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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 15:03:55 -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/21/t1195682241mywrjtolkrpxkqw.htm/, Retrieved Tue, 07 May 2024 18:37:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5899, Retrieved Tue, 07 May 2024 18:37:17 +0000

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No (this computation is public)

User-defined keywords

Seasonal dummies

Estimated Impact

271

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

-       [Multiple Regression] [Workshop 3 Q3] [2007-11-21 22:03:55] [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=5899&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=5899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5899&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] = + 601.951152073733 + 1.24423963133640x[t] -18.9880184331796M1[t] -24.1953917050691M2[t] -40.7465437788018M3[t] -39M4[t] -37.2488479262673M5[t] -41M6[t] -50.9953917050691M7[t] -57.9953917050691M8[t] -64.8976958525346M9[t] -64.9953917050692M10[t] -10.4000000000000M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  601.951152073733 +  1.24423963133640x[t] -18.9880184331796M1[t] -24.1953917050691M2[t] -40.7465437788018M3[t] -39M4[t] -37.2488479262673M5[t] -41M6[t] -50.9953917050691M7[t] -57.9953917050691M8[t] -64.8976958525346M9[t] -64.9953917050692M10[t] -10.4000000000000M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5899&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  601.951152073733 +  1.24423963133640x[t] -18.9880184331796M1[t] -24.1953917050691M2[t] -40.7465437788018M3[t] -39M4[t] -37.2488479262673M5[t] -41M6[t] -50.9953917050691M7[t] -57.9953917050691M8[t] -64.8976958525346M9[t] -64.9953917050692M10[t] -10.4000000000000M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5899&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] = + 601.951152073733 + 1.24423963133640x[t] -18.9880184331796M1[t] -24.1953917050691M2[t] -40.7465437788018M3[t] -39M4[t] -37.2488479262673M5[t] -41M6[t] -50.9953917050691M7[t] -57.9953917050691M8[t] -64.8976958525346M9[t] -64.9953917050692M10[t] -10.4000000000000M11[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)	601.951152073733	15.458534	38.9397	0	0
x	1.24423963133640	12.678314	0.0981	0.92223	0.461115
M1	-18.9880184331796	22.153819	-0.8571	0.395649	0.197825
M2	-24.1953917050691	23.831633	-1.0153	0.315071	0.157535
M3	-40.7465437788018	22.867873	-1.7818	0.081105	0.040552
M4	-39	21.565559	-1.8084	0.076805	0.038402
M5	-37.2488479262673	21.714118	-1.7154	0.092718	0.046359
M6	-41	21.565559	-1.9012	0.063291	0.031646
M7	-50.9953917050691	23.831633	-2.1398	0.037481	0.01874
M8	-57.9953917050691	23.831633	-2.4335	0.018725	0.009362
M9	-64.8976958525346	22.153819	-2.9294	0.005183	0.002592
M10	-64.9953917050692	23.831633	-2.7273	0.008892	0.004446
M11	-10.4000000000000	21.565559	-0.4823	0.63182	0.31591

