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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 03:02:58 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258711425ikxagdwhyzmz9zy.htm/, Retrieved Sat, 20 Apr 2024 12:41:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58003, Retrieved Sat, 20 Apr 2024 12:41:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

154

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [SHWWS7model4] [2009-11-20 10:02:58] [db49399df1e4a3dbe31268849cebfd7f] [Current]

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Dataseries X:

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Histogram

Boxplots

130	0	135	139	149	161
127	0	130	135	139	149
122	0	127	130	135	139
117	0	122	127	130	135
112	0	117	122	127	130
113	0	112	117	122	127
149	0	113	112	117	122
157	0	149	113	112	117
157	0	157	149	113	112
147	0	157	157	149	113
137	0	147	157	157	149
132	0	137	147	157	157
125	0	132	137	147	157
123	0	125	132	137	147
117	0	123	125	132	137
114	0	117	123	125	132
111	0	114	117	123	125
112	0	111	114	117	123
144	0	112	111	114	117
150	0	144	112	111	114
149	0	150	144	112	111
134	0	149	150	144	112
123	0	134	149	150	144
116	0	123	134	149	150
117	0	116	123	134	149
111	0	117	116	123	134
105	0	111	117	116	123
102	0	105	111	117	116
95	0	102	105	111	117
93	0	95	102	105	111
124	0	93	95	102	105
130	0	124	93	95	102
124	0	130	124	93	95
115	0	124	130	124	93
106	0	115	124	130	124
105	0	106	115	124	130
105	1	105	106	115	124
101	1	105	105	106	115
95	1	101	105	105	106
93	1	95	101	105	105
84	1	93	95	101	105
87	1	84	93	95	101
116	1	87	84	93	95
120	1	116	87	84	93
117	1	120	116	87	84
109	1	117	120	116	87
105	1	109	117	120	116
107	1	105	109	117	120
109	1	107	105	109	117
109	1	109	107	105	109
108	1	109	109	107	105
107	1	108	109	109	107
99	1	107	108	109	109
103	1	99	107	108	109
131	1	103	99	107	108
137	1	131	103	99	107

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58003&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]4 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=58003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 18.7759413459670 + 0.43897739128912X[t] + 1.06333051395152Y1[t] + 0.249611180197316Y2[t] -0.349662551162838Y3[t] -0.075810088056322Y4[t] -0.408726804135841M1[t] -4.56723252040138M2[t] -7.36961206330479M3[t] -5.0991696927366M4[t] -8.4347111814441M5[t] -1.36184987808146M6[t] + 28.6785006089940M7[t] -1.22253043329851M8[t] -18.4328814476152M9[t] -16.4517178213962M10[t] -8.5643761303616M11[t] -0.0744452192710236t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  18.7759413459670 +  0.43897739128912X[t] +  1.06333051395152Y1[t] +  0.249611180197316Y2[t] -0.349662551162838Y3[t] -0.075810088056322Y4[t] -0.408726804135841M1[t] -4.56723252040138M2[t] -7.36961206330479M3[t] -5.0991696927366M4[t] -8.4347111814441M5[t] -1.36184987808146M6[t] +  28.6785006089940M7[t] -1.22253043329851M8[t] -18.4328814476152M9[t] -16.4517178213962M10[t] -8.5643761303616M11[t] -0.0744452192710236t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58003&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  18.7759413459670 +  0.43897739128912X[t] +  1.06333051395152Y1[t] +  0.249611180197316Y2[t] -0.349662551162838Y3[t] -0.075810088056322Y4[t] -0.408726804135841M1[t] -4.56723252040138M2[t] -7.36961206330479M3[t] -5.0991696927366M4[t] -8.4347111814441M5[t] -1.36184987808146M6[t] +  28.6785006089940M7[t] -1.22253043329851M8[t] -18.4328814476152M9[t] -16.4517178213962M10[t] -8.5643761303616M11[t] -0.0744452192710236t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 18.7759413459670 + 0.43897739128912X[t] + 1.06333051395152Y1[t] + 0.249611180197316Y2[t] -0.349662551162838Y3[t] -0.075810088056322Y4[t] -0.408726804135841M1[t] -4.56723252040138M2[t] -7.36961206330479M3[t] -5.0991696927366M4[t] -8.4347111814441M5[t] -1.36184987808146M6[t] + 28.6785006089940M7[t] -1.22253043329851M8[t] -18.4328814476152M9[t] -16.4517178213962M10[t] -8.5643761303616M11[t] -0.0744452192710236t + 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)	18.7759413459670	9.864848	1.9033	0.064594	0.032297
X	0.43897739128912	1.456328	0.3014	0.764732	0.382366
Y1	1.06333051395152	0.162203	6.5555	0	0
Y2	0.249611180197316	0.236701	1.0545	0.298294	0.149147
Y3	-0.349662551162838	0.244213	-1.4318	0.160377	0.080189
Y4	-0.075810088056322	0.184596	-0.4107	0.683613	0.341807
M1	-0.408726804135841	2.593196	-0.1576	0.875595	0.437797
M2	-4.56723252040138	2.708624	-1.6862	0.099956	0.049978
M3	-7.36961206330479	2.486263	-2.9641	0.005217	0.002609
M4	-5.0991696927366	2.404027	-2.1211	0.040496	0.020248
M5	-8.4347111814441	2.38102	-3.5425	0.001068	0.000534
M6	-1.36184987808146	2.590078	-0.5258	0.602086	0.301043
M7	28.6785006089940	2.711993	10.5747	0	0
M8	-1.22253043329851	6.718863	-0.182	0.856585	0.428293
M9	-18.4328814476152	7.221391	-2.5525	0.014835	0.007418
M10	-16.4517178213962	6.61876	-2.4856	0.017448	0.008724
M11	-8.5643761303616	2.682452	-3.1927	0.002829	0.001414
t	-0.0744452192710236	0.054226	-1.3729	0.177841	0.088921

