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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 15 Nov 2007 08:42:40 -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/t1195141023b8e06nn5g4zxywl.htm/, Retrieved Sat, 04 May 2024 12:15:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14461, Retrieved Sat, 04 May 2024 12:15:50 +0000

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No (this computation is public)

User-defined keywords

W9Q3G7

Estimated Impact

191

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 15:42:40] [923db922542fbe09e7ff87bb31b2f310] [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=14461&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=14461&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14461&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] = + 146.931317512971 + 5.83579994896655X[t] + 0.101213765254304M1[t] -6.77126291530474M2[t] -15.6404133100038M3[t] -24.1513303118304M4[t] -27.4383806810127M5[t] -28.9741977423784M6[t] -31.3707148122497M7[t] -35.5184651899375M8[t] -40.832882234292M9[t] -42.8985325864632M10[t] -8.99154961380658M11[t] -0.0189162889788047t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  146.931317512971 +  5.83579994896655X[t] +  0.101213765254304M1[t] -6.77126291530474M2[t] -15.6404133100038M3[t] -24.1513303118304M4[t] -27.4383806810127M5[t] -28.9741977423784M6[t] -31.3707148122497M7[t] -35.5184651899375M8[t] -40.832882234292M9[t] -42.8985325864632M10[t] -8.99154961380658M11[t] -0.0189162889788047t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14461&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  146.931317512971 +  5.83579994896655X[t] +  0.101213765254304M1[t] -6.77126291530474M2[t] -15.6404133100038M3[t] -24.1513303118304M4[t] -27.4383806810127M5[t] -28.9741977423784M6[t] -31.3707148122497M7[t] -35.5184651899375M8[t] -40.832882234292M9[t] -42.8985325864632M10[t] -8.99154961380658M11[t] -0.0189162889788047t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14461&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14461&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] = + 146.931317512971 + 5.83579994896655X[t] + 0.101213765254304M1[t] -6.77126291530474M2[t] -15.6404133100038M3[t] -24.1513303118304M4[t] -27.4383806810127M5[t] -28.9741977423784M6[t] -31.3707148122497M7[t] -35.5184651899375M8[t] -40.832882234292M9[t] -42.8985325864632M10[t] -8.99154961380658M11[t] -0.0189162889788047t + 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)	146.931317512971	5.488206	26.7722	0	0
X	5.83579994896655	3.148062	1.8538	0.068773	0.034386
M1	0.101213765254304	5.528352	0.0183	0.985455	0.492727
M2	-6.77126291530474	5.709779	-1.1859	0.240413	0.120207
M3	-15.6404133100038	6.097814	-2.5649	0.012883	0.006442
M4	-24.1513303118304	5.435809	-4.443	4e-05	2e-05
M5	-27.4383806810127	5.446938	-5.0374	5e-06	2e-06
M6	-28.9741977423784	5.461967	-5.3047	2e-06	1e-06
M7	-31.3707148122497	5.843621	-5.3684	1e-06	1e-06
M8	-35.5184651899375	5.835969	-6.0861	0	0
M9	-40.832882234292	5.82882	-7.0053	0	0
M10	-42.8985325864632	5.44746	-7.875	0	0
M11	-8.99154961380658	5.442336	-1.6521	0.103817	0.051908
t	-0.0189162889788047	0.054725	-0.3457	0.730827	0.365414

\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) & 146.931317512971 & 5.488206 & 26.7722 & 0 & 0 \tabularnewline
X & 5.83579994896655 & 3.148062 & 1.8538 & 0.068773 & 0.034386 \tabularnewline
M1 & 0.101213765254304 & 5.528352 & 0.0183 & 0.985455 & 0.492727 \tabularnewline
M2 & -6.77126291530474 & 5.709779 & -1.1859 & 0.240413 & 0.120207 \tabularnewline
M3 & -15.6404133100038 & 6.097814 & -2.5649 & 0.012883 & 0.006442 \tabularnewline
