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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 14 Dec 2015 18:03:45 +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/14/t14501162882001fxpidc5rugs.htm/, Retrieved Thu, 16 May 2024 06:18:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286365, Retrieved Thu, 16 May 2024 06:18:45 +0000

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

-       [Multiple Regression] [Multiple regressi...] [2015-12-14 18:03:45] [2ea4f5baf6c33ea976d37beb530b55ab] [Current]

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7.1
6.8
6.5
6.1
5.7
5.6
5.7
5.8
5.9
6.3
6.5
6.3
6.4
6.3
6.3
6.2
6.2
6.2
6.4
6.5
6.5
6.7
6.7
6.3
6.2
6.3
6.5
6.9
7
7
6.9
6.7
6.7
7.1
7.1
6.9
7
6.9
6.9
6.8
6.5
6.2
5.9
5.8
6.1
7
7.4
7.3
7.2
7.1
7.1
7.1
7.1
6.9
6.6
6.4
6.5
6.9
6.9
6.7

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=286365&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=286365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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
V_25[t] = + 6.2125 + 0.228958M1[t] + 0.115417M2[t] + 0.081875M3[t] + 0.0283333M4[t] -0.105208M5[t] -0.23875M6[t] -0.332292M7[t] -0.405833M8[t] -0.319375M9[t] + 0.127083M10[t] + 0.233542M11[t] + 0.0135417t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
V_25[t] =  +  6.2125 +  0.228958M1[t] +  0.115417M2[t] +  0.081875M3[t] +  0.0283333M4[t] -0.105208M5[t] -0.23875M6[t] -0.332292M7[t] -0.405833M8[t] -0.319375M9[t] +  0.127083M10[t] +  0.233542M11[t] +  0.0135417t  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286365&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]V_25[t] =  +  6.2125 +  0.228958M1[t] +  0.115417M2[t] +  0.081875M3[t] +  0.0283333M4[t] -0.105208M5[t] -0.23875M6[t] -0.332292M7[t] -0.405833M8[t] -0.319375M9[t] +  0.127083M10[t] +  0.233542M11[t] +  0.0135417t  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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
V_25[t] = + 6.2125 + 0.228958M1[t] + 0.115417M2[t] + 0.081875M3[t] + 0.0283333M4[t] -0.105208M5[t] -0.23875M6[t] -0.332292M7[t] -0.405833M8[t] -0.319375M9[t] + 0.127083M10[t] + 0.233542M11[t] + 0.0135417t + 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)	+6.213	0.1837	+3.3820e+01	1.215e-34	6.074e-35
M1	+0.229	0.2235	+1.0250e+00	0.3108	0.1554
M2	+0.1154	0.2231	+5.1720e-01	0.6074	0.3037
M3	+0.08188	0.2228	+3.6740e-01	0.715	0.3575
M4	+0.02833	0.2226	+1.2730e-01	0.8992	0.4496
M5	-0.1052	0.2223	-4.7320e-01	0.6383	0.3191
M6	-0.2387	0.2221	-1.0750e+00	0.2879	0.144
M7	-0.3323	0.222	-1.4970e+00	0.141	0.07052
M8	-0.4058	0.2218	-1.8300e+00	0.07364	0.03682
M9	-0.3194	0.2217	-1.4410e+00	0.1563	0.07816
M10	+0.1271	0.2216	+5.7350e-01	0.5691	0.2845
M11	+0.2335	0.2216	+1.0540e+00	0.2972	0.1486
