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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 17 Dec 2007 13:01:29 -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/Dec/17/t1197920702hpwx5e66cf0s4bm.htm/, Retrieved Fri, 03 May 2024 20:07:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4420, Retrieved Fri, 03 May 2024 20:07:52 +0000

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Estimated Impact

165

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

-       [Multiple Regression] [] [2007-12-17 20:01:29] [ba3202e2798d2e4685d19d988e9c69df] [Current]

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85,6	92,81	88	75,6
89	59,04	88,4	48,7
97,5	72,81	95	111,7
104	91,81	101,8	119,5
99,4	68,07	107,6	103,4
103,2	49,16	118,9	96,3
103	124,61	126,9	96,6
91,2	109,89	106,3	110,4
85,9	110,51	109,2	104,4
80,7	114,77	104,6	110,7
86,7	92,37	100,8	93,6
80,7	103,63	92,1	114,8
81,5	90,43	86,4	74,9
83,4	65,86	96	69,8
83,5	83,33	98,5	104,2
89,5	94,49	112	109,3
85,8	68,98	113,9	92,7
77,4	55,46	120	91,7
67,5	132,89	126,7	84,4
63,7	121,71	112,8	94,5
59,4	127,01	116,2	103,6
62	134,04	110,6	105,9
62,4	106,48	105	108
58,1	117,55	101,2	119,9
58	101,61	99,3	84,5
56,3	82,66	101,9	76,7
61,4	89,28	106,4	120,5
59,8	109,24	118,9	119,6
54,3	88,16	121,9	102,3
47	59,23	132	101,7
50,5	164,21	121,4	86,9
48,1	125,13	117	93,6
58,8	152,68	122,7	113,6
70,4	132,96	113	106,7
71,9	112,42	104	96,1
73,3	136,43	101,2	124,6
83,5	107,32	100,8	72,5
90,1	87,61	98,9	89
101,3	97,86	103	115,3
98,3	106,60	117,8	119,1
106,7	92,17	126,6	104,4
109,9	65,31	127,6	104,9
111,1	161,49	115,8	76,9
119	162,25	114,8	95,3
120,7	175,13	119,2	114,9
104,5	147,28	109,9	98,9
121,6	144,48	98,9	102,9
129,6	122,67	98,6	90
124,5	102,27	96,6	81
130,1	88,64	96,7	66,2
142,3	89,59	103,5	86,7
140	112,20	115,3	86,7
143,3	91,98	122,5	103,4
113,4	57,85	125,3	89,5
113,8	160,49	111,2	113,7
120,7	128,33	110,7	120,2
112,9	140,69	114,2	137,8
115,5	126,61	105,6	99,1
121,9	129,27	95,5	110,4
119,3	124,27	97,3	112,3
111	112,90	95,5	82,2
114,2	92,54	96,3	72,2
113,5	85,70	100,2	106,7
94	116,72	113,4	106,4
83,2	92,08	121,4	110
82,8	58,98	122,1	87,5
85,8	154,50	119,3	79,7
88,7	145,55	110,8	83,3
105,3	146,60	110,1	91,8
113,1	143,51	99,7	89,2
113,8	113,52	104,8	90,6
109,4	104,80	105,4	92,6

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4420&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4420&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4420&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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation
olie[t] = + 131.058720667153 + 0.0777048133057692wagens[t] -0.365660000574707electric[t] -0.0686328689875479vervoers[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
olie[t] =  +  131.058720667153 +  0.0777048133057692wagens[t] -0.365660000574707electric[t] -0.0686328689875479vervoers[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4420&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]olie[t] =  +  131.058720667153 +  0.0777048133057692wagens[t] -0.365660000574707electric[t] -0.0686328689875479vervoers[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4420&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4420&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
olie[t] = + 131.058720667153 + 0.0777048133057692wagens[t] -0.365660000574707electric[t] -0.0686328689875479vervoers[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)	131.058720667153	32.037171	4.0908	0.000116	5.8e-05
wagens	0.0777048133057692	0.099594	0.7802	0.437971	0.218985
electric	-0.365660000574707	0.28047	-1.3037	0.196718	0.098359
vervoers	-0.0686328689875479	0.191959	-0.3575	0.721796	0.360898

