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

Thu, 15 Nov 2007 08:39:50 -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/15/t1195140894h1dlcc5cs0gmujn.htm/, Retrieved Sat, 04 May 2024 12:05:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14460, Retrieved Sat, 04 May 2024 12:05:12 +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

W9Q3G7

Estimated Impact

187

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

-       [Multiple Regression] [multiple regressi...] [2007-11-15 15:39:50] [923db922542fbe09e7ff87bb31b2f310] [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=14460&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=14460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14460&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 145.890405293631 + 6.13151364764265X[t] + 0.357733664185238M1[t] -6.43424317617864M2[t] -15.2237386269644M3[t] -24M4[t] -27.3552522746071M5[t] -28.8114143920596M6[t] -31.0789909015716M7[t] -35.2456575682382M8[t] -40.5789909015715M9[t] -42.8114143920596M10[t] -9.02191894127379M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  145.890405293631 +  6.13151364764265X[t] +  0.357733664185238M1[t] -6.43424317617864M2[t] -15.2237386269644M3[t] -24M4[t] -27.3552522746071M5[t] -28.8114143920596M6[t] -31.0789909015716M7[t] -35.2456575682382M8[t] -40.5789909015715M9[t] -42.8114143920596M10[t] -9.02191894127379M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14460&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  145.890405293631 +  6.13151364764265X[t] +  0.357733664185238M1[t] -6.43424317617864M2[t] -15.2237386269644M3[t] -24M4[t] -27.3552522746071M5[t] -28.8114143920596M6[t] -31.0789909015716M7[t] -35.2456575682382M8[t] -40.5789909015715M9[t] -42.8114143920596M10[t] -9.02191894127379M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14460&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 145.890405293631 + 6.13151364764265X[t] + 0.357733664185238M1[t] -6.43424317617864M2[t] -15.2237386269644M3[t] -24M4[t] -27.3552522746071M5[t] -28.8114143920596M6[t] -31.0789909015716M7[t] -35.2456575682382M8[t] -40.5789909015715M9[t] -42.8114143920596M10[t] -9.02191894127379M11[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)	145.890405293631	4.554462	32.0324	0	0
X	6.13151364764265	3.007277	2.0389	0.045874	0.022937
M1	0.357733664185238	5.43797	0.0658	0.947768	0.473884
M2	-6.43424317617864	5.584484	-1.1522	0.253824	0.126912
M3	-15.2237386269644	5.933455	-2.5657	0.012812	0.006406
M4	-24	5.378246	-4.4624	3.6e-05	1.8e-05
M5	-27.3552522746071	5.40155	-5.0643	4e-06	2e-06
M6	-28.8114143920596	5.40155	-5.3339	2e-06	1e-06
M7	-31.0789909015716	5.73977	-5.4147	1e-06	1e-06
M8	-35.2456575682382	5.73977	-6.1406	0	0
M9	-40.5789909015715	5.73977	-7.0698	0	0
M10	-42.8114143920596	5.40155	-7.9258	0	0
M11	-9.02191894127379	5.40155	-1.6702	0.10008	0.05004

\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) & 145.890405293631 & 4.554462 & 32.0324 & 0 & 0 \tabularnewline
X & 6.13151364764265 & 3.007277 & 2.0389 & 0.045874 & 0.022937 \tabularnewline
M1 & 0.357733664185238 & 5.43797 & 0.0658 & 0.947768 & 0.473884 \tabularnewline
M2 & -6.43424317617864 & 5.584484 & -1.1522 & 0.253824 & 0.126912 \tabularnewline
M3 & -15.2237386269644 & 5.933455 & -2.5657 & 0.012812 & 0.006406 \tabularnewline
M4 & -24 & 5.378246 & -4.4624 & 3.6e-05 & 1.8e-05 \tabularnewline
M5 & -27.3552522746071 & 5.40155 & -5.0643 & 4e-06 & 2e-06 \tabularnewline
M6 & -28.8114143920596 & 5.40155 & -5.3339 & 2e-06 & 1e-06 \tabularnewline