t	+0.01354	0.002665	+5.0820e+00	6.378e-06	3.189e-06

\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) & +6.213 &  0.1837 & +3.3820e+01 &  1.215e-34 &  6.074e-35 \tabularnewline
M1 & +0.229 &  0.2235 & +1.0250e+00 &  0.3108 &  0.1554 \tabularnewline
M2 & +0.1154 &  0.2231 & +5.1720e-01 &  0.6074 &  0.3037 \tabularnewline
M3 & +0.08188 &  0.2228 & +3.6740e-01 &  0.715 &  0.3575 \tabularnewline
M4 & +0.02833 &  0.2226 & +1.2730e-01 &  0.8992 &  0.4496 \tabularnewline
M5 & -0.1052 &  0.2223 & -4.7320e-01 &  0.6383 &  0.3191 \tabularnewline
M6 & -0.2387 &  0.2221 & -1.0750e+00 &  0.2879 &  0.144 \tabularnewline
M7 & -0.3323 &  0.222 & -1.4970e+00 &  0.141 &  0.07052 \tabularnewline
M8 & -0.4058 &  0.2218 & -1.8300e+00 &  0.07364 &  0.03682 \tabularnewline
M9 & -0.3194 &  0.2217 & -1.4410e+00 &  0.1563 &  0.07816 \tabularnewline
M10 & +0.1271 &  0.2216 & +5.7350e-01 &  0.5691 &  0.2845 \tabularnewline
M11 & +0.2335 &  0.2216 & +1.0540e+00 &  0.2972 &  0.1486 \tabularnewline
t & +0.01354 &  0.002665 & +5.0820e+00 &  6.378e-06 &  3.189e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286365&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]+6.213[/C][C] 0.1837[/C][C]+3.3820e+01[/C][C] 1.215e-34[/C][C] 6.074e-35[/C][/ROW]
[ROW][C]M1[/C][C]+0.229[/C][C] 0.2235[/C][C]+1.0250e+00[/C][C] 0.3108[/C][C] 0.1554[/C][/ROW]
[ROW][C]M2[/C][C]+0.1154[/C][C] 0.2231[/C][C]+5.1720e-01[/C][C] 0.6074[/C][C] 0.3037[/C][/ROW]
[ROW][C]M3[/C][C]+0.08188[/C][C] 0.2228[/C][C]+3.6740e-01[/C][C] 0.715[/C][C] 0.3575[/C][/ROW]
[ROW][C]M4[/C][C]+0.02833[/C][C] 0.2226[/C][C]+1.2730e-01[/C][C] 0.8992[/C][C] 0.4496[/C][/ROW]
[ROW][C]M5[/C][C]-0.1052[/C][C] 0.2223[/C][C]-4.7320e-01[/C][C] 0.6383[/C][C] 0.3191[/C][/ROW]
[ROW][C]M6[/C][C]-0.2387[/C][C] 0.2221[/C][C]-1.0750e+00[/C][C] 0.2879[/C][C] 0.144[/C][/ROW]
[ROW][C]M7[/C][C]-0.3323[/C][C] 0.222[/C][C]-1.4970e+00[/C][C] 0.141[/C][C] 0.07052[/C][/ROW]
[ROW][C]M8[/C][C]-0.4058[/C][C] 0.2218[/C][C]-1.8300e+00[/C][C] 0.07364[/C][C] 0.03682[/C][/ROW]
[ROW][C]M9[/C][C]-0.3194[/C][C] 0.2217[/C][C]-1.4410e+00[/C][C] 0.1563[/C][C] 0.07816[/C][/ROW]
[ROW][C]M10[/C][C]+0.1271[/C][C] 0.2216[/C][C]+5.7350e-01[/C][C] 0.5691[/C][C] 0.2845[/C][/ROW]
[ROW][C]M11[/C][C]+0.2335[/C][C] 0.2216[/C][C]+1.0540e+00[/C][C] 0.2972[/C][C] 0.1486[/C][/ROW]
[ROW][C]t[/C][C]+0.01354[/C][C] 0.002665[/C][C]+5.0820e+00[/C][C] 6.378e-06[/C][C] 3.189e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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)	+6.213	0.1837	+3.3820e+01	1.215e-34	6.074e-35
M1	+0.229	0.2235	+1.0250e+00	0.3108	0.1554
M2	+0.1154	0.2231	+5.1720e-01	0.6074	0.3037
M3	+0.08188	0.2228	+3.6740e-01	0.715	0.3575
M4	+0.02833	0.2226	+1.2730e-01	0.8992	0.4496
M5	-0.1052	0.2223	-4.7320e-01	0.6383	0.3191
