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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 04 Dec 2015 09:57:11 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/04/t1449223635sphs2ss2wxuoaph.htm/, Retrieved Thu, 16 May 2024 10:07:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285049, Retrieved Thu, 16 May 2024 10:07:36 +0000

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Estimated Impact

108

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

-       [Multiple Regression] [multiple regressi...] [2015-12-04 09:57:11] [201263e50fe1652009691bd5c495bb3d] [Current]

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Dataseries X:

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21.6 6.5
21.6 6.2
21.6 6.3
19.4 6.4
19.4 6.3
19.4 6.1
15.9 5.7
15.9 5.6
15.9 5.6
21.8 6.2
21.8 6.3
21.8 6.2
17.6 6
17.6 5.9
17.6 6
19 6.1
19 6.1
19 6
16.3 6
16.3 6
16.3 5.9
22.5 6.1
22.5 6.3
22.5 6.5
23.8 7.1
23.8 7.5
23.8 7.6
24.6 7.6
24.6 7.4
24.6 7.1
22.7 6.9
22.7 6.8
22.7 6.8
25.2 7.3
25.2 7.3
25.2 7.3
26.4 7.2
26.4 7.2
26.4 7.4
26 7.7
26 7.8
26 7.9
23.2 7.9
23.2 7.8
23.2 7.7
22.7 7.9
22.7 7.8
22.7 7.6
24 7.5
24 7.4
24 7.7
20.7 8.2
20.7 8.4
20.7 8.4
23.8 8.2
23.8 8
23.8 8
27.1 8.2
27.1 8.2
27.1 8

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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Multiple Linear Regression - Estimated Regression Equation
M-25[t] = + 1.09921 + 1.27678M_25[t] + 0.758206`M-25(t-1)`[t] -0.00741498`M-25(t-2)`[t] -0.20449`M-25(t-3)`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
M-25[t] =  +  1.09921 +  1.27678M_25[t] +  0.758206`M-25(t-1)`[t] -0.00741498`M-25(t-2)`[t] -0.20449`M-25(t-3)`[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]M-25[t] =  +  1.09921 +  1.27678M_25[t] +  0.758206`M-25(t-1)`[t] -0.00741498`M-25(t-2)`[t] -0.20449`M-25(t-3)`[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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
M-25[t] = + 1.09921 + 1.27678M_25[t] + 0.758206`M-25(t-1)`[t] -0.00741498`M-25(t-2)`[t] -0.20449`M-25(t-3)`[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)	+1.099	1.851	+5.9400e-01	0.5551	0.2776
M_25	+1.277	0.3982	+3.2060e+00	0.002303	0.001151
`M-25(t-1)`	+0.7582	0.137	+5.5330e+00	1.042e-06	5.21e-07
`M-25(t-2)`	-0.007415	0.1726	-4.2950e-02	0.9659	0.483
`M-25(t-3)`	-0.2045	0.1345	-1.5200e+00	0.1345	0.06725

\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) & +1.099 &  1.851 & +5.9400e-01 &  0.5551 &  0.2776 \tabularnewline
M_25 & +1.277 &  0.3982 & +3.2060e+00 &  0.002303 &  0.001151 \tabularnewline
`M-25(t-1)` & +0.7582 &  0.137 & +5.5330e+00 &  1.042e-06 &  5.21e-07 \tabularnewline
`M-25(t-2)` & -0.007415 &  0.1726 & -4.2950e-02 &  0.9659 &  0.483 \tabularnewline
`M-25(t-3)` & -0.2045 &  0.1345 & -1.5200e+00 &  0.1345 &  0.06725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&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]+1.099[/C][C] 1.851[/C][C]+5.9400e-01[/C][C] 0.5551[/C][C] 0.2776[/C][/ROW]
[ROW][C]M_25[/C][C]+1.277[/C][C] 0.3982[/C][C]+3.2060e+00[/C][C] 0.002303[/C][C] 0.001151[/C][/ROW]
[ROW][C]`M-25(t-1)`[/C][C]+0.7582[/C][C] 0.137[/C][C]+5.5330e+00[/C][C] 1.042e-06[/C][C] 5.21e-07[/C][/ROW]
[ROW][C]`M-25(t-2)`[/C][C]-0.007415[/C][C] 0.1726[/C][C]-4.2950e-02[/C][C] 0.9659[/C][C] 0.483[/C][/ROW]
[ROW][C]`M-25(t-3)`[/C][C]-0.2045[/C][C] 0.1345[/C][C]-1.5200e+00[/C][C] 0.1345[/C][C] 0.06725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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)	+1.099	1.851	+5.9400e-01	0.5551	0.2776
M_25	+1.277	0.3982	+3.2060e+00	0.002303	0.001151
`M-25(t-1)`	+0.7582	0.137	+5.5330e+00	1.042e-06	5.21e-07
`M-25(t-2)`	-0.007415	0.1726	-4.2950e-02	0.9659	0.483
`M-25(t-3)`	-0.2045	0.1345	-1.5200e+00	0.1345	0.06725

