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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sun, 07 Dec 2014 13:43:54 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/07/t1417959881yjs5wxn24otrbyr.htm/, Retrieved Thu, 16 May 2024 13:18:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263779, Retrieved Thu, 16 May 2024 13:18:59 +0000

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-       [Multiple Regression] [Paper] [2014-12-07 13:43:54] [58179e1d3a5a39b9daf58e365d8a3352] [Current]

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26 50 4 13 12 13 13 21 2 12.9
37 54 5 14 11 11 11 22 0 12.8
67 71 4 16 13 14 10 18 0 7.4
43 54 4 14 11 15 9 23 4 6.7
52 65 9 13 10 14 8 12 0 12.6
52 73 8 15 7 11 26 20 -1 14.8
43 52 11 13 10 13 10 22 0 13.3
84 84 4 20 15 16 10 21 1 11.1
67 42 4 17 12 14 8 19 0 8.2
49 66 6 15 12 14 13 22 3 11.4
70 65 4 16 10 15 11 15 -1 6.4
58 73 4 17 14 13 12 19 4 12
68 75 4 11 6 14 24 18 1 6.3
62 72 11 16 12 11 21 15 0 11.3
43 66 4 16 14 12 5 20 -2 11.9
56 70 4 15 11 14 14 21 -4 9.3
74 81 6 14 12 12 9 15 2 10
63 69 8 16 13 15 17 23 2 13.8
58 71 5 17 11 14 18 21 -4 10.8
63 68 9 15 7 12 23 25 2 11.7
53 70 4 14 11 12 9 9 2 10.9
57 68 7 14 7 12 14 30 0 16.1
64 67 4 15 12 14 10 23 -3 9.9
53 76 4 17 13 16 8 16 2 11.5
29 70 7 14 9 12 10 16 0 8.3
54 60 12 16 11 12 19 19 4 11.7
58 72 7 15 12 14 11 25 2 9
51 71 8 16 12 15 12 23 2 10.8
54 70 4 8 5 14 11 10 -4 10.4
56 64 9 17 13 13 10 14 3 12.7
47 76 4 10 6 16 14 26 2 11.8
50 68 4 16 6 15 11 24 -1 13
35 76 4 16 12 13 13 24 -3 10.8
30 65 7 16 11 16 15 18 0 12.3
68 67 4 8 6 16 15 23 1 11.3
56 75 4 14 11 15 14 23 -3 11.6
43 60 4 16 12 13 12 19 3 10.9
67 73 4 19 13 12 13 21 0 12.1
62 63 4 19 14 14 7 18 0 13.3
57 70 4 14 12 14 8 27 0 10.1
54 66 12 13 14 10 20 13 3 14.3
61 64 4 15 11 16 16 28 0 9.3
56 70 5 11 10 14 11 23 2 12.5
41 75 15 9 7 14 26 21 -1 7.6
53 60 10 12 7 15 15 19 3 9.2
46 66 5 13 10 16 20 17 2 14.5
51 59 9 17 12 15 15 25 2 12.3
37 78 4 7 5 13 17 14 -2 12.6
42 67 7 15 10 12 19 16 0 13
38 59 5 12 12 12 13 24 -2 12.6
66 66 4 15 11 14 8 20 0 13.2
53 71 4 16 12 15 9 24 6 7.7
49 66 4 14 11 11 12 22 0 10.5
49 72 4 16 12 14 9 22 -2 10.9
59 71 6 13 10 16 14 20 1 4.3
40 59 10 16 9 13 14 10 0 10.3
63 78 4 10 7 11 13 22 2 11.4
34 65 11 12 9 12 16 20 2 5.6
32 65 14 14 10 12 14 22 -3 8.8
67 71 4 16 12 14 11 20 1 9
61 72 4 18 14 12 11 17 -4 9.6
60 66 5 12 9 13 14 18 1 6.4
63 69 4 15 12 14 15 19 0 11.6

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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	'Gertrude Mary Cox' @ cox.wessa.net