M6	-0.2387	0.2221	-1.0750e+00	0.2879	0.144
M7	-0.3323	0.222	-1.4970e+00	0.141	0.07052
M8	-0.4058	0.2218	-1.8300e+00	0.07364	0.03682
M9	-0.3194	0.2217	-1.4410e+00	0.1563	0.07816
M10	+0.1271	0.2216	+5.7350e-01	0.5691	0.2845
M11	+0.2335	0.2216	+1.0540e+00	0.2972	0.1486
t	+0.01354	0.002665	+5.0820e+00	6.378e-06	3.189e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.7093
R-squared	0.5031
Adjusted R-squared	0.3763
F-TEST (value)	3.966
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	0.0003134
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.3503
Sum Squared Residuals	5.767

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.7093 \tabularnewline
R-squared &  0.5031 \tabularnewline
Adjusted R-squared &  0.3763 \tabularnewline
F-TEST (value) &  3.966 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value &  0.0003134 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  0.3503 \tabularnewline
Sum Squared Residuals &  5.767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286365&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.7093[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.5031[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.3763[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 3.966[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C] 0.0003134[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 0.3503[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 5.767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286365&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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	0.7093
R-squared	0.5031
Adjusted R-squared	0.3763
F-TEST (value)	3.966
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	0.0003134
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.3503
Sum Squared Residuals	5.767

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.1	6.455	0.645
2	6.8	6.355	0.445
3	6.5	6.335	0.165
4	6.1	6.295	-0.195
5	5.7	6.175	-0.475
6	5.6	6.055	-0.455
7	5.7	5.975	-0.275
8	5.8	5.915	-0.115
9	5.9	6.015	-0.115
10	6.3	6.475	-0.175
11	6.5	6.595	-0.095
12	6.3	6.375	-0.075
13	6.4	6.617	-0.2175
14	6.3	6.518	-0.2175
15	6.3	6.497	-0.1975
16	6.2	6.457	-0.2575
17	6.2	6.338	-0.1375
18	6.2	6.218	-0.0175
19	6.4	6.138	0.2625
20	6.5	6.077	0.4225
21	6.5	6.178	0.3225
22	6.7	6.638	0.0625
23	6.7	6.758	-0.0575
24	6.3	6.537	-0.2375
25	6.2	6.78	-0.58
26	6.3	6.68	-0.38
27	6.5	6.66	-0.16
28	6.9	6.62	0.28
29	7	6.5	0.5
30	7	6.38	0.62
31	6.9	6.3	0.6
32	6.7	6.24	0.46
33	6.7	6.34	0.36
34	7.1	6.8	0.3
35	7.1	6.92	0.18
36	6.9	6.7	0.2
37	7	6.942	0.0575
38	6.9	6.843	0.0575
39	6.9	6.822	0.0775
40	6.8	6.782	0.0175
41	6.5	6.662	-0.1625
42	6.2	6.543	-0.3425
43	5.9	6.463	-0.5625
44	5.8	6.402	-0.6025
45	6.1	6.503	-0.4025
46	7	6.963	0.0375
