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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 22 Dec 2008 15:26:41 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t1229984840dvnete2bldoi8c8.htm/, Retrieved Sun, 12 May 2024 12:40:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36243, Retrieved Sun, 12 May 2024 12:40:14 +0000

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Estimated Impact

191

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
F    D  [Multiple Regression] [Case seatbelt law...] [2008-11-24 09:36:19] [b82ef11dce0545f3fd4676ec3ebed828]
-    D    [Multiple Regression] [Paper: Multiple R...] [2008-12-14 13:42:08] [9e54d1454d464f1bf9ee4a54d5d56945]
-   PD      [Multiple Regression] [Paper: Multiple R...] [2008-12-16 18:26:09] [9e54d1454d464f1bf9ee4a54d5d56945]
-               [Multiple Regression] [] [2008-12-22 22:26:41] [27189814204044fdc56e2241a9375b9f] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36243&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36243&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 20.8533123028391 + 12.9760252365931x[t] -3.35047318611986M1[t] -7.2873291272345M2[t] -0.687329127234502M3[t] -0.220662460567836M4[t] -0.653995793901169M5[t] -4.12066246056783M6[t] -0.320662460567832M7[t] -1.9373291272345M8[t] + 1.09600420609883M9[t] -0.103995793901166M10[t] -2.70000000000001M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  20.8533123028391 +  12.9760252365931x[t] -3.35047318611986M1[t] -7.2873291272345M2[t] -0.687329127234502M3[t] -0.220662460567836M4[t] -0.653995793901169M5[t] -4.12066246056783M6[t] -0.320662460567832M7[t] -1.9373291272345M8[t] +  1.09600420609883M9[t] -0.103995793901166M10[t] -2.70000000000001M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36243&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  20.8533123028391 +  12.9760252365931x[t] -3.35047318611986M1[t] -7.2873291272345M2[t] -0.687329127234502M3[t] -0.220662460567836M4[t] -0.653995793901169M5[t] -4.12066246056783M6[t] -0.320662460567832M7[t] -1.9373291272345M8[t] +  1.09600420609883M9[t] -0.103995793901166M10[t] -2.70000000000001M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36243&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 20.8533123028391 + 12.9760252365931x[t] -3.35047318611986M1[t] -7.2873291272345M2[t] -0.687329127234502M3[t] -0.220662460567836M4[t] -0.653995793901169M5[t] -4.12066246056783M6[t] -0.320662460567832M7[t] -1.9373291272345M8[t] + 1.09600420609883M9[t] -0.103995793901166M10[t] -2.70000000000001M11[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)	20.8533123028391	3.248691	6.419	0	0
x	12.9760252365931	1.813153	7.1566	0	0
M1	-3.35047318611986	3.925176	-0.8536	0.39673	0.198365
M2	-7.2873291272345	4.078394	-1.7868	0.07902	0.03951
M3	-0.687329127234502	4.078394	-0.1685	0.866734	0.433367
M4	-0.220662460567836	4.078394	-0.0541	0.957031	0.478516
M5	-0.653995793901169	4.078394	-0.1604	0.873139	0.43657
M6	-4.12066246056783	4.078394	-1.0104	0.316378	0.158189
M7	-0.320662460567832	4.078394	-0.0786	0.937593	0.468796
M8	-1.9373291272345	4.078394	-0.475	0.636496	0.318248
M9	1.09600420609883	4.078394	0.2687	0.789056	0.394528