\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) & 18.7759413459670 & 9.864848 & 1.9033 & 0.064594 & 0.032297 \tabularnewline
X & 0.43897739128912 & 1.456328 & 0.3014 & 0.764732 & 0.382366 \tabularnewline
Y1 & 1.06333051395152 & 0.162203 & 6.5555 & 0 & 0 \tabularnewline
Y2 & 0.249611180197316 & 0.236701 & 1.0545 & 0.298294 & 0.149147 \tabularnewline
Y3 & -0.349662551162838 & 0.244213 & -1.4318 & 0.160377 & 0.080189 \tabularnewline
Y4 & -0.075810088056322 & 0.184596 & -0.4107 & 0.683613 & 0.341807 \tabularnewline
M1 & -0.408726804135841 & 2.593196 & -0.1576 & 0.875595 & 0.437797 \tabularnewline
M2 & -4.56723252040138 & 2.708624 & -1.6862 & 0.099956 & 0.049978 \tabularnewline
M3 & -7.36961206330479 & 2.486263 & -2.9641 & 0.005217 & 0.002609 \tabularnewline
M4 & -5.0991696927366 & 2.404027 & -2.1211 & 0.040496 & 0.020248 \tabularnewline
M5 & -8.4347111814441 & 2.38102 & -3.5425 & 0.001068 & 0.000534 \tabularnewline
M6 & -1.36184987808146 & 2.590078 & -0.5258 & 0.602086 & 0.301043 \tabularnewline
M7 & 28.6785006089940 & 2.711993 & 10.5747 & 0 & 0 \tabularnewline
M8 & -1.22253043329851 & 6.718863 & -0.182 & 0.856585 & 0.428293 \tabularnewline
M9 & -18.4328814476152 & 7.221391 & -2.5525 & 0.014835 & 0.007418 \tabularnewline
M10 & -16.4517178213962 & 6.61876 & -2.4856 & 0.017448 & 0.008724 \tabularnewline
M11 & -8.5643761303616 & 2.682452 & -3.1927 & 0.002829 & 0.001414 \tabularnewline
t & -0.0744452192710236 & 0.054226 & -1.3729 & 0.177841 & 0.088921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58003&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]18.7759413459670[/C][C]9.864848[/C][C]1.9033[/C][C]0.064594[/C][C]0.032297[/C][/ROW]
[ROW][C]X[/C][C]0.43897739128912[/C][C]1.456328[/C][C]0.3014[/C][C]0.764732[/C][C]0.382366[/C][/ROW]
[ROW][C]Y1[/C][C]1.06333051395152[/C][C]0.162203[/C][C]6.5555[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]0.249611180197316[/C][C]0.236701[/C][C]1.0545[/C][C]0.298294[/C][C]0.149147[/C][/ROW]
[ROW][C]Y3[/C][C]-0.349662551162838[/C][C]0.244213[/C][C]-1.4318[/C][C]0.160377[/C][C]0.080189[/C][/ROW]
[ROW][C]Y4[/C][C]-0.075810088056322[/C][C]0.184596[/C][C]-0.4107[/C][C]0.683613[/C][C]0.341807[/C][/ROW]
[ROW][C]M1[/C][C]-0.408726804135841[/C][C]2.593196[/C][C]-0.1576[/C][C]0.875595[/C][C]0.437797[/C][/ROW]