47	7.4	7.082	0.3175
48	7.3	6.862	0.4375
49	7.2	7.105	0.095
50	7.1	7.005	0.095
51	7.1	6.985	0.115
52	7.1	6.945	0.155
53	7.1	6.825	0.275
54	6.9	6.705	0.195
55	6.6	6.625	-0.025
56	6.4	6.565	-0.165
57	6.5	6.665	-0.165
58	6.9	7.125	-0.225
59	6.9	7.245	-0.345
60	6.7	7.025	-0.325

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  7.1 &  6.455 &  0.645 \tabularnewline
2 &  6.8 &  6.355 &  0.445 \tabularnewline
3 &  6.5 &  6.335 &  0.165 \tabularnewline
4 &  6.1 &  6.295 & -0.195 \tabularnewline
5 &  5.7 &  6.175 & -0.475 \tabularnewline
6 &  5.6 &  6.055 & -0.455 \tabularnewline
7 &  5.7 &  5.975 & -0.275 \tabularnewline
8 &  5.8 &  5.915 & -0.115 \tabularnewline
9 &  5.9 &  6.015 & -0.115 \tabularnewline
10 &  6.3 &  6.475 & -0.175 \tabularnewline
11 &  6.5 &  6.595 & -0.095 \tabularnewline
12 &  6.3 &  6.375 & -0.075 \tabularnewline
13 &  6.4 &  6.617 & -0.2175 \tabularnewline
14 &  6.3 &  6.518 & -0.2175 \tabularnewline
15 &  6.3 &  6.497 & -0.1975 \tabularnewline
16 &  6.2 &  6.457 & -0.2575 \tabularnewline
17 &  6.2 &  6.338 & -0.1375 \tabularnewline
18 &  6.2 &  6.218 & -0.0175 \tabularnewline
19 &  6.4 &  6.138 &  0.2625 \tabularnewline
20 &  6.5 &  6.077 &  0.4225 \tabularnewline
21 &  6.5 &  6.178 &  0.3225 \tabularnewline
22 &  6.7 &  6.638 &  0.0625 \tabularnewline
23 &  6.7 &  6.758 & -0.0575 \tabularnewline
24 &  6.3 &  6.537 & -0.2375 \tabularnewline
25 &  6.2 &  6.78 & -0.58 \tabularnewline
26 &  6.3 &  6.68 & -0.38 \tabularnewline
27 &  6.5 &  6.66 & -0.16 \tabularnewline
28 &  6.9 &  6.62 &  0.28 \tabularnewline
29 &  7 &  6.5 &  0.5 \tabularnewline
30 &  7 &  6.38 &  0.62 \tabularnewline
31 &  6.9 &  6.3 &  0.6 \tabularnewline
32 &  6.7 &  6.24 &  0.46 \tabularnewline
33 &  6.7 &  6.34 &  0.36 \tabularnewline
34 &  7.1 &  6.8 &  0.3 \tabularnewline
35 &  7.1 &  6.92 &  0.18 \tabularnewline
36 &  6.9 &  6.7 &  0.2 \tabularnewline
37 &  7 &  6.942 &  0.0575 \tabularnewline
38 &  6.9 &  6.843 &  0.0575 \tabularnewline
39 &  6.9 &  6.822 &  0.0775 \tabularnewline
40 &  6.8 &  6.782 &  0.0175 \tabularnewline
41 &  6.5 &  6.662 & -0.1625 \tabularnewline
42 &  6.2 &  6.543 & -0.3425 \tabularnewline
43 &  5.9 &  6.463 & -0.5625 \tabularnewline
44 &  5.8 &  6.402 & -0.6025 \tabularnewline
45 &  6.1 &  6.503 & -0.4025 \tabularnewline
46 &  7 &  6.963 &  0.0375 \tabularnewline
47 &  7.4 &  7.082 &  0.3175 \tabularnewline
48 &  7.3 &  6.862 &  0.4375 \tabularnewline
49 &  7.2 &  7.105 &  0.095 \tabularnewline
50 &  7.1 &  7.005 &  0.095 \tabularnewline
51 &  7.1 &  6.985 &  0.115 \tabularnewline
52 &  7.1 &  6.945 &  0.155 \tabularnewline
53 &  7.1 &  6.825 &  0.275 \tabularnewline
54 &  6.9 &  6.705 &  0.195 \tabularnewline
55 &  6.6 &  6.625 & -0.025 \tabularnewline