Multiple Linear Regression - Regression Statistics
Multiple R	0.8798
R-squared	0.7741
Adjusted R-squared	0.7568
F-TEST (value)	44.55
F-TEST (DF numerator)	4
F-TEST (DF denominator)	52
p-value	3.331e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.602
Sum Squared Residuals	133.4

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.8798 \tabularnewline
R-squared &  0.7741 \tabularnewline
Adjusted R-squared &  0.7568 \tabularnewline
F-TEST (value) &  44.55 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 52 \tabularnewline
p-value &  3.331e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  1.602 \tabularnewline
Sum Squared Residuals &  133.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.8798[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.7741[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.7568[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 44.55[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]4[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]52[/C][/ROW]
[ROW][C]p-value[/C][C] 3.331e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 1.602[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 133.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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	0.8798
R-squared	0.7741
Adjusted R-squared	0.7568
F-TEST (value)	44.55
F-TEST (DF numerator)	4
F-TEST (DF denominator)	52
p-value	3.331e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.602
Sum Squared Residuals	133.4

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	19.4	21.07	-1.671
2	19.4	19.27	0.125
3	19.4	19.04	0.364
4	15.9	18.98	-3.075
5	15.9	16.19	-0.2937
6	15.9	16.22	-0.3197
7	21.8	17.7	4.099
8	21.8	22.3	-0.5026
9	21.8	22.13	-0.3311
10	17.6	20.67	-3.069
11	17.6	17.36	0.2429
12	17.6	17.52	0.08404
13	19	18.5	0.4975
14	19	19.56	-0.564
15	19	19.43	-0.4259
16	16.3	19.14	-2.84
17	16.3	17.09	-0.7925
18	16.3	16.98	-0.6848
19	22.5	17.79	4.708
20	22.5	22.75	-0.2485
21	22.5	22.96	-0.4579
22	23.8	22.46	1.344
23	23.8	23.95	-0.1525
24	23.8	24.07	-0.2706
25	24.6	23.8	0.7953
26	24.6	24.16	0.4441
27	24.6	23.77	0.833
28	22.7	23.35	-0.648
29	22.7	21.78	0.9202
30	22.7	21.79	0.9062
31	25.2	22.82	2.379
32	25.2	24.72	0.4837
33	25.2	24.7	0.5022
34	26.4	24.06	2.341
35	26.4	24.97	1.431
36	26.4	25.22	1.185
37	26	25.35	0.6472
38	26	25.18	0.8228
39	26	25.31	0.6922
40	23.2	25.39	-2.19
41	23.2	23.14	0.06102
42	23.2	23.03	0.1679
43	22.7	23.86	-1.16
44	22.7	23.35	-0.6532
45	22.7	23.1	-0.4016
46	24	23.08	0.9239
47	24	23.93	0.06588
48	24	24.31	-0.3075
49	20.7	24.68	-3.98
50	20.7	22.43	-1.733
51	20.7	22.46	-1.758
52	23.8	22.88	0.9227
53	23.8	24.97	-1.172
54	23.8	24.95	-1.149
55	27.1	24.57	2.529
56	27.1	27.07	0.02711
57	27.1	26.79	0.3069