M7 & -31.0789909015716 & 5.73977 & -5.4147 & 1e-06 & 1e-06 \tabularnewline
M8 & -35.2456575682382 & 5.73977 & -6.1406 & 0 & 0 \tabularnewline
M9 & -40.5789909015715 & 5.73977 & -7.0698 & 0 & 0 \tabularnewline
M10 & -42.8114143920596 & 5.40155 & -7.9258 & 0 & 0 \tabularnewline
M11 & -9.02191894127379 & 5.40155 & -1.6702 & 0.10008 & 0.05004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14460&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]145.890405293631[/C][C]4.554462[/C][C]32.0324[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]6.13151364764265[/C][C]3.007277[/C][C]2.0389[/C][C]0.045874[/C][C]0.022937[/C][/ROW]
[ROW][C]M1[/C][C]0.357733664185238[/C][C]5.43797[/C][C]0.0658[/C][C]0.947768[/C][C]0.473884[/C][/ROW]
[ROW][C]M2[/C][C]-6.43424317617864[/C][C]5.584484[/C][C]-1.1522[/C][C]0.253824[/C][C]0.126912[/C][/ROW]
[ROW][C]M3[/C][C]-15.2237386269644[/C][C]5.933455[/C][C]-2.5657[/C][C]0.012812[/C][C]0.006406[/C][/ROW]
[ROW][C]M4[/C][C]-24[/C][C]5.378246[/C][C]-4.4624[/C][C]3.6e-05[/C][C]1.8e-05[/C][/ROW]
[ROW][C]M5[/C][C]-27.3552522746071[/C][C]5.40155[/C][C]-5.0643[/C][C]4e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M6[/C][C]-28.8114143920596[/C][C]5.40155[/C][C]-5.3339[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M7[/C][C]-31.0789909015716[/C][C]5.73977[/C][C]-5.4147[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M8[/C][C]-35.2456575682382[/C][C]5.73977[/C][C]-6.1406[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-40.5789909015715[/C][C]5.73977[/C][C]-7.0698[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-42.8114143920596[/C][C]5.40155[/C][C]-7.9258[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-9.02191894127379[/C][C]5.40155[/C][C]-1.6702[/C][C]0.10008[/C][C]0.05004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14460&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)	145.890405293631	4.554462	32.0324	0	0
X	6.13151364764265	3.007277	2.0389	0.045874	0.022937
M1	0.357733664185238	5.43797	0.0658	0.947768	0.473884
M2	-6.43424317617864	5.584484	-1.1522	0.253824	0.126912
M3	-15.2237386269644	5.933455	-2.5657	0.012812	0.006406
M4	-24	5.378246	-4.4624	3.6e-05	1.8e-05
M5	-27.3552522746071	5.40155	-5.0643	4e-06	2e-06
M6	-28.8114143920596	5.40155	-5.3339	2e-06	1e-06
M7	-31.0789909015716	5.73977	-5.4147	1e-06	1e-06
M8	-35.2456575682382	5.73977	-6.1406	0	0
M9	-40.5789909015715	5.73977	-7.0698	0	0
M10	-42.8114143920596	5.40155	-7.9258	0	0
M11	-9.02191894127379	5.40155	-1.6702	0.10008	0.05004

Multiple Linear Regression - Regression Statistics
Multiple R	0.875387351584385
R-squared	0.766303015313923
Adjusted R-squared	0.719563618376708
F-TEST (value)	16.3952268434976
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	1.03250741290140e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.31539581111443
Sum Squared Residuals	5206.5959470637

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.875387351584385 \tabularnewline
R-squared & 0.766303015313923 \tabularnewline
Adjusted R-squared & 0.719563618376708 \tabularnewline
F-TEST (value) & 16.3952268434976 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 60 \tabularnewline
p-value & 1.03250741290140e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9.31539581111443 \tabularnewline
Sum Squared Residuals & 5206.5959470637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14460&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.875387351584385[/C][/ROW]
