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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 11:11:14 -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/20/t1258740748h7f4hqex39h4lpm.htm/, Retrieved Thu, 18 Apr 2024 19:55:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58384, Retrieved Thu, 18 Apr 2024 19:55:57 +0000

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133

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-     [Multiple Regression] [Indicator voor he...] [2009-11-19 10:17:29] [8b10896fd8c0913ff1dc4e6dd35f743c]
- R  D    [Multiple Regression] [model 3] [2009-11-20 18:11:14] [18c0746232b29e9668aa6bedcb8dd698] [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	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=58384&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=58384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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
Rvnp[t] = + 38.2335095393206 -0.764949810543109Svdg[t] -3.59272407985997M1[t] -6.99181657027631M2[t] -5.0113105763478M3[t] -4.21864397615723M4[t] -4.17195730018391M5[t] -5.03620035897094M6[t] -7.09137315251833M7[t] -5.32674670389328M8[t] -2.80212025526823M9[t] -1.73337335194664M10[t] -1.26565656229918M11[t] -0.313696713864699t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Rvnp[t] =  +  38.2335095393206 -0.764949810543109Svdg[t] -3.59272407985997M1[t] -6.99181657027631M2[t] -5.0113105763478M3[t] -4.21864397615723M4[t] -4.17195730018391M5[t] -5.03620035897094M6[t] -7.09137315251833M7[t] -5.32674670389328M8[t] -2.80212025526823M9[t] -1.73337335194664M10[t] -1.26565656229918M11[t] -0.313696713864699t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58384&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Rvnp[t] =  +  38.2335095393206 -0.764949810543109Svdg[t] -3.59272407985997M1[t] -6.99181657027631M2[t] -5.0113105763478M3[t] -4.21864397615723M4[t] -4.17195730018391M5[t] -5.03620035897094M6[t] -7.09137315251833M7[t] -5.32674670389328M8[t] -2.80212025526823M9[t] -1.73337335194664M10[t] -1.26565656229918M11[t] -0.313696713864699t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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
Rvnp[t] = + 38.2335095393206 -0.764949810543109Svdg[t] -3.59272407985997M1[t] -6.99181657027631M2[t] -5.0113105763478M3[t] -4.21864397615723M4[t] -4.17195730018391M5[t] -5.03620035897094M6[t] -7.09137315251833M7[t] -5.32674670389328M8[t] -2.80212025526823M9[t] -1.73337335194664M10[t] -1.26565656229918M11[t] -0.313696713864699t + 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)	38.2335095393206	10.70384	3.5719	0.000844	0.000422
Svdg	-0.764949810543109	0.414666	-1.8447	0.07152	0.03576
M1	-3.59272407985997	6.680476	-0.5378	0.593311	0.296656
M2	-6.99181657027631	7.066713	-0.9894	0.327643	0.163821
M3	-5.0113105763478	6.651337	-0.7534	0.455031	0.227516
M4	-4.21864397615723	6.609334	-0.6383	0.526453	0.263226
M5	-4.17195730018391	6.592397	-0.6328	0.529969	0.264985
M6	-5.03620035897094	6.608617	-0.7621	0.449911	0.224955
M7	-7.09137315251833	6.754597	-1.0499	0.299268	0.149634
M8	-5.32674670389328	6.625689	-0.804	0.425559	0.21278
M9	-2.80212025526823	6.571308	-0.4264	0.671793	0.335896
M10	-1.73337335194664	6.580854	-0.2634	0.793421	0.396711
M11	-1.26565656229918	6.582159	-0.1923	0.848365	0.424182
t	-0.313696713864699	0.147594	-2.1254	0.038955	0.019478

\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) & 38.2335095393206 & 10.70384 & 3.5719 & 0.000844 & 0.000422 \tabularnewline
Svdg & -0.764949810543109 & 0.414666 & -1.8447 & 0.07152 & 0.03576 \tabularnewline
M1 & -3.59272407985997 & 6.680476 & -0.5378 & 0.593311 & 0.296656 \tabularnewline
M2 & -6.99181657027631 & 7.066713 & -0.9894 & 0.327643 & 0.163821 \tabularnewline
M3 & -5.0113105763478 & 6.651337 & -0.7534 & 0.455031 & 0.227516 \tabularnewline
M4 & -4.21864397615723 & 6.609334 & -0.6383 & 0.526453 & 0.263226 \tabularnewline