M4 & -24.1513303118304 & 5.435809 & -4.443 & 4e-05 & 2e-05 \tabularnewline
M5 & -27.4383806810127 & 5.446938 & -5.0374 & 5e-06 & 2e-06 \tabularnewline
M6 & -28.9741977423784 & 5.461967 & -5.3047 & 2e-06 & 1e-06 \tabularnewline
M7 & -31.3707148122497 & 5.843621 & -5.3684 & 1e-06 & 1e-06 \tabularnewline
M8 & -35.5184651899375 & 5.835969 & -6.0861 & 0 & 0 \tabularnewline
M9 & -40.832882234292 & 5.82882 & -7.0053 & 0 & 0 \tabularnewline
M10 & -42.8985325864632 & 5.44746 & -7.875 & 0 & 0 \tabularnewline
M11 & -8.99154961380658 & 5.442336 & -1.6521 & 0.103817 & 0.051908 \tabularnewline
t & -0.0189162889788047 & 0.054725 & -0.3457 & 0.730827 & 0.365414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14461&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]146.931317512971[/C][C]5.488206[/C][C]26.7722[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]5.83579994896655[/C][C]3.148062[/C][C]1.8538[/C][C]0.068773[/C][C]0.034386[/C][/ROW]
[ROW][C]M1[/C][C]0.101213765254304[/C][C]5.528352[/C][C]0.0183[/C][C]0.985455[/C][C]0.492727[/C][/ROW]
[ROW][C]M2[/C][C]-6.77126291530474[/C][C]5.709779[/C][C]-1.1859[/C][C]0.240413[/C][C]0.120207[/C][/ROW]
[ROW][C]M3[/C][C]-15.6404133100038[/C][C]6.097814[/C][C]-2.5649[/C][C]0.012883[/C][C]0.006442[/C][/ROW]
[ROW][C]M4[/C][C]-24.1513303118304[/C][C]5.435809[/C][C]-4.443[/C][C]4e-05[/C][C]2e-05[/C][/ROW]
[ROW][C]M5[/C][C]-27.4383806810127[/C][C]5.446938[/C][C]-5.0374[/C][C]5e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M6[/C][C]-28.9741977423784[/C][C]5.461967[/C][C]-5.3047[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M7[/C][C]-31.3707148122497[/C][C]5.843621[/C][C]-5.3684[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M8[/C][C]-35.5184651899375[/C][C]5.835969[/C][C]-6.0861[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-40.832882234292[/C][C]5.82882[/C][C]-7.0053[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-42.8985325864632[/C][C]5.44746[/C][C]-7.875[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-8.99154961380658[/C][C]5.442336[/C][C]-1.6521[/C][C]0.103817[/C][C]0.051908[/C][/ROW]
[ROW][C]t[/C][C]-0.0189162889788047[/C][C]0.054725[/C][C]-0.3457[/C][C]0.730827[/C][C]0.365414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14461&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14461&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)	146.931317512971	5.488206	26.7722	0	0
X	5.83579994896655	3.148062	1.8538	0.068773	0.034386
M1	0.101213765254304	5.528352	0.0183	0.985455	0.492727
M2	-6.77126291530474	5.709779	-1.1859	0.240413	0.120207
M3	-15.6404133100038	6.097814	-2.5649	0.012883	0.006442
M4	-24.1513303118304	5.435809	-4.443	4e-05	2e-05
M5	-27.4383806810127	5.446938	-5.0374	5e-06	2e-06
M6	-28.9741977423784	5.461967	-5.3047	2e-06	1e-06
M7	-31.3707148122497	5.843621	-5.3684	1e-06	1e-06
M8	-35.5184651899375	5.835969	-6.0861	0	0
M9	-40.832882234292	5.82882	-7.0053	0	0
M10	-42.8985325864632	5.44746	-7.875	0	0
M11	-8.99154961380658	5.442336	-1.6521	0.103817	0.051908
t	-0.0189162889788047	0.054725	-0.3457	0.730827	0.365414

Multiple Linear Regression - Regression Statistics
Multiple R	0.875657079533982
R-squared	0.766775320937982
Adjusted R-squared	0.715386832331097
F-TEST (value)	14.9211494971900
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	4.08562073062058e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.38451061286577
Sum Squared Residuals	5196.07332713642

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.875657079533982 \tabularnewline
R-squared & 0.766775320937982 \tabularnewline
Adjusted R-squared & 0.715386832331097 \tabularnewline