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  19.4 &  21.07 & -1.671 \tabularnewline
2 &  19.4 &  19.27 &  0.125 \tabularnewline
3 &  19.4 &  19.04 &  0.364 \tabularnewline
4 &  15.9 &  18.98 & -3.075 \tabularnewline
5 &  15.9 &  16.19 & -0.2937 \tabularnewline
6 &  15.9 &  16.22 & -0.3197 \tabularnewline
7 &  21.8 &  17.7 &  4.099 \tabularnewline
8 &  21.8 &  22.3 & -0.5026 \tabularnewline
9 &  21.8 &  22.13 & -0.3311 \tabularnewline
10 &  17.6 &  20.67 & -3.069 \tabularnewline
11 &  17.6 &  17.36 &  0.2429 \tabularnewline
12 &  17.6 &  17.52 &  0.08404 \tabularnewline
13 &  19 &  18.5 &  0.4975 \tabularnewline
14 &  19 &  19.56 & -0.564 \tabularnewline
15 &  19 &  19.43 & -0.4259 \tabularnewline
16 &  16.3 &  19.14 & -2.84 \tabularnewline
17 &  16.3 &  17.09 & -0.7925 \tabularnewline
18 &  16.3 &  16.98 & -0.6848 \tabularnewline
19 &  22.5 &  17.79 &  4.708 \tabularnewline
20 &  22.5 &  22.75 & -0.2485 \tabularnewline
21 &  22.5 &  22.96 & -0.4579 \tabularnewline
22 &  23.8 &  22.46 &  1.344 \tabularnewline
23 &  23.8 &  23.95 & -0.1525 \tabularnewline
24 &  23.8 &  24.07 & -0.2706 \tabularnewline
25 &  24.6 &  23.8 &  0.7953 \tabularnewline
26 &  24.6 &  24.16 &  0.4441 \tabularnewline
27 &  24.6 &  23.77 &  0.833 \tabularnewline
28 &  22.7 &  23.35 & -0.648 \tabularnewline
29 &  22.7 &  21.78 &  0.9202 \tabularnewline
30 &  22.7 &  21.79 &  0.9062 \tabularnewline
31 &  25.2 &  22.82 &  2.379 \tabularnewline
32 &  25.2 &  24.72 &  0.4837 \tabularnewline
33 &  25.2 &  24.7 &  0.5022 \tabularnewline
34 &  26.4 &  24.06 &  2.341 \tabularnewline
35 &  26.4 &  24.97 &  1.431 \tabularnewline
36 &  26.4 &  25.22 &  1.185 \tabularnewline
37 &  26 &  25.35 &  0.6472 \tabularnewline
38 &  26 &  25.18 &  0.8228 \tabularnewline
39 &  26 &  25.31 &  0.6922 \tabularnewline
40 &  23.2 &  25.39 & -2.19 \tabularnewline
41 &  23.2 &  23.14 &  0.06102 \tabularnewline
42 &  23.2 &  23.03 &  0.1679 \tabularnewline
43 &  22.7 &  23.86 & -1.16 \tabularnewline
44 &  22.7 &  23.35 & -0.6532 \tabularnewline
45 &  22.7 &  23.1 & -0.4016 \tabularnewline
46 &  24 &  23.08 &  0.9239 \tabularnewline
47 &  24 &  23.93 &  0.06588 \tabularnewline
48 &  24 &  24.31 & -0.3075 \tabularnewline
49 &  20.7 &  24.68 & -3.98 \tabularnewline
50 &  20.7 &  22.43 & -1.733 \tabularnewline
51 &  20.7 &  22.46 & -1.758 \tabularnewline
52 &  23.8 &  22.88 &  0.9227 \tabularnewline
53 &  23.8 &  24.97 & -1.172 \tabularnewline