\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) & 601.951152073733 & 15.458534 & 38.9397 & 0 & 0 \tabularnewline
x & 1.24423963133640 & 12.678314 & 0.0981 & 0.92223 & 0.461115 \tabularnewline
M1 & -18.9880184331796 & 22.153819 & -0.8571 & 0.395649 & 0.197825 \tabularnewline
M2 & -24.1953917050691 & 23.831633 & -1.0153 & 0.315071 & 0.157535 \tabularnewline
M3 & -40.7465437788018 & 22.867873 & -1.7818 & 0.081105 & 0.040552 \tabularnewline
M4 & -39 & 21.565559 & -1.8084 & 0.076805 & 0.038402 \tabularnewline
M5 & -37.2488479262673 & 21.714118 & -1.7154 & 0.092718 & 0.046359 \tabularnewline
M6 & -41 & 21.565559 & -1.9012 & 0.063291 & 0.031646 \tabularnewline
M7 & -50.9953917050691 & 23.831633 & -2.1398 & 0.037481 & 0.01874 \tabularnewline
M8 & -57.9953917050691 & 23.831633 & -2.4335 & 0.018725 & 0.009362 \tabularnewline
M9 & -64.8976958525346 & 22.153819 & -2.9294 & 0.005183 & 0.002592 \tabularnewline
M10 & -64.9953917050692 & 23.831633 & -2.7273 & 0.008892 & 0.004446 \tabularnewline
M11 & -10.4000000000000 & 21.565559 & -0.4823 & 0.63182 & 0.31591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5899&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]601.951152073733[/C][C]15.458534[/C][C]38.9397[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]1.24423963133640[/C][C]12.678314[/C][C]0.0981[/C][C]0.92223[/C][C]0.461115[/C][/ROW]
[ROW][C]M1[/C][C]-18.9880184331796[/C][C]22.153819[/C][C]-0.8571[/C][C]0.395649[/C][C]0.197825[/C][/ROW]
[ROW][C]M2[/C][C]-24.1953917050691[/C][C]23.831633[/C][C]-1.0153[/C][C]0.315071[/C][C]0.157535[/C][/ROW]
[ROW][C]M3[/C][C]-40.7465437788018[/C][C]22.867873[/C][C]-1.7818[/C][C]0.081105[/C][C]0.040552[/C][/ROW]
[ROW][C]M4[/C][C]-39[/C][C]21.565559[/C][C]-1.8084[/C][C]0.076805[/C][C]0.038402[/C][/ROW]
[ROW][C]M5[/C][C]-37.2488479262673[/C][C]21.714118[/C][C]-1.7154[/C][C]0.092718[/C][C]0.046359[/C][/ROW]
[ROW][C]M6[/C][C]-41[/C][C]21.565559[/C][C]-1.9012[/C][C]0.063291[/C][C]0.031646[/C][/ROW]
[ROW][C]M7[/C][C]-50.9953917050691[/C][C]23.831633[/C][C]-2.1398[/C][C]0.037481[/C][C]0.01874[/C][/ROW]
[ROW][C]M8[/C][C]-57.9953917050691[/C][C]23.831633[/C][C]-2.4335[/C][C]0.018725[/C][C]0.009362[/C][/ROW]
[ROW][C]M9[/C][C]-64.8976958525346[/C][C]22.153819[/C][C]-2.9294[/C][C]0.005183[/C][C]0.002592[/C][/ROW]
[ROW][C]M10[/C][C]-64.9953917050692[/C][C]23.831633[/C][C]-2.7273[/C][C]0.008892[/C][C]0.004446[/C][/ROW]
[ROW][C]M11[/C][C]-10.4000000000000[/C][C]21.565559[/C][C]-0.4823[/C][C]0.63182[/C][C]0.31591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5899&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)	601.951152073733	15.458534	38.9397	0	0
x	1.24423963133640	12.678314	0.0981	0.92223	0.461115
M1	-18.9880184331796	22.153819	-0.8571	0.395649	0.197825
M2	-24.1953917050691	23.831633	-1.0153	0.315071	0.157535
M3	-40.7465437788018	22.867873	-1.7818	0.081105	0.040552
M4	-39	21.565559	-1.8084	0.076805	0.038402
M5	-37.2488479262673	21.714118	-1.7154	0.092718	0.046359
M6	-41	21.565559	-1.9012	0.063291	0.031646
M7	-50.9953917050691	23.831633	-2.1398	0.037481	0.01874
M8	-57.9953917050691	23.831633	-2.4335	0.018725	0.009362
M9	-64.8976958525346	22.153819	-2.9294	0.005183	0.002592
M10	-64.9953917050692	23.831633	-2.7273	0.008892	0.004446
M11	-10.4000000000000	21.565559	-0.4823	0.63182	0.31591

Multiple Linear Regression - Regression Statistics
Multiple R	0.547179904465269
R-squared	0.299405847850621
Adjusted R-squared	0.124257309813276
F-TEST (value)	1.70943960598051
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.0943120423223625
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	34.0981432300322
Sum Squared Residuals	55808.8018433179