56 &  6.4 &  6.565 & -0.165 \tabularnewline
57 &  6.5 &  6.665 & -0.165 \tabularnewline
58 &  6.9 &  7.125 & -0.225 \tabularnewline
59 &  6.9 &  7.245 & -0.345 \tabularnewline
60 &  6.7 &  7.025 & -0.325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286365&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] 7.1[/C][C] 6.455[/C][C] 0.645[/C][/ROW]
[ROW][C]2[/C][C] 6.8[/C][C] 6.355[/C][C] 0.445[/C][/ROW]
[ROW][C]3[/C][C] 6.5[/C][C] 6.335[/C][C] 0.165[/C][/ROW]
[ROW][C]4[/C][C] 6.1[/C][C] 6.295[/C][C]-0.195[/C][/ROW]
[ROW][C]5[/C][C] 5.7[/C][C] 6.175[/C][C]-0.475[/C][/ROW]
[ROW][C]6[/C][C] 5.6[/C][C] 6.055[/C][C]-0.455[/C][/ROW]
[ROW][C]7[/C][C] 5.7[/C][C] 5.975[/C][C]-0.275[/C][/ROW]
[ROW][C]8[/C][C] 5.8[/C][C] 5.915[/C][C]-0.115[/C][/ROW]
[ROW][C]9[/C][C] 5.9[/C][C] 6.015[/C][C]-0.115[/C][/ROW]
[ROW][C]10[/C][C] 6.3[/C][C] 6.475[/C][C]-0.175[/C][/ROW]
[ROW][C]11[/C][C] 6.5[/C][C] 6.595[/C][C]-0.095[/C][/ROW]
[ROW][C]12[/C][C] 6.3[/C][C] 6.375[/C][C]-0.075[/C][/ROW]
[ROW][C]13[/C][C] 6.4[/C][C] 6.617[/C][C]-0.2175[/C][/ROW]
[ROW][C]14[/C][C] 6.3[/C][C] 6.518[/C][C]-0.2175[/C][/ROW]
[ROW][C]15[/C][C] 6.3[/C][C] 6.497[/C][C]-0.1975[/C][/ROW]
[ROW][C]16[/C][C] 6.2[/C][C] 6.457[/C][C]-0.2575[/C][/ROW]
[ROW][C]17[/C][C] 6.2[/C][C] 6.338[/C][C]-0.1375[/C][/ROW]
[ROW][C]18[/C][C] 6.2[/C][C] 6.218[/C][C]-0.0175[/C][/ROW]
[ROW][C]19[/C][C] 6.4[/C][C] 6.138[/C][C] 0.2625[/C][/ROW]
[ROW][C]20[/C][C] 6.5[/C][C] 6.077[/C][C] 0.4225[/C][/ROW]
[ROW][C]21[/C][C] 6.5[/C][C] 6.178[/C][C] 0.3225[/C][/ROW]
[ROW][C]22[/C][C] 6.7[/C][C] 6.638[/C][C] 0.0625[/C][/ROW]
[ROW][C]23[/C][C] 6.7[/C][C] 6.758[/C][C]-0.0575[/C][/ROW]
[ROW][C]24[/C][C] 6.3[/C][C] 6.537[/C][C]-0.2375[/C][/ROW]
[ROW][C]25[/C][C] 6.2[/C][C] 6.78[/C][C]-0.58[/C][/ROW]
[ROW][C]26[/C][C] 6.3[/C][C] 6.68[/C][C]-0.38[/C][/ROW]
[ROW][C]27[/C][C] 6.5[/C][C] 6.66[/C][C]-0.16[/C][/ROW]
[ROW][C]28[/C][C] 6.9[/C][C] 6.62[/C][C] 0.28[/C][/ROW]
[ROW][C]29[/C][C] 7[/C][C] 6.5[/C][C] 0.5[/C][/ROW]
[ROW][C]30[/C][C] 7[/C][C] 6.38[/C][C] 0.62[/C][/ROW]
[ROW][C]31[/C][C] 6.9[/C][C] 6.3[/C][C] 0.6[/C][/ROW]
[ROW][C]32[/C][C] 6.7[/C][C] 6.24[/C][C] 0.46[/C][/ROW]
[ROW][C]33[/C][C] 6.7[/C][C] 6.34[/C][C] 0.36[/C][/ROW]
[ROW][C]34[/C][C] 7.1[/C][C] 6.8[/C][C] 0.3[/C][/ROW]
[ROW][C]35[/C][C] 7.1[/C][C] 6.92[/C][C] 0.18[/C][/ROW]
[ROW][C]36[/C][C] 6.9[/C][C] 6.7[/C][C] 0.2[/C][/ROW]
[ROW][C]37[/C][C] 7[/C][C] 6.942[/C][C] 0.0575[/C][/ROW]
[ROW][C]38[/C][C] 6.9[/C][C] 6.843[/C][C] 0.0575[/C][/ROW]
[ROW][C]39[/C][C] 6.9[/C][C] 6.822[/C][C] 0.0775[/C][/ROW]
[ROW][C]40[/C][C] 6.8[/C][C] 6.782[/C][C] 0.0175[/C][/ROW]
[ROW][C]41[/C][C] 6.5[/C][C] 6.662[/C][C]-0.1625[/C][/ROW]
[ROW][C]42[/C][C] 6.2[/C][C] 6.543[/C][C]-0.3425[/C][/ROW]
[ROW][C]43[/C][C] 5.9[/C][C] 6.463[/C][C]-0.5625[/C][/ROW]
