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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 16 Nov 2007 08:23:36 -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/16/t1195226316nby13m7sfs6t6ju.htm/, Retrieved Mon, 06 May 2024 03:04:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14462, Retrieved Mon, 06 May 2024 03:04:21 +0000

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No (this computation is public)

User-defined keywords

Rik, workshop 8, eigen gegevens, regressie analyse, EDA

Estimated Impact

263

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

-       [Multiple Regression] [Q3_WS8_Rik] [2007-11-16 15:23:36] [ca2982e42f0130f9b90c1847cba83896] [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=14462&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=14462&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14462&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
Werklh[t] = + 611.764523175355 -14.3070561873757LisStr[t] -52.9865133386884`9/11 `[t] -3.54164235685386M1[t] -7.7223382516665M2[t] -24.6711622204371M3[t] -23.8378288871039M4[t] -30.1689144435519M5[t] -33.668914443552M6[t] -42.0022477768852M7[t] -49.3355811102186M8[t] -56.5022477768852M9[t] -56.0022477768852M10[t] -1.16891444355192M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werklh[t] =  +  611.764523175355 -14.3070561873757LisStr[t] -52.9865133386884`9/11
`[t] -3.54164235685386M1[t] -7.7223382516665M2[t] -24.6711622204371M3[t] -23.8378288871039M4[t] -30.1689144435519M5[t] -33.668914443552M6[t] -42.0022477768852M7[t] -49.3355811102186M8[t] -56.5022477768852M9[t] -56.0022477768852M10[t] -1.16891444355192M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14462&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werklh[t] =  +  611.764523175355 -14.3070561873757LisStr[t] -52.9865133386884`9/11
`[t] -3.54164235685386M1[t] -7.7223382516665M2[t] -24.6711622204371M3[t] -23.8378288871039M4[t] -30.1689144435519M5[t] -33.668914443552M6[t] -42.0022477768852M7[t] -49.3355811102186M8[t] -56.5022477768852M9[t] -56.0022477768852M10[t] -1.16891444355192M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14462&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14462&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
Werklh[t] = + 611.764523175355 -14.3070561873757LisStr[t] -52.9865133386884`9/11 `[t] -3.54164235685386M1[t] -7.7223382516665M2[t] -24.6711622204371M3[t] -23.8378288871039M4[t] -30.1689144435519M5[t] -33.668914443552M6[t] -42.0022477768852M7[t] -49.3355811102186M8[t] -56.5022477768852M9[t] -56.0022477768852M10[t] -1.16891444355192M11[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)	611.764523175355	9.463543	64.6443	0	0
LisStr	-14.3070561873757	6.378918	-2.2429	0.028675	0.014338
`9/11 `	-52.9865133386884	4.005741	-13.2276	0	0
M1	-3.54164235685386	12.254717	-0.289	0.773593	0.386796
M2	-7.7223382516665	12.746818	-0.6058	0.546955	0.273477
M3	-24.6711622204371	12.75693	-1.9339	0.057921	0.028961
M4	-23.8378288871039	12.75693	-1.8686	0.066643	0.033322
M5	-30.1689144435519	12.704413	-2.3747	0.020835	0.010417
M6	-33.668914443552	12.704413	-2.6502	0.010311	0.005155