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.547179904465269 \tabularnewline
R-squared & 0.299405847850621 \tabularnewline
Adjusted R-squared & 0.124257309813276 \tabularnewline
F-TEST (value) & 1.70943960598051 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.0943120423223625 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 34.0981432300322 \tabularnewline
Sum Squared Residuals & 55808.8018433179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5899&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.547179904465269[/C][/ROW]
[ROW][C]R-squared[/C][C]0.299405847850621[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.124257309813276[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.70943960598051[/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]0.0943120423223625[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]34.0981432300322[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]55808.8018433179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5899&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5899&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	0.547179904465269
R-squared	0.299405847850621
Adjusted R-squared	0.124257309813276
F-TEST (value)	1.70943960598051
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.0943120423223625
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	34.0981432300322
Sum Squared Residuals	55808.8018433179

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	523	582.963133640553	-59.9631336405528
2	519	579	-59.9999999999999
3	509	562.448847926267	-53.4488479262673
4	512	564.195391705069	-52.1953917050690
5	519	564.702304147465	-45.7023041474655
6	517	560.951152073733	-43.9511520737328
7	510	552.2	-42.2
8	509	545.2	-36.2
9	501	537.053456221198	-36.0534562211981
10	507	538.2	-31.2000000000000
11	569	591.551152073733	-22.5511520737328
12	580	601.951152073733	-21.9511520737327
13	578	584.20737327189	-6.20737327188945
14	565	579	-14
15	547	561.204608294931	-14.2046082949309
16	555	562.951152073733	-7.95115207373274
17	562	564.702304147465	-2.70230414746545
18	561	560.951152073733	0.0488479262672605
19	555	552.2	2.80000000000001
20	544	545.2	-1.19999999999999
21	537	538.297695852535	-1.29769585253455
22	543	538.2	4.80000000000003
23	594	592.795391705069	1.20460829493088
24	611	601.951152073733	9.04884792626725
25	613	584.20737327189	28.7926267281105
26	611	579	32
27	594	562.448847926267	31.5511520737327
28	595	562.951152073733	32.0488479262673
29	591	564.702304147465	26.2976958525345
30	589	560.951152073733	28.0488479262673
31	584	552.2	31.8
32	573	545.2	27.8
33	567	537.053456221198	29.9465437788018
34	569	538.2	30.8
35	621	591.551152073733	29.4488479262673
36	629	601.951152073733	27.0488479262673
37	628	584.20737327189	43.7926267281105
38	612	579	33
39	595	562.448847926267	32.5511520737327
40	597	562.951152073733	34.0488479262673
41	593	565.946543778802	27.0534562211982
42	590	560.951152073733	29.0488479262673
43	580	552.2	27.8
44	574	545.2	28.8
45	573	538.297695852535	34.7023041474654
46	573	538.2	34.8
47	620	591.551152073733	28.4488479262673
48	626	601.951152073733	24.0488479262673
49	620	584.20737327189	35.7926267281105
50	588	579	9
51	566	562.448847926267	3.55115207373273
52	557	562.951152073733	-5.95115207373274
53	561	565.946543778802	-4.94654377880181
54	549	562.195391705069	-13.1953917050691
55	532	552.2	-20.2
56	526	545.2	-19.2
57	511	538.297695852535	-27.2976958525345
58	499	538.2	-39.2
59	555	591.551152073733	-36.5511520737327
60	565	603.195391705069	-38.1953917050691
61	542	584.20737327189	-42.2073732718895

