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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Thu, 15 Nov 2007 05:27:22 -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/15/t1195129424t68y3ljegaa64rz.htm/, Retrieved Sat, 04 May 2024 17:15:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14452, Retrieved Sat, 04 May 2024 17:15:56 +0000

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Estimated Impact

262

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

-       [Multiple Regression] [] [2007-11-15 12:27:22] [0bbb5142800af364af4806d34f5150ff] [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=14452&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=14452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14452&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
-25[t] = + 163.547479367605 + 11.0329123993239`invloed>25`[t] -2.87383580259192M1[t] -11.0864903384044M2[t] -21.5772927645752M3[t] -24.9014285240794M4[t] -26.8922309502502M5[t] -30.0497000430877M6[t] -35.0405024692585M7[t] -38.8646382287627M8[t] -43.8554406549335M9[t] -42.6795764144377M10[t] -8.3425309071625M11[t] -0.342530907162507t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
-25[t] =  +  163.547479367605 +  11.0329123993239`invloed>25`[t] -2.87383580259192M1[t] -11.0864903384044M2[t] -21.5772927645752M3[t] -24.9014285240794M4[t] -26.8922309502502M5[t] -30.0497000430877M6[t] -35.0405024692585M7[t] -38.8646382287627M8[t] -43.8554406549335M9[t] -42.6795764144377M10[t] -8.3425309071625M11[t] -0.342530907162507t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14452&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]-25[t] =  +  163.547479367605 +  11.0329123993239`invloed>25`[t] -2.87383580259192M1[t] -11.0864903384044M2[t] -21.5772927645752M3[t] -24.9014285240794M4[t] -26.8922309502502M5[t] -30.0497000430877M6[t] -35.0405024692585M7[t] -38.8646382287627M8[t] -43.8554406549335M9[t] -42.6795764144377M10[t] -8.3425309071625M11[t] -0.342530907162507t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14452&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
-25[t] = + 163.547479367605 + 11.0329123993239`invloed>25`[t] -2.87383580259192M1[t] -11.0864903384044M2[t] -21.5772927645752M3[t] -24.9014285240794M4[t] -26.8922309502502M5[t] -30.0497000430877M6[t] -35.0405024692585M7[t] -38.8646382287627M8[t] -43.8554406549335M9[t] -42.6795764144377M10[t] -8.3425309071625M11[t] -0.342530907162507t + 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)	163.547479367605	3.481595	46.9749	0	0
`invloed>25`	11.0329123993239	1.422543	7.7558	0	0
M1	-2.87383580259192	3.784525	-0.7594	0.450658	0.225329
M2	-11.0864903384044	3.943247	-2.8115	0.006683	0.003342
M3	-21.5772927645752	3.938527	-5.4785	1e-06	0
M4	-24.9014285240794	3.934542	-6.3289	0	0
M5	-26.8922309502502	3.931293	-6.8406	0	0
M6	-30.0497000430877	3.928782	-7.6486	0	0
M7	-35.0405024692585	3.927011	-8.9229	0	0
M8	-38.8646382287627	3.92598	-9.8993	0	0
M9	-43.8554406549335	3.92569	-11.1714	0	0
M10	-42.6795764144377	3.926142	-10.8706	0	0
M11	-8.3425309071625	3.92248	-2.1269	0.037624	0.018812
t	-0.342530907162507	0.053949	-6.3492	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) & 163.547479367605 & 3.481595 & 46.9749 & 0 & 0 \tabularnewline
`invloed>25` & 11.0329123993239 & 1.422543 & 7.7558 & 0 & 0 \tabularnewline
M1 & -2.87383580259192 & 3.784525 & -0.7594 & 0.450658 & 0.225329 \tabularnewline
M2 & -11.0864903384044 & 3.943247 & -2.8115 & 0.006683 & 0.003342 \tabularnewline
M3 & -21.5772927645752 & 3.938527 & -5.4785 & 1e-06 & 0 \tabularnewline
