Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 19 Nov 2007 04:24:31 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/19/t1195471152pz5yc8g51t9tbk5.htm/, Retrieved Fri, 03 May 2024 14:26:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5712, Retrieved Fri, 03 May 2024 14:26:38 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Q3 The Seatbelt Law

Estimated Impact

204

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

-       [Multiple Regression] [Q3 The Seatbelt Law] [2007-11-19 11:24:31] [0cecb02636bfe8ebd97a7fef80b2b9e7] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=5712&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=5712&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5712&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
Investeringsgoederen[t] = + 99.0459962049336 -4.73984819734343`Dummy `[t] + 2.56438330170773M1[t] -5.15855787476282M2[t] -4.1614990512334M3[t] -11.9044402277040M4[t] -5.88738140417458M5[t] + 15.0096774193548M6[t] -2.73326375711576M7[t] -0.188235294117634M8[t] + 16.7888235294117M9[t] -24.5541176470588M10[t] -29.6370588235294M11[t] + 0.582941176470588t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Investeringsgoederen[t] =  +  99.0459962049336 -4.73984819734343`Dummy
`[t] +  2.56438330170773M1[t] -5.15855787476282M2[t] -4.1614990512334M3[t] -11.9044402277040M4[t] -5.88738140417458M5[t] +  15.0096774193548M6[t] -2.73326375711576M7[t] -0.188235294117634M8[t] +  16.7888235294117M9[t] -24.5541176470588M10[t] -29.6370588235294M11[t] +  0.582941176470588t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5712&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Investeringsgoederen[t] =  +  99.0459962049336 -4.73984819734343`Dummy
`[t] +  2.56438330170773M1[t] -5.15855787476282M2[t] -4.1614990512334M3[t] -11.9044402277040M4[t] -5.88738140417458M5[t] +  15.0096774193548M6[t] -2.73326375711576M7[t] -0.188235294117634M8[t] +  16.7888235294117M9[t] -24.5541176470588M10[t] -29.6370588235294M11[t] +  0.582941176470588t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5712&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5712&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
Investeringsgoederen[t] = + 99.0459962049336 -4.73984819734343`Dummy `[t] + 2.56438330170773M1[t] -5.15855787476282M2[t] -4.1614990512334M3[t] -11.9044402277040M4[t] -5.88738140417458M5[t] + 15.0096774193548M6[t] -2.73326375711576M7[t] -0.188235294117634M8[t] + 16.7888235294117M9[t] -24.5541176470588M10[t] -29.6370588235294M11[t] + 0.582941176470588t + 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)	99.0459962049336	3.479393	28.4665	0	0
`Dummy `	-4.73984819734343	3.165266	-1.4975	0.141105	0.070553
M1	2.56438330170773	4.233385	0.6058	0.547657	0.273828
M2	-5.15855787476282	4.225736	-1.2207	0.228402	0.114201
M3	-4.1614990512334	4.219777	-0.9862	0.329199	0.1646
M4	-11.9044402277040	4.215516	-2.824	0.006989	0.003494
M5	-5.88738140417458	4.212957	-1.3974	0.168983	0.084492
M6	15.0096774193548	4.212103	3.5635	0.000866	0.000433
M7	-2.73326375711576	4.212957	-0.6488	0.519709	0.259855
M8	-0.188235294117634	4.208908	-0.0447	0.964522	0.482261
M9	16.7888235294117	4.202926	3.9946	0.000232	0.000116
M10	-24.5541176470588	4.198647	-5.8481	0	0
M11	-29.6370588235294	4.196078	-7.063	0	0
t	0.582941176470588	0.084791	6.875	0	0