[ROW][C]R-squared[/C][C]0.766303015313923[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.719563618376708[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]16.3952268434976[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]60[/C][/ROW]
[ROW][C]p-value[/C][C]1.03250741290140e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9.31539581111443[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5206.5959470637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14460&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14460&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	0.875387351584385
R-squared	0.766303015313923
Adjusted R-squared	0.719563618376708
F-TEST (value)	16.3952268434976
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	1.03250741290140e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.31539581111443
Sum Squared Residuals	5206.5959470637

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	140	152.379652605459	-12.3796526054593
2	132	139.456162117452	-7.45616211745239
3	117	130.666666666667	-13.6666666666667
4	114	128.021918941274	-14.0219189412737
5	113	124.666666666667	-11.6666666666667
6	110	123.210504549214	-13.2105045492142
7	107	114.811414392060	-7.81141439205963
8	103	110.644747725393	-7.64474772539285
9	98	105.311414392060	-7.31141439205952
10	98	109.210504549214	-11.2105045492143
11	137	143	-6.00000000000002
12	148	145.890405293631	2.10959470636889
13	147	146.248138957816	0.751861042183654
14	139	145.587675765095	-6.58767576509511
15	130	130.666666666667	-0.666666666666664
16	128	128.021918941274	-0.0219189412737837
17	127	124.666666666667	2.33333333333333
18	123	123.210504549214	-0.210504549214221
19	118	114.811414392060	3.18858560794045
20	114	116.776261373036	-2.77626137303555
21	108	105.311414392060	2.68858560794044
22	111	109.210504549214	1.78949545078580
23	151	143	8
24	159	152.021918941274	6.97808105872622
25	158	146.248138957816	11.7518610421837
26	148	139.456162117452	8.54383788254755
27	138	130.666666666667	7.33333333333334
28	137	128.021918941274	8.97808105872621
29	136	124.666666666667	11.3333333333333
30	133	123.210504549214	9.78949545078578
31	126	120.942928039702	5.05707196029781
32	120	110.644747725393	9.3552522746071
33	114	105.311414392060	8.68858560794044
34	116	109.210504549214	6.78949545078579
35	153	143	10
36	162	152.021918941274	9.97808105872622
37	161	152.379652605459	8.620347394541
38	149	145.587675765095	3.41232423490489
39	139	130.666666666667	8.33333333333334
40	135	128.021918941274	6.97808105872621
41	130	124.666666666667	5.33333333333333
42	127	123.210504549214	3.78949545078578
43	122	114.811414392060	7.18858560794046
44	117	110.644747725393	6.3552522746071
45	112	105.311414392060	6.68858560794044
46	113	109.210504549214	3.78949545078579
47	149	143	6
48	157	152.021918941274	4.97808105872621
49	157	146.248138957816	10.7518610421837
50	147	139.456162117452	7.54383788254755
51	137	130.666666666667	6.33333333333333
52	132	128.021918941274	3.97808105872621
53	125	124.666666666667	0.333333333333333
54	123	117.078990901572	5.92100909842843
55	117	114.811414392060	2.18858560794045
56	114	110.644747725393	3.3552522746071
57	111	111.442928039702	-0.442928039702218
58	112	103.078990901572	8.92100909842845
59	144	143	1.00000000000000
60	150	152.021918941274	-2.02191894127378
61	149	146.248138957816	2.75186104218366
62	134	139.456162117452	-5.45616211745245
63	123	130.666666666667	-7.66666666666666
64	116	121.890405293631	-5.89040529363112
65	117	124.666666666667	-7.66666666666667
66	111	117.078990901572	-6.07899090157157