54 &  23.8 &  24.95 & -1.149 \tabularnewline
55 &  27.1 &  24.57 &  2.529 \tabularnewline
56 &  27.1 &  27.07 &  0.02711 \tabularnewline
57 &  27.1 &  26.79 &  0.3069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&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] 19.4[/C][C] 21.07[/C][C]-1.671[/C][/ROW]
[ROW][C]2[/C][C] 19.4[/C][C] 19.27[/C][C] 0.125[/C][/ROW]
[ROW][C]3[/C][C] 19.4[/C][C] 19.04[/C][C] 0.364[/C][/ROW]
[ROW][C]4[/C][C] 15.9[/C][C] 18.98[/C][C]-3.075[/C][/ROW]
[ROW][C]5[/C][C] 15.9[/C][C] 16.19[/C][C]-0.2937[/C][/ROW]
[ROW][C]6[/C][C] 15.9[/C][C] 16.22[/C][C]-0.3197[/C][/ROW]
[ROW][C]7[/C][C] 21.8[/C][C] 17.7[/C][C] 4.099[/C][/ROW]
[ROW][C]8[/C][C] 21.8[/C][C] 22.3[/C][C]-0.5026[/C][/ROW]
[ROW][C]9[/C][C] 21.8[/C][C] 22.13[/C][C]-0.3311[/C][/ROW]
[ROW][C]10[/C][C] 17.6[/C][C] 20.67[/C][C]-3.069[/C][/ROW]
[ROW][C]11[/C][C] 17.6[/C][C] 17.36[/C][C] 0.2429[/C][/ROW]
[ROW][C]12[/C][C] 17.6[/C][C] 17.52[/C][C] 0.08404[/C][/ROW]
[ROW][C]13[/C][C] 19[/C][C] 18.5[/C][C] 0.4975[/C][/ROW]
[ROW][C]14[/C][C] 19[/C][C] 19.56[/C][C]-0.564[/C][/ROW]
[ROW][C]15[/C][C] 19[/C][C] 19.43[/C][C]-0.4259[/C][/ROW]
[ROW][C]16[/C][C] 16.3[/C][C] 19.14[/C][C]-2.84[/C][/ROW]
[ROW][C]17[/C][C] 16.3[/C][C] 17.09[/C][C]-0.7925[/C][/ROW]
[ROW][C]18[/C][C] 16.3[/C][C] 16.98[/C][C]-0.6848[/C][/ROW]
[ROW][C]19[/C][C] 22.5[/C][C] 17.79[/C][C] 4.708[/C][/ROW]
[ROW][C]20[/C][C] 22.5[/C][C] 22.75[/C][C]-0.2485[/C][/ROW]
[ROW][C]21[/C][C] 22.5[/C][C] 22.96[/C][C]-0.4579[/C][/ROW]
[ROW][C]22[/C][C] 23.8[/C][C] 22.46[/C][C] 1.344[/C][/ROW]
[ROW][C]23[/C][C] 23.8[/C][C] 23.95[/C][C]-0.1525[/C][/ROW]
[ROW][C]24[/C][C] 23.8[/C][C] 24.07[/C][C]-0.2706[/C][/ROW]
[ROW][C]25[/C][C] 24.6[/C][C] 23.8[/C][C] 0.7953[/C][/ROW]
[ROW][C]26[/C][C] 24.6[/C][C] 24.16[/C][C] 0.4441[/C][/ROW]
[ROW][C]27[/C][C] 24.6[/C][C] 23.77[/C][C] 0.833[/C][/ROW]
[ROW][C]28[/C][C] 22.7[/C][C] 23.35[/C][C]-0.648[/C][/ROW]
[ROW][C]29[/C][C] 22.7[/C][C] 21.78[/C][C] 0.9202[/C][/ROW]
[ROW][C]30[/C][C] 22.7[/C][C] 21.79[/C][C] 0.9062[/C][/ROW]
[ROW][C]31[/C][C] 25.2[/C][C] 22.82[/C][C] 2.379[/C][/ROW]
[ROW][C]32[/C][C] 25.2[/C][C] 24.72[/C][C] 0.4837[/C][/ROW]
[ROW][C]33[/C][C] 25.2[/C][C] 24.7[/C][C] 0.5022[/C][/ROW]
[ROW][C]34[/C][C] 26.4[/C][C] 24.06[/C][C] 2.341[/C][/ROW]
[ROW][C]35[/C][C] 26.4[/C][C] 24.97[/C][C] 1.431[/C][/ROW]
[ROW][C]36[/C][C] 26.4[/C][C] 25.22[/C][C] 1.185[/C][/ROW]
[ROW][C]37[/C][C] 26[/C][C] 25.35[/C][C] 0.6472[/C][/ROW]
