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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 21 Nov 2007 16:18:19 -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/2007/Nov/22/t11956866845nqccbwax0i6ekn.htm/, Retrieved Fri, 03 May 2024 01:56:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5904, Retrieved Fri, 03 May 2024 01:56:22 +0000

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No (this computation is public)

User-defined keywords

Seasonal dummies

Estimated Impact

187

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

-       [Multiple Regression] [Workshop Q3 herst...] [2007-11-21 23:18:19] [44cf2be50bc8700e14714598feda9df9] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5904&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5904&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 598.544186046512 + 18.2790697674418x[t] -20.6372093023255M1[t] -30.5116279069767M2[t] -47.3116279069768M3[t] -42.6558139534884M4[t] -33.3441860465117M5[t] -37.3441860465116M6[t] -46.3441860465116M7[t] -53.3441860465116M8[t] -60.7441860465116M9[t] -60.3441860465116M10[t] -6.74418604651162M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  598.544186046512 +  18.2790697674418x[t] -20.6372093023255M1[t] -30.5116279069767M2[t] -47.3116279069768M3[t] -42.6558139534884M4[t] -33.3441860465117M5[t] -37.3441860465116M6[t] -46.3441860465116M7[t] -53.3441860465116M8[t] -60.7441860465116M9[t] -60.3441860465116M10[t] -6.74418604651162M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5904&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  598.544186046512 +  18.2790697674418x[t] -20.6372093023255M1[t] -30.5116279069767M2[t] -47.3116279069768M3[t] -42.6558139534884M4[t] -33.3441860465117M5[t] -37.3441860465116M6[t] -46.3441860465116M7[t] -53.3441860465116M8[t] -60.7441860465116M9[t] -60.3441860465116M10[t] -6.74418604651162M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5904&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] = + 598.544186046512 + 18.2790697674418x[t] -20.6372093023255M1[t] -30.5116279069767M2[t] -47.3116279069768M3[t] -42.6558139534884M4[t] -33.3441860465117M5[t] -37.3441860465116M6[t] -46.3441860465116M7[t] -53.3441860465116M8[t] -60.7441860465116M9[t] -60.3441860465116M10[t] -6.74418604651162M11[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)	598.544186046512	15.245865	39.2594	0	0
x	18.2790697674418	13.995477	1.3061	0.197753	0.098877
M1	-20.6372093023255	20.377722	-1.0127	0.316265	0.158133
M2	-30.5116279069767	21.921284	-1.3919	0.170377	0.085189
M3	-47.3116279069768	21.921284	-2.1583	0.03594	0.01797
M4	-42.6558139534884	21.378444	-1.9953	0.051706	0.025853
M5	-33.3441860465117	21.378444	-1.5597	0.125398	0.062699
M6	-37.3441860465116	21.378444	-1.7468	0.087066	0.043533
M7	-46.3441860465116	21.378444	-2.1678	0.035164	0.017582
M8	-53.3441860465116	21.378444	-2.4952	0.016079	0.00804
M9	-60.7441860465116	21.378444	-2.8414	0.006574	0.003287
M10	-60.3441860465116	21.378444	-2.8227	0.006911	0.003456
M11	-6.74418604651162	21.378444	-0.3155	0.753775	0.376887