M7	-42.0022477768852	12.704413	-3.3061	0.001613	0.000807
M8	-49.3355811102186	12.704413	-3.8833	0.000263	0.000131
M9	-56.5022477768852	12.704413	-4.4475	3.9e-05	2e-05
M10	-56.0022477768852	12.704413	-4.4081	4.5e-05	2.2e-05
M11	-1.16891444355192	12.704413	-0.092	0.927003	0.463501

\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) & 611.764523175355 & 9.463543 & 64.6443 & 0 & 0 \tabularnewline
LisStr & -14.3070561873757 & 6.378918 & -2.2429 & 0.028675 & 0.014338 \tabularnewline
`9/11
` & -52.9865133386884 & 4.005741 & -13.2276 & 0 & 0 \tabularnewline
M1 & -3.54164235685386 & 12.254717 & -0.289 & 0.773593 & 0.386796 \tabularnewline
M2 & -7.7223382516665 & 12.746818 & -0.6058 & 0.546955 & 0.273477 \tabularnewline
M3 & -24.6711622204371 & 12.75693 & -1.9339 & 0.057921 & 0.028961 \tabularnewline
M4 & -23.8378288871039 & 12.75693 & -1.8686 & 0.066643 & 0.033322 \tabularnewline
M5 & -30.1689144435519 & 12.704413 & -2.3747 & 0.020835 & 0.010417 \tabularnewline
M6 & -33.668914443552 & 12.704413 & -2.6502 & 0.010311 & 0.005155 \tabularnewline
M7 & -42.0022477768852 & 12.704413 & -3.3061 & 0.001613 & 0.000807 \tabularnewline
M8 & -49.3355811102186 & 12.704413 & -3.8833 & 0.000263 & 0.000131 \tabularnewline
M9 & -56.5022477768852 & 12.704413 & -4.4475 & 3.9e-05 & 2e-05 \tabularnewline
M10 & -56.0022477768852 & 12.704413 & -4.4081 & 4.5e-05 & 2.2e-05 \tabularnewline
M11 & -1.16891444355192 & 12.704413 & -0.092 & 0.927003 & 0.463501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14462&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]611.764523175355[/C][C]9.463543[/C][C]64.6443[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]LisStr[/C][C]-14.3070561873757[/C][C]6.378918[/C][C]-2.2429[/C][C]0.028675[/C][C]0.014338[/C][/ROW]
[ROW][C]`9/11
`[/C][C]-52.9865133386884[/C][C]4.005741[/C][C]-13.2276[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-3.54164235685386[/C][C]12.254717[/C][C]-0.289[/C][C]0.773593[/C][C]0.386796[/C][/ROW]
[ROW][C]M2[/C][C]-7.7223382516665[/C][C]12.746818[/C][C]-0.6058[/C][C]0.546955[/C][C]0.273477[/C][/ROW]
[ROW][C]M3[/C][C]-24.6711622204371[/C][C]12.75693[/C][C]-1.9339[/C][C]0.057921[/C][C]0.028961[/C][/ROW]
[ROW][C]M4[/C][C]-23.8378288871039[/C][C]12.75693[/C][C]-1.8686[/C][C]0.066643[/C][C]0.033322[/C][/ROW]
[ROW][C]M5[/C][C]-30.1689144435519[/C][C]12.704413[/C][C]-2.3747[/C][C]0.020835[/C][C]0.010417[/C][/ROW]
[ROW][C]M6[/C][C]-33.668914443552[/C][C]12.704413[/C][C]-2.6502[/C][C]0.010311[/C][C]0.005155[/C][/ROW]
[ROW][C]M7[/C][C]-42.0022477768852[/C][C]12.704413[/C][C]-3.3061[/C][C]0.001613[/C][C]0.000807[/C][/ROW]
[ROW][C]M8[/C][C]-49.3355811102186[/C][C]12.704413[/C][C]-3.8833[/C][C]0.000263[/C][C]0.000131[/C][/ROW]
[ROW][C]M9[/C][C]-56.5022477768852[/C][C]12.704413[/C][C]-4.4475[/C][C]3.9e-05[/C][C]2e-05[/C][/ROW]
[ROW][C]M10[/C][C]-56.0022477768852[/C][C]12.704413[/C][C]-4.4081[/C][C]4.5e-05[/C][C]2.2e-05[/C][/ROW]
[ROW][C]M11[/C][C]-1.16891444355192[/C][C]12.704413[/C][C]-0.092[/C][C]0.927003[/C][C]0.463501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14462&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14462&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)	611.764523175355	9.463543	64.6443	0	0