\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) & 99.0459962049336 & 3.479393 & 28.4665 & 0 & 0 \tabularnewline
`Dummy
` & -4.73984819734343 & 3.165266 & -1.4975 & 0.141105 & 0.070553 \tabularnewline
M1 & 2.56438330170773 & 4.233385 & 0.6058 & 0.547657 & 0.273828 \tabularnewline
M2 & -5.15855787476282 & 4.225736 & -1.2207 & 0.228402 & 0.114201 \tabularnewline
M3 & -4.1614990512334 & 4.219777 & -0.9862 & 0.329199 & 0.1646 \tabularnewline
M4 & -11.9044402277040 & 4.215516 & -2.824 & 0.006989 & 0.003494 \tabularnewline
M5 & -5.88738140417458 & 4.212957 & -1.3974 & 0.168983 & 0.084492 \tabularnewline
M6 & 15.0096774193548 & 4.212103 & 3.5635 & 0.000866 & 0.000433 \tabularnewline
M7 & -2.73326375711576 & 4.212957 & -0.6488 & 0.519709 & 0.259855 \tabularnewline
M8 & -0.188235294117634 & 4.208908 & -0.0447 & 0.964522 & 0.482261 \tabularnewline
M9 & 16.7888235294117 & 4.202926 & 3.9946 & 0.000232 & 0.000116 \tabularnewline
M10 & -24.5541176470588 & 4.198647 & -5.8481 & 0 & 0 \tabularnewline
M11 & -29.6370588235294 & 4.196078 & -7.063 & 0 & 0 \tabularnewline
t & 0.582941176470588 & 0.084791 & 6.875 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5712&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]99.0459962049336[/C][C]3.479393[/C][C]28.4665[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Dummy
`[/C][C]-4.73984819734343[/C][C]3.165266[/C][C]-1.4975[/C][C]0.141105[/C][C]0.070553[/C][/ROW]
[ROW][C]M1[/C][C]2.56438330170773[/C][C]4.233385[/C][C]0.6058[/C][C]0.547657[/C][C]0.273828[/C][/ROW]
[ROW][C]M2[/C][C]-5.15855787476282[/C][C]4.225736[/C][C]-1.2207[/C][C]0.228402[/C][C]0.114201[/C][/ROW]
[ROW][C]M3[/C][C]-4.1614990512334[/C][C]4.219777[/C][C]-0.9862[/C][C]0.329199[/C][C]0.1646[/C][/ROW]
[ROW][C]M4[/C][C]-11.9044402277040[/C][C]4.215516[/C][C]-2.824[/C][C]0.006989[/C][C]0.003494[/C][/ROW]
[ROW][C]M5[/C][C]-5.88738140417458[/C][C]4.212957[/C][C]-1.3974[/C][C]0.168983[/C][C]0.084492[/C][/ROW]
[ROW][C]M6[/C][C]15.0096774193548[/C][C]4.212103[/C][C]3.5635[/C][C]0.000866[/C][C]0.000433[/C][/ROW]
[ROW][C]M7[/C][C]-2.73326375711576[/C][C]4.212957[/C][C]-0.6488[/C][C]0.519709[/C][C]0.259855[/C][/ROW]
[ROW][C]M8[/C][C]-0.188235294117634[/C][C]4.208908[/C][C]-0.0447[/C][C]0.964522[/C][C]0.482261[/C][/ROW]
[ROW][C]M9[/C][C]16.7888235294117[/C][C]4.202926[/C][C]3.9946[/C][C]0.000232[/C][C]0.000116[/C][/ROW]
[ROW][C]M10[/C][C]-24.5541176470588[/C][C]4.198647[/C][C]-5.8481[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-29.6370588235294[/C][C]4.196078[/C][C]-7.063[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]0.582941176470588[/C][C]0.084791[/C][C]6.875[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5712&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5712&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)	99.0459962049336	3.479393	28.4665	0	0
`Dummy `	-4.73984819734343	3.165266	-1.4975	0.141105	0.070553
M1	2.56438330170773	4.233385	0.6058	0.547657	0.273828
M2	-5.15855787476282	4.225736	-1.2207	0.228402	0.114201
M3	-4.1614990512334	4.219777	-0.9862	0.329199	0.1646
M4	-11.9044402277040	4.215516	-2.824	0.006989	0.003494
M5	-5.88738140417458	4.212957	-1.3974	0.168983	0.084492
M6	15.0096774193548	4.212103	3.5635	0.000866	0.000433
M7	-2.73326375711576	4.212957	-0.6488	0.519709	0.259855
M8	-0.188235294117634	4.208908	-0.0447	0.964522	0.482261
M9	16.7888235294117	4.202926	3.9946	0.000232	0.000116
M10	-24.5541176470588	4.198647	-5.8481	0	0
M11	-29.6370588235294	4.196078	-7.063	0	0
t	0.582941176470588	0.084791	6.875	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.933719555032695
R-squared	0.871832207450453
Adjusted R-squared	0.835610874773407
F-TEST (value)	24.0695784228544
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	3.33066907387547e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.63322668312216
Sum Squared Residuals	2023.98602656545

