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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 16 Dec 2015 18:50:45 +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/16/t1450291907at9snsbnbwncpay.htm/, Retrieved Thu, 16 May 2024 18:33:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286735, Retrieved Thu, 16 May 2024 18:33:18 +0000

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Original text written by user:

hier wordt een vijf ingevuld bij degree of predetermination

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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...] [2015-12-16 18:50:45] [7b9f7e1283e2b89337d884e38fbaf01c] [Current]

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-27 1.9
-29 2
-33 2
-27 1.8
-22 1.6
-23 1.4
-23 0.2
-15 0.3
-15 0.4
-24 0.7
-18 1
-14 1.1
-7 0.8
-12 0.8
-12 1
-15 1.1
-16 1
-17 0.8
-13 1.6
-8 1.5
-13 1.6
-13 1.6
-11 1.6
-16 1.9
-5 2
-3 1.9
-7 2
-10 2.1
-10 2.3
-11 2.3
-11 2.6
-19 2.6
-30 2.7
-38 2.6
-36 2.6
-40 2.4
-34 2.5
-35 2.5
-38 2.5
-32 2.4
-37 2.1
-39 2.1
-31 2.3
-30 2.3
-29 2.3
-36 2.9
-41 2.8
-42 2.9
-33 3
-43 3
-41 2.9
-34 2.6
-32 2.8
-36 2.9
-37 3.1
-30 2.8
-32 2.4
-30 1.6
-21 1.5
-19 1.7
-9 1.4
-8 1.1
-6 0.8
-4 1.2
-1 0.8
-2 0.9
-1 0.9
-4 1
-8 0.9
-6 1.1
-11 1
-11 0.7

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=286735&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=286735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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
Consumentenvertrouwen[t] = + 0.900876 -2.69041Inflatie[t] + 0.815511`Consumentenvertrouwen(t-1)`[t] -0.0752965`Consumentenvertrouwen(t-2)`[t] + 0.171665`Consumentenvertrouwen(t-3)`[t] -0.0230095`Consumentenvertrouwen(t-4)`[t] -0.0829487`Consumentenvertrouwen(t-5)`[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Consumentenvertrouwen[t] =  +  0.900876 -2.69041Inflatie[t] +  0.815511`Consumentenvertrouwen(t-1)`[t] -0.0752965`Consumentenvertrouwen(t-2)`[t] +  0.171665`Consumentenvertrouwen(t-3)`[t] -0.0230095`Consumentenvertrouwen(t-4)`[t] -0.0829487`Consumentenvertrouwen(t-5)`[t]  + e[t] \tabularnewline
Warning: you did not specify the column number of the endogenous series! The first column was selected by default. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286735&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Consumentenvertrouwen[t] =  +  0.900876 -2.69041Inflatie[t] +  0.815511`Consumentenvertrouwen(t-1)`[t] -0.0752965`Consumentenvertrouwen(t-2)`[t] +  0.171665`Consumentenvertrouwen(t-3)`[t] -0.0230095`Consumentenvertrouwen(t-4)`[t] -0.0829487`Consumentenvertrouwen(t-5)`[t]  + e[t][/C][/ROW]
[ROW][C]Warning: you did not specify the column number of the endogenous series! The first column was selected by default.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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
Consumentenvertrouwen[t] = + 0.900876 -2.69041Inflatie[t] + 0.815511`Consumentenvertrouwen(t-1)`[t] -0.0752965`Consumentenvertrouwen(t-2)`[t] + 0.171665`Consumentenvertrouwen(t-3)`[t] -0.0230095`Consumentenvertrouwen(t-4)`[t] -0.0829487`Consumentenvertrouwen(t-5)`[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+0.9009	1.591	+5.6630e-01	0.5733	0.2867
Inflatie	-2.69	0.9814	-2.7410e+00	0.008049	0.004024
`Consumentenvertrouwen(t-1)`	+0.8155	0.1284	+6.3520e+00	3.144e-08	1.572e-08
`Consumentenvertrouwen(t-2)`	-0.0753	0.1672	-4.5040e-01	0.654	0.327
`Consumentenvertrouwen(t-3)`	+0.1717	0.1642	+1.0450e+00	0.3001	0.15
`Consumentenvertrouwen(t-4)`	-0.02301	0.1662	-1.3850e-01	0.8903	0.4452
`Consumentenvertrouwen(t-5)`	-0.08295	0.122	-6.7970e-01	0.4993	0.2497