M5 & -4.17195730018391 & 6.592397 & -0.6328 & 0.529969 & 0.264985 \tabularnewline
M6 & -5.03620035897094 & 6.608617 & -0.7621 & 0.449911 & 0.224955 \tabularnewline
M7 & -7.09137315251833 & 6.754597 & -1.0499 & 0.299268 & 0.149634 \tabularnewline
M8 & -5.32674670389328 & 6.625689 & -0.804 & 0.425559 & 0.21278 \tabularnewline
M9 & -2.80212025526823 & 6.571308 & -0.4264 & 0.671793 & 0.335896 \tabularnewline
M10 & -1.73337335194664 & 6.580854 & -0.2634 & 0.793421 & 0.396711 \tabularnewline
M11 & -1.26565656229918 & 6.582159 & -0.1923 & 0.848365 & 0.424182 \tabularnewline
t & -0.313696713864699 & 0.147594 & -2.1254 & 0.038955 & 0.019478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58384&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]38.2335095393206[/C][C]10.70384[/C][C]3.5719[/C][C]0.000844[/C][C]0.000422[/C][/ROW]
[ROW][C]Svdg[/C][C]-0.764949810543109[/C][C]0.414666[/C][C]-1.8447[/C][C]0.07152[/C][C]0.03576[/C][/ROW]
[ROW][C]M1[/C][C]-3.59272407985997[/C][C]6.680476[/C][C]-0.5378[/C][C]0.593311[/C][C]0.296656[/C][/ROW]
[ROW][C]M2[/C][C]-6.99181657027631[/C][C]7.066713[/C][C]-0.9894[/C][C]0.327643[/C][C]0.163821[/C][/ROW]
[ROW][C]M3[/C][C]-5.0113105763478[/C][C]6.651337[/C][C]-0.7534[/C][C]0.455031[/C][C]0.227516[/C][/ROW]
[ROW][C]M4[/C][C]-4.21864397615723[/C][C]6.609334[/C][C]-0.6383[/C][C]0.526453[/C][C]0.263226[/C][/ROW]
[ROW][C]M5[/C][C]-4.17195730018391[/C][C]6.592397[/C][C]-0.6328[/C][C]0.529969[/C][C]0.264985[/C][/ROW]
[ROW][C]M6[/C][C]-5.03620035897094[/C][C]6.608617[/C][C]-0.7621[/C][C]0.449911[/C][C]0.224955[/C][/ROW]
[ROW][C]M7[/C][C]-7.09137315251833[/C][C]6.754597[/C][C]-1.0499[/C][C]0.299268[/C][C]0.149634[/C][/ROW]
[ROW][C]M8[/C][C]-5.32674670389328[/C][C]6.625689[/C][C]-0.804[/C][C]0.425559[/C][C]0.21278[/C][/ROW]
[ROW][C]M9[/C][C]-2.80212025526823[/C][C]6.571308[/C][C]-0.4264[/C][C]0.671793[/C][C]0.335896[/C][/ROW]
[ROW][C]M10[/C][C]-1.73337335194664[/C][C]6.580854[/C][C]-0.2634[/C][C]0.793421[/C][C]0.396711[/C][/ROW]
[ROW][C]M11[/C][C]-1.26565656229918[/C][C]6.582159[/C][C]-0.1923[/C][C]0.848365[/C][C]0.424182[/C][/ROW]
[ROW][C]t[/C][C]-0.313696713864699[/C][C]0.147594[/C][C]-2.1254[/C][C]0.038955[/C][C]0.019478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58384&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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)	38.2335095393206	10.70384	3.5719	0.000844	0.000422
Svdg	-0.764949810543109	0.414666	-1.8447	0.07152	0.03576
M1	-3.59272407985997	6.680476	-0.5378	0.593311	0.296656
M2	-6.99181657027631	7.066713	-0.9894	0.327643	0.163821
M3	-5.0113105763478	6.651337	-0.7534	0.455031	0.227516
M4	-4.21864397615723	6.609334	-0.6383	0.526453	0.263226
M5	-4.17195730018391	6.592397	-0.6328	0.529969	0.264985
M6	-5.03620035897094	6.608617	-0.7621	0.449911	0.224955
M7	-7.09137315251833	6.754597	-1.0499	0.299268	0.149634
M8	-5.32674670389328	6.625689	-0.804	0.425559	0.21278
M9	-2.80212025526823	6.571308	-0.4264	0.671793	0.335896
M10	-1.73337335194664	6.580854	-0.2634	0.793421	0.396711
M11	-1.26565656229918	6.582159	-0.1923	0.848365	0.424182
t	-0.313696713864699	0.147594	-2.1254	0.038955	0.019478

Multiple Linear Regression - Regression Statistics
Multiple R	0.324935060040943
R-squared	0.105582793243811
Adjusted R-squared	-0.147187286926416
F-TEST (value)	0.417702890993692
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.955563158999425
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.3815051824122
Sum Squared Residuals	4957.67989321279

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.324935060040943 \tabularnewline
R-squared & 0.105582793243811 \tabularnewline
Adjusted R-squared & -0.147187286926416 \tabularnewline
F-TEST (value) & 0.417702890993692 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.955563158999425 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 10.3815051824122 \tabularnewline