M10	-0.103995793901166	4.078394	-0.0255	0.979741	0.489871
M11	-2.70000000000001	4.067183	-0.6639	0.509329	0.254665

\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) & 20.8533123028391 & 3.248691 & 6.419 & 0 & 0 \tabularnewline
x & 12.9760252365931 & 1.813153 & 7.1566 & 0 & 0 \tabularnewline
M1 & -3.35047318611986 & 3.925176 & -0.8536 & 0.39673 & 0.198365 \tabularnewline
M2 & -7.2873291272345 & 4.078394 & -1.7868 & 0.07902 & 0.03951 \tabularnewline
M3 & -0.687329127234502 & 4.078394 & -0.1685 & 0.866734 & 0.433367 \tabularnewline
M4 & -0.220662460567836 & 4.078394 & -0.0541 & 0.957031 & 0.478516 \tabularnewline
M5 & -0.653995793901169 & 4.078394 & -0.1604 & 0.873139 & 0.43657 \tabularnewline
M6 & -4.12066246056783 & 4.078394 & -1.0104 & 0.316378 & 0.158189 \tabularnewline
M7 & -0.320662460567832 & 4.078394 & -0.0786 & 0.937593 & 0.468796 \tabularnewline
M8 & -1.9373291272345 & 4.078394 & -0.475 & 0.636496 & 0.318248 \tabularnewline
M9 & 1.09600420609883 & 4.078394 & 0.2687 & 0.789056 & 0.394528 \tabularnewline
M10 & -0.103995793901166 & 4.078394 & -0.0255 & 0.979741 & 0.489871 \tabularnewline
M11 & -2.70000000000001 & 4.067183 & -0.6639 & 0.509329 & 0.254665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36243&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]20.8533123028391[/C][C]3.248691[/C][C]6.419[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]12.9760252365931[/C][C]1.813153[/C][C]7.1566[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-3.35047318611986[/C][C]3.925176[/C][C]-0.8536[/C][C]0.39673[/C][C]0.198365[/C][/ROW]
[ROW][C]M2[/C][C]-7.2873291272345[/C][C]4.078394[/C][C]-1.7868[/C][C]0.07902[/C][C]0.03951[/C][/ROW]
[ROW][C]M3[/C][C]-0.687329127234502[/C][C]4.078394[/C][C]-0.1685[/C][C]0.866734[/C][C]0.433367[/C][/ROW]
[ROW][C]M4[/C][C]-0.220662460567836[/C][C]4.078394[/C][C]-0.0541[/C][C]0.957031[/C][C]0.478516[/C][/ROW]
[ROW][C]M5[/C][C]-0.653995793901169[/C][C]4.078394[/C][C]-0.1604[/C][C]0.873139[/C][C]0.43657[/C][/ROW]
[ROW][C]M6[/C][C]-4.12066246056783[/C][C]4.078394[/C][C]-1.0104[/C][C]0.316378[/C][C]0.158189[/C][/ROW]
[ROW][C]M7[/C][C]-0.320662460567832[/C][C]4.078394[/C][C]-0.0786[/C][C]0.937593[/C][C]0.468796[/C][/ROW]
[ROW][C]M8[/C][C]-1.9373291272345[/C][C]4.078394[/C][C]-0.475[/C][C]0.636496[/C][C]0.318248[/C][/ROW]
[ROW][C]M9[/C][C]1.09600420609883[/C][C]4.078394[/C][C]0.2687[/C][C]0.789056[/C][C]0.394528[/C][/ROW]
[ROW][C]M10[/C][C]-0.103995793901166[/C][C]4.078394[/C][C]-0.0255[/C][C]0.979741[/C][C]0.489871[/C][/ROW]
[ROW][C]M11[/C][C]-2.70000000000001[/C][C]4.067183[/C][C]-0.6639[/C][C]0.509329[/C][C]0.254665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36243&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)	20.8533123028391	3.248691	6.419	0	0
x	12.9760252365931	1.813153	7.1566	0	0
M1	-3.35047318611986	3.925176	-0.8536	0.39673	0.198365
M2	-7.2873291272345	4.078394	-1.7868	0.07902	0.03951
M3	-0.687329127234502	4.078394	-0.1685	0.866734	0.433367
M4	-0.220662460567836	4.078394	-0.0541	0.957031	0.478516
M5	-0.653995793901169	4.078394	-0.1604	0.873139	0.43657
M6	-4.12066246056783	4.078394	-1.0104	0.316378	0.158189
M7	-0.320662460567832	4.078394	-0.0786	0.937593	0.468796
M8	-1.9373291272345	4.078394	-0.475	0.636496	0.318248
