361720807726[/C][C]-3.43617208077261[/C][/ROW]
[ROW][C]40[/C][C]10[/C][C]14.9516481762311[/C][C]-4.95164817623114[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]16.7551281028015[/C][C]-7.7551281028015[/C][/ROW]
[ROW][C]42[/C][C]9[/C][C]16.2766940697582[/C][C]-7.27669406975816[/C][/ROW]
[ROW][C]43[/C][C]6[/C][C]11.1913001835741[/C][C]-5.19130018357411[/C][/ROW]
[ROW][C]44[/C][C]11[/C][C]11.3886902386463[/C][C]-0.388690238646338[/C][/ROW]
[ROW][C]45[/C][C]9[/C][C]10.7041663341049[/C][C]-1.70416633410488[/C][/ROW]
[ROW][C]46[/C][C]10[/C][C]8.82225237449118[/C][C]1.17774762550882[/C][/ROW]
[ROW][C]47[/C][C]9[/C][C]11.5490382313034[/C][C]-2.54903823130338[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]13.7119961688882[/C][C]2.28800383111182[/C][/ROW]
[ROW][C]49[/C][C]10[/C][C]12.1536169420278[/C][C]-2.15361694202782[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]10.2309521909171[/C][C]-3.23095219091708[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]12.8283422459893[/C][C]-5.8283422459893[/C][/ROW]
[ROW][C]52[/C][C]14[/C][C]15.7533881395163[/C][C]-1.75338813951632[/C][/ROW]
[ROW][C]53[/C][C]11[/C][C]13.5481682496608[/C][C]-2.54816824966079[/C][/ROW]
[ROW][C]54[/C][C]10[/C][C]12.6688642349749[/C][C]-2.66886423497486[/C][/ROW]
[ROW][C]55[/C][C]6[/C][C]13.9973900550722[/C][C]-7.99739005507223[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]17.8026099449278[/C][C]-9.80260994492777[/C][/ROW]
[ROW][C]57[/C][C]13[/C][C]19.9241759118844[/C][C]-6.92417591188443[/C][/ROW]
[ROW][C]58[/C][C]12[/C][C]19.6457418788411[/C][C]-7.64574187884109[/C][/ROW]
[ROW][C]59[/C][C]15[/C][C]22.7733977172959[/C][C]-7.77339771729588[/C][/ROW]
[ROW][C]60[/C][C]16[/C][C]23.7337457099529[/C][C]-7.73374570995291[/C][/ROW]
[ROW][C]61[/C][C]16[/C][C]22.1753664830926[/C][C]-6.17536648309255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64963&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&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	24	18.1666666666667	5.83333333333329
2	22	16.6448718971985	5.35512810280152
3	25	21.2466118604837	3.75338813951632
4	24	20.5638279192274	3.43617208077261
5	29	21.5655678825126	7.43443211748743
6	26	21.8888738127544	4.11112618724559
7	26	16.0017399632852	9.99826003671482
8	21	14.5956500917870	6.40434990821295
9	23	15.5146061138159	7.48539388618406
10	22	14.0335621358448	7.96643786415516
11	21	14.7559980844441	6.24400191555591
12	16	12.1085162423178	3.89148375768218
13	19	16.9640567217389	2.03594327826111
14	16	15.0413919706281	0.958608029371852
15	25	20.4448718971985	4.5551281028015
16	27	20.96469790087	6.03530209913002
17	23	20.7638279192274	2.23617208077261
18	22	18.2810439779711	3.71895602202889
19	23	15.2	7.8
20	20	17.8026099449278	2.19739005507223
21	24	20.7259158751696	3.27408412483039
22	23	21.2492218054114	1.75077819458855
23	20	17.9629579375848	2.03704206241520
24	21	20.1259158751696	0.874084124830393
25	22	22.1753664830925	-0.175366483092550
26	17	19.8518317503392	-2.85183175033922
27	21	20.0440019155559	0.95599808444409
28	19	21.7664378641552	-2.76643786415516
29	23	22.3673078457978	0.63269215420225
30	22	19.8845239045415	2.11547609545854
31	15	19.6095697980685	-4.60956979806848
32	23	21.4104397797111	1.58956022028893
33	21	23.1311357650251	-2.13113576502514
34	18	21.2492218054114	-3.24922180541145
35	18	15.9586080293719	2.04139197062814
36	18	17.3198260036715	0.680173996328518
37	18	17.3649267033815	0.635073296618521
38	10	10.2309521909171	-0.230952190917076
39	13	16.4361720807726	-3.43617208077261
40	10	14.9516481762311	-4.95164817623114