67	105	114.811414392060	-9.81141439205955
68	102	110.644747725393	-8.6447477253929
69	95	105.311414392060	-10.3114143920596
70	93	103.078990901572	-10.0789909015715
71	124	143	-19
72	130	152.021918941274	-22.0219189412738
73	124	146.248138957816	-22.2481389578163

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 140 & 152.379652605459 & -12.3796526054593 \tabularnewline
2 & 132 & 139.456162117452 & -7.45616211745239 \tabularnewline
3 & 117 & 130.666666666667 & -13.6666666666667 \tabularnewline
4 & 114 & 128.021918941274 & -14.0219189412737 \tabularnewline
5 & 113 & 124.666666666667 & -11.6666666666667 \tabularnewline
6 & 110 & 123.210504549214 & -13.2105045492142 \tabularnewline
7 & 107 & 114.811414392060 & -7.81141439205963 \tabularnewline
8 & 103 & 110.644747725393 & -7.64474772539285 \tabularnewline
9 & 98 & 105.311414392060 & -7.31141439205952 \tabularnewline
10 & 98 & 109.210504549214 & -11.2105045492143 \tabularnewline
11 & 137 & 143 & -6.00000000000002 \tabularnewline
12 & 148 & 145.890405293631 & 2.10959470636889 \tabularnewline
13 & 147 & 146.248138957816 & 0.751861042183654 \tabularnewline
14 & 139 & 145.587675765095 & -6.58767576509511 \tabularnewline
15 & 130 & 130.666666666667 & -0.666666666666664 \tabularnewline
16 & 128 & 128.021918941274 & -0.0219189412737837 \tabularnewline
17 & 127 & 124.666666666667 & 2.33333333333333 \tabularnewline
18 & 123 & 123.210504549214 & -0.210504549214221 \tabularnewline
19 & 118 & 114.811414392060 & 3.18858560794045 \tabularnewline
20 & 114 & 116.776261373036 & -2.77626137303555 \tabularnewline
21 & 108 & 105.311414392060 & 2.68858560794044 \tabularnewline
22 & 111 & 109.210504549214 & 1.78949545078580 \tabularnewline
23 & 151 & 143 & 8 \tabularnewline
24 & 159 & 152.021918941274 & 6.97808105872622 \tabularnewline
25 & 158 & 146.248138957816 & 11.7518610421837 \tabularnewline
26 & 148 & 139.456162117452 & 8.54383788254755 \tabularnewline
27 & 138 & 130.666666666667 & 7.33333333333334 \tabularnewline
28 & 137 & 128.021918941274 & 8.97808105872621 \tabularnewline
29 & 136 & 124.666666666667 & 11.3333333333333 \tabularnewline
30 & 133 & 123.210504549214 & 9.78949545078578 \tabularnewline
31 & 126 & 120.942928039702 & 5.05707196029781 \tabularnewline
32 & 120 & 110.644747725393 & 9.3552522746071 \tabularnewline
33 & 114 & 105.311414392060 & 8.68858560794044 \tabularnewline
34 & 116 & 109.210504549214 & 6.78949545078579 \tabularnewline
35 & 153 & 143 & 10 \tabularnewline
36 & 162 & 152.021918941274 & 9.97808105872622 \tabularnewline
37 & 161 & 152.379652605459 & 8.620347394541 \tabularnewline
38 & 149 & 145.587675765095 & 3.41232423490489 \tabularnewline
39 & 139 & 130.666666666667 & 8.33333333333334 \tabularnewline
40 & 135 & 128.021918941274 & 6.97808105872621 \tabularnewline
41 & 130 & 124.666666666667 & 5.33333333333333 \tabularnewline
42 & 127 & 123.210504549214 & 3.78949545078578 \tabularnewline
43 & 122 & 114.811414392060 & 7.18858560794046 \tabularnewline
44 & 117 & 110.644747725393 & 6.3552522746071 \tabularnewline
45 & 112 & 105.311414392060 & 6.68858560794044 \tabularnewline
46 & 113 & 109.210504549214 & 3.78949545078579 \tabularnewline
47 & 149 & 143 & 6 \tabularnewline
48 & 157 & 152.021918941274 & 4.97808105872621 \tabularnewline
49 & 157 & 146.248138957816 & 10.7518610421837 \tabularnewline
50 & 147 & 139.456162117452 & 7.54383788254755 \tabularnewline
51 & 137 & 130.666666666667 & 6.33333333333333 \tabularnewline
52 & 132 & 128.021918941274 & 3.97808105872621 \tabularnewline