M9	1.09600420609883	4.078394	0.2687	0.789056	0.394528
M10	-0.103995793901166	4.078394	-0.0255	0.979741	0.489871
M11	-2.70000000000001	4.067183	-0.6639	0.509329	0.254665

Multiple Linear Regression - Regression Statistics
Multiple R	0.705897895720123
R-squared	0.498291839182097
Adjusted R-squared	0.397950207018517
F-TEST (value)	4.96595309880713
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	1.21898229794581e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.04456831125253
Sum Squared Residuals	2977.55656151419

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.705897895720123 \tabularnewline
R-squared & 0.498291839182097 \tabularnewline
Adjusted R-squared & 0.397950207018517 \tabularnewline
F-TEST (value) & 4.96595309880713 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 60 \tabularnewline
p-value & 1.21898229794581e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 7.04456831125253 \tabularnewline
Sum Squared Residuals & 2977.55656151419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36243&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.705897895720123[/C][/ROW]
[ROW][C]R-squared[/C][C]0.498291839182097[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.397950207018517[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.96595309880713[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]60[/C][/ROW]
[ROW][C]p-value[/C][C]1.21898229794581e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]7.04456831125253[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2977.55656151419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36243&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36243&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	0.705897895720123
R-squared	0.498291839182097
Adjusted R-squared	0.397950207018517
F-TEST (value)	4.96595309880713
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	1.21898229794581e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.04456831125253
Sum Squared Residuals	2977.55656151419

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	17.3	17.5028391167191	-0.202839116719124
2	15.4	13.5659831756047	1.83401682439533
3	16.9	20.1659831756046	-3.26598317560462
4	20.8	20.6326498422713	0.167350157728703
5	16.4	20.1993165089380	-3.79931650893796
6	11.3	16.7326498422713	-5.43264984227129
7	17.5	20.5326498422713	-3.0326498422713
8	16.6	18.9159831756046	-2.31598317560463
9	17.5	21.9493165089380	-4.44931650893796
10	19.5	20.7493165089380	-1.24931650893796
11	18.8	18.1533123028391	0.646687697160882
12	20.2	20.8533123028391	-0.653312302839126
13	19.2	17.5028391167193	1.69716088328073
14	14.4	13.5659831756046	0.834016824395377
15	24.5	20.1659831756046	4.33401682439537
16	25.7	20.6326498422713	5.0673501577287
17	27.1	20.1993165089380	6.90068349106204
18	21	16.7326498422713	4.2673501577287
19	18.6	20.5326498422713	-1.93264984227130
20	20	18.9159831756046	1.08401682439537
21	21.8	21.9493165089380	-0.149316508937964
22	20.4	20.7493165089380	-0.349316508937965
23	18	31.1293375394322	-13.1293375394322
24	21.5	33.8293375394322	-12.3293375394322
25	19.1	30.4788643533123	-11.3788643533123
26	19.7	26.5420084121977	-6.84200841219768
