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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 24 Aug 2012 03:12:18 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/24/t13457929549lzft1eha6629la.htm/, Retrieved Sat, 27 Apr 2024 23:53:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169492, Retrieved Sat, 27 Apr 2024 23:53:02 +0000

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No (this computation is public)

User-defined keywords

as above

Estimated Impact

169

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

-       [Multiple Regression] [CWR multivariate ...] [2012-08-24 07:12:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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48	81	0	4	1	6	0	1	6
56	38	1	4	1	3	0	1	6
47	89	0	1	1	2	0	1	6
48	80	1	2	1	2	0	2	6
45	79	1	2	1	2	0	1	6
56	61	1	2	1	1	0	1	6
48	42	0	2	1	2	0	1	6
45	67	0	2	2	2	0	1	6
52	47	1	2	1	2	0	1	6
47	55	1	2	2	3	0	1	7
52	85	1	4	1	2	0	1	7
60	75	0	4	1	3	0	1	7
45	66	0	4	1	2	0	1	7
48	53	1	4	1	2	0	2	7
56	67	0	1	1	1	0	1	7
60	63	1	2	1	4	0	2	7
52	51	1	4	1	2	0	2	7
60	41	1	4	1	1	0	2	7
47	59	1	1	1	1	0	2	7
52	44	0	1	1	5	0	1	7
47	48	0	1	1	1	0	1	7
59	60	1	2	1	2	0	2	8
48	84	1	2	1	2	0	1	8
61	67	0	2	2	1	0	1	8
60	38	1	2	1	7	0	1	8
45	46	0	4	1	2	0	1	8
63	36	0	2	1	1	0	1	8
41	79	0	4	1	2	0	1	8
49	32	1	1	1	1	0	2	8
63	65	0	4	1	3	1	1	7
54	79	1	4	1	4	1	1	7
55	67	1	4	1	4	1	2	7
70	73	1	2	2	1	1	1	7
43	74	1	4	1	3	1	2	7
58	61	0	4	1	4	1	2	7
56	69	1	4	1	2	1	2	7
50	55	0	4	1	4	1	2	7
32	75	1	4	1	2	1	2	7
59	29	0	2	1	5	1	1	7
58	66	0	1	1	3	1	1	7
56	48	0	2	1	3	1	1	7
50	64	1	4	1	1	1	1	7
32	52	1	4	1	1	1	1	7
36	31	0	2	1	1	1	1	10
46	85	1	4	1	5	1	1	10
47	58	1	2	3	3	1	1	10
67	75	0	4	2	6	1	1	10
61	46	0	1	3	5	1	1	10
49	53	1	1	1	4	1	1	10
49	80	1	4	1	3	1	2	10
56	67	1	4	1	1	1	2	10
56	58	1	4	1	5	1	2	10
52	70	1	4	1	4	1	2	10
49	77	1	4	1	1	1	2	10
55	58	0	4	1	9	1	1	10
56	65	0	4	1	4	1	2	10

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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	5 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation
Sat[t] = + 48.7716447324039 -0.0329259567701882Age[t] -1.54456830512478MF[t] -0.462010688776791Rm[t] + 3.31334019308661PubPr[t] + 1.18532954135618LOS[t] -0.188414089256728OorG[t] + 2.14873852674129type[t] -0.333101201099572`wr `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Sat[t] =  +  48.7716447324039 -0.0329259567701882Age[t] -1.54456830512478MF[t] -0.462010688776791Rm[t] +  3.31334019308661PubPr[t] +  1.18532954135618LOS[t] -0.188414089256728OorG[t] +  2.14873852674129type[t] -0.333101201099572`wr
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Sat[t] =  +  48.7716447324039 -0.0329259567701882Age[t] -1.54456830512478MF[t] -0.462010688776791Rm[t] +  3.31334019308661PubPr[t] +  1.18532954135618LOS[t] -0.188414089256728OorG[t] +  2.14873852674129type[t] -0.333101201099572`wr
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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
Sat[t] = + 48.7716447324039 -0.0329259567701882Age[t] -1.54456830512478MF[t] -0.462010688776791Rm[t] + 3.31334019308661PubPr[t] + 1.18532954135618LOS[t] -0.188414089256728OorG[t] + 2.14873852674129type[t] -0.333101201099572`wr `[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	48.7716447324039	8.495137	5.7411	1e-06	0
Age	-0.0329259567701882	0.07281	-0.4522	0.653194	0.326597
MF	-1.54456830512478	2.37937	-0.6492	0.519401	0.259701
Rm	-0.462010688776791	1.042953	-0.443	0.65981	0.329905
PubPr	3.31334019308661	2.593253	1.2777	0.207638	0.103819
LOS	1.18532954135618	0.669969	1.7692	0.083344	0.041672
OorG	-0.188414089256728	2.631239	-0.0716	0.943219	0.471609
type	2.14873852674129	2.622467	0.8194	0.416718	0.208359
`wr `	-0.333101201099572	0.936702	-0.3556	0.723723	0.361862