[ROW][C]M2[/C][C]-4.56723252040138[/C][C]2.708624[/C][C]-1.6862[/C][C]0.099956[/C][C]0.049978[/C][/ROW]
[ROW][C]M3[/C][C]-7.36961206330479[/C][C]2.486263[/C][C]-2.9641[/C][C]0.005217[/C][C]0.002609[/C][/ROW]
[ROW][C]M4[/C][C]-5.0991696927366[/C][C]2.404027[/C][C]-2.1211[/C][C]0.040496[/C][C]0.020248[/C][/ROW]
[ROW][C]M5[/C][C]-8.4347111814441[/C][C]2.38102[/C][C]-3.5425[/C][C]0.001068[/C][C]0.000534[/C][/ROW]
[ROW][C]M6[/C][C]-1.36184987808146[/C][C]2.590078[/C][C]-0.5258[/C][C]0.602086[/C][C]0.301043[/C][/ROW]
[ROW][C]M7[/C][C]28.6785006089940[/C][C]2.711993[/C][C]10.5747[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-1.22253043329851[/C][C]6.718863[/C][C]-0.182[/C][C]0.856585[/C][C]0.428293[/C][/ROW]
[ROW][C]M9[/C][C]-18.4328814476152[/C][C]7.221391[/C][C]-2.5525[/C][C]0.014835[/C][C]0.007418[/C][/ROW]
[ROW][C]M10[/C][C]-16.4517178213962[/C][C]6.61876[/C][C]-2.4856[/C][C]0.017448[/C][C]0.008724[/C][/ROW]
[ROW][C]M11[/C][C]-8.5643761303616[/C][C]2.682452[/C][C]-3.1927[/C][C]0.002829[/C][C]0.001414[/C][/ROW]
[ROW][C]t[/C][C]-0.0744452192710236[/C][C]0.054226[/C][C]-1.3729[/C][C]0.177841[/C][C]0.088921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&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)	18.7759413459670	9.864848	1.9033	0.064594	0.032297
X	0.43897739128912	1.456328	0.3014	0.764732	0.382366
Y1	1.06333051395152	0.162203	6.5555	0	0
Y2	0.249611180197316	0.236701	1.0545	0.298294	0.149147
Y3	-0.349662551162838	0.244213	-1.4318	0.160377	0.080189
Y4	-0.075810088056322	0.184596	-0.4107	0.683613	0.341807
M1	-0.408726804135841	2.593196	-0.1576	0.875595	0.437797
M2	-4.56723252040138	2.708624	-1.6862	0.099956	0.049978
M3	-7.36961206330479	2.486263	-2.9641	0.005217	0.002609
M4	-5.0991696927366	2.404027	-2.1211	0.040496	0.020248
M5	-8.4347111814441	2.38102	-3.5425	0.001068	0.000534
M6	-1.36184987808146	2.590078	-0.5258	0.602086	0.301043
M7	28.6785006089940	2.711993	10.5747	0	0
M8	-1.22253043329851	6.718863	-0.182	0.856585	0.428293
M9	-18.4328814476152	7.221391	-2.5525	0.014835	0.007418
M10	-16.4517178213962	6.61876	-2.4856	0.017448	0.008724
M11	-8.5643761303616	2.682452	-3.1927	0.002829	0.001414
t	-0.0744452192710236	0.054226	-1.3729	0.177841	0.088921