LisStr	-14.3070561873757	6.378918	-2.2429	0.028675	0.014338
`9/11 `	-52.9865133386884	4.005741	-13.2276	0	0
M1	-3.54164235685386	12.254717	-0.289	0.773593	0.386796
M2	-7.7223382516665	12.746818	-0.6058	0.546955	0.273477
M3	-24.6711622204371	12.75693	-1.9339	0.057921	0.028961
M4	-23.8378288871039	12.75693	-1.8686	0.066643	0.033322
M5	-30.1689144435519	12.704413	-2.3747	0.020835	0.010417
M6	-33.668914443552	12.704413	-2.6502	0.010311	0.005155
M7	-42.0022477768852	12.704413	-3.3061	0.001613	0.000807
M8	-49.3355811102186	12.704413	-3.8833	0.000263	0.000131
M9	-56.5022477768852	12.704413	-4.4475	3.9e-05	2e-05
M10	-56.0022477768852	12.704413	-4.4081	4.5e-05	2.2e-05
M11	-1.16891444355192	12.704413	-0.092	0.927003	0.463501

Multiple Linear Regression - Regression Statistics
Multiple R	0.90349926934115
R-squared	0.816310929699992
Adjusted R-squared	0.775837066752533
F-TEST (value)	20.1688415746151
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	21.9742835076412
Sum Squared Residuals	28489.2790047774

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.90349926934115 \tabularnewline
R-squared & 0.816310929699992 \tabularnewline
Adjusted R-squared & 0.775837066752533 \tabularnewline
F-TEST (value) & 20.1688415746151 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 21.9742835076412 \tabularnewline
Sum Squared Residuals & 28489.2790047774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14462&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.90349926934115[/C][/ROW]
[ROW][C]R-squared[/C][C]0.816310929699992[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.775837066752533[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]20.1688415746151[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]21.9742835076412[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]28489.2790047774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14462&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14462&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	0.90349926934115
R-squared	0.816310929699992
Adjusted R-squared	0.775837066752533
F-TEST (value)	20.1688415746151
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	21.9742835076412
Sum Squared Residuals	28489.2790047774

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	513	502.249854141123	10.750145858877
2	503	498.069158246311	4.93084175368863
3	471	481.12033427754	-10.1203342775403
4	471	481.953667610874	-10.9536676108739
5	476	475.622582054426	0.377417945574162
6	475	472.122582054426	2.87741794557407
7	470	463.789248721093	6.21075127890751
8	461	456.455915387759	4.54408461224077
9	455	449.289248721092	5.71075127890764
10	456	449.789248721093	6.21075127890741
11	517	504.622582054426	12.3774179455741
12	525	558.778009836666	-33.7780098366662
13	523	555.236367479812	-32.2363674798124
14	519	551.055671585	-32.0556715849998
15	509	534.106847616229	-25.1068476162292
16	512	534.940180949562	-22.9401809495624
17	519	528.609095393114	-9.60909539311436
18	517	525.109095393114	-8.10909539311434
19	510	516.775762059781	-6.77576205978102
20	509	509.442428726448	-0.442428726447690
21	501	502.275762059781	-1.27576205978107