Multiple Linear Regression - Estimated Regression Equation
TOT[t] = + 13.5189 -0.0260675AMS.I[t] -0.00040861AMS.E[t] -0.0821243AMS.A[t] + 0.144752CONFSTATTOT[t] -0.00492907CONFSOFTTOT[t] -0.341381STRESSTOT[t] + 0.0630965CESDTOT[t] + 0.0466NUMERACYTOT[t] + 0.0255257DECTESTTOT[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TOT[t] =  +  13.5189 -0.0260675AMS.I[t] -0.00040861AMS.E[t] -0.0821243AMS.A[t] +  0.144752CONFSTATTOT[t] -0.00492907CONFSOFTTOT[t] -0.341381STRESSTOT[t] +  0.0630965CESDTOT[t] +  0.0466NUMERACYTOT[t] +  0.0255257DECTESTTOT[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TOT[t] =  +  13.5189 -0.0260675AMS.I[t] -0.00040861AMS.E[t] -0.0821243AMS.A[t] +  0.144752CONFSTATTOT[t] -0.00492907CONFSOFTTOT[t] -0.341381STRESSTOT[t] +  0.0630965CESDTOT[t] +  0.0466NUMERACYTOT[t] +  0.0255257DECTESTTOT[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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
TOT[t] = + 13.5189 -0.0260675AMS.I[t] -0.00040861AMS.E[t] -0.0821243AMS.A[t] + 0.144752CONFSTATTOT[t] -0.00492907CONFSOFTTOT[t] -0.341381STRESSTOT[t] + 0.0630965CESDTOT[t] + 0.0466NUMERACYTOT[t] + 0.0255257DECTESTTOT[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)	13.5189	5.04492	2.68	0.00979548	0.00489774
AMS.I	-0.0260675	0.0310498	-0.8395	0.404939	0.202469
AMS.E	-0.00040861	0.047967	-0.008519	0.993235	0.496618
AMS.A	-0.0821243	0.13912	-0.5903	0.557489	0.278745
CONFSTATTOT	0.144752	0.18531	0.7811	0.438199	0.219099
CONFSOFTTOT	-0.00492907	0.208261	-0.02367	0.981206	0.490603
STRESSTOT	-0.341381	0.222698	-1.533	0.131242	0.0656208
CESDTOT	0.0630965	0.090916	0.694	0.490708	0.245354
NUMERACYTOT	0.0466	0.0758551	0.6143	0.541626	0.270813
DECTESTTOT	0.0255257	0.15133	0.1687	0.866693	0.433347

\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) & 13.5189 & 5.04492 & 2.68 & 0.00979548 & 0.00489774 \tabularnewline
AMS.I & -0.0260675 & 0.0310498 & -0.8395 & 0.404939 & 0.202469 \tabularnewline
AMS.E & -0.00040861 & 0.047967 & -0.008519 & 0.993235 & 0.496618 \tabularnewline
AMS.A & -0.0821243 & 0.13912 & -0.5903 & 0.557489 & 0.278745 \tabularnewline
CONFSTATTOT & 0.144752 & 0.18531 & 0.7811 & 0.438199 & 0.219099 \tabularnewline
CONFSOFTTOT & -0.00492907 & 0.208261 & -0.02367 & 0.981206 & 0.490603 \tabularnewline
STRESSTOT & -0.341381 & 0.222698 & -1.533 & 0.131242 & 0.0656208 \tabularnewline
CESDTOT & 0.0630965 & 0.090916 & 0.694 & 0.490708 & 0.245354 \tabularnewline
NUMERACYTOT & 0.0466 & 0.0758551 & 0.6143 & 0.541626 & 0.270813 \tabularnewline
DECTESTTOT & 0.0255257 & 0.15133 & 0.1687 & 0.866693 & 0.433347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&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]13.5189[/C][C]5.04492[/C][C]2.68[/C][C]0.00979548[/C][C]0.00489774[/C][/ROW]
[ROW][C]AMS.I[/C][C]-0.0260675[/C][C]0.0310498[/C][C]-0.8395[/C][C]0.404939[/C][C]0.202469[/C][/ROW]
[ROW][C]AMS.E[/C][C]-0.00040861[/C][C]0.047967[/C][C]-0.008519[/C][C]0.993235[/C][C]0.496618[/C][/ROW]
[ROW][C]AMS.A[/C][C]-0.0821243[/C][C]0.13912[/C][C]-0.5903[/C][C]0.557489[/C][C]0.278745[/C][/ROW]
[ROW][C]CONFSTATTOT[/C][C]0.144752[/C][C]0.18531[/C][C]0.7811[/C][C]0.438199[/C][C]0.219099[/C][/ROW]
[ROW][C]CONFSOFTTOT[/C][C]-0.00492907[/C][C]0.208261[/C][C]-0.02367[/C][C]0.981206[/C][C]0.490603[/C][/ROW]
[ROW][C]STRESSTOT[/C][C]-0.341381[/C][C]0.222698[/C][C]-1.533[/C][C]0.131242[/C][C]0.0656208[/C][/ROW]
[ROW][C]CESDTOT[/C][C]0.0630965[/C][C]0.090916[/C][C]0.694[/C][C]0.490708[/C][C]0.245354[/C][/ROW]
[ROW][C]NUMERACYTOT[/C][C]0.0466[/C][C]0.0758551[/C][C]0.6143[/C][C]0.541626[/C][C]0.270813[/C][/ROW]
[ROW][C]DECTESTTOT[/C][C]0.0255257[/C][C]0.15133[/C][C]0.1687[/C][C]0.866693[/C][C]0.433347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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)	13.5189	5.04492	2.68	0.00979548	0.00489774
AMS.I	-0.0260675	0.0310498	-0.8395	0.404939	0.202469
AMS.E	-0.00040861	0.047967	-0.008519	0.993235	0.496618
AMS.A	-0.0821243	0.13912	-0.5903	0.557489	0.278745
CONFSTATTOT	0.144752	0.18531	0.7811	0.438199	0.219099
CONFSOFTTOT	-0.00492907	0.208261	-0.02367	0.981206	0.490603
STRESSTOT	-0.341381	0.222698	-1.533	0.131242	0.0656208
CESDTOT	0.0630965	0.090916	0.694	0.490708	0.245354
NUMERACYTOT	0.0466	0.0758551	0.6143	0.541626	0.270813
DECTESTTOT	0.0255257	0.15133	0.1687	0.866693	0.433347