Multiple Linear Regression - Regression Statistics
Multiple R	0.99241266276863
R-squared	0.984882893223523
Adjusted R-squared	0.978119977034046
F-TEST (value)	145.629912545128
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.569251592751
Sum Squared Residuals	250.840042380435

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99241266276863 \tabularnewline
R-squared & 0.984882893223523 \tabularnewline
Adjusted R-squared & 0.978119977034046 \tabularnewline
F-TEST (value) & 145.629912545128 \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 & 2.569251592751 \tabularnewline
Sum Squared Residuals & 250.840042380435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58003&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99241266276863[/C][/ROW]
[ROW][C]R-squared[/C][C]0.984882893223523[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.978119977034046[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]145.629912545128[/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]2.569251592751[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]250.840042380435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58003&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&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	0.99241266276863
R-squared	0.984882893223523
Adjusted R-squared	0.978119977034046
F-TEST (value)	145.629912545128
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.569251592751
Sum Squared Residuals	250.840042380435

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	130	132.233198453111	-2.23319845311130
2	127	126.091496795332	0.908503204667906
3	122	120.933375675531	1.06662432446888
4	117	119.115439824518	-2.11543982451822
5	112	110.568782739566	1.43121726043434
6	113	112.978233372896	0.0217666271037571
7	149	144.886776449761	4.1132235502386
8	157	155.568173066746	1.43182693325432
9	157	155.805411320992	1.19458867900772
10	147	147.045357239600	-0.0453572396002797
11	137	138.698484992518	-1.69848499251837
12	132	133.45251825767	-1.45251825767001
13	125	128.653207374161	-3.65320737416081
14	123	119.983613332169	3.0163866678314
15	117	115.739262917087	1.26073708291266
16	114	113.882742922702	0.117257077297759
17	111	107.015093310405	3.98490668959482
18	112	112.32427979514	-0.324279795139979
19	144	144.108530218130	-0.108530218130399
20	150	149.685659500870	0.314340499129698
21	149	146.646171830312	2.35382816968805
22	134	137.722215079225	-3.72221507922515
23	123	124.811644536739	-1.81164453673928
24	116	117.755574114228	-1.75557411422830
25	117	112.404113866489	4.59588613351077
26	111	112.470654567159	-1.47065456715903
27	105	106.745006728232	-1.74500672823222
28	102	101.244361779868	0.75563822013222
29	95	95.1688816677715	-0.168881667771513
30	93	96.5279864489255	-3.52798644892551
31	124	124.123800609272	-0.123800609272107
32	130	129.28741604212	0.712583957880102
33	124	127.350545197078	-3.35054519707804
34	115	113.687028691565	1.31297130843456
35	106	105.984195419858	0.0158045801415627
36	105	104.300765862249	0.699234137751412
37	105	104.548563583207	0.451436416793032
38	101	103.895255220446	-2.89525522044554
39	95	97.7970617461348	-2.79706174613477
40	93	92.6904411809899	0.309558819010125
41	84	87.0547765685758	-3.05477656857577
42	87	86.3852113259114	0.614788674088596
43	116	118.448793144458	-2.44879314445813
44	120	123.357318464659	-3.35731846465881
45	117	117.197871651618	-0.19787165161773
46	109	106.545398989609	2.45460101039087
47	105	101.505675050884	3.49432494911609
48	107	104.491141765853	2.50885823414690
49	109	108.160916723032	0.83908327696831
50	109	108.558980084895	0.441019915105264
51	108	105.785292933015	2.21470706698545
52	107	106.067014291922	0.932985708078123
53	99	101.192465713682	-2.19246571368187
54	103	99.7842890571269	3.21571094287314
55	131	132.432099578378	-1.43209957837797
56	137	136.101432925605	0.898567074394699