\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) & 48.7716447324039 & 8.495137 & 5.7411 & 1e-06 & 0 \tabularnewline
Age & -0.0329259567701882 & 0.07281 & -0.4522 & 0.653194 & 0.326597 \tabularnewline
MF & -1.54456830512478 & 2.37937 & -0.6492 & 0.519401 & 0.259701 \tabularnewline
Rm & -0.462010688776791 & 1.042953 & -0.443 & 0.65981 & 0.329905 \tabularnewline
PubPr & 3.31334019308661 & 2.593253 & 1.2777 & 0.207638 & 0.103819 \tabularnewline
LOS & 1.18532954135618 & 0.669969 & 1.7692 & 0.083344 & 0.041672 \tabularnewline
OorG & -0.188414089256728 & 2.631239 & -0.0716 & 0.943219 & 0.471609 \tabularnewline
type & 2.14873852674129 & 2.622467 & 0.8194 & 0.416718 & 0.208359 \tabularnewline
`wr
` & -0.333101201099572 & 0.936702 & -0.3556 & 0.723723 & 0.361862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&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]48.7716447324039[/C][C]8.495137[/C][C]5.7411[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]Age[/C][C]-0.0329259567701882[/C][C]0.07281[/C][C]-0.4522[/C][C]0.653194[/C][C]0.326597[/C][/ROW]
[ROW][C]MF[/C][C]-1.54456830512478[/C][C]2.37937[/C][C]-0.6492[/C][C]0.519401[/C][C]0.259701[/C][/ROW]
[ROW][C]Rm[/C][C]-0.462010688776791[/C][C]1.042953[/C][C]-0.443[/C][C]0.65981[/C][C]0.329905[/C][/ROW]
[ROW][C]PubPr[/C][C]3.31334019308661[/C][C]2.593253[/C][C]1.2777[/C][C]0.207638[/C][C]0.103819[/C][/ROW]
[ROW][C]LOS[/C][C]1.18532954135618[/C][C]0.669969[/C][C]1.7692[/C][C]0.083344[/C][C]0.041672[/C][/ROW]
[ROW][C]OorG[/C][C]-0.188414089256728[/C][C]2.631239[/C][C]-0.0716[/C][C]0.943219[/C][C]0.471609[/C][/ROW]
[ROW][C]type[/C][C]2.14873852674129[/C][C]2.622467[/C][C]0.8194[/C][C]0.416718[/C][C]0.208359[/C][/ROW]
[ROW][C]`wr
`[/C][C]-0.333101201099572[/C][C]0.936702[/C][C]-0.3556[/C][C]0.723723[/C][C]0.361862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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)	48.7716447324039	8.495137	5.7411	1e-06	0
Age	-0.0329259567701882	0.07281	-0.4522	0.653194	0.326597
MF	-1.54456830512478	2.37937	-0.6492	0.519401	0.259701
Rm	-0.462010688776791	1.042953	-0.443	0.65981	0.329905
PubPr	3.31334019308661	2.593253	1.2777	0.207638	0.103819
LOS	1.18532954135618	0.669969	1.7692	0.083344	0.041672
OorG	-0.188414089256728	2.631239	-0.0716	0.943219	0.471609
type	2.14873852674129	2.622467	0.8194	0.416718	0.208359
`wr `	-0.333101201099572	0.936702	-0.3556	0.723723	0.361862

Multiple Linear Regression - Regression Statistics
Multiple R	0.354064251111079
R-squared	0.125361493914849
Adjusted R-squared	-0.0235131454187933
F-TEST (value)	0.842060773251661
F-TEST (DF numerator)	8
F-TEST (DF denominator)	47
p-value	0.570853717890965
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.79841587553479
Sum Squared Residuals	2858.31863788627

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.354064251111079 \tabularnewline
R-squared & 0.125361493914849 \tabularnewline
Adjusted R-squared & -0.0235131454187933 \tabularnewline
F-TEST (value) & 0.842060773251661 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.570853717890965 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 7.79841587553479 \tabularnewline
Sum Squared Residuals & 2858.31863788627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.354064251111079[/C][/ROW]
[ROW][C]R-squared[/C][C]0.125361493914849[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.0235131454187933[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.842060773251661[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0.570853717890965[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]7.79841587553479[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2858.31863788627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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	0.354064251111079
R-squared	0.125361493914849
Adjusted R-squared	-0.0235131454187933
F-TEST (value)	0.842060773251661
F-TEST (DF numerator)	8
F-TEST (DF denominator)	47
p-value	0.570853717890965
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.79841587553479
Sum Squared Residuals	2858.31863788627