M4 & -24.9014285240794 & 3.934542 & -6.3289 & 0 & 0 \tabularnewline
M5 & -26.8922309502502 & 3.931293 & -6.8406 & 0 & 0 \tabularnewline
M6 & -30.0497000430877 & 3.928782 & -7.6486 & 0 & 0 \tabularnewline
M7 & -35.0405024692585 & 3.927011 & -8.9229 & 0 & 0 \tabularnewline
M8 & -38.8646382287627 & 3.92598 & -9.8993 & 0 & 0 \tabularnewline
M9 & -43.8554406549335 & 3.92569 & -11.1714 & 0 & 0 \tabularnewline
M10 & -42.6795764144377 & 3.926142 & -10.8706 & 0 & 0 \tabularnewline
M11 & -8.3425309071625 & 3.92248 & -2.1269 & 0.037624 & 0.018812 \tabularnewline
t & -0.342530907162507 & 0.053949 & -6.3492 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14452&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]163.547479367605[/C][C]3.481595[/C][C]46.9749[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`invloed>25`[/C][C]11.0329123993239[/C][C]1.422543[/C][C]7.7558[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-2.87383580259192[/C][C]3.784525[/C][C]-0.7594[/C][C]0.450658[/C][C]0.225329[/C][/ROW]
[ROW][C]M2[/C][C]-11.0864903384044[/C][C]3.943247[/C][C]-2.8115[/C][C]0.006683[/C][C]0.003342[/C][/ROW]
[ROW][C]M3[/C][C]-21.5772927645752[/C][C]3.938527[/C][C]-5.4785[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-24.9014285240794[/C][C]3.934542[/C][C]-6.3289[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-26.8922309502502[/C][C]3.931293[/C][C]-6.8406[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-30.0497000430877[/C][C]3.928782[/C][C]-7.6486[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]-35.0405024692585[/C][C]3.927011[/C][C]-8.9229[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-38.8646382287627[/C][C]3.92598[/C][C]-9.8993[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-43.8554406549335[/C][C]3.92569[/C][C]-11.1714[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-42.6795764144377[/C][C]3.926142[/C][C]-10.8706[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-8.3425309071625[/C][C]3.92248[/C][C]-2.1269[/C][C]0.037624[/C][C]0.018812[/C][/ROW]
[ROW][C]t[/C][C]-0.342530907162507[/C][C]0.053949[/C][C]-6.3492[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14452&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)	163.547479367605	3.481595	46.9749	0	0
`invloed>25`	11.0329123993239	1.422543	7.7558	0	0
M1	-2.87383580259192	3.784525	-0.7594	0.450658	0.225329
M2	-11.0864903384044	3.943247	-2.8115	0.006683	0.003342
M3	-21.5772927645752	3.938527	-5.4785	1e-06	0
M4	-24.9014285240794	3.934542	-6.3289	0	0
M5	-26.8922309502502	3.931293	-6.8406	0	0
M6	-30.0497000430877	3.928782	-7.6486	0	0
M7	-35.0405024692585	3.927011	-8.9229	0	0
M8	-38.8646382287627	3.92598	-9.8993	0	0
M9	-43.8554406549335	3.92569	-11.1714	0	0
M10	-42.6795764144377	3.926142	-10.8706	0	0
M11	-8.3425309071625	3.92248	-2.1269	0.037624	0.018812
t	-0.342530907162507	0.053949	-6.3492	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.936903713692415
R-squared	0.877788568730638
Adjusted R-squared	0.850860626247559
F-TEST (value)	32.5976843304014
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.79329216225658
Sum Squared Residuals	2722.78028570483

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.936903713692415 \tabularnewline
R-squared & 0.877788568730638 \tabularnewline
Adjusted R-squared & 0.850860626247559 \tabularnewline
F-TEST (value) & 32.5976843304014 \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 & 6.79329216225658 \tabularnewline
Sum Squared Residuals & 2722.78028570483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14452&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.936903713692415[/C][/ROW]