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 130 & 132.233198453111 & -2.23319845311130 \tabularnewline
2 & 127 & 126.091496795332 & 0.908503204667906 \tabularnewline
3 & 122 & 120.933375675531 & 1.06662432446888 \tabularnewline
4 & 117 & 119.115439824518 & -2.11543982451822 \tabularnewline
5 & 112 & 110.568782739566 & 1.43121726043434 \tabularnewline
6 & 113 & 112.978233372896 & 0.0217666271037571 \tabularnewline
7 & 149 & 144.886776449761 & 4.1132235502386 \tabularnewline
8 & 157 & 155.568173066746 & 1.43182693325432 \tabularnewline
9 & 157 & 155.805411320992 & 1.19458867900772 \tabularnewline
10 & 147 & 147.045357239600 & -0.0453572396002797 \tabularnewline
11 & 137 & 138.698484992518 & -1.69848499251837 \tabularnewline
12 & 132 & 133.45251825767 & -1.45251825767001 \tabularnewline
13 & 125 & 128.653207374161 & -3.65320737416081 \tabularnewline
14 & 123 & 119.983613332169 & 3.0163866678314 \tabularnewline
15 & 117 & 115.739262917087 & 1.26073708291266 \tabularnewline
16 & 114 & 113.882742922702 & 0.117257077297759 \tabularnewline
17 & 111 & 107.015093310405 & 3.98490668959482 \tabularnewline
18 & 112 & 112.32427979514 & -0.324279795139979 \tabularnewline
19 & 144 & 144.108530218130 & -0.108530218130399 \tabularnewline
20 & 150 & 149.685659500870 & 0.314340499129698 \tabularnewline
21 & 149 & 146.646171830312 & 2.35382816968805 \tabularnewline
22 & 134 & 137.722215079225 & -3.72221507922515 \tabularnewline
23 & 123 & 124.811644536739 & -1.81164453673928 \tabularnewline
24 & 116 & 117.755574114228 & -1.75557411422830 \tabularnewline
25 & 117 & 112.404113866489 & 4.59588613351077 \tabularnewline
26 & 111 & 112.470654567159 & -1.47065456715903 \tabularnewline
27 & 105 & 106.745006728232 & -1.74500672823222 \tabularnewline
28 & 102 & 101.244361779868 & 0.75563822013222 \tabularnewline
29 & 95 & 95.1688816677715 & -0.168881667771513 \tabularnewline
30 & 93 & 96.5279864489255 & -3.52798644892551 \tabularnewline
31 & 124 & 124.123800609272 & -0.123800609272107 \tabularnewline
32 & 130 & 129.28741604212 & 0.712583957880102 \tabularnewline
33 & 124 & 127.350545197078 & -3.35054519707804 \tabularnewline
34 & 115 & 113.687028691565 & 1.31297130843456 \tabularnewline
35 & 106 & 105.984195419858 & 0.0158045801415627 \tabularnewline
36 & 105 & 104.300765862249 & 0.699234137751412 \tabularnewline
37 & 105 & 104.548563583207 & 0.451436416793032 \tabularnewline
38 & 101 & 103.895255220446 & -2.89525522044554 \tabularnewline
39 & 95 & 97.7970617461348 & -2.79706174613477 \tabularnewline
40 & 93 & 92.6904411809899 & 0.309558819010125 \tabularnewline
41 & 84 & 87.0547765685758 & -3.05477656857577 \tabularnewline
42 & 87 & 86.3852113259114 & 0.614788674088596 \tabularnewline
43 & 116 & 118.448793144458 & -2.44879314445813 \tabularnewline
44 & 120 & 123.357318464659 & -3.35731846465881 \tabularnewline
45 & 117 & 117.197871651618 & -0.19787165161773 \tabularnewline
46 & 109 & 106.545398989609 & 2.45460101039087 \tabularnewline
47 & 105 & 101.505675050884 & 3.49432494911609 \tabularnewline
48 & 107 & 104.491141765853 & 2.50885823414690 \tabularnewline
49 & 109 & 108.160916723032 & 0.83908327696831 \tabularnewline
50 & 109 & 108.558980084895 & 0.441019915105264 \tabularnewline
51 & 108 & 105.785292933015 & 2.21470706698545 \tabularnewline
52 & 107 & 106.067014291922 & 0.932985708078123 \tabularnewline
53 & 99 & 101.192465713682 & -2.19246571368187 \tabularnewline
54 & 103 & 99.7842890571269 & 3.21571094287314 \tabularnewline
55 & 131 & 132.432099578378 & -1.43209957837797 \tabularnewline
