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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 20 Dec 2009 04:10:48 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/20/t12613076061whrt61i4saljbh.htm/, Retrieved Sat, 27 Apr 2024 11:14:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69838, Retrieved Sat, 27 Apr 2024 11:14:15 +0000

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Estimated Impact

107

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

-       [Multiple Regression] [Model 4] [2009-12-20 11:10:48] [e458b4e05bf28a297f8af8d9f96e59d6] [Current]

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86,0	88,4	90,7	95,3	100,0	94,7
86,0	86,0	88,4	90,7	95,3	110,6
95,3	86,0	86,0	88,4	90,7	71,3
95,3	95,3	86,0	86,0	88,4	104,1
88,4	95,3	95,3	86,0	86,0	112,3
86,0	88,4	95,3	95,3	86,0	110,2
81,4	86,0	88,4	95,3	95,3	112,9
83,7	81,4	86,0	88,4	95,3	95,1
95,3	83,7	81,4	86,0	88,4	103,1
88,4	95,3	83,7	81,4	86,0	101,9
86,0	88,4	95,3	83,7	81,4	100,4
83,7	86,0	88,4	95,3	83,7	106,9
76,7	83,7	86,0	88,4	95,3	100,7
79,1	76,7	83,7	86,0	88,4	114,3
86,0	79,1	76,7	83,7	86,0	73,3
86,0	86,0	79,1	76,7	83,7	105,9
79,1	86,0	86,0	79,1	76,7	113,9
76,7	79,1	86,0	86,0	79,1	112,1
69,8	76,7	79,1	86,0	86,0	117,5
69,8	69,8	76,7	79,1	86,0	97,5
76,7	69,8	69,8	76,7	79,1	112,3
69,8	76,7	69,8	69,8	76,7	106,9
67,4	69,8	76,7	69,8	69,8	120,9
65,1	67,4	69,8	76,7	69,8	92,7
58,1	65,1	67,4	69,8	76,7	110,9
60,5	58,1	65,1	67,4	69,8	116,5
65,1	60,5	58,1	65,1	67,4	77,1
62,8	65,1	60,5	58,1	65,1	113,1
55,8	62,8	65,1	60,5	58,1	115,9
51,2	55,8	62,8	65,1	60,5	123,5
48,8	51,2	55,8	62,8	65,1	123,6
48,8	48,8	51,2	55,8	62,8	101,5
53,5	48,8	48,8	51,2	55,8	121,0
48,8	53,5	48,8	48,8	51,2	112,2
46,5	48,8	53,5	48,8	48,8	126,0
44,2	46,5	48,8	53,5	48,8	101,8
39,5	44,2	46,5	48,8	53,5	117,9
41,9	39,5	44,2	46,5	48,8	122,2
48,8	41,9	39,5	44,2	46,5	82,7
46,5	48,8	41,9	39,5	44,2	120,5
41,9	46,5	48,8	41,9	39,5	120,3
39,5	41,9	46,5	48,8	41,9	134,2
37,2	39,5	41,9	46,5	48,8	128,2
37,2	37,2	39,5	41,9	46,5	100,5
41,9	37,2	37,2	39,5	41,9	126,0
39,5	41,9	37,2	37,2	39,5	122,9
39,5	39,5	41,9	37,2	37,2	106,1
34,9	39,5	39,5	41,9	37,2	130,4
34,9	34,9	39,5	39,5	41,9	121,3
34,9	34,9	34,9	39,5	39,5	126,1
41,9	34,9	34,9	34,9	39,5	88,7
41,9	41,9	34,9	34,9	34,9	118,7
39,5	41,9	41,9	34,9	34,9	129,3
39,5	39,5	41,9	41,9	34,9	136,2
41,9	39,5	39,5	41,9	41,9	123,0
46,5	41,9	39,5	39,5	41,9	103,5

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' @ 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69838&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Werkloosheid(Y(t))[t] = + 2.85103732321234 + 0.976127794666543`Y(t-1)`[t] + 0.236365899150279`Y(t-2)`[t] + 0.134593358559729`Y(t-3)`[t] -0.341976205796012`Y(t-4)`[t] -0.0864265177172897Productie[t] + 2.5704281506859M1[t] + 8.0452757771165M2[t] + 10.6852562679373M3[t] + 5.13454323216124M4[t] -2.36138688814796M5[t] + 0.840375791480767M6[t] + 3.94041195459863M7[t] + 7.0899908939364M8[t] + 13.9240510104693M9[t] + 0.826377650593013M10[t] + 1.18103914539342M11[t] + 0.0648222506919648t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkloosheid(Y(t))[t] =  +  2.85103732321234 +  0.976127794666543`Y(t-1)`[t] +  0.236365899150279`Y(t-2)`[t] +  0.134593358559729`Y(t-3)`[t] -0.341976205796012`Y(t-4)`[t] -0.0864265177172897Productie[t] +  2.5704281506859M1[t] +  8.0452757771165M2[t] +  10.6852562679373M3[t] +  5.13454323216124M4[t] -2.36138688814796M5[t] +  0.840375791480767M6[t] +  3.94041195459863M7[t] +  7.0899908939364M8[t] +  13.9240510104693M9[t] +  0.826377650593013M10[t] +  1.18103914539342M11[t] +  0.0648222506919648t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69838&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkloosheid(Y(t))[t] =  +  2.85103732321234 +  0.976127794666543`Y(t-1)`[t] +  0.236365899150279`Y(t-2)`[t] +  0.134593358559729`Y(t-3)`[t] -0.341976205796012`Y(t-4)`[t] -0.0864265177172897Productie[t] +  2.5704281506859M1[t] +  8.0452757771165M2[t] +  10.6852562679373M3[t] +  5.13454323216124M4[t] -2.36138688814796M5[t] +  0.840375791480767M6[t] +  3.94041195459863M7[t] +  7.0899908939364M8[t] +  13.9240510104693M9[t] +  0.826377650593013M10[t] +  1.18103914539342M11[t] +  0.0648222506919648t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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
Werkloosheid(Y(t))[t] = + 2.85103732321234 + 0.976127794666543`Y(t-1)`[t] + 0.236365899150279`Y(t-2)`[t] + 0.134593358559729`Y(t-3)`[t] -0.341976205796012`Y(t-4)`[t] -0.0864265177172897Productie[t] + 2.5704281506859M1[t] + 8.0452757771165M2[t] + 10.6852562679373M3[t] + 5.13454323216124M4[t] -2.36138688814796M5[t] + 0.840375791480767M6[t] + 3.94041195459863M7[t] + 7.0899908939364M8[t] + 13.9240510104693M9[t] + 0.826377650593013M10[t] + 1.18103914539342M11[t] + 0.0648222506919648t + 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)	2.85103732321234	10.306593	0.2766	0.783569	0.391784
`Y(t-1)`	0.976127794666543	0.151884	6.4268	0	0
`Y(t-2)`	0.236365899150279	0.217164	1.0884	0.283264	0.141632
`Y(t-3)`	0.134593358559729	0.216229	0.6225	0.537359	0.268679
`Y(t-4)`	-0.341976205796012	0.173163	-1.9749	0.05558	0.02779
Productie	-0.0864265177172897	0.055892	-1.5463	0.130315	0.065158
M1	2.5704281506859	2.406703	1.068	0.292246	0.146123
M2	8.0452757771165	2.084308	3.8599	0.000427	0.000213
M3	10.6852562679373	2.782161	3.8406	0.000452	0.000226
M4	5.13454323216124	2.873556	1.7868	0.081945	0.040973
M5	-2.36138688814796	2.513384	-0.9395	0.353395	0.176698
M6	0.840375791480767	1.792159	0.4689	0.641807	0.320904
M7	3.94041195459863	2.04567	1.9262	0.061582	0.030791
M8	7.0899908939364	2.597087	2.73	0.009546	0.004773
M9	13.9240510104693	2.239463	6.2176	0	0
M10	0.826377650593013	2.851568	0.2898	0.773547	0.386773
M11	1.18103914539342	2.563276	0.4608	0.647601	0.323801
t	0.0648222506919648	0.095957	0.6755	0.503428	0.251714

\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) & 2.85103732321234 & 10.306593 & 0.2766 & 0.783569 & 0.391784 \tabularnewline
`Y(t-1)` & 0.976127794666543 & 0.151884 & 6.4268 & 0 & 0 \tabularnewline
`Y(t-2)` & 0.236365899150279 & 0.217164 & 1.0884 & 0.283264 & 0.141632 \tabularnewline
`Y(t-3)` & 0.134593358559729 & 0.216229 & 0.6225 & 0.537359 & 0.268679 \tabularnewline
`Y(t-4)` & -0.341976205796012 & 0.173163 & -1.9749 & 0.05558 & 0.02779 \tabularnewline
Productie & -0.0864265177172897 & 0.055892 & -1.5463 & 0.130315 & 0.065158 \tabularnewline
M1 & 2.5704281506859 & 2.406703 & 1.068 & 0.292246 & 0.146123 \tabularnewline
M2 & 8.0452757771165 & 2.084308 & 3.8599 & 0.000427 & 0.000213 \tabularnewline
M3 & 10.6852562679373 & 2.782161 & 3.8406 & 0.000452 & 0.000226 \tabularnewline
M4 & 5.13454323216124 & 2.873556 & 1.7868 & 0.081945 & 0.040973 \tabularnewline
M5 & -2.36138688814796 & 2.513384 & -0.9395 & 0.353395 & 0.176698 \tabularnewline
M6 & 0.840375791480767 & 1.792159 & 0.4689 & 0.641807 & 0.320904 \tabularnewline
M7 & 3.94041195459863 & 2.04567 & 1.9262 & 0.061582 & 0.030791 \tabularnewline
M8 & 7.0899908939364 & 2.597087 & 2.73 & 0.009546 & 0.004773 \tabularnewline
M9 & 13.9240510104693 & 2.239463 & 6.2176 & 0 & 0 \tabularnewline
M10 & 0.826377650593013 & 2.851568 & 0.2898 & 0.773547 & 0.386773 \tabularnewline
M11 & 1.18103914539342 & 2.563276 & 0.4608 & 0.647601 & 0.323801 \tabularnewline
