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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 15 Nov 2007 06:06:06 -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/t11951316583fqla84frjxuph3.htm/, Retrieved Sat, 04 May 2024 14:01:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14456, Retrieved Sat, 04 May 2024 14:01:59 +0000

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Estimated Impact

245

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

-       [Multiple Regression] [-25 tov economisc...] [2007-11-15 13:06:06] [c56f8008888e950480d69a6e2ce38f45] [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=14456&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=14456&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14456&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] = + 150.040609137056 -1.43908629441624eco[t] -3.47969543147209M1[t] -9.739847715736M2[t] -20.3333333333333M3[t] -24.2398477157360M4[t] -26.0934856175973M5[t] -29.3536379018613M6[t] -34.4471235194585M7[t] -38.3739424703892M8[t] -44.4268189509306M9[t] -43.1137901861252M10[t] -8M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
<25[t] =  +  150.040609137056 -1.43908629441624eco[t] -3.47969543147209M1[t] -9.739847715736M2[t] -20.3333333333333M3[t] -24.2398477157360M4[t] -26.0934856175973M5[t] -29.3536379018613M6[t] -34.4471235194585M7[t] -38.3739424703892M8[t] -44.4268189509306M9[t] -43.1137901861252M10[t] -8M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14456&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]<25[t] =  +  150.040609137056 -1.43908629441624eco[t] -3.47969543147209M1[t] -9.739847715736M2[t] -20.3333333333333M3[t] -24.2398477157360M4[t] -26.0934856175973M5[t] -29.3536379018613M6[t] -34.4471235194585M7[t] -38.3739424703892M8[t] -44.4268189509306M9[t] -43.1137901861252M10[t] -8M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14456&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14456&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] = + 150.040609137056 -1.43908629441624eco[t] -3.47969543147209M1[t] -9.739847715736M2[t] -20.3333333333333M3[t] -24.2398477157360M4[t] -26.0934856175973M5[t] -29.3536379018613M6[t] -34.4471235194585M7[t] -38.3739424703892M8[t] -44.4268189509306M9[t] -43.1137901861252M10[t] -8M11[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)	150.040609137056	3.962288	37.8672	0	0
eco	-1.43908629441624	1.174101	-1.2257	0.225104	0.112552
M1	-3.47969543147209	5.307729	-0.6556	0.514594	0.257297
M2	-9.739847715736	5.496581	-1.772	0.081475	0.040737
M3	-20.3333333333333	5.493097	-3.7016	0.000468	0.000234
M4	-24.2398477157360	5.496581	-4.41	4.4e-05	2.2e-05
M5	-26.0934856175973	5.496581	-4.7472	1.3e-05	7e-06
M6	-29.3536379018613	5.507021	-5.3302	2e-06	1e-06
M7	-34.4471235194585	5.524377	-6.2355	0	0
M8	-38.3739424703892	5.548584	-6.916	0	0
M9	-44.4268189509306	5.496581	-8.0826	0	0
M10	-43.1137901861252	5.524377	-7.8043	0	0
M11	-8	5.493097	-1.4564	0.150503	0.075251

\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) & 150.040609137056 & 3.962288 & 37.8672 & 0 & 0 \tabularnewline
eco & -1.43908629441624 & 1.174101 & -1.2257 & 0.225104 & 0.112552 \tabularnewline
M1 & -3.47969543147209 & 5.307729 & -0.6556 & 0.514594 & 0.257297 \tabularnewline
M2 & -9.739847715736 & 5.496581 & -1.772 & 0.081475 & 0.040737 \tabularnewline
M3 & -20.3333333333333 & 5.493097 & -3.7016 & 0.000468 & 0.000234 \tabularnewline
M4 & -24.2398477157360 & 5.496581 & -4.41 & 4.4e-05 & 2.2e-05 \tabularnewline
M5 & -26.0934856175973 & 5.496581 & -4.7472 & 1.3e-05 & 7e-06 \tabularnewline