56 & 137 & 136.101432925605 & 0.898567074394699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58003&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]130[/C][C]132.233198453111[/C][C]-2.23319845311130[/C][/ROW]
[ROW][C]2[/C][C]127[/C][C]126.091496795332[/C][C]0.908503204667906[/C][/ROW]
[ROW][C]3[/C][C]122[/C][C]120.933375675531[/C][C]1.06662432446888[/C][/ROW]
[ROW][C]4[/C][C]117[/C][C]119.115439824518[/C][C]-2.11543982451822[/C][/ROW]
[ROW][C]5[/C][C]112[/C][C]110.568782739566[/C][C]1.43121726043434[/C][/ROW]
[ROW][C]6[/C][C]113[/C][C]112.978233372896[/C][C]0.0217666271037571[/C][/ROW]
[ROW][C]7[/C][C]149[/C][C]144.886776449761[/C][C]4.1132235502386[/C][/ROW]
[ROW][C]8[/C][C]157[/C][C]155.568173066746[/C][C]1.43182693325432[/C][/ROW]
[ROW][C]9[/C][C]157[/C][C]155.805411320992[/C][C]1.19458867900772[/C][/ROW]
[ROW][C]10[/C][C]147[/C][C]147.045357239600[/C][C]-0.0453572396002797[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]138.698484992518[/C][C]-1.69848499251837[/C][/ROW]
[ROW][C]12[/C][C]132[/C][C]133.45251825767[/C][C]-1.45251825767001[/C][/ROW]
[ROW][C]13[/C][C]125[/C][C]128.653207374161[/C][C]-3.65320737416081[/C][/ROW]
[ROW][C]14[/C][C]123[/C][C]119.983613332169[/C][C]3.0163866678314[/C][/ROW]
[ROW][C]15[/C][C]117[/C][C]115.739262917087[/C][C]1.26073708291266[/C][/ROW]
[ROW][C]16[/C][C]114[/C][C]113.882742922702[/C][C]0.117257077297759[/C][/ROW]
[ROW][C]17[/C][C]111[/C][C]107.015093310405[/C][C]3.98490668959482[/C][/ROW]
[ROW][C]18[/C][C]112[/C][C]112.32427979514[/C][C]-0.324279795139979[/C][/ROW]
[ROW][C]19[/C][C]144[/C][C]144.108530218130[/C][C]-0.108530218130399[/C][/ROW]
[ROW][C]20[/C][C]150[/C][C]149.685659500870[/C][C]0.314340499129698[/C][/ROW]
[ROW][C]21[/C][C]149[/C][C]146.646171830312[/C][C]2.35382816968805[/C][/ROW]
[ROW][C]22[/C][C]134[/C][C]137.722215079225[/C][C]-3.72221507922515[/C][/ROW]
[ROW][C]23[/C][C]123[/C][C]124.811644536739[/C][C]-1.81164453673928[/C][/ROW]
[ROW][C]24[/C][C]116[/C][C]117.755574114228[/C][C]-1.75557411422830[/C][/ROW]
[ROW][C]25[/C][C]117[/C][C]112.404113866489[/C][C]4.59588613351077[/C][/ROW]
[ROW][C]26[/C][C]111[/C][C]112.470654567159[/C][C]-1.47065456715903[/C][/ROW]
[ROW][C]27[/C][C]105[/C][C]106.745006728232[/C][C]-1.74500672823222[/C][/ROW]
[ROW][C]28[/C][C]102[/C][C]101.244361779868[/C][C]0.75563822013222[/C][/ROW]
[ROW][C]29[/C][C]95[/C][C]95.1688816677715[/C][C]-0.168881667771513[/C][/ROW]
[ROW][C]30[/C][C]93[/C][C]96.5279864489255[/C][C]-3.52798644892551[/C][/ROW]
[ROW][C]31[/C][C]124[/C][C]124.123800609272[/C][C]-0.123800609272107[/C][/ROW]
[ROW][C]32[/C][C]130[/C][C]129.28741604212[/C][C]0.712583957880102[/C][/ROW]
[ROW][C]33[/C][C]124[/C][C]127.350545197078[/C][C]-3.35054519707804[/C][/ROW]
[ROW][C]34[/C][C]115[/C][C]113.687028691565[/C][C]1.31297130843456[/C][/ROW]
[ROW][C]35[/C][C]106[/C][C]105.984195419858[/C][C]0.0158045801415627[/C][/ROW]
[ROW][C]36[/C][C]105[/C][C]104.300765862249[/C][C]0.699234137751412[/C][/ROW]
[ROW][C]37[/C][C]105[/C][C]104.548563583207[/C][C]0.451436416793032[/C][/ROW]
[ROW][C]38[/C][C]101[/C][C]103.895255220446[/C][C]-2.89525522044554[/C][/ROW]
[ROW][C]39[/C][C]95[/C][C]97.7970617461348[/C][C]-2.79706174613477[/C][/ROW]
[ROW][C]40[/C][C]93[/C][C]92.6904411809899[/C][C]0.309558819010125[/C][/ROW]
[ROW][C]41[/C][C]84[/C][C]87.0547765685758[/C][C]-3.05477656857577[/C][/ROW]
[ROW][C]42[/C][C]87[/C][C]86.3852113259114[/C][C]0.614788674088596[/C][/ROW]
[ROW][C]43[/C][C]116[/C][C]118.448793144458[/C][C]-2.44879314445813[/C][/ROW]
