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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 18 Nov 2009 09:31:41 -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/Nov/18/t1258561955hq9llce776tdpu6.htm/, Retrieved Fri, 05 Dec 2025 06:19:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57519, Retrieved Fri, 05 Dec 2025 06:19:12 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

451

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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [WS7 (t-1)] [2009-11-18 16:31:41] [82f421ff86a0429b20e3ed68bd89f1bd] [Current]

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Dataseries X:

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7,59	43,14	7,59
7,57	43,39	7,59
7,57	43,46	7,57
7,59	43,54	7,57
7,6	43,62	7,59
7,64	44,01	7,6
7,64	44,5	7,64
7,76	44,73	7,64
7,76	44,89	7,76
7,76	45,09	7,76
7,77	45,17	7,76
7,83	45,24	7,77
7,94	45,42	7,83
7,94	45,67	7,94
7,94	45,68	7,94
8,09	46,56	7,94
8,18	46,72	8,09
8,26	47,01	8,18
8,28	47,26	8,26
8,28	47,49	8,28
8,28	47,51	8,28
8,29	47,52	8,28
8,3	47,66	8,29
8,3	47,71	8,3
8,31	47,87	8,3
8,33	48	8,31
8,33	48	8,33
8,34	48,05	8,33
8,48	48,25	8,34
8,59	48,72	8,48
8,67	48,94	8,59
8,67	49,16	8,67
8,67	49,18	8,67
8,71	49,25	8,67
8,72	49,34	8,71
8,72	49,49	8,72
8,72	49,57	8,72
8,74	49,63	8,72
8,74	49,67	8,74
8,74	49,7	8,74
8,74	49,8	8,74
8,79	50,09	8,74
8,85	50,49	8,79
8,86	50,73	8,85
8,87	51,12	8,86
8,92	51,15	8,87
8,96	51,41	8,92
8,97	51,61	8,96
8,99	52,06	8,97
8,98	52,17	8,99
8,98	52,18	8,98
9,01	52,19	8,98
9,01	52,74	9,01
9,03	53,05	9,01
9,05	53,38	9,03
9,05	53,78	9,05

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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&T=0

As an alternative you can also use a QR Code:

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

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.561884252914864 + 0.0216620241930846X[t] + 0.954028194605642Y1[t] + 0.00892343909083954M1[t] -0.01646835463777M2[t] -0.0161527040647591M3[t] + 0.0240851904459348M4[t] + 0.0300806045896479M5[t] + 0.039492462372239M6[t] + 0.0137159261098806M7[t] + 0.00243905630834483M8[t] -0.0181185568513062M9[t] + 0.005604485378458M10[t] -0.00104613834295537M11[t] -0.00278691959124200t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.561884252914864 +  0.0216620241930846X[t] +  0.954028194605642Y1[t] +  0.00892343909083954M1[t] -0.01646835463777M2[t] -0.0161527040647591M3[t] +  0.0240851904459348M4[t] +  0.0300806045896479M5[t] +  0.039492462372239M6[t] +  0.0137159261098806M7[t] +  0.00243905630834483M8[t] -0.0181185568513062M9[t] +  0.005604485378458M10[t] -0.00104613834295537M11[t] -0.00278691959124200t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.561884252914864 +  0.0216620241930846X[t] +  0.954028194605642Y1[t] +  0.00892343909083954M1[t] -0.01646835463777M2[t] -0.0161527040647591M3[t] +  0.0240851904459348M4[t] +  0.0300806045896479M5[t] +  0.039492462372239M6[t] +  0.0137159261098806M7[t] +  0.00243905630834483M8[t] -0.0181185568513062M9[t] +  0.005604485378458M10[t] -0.00104613834295537M11[t] -0.00278691959124200t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&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
Y[t] = -0.561884252914864 + 0.0216620241930846X[t] + 0.954028194605642Y1[t] + 0.00892343909083954M1[t] -0.01646835463777M2[t] -0.0161527040647591M3[t] + 0.0240851904459348M4[t] + 0.0300806045896479M5[t] + 0.039492462372239M6[t] + 0.0137159261098806M7[t] + 0.00243905630834483M8[t] -0.0181185568513062M9[t] + 0.005604485378458M10[t] -0.00104613834295537M11[t] -0.00278691959124200t + 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)	-0.561884252914864	0.832539	-0.6749	0.503525	0.251762
X	0.0216620241930846	0.01811	1.1961	0.238518	0.119259
Y1	0.954028194605642	0.064319	14.8327	0	0
M1	0.00892343909083954	0.026233	0.3402	0.735472	0.367736
M2	-0.01646835463777	0.026221	-0.6281	0.53345	0.266725
M3	-0.0161527040647591	0.026455	-0.6106	0.544856	0.272428
M4	0.0240851904459348	0.026581	0.9061	0.370173	0.185086
M5	0.0300806045896479	0.026429	1.1382	0.261656	0.130828
M6	0.039492462372239	0.026322	1.5003	0.141189	0.070594
M7	0.0137159261098806	0.026509	0.5174	0.607657	0.303829
M8	0.00243905630834483	0.026793	0.091	0.927908	0.463954
M9	-0.0181185568513062	0.027897	-0.6495	0.519652	0.259826
M10	0.005604485378458	0.027659	0.2026	0.840428	0.420214
M11	-0.00104613834295537	0.02762	-0.0379	0.969971	0.484985
t	-0.00278691959124200	0.003377	-0.8254	0.413944	0.206972

