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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sun, 06 Dec 2015 20:58:13 +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/06/t1449435513xawugczcfmlixbj.htm/, Retrieved Thu, 16 May 2024 15:45:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285322, Retrieved Thu, 16 May 2024 15:45:53 +0000

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User-defined keywords

regressie 3

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

-       [Multiple Regression] [Paper 3] [2015-12-06 20:58:13] [fb7ef44ef6cdfac67cf9078e3093d323] [Current]
- R P     [Multiple Regression] [Statistiek 3] [2015-12-17 12:55:19] [7c4d8ff25a79c0ca04f65cc37f1af957] 

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Dataseries X:

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-5	-6	50	19	-29
-1	-3	53	20	-29
-2	-4	50	21	-29
-5	-7	50	20	-27
-4	-7	51	21	-29
-6	-7	53	19	-24
-2	-3	49	22	-29
-2	0	54	20	-21
-2	-5	57	18	-20
-2	-3	58	16	-26
2	3	56	17	-19
1	2	60	18	-22
-8	-7	55	19	-22
-1	-1	54	18	-15
1	0	52	20	-16
-1	-3	55	21	-22
2	4	56	18	-21
2	2	54	19	-11
1	3	53	19	-10
-1	0	59	19	-6
-2	-10	62	21	-8
-2	-10	63	19	-15
-1	-9	64	19	-16
-8	-22	75	17	-24
-4	-16	77	16	-27
-6	-18	79	16	-33
-3	-14	77	17	-29
-3	-12	82	16	-34
-7	-17	83	15	-37
-9	-23	81	16	-31
-11	-28	78	16	-33
-13	-31	79	16	-25
-11	-21	79	18	-27
-9	-19	73	19	-21
-17	-22	72	16	-32
-22	-22	67	16	-31
-25	-25	67	16	-32
-20	-16	50	18	-30
-24	-22	45	16	-34
-24	-21	39	15	-35
-22	-10	39	15	-37
-19	-7	37	16	-32
-18	-5	30	18	-28
-17	-4	24	16	-26
-11	7	27	19	-24
-11	6	19	19	-27
-12	3	19	18	-26
-10	10	25	17	-27
-15	0	16	19	-27
-15	-2	20	22	-24
-15	-1	25	19	-28
-13	2	34	19	-23
-8	8	39	16	-23
-13	-6	40	18	-29
-9	-4	38	20	-25
-7	4	42	17	-24
-4	7	46	17	-20
-4	3	48	17	-22
-2	3	51	20	-24
0	8	55	21	-27
-2	3	52	19	-25
-3	-3	55	18	-26
1	4	58	20	-24
-2	-5	72	17	-26
-1	-1	70	15	-22
1	5	70	17	-20
-3	0	63	18	-26
-4	-6	66	20	-22
-9	-13	65	19	-29
-9	-15	55	20	-30
-7	-8	57	22	-26
-14	-20	60	20	-30
-12	-10	63	21	-33
-16	-22	65	19	-33
-20	-25	61	22	-31
-12	-10	65	19	-36
-12	-8	63	21	-43
-10	-9	59	19	-40
-10	-5	56	21	-38
-13	-7	54	18	-41
-16	-11	56	18	-38
-14	-11	54	20	-40
-17	-16	58	19	-41
-24	-28	59	19	-45
-25	-27	60	17	-54
-23	-23	57	18	-47
-17	-10	54	17	-44
-24	-22	52	18	-47
-20	-15	50	19	-47
-19	-14	51	17	-45
-18	-12	47	19	-42
-16	-10	51	19	-42
-12	1	46	17	-39
-7	9	44	19	-35
-6	7	39	21	-29
-6	9	43	20	-37
-5	7	46	19	-35
-4	12	43	21	-32
-4	10	34	20	-33
-8	7	36	18	-37
-9	4	34	18	-36
-6	5	38	16	-34
-7	5	32	18	-38
-10	-1	38	19	-33
-11	-5	30	18	-41
-11	-6	17	18	-39
-12	-9	14	17	-40
-14	-15	18	18	-42
-12	-10	18	19	-45
-9	-5	13	18	-39
-5	2	9	19	-44
-6	-1	12	19	-44
-6	0	19	20	-43
-3	4	20	21	-39
-2	8	25	17	-38
-6	-1	26	20	-43
-6	-4	29	21	-46
-10	-10	28	18	-42
-8	-6	30	19	-45
-4	-2	38	20	-46