[ROW][C]44[/C][C] 5.8[/C][C] 6.402[/C][C]-0.6025[/C][/ROW]
[ROW][C]45[/C][C] 6.1[/C][C] 6.503[/C][C]-0.4025[/C][/ROW]
[ROW][C]46[/C][C] 7[/C][C] 6.963[/C][C] 0.0375[/C][/ROW]
[ROW][C]47[/C][C] 7.4[/C][C] 7.082[/C][C] 0.3175[/C][/ROW]
[ROW][C]48[/C][C] 7.3[/C][C] 6.862[/C][C] 0.4375[/C][/ROW]
[ROW][C]49[/C][C] 7.2[/C][C] 7.105[/C][C] 0.095[/C][/ROW]
[ROW][C]50[/C][C] 7.1[/C][C] 7.005[/C][C] 0.095[/C][/ROW]
[ROW][C]51[/C][C] 7.1[/C][C] 6.985[/C][C] 0.115[/C][/ROW]
[ROW][C]52[/C][C] 7.1[/C][C] 6.945[/C][C] 0.155[/C][/ROW]
[ROW][C]53[/C][C] 7.1[/C][C] 6.825[/C][C] 0.275[/C][/ROW]
[ROW][C]54[/C][C] 6.9[/C][C] 6.705[/C][C] 0.195[/C][/ROW]
[ROW][C]55[/C][C] 6.6[/C][C] 6.625[/C][C]-0.025[/C][/ROW]
[ROW][C]56[/C][C] 6.4[/C][C] 6.565[/C][C]-0.165[/C][/ROW]
[ROW][C]57[/C][C] 6.5[/C][C] 6.665[/C][C]-0.165[/C][/ROW]
[ROW][C]58[/C][C] 6.9[/C][C] 7.125[/C][C]-0.225[/C][/ROW]
[ROW][C]59[/C][C] 6.9[/C][C] 7.245[/C][C]-0.345[/C][/ROW]
[ROW][C]60[/C][C] 6.7[/C][C] 7.025[/C][C]-0.325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286365&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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	7.1	6.455	0.645
2	6.8	6.355	0.445
3	6.5	6.335	0.165
4	6.1	6.295	-0.195
5	5.7	6.175	-0.475
6	5.6	6.055	-0.455
7	5.7	5.975	-0.275
8	5.8	5.915	-0.115
9	5.9	6.015	-0.115
10	6.3	6.475	-0.175
11	6.5	6.595	-0.095
12	6.3	6.375	-0.075
13	6.4	6.617	-0.2175
14	6.3	6.518	-0.2175
15	6.3	6.497	-0.1975
16	6.2	6.457	-0.2575
17	6.2	6.338	-0.1375
18	6.2	6.218	-0.0175
19	6.4	6.138	0.2625
20	6.5	6.077	0.4225
21	6.5	6.178	0.3225
22	6.7	6.638	0.0625
23	6.7	6.758	-0.0575
24	6.3	6.537	-0.2375
25	6.2	6.78	-0.58
26	6.3	6.68	-0.38
27	6.5	6.66	-0.16
28	6.9	6.62	0.28
29	7	6.5	0.5
30	7	6.38	0.62
31	6.9	6.3	0.6
32	6.7	6.24	0.46
33	6.7	6.34	0.36
34	7.1	6.8	0.3
35	7.1	6.92	0.18
36	6.9	6.7	0.2
37	7	6.942	0.0575
38	6.9	6.843	0.0575
39	6.9	6.822	0.0775
40	6.8	6.782	0.0175
41	6.5	6.662	-0.1625
42	6.2	6.543	-0.3425
43	5.9	6.463	-0.5625
44	5.8	6.402	-0.6025
45	6.1	6.503	-0.4025
46	7	6.963	0.0375
47	7.4	7.082	0.3175
48	7.3	6.862	0.4375
49	7.2	7.105	0.095
50	7.1	7.005	0.095
51	7.1	6.985	0.115
52	7.1	6.945	0.155
53	7.1	6.825	0.275
54	6.9	6.705	0.195
55	6.6	6.625	-0.025
56	6.4	6.565	-0.165
57	6.5	6.665	-0.165
58	6.9	7.125	-0.225
59	6.9	7.245	-0.345
60	6.7	7.025	-0.325

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.3128	0.6256	0.6872
17	0.5445	0.911	0.4555
18	0.6361	0.7279	0.3639
19	0.6733	0.6534	0.3267
20	0.6781	0.6438	0.3219
21	0.6268	0.7465	0.3732
22	0.526	0.948	0.474
23	0.425	0.85	0.575
24	0.3787	0.7573	0.6213
25	0.6054	0.7891	0.3946
26	0.6443	0.7114	0.3557
27	0.6175	0.7651	0.3825
28	0.6387	0.7226	0.3613
29	0.7103	0.5794	0.2897
30	0.7699	0.4603	0.2301
31	0.8171	0.3658	0.1829
32	0.8533	0.2933	0.1467
33	0.8649	0.2703	0.1351