[ROW][C]38[/C][C] 26[/C][C] 25.18[/C][C] 0.8228[/C][/ROW]
[ROW][C]39[/C][C] 26[/C][C] 25.31[/C][C] 0.6922[/C][/ROW]
[ROW][C]40[/C][C] 23.2[/C][C] 25.39[/C][C]-2.19[/C][/ROW]
[ROW][C]41[/C][C] 23.2[/C][C] 23.14[/C][C] 0.06102[/C][/ROW]
[ROW][C]42[/C][C] 23.2[/C][C] 23.03[/C][C] 0.1679[/C][/ROW]
[ROW][C]43[/C][C] 22.7[/C][C] 23.86[/C][C]-1.16[/C][/ROW]
[ROW][C]44[/C][C] 22.7[/C][C] 23.35[/C][C]-0.6532[/C][/ROW]
[ROW][C]45[/C][C] 22.7[/C][C] 23.1[/C][C]-0.4016[/C][/ROW]
[ROW][C]46[/C][C] 24[/C][C] 23.08[/C][C] 0.9239[/C][/ROW]
[ROW][C]47[/C][C] 24[/C][C] 23.93[/C][C] 0.06588[/C][/ROW]
[ROW][C]48[/C][C] 24[/C][C] 24.31[/C][C]-0.3075[/C][/ROW]
[ROW][C]49[/C][C] 20.7[/C][C] 24.68[/C][C]-3.98[/C][/ROW]
[ROW][C]50[/C][C] 20.7[/C][C] 22.43[/C][C]-1.733[/C][/ROW]
[ROW][C]51[/C][C] 20.7[/C][C] 22.46[/C][C]-1.758[/C][/ROW]
[ROW][C]52[/C][C] 23.8[/C][C] 22.88[/C][C] 0.9227[/C][/ROW]
[ROW][C]53[/C][C] 23.8[/C][C] 24.97[/C][C]-1.172[/C][/ROW]
[ROW][C]54[/C][C] 23.8[/C][C] 24.95[/C][C]-1.149[/C][/ROW]
[ROW][C]55[/C][C] 27.1[/C][C] 24.57[/C][C] 2.529[/C][/ROW]
[ROW][C]56[/C][C] 27.1[/C][C] 27.07[/C][C] 0.02711[/C][/ROW]
[ROW][C]57[/C][C] 27.1[/C][C] 26.79[/C][C] 0.3069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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	19.4	21.07	-1.671
2	19.4	19.27	0.125
3	19.4	19.04	0.364
4	15.9	18.98	-3.075
5	15.9	16.19	-0.2937
6	15.9	16.22	-0.3197
7	21.8	17.7	4.099
8	21.8	22.3	-0.5026
9	21.8	22.13	-0.3311
10	17.6	20.67	-3.069
11	17.6	17.36	0.2429
12	17.6	17.52	0.08404
13	19	18.5	0.4975
14	19	19.56	-0.564
15	19	19.43	-0.4259
16	16.3	19.14	-2.84
17	16.3	17.09	-0.7925
18	16.3	16.98	-0.6848
19	22.5	17.79	4.708
20	22.5	22.75	-0.2485
21	22.5	22.96	-0.4579
22	23.8	22.46	1.344
23	23.8	23.95	-0.1525
24	23.8	24.07	-0.2706
25	24.6	23.8	0.7953
26	24.6	24.16	0.4441
27	24.6	23.77	0.833
28	22.7	23.35	-0.648
29	22.7	21.78	0.9202
30	22.7	21.79	0.9062
31	25.2	22.82	2.379
32	25.2	24.72	0.4837
33	25.2	24.7	0.5022
34	26.4	24.06	2.341
35	26.4	24.97	1.431
36	26.4	25.22	1.185
37	26	25.35	0.6472
38	26	25.18	0.8228
39	26	25.31	0.6922
40	23.2	25.39	-2.19
41	23.2	23.14	0.06102
42	23.2	23.03	0.1679
43	22.7	23.86	-1.16
44	22.7	23.35	-0.6532
45	22.7	23.1	-0.4016
46	24	23.08	0.9239
47	24	23.93	0.06588
48	24	24.31	-0.3075
49	20.7	24.68	-3.98
50	20.7	22.43	-1.733
51	20.7	22.46	-1.758
52	23.8	22.88	0.9227
53	23.8	24.97	-1.172
54	23.8	24.95	-1.149
55	27.1	24.57	2.529
56	27.1	27.07	0.02711
57	27.1	26.79	0.3069