22	507	502.775762059781	4.22423794021898
23	569	557.609095393114	11.3909046068857
24	580	558.778009836666	21.2219901633337
25	578	555.236367479812	22.7636325201876
26	565	551.055671585	13.9443284150002
27	547	534.106847616229	12.8931523837708
28	555	534.940180949562	20.0598190504376
29	562	581.595608731803	-19.5956087318028
30	561	578.095608731803	-17.0956087318028
31	555	569.76227539847	-14.7622753984695
32	544	562.428942065136	-18.4289420651362
33	537	555.26227539847	-18.2622753984696
34	543	555.76227539847	-12.7622753984695
35	594	610.595608731803	-16.5956087318028
36	611	611.764523175355	-0.764523175354762
37	613	608.222880818501	4.77711918149906
38	611	604.042184923688	6.95781507631172
39	594	587.093360954918	6.90663904508235
40	595	587.926694288251	7.07330571174907
41	591	581.595608731803	9.40439126819715
42	589	578.095608731803	10.9043912681972
43	584	569.76227539847	14.2377246015305
44	573	562.428942065136	10.5710579348638
45	567	555.26227539847	11.7377246015305
46	569	555.76227539847	13.2377246015305
47	621	610.595608731803	10.4043912681972
48	629	611.764523175355	17.2354768246452
49	628	608.222880818501	19.7771191814991
50	612	604.042184923688	7.95781507631172
51	595	572.786304767542	22.2136952324581
52	597	573.619638100875	23.3803618991249
53	593	567.288552544427	25.7114474555730
54	590	563.788552544427	26.2114474555730
55	580	555.455219211094	24.5447807889063
56	574	548.12188587776	25.8781141222396
57	573	540.955219211094	32.0447807889063
58	573	541.455219211094	31.5447807889063
59	620	596.288552544427	23.7114474555730
60	626	597.457466987979	28.542533012021
61	620	593.915824631125	26.0841753688749
62	588	589.735128736313	-1.73512873631249
63	566	572.786304767542	-6.78630476754185
64	557	573.619638100875	-16.6196381008751
65	561	567.288552544427	-6.28855254442706
66	549	563.788552544427	-14.7885525444270
67	532	555.455219211094	-23.4552192110937
68	526	548.12188587776	-22.1218858777604
69	511	540.955219211094	-29.9552192110937
70	499	541.455219211094	-42.4552192110937
71	555	596.288552544427	-41.288552544427
72	565	597.457466987979	-32.457466987979
73	542	593.915824631125	-51.9158246311251

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 513 & 502.249854141123 & 10.750145858877 \tabularnewline
2 & 503 & 498.069158246311 & 4.93084175368863 \tabularnewline
3 & 471 & 481.12033427754 & -10.1203342775403 \tabularnewline
4 & 471 & 481.953667610874 & -10.9536676108739 \tabularnewline
5 & 476 & 475.622582054426 & 0.377417945574162 \tabularnewline
6 & 475 & 472.122582054426 & 2.87741794557407 \tabularnewline
7 & 470 & 463.789248721093 & 6.21075127890751 \tabularnewline
8 & 461 & 456.455915387759 & 4.54408461224077 \tabularnewline
9 & 455 & 449.289248721092 & 5.71075127890764 \tabularnewline
10 & 456 & 449.789248721093 & 6.21075127890741 \tabularnewline
11 & 517 & 504.622582054426 & 12.3774179455741 \tabularnewline
12 & 525 & 558.778009836666 & -33.7780098366662 \tabularnewline
13 & 523 & 555.236367479812 & -32.2363674798124 \tabularnewline
14 & 519 & 551.055671585 & -32.0556715849998 \tabularnewline
15 & 509 & 534.106847616229 & -25.1068476162292 \tabularnewline