M6 & -29.3536379018613 & 5.507021 & -5.3302 & 2e-06 & 1e-06 \tabularnewline
M7 & -34.4471235194585 & 5.524377 & -6.2355 & 0 & 0 \tabularnewline
M8 & -38.3739424703892 & 5.548584 & -6.916 & 0 & 0 \tabularnewline
M9 & -44.4268189509306 & 5.496581 & -8.0826 & 0 & 0 \tabularnewline
M10 & -43.1137901861252 & 5.524377 & -7.8043 & 0 & 0 \tabularnewline
M11 & -8 & 5.493097 & -1.4564 & 0.150503 & 0.075251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14456&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]150.040609137056[/C][C]3.962288[/C][C]37.8672[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]eco[/C][C]-1.43908629441624[/C][C]1.174101[/C][C]-1.2257[/C][C]0.225104[/C][C]0.112552[/C][/ROW]
[ROW][C]M1[/C][C]-3.47969543147209[/C][C]5.307729[/C][C]-0.6556[/C][C]0.514594[/C][C]0.257297[/C][/ROW]
[ROW][C]M2[/C][C]-9.739847715736[/C][C]5.496581[/C][C]-1.772[/C][C]0.081475[/C][C]0.040737[/C][/ROW]
[ROW][C]M3[/C][C]-20.3333333333333[/C][C]5.493097[/C][C]-3.7016[/C][C]0.000468[/C][C]0.000234[/C][/ROW]
[ROW][C]M4[/C][C]-24.2398477157360[/C][C]5.496581[/C][C]-4.41[/C][C]4.4e-05[/C][C]2.2e-05[/C][/ROW]
[ROW][C]M5[/C][C]-26.0934856175973[/C][C]5.496581[/C][C]-4.7472[/C][C]1.3e-05[/C][C]7e-06[/C][/ROW]
[ROW][C]M6[/C][C]-29.3536379018613[/C][C]5.507021[/C][C]-5.3302[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M7[/C][C]-34.4471235194585[/C][C]5.524377[/C][C]-6.2355[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-38.3739424703892[/C][C]5.548584[/C][C]-6.916[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-44.4268189509306[/C][C]5.496581[/C][C]-8.0826[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-43.1137901861252[/C][C]5.524377[/C][C]-7.8043[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-8[/C][C]5.493097[/C][C]-1.4564[/C][C]0.150503[/C][C]0.075251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14456&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14456&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)	150.040609137056	3.962288	37.8672	0	0
eco	-1.43908629441624	1.174101	-1.2257	0.225104	0.112552
M1	-3.47969543147209	5.307729	-0.6556	0.514594	0.257297
M2	-9.739847715736	5.496581	-1.772	0.081475	0.040737
M3	-20.3333333333333	5.493097	-3.7016	0.000468	0.000234
M4	-24.2398477157360	5.496581	-4.41	4.4e-05	2.2e-05
M5	-26.0934856175973	5.496581	-4.7472	1.3e-05	7e-06
M6	-29.3536379018613	5.507021	-5.3302	2e-06	1e-06
M7	-34.4471235194585	5.524377	-6.2355	0	0
M8	-38.3739424703892	5.548584	-6.916	0	0
M9	-44.4268189509306	5.496581	-8.0826	0	0
M10	-43.1137901861252	5.524377	-7.8043	0	0
M11	-8	5.493097	-1.4564	0.150503	0.075251

Multiple Linear Regression - Regression Statistics
Multiple R	0.869606485316494
R-squared	0.756215439304505
Adjusted R-squared	0.707458527165406
F-TEST (value)	15.509912464249
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	3.44169137633799e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.51432225516791
Sum Squared Residuals	5431.339678511

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.869606485316494 \tabularnewline
R-squared & 0.756215439304505 \tabularnewline
Adjusted R-squared & 0.707458527165406 \tabularnewline
F-TEST (value) & 15.509912464249 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 60 \tabularnewline
p-value & 3.44169137633799e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9.51432225516791 \tabularnewline
Sum Squared Residuals & 5431.339678511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14456&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.869606485316494[/C][/ROW]