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285322&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285322&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285322&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Multiple Linear Regression - Estimated Regression Equation
consumentenvertrouwen[t] = -15.0344 + 0.478158vooruitz_economie[t] -0.00355933cons_prijzen_12m[t] -0.0303923fin_sit_gezinnen[t] -0.228762gunstig_sparen[t] + 0.0590081`consumentenvertrouwen(t-1)`[t] -0.0553338`consumentenvertrouwen(t-2)`[t] + 0.271837`consumentenvertrouwen(t-3)`[t] -0.398677`consumentenvertrouwen(t-4)`[t] + 0.36045`consumentenvertrouwen(t-1s)`[t] + 0.195034`consumentenvertrouwen(t-2s)`[t] + 0.143529`consumentenvertrouwen(t-3s)`[t] -0.418048`consumentenvertrouwen(t-4s)`[t] -0.138318`consumentenvertrouwen(t-5s)`[t] -0.137215`consumentenvertrouwen(t-6s)`[t] -0.265878`consumentenvertrouwen(t-7s)`[t] + 0.238537`consumentenvertrouwen(t-8s)`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
consumentenvertrouwen[t] =  -15.0344 +  0.478158vooruitz_economie[t] -0.00355933cons_prijzen_12m[t] -0.0303923fin_sit_gezinnen[t] -0.228762gunstig_sparen[t] +  0.0590081`consumentenvertrouwen(t-1)`[t] -0.0553338`consumentenvertrouwen(t-2)`[t] +  0.271837`consumentenvertrouwen(t-3)`[t] -0.398677`consumentenvertrouwen(t-4)`[t] +  0.36045`consumentenvertrouwen(t-1s)`[t] +  0.195034`consumentenvertrouwen(t-2s)`[t] +  0.143529`consumentenvertrouwen(t-3s)`[t] -0.418048`consumentenvertrouwen(t-4s)`[t] -0.138318`consumentenvertrouwen(t-5s)`[t] -0.137215`consumentenvertrouwen(t-6s)`[t] -0.265878`consumentenvertrouwen(t-7s)`[t] +  0.238537`consumentenvertrouwen(t-8s)`[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285322&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]consumentenvertrouwen[t] =  -15.0344 +  0.478158vooruitz_economie[t] -0.00355933cons_prijzen_12m[t] -0.0303923fin_sit_gezinnen[t] -0.228762gunstig_sparen[t] +  0.0590081`consumentenvertrouwen(t-1)`[t] -0.0553338`consumentenvertrouwen(t-2)`[t] +  0.271837`consumentenvertrouwen(t-3)`[t] -0.398677`consumentenvertrouwen(t-4)`[t] +  0.36045`consumentenvertrouwen(t-1s)`[t] +  0.195034`consumentenvertrouwen(t-2s)`[t] +  0.143529`consumentenvertrouwen(t-3s)`[t] -0.418048`consumentenvertrouwen(t-4s)`[t] -0.138318`consumentenvertrouwen(t-5s)`[t] -0.137215`consumentenvertrouwen(t-6s)`[t] -0.265878`consumentenvertrouwen(t-7s)`[t] +  0.238537`consumentenvertrouwen(t-8s)`[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285322&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285322&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] = -15.0344 + 0.478158vooruitz_economie[t] -0.00355933cons_prijzen_12m[t] -0.0303923fin_sit_gezinnen[t] -0.228762gunstig_sparen[t] + 0.0590081`consumentenvertrouwen(t-1)`[t] -0.0553338`consumentenvertrouwen(t-2)`[t] + 0.271837`consumentenvertrouwen(t-3)`[t] -0.398677`consumentenvertrouwen(t-4)`[t] + 0.36045`consumentenvertrouwen(t-1s)`[t] + 0.195034`consumentenvertrouwen(t-2s)`[t] + 0.143529`consumentenvertrouwen(t-3s)`[t] -0.418048`consumentenvertrouwen(t-4s)`[t] -0.138318`consumentenvertrouwen(t-5s)`[t] -0.137215`consumentenvertrouwen(t-6s)`[t] -0.265878`consumentenvertrouwen(t-7s)`[t] + 0.238537`consumentenvertrouwen(t-8s)`[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)	-15.03	7.019	-2.1420e+00	0.1216	0.06081
vooruitz_economie	+0.4782	0.06488	+7.3690e+00	0.005166	0.002583
cons_prijzen_12m	-0.003559	0.08208	-4.3370e-02	0.9681	0.4841
fin_sit_gezinnen	-0.03039	0.3247	-9.3590e-02	0.9313	0.4657
gunstig_sparen	-0.2288	0.213	-1.0740e+00	0.3616	0.1808
`consumentenvertrouwen(t-1)`	+0.05901	0.1219	+4.8420e-01	0.6614	0.3307
`consumentenvertrouwen(t-2)`	-0.05533	0.1505	-3.6760e-01	0.7376	0.3688
`consumentenvertrouwen(t-3)`	+0.2718	0.135	+2.0140e+00	0.1375	0.06875
`consumentenvertrouwen(t-4)`	-0.3987	0.2714	-1.4690e+00	0.2381	0.1191
`consumentenvertrouwen(t-1s)`	+0.3604	0.2506	+1.4380e+00	0.246	0.123
`consumentenvertrouwen(t-2s)`	+0.195	0.1523	+1.2810e+00	0.2903	0.1451
`consumentenvertrouwen(t-3s)`	+0.1435	0.1629	+8.8110e-01	0.4432	0.2216
`consumentenvertrouwen(t-4s)`	-0.418	0.151	-2.7680e+00	0.0697	0.03485
`consumentenvertrouwen(t-5s)`	-0.1383	0.2192	-6.3100e-01	0.5728	0.2864
`consumentenvertrouwen(t-6s)`	-0.1372	0.1038	-1.3220e+00	0.278	0.139
`consumentenvertrouwen(t-7s)`	-0.2659	0.1805	-1.4730e+00	0.2372	0.1186
`consumentenvertrouwen(t-8s)`	+0.2385	0.1492	+1.5990e+00	0.2081	0.1041