53 & 125 & 124.666666666667 & 0.333333333333333 \tabularnewline
54 & 123 & 117.078990901572 & 5.92100909842843 \tabularnewline
55 & 117 & 114.811414392060 & 2.18858560794045 \tabularnewline
56 & 114 & 110.644747725393 & 3.3552522746071 \tabularnewline
57 & 111 & 111.442928039702 & -0.442928039702218 \tabularnewline
58 & 112 & 103.078990901572 & 8.92100909842845 \tabularnewline
59 & 144 & 143 & 1.00000000000000 \tabularnewline
60 & 150 & 152.021918941274 & -2.02191894127378 \tabularnewline
61 & 149 & 146.248138957816 & 2.75186104218366 \tabularnewline
62 & 134 & 139.456162117452 & -5.45616211745245 \tabularnewline
63 & 123 & 130.666666666667 & -7.66666666666666 \tabularnewline
64 & 116 & 121.890405293631 & -5.89040529363112 \tabularnewline
65 & 117 & 124.666666666667 & -7.66666666666667 \tabularnewline
66 & 111 & 117.078990901572 & -6.07899090157157 \tabularnewline
67 & 105 & 114.811414392060 & -9.81141439205955 \tabularnewline
68 & 102 & 110.644747725393 & -8.6447477253929 \tabularnewline
69 & 95 & 105.311414392060 & -10.3114143920596 \tabularnewline
70 & 93 & 103.078990901572 & -10.0789909015715 \tabularnewline
71 & 124 & 143 & -19 \tabularnewline
72 & 130 & 152.021918941274 & -22.0219189412738 \tabularnewline
73 & 124 & 146.248138957816 & -22.2481389578163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14460&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]152.379652605459[/C][C]-12.3796526054593[/C][/ROW]
[ROW][C]2[/C][C]132[/C][C]139.456162117452[/C][C]-7.45616211745239[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]130.666666666667[/C][C]-13.6666666666667[/C][/ROW]
[ROW][C]4[/C][C]114[/C][C]128.021918941274[/C][C]-14.0219189412737[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]124.666666666667[/C][C]-11.6666666666667[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]123.210504549214[/C][C]-13.2105045492142[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]114.811414392060[/C][C]-7.81141439205963[/C][/ROW]
[ROW][C]8[/C][C]103[/C][C]110.644747725393[/C][C]-7.64474772539285[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]105.311414392060[/C][C]-7.31141439205952[/C][/ROW]
[ROW][C]10[/C][C]98[/C][C]109.210504549214[/C][C]-11.2105045492143[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]143[/C][C]-6.00000000000002[/C][/ROW]
[ROW][C]12[/C][C]148[/C][C]145.890405293631[/C][C]2.10959470636889[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]146.248138957816[/C][C]0.751861042183654[/C][/ROW]
[ROW][C]14[/C][C]139[/C][C]145.587675765095[/C][C]-6.58767576509511[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]130.666666666667[/C][C]-0.666666666666664[/C][/ROW]
[ROW][C]16[/C][C]128[/C][C]128.021918941274[/C][C]-0.0219189412737837[/C][/ROW]
[ROW][C]17[/C][C]127[/C][C]124.666666666667[/C][C]2.33333333333333[/C][/ROW]
[ROW][C]18[/C][C]123[/C][C]123.210504549214[/C][C]-0.210504549214221[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]114.811414392060[/C][C]3.18858560794045[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]116.776261373036[/C][C]-2.77626137303555[/C][/ROW]
[ROW][C]21[/C][C]108[/C][C]105.311414392060[/C][C]2.68858560794044[/C][/ROW]
[ROW][C]22[/C][C]111[/C][C]109.210504549214[/C][C]1.78949545078580[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]143[/C][C]8[/C][/ROW]
[ROW][C]24[/C][C]159[/C][C]152.021918941274[/C][C]6.97808105872622[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]146.248138957816[/C][C]11.7518610421837[/C][/ROW]