Multiple Linear Regression - Regression Statistics
Multiple R	0.29436
R-squared	0.0866477
Adjusted R-squared	-0.0684499
F-TEST (value)	0.558666
F-TEST (DF numerator)	9
F-TEST (DF denominator)	53
p-value	0.824326
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.48064
Sum Squared Residuals	326.14

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.29436 \tabularnewline
R-squared & 0.0866477 \tabularnewline
Adjusted R-squared & -0.0684499 \tabularnewline
F-TEST (value) & 0.558666 \tabularnewline
F-TEST (DF numerator) & 9 \tabularnewline
F-TEST (DF denominator) & 53 \tabularnewline
p-value & 0.824326 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.48064 \tabularnewline
Sum Squared Residuals & 326.14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.29436[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0866477[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.0684499[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.558666[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]9[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]53[/C][/ROW]
[ROW][C]p-value[/C][C]0.824326[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.48064[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]326.14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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	0.29436
R-squared	0.0866477
Adjusted R-squared	-0.0684499
F-TEST (value)	0.558666
F-TEST (DF numerator)	9
F-TEST (DF denominator)	53
p-value	0.824326
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.48064
Sum Squared Residuals	326.14

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	12.9	11.7268	1.17321
2	12.8	12.0581	0.741914
3	7.4	10.3572	-2.95725
4	6.7	10.6408	-3.94079
5	12.6	9.51483	3.08517
6	14.8	12.4051	2.39487
7	13.3	10.5241	2.77593
8	11.1	9.9605	1.1395
9	8.2	10.4392	-2.23918
10	11.4	10.9767	0.4233
11	6.4	9.85267	-3.45267
12	12	11.3471	0.652864
13	6.3	10.5492	-4.24917
14	11.3	11.4956	-0.195639
15	11.9	11.3894	0.510593
16	9.3	10.7996	-1.49959
17	10	10.2528	-0.252782
18	13.8	10.5182	3.28182
19	10.8	11.2068	-0.406809
20	11.7	11.8172	-0.117211
21	10.9	10.6943	0.20573
22	16.1	11.6072	4.49281
23	9.9	10.4537	-0.553684
24	11.5	10.0138	1.4862
25	8.3	11.4216	-3.12162
26	11.7	11.4528	0.247184
27	9	10.6456	-1.6456
28	10.8	10.5196	0.280378
29	10.4	9.16614	1.23386
30	12.7	10.6125	2.08746
31	11.8	10.036	1.76398
32	13	10.8119	2.18809
33	10.8	11.928	-1.12798
34	12.3	10.7204	1.5796
35	11.3	9.10055	2.19945
36	11.6	10.4301	1.16986
37	10.9	11.583	-0.683041
38	12.1	11.8025	0.297463
39	13.3	10.7309	2.56911
40	10.1	10.627	-0.526962
41	14.3	11.4421	2.85795
42	9.3	10.5434	-1.24344
43	12.5	10.2004	2.29955
44	7.6	10.2701	-2.67013
45	9.2	9.78179	-0.581786
46	14.5	10.3578	4.14223
47	12.3	10.8696	1.43036
48	12.6	10.4187	2.18132
49	13	11.7917	1.20834
50	12.6	11.5625	1.0375
51	13.2	10.2175	2.98253
52	7.7	10.7554	-3.0554
53	10.5	11.8856	-1.38559
54	10.9	10.9032	-0.00323384
55	4.3	9.67042	-5.37042
56	10.3	10.8139	-0.513909
57	11.4	11.0706	0.329398
58	5.6	11.2914	-5.69136
59	8.8	11.2211	-2.42107
60	9	10.544	-1.544
61	9.6	11.395	-1.79497
62	6.4	10.5196	-4.11964
63	11.6	10.6846	0.915406