\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) & -15.03 &  7.019 & -2.1420e+00 &  0.1216 &  0.06081 \tabularnewline
vooruitz_economie & +0.4782 &  0.06488 & +7.3690e+00 &  0.005166 &  0.002583 \tabularnewline
cons_prijzen_12m & -0.003559 &  0.08208 & -4.3370e-02 &  0.9681 &  0.4841 \tabularnewline
fin_sit_gezinnen & -0.03039 &  0.3247 & -9.3590e-02 &  0.9313 &  0.4657 \tabularnewline
gunstig_sparen & -0.2288 &  0.213 & -1.0740e+00 &  0.3616 &  0.1808 \tabularnewline
`consumentenvertrouwen(t-1)` & +0.05901 &  0.1219 & +4.8420e-01 &  0.6614 &  0.3307 \tabularnewline
`consumentenvertrouwen(t-2)` & -0.05533 &  0.1505 & -3.6760e-01 &  0.7376 &  0.3688 \tabularnewline
`consumentenvertrouwen(t-3)` & +0.2718 &  0.135 & +2.0140e+00 &  0.1375 &  0.06875 \tabularnewline
`consumentenvertrouwen(t-4)` & -0.3987 &  0.2714 & -1.4690e+00 &  0.2381 &  0.1191 \tabularnewline
`consumentenvertrouwen(t-1s)` & +0.3604 &  0.2506 & +1.4380e+00 &  0.246 &  0.123 \tabularnewline
`consumentenvertrouwen(t-2s)` & +0.195 &  0.1523 & +1.2810e+00 &  0.2903 &  0.1451 \tabularnewline
`consumentenvertrouwen(t-3s)` & +0.1435 &  0.1629 & +8.8110e-01 &  0.4432 &  0.2216 \tabularnewline
`consumentenvertrouwen(t-4s)` & -0.418 &  0.151 & -2.7680e+00 &  0.0697 &  0.03485 \tabularnewline
`consumentenvertrouwen(t-5s)` & -0.1383 &  0.2192 & -6.3100e-01 &  0.5728 &  0.2864 \tabularnewline
`consumentenvertrouwen(t-6s)` & -0.1372 &  0.1038 & -1.3220e+00 &  0.278 &  0.139 \tabularnewline
`consumentenvertrouwen(t-7s)` & -0.2659 &  0.1805 & -1.4730e+00 &  0.2372 &  0.1186 \tabularnewline
`consumentenvertrouwen(t-8s)` & +0.2385 &  0.1492 & +1.5990e+00 &  0.2081 &  0.1041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285322&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]-15.03[/C][C] 7.019[/C][C]-2.1420e+00[/C][C] 0.1216[/C][C] 0.06081[/C][/ROW]
[ROW][C]vooruitz_economie[/C][C]+0.4782[/C][C] 0.06488[/C][C]+7.3690e+00[/C][C] 0.005166[/C][C] 0.002583[/C][/ROW]
[ROW][C]cons_prijzen_12m[/C][C]-0.003559[/C][C] 0.08208[/C][C]-4.3370e-02[/C][C] 0.9681[/C][C] 0.4841[/C][/ROW]
[ROW][C]fin_sit_gezinnen[/C][C]-0.03039[/C][C] 0.3247[/C][C]-9.3590e-02[/C][C] 0.9313[/C][C] 0.4657[/C][/ROW]
[ROW][C]gunstig_sparen[/C][C]-0.2288[/C][C] 0.213[/C][C]-1.0740e+00[/C][C] 0.3616[/C][C] 0.1808[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-1)`[/C][C]+0.05901[/C][C] 0.1219[/C][C]+4.8420e-01[/C][C] 0.6614[/C][C] 0.3307[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-2)`[/C][C]-0.05533[/C][C] 0.1505[/C][C]-3.6760e-01[/C][C] 0.7376[/C][C] 