41	9	16.7551281028015	-7.7551281028015
42	9	16.2766940697582	-7.27669406975816
43	6	11.1913001835741	-5.19130018357411
44	11	11.3886902386463	-0.388690238646338
45	9	10.7041663341049	-1.70416633410488
46	10	8.82225237449118	1.17774762550882
47	9	11.5490382313034	-2.54903823130338
48	16	13.7119961688882	2.28800383111182
49	10	12.1536169420278	-2.15361694202782
50	7	10.2309521909171	-3.23095219091708
51	7	12.8283422459893	-5.8283422459893
52	14	15.7533881395163	-1.75338813951632
53	11	13.5481682496608	-2.54816824966079
54	10	12.6688642349749	-2.66886423497486
55	6	13.9973900550722	-7.99739005507223
56	8	17.8026099449278	-9.80260994492777
57	13	19.9241759118844	-6.92417591188443
58	12	19.6457418788411	-7.64574187884109
59	15	22.7733977172959	-7.77339771729588
60	16	23.7337457099529	-7.73374570995291
61	16	22.1753664830926	-6.17536648309255

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0343445118019451	0.0686890236038901	0.965655488198055
17	0.0260192889578656	0.0520385779157311	0.973980711042134
18	0.0638090292559883	0.127618058511977	0.936190970744012
19	0.0545697298288899	0.109139459657780	0.94543027017111
20	0.102010460358928	0.204020920717856	0.897989539641072
21	0.101605476698440	0.203210953396880	0.89839452330156
22	0.0843411421510161	0.168682284302032	0.915658857848984
23	0.0629388088607004	0.125877617721401	0.9370611911393
24	0.0390410090077631	0.0780820180155262	0.960958990992237
25	0.0244545086943207	0.0489090173886414	0.97554549130568
26	0.0208573148729593	0.0417146297459187	0.97914268512704
27	0.0264345199960455	0.0528690399920911	0.973565480003954
28	0.0582830234172677	0.116566046834535	0.941716976582732
29	0.0745209097453136	0.149041819490627	0.925479090254686
30	0.107397316201122	0.214794632402244	0.892602683798878
31	0.338942778746247	0.677885557492493	0.661057221253753
32	0.552326697845922	0.895346604308156	0.447673302154078
33	0.664991082529348	0.670017834941304	0.335008917470652
34	0.722191795481039	0.555616409037922	0.277808204518961
35	0.828017922151875	0.343964155696251	0.171982077848125
36	0.782701180013068	0.434597639973865	0.217298819986932
37	0.85231620676747	0.295367586465062	0.147683793232531
38	0.883361289061262	0.233277421877477	0.116638710938738
39	0.951956653499143	0.0960866930017131	0.0480433465008566
40	0.972764913807646	0.0544701723847089	0.0272350861923545
41	0.980347872462071	0.0393042550758582	0.0196521275379291
42	0.974190727130412	0.0516185457391762	0.0258092728695881
43	0.951579382240186	0.0968412355196279	0.0484206177598139
44	0.965121969359513	0.0697560612809735	0.0348780306404868
45	0.903899332675134	0.192201334649732	0.0961006673248658

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0343445118019451 & 0.0686890236038901 & 0.965655488198055 \tabularnewline
17 & 0.0260192889578656 & 0.0520385779157311 & 0.973980711042134 \tabularnewline
18 & 0.0638090292559883 & 0.127618058511977 & 0.936190970744012 \tabularnewline
19 & 0.0545697298288899 & 0.109139459657780 & 0.94543027017111 \tabularnewline
20 & 0.102010460358928 & 0.204020920717856 & 0.897989539641072 \tabularnewline
21 & 0.101605476698440 & 0.203210953396880 & 0.89839452330156 \tabularnewline
22 & 0.0843411421510161 & 0.168682284302032 & 0.915658857848984 \tabularnewline
23 & 0.0629388088607004 & 0.125877617721401 & 0.9370611911393 \tabularnewline
24 & 0.0390410090077631 & 0.0780820180155262 & 0.960958990992237 \tabularnewline
25 & 0.0244545086943207 & 0.0489090173886414 & 0.97554549130568 \tabularnewline
26 & 0.0208573148729593 & 0.0417146297459187 & 0.97914268512704 \tabularnewline