[ROW][C]26[/C][C]148[/C][C]139.456162117452[/C][C]8.54383788254755[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]130.666666666667[/C][C]7.33333333333334[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]128.021918941274[/C][C]8.97808105872621[/C][/ROW]
[ROW][C]29[/C][C]136[/C][C]124.666666666667[/C][C]11.3333333333333[/C][/ROW]
[ROW][C]30[/C][C]133[/C][C]123.210504549214[/C][C]9.78949545078578[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]120.942928039702[/C][C]5.05707196029781[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]110.644747725393[/C][C]9.3552522746071[/C][/ROW]
[ROW][C]33[/C][C]114[/C][C]105.311414392060[/C][C]8.68858560794044[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]109.210504549214[/C][C]6.78949545078579[/C][/ROW]
[ROW][C]35[/C][C]153[/C][C]143[/C][C]10[/C][/ROW]
[ROW][C]36[/C][C]162[/C][C]152.021918941274[/C][C]9.97808105872622[/C][/ROW]
[ROW][C]37[/C][C]161[/C][C]152.379652605459[/C][C]8.620347394541[/C][/ROW]
[ROW][C]38[/C][C]149[/C][C]145.587675765095[/C][C]3.41232423490489[/C][/ROW]
[ROW][C]39[/C][C]139[/C][C]130.666666666667[/C][C]8.33333333333334[/C][/ROW]
[ROW][C]40[/C][C]135[/C][C]128.021918941274[/C][C]6.97808105872621[/C][/ROW]
[ROW][C]41[/C][C]130[/C][C]124.666666666667[/C][C]5.33333333333333[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]123.210504549214[/C][C]3.78949545078578[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]114.811414392060[/C][C]7.18858560794046[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]110.644747725393[/C][C]6.3552522746071[/C][/ROW]
[ROW][C]45[/C][C]112[/C][C]105.311414392060[/C][C]6.68858560794044[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]109.210504549214[/C][C]3.78949545078579[/C][/ROW]
[ROW][C]47[/C][C]149[/C][C]143[/C][C]6[/C][/ROW]
[ROW][C]48[/C][C]157[/C][C]152.021918941274[/C][C]4.97808105872621[/C][/ROW]
[ROW][C]49[/C][C]157[/C][C]146.248138957816[/C][C]10.7518610421837[/C][/ROW]
[ROW][C]50[/C][C]147[/C][C]139.456162117452[/C][C]7.54383788254755[/C][/ROW]
[ROW][C]51[/C][C]137[/C][C]130.666666666667[/C][C]6.33333333333333[/C][/ROW]
[ROW][C]52[/C][C]132[/C][C]128.021918941274[/C][C]3.97808105872621[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]124.666666666667[/C][C]0.333333333333333[/C][/ROW]
[ROW][C]54[/C][C]123[/C][C]117.078990901572[/C][C]5.92100909842843[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]114.811414392060[/C][C]2.18858560794045[/C][/ROW]
[ROW][C]56[/C][C]114[/C][C]110.644747725393[/C][C]3.3552522746071[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]111.442928039702[/C][C]-0.442928039702218[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]103.078990901572[/C][C]8.92100909842845[/C][/ROW]
[ROW][C]59[/C][C]144[/C][C]143[/C][C]1.00000000000000[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]152.021918941274[/C][C]-2.02191894127378[/C][/ROW]
[ROW][C]61[/C][C]149[/C][C]146.248138957816[/C][C]2.75186104218366[/C][/ROW]
[ROW][C]62[/C][C]134[/C][C]139.456162117452[/C][C]-5.45616211745245[/C][/ROW]
[ROW][C]63[/C][C]123[/C][C]130.666666666667[/C][C]-7.66666666666666[/C][/ROW]
[ROW][C]64[/C][C]116[/C][C]121.890405293631[/C][C]-5.89040529363112[/C][/ROW]
[ROW][C]65[/C][C]117[/C][C]124.666666666667[/C][C]-7.66666666666667[/C][/ROW]
[ROW][C]66[/C][C]111[/C][C]117.078990901572[/C][C]-6.07899090157157[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]114.811414392060[/C][C]-9.81141439205955[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]110.644747725393[/C][C]-8.6447477253929[/C][/ROW]