0.3688[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-3)`[/C][C]+0.2718[/C][C] 0.135[/C][C]+2.0140e+00[/C][C] 0.1375[/C][C] 0.06875[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-4)`[/C][C]-0.3987[/C][C] 0.2714[/C][C]-1.4690e+00[/C][C] 0.2381[/C][C] 0.1191[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-1s)`[/C][C]+0.3604[/C][C] 0.2506[/C][C]+1.4380e+00[/C][C] 0.246[/C][C] 0.123[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-2s)`[/C][C]+0.195[/C][C] 0.1523[/C][C]+1.2810e+00[/C][C] 0.2903[/C][C] 0.1451[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-3s)`[/C][C]+0.1435[/C][C] 0.1629[/C][C]+8.8110e-01[/C][C] 0.4432[/C][C] 0.2216[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-4s)`[/C][C]-0.418[/C][C] 0.151[/C][C]-2.7680e+00[/C][C] 0.0697[/C][C] 0.03485[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-5s)`[/C][C]-0.1383[/C][C] 0.2192[/C][C]-6.3100e-01[/C][C] 0.5728[/C][C] 0.2864[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-6s)`[/C][C]-0.1372[/C][C] 0.1038[/C][C]-1.3220e+00[/C][C] 0.278[/C][C] 0.139[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-7s)`[/C][C]-0.2659[/C][C] 0.1805[/C][C]-1.4730e+00[/C][C] 0.2372[/C][C] 0.1186[/C][/ROW]
[ROW][C]`consumentenvertrouwen(t-8s)`[/C][C]+0.2385[/C][C] 0.1492[/C][C]+1.5990e+00[/C][C] 0.2081[/C][C] 0.1041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285322&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285322&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)	-15.03	7.019	-2.1420e+00	0.1216	0.06081
vooruitz_economie	+0.4782	0.06488	+7.3690e+00	0.005166	0.002583
cons_prijzen_12m	-0.003559	0.08208	-4.3370e-02	0.9681	0.4841
fin_sit_gezinnen	-0.03039	0.3247	-9.3590e-02	0.9313	0.4657
gunstig_sparen	-0.2288	0.213	-1.0740e+00	0.3616	0.1808
`consumentenvertrouwen(t-1)`	+0.05901	0.1219	+4.8420e-01	0.6614	0.3307
`consumentenvertrouwen(t-2)`	-0.05533	0.1505	-3.6760e-01	0.7376	0.3688
`consumentenvertrouwen(t-3)`	+0.2718	0.135	+2.0140e+00	0.1375	0.06875
`consumentenvertrouwen(t-4)`	-0.3987	0.2714	-1.4690e+00	0.2381	0.1191
`consumentenvertrouwen(t-1s)`	+0.3604	0.2506	+1.4380e+00	0.246	0.123
`consumentenvertrouwen(t-2s)`	+0.195	0.1523	+1.2810e+00	0.2903	0.1451
`consumentenvertrouwen(t-3s)`	+0.1435	0.1629	+8.8110e-01	0.4432	0.2216
`consumentenvertrouwen(t-4s)`	-0.418	0.151	-2.7680e+00	0.0697	0.03485
`consumentenvertrouwen(t-5s)`	-0.1383	0.2192	-6.3100e-01	0.5728	0.2864
`consumentenvertrouwen(t-6s)`	-0.1372	0.1038	-1.3220e+00	0.278	0.139
`consumentenvertrouwen(t-7s)`	-0.2659	0.1805	-1.4730e+00	0.2372	0.1186
`consumentenvertrouwen(t-8s)`	+0.2385	0.1492	+1.5990e+00	0.2081	0.1041