\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) & +0.9009 &  1.591 & +5.6630e-01 &  0.5733 &  0.2867 \tabularnewline
Inflatie & -2.69 &  0.9814 & -2.7410e+00 &  0.008049 &  0.004024 \tabularnewline
`Consumentenvertrouwen(t-1)` & +0.8155 &  0.1284 & +6.3520e+00 &  3.144e-08 &  1.572e-08 \tabularnewline
`Consumentenvertrouwen(t-2)` & -0.0753 &  0.1672 & -4.5040e-01 &  0.654 &  0.327 \tabularnewline
`Consumentenvertrouwen(t-3)` & +0.1717 &  0.1642 & +1.0450e+00 &  0.3001 &  0.15 \tabularnewline
`Consumentenvertrouwen(t-4)` & -0.02301 &  0.1662 & -1.3850e-01 &  0.8903 &  0.4452 \tabularnewline
`Consumentenvertrouwen(t-5)` & -0.08295 &  0.122 & -6.7970e-01 &  0.4993 &  0.2497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286735&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]+0.9009[/C][C] 1.591[/C][C]+5.6630e-01[/C][C] 0.5733[/C][C] 0.2867[/C][/ROW]
[ROW][C]Inflatie[/C][C]-2.69[/C][C] 0.9814[/C][C]-2.7410e+00[/C][C] 0.008049[/C][C] 0.004024[/C][/ROW]
[ROW][C]`Consumentenvertrouwen(t-1)`[/C][C]+0.8155[/C][C] 0.1284[/C][C]+6.3520e+00[/C][C] 3.144e-08[/C][C] 1.572e-08[/C][/ROW]
[ROW][C]`Consumentenvertrouwen(t-2)`[/C][C]-0.0753[/C][C] 0.1672[/C][C]-4.5040e-01[/C][C] 0.654[/C][C] 0.327[/C][/ROW]
[ROW][C]`Consumentenvertrouwen(t-3)`[/C][C]+0.1717[/C][C] 0.1642[/C][C]+1.0450e+00[/C][C] 0.3001[/C][C] 0.15[/C][/ROW]
[ROW][C]`Consumentenvertrouwen(t-4)`[/C][C]-0.02301[/C][C] 0.1662[/C][C]-1.3850e-01[/C][C] 0.8903[/C][C] 0.4452[/C][/ROW]
[ROW][C]`Consumentenvertrouwen(t-5)`[/C][C]-0.08295[/C][C] 0.122[/C][C]-6.7970e-01[/C][C] 0.4993[/C][C] 0.2497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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)	+0.9009	1.591	+5.6630e-01	0.5733	0.2867
Inflatie	-2.69	0.9814	-2.7410e+00	0.008049	0.004024
`Consumentenvertrouwen(t-1)`	+0.8155	0.1284	+6.3520e+00	3.144e-08	1.572e-08
`Consumentenvertrouwen(t-2)`	-0.0753	0.1672	-4.5040e-01	0.654	0.327
`Consumentenvertrouwen(t-3)`	+0.1717	0.1642	+1.0450e+00	0.3001	0.15
`Consumentenvertrouwen(t-4)`	-0.02301	0.1662	-1.3850e-01	0.8903	0.4452
`Consumentenvertrouwen(t-5)`	-0.08295	0.122	-6.7970e-01	0.4993	0.2497

Multiple Linear Regression - Regression Statistics
Multiple R	0.9364
R-squared	0.8768
Adjusted R-squared	0.8645
F-TEST (value)	71.15
F-TEST (DF numerator)	6
F-TEST (DF denominator)	60
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.723
Sum Squared Residuals	1339

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.9364 \tabularnewline
R-squared &  0.8768 \tabularnewline
Adjusted R-squared &  0.8645 \tabularnewline
F-TEST (value) &  71.15 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 60 \tabularnewline
p-value &  0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  4.723 \tabularnewline
Sum Squared Residuals &  1339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286735&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.9364[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.8768[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.8645[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 71.15[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]60[/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] 4.723[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 1339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286735&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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	0.9364
R-squared	0.8768
Adjusted R-squared	0.8645
F-TEST (value)	71.15
F-TEST (DF numerator)	6
F-TEST (DF denominator)	60
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.723
Sum Squared Residuals	1339

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	-23	-21.53	-1.468
2	-23	-18.21	-4.792
3	-15	-17.35	2.349
4	-15	-11.88	-3.121
5	-24	-13.68	-10.32
6	-18	-20.37	2.37
7	-14	-15.25	1.253
8	-7	-13.84	6.844
9	-12	-7.199	-4.801
10	-12	-11.05	-0.953
11	-15	-10.33	-4.672
12	-16	-13.86	-2.144
13	-17	-14.37	-2.627
14	-13	-17.37	4.366
15	-8	-13.86	5.862
16	-13	-10.25	-2.745
17	-13	-13.92	0.9164
18	-11	-12.69	1.691
19	-16	-13.17	-2.828
20	-5	-17.97	12.97
21	-3	-7.595	4.595
22	-7	-7.965	0.9652
23	-10	-9.809	-0.1906
24	-10	-11.99	1.988
25	-11	-13.41	2.407
26	-11	-15.62	4.619
27	-19	-15.14	-3.858
28	-30	-21.86	-8.142
29	-38	-29.93	-8.065
30	-36	-36.92	0.9208
31	-40	-35.85	-4.146
32	-34	-39.99	5.992
33	-35	-33.36	-1.642
34	-38	-34.69	-3.306
35	-32	-35.84	3.84
36	-37	-29.89	-7.108
37	-39	-35.41	-3.589
38	-31	-36.02	5.022
39	-30	-30.09	0.09459
40	-29	-30.61	1.607
41	-36	-29.65	-6.353
42	-41	-35.01	-5.991
43	-42	-39.34	-2.657
44	-33	-41.36	8.359
45	-43	-34.72	-8.276
46	-41	-42.76	1.764
47	-34	-37.59	3.59
48	-32	-34.41	2.411
49	-36	-33.75	-2.251
50	-37	-35.71	-1.285
51	-30	-35.41	5.406
52	-32	-29.86	-2.141
53	-30	-30.11	0.1101
54	-21	-26.5	5.503
55	-19	-20.27	1.274
56	-9	-18.7	9.704
57	-8	-8.228	0.2279
58	-6	-7.388	1.388
59	-4	-5.984	1.984
60	-1	-3.652	2.652
61	-2	-2.134	0.1342
62	-1	-2.961	1.961
63	-4	-2.036	-1.964
64	-8	-4.696	-3.304
65	-6	-8.324	2.324
66	-11	-6.578	-4.422
67	-11	-10.7	-0.3004