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -0.561884252914864 & 0.832539 & -0.6749 & 0.503525 & 0.251762 \tabularnewline
X & 0.0216620241930846 & 0.01811 & 1.1961 & 0.238518 & 0.119259 \tabularnewline
Y1 & 0.954028194605642 & 0.064319 & 14.8327 & 0 & 0 \tabularnewline
M1 & 0.00892343909083954 & 0.026233 & 0.3402 & 0.735472 & 0.367736 \tabularnewline
M2 & -0.01646835463777 & 0.026221 & -0.6281 & 0.53345 & 0.266725 \tabularnewline
M3 & -0.0161527040647591 & 0.026455 & -0.6106 & 0.544856 & 0.272428 \tabularnewline
M4 & 0.0240851904459348 & 0.026581 & 0.9061 & 0.370173 & 0.185086 \tabularnewline
M5 & 0.0300806045896479 & 0.026429 & 1.1382 & 0.261656 & 0.130828 \tabularnewline
M6 & 0.039492462372239 & 0.026322 & 1.5003 & 0.141189 & 0.070594 \tabularnewline
M7 & 0.0137159261098806 & 0.026509 & 0.5174 & 0.607657 & 0.303829 \tabularnewline
M8 & 0.00243905630834483 & 0.026793 & 0.091 & 0.927908 & 0.463954 \tabularnewline
M9 & -0.0181185568513062 & 0.027897 & -0.6495 & 0.519652 & 0.259826 \tabularnewline
M10 & 0.005604485378458 & 0.027659 & 0.2026 & 0.840428 & 0.420214 \tabularnewline
M11 & -0.00104613834295537 & 0.02762 & -0.0379 & 0.969971 & 0.484985 \tabularnewline
t & -0.00278691959124200 & 0.003377 & -0.8254 & 0.413944 & 0.206972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-0.561884252914864[/C][C]0.832539[/C][C]-0.6749[/C][C]0.503525[/C][C]0.251762[/C][/ROW]
[ROW][C]X[/C][C]0.0216620241930846[/C][C]0.01811[/C][C]1.1961[/C][C]0.238518[/C][C]0.119259[/C][/ROW]
[ROW][C]Y1[/C][C]0.954028194605642[/C][C]0.064319[/C][C]14.8327[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.00892343909083954[/C][C]0.026233[/C][C]0.3402[/C][C]0.735472[/C][C]0.367736[/C][/ROW]
[ROW][C]M2[/C][C]-0.01646835463777[/C][C]0.026221[/C][C]-0.6281[/C][C]0.53345[/C][C]0.266725[/C][/ROW]
[ROW][C]M3[/C][C]-0.0161527040647591[/C][C]0.026455[/C][C]-0.6106[/C][C]0.544856[/C][C]0.272428[/C][/ROW]
[ROW][C]M4[/C][C]0.0240851904459348[/C][C]0.026581[/C][C]0.9061[/C][C]0.370173[/C][C]0.185086[/C][/ROW]
[ROW][C]M5[/C][C]0.0300806045896479[/C][C]0.026429[/C][C]1.1382[/C][C]0.261656[/C][C]0.130828[/C][/ROW]
[ROW][C]M6[/C][C]0.039492462372239[/C][C]0.026322[/C][C]1.5003[/C][C]0.141189[/C][C]0.070594[/C][/ROW]
[ROW][C]M7[/C][C]0.0137159261098806[/C][C]0.026509[/C][C]0.5174[/C][C]0.607657[/C][C]0.303829[/C][/ROW]
[ROW][C]M8[/C][C]0.00243905630834483[/C][C]0.026793[/C][C]0.091[/C][C]0.927908[/C][C]0.463954[/C][/ROW]
[ROW][C]M9[/C][C]-0.0181185568513062[/C][C]0.027897[/C][C]-0.6495[/C][C]0.519652[/C][C]0.259826[/C][/ROW]
[ROW][C]M10[/C][C]0.005604485378458[/C][C]0.027659[/C][C]0.2026[/C][C]0.840428[/C][C]0.420214[/C][/ROW]
[ROW][C]M11[/C][C]-0.00104613834295537[/C][C]0.02762[/C][C]-0.0379[/C][C]0.969971[/C][C]0.484985[/C][/ROW]
[ROW][C]t[/C][C]-0.00278691959124200[/C][C]0.003377[/C][C]-0.8254[/C][C]0.413944[/C][C]0.206972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	-0.561884252914864	0.832539	-0.6749	0.503525	0.251762
X	0.0216620241930846	0.01811	1.1961	0.238518	0.119259
Y1	0.954028194605642	0.064319	14.8327	0	0
M1	0.00892343909083954	0.026233	0.3402	0.735472	0.367736
M2	-0.01646835463777	0.026221	-0.6281	0.53345	0.266725
M3	-0.0161527040647591	0.026455	-0.6106	0.544856	0.272428
M4	0.0240851904459348	0.026581	0.9061	0.370173	0.185086
M5	0.0300806045896479	0.026429	1.1382	0.261656	0.130828
M6	0.039492462372239	0.026322	1.5003	0.141189	0.070594
M7	0.0137159261098806	0.026509	0.5174	0.607657	0.303829
M8	0.00243905630834483	0.026793	0.091	0.927908	0.463954
M9	-0.0181185568513062	0.027897	-0.6495	0.519652	0.259826
M10	0.005604485378458	0.027659	0.2026	0.840428	0.420214
M11	-0.00104613834295537	0.02762	-0.0379	0.969971	0.484985
t	-0.00278691959124200	0.003377	-0.8254	0.413944	0.206972