t & 0.0648222506919648 & 0.095957 & 0.6755 & 0.503428 & 0.251714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69838&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]2.85103732321234[/C][C]10.306593[/C][C]0.2766[/C][C]0.783569[/C][C]0.391784[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.976127794666543[/C][C]0.151884[/C][C]6.4268[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.236365899150279[/C][C]0.217164[/C][C]1.0884[/C][C]0.283264[/C][C]0.141632[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]0.134593358559729[/C][C]0.216229[/C][C]0.6225[/C][C]0.537359[/C][C]0.268679[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.341976205796012[/C][C]0.173163[/C][C]-1.9749[/C][C]0.05558[/C][C]0.02779[/C][/ROW]
[ROW][C]Productie[/C][C]-0.0864265177172897[/C][C]0.055892[/C][C]-1.5463[/C][C]0.130315[/C][C]0.065158[/C][/ROW]
[ROW][C]M1[/C][C]2.5704281506859[/C][C]2.406703[/C][C]1.068[/C][C]0.292246[/C][C]0.146123[/C][/ROW]
[ROW][C]M2[/C][C]8.0452757771165[/C][C]2.084308[/C][C]3.8599[/C][C]0.000427[/C][C]0.000213[/C][/ROW]
[ROW][C]M3[/C][C]10.6852562679373[/C][C]2.782161[/C][C]3.8406[/C][C]0.000452[/C][C]0.000226[/C][/ROW]
[ROW][C]M4[/C][C]5.13454323216124[/C][C]2.873556[/C][C]1.7868[/C][C]0.081945[/C][C]0.040973[/C][/ROW]
[ROW][C]M5[/C][C]-2.36138688814796[/C][C]2.513384[/C][C]-0.9395[/C][C]0.353395[/C][C]0.176698[/C][/ROW]
[ROW][C]M6[/C][C]0.840375791480767[/C][C]1.792159[/C][C]0.4689[/C][C]0.641807[/C][C]0.320904[/C][/ROW]
[ROW][C]M7[/C][C]3.94041195459863[/C][C]2.04567[/C][C]1.9262[/C][C]0.061582[/C][C]0.030791[/C][/ROW]
[ROW][C]M8[/C][C]7.0899908939364[/C][C]2.597087[/C][C]2.73[/C][C]0.009546[/C][C]0.004773[/C][/ROW]
[ROW][C]M9[/C][C]13.9240510104693[/C][C]2.239463[/C][C]6.2176[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]0.826377650593013[/C][C]2.851568[/C][C]0.2898[/C][C]0.773547[/C][C]0.386773[/C][/ROW]
[ROW][C]M11[/C][C]1.18103914539342[/C][C]2.563276[/C][C]0.4608[/C][C]0.647601[/C][C]0.323801[/C][/ROW]
[ROW][C]t[/C][C]0.0648222506919648[/C][C]0.095957[/C][C]0.6755[/C][C]0.503428[/C][C]0.251714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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)	2.85103732321234	10.306593	0.2766	0.783569	0.391784
`Y(t-1)`	0.976127794666543	0.151884	6.4268	0	0
`Y(t-2)`	0.236365899150279	0.217164	1.0884	0.283264	0.141632
`Y(t-3)`	0.134593358559729	0.216229	0.6225	0.537359	0.268679
`Y(t-4)`	-0.341976205796012	0.173163	-1.9749	0.05558	0.02779
Productie	-0.0864265177172897	0.055892	-1.5463	0.130315	0.065158
M1	2.5704281506859	2.406703	1.068	0.292246	0.146123
M2	8.0452757771165	2.084308	3.8599	0.000427	0.000213
M3	10.6852562679373	2.782161	3.8406	0.000452	0.000226
M4	5.13454323216124	2.873556	1.7868	0.081945	0.040973
M5	-2.36138688814796	2.513384	-0.9395	0.353395	0.176698
M6	0.840375791480767	1.792159	0.4689	0.641807	0.320904
M7	3.94041195459863	2.04567	1.9262	0.061582	0.030791
M8	7.0899908939364	2.597087	2.73	0.009546	0.004773
M9	13.9240510104693	2.239463	6.2176	0	0
M10	0.826377650593013	2.851568	0.2898	0.773547	0.386773
M11	1.18103914539342	2.563276	0.4608	0.647601	0.323801
t	0.0648222506919648	0.095957	0.6755	0.503428	0.251714

Multiple Linear Regression - Regression Statistics
Multiple R	0.99638054568302
R-squared	0.992774191815591
Adjusted R-squared	0.989541593417303
F-TEST (value)	307.113371194316
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.03448320450095
Sum Squared Residuals	157.286632557065

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99638054568302 \tabularnewline
R-squared & 0.992774191815591 \tabularnewline
Adjusted R-squared & 0.989541593417303 \tabularnewline
F-TEST (value) & 307.113371194316 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.03448320450095 \tabularnewline
Sum Squared Residuals & 157.286632557065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69838&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99638054568302[/C][/ROW]