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -23 & -21.53 & -1.468 \tabularnewline
2 & -23 & -18.21 & -4.792 \tabularnewline
3 & -15 & -17.35 &  2.349 \tabularnewline
4 & -15 & -11.88 & -3.121 \tabularnewline
5 & -24 & -13.68 & -10.32 \tabularnewline
6 & -18 & -20.37 &  2.37 \tabularnewline
7 & -14 & -15.25 &  1.253 \tabularnewline
8 & -7 & -13.84 &  6.844 \tabularnewline
9 & -12 & -7.199 & -4.801 \tabularnewline
10 & -12 & -11.05 & -0.953 \tabularnewline
11 & -15 & -10.33 & -4.672 \tabularnewline
12 & -16 & -13.86 & -2.144 \tabularnewline
13 & -17 & -14.37 & -2.627 \tabularnewline
14 & -13 & -17.37 &  4.366 \tabularnewline
15 & -8 & -13.86 &  5.862 \tabularnewline
16 & -13 & -10.25 & -2.745 \tabularnewline
17 & -13 & -13.92 &  0.9164 \tabularnewline
18 & -11 & -12.69 &  1.691 \tabularnewline
19 & -16 & -13.17 & -2.828 \tabularnewline
20 & -5 & -17.97 &  12.97 \tabularnewline
21 & -3 & -7.595 &  4.595 \tabularnewline
22 & -7 & -7.965 &  0.9652 \tabularnewline
23 & -10 & -9.809 & -0.1906 \tabularnewline
24 & -10 & -11.99 &  1.988 \tabularnewline
25 & -11 & -13.41 &  2.407 \tabularnewline
26 & -11 & -15.62 &  4.619 \tabularnewline
27 & -19 & -15.14 & -3.858 \tabularnewline
28 & -30 & -21.86 & -8.142 \tabularnewline
29 & -38 & -29.93 & -8.065 \tabularnewline
30 & -36 & -36.92 &  0.9208 \tabularnewline
31 & -40 & -35.85 & -4.146 \tabularnewline
32 & -34 & -39.99 &  5.992 \tabularnewline
33 & -35 & -33.36 & -1.642 \tabularnewline
34 & -38 & -34.69 & -3.306 \tabularnewline
35 & -32 & -35.84 &  3.84 \tabularnewline
36 & -37 & -29.89 & -7.108 \tabularnewline
37 & -39 & -35.41 & -3.589 \tabularnewline
38 & -31 & -36.02 &  5.022 \tabularnewline
39 & -30 & -30.09 &  0.09459 \tabularnewline
40 & -29 & -30.61 &  1.607 \tabularnewline
41 & -36 & -29.65 & -6.353 \tabularnewline
42 & -41 & -35.01 & -5.991 \tabularnewline
43 & -42 & -39.34 & -2.657 \tabularnewline
44 & -33 & -41.36 &  8.359 \tabularnewline
45 & -43 & -34.72 & -8.276 \tabularnewline
46 & -41 & -42.76 &  1.764 \tabularnewline
47 & -34 & -37.59 &  3.59 \tabularnewline
48 & -32 & -34.41 &  2.411 \tabularnewline
49 & -36 & -33.75 & -2.251 \tabularnewline
50 & -37 & -35.71 & -1.285 \tabularnewline
51 & -30 & -35.41 &  5.406 \tabularnewline
52 & -32 & -29.86 & -2.141 \tabularnewline
53 & -30 & -30.11 &  0.1101 \tabularnewline
54 & -21 & -26.5 &  5.503 \tabularnewline
55 & -19 & -20.27 &  1.274 \tabularnewline
56 & -9 & -18.7 &  9.704 \tabularnewline
57 & -8 & -8.228 &  0.2279 \tabularnewline
58 & -6 & -7.388 &  1.388 \tabularnewline
59 & -4 & -5.984 &  1.984 \tabularnewline
60 & -1 & -3.652 &  2.652 \tabularnewline
61 & -2 & -2.134 &  0.1342 \tabularnewline
62 & -1 & -2.961 &  1.961 \tabularnewline
63 & -4 & -2.036 & -1.964 \tabularnewline
64 & -8 & -4.696 & -3.304 \tabularnewline