F-TEST (value) & 14.9211494971900 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 4.08562073062058e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9.38451061286577 \tabularnewline
Sum Squared Residuals & 5196.07332713642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14461&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.875657079533982[/C][/ROW]
[ROW][C]R-squared[/C][C]0.766775320937982[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.715386832331097[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]14.9211494971900[/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]4.08562073062058e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9.38451061286577[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5196.07332713642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14461&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14461&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	0.875657079533982
R-squared	0.766775320937982
Adjusted R-squared	0.715386832331097
F-TEST (value)	14.9211494971900
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	4.08562073062058e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.38451061286577
Sum Squared Residuals	5196.07332713642

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	140	152.849414938213	-12.8494149382133
2	132	140.122222019709	-8.12222201970856
3	117	131.234155336031	-14.2341553360308
4	114	128.540121994192	-14.5401219941919
5	113	125.234155336031	-12.2341553360308
6	110	123.679421985686	-13.6794219856863
7	107	115.428188677870	-8.42818867786978
8	103	111.261522011203	-8.26152201120301
9	98	105.928188677870	-7.92818867786968
10	98	109.679421985686	-11.6794219856864
11	137	143.567488669364	-6.56748866936416
12	148	146.704322045225	1.29567795477467
13	147	146.786619521501	0.213380478499176
14	139	145.731026500930	-6.73102650092954
15	130	131.007159868285	-1.00715986828514
16	128	128.313126526446	-0.313126526446249
17	127	125.007159868285	1.99284013171485
18	123	123.452426517941	-0.45242651794067
19	118	115.201193210124	2.79880678987595
20	114	116.870326492424	-2.87032649242395
21	108	105.701193210124	2.29880678987594
22	111	109.452426517941	1.54757348205935
23	151	143.340493201618	7.65950679838152
24	159	152.313126526446	6.68687347355375
25	158	146.559624053755	11.4403759462448
26	148	139.668231084217	8.3317689157827
27	138	130.780164400539	7.21983559946051
28	137	128.086131058701	8.9138689412994
29	136	124.780164400539	11.2198355994605
30	133	123.225431050195	9.774568949805
31	126	120.809997691345	5.19000230865507
32	120	110.807531075712	9.19246892428826
33	114	105.474197742378	8.5258022576216
34	116	109.225431050195	6.774568949805
35	153	143.113497733873	9.88650226612718
36	162	152.086131058701	9.91386894129941
37	161	152.168428534976	8.83157146502393
38	149	145.277035565438	3.72296443456178
39	139	130.553168932794	8.44683106720616
40	135	127.859135590955	7.14086440904506
41	130	124.553168932794	5.44683106720616
42	127	122.998435582449	4.00156441755064
43	122	114.747202274633	7.25279772536727
44	117	110.580535607966	6.41946439203391
45	112	105.247202274633	6.75279772536725
46	113	108.998435582449	4.00156441755065
47	149	142.886502266127	6.11349773387283
48	157	151.859135590955	5.14086440904506
49	157	146.105633118264	10.8943668817361
50	147	139.214240148726	7.785759851274
51	137	130.326173465048	6.67382653495182
52	132	127.632140123209	4.36785987679072
53	125	124.326173465048	0.67382653495182
54	123	116.935640165737	6.06435983426286
55	117	114.520206806887	2.47979319311292
56	114	110.353540140220	3.64645985977957
57	111	110.856006755854	0.143993244146354
58	112	102.935640165737	9.06435983426287
59	144	142.659506798381	1.34049320161849
60	150	151.632140123209	-1.63214012320928