34	0.8426	0.3147	0.1574
35	0.7872	0.4255	0.2128
36	0.7223	0.5554	0.2777
37	0.6267	0.7466	0.3733
38	0.5192	0.9615	0.4808
39	0.4058	0.8116	0.5942
40	0.2994	0.5988	0.7006
41	0.2535	0.5071	0.7465
42	0.2767	0.5534	0.7233
43	0.3943	0.7886	0.6057
44	0.5643	0.8715	0.4357

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 &  0.3128 &  0.6256 &  0.6872 \tabularnewline
17 &  0.5445 &  0.911 &  0.4555 \tabularnewline
18 &  0.6361 &  0.7279 &  0.3639 \tabularnewline
19 &  0.6733 &  0.6534 &  0.3267 \tabularnewline
20 &  0.6781 &  0.6438 &  0.3219 \tabularnewline
21 &  0.6268 &  0.7465 &  0.3732 \tabularnewline
22 &  0.526 &  0.948 &  0.474 \tabularnewline
23 &  0.425 &  0.85 &  0.575 \tabularnewline
24 &  0.3787 &  0.7573 &  0.6213 \tabularnewline
25 &  0.6054 &  0.7891 &  0.3946 \tabularnewline
26 &  0.6443 &  0.7114 &  0.3557 \tabularnewline
27 &  0.6175 &  0.7651 &  0.3825 \tabularnewline
28 &  0.6387 &  0.7226 &  0.3613 \tabularnewline
29 &  0.7103 &  0.5794 &  0.2897 \tabularnewline
30 &  0.7699 &  0.4603 &  0.2301 \tabularnewline
31 &  0.8171 &  0.3658 &  0.1829 \tabularnewline
32 &  0.8533 &  0.2933 &  0.1467 \tabularnewline
33 &  0.8649 &  0.2703 &  0.1351 \tabularnewline
34 &  0.8426 &  0.3147 &  0.1574 \tabularnewline
35 &  0.7872 &  0.4255 &  0.2128 \tabularnewline
36 &  0.7223 &  0.5554 &  0.2777 \tabularnewline
37 &  0.6267 &  0.7466 &  0.3733 \tabularnewline
38 &  0.5192 &  0.9615 &  0.4808 \tabularnewline
39 &  0.4058 &  0.8116 &  0.5942 \tabularnewline
40 &  0.2994 &  0.5988 &  0.7006 \tabularnewline
41 &  0.2535 &  0.5071 &  0.7465 \tabularnewline
42 &  0.2767 &  0.5534 &  0.7233 \tabularnewline
43 &  0.3943 &  0.7886 &  0.6057 \tabularnewline
44 &  0.5643 &  0.8715 &  0.4357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286365&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]16[/C][C] 0.3128[/C][C] 0.6256[/C][C] 0.6872[/C][/ROW]
[ROW][C]17[/C][C] 0.5445[/C][C] 0.911[/C][C] 0.4555[/C][/ROW]
[ROW][C]18[/C][C] 0.6361[/C][C] 0.7279[/C][C] 0.3639[/C][/ROW]
[ROW][C]19[/C][C] 0.6733[/C][C] 0.6534[/C][C] 0.3267[/C][/ROW]
[ROW][C]20[/C][C] 0.6781[/C][C] 0.6438[/C][C] 0.3219[/C][/ROW]
[ROW][C]21[/C][C] 0.6268[/C][C] 0.7465[/C][C] 0.3732[/C][/ROW]
[ROW][C]22[/C][C] 0.526[/C][C] 0.948[/C][C] 0.474[/C][/ROW]
[ROW][C]23[/C][C] 0.425[/C][C] 0.85[/C][C] 0.575[/C][/ROW]
[ROW][C]24[/C][C] 0.3787[/C][C] 0.7573[/C][C] 0.6213[/C][/ROW]
[ROW][C]25[/C][C] 0.6054[/C][C] 0.7891[/C][C] 0.3946[/C][/ROW]
[ROW][C]26[/C][C] 0.6443[/C][C] 0.7114[/C][C] 0.3557[/C][/ROW]
[ROW][C]27[/C][C] 0.6175[/C][C] 0.7651[/C][C] 0.3825[/C][/ROW]
[ROW][C]28[/C][C] 0.6387[/C][C] 0.7226[/C][C] 0.3613[/C][/ROW]
[ROW][C]29[/C][C] 0.7103[/C][C] 0.5794[/C][C] 0.2897[/C][/ROW]
[ROW][C]30[/C][C] 0.7699[/C][C] 0.4603[/C][C] 0.2301[/C][/ROW]