[ROW][C]R-squared[/C][C]0.756215439304505[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.707458527165406[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.509912464249[/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]3.44169137633799e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9.51432225516791[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5431.339678511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14456&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14456&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	0.869606485316494
R-squared	0.756215439304505
Adjusted R-squared	0.707458527165406
F-TEST (value)	15.509912464249
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	3.44169137633799e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.51432225516791
Sum Squared Residuals	5431.339678511

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	140	148.000000000000	-8.00000000000028
2	132	143.178934010152	-11.1789340101523
3	117	132.585448392555	-15.5854483925550
4	114	127.239847715736	-13.2398477157361
5	113	122.508037225042	-9.50803722504226
6	110	119.247884940778	-9.24788494077836
7	107	114.154399323181	-7.15439932318104
8	103	110.227580372250	-7.22758037225039
9	98	104.174703891709	-6.17470389170896
10	98	105.487732656514	-7.48773265651439
11	137	142.040609137056	-5.04060913705584
12	148	151.479695431472	-3.47969543147208
13	147	148	-0.99999999999996
14	139	141.739847715736	-2.73984771573605
15	130	131.146362098139	-1.14636209813874
16	128	127.239847715736	0.760152284263968
17	127	126.825296108291	0.174703891708963
18	123	123.565143824027	-0.565143824027069
19	118	118.471658206430	-0.471658206429764
20	114	113.105752961083	0.894247038917088
21	108	107.052876480541	0.947123519458542
22	111	108.365905245347	2.63409475465314
23	151	143.479695431472	7.52030456852792
24	159	151.479695431472	7.52030456852793
25	158	148	10.0000000000000
26	148	141.739847715736	6.26015228426396
27	138	129.707275803722	8.2927241962775
28	137	125.800761421320	11.1992385786802
29	136	122.508037225042	13.4919627749577
30	133	119.247884940778	13.7521150592217
31	126	114.154399323181	11.8456006768189
32	120	110.227580372250	9.77241962774957
33	114	107.052876480541	6.94712351945854
34	116	105.487732656514	10.5122673434856
35	153	143.479695431472	9.52030456852792
36	162	148.601522842640	13.3984771573604
37	161	146.560913705584	14.4390862944163
38	149	141.739847715736	7.26015228426396
39	139	131.146362098139	7.85363790186126
40	135	127.239847715736	7.76015228426397
41	130	125.386209813875	4.61379018612521
42	127	122.126057529611	4.87394247038918
43	122	114.154399323181	7.84560067681895
44	117	113.105752961083	3.89424703891709
45	112	108.491962774958	3.50803722504232
46	113	109.804991539763	3.19500846023689
47	149	144.918781725888	4.08121827411169
48	157	151.479695431472	5.52030456852794
49	157	149.439086294416	7.5609137055838
50	147	141.739847715736	5.26015228426396
51	137	131.146362098139	5.85363790186126
52	132	127.239847715736	4.76015228426397
53	125	125.386209813875	-0.386209813874792
54	123	122.126057529611	0.873942470389178
55	117	117.032571912014	-0.0325719120135387
56	114	113.105752961083	0.894247038917088
57	111	107.052876480541	3.94712351945854
58	112	108.365905245347	3.63409475465314
59	144	142.040609137056	1.95939086294416
60	150	151.479695431472	-1.47969543147207
61	149	148	1.00000000000005
62	134	138.861675126904	-4.86167512690357
63	123	128.268189509306	-5.26818950930626
64	116	127.239847715736	-11.2398477157360
65	117	125.386209813875	-8.3862098138748
66	111	120.686971235195	-9.68697123519459
67	105	117.032571912014	-12.0325719120135