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 523 & 582.963133640553 & -59.9631336405528 \tabularnewline
2 & 519 & 579 & -59.9999999999999 \tabularnewline
3 & 509 & 562.448847926267 & -53.4488479262673 \tabularnewline
4 & 512 & 564.195391705069 & -52.1953917050690 \tabularnewline
5 & 519 & 564.702304147465 & -45.7023041474655 \tabularnewline
6 & 517 & 560.951152073733 & -43.9511520737328 \tabularnewline
7 & 510 & 552.2 & -42.2 \tabularnewline
8 & 509 & 545.2 & -36.2 \tabularnewline
9 & 501 & 537.053456221198 & -36.0534562211981 \tabularnewline
10 & 507 & 538.2 & -31.2000000000000 \tabularnewline
11 & 569 & 591.551152073733 & -22.5511520737328 \tabularnewline
12 & 580 & 601.951152073733 & -21.9511520737327 \tabularnewline
13 & 578 & 584.20737327189 & -6.20737327188945 \tabularnewline
14 & 565 & 579 & -14 \tabularnewline
15 & 547 & 561.204608294931 & -14.2046082949309 \tabularnewline
16 & 555 & 562.951152073733 & -7.95115207373274 \tabularnewline
17 & 562 & 564.702304147465 & -2.70230414746545 \tabularnewline
18 & 561 & 560.951152073733 & 0.0488479262672605 \tabularnewline
19 & 555 & 552.2 & 2.80000000000001 \tabularnewline
20 & 544 & 545.2 & -1.19999999999999 \tabularnewline
21 & 537 & 538.297695852535 & -1.29769585253455 \tabularnewline
22 & 543 & 538.2 & 4.80000000000003 \tabularnewline
23 & 594 & 592.795391705069 & 1.20460829493088 \tabularnewline
24 & 611 & 601.951152073733 & 9.04884792626725 \tabularnewline
25 & 613 & 584.20737327189 & 28.7926267281105 \tabularnewline
26 & 611 & 579 & 32 \tabularnewline
27 & 594 & 562.448847926267 & 31.5511520737327 \tabularnewline
28 & 595 & 562.951152073733 & 32.0488479262673 \tabularnewline
29 & 591 & 564.702304147465 & 26.2976958525345 \tabularnewline
30 & 589 & 560.951152073733 & 28.0488479262673 \tabularnewline
31 & 584 & 552.2 & 31.8 \tabularnewline
32 & 573 & 545.2 & 27.8 \tabularnewline
33 & 567 & 537.053456221198 & 29.9465437788018 \tabularnewline
34 & 569 & 538.2 & 30.8 \tabularnewline
35 & 621 & 591.551152073733 & 29.4488479262673 \tabularnewline
36 & 629 & 601.951152073733 & 27.0488479262673 \tabularnewline
37 & 628 & 584.20737327189 & 43.7926267281105 \tabularnewline
38 & 612 & 579 & 33 \tabularnewline
39 & 595 & 562.448847926267 & 32.5511520737327 \tabularnewline
40 & 597 & 562.951152073733 & 34.0488479262673 \tabularnewline
41 & 593 & 565.946543778802 & 27.0534562211982 \tabularnewline
42 & 590 & 560.951152073733 & 29.0488479262673 \tabularnewline
43 & 580 & 552.2 & 27.8 \tabularnewline
44 & 574 & 545.2 & 28.8 \tabularnewline
45 & 573 & 538.297695852535 & 34.7023041474654 \tabularnewline
46 & 573 & 538.2 & 34.8 \tabularnewline
47 & 620 & 591.551152073733 & 28.4488479262673 \tabularnewline
48 & 626 & 601.951152073733 & 24.0488479262673 \tabularnewline
49 & 620 & 584.20737327189 & 35.7926267281105 \tabularnewline
50 & 588 & 579 & 9 \tabularnewline
51 & 566 & 562.448847926267 & 3.55115207373273 \tabularnewline
52 & 557 & 562.951152073733 & -5.95115207373274 \tabularnewline
53 & 561 & 565.946543778802 & -4.94654377880181 \tabularnewline
54 & 549 & 562.195391705069 & -13.1953917050691 \tabularnewline
55 & 532 & 552.2 & -20.2 \tabularnewline
56 & 526 & 545.2 & -19.2 \tabularnewline
57 & 511 & 538.297695852535 & -27.2976958525345 \tabularnewline