65 & -6 & -8.324 &  2.324 \tabularnewline
66 & -11 & -6.578 & -4.422 \tabularnewline
67 & -11 & -10.7 & -0.3004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286735&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]-23[/C][C]-21.53[/C][C]-1.468[/C][/ROW]
[ROW][C]2[/C][C]-23[/C][C]-18.21[/C][C]-4.792[/C][/ROW]
[ROW][C]3[/C][C]-15[/C][C]-17.35[/C][C] 2.349[/C][/ROW]
[ROW][C]4[/C][C]-15[/C][C]-11.88[/C][C]-3.121[/C][/ROW]
[ROW][C]5[/C][C]-24[/C][C]-13.68[/C][C]-10.32[/C][/ROW]
[ROW][C]6[/C][C]-18[/C][C]-20.37[/C][C] 2.37[/C][/ROW]
[ROW][C]7[/C][C]-14[/C][C]-15.25[/C][C] 1.253[/C][/ROW]
[ROW][C]8[/C][C]-7[/C][C]-13.84[/C][C] 6.844[/C][/ROW]
[ROW][C]9[/C][C]-12[/C][C]-7.199[/C][C]-4.801[/C][/ROW]
[ROW][C]10[/C][C]-12[/C][C]-11.05[/C][C]-0.953[/C][/ROW]
[ROW][C]11[/C][C]-15[/C][C]-10.33[/C][C]-4.672[/C][/ROW]
[ROW][C]12[/C][C]-16[/C][C]-13.86[/C][C]-2.144[/C][/ROW]
[ROW][C]13[/C][C]-17[/C][C]-14.37[/C][C]-2.627[/C][/ROW]
[ROW][C]14[/C][C]-13[/C][C]-17.37[/C][C] 4.366[/C][/ROW]
[ROW][C]15[/C][C]-8[/C][C]-13.86[/C][C] 5.862[/C][/ROW]
[ROW][C]16[/C][C]-13[/C][C]-10.25[/C][C]-2.745[/C][/ROW]
[ROW][C]17[/C][C]-13[/C][C]-13.92[/C][C] 0.9164[/C][/ROW]
[ROW][C]18[/C][C]-11[/C][C]-12.69[/C][C] 1.691[/C][/ROW]
[ROW][C]19[/C][C]-16[/C][C]-13.17[/C][C]-2.828[/C][/ROW]
[ROW][C]20[/C][C]-5[/C][C]-17.97[/C][C] 12.97[/C][/ROW]
[ROW][C]21[/C][C]-3[/C][C]-7.595[/C][C] 4.595[/C][/ROW]
[ROW][C]22[/C][C]-7[/C][C]-7.965[/C][C] 0.9652[/C][/ROW]
[ROW][C]23[/C][C]-10[/C][C]-9.809[/C][C]-0.1906[/C][/ROW]
[ROW][C]24[/C][C]-10[/C][C]-11.99[/C][C] 1.988[/C][/ROW]
[ROW][C]25[/C][C]-11[/C][C]-13.41[/C][C] 2.407[/C][/ROW]
[ROW][C]26[/C][C]-11[/C][C]-15.62[/C][C] 4.619[/C][/ROW]
[ROW][C]27[/C][C]-19[/C][C]-15.14[/C][C]-3.858[/C][/ROW]
[ROW][C]28[/C][C]-30[/C][C]-21.86[/C][C]-8.142[/C][/ROW]
[ROW][C]29[/C][C]-38[/C][C]-29.93[/C][C]-8.065[/C][/ROW]
[ROW][C]30[/C][C]-36[/C][C]-36.92[/C][C] 0.9208[/C][/ROW]
[ROW][C]31[/C][C]-40[/C][C]-35.85[/C][C]-4.146[/C][/ROW]
[ROW][C]32[/C][C]-34[/C][C]-39.99[/C][C] 5.992[/C][/ROW]
[ROW][C]33[/C][C]-35[/C][C]-33.36[/C][C]-1.642[/C][/ROW]
[ROW][C]34[/C][C]-38[/C][C]-34.69[/C][C]-3.306[/C][/ROW]
[ROW][C]35[/C][C]-32[/C][C]-35.84[/C][C] 3.84[/C][/ROW]
[ROW][C]36[/C][C]-37[/C][C]-29.89[/C][C]-7.108[/C][/ROW]
[ROW][C]37[/C][C]-39[/C][C]-35.41[/C][C]-3.589[/C][/ROW]
[ROW][C]38[/C][C]-31[/C][C]-36.02[/C][C] 5.022[/C][/ROW]
[ROW][C]39[/C][C]-30[/C][C]-30.09[/C][C] 0.09459[/C][/ROW]
[ROW][C]40[/C][C]-29[/C][C]-30.61[/C][C] 1.607[/C][/ROW]
[ROW][C]41[/C][C]-36[/C][C]-29.65[/C][C]-6.353[/C][/ROW]
[ROW][C]42[/C][C]-41[/C][C]-35.01[/C][C]-5.991[/C][/ROW]
[ROW][C]43[/C][C]-42[/C][C]-39.34[/C][C]-2.657[/C][/ROW]
[ROW][C]44[/C][C]-33[/C][C]-41.36[/C][C] 8.359[/C][/ROW]
[ROW][C]45[/C][C]-43[/C][C]-34.72[/C][C]-8.276[/C][/ROW]