[ROW][C]R-squared[/C][C]0.992774191815591[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.989541593417303[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]307.113371194316[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.03448320450095[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]157.286632557065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69838&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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	0.99638054568302
R-squared	0.992774191815591
Adjusted R-squared	0.989541593417303
F-TEST (value)	307.113371194316
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.03448320450095
Sum Squared Residuals	157.286632557065

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	86	83.6589070893564	2.34109291064364
2	86	85.9262057773954	0.0737942226046428
3	95.3	92.7238183292111	2.57618167078890
4	95.3	93.9446474661863	1.35535253381374
5	88.4	88.8237879072953	-0.423787907295282
6	86	86.7883049762286	-0.788304976228623
7	81.4	82.5658016669622	-1.16580166696223
8	83.7	81.3324346848708	2.36756531512918
9	95.3	90.7343274614483	4.56567253855169
10	88.4	89.8735256042379	-1.47352560423791
11	86	88.3118670445993	-2.31186704459934
12	83.7	83.4349840593609	0.265015940639098
13	76.7	78.8980886235964	-2.19808862359638
14	79.1	77.9224334885015	1.17756651149850
15	86	85.3700470387939	0.629952961206113
16	86	84.2136034806987	1.78639651930127
17	79.1	80.4388656745955	-1.33886567459555
18	76.7	77.2336878337599	-0.533687833759903
19	69.8	73.5985758205673	-3.79857582056726
20	69.8	70.3102532497208	-0.510253249720842
21	76.7	76.3357102100421	0.364289789957942
22	69.8	70.3968927995785	-0.596892799578531
23	67.4	66.8616840379591	0.538315962040915
24	65.1	65.1377577056107	-0.0377577056107264
25	58.1	60.0993434047856	-1.99934340478557
26	60.5	59.815100411429	0.684899588570984
27	65.1	67.1244315333738	-2.02443153337376
28	62.8	63.4290438873068	-0.629043887306756
29	55.8	57.3149884775548	-1.51498847755478
30	51.2	52.346582297977	-1.14658229797695
31	48.8	47.475393639148	1.32460636085203
32	48.8	49.0142227908515	-0.214222790851544
33	53.5	55.435213895826	-1.93521389582595
34	48.8	49.0007832636048	-0.200783263604812
35	46.5	45.5714430495826	0.928556950417436
36	44.2	43.8233230151309	0.376676984869109
37	39.5	40.0384940330097	-0.538494033009721
38	41.9	41.3728111235234	0.52718887647657
39	48.8	49.2002288447059	-0.400228844705945
40	46.5	47.9039321191682	-1.40393211916824
41	41.9	41.8062525572829	0.0937474427170518
42	39.5	38.9456307479733	0.554369252026719
43	37.2	36.529857880116	0.670142119884006
44	37.2	39.493317349177	-2.29331734917701
45	41.9	44.8947484326837	-2.99474843268369
46	39.5	37.2287983325787	2.27120166742125
47	39.5	38.655005867859	0.844994132140992
48	34.9	35.5039352198975	-0.603935219897477
49	34.9	32.5051668492520	2.39483315074803
50	34.9	37.3634491991507	-2.46344919915070
51	41.9	42.6814742539153	-0.781474253915302
52	41.9	43.00877304664	-1.10877304664000
53	39.5	36.3161053832714	3.18389461672855
54	39.5	37.5857941440612	1.91420585593875
55	41.9	38.9303709932065	2.96962900679346
56	46.5	45.8497719253798	0.650228074620219

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 86 & 83.6589070893564 & 2.34109291064364 \tabularnewline
2 & 86 & 85.9262057773954 & 0.0737942226046428 \tabularnewline
3 & 95.3 & 92.7238183292111 & 2.57618167078890 \tabularnewline
4 & 95.3 & 93.9446474661863 & 1.35535253381374 \tabularnewline
5 & 88.4 & 88.8237879072953 & -0.423787907295282 \tabularnewline
6 & 86 & 86.7883049762286 & -0.788304976228623 \tabularnewline
7 & 81.4 & 82.5658016669622 & -1.16580166696223 \tabularnewline
8 & 83.7 & 81.3324346848708 & 2.36756531512918 \tabularnewline
9 & 95.3 & 90.7343274614483 & 4.56567253855169 \tabularnewline