16 & 512 & 534.940180949562 & -22.9401809495624 \tabularnewline
17 & 519 & 528.609095393114 & -9.60909539311436 \tabularnewline
18 & 517 & 525.109095393114 & -8.10909539311434 \tabularnewline
19 & 510 & 516.775762059781 & -6.77576205978102 \tabularnewline
20 & 509 & 509.442428726448 & -0.442428726447690 \tabularnewline
21 & 501 & 502.275762059781 & -1.27576205978107 \tabularnewline
22 & 507 & 502.775762059781 & 4.22423794021898 \tabularnewline
23 & 569 & 557.609095393114 & 11.3909046068857 \tabularnewline
24 & 580 & 558.778009836666 & 21.2219901633337 \tabularnewline
25 & 578 & 555.236367479812 & 22.7636325201876 \tabularnewline
26 & 565 & 551.055671585 & 13.9443284150002 \tabularnewline
27 & 547 & 534.106847616229 & 12.8931523837708 \tabularnewline
28 & 555 & 534.940180949562 & 20.0598190504376 \tabularnewline
29 & 562 & 581.595608731803 & -19.5956087318028 \tabularnewline
30 & 561 & 578.095608731803 & -17.0956087318028 \tabularnewline
31 & 555 & 569.76227539847 & -14.7622753984695 \tabularnewline
32 & 544 & 562.428942065136 & -18.4289420651362 \tabularnewline
33 & 537 & 555.26227539847 & -18.2622753984696 \tabularnewline
34 & 543 & 555.76227539847 & -12.7622753984695 \tabularnewline
35 & 594 & 610.595608731803 & -16.5956087318028 \tabularnewline
36 & 611 & 611.764523175355 & -0.764523175354762 \tabularnewline
37 & 613 & 608.222880818501 & 4.77711918149906 \tabularnewline
38 & 611 & 604.042184923688 & 6.95781507631172 \tabularnewline
39 & 594 & 587.093360954918 & 6.90663904508235 \tabularnewline
40 & 595 & 587.926694288251 & 7.07330571174907 \tabularnewline
41 & 591 & 581.595608731803 & 9.40439126819715 \tabularnewline
42 & 589 & 578.095608731803 & 10.9043912681972 \tabularnewline
43 & 584 & 569.76227539847 & 14.2377246015305 \tabularnewline
44 & 573 & 562.428942065136 & 10.5710579348638 \tabularnewline
45 & 567 & 555.26227539847 & 11.7377246015305 \tabularnewline
46 & 569 & 555.76227539847 & 13.2377246015305 \tabularnewline
47 & 621 & 610.595608731803 & 10.4043912681972 \tabularnewline
48 & 629 & 611.764523175355 & 17.2354768246452 \tabularnewline
49 & 628 & 608.222880818501 & 19.7771191814991 \tabularnewline
50 & 612 & 604.042184923688 & 7.95781507631172 \tabularnewline
51 & 595 & 572.786304767542 & 22.2136952324581 \tabularnewline
52 & 597 & 573.619638100875 & 23.3803618991249 \tabularnewline
53 & 593 & 567.288552544427 & 25.7114474555730 \tabularnewline
54 & 590 & 563.788552544427 & 26.2114474555730 \tabularnewline
55 & 580 & 555.455219211094 & 24.5447807889063 \tabularnewline
56 & 574 & 548.12188587776 & 25.8781141222396 \tabularnewline
57 & 573 & 540.955219211094 & 32.0447807889063 \tabularnewline
58 & 573 & 541.455219211094 & 31.5447807889063 \tabularnewline
59 & 620 & 596.288552544427 & 23.7114474555730 \tabularnewline
60 & 626 & 597.457466987979 & 28.542533012021 \tabularnewline
61 & 620 & 593.915824631125 & 26.0841753688749 \tabularnewline
62 & 588 & 589.735128736313 & -1.73512873631249 \tabularnewline
63 & 566 & 572.786304767542 & -6.78630476754185 \tabularnewline
64 & 557 & 573.619638100875 & -16.6196381008751 \tabularnewline
65 & 561 & 567.288552544427 & -6.28855254442706 \tabularnewline