27	26	33.1420084121977	-7.14200841219768
28	26.3	33.6086750788644	-7.30867507886435
29	24.6	33.175341745531	-8.57534174553101
30	22.4	29.7086750788644	-7.30867507886435
31	32	33.5086750788643	-1.50867507886435
32	24	31.8920084121977	-7.89200841219768
33	30	34.925341745531	-4.92534174553102
34	24.1	33.725341745531	-9.62534174553102
35	26.3	31.1293375394322	-4.82933753943218
36	29.8	33.8293375394322	-4.02933753943218
37	21.9	30.4788643533123	-8.57886435331232
38	22.8	26.5420084121977	-3.74200841219768
39	29.2	33.1420084121977	-3.94200841219768
40	27.5	33.6086750788644	-6.10867507886435
41	27.4	33.175341745531	-5.77534174553102
42	31	29.7086750788643	1.29132492113565
43	26.1	33.5086750788643	-7.40867507886435
44	22.2	31.8920084121977	-9.69200841219768
45	34	34.925341745531	-0.925341745531018
46	26.9	33.725341745531	-6.82534174553102
47	31.9	31.1293375394322	0.770662460567823
48	34.2	33.8293375394322	0.370662460567821
49	31.2	30.4788643533123	0.721135646687679
50	28.5	26.5420084121977	1.95799158780232
51	37.1	33.1420084121977	3.95799158780232
52	36	33.6086750788644	2.39132492113565
53	34.8	33.175341745531	1.62465825446898
54	32.1	29.7086750788643	2.39132492113565
55	37.2	33.5086750788643	3.69132492113565
56	36.3	31.8920084121977	4.40799158780231
57	39.5	34.925341745531	4.57465825446898
58	37.1	33.725341745531	3.37465825446898
59	35.6	31.1293375394322	4.47066246056783
60	36.2	33.8293375394322	2.37066246056782
61	35.9	30.4788643533123	5.42113564668768
62	32.5	26.5420084121977	5.95799158780232
63	39.2	33.1420084121977	6.05799158780232
64	39.4	33.6086750788644	5.79132492113564
65	42.8	33.175341745531	9.62465825446898
66	34.5	29.7086750788643	4.79132492113565
67	43.7	33.5086750788643	10.1913249211357
68	46.3	31.8920084121977	14.4079915878023
69	40.8	34.925341745531	5.87465825446898
70	48.4	33.725341745531	14.674658254469
71	43.2	31.1293375394322	12.0706624605678
72	48.1	33.8293375394322	14.2706624605678
73	42.8	30.4788643533123	12.3211356466877

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 17.3 & 17.5028391167191 & -0.202839116719124 \tabularnewline
2 & 15.4 & 13.5659831756047 & 1.83401682439533 \tabularnewline
3 & 16.9 & 20.1659831756046 & -3.26598317560462 \tabularnewline
4 & 20.8 & 20.6326498422713 & 0.167350157728703 \tabularnewline
5 & 16.4 & 20.1993165089380 & -3.79931650893796 \tabularnewline
6 & 11.3 & 16.7326498422713 & -5.43264984227129 \tabularnewline
7 & 17.5 & 20.5326498422713 & -3.0326498422713 \tabularnewline
8 & 16.6 & 18.9159831756046 & -2.31598317560463 \tabularnewline
9 & 17.5 & 21.9493165089380 & -4.44931650893796 \tabularnewline
10 & 19.5 & 20.7493165089380 & -1.24931650893796 \tabularnewline
11 & 18.8 & 18.1533123028391 & 0.646687697160882 \tabularnewline
12 & 20.2 & 20.8533123028391 & -0.653312302839126 \tabularnewline
13 & 19.2 & 17.5028391167193 & 1.69716088328073 \tabularnewline
14 & 14.4 & 13.5659831756046 & 0.834016824395377 \tabularnewline
15 & 24.5 & 20.1659831756046 & 4.33401682439537 \tabularnewline
16 & 25.7 & 20.6326498422713 & 5.0673501577287 \tabularnewline
17 & 27.1 & 20.1993165089380 & 6.90068349106204 \tabularnewline
18 & 21 & 16.7326498422713 & 4.2673501577287 \tabularnewline
19 & 18.6 & 20.5326498422713 & -1.93264984227130 \tabularnewline