[ROW][C]R-squared[/C][C]0.877788568730638[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.850860626247559[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]32.5976843304014[/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]6.79329216225658[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2722.78028570483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14452&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	0.936903713692415
R-squared	0.877788568730638
Adjusted R-squared	0.850860626247559
F-TEST (value)	32.5976843304014
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.79329216225658
Sum Squared Residuals	2722.78028570483

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	140	149.298200258527	-9.29820025852665
2	132	140.743014815551	-8.74301481555134
3	117	129.909681482218	-12.909681482218
4	114	126.243014815551	-12.2430148155514
5	113	123.909681482218	-10.9096814822180
6	110	120.409681482218	-10.4096814822181
7	107	115.076348148885	-8.07634814888472
8	103	110.909681482218	-7.90968148221798
9	98	105.576348148885	-7.5763481488847
10	98	106.409681482218	-8.40968148221801
11	137	140.404196082331	-3.40419608233070
12	148	148.404196082331	-0.404196082330704
13	147	145.187829372576	1.81217062742375
14	139	136.632643929601	2.36735607039873
15	130	125.799310596268	4.20068940373207
16	128	122.132643929601	5.86735607039874
17	127	119.799310596268	7.20068940373206
18	123	116.299310596268	6.70068940373208
19	118	110.965977262935	7.03402273706541
20	114	106.799310596268	7.20068940373207
21	108	101.465977262935	6.53402273706542
22	111	102.299310596268	8.70068940373207
23	151	147.326737595704	3.67326240429553
24	159	155.326737595704	3.67326240429554
25	158	152.11037088595	5.88962911404997
26	148	143.555185442975	4.44481455702496
27	138	132.721852109642	5.2781478903583
28	137	129.055185442975	7.94481455702497
29	136	126.721852109642	9.27814789035829
30	133	123.221852109642	9.7781478903583
31	126	117.888518776308	8.11148122369164
32	120	113.721852109642	6.27814789035829
33	114	108.388518776308	5.61148122369164
34	116	109.221852109642	6.7781478903583
35	153	143.216366709754	9.7836332902456
36	162	151.216366709754	10.7836332902456
37	161	148	13.0000000000000
38	149	150.477726956349	-1.47772695634882
39	139	139.644393623015	-0.644393623015476
40	135	135.977726956349	-0.97772695634881
41	130	133.644393623016	-3.64439362301549
42	127	130.144393623015	-3.14439362301548
43	122	124.811060289682	-2.81106028968214
44	117	120.644393623015	-3.64439362301549
45	112	115.311060289682	-3.31106028968215
46	113	116.144393623015	-3.14439362301549
47	149	150.138908223128	-1.13890822312817
48	157	158.138908223128	-1.13890822312816
49	157	154.922541513374	2.07745848662627
50	147	146.367356070399	0.632643929601259
51	137	135.534022737065	1.46597726293460
52	132	131.867356070399	0.132643929601268
53	125	129.534022737065	-4.53402273706541
54	123	126.034022737065	-3.0340227370654
55	117	120.700689403732	-3.70068940373206
56	114	116.534022737065	-2.53402273706541
57	111	111.200689403732	-0.200689403732075
58	112	112.034022737065	-0.0340227370654120
59	144	146.028537337178	-2.02853733717810
60	150	154.028537337178	-4.02853733717808
61	149	150.812170627424	-1.81217062742366
62	134	131.224072785125	2.77592721487519
63	123	120.390739451791	2.60926054820853
64	116	116.724072785125	-0.724072785124802
65	117	114.390739451791	2.60926054820853
66	111	110.890739451791	0.109260548208544
67	105	105.557406118458	-0.557406118458123
68	102	101.390739451791	0.609260548208527
69	95	96.0574061184581	-1.05740611845812