10 & 88.4 & 89.8735256042379 & -1.47352560423791 \tabularnewline
11 & 86 & 88.3118670445993 & -2.31186704459934 \tabularnewline
12 & 83.7 & 83.4349840593609 & 0.265015940639098 \tabularnewline
13 & 76.7 & 78.8980886235964 & -2.19808862359638 \tabularnewline
14 & 79.1 & 77.9224334885015 & 1.17756651149850 \tabularnewline
15 & 86 & 85.3700470387939 & 0.629952961206113 \tabularnewline
16 & 86 & 84.2136034806987 & 1.78639651930127 \tabularnewline
17 & 79.1 & 80.4388656745955 & -1.33886567459555 \tabularnewline
18 & 76.7 & 77.2336878337599 & -0.533687833759903 \tabularnewline
19 & 69.8 & 73.5985758205673 & -3.79857582056726 \tabularnewline
20 & 69.8 & 70.3102532497208 & -0.510253249720842 \tabularnewline
21 & 76.7 & 76.3357102100421 & 0.364289789957942 \tabularnewline
22 & 69.8 & 70.3968927995785 & -0.596892799578531 \tabularnewline
23 & 67.4 & 66.8616840379591 & 0.538315962040915 \tabularnewline
24 & 65.1 & 65.1377577056107 & -0.0377577056107264 \tabularnewline
25 & 58.1 & 60.0993434047856 & -1.99934340478557 \tabularnewline
26 & 60.5 & 59.815100411429 & 0.684899588570984 \tabularnewline
27 & 65.1 & 67.1244315333738 & -2.02443153337376 \tabularnewline
28 & 62.8 & 63.4290438873068 & -0.629043887306756 \tabularnewline
29 & 55.8 & 57.3149884775548 & -1.51498847755478 \tabularnewline
30 & 51.2 & 52.346582297977 & -1.14658229797695 \tabularnewline
31 & 48.8 & 47.475393639148 & 1.32460636085203 \tabularnewline
32 & 48.8 & 49.0142227908515 & -0.214222790851544 \tabularnewline
33 & 53.5 & 55.435213895826 & -1.93521389582595 \tabularnewline
34 & 48.8 & 49.0007832636048 & -0.200783263604812 \tabularnewline
35 & 46.5 & 45.5714430495826 & 0.928556950417436 \tabularnewline
36 & 44.2 & 43.8233230151309 & 0.376676984869109 \tabularnewline
37 & 39.5 & 40.0384940330097 & -0.538494033009721 \tabularnewline
38 & 41.9 & 41.3728111235234 & 0.52718887647657 \tabularnewline
39 & 48.8 & 49.2002288447059 & -0.400228844705945 \tabularnewline
40 & 46.5 & 47.9039321191682 & -1.40393211916824 \tabularnewline
41 & 41.9 & 41.8062525572829 & 0.0937474427170518 \tabularnewline
42 & 39.5 & 38.9456307479733 & 0.554369252026719 \tabularnewline
43 & 37.2 & 36.529857880116 & 0.670142119884006 \tabularnewline
44 & 37.2 & 39.493317349177 & -2.29331734917701 \tabularnewline
45 & 41.9 & 44.8947484326837 & -2.99474843268369 \tabularnewline
46 & 39.5 & 37.2287983325787 & 2.27120166742125 \tabularnewline
47 & 39.5 & 38.655005867859 & 0.844994132140992 \tabularnewline
48 & 34.9 & 35.5039352198975 & -0.603935219897477 \tabularnewline
49 & 34.9 & 32.5051668492520 & 2.39483315074803 \tabularnewline
50 & 34.9 & 37.3634491991507 & -2.46344919915070 \tabularnewline
51 & 41.9 & 42.6814742539153 & -0.781474253915302 \tabularnewline
52 & 41.9 & 43.00877304664 & -1.10877304664000 \tabularnewline
53 & 39.5 & 36.3161053832714 & 3.18389461672855 \tabularnewline
54 & 39.5 & 37.5857941440612 & 1.91420585593875 \tabularnewline
55 & 41.9 & 38.9303709932065 & 2.96962900679346 \tabularnewline
56 & 46.5 & 45.8497719253798 & 0.650228074620219 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69838&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]86[/C][C]83.6589070893564[/C][C]2.34109291064364[/C][/ROW]
[ROW][C]2[/C][C]86[/C][C]85.9262057773954[/C][C]0.0737942226046428[/C][/ROW]
[ROW][C]3[/C][C]95.3[/C][C]92.7238183292111[/C][C]2.57618167078890[/C][/ROW]
[ROW][C]4[/C][C]95.3[/C][C]93.9446474661863[/C][C]1.35535253381374[/C][/ROW]
[ROW][C]5[/C][C]88.4[/C][C]88.8237879072953[/C][C]-0.423787907295282[/C][/ROW]
[ROW][C]6[/C][C]86[/C][C]86.7883049762286[/C][C]-0.788304976228623[/C][/ROW]
[ROW][C]7[/C][C]81.4[/C][C]82.5658016669622[/C][C]-1.16580166696223[/C][/ROW]
[ROW][C]8[/C][C]83.7[/C][C]81.3324346848708[/C][C]2.36756531512918[/C][/ROW]