68	102	110.227580372250	-8.22758037225043
69	95	104.174703891709	-9.17470389170897
70	93	105.487732656514	-12.4877326565144
71	124	142.040609137056	-18.0406091370558
72	130	151.479695431472	-21.4796954314721
73	124	148	-24.0000000000000

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 140 & 148.000000000000 & -8.00000000000028 \tabularnewline
2 & 132 & 143.178934010152 & -11.1789340101523 \tabularnewline
3 & 117 & 132.585448392555 & -15.5854483925550 \tabularnewline
4 & 114 & 127.239847715736 & -13.2398477157361 \tabularnewline
5 & 113 & 122.508037225042 & -9.50803722504226 \tabularnewline
6 & 110 & 119.247884940778 & -9.24788494077836 \tabularnewline
7 & 107 & 114.154399323181 & -7.15439932318104 \tabularnewline
8 & 103 & 110.227580372250 & -7.22758037225039 \tabularnewline
9 & 98 & 104.174703891709 & -6.17470389170896 \tabularnewline
10 & 98 & 105.487732656514 & -7.48773265651439 \tabularnewline
11 & 137 & 142.040609137056 & -5.04060913705584 \tabularnewline
12 & 148 & 151.479695431472 & -3.47969543147208 \tabularnewline
13 & 147 & 148 & -0.99999999999996 \tabularnewline
14 & 139 & 141.739847715736 & -2.73984771573605 \tabularnewline
15 & 130 & 131.146362098139 & -1.14636209813874 \tabularnewline
16 & 128 & 127.239847715736 & 0.760152284263968 \tabularnewline
17 & 127 & 126.825296108291 & 0.174703891708963 \tabularnewline
18 & 123 & 123.565143824027 & -0.565143824027069 \tabularnewline
19 & 118 & 118.471658206430 & -0.471658206429764 \tabularnewline
20 & 114 & 113.105752961083 & 0.894247038917088 \tabularnewline
21 & 108 & 107.052876480541 & 0.947123519458542 \tabularnewline
22 & 111 & 108.365905245347 & 2.63409475465314 \tabularnewline
23 & 151 & 143.479695431472 & 7.52030456852792 \tabularnewline
24 & 159 & 151.479695431472 & 7.52030456852793 \tabularnewline
25 & 158 & 148 & 10.0000000000000 \tabularnewline
26 & 148 & 141.739847715736 & 6.26015228426396 \tabularnewline
27 & 138 & 129.707275803722 & 8.2927241962775 \tabularnewline
28 & 137 & 125.800761421320 & 11.1992385786802 \tabularnewline
29 & 136 & 122.508037225042 & 13.4919627749577 \tabularnewline
30 & 133 & 119.247884940778 & 13.7521150592217 \tabularnewline
31 & 126 & 114.154399323181 & 11.8456006768189 \tabularnewline
32 & 120 & 110.227580372250 & 9.77241962774957 \tabularnewline
33 & 114 & 107.052876480541 & 6.94712351945854 \tabularnewline
34 & 116 & 105.487732656514 & 10.5122673434856 \tabularnewline
35 & 153 & 143.479695431472 & 9.52030456852792 \tabularnewline
36 & 162 & 148.601522842640 & 13.3984771573604 \tabularnewline
37 & 161 & 146.560913705584 & 14.4390862944163 \tabularnewline
38 & 149 & 141.739847715736 & 7.26015228426396 \tabularnewline
39 & 139 & 131.146362098139 & 7.85363790186126 \tabularnewline
40 & 135 & 127.239847715736 & 7.76015228426397 \tabularnewline
41 & 130 & 125.386209813875 & 4.61379018612521 \tabularnewline
42 & 127 & 122.126057529611 & 4.87394247038918 \tabularnewline
43 & 122 & 114.154399323181 & 7.84560067681895 \tabularnewline
44 & 117 & 113.105752961083 & 3.89424703891709 \tabularnewline
45 & 112 & 108.491962774958 & 3.50803722504232 \tabularnewline
46 & 113 & 109.804991539763 & 3.19500846023689 \tabularnewline
47 & 149 & 144.918781725888 & 4.08121827411169 \tabularnewline
48 & 157 & 151.479695431472 & 5.52030456852794 \tabularnewline
49 & 157 & 149.439086294416 & 7.5609137055838 \tabularnewline
50 & 147 & 141.739847715736 & 5.26015228426396 \tabularnewline
51 & 137 & 131.146362098139 & 5.85363790186126 \tabularnewline
52 & 132 & 127.239847715736 & 4.76015228426397 \tabularnewline