Multiple Linear Regression - Regression Statistics
Multiple R	0.997625025332438
R-squared	0.995255691169548
Adjusted R-squared	0.993635683276223
F-TEST (value)	614.352371534885
F-TEST (DF numerator)	14
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0390228580478303
Sum Squared Residuals	0.0624341214590656

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.997625025332438 \tabularnewline
R-squared & 0.995255691169548 \tabularnewline
Adjusted R-squared & 0.993635683276223 \tabularnewline
F-TEST (value) & 614.352371534885 \tabularnewline
F-TEST (DF numerator) & 14 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0390228580478303 \tabularnewline
Sum Squared Residuals & 0.0624341214590656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.997625025332438[/C][/ROW]
[ROW][C]R-squared[/C][C]0.995255691169548[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.993635683276223[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]614.352371534885[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]14[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/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]0.0390228580478303[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0624341214590656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&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	0.997625025332438
R-squared	0.995255691169548
Adjusted R-squared	0.993635683276223
F-TEST (value)	614.352371534885
F-TEST (DF numerator)	14
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0390228580478303
Sum Squared Residuals	0.0624341214590656

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.59	7.61982598733123	-0.0298259873312309
2	7.57	7.59706278005965	-0.0270627800596501
3	7.57	7.57702728884282	-0.00702728884282097
4	7.59	7.61621122569772	-0.0262112256977200
5	7.6	7.64023324607775	-0.0402332460777503
6	7.64	7.66484665565046	-0.0248466556504587
7	7.64	7.6850587194357	-0.0450587194356954
8	7.76	7.67597719560733	0.084022804392673
9	7.76	7.77058197008	-0.0105819700800046
10	7.76	7.79585049755714	-0.0358504975571439
11	7.77	7.78814591617993	-0.0181459161799354
12	7.83	7.79746175857122	0.0325382414287795
13	7.94	7.86473913410191	0.0752608658980881
14	7.94	7.94691902823695	-0.00691902823695242
15	7.94	7.94466437946065	-0.00466437946065205
16	8.09	8.00117793567002	0.088822064329981
17	8.18	8.15095658328423	0.0290434167157706
18	8.26	8.24972604600608	0.0102739539939193
19	8.28	8.3029003517692	-0.0229003517692032
20	8.28	8.31289939183295	-0.0328993918329474
21	8.28	8.28998809956592	-0.00998809956591605
22	8.29	8.31114084244637	-0.0211408424463694
23	8.3	8.3142762644668	-0.0142762644668003
24	8.3	8.32315886637423	-0.0231588663742259
25	8.31	8.33276130974472	-0.0227613097447171
26	8.33	8.31693894151602	0.0130610584839767
27	8.33	8.3335482363899	-0.00354823638990462
28	8.34	8.37208231251901	-0.0320823125190109
29	8.48	8.38916349385616	0.0908365061438454
30	8.59	8.53953353066304	0.0504664693369556
31	8.67	8.62067882153854	0.0493211784614574
32	8.67	8.6877029330367	-0.0177029330366948
33	8.67	8.66479164076966	0.00520835923033638
34	8.71	8.6872441051017	0.0227558948982992
35	8.72	8.71791727175065	0.00208272824935013
36	8.72	8.72896607607738	-0.00896607607738213
37	8.72	8.73683555751243	-0.0168355575124263
38	8.74	8.70995656564416	0.0300434343558396
39	8.74	8.72743234148576	0.0125676585142350
40	8.74	8.765533177131	-0.0255331771310095
41	8.74	8.77090787410279	-0.0309078741027889
42	8.79	8.78381479931013	0.00618520068986623
43	8.85	8.81161756286405	0.0383824371359523
44	8.86	8.85999435095395	5.64904605067666e-06
45	8.87	8.85463828958441	0.0153617104155843
46	8.92	8.88576455489479	0.034235445105214
47	8.96	8.92966054760262	0.0303394523973856
48	8.97	8.97041329897717	-0.000413298977171437
49	8.99	8.99583801130971	-0.00583801130971378
50	8.98	8.98912268454322	-0.00912268454321379
51	8.98	8.97732775382086	0.00267224617914272
52	9.01	9.01499534898224	-0.00499534898224064
53	9.01	9.05873880267908	-0.0487388026790768
54	9.03	9.07207896837028	-0.0420789683702824
55	9.05	9.06974454439251	-0.0197445443925112
56	9.05	9.08342612856908	-0.0334261285690814