[ROW][C]9[/C][C]95.3[/C][C]90.7343274614483[/C][C]4.56567253855169[/C][/ROW]
[ROW][C]10[/C][C]88.4[/C][C]89.8735256042379[/C][C]-1.47352560423791[/C][/ROW]
[ROW][C]11[/C][C]86[/C][C]88.3118670445993[/C][C]-2.31186704459934[/C][/ROW]
[ROW][C]12[/C][C]83.7[/C][C]83.4349840593609[/C][C]0.265015940639098[/C][/ROW]
[ROW][C]13[/C][C]76.7[/C][C]78.8980886235964[/C][C]-2.19808862359638[/C][/ROW]
[ROW][C]14[/C][C]79.1[/C][C]77.9224334885015[/C][C]1.17756651149850[/C][/ROW]
[ROW][C]15[/C][C]86[/C][C]85.3700470387939[/C][C]0.629952961206113[/C][/ROW]
[ROW][C]16[/C][C]86[/C][C]84.2136034806987[/C][C]1.78639651930127[/C][/ROW]
[ROW][C]17[/C][C]79.1[/C][C]80.4388656745955[/C][C]-1.33886567459555[/C][/ROW]
[ROW][C]18[/C][C]76.7[/C][C]77.2336878337599[/C][C]-0.533687833759903[/C][/ROW]
[ROW][C]19[/C][C]69.8[/C][C]73.5985758205673[/C][C]-3.79857582056726[/C][/ROW]
[ROW][C]20[/C][C]69.8[/C][C]70.3102532497208[/C][C]-0.510253249720842[/C][/ROW]
[ROW][C]21[/C][C]76.7[/C][C]76.3357102100421[/C][C]0.364289789957942[/C][/ROW]
[ROW][C]22[/C][C]69.8[/C][C]70.3968927995785[/C][C]-0.596892799578531[/C][/ROW]
[ROW][C]23[/C][C]67.4[/C][C]66.8616840379591[/C][C]0.538315962040915[/C][/ROW]
[ROW][C]24[/C][C]65.1[/C][C]65.1377577056107[/C][C]-0.0377577056107264[/C][/ROW]
[ROW][C]25[/C][C]58.1[/C][C]60.0993434047856[/C][C]-1.99934340478557[/C][/ROW]
[ROW][C]26[/C][C]60.5[/C][C]59.815100411429[/C][C]0.684899588570984[/C][/ROW]
[ROW][C]27[/C][C]65.1[/C][C]67.1244315333738[/C][C]-2.02443153337376[/C][/ROW]
[ROW][C]28[/C][C]62.8[/C][C]63.4290438873068[/C][C]-0.629043887306756[/C][/ROW]
[ROW][C]29[/C][C]55.8[/C][C]57.3149884775548[/C][C]-1.51498847755478[/C][/ROW]
[ROW][C]30[/C][C]51.2[/C][C]52.346582297977[/C][C]-1.14658229797695[/C][/ROW]
[ROW][C]31[/C][C]48.8[/C][C]47.475393639148[/C][C]1.32460636085203[/C][/ROW]
[ROW][C]32[/C][C]48.8[/C][C]49.0142227908515[/C][C]-0.214222790851544[/C][/ROW]
[ROW][C]33[/C][C]53.5[/C][C]55.435213895826[/C][C]-1.93521389582595[/C][/ROW]
[ROW][C]34[/C][C]48.8[/C][C]49.0007832636048[/C][C]-0.200783263604812[/C][/ROW]
[ROW][C]35[/C][C]46.5[/C][C]45.5714430495826[/C][C]0.928556950417436[/C][/ROW]
[ROW][C]36[/C][C]44.2[/C][C]43.8233230151309[/C][C]0.376676984869109[/C][/ROW]
[ROW][C]37[/C][C]39.5[/C][C]40.0384940330097[/C][C]-0.538494033009721[/C][/ROW]
[ROW][C]38[/C][C]41.9[/C][C]41.3728111235234[/C][C]0.52718887647657[/C][/ROW]
[ROW][C]39[/C][C]48.8[/C][C]49.2002288447059[/C][C]-0.400228844705945[/C][/ROW]
[ROW][C]40[/C][C]46.5[/C][C]47.9039321191682[/C][C]-1.40393211916824[/C][/ROW]
[ROW][C]41[/C][C]41.9[/C][C]41.8062525572829[/C][C]0.0937474427170518[/C][/ROW]
[ROW][C]42[/C][C]39.5[/C][C]38.9456307479733[/C][C]0.554369252026719[/C][/ROW]
[ROW][C]43[/C][C]37.2[/C][C]36.529857880116[/C][C]0.670142119884006[/C][/ROW]
[ROW][C]44[/C][C]37.2[/C][C]39.493317349177[/C][C]-2.29331734917701[/C][/ROW]
[ROW][C]45[/C][C]41.9[/C][C]44.8947484326837[/C][C]-2.99474843268369[/C][/ROW]
[ROW][C]46[/C][C]39.5[/C][C]37.2287983325787[/C][C]2.27120166742125[/C][/ROW]
[ROW][C]47[/C][C]39.5[/C][C]38.655005867859[/C][C]0.844994132140992[/C][/ROW]
[ROW][C]48[/C][C]34.9[/C][C]35.5039352198975[/C][C]-0.603935219897477[/C][/ROW]
[ROW][C]49[/C][C]34.9[/C][C]32.5051668492520[/C][C]2.39483315074803[/C][/ROW]
[ROW][C]50[/C][C]34.9[/C][C]37.3634491991507[/C][C]-2.46344919915070[/C][/ROW]
[ROW][C]51[/C][C]41.9[/C][C]42.6814742539153[/C][C]-0.781474253915302[/C][/ROW]
[ROW][C]52[/C][C]41.9[/C][C]43.00877304664[/C][C]-1.10877304664000[/C][/ROW]
[ROW][C]53[/C][C]39.5[/C][C]36.3161053832714[/C][C]3.18389461672855[/C][/ROW]
[ROW][C]54[/C][C]39.5[/C][C]37.5857941440612[/C][C]1.91420585593875[/C][/ROW]
[ROW][C]55[/C][C]41.9[/C][C]38.9303709932065[/C][C]2.96962900679346[/C][/ROW]