Multiple Linear Regression - Regression Statistics
Multiple R	0.9971
R-squared	0.9943
Adjusted R-squared	0.9637
F-TEST (value)	32.54
F-TEST (DF numerator)	16
F-TEST (DF denominator)	3
p-value	0.007538
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.622
Sum Squared Residuals	1.161

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.9971 \tabularnewline
R-squared &  0.9943 \tabularnewline
Adjusted R-squared &  0.9637 \tabularnewline
F-TEST (value) &  32.54 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 3 \tabularnewline
p-value &  0.007538 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  0.622 \tabularnewline
Sum Squared Residuals &  1.161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285322&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.9971[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.9943[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.9637[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 32.54[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]3[/C][/ROW]
[ROW][C]p-value[/C][C] 0.007538[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 0.622[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 1.161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285322&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285322&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	0.9971
R-squared	0.9943
Adjusted R-squared	0.9637
F-TEST (value)	32.54
F-TEST (DF numerator)	16
F-TEST (DF denominator)	3
p-value	0.007538
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.622
Sum Squared Residuals	1.161

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	-9	-8.73	-0.2699
2	-6	-6.389	0.389
3	-7	-6.898	-0.1019
4	-10	-10.04	0.04073
5	-11	-10.93	-0.07455
6	-11	-11.26	0.2578
7	-12	-11.63	-0.3666
8	-14	-14.4	0.3982
9	-12	-11.83	-0.1659
10	-9	-8.701	-0.299
11	-5	-5.153	0.1526
12	-6	-6.345	0.3451
13	-6	-5.598	-0.4015
14	-3	-3.149	0.1491
15	-2	-1.942	-0.0585
16	-6	-5.967	-0.03285
17	-6	-6.161	0.1615
18	-10	-9.823	-0.1769
19	-8	-8.19	0.1897
20	-4	-3.864	-0.1362