66 & 549 & 563.788552544427 & -14.7885525444270 \tabularnewline
67 & 532 & 555.455219211094 & -23.4552192110937 \tabularnewline
68 & 526 & 548.12188587776 & -22.1218858777604 \tabularnewline
69 & 511 & 540.955219211094 & -29.9552192110937 \tabularnewline
70 & 499 & 541.455219211094 & -42.4552192110937 \tabularnewline
71 & 555 & 596.288552544427 & -41.288552544427 \tabularnewline
72 & 565 & 597.457466987979 & -32.457466987979 \tabularnewline
73 & 542 & 593.915824631125 & -51.9158246311251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14462&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]513[/C][C]502.249854141123[/C][C]10.750145858877[/C][/ROW]
[ROW][C]2[/C][C]503[/C][C]498.069158246311[/C][C]4.93084175368863[/C][/ROW]
[ROW][C]3[/C][C]471[/C][C]481.12033427754[/C][C]-10.1203342775403[/C][/ROW]
[ROW][C]4[/C][C]471[/C][C]481.953667610874[/C][C]-10.9536676108739[/C][/ROW]
[ROW][C]5[/C][C]476[/C][C]475.622582054426[/C][C]0.377417945574162[/C][/ROW]
[ROW][C]6[/C][C]475[/C][C]472.122582054426[/C][C]2.87741794557407[/C][/ROW]
[ROW][C]7[/C][C]470[/C][C]463.789248721093[/C][C]6.21075127890751[/C][/ROW]
[ROW][C]8[/C][C]461[/C][C]456.455915387759[/C][C]4.54408461224077[/C][/ROW]
[ROW][C]9[/C][C]455[/C][C]449.289248721092[/C][C]5.71075127890764[/C][/ROW]
[ROW][C]10[/C][C]456[/C][C]449.789248721093[/C][C]6.21075127890741[/C][/ROW]
[ROW][C]11[/C][C]517[/C][C]504.622582054426[/C][C]12.3774179455741[/C][/ROW]
[ROW][C]12[/C][C]525[/C][C]558.778009836666[/C][C]-33.7780098366662[/C][/ROW]
[ROW][C]13[/C][C]523[/C][C]555.236367479812[/C][C]-32.2363674798124[/C][/ROW]
[ROW][C]14[/C][C]519[/C][C]551.055671585[/C][C]-32.0556715849998[/C][/ROW]
[ROW][C]15[/C][C]509[/C][C]534.106847616229[/C][C]-25.1068476162292[/C][/ROW]
[ROW][C]16[/C][C]512[/C][C]534.940180949562[/C][C]-22.9401809495624[/C][/ROW]
[ROW][C]17[/C][C]519[/C][C]528.609095393114[/C][C]-9.60909539311436[/C][/ROW]
[ROW][C]18[/C][C]517[/C][C]525.109095393114[/C][C]-8.10909539311434[/C][/ROW]
[ROW][C]19[/C][C]510[/C][C]516.775762059781[/C][C]-6.77576205978102[/C][/ROW]
[ROW][C]20[/C][C]509[/C][C]509.442428726448[/C][C]-0.442428726447690[/C][/ROW]
[ROW][C]21[/C][C]501[/C][C]502.275762059781[/C][C]-1.27576205978107[/C][/ROW]
[ROW][C]22[/C][C]507[/C][C]502.775762059781[/C][C]4.22423794021898[/C][/ROW]
[ROW][C]23[/C][C]569[/C][C]557.609095393114[/C][C]11.3909046068857[/C][/ROW]
[ROW][C]24[/C][C]580[/C][C]558.778009836666[/C][C]21.2219901633337[/C][/ROW]
[ROW][C]25[/C][C]578[/C][C]555.236367479812[/C][C]22.7636325201876[/C][/ROW]
[ROW][C]26[/C][C]565[/C][C]551.055671585[/C][C]13.9443284150002[/C][/ROW]
[ROW][C]27[/C][C]547[/C][C]534.106847616229[/C][C]12.8931523837708[/C][/ROW]
[ROW][C]28[/C][C]555[/C][C]534.940180949562[/C][C]20.0598190504376[/C][/ROW]
[ROW][C]29[/C][C]562[/C][C]581.595608731803[/C][C]-19.5956087318028[/C][/ROW]
[ROW][C]30[/C][C]561[/C][C]578.095608731803[/C][C]-17.0956087318028[/C][/ROW]
[ROW][C]31[/C][C]555[/C][C]569.76227539847[/C][C]-14.7622753984695[/C][/ROW]
[ROW][C]32[/C][C]544[/C][C]562.428942065136[/C][C]-18.4289420651362[/C][/ROW]
[ROW][C]33[/C][C]537[/C][C]555.26227539847[/C][C]-18.2622753984696[/C][/ROW]
[ROW][C]34[/C][C]543[/C][C]555.76227539847[/C][C]-12.7622753984695[/C][/ROW]