58 & 499 & 538.2 & -39.2 \tabularnewline
59 & 555 & 591.551152073733 & -36.5511520737327 \tabularnewline
60 & 565 & 603.195391705069 & -38.1953917050691 \tabularnewline
61 & 542 & 584.20737327189 & -42.2073732718895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5899&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]582.963133640553[/C][C]-59.9631336405528[/C][/ROW]
[ROW][C]2[/C][C]519[/C][C]579[/C][C]-59.9999999999999[/C][/ROW]
[ROW][C]3[/C][C]509[/C][C]562.448847926267[/C][C]-53.4488479262673[/C][/ROW]
[ROW][C]4[/C][C]512[/C][C]564.195391705069[/C][C]-52.1953917050690[/C][/ROW]
[ROW][C]5[/C][C]519[/C][C]564.702304147465[/C][C]-45.7023041474655[/C][/ROW]
[ROW][C]6[/C][C]517[/C][C]560.951152073733[/C][C]-43.9511520737328[/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]-36.2[/C][/ROW]
[ROW][C]9[/C][C]501[/C][C]537.053456221198[/C][C]-36.0534562211981[/C][/ROW]
[ROW][C]10[/C][C]507[/C][C]538.2[/C][C]-31.2000000000000[/C][/ROW]
[ROW][C]11[/C][C]569[/C][C]591.551152073733[/C][C]-22.5511520737328[/C][/ROW]
[ROW][C]12[/C][C]580[/C][C]601.951152073733[/C][C]-21.9511520737327[/C][/ROW]
[ROW][C]13[/C][C]578[/C][C]584.20737327189[/C][C]-6.20737327188945[/C][/ROW]
[ROW][C]14[/C][C]565[/C][C]579[/C][C]-14[/C][/ROW]
[ROW][C]15[/C][C]547[/C][C]561.204608294931[/C][C]-14.2046082949309[/C][/ROW]
[ROW][C]16[/C][C]555[/C][C]562.951152073733[/C][C]-7.95115207373274[/C][/ROW]
[ROW][C]17[/C][C]562[/C][C]564.702304147465[/C][C]-2.70230414746545[/C][/ROW]
[ROW][C]18[/C][C]561[/C][C]560.951152073733[/C][C]0.0488479262672605[/C][/ROW]
[ROW][C]19[/C][C]555[/C][C]552.2[/C][C]2.80000000000001[/C][/ROW]
[ROW][C]20[/C][C]544[/C][C]545.2[/C][C]-1.19999999999999[/C][/ROW]
[ROW][C]21[/C][C]537[/C][C]538.297695852535[/C][C]-1.29769585253455[/C][/ROW]
[ROW][C]22[/C][C]543[/C][C]538.2[/C][C]4.80000000000003[/C][/ROW]
[ROW][C]23[/C][C]594[/C][C]592.795391705069[/C][C]1.20460829493088[/C][/ROW]
[ROW][C]24[/C][C]611[/C][C]601.951152073733[/C][C]9.04884792626725[/C][/ROW]
[ROW][C]25[/C][C]613[/C][C]584.20737327189[/C][C]28.7926267281105[/C][/ROW]
[ROW][C]26[/C][C]611[/C][C]579[/C][C]32[/C][/ROW]
[ROW][C]27[/C][C]594[/C][C]562.448847926267[/C][C]31.5511520737327[/C][/ROW]
[ROW][C]28[/C][C]595[/C][C]562.951152073733[/C][C]32.0488479262673[/C][/ROW]
[ROW][C]29[/C][C]591[/C][C]564.702304147465[/C][C]26.2976958525345[/C][/ROW]
[ROW][C]30[/C][C]589[/C][C]560.951152073733[/C][C]28.0488479262673[/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]537.053456221198[/C][C]29.9465437788018[/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]591.551152073733[/C][C]29.4488479262673[/C][/ROW]
[ROW][C]36[/C][C]629[/C][C]601.951152073733[/C][C]27.0488479262673[/C][/ROW]
[ROW][C]37[/C][C]628[/C][C]584.20737327189[/C][C]43.7926267281105[/C][/ROW]
[ROW][C]38[/C][C]612[/C][C]579[/C][C]33[/C][/ROW]
[ROW][C]39[/C][C]595[/C][C]562.448847926267[/C][C]32.5511520737327[/C][/ROW]
[ROW][C]40[/C][C]597[/C][C]562.951152073733[/C][C]34.0488479262673[/C][/ROW]
[ROW][C]41[/C][C]593[/C][C]565.946543778802[/C][C]27.0534562211982[/C][/ROW]
[ROW][C]42[/C][C]590[/C][C]560.951152073733[/C][C]29.0488479262673[/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]538.297695852535[/C][C]34.7023041474654[/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]591.551152073733[/C][C]28.4488479262673[/C][/ROW]