\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) & 131.058720667153 & 32.037171 & 4.0908 & 0.000116 & 5.8e-05 \tabularnewline
wagens & 0.0777048133057692 & 0.099594 & 0.7802 & 0.437971 & 0.218985 \tabularnewline
electric & -0.365660000574707 & 0.28047 & -1.3037 & 0.196718 & 0.098359 \tabularnewline
vervoers & -0.0686328689875479 & 0.191959 & -0.3575 & 0.721796 & 0.360898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4420&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]131.058720667153[/C][C]32.037171[/C][C]4.0908[/C][C]0.000116[/C][C]5.8e-05[/C][/ROW]
[ROW][C]wagens[/C][C]0.0777048133057692[/C][C]0.099594[/C][C]0.7802[/C][C]0.437971[/C][C]0.218985[/C][/ROW]
[ROW][C]electric[/C][C]-0.365660000574707[/C][C]0.28047[/C][C]-1.3037[/C][C]0.196718[/C][C]0.098359[/C][/ROW]
[ROW][C]vervoers[/C][C]-0.0686328689875479[/C][C]0.191959[/C][C]-0.3575[/C][C]0.721796[/C][C]0.360898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4420&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4420&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)	131.058720667153	32.037171	4.0908	0.000116	5.8e-05
wagens	0.0777048133057692	0.099594	0.7802	0.437971	0.218985
electric	-0.365660000574707	0.28047	-1.3037	0.196718	0.098359
vervoers	-0.0686328689875479	0.191959	-0.3575	0.721796	0.360898

Multiple Linear Regression - Regression Statistics
Multiple R	0.189440361235054
R-squared	0.0358876504648676
Adjusted R-squared	-0.00664671789697646
F-TEST (value)	0.843733005732395
F-TEST (DF numerator)	3
F-TEST (DF denominator)	68
p-value	0.474688991216682
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	24.6583433727325
Sum Squared Residuals	41346.3050563555

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.189440361235054 \tabularnewline
R-squared & 0.0358876504648676 \tabularnewline
Adjusted R-squared & -0.00664671789697646 \tabularnewline
F-TEST (value) & 0.843733005732395 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 68 \tabularnewline
p-value & 0.474688991216682 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 24.6583433727325 \tabularnewline
Sum Squared Residuals & 41346.3050563555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4420&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.189440361235054[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0358876504648676[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.00664671789697646[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.843733005732395[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]68[/C][/ROW]
[ROW][C]p-value[/C][C]0.474688991216682[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]24.6583433727325[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]41346.3050563555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4420&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4420&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	0.189440361235054
R-squared	0.0358876504648676
Adjusted R-squared	-0.00664671789697646
F-TEST (value)	0.843733005732395
F-TEST (DF numerator)	3
F-TEST (DF denominator)	68
p-value	0.474688991216682
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	24.6583433727325
Sum Squared Residuals	41346.3050563555

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	85.6	100.903779444029	-15.3037794440286
2	89	99.9796480742283	-10.9796480742283
3	97.5	94.3124166034401	3.18758339655989
4	104	92.7669836742388	11.2330163257612
5	99.4	89.9064325937261	9.4935674062739
6	103.2	84.7923699374314	18.4076300625686
7	103	87.7093282360578	15.2906717639422
8	91.2	93.1509758040077	-1.95097580400765
9	85.9	92.5505360005159	-6.65053600051587
10	80.7	94.1312074332206	-13.4312074332205
11	86.7	94.9537496770423	-8.25374967704227
12	80.7	97.5549310573292	-16.8549310573292
13	81.5	101.351940997572	-19.851940997572
14	83.4	96.2824253609686	-12.8824253609686
15	83.5	94.364807754812	-10.8648077548119
16	89.5	89.9455558317093	-0.445555831709287
17	85.8	88.4078576683805	-2.60785766838047
18	77.4	85.1953954579683	-7.7953954579683
19	67.5	89.2631770919926	-21.7631770919926
20	63.7	92.7839193104483	-29.0839193104483
21	59.4	91.3279517112282	-31.9279517112282
22	62	93.7640569533147	-31.7640569533147
23	62.4	93.5260792769522	-31.1260792769522
24	58.1	94.9590484214792	-36.8590484214792
25	58	96.8447912606363	-38.8447912606363
26	56.3	94.9569054251006	-38.6569054251006
27	61.4	90.819721624944	-29.4197216249440
28	59.8	87.8617292734322	-28.0617292734322
29	54.3	86.314080440707	-32.014080440707
30	47	80.4140939073591	-33.4140939073591
31	50.5	93.4633076753063	-42.9633076753063
32	48.1	91.575667351629	-43.475667351629
33	58.8	90.2595155751762	-31.4595155751762
34	70.4	92.7476454583751	-22.3476454583751
35	71.9	95.170037009515	-23.270037009515
36	73.3	96.1035408124506	-22.8035408124506
37	83.5	97.5635901716008	-14.0635901716008
38	90.1	95.5943399641415	-5.49433996414148
39	101.3	93.0865638437968	8.2134361562032
40	98.3	88.0931310014309	10.2068689985691
41	106.7	84.7629457144882	21.9370542855118
42	109.9	82.2758179940267	27.6241820059733
43	111.1	95.9859752762085	15.1140247237915
44	119	95.1478461455247	23.8521538544753
45	120.7	93.1945759062183	27.5054240937816
46	104.5	95.5292607647982	8.97073923520178
47	121.6	99.0594158179136	22.5405841820863
48	129.6	98.3597358498266	31.2402641501734
49	124.5	98.1235734804263	26.3764265195737
50	130.1	98.0436573360269	32.0563426639731
51	142.3	94.2240150905146	48.0759849094854
52	140	91.6661329125765	48.3338670874235
53	143.3	86.316020671304	56.9839793286961
54	113.4	83.5941042704958	29.8058957295043
55	113.8	95.0646168868046	18.7353831131954
56	120.7	92.3023464427594	28.3976535572406
57	112.9	90.7750294390264	22.1249705609737
58	115.5	95.4817137024417	20.0182862975583
59	121.9	98.6060230920803	23.2939769079197
60	119.3	97.4289085734406	21.8710914265594
61	111	99.2694422037137	11.7305577962863
62	114.2	98.081172894224	16.1188271057760
63	113.5	93.7557639889007	19.7442360110993
64	94	91.3600451507558	2.63995484924417
65	83.2	86.2730402179489	-3.07304021794885
66	82.8	84.9892884493454	-2.18928844934544
67	85.8	93.9708365960246	-8.17083659602456
68	88.7	96.1364101934678	-7.43641019346775
69	105.3	95.890582861447	9.40941713855305
70	113.1	99.6317844536767	13.4682155463233
71	113.8	95.3404650831231	18.4595349168769
72	109.4	94.3062173727769	15.0937826272231