\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) & 598.544186046512 & 15.245865 & 39.2594 & 0 & 0 \tabularnewline
x & 18.2790697674418 & 13.995477 & 1.3061 & 0.197753 & 0.098877 \tabularnewline
M1 & -20.6372093023255 & 20.377722 & -1.0127 & 0.316265 & 0.158133 \tabularnewline
M2 & -30.5116279069767 & 21.921284 & -1.3919 & 0.170377 & 0.085189 \tabularnewline
M3 & -47.3116279069768 & 21.921284 & -2.1583 & 0.03594 & 0.01797 \tabularnewline
M4 & -42.6558139534884 & 21.378444 & -1.9953 & 0.051706 & 0.025853 \tabularnewline
M5 & -33.3441860465117 & 21.378444 & -1.5597 & 0.125398 & 0.062699 \tabularnewline
M6 & -37.3441860465116 & 21.378444 & -1.7468 & 0.087066 & 0.043533 \tabularnewline
M7 & -46.3441860465116 & 21.378444 & -2.1678 & 0.035164 & 0.017582 \tabularnewline
M8 & -53.3441860465116 & 21.378444 & -2.4952 & 0.016079 & 0.00804 \tabularnewline
M9 & -60.7441860465116 & 21.378444 & -2.8414 & 0.006574 & 0.003287 \tabularnewline
M10 & -60.3441860465116 & 21.378444 & -2.8227 & 0.006911 & 0.003456 \tabularnewline
M11 & -6.74418604651162 & 21.378444 & -0.3155 & 0.753775 & 0.376887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5904&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]598.544186046512[/C][C]15.245865[/C][C]39.2594[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]18.2790697674418[/C][C]13.995477[/C][C]1.3061[/C][C]0.197753[/C][C]0.098877[/C][/ROW]
[ROW][C]M1[/C][C]-20.6372093023255[/C][C]20.377722[/C][C]-1.0127[/C][C]0.316265[/C][C]0.158133[/C][/ROW]
[ROW][C]M2[/C][C]-30.5116279069767[/C][C]21.921284[/C][C]-1.3919[/C][C]0.170377[/C][C]0.085189[/C][/ROW]
[ROW][C]M3[/C][C]-47.3116279069768[/C][C]21.921284[/C][C]-2.1583[/C][C]0.03594[/C][C]0.01797[/C][/ROW]
[ROW][C]M4[/C][C]-42.6558139534884[/C][C]21.378444[/C][C]-1.9953[/C][C]0.051706[/C][C]0.025853[/C][/ROW]
[ROW][C]M5[/C][C]-33.3441860465117[/C][C]21.378444[/C][C]-1.5597[/C][C]0.125398[/C][C]0.062699[/C][/ROW]
[ROW][C]M6[/C][C]-37.3441860465116[/C][C]21.378444[/C][C]-1.7468[/C][C]0.087066[/C][C]0.043533[/C][/ROW]
[ROW][C]M7[/C][C]-46.3441860465116[/C][C]21.378444[/C][C]-2.1678[/C][C]0.035164[/C][C]0.017582[/C][/ROW]
[ROW][C]M8[/C][C]-53.3441860465116[/C][C]21.378444[/C][C]-2.4952[/C][C]0.016079[/C][C]0.00804[/C][/ROW]
[ROW][C]M9[/C][C]-60.7441860465116[/C][C]21.378444[/C][C]-2.8414[/C][C]0.006574[/C][C]0.003287[/C][/ROW]
[ROW][C]M10[/C][C]-60.3441860465116[/C][C]21.378444[/C][C]-2.8227[/C][C]0.006911[/C][C]0.003456[/C][/ROW]
[ROW][C]M11[/C][C]-6.74418604651162[/C][C]21.378444[/C][C]-0.3155[/C][C]0.753775[/C][C]0.376887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5904&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5904&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)	598.544186046512	15.245865	39.2594	0	0
x	18.2790697674418	13.995477	1.3061	0.197753	0.098877
M1	-20.6372093023255	20.377722	-1.0127	0.316265	0.158133
M2	-30.5116279069767	21.921284	-1.3919	0.170377	0.085189
M3	-47.3116279069768	21.921284	-2.1583	0.03594	0.01797
M4	-42.6558139534884	21.378444	-1.9953	0.051706	0.025853
M5	-33.3441860465117	21.378444	-1.5597	0.125398	0.062699
M6	-37.3441860465116	21.378444	-1.7468	0.087066	0.043533
M7	-46.3441860465116	21.378444	-2.1678	0.035164	0.017582
M8	-53.3441860465116	21.378444	-2.4952	0.016079	0.00804
M9	-60.7441860465116	21.378444	-2.8414	0.006574	0.003287
M10	-60.3441860465116	21.378444	-2.8227	0.006911	0.003456
M11	-6.74418604651162	21.378444	-0.3155	0.753775	0.376887

Multiple Linear Regression - Regression Statistics
Multiple R	0.568606440562468
R-squared	0.32331328424912
Adjusted R-squared	0.154141605311400
F-TEST (value)	1.91115490653815
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.0566763849716443
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	33.5113020388806
Sum Squared Residuals	53904.3534883721