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12.9 & 11.7268 & 1.17321 \tabularnewline
2 & 12.8 & 12.0581 & 0.741914 \tabularnewline
3 & 7.4 & 10.3572 & -2.95725 \tabularnewline
4 & 6.7 & 10.6408 & -3.94079 \tabularnewline
5 & 12.6 & 9.51483 & 3.08517 \tabularnewline
6 & 14.8 & 12.4051 & 2.39487 \tabularnewline
7 & 13.3 & 10.5241 & 2.77593 \tabularnewline
8 & 11.1 & 9.9605 & 1.1395 \tabularnewline
9 & 8.2 & 10.4392 & -2.23918 \tabularnewline
10 & 11.4 & 10.9767 & 0.4233 \tabularnewline
11 & 6.4 & 9.85267 & -3.45267 \tabularnewline
12 & 12 & 11.3471 & 0.652864 \tabularnewline
13 & 6.3 & 10.5492 & -4.24917 \tabularnewline
14 & 11.3 & 11.4956 & -0.195639 \tabularnewline
15 & 11.9 & 11.3894 & 0.510593 \tabularnewline
16 & 9.3 & 10.7996 & -1.49959 \tabularnewline
17 & 10 & 10.2528 & -0.252782 \tabularnewline
18 & 13.8 & 10.5182 & 3.28182 \tabularnewline
19 & 10.8 & 11.2068 & -0.406809 \tabularnewline
20 & 11.7 & 11.8172 & -0.117211 \tabularnewline
21 & 10.9 & 10.6943 & 0.20573 \tabularnewline
22 & 16.1 & 11.6072 & 4.49281 \tabularnewline
23 & 9.9 & 10.4537 & -0.553684 \tabularnewline
24 & 11.5 & 10.0138 & 1.4862 \tabularnewline
25 & 8.3 & 11.4216 & -3.12162 \tabularnewline
26 & 11.7 & 11.4528 & 0.247184 \tabularnewline
27 & 9 & 10.6456 & -1.6456 \tabularnewline
28 & 10.8 & 10.5196 & 0.280378 \tabularnewline
29 & 10.4 & 9.16614 & 1.23386 \tabularnewline
30 & 12.7 & 10.6125 & 2.08746 \tabularnewline
31 & 11.8 & 10.036 & 1.76398 \tabularnewline
32 & 13 & 10.8119 & 2.18809 \tabularnewline
33 & 10.8 & 11.928 & -1.12798 \tabularnewline
34 & 12.3 & 10.7204 & 1.5796 \tabularnewline
35 & 11.3 & 9.10055 & 2.19945 \tabularnewline
36 & 11.6 & 10.4301 & 1.16986 \tabularnewline
37 & 10.9 & 11.583 & -0.683041 \tabularnewline
38 & 12.1 & 11.8025 & 0.297463 \tabularnewline
39 & 13.3 & 10.7309 & 2.56911 \tabularnewline
40 & 10.1 & 10.627 & -0.526962 \tabularnewline
41 & 14.3 & 11.4421 & 2.85795 \tabularnewline
42 & 9.3 & 10.5434 & -1.24344 \tabularnewline
43 & 12.5 & 10.2004 & 2.29955 \tabularnewline
44 & 7.6 & 10.2701 & -2.67013 \tabularnewline
45 & 9.2 & 9.78179 & -0.581786 \tabularnewline
46 & 14.5 & 10.3578 & 4.14223 \tabularnewline
47 & 12.3 & 10.8696 & 1.43036 \tabularnewline
48 & 12.6 & 10.4187 & 2.18132 \tabularnewline
49 & 13 & 11.7917 & 1.20834 \tabularnewline
50 & 12.6 & 11.5625 & 1.0375 \tabularnewline
51 & 13.2 & 10.2175 & 2.98253 \tabularnewline
52 & 7.7 & 10.7554 & -3.0554 \tabularnewline
53 & 10.5 & 11.8856 & -1.38559 \tabularnewline
54 & 10.9 & 10.9032 & -0.00323384 \tabularnewline
55 & 4.3 & 9.67042 & -5.37042 \tabularnewline
56 & 10.3 & 10.8139 & -0.513909 \tabularnewline
57 & 11.4 & 11.0706 & 0.329398 \tabularnewline
58 & 5.6 & 11.2914 & -5.69136 \tabularnewline
59 & 8.8 & 11.2211 & -2.42107 \tabularnewline
60 & 9 & 10.544 & -1.544 \tabularnewline
61 & 9.6 & 11.395 & -1.79497 \tabularnewline
62 & 6.4 & 10.5196 & -4.11964 \tabularnewline
63 & 11.6 & 10.6846 & 0.915406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&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]12.9[/C][C]11.7268[/C][C]1.17321[/C][/ROW]
[ROW][C]2[/C][C]12.8[/C][C]12.0581[/C][C]0.741914[/C][/ROW]
[ROW][C]3[/C][C]7.4[/C][C]10.3572[/C][C]-2.95725[/C][/ROW]
[ROW][C]4[/C][C]6.7[/C][C]10.6408[/C][C]-3.94079[/C][/ROW]
[ROW][C]5[/C][C]12.6[/C][C]9.51483[/C][C]3.08517[/C][/ROW]
[ROW][C]6[/C][C]14.8[/C][C]12.4051[/C][C]2.39487[/C][/ROW]
[ROW][C]7[/C][C]13.3[/C][C]10.5241[/C][C]2.77593[/C][/ROW]
[ROW][C]8[/C][C]11.1[/C][C]9.9605[/C][C]1.1395[/C][/ROW]
[ROW][C]9[/C][C]8.2[/C][C]10.4392[/C][C]-2.23918[/C][/ROW]
[ROW][C]10[/C][C]11.4[/C][C]10.9767[/C][C]0.4233[/C][/ROW]
[ROW][C]11[/C][C]6.4[/C][C]9.85267[/C][C]-3.45267[/C][/ROW]
[ROW][C]12[/C][C]12[/C][C]11.3471[/C][C]0.652864[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]10.5492[/C][C]-4.24917[/C][/ROW]
[ROW][C]14[/C][C]11.3[/C][C]11.4956[/C][C]-0.195639[/C][/ROW]
[ROW][C]15[/C][C]11.9[/C][C]11.3894[/C][C]0.510593[/C][/ROW]
[ROW][C]16[/C][C]9.3[/C][C]10.7996[/C][C]-1.49959[/C][/ROW]
[ROW][C]17[/C][C]10[/C][C]10.2528[/C][C]-0.252782[/C][/ROW]
[ROW][C]18[/C][C]13.8[/C][C]10.5182[/C][C]3.28182[/C][/ROW]
[ROW][C]19[/C][C]10.8[/C][C]11.2068[/C][C]-0.406809[/C][/ROW]
[ROW][C]20[/C][C]11.7[/C][C]11.8172[/C][C]-0.117211[/C][/ROW]