[ROW][C]56[/C][C]46.5[/C][C]45.8497719253798[/C][C]0.650228074620219[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69838&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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	86	83.6589070893564	2.34109291064364
2	86	85.9262057773954	0.0737942226046428
3	95.3	92.7238183292111	2.57618167078890
4	95.3	93.9446474661863	1.35535253381374
5	88.4	88.8237879072953	-0.423787907295282
6	86	86.7883049762286	-0.788304976228623
7	81.4	82.5658016669622	-1.16580166696223
8	83.7	81.3324346848708	2.36756531512918
9	95.3	90.7343274614483	4.56567253855169
10	88.4	89.8735256042379	-1.47352560423791
11	86	88.3118670445993	-2.31186704459934
12	83.7	83.4349840593609	0.265015940639098
13	76.7	78.8980886235964	-2.19808862359638
14	79.1	77.9224334885015	1.17756651149850
15	86	85.3700470387939	0.629952961206113
16	86	84.2136034806987	1.78639651930127
17	79.1	80.4388656745955	-1.33886567459555
18	76.7	77.2336878337599	-0.533687833759903
19	69.8	73.5985758205673	-3.79857582056726
20	69.8	70.3102532497208	-0.510253249720842
21	76.7	76.3357102100421	0.364289789957942
22	69.8	70.3968927995785	-0.596892799578531
23	67.4	66.8616840379591	0.538315962040915
24	65.1	65.1377577056107	-0.0377577056107264
25	58.1	60.0993434047856	-1.99934340478557
26	60.5	59.815100411429	0.684899588570984
27	65.1	67.1244315333738	-2.02443153337376
28	62.8	63.4290438873068	-0.629043887306756
29	55.8	57.3149884775548	-1.51498847755478
30	51.2	52.346582297977	-1.14658229797695
31	48.8	47.475393639148	1.32460636085203
32	48.8	49.0142227908515	-0.214222790851544
33	53.5	55.435213895826	-1.93521389582595
34	48.8	49.0007832636048	-0.200783263604812
35	46.5	45.5714430495826	0.928556950417436
36	44.2	43.8233230151309	0.376676984869109
37	39.5	40.0384940330097	-0.538494033009721
38	41.9	41.3728111235234	0.52718887647657
39	48.8	49.2002288447059	-0.400228844705945
40	46.5	47.9039321191682	-1.40393211916824
41	41.9	41.8062525572829	0.0937474427170518
42	39.5	38.9456307479733	0.554369252026719
43	37.2	36.529857880116	0.670142119884006
44	37.2	39.493317349177	-2.29331734917701
45	41.9	44.8947484326837	-2.99474843268369
46	39.5	37.2287983325787	2.27120166742125
47	39.5	38.655005867859	0.844994132140992
48	34.9	35.5039352198975	-0.603935219897477
49	34.9	32.5051668492520	2.39483315074803
50	34.9	37.3634491991507	-2.46344919915070
51	41.9	42.6814742539153	-0.781474253915302
52	41.9	43.00877304664	-1.10877304664000
53	39.5	36.3161053832714	3.18389461672855
54	39.5	37.5857941440612	1.91420585593875
55	41.9	38.9303709932065	2.96962900679346
56	46.5	45.8497719253798	0.650228074620219

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.511403350885411	0.977193298229179	0.488596649114589
22	0.344657621482333	0.689315242964666	0.655342378517667
23	0.841910465743089	0.316179068513823	0.158089534256911
24	0.749249662393189	0.501500675213622	0.250750337606811
25	0.707882230510599	0.584235538978803	0.292117769489401
26	0.645280988208059	0.709438023583883	0.354719011791941
27	0.579009633017837	0.841980733964325	0.420990366982163
28	0.495760638547543	0.991521277095086	0.504239361452457
29	0.432083966257842	0.864167932515684	0.567916033742158
30	0.492270091696039	0.984540183392078	0.507729908303961
31	0.582569273483456	0.834861453033089	0.417430726516544
32	0.447762107908364	0.895524215816728	0.552237892091636
33	0.401742253161213	0.803484506322425	0.598257746838787
34	0.410191879457695	0.82038375891539	0.589808120542305
35	0.303597315841075	0.60719463168215	0.696402684158925

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.511403350885411 & 0.977193298229179 & 0.488596649114589 \tabularnewline
22 & 0.344657621482333 & 0.689315242964666 & 0.655342378517667 \tabularnewline