53 & 125 & 125.386209813875 & -0.386209813874792 \tabularnewline
54 & 123 & 122.126057529611 & 0.873942470389178 \tabularnewline
55 & 117 & 117.032571912014 & -0.0325719120135387 \tabularnewline
56 & 114 & 113.105752961083 & 0.894247038917088 \tabularnewline
57 & 111 & 107.052876480541 & 3.94712351945854 \tabularnewline
58 & 112 & 108.365905245347 & 3.63409475465314 \tabularnewline
59 & 144 & 142.040609137056 & 1.95939086294416 \tabularnewline
60 & 150 & 151.479695431472 & -1.47969543147207 \tabularnewline
61 & 149 & 148 & 1.00000000000005 \tabularnewline
62 & 134 & 138.861675126904 & -4.86167512690357 \tabularnewline
63 & 123 & 128.268189509306 & -5.26818950930626 \tabularnewline
64 & 116 & 127.239847715736 & -11.2398477157360 \tabularnewline
65 & 117 & 125.386209813875 & -8.3862098138748 \tabularnewline
66 & 111 & 120.686971235195 & -9.68697123519459 \tabularnewline
67 & 105 & 117.032571912014 & -12.0325719120135 \tabularnewline
68 & 102 & 110.227580372250 & -8.22758037225043 \tabularnewline
69 & 95 & 104.174703891709 & -9.17470389170897 \tabularnewline
70 & 93 & 105.487732656514 & -12.4877326565144 \tabularnewline
71 & 124 & 142.040609137056 & -18.0406091370558 \tabularnewline
72 & 130 & 151.479695431472 & -21.4796954314721 \tabularnewline
73 & 124 & 148 & -24.0000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14456&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]148.000000000000[/C][C]-8.00000000000028[/C][/ROW]
[ROW][C]2[/C][C]132[/C][C]143.178934010152[/C][C]-11.1789340101523[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]132.585448392555[/C][C]-15.5854483925550[/C][/ROW]
[ROW][C]4[/C][C]114[/C][C]127.239847715736[/C][C]-13.2398477157361[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]122.508037225042[/C][C]-9.50803722504226[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]119.247884940778[/C][C]-9.24788494077836[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]114.154399323181[/C][C]-7.15439932318104[/C][/ROW]
[ROW][C]8[/C][C]103[/C][C]110.227580372250[/C][C]-7.22758037225039[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]104.174703891709[/C][C]-6.17470389170896[/C][/ROW]
[ROW][C]10[/C][C]98[/C][C]105.487732656514[/C][C]-7.48773265651439[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]142.040609137056[/C][C]-5.04060913705584[/C][/ROW]
[ROW][C]12[/C][C]148[/C][C]151.479695431472[/C][C]-3.47969543147208[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]148[/C][C]-0.99999999999996[/C][/ROW]
[ROW][C]14[/C][C]139[/C][C]141.739847715736[/C][C]-2.73984771573605[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]131.146362098139[/C][C]-1.14636209813874[/C][/ROW]
[ROW][C]16[/C][C]128[/C][C]127.239847715736[/C][C]0.760152284263968[/C][/ROW]
[ROW][C]17[/C][C]127[/C][C]126.825296108291[/C][C]0.174703891708963[/C][/ROW]
[ROW][C]18[/C][C]123[/C][C]123.565143824027[/C][C]-0.565143824027069[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]118.471658206430[/C][C]-0.471658206429764[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]113.105752961083[/C][C]0.894247038917088[/C][/ROW]
[ROW][C]21[/C][C]108[/C][C]107.052876480541[/C][C]0.947123519458542[/C][/ROW]
[ROW][C]22[/C][C]111[/C][C]108.365905245347[/C][C]2.63409475465314[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]143.479695431472[/C][C]7.52030456852792[/C][/ROW]
[ROW][C]24[/C][C]159[/C][C]151.479695431472[/C][C]7.52030456852793[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]148[/C][C]10.0000000000000[/C][/ROW]