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.568606440562468 \tabularnewline
R-squared & 0.32331328424912 \tabularnewline
Adjusted R-squared & 0.154141605311400 \tabularnewline
F-TEST (value) & 1.91115490653815 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.0566763849716443 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 33.5113020388806 \tabularnewline
Sum Squared Residuals & 53904.3534883721 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5904&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.568606440562468[/C][/ROW]
[ROW][C]R-squared[/C][C]0.32331328424912[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.154141605311400[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.91115490653815[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.0566763849716443[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]33.5113020388806[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]53904.3534883721[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5904&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5904&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	0.568606440562468
R-squared	0.32331328424912
Adjusted R-squared	0.154141605311400
F-TEST (value)	1.91115490653815
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.0566763849716443
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	33.5113020388806
Sum Squared Residuals	53904.3534883721

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	523	577.906976744186	-54.9069767441859
2	519	568.032558139535	-49.0325581395349
3	509	551.232558139535	-42.2325581395348
4	512	555.888372093023	-43.8883720930234
5	519	565.2	-46.2
6	517	561.2	-44.2000000000001
7	510	552.2	-42.2
8	509	545.2	-36.2000000000000
9	501	537.8	-36.8
10	507	538.2	-31.2
11	569	591.8	-22.8
12	580	598.544186046512	-18.5441860465116
13	578	596.186046511628	-18.1860465116280
14	565	586.311627906977	-21.3116279069767
15	547	569.511627906977	-22.5116279069767
16	555	555.888372093023	-0.888372093023233
17	562	565.2	-3.20000000000000
18	561	561.2	-0.200000000000016
19	555	552.2	2.79999999999999
20	544	545.2	-1.20000000000001
21	537	537.8	-0.800000000000014
22	543	538.2	4.8
23	594	591.8	2.20000000000000
24	611	616.823255813953	-5.82325581395349
25	613	596.186046511628	16.8139534883720
26	611	586.311627906977	24.6883720930232
27	594	569.511627906977	24.4883720930233
28	595	574.167441860465	20.8325581395349
29	591	565.2	25.8
30	589	561.2	27.8
31	584	552.2	31.8
32	573	545.2	27.8
33	567	537.8	29.2
34	569	538.2	30.8
35	621	591.8	29.2
36	629	598.544186046512	30.4558139534884
37	628	577.906976744186	50.0930232558139
38	612	568.032558139535	43.9674418604651
39	595	551.232558139535	43.7674418604651
40	597	555.888372093023	41.1116279069768
41	593	565.2	27.8
42	590	561.2	28.8
43	580	552.2	27.8
44	574	545.2	28.8
45	573	537.8	35.2
46	573	538.2	34.8
47	620	591.8	28.2
48	626	598.544186046512	27.4558139534884
49	620	577.906976744186	42.0930232558139
50	588	586.311627906977	1.68837209302325
51	566	569.511627906977	-3.51162790697674
52	557	574.167441860465	-17.1674418604651
53	561	565.2	-4.2
54	549	561.2	-12.2000000000000
55	532	552.2	-20.2
56	526	545.2	-19.2
57	511	537.8	-26.8
58	499	538.2	-39.2
59	555	591.8	-36.8
60	565	598.544186046512	-33.5441860465116
61	542	577.906976744186	-35.9069767441861