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.933719555032695 \tabularnewline
R-squared & 0.871832207450453 \tabularnewline
Adjusted R-squared & 0.835610874773407 \tabularnewline
F-TEST (value) & 24.0695784228544 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 3.33066907387547e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.63322668312216 \tabularnewline
Sum Squared Residuals & 2023.98602656545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5712&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.933719555032695[/C][/ROW]
[ROW][C]R-squared[/C][C]0.871832207450453[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.835610874773407[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]24.0695784228544[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]3.33066907387547e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]6.63322668312216[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2023.98602656545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5712&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5712&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	0.933719555032695
R-squared	0.871832207450453
Adjusted R-squared	0.835610874773407
F-TEST (value)	24.0695784228544
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	3.33066907387547e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.63322668312216
Sum Squared Residuals	2023.98602656545

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	126.6	102.193320683112	24.4066793168879
2	93.9	95.053320683112	-1.15332068311196
3	89.8	96.633320683112	-6.83332068311195
4	93.4	89.473320683112	3.92667931688806
5	101.5	96.073320683112	5.42667931688804
6	110.4	117.553320683112	-7.15332068311196
7	105.9	100.393320683112	5.50667931688806
8	108.4	103.521290322581	4.87870967741936
9	113.9	121.081290322581	-7.18129032258064
10	86.1	80.3212903225807	5.77870967741932
11	69.4	75.8212903225806	-6.42129032258055
12	101.2	106.041290322581	-4.84129032258067
13	100.5	109.188614800759	-8.68861480075898
14	98	102.048614800759	-4.04861480075899
15	106.6	103.628614800759	2.97138519924099
16	90.1	96.468614800759	-6.36861480075901
17	96.9	103.068614800759	-6.168614800759
18	125.9	124.548614800759	1.35138519924101
19	112	107.388614800759	4.611385199241
20	100	105.776736242884	-5.77673624288427
21	123.9	123.336736242884	0.563263757115755
22	79.8	82.5767362428843	-2.77673624288425
23	83.4	78.0767362428843	5.32326375711572
24	113.6	108.296736242884	5.30326375711572
25	112.9	111.444060721063	1.45593927893742
26	104	104.304060721063	-0.30406072106263
27	109.9	105.884060721063	4.01593927893738
28	99	98.7240607210626	0.275939278937370
29	106.3	105.324060721063	0.975939278937373
30	128.9	126.804060721063	2.09593927893738
31	111.1	109.644060721063	1.45593927893737
32	102.9	112.772030360531	-9.8720303605313
33	130	130.332030360531	-0.332030360531307
34	87	89.5720303605313	-2.5720303605313
35	87.5	85.0720303605313	2.42796963946867
36	117.6	115.292030360531	2.30796963946867
37	103.4	118.439354838710	-15.0393548387096
38	110.8	111.299354838710	-0.499354838709688
39	112.6	112.879354838710	-0.279354838709688
40	102.5	105.719354838710	-3.21935483870968
41	112.4	112.319354838710	0.080645161290322
42	135.6	133.799354838710	1.80064516129031
43	105.1	116.639354838710	-11.5393548387097
44	127.7	119.767324478178	7.93267552182163
45	137	137.327324478178	-0.327324478178366
46	91	96.5673244781783	-5.56732447817835
47	90.5	92.0673244781784	-1.56732447817839
48	122.4	122.287324478178	0.112675521821624
49	123.3	125.434648956357	-2.13464895635669
50	124.3	118.294648956357	6.00535104364326
51	120	119.874648956357	0.125351043643261
52	118.1	112.714648956357	5.38535104364326
53	119	119.314648956357	-0.314648956356736
54	142.7	140.794648956357	1.90535104364325
55	123.6	123.634648956357	-0.034648956356742
56	129.6	126.762618595825	2.83738140417457
57	151.6	144.322618595825	7.27738140417457
58	108.7	103.562618595825	5.13738140417459
59	99.3	99.0626185958254	0.237381404174553
60	126.4	129.282618595825	-2.88261859582543