27 & 0.0264345199960455 & 0.0528690399920911 & 0.973565480003954 \tabularnewline
28 & 0.0582830234172677 & 0.116566046834535 & 0.941716976582732 \tabularnewline
29 & 0.0745209097453136 & 0.149041819490627 & 0.925479090254686 \tabularnewline
30 & 0.107397316201122 & 0.214794632402244 & 0.892602683798878 \tabularnewline
31 & 0.338942778746247 & 0.677885557492493 & 0.661057221253753 \tabularnewline
32 & 0.552326697845922 & 0.895346604308156 & 0.447673302154078 \tabularnewline
33 & 0.664991082529348 & 0.670017834941304 & 0.335008917470652 \tabularnewline
34 & 0.722191795481039 & 0.555616409037922 & 0.277808204518961 \tabularnewline
35 & 0.828017922151875 & 0.343964155696251 & 0.171982077848125 \tabularnewline
36 & 0.782701180013068 & 0.434597639973865 & 0.217298819986932 \tabularnewline
37 & 0.85231620676747 & 0.295367586465062 & 0.147683793232531 \tabularnewline
38 & 0.883361289061262 & 0.233277421877477 & 0.116638710938738 \tabularnewline
39 & 0.951956653499143 & 0.0960866930017131 & 0.0480433465008566 \tabularnewline
40 & 0.972764913807646 & 0.0544701723847089 & 0.0272350861923545 \tabularnewline
41 & 0.980347872462071 & 0.0393042550758582 & 0.0196521275379291 \tabularnewline
42 & 0.974190727130412 & 0.0516185457391762 & 0.0258092728695881 \tabularnewline
43 & 0.951579382240186 & 0.0968412355196279 & 0.0484206177598139 \tabularnewline
44 & 0.965121969359513 & 0.0697560612809735 & 0.0348780306404868 \tabularnewline
45 & 0.903899332675134 & 0.192201334649732 & 0.0961006673248658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&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]0.0343445118019451[/C][C]0.0686890236038901[/C][C]0.965655488198055[/C][/ROW]
[ROW][C]17[/C][C]0.0260192889578656[/C][C]0.0520385779157311[/C][C]0.973980711042134[/C][/ROW]
[ROW][C]18[/C][C]0.0638090292559883[/C][C]0.127618058511977[/C][C]0.936190970744012[/C][/ROW]
[ROW][C]19[/C][C]0.0545697298288899[/C][C]0.109139459657780[/C][C]0.94543027017111[/C][/ROW]
[ROW][C]20[/C][C]0.102010460358928[/C][C]0.204020920717856[/C][C]0.897989539641072[/C][/ROW]
[ROW][C]21[/C][C]0.101605476698440[/C][C]0.203210953396880[/C][C]0.89839452330156[/C][/ROW]
[ROW][C]22[/C][C]0.0843411421510161[/C][C]0.168682284302032[/C][C]0.915658857848984[/C][/ROW]
[ROW][C]23[/C][C]0.0629388088607004[/C][C]0.125877617721401[/C][C]0.9370611911393[/C][/ROW]
[ROW][C]24[/C][C]0.0390410090077631[/C][C]0.0780820180155262[/C][C]0.960958990992237[/C][/ROW]
[ROW][C]25[/C][C]0.0244545086943207[/C][C]0.0489090173886414[/C][C]0.97554549130568[/C][/ROW]
[ROW][C]26[/C][C]0.0208573148729593[/C][C]0.0417146297459187[/C][C]0.97914268512704[/C][/ROW]
[ROW][C]27[/C][C]0.0264345199960455[/C][C]0.0528690399920911[/C][C]0.973565480003954[/C][/ROW]
[ROW][C]28[/C][C]0.0582830234172677[/C][C]0.116566046834535[/C][C]0.941716976582732[/C][/ROW]
[ROW][C]29[/C][C]0.0745209097453136[/C][C]0.149041819490627[/C][C]0.925479090254686[/C][/ROW]
[ROW][C]30[/C][C]0.107397316201122[/C][C]0.214794632402244[/C][C]0.892602683798878[/C][/ROW]
[ROW][C]31[/C][C]0.338942778746247[/C][C]0.677885557492493[/C][C]0.661057221253753[/C][/ROW]
[ROW][C]32[/C][C]0.552326697845922[/C][C]0.895346604308156[/C][C]0.447673302154078[/C][/ROW]
[ROW][C]33[/C][C]0.664991082529348[/C][C]0.670017834941304[/C][C]0.335008917470652[/C][/ROW]
[ROW][C]34[/C][C]0.722191795481039[/C][C]0.555616409037922[/C][C]0.277808204518961[/C][/ROW]
[ROW][C]35[/C][C]0.828017922151875[/C][C]0.343964155696251[/C][C]0.171982077848125[/C][/ROW]
[ROW][C]36[/C][C]0.782701180013068[/C][C]0.434597639973865[/C][C]0.217298819986932[/C][/ROW]