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -9 & -8.73 & -0.2699 \tabularnewline
2 & -6 & -6.389 &  0.389 \tabularnewline
3 & -7 & -6.898 & -0.1019 \tabularnewline
4 & -10 & -10.04 &  0.04073 \tabularnewline
5 & -11 & -10.93 & -0.07455 \tabularnewline
6 & -11 & -11.26 &  0.2578 \tabularnewline
7 & -12 & -11.63 & -0.3666 \tabularnewline
8 & -14 & -14.4 &  0.3982 \tabularnewline
9 & -12 & -11.83 & -0.1659 \tabularnewline
10 & -9 & -8.701 & -0.299 \tabularnewline
11 & -5 & -5.153 &  0.1526 \tabularnewline
12 & -6 & -6.345 &  0.3451 \tabularnewline
13 & -6 & -5.598 & -0.4015 \tabularnewline
14 & -3 & -3.149 &  0.1491 \tabularnewline
15 & -2 & -1.942 & -0.0585 \tabularnewline
16 & -6 & -5.967 & -0.03285 \tabularnewline
17 & -6 & -6.161 &  0.1615 \tabularnewline
18 & -10 & -9.823 & -0.1769 \tabularnewline
19 & -8 & -8.19 &  0.1897 \tabularnewline
20 & -4 & -3.864 & -0.1362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285322&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]-9[/C][C]-8.73[/C][C]-0.2699[/C][/ROW]
[ROW][C]2[/C][C]-6[/C][C]-6.389[/C][C] 0.389[/C][/ROW]
[ROW][C]3[/C][C]-7[/C][C]-6.898[/C][C]-0.1019[/C][/ROW]
[ROW][C]4[/C][C]-10[/C][C]-10.04[/C][C] 0.04073[/C][/ROW]
[ROW][C]5[/C][C]-11[/C][C]-10.93[/C][C]-0.07455[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-11.26[/C][C] 0.2578[/C][/ROW]
[ROW][C]7[/C][C]-12[/C][C]-11.63[/C][C]-0.3666[/C][/ROW]
[ROW][C]8[/C][C]-14[/C][C]-14.4[/C][C] 0.3982[/C][/ROW]
[ROW][C]9[/C][C]-12[/C][C]-11.83[/C][C]-0.1659[/C][/ROW]
[ROW][C]10[/C][C]-9[/C][C]-8.701[/C][C]-0.299[/C][/ROW]
[ROW][C]11[/C][C]-5[/C][C]-5.153[/C][C] 0.1526[/C][/ROW]
[ROW][C]12[/C][C]-6[/C][C]-6.345[/C][C] 0.3451[/C][/ROW]
[ROW][C]13[/C][C]-6[/C][C]-5.598[/C][C]-0.4015[/C][/ROW]
[ROW][C]14[/C][C]-3[/C][C]-3.149[/C][C] 0.1491[/C][/ROW]
[ROW][C]15[/C][C]-2[/C][C]-1.942[/C][C]-0.0585[/C][/ROW]
[ROW][C]16[/C][C]-6[/C][C]-5.967[/C][C]-0.03285[/C][/ROW]
[ROW][C]17[/C][C]-6[/C][C]-6.161[/C][C] 0.1615[/C][/ROW]
[ROW][C]18[/C][C]-10[/C][C]-9.823[/C][C]-0.1769[/C][/ROW]
[ROW][C]19[/C][C]-8[/C][C]-8.19[/C][C] 0.1897[/C][/ROW]
[ROW][C]20[/C][C]-4[/C][C]-3.864[/C][C]-0.1362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285322&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285322&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	-9	-8.73	-0.2699
2	-6	-6.389	0.389
3	-7	-6.898	-0.1019
4	-10	-10.04	0.04073
5	-11	-10.93	-0.07455
6	-11	-11.26	0.2578
7	-12	-11.63	-0.3666
8	-14	-14.4	0.3982
9	-12	-11.83	-0.1659
10	-9	-8.701	-0.299
11	-5	-5.153	0.1526
12	-6	-6.345	0.3451
13	-6	-5.598	-0.4015
14	-3	-3.149	0.1491
15	-2	-1.942	-0.0585
16	-6	-5.967	-0.03285
17	-6	-6.161	0.1615
18	-10	-9.823	-0.1769
19	-8	-8.19	0.1897
20	-4	-3.864	-0.1362

Figure 1

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Figure 3

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Figure 4

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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 = 4 ; par5 = 12 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 4 ; par5 = 8 ;

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

par5 <- '6'
par4 <- '4'
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'){
(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