70	93	96.8907394517915	-3.89073945179146
71	124	130.885254051904	-6.88525405190416
72	130	138.885254051904	-8.88525405190415
73	124	135.668887342150	-11.6688873421497

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 140 & 149.298200258527 & -9.29820025852665 \tabularnewline
2 & 132 & 140.743014815551 & -8.74301481555134 \tabularnewline
3 & 117 & 129.909681482218 & -12.909681482218 \tabularnewline
4 & 114 & 126.243014815551 & -12.2430148155514 \tabularnewline
5 & 113 & 123.909681482218 & -10.9096814822180 \tabularnewline
6 & 110 & 120.409681482218 & -10.4096814822181 \tabularnewline
7 & 107 & 115.076348148885 & -8.07634814888472 \tabularnewline
8 & 103 & 110.909681482218 & -7.90968148221798 \tabularnewline
9 & 98 & 105.576348148885 & -7.5763481488847 \tabularnewline
10 & 98 & 106.409681482218 & -8.40968148221801 \tabularnewline
11 & 137 & 140.404196082331 & -3.40419608233070 \tabularnewline
12 & 148 & 148.404196082331 & -0.404196082330704 \tabularnewline
13 & 147 & 145.187829372576 & 1.81217062742375 \tabularnewline
14 & 139 & 136.632643929601 & 2.36735607039873 \tabularnewline
15 & 130 & 125.799310596268 & 4.20068940373207 \tabularnewline
16 & 128 & 122.132643929601 & 5.86735607039874 \tabularnewline
17 & 127 & 119.799310596268 & 7.20068940373206 \tabularnewline
18 & 123 & 116.299310596268 & 6.70068940373208 \tabularnewline
19 & 118 & 110.965977262935 & 7.03402273706541 \tabularnewline
20 & 114 & 106.799310596268 & 7.20068940373207 \tabularnewline
21 & 108 & 101.465977262935 & 6.53402273706542 \tabularnewline
22 & 111 & 102.299310596268 & 8.70068940373207 \tabularnewline
23 & 151 & 147.326737595704 & 3.67326240429553 \tabularnewline
24 & 159 & 155.326737595704 & 3.67326240429554 \tabularnewline
25 & 158 & 152.11037088595 & 5.88962911404997 \tabularnewline
26 & 148 & 143.555185442975 & 4.44481455702496 \tabularnewline
27 & 138 & 132.721852109642 & 5.2781478903583 \tabularnewline
28 & 137 & 129.055185442975 & 7.94481455702497 \tabularnewline
29 & 136 & 126.721852109642 & 9.27814789035829 \tabularnewline
30 & 133 & 123.221852109642 & 9.7781478903583 \tabularnewline
31 & 126 & 117.888518776308 & 8.11148122369164 \tabularnewline
32 & 120 & 113.721852109642 & 6.27814789035829 \tabularnewline
33 & 114 & 108.388518776308 & 5.61148122369164 \tabularnewline
34 & 116 & 109.221852109642 & 6.7781478903583 \tabularnewline
35 & 153 & 143.216366709754 & 9.7836332902456 \tabularnewline
36 & 162 & 151.216366709754 & 10.7836332902456 \tabularnewline
37 & 161 & 148 & 13.0000000000000 \tabularnewline
38 & 149 & 150.477726956349 & -1.47772695634882 \tabularnewline
39 & 139 & 139.644393623015 & -0.644393623015476 \tabularnewline
40 & 135 & 135.977726956349 & -0.97772695634881 \tabularnewline
41 & 130 & 133.644393623016 & -3.64439362301549 \tabularnewline
42 & 127 & 130.144393623015 & -3.14439362301548 \tabularnewline
43 & 122 & 124.811060289682 & -2.81106028968214 \tabularnewline
44 & 117 & 120.644393623015 & -3.64439362301549 \tabularnewline
45 & 112 & 115.311060289682 & -3.31106028968215 \tabularnewline
46 & 113 & 116.144393623015 & -3.14439362301549 \tabularnewline
47 & 149 & 150.138908223128 & -1.13890822312817 \tabularnewline
48 & 157 & 158.138908223128 & -1.13890822312816 \tabularnewline
49 & 157 & 154.922541513374 & 2.07745848662627 \tabularnewline
50 & 147 & 146.367356070399 & 0.632643929601259 \tabularnewline
51 & 137 & 135.534022737065 & 1.46597726293460 \tabularnewline
52 & 132 & 131.867356070399 & 0.132643929601268 \tabularnewline
53 & 125 & 129.534022737065 & -4.53402273706541 \tabularnewline
54 & 123 & 126.034022737065 & -3.0340227370654 \tabularnewline