[ROW][C]37[/C][C]0.85231620676747[/C][C]0.295367586465062[/C][C]0.147683793232531[/C][/ROW]
[ROW][C]38[/C][C]0.883361289061262[/C][C]0.233277421877477[/C][C]0.116638710938738[/C][/ROW]
[ROW][C]39[/C][C]0.951956653499143[/C][C]0.0960866930017131[/C][C]0.0480433465008566[/C][/ROW]
[ROW][C]40[/C][C]0.972764913807646[/C][C]0.0544701723847089[/C][C]0.0272350861923545[/C][/ROW]
[ROW][C]41[/C][C]0.980347872462071[/C][C]0.0393042550758582[/C][C]0.0196521275379291[/C][/ROW]
[ROW][C]42[/C][C]0.974190727130412[/C][C]0.0516185457391762[/C][C]0.0258092728695881[/C][/ROW]
[ROW][C]43[/C][C]0.951579382240186[/C][C]0.0968412355196279[/C][C]0.0484206177598139[/C][/ROW]
[ROW][C]44[/C][C]0.965121969359513[/C][C]0.0697560612809735[/C][C]0.0348780306404868[/C][/ROW]
[ROW][C]45[/C][C]0.903899332675134[/C][C]0.192201334649732[/C][C]0.0961006673248658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64963&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&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	0.0343445118019451	0.0686890236038901	0.965655488198055
17	0.0260192889578656	0.0520385779157311	0.973980711042134
18	0.0638090292559883	0.127618058511977	0.936190970744012
19	0.0545697298288899	0.109139459657780	0.94543027017111
20	0.102010460358928	0.204020920717856	0.897989539641072
21	0.101605476698440	0.203210953396880	0.89839452330156
22	0.0843411421510161	0.168682284302032	0.915658857848984
23	0.0629388088607004	0.125877617721401	0.9370611911393
24	0.0390410090077631	0.0780820180155262	0.960958990992237
25	0.0244545086943207	0.0489090173886414	0.97554549130568
26	0.0208573148729593	0.0417146297459187	0.97914268512704
27	0.0264345199960455	0.0528690399920911	0.973565480003954
28	0.0582830234172677	0.116566046834535	0.941716976582732
29	0.0745209097453136	0.149041819490627	0.925479090254686
30	0.107397316201122	0.214794632402244	0.892602683798878
31	0.338942778746247	0.677885557492493	0.661057221253753
32	0.552326697845922	0.895346604308156	0.447673302154078
33	0.664991082529348	0.670017834941304	0.335008917470652
34	0.722191795481039	0.555616409037922	0.277808204518961
35	0.828017922151875	0.343964155696251	0.171982077848125
36	0.782701180013068	0.434597639973865	0.217298819986932
37	0.85231620676747	0.295367586465062	0.147683793232531
38	0.883361289061262	0.233277421877477	0.116638710938738
39	0.951956653499143	0.0960866930017131	0.0480433465008566
40	0.972764913807646	0.0544701723847089	0.0272350861923545
41	0.980347872462071	0.0393042550758582	0.0196521275379291
42	0.974190727130412	0.0516185457391762	0.0258092728695881
43	0.951579382240186	0.0968412355196279	0.0484206177598139
44	0.965121969359513	0.0697560612809735	0.0348780306404868
45	0.903899332675134	0.192201334649732	0.0961006673248658

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	3	0.1	NOK
10% type I error level	12	0.4	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 3 & 0.1 & NOK \tabularnewline
10% type I error level & 12 & 0.4 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64963&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]3[/C][C]0.1[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.4[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64963&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64963&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	3	0.1	NOK
10% type I error level	12	0.4	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

PNG link

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PDF link

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