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	48	54.832048240279	-6.83204824027897
2	56	51.1473074522038	4.85269254779624
3	47	51.2133544870231	-4.21335448702315
4	48	51.6518476307946	-3.65184763079456
5	45	49.5360350608235	-4.53603506082346
6	56	48.9433727413307	7.05662725866934
7	48	52.2988637664452	-4.2988637664452
8	45	54.7890550402771	-9.78905504027711
9	52	50.5896656774695	1.41033432253053
10	47	54.4918265566512	-7.49182655665118
11	52	48.0813567415492	3.91864325845083
12	60	51.140514155732	8.85948584426798
13	45	50.2515182253075	-5.25151822530753
14	48	51.2837258849365	-3.28372588493649
15	56	50.4192947935115	5.58070520648846
16	60	54.2491467775005	5.75085322249946
17	52	51.3495777984769	0.650422201523139
18	60	50.4935078248226	9.50649217517743
19	47	51.2868726692896	-4.28687266928955
20	52	55.9179099646506	-3.91790996465058
21	47	51.0448879721451	-4.04488797214511
22	59	51.6441643639992	7.35583563600082
23	48	48.7052028747734	-0.705202874773368
24	61	52.9375230967218	8.06247690327821
25	60	56.1464445929829	3.85355540701709
26	45	50.5769361596117	-5.57693615961172
27	63	50.644887563511	12.355112436489
28	41	49.4903795861955	-8.49037958619551
29	49	51.8427723009851	-2.84277230098506
30	63	51.2813596341772	11.7186403658228
31	54	50.4611574756259	3.53884252437407
32	55	53.0050074836095	1.99499251639052
33	70	51.3400861628187	18.6599138371813
34	43	51.589196244862	-8.58919624486198
35	58	54.7471315293554	3.25286847064461
36	56	50.5684964873567	5.43150351264325
37	50	54.9446872699765	-4.94468726997652
38	32	50.3709407467356	-18.3709407467356
39	59	55.7613745381699	3.23862546183012
40	58	52.6344657437374	5.36553425626265
41	56	52.765122276824	3.23487772317605
42	50	47.3990582031102	2.60094179688978
43	32	47.7941696843525	-15.7941696843525
44	36	49.9549008559061	-13.9549008559061
45	46	50.4496276730623	-4.44962767306226
46	47	56.5186711868718	-9.51867118687178
47	67	56.8221252803317	10.1778747196683
48	61	61.291020744728	-0.291020744727972
49	49	51.7039608146825	-2.70396081468248
50	49	50.3923369009421	-1.39233690094214
51	56	48.4497152562422	7.55028474375777
52	56	53.4873670325986	2.51263296740137
53	52	51.9069260100002	0.093073989999803
54	49	48.1204556885403	0.879544311459653
55	55	57.6245149764068	-2.62451497640683
56	56	53.6161240989759	2.38387590102408