20 & 20 & 18.9159831756046 & 1.08401682439537 \tabularnewline
21 & 21.8 & 21.9493165089380 & -0.149316508937964 \tabularnewline
22 & 20.4 & 20.7493165089380 & -0.349316508937965 \tabularnewline
23 & 18 & 31.1293375394322 & -13.1293375394322 \tabularnewline
24 & 21.5 & 33.8293375394322 & -12.3293375394322 \tabularnewline
25 & 19.1 & 30.4788643533123 & -11.3788643533123 \tabularnewline
26 & 19.7 & 26.5420084121977 & -6.84200841219768 \tabularnewline
27 & 26 & 33.1420084121977 & -7.14200841219768 \tabularnewline
28 & 26.3 & 33.6086750788644 & -7.30867507886435 \tabularnewline
29 & 24.6 & 33.175341745531 & -8.57534174553101 \tabularnewline
30 & 22.4 & 29.7086750788644 & -7.30867507886435 \tabularnewline
31 & 32 & 33.5086750788643 & -1.50867507886435 \tabularnewline
32 & 24 & 31.8920084121977 & -7.89200841219768 \tabularnewline
33 & 30 & 34.925341745531 & -4.92534174553102 \tabularnewline
34 & 24.1 & 33.725341745531 & -9.62534174553102 \tabularnewline
35 & 26.3 & 31.1293375394322 & -4.82933753943218 \tabularnewline
36 & 29.8 & 33.8293375394322 & -4.02933753943218 \tabularnewline
37 & 21.9 & 30.4788643533123 & -8.57886435331232 \tabularnewline
38 & 22.8 & 26.5420084121977 & -3.74200841219768 \tabularnewline
39 & 29.2 & 33.1420084121977 & -3.94200841219768 \tabularnewline
40 & 27.5 & 33.6086750788644 & -6.10867507886435 \tabularnewline
41 & 27.4 & 33.175341745531 & -5.77534174553102 \tabularnewline
42 & 31 & 29.7086750788643 & 1.29132492113565 \tabularnewline
43 & 26.1 & 33.5086750788643 & -7.40867507886435 \tabularnewline
44 & 22.2 & 31.8920084121977 & -9.69200841219768 \tabularnewline
45 & 34 & 34.925341745531 & -0.925341745531018 \tabularnewline
46 & 26.9 & 33.725341745531 & -6.82534174553102 \tabularnewline
47 & 31.9 & 31.1293375394322 & 0.770662460567823 \tabularnewline
48 & 34.2 & 33.8293375394322 & 0.370662460567821 \tabularnewline
49 & 31.2 & 30.4788643533123 & 0.721135646687679 \tabularnewline
50 & 28.5 & 26.5420084121977 & 1.95799158780232 \tabularnewline
51 & 37.1 & 33.1420084121977 & 3.95799158780232 \tabularnewline
52 & 36 & 33.6086750788644 & 2.39132492113565 \tabularnewline
53 & 34.8 & 33.175341745531 & 1.62465825446898 \tabularnewline
54 & 32.1 & 29.7086750788643 & 2.39132492113565 \tabularnewline
55 & 37.2 & 33.5086750788643 & 3.69132492113565 \tabularnewline
56 & 36.3 & 31.8920084121977 & 4.40799158780231 \tabularnewline
57 & 39.5 & 34.925341745531 & 4.57465825446898 \tabularnewline
58 & 37.1 & 33.725341745531 & 3.37465825446898 \tabularnewline
59 & 35.6 & 31.1293375394322 & 4.47066246056783 \tabularnewline
60 & 36.2 & 33.8293375394322 & 2.37066246056782 \tabularnewline
61 & 35.9 & 30.4788643533123 & 5.42113564668768 \tabularnewline
62 & 32.5 & 26.5420084121977 & 5.95799158780232 \tabularnewline
63 & 39.2 & 33.1420084121977 & 6.05799158780232 \tabularnewline
64 & 39.4 & 33.6086750788644 & 5.79132492113564 \tabularnewline
65 & 42.8 & 33.175341745531 & 9.62465825446898 \tabularnewline
66 & 34.5 & 29.7086750788643 & 4.79132492113565 \tabularnewline
67 & 43.7 & 33.5086750788643 & 10.1913249211357 \tabularnewline
68 & 46.3 & 31.8920084121977 & 14.4079915878023 \tabularnewline