[ROW][C]21[/C][C]10.9[/C][C]10.6943[/C][C]0.20573[/C][/ROW]
[ROW][C]22[/C][C]16.1[/C][C]11.6072[/C][C]4.49281[/C][/ROW]
[ROW][C]23[/C][C]9.9[/C][C]10.4537[/C][C]-0.553684[/C][/ROW]
[ROW][C]24[/C][C]11.5[/C][C]10.0138[/C][C]1.4862[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]11.4216[/C][C]-3.12162[/C][/ROW]
[ROW][C]26[/C][C]11.7[/C][C]11.4528[/C][C]0.247184[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]10.6456[/C][C]-1.6456[/C][/ROW]
[ROW][C]28[/C][C]10.8[/C][C]10.5196[/C][C]0.280378[/C][/ROW]
[ROW][C]29[/C][C]10.4[/C][C]9.16614[/C][C]1.23386[/C][/ROW]
[ROW][C]30[/C][C]12.7[/C][C]10.6125[/C][C]2.08746[/C][/ROW]
[ROW][C]31[/C][C]11.8[/C][C]10.036[/C][C]1.76398[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]10.8119[/C][C]2.18809[/C][/ROW]
[ROW][C]33[/C][C]10.8[/C][C]11.928[/C][C]-1.12798[/C][/ROW]
[ROW][C]34[/C][C]12.3[/C][C]10.7204[/C][C]1.5796[/C][/ROW]
[ROW][C]35[/C][C]11.3[/C][C]9.10055[/C][C]2.19945[/C][/ROW]
[ROW][C]36[/C][C]11.6[/C][C]10.4301[/C][C]1.16986[/C][/ROW]
[ROW][C]37[/C][C]10.9[/C][C]11.583[/C][C]-0.683041[/C][/ROW]
[ROW][C]38[/C][C]12.1[/C][C]11.8025[/C][C]0.297463[/C][/ROW]
[ROW][C]39[/C][C]13.3[/C][C]10.7309[/C][C]2.56911[/C][/ROW]
[ROW][C]40[/C][C]10.1[/C][C]10.627[/C][C]-0.526962[/C][/ROW]
[ROW][C]41[/C][C]14.3[/C][C]11.4421[/C][C]2.85795[/C][/ROW]
[ROW][C]42[/C][C]9.3[/C][C]10.5434[/C][C]-1.24344[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]10.2004[/C][C]2.29955[/C][/ROW]
[ROW][C]44[/C][C]7.6[/C][C]10.2701[/C][C]-2.67013[/C][/ROW]
[ROW][C]45[/C][C]9.2[/C][C]9.78179[/C][C]-0.581786[/C][/ROW]
[ROW][C]46[/C][C]14.5[/C][C]10.3578[/C][C]4.14223[/C][/ROW]
[ROW][C]47[/C][C]12.3[/C][C]10.8696[/C][C]1.43036[/C][/ROW]
[ROW][C]48[/C][C]12.6[/C][C]10.4187[/C][C]2.18132[/C][/ROW]
[ROW][C]49[/C][C]13[/C][C]11.7917[/C][C]1.20834[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]11.5625[/C][C]1.0375[/C][/ROW]
[ROW][C]51[/C][C]13.2[/C][C]10.2175[/C][C]2.98253[/C][/ROW]
[ROW][C]52[/C][C]7.7[/C][C]10.7554[/C][C]-3.0554[/C][/ROW]
[ROW][C]53[/C][C]10.5[/C][C]11.8856[/C][C]-1.38559[/C][/ROW]
[ROW][C]54[/C][C]10.9[/C][C]10.9032[/C][C]-0.00323384[/C][/ROW]
[ROW][C]55[/C][C]4.3[/C][C]9.67042[/C][C]-5.37042[/C][/ROW]
[ROW][C]56[/C][C]10.3[/C][C]10.8139[/C][C]-0.513909[/C][/ROW]
[ROW][C]57[/C][C]11.4[/C][C]11.0706[/C][C]0.329398[/C][/ROW]
[ROW][C]58[/C][C]5.6[/C][C]11.2914[/C][C]-5.69136[/C][/ROW]
[ROW][C]59[/C][C]8.8[/C][C]11.2211[/C][C]-2.42107[/C][/ROW]
[ROW][C]60[/C][C]9[/C][C]10.544[/C][C]-1.544[/C][/ROW]
[ROW][C]61[/C][C]9.6[/C][C]11.395[/C][C]-1.79497[/C][/ROW]
[ROW][C]62[/C][C]6.4[/C][C]10.5196[/C][C]-4.11964[/C][/ROW]
[ROW][C]63[/C][C]11.6[/C][C]10.6846[/C][C]0.915406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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	12.9	11.7268	1.17321
2	12.8	12.0581	0.741914
3	7.4	10.3572	-2.95725
4	6.7	10.6408	-3.94079
5	12.6	9.51483	3.08517
6	14.8	12.4051	2.39487
7	13.3	10.5241	2.77593
8	11.1	9.9605	1.1395
9	8.2	10.4392	-2.23918
10	11.4	10.9767	0.4233
11	6.4	9.85267	-3.45267
12	12	11.3471	0.652864
13	6.3	10.5492	-4.24917
14	11.3	11.4956	-0.195639
15	11.9	11.3894	0.510593
16	9.3	10.7996	-1.49959
17	10	10.2528	-0.252782
18	13.8	10.5182	3.28182
19	10.8	11.2068	-0.406809
20	11.7	11.8172	-0.117211
21	10.9	10.6943	0.20573
22	16.1	11.6072	4.49281
23	9.9	10.4537	-0.553684
24	11.5	10.0138	1.4862
25	8.3	11.4216	-3.12162
26	11.7	11.4528	0.247184
27	9	10.6456	-1.6456
28	10.8	10.5196	0.280378
29	10.4	9.16614	1.23386
30	12.7	10.6125	2.08746
31	11.8	10.036	1.76398
32	13	10.8119	2.18809
33	10.8	11.928	-1.12798
34	12.3	10.7204	1.5796
35	11.3	9.10055	2.19945
36	11.6	10.4301	1.16986
37	10.9	11.583	-0.683041
38	12.1	11.8025	0.297463
39	13.3	10.7309	2.56911
40	10.1	10.627	-0.526962
41	14.3	11.4421	2.85795
42	9.3	10.5434	-1.24344
43	12.5	10.2004	2.29955
44	7.6	10.2701	-2.67013
45	9.2	9.78179	-0.581786
46	14.5	10.3578	4.14223
47	12.3	10.8696	1.43036
48	12.6	10.4187	2.18132
49	13	11.7917	1.20834
50	12.6	11.5625	1.0375
51	13.2	10.2175	2.98253
52	7.7	10.7554	-3.0554
53	10.5	11.8856	-1.38559
54	10.9	10.9032	-0.00323384
55	4.3	9.67042	-5.37042
56	10.3	10.8139	-0.513909
57	11.4	11.0706	0.329398
58	5.6	11.2914	-5.69136
59	8.8	11.2211	-2.42107
60	9	10.544	-1.544
61	9.6	11.395	-1.79497
62	6.4	10.5196	-4.11964
63	11.6	10.6846	0.915406