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 48 & 54.832048240279 & -6.83204824027897 \tabularnewline
2 & 56 & 51.1473074522038 & 4.85269254779624 \tabularnewline
3 & 47 & 51.2133544870231 & -4.21335448702315 \tabularnewline
4 & 48 & 51.6518476307946 & -3.65184763079456 \tabularnewline
5 & 45 & 49.5360350608235 & -4.53603506082346 \tabularnewline
6 & 56 & 48.9433727413307 & 7.05662725866934 \tabularnewline
7 & 48 & 52.2988637664452 & -4.2988637664452 \tabularnewline
8 & 45 & 54.7890550402771 & -9.78905504027711 \tabularnewline
9 & 52 & 50.5896656774695 & 1.41033432253053 \tabularnewline
10 & 47 & 54.4918265566512 & -7.49182655665118 \tabularnewline
11 & 52 & 48.0813567415492 & 3.91864325845083 \tabularnewline
12 & 60 & 51.140514155732 & 8.85948584426798 \tabularnewline
13 & 45 & 50.2515182253075 & -5.25151822530753 \tabularnewline
14 & 48 & 51.2837258849365 & -3.28372588493649 \tabularnewline
15 & 56 & 50.4192947935115 & 5.58070520648846 \tabularnewline
16 & 60 & 54.2491467775005 & 5.75085322249946 \tabularnewline
17 & 52 & 51.3495777984769 & 0.650422201523139 \tabularnewline
18 & 60 & 50.4935078248226 & 9.50649217517743 \tabularnewline
19 & 47 & 51.2868726692896 & -4.28687266928955 \tabularnewline
20 & 52 & 55.9179099646506 & -3.91790996465058 \tabularnewline
21 & 47 & 51.0448879721451 & -4.04488797214511 \tabularnewline
22 & 59 & 51.6441643639992 & 7.35583563600082 \tabularnewline
23 & 48 & 48.7052028747734 & -0.705202874773368 \tabularnewline
24 & 61 & 52.9375230967218 & 8.06247690327821 \tabularnewline
25 & 60 & 56.1464445929829 & 3.85355540701709 \tabularnewline
26 & 45 & 50.5769361596117 & -5.57693615961172 \tabularnewline
27 & 63 & 50.644887563511 & 12.355112436489 \tabularnewline
28 & 41 & 49.4903795861955 & -8.49037958619551 \tabularnewline
29 & 49 & 51.8427723009851 & -2.84277230098506 \tabularnewline
30 & 63 & 51.2813596341772 & 11.7186403658228 \tabularnewline
31 & 54 & 50.4611574756259 & 3.53884252437407 \tabularnewline
32 & 55 & 53.0050074836095 & 1.99499251639052 \tabularnewline
33 & 70 & 51.3400861628187 & 18.6599138371813 \tabularnewline
34 & 43 & 51.589196244862 & -8.58919624486198 \tabularnewline
35 & 58 & 54.7471315293554 & 3.25286847064461 \tabularnewline
36 & 56 & 50.5684964873567 & 5.43150351264325 \tabularnewline
37 & 50 & 54.9446872699765 & -4.94468726997652 \tabularnewline
38 & 32 & 50.3709407467356 & -18.3709407467356 \tabularnewline
39 & 59 & 55.7613745381699 & 3.23862546183012 \tabularnewline
40 & 58 & 52.6344657437374 & 5.36553425626265 \tabularnewline
41 & 56 & 52.765122276824 & 3.23487772317605 \tabularnewline
42 & 50 & 47.3990582031102 & 2.60094179688978 \tabularnewline
43 & 32 & 47.7941696843525 & -15.7941696843525 \tabularnewline
44 & 36 & 49.9549008559061 & -13.9549008559061 \tabularnewline
45 & 46 & 50.4496276730623 & -4.44962767306226 \tabularnewline
46 & 47 & 56.5186711868718 & -9.51867118687178 \tabularnewline
47 & 67 & 56.8221252803317 & 10.1778747196683 \tabularnewline
48 & 61 & 61.291020744728 & -0.291020744727972 \tabularnewline
49 & 49 & 51.7039608146825 & -2.70396081468248 \tabularnewline
50 & 49 & 50.3923369009421 & -1.39233690094214 \tabularnewline
51 & 56 & 48.4497152562422 & 7.55028474375777 \tabularnewline
52 & 56 & 53.4873670325986 & 2.51263296740137 \tabularnewline
53 & 52 & 51.9069260100002 & 0.093073989999803 \tabularnewline
54 & 49 & 48.1204556885403 & 0.879544311459653 \tabularnewline
55 & 55 & 57.6245149764068 & -2.62451497640683 \tabularnewline
56 & 56 & 53.6161240989759 & 2.38387590102408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&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]48[/C][C]54.832048240279[/C][C]-6.83204824027897[/C][/ROW]
[ROW][C]2[/C][C]56[/C][C]51.1473074522038[/C][C]4.85269254779624[/C][/ROW]
[ROW][C]3[/C][C]47[/C][C]51.2133544870231[/C][C]-4.21335448702315[/C][/ROW]
[ROW][C]4[/C][C]48[/C][C]51.6518476307946[/C][C]-3.65184763079456[/C][/ROW]
[ROW][C]5[/C][C]45[/C][C]49.5360350608235[/C][C]-4.53603506082346[/C][/ROW]
[ROW][C]6[/C][C]56[/C][C]48.9433727413307[/C][C]7.05662725866934[/C][/ROW]
[ROW][C]7[/C][C]48[/C][C]52.2988637664452[/C][C]-4.2988637664452[/C][/ROW]
[ROW][C]8[/C][C]45[/C][C]54.7890550402771[/C][C]-9.78905504027711[/C][/ROW]
[ROW][C]9[/C][C]52[/C][C]50.5896656774695[/C][C]1.41033432253053[/C][/ROW]
[ROW][C]10[/C][C]47[/C][C]54.4918265566512[/C][C]-7.49182655665118[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]48.0813567415492[/C][C]3.91864325845083[/C][/ROW]
[ROW][C]12[/C][C]60[/C][C]51.140514155732[/C][C]8.85948584426798[/C][/ROW]
[ROW][C]13[/C][C]45[/C][C]50.2515182253075[/C][C]-5.25151822530753[/C][/ROW]
[ROW][C]14[/C][C]48[/C][C]51.2837258849365[/C][C]-3.28372588493649[/C][/ROW]
[ROW][C]15[/C][C]56[/C][C]50.4192947935115[/C][C]5.58070520648846[/C][/ROW]
[ROW][C]16[/C][C]60[/C][C]54.2491467775005[/C][C]5.75085322249946[/C][/ROW]
[ROW][C]17[/C][C]52[/C][C]51.3495777984769[/C][C]0.650422201523139[/C][/ROW]
[ROW][C]18[/C][C]60[/C][C]50.4935078248226[/C][C]9.50649217517743[/C][/ROW]
[ROW][C]19[/C][C]47[/C][C]51.2868726692896[/C][C]-4.28687266928955[/C][/ROW]
[ROW][C]20[/C][C]52[/C][C]55.9179099646506[/C][C]-3.91790996465058[/C][/ROW]