69 & 40.8 & 34.925341745531 & 5.87465825446898 \tabularnewline
70 & 48.4 & 33.725341745531 & 14.674658254469 \tabularnewline
71 & 43.2 & 31.1293375394322 & 12.0706624605678 \tabularnewline
72 & 48.1 & 33.8293375394322 & 14.2706624605678 \tabularnewline
73 & 42.8 & 30.4788643533123 & 12.3211356466877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36243&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]17.3[/C][C]17.5028391167191[/C][C]-0.202839116719124[/C][/ROW]
[ROW][C]2[/C][C]15.4[/C][C]13.5659831756047[/C][C]1.83401682439533[/C][/ROW]
[ROW][C]3[/C][C]16.9[/C][C]20.1659831756046[/C][C]-3.26598317560462[/C][/ROW]
[ROW][C]4[/C][C]20.8[/C][C]20.6326498422713[/C][C]0.167350157728703[/C][/ROW]
[ROW][C]5[/C][C]16.4[/C][C]20.1993165089380[/C][C]-3.79931650893796[/C][/ROW]
[ROW][C]6[/C][C]11.3[/C][C]16.7326498422713[/C][C]-5.43264984227129[/C][/ROW]
[ROW][C]7[/C][C]17.5[/C][C]20.5326498422713[/C][C]-3.0326498422713[/C][/ROW]
[ROW][C]8[/C][C]16.6[/C][C]18.9159831756046[/C][C]-2.31598317560463[/C][/ROW]
[ROW][C]9[/C][C]17.5[/C][C]21.9493165089380[/C][C]-4.44931650893796[/C][/ROW]
[ROW][C]10[/C][C]19.5[/C][C]20.7493165089380[/C][C]-1.24931650893796[/C][/ROW]
[ROW][C]11[/C][C]18.8[/C][C]18.1533123028391[/C][C]0.646687697160882[/C][/ROW]
[ROW][C]12[/C][C]20.2[/C][C]20.8533123028391[/C][C]-0.653312302839126[/C][/ROW]
[ROW][C]13[/C][C]19.2[/C][C]17.5028391167193[/C][C]1.69716088328073[/C][/ROW]
[ROW][C]14[/C][C]14.4[/C][C]13.5659831756046[/C][C]0.834016824395377[/C][/ROW]
[ROW][C]15[/C][C]24.5[/C][C]20.1659831756046[/C][C]4.33401682439537[/C][/ROW]
[ROW][C]16[/C][C]25.7[/C][C]20.6326498422713[/C][C]5.0673501577287[/C][/ROW]
[ROW][C]17[/C][C]27.1[/C][C]20.1993165089380[/C][C]6.90068349106204[/C][/ROW]
[ROW][C]18[/C][C]21[/C][C]16.7326498422713[/C][C]4.2673501577287[/C][/ROW]
[ROW][C]19[/C][C]18.6[/C][C]20.5326498422713[/C][C]-1.93264984227130[/C][/ROW]
[ROW][C]20[/C][C]20[/C][C]18.9159831756046[/C][C]1.08401682439537[/C][/ROW]
[ROW][C]21[/C][C]21.8[/C][C]21.9493165089380[/C][C]-0.149316508937964[/C][/ROW]
[ROW][C]22[/C][C]20.4[/C][C]20.7493165089380[/C][C]-0.349316508937965[/C][/ROW]
[ROW][C]23[/C][C]18[/C][C]31.1293375394322[/C][C]-13.1293375394322[/C][/ROW]
[ROW][C]24[/C][C]21.5[/C][C]33.8293375394322[/C][C]-12.3293375394322[/C][/ROW]
[ROW][C]25[/C][C]19.1[/C][C]30.4788643533123[/C][C]-11.3788643533123[/C][/ROW]
[ROW][C]26[/C][C]19.7[/C][C]26.5420084121977[/C][C]-6.84200841219768[/C][/ROW]
[ROW][C]27[/C][C]26[/C][C]33.1420084121977[/C][C]-7.14200841219768[/C][/ROW]
[ROW][C]28[/C][C]26.3[/C][C]33.6086750788644[/C][C]-7.30867507886435[/C][/ROW]
[ROW][C]29[/C][C]24.6[/C][C]33.175341745531[/C][C]-8.57534174553101[/C][/ROW]
[ROW][C]30[/C][C]22.4[/C][C]29.7086750788644[/C][C]-7.30867507886435[/C][/ROW]
[ROW][C]31[/C][C]32[/C][C]33.5086750788643[/C][C]-1.50867507886435[/C][/ROW]
[ROW][C]32[/C][C]24[/C][C]31.8920084121977[/C][C]-7.89200841219768[/C][/ROW]
[ROW][C]33[/C][C]30[/C][C]34.925341745531[/C][C]-4.92534174553102[/C][/ROW]
[ROW][C]34[/C][C]24.1[/C][C]33.725341745531[/C][C]-9.62534174553102[/C][/ROW]
[ROW][C]35[/C][C]26.3[/C][C]31.1293375394322[/C][C]-4.82933753943218[/C][/ROW]
[ROW][C]36[/C][C]29.8[/C][C]33.8293375394322[/C][C]-4.02933753943218[/C][/ROW]