[ROW][C]46[/C][C]-41[/C][C]-42.76[/C][C] 1.764[/C][/ROW]
[ROW][C]47[/C][C]-34[/C][C]-37.59[/C][C] 3.59[/C][/ROW]
[ROW][C]48[/C][C]-32[/C][C]-34.41[/C][C] 2.411[/C][/ROW]
[ROW][C]49[/C][C]-36[/C][C]-33.75[/C][C]-2.251[/C][/ROW]
[ROW][C]50[/C][C]-37[/C][C]-35.71[/C][C]-1.285[/C][/ROW]
[ROW][C]51[/C][C]-30[/C][C]-35.41[/C][C] 5.406[/C][/ROW]
[ROW][C]52[/C][C]-32[/C][C]-29.86[/C][C]-2.141[/C][/ROW]
[ROW][C]53[/C][C]-30[/C][C]-30.11[/C][C] 0.1101[/C][/ROW]
[ROW][C]54[/C][C]-21[/C][C]-26.5[/C][C] 5.503[/C][/ROW]
[ROW][C]55[/C][C]-19[/C][C]-20.27[/C][C] 1.274[/C][/ROW]
[ROW][C]56[/C][C]-9[/C][C]-18.7[/C][C] 9.704[/C][/ROW]
[ROW][C]57[/C][C]-8[/C][C]-8.228[/C][C] 0.2279[/C][/ROW]
[ROW][C]58[/C][C]-6[/C][C]-7.388[/C][C] 1.388[/C][/ROW]
[ROW][C]59[/C][C]-4[/C][C]-5.984[/C][C] 1.984[/C][/ROW]
[ROW][C]60[/C][C]-1[/C][C]-3.652[/C][C] 2.652[/C][/ROW]
[ROW][C]61[/C][C]-2[/C][C]-2.134[/C][C] 0.1342[/C][/ROW]
[ROW][C]62[/C][C]-1[/C][C]-2.961[/C][C] 1.961[/C][/ROW]
[ROW][C]63[/C][C]-4[/C][C]-2.036[/C][C]-1.964[/C][/ROW]
[ROW][C]64[/C][C]-8[/C][C]-4.696[/C][C]-3.304[/C][/ROW]
[ROW][C]65[/C][C]-6[/C][C]-8.324[/C][C] 2.324[/C][/ROW]
[ROW][C]66[/C][C]-11[/C][C]-6.578[/C][C]-4.422[/C][/ROW]
[ROW][C]67[/C][C]-11[/C][C]-10.7[/C][C]-0.3004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286735&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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	-23	-21.53	-1.468
2	-23	-18.21	-4.792
3	-15	-17.35	2.349
4	-15	-11.88	-3.121
5	-24	-13.68	-10.32
6	-18	-20.37	2.37
7	-14	-15.25	1.253
8	-7	-13.84	6.844
9	-12	-7.199	-4.801
10	-12	-11.05	-0.953
11	-15	-10.33	-4.672
12	-16	-13.86	-2.144
13	-17	-14.37	-2.627
14	-13	-17.37	4.366
15	-8	-13.86	5.862
16	-13	-10.25	-2.745
17	-13	-13.92	0.9164
18	-11	-12.69	1.691
19	-16	-13.17	-2.828
20	-5	-17.97	12.97
21	-3	-7.595	4.595
22	-7	-7.965	0.9652
23	-10	-9.809	-0.1906
24	-10	-11.99	1.988
25	-11	-13.41	2.407
26	-11	-15.62	4.619
27	-19	-15.14	-3.858
28	-30	-21.86	-8.142
29	-38	-29.93	-8.065
30	-36	-36.92	0.9208
31	-40	-35.85	-4.146
32	-34	-39.99	5.992
33	-35	-33.36	-1.642
34	-38	-34.69	-3.306
35	-32	-35.84	3.84
36	-37	-29.89	-7.108
37	-39	-35.41	-3.589
38	-31	-36.02	5.022
39	-30	-30.09	0.09459
40	-29	-30.61	1.607
41	-36	-29.65	-6.353
42	-41	-35.01	-5.991
43	-42	-39.34	-2.657
44	-33	-41.36	8.359
45	-43	-34.72	-8.276
46	-41	-42.76	1.764
47	-34	-37.59	3.59
48	-32	-34.41	2.411
49	-36	-33.75	-2.251
50	-37	-35.71	-1.285
51	-30	-35.41	5.406
52	-32	-29.86	-2.141
53	-30	-30.11	0.1101
54	-21	-26.5	5.503
55	-19	-20.27	1.274
56	-9	-18.7	9.704
57	-8	-8.228	0.2279
58	-6	-7.388	1.388
59	-4	-5.984	1.984
60	-1	-3.652	2.652
61	-2	-2.134	0.1342
62	-1	-2.961	1.961
63	-4	-2.036	-1.964
64	-8	-4.696	-3.304
65	-6	-8.324	2.324
66	-11	-6.578	-4.422
67	-11	-10.7	-0.3004