[ROW][C]35[/C][C]594[/C][C]610.595608731803[/C][C]-16.5956087318028[/C][/ROW]
[ROW][C]36[/C][C]611[/C][C]611.764523175355[/C][C]-0.764523175354762[/C][/ROW]
[ROW][C]37[/C][C]613[/C][C]608.222880818501[/C][C]4.77711918149906[/C][/ROW]
[ROW][C]38[/C][C]611[/C][C]604.042184923688[/C][C]6.95781507631172[/C][/ROW]
[ROW][C]39[/C][C]594[/C][C]587.093360954918[/C][C]6.90663904508235[/C][/ROW]
[ROW][C]40[/C][C]595[/C][C]587.926694288251[/C][C]7.07330571174907[/C][/ROW]
[ROW][C]41[/C][C]591[/C][C]581.595608731803[/C][C]9.40439126819715[/C][/ROW]
[ROW][C]42[/C][C]589[/C][C]578.095608731803[/C][C]10.9043912681972[/C][/ROW]
[ROW][C]43[/C][C]584[/C][C]569.76227539847[/C][C]14.2377246015305[/C][/ROW]
[ROW][C]44[/C][C]573[/C][C]562.428942065136[/C][C]10.5710579348638[/C][/ROW]
[ROW][C]45[/C][C]567[/C][C]555.26227539847[/C][C]11.7377246015305[/C][/ROW]
[ROW][C]46[/C][C]569[/C][C]555.76227539847[/C][C]13.2377246015305[/C][/ROW]
[ROW][C]47[/C][C]621[/C][C]610.595608731803[/C][C]10.4043912681972[/C][/ROW]
[ROW][C]48[/C][C]629[/C][C]611.764523175355[/C][C]17.2354768246452[/C][/ROW]
[ROW][C]49[/C][C]628[/C][C]608.222880818501[/C][C]19.7771191814991[/C][/ROW]
[ROW][C]50[/C][C]612[/C][C]604.042184923688[/C][C]7.95781507631172[/C][/ROW]
[ROW][C]51[/C][C]595[/C][C]572.786304767542[/C][C]22.2136952324581[/C][/ROW]
[ROW][C]52[/C][C]597[/C][C]573.619638100875[/C][C]23.3803618991249[/C][/ROW]
[ROW][C]53[/C][C]593[/C][C]567.288552544427[/C][C]25.7114474555730[/C][/ROW]
[ROW][C]54[/C][C]590[/C][C]563.788552544427[/C][C]26.2114474555730[/C][/ROW]
[ROW][C]55[/C][C]580[/C][C]555.455219211094[/C][C]24.5447807889063[/C][/ROW]
[ROW][C]56[/C][C]574[/C][C]548.12188587776[/C][C]25.8781141222396[/C][/ROW]
[ROW][C]57[/C][C]573[/C][C]540.955219211094[/C][C]32.0447807889063[/C][/ROW]
[ROW][C]58[/C][C]573[/C][C]541.455219211094[/C][C]31.5447807889063[/C][/ROW]
[ROW][C]59[/C][C]620[/C][C]596.288552544427[/C][C]23.7114474555730[/C][/ROW]
[ROW][C]60[/C][C]626[/C][C]597.457466987979[/C][C]28.542533012021[/C][/ROW]
[ROW][C]61[/C][C]620[/C][C]593.915824631125[/C][C]26.0841753688749[/C][/ROW]
[ROW][C]62[/C][C]588[/C][C]589.735128736313[/C][C]-1.73512873631249[/C][/ROW]
[ROW][C]63[/C][C]566[/C][C]572.786304767542[/C][C]-6.78630476754185[/C][/ROW]
[ROW][C]64[/C][C]557[/C][C]573.619638100875[/C][C]-16.6196381008751[/C][/ROW]
[ROW][C]65[/C][C]561[/C][C]567.288552544427[/C][C]-6.28855254442706[/C][/ROW]
[ROW][C]66[/C][C]549[/C][C]563.788552544427[/C][C]-14.7885525444270[/C][/ROW]
[ROW][C]67[/C][C]532[/C][C]555.455219211094[/C][C]-23.4552192110937[/C][/ROW]
[ROW][C]68[/C][C]526[/C][C]548.12188587776[/C][C]-22.1218858777604[/C][/ROW]
[ROW][C]69[/C][C]511[/C][C]540.955219211094[/C][C]-29.9552192110937[/C][/ROW]
[ROW][C]70[/C][C]499[/C][C]541.455219211094[/C][C]-42.4552192110937[/C][/ROW]
[ROW][C]71[/C][C]555[/C][C]596.288552544427[/C][C]-41.288552544427[/C][/ROW]
[ROW][C]72[/C][C]565[/C][C]597.457466987979[/C][C]-32.457466987979[/C][/ROW]
[ROW][C]73[/C][C]542[/C][C]593.915824631125[/C][C]-51.9158246311251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14462&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14462&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	513	502.249854141123	10.750145858877