[ROW][C]31[/C][C] 0.8171[/C][C] 0.3658[/C][C] 0.1829[/C][/ROW]
[ROW][C]32[/C][C] 0.8533[/C][C] 0.2933[/C][C] 0.1467[/C][/ROW]
[ROW][C]33[/C][C] 0.8649[/C][C] 0.2703[/C][C] 0.1351[/C][/ROW]
[ROW][C]34[/C][C] 0.8426[/C][C] 0.3147[/C][C] 0.1574[/C][/ROW]
[ROW][C]35[/C][C] 0.7872[/C][C] 0.4255[/C][C] 0.2128[/C][/ROW]
[ROW][C]36[/C][C] 0.7223[/C][C] 0.5554[/C][C] 0.2777[/C][/ROW]
[ROW][C]37[/C][C] 0.6267[/C][C] 0.7466[/C][C] 0.3733[/C][/ROW]
[ROW][C]38[/C][C] 0.5192[/C][C] 0.9615[/C][C] 0.4808[/C][/ROW]
[ROW][C]39[/C][C] 0.4058[/C][C] 0.8116[/C][C] 0.5942[/C][/ROW]
[ROW][C]40[/C][C] 0.2994[/C][C] 0.5988[/C][C] 0.7006[/C][/ROW]
[ROW][C]41[/C][C] 0.2535[/C][C] 0.5071[/C][C] 0.7465[/C][/ROW]
[ROW][C]42[/C][C] 0.2767[/C][C] 0.5534[/C][C] 0.7233[/C][/ROW]
[ROW][C]43[/C][C] 0.3943[/C][C] 0.7886[/C][C] 0.6057[/C][/ROW]
[ROW][C]44[/C][C] 0.5643[/C][C] 0.8715[/C][C] 0.4357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286365&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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
16	0.3128	0.6256	0.6872
17	0.5445	0.911	0.4555
18	0.6361	0.7279	0.3639
19	0.6733	0.6534	0.3267
20	0.6781	0.6438	0.3219
21	0.6268	0.7465	0.3732
22	0.526	0.948	0.474
23	0.425	0.85	0.575
24	0.3787	0.7573	0.6213
25	0.6054	0.7891	0.3946
26	0.6443	0.7114	0.3557
27	0.6175	0.7651	0.3825
28	0.6387	0.7226	0.3613
29	0.7103	0.5794	0.2897
30	0.7699	0.4603	0.2301
31	0.8171	0.3658	0.1829
32	0.8533	0.2933	0.1467
33	0.8649	0.2703	0.1351
34	0.8426	0.3147	0.1574
35	0.7872	0.4255	0.2128
36	0.7223	0.5554	0.2777
37	0.6267	0.7466	0.3733
38	0.5192	0.9615	0.4808
39	0.4058	0.8116	0.5942
40	0.2994	0.5988	0.7006
41	0.2535	0.5071	0.7465
42	0.2767	0.5534	0.7233
43	0.3943	0.7886	0.6057
44	0.5643	0.8715	0.4357

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=286365&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=286365&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286365&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 ; par4 = ; par5 = ;

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

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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s=12)'){
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s=12)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,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(par5 > 0) {
x2 <- array(0, dim=c(n-par5*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*12)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*12-j*12,par1]
}
}
x <- cbind(x[(par5*12+1):n,], x2)
n <- n - par5*12
}
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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
(k <- length(x[n,]))
head(x)
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