[ROW][C]37[/C][C]21.9[/C][C]30.4788643533123[/C][C]-8.57886435331232[/C][/ROW]
[ROW][C]38[/C][C]22.8[/C][C]26.5420084121977[/C][C]-3.74200841219768[/C][/ROW]
[ROW][C]39[/C][C]29.2[/C][C]33.1420084121977[/C][C]-3.94200841219768[/C][/ROW]
[ROW][C]40[/C][C]27.5[/C][C]33.6086750788644[/C][C]-6.10867507886435[/C][/ROW]
[ROW][C]41[/C][C]27.4[/C][C]33.175341745531[/C][C]-5.77534174553102[/C][/ROW]
[ROW][C]42[/C][C]31[/C][C]29.7086750788643[/C][C]1.29132492113565[/C][/ROW]
[ROW][C]43[/C][C]26.1[/C][C]33.5086750788643[/C][C]-7.40867507886435[/C][/ROW]
[ROW][C]44[/C][C]22.2[/C][C]31.8920084121977[/C][C]-9.69200841219768[/C][/ROW]
[ROW][C]45[/C][C]34[/C][C]34.925341745531[/C][C]-0.925341745531018[/C][/ROW]
[ROW][C]46[/C][C]26.9[/C][C]33.725341745531[/C][C]-6.82534174553102[/C][/ROW]
[ROW][C]47[/C][C]31.9[/C][C]31.1293375394322[/C][C]0.770662460567823[/C][/ROW]
[ROW][C]48[/C][C]34.2[/C][C]33.8293375394322[/C][C]0.370662460567821[/C][/ROW]
[ROW][C]49[/C][C]31.2[/C][C]30.4788643533123[/C][C]0.721135646687679[/C][/ROW]
[ROW][C]50[/C][C]28.5[/C][C]26.5420084121977[/C][C]1.95799158780232[/C][/ROW]
[ROW][C]51[/C][C]37.1[/C][C]33.1420084121977[/C][C]3.95799158780232[/C][/ROW]
[ROW][C]52[/C][C]36[/C][C]33.6086750788644[/C][C]2.39132492113565[/C][/ROW]
[ROW][C]53[/C][C]34.8[/C][C]33.175341745531[/C][C]1.62465825446898[/C][/ROW]
[ROW][C]54[/C][C]32.1[/C][C]29.7086750788643[/C][C]2.39132492113565[/C][/ROW]
[ROW][C]55[/C][C]37.2[/C][C]33.5086750788643[/C][C]3.69132492113565[/C][/ROW]
[ROW][C]56[/C][C]36.3[/C][C]31.8920084121977[/C][C]4.40799158780231[/C][/ROW]
[ROW][C]57[/C][C]39.5[/C][C]34.925341745531[/C][C]4.57465825446898[/C][/ROW]
[ROW][C]58[/C][C]37.1[/C][C]33.725341745531[/C][C]3.37465825446898[/C][/ROW]
[ROW][C]59[/C][C]35.6[/C][C]31.1293375394322[/C][C]4.47066246056783[/C][/ROW]
[ROW][C]60[/C][C]36.2[/C][C]33.8293375394322[/C][C]2.37066246056782[/C][/ROW]
[ROW][C]61[/C][C]35.9[/C][C]30.4788643533123[/C][C]5.42113564668768[/C][/ROW]
[ROW][C]62[/C][C]32.5[/C][C]26.5420084121977[/C][C]5.95799158780232[/C][/ROW]
[ROW][C]63[/C][C]39.2[/C][C]33.1420084121977[/C][C]6.05799158780232[/C][/ROW]
[ROW][C]64[/C][C]39.4[/C][C]33.6086750788644[/C][C]5.79132492113564[/C][/ROW]
[ROW][C]65[/C][C]42.8[/C][C]33.175341745531[/C][C]9.62465825446898[/C][/ROW]
[ROW][C]66[/C][C]34.5[/C][C]29.7086750788643[/C][C]4.79132492113565[/C][/ROW]
[ROW][C]67[/C][C]43.7[/C][C]33.5086750788643[/C][C]10.1913249211357[/C][/ROW]
[ROW][C]68[/C][C]46.3[/C][C]31.8920084121977[/C][C]14.4079915878023[/C][/ROW]
[ROW][C]69[/C][C]40.8[/C][C]34.925341745531[/C][C]5.87465825446898[/C][/ROW]
[ROW][C]70[/C][C]48.4[/C][C]33.725341745531[/C][C]14.674658254469[/C][/ROW]
[ROW][C]71[/C][C]43.2[/C][C]31.1293375394322[/C][C]12.0706624605678[/C][/ROW]
[ROW][C]72[/C][C]48.1[/C][C]33.8293375394322[/C][C]14.2706624605678[/C][/ROW]
[ROW][C]73[/C][C]42.8[/C][C]30.4788643533123[/C][C]12.3211356466877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36243&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36243&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	17.3	17.5028391167191	-0.202839116719124
2	15.4	13.5659831756047	1.83401682439533
3	16.9	20.1659831756046	-3.26598317560462
4	20.8	20.6326498422713	0.167350157728703