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 523 & 577.906976744186 & -54.9069767441859 \tabularnewline
2 & 519 & 568.032558139535 & -49.0325581395349 \tabularnewline
3 & 509 & 551.232558139535 & -42.2325581395348 \tabularnewline
4 & 512 & 555.888372093023 & -43.8883720930234 \tabularnewline
5 & 519 & 565.2 & -46.2 \tabularnewline
6 & 517 & 561.2 & -44.2000000000001 \tabularnewline
7 & 510 & 552.2 & -42.2 \tabularnewline
8 & 509 & 545.2 & -36.2000000000000 \tabularnewline
9 & 501 & 537.8 & -36.8 \tabularnewline
10 & 507 & 538.2 & -31.2 \tabularnewline
11 & 569 & 591.8 & -22.8 \tabularnewline
12 & 580 & 598.544186046512 & -18.5441860465116 \tabularnewline
13 & 578 & 596.186046511628 & -18.1860465116280 \tabularnewline
14 & 565 & 586.311627906977 & -21.3116279069767 \tabularnewline
15 & 547 & 569.511627906977 & -22.5116279069767 \tabularnewline
16 & 555 & 555.888372093023 & -0.888372093023233 \tabularnewline
17 & 562 & 565.2 & -3.20000000000000 \tabularnewline
18 & 561 & 561.2 & -0.200000000000016 \tabularnewline
19 & 555 & 552.2 & 2.79999999999999 \tabularnewline
20 & 544 & 545.2 & -1.20000000000001 \tabularnewline
21 & 537 & 537.8 & -0.800000000000014 \tabularnewline
22 & 543 & 538.2 & 4.8 \tabularnewline
23 & 594 & 591.8 & 2.20000000000000 \tabularnewline
24 & 611 & 616.823255813953 & -5.82325581395349 \tabularnewline
25 & 613 & 596.186046511628 & 16.8139534883720 \tabularnewline
26 & 611 & 586.311627906977 & 24.6883720930232 \tabularnewline
27 & 594 & 569.511627906977 & 24.4883720930233 \tabularnewline
28 & 595 & 574.167441860465 & 20.8325581395349 \tabularnewline
29 & 591 & 565.2 & 25.8 \tabularnewline
30 & 589 & 561.2 & 27.8 \tabularnewline
31 & 584 & 552.2 & 31.8 \tabularnewline
32 & 573 & 545.2 & 27.8 \tabularnewline
33 & 567 & 537.8 & 29.2 \tabularnewline
34 & 569 & 538.2 & 30.8 \tabularnewline
35 & 621 & 591.8 & 29.2 \tabularnewline
36 & 629 & 598.544186046512 & 30.4558139534884 \tabularnewline
37 & 628 & 577.906976744186 & 50.0930232558139 \tabularnewline
38 & 612 & 568.032558139535 & 43.9674418604651 \tabularnewline
39 & 595 & 551.232558139535 & 43.7674418604651 \tabularnewline
40 & 597 & 555.888372093023 & 41.1116279069768 \tabularnewline
41 & 593 & 565.2 & 27.8 \tabularnewline
42 & 590 & 561.2 & 28.8 \tabularnewline
43 & 580 & 552.2 & 27.8 \tabularnewline
44 & 574 & 545.2 & 28.8 \tabularnewline
45 & 573 & 537.8 & 35.2 \tabularnewline
46 & 573 & 538.2 & 34.8 \tabularnewline
47 & 620 & 591.8 & 28.2 \tabularnewline
48 & 626 & 598.544186046512 & 27.4558139534884 \tabularnewline
49 & 620 & 577.906976744186 & 42.0930232558139 \tabularnewline
50 & 588 & 586.311627906977 & 1.68837209302325 \tabularnewline
51 & 566 & 569.511627906977 & -3.51162790697674 \tabularnewline
52 & 557 & 574.167441860465 & -17.1674418604651 \tabularnewline
53 & 561 & 565.2 & -4.2 \tabularnewline
54 & 549 & 561.2 & -12.2000000000000 \tabularnewline
55 & 532 & 552.2 & -20.2 \tabularnewline
56 & 526 & 545.2 & -19.2 \tabularnewline
57 & 511 & 537.8 & -26.8 \tabularnewline
58 & 499 & 538.2 & -39.2 \tabularnewline
59 & 555 & 591.8 & -36.8 \tabularnewline
60 & 565 & 598.544186046512 & -33.5441860465116 \tabularnewline