2	503	498.069158246311	4.93084175368863
3	471	481.12033427754	-10.1203342775403
4	471	481.953667610874	-10.9536676108739
5	476	475.622582054426	0.377417945574162
6	475	472.122582054426	2.87741794557407
7	470	463.789248721093	6.21075127890751
8	461	456.455915387759	4.54408461224077
9	455	449.289248721092	5.71075127890764
10	456	449.789248721093	6.21075127890741
11	517	504.622582054426	12.3774179455741
12	525	558.778009836666	-33.7780098366662
13	523	555.236367479812	-32.2363674798124
14	519	551.055671585	-32.0556715849998
15	509	534.106847616229	-25.1068476162292
16	512	534.940180949562	-22.9401809495624
17	519	528.609095393114	-9.60909539311436
18	517	525.109095393114	-8.10909539311434
19	510	516.775762059781	-6.77576205978102
20	509	509.442428726448	-0.442428726447690
21	501	502.275762059781	-1.27576205978107
22	507	502.775762059781	4.22423794021898
23	569	557.609095393114	11.3909046068857
24	580	558.778009836666	21.2219901633337
25	578	555.236367479812	22.7636325201876
26	565	551.055671585	13.9443284150002
27	547	534.106847616229	12.8931523837708
28	555	534.940180949562	20.0598190504376
29	562	581.595608731803	-19.5956087318028
30	561	578.095608731803	-17.0956087318028
31	555	569.76227539847	-14.7622753984695
32	544	562.428942065136	-18.4289420651362
33	537	555.26227539847	-18.2622753984696
34	543	555.76227539847	-12.7622753984695
35	594	610.595608731803	-16.5956087318028
36	611	611.764523175355	-0.764523175354762
37	613	608.222880818501	4.77711918149906
38	611	604.042184923688	6.95781507631172
39	594	587.093360954918	6.90663904508235
40	595	587.926694288251	7.07330571174907
41	591	581.595608731803	9.40439126819715
42	589	578.095608731803	10.9043912681972
43	584	569.76227539847	14.2377246015305
44	573	562.428942065136	10.5710579348638
45	567	555.26227539847	11.7377246015305
46	569	555.76227539847	13.2377246015305
47	621	610.595608731803	10.4043912681972
48	629	611.764523175355	17.2354768246452
49	628	608.222880818501	19.7771191814991
50	612	604.042184923688	7.95781507631172
51	595	572.786304767542	22.2136952324581
52	597	573.619638100875	23.3803618991249
53	593	567.288552544427	25.7114474555730
54	590	563.788552544427	26.2114474555730
55	580	555.455219211094	24.5447807889063
56	574	548.12188587776	25.8781141222396
57	573	540.955219211094	32.0447807889063
58	573	541.455219211094	31.5447807889063
59	620	596.288552544427	23.7114474555730
60	626	597.457466987979	28.542533012021
61	620	593.915824631125	26.0841753688749
62	588	589.735128736313	-1.73512873631249
63	566	572.786304767542	-6.78630476754185
64	557	573.619638100875	-16.6196381008751
65	561	567.288552544427	-6.28855254442706
66	549	563.788552544427	-14.7885525444270
67	532	555.455219211094	-23.4552192110937
68	526	548.12188587776	-22.1218858777604
69	511	540.955219211094	-29.9552192110937
70	499	541.455219211094	-42.4552192110937
71	555	596.288552544427	-41.288552544427
72	565	597.457466987979	-32.457466987979
73	542	593.915824631125	-51.9158246311251

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 = Do not include Seasonal 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