[ROW][C]26[/C][C]148[/C][C]141.739847715736[/C][C]6.26015228426396[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]129.707275803722[/C][C]8.2927241962775[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]125.800761421320[/C][C]11.1992385786802[/C][/ROW]
[ROW][C]29[/C][C]136[/C][C]122.508037225042[/C][C]13.4919627749577[/C][/ROW]
[ROW][C]30[/C][C]133[/C][C]119.247884940778[/C][C]13.7521150592217[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]114.154399323181[/C][C]11.8456006768189[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]110.227580372250[/C][C]9.77241962774957[/C][/ROW]
[ROW][C]33[/C][C]114[/C][C]107.052876480541[/C][C]6.94712351945854[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]105.487732656514[/C][C]10.5122673434856[/C][/ROW]
[ROW][C]35[/C][C]153[/C][C]143.479695431472[/C][C]9.52030456852792[/C][/ROW]
[ROW][C]36[/C][C]162[/C][C]148.601522842640[/C][C]13.3984771573604[/C][/ROW]
[ROW][C]37[/C][C]161[/C][C]146.560913705584[/C][C]14.4390862944163[/C][/ROW]
[ROW][C]38[/C][C]149[/C][C]141.739847715736[/C][C]7.26015228426396[/C][/ROW]
[ROW][C]39[/C][C]139[/C][C]131.146362098139[/C][C]7.85363790186126[/C][/ROW]
[ROW][C]40[/C][C]135[/C][C]127.239847715736[/C][C]7.76015228426397[/C][/ROW]
[ROW][C]41[/C][C]130[/C][C]125.386209813875[/C][C]4.61379018612521[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]122.126057529611[/C][C]4.87394247038918[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]114.154399323181[/C][C]7.84560067681895[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]113.105752961083[/C][C]3.89424703891709[/C][/ROW]
[ROW][C]45[/C][C]112[/C][C]108.491962774958[/C][C]3.50803722504232[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]109.804991539763[/C][C]3.19500846023689[/C][/ROW]
[ROW][C]47[/C][C]149[/C][C]144.918781725888[/C][C]4.08121827411169[/C][/ROW]
[ROW][C]48[/C][C]157[/C][C]151.479695431472[/C][C]5.52030456852794[/C][/ROW]
[ROW][C]49[/C][C]157[/C][C]149.439086294416[/C][C]7.5609137055838[/C][/ROW]
[ROW][C]50[/C][C]147[/C][C]141.739847715736[/C][C]5.26015228426396[/C][/ROW]
[ROW][C]51[/C][C]137[/C][C]131.146362098139[/C][C]5.85363790186126[/C][/ROW]
[ROW][C]52[/C][C]132[/C][C]127.239847715736[/C][C]4.76015228426397[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]125.386209813875[/C][C]-0.386209813874792[/C][/ROW]
[ROW][C]54[/C][C]123[/C][C]122.126057529611[/C][C]0.873942470389178[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]117.032571912014[/C][C]-0.0325719120135387[/C][/ROW]
[ROW][C]56[/C][C]114[/C][C]113.105752961083[/C][C]0.894247038917088[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]107.052876480541[/C][C]3.94712351945854[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]108.365905245347[/C][C]3.63409475465314[/C][/ROW]
[ROW][C]59[/C][C]144[/C][C]142.040609137056[/C][C]1.95939086294416[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]151.479695431472[/C][C]-1.47969543147207[/C][/ROW]
[ROW][C]61[/C][C]149[/C][C]148[/C][C]1.00000000000005[/C][/ROW]
[ROW][C]62[/C][C]134[/C][C]138.861675126904[/C][C]-4.86167512690357[/C][/ROW]
[ROW][C]63[/C][C]123[/C][C]128.268189509306[/C][C]-5.26818950930626[/C][/ROW]
[ROW][C]64[/C][C]116[/C][C]127.239847715736[/C][C]-11.2398477157360[/C][/ROW]
[ROW][C]65[/C][C]117[/C][C]125.386209813875[/C][C]-8.3862098138748[/C][/ROW]
[ROW][C]66[/C][C]111[/C][C]120.686971235195[/C][C]-9.68697123519459[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]117.032571912014[/C][C]-12.0325719120135[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]110.227580372250[/C][C]-8.22758037225043[/C][/ROW]
[ROW][C]69[/C][C]95[/C][C]104.174703891709[/C][C]-9.17470389170897[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]105.487732656514[/C][C]-12.4877326565144[/C][/ROW]