[ROW][C]44[/C][C]120[/C][C]123.357318464659[/C][C]-3.35731846465881[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]117.197871651618[/C][C]-0.19787165161773[/C][/ROW]
[ROW][C]46[/C][C]109[/C][C]106.545398989609[/C][C]2.45460101039087[/C][/ROW]
[ROW][C]47[/C][C]105[/C][C]101.505675050884[/C][C]3.49432494911609[/C][/ROW]
[ROW][C]48[/C][C]107[/C][C]104.491141765853[/C][C]2.50885823414690[/C][/ROW]
[ROW][C]49[/C][C]109[/C][C]108.160916723032[/C][C]0.83908327696831[/C][/ROW]
[ROW][C]50[/C][C]109[/C][C]108.558980084895[/C][C]0.441019915105264[/C][/ROW]
[ROW][C]51[/C][C]108[/C][C]105.785292933015[/C][C]2.21470706698545[/C][/ROW]
[ROW][C]52[/C][C]107[/C][C]106.067014291922[/C][C]0.932985708078123[/C][/ROW]
[ROW][C]53[/C][C]99[/C][C]101.192465713682[/C][C]-2.19246571368187[/C][/ROW]
[ROW][C]54[/C][C]103[/C][C]99.7842890571269[/C][C]3.21571094287314[/C][/ROW]
[ROW][C]55[/C][C]131[/C][C]132.432099578378[/C][C]-1.43209957837797[/C][/ROW]
[ROW][C]56[/C][C]137[/C][C]136.101432925605[/C][C]0.898567074394699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58003&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&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	130	132.233198453111	-2.23319845311130
2	127	126.091496795332	0.908503204667906
3	122	120.933375675531	1.06662432446888
4	117	119.115439824518	-2.11543982451822
5	112	110.568782739566	1.43121726043434
6	113	112.978233372896	0.0217666271037571
7	149	144.886776449761	4.1132235502386
8	157	155.568173066746	1.43182693325432
9	157	155.805411320992	1.19458867900772
10	147	147.045357239600	-0.0453572396002797
11	137	138.698484992518	-1.69848499251837
12	132	133.45251825767	-1.45251825767001
13	125	128.653207374161	-3.65320737416081
14	123	119.983613332169	3.0163866678314
15	117	115.739262917087	1.26073708291266
16	114	113.882742922702	0.117257077297759
17	111	107.015093310405	3.98490668959482
18	112	112.32427979514	-0.324279795139979
19	144	144.108530218130	-0.108530218130399
20	150	149.685659500870	0.314340499129698
21	149	146.646171830312	2.35382816968805
22	134	137.722215079225	-3.72221507922515
23	123	124.811644536739	-1.81164453673928
24	116	117.755574114228	-1.75557411422830
25	117	112.404113866489	4.59588613351077
26	111	112.470654567159	-1.47065456715903
27	105	106.745006728232	-1.74500672823222
28	102	101.244361779868	0.75563822013222
29	95	95.1688816677715	-0.168881667771513
30	93	96.5279864489255	-3.52798644892551
31	124	124.123800609272	-0.123800609272107
32	130	129.28741604212	0.712583957880102
33	124	127.350545197078	-3.35054519707804
34	115	113.687028691565	1.31297130843456
35	106	105.984195419858	0.0158045801415627
36	105	104.300765862249	0.699234137751412
37	105	104.548563583207	0.451436416793032
38	101	103.895255220446	-2.89525522044554
39	95	97.7970617461348	-2.79706174613477
40	93	92.6904411809899	0.309558819010125
41	84	87.0547765685758	-3.05477656857577
42	87	86.3852113259114	0.614788674088596
43	116	118.448793144458	-2.44879314445813
44	120	123.357318464659	-3.35731846465881
45	117	117.197871651618	-0.19787165161773
46	109	106.545398989609	2.45460101039087
47	105	101.505675050884	3.49432494911609
48	107	104.491141765853	2.50885823414690
49	109	108.160916723032	0.83908327696831
50	109	108.558980084895	0.441019915105264
51	108	105.785292933015	2.21470706698545
52	107	106.067014291922	0.932985708078123
53	99	101.192465713682	-2.19246571368187
54	103	99.7842890571269	3.21571094287314
55	131	132.432099578378	-1.43209957837797
56	137	136.101432925605	0.898567074394699