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
13	0.388704	0.777409	0.611296
14	0.662733	0.674533	0.337267
15	0.575986	0.848027	0.424014
16	0.459408	0.918816	0.540592
17	0.348382	0.696763	0.651618
18	0.383236	0.766472	0.616764
19	0.286493	0.572985	0.713507
20	0.212465	0.42493	0.787535
21	0.155292	0.310584	0.844708
22	0.278468	0.556936	0.721532
23	0.207262	0.414523	0.792738
24	0.147955	0.295909	0.852045
25	0.411517	0.823033	0.588483
26	0.372326	0.744653	0.627674
27	0.400877	0.801754	0.599123
28	0.337075	0.67415	0.662925
29	0.329894	0.659787	0.670106
30	0.305915	0.611831	0.694085
31	0.276949	0.553899	0.723051
32	0.293461	0.586921	0.706539
33	0.243362	0.486723	0.756638
34	0.199604	0.399209	0.800396
35	0.17258	0.345159	0.82742
36	0.130903	0.261806	0.869097
37	0.0969744	0.193949	0.903026
38	0.0727601	0.14552	0.92724
39	0.0801793	0.160359	0.919821
40	0.0555236	0.111047	0.944476
41	0.0635716	0.127143	0.936428
42	0.0930961	0.186192	0.906904
43	0.24262	0.485239	0.75738
44	0.279521	0.559042	0.720479
45	0.205285	0.41057	0.794715
46	0.317515	0.63503	0.682485
47	0.227225	0.45445	0.772775
48	0.238976	0.477952	0.761024
49	0.168484	0.336969	0.831516
50	0.216996	0.433992	0.783004