55 & 117 & 120.700689403732 & -3.70068940373206 \tabularnewline
56 & 114 & 116.534022737065 & -2.53402273706541 \tabularnewline
57 & 111 & 111.200689403732 & -0.200689403732075 \tabularnewline
58 & 112 & 112.034022737065 & -0.0340227370654120 \tabularnewline
59 & 144 & 146.028537337178 & -2.02853733717810 \tabularnewline
60 & 150 & 154.028537337178 & -4.02853733717808 \tabularnewline
61 & 149 & 150.812170627424 & -1.81217062742366 \tabularnewline
62 & 134 & 131.224072785125 & 2.77592721487519 \tabularnewline
63 & 123 & 120.390739451791 & 2.60926054820853 \tabularnewline
64 & 116 & 116.724072785125 & -0.724072785124802 \tabularnewline
65 & 117 & 114.390739451791 & 2.60926054820853 \tabularnewline
66 & 111 & 110.890739451791 & 0.109260548208544 \tabularnewline
67 & 105 & 105.557406118458 & -0.557406118458123 \tabularnewline
68 & 102 & 101.390739451791 & 0.609260548208527 \tabularnewline
69 & 95 & 96.0574061184581 & -1.05740611845812 \tabularnewline
70 & 93 & 96.8907394517915 & -3.89073945179146 \tabularnewline
71 & 124 & 130.885254051904 & -6.88525405190416 \tabularnewline
72 & 130 & 138.885254051904 & -8.88525405190415 \tabularnewline
73 & 124 & 135.668887342150 & -11.6688873421497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14452&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]140[/C][C]149.298200258527[/C][C]-9.29820025852665[/C][/ROW]
[ROW][C]2[/C][C]132[/C][C]140.743014815551[/C][C]-8.74301481555134[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]129.909681482218[/C][C]-12.909681482218[/C][/ROW]
[ROW][C]4[/C][C]114[/C][C]126.243014815551[/C][C]-12.2430148155514[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]123.909681482218[/C][C]-10.9096814822180[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]120.409681482218[/C][C]-10.4096814822181[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]115.076348148885[/C][C]-8.07634814888472[/C][/ROW]
[ROW][C]8[/C][C]103[/C][C]110.909681482218[/C][C]-7.90968148221798[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]105.576348148885[/C][C]-7.5763481488847[/C][/ROW]
[ROW][C]10[/C][C]98[/C][C]106.409681482218[/C][C]-8.40968148221801[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]140.404196082331[/C][C]-3.40419608233070[/C][/ROW]
[ROW][C]12[/C][C]148[/C][C]148.404196082331[/C][C]-0.404196082330704[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]145.187829372576[/C][C]1.81217062742375[/C][/ROW]
[ROW][C]14[/C][C]139[/C][C]136.632643929601[/C][C]2.36735607039873[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]125.799310596268[/C][C]4.20068940373207[/C][/ROW]
[ROW][C]16[/C][C]128[/C][C]122.132643929601[/C][C]5.86735607039874[/C][/ROW]
[ROW][C]17[/C][C]127[/C][C]119.799310596268[/C][C]7.20068940373206[/C][/ROW]
[ROW][C]18[/C][C]123[/C][C]116.299310596268[/C][C]6.70068940373208[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]110.965977262935[/C][C]7.03402273706541[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]106.799310596268[/C][C]7.20068940373207[/C][/ROW]
[ROW][C]21[/C][C]108[/C][C]101.465977262935[/C][C]6.53402273706542[/C][/ROW]
[ROW][C]22[/C][C]111[/C][C]102.299310596268[/C][C]8.70068940373207[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]147.326737595704[/C][C]3.67326240429553[/C][/ROW]
[ROW][C]24[/C][C]159[/C][C]155.326737595704[/C][C]3.67326240429554[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]152.11037088595[/C][C]5.88962911404997[/C][/ROW]