61	149	145.878637650518	3.1213623494818
62	134	138.987244680980	-4.98724468098035
63	123	130.099177997303	-7.09917799730252
64	116	121.569344706497	-5.56934470649707
65	117	124.099177997303	-7.09917799730252
66	111	116.708644697991	-5.70864469799149
67	105	114.293211339141	-9.29321133914142
68	102	110.126544672475	-8.12654467247477
69	95	104.793211339141	-9.79321133914144
70	93	102.708644697991	-9.70864469799148
71	124	142.432511330636	-18.4325113306359
72	130	151.405144655464	-21.4051446554636
73	124	145.651642182773	-21.6516421827725

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 140 & 152.849414938213 & -12.8494149382133 \tabularnewline
2 & 132 & 140.122222019709 & -8.12222201970856 \tabularnewline
3 & 117 & 131.234155336031 & -14.2341553360308 \tabularnewline
4 & 114 & 128.540121994192 & -14.5401219941919 \tabularnewline
5 & 113 & 125.234155336031 & -12.2341553360308 \tabularnewline
6 & 110 & 123.679421985686 & -13.6794219856863 \tabularnewline
7 & 107 & 115.428188677870 & -8.42818867786978 \tabularnewline
8 & 103 & 111.261522011203 & -8.26152201120301 \tabularnewline
9 & 98 & 105.928188677870 & -7.92818867786968 \tabularnewline
10 & 98 & 109.679421985686 & -11.6794219856864 \tabularnewline
11 & 137 & 143.567488669364 & -6.56748866936416 \tabularnewline
12 & 148 & 146.704322045225 & 1.29567795477467 \tabularnewline
13 & 147 & 146.786619521501 & 0.213380478499176 \tabularnewline
14 & 139 & 145.731026500930 & -6.73102650092954 \tabularnewline
15 & 130 & 131.007159868285 & -1.00715986828514 \tabularnewline
16 & 128 & 128.313126526446 & -0.313126526446249 \tabularnewline
17 & 127 & 125.007159868285 & 1.99284013171485 \tabularnewline
18 & 123 & 123.452426517941 & -0.45242651794067 \tabularnewline
19 & 118 & 115.201193210124 & 2.79880678987595 \tabularnewline
20 & 114 & 116.870326492424 & -2.87032649242395 \tabularnewline
21 & 108 & 105.701193210124 & 2.29880678987594 \tabularnewline
22 & 111 & 109.452426517941 & 1.54757348205935 \tabularnewline
23 & 151 & 143.340493201618 & 7.65950679838152 \tabularnewline
24 & 159 & 152.313126526446 & 6.68687347355375 \tabularnewline
25 & 158 & 146.559624053755 & 11.4403759462448 \tabularnewline
26 & 148 & 139.668231084217 & 8.3317689157827 \tabularnewline
27 & 138 & 130.780164400539 & 7.21983559946051 \tabularnewline
28 & 137 & 128.086131058701 & 8.9138689412994 \tabularnewline
29 & 136 & 124.780164400539 & 11.2198355994605 \tabularnewline
30 & 133 & 123.225431050195 & 9.774568949805 \tabularnewline
31 & 126 & 120.809997691345 & 5.19000230865507 \tabularnewline
32 & 120 & 110.807531075712 & 9.19246892428826 \tabularnewline
33 & 114 & 105.474197742378 & 8.5258022576216 \tabularnewline
34 & 116 & 109.225431050195 & 6.774568949805 \tabularnewline
35 & 153 & 143.113497733873 & 9.88650226612718 \tabularnewline
36 & 162 & 152.086131058701 & 9.91386894129941 \tabularnewline
37 & 161 & 152.168428534976 & 8.83157146502393 \tabularnewline
38 & 149 & 145.277035565438 & 3.72296443456178 \tabularnewline
39 & 139 & 130.553168932794 & 8.44683106720616 \tabularnewline
40 & 135 & 127.859135590955 & 7.14086440904506 \tabularnewline
41 & 130 & 124.553168932794 & 5.44683106720616 \tabularnewline
42 & 127 & 122.998435582449 & 4.00156441755064 \tabularnewline
43 & 122 & 114.747202274633 & 7.25279772536727 \tabularnewline
44 & 117 & 110.580535607966 & 6.41946439203391 \tabularnewline
45 & 112 & 105.247202274633 & 6.75279772536725 \tabularnewline
46 & 113 & 108.998435582449 & 4.00156441755065 \tabularnewline
47 & 149 & 142.886502266127 & 6.11349773387283 \tabularnewline
48 & 157 & 151.859135590955 & 5.14086440904506 \tabularnewline