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.59 & 7.61982598733123 & -0.0298259873312309 \tabularnewline
2 & 7.57 & 7.59706278005965 & -0.0270627800596501 \tabularnewline
3 & 7.57 & 7.57702728884282 & -0.00702728884282097 \tabularnewline
4 & 7.59 & 7.61621122569772 & -0.0262112256977200 \tabularnewline
5 & 7.6 & 7.64023324607775 & -0.0402332460777503 \tabularnewline
6 & 7.64 & 7.66484665565046 & -0.0248466556504587 \tabularnewline
7 & 7.64 & 7.6850587194357 & -0.0450587194356954 \tabularnewline
8 & 7.76 & 7.67597719560733 & 0.084022804392673 \tabularnewline
9 & 7.76 & 7.77058197008 & -0.0105819700800046 \tabularnewline
10 & 7.76 & 7.79585049755714 & -0.0358504975571439 \tabularnewline
11 & 7.77 & 7.78814591617993 & -0.0181459161799354 \tabularnewline
12 & 7.83 & 7.79746175857122 & 0.0325382414287795 \tabularnewline
13 & 7.94 & 7.86473913410191 & 0.0752608658980881 \tabularnewline
14 & 7.94 & 7.94691902823695 & -0.00691902823695242 \tabularnewline
15 & 7.94 & 7.94466437946065 & -0.00466437946065205 \tabularnewline
16 & 8.09 & 8.00117793567002 & 0.088822064329981 \tabularnewline
17 & 8.18 & 8.15095658328423 & 0.0290434167157706 \tabularnewline
18 & 8.26 & 8.24972604600608 & 0.0102739539939193 \tabularnewline
19 & 8.28 & 8.3029003517692 & -0.0229003517692032 \tabularnewline
20 & 8.28 & 8.31289939183295 & -0.0328993918329474 \tabularnewline
21 & 8.28 & 8.28998809956592 & -0.00998809956591605 \tabularnewline
22 & 8.29 & 8.31114084244637 & -0.0211408424463694 \tabularnewline
23 & 8.3 & 8.3142762644668 & -0.0142762644668003 \tabularnewline
24 & 8.3 & 8.32315886637423 & -0.0231588663742259 \tabularnewline
25 & 8.31 & 8.33276130974472 & -0.0227613097447171 \tabularnewline
26 & 8.33 & 8.31693894151602 & 0.0130610584839767 \tabularnewline
27 & 8.33 & 8.3335482363899 & -0.00354823638990462 \tabularnewline
28 & 8.34 & 8.37208231251901 & -0.0320823125190109 \tabularnewline
29 & 8.48 & 8.38916349385616 & 0.0908365061438454 \tabularnewline
30 & 8.59 & 8.53953353066304 & 0.0504664693369556 \tabularnewline
31 & 8.67 & 8.62067882153854 & 0.0493211784614574 \tabularnewline
32 & 8.67 & 8.6877029330367 & -0.0177029330366948 \tabularnewline
33 & 8.67 & 8.66479164076966 & 0.00520835923033638 \tabularnewline
34 & 8.71 & 8.6872441051017 & 0.0227558948982992 \tabularnewline
35 & 8.72 & 8.71791727175065 & 0.00208272824935013 \tabularnewline
36 & 8.72 & 8.72896607607738 & -0.00896607607738213 \tabularnewline
37 & 8.72 & 8.73683555751243 & -0.0168355575124263 \tabularnewline
38 & 8.74 & 8.70995656564416 & 0.0300434343558396 \tabularnewline
39 & 8.74 & 8.72743234148576 & 0.0125676585142350 \tabularnewline
40 & 8.74 & 8.765533177131 & -0.0255331771310095 \tabularnewline
41 & 8.74 & 8.77090787410279 & -0.0309078741027889 \tabularnewline
42 & 8.79 & 8.78381479931013 & 0.00618520068986623 \tabularnewline
43 & 8.85 & 8.81161756286405 & 0.0383824371359523 \tabularnewline
44 & 8.86 & 8.85999435095395 & 5.64904605067666e-06 \tabularnewline
45 & 8.87 & 8.85463828958441 & 0.0153617104155843 \tabularnewline
46 & 8.92 & 8.88576455489479 & 0.034235445105214 \tabularnewline
47 & 8.96 & 8.92966054760262 & 0.0303394523973856 \tabularnewline
48 & 8.97 & 8.97041329897717 & -0.000413298977171437 \tabularnewline
49 & 8.99 & 8.99583801130971 & -0.00583801130971378 \tabularnewline
50 & 8.98 & 8.98912268454322 & -0.00912268454321379 \tabularnewline
51 & 8.98 & 8.97732775382086 & 0.00267224617914272 \tabularnewline
52 & 9.01 & 9.01499534898224 & -0.00499534898224064 \tabularnewline
53 & 9.01 & 9.05873880267908 & -0.0487388026790768 \tabularnewline
54 & 9.03 & 9.07207896837028 & -0.0420789683702824 \tabularnewline