[ROW][C]21[/C][C]47[/C][C]51.0448879721451[/C][C]-4.04488797214511[/C][/ROW]
[ROW][C]22[/C][C]59[/C][C]51.6441643639992[/C][C]7.35583563600082[/C][/ROW]
[ROW][C]23[/C][C]48[/C][C]48.7052028747734[/C][C]-0.705202874773368[/C][/ROW]
[ROW][C]24[/C][C]61[/C][C]52.9375230967218[/C][C]8.06247690327821[/C][/ROW]
[ROW][C]25[/C][C]60[/C][C]56.1464445929829[/C][C]3.85355540701709[/C][/ROW]
[ROW][C]26[/C][C]45[/C][C]50.5769361596117[/C][C]-5.57693615961172[/C][/ROW]
[ROW][C]27[/C][C]63[/C][C]50.644887563511[/C][C]12.355112436489[/C][/ROW]
[ROW][C]28[/C][C]41[/C][C]49.4903795861955[/C][C]-8.49037958619551[/C][/ROW]
[ROW][C]29[/C][C]49[/C][C]51.8427723009851[/C][C]-2.84277230098506[/C][/ROW]
[ROW][C]30[/C][C]63[/C][C]51.2813596341772[/C][C]11.7186403658228[/C][/ROW]
[ROW][C]31[/C][C]54[/C][C]50.4611574756259[/C][C]3.53884252437407[/C][/ROW]
[ROW][C]32[/C][C]55[/C][C]53.0050074836095[/C][C]1.99499251639052[/C][/ROW]
[ROW][C]33[/C][C]70[/C][C]51.3400861628187[/C][C]18.6599138371813[/C][/ROW]
[ROW][C]34[/C][C]43[/C][C]51.589196244862[/C][C]-8.58919624486198[/C][/ROW]
[ROW][C]35[/C][C]58[/C][C]54.7471315293554[/C][C]3.25286847064461[/C][/ROW]
[ROW][C]36[/C][C]56[/C][C]50.5684964873567[/C][C]5.43150351264325[/C][/ROW]
[ROW][C]37[/C][C]50[/C][C]54.9446872699765[/C][C]-4.94468726997652[/C][/ROW]
[ROW][C]38[/C][C]32[/C][C]50.3709407467356[/C][C]-18.3709407467356[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]55.7613745381699[/C][C]3.23862546183012[/C][/ROW]
[ROW][C]40[/C][C]58[/C][C]52.6344657437374[/C][C]5.36553425626265[/C][/ROW]
[ROW][C]41[/C][C]56[/C][C]52.765122276824[/C][C]3.23487772317605[/C][/ROW]
[ROW][C]42[/C][C]50[/C][C]47.3990582031102[/C][C]2.60094179688978[/C][/ROW]
[ROW][C]43[/C][C]32[/C][C]47.7941696843525[/C][C]-15.7941696843525[/C][/ROW]
[ROW][C]44[/C][C]36[/C][C]49.9549008559061[/C][C]-13.9549008559061[/C][/ROW]
[ROW][C]45[/C][C]46[/C][C]50.4496276730623[/C][C]-4.44962767306226[/C][/ROW]
[ROW][C]46[/C][C]47[/C][C]56.5186711868718[/C][C]-9.51867118687178[/C][/ROW]
[ROW][C]47[/C][C]67[/C][C]56.8221252803317[/C][C]10.1778747196683[/C][/ROW]
[ROW][C]48[/C][C]61[/C][C]61.291020744728[/C][C]-0.291020744727972[/C][/ROW]
[ROW][C]49[/C][C]49[/C][C]51.7039608146825[/C][C]-2.70396081468248[/C][/ROW]
[ROW][C]50[/C][C]49[/C][C]50.3923369009421[/C][C]-1.39233690094214[/C][/ROW]
[ROW][C]51[/C][C]56[/C][C]48.4497152562422[/C][C]7.55028474375777[/C][/ROW]
[ROW][C]52[/C][C]56[/C][C]53.4873670325986[/C][C]2.51263296740137[/C][/ROW]
[ROW][C]53[/C][C]52[/C][C]51.9069260100002[/C][C]0.093073989999803[/C][/ROW]
[ROW][C]54[/C][C]49[/C][C]48.1204556885403[/C][C]0.879544311459653[/C][/ROW]
[ROW][C]55[/C][C]55[/C][C]57.6245149764068[/C][C]-2.62451497640683[/C][/ROW]
[ROW][C]56[/C][C]56[/C][C]53.6161240989759[/C][C]2.38387590102408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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	48	54.832048240279	-6.83204824027897
2	56	51.1473074522038	4.85269254779624
3	47	51.2133544870231	-4.21335448702315
4	48	51.6518476307946	-3.65184763079456
5	45	49.5360350608235	-4.53603506082346
6	56	48.9433727413307	7.05662725866934
7	48	52.2988637664452	-4.2988637664452
8	45	54.7890550402771	-9.78905504027711
9	52	50.5896656774695	1.41033432253053
10	47	54.4918265566512	-7.49182655665118
11	52	48.0813567415492	3.91864325845083
12	60	51.140514155732	8.85948584426798
13	45	50.2515182253075	-5.25151822530753
14	48	51.2837258849365	-3.28372588493649
15	56	50.4192947935115	5.58070520648846
16	60	54.2491467775005	5.75085322249946
17	52	51.3495777984769	0.650422201523139
18	60	50.4935078248226	9.50649217517743
19	47	51.2868726692896	-4.28687266928955
20	52	55.9179099646506	-3.91790996465058
21	47	51.0448879721451	-4.04488797214511
22	59	51.6441643639992	7.35583563600082
23	48	48.7052028747734	-0.705202874773368
24	61	52.9375230967218	8.06247690327821
25	60	56.1464445929829	3.85355540701709
26	45	50.5769361596117	-5.57693615961172
27	63	50.644887563511	12.355112436489
28	41	49.4903795861955	-8.49037958619551
29	49	51.8427723009851	-2.84277230098506
30	63	51.2813596341772	11.7186403658228
31	54	50.4611574756259	3.53884252437407
32	55	53.0050074836095	1.99499251639052
33	70	51.3400861628187	18.6599138371813
34	43	51.589196244862	-8.58919624486198
35	58	54.7471315293554	3.25286847064461
36	56	50.5684964873567	5.43150351264325
37	50	54.9446872699765	-4.94468726997652
38	32	50.3709407467356	-18.3709407467356
39	59	55.7613745381699	3.23862546183012
40	58	52.6344657437374	5.36553425626265
41	56	52.765122276824	3.23487772317605
42	50	47.3990582031102	2.60094179688978
43	32	47.7941696843525	-15.7941696843525
44	36	49.9549008559061	-13.9549008559061
45	46	50.4496276730623	-4.44962767306226
46	47	56.5186711868718	-9.51867118687178
47	67	56.8221252803317	10.1778747196683
48	61	61.291020744728	-0.291020744727972
49	49	51.7039608146825	-2.70396081468248
50	49	50.3923369009421	-1.39233690094214
51	56	48.4497152562422	7.55028474375777
52	56	53.4873670325986	2.51263296740137
53	52	51.9069260100002	0.093073989999803
54	49	48.1204556885403	0.879544311459653
55	55	57.6245149764068	-2.62451497640683
56	56	53.6161240989759	2.38387590102408