49 & 157 & 146.105633118264 & 10.8943668817361 \tabularnewline
50 & 147 & 139.214240148726 & 7.785759851274 \tabularnewline
51 & 137 & 130.326173465048 & 6.67382653495182 \tabularnewline
52 & 132 & 127.632140123209 & 4.36785987679072 \tabularnewline
53 & 125 & 124.326173465048 & 0.67382653495182 \tabularnewline
54 & 123 & 116.935640165737 & 6.06435983426286 \tabularnewline
55 & 117 & 114.520206806887 & 2.47979319311292 \tabularnewline
56 & 114 & 110.353540140220 & 3.64645985977957 \tabularnewline
57 & 111 & 110.856006755854 & 0.143993244146354 \tabularnewline
58 & 112 & 102.935640165737 & 9.06435983426287 \tabularnewline
59 & 144 & 142.659506798381 & 1.34049320161849 \tabularnewline
60 & 150 & 151.632140123209 & -1.63214012320928 \tabularnewline
61 & 149 & 145.878637650518 & 3.1213623494818 \tabularnewline
62 & 134 & 138.987244680980 & -4.98724468098035 \tabularnewline
63 & 123 & 130.099177997303 & -7.09917799730252 \tabularnewline
64 & 116 & 121.569344706497 & -5.56934470649707 \tabularnewline
65 & 117 & 124.099177997303 & -7.09917799730252 \tabularnewline
66 & 111 & 116.708644697991 & -5.70864469799149 \tabularnewline
67 & 105 & 114.293211339141 & -9.29321133914142 \tabularnewline
68 & 102 & 110.126544672475 & -8.12654467247477 \tabularnewline
69 & 95 & 104.793211339141 & -9.79321133914144 \tabularnewline
70 & 93 & 102.708644697991 & -9.70864469799148 \tabularnewline
71 & 124 & 142.432511330636 & -18.4325113306359 \tabularnewline
72 & 130 & 151.405144655464 & -21.4051446554636 \tabularnewline
73 & 124 & 145.651642182773 & -21.6516421827725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14461&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]152.849414938213[/C][C]-12.8494149382133[/C][/ROW]
[ROW][C]2[/C][C]132[/C][C]140.122222019709[/C][C]-8.12222201970856[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]131.234155336031[/C][C]-14.2341553360308[/C][/ROW]
[ROW][C]4[/C][C]114[/C][C]128.540121994192[/C][C]-14.5401219941919[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]125.234155336031[/C][C]-12.2341553360308[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]123.679421985686[/C][C]-13.6794219856863[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]115.428188677870[/C][C]-8.42818867786978[/C][/ROW]
[ROW][C]8[/C][C]103[/C][C]111.261522011203[/C][C]-8.26152201120301[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]105.928188677870[/C][C]-7.92818867786968[/C][/ROW]
[ROW][C]10[/C][C]98[/C][C]109.679421985686[/C][C]-11.6794219856864[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]143.567488669364[/C][C]-6.56748866936416[/C][/ROW]
[ROW][C]12[/C][C]148[/C][C]146.704322045225[/C][C]1.29567795477467[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]146.786619521501[/C][C]0.213380478499176[/C][/ROW]
[ROW][C]14[/C][C]139[/C][C]145.731026500930[/C][C]-6.73102650092954[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]131.007159868285[/C][C]-1.00715986828514[/C][/ROW]
[ROW][C]16[/C][C]128[/C][C]128.313126526446[/C][C]-0.313126526446249[/C][/ROW]
[ROW][C]17[/C][C]127[/C][C]125.007159868285[/C][C]1.99284013171485[/C][/ROW]
[ROW][C]18[/C][C]123[/C][C]123.452426517941[/C][C]-0.45242651794067[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]115.201193210124[/C][C]2.79880678987595[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]116.870326492424[/C][C]-2.87032649242395[/C][/ROW]
[ROW][C]21[/C][C]108[/C][C]105.701193210124[/C][C]2.29880678987594[/C][/ROW]
[ROW][C]22[/C][C]111[/C][C]109.452426517941[/C][C]1.54757348205935[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]143.340493201618[/C][C]7.65950679838152[/C][/ROW]