Sum Squared Residuals & 4957.67989321279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58384&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.324935060040943[/C][/ROW]
[ROW][C]R-squared[/C][C]0.105582793243811[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.147187286926416[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.417702890993692[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0.955563158999425[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]10.3815051824122[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4957.67989321279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58384&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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	0.324935060040943
R-squared	0.105582793243811
Adjusted R-squared	-0.147187286926416
F-TEST (value)	0.417702890993692
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.955563158999425
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.3815051824122
Sum Squared Residuals	4957.67989321279

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	12.6	20.5579921558200	-7.95799215582005
2	15.7	18.3751025726251	-2.67510257262514
3	13.2	17.7470624210596	-4.54706242105963
4	20.3	18.9909821179286	1.30901788207140
5	12.8	14.8992230273217	-2.09922302732167
6	8	16.0161326862993	-8.01613268629927
7	0.9	13.6472631788872	-12.7472631788872
8	3.6	18.9229419663631	-15.3229419663631
9	14.1	19.6039720800372	-5.50397208003723
10	21.7	21.1239720800372	0.576027919962784
11	24.5	22.0429419663631	2.45705803363691
12	18.9	26.8196508675131	-7.91965086751312
13	13.9	20.6183806421591	-6.71838064215912
14	11	19.2004408695074	-8.2004408695074
15	5.8	13.9827018546832	-8.18270185468324
16	15.5	12.9317721199229	2.56822788007711
17	22.4	15.7245613242039	6.67543867579605
18	31.7	15.3115713620953	16.3884286379047
19	30.3	12.1777520441401	18.1222479558599
20	31.4	15.9235312105298	15.4764687894702
21	20.2	15.0746617031177	5.12533829688227
22	19.7	16.5946617031177	3.10533829688227
23	10.8	19.0435312105298	-8.24353121052981
24	13.2	19.2305412484212	-6.03054124842119
25	15.1	14.5591706441534	0.540829355846585
26	15.6	14.6711304925879	0.928869507412083
27	15.5	13.2781405304793	2.2218594695207
28	12.7	15.2870100378914	-2.58701003789138
29	10.9	11.9602007578276	-1.06020075782757
30	10	11.5472107957189	-1.54721079571894
31	9.1	14.5329899621086	-5.43298996210862
32	10.3	9.8643212125241	0.435678787475895
33	16.9	13.6051505683707	3.29484943162933
34	22	16.6550501894569	5.34494981054311
35	27.6	16.8090702652396	10.7909297347604
36	28.9	17.7610301136741	11.1389698863259
37	31	13.8546093199495	17.1453906800505
38	32.9	16.2614186000133	16.6385813999867
39	38.1	15.6333784484478	22.4666215515522
40	28.8	18.4071977664030	10.3928022335970
41	29	18.9051375390547	10.0948624609453
42	21.8	17.7271977664030	4.07280223359703
43	28.8	17.6531776906202	11.1468223093798
44	25.6	15.2793583726650	10.3206416273350
45	28.2	19.0201877285116	9.17981227148841
46	20.2	19.0102881074254	1.18971189257462
47	17.9	19.9292579937512	-2.02925799375125
48	16.3	15.5265691683840	0.773430831616032
49	13.2	16.2098472379180	-3.00984723791795
50	8.1	14.7919074652662	-6.69190746526624
51	4.5	16.4587167453301	-11.9587167453301
52	-0.1	11.5830379578542	-11.6830379578542
53	0	13.6108773515921	-13.6108773515921
54	2.3	13.1978873894835	-10.8978873894835
55	2.8	13.8888171242438	-11.0888171242438
56	2.9	13.8098472379180	-10.9098472379180
57	0.1	12.1960279199628	-12.0960279199628
58	3.5	13.7160279199628	-10.2160279199628
59	8.6	11.5751985641162	-2.97519856411621
60	13.8	11.7622086020076	2.03779139799241

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 12.6 & 20.5579921558200 & -7.95799215582005 \tabularnewline
2 & 15.7 & 18.3751025726251 & -2.67510257262514 \tabularnewline
3 & 13.2 & 17.7470624210596 & -4.54706242105963 \tabularnewline