[ROW][C]48[/C][C]626[/C][C]601.951152073733[/C][C]24.0488479262673[/C][/ROW]
[ROW][C]49[/C][C]620[/C][C]584.20737327189[/C][C]35.7926267281105[/C][/ROW]
[ROW][C]50[/C][C]588[/C][C]579[/C][C]9[/C][/ROW]
[ROW][C]51[/C][C]566[/C][C]562.448847926267[/C][C]3.55115207373273[/C][/ROW]
[ROW][C]52[/C][C]557[/C][C]562.951152073733[/C][C]-5.95115207373274[/C][/ROW]
[ROW][C]53[/C][C]561[/C][C]565.946543778802[/C][C]-4.94654377880181[/C][/ROW]
[ROW][C]54[/C][C]549[/C][C]562.195391705069[/C][C]-13.1953917050691[/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]538.297695852535[/C][C]-27.2976958525345[/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]591.551152073733[/C][C]-36.5511520737327[/C][/ROW]
[ROW][C]60[/C][C]565[/C][C]603.195391705069[/C][C]-38.1953917050691[/C][/ROW]
[ROW][C]61[/C][C]542[/C][C]584.20737327189[/C][C]-42.2073732718895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5899&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5899&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	582.963133640553	-59.9631336405528
2	519	579	-59.9999999999999
3	509	562.448847926267	-53.4488479262673
4	512	564.195391705069	-52.1953917050690
5	519	564.702304147465	-45.7023041474655
6	517	560.951152073733	-43.9511520737328
7	510	552.2	-42.2
8	509	545.2	-36.2
9	501	537.053456221198	-36.0534562211981
10	507	538.2	-31.2000000000000
11	569	591.551152073733	-22.5511520737328
12	580	601.951152073733	-21.9511520737327
13	578	584.20737327189	-6.20737327188945
14	565	579	-14
15	547	561.204608294931	-14.2046082949309
16	555	562.951152073733	-7.95115207373274
17	562	564.702304147465	-2.70230414746545
18	561	560.951152073733	0.0488479262672605
19	555	552.2	2.80000000000001
20	544	545.2	-1.19999999999999
21	537	538.297695852535	-1.29769585253455
22	543	538.2	4.80000000000003
23	594	592.795391705069	1.20460829493088
24	611	601.951152073733	9.04884792626725
25	613	584.20737327189	28.7926267281105
26	611	579	32
27	594	562.448847926267	31.5511520737327
28	595	562.951152073733	32.0488479262673
29	591	564.702304147465	26.2976958525345
30	589	560.951152073733	28.0488479262673
31	584	552.2	31.8
32	573	545.2	27.8
33	567	537.053456221198	29.9465437788018
34	569	538.2	30.8
35	621	591.551152073733	29.4488479262673
36	629	601.951152073733	27.0488479262673
37	628	584.20737327189	43.7926267281105
38	612	579	33
39	595	562.448847926267	32.5511520737327
40	597	562.951152073733	34.0488479262673
41	593	565.946543778802	27.0534562211982
42	590	560.951152073733	29.0488479262673
43	580	552.2	27.8
44	574	545.2	28.8
45	573	538.297695852535	34.7023041474654
46	573	538.2	34.8
47	620	591.551152073733	28.4488479262673
48	626	601.951152073733	24.0488479262673
49	620	584.20737327189	35.7926267281105
50	588	579	9
51	566	562.448847926267	3.55115207373273
52	557	562.951152073733	-5.95115207373274
53	561	565.946543778802	-4.94654377880181
54	549	562.195391705069	-13.1953917050691
55	532	552.2	-20.2
56	526	545.2	-19.2
57	511	538.297695852535	-27.2976958525345
58	499	538.2	-39.2
59	555	591.551152073733	-36.5511520737327
60	565	603.195391705069	-38.1953917050691
61	542	584.20737327189	-42.2073732718895

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