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
13 & 0.388704 & 0.777409 & 0.611296 \tabularnewline
14 & 0.662733 & 0.674533 & 0.337267 \tabularnewline
15 & 0.575986 & 0.848027 & 0.424014 \tabularnewline
16 & 0.459408 & 0.918816 & 0.540592 \tabularnewline
17 & 0.348382 & 0.696763 & 0.651618 \tabularnewline
18 & 0.383236 & 0.766472 & 0.616764 \tabularnewline
19 & 0.286493 & 0.572985 & 0.713507 \tabularnewline
20 & 0.212465 & 0.42493 & 0.787535 \tabularnewline
21 & 0.155292 & 0.310584 & 0.844708 \tabularnewline
22 & 0.278468 & 0.556936 & 0.721532 \tabularnewline
23 & 0.207262 & 0.414523 & 0.792738 \tabularnewline
24 & 0.147955 & 0.295909 & 0.852045 \tabularnewline
25 & 0.411517 & 0.823033 & 0.588483 \tabularnewline
26 & 0.372326 & 0.744653 & 0.627674 \tabularnewline
27 & 0.400877 & 0.801754 & 0.599123 \tabularnewline
28 & 0.337075 & 0.67415 & 0.662925 \tabularnewline
29 & 0.329894 & 0.659787 & 0.670106 \tabularnewline
30 & 0.305915 & 0.611831 & 0.694085 \tabularnewline
31 & 0.276949 & 0.553899 & 0.723051 \tabularnewline
32 & 0.293461 & 0.586921 & 0.706539 \tabularnewline
33 & 0.243362 & 0.486723 & 0.756638 \tabularnewline
34 & 0.199604 & 0.399209 & 0.800396 \tabularnewline
35 & 0.17258 & 0.345159 & 0.82742 \tabularnewline
36 & 0.130903 & 0.261806 & 0.869097 \tabularnewline
37 & 0.0969744 & 0.193949 & 0.903026 \tabularnewline
38 & 0.0727601 & 0.14552 & 0.92724 \tabularnewline
39 & 0.0801793 & 0.160359 & 0.919821 \tabularnewline
40 & 0.0555236 & 0.111047 & 0.944476 \tabularnewline
41 & 0.0635716 & 0.127143 & 0.936428 \tabularnewline
42 & 0.0930961 & 0.186192 & 0.906904 \tabularnewline
43 & 0.24262 & 0.485239 & 0.75738 \tabularnewline
44 & 0.279521 & 0.559042 & 0.720479 \tabularnewline
45 & 0.205285 & 0.41057 & 0.794715 \tabularnewline
46 & 0.317515 & 0.63503 & 0.682485 \tabularnewline
47 & 0.227225 & 0.45445 & 0.772775 \tabularnewline
48 & 0.238976 & 0.477952 & 0.761024 \tabularnewline
49 & 0.168484 & 0.336969 & 0.831516 \tabularnewline
50 & 0.216996 & 0.433992 & 0.783004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&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]13[/C][C]0.388704[/C][C]0.777409[/C][C]0.611296[/C][/ROW]
[ROW][C]14[/C][C]0.662733[/C][C]0.674533[/C][C]0.337267[/C][/ROW]
[ROW][C]15[/C][C]0.575986[/C][C]0.848027[/C][C]0.424014[/C][/ROW]
[ROW][C]16[/C][C]0.459408[/C][C]0.918816[/C][C]0.540592[/C][/ROW]
[ROW][C]17[/C][C]0.348382[/C][C]0.696763[/C][C]0.651618[/C][/ROW]
[ROW][C]18[/C][C]0.383236[/C][C]0.766472[/C][C]0.616764[/C][/ROW]
[ROW][C]19[/C][C]0.286493[/C][C]0.572985[/C][C]0.713507[/C][/ROW]
[ROW][C]20[/C][C]0.212465[/C][C]0.42493[/C][C]0.787535[/C][/ROW]
[ROW][C]21[/C][C]0.155292[/C][C]0.310584[/C][C]0.844708[/C][/ROW]
[ROW][C]22[/C][C]0.278468[/C][C]0.556936[/C][C]0.721532[/C][/ROW]
[ROW][C]23[/C][C]0.207262[/C][C]0.414523[/C][C]0.792738[/C][/ROW]
[ROW][C]24[/C][C]0.147955[/C][C]0.295909[/C][C]0.852045[/C][/ROW]
[ROW][C]25[/C][C]0.411517[/C][C]0.823033[/C][C]0.588483[/C][/ROW]
[ROW][C]26[/C][C]0.372326[/C][C]0.744653[/C][C]0.627674[/C][/ROW]
[ROW][C]27[/C][C]0.400877[/C][C]0.801754[/C][C]0.599123[/C][/ROW]
[ROW][C]28[/C][C]0.337075[/C][C]0.67415[/C][C]0.662925[/C][/ROW]
[ROW][C]29[/C][C]0.329894[/C][C]0.659787[/C][C]0.670106[/C][/ROW]
[ROW][C]30[/C][C]0.305915[/C][C]0.611831[/C][C]0.694085[/C][/ROW]
[ROW][C]31[/C][C]0.276949[/C][C]0.553899[/C][C]0.723051[/C][/ROW]
[ROW][C]32[/C][C]0.293461[/C][C]0.586921[/C][C]0.706539[/C][/ROW]