55 & 9.05 & 9.06974454439251 & -0.0197445443925112 \tabularnewline
56 & 9.05 & 9.08342612856908 & -0.0334261285690814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&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]7.59[/C][C]7.61982598733123[/C][C]-0.0298259873312309[/C][/ROW]
[ROW][C]2[/C][C]7.57[/C][C]7.59706278005965[/C][C]-0.0270627800596501[/C][/ROW]
[ROW][C]3[/C][C]7.57[/C][C]7.57702728884282[/C][C]-0.00702728884282097[/C][/ROW]
[ROW][C]4[/C][C]7.59[/C][C]7.61621122569772[/C][C]-0.0262112256977200[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]7.64023324607775[/C][C]-0.0402332460777503[/C][/ROW]
[ROW][C]6[/C][C]7.64[/C][C]7.66484665565046[/C][C]-0.0248466556504587[/C][/ROW]
[ROW][C]7[/C][C]7.64[/C][C]7.6850587194357[/C][C]-0.0450587194356954[/C][/ROW]
[ROW][C]8[/C][C]7.76[/C][C]7.67597719560733[/C][C]0.084022804392673[/C][/ROW]
[ROW][C]9[/C][C]7.76[/C][C]7.77058197008[/C][C]-0.0105819700800046[/C][/ROW]
[ROW][C]10[/C][C]7.76[/C][C]7.79585049755714[/C][C]-0.0358504975571439[/C][/ROW]
[ROW][C]11[/C][C]7.77[/C][C]7.78814591617993[/C][C]-0.0181459161799354[/C][/ROW]
[ROW][C]12[/C][C]7.83[/C][C]7.79746175857122[/C][C]0.0325382414287795[/C][/ROW]
[ROW][C]13[/C][C]7.94[/C][C]7.86473913410191[/C][C]0.0752608658980881[/C][/ROW]
[ROW][C]14[/C][C]7.94[/C][C]7.94691902823695[/C][C]-0.00691902823695242[/C][/ROW]
[ROW][C]15[/C][C]7.94[/C][C]7.94466437946065[/C][C]-0.00466437946065205[/C][/ROW]
[ROW][C]16[/C][C]8.09[/C][C]8.00117793567002[/C][C]0.088822064329981[/C][/ROW]
[ROW][C]17[/C][C]8.18[/C][C]8.15095658328423[/C][C]0.0290434167157706[/C][/ROW]
[ROW][C]18[/C][C]8.26[/C][C]8.24972604600608[/C][C]0.0102739539939193[/C][/ROW]
[ROW][C]19[/C][C]8.28[/C][C]8.3029003517692[/C][C]-0.0229003517692032[/C][/ROW]
[ROW][C]20[/C][C]8.28[/C][C]8.31289939183295[/C][C]-0.0328993918329474[/C][/ROW]
[ROW][C]21[/C][C]8.28[/C][C]8.28998809956592[/C][C]-0.00998809956591605[/C][/ROW]
[ROW][C]22[/C][C]8.29[/C][C]8.31114084244637[/C][C]-0.0211408424463694[/C][/ROW]
[ROW][C]23[/C][C]8.3[/C][C]8.3142762644668[/C][C]-0.0142762644668003[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]8.32315886637423[/C][C]-0.0231588663742259[/C][/ROW]
[ROW][C]25[/C][C]8.31[/C][C]8.33276130974472[/C][C]-0.0227613097447171[/C][/ROW]
[ROW][C]26[/C][C]8.33[/C][C]8.31693894151602[/C][C]0.0130610584839767[/C][/ROW]
[ROW][C]27[/C][C]8.33[/C][C]8.3335482363899[/C][C]-0.00354823638990462[/C][/ROW]
[ROW][C]28[/C][C]8.34[/C][C]8.37208231251901[/C][C]-0.0320823125190109[/C][/ROW]
[ROW][C]29[/C][C]8.48[/C][C]8.38916349385616[/C][C]0.0908365061438454[/C][/ROW]
[ROW][C]30[/C][C]8.59[/C][C]8.53953353066304[/C][C]0.0504664693369556[/C][/ROW]
[ROW][C]31[/C][C]8.67[/C][C]8.62067882153854[/C][C]0.0493211784614574[/C][/ROW]
[ROW][C]32[/C][C]8.67[/C][C]8.6877029330367[/C][C]-0.0177029330366948[/C][/ROW]
[ROW][C]33[/C][C]8.67[/C][C]8.66479164076966[/C][C]0.00520835923033638[/C][/ROW]
[ROW][C]34[/C][C]8.71[/C][C]8.6872441051017[/C][C]0.0227558948982992[/C][/ROW]
[ROW][C]35[/C][C]8.72[/C][C]8.71791727175065[/C][C]0.00208272824935013[/C][/ROW]
[ROW][C]36[/C][C]8.72[/C][C]8.72896607607738[/C][C]-0.00896607607738213[/C][/ROW]
[ROW][C]37[/C][C]8.72[/C][C]8.73683555751243[/C][C]-0.0168355575124263[/C][/ROW]
[ROW][C]38[/C][C]8.74[/C][C]8.70995656564416[/C][C]0.0300434343558396[/C][/ROW]
[ROW][C]39[/C][C]8.74[/C][C]8.72743234148576[/C][C]0.0125676585142350[/C][/ROW]
[ROW][C]40[/C][C]8.74[/C][C]8.765533177131[/C][C]-0.0255331771310095[/C][/ROW]
[ROW][C]41[/C][C]8.74[/C][C]8.77090787410279[/C][C]-0.0309078741027889[/C][/ROW]
[ROW][C]42[/C][C]8.79[/C][C]8.78381479931013[/C][C]0.00618520068986623[/C][/ROW]
[ROW][C]43[/C][C]8.85[/C][C]8.81161756286405[/C][C]0.0383824371359523[/C][/ROW]