[ROW][C]69[/C][C]95[/C][C]105.311414392060[/C][C]-10.3114143920596[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]103.078990901572[/C][C]-10.0789909015715[/C][/ROW]
[ROW][C]71[/C][C]124[/C][C]143[/C][C]-19[/C][/ROW]
[ROW][C]72[/C][C]130[/C][C]152.021918941274[/C][C]-22.0219189412738[/C][/ROW]
[ROW][C]73[/C][C]124[/C][C]146.248138957816[/C][C]-22.2481389578163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14460&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14460&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	152.379652605459	-12.3796526054593
2	132	139.456162117452	-7.45616211745239
3	117	130.666666666667	-13.6666666666667
4	114	128.021918941274	-14.0219189412737
5	113	124.666666666667	-11.6666666666667
6	110	123.210504549214	-13.2105045492142
7	107	114.811414392060	-7.81141439205963
8	103	110.644747725393	-7.64474772539285
9	98	105.311414392060	-7.31141439205952
10	98	109.210504549214	-11.2105045492143
11	137	143	-6.00000000000002
12	148	145.890405293631	2.10959470636889
13	147	146.248138957816	0.751861042183654
14	139	145.587675765095	-6.58767576509511
15	130	130.666666666667	-0.666666666666664
16	128	128.021918941274	-0.0219189412737837
17	127	124.666666666667	2.33333333333333
18	123	123.210504549214	-0.210504549214221
19	118	114.811414392060	3.18858560794045
20	114	116.776261373036	-2.77626137303555
21	108	105.311414392060	2.68858560794044
22	111	109.210504549214	1.78949545078580
23	151	143	8
24	159	152.021918941274	6.97808105872622
25	158	146.248138957816	11.7518610421837
26	148	139.456162117452	8.54383788254755
27	138	130.666666666667	7.33333333333334
28	137	128.021918941274	8.97808105872621
29	136	124.666666666667	11.3333333333333
30	133	123.210504549214	9.78949545078578
31	126	120.942928039702	5.05707196029781
32	120	110.644747725393	9.3552522746071
33	114	105.311414392060	8.68858560794044
34	116	109.210504549214	6.78949545078579
35	153	143	10
36	162	152.021918941274	9.97808105872622
37	161	152.379652605459	8.620347394541
38	149	145.587675765095	3.41232423490489
39	139	130.666666666667	8.33333333333334
40	135	128.021918941274	6.97808105872621
41	130	124.666666666667	5.33333333333333
42	127	123.210504549214	3.78949545078578
43	122	114.811414392060	7.18858560794046
44	117	110.644747725393	6.3552522746071
45	112	105.311414392060	6.68858560794044
46	113	109.210504549214	3.78949545078579
47	149	143	6
48	157	152.021918941274	4.97808105872621
49	157	146.248138957816	10.7518610421837
50	147	139.456162117452	7.54383788254755
51	137	130.666666666667	6.33333333333333
52	132	128.021918941274	3.97808105872621
53	125	124.666666666667	0.333333333333333
54	123	117.078990901572	5.92100909842843
55	117	114.811414392060	2.18858560794045
56	114	110.644747725393	3.3552522746071
57	111	111.442928039702	-0.442928039702218
58	112	103.078990901572	8.92100909842845
59	144	143	1.00000000000000
60	150	152.021918941274	-2.02191894127378
61	149	146.248138957816	2.75186104218366
62	134	139.456162117452	-5.45616211745245
63	123	130.666666666667	-7.66666666666666
64	116	121.890405293631	-5.89040529363112
65	117	124.666666666667	-7.66666666666667
66	111	117.078990901572	-6.07899090157157
67	105	114.811414392060	-9.81141439205955
68	102	110.644747725393	-8.6447477253929
69	95	105.311414392060	-10.3114143920596
70	93	103.078990901572	-10.0789909015715
71	124	143	-19
72	130	152.021918941274	-22.0219189412738
73	124	146.248138957816	-22.2481389578163

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 = 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