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.8061	0.3878	0.1939
11	0.7601	0.4797	0.2399
12	0.7754	0.4492	0.2246
13	0.7005	0.5989	0.2995
14	0.6334	0.7333	0.3666
15	0.6529	0.6942	0.3471
16	0.5666	0.8668	0.4334
17	0.4747	0.9493	0.5253
18	0.3788	0.7576	0.6212
19	0.381	0.762	0.619
20	0.6736	0.6528	0.3264
21	0.6724	0.6552	0.3276
22	0.6052	0.7895	0.3948
23	0.5283	0.9433	0.4717
24	0.4742	0.9483	0.5258
25	0.4687	0.9374	0.5313
26	0.5648	0.8704	0.4352
27	0.6968	0.6064	0.3032
28	0.8595	0.2811	0.1405
29	0.9133	0.1735	0.08674
30	0.8816	0.2368	0.1184
31	0.8627	0.2745	0.1373
32	0.9012	0.1977	0.09885
33	0.8644	0.2713	0.1356
34	0.8328	0.3343	0.1672
35	0.8175	0.3649	0.1825
36	0.9043	0.1913	0.09567
37	0.9223	0.1554	0.07768
38	0.9141	0.1718	0.08588
39	0.8819	0.2363	0.1181
40	0.8435	0.313	0.1565
41	0.8368	0.3264	0.1632
42	0.9121	0.1757	0.08786
43	0.9201	0.1598	0.07991
44	0.9808	0.03847	0.01924
45	0.9834	0.0332	0.0166
46	0.9716	0.05673	0.02837
47	0.9565	0.08704	0.04352
48	0.9468	0.1064	0.05322
49	0.9135	0.1729	0.08646
50	0.9471	0.1059	0.05293
51	0.9221	0.1558	0.07791
52	0.8834	0.2332	0.1166
53	0.9628	0.07434	0.03717
54	0.9288	0.1424	0.07121
55	0.8885	0.2229	0.1115
56	0.9147	0.1707	0.08534
57	0.8097	0.3805	0.1903