[ROW][C]33[/C][C]0.243362[/C][C]0.486723[/C][C]0.756638[/C][/ROW]
[ROW][C]34[/C][C]0.199604[/C][C]0.399209[/C][C]0.800396[/C][/ROW]
[ROW][C]35[/C][C]0.17258[/C][C]0.345159[/C][C]0.82742[/C][/ROW]
[ROW][C]36[/C][C]0.130903[/C][C]0.261806[/C][C]0.869097[/C][/ROW]
[ROW][C]37[/C][C]0.0969744[/C][C]0.193949[/C][C]0.903026[/C][/ROW]
[ROW][C]38[/C][C]0.0727601[/C][C]0.14552[/C][C]0.92724[/C][/ROW]
[ROW][C]39[/C][C]0.0801793[/C][C]0.160359[/C][C]0.919821[/C][/ROW]
[ROW][C]40[/C][C]0.0555236[/C][C]0.111047[/C][C]0.944476[/C][/ROW]
[ROW][C]41[/C][C]0.0635716[/C][C]0.127143[/C][C]0.936428[/C][/ROW]
[ROW][C]42[/C][C]0.0930961[/C][C]0.186192[/C][C]0.906904[/C][/ROW]
[ROW][C]43[/C][C]0.24262[/C][C]0.485239[/C][C]0.75738[/C][/ROW]
[ROW][C]44[/C][C]0.279521[/C][C]0.559042[/C][C]0.720479[/C][/ROW]
[ROW][C]45[/C][C]0.205285[/C][C]0.41057[/C][C]0.794715[/C][/ROW]
[ROW][C]46[/C][C]0.317515[/C][C]0.63503[/C][C]0.682485[/C][/ROW]
[ROW][C]47[/C][C]0.227225[/C][C]0.45445[/C][C]0.772775[/C][/ROW]
[ROW][C]48[/C][C]0.238976[/C][C]0.477952[/C][C]0.761024[/C][/ROW]
[ROW][C]49[/C][C]0.168484[/C][C]0.336969[/C][C]0.831516[/C][/ROW]
[ROW][C]50[/C][C]0.216996[/C][C]0.433992[/C][C]0.783004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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
13	0.388704	0.777409	0.611296
14	0.662733	0.674533	0.337267
15	0.575986	0.848027	0.424014
16	0.459408	0.918816	0.540592
17	0.348382	0.696763	0.651618
18	0.383236	0.766472	0.616764
19	0.286493	0.572985	0.713507
20	0.212465	0.42493	0.787535
21	0.155292	0.310584	0.844708
22	0.278468	0.556936	0.721532
23	0.207262	0.414523	0.792738
24	0.147955	0.295909	0.852045
25	0.411517	0.823033	0.588483
26	0.372326	0.744653	0.627674
27	0.400877	0.801754	0.599123
28	0.337075	0.67415	0.662925
29	0.329894	0.659787	0.670106
30	0.305915	0.611831	0.694085
31	0.276949	0.553899	0.723051
32	0.293461	0.586921	0.706539
33	0.243362	0.486723	0.756638
34	0.199604	0.399209	0.800396
35	0.17258	0.345159	0.82742
36	0.130903	0.261806	0.869097
37	0.0969744	0.193949	0.903026
38	0.0727601	0.14552	0.92724
39	0.0801793	0.160359	0.919821
40	0.0555236	0.111047	0.944476
41	0.0635716	0.127143	0.936428
42	0.0930961	0.186192	0.906904
43	0.24262	0.485239	0.75738
44	0.279521	0.559042	0.720479
45	0.205285	0.41057	0.794715
46	0.317515	0.63503	0.682485
47	0.227225	0.45445	0.772775
48	0.238976	0.477952	0.761024
49	0.168484	0.336969	0.831516
50	0.216996	0.433992	0.783004

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	0	0	OK
10% type I error level	0	0	OK

\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 & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263779&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263779&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263779&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	0	0	OK
10% type I error level	0	0	OK

Figure 1

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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 = 10 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 10 ; par2 = Do not include Seasonal 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
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, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
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,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant1,6))
a<-table.element(a,signif(numsignificant1/numgqtests,6))
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code