[ROW][C]24[/C][C]159[/C][C]152.313126526446[/C][C]6.68687347355375[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]146.559624053755[/C][C]11.4403759462448[/C][/ROW]
[ROW][C]26[/C][C]148[/C][C]139.668231084217[/C][C]8.3317689157827[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]130.780164400539[/C][C]7.21983559946051[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]128.086131058701[/C][C]8.9138689412994[/C][/ROW]
[ROW][C]29[/C][C]136[/C][C]124.780164400539[/C][C]11.2198355994605[/C][/ROW]
[ROW][C]30[/C][C]133[/C][C]123.225431050195[/C][C]9.774568949805[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]120.809997691345[/C][C]5.19000230865507[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]110.807531075712[/C][C]9.19246892428826[/C][/ROW]
[ROW][C]33[/C][C]114[/C][C]105.474197742378[/C][C]8.5258022576216[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]109.225431050195[/C][C]6.774568949805[/C][/ROW]
[ROW][C]35[/C][C]153[/C][C]143.113497733873[/C][C]9.88650226612718[/C][/ROW]
[ROW][C]36[/C][C]162[/C][C]152.086131058701[/C][C]9.91386894129941[/C][/ROW]
[ROW][C]37[/C][C]161[/C][C]152.168428534976[/C][C]8.83157146502393[/C][/ROW]
[ROW][C]38[/C][C]149[/C][C]145.277035565438[/C][C]3.72296443456178[/C][/ROW]
[ROW][C]39[/C][C]139[/C][C]130.553168932794[/C][C]8.44683106720616[/C][/ROW]
[ROW][C]40[/C][C]135[/C][C]127.859135590955[/C][C]7.14086440904506[/C][/ROW]
[ROW][C]41[/C][C]130[/C][C]124.553168932794[/C][C]5.44683106720616[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]122.998435582449[/C][C]4.00156441755064[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]114.747202274633[/C][C]7.25279772536727[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]110.580535607966[/C][C]6.41946439203391[/C][/ROW]
[ROW][C]45[/C][C]112[/C][C]105.247202274633[/C][C]6.75279772536725[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]108.998435582449[/C][C]4.00156441755065[/C][/ROW]
[ROW][C]47[/C][C]149[/C][C]142.886502266127[/C][C]6.11349773387283[/C][/ROW]
[ROW][C]48[/C][C]157[/C][C]151.859135590955[/C][C]5.14086440904506[/C][/ROW]
[ROW][C]49[/C][C]157[/C][C]146.105633118264[/C][C]10.8943668817361[/C][/ROW]
[ROW][C]50[/C][C]147[/C][C]139.214240148726[/C][C]7.785759851274[/C][/ROW]
[ROW][C]51[/C][C]137[/C][C]130.326173465048[/C][C]6.67382653495182[/C][/ROW]
[ROW][C]52[/C][C]132[/C][C]127.632140123209[/C][C]4.36785987679072[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]124.326173465048[/C][C]0.67382653495182[/C][/ROW]
[ROW][C]54[/C][C]123[/C][C]116.935640165737[/C][C]6.06435983426286[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]114.520206806887[/C][C]2.47979319311292[/C][/ROW]
[ROW][C]56[/C][C]114[/C][C]110.353540140220[/C][C]3.64645985977957[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]110.856006755854[/C][C]0.143993244146354[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]102.935640165737[/C][C]9.06435983426287[/C][/ROW]
[ROW][C]59[/C][C]144[/C][C]142.659506798381[/C][C]1.34049320161849[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]151.632140123209[/C][C]-1.63214012320928[/C][/ROW]
[ROW][C]61[/C][C]149[/C][C]145.878637650518[/C][C]3.1213623494818[/C][/ROW]
[ROW][C]62[/C][C]134[/C][C]138.987244680980[/C][C]-4.98724468098035[/C][/ROW]
[ROW][C]63[/C][C]123[/C][C]130.099177997303[/C][C]-7.09917799730252[/C][/ROW]
[ROW][C]64[/C][C]116[/C][C]121.569344706497[/C][C]-5.56934470649707[/C][/ROW]
[ROW][C]65[/C][C]117[/C][C]124.099177997303[/C][C]-7.09917799730252[/C][/ROW]
[ROW][C]66[/C][C]111[/C][C]116.708644697991[/C][C]-5.70864469799149[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]114.293211339141[/C][C]-9.29321133914142[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]110.126544672475[/C][C]-8.12654467247477[/C][/ROW]