[ROW][C]44[/C][C]8.86[/C][C]8.85999435095395[/C][C]5.64904605067666e-06[/C][/ROW]
[ROW][C]45[/C][C]8.87[/C][C]8.85463828958441[/C][C]0.0153617104155843[/C][/ROW]
[ROW][C]46[/C][C]8.92[/C][C]8.88576455489479[/C][C]0.034235445105214[/C][/ROW]
[ROW][C]47[/C][C]8.96[/C][C]8.92966054760262[/C][C]0.0303394523973856[/C][/ROW]
[ROW][C]48[/C][C]8.97[/C][C]8.97041329897717[/C][C]-0.000413298977171437[/C][/ROW]
[ROW][C]49[/C][C]8.99[/C][C]8.99583801130971[/C][C]-0.00583801130971378[/C][/ROW]
[ROW][C]50[/C][C]8.98[/C][C]8.98912268454322[/C][C]-0.00912268454321379[/C][/ROW]
[ROW][C]51[/C][C]8.98[/C][C]8.97732775382086[/C][C]0.00267224617914272[/C][/ROW]
[ROW][C]52[/C][C]9.01[/C][C]9.01499534898224[/C][C]-0.00499534898224064[/C][/ROW]
[ROW][C]53[/C][C]9.01[/C][C]9.05873880267908[/C][C]-0.0487388026790768[/C][/ROW]
[ROW][C]54[/C][C]9.03[/C][C]9.07207896837028[/C][C]-0.0420789683702824[/C][/ROW]
[ROW][C]55[/C][C]9.05[/C][C]9.06974454439251[/C][C]-0.0197445443925112[/C][/ROW]
[ROW][C]56[/C][C]9.05[/C][C]9.08342612856908[/C][C]-0.0334261285690814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&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	7.59	7.61982598733123	-0.0298259873312309
2	7.57	7.59706278005965	-0.0270627800596501
3	7.57	7.57702728884282	-0.00702728884282097
4	7.59	7.61621122569772	-0.0262112256977200
5	7.6	7.64023324607775	-0.0402332460777503
6	7.64	7.66484665565046	-0.0248466556504587
7	7.64	7.6850587194357	-0.0450587194356954
8	7.76	7.67597719560733	0.084022804392673
9	7.76	7.77058197008	-0.0105819700800046
10	7.76	7.79585049755714	-0.0358504975571439
11	7.77	7.78814591617993	-0.0181459161799354
12	7.83	7.79746175857122	0.0325382414287795
13	7.94	7.86473913410191	0.0752608658980881
14	7.94	7.94691902823695	-0.00691902823695242
15	7.94	7.94466437946065	-0.00466437946065205
16	8.09	8.00117793567002	0.088822064329981
17	8.18	8.15095658328423	0.0290434167157706
18	8.26	8.24972604600608	0.0102739539939193
19	8.28	8.3029003517692	-0.0229003517692032
20	8.28	8.31289939183295	-0.0328993918329474
21	8.28	8.28998809956592	-0.00998809956591605
22	8.29	8.31114084244637	-0.0211408424463694
23	8.3	8.3142762644668	-0.0142762644668003
24	8.3	8.32315886637423	-0.0231588663742259
25	8.31	8.33276130974472	-0.0227613097447171
26	8.33	8.31693894151602	0.0130610584839767
27	8.33	8.3335482363899	-0.00354823638990462
28	8.34	8.37208231251901	-0.0320823125190109
29	8.48	8.38916349385616	0.0908365061438454
30	8.59	8.53953353066304	0.0504664693369556
31	8.67	8.62067882153854	0.0493211784614574
32	8.67	8.6877029330367	-0.0177029330366948
33	8.67	8.66479164076966	0.00520835923033638
34	8.71	8.6872441051017	0.0227558948982992
35	8.72	8.71791727175065	0.00208272824935013
36	8.72	8.72896607607738	-0.00896607607738213
37	8.72	8.73683555751243	-0.0168355575124263
38	8.74	8.70995656564416	0.0300434343558396
39	8.74	8.72743234148576	0.0125676585142350
40	8.74	8.765533177131	-0.0255331771310095
41	8.74	8.77090787410279	-0.0309078741027889
42	8.79	8.78381479931013	0.00618520068986623
43	8.85	8.81161756286405	0.0383824371359523
44	8.86	8.85999435095395	5.64904605067666e-06
45	8.87	8.85463828958441	0.0153617104155843
46	8.92	8.88576455489479	0.034235445105214
47	8.96	8.92966054760262	0.0303394523973856
48	8.97	8.97041329897717	-0.000413298977171437
49	8.99	8.99583801130971	-0.00583801130971378
50	8.98	8.98912268454322	-0.00912268454321379
51	8.98	8.97732775382086	0.00267224617914272
52	9.01	9.01499534898224	-0.00499534898224064
53	9.01	9.05873880267908	-0.0487388026790768
54	9.03	9.07207896837028	-0.0420789683702824
55	9.05	9.06974454439251	-0.0197445443925112
56	9.05	9.08342612856908	-0.0334261285690814