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.1192	0.2384	0.8808
9	0.1036	0.2071	0.8964
10	0.06611	0.1322	0.9339
11	0.03682	0.07363	0.9632
12	0.01531	0.03063	0.9847
13	0.01794	0.03588	0.9821
14	0.01351	0.02702	0.9865
15	0.006222	0.01244	0.9938
16	0.07796	0.1559	0.922
17	0.1933	0.3866	0.8067
18	0.2515	0.503	0.7485
19	0.5848	0.8305	0.4152
20	0.5376	0.9247	0.4624
21	0.4946	0.9891	0.5054
22	0.419	0.8381	0.581
23	0.4782	0.9564	0.5218
24	0.468	0.936	0.532
25	0.3941	0.7882	0.6059
26	0.3437	0.6874	0.6563
27	0.3989	0.7978	0.6011
28	0.4502	0.9004	0.5498
29	0.4664	0.9328	0.5336
30	0.4667	0.9333	0.5333
31	0.4656	0.9312	0.5344
32	0.3906	0.7811	0.6094
33	0.3208	0.6415	0.6792
34	0.4154	0.8307	0.5846
35	0.4088	0.8175	0.5912
36	0.3493	0.6985	0.6507
37	0.2792	0.5584	0.7208
38	0.2343	0.4685	0.7657
39	0.2115	0.423	0.7885
40	0.3466	0.6932	0.6534
41	0.2968	0.5937	0.7032
42	0.2392	0.4785	0.7608
43	0.2379	0.4757	0.7621
44	0.1881	0.3762	0.8119
45	0.1316	0.2632	0.8684
46	0.08946	0.1789	0.9105
47	0.05049	0.101	0.9495
48	0.02823	0.05647	0.9718
49	0.162	0.3241	0.838