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 &  0.8061 &  0.3878 &  0.1939 \tabularnewline
11 &  0.7601 &  0.4797 &  0.2399 \tabularnewline
12 &  0.7754 &  0.4492 &  0.2246 \tabularnewline
13 &  0.7005 &  0.5989 &  0.2995 \tabularnewline
14 &  0.6334 &  0.7333 &  0.3666 \tabularnewline
15 &  0.6529 &  0.6942 &  0.3471 \tabularnewline
16 &  0.5666 &  0.8668 &  0.4334 \tabularnewline
17 &  0.4747 &  0.9493 &  0.5253 \tabularnewline
18 &  0.3788 &  0.7576 &  0.6212 \tabularnewline
19 &  0.381 &  0.762 &  0.619 \tabularnewline
20 &  0.6736 &  0.6528 &  0.3264 \tabularnewline
21 &  0.6724 &  0.6552 &  0.3276 \tabularnewline
22 &  0.6052 &  0.7895 &  0.3948 \tabularnewline
23 &  0.5283 &  0.9433 &  0.4717 \tabularnewline
24 &  0.4742 &  0.9483 &  0.5258 \tabularnewline
25 &  0.4687 &  0.9374 &  0.5313 \tabularnewline
26 &  0.5648 &  0.8704 &  0.4352 \tabularnewline
27 &  0.6968 &  0.6064 &  0.3032 \tabularnewline
28 &  0.8595 &  0.2811 &  0.1405 \tabularnewline
29 &  0.9133 &  0.1735 &  0.08674 \tabularnewline
30 &  0.8816 &  0.2368 &  0.1184 \tabularnewline
31 &  0.8627 &  0.2745 &  0.1373 \tabularnewline
32 &  0.9012 &  0.1977 &  0.09885 \tabularnewline
33 &  0.8644 &  0.2713 &  0.1356 \tabularnewline
34 &  0.8328 &  0.3343 &  0.1672 \tabularnewline
35 &  0.8175 &  0.3649 &  0.1825 \tabularnewline
36 &  0.9043 &  0.1913 &  0.09567 \tabularnewline
37 &  0.9223 &  0.1554 &  0.07768 \tabularnewline
38 &  0.9141 &  0.1718 &  0.08588 \tabularnewline
39 &  0.8819 &  0.2363 &  0.1181 \tabularnewline
40 &  0.8435 &  0.313 &  0.1565 \tabularnewline
41 &  0.8368 &  0.3264 &  0.1632 \tabularnewline
42 &  0.9121 &  0.1757 &  0.08786 \tabularnewline
43 &  0.9201 &  0.1598 &  0.07991 \tabularnewline
44 &  0.9808 &  0.03847 &  0.01924 \tabularnewline
45 &  0.9834 &  0.0332 &  0.0166 \tabularnewline
46 &  0.9716 &  0.05673 &  0.02837 \tabularnewline
47 &  0.9565 &  0.08704 &  0.04352 \tabularnewline
48 &  0.9468 &  0.1064 &  0.05322 \tabularnewline
49 &  0.9135 &  0.1729 &  0.08646 \tabularnewline
50 &  0.9471 &  0.1059 &  0.05293 \tabularnewline
51 &  0.9221 &  0.1558 &  0.07791 \tabularnewline
52 &  0.8834 &  0.2332 &  0.1166 \tabularnewline
53 &  0.9628 &  0.07434 &  0.03717 \tabularnewline
54 &  0.9288 &  0.1424 &  0.07121 \tabularnewline
55 &  0.8885 &  0.2229 &  0.1115 \tabularnewline
56 &  0.9147 &  0.1707 &  0.08534 \tabularnewline
57 &  0.8097 &  0.3805 &  0.1903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286735&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]10[/C][C] 0.8061[/C][C] 0.3878[/C][C] 0.1939[/C][/ROW]
[ROW][C]11[/C][C] 0.7601[/C][C] 0.4797[/C][C] 0.2399[/C][/ROW]
[ROW][C]12[/C][C] 0.7754[/C][C] 0.4492[/C][C] 0.2246[/C][/ROW]
[ROW][C]13[/C][C] 0.7005[/C][C] 0.5989[/C][C] 0.2995[/C][/ROW]
[ROW][C]14[/C][C] 0.6334[/C][C] 0.7333[/C][C] 0.3666[/C][/ROW]
[ROW][C]15[/C][C] 0.6529[/C][C] 0.6942[/C][C] 0.3471[/C][/ROW]
[ROW][C]16[/C][C] 0.5666[/C][C] 0.8668[/C][C] 0.4334[/C][/ROW]
[ROW][C]17[/C][C] 0.4747[/C][C] 0.9493[/C][C] 0.5253[/C][/ROW]
[ROW][C]18[/C][C] 0.3788[/C][C] 0.7576[/C][C] 0.6212[/C][/ROW]
[ROW][C]19[/C][C] 0.381[/C][C] 0.762[/C][C] 0.619[/C][/ROW]
[ROW][C]20[/C][C] 0.6736[/C][C] 0.6528[/C][C] 0.3264[/C][/ROW]
[ROW][C]21[/C][C] 0.6724[/C][C] 0.6552[/C][C] 0.3276[/C][/ROW]
[ROW][C]22[/C][C] 0.6052[/C][C] 0.7895[/C][C] 0.3948[/C][/ROW]
[ROW][C]23[/C][C] 0.5283[/C][C] 0.9433[/C][C] 0.4717[/C][/ROW]
[ROW][C]24[/C][C] 0.4742[/C][C] 0.9483[/C][C] 0.5258[/C][/ROW]
[ROW][C]25[/C][C] 0.4687[/C][C] 0.9374[/C][C] 0.5313[/C][/ROW]
[ROW][C]26[/C][C] 0.5648[/C][C] 0.8704[/C][C] 0.4352[/C][/ROW]
[ROW][C]27[/C][C] 0.6968[/C][C] 0.6064[/C][C] 0.3032[/C][/ROW]
[ROW][C]28[/C][C] 0.8595[/C][C] 0.2811[/C][C] 0.1405[/C][/ROW]
[ROW][C]29[/C][C] 0.9133[/C][C] 0.1735[/C][C] 0.08674[/C][/ROW]
[ROW][C]30[/C][C] 0.8816[/C][C] 0.2368[/C][C] 0.1184[/C][/ROW]
[ROW][C]31[/C][C] 0.8627[/C][C] 0.2745[/C][C] 0.1373[/C][/ROW]