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.249958727363467	0.499917454726934	0.750041272636533
22	0.77455260270758	0.450894794584840	0.225447397292420
23	0.664279642287847	0.671440715424307	0.335720357712153
24	0.561926616149368	0.876146767701265	0.438073383850632
25	0.766115767680358	0.467768464639284	0.233884232319642
26	0.77241699970985	0.455166000580301	0.227583000290151
27	0.755418740625895	0.48916251874821	0.244581259374105
28	0.669902495308256	0.660195009383487	0.330097504691744
29	0.771208230255386	0.457583539489228	0.228791769744614
30	0.783425491009329	0.433149017981343	0.216574508990671
31	0.909450811272196	0.181098377455609	0.0905491887278044
32	0.921487528457456	0.157024943085087	0.0785124715425436
33	0.893089977647141	0.213820044705717	0.106910022352859
34	0.909606872183835	0.180786255632330	0.0903931278161648
35	0.855002073601457	0.289995852797087	0.144997926398543

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.249958727363467 & 0.499917454726934 & 0.750041272636533 \tabularnewline
22 & 0.77455260270758 & 0.450894794584840 & 0.225447397292420 \tabularnewline
23 & 0.664279642287847 & 0.671440715424307 & 0.335720357712153 \tabularnewline
24 & 0.561926616149368 & 0.876146767701265 & 0.438073383850632 \tabularnewline
25 & 0.766115767680358 & 0.467768464639284 & 0.233884232319642 \tabularnewline
26 & 0.77241699970985 & 0.455166000580301 & 0.227583000290151 \tabularnewline
27 & 0.755418740625895 & 0.48916251874821 & 0.244581259374105 \tabularnewline
28 & 0.669902495308256 & 0.660195009383487 & 0.330097504691744 \tabularnewline
29 & 0.771208230255386 & 0.457583539489228 & 0.228791769744614 \tabularnewline
30 & 0.783425491009329 & 0.433149017981343 & 0.216574508990671 \tabularnewline
31 & 0.909450811272196 & 0.181098377455609 & 0.0905491887278044 \tabularnewline
32 & 0.921487528457456 & 0.157024943085087 & 0.0785124715425436 \tabularnewline
33 & 0.893089977647141 & 0.213820044705717 & 0.106910022352859 \tabularnewline
34 & 0.909606872183835 & 0.180786255632330 & 0.0903931278161648 \tabularnewline
35 & 0.855002073601457 & 0.289995852797087 & 0.144997926398543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58003&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]0.249958727363467[/C][C]0.499917454726934[/C][C]0.750041272636533[/C][/ROW]
[ROW][C]22[/C][C]0.77455260270758[/C][C]0.450894794584840[/C][C]0.225447397292420[/C][/ROW]
[ROW][C]23[/C][C]0.664279642287847[/C][C]0.671440715424307[/C][C]0.335720357712153[/C][/ROW]
[ROW][C]24[/C][C]0.561926616149368[/C][C]0.876146767701265[/C][C]0.438073383850632[/C][/ROW]
[ROW][C]25[/C][C]0.766115767680358[/C][C]0.467768464639284[/C][C]0.233884232319642[/C][/ROW]
[ROW][C]26[/C][C]0.77241699970985[/C][C]0.455166000580301[/C][C]0.227583000290151[/C][/ROW]
[ROW][C]27[/C][C]0.755418740625895[/C][C]0.48916251874821[/C][C]0.244581259374105[/C][/ROW]
[ROW][C]28[/C][C]0.669902495308256[/C][C]0.660195009383487[/C][C]0.330097504691744[/C][/ROW]
[ROW][C]29[/C][C]0.771208230255386[/C][C]0.457583539489228[/C][C]0.228791769744614[/C][/ROW]
[ROW][C]30[/C][C]0.783425491009329[/C][C]0.433149017981343[/C][C]0.216574508990671[/C][/ROW]
[ROW][C]31[/C][C]0.909450811272196[/C][C]0.181098377455609[/C][C]0.0905491887278044[/C][/ROW]
[ROW][C]32[/C][C]0.921487528457456[/C][C]0.157024943085087[/C][C]0.0785124715425436[/C][/ROW]
[ROW][C]33[/C][C]0.893089977647141[/C][C]0.213820044705717[/C][C]0.106910022352859[/C][/ROW]
[ROW][C]34[/C][C]0.909606872183835[/C][C]0.180786255632330[/C][C]0.0903931278161648[/C][/ROW]
[ROW][C]35[/C][C]0.855002073601457[/C][C]0.289995852797087[/C][C]0.144997926398543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58003&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&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	0.249958727363467	0.499917454726934	0.750041272636533
22	0.77455260270758	0.450894794584840	0.225447397292420
23	0.664279642287847	0.671440715424307	0.335720357712153
24	0.561926616149368	0.876146767701265	0.438073383850632
25	0.766115767680358	0.467768464639284	0.233884232319642
26	0.77241699970985	0.455166000580301	0.227583000290151
27	0.755418740625895	0.48916251874821	0.244581259374105
28	0.669902495308256	0.660195009383487	0.330097504691744
29	0.771208230255386	0.457583539489228	0.228791769744614
30	0.783425491009329	0.433149017981343	0.216574508990671
31	0.909450811272196	0.181098377455609	0.0905491887278044
32	0.921487528457456	0.157024943085087	0.0785124715425436
33	0.893089977647141	0.213820044705717	0.106910022352859
34	0.909606872183835	0.180786255632330	0.0903931278161648
35	0.855002073601457	0.289995852797087	0.144997926398543

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=58003&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=58003&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58003&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

PNG link

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PDF link

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