4 & 20.3 & 18.9909821179286 & 1.30901788207140 \tabularnewline
5 & 12.8 & 14.8992230273217 & -2.09922302732167 \tabularnewline
6 & 8 & 16.0161326862993 & -8.01613268629927 \tabularnewline
7 & 0.9 & 13.6472631788872 & -12.7472631788872 \tabularnewline
8 & 3.6 & 18.9229419663631 & -15.3229419663631 \tabularnewline
9 & 14.1 & 19.6039720800372 & -5.50397208003723 \tabularnewline
10 & 21.7 & 21.1239720800372 & 0.576027919962784 \tabularnewline
11 & 24.5 & 22.0429419663631 & 2.45705803363691 \tabularnewline
12 & 18.9 & 26.8196508675131 & -7.91965086751312 \tabularnewline
13 & 13.9 & 20.6183806421591 & -6.71838064215912 \tabularnewline
14 & 11 & 19.2004408695074 & -8.2004408695074 \tabularnewline
15 & 5.8 & 13.9827018546832 & -8.18270185468324 \tabularnewline
16 & 15.5 & 12.9317721199229 & 2.56822788007711 \tabularnewline
17 & 22.4 & 15.7245613242039 & 6.67543867579605 \tabularnewline
18 & 31.7 & 15.3115713620953 & 16.3884286379047 \tabularnewline
19 & 30.3 & 12.1777520441401 & 18.1222479558599 \tabularnewline
20 & 31.4 & 15.9235312105298 & 15.4764687894702 \tabularnewline
21 & 20.2 & 15.0746617031177 & 5.12533829688227 \tabularnewline
22 & 19.7 & 16.5946617031177 & 3.10533829688227 \tabularnewline
23 & 10.8 & 19.0435312105298 & -8.24353121052981 \tabularnewline
24 & 13.2 & 19.2305412484212 & -6.03054124842119 \tabularnewline
25 & 15.1 & 14.5591706441534 & 0.540829355846585 \tabularnewline
26 & 15.6 & 14.6711304925879 & 0.928869507412083 \tabularnewline
27 & 15.5 & 13.2781405304793 & 2.2218594695207 \tabularnewline
28 & 12.7 & 15.2870100378914 & -2.58701003789138 \tabularnewline
29 & 10.9 & 11.9602007578276 & -1.06020075782757 \tabularnewline
30 & 10 & 11.5472107957189 & -1.54721079571894 \tabularnewline
31 & 9.1 & 14.5329899621086 & -5.43298996210862 \tabularnewline
32 & 10.3 & 9.8643212125241 & 0.435678787475895 \tabularnewline
33 & 16.9 & 13.6051505683707 & 3.29484943162933 \tabularnewline
34 & 22 & 16.6550501894569 & 5.34494981054311 \tabularnewline
35 & 27.6 & 16.8090702652396 & 10.7909297347604 \tabularnewline
36 & 28.9 & 17.7610301136741 & 11.1389698863259 \tabularnewline
37 & 31 & 13.8546093199495 & 17.1453906800505 \tabularnewline
38 & 32.9 & 16.2614186000133 & 16.6385813999867 \tabularnewline
39 & 38.1 & 15.6333784484478 & 22.4666215515522 \tabularnewline
40 & 28.8 & 18.4071977664030 & 10.3928022335970 \tabularnewline
41 & 29 & 18.9051375390547 & 10.0948624609453 \tabularnewline
42 & 21.8 & 17.7271977664030 & 4.07280223359703 \tabularnewline
43 & 28.8 & 17.6531776906202 & 11.1468223093798 \tabularnewline
44 & 25.6 & 15.2793583726650 & 10.3206416273350 \tabularnewline
45 & 28.2 & 19.0201877285116 & 9.17981227148841 \tabularnewline
46 & 20.2 & 19.0102881074254 & 1.18971189257462 \tabularnewline
47 & 17.9 & 19.9292579937512 & -2.02925799375125 \tabularnewline
48 & 16.3 & 15.5265691683840 & 0.773430831616032 \tabularnewline
49 & 13.2 & 16.2098472379180 & -3.00984723791795 \tabularnewline
50 & 8.1 & 14.7919074652662 & -6.69190746526624 \tabularnewline
51 & 4.5 & 16.4587167453301 & -11.9587167453301 \tabularnewline
52 & -0.1 & 11.5830379578542 & -11.6830379578542 \tabularnewline
53 & 0 & 13.6108773515921 & -13.6108773515921 \tabularnewline
54 & 2.3 & 13.1978873894835 & -10.8978873894835 \tabularnewline
55 & 2.8 & 13.8888171242438 & -11.0888171242438 \tabularnewline
56 & 2.9 & 13.8098472379180 & -10.9098472379180 \tabularnewline
57 & 0.1 & 12.1960279199628 & -12.0960279199628 \tabularnewline
58 & 3.5 & 13.7160279199628 & -10.2160279199628 \tabularnewline
59 & 8.6 & 11.5751985641162 & -2.97519856411621 \tabularnewline
60 & 13.8 & 11.7622086020076 & 2.03779139799241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58384&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]12.6[/C][C]20.5579921558200[/C][C]-7.95799215582005[/C][/ROW]
[ROW][C]2[/C][C]15.7[/C][C]18.3751025726251[/C][C]-2.67510257262514[/C][/ROW]