5	16.4	20.1993165089380	-3.79931650893796
6	11.3	16.7326498422713	-5.43264984227129
7	17.5	20.5326498422713	-3.0326498422713
8	16.6	18.9159831756046	-2.31598317560463
9	17.5	21.9493165089380	-4.44931650893796
10	19.5	20.7493165089380	-1.24931650893796
11	18.8	18.1533123028391	0.646687697160882
12	20.2	20.8533123028391	-0.653312302839126
13	19.2	17.5028391167193	1.69716088328073
14	14.4	13.5659831756046	0.834016824395377
15	24.5	20.1659831756046	4.33401682439537
16	25.7	20.6326498422713	5.0673501577287
17	27.1	20.1993165089380	6.90068349106204
18	21	16.7326498422713	4.2673501577287
19	18.6	20.5326498422713	-1.93264984227130
20	20	18.9159831756046	1.08401682439537
21	21.8	21.9493165089380	-0.149316508937964
22	20.4	20.7493165089380	-0.349316508937965
23	18	31.1293375394322	-13.1293375394322
24	21.5	33.8293375394322	-12.3293375394322
25	19.1	30.4788643533123	-11.3788643533123
26	19.7	26.5420084121977	-6.84200841219768
27	26	33.1420084121977	-7.14200841219768
28	26.3	33.6086750788644	-7.30867507886435
29	24.6	33.175341745531	-8.57534174553101
30	22.4	29.7086750788644	-7.30867507886435
31	32	33.5086750788643	-1.50867507886435
32	24	31.8920084121977	-7.89200841219768
33	30	34.925341745531	-4.92534174553102
34	24.1	33.725341745531	-9.62534174553102
35	26.3	31.1293375394322	-4.82933753943218
36	29.8	33.8293375394322	-4.02933753943218
37	21.9	30.4788643533123	-8.57886435331232
38	22.8	26.5420084121977	-3.74200841219768
39	29.2	33.1420084121977	-3.94200841219768
40	27.5	33.6086750788644	-6.10867507886435
41	27.4	33.175341745531	-5.77534174553102
42	31	29.7086750788643	1.29132492113565
43	26.1	33.5086750788643	-7.40867507886435
44	22.2	31.8920084121977	-9.69200841219768
45	34	34.925341745531	-0.925341745531018
46	26.9	33.725341745531	-6.82534174553102
47	31.9	31.1293375394322	0.770662460567823
48	34.2	33.8293375394322	0.370662460567821
49	31.2	30.4788643533123	0.721135646687679
50	28.5	26.5420084121977	1.95799158780232
51	37.1	33.1420084121977	3.95799158780232
52	36	33.6086750788644	2.39132492113565
53	34.8	33.175341745531	1.62465825446898
54	32.1	29.7086750788643	2.39132492113565
55	37.2	33.5086750788643	3.69132492113565
56	36.3	31.8920084121977	4.40799158780231
57	39.5	34.925341745531	4.57465825446898
58	37.1	33.725341745531	3.37465825446898
59	35.6	31.1293375394322	4.47066246056783
60	36.2	33.8293375394322	2.37066246056782
61	35.9	30.4788643533123	5.42113564668768
62	32.5	26.5420084121977	5.95799158780232
63	39.2	33.1420084121977	6.05799158780232
64	39.4	33.6086750788644	5.79132492113564
65	42.8	33.175341745531	9.62465825446898
66	34.5	29.7086750788643	4.79132492113565
67	43.7	33.5086750788643	10.1913249211357
68	46.3	31.8920084121977	14.4079915878023
69	40.8	34.925341745531	5.87465825446898
70	48.4	33.725341745531	14.674658254469
71	43.2	31.1293375394322	12.0706624605678
72	48.1	33.8293375394322	14.2706624605678
73	42.8	30.4788643533123	12.3211356466877

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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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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

library(lattice)
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code