[ROW][C]32[/C][C] 0.9012[/C][C] 0.1977[/C][C] 0.09885[/C][/ROW]
[ROW][C]33[/C][C] 0.8644[/C][C] 0.2713[/C][C] 0.1356[/C][/ROW]
[ROW][C]34[/C][C] 0.8328[/C][C] 0.3343[/C][C] 0.1672[/C][/ROW]
[ROW][C]35[/C][C] 0.8175[/C][C] 0.3649[/C][C] 0.1825[/C][/ROW]
[ROW][C]36[/C][C] 0.9043[/C][C] 0.1913[/C][C] 0.09567[/C][/ROW]
[ROW][C]37[/C][C] 0.9223[/C][C] 0.1554[/C][C] 0.07768[/C][/ROW]
[ROW][C]38[/C][C] 0.9141[/C][C] 0.1718[/C][C] 0.08588[/C][/ROW]
[ROW][C]39[/C][C] 0.8819[/C][C] 0.2363[/C][C] 0.1181[/C][/ROW]
[ROW][C]40[/C][C] 0.8435[/C][C] 0.313[/C][C] 0.1565[/C][/ROW]
[ROW][C]41[/C][C] 0.8368[/C][C] 0.3264[/C][C] 0.1632[/C][/ROW]
[ROW][C]42[/C][C] 0.9121[/C][C] 0.1757[/C][C] 0.08786[/C][/ROW]
[ROW][C]43[/C][C] 0.9201[/C][C] 0.1598[/C][C] 0.07991[/C][/ROW]
[ROW][C]44[/C][C] 0.9808[/C][C] 0.03847[/C][C] 0.01924[/C][/ROW]
[ROW][C]45[/C][C] 0.9834[/C][C] 0.0332[/C][C] 0.0166[/C][/ROW]
[ROW][C]46[/C][C] 0.9716[/C][C] 0.05673[/C][C] 0.02837[/C][/ROW]
[ROW][C]47[/C][C] 0.9565[/C][C] 0.08704[/C][C] 0.04352[/C][/ROW]
[ROW][C]48[/C][C] 0.9468[/C][C] 0.1064[/C][C] 0.05322[/C][/ROW]
[ROW][C]49[/C][C] 0.9135[/C][C] 0.1729[/C][C] 0.08646[/C][/ROW]
[ROW][C]50[/C][C] 0.9471[/C][C] 0.1059[/C][C] 0.05293[/C][/ROW]
[ROW][C]51[/C][C] 0.9221[/C][C] 0.1558[/C][C] 0.07791[/C][/ROW]
[ROW][C]52[/C][C] 0.8834[/C][C] 0.2332[/C][C] 0.1166[/C][/ROW]
[ROW][C]53[/C][C] 0.9628[/C][C] 0.07434[/C][C] 0.03717[/C][/ROW]
[ROW][C]54[/C][C] 0.9288[/C][C] 0.1424[/C][C] 0.07121[/C][/ROW]
[ROW][C]55[/C][C] 0.8885[/C][C] 0.2229[/C][C] 0.1115[/C][/ROW]
[ROW][C]56[/C][C] 0.9147[/C][C] 0.1707[/C][C] 0.08534[/C][/ROW]
[ROW][C]57[/C][C] 0.8097[/C][C] 0.3805[/C][C] 0.1903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286735&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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
10	0.8061	0.3878	0.1939
11	0.7601	0.4797	0.2399
12	0.7754	0.4492	0.2246
13	0.7005	0.5989	0.2995
14	0.6334	0.7333	0.3666
15	0.6529	0.6942	0.3471
16	0.5666	0.8668	0.4334
17	0.4747	0.9493	0.5253
18	0.3788	0.7576	0.6212
19	0.381	0.762	0.619
20	0.6736	0.6528	0.3264
21	0.6724	0.6552	0.3276
22	0.6052	0.7895	0.3948
23	0.5283	0.9433	0.4717
24	0.4742	0.9483	0.5258
25	0.4687	0.9374	0.5313
26	0.5648	0.8704	0.4352
27	0.6968	0.6064	0.3032
28	0.8595	0.2811	0.1405
29	0.9133	0.1735	0.08674
30	0.8816	0.2368	0.1184
31	0.8627	0.2745	0.1373
32	0.9012	0.1977	0.09885
33	0.8644	0.2713	0.1356
34	0.8328	0.3343	0.1672
35	0.8175	0.3649	0.1825
36	0.9043	0.1913	0.09567
37	0.9223	0.1554	0.07768
38	0.9141	0.1718	0.08588
39	0.8819	0.2363	0.1181
40	0.8435	0.313	0.1565
41	0.8368	0.3264	0.1632
42	0.9121	0.1757	0.08786
43	0.9201	0.1598	0.07991
44	0.9808	0.03847	0.01924
45	0.9834	0.0332	0.0166
46	0.9716	0.05673	0.02837
47	0.9565	0.08704	0.04352
48	0.9468	0.1064	0.05322
49	0.9135	0.1729	0.08646
50	0.9471	0.1059	0.05293
51	0.9221	0.1558	0.07791
52	0.8834	0.2332	0.1166
53	0.9628	0.07434	0.03717
54	0.9288	0.1424	0.07121
55	0.8885	0.2229	0.1115
56	0.9147	0.1707	0.08534
57	0.8097	0.3805	0.1903

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	2	0.0416667	OK
10% type I error level	5	0.104167	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 & 2 & 0.0416667 & OK \tabularnewline
10% type I error level & 5 & 0.104167 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286735&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]2[/C][C]0.0416667[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.104167[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286735&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286735&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	2	0.0416667	OK
10% type I error level	5	0.104167	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):

par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 5 ;

Parameters (R input):

par1 = ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 5 ; 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