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 126.6 & 102.193320683112 & 24.4066793168879 \tabularnewline
2 & 93.9 & 95.053320683112 & -1.15332068311196 \tabularnewline
3 & 89.8 & 96.633320683112 & -6.83332068311195 \tabularnewline
4 & 93.4 & 89.473320683112 & 3.92667931688806 \tabularnewline
5 & 101.5 & 96.073320683112 & 5.42667931688804 \tabularnewline
6 & 110.4 & 117.553320683112 & -7.15332068311196 \tabularnewline
7 & 105.9 & 100.393320683112 & 5.50667931688806 \tabularnewline
8 & 108.4 & 103.521290322581 & 4.87870967741936 \tabularnewline
9 & 113.9 & 121.081290322581 & -7.18129032258064 \tabularnewline
10 & 86.1 & 80.3212903225807 & 5.77870967741932 \tabularnewline
11 & 69.4 & 75.8212903225806 & -6.42129032258055 \tabularnewline
12 & 101.2 & 106.041290322581 & -4.84129032258067 \tabularnewline
13 & 100.5 & 109.188614800759 & -8.68861480075898 \tabularnewline
14 & 98 & 102.048614800759 & -4.04861480075899 \tabularnewline
15 & 106.6 & 103.628614800759 & 2.97138519924099 \tabularnewline
16 & 90.1 & 96.468614800759 & -6.36861480075901 \tabularnewline
17 & 96.9 & 103.068614800759 & -6.168614800759 \tabularnewline
18 & 125.9 & 124.548614800759 & 1.35138519924101 \tabularnewline
19 & 112 & 107.388614800759 & 4.611385199241 \tabularnewline
20 & 100 & 105.776736242884 & -5.77673624288427 \tabularnewline
21 & 123.9 & 123.336736242884 & 0.563263757115755 \tabularnewline
22 & 79.8 & 82.5767362428843 & -2.77673624288425 \tabularnewline
23 & 83.4 & 78.0767362428843 & 5.32326375711572 \tabularnewline
24 & 113.6 & 108.296736242884 & 5.30326375711572 \tabularnewline
25 & 112.9 & 111.444060721063 & 1.45593927893742 \tabularnewline
26 & 104 & 104.304060721063 & -0.30406072106263 \tabularnewline
27 & 109.9 & 105.884060721063 & 4.01593927893738 \tabularnewline
28 & 99 & 98.7240607210626 & 0.275939278937370 \tabularnewline
29 & 106.3 & 105.324060721063 & 0.975939278937373 \tabularnewline
30 & 128.9 & 126.804060721063 & 2.09593927893738 \tabularnewline
31 & 111.1 & 109.644060721063 & 1.45593927893737 \tabularnewline
32 & 102.9 & 112.772030360531 & -9.8720303605313 \tabularnewline
33 & 130 & 130.332030360531 & -0.332030360531307 \tabularnewline
34 & 87 & 89.5720303605313 & -2.5720303605313 \tabularnewline
35 & 87.5 & 85.0720303605313 & 2.42796963946867 \tabularnewline
36 & 117.6 & 115.292030360531 & 2.30796963946867 \tabularnewline
37 & 103.4 & 118.439354838710 & -15.0393548387096 \tabularnewline
38 & 110.8 & 111.299354838710 & -0.499354838709688 \tabularnewline
39 & 112.6 & 112.879354838710 & -0.279354838709688 \tabularnewline
40 & 102.5 & 105.719354838710 & -3.21935483870968 \tabularnewline
41 & 112.4 & 112.319354838710 & 0.080645161290322 \tabularnewline
42 & 135.6 & 133.799354838710 & 1.80064516129031 \tabularnewline
43 & 105.1 & 116.639354838710 & -11.5393548387097 \tabularnewline
44 & 127.7 & 119.767324478178 & 7.93267552182163 \tabularnewline