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.266571474917888	0.533142949835777	0.733428525082112
13	0.399622397801117	0.799244795602234	0.600377602198883
14	0.279145925479964	0.558291850959927	0.720854074520036
15	0.217620809981041	0.435241619962083	0.782379190018959
16	0.183425423625557	0.366850847251114	0.816574576374443
17	0.109965199537896	0.219930399075792	0.890034800462104
18	0.115086914963588	0.230173829927177	0.884913085036412
19	0.111293234498684	0.222586468997368	0.888706765501316
20	0.0819192557674437	0.163838511534887	0.918080744232556
21	0.0670519003542013	0.134103800708403	0.932948099645799
22	0.0458825738949691	0.0917651477899382	0.954117426105031
23	0.0386232919053569	0.0772465838107138	0.961376708094643
24	0.0531950475877376	0.106390095175475	0.946804952412262
25	0.0341406524705728	0.0682813049411455	0.965859347529427
26	0.0460599814478109	0.0921199628956219	0.953940018552189
27	0.0780938031962739	0.156187606392548	0.921906196803726
28	0.118959051108651	0.237918102217302	0.881040948891349
29	0.107175679070781	0.214351358141561	0.892824320929219
30	0.0867454549780464	0.173490909956093	0.913254545021954
31	0.0679795395698259	0.135959079139652	0.932020460430174
32	0.0475460293291161	0.0950920586582322	0.952453970670884
33	0.148803670522008	0.297607341044015	0.851196329477992
34	0.209219471078992	0.418438942157984	0.790780528921008
35	0.149570060916446	0.299140121832893	0.850429939083554
36	0.13660402992852	0.27320805985704	0.86339597007148
37	0.107814043736658	0.215628087473315	0.892185956263342
38	0.686199659202014	0.627600681595971	0.313800340797986
39	0.620194363961597	0.759611272076807	0.379805636038404
40	0.52814744272953	0.94370511454094	0.47185255727047
41	0.403374449184084	0.806748898368168	0.596625550815916
42	0.498620673309765	0.99724134661953	0.501379326690235
43	0.463358176932463	0.926716353864927	0.536641823067537
44	0.53106436326342	0.937871273473161	0.46893563673658