[ROW][C]26[/C][C]148[/C][C]143.555185442975[/C][C]4.44481455702496[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]132.721852109642[/C][C]5.2781478903583[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]129.055185442975[/C][C]7.94481455702497[/C][/ROW]
[ROW][C]29[/C][C]136[/C][C]126.721852109642[/C][C]9.27814789035829[/C][/ROW]
[ROW][C]30[/C][C]133[/C][C]123.221852109642[/C][C]9.7781478903583[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]117.888518776308[/C][C]8.11148122369164[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]113.721852109642[/C][C]6.27814789035829[/C][/ROW]
[ROW][C]33[/C][C]114[/C][C]108.388518776308[/C][C]5.61148122369164[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]109.221852109642[/C][C]6.7781478903583[/C][/ROW]
[ROW][C]35[/C][C]153[/C][C]143.216366709754[/C][C]9.7836332902456[/C][/ROW]
[ROW][C]36[/C][C]162[/C][C]151.216366709754[/C][C]10.7836332902456[/C][/ROW]
[ROW][C]37[/C][C]161[/C][C]148[/C][C]13.0000000000000[/C][/ROW]
[ROW][C]38[/C][C]149[/C][C]150.477726956349[/C][C]-1.47772695634882[/C][/ROW]
[ROW][C]39[/C][C]139[/C][C]139.644393623015[/C][C]-0.644393623015476[/C][/ROW]
[ROW][C]40[/C][C]135[/C][C]135.977726956349[/C][C]-0.97772695634881[/C][/ROW]
[ROW][C]41[/C][C]130[/C][C]133.644393623016[/C][C]-3.64439362301549[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]130.144393623015[/C][C]-3.14439362301548[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]124.811060289682[/C][C]-2.81106028968214[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]120.644393623015[/C][C]-3.64439362301549[/C][/ROW]
[ROW][C]45[/C][C]112[/C][C]115.311060289682[/C][C]-3.31106028968215[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]116.144393623015[/C][C]-3.14439362301549[/C][/ROW]
[ROW][C]47[/C][C]149[/C][C]150.138908223128[/C][C]-1.13890822312817[/C][/ROW]
[ROW][C]48[/C][C]157[/C][C]158.138908223128[/C][C]-1.13890822312816[/C][/ROW]
[ROW][C]49[/C][C]157[/C][C]154.922541513374[/C][C]2.07745848662627[/C][/ROW]
[ROW][C]50[/C][C]147[/C][C]146.367356070399[/C][C]0.632643929601259[/C][/ROW]
[ROW][C]51[/C][C]137[/C][C]135.534022737065[/C][C]1.46597726293460[/C][/ROW]
[ROW][C]52[/C][C]132[/C][C]131.867356070399[/C][C]0.132643929601268[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]129.534022737065[/C][C]-4.53402273706541[/C][/ROW]
[ROW][C]54[/C][C]123[/C][C]126.034022737065[/C][C]-3.0340227370654[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]120.700689403732[/C][C]-3.70068940373206[/C][/ROW]
[ROW][C]56[/C][C]114[/C][C]116.534022737065[/C][C]-2.53402273706541[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]111.200689403732[/C][C]-0.200689403732075[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]112.034022737065[/C][C]-0.0340227370654120[/C][/ROW]
[ROW][C]59[/C][C]144[/C][C]146.028537337178[/C][C]-2.02853733717810[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]154.028537337178[/C][C]-4.02853733717808[/C][/ROW]
[ROW][C]61[/C][C]149[/C][C]150.812170627424[/C][C]-1.81217062742366[/C][/ROW]
[ROW][C]62[/C][C]134[/C][C]131.224072785125[/C][C]2.77592721487519[/C][/ROW]
[ROW][C]63[/C][C]123[/C][C]120.390739451791[/C][C]2.60926054820853[/C][/ROW]
[ROW][C]64[/C][C]116[/C][C]116.724072785125[/C][C]-0.724072785124802[/C][/ROW]
[ROW][C]65[/C][C]117[/C][C]114.390739451791[/C][C]2.60926054820853[/C][/ROW]
[ROW][C]66[/C][C]111[/C][C]110.890739451791[/C][C]0.109260548208544[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]105.557406118458[/C][C]-0.557406118458123[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]101.390739451791[/C][C]0.609260548208527[/C][/ROW]
[ROW][C]69[/C][C]95[/C][C]96.0574061184581[/C][C]-1.05740611845812[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]96.8907394517915[/C][C]-3.89073945179146[/C][/ROW]