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
18	0.0929443758367375	0.185888751673475	0.907055624163262
19	0.136215763971520	0.272431527943041	0.86378423602848
20	0.550926283643784	0.898147432712431	0.449073716356216
21	0.415711210550199	0.831422421100398	0.584288789449801
22	0.441144309928186	0.882288619856372	0.558855690071814
23	0.375231144649479	0.750462289298959	0.62476885535052
24	0.341100139082017	0.682200278164034	0.658899860917983
25	0.57512138820161	0.84975722359678	0.42487861179839
26	0.49581039557606	0.99162079115212	0.50418960442394
27	0.507937804768412	0.984124390463175	0.492062195231588
28	0.897566847501053	0.204866304997894	0.102433152498947
29	0.964568832763564	0.0708623344728717	0.0354311672364359
30	0.986886969401222	0.0262260611975562	0.0131130305987781
31	0.9992224870669	0.00155502586620131	0.000777512933100656
32	0.998228386597077	0.00354322680584651	0.00177161340292326
33	0.995965829671242	0.00806834065751614	0.00403417032875807
34	0.994400418309138	0.0111991633817234	0.00559958169086169
35	0.984462935638214	0.0310741287235725	0.0155370643617862
36	0.9640434052416	0.0719131895167986	0.0359565947583993
37	0.928591154038824	0.142817691922352	0.071408845961176
38	0.896376776526153	0.207246446947694	0.103623223473847