61 & 542 & 577.906976744186 & -35.9069767441861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5904&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]523[/C][C]577.906976744186[/C][C]-54.9069767441859[/C][/ROW]
[ROW][C]2[/C][C]519[/C][C]568.032558139535[/C][C]-49.0325581395349[/C][/ROW]
[ROW][C]3[/C][C]509[/C][C]551.232558139535[/C][C]-42.2325581395348[/C][/ROW]
[ROW][C]4[/C][C]512[/C][C]555.888372093023[/C][C]-43.8883720930234[/C][/ROW]
[ROW][C]5[/C][C]519[/C][C]565.2[/C][C]-46.2[/C][/ROW]
[ROW][C]6[/C][C]517[/C][C]561.2[/C][C]-44.2000000000001[/C][/ROW]
[ROW][C]7[/C][C]510[/C][C]552.2[/C][C]-42.2[/C][/ROW]
[ROW][C]8[/C][C]509[/C][C]545.2[/C][C]-36.2000000000000[/C][/ROW]
[ROW][C]9[/C][C]501[/C][C]537.8[/C][C]-36.8[/C][/ROW]
[ROW][C]10[/C][C]507[/C][C]538.2[/C][C]-31.2[/C][/ROW]
[ROW][C]11[/C][C]569[/C][C]591.8[/C][C]-22.8[/C][/ROW]
[ROW][C]12[/C][C]580[/C][C]598.544186046512[/C][C]-18.5441860465116[/C][/ROW]
[ROW][C]13[/C][C]578[/C][C]596.186046511628[/C][C]-18.1860465116280[/C][/ROW]
[ROW][C]14[/C][C]565[/C][C]586.311627906977[/C][C]-21.3116279069767[/C][/ROW]
[ROW][C]15[/C][C]547[/C][C]569.511627906977[/C][C]-22.5116279069767[/C][/ROW]
[ROW][C]16[/C][C]555[/C][C]555.888372093023[/C][C]-0.888372093023233[/C][/ROW]
[ROW][C]17[/C][C]562[/C][C]565.2[/C][C]-3.20000000000000[/C][/ROW]
[ROW][C]18[/C][C]561[/C][C]561.2[/C][C]-0.200000000000016[/C][/ROW]
[ROW][C]19[/C][C]555[/C][C]552.2[/C][C]2.79999999999999[/C][/ROW]
[ROW][C]20[/C][C]544[/C][C]545.2[/C][C]-1.20000000000001[/C][/ROW]
[ROW][C]21[/C][C]537[/C][C]537.8[/C][C]-0.800000000000014[/C][/ROW]
[ROW][C]22[/C][C]543[/C][C]538.2[/C][C]4.8[/C][/ROW]
[ROW][C]23[/C][C]594[/C][C]591.8[/C][C]2.20000000000000[/C][/ROW]
[ROW][C]24[/C][C]611[/C][C]616.823255813953[/C][C]-5.82325581395349[/C][/ROW]
[ROW][C]25[/C][C]613[/C][C]596.186046511628[/C][C]16.8139534883720[/C][/ROW]
[ROW][C]26[/C][C]611[/C][C]586.311627906977[/C][C]24.6883720930232[/C][/ROW]
[ROW][C]27[/C][C]594[/C][C]569.511627906977[/C][C]24.4883720930233[/C][/ROW]
[ROW][C]28[/C][C]595[/C][C]574.167441860465[/C][C]20.8325581395349[/C][/ROW]
[ROW][C]29[/C][C]591[/C][C]565.2[/C][C]25.8[/C][/ROW]
[ROW][C]30[/C][C]589[/C][C]561.2[/C][C]27.8[/C][/ROW]
[ROW][C]31[/C][C]584[/C][C]552.2[/C][C]31.8[/C][/ROW]
[ROW][C]32[/C][C]573[/C][C]545.2[/C][C]27.8[/C][/ROW]
[ROW][C]33[/C][C]567[/C][C]537.8[/C][C]29.2[/C][/ROW]
[ROW][C]34[/C][C]569[/C][C]538.2[/C][C]30.8[/C][/ROW]
[ROW][C]35[/C][C]621[/C][C]591.8[/C][C]29.2[/C][/ROW]
[ROW][C]36[/C][C]629[/C][C]598.544186046512[/C][C]30.4558139534884[/C][/ROW]
[ROW][C]37[/C][C]628[/C][C]577.906976744186[/C][C]50.0930232558139[/C][/ROW]
[ROW][C]38[/C][C]612[/C][C]568.032558139535[/C][C]43.9674418604651[/C][/ROW]
[ROW][C]39[/C][C]595[/C][C]551.232558139535[/C][C]43.7674418604651[/C][/ROW]
[ROW][C]40[/C][C]597[/C][C]555.888372093023[/C][C]41.1116279069768[/C][/ROW]
[ROW][C]41[/C][C]593[/C][C]565.2[/C][C]27.8[/C][/ROW]
[ROW][C]42[/C][C]590[/C][C]561.2[/C][C]28.8[/C][/ROW]
[ROW][C]43[/C][C]580[/C][C]552.2[/C][C]27.8[/C][/ROW]
[ROW][C]44[/C][C]574[/C][C]545.2[/C][C]28.8[/C][/ROW]
[ROW][C]45[/C][C]573[/C][C]537.8[/C][C]35.2[/C][/ROW]