45 & 137 & 137.327324478178 & -0.327324478178366 \tabularnewline
46 & 91 & 96.5673244781783 & -5.56732447817835 \tabularnewline
47 & 90.5 & 92.0673244781784 & -1.56732447817839 \tabularnewline
48 & 122.4 & 122.287324478178 & 0.112675521821624 \tabularnewline
49 & 123.3 & 125.434648956357 & -2.13464895635669 \tabularnewline
50 & 124.3 & 118.294648956357 & 6.00535104364326 \tabularnewline
51 & 120 & 119.874648956357 & 0.125351043643261 \tabularnewline
52 & 118.1 & 112.714648956357 & 5.38535104364326 \tabularnewline
53 & 119 & 119.314648956357 & -0.314648956356736 \tabularnewline
54 & 142.7 & 140.794648956357 & 1.90535104364325 \tabularnewline
55 & 123.6 & 123.634648956357 & -0.034648956356742 \tabularnewline
56 & 129.6 & 126.762618595825 & 2.83738140417457 \tabularnewline
57 & 151.6 & 144.322618595825 & 7.27738140417457 \tabularnewline
58 & 108.7 & 103.562618595825 & 5.13738140417459 \tabularnewline
59 & 99.3 & 99.0626185958254 & 0.237381404174553 \tabularnewline
60 & 126.4 & 129.282618595825 & -2.88261859582543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5712&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]126.6[/C][C]102.193320683112[/C][C]24.4066793168879[/C][/ROW]
[ROW][C]2[/C][C]93.9[/C][C]95.053320683112[/C][C]-1.15332068311196[/C][/ROW]
[ROW][C]3[/C][C]89.8[/C][C]96.633320683112[/C][C]-6.83332068311195[/C][/ROW]
[ROW][C]4[/C][C]93.4[/C][C]89.473320683112[/C][C]3.92667931688806[/C][/ROW]
[ROW][C]5[/C][C]101.5[/C][C]96.073320683112[/C][C]5.42667931688804[/C][/ROW]
[ROW][C]6[/C][C]110.4[/C][C]117.553320683112[/C][C]-7.15332068311196[/C][/ROW]
[ROW][C]7[/C][C]105.9[/C][C]100.393320683112[/C][C]5.50667931688806[/C][/ROW]
[ROW][C]8[/C][C]108.4[/C][C]103.521290322581[/C][C]4.87870967741936[/C][/ROW]
[ROW][C]9[/C][C]113.9[/C][C]121.081290322581[/C][C]-7.18129032258064[/C][/ROW]
[ROW][C]10[/C][C]86.1[/C][C]80.3212903225807[/C][C]5.77870967741932[/C][/ROW]
[ROW][C]11[/C][C]69.4[/C][C]75.8212903225806[/C][C]-6.42129032258055[/C][/ROW]
[ROW][C]12[/C][C]101.2[/C][C]106.041290322581[/C][C]-4.84129032258067[/C][/ROW]
[ROW][C]13[/C][C]100.5[/C][C]109.188614800759[/C][C]-8.68861480075898[/C][/ROW]
[ROW][C]14[/C][C]98[/C][C]102.048614800759[/C][C]-4.04861480075899[/C][/ROW]
[ROW][C]15[/C][C]106.6[/C][C]103.628614800759[/C][C]2.97138519924099[/C][/ROW]
[ROW][C]16[/C][C]90.1[/C][C]96.468614800759[/C][C]-6.36861480075901[/C][/ROW]
[ROW][C]17[/C][C]96.9[/C][C]103.068614800759[/C][C]-6.168614800759[/C][/ROW]
[ROW][C]18[/C][C]125.9[/C][C]124.548614800759[/C][C]1.35138519924101[/C][/ROW]
[ROW][C]19[/C][C]112[/C][C]107.388614800759[/C][C]4.611385199241[/C][/ROW]
[ROW][C]20[/C][C]100[/C][C]105.776736242884[/C][C]-5.77673624288427[/C][/ROW]
[ROW][C]21[/C][C]123.9[/C][C]123.336736242884[/C][C]0.563263757115755[/C][/ROW]
[ROW][C]22[/C][C]79.8[/C][C]82.5767362428843[/C][C]-2.77673624288425[/C][/ROW]
[ROW][C]23[/C][C]83.4[/C][C]78.0767362428843[/C][C]5.32326375711572[/C][/ROW]