[ROW][C]69[/C][C]95[/C][C]104.793211339141[/C][C]-9.79321133914144[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]102.708644697991[/C][C]-9.70864469799148[/C][/ROW]
[ROW][C]71[/C][C]124[/C][C]142.432511330636[/C][C]-18.4325113306359[/C][/ROW]
[ROW][C]72[/C][C]130[/C][C]151.405144655464[/C][C]-21.4051446554636[/C][/ROW]
[ROW][C]73[/C][C]124[/C][C]145.651642182773[/C][C]-21.6516421827725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14461&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14461&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	152.849414938213	-12.8494149382133
2	132	140.122222019709	-8.12222201970856
3	117	131.234155336031	-14.2341553360308
4	114	128.540121994192	-14.5401219941919
5	113	125.234155336031	-12.2341553360308
6	110	123.679421985686	-13.6794219856863
7	107	115.428188677870	-8.42818867786978
8	103	111.261522011203	-8.26152201120301
9	98	105.928188677870	-7.92818867786968
10	98	109.679421985686	-11.6794219856864
11	137	143.567488669364	-6.56748866936416
12	148	146.704322045225	1.29567795477467
13	147	146.786619521501	0.213380478499176
14	139	145.731026500930	-6.73102650092954
15	130	131.007159868285	-1.00715986828514
16	128	128.313126526446	-0.313126526446249
17	127	125.007159868285	1.99284013171485
18	123	123.452426517941	-0.45242651794067
19	118	115.201193210124	2.79880678987595
20	114	116.870326492424	-2.87032649242395
21	108	105.701193210124	2.29880678987594
22	111	109.452426517941	1.54757348205935
23	151	143.340493201618	7.65950679838152
24	159	152.313126526446	6.68687347355375
25	158	146.559624053755	11.4403759462448
26	148	139.668231084217	8.3317689157827
27	138	130.780164400539	7.21983559946051
28	137	128.086131058701	8.9138689412994
29	136	124.780164400539	11.2198355994605
30	133	123.225431050195	9.774568949805
31	126	120.809997691345	5.19000230865507
32	120	110.807531075712	9.19246892428826
33	114	105.474197742378	8.5258022576216
34	116	109.225431050195	6.774568949805
35	153	143.113497733873	9.88650226612718
36	162	152.086131058701	9.91386894129941
37	161	152.168428534976	8.83157146502393
38	149	145.277035565438	3.72296443456178
39	139	130.553168932794	8.44683106720616
40	135	127.859135590955	7.14086440904506
41	130	124.553168932794	5.44683106720616
42	127	122.998435582449	4.00156441755064
43	122	114.747202274633	7.25279772536727
44	117	110.580535607966	6.41946439203391
45	112	105.247202274633	6.75279772536725
46	113	108.998435582449	4.00156441755065
47	149	142.886502266127	6.11349773387283
48	157	151.859135590955	5.14086440904506
49	157	146.105633118264	10.8943668817361
50	147	139.214240148726	7.785759851274
51	137	130.326173465048	6.67382653495182
52	132	127.632140123209	4.36785987679072
53	125	124.326173465048	0.67382653495182
54	123	116.935640165737	6.06435983426286
55	117	114.520206806887	2.47979319311292
56	114	110.353540140220	3.64645985977957
57	111	110.856006755854	0.143993244146354
58	112	102.935640165737	9.06435983426287
59	144	142.659506798381	1.34049320161849
60	150	151.632140123209	-1.63214012320928
61	149	145.878637650518	3.1213623494818
62	134	138.987244680980	-4.98724468098035
63	123	130.099177997303	-7.09917799730252
64	116	121.569344706497	-5.56934470649707
65	117	124.099177997303	-7.09917799730252
66	111	116.708644697991	-5.70864469799149
67	105	114.293211339141	-9.29321133914142
68	102	110.126544672475	-8.12654467247477
69	95	104.793211339141	-9.79321133914144
70	93	102.708644697991	-9.70864469799148
71	124	142.432511330636	-18.4325113306359
72	130	151.405144655464	-21.4051446554636
73	124	145.651642182773	-21.6516421827725

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