[ROW][C]3[/C][C]13.2[/C][C]17.7470624210596[/C][C]-4.54706242105963[/C][/ROW]
[ROW][C]4[/C][C]20.3[/C][C]18.9909821179286[/C][C]1.30901788207140[/C][/ROW]
[ROW][C]5[/C][C]12.8[/C][C]14.8992230273217[/C][C]-2.09922302732167[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]16.0161326862993[/C][C]-8.01613268629927[/C][/ROW]
[ROW][C]7[/C][C]0.9[/C][C]13.6472631788872[/C][C]-12.7472631788872[/C][/ROW]
[ROW][C]8[/C][C]3.6[/C][C]18.9229419663631[/C][C]-15.3229419663631[/C][/ROW]
[ROW][C]9[/C][C]14.1[/C][C]19.6039720800372[/C][C]-5.50397208003723[/C][/ROW]
[ROW][C]10[/C][C]21.7[/C][C]21.1239720800372[/C][C]0.576027919962784[/C][/ROW]
[ROW][C]11[/C][C]24.5[/C][C]22.0429419663631[/C][C]2.45705803363691[/C][/ROW]
[ROW][C]12[/C][C]18.9[/C][C]26.8196508675131[/C][C]-7.91965086751312[/C][/ROW]
[ROW][C]13[/C][C]13.9[/C][C]20.6183806421591[/C][C]-6.71838064215912[/C][/ROW]
[ROW][C]14[/C][C]11[/C][C]19.2004408695074[/C][C]-8.2004408695074[/C][/ROW]
[ROW][C]15[/C][C]5.8[/C][C]13.9827018546832[/C][C]-8.18270185468324[/C][/ROW]
[ROW][C]16[/C][C]15.5[/C][C]12.9317721199229[/C][C]2.56822788007711[/C][/ROW]
[ROW][C]17[/C][C]22.4[/C][C]15.7245613242039[/C][C]6.67543867579605[/C][/ROW]
[ROW][C]18[/C][C]31.7[/C][C]15.3115713620953[/C][C]16.3884286379047[/C][/ROW]
[ROW][C]19[/C][C]30.3[/C][C]12.1777520441401[/C][C]18.1222479558599[/C][/ROW]
[ROW][C]20[/C][C]31.4[/C][C]15.9235312105298[/C][C]15.4764687894702[/C][/ROW]
[ROW][C]21[/C][C]20.2[/C][C]15.0746617031177[/C][C]5.12533829688227[/C][/ROW]
[ROW][C]22[/C][C]19.7[/C][C]16.5946617031177[/C][C]3.10533829688227[/C][/ROW]
[ROW][C]23[/C][C]10.8[/C][C]19.0435312105298[/C][C]-8.24353121052981[/C][/ROW]
[ROW][C]24[/C][C]13.2[/C][C]19.2305412484212[/C][C]-6.03054124842119[/C][/ROW]
[ROW][C]25[/C][C]15.1[/C][C]14.5591706441534[/C][C]0.540829355846585[/C][/ROW]
[ROW][C]26[/C][C]15.6[/C][C]14.6711304925879[/C][C]0.928869507412083[/C][/ROW]
[ROW][C]27[/C][C]15.5[/C][C]13.2781405304793[/C][C]2.2218594695207[/C][/ROW]
[ROW][C]28[/C][C]12.7[/C][C]15.2870100378914[/C][C]-2.58701003789138[/C][/ROW]
[ROW][C]29[/C][C]10.9[/C][C]11.9602007578276[/C][C]-1.06020075782757[/C][/ROW]
[ROW][C]30[/C][C]10[/C][C]11.5472107957189[/C][C]-1.54721079571894[/C][/ROW]
[ROW][C]31[/C][C]9.1[/C][C]14.5329899621086[/C][C]-5.43298996210862[/C][/ROW]
[ROW][C]32[/C][C]10.3[/C][C]9.8643212125241[/C][C]0.435678787475895[/C][/ROW]
[ROW][C]33[/C][C]16.9[/C][C]13.6051505683707[/C][C]3.29484943162933[/C][/ROW]
[ROW][C]34[/C][C]22[/C][C]16.6550501894569[/C][C]5.34494981054311[/C][/ROW]
[ROW][C]35[/C][C]27.6[/C][C]16.8090702652396[/C][C]10.7909297347604[/C][/ROW]
[ROW][C]36[/C][C]28.9[/C][C]17.7610301136741[/C][C]11.1389698863259[/C][/ROW]
[ROW][C]37[/C][C]31[/C][C]13.8546093199495[/C][C]17.1453906800505[/C][/ROW]
[ROW][C]38[/C][C]32.9[/C][C]16.2614186000133[/C][C]16.6385813999867[/C][/ROW]
[ROW][C]39[/C][C]38.1[/C][C]15.6333784484478[/C][C]22.4666215515522[/C][/ROW]
[ROW][C]40[/C][C]28.8[/C][C]18.4071977664030[/C][C]10.3928022335970[/C][/ROW]
[ROW][C]41[/C][C]29[/C][C]18.9051375390547[/C][C]10.0948624609453[/C][/ROW]
[ROW][C]42[/C][C]21.8[/C][C]17.7271977664030[/C][C]4.07280223359703[/C][/ROW]
[ROW][C]43[/C][C]28.8[/C][C]17.6531776906202[/C][C]11.1468223093798[/C][/ROW]
[ROW][C]44[/C][C]25.6[/C][C]15.2793583726650[/C][C]10.3206416273350[/C][/ROW]
[ROW][C]45[/C][C]28.2[/C][C]19.0201877285116[/C][C]9.17981227148841[/C][/ROW]
[ROW][C]46[/C][C]20.2[/C][C]19.0102881074254[/C][C]1.18971189257462[/C][/ROW]
[ROW][C]47[/C][C]17.9[/C][C]19.9292579937512[/C][C]-2.02925799375125[/C][/ROW]
[ROW][C]48[/C][C]16.3[/C][C]15.5265691683840[/C][C]0.773430831616032[/C][/ROW]
[ROW][C]49[/C][C]13.2[/C][C]16.2098472379180[/C][C]-3.00984723791795[/C][/ROW]
[ROW][C]50[/C][C]8.1[/C][C]14.7919074652662[/C][C]-6.69190746526624[/C][/ROW]
[ROW][C]51[/C][C]4.5[/C][C]16.4587167453301[/C][C]-11.9587167453301[/C][/ROW]