[ROW][C]24[/C][C]113.6[/C][C]108.296736242884[/C][C]5.30326375711572[/C][/ROW]
[ROW][C]25[/C][C]112.9[/C][C]111.444060721063[/C][C]1.45593927893742[/C][/ROW]
[ROW][C]26[/C][C]104[/C][C]104.304060721063[/C][C]-0.30406072106263[/C][/ROW]
[ROW][C]27[/C][C]109.9[/C][C]105.884060721063[/C][C]4.01593927893738[/C][/ROW]
[ROW][C]28[/C][C]99[/C][C]98.7240607210626[/C][C]0.275939278937370[/C][/ROW]
[ROW][C]29[/C][C]106.3[/C][C]105.324060721063[/C][C]0.975939278937373[/C][/ROW]
[ROW][C]30[/C][C]128.9[/C][C]126.804060721063[/C][C]2.09593927893738[/C][/ROW]
[ROW][C]31[/C][C]111.1[/C][C]109.644060721063[/C][C]1.45593927893737[/C][/ROW]
[ROW][C]32[/C][C]102.9[/C][C]112.772030360531[/C][C]-9.8720303605313[/C][/ROW]
[ROW][C]33[/C][C]130[/C][C]130.332030360531[/C][C]-0.332030360531307[/C][/ROW]
[ROW][C]34[/C][C]87[/C][C]89.5720303605313[/C][C]-2.5720303605313[/C][/ROW]
[ROW][C]35[/C][C]87.5[/C][C]85.0720303605313[/C][C]2.42796963946867[/C][/ROW]
[ROW][C]36[/C][C]117.6[/C][C]115.292030360531[/C][C]2.30796963946867[/C][/ROW]
[ROW][C]37[/C][C]103.4[/C][C]118.439354838710[/C][C]-15.0393548387096[/C][/ROW]
[ROW][C]38[/C][C]110.8[/C][C]111.299354838710[/C][C]-0.499354838709688[/C][/ROW]
[ROW][C]39[/C][C]112.6[/C][C]112.879354838710[/C][C]-0.279354838709688[/C][/ROW]
[ROW][C]40[/C][C]102.5[/C][C]105.719354838710[/C][C]-3.21935483870968[/C][/ROW]
[ROW][C]41[/C][C]112.4[/C][C]112.319354838710[/C][C]0.080645161290322[/C][/ROW]
[ROW][C]42[/C][C]135.6[/C][C]133.799354838710[/C][C]1.80064516129031[/C][/ROW]
[ROW][C]43[/C][C]105.1[/C][C]116.639354838710[/C][C]-11.5393548387097[/C][/ROW]
[ROW][C]44[/C][C]127.7[/C][C]119.767324478178[/C][C]7.93267552182163[/C][/ROW]
[ROW][C]45[/C][C]137[/C][C]137.327324478178[/C][C]-0.327324478178366[/C][/ROW]
[ROW][C]46[/C][C]91[/C][C]96.5673244781783[/C][C]-5.56732447817835[/C][/ROW]
[ROW][C]47[/C][C]90.5[/C][C]92.0673244781784[/C][C]-1.56732447817839[/C][/ROW]
[ROW][C]48[/C][C]122.4[/C][C]122.287324478178[/C][C]0.112675521821624[/C][/ROW]
[ROW][C]49[/C][C]123.3[/C][C]125.434648956357[/C][C]-2.13464895635669[/C][/ROW]
[ROW][C]50[/C][C]124.3[/C][C]118.294648956357[/C][C]6.00535104364326[/C][/ROW]
[ROW][C]51[/C][C]120[/C][C]119.874648956357[/C][C]0.125351043643261[/C][/ROW]
[ROW][C]52[/C][C]118.1[/C][C]112.714648956357[/C][C]5.38535104364326[/C][/ROW]
[ROW][C]53[/C][C]119[/C][C]119.314648956357[/C][C]-0.314648956356736[/C][/ROW]
[ROW][C]54[/C][C]142.7[/C][C]140.794648956357[/C][C]1.90535104364325[/C][/ROW]
[ROW][C]55[/C][C]123.6[/C][C]123.634648956357[/C][C]-0.034648956356742[/C][/ROW]
[ROW][C]56[/C][C]129.6[/C][C]126.762618595825[/C][C]2.83738140417457[/C][/ROW]
[ROW][C]57[/C][C]151.6[/C][C]144.322618595825[/C][C]7.27738140417457[/C][/ROW]
[ROW][C]58[/C][C]108.7[/C][C]103.562618595825[/C][C]5.13738140417459[/C][/ROW]
[ROW][C]59[/C][C]99.3[/C][C]99.0626185958254[/C][C]0.237381404174553[/C][/ROW]