23 & 0.841910465743089 & 0.316179068513823 & 0.158089534256911 \tabularnewline
24 & 0.749249662393189 & 0.501500675213622 & 0.250750337606811 \tabularnewline
25 & 0.707882230510599 & 0.584235538978803 & 0.292117769489401 \tabularnewline
26 & 0.645280988208059 & 0.709438023583883 & 0.354719011791941 \tabularnewline
27 & 0.579009633017837 & 0.841980733964325 & 0.420990366982163 \tabularnewline
28 & 0.495760638547543 & 0.991521277095086 & 0.504239361452457 \tabularnewline
29 & 0.432083966257842 & 0.864167932515684 & 0.567916033742158 \tabularnewline
30 & 0.492270091696039 & 0.984540183392078 & 0.507729908303961 \tabularnewline
31 & 0.582569273483456 & 0.834861453033089 & 0.417430726516544 \tabularnewline
32 & 0.447762107908364 & 0.895524215816728 & 0.552237892091636 \tabularnewline
33 & 0.401742253161213 & 0.803484506322425 & 0.598257746838787 \tabularnewline
34 & 0.410191879457695 & 0.82038375891539 & 0.589808120542305 \tabularnewline
35 & 0.303597315841075 & 0.60719463168215 & 0.696402684158925 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69838&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]21[/C][C]0.511403350885411[/C][C]0.977193298229179[/C][C]0.488596649114589[/C][/ROW]
[ROW][C]22[/C][C]0.344657621482333[/C][C]0.689315242964666[/C][C]0.655342378517667[/C][/ROW]
[ROW][C]23[/C][C]0.841910465743089[/C][C]0.316179068513823[/C][C]0.158089534256911[/C][/ROW]
[ROW][C]24[/C][C]0.749249662393189[/C][C]0.501500675213622[/C][C]0.250750337606811[/C][/ROW]
[ROW][C]25[/C][C]0.707882230510599[/C][C]0.584235538978803[/C][C]0.292117769489401[/C][/ROW]
[ROW][C]26[/C][C]0.645280988208059[/C][C]0.709438023583883[/C][C]0.354719011791941[/C][/ROW]
[ROW][C]27[/C][C]0.579009633017837[/C][C]0.841980733964325[/C][C]0.420990366982163[/C][/ROW]
[ROW][C]28[/C][C]0.495760638547543[/C][C]0.991521277095086[/C][C]0.504239361452457[/C][/ROW]
[ROW][C]29[/C][C]0.432083966257842[/C][C]0.864167932515684[/C][C]0.567916033742158[/C][/ROW]
[ROW][C]30[/C][C]0.492270091696039[/C][C]0.984540183392078[/C][C]0.507729908303961[/C][/ROW]
[ROW][C]31[/C][C]0.582569273483456[/C][C]0.834861453033089[/C][C]0.417430726516544[/C][/ROW]
[ROW][C]32[/C][C]0.447762107908364[/C][C]0.895524215816728[/C][C]0.552237892091636[/C][/ROW]
[ROW][C]33[/C][C]0.401742253161213[/C][C]0.803484506322425[/C][C]0.598257746838787[/C][/ROW]
[ROW][C]34[/C][C]0.410191879457695[/C][C]0.82038375891539[/C][C]0.589808120542305[/C][/ROW]
[ROW][C]35[/C][C]0.303597315841075[/C][C]0.60719463168215[/C][C]0.696402684158925[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69838&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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
21	0.511403350885411	0.977193298229179	0.488596649114589
22	0.344657621482333	0.689315242964666	0.655342378517667
23	0.841910465743089	0.316179068513823	0.158089534256911
24	0.749249662393189	0.501500675213622	0.250750337606811
25	0.707882230510599	0.584235538978803	0.292117769489401
26	0.645280988208059	0.709438023583883	0.354719011791941
27	0.579009633017837	0.841980733964325	0.420990366982163
28	0.495760638547543	0.991521277095086	0.504239361452457
29	0.432083966257842	0.864167932515684	0.567916033742158
30	0.492270091696039	0.984540183392078	0.507729908303961
31	0.582569273483456	0.834861453033089	0.417430726516544
32	0.447762107908364	0.895524215816728	0.552237892091636
33	0.401742253161213	0.803484506322425	0.598257746838787
34	0.410191879457695	0.82038375891539	0.589808120542305
35	0.303597315841075	0.60719463168215	0.696402684158925

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=69838&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=69838&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69838&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