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 & 0.266571474917888 & 0.533142949835777 & 0.733428525082112 \tabularnewline
13 & 0.399622397801117 & 0.799244795602234 & 0.600377602198883 \tabularnewline
14 & 0.279145925479964 & 0.558291850959927 & 0.720854074520036 \tabularnewline
15 & 0.217620809981041 & 0.435241619962083 & 0.782379190018959 \tabularnewline
16 & 0.183425423625557 & 0.366850847251114 & 0.816574576374443 \tabularnewline
17 & 0.109965199537896 & 0.219930399075792 & 0.890034800462104 \tabularnewline
18 & 0.115086914963588 & 0.230173829927177 & 0.884913085036412 \tabularnewline
19 & 0.111293234498684 & 0.222586468997368 & 0.888706765501316 \tabularnewline
20 & 0.0819192557674437 & 0.163838511534887 & 0.918080744232556 \tabularnewline
21 & 0.0670519003542013 & 0.134103800708403 & 0.932948099645799 \tabularnewline
22 & 0.0458825738949691 & 0.0917651477899382 & 0.954117426105031 \tabularnewline
23 & 0.0386232919053569 & 0.0772465838107138 & 0.961376708094643 \tabularnewline
24 & 0.0531950475877376 & 0.106390095175475 & 0.946804952412262 \tabularnewline
25 & 0.0341406524705728 & 0.0682813049411455 & 0.965859347529427 \tabularnewline
26 & 0.0460599814478109 & 0.0921199628956219 & 0.953940018552189 \tabularnewline
27 & 0.0780938031962739 & 0.156187606392548 & 0.921906196803726 \tabularnewline
28 & 0.118959051108651 & 0.237918102217302 & 0.881040948891349 \tabularnewline
29 & 0.107175679070781 & 0.214351358141561 & 0.892824320929219 \tabularnewline
30 & 0.0867454549780464 & 0.173490909956093 & 0.913254545021954 \tabularnewline
31 & 0.0679795395698259 & 0.135959079139652 & 0.932020460430174 \tabularnewline
32 & 0.0475460293291161 & 0.0950920586582322 & 0.952453970670884 \tabularnewline
33 & 0.148803670522008 & 0.297607341044015 & 0.851196329477992 \tabularnewline
34 & 0.209219471078992 & 0.418438942157984 & 0.790780528921008 \tabularnewline
35 & 0.149570060916446 & 0.299140121832893 & 0.850429939083554 \tabularnewline
36 & 0.13660402992852 & 0.27320805985704 & 0.86339597007148 \tabularnewline
37 & 0.107814043736658 & 0.215628087473315 & 0.892185956263342 \tabularnewline
38 & 0.686199659202014 & 0.627600681595971 & 0.313800340797986 \tabularnewline
39 & 0.620194363961597 & 0.759611272076807 & 0.379805636038404 \tabularnewline
40 & 0.52814744272953 & 0.94370511454094 & 0.47185255727047 \tabularnewline
41 & 0.403374449184084 & 0.806748898368168 & 0.596625550815916 \tabularnewline
42 & 0.498620673309765 & 0.99724134661953 & 0.501379326690235 \tabularnewline
43 & 0.463358176932463 & 0.926716353864927 & 0.536641823067537 \tabularnewline
44 & 0.53106436326342 & 0.937871273473161 & 0.46893563673658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&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]12[/C][C]0.266571474917888[/C][C]0.533142949835777[/C][C]0.733428525082112[/C][/ROW]
[ROW][C]13[/C][C]0.399622397801117[/C][C]0.799244795602234[/C][C]0.600377602198883[/C][/ROW]
[ROW][C]14[/C][C]0.279145925479964[/C][C]0.558291850959927[/C][C]0.720854074520036[/C][/ROW]
[ROW][C]15[/C][C]0.217620809981041[/C][C]0.435241619962083[/C][C]0.782379190018959[/C][/ROW]
[ROW][C]16[/C][C]0.183425423625557[/C][C]0.366850847251114[/C][C]0.816574576374443[/C][/ROW]
[ROW][C]17[/C][C]0.109965199537896[/C][C]0.219930399075792[/C][C]0.890034800462104[/C][/ROW]
[ROW][C]18[/C][C]0.115086914963588[/C][C]0.230173829927177[/C][C]0.884913085036412[/C][/ROW]
[ROW][C]19[/C][C]0.111293234498684[/C][C]0.222586468997368[/C][C]0.888706765501316[/C][/ROW]
[ROW][C]20[/C][C]0.0819192557674437[/C][C]0.163838511534887[/C][C]0.918080744232556[/C][/ROW]
[ROW][C]21[/C][C]0.0670519003542013[/C][C]0.134103800708403[/C][C]0.932948099645799[/C][/ROW]
[ROW][C]22[/C][C]0.0458825738949691[/C][C]0.0917651477899382[/C][C]0.954117426105031[/C][/ROW]
[ROW][C]23[/C][C]0.0386232919053569[/C][C]0.0772465838107138[/C][C]0.961376708094643[/C][/ROW]
[ROW][C]24[/C][C]0.0531950475877376[/C][C]0.106390095175475[/C][C]0.946804952412262[/C][/ROW]
[ROW][C]25[/C][C]0.0341406524705728[/C][C]0.0682813049411455[/C][C]0.965859347529427[/C][/ROW]
[ROW][C]26[/C][C]0.0460599814478109[/C][C]0.0921199628956219[/C][C]0.953940018552189[/C][/ROW]
[ROW][C]27[/C][C]0.0780938031962739[/C][C]0.156187606392548[/C][C]0.921906196803726[/C][/ROW]