[ROW][C]71[/C][C]124[/C][C]142.040609137056[/C][C]-18.0406091370558[/C][/ROW]
[ROW][C]72[/C][C]130[/C][C]151.479695431472[/C][C]-21.4796954314721[/C][/ROW]
[ROW][C]73[/C][C]124[/C][C]148[/C][C]-24.0000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14456&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14456&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	148.000000000000	-8.00000000000028
2	132	143.178934010152	-11.1789340101523
3	117	132.585448392555	-15.5854483925550
4	114	127.239847715736	-13.2398477157361
5	113	122.508037225042	-9.50803722504226
6	110	119.247884940778	-9.24788494077836
7	107	114.154399323181	-7.15439932318104
8	103	110.227580372250	-7.22758037225039
9	98	104.174703891709	-6.17470389170896
10	98	105.487732656514	-7.48773265651439
11	137	142.040609137056	-5.04060913705584
12	148	151.479695431472	-3.47969543147208
13	147	148	-0.99999999999996
14	139	141.739847715736	-2.73984771573605
15	130	131.146362098139	-1.14636209813874
16	128	127.239847715736	0.760152284263968
17	127	126.825296108291	0.174703891708963
18	123	123.565143824027	-0.565143824027069
19	118	118.471658206430	-0.471658206429764
20	114	113.105752961083	0.894247038917088
21	108	107.052876480541	0.947123519458542
22	111	108.365905245347	2.63409475465314
23	151	143.479695431472	7.52030456852792
24	159	151.479695431472	7.52030456852793
25	158	148	10.0000000000000
26	148	141.739847715736	6.26015228426396
27	138	129.707275803722	8.2927241962775
28	137	125.800761421320	11.1992385786802
29	136	122.508037225042	13.4919627749577
30	133	119.247884940778	13.7521150592217
31	126	114.154399323181	11.8456006768189
32	120	110.227580372250	9.77241962774957
33	114	107.052876480541	6.94712351945854
34	116	105.487732656514	10.5122673434856
35	153	143.479695431472	9.52030456852792
36	162	148.601522842640	13.3984771573604
37	161	146.560913705584	14.4390862944163
38	149	141.739847715736	7.26015228426396
39	139	131.146362098139	7.85363790186126
40	135	127.239847715736	7.76015228426397
41	130	125.386209813875	4.61379018612521
42	127	122.126057529611	4.87394247038918
43	122	114.154399323181	7.84560067681895
44	117	113.105752961083	3.89424703891709
45	112	108.491962774958	3.50803722504232
46	113	109.804991539763	3.19500846023689
47	149	144.918781725888	4.08121827411169
48	157	151.479695431472	5.52030456852794
49	157	149.439086294416	7.5609137055838
50	147	141.739847715736	5.26015228426396
51	137	131.146362098139	5.85363790186126
52	132	127.239847715736	4.76015228426397
53	125	125.386209813875	-0.386209813874792
54	123	122.126057529611	0.873942470389178
55	117	117.032571912014	-0.0325719120135387
56	114	113.105752961083	0.894247038917088
57	111	107.052876480541	3.94712351945854
58	112	108.365905245347	3.63409475465314
59	144	142.040609137056	1.95939086294416
60	150	151.479695431472	-1.47969543147207
61	149	148	1.00000000000005
62	134	138.861675126904	-4.86167512690357
63	123	128.268189509306	-5.26818950930626
64	116	127.239847715736	-11.2398477157360
65	117	125.386209813875	-8.3862098138748
66	111	120.686971235195	-9.68697123519459
67	105	117.032571912014	-12.0325719120135
68	102	110.227580372250	-8.22758037225043
69	95	104.174703891709	-9.17470389170897
70	93	105.487732656514	-12.4877326565144
71	124	142.040609137056	-18.0406091370558
72	130	151.479695431472	-21.4796954314721
73	124	148	-24.0000000000000

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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 = 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