[ROW][C]52[/C][C]-0.1[/C][C]11.5830379578542[/C][C]-11.6830379578542[/C][/ROW]
[ROW][C]53[/C][C]0[/C][C]13.6108773515921[/C][C]-13.6108773515921[/C][/ROW]
[ROW][C]54[/C][C]2.3[/C][C]13.1978873894835[/C][C]-10.8978873894835[/C][/ROW]
[ROW][C]55[/C][C]2.8[/C][C]13.8888171242438[/C][C]-11.0888171242438[/C][/ROW]
[ROW][C]56[/C][C]2.9[/C][C]13.8098472379180[/C][C]-10.9098472379180[/C][/ROW]
[ROW][C]57[/C][C]0.1[/C][C]12.1960279199628[/C][C]-12.0960279199628[/C][/ROW]
[ROW][C]58[/C][C]3.5[/C][C]13.7160279199628[/C][C]-10.2160279199628[/C][/ROW]
[ROW][C]59[/C][C]8.6[/C][C]11.5751985641162[/C][C]-2.97519856411621[/C][/ROW]
[ROW][C]60[/C][C]13.8[/C][C]11.7622086020076[/C][C]2.03779139799241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58384&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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	12.6	20.5579921558200	-7.95799215582005
2	15.7	18.3751025726251	-2.67510257262514
3	13.2	17.7470624210596	-4.54706242105963
4	20.3	18.9909821179286	1.30901788207140
5	12.8	14.8992230273217	-2.09922302732167
6	8	16.0161326862993	-8.01613268629927
7	0.9	13.6472631788872	-12.7472631788872
8	3.6	18.9229419663631	-15.3229419663631
9	14.1	19.6039720800372	-5.50397208003723
10	21.7	21.1239720800372	0.576027919962784
11	24.5	22.0429419663631	2.45705803363691
12	18.9	26.8196508675131	-7.91965086751312
13	13.9	20.6183806421591	-6.71838064215912
14	11	19.2004408695074	-8.2004408695074
15	5.8	13.9827018546832	-8.18270185468324
16	15.5	12.9317721199229	2.56822788007711
17	22.4	15.7245613242039	6.67543867579605
18	31.7	15.3115713620953	16.3884286379047
19	30.3	12.1777520441401	18.1222479558599
20	31.4	15.9235312105298	15.4764687894702
21	20.2	15.0746617031177	5.12533829688227
22	19.7	16.5946617031177	3.10533829688227
23	10.8	19.0435312105298	-8.24353121052981
24	13.2	19.2305412484212	-6.03054124842119
25	15.1	14.5591706441534	0.540829355846585
26	15.6	14.6711304925879	0.928869507412083
27	15.5	13.2781405304793	2.2218594695207
28	12.7	15.2870100378914	-2.58701003789138
29	10.9	11.9602007578276	-1.06020075782757
30	10	11.5472107957189	-1.54721079571894
31	9.1	14.5329899621086	-5.43298996210862
32	10.3	9.8643212125241	0.435678787475895
33	16.9	13.6051505683707	3.29484943162933
34	22	16.6550501894569	5.34494981054311
35	27.6	16.8090702652396	10.7909297347604
36	28.9	17.7610301136741	11.1389698863259
37	31	13.8546093199495	17.1453906800505
38	32.9	16.2614186000133	16.6385813999867
39	38.1	15.6333784484478	22.4666215515522
40	28.8	18.4071977664030	10.3928022335970
41	29	18.9051375390547	10.0948624609453
42	21.8	17.7271977664030	4.07280223359703
43	28.8	17.6531776906202	11.1468223093798
44	25.6	15.2793583726650	10.3206416273350
45	28.2	19.0201877285116	9.17981227148841
46	20.2	19.0102881074254	1.18971189257462
47	17.9	19.9292579937512	-2.02925799375125
48	16.3	15.5265691683840	0.773430831616032
49	13.2	16.2098472379180	-3.00984723791795
50	8.1	14.7919074652662	-6.69190746526624
51	4.5	16.4587167453301	-11.9587167453301
52	-0.1	11.5830379578542	-11.6830379578542
53	0	13.6108773515921	-13.6108773515921
54	2.3	13.1978873894835	-10.8978873894835
55	2.8	13.8888171242438	-11.0888171242438
56	2.9	13.8098472379180	-10.9098472379180
57	0.1	12.1960279199628	-12.0960279199628
58	3.5	13.7160279199628	-10.2160279199628
59	8.6	11.5751985641162	-2.97519856411621
60	13.8	11.7622086020076	2.03779139799241

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.111780849272206	0.223561698544412	0.888219150727794
18	0.443199970935922	0.886399941871844	0.556800029064078
19	0.710760990084942	0.578478019830116	0.289239009915058
20	0.7805086115887	0.4389827768226	0.2194913884113
21	0.676590160506361	0.646819678987278	0.323409839493639
22	0.5840496286447	0.8319007427106	0.4159503713553
23	0.694053223113498	0.611893553773005	0.305946776886502
24	0.757001413451101	0.485997173097798	0.242998586548899
25	0.717404683816405	0.56519063236719	0.282595316183595