[ROW][C]71[/C][C]124[/C][C]130.885254051904[/C][C]-6.88525405190416[/C][/ROW]
[ROW][C]72[/C][C]130[/C][C]138.885254051904[/C][C]-8.88525405190415[/C][/ROW]
[ROW][C]73[/C][C]124[/C][C]135.668887342150[/C][C]-11.6688873421497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14452&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14452&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	140	149.298200258527	-9.29820025852665
2	132	140.743014815551	-8.74301481555134
3	117	129.909681482218	-12.909681482218
4	114	126.243014815551	-12.2430148155514
5	113	123.909681482218	-10.9096814822180
6	110	120.409681482218	-10.4096814822181
7	107	115.076348148885	-8.07634814888472
8	103	110.909681482218	-7.90968148221798
9	98	105.576348148885	-7.5763481488847
10	98	106.409681482218	-8.40968148221801
11	137	140.404196082331	-3.40419608233070
12	148	148.404196082331	-0.404196082330704
13	147	145.187829372576	1.81217062742375
14	139	136.632643929601	2.36735607039873
15	130	125.799310596268	4.20068940373207
16	128	122.132643929601	5.86735607039874
17	127	119.799310596268	7.20068940373206
18	123	116.299310596268	6.70068940373208
19	118	110.965977262935	7.03402273706541
20	114	106.799310596268	7.20068940373207
21	108	101.465977262935	6.53402273706542
22	111	102.299310596268	8.70068940373207
23	151	147.326737595704	3.67326240429553
24	159	155.326737595704	3.67326240429554
25	158	152.11037088595	5.88962911404997
26	148	143.555185442975	4.44481455702496
27	138	132.721852109642	5.2781478903583
28	137	129.055185442975	7.94481455702497
29	136	126.721852109642	9.27814789035829
30	133	123.221852109642	9.7781478903583
31	126	117.888518776308	8.11148122369164
32	120	113.721852109642	6.27814789035829
33	114	108.388518776308	5.61148122369164
34	116	109.221852109642	6.7781478903583
35	153	143.216366709754	9.7836332902456
36	162	151.216366709754	10.7836332902456
37	161	148	13.0000000000000
38	149	150.477726956349	-1.47772695634882
39	139	139.644393623015	-0.644393623015476
40	135	135.977726956349	-0.97772695634881
41	130	133.644393623016	-3.64439362301549
42	127	130.144393623015	-3.14439362301548
43	122	124.811060289682	-2.81106028968214
44	117	120.644393623015	-3.64439362301549
45	112	115.311060289682	-3.31106028968215
46	113	116.144393623015	-3.14439362301549
47	149	150.138908223128	-1.13890822312817
48	157	158.138908223128	-1.13890822312816
49	157	154.922541513374	2.07745848662627
50	147	146.367356070399	0.632643929601259
51	137	135.534022737065	1.46597726293460
52	132	131.867356070399	0.132643929601268
53	125	129.534022737065	-4.53402273706541
54	123	126.034022737065	-3.0340227370654
55	117	120.700689403732	-3.70068940373206
56	114	116.534022737065	-2.53402273706541
57	111	111.200689403732	-0.200689403732075
58	112	112.034022737065	-0.0340227370654120
59	144	146.028537337178	-2.02853733717810
60	150	154.028537337178	-4.02853733717808
61	149	150.812170627424	-1.81217062742366
62	134	131.224072785125	2.77592721487519
63	123	120.390739451791	2.60926054820853
64	116	116.724072785125	-0.724072785124802
65	117	114.390739451791	2.60926054820853
66	111	110.890739451791	0.109260548208544
67	105	105.557406118458	-0.557406118458123
68	102	101.390739451791	0.609260548208527
69	95	96.0574061184581	-1.05740611845812
70	93	96.8907394517915	-3.89073945179146
71	124	130.885254051904	-6.88525405190416
72	130	138.885254051904	-8.88525405190415
73	124	135.668887342150	-11.6688873421497

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 = 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