[ROW][C]28[/C][C]0.118959051108651[/C][C]0.237918102217302[/C][C]0.881040948891349[/C][/ROW]
[ROW][C]29[/C][C]0.107175679070781[/C][C]0.214351358141561[/C][C]0.892824320929219[/C][/ROW]
[ROW][C]30[/C][C]0.0867454549780464[/C][C]0.173490909956093[/C][C]0.913254545021954[/C][/ROW]
[ROW][C]31[/C][C]0.0679795395698259[/C][C]0.135959079139652[/C][C]0.932020460430174[/C][/ROW]
[ROW][C]32[/C][C]0.0475460293291161[/C][C]0.0950920586582322[/C][C]0.952453970670884[/C][/ROW]
[ROW][C]33[/C][C]0.148803670522008[/C][C]0.297607341044015[/C][C]0.851196329477992[/C][/ROW]
[ROW][C]34[/C][C]0.209219471078992[/C][C]0.418438942157984[/C][C]0.790780528921008[/C][/ROW]
[ROW][C]35[/C][C]0.149570060916446[/C][C]0.299140121832893[/C][C]0.850429939083554[/C][/ROW]
[ROW][C]36[/C][C]0.13660402992852[/C][C]0.27320805985704[/C][C]0.86339597007148[/C][/ROW]
[ROW][C]37[/C][C]0.107814043736658[/C][C]0.215628087473315[/C][C]0.892185956263342[/C][/ROW]
[ROW][C]38[/C][C]0.686199659202014[/C][C]0.627600681595971[/C][C]0.313800340797986[/C][/ROW]
[ROW][C]39[/C][C]0.620194363961597[/C][C]0.759611272076807[/C][C]0.379805636038404[/C][/ROW]
[ROW][C]40[/C][C]0.52814744272953[/C][C]0.94370511454094[/C][C]0.47185255727047[/C][/ROW]
[ROW][C]41[/C][C]0.403374449184084[/C][C]0.806748898368168[/C][C]0.596625550815916[/C][/ROW]
[ROW][C]42[/C][C]0.498620673309765[/C][C]0.99724134661953[/C][C]0.501379326690235[/C][/ROW]
[ROW][C]43[/C][C]0.463358176932463[/C][C]0.926716353864927[/C][C]0.536641823067537[/C][/ROW]
[ROW][C]44[/C][C]0.53106436326342[/C][C]0.937871273473161[/C][C]0.46893563673658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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
12	0.266571474917888	0.533142949835777	0.733428525082112
13	0.399622397801117	0.799244795602234	0.600377602198883
14	0.279145925479964	0.558291850959927	0.720854074520036
15	0.217620809981041	0.435241619962083	0.782379190018959
16	0.183425423625557	0.366850847251114	0.816574576374443
17	0.109965199537896	0.219930399075792	0.890034800462104
18	0.115086914963588	0.230173829927177	0.884913085036412
19	0.111293234498684	0.222586468997368	0.888706765501316
20	0.0819192557674437	0.163838511534887	0.918080744232556
21	0.0670519003542013	0.134103800708403	0.932948099645799
22	0.0458825738949691	0.0917651477899382	0.954117426105031
23	0.0386232919053569	0.0772465838107138	0.961376708094643
24	0.0531950475877376	0.106390095175475	0.946804952412262
25	0.0341406524705728	0.0682813049411455	0.965859347529427
26	0.0460599814478109	0.0921199628956219	0.953940018552189
27	0.0780938031962739	0.156187606392548	0.921906196803726
28	0.118959051108651	0.237918102217302	0.881040948891349
29	0.107175679070781	0.214351358141561	0.892824320929219
30	0.0867454549780464	0.173490909956093	0.913254545021954
31	0.0679795395698259	0.135959079139652	0.932020460430174
32	0.0475460293291161	0.0950920586582322	0.952453970670884
33	0.148803670522008	0.297607341044015	0.851196329477992
34	0.209219471078992	0.418438942157984	0.790780528921008
35	0.149570060916446	0.299140121832893	0.850429939083554
36	0.13660402992852	0.27320805985704	0.86339597007148
37	0.107814043736658	0.215628087473315	0.892185956263342
38	0.686199659202014	0.627600681595971	0.313800340797986
39	0.620194363961597	0.759611272076807	0.379805636038404
40	0.52814744272953	0.94370511454094	0.47185255727047
41	0.403374449184084	0.806748898368168	0.596625550815916
42	0.498620673309765	0.99724134661953	0.501379326690235
43	0.463358176932463	0.926716353864927	0.536641823067537
44	0.53106436326342	0.937871273473161	0.46893563673658

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	5	0.151515151515152	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 5 & 0.151515151515152 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169492&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]5[/C][C]0.151515151515152[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169492&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169492&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	5	0.151515151515152	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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$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