26	0.670868609281358	0.658262781437284	0.329131390718642
27	0.599706365898895	0.80058726820221	0.400293634101105
28	0.653966143881173	0.692067712237654	0.346033856118827
29	0.611044312373871	0.777911375252257	0.388955687626129
30	0.574677226369177	0.850645547261646	0.425322773630823
31	0.651886823626854	0.696226352746292	0.348113176373146
32	0.631591957570217	0.736816084859567	0.368408042429783
33	0.635649885764143	0.728700228471715	0.364350114235857
34	0.634134665376294	0.731730669247412	0.365865334623706
35	0.670784666501184	0.658430666997632	0.329215333498816
36	0.820700085647692	0.358599828704615	0.179299914352308
37	0.81780175201184	0.364396495976319	0.182198247988160
38	0.754323776264018	0.491352447471964	0.245676223735982
39	0.74668728423805	0.506625431523899	0.253312715761950
40	0.700482288713771	0.599035422572457	0.299517711286229
41	0.670380602507146	0.659238794985708	0.329619397492854
42	0.533269911709523	0.933460176580955	0.466730088290477
43	0.434755036258003	0.869510072516006	0.565244963741997

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.111780849272206 & 0.223561698544412 & 0.888219150727794 \tabularnewline
18 & 0.443199970935922 & 0.886399941871844 & 0.556800029064078 \tabularnewline
19 & 0.710760990084942 & 0.578478019830116 & 0.289239009915058 \tabularnewline
20 & 0.7805086115887 & 0.4389827768226 & 0.2194913884113 \tabularnewline
21 & 0.676590160506361 & 0.646819678987278 & 0.323409839493639 \tabularnewline
22 & 0.5840496286447 & 0.8319007427106 & 0.4159503713553 \tabularnewline
23 & 0.694053223113498 & 0.611893553773005 & 0.305946776886502 \tabularnewline
24 & 0.757001413451101 & 0.485997173097798 & 0.242998586548899 \tabularnewline
25 & 0.717404683816405 & 0.56519063236719 & 0.282595316183595 \tabularnewline
26 & 0.670868609281358 & 0.658262781437284 & 0.329131390718642 \tabularnewline
27 & 0.599706365898895 & 0.80058726820221 & 0.400293634101105 \tabularnewline
28 & 0.653966143881173 & 0.692067712237654 & 0.346033856118827 \tabularnewline
29 & 0.611044312373871 & 0.777911375252257 & 0.388955687626129 \tabularnewline
30 & 0.574677226369177 & 0.850645547261646 & 0.425322773630823 \tabularnewline
31 & 0.651886823626854 & 0.696226352746292 & 0.348113176373146 \tabularnewline
32 & 0.631591957570217 & 0.736816084859567 & 0.368408042429783 \tabularnewline
33 & 0.635649885764143 & 0.728700228471715 & 0.364350114235857 \tabularnewline
34 & 0.634134665376294 & 0.731730669247412 & 0.365865334623706 \tabularnewline
35 & 0.670784666501184 & 0.658430666997632 & 0.329215333498816 \tabularnewline
36 & 0.820700085647692 & 0.358599828704615 & 0.179299914352308 \tabularnewline
37 & 0.81780175201184 & 0.364396495976319 & 0.182198247988160 \tabularnewline
38 & 0.754323776264018 & 0.491352447471964 & 0.245676223735982 \tabularnewline
39 & 0.74668728423805 & 0.506625431523899 & 0.253312715761950 \tabularnewline
40 & 0.700482288713771 & 0.599035422572457 & 0.299517711286229 \tabularnewline
41 & 0.670380602507146 & 0.659238794985708 & 0.329619397492854 \tabularnewline
42 & 0.533269911709523 & 0.933460176580955 & 0.466730088290477 \tabularnewline
43 & 0.434755036258003 & 0.869510072516006 & 0.565244963741997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58384&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]17[/C][C]0.111780849272206[/C][C]0.223561698544412[/C][C]0.888219150727794[/C][/ROW]
[ROW][C]18[/C][C]0.443199970935922[/C][C]0.886399941871844[/C][C]0.556800029064078[/C][/ROW]
[ROW][C]19[/C][C]0.710760990084942[/C][C]0.578478019830116[/C][C]0.289239009915058[/C][/ROW]
[ROW][C]20[/C][C]0.7805086115887[/C][C]0.4389827768226[/C][C]0.2194913884113[/C][/ROW]
[ROW][C]21[/C][C]0.676590160506361[/C][C]0.646819678987278[/C][C]0.323409839493639[/C][/ROW]
[ROW][C]22[/C][C]0.5840496286447[/C][C]0.8319007427106[/C][C]0.4159503713553[/C][/ROW]