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
8 &  0.1192 &  0.2384 &  0.8808 \tabularnewline
9 &  0.1036 &  0.2071 &  0.8964 \tabularnewline
10 &  0.06611 &  0.1322 &  0.9339 \tabularnewline
11 &  0.03682 &  0.07363 &  0.9632 \tabularnewline
12 &  0.01531 &  0.03063 &  0.9847 \tabularnewline
13 &  0.01794 &  0.03588 &  0.9821 \tabularnewline
14 &  0.01351 &  0.02702 &  0.9865 \tabularnewline
15 &  0.006222 &  0.01244 &  0.9938 \tabularnewline
16 &  0.07796 &  0.1559 &  0.922 \tabularnewline
17 &  0.1933 &  0.3866 &  0.8067 \tabularnewline
18 &  0.2515 &  0.503 &  0.7485 \tabularnewline
19 &  0.5848 &  0.8305 &  0.4152 \tabularnewline
20 &  0.5376 &  0.9247 &  0.4624 \tabularnewline
21 &  0.4946 &  0.9891 &  0.5054 \tabularnewline
22 &  0.419 &  0.8381 &  0.581 \tabularnewline
23 &  0.4782 &  0.9564 &  0.5218 \tabularnewline
24 &  0.468 &  0.936 &  0.532 \tabularnewline
25 &  0.3941 &  0.7882 &  0.6059 \tabularnewline
26 &  0.3437 &  0.6874 &  0.6563 \tabularnewline
27 &  0.3989 &  0.7978 &  0.6011 \tabularnewline
28 &  0.4502 &  0.9004 &  0.5498 \tabularnewline
29 &  0.4664 &  0.9328 &  0.5336 \tabularnewline
30 &  0.4667 &  0.9333 &  0.5333 \tabularnewline
31 &  0.4656 &  0.9312 &  0.5344 \tabularnewline
32 &  0.3906 &  0.7811 &  0.6094 \tabularnewline
33 &  0.3208 &  0.6415 &  0.6792 \tabularnewline
34 &  0.4154 &  0.8307 &  0.5846 \tabularnewline
35 &  0.4088 &  0.8175 &  0.5912 \tabularnewline
36 &  0.3493 &  0.6985 &  0.6507 \tabularnewline
37 &  0.2792 &  0.5584 &  0.7208 \tabularnewline
38 &  0.2343 &  0.4685 &  0.7657 \tabularnewline
39 &  0.2115 &  0.423 &  0.7885 \tabularnewline
40 &  0.3466 &  0.6932 &  0.6534 \tabularnewline
41 &  0.2968 &  0.5937 &  0.7032 \tabularnewline
42 &  0.2392 &  0.4785 &  0.7608 \tabularnewline
43 &  0.2379 &  0.4757 &  0.7621 \tabularnewline
44 &  0.1881 &  0.3762 &  0.8119 \tabularnewline
45 &  0.1316 &  0.2632 &  0.8684 \tabularnewline
46 &  0.08946 &  0.1789 &  0.9105 \tabularnewline
47 &  0.05049 &  0.101 &  0.9495 \tabularnewline
48 &  0.02823 &  0.05647 &  0.9718 \tabularnewline
49 &  0.162 &  0.3241 &  0.838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&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]8[/C][C] 0.1192[/C][C] 0.2384[/C][C] 0.8808[/C][/ROW]
[ROW][C]9[/C][C] 0.1036[/C][C] 0.2071[/C][C] 0.8964[/C][/ROW]
[ROW][C]10[/C][C] 0.06611[/C][C] 0.1322[/C][C] 0.9339[/C][/ROW]
[ROW][C]11[/C][C] 0.03682[/C][C] 0.07363[/C][C] 0.9632[/C][/ROW]
[ROW][C]12[/C][C] 0.01531[/C][C] 0.03063[/C][C] 0.9847[/C][/ROW]
[ROW][C]13[/C][C] 0.01794[/C][C] 0.03588[/C][C] 0.9821[/C][/ROW]
[ROW][C]14[/C][C] 0.01351[/C][C] 0.02702[/C][C] 0.9865[/C][/ROW]
[ROW][C]15[/C][C] 0.006222[/C][C] 0.01244[/C][C] 0.9938[/C][/ROW]
[ROW][C]16[/C][C] 0.07796[/C][C] 0.1559[/C][C] 0.922[/C][/ROW]
[ROW][C]17[/C][C] 0.1933[/C][C] 0.3866[/C][C] 0.8067[/C][/ROW]
[ROW][C]18[/C][C] 0.2515[/C][C] 0.503[/C][C] 0.7485[/C][/ROW]
[ROW][C]19[/C][C] 0.5848[/C][C] 0.8305[/C][C] 0.4152[/C][/ROW]
[ROW][C]20[/C][C] 0.5376[/C][C] 0.9247[/C][C] 0.4624[/C][/ROW]
[ROW][C]21[/C][C] 0.4946[/C][C] 0.9891[/C][C] 0.5054[/C][/ROW]
[ROW][C]22[/C][C] 0.419[/C][C] 0.8381[/C][C] 0.581[/C][/ROW]
[ROW][C]23[/C][C] 0.4782[/C][C] 0.9564[/C][C] 0.5218[/C][/ROW]
[ROW][C]24[/C][C] 0.468[/C][C] 0.936[/C][C] 0.532[/C][/ROW]
[ROW][C]25[/C][C] 0.3941[/C][C] 0.7882[/C][C] 0.6059[/C][/ROW]
[ROW][C]26[/C][C] 0.3437[/C][C] 0.6874[/C][C] 0.6563[/C][/ROW]
[ROW][C]27[/C][C] 0.3989[/C][C] 0.7978[/C][C] 0.6011[/C][/ROW]
[ROW][C]28[/C][C] 0.4502[/C][C] 0.9004[/C][C] 0.5498[/C][/ROW]
[ROW][C]29[/C][C] 0.4664[/C][C] 0.9328[/C][C] 0.5336[/C][/ROW]
[ROW][C]30[/C][C] 0.4667[/C][C] 0.9333[/C][C] 0.5333[/C][/ROW]
[ROW][C]31[/C][C] 0.4656[/C][C] 0.9312[/C][C] 0.5344[/C][/ROW]
[ROW][C]32[/C][C] 0.3906[/C][C] 0.7811[/C][C] 0.6094[/C][/ROW]