[ROW][C]46[/C][C]573[/C][C]538.2[/C][C]34.8[/C][/ROW]
[ROW][C]47[/C][C]620[/C][C]591.8[/C][C]28.2[/C][/ROW]
[ROW][C]48[/C][C]626[/C][C]598.544186046512[/C][C]27.4558139534884[/C][/ROW]
[ROW][C]49[/C][C]620[/C][C]577.906976744186[/C][C]42.0930232558139[/C][/ROW]
[ROW][C]50[/C][C]588[/C][C]586.311627906977[/C][C]1.68837209302325[/C][/ROW]
[ROW][C]51[/C][C]566[/C][C]569.511627906977[/C][C]-3.51162790697674[/C][/ROW]
[ROW][C]52[/C][C]557[/C][C]574.167441860465[/C][C]-17.1674418604651[/C][/ROW]
[ROW][C]53[/C][C]561[/C][C]565.2[/C][C]-4.2[/C][/ROW]
[ROW][C]54[/C][C]549[/C][C]561.2[/C][C]-12.2000000000000[/C][/ROW]
[ROW][C]55[/C][C]532[/C][C]552.2[/C][C]-20.2[/C][/ROW]
[ROW][C]56[/C][C]526[/C][C]545.2[/C][C]-19.2[/C][/ROW]
[ROW][C]57[/C][C]511[/C][C]537.8[/C][C]-26.8[/C][/ROW]
[ROW][C]58[/C][C]499[/C][C]538.2[/C][C]-39.2[/C][/ROW]
[ROW][C]59[/C][C]555[/C][C]591.8[/C][C]-36.8[/C][/ROW]
[ROW][C]60[/C][C]565[/C][C]598.544186046512[/C][C]-33.5441860465116[/C][/ROW]
[ROW][C]61[/C][C]542[/C][C]577.906976744186[/C][C]-35.9069767441861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5904&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5904&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	523	577.906976744186	-54.9069767441859
2	519	568.032558139535	-49.0325581395349
3	509	551.232558139535	-42.2325581395348
4	512	555.888372093023	-43.8883720930234
5	519	565.2	-46.2
6	517	561.2	-44.2000000000001
7	510	552.2	-42.2
8	509	545.2	-36.2000000000000
9	501	537.8	-36.8
10	507	538.2	-31.2
11	569	591.8	-22.8
12	580	598.544186046512	-18.5441860465116
13	578	596.186046511628	-18.1860465116280
14	565	586.311627906977	-21.3116279069767
15	547	569.511627906977	-22.5116279069767
16	555	555.888372093023	-0.888372093023233
17	562	565.2	-3.20000000000000
18	561	561.2	-0.200000000000016
19	555	552.2	2.79999999999999
20	544	545.2	-1.20000000000001
21	537	537.8	-0.800000000000014
22	543	538.2	4.8
23	594	591.8	2.20000000000000
24	611	616.823255813953	-5.82325581395349
25	613	596.186046511628	16.8139534883720
26	611	586.311627906977	24.6883720930232
27	594	569.511627906977	24.4883720930233
28	595	574.167441860465	20.8325581395349
29	591	565.2	25.8
30	589	561.2	27.8
31	584	552.2	31.8
32	573	545.2	27.8
33	567	537.8	29.2
34	569	538.2	30.8
35	621	591.8	29.2
36	629	598.544186046512	30.4558139534884
37	628	577.906976744186	50.0930232558139
38	612	568.032558139535	43.9674418604651
39	595	551.232558139535	43.7674418604651
40	597	555.888372093023	41.1116279069768
41	593	565.2	27.8
42	590	561.2	28.8
43	580	552.2	27.8
44	574	545.2	28.8
45	573	537.8	35.2
46	573	538.2	34.8
47	620	591.8	28.2
48	626	598.544186046512	27.4558139534884
49	620	577.906976744186	42.0930232558139
50	588	586.311627906977	1.68837209302325
51	566	569.511627906977	-3.51162790697674
52	557	574.167441860465	-17.1674418604651
53	561	565.2	-4.2
54	549	561.2	-12.2000000000000
55	532	552.2	-20.2
56	526	545.2	-19.2
57	511	537.8	-26.8
58	499	538.2	-39.2
59	555	591.8	-36.8
60	565	598.544186046512	-33.5441860465116
61	542	577.906976744186	-35.9069767441861

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 ;

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