[ROW][C]60[/C][C]126.4[/C][C]129.282618595825[/C][C]-2.88261859582543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5712&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5712&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	126.6	102.193320683112	24.4066793168879
2	93.9	95.053320683112	-1.15332068311196
3	89.8	96.633320683112	-6.83332068311195
4	93.4	89.473320683112	3.92667931688806
5	101.5	96.073320683112	5.42667931688804
6	110.4	117.553320683112	-7.15332068311196
7	105.9	100.393320683112	5.50667931688806
8	108.4	103.521290322581	4.87870967741936
9	113.9	121.081290322581	-7.18129032258064
10	86.1	80.3212903225807	5.77870967741932
11	69.4	75.8212903225806	-6.42129032258055
12	101.2	106.041290322581	-4.84129032258067
13	100.5	109.188614800759	-8.68861480075898
14	98	102.048614800759	-4.04861480075899
15	106.6	103.628614800759	2.97138519924099
16	90.1	96.468614800759	-6.36861480075901
17	96.9	103.068614800759	-6.168614800759
18	125.9	124.548614800759	1.35138519924101
19	112	107.388614800759	4.611385199241
20	100	105.776736242884	-5.77673624288427
21	123.9	123.336736242884	0.563263757115755
22	79.8	82.5767362428843	-2.77673624288425
23	83.4	78.0767362428843	5.32326375711572
24	113.6	108.296736242884	5.30326375711572
25	112.9	111.444060721063	1.45593927893742
26	104	104.304060721063	-0.30406072106263
27	109.9	105.884060721063	4.01593927893738
28	99	98.7240607210626	0.275939278937370
29	106.3	105.324060721063	0.975939278937373
30	128.9	126.804060721063	2.09593927893738
31	111.1	109.644060721063	1.45593927893737
32	102.9	112.772030360531	-9.8720303605313
33	130	130.332030360531	-0.332030360531307
34	87	89.5720303605313	-2.5720303605313
35	87.5	85.0720303605313	2.42796963946867
36	117.6	115.292030360531	2.30796963946867
37	103.4	118.439354838710	-15.0393548387096
38	110.8	111.299354838710	-0.499354838709688
39	112.6	112.879354838710	-0.279354838709688
40	102.5	105.719354838710	-3.21935483870968
41	112.4	112.319354838710	0.080645161290322
42	135.6	133.799354838710	1.80064516129031
43	105.1	116.639354838710	-11.5393548387097
44	127.7	119.767324478178	7.93267552182163
45	137	137.327324478178	-0.327324478178366
46	91	96.5673244781783	-5.56732447817835
47	90.5	92.0673244781784	-1.56732447817839
48	122.4	122.287324478178	0.112675521821624
49	123.3	125.434648956357	-2.13464895635669
50	124.3	118.294648956357	6.00535104364326
51	120	119.874648956357	0.125351043643261
52	118.1	112.714648956357	5.38535104364326
53	119	119.314648956357	-0.314648956356736
54	142.7	140.794648956357	1.90535104364325
55	123.6	123.634648956357	-0.034648956356742
56	129.6	126.762618595825	2.83738140417457
57	151.6	144.322618595825	7.27738140417457
58	108.7	103.562618595825	5.13738140417459
59	99.3	99.0626185958254	0.237381404174553
60	126.4	129.282618595825	-2.88261859582543

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

Postscript link

PDF link

Figure 9

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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