[ROW][C]33[/C][C] 0.3208[/C][C] 0.6415[/C][C] 0.6792[/C][/ROW]
[ROW][C]34[/C][C] 0.4154[/C][C] 0.8307[/C][C] 0.5846[/C][/ROW]
[ROW][C]35[/C][C] 0.4088[/C][C] 0.8175[/C][C] 0.5912[/C][/ROW]
[ROW][C]36[/C][C] 0.3493[/C][C] 0.6985[/C][C] 0.6507[/C][/ROW]
[ROW][C]37[/C][C] 0.2792[/C][C] 0.5584[/C][C] 0.7208[/C][/ROW]
[ROW][C]38[/C][C] 0.2343[/C][C] 0.4685[/C][C] 0.7657[/C][/ROW]
[ROW][C]39[/C][C] 0.2115[/C][C] 0.423[/C][C] 0.7885[/C][/ROW]
[ROW][C]40[/C][C] 0.3466[/C][C] 0.6932[/C][C] 0.6534[/C][/ROW]
[ROW][C]41[/C][C] 0.2968[/C][C] 0.5937[/C][C] 0.7032[/C][/ROW]
[ROW][C]42[/C][C] 0.2392[/C][C] 0.4785[/C][C] 0.7608[/C][/ROW]
[ROW][C]43[/C][C] 0.2379[/C][C] 0.4757[/C][C] 0.7621[/C][/ROW]
[ROW][C]44[/C][C] 0.1881[/C][C] 0.3762[/C][C] 0.8119[/C][/ROW]
[ROW][C]45[/C][C] 0.1316[/C][C] 0.2632[/C][C] 0.8684[/C][/ROW]
[ROW][C]46[/C][C] 0.08946[/C][C] 0.1789[/C][C] 0.9105[/C][/ROW]
[ROW][C]47[/C][C] 0.05049[/C][C] 0.101[/C][C] 0.9495[/C][/ROW]
[ROW][C]48[/C][C] 0.02823[/C][C] 0.05647[/C][C] 0.9718[/C][/ROW]
[ROW][C]49[/C][C] 0.162[/C][C] 0.3241[/C][C] 0.838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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
8	0.1192	0.2384	0.8808
9	0.1036	0.2071	0.8964
10	0.06611	0.1322	0.9339
11	0.03682	0.07363	0.9632
12	0.01531	0.03063	0.9847
13	0.01794	0.03588	0.9821
14	0.01351	0.02702	0.9865
15	0.006222	0.01244	0.9938
16	0.07796	0.1559	0.922
17	0.1933	0.3866	0.8067
18	0.2515	0.503	0.7485
19	0.5848	0.8305	0.4152
20	0.5376	0.9247	0.4624
21	0.4946	0.9891	0.5054
22	0.419	0.8381	0.581
23	0.4782	0.9564	0.5218
24	0.468	0.936	0.532
25	0.3941	0.7882	0.6059
26	0.3437	0.6874	0.6563
27	0.3989	0.7978	0.6011
28	0.4502	0.9004	0.5498
29	0.4664	0.9328	0.5336
30	0.4667	0.9333	0.5333
31	0.4656	0.9312	0.5344
32	0.3906	0.7811	0.6094
33	0.3208	0.6415	0.6792
34	0.4154	0.8307	0.5846
35	0.4088	0.8175	0.5912
36	0.3493	0.6985	0.6507
37	0.2792	0.5584	0.7208
38	0.2343	0.4685	0.7657
39	0.2115	0.423	0.7885
40	0.3466	0.6932	0.6534
41	0.2968	0.5937	0.7032
42	0.2392	0.4785	0.7608
43	0.2379	0.4757	0.7621
44	0.1881	0.3762	0.8119
45	0.1316	0.2632	0.8684
46	0.08946	0.1789	0.9105
47	0.05049	0.101	0.9495
48	0.02823	0.05647	0.9718
49	0.162	0.3241	0.838

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	4	0.0952381	NOK
10% type I error level	6	0.142857	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 & 4 & 0.0952381 & NOK \tabularnewline
10% type I error level & 6 & 0.142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285049&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]4[/C][C]0.0952381[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]6[/C][C]0.142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285049&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285049&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	4	0.0952381	NOK
10% type I error level	6	0.142857	NOK

Figure 1

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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 ; par4 = 3 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 3 ; par5 = ;

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

par5 <- ''
par4 <- ''
par3 <- 'No Linear Trend'
par2 <- 'Do not include Seasonal Dummies'
par1 <- '1'
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
x <- na.omit(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(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
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+par4,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1+par4,])
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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, mywarning)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
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,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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