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
18 & 0.0929443758367375 & 0.185888751673475 & 0.907055624163262 \tabularnewline
19 & 0.136215763971520 & 0.272431527943041 & 0.86378423602848 \tabularnewline
20 & 0.550926283643784 & 0.898147432712431 & 0.449073716356216 \tabularnewline
21 & 0.415711210550199 & 0.831422421100398 & 0.584288789449801 \tabularnewline
22 & 0.441144309928186 & 0.882288619856372 & 0.558855690071814 \tabularnewline
23 & 0.375231144649479 & 0.750462289298959 & 0.62476885535052 \tabularnewline
24 & 0.341100139082017 & 0.682200278164034 & 0.658899860917983 \tabularnewline
25 & 0.57512138820161 & 0.84975722359678 & 0.42487861179839 \tabularnewline
26 & 0.49581039557606 & 0.99162079115212 & 0.50418960442394 \tabularnewline
27 & 0.507937804768412 & 0.984124390463175 & 0.492062195231588 \tabularnewline
28 & 0.897566847501053 & 0.204866304997894 & 0.102433152498947 \tabularnewline
29 & 0.964568832763564 & 0.0708623344728717 & 0.0354311672364359 \tabularnewline
30 & 0.986886969401222 & 0.0262260611975562 & 0.0131130305987781 \tabularnewline
31 & 0.9992224870669 & 0.00155502586620131 & 0.000777512933100656 \tabularnewline
32 & 0.998228386597077 & 0.00354322680584651 & 0.00177161340292326 \tabularnewline
33 & 0.995965829671242 & 0.00806834065751614 & 0.00403417032875807 \tabularnewline
34 & 0.994400418309138 & 0.0111991633817234 & 0.00559958169086169 \tabularnewline
35 & 0.984462935638214 & 0.0310741287235725 & 0.0155370643617862 \tabularnewline
36 & 0.9640434052416 & 0.0719131895167986 & 0.0359565947583993 \tabularnewline
37 & 0.928591154038824 & 0.142817691922352 & 0.071408845961176 \tabularnewline
38 & 0.896376776526153 & 0.207246446947694 & 0.103623223473847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&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]18[/C][C]0.0929443758367375[/C][C]0.185888751673475[/C][C]0.907055624163262[/C][/ROW]
[ROW][C]19[/C][C]0.136215763971520[/C][C]0.272431527943041[/C][C]0.86378423602848[/C][/ROW]
[ROW][C]20[/C][C]0.550926283643784[/C][C]0.898147432712431[/C][C]0.449073716356216[/C][/ROW]
[ROW][C]21[/C][C]0.415711210550199[/C][C]0.831422421100398[/C][C]0.584288789449801[/C][/ROW]
[ROW][C]22[/C][C]0.441144309928186[/C][C]0.882288619856372[/C][C]0.558855690071814[/C][/ROW]
[ROW][C]23[/C][C]0.375231144649479[/C][C]0.750462289298959[/C][C]0.62476885535052[/C][/ROW]
[ROW][C]24[/C][C]0.341100139082017[/C][C]0.682200278164034[/C][C]0.658899860917983[/C][/ROW]
[ROW][C]25[/C][C]0.57512138820161[/C][C]0.84975722359678[/C][C]0.42487861179839[/C][/ROW]
[ROW][C]26[/C][C]0.49581039557606[/C][C]0.99162079115212[/C][C]0.50418960442394[/C][/ROW]
[ROW][C]27[/C][C]0.507937804768412[/C][C]0.984124390463175[/C][C]0.492062195231588[/C][/ROW]
[ROW][C]28[/C][C]0.897566847501053[/C][C]0.204866304997894[/C][C]0.102433152498947[/C][/ROW]
[ROW][C]29[/C][C]0.964568832763564[/C][C]0.0708623344728717[/C][C]0.0354311672364359[/C][/ROW]
[ROW][C]30[/C][C]0.986886969401222[/C][C]0.0262260611975562[/C][C]0.0131130305987781[/C][/ROW]
[ROW][C]31[/C][C]0.9992224870669[/C][C]0.00155502586620131[/C][C]0.000777512933100656[/C][/ROW]
[ROW][C]32[/C][C]0.998228386597077[/C][C]0.00354322680584651[/C][C]0.00177161340292326[/C][/ROW]
[ROW][C]33[/C][C]0.995965829671242[/C][C]0.00806834065751614[/C][C]0.00403417032875807[/C][/ROW]
[ROW][C]34[/C][C]0.994400418309138[/C][C]0.0111991633817234[/C][C]0.00559958169086169[/C][/ROW]
[ROW][C]35[/C][C]0.984462935638214[/C][C]0.0310741287235725[/C][C]0.0155370643617862[/C][/ROW]
[ROW][C]36[/C][C]0.9640434052416[/C][C]0.0719131895167986[/C][C]0.0359565947583993[/C][/ROW]
[ROW][C]37[/C][C]0.928591154038824[/C][C]0.142817691922352[/C][C]0.071408845961176[/C][/ROW]
[ROW][C]38[/C][C]0.896376776526153[/C][C]0.207246446947694[/C][C]0.103623223473847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&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
18	0.0929443758367375	0.185888751673475	0.907055624163262
19	0.136215763971520	0.272431527943041	0.86378423602848
20	0.550926283643784	0.898147432712431	0.449073716356216
21	0.415711210550199	0.831422421100398	0.584288789449801
22	0.441144309928186	0.882288619856372	0.558855690071814
23	0.375231144649479	0.750462289298959	0.62476885535052
24	0.341100139082017	0.682200278164034	0.658899860917983
25	0.57512138820161	0.84975722359678	0.42487861179839
26	0.49581039557606	0.99162079115212	0.50418960442394
27	0.507937804768412	0.984124390463175	0.492062195231588
28	0.897566847501053	0.204866304997894	0.102433152498947
29	0.964568832763564	0.0708623344728717	0.0354311672364359
30	0.986886969401222	0.0262260611975562	0.0131130305987781
31	0.9992224870669	0.00155502586620131	0.000777512933100656
32	0.998228386597077	0.00354322680584651	0.00177161340292326
33	0.995965829671242	0.00806834065751614	0.00403417032875807
34	0.994400418309138	0.0111991633817234	0.00559958169086169
35	0.984462935638214	0.0310741287235725	0.0155370643617862
36	0.9640434052416	0.0719131895167986	0.0359565947583993
37	0.928591154038824	0.142817691922352	0.071408845961176
38	0.896376776526153	0.207246446947694	0.103623223473847

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	3	0.142857142857143	NOK
5% type I error level	6	0.285714285714286	NOK
10% type I error level	8	0.380952380952381	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 & 3 & 0.142857142857143 & NOK \tabularnewline
5% type I error level & 6 & 0.285714285714286 & NOK \tabularnewline
10% type I error level & 8 & 0.380952380952381 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57519&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]3[/C][C]0.142857142857143[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]6[/C][C]0.285714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.380952380952381[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57519&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57519&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	3	0.142857142857143	NOK
5% type I error level	6	0.285714285714286	NOK
10% type I error level	8	0.380952380952381	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 ;

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