[ROW][C]23[/C][C]0.694053223113498[/C][C]0.611893553773005[/C][C]0.305946776886502[/C][/ROW]
[ROW][C]24[/C][C]0.757001413451101[/C][C]0.485997173097798[/C][C]0.242998586548899[/C][/ROW]
[ROW][C]25[/C][C]0.717404683816405[/C][C]0.56519063236719[/C][C]0.282595316183595[/C][/ROW]
[ROW][C]26[/C][C]0.670868609281358[/C][C]0.658262781437284[/C][C]0.329131390718642[/C][/ROW]
[ROW][C]27[/C][C]0.599706365898895[/C][C]0.80058726820221[/C][C]0.400293634101105[/C][/ROW]
[ROW][C]28[/C][C]0.653966143881173[/C][C]0.692067712237654[/C][C]0.346033856118827[/C][/ROW]
[ROW][C]29[/C][C]0.611044312373871[/C][C]0.777911375252257[/C][C]0.388955687626129[/C][/ROW]
[ROW][C]30[/C][C]0.574677226369177[/C][C]0.850645547261646[/C][C]0.425322773630823[/C][/ROW]
[ROW][C]31[/C][C]0.651886823626854[/C][C]0.696226352746292[/C][C]0.348113176373146[/C][/ROW]
[ROW][C]32[/C][C]0.631591957570217[/C][C]0.736816084859567[/C][C]0.368408042429783[/C][/ROW]
[ROW][C]33[/C][C]0.635649885764143[/C][C]0.728700228471715[/C][C]0.364350114235857[/C][/ROW]
[ROW][C]34[/C][C]0.634134665376294[/C][C]0.731730669247412[/C][C]0.365865334623706[/C][/ROW]
[ROW][C]35[/C][C]0.670784666501184[/C][C]0.658430666997632[/C][C]0.329215333498816[/C][/ROW]
[ROW][C]36[/C][C]0.820700085647692[/C][C]0.358599828704615[/C][C]0.179299914352308[/C][/ROW]
[ROW][C]37[/C][C]0.81780175201184[/C][C]0.364396495976319[/C][C]0.182198247988160[/C][/ROW]
[ROW][C]38[/C][C]0.754323776264018[/C][C]0.491352447471964[/C][C]0.245676223735982[/C][/ROW]
[ROW][C]39[/C][C]0.74668728423805[/C][C]0.506625431523899[/C][C]0.253312715761950[/C][/ROW]
[ROW][C]40[/C][C]0.700482288713771[/C][C]0.599035422572457[/C][C]0.299517711286229[/C][/ROW]
[ROW][C]41[/C][C]0.670380602507146[/C][C]0.659238794985708[/C][C]0.329619397492854[/C][/ROW]
[ROW][C]42[/C][C]0.533269911709523[/C][C]0.933460176580955[/C][C]0.466730088290477[/C][/ROW]
[ROW][C]43[/C][C]0.434755036258003[/C][C]0.869510072516006[/C][C]0.565244963741997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58384&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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
17	0.111780849272206	0.223561698544412	0.888219150727794
18	0.443199970935922	0.886399941871844	0.556800029064078
19	0.710760990084942	0.578478019830116	0.289239009915058
20	0.7805086115887	0.4389827768226	0.2194913884113
21	0.676590160506361	0.646819678987278	0.323409839493639
22	0.5840496286447	0.8319007427106	0.4159503713553
23	0.694053223113498	0.611893553773005	0.305946776886502
24	0.757001413451101	0.485997173097798	0.242998586548899
25	0.717404683816405	0.56519063236719	0.282595316183595
26	0.670868609281358	0.658262781437284	0.329131390718642
27	0.599706365898895	0.80058726820221	0.400293634101105
28	0.653966143881173	0.692067712237654	0.346033856118827
29	0.611044312373871	0.777911375252257	0.388955687626129
30	0.574677226369177	0.850645547261646	0.425322773630823
31	0.651886823626854	0.696226352746292	0.348113176373146
32	0.631591957570217	0.736816084859567	0.368408042429783
33	0.635649885764143	0.728700228471715	0.364350114235857
34	0.634134665376294	0.731730669247412	0.365865334623706
35	0.670784666501184	0.658430666997632	0.329215333498816
36	0.820700085647692	0.358599828704615	0.179299914352308
37	0.81780175201184	0.364396495976319	0.182198247988160
38	0.754323776264018	0.491352447471964	0.245676223735982
39	0.74668728423805	0.506625431523899	0.253312715761950
40	0.700482288713771	0.599035422572457	0.299517711286229
41	0.670380602507146	0.659238794985708	0.329619397492854
42	0.533269911709523	0.933460176580955	0.466730088290477
43	0.434755036258003	0.869510072516006	0.565244963741997

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=58384&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=58384&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58384&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 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