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 85.6 & 100.903779444029 & -15.3037794440286 \tabularnewline
2 & 89 & 99.9796480742283 & -10.9796480742283 \tabularnewline
3 & 97.5 & 94.3124166034401 & 3.18758339655989 \tabularnewline
4 & 104 & 92.7669836742388 & 11.2330163257612 \tabularnewline
5 & 99.4 & 89.9064325937261 & 9.4935674062739 \tabularnewline
6 & 103.2 & 84.7923699374314 & 18.4076300625686 \tabularnewline
7 & 103 & 87.7093282360578 & 15.2906717639422 \tabularnewline
8 & 91.2 & 93.1509758040077 & -1.95097580400765 \tabularnewline
9 & 85.9 & 92.5505360005159 & -6.65053600051587 \tabularnewline
10 & 80.7 & 94.1312074332206 & -13.4312074332205 \tabularnewline
11 & 86.7 & 94.9537496770423 & -8.25374967704227 \tabularnewline
12 & 80.7 & 97.5549310573292 & -16.8549310573292 \tabularnewline
13 & 81.5 & 101.351940997572 & -19.851940997572 \tabularnewline
14 & 83.4 & 96.2824253609686 & -12.8824253609686 \tabularnewline
15 & 83.5 & 94.364807754812 & -10.8648077548119 \tabularnewline
16 & 89.5 & 89.9455558317093 & -0.445555831709287 \tabularnewline
17 & 85.8 & 88.4078576683805 & -2.60785766838047 \tabularnewline
18 & 77.4 & 85.1953954579683 & -7.7953954579683 \tabularnewline
19 & 67.5 & 89.2631770919926 & -21.7631770919926 \tabularnewline
20 & 63.7 & 92.7839193104483 & -29.0839193104483 \tabularnewline
21 & 59.4 & 91.3279517112282 & -31.9279517112282 \tabularnewline
22 & 62 & 93.7640569533147 & -31.7640569533147 \tabularnewline
23 & 62.4 & 93.5260792769522 & -31.1260792769522 \tabularnewline
24 & 58.1 & 94.9590484214792 & -36.8590484214792 \tabularnewline
25 & 58 & 96.8447912606363 & -38.8447912606363 \tabularnewline
26 & 56.3 & 94.9569054251006 & -38.6569054251006 \tabularnewline
27 & 61.4 & 90.819721624944 & -29.4197216249440 \tabularnewline
28 & 59.8 & 87.8617292734322 & -28.0617292734322 \tabularnewline
29 & 54.3 & 86.314080440707 & -32.014080440707 \tabularnewline
30 & 47 & 80.4140939073591 & -33.4140939073591 \tabularnewline
31 & 50.5 & 93.4633076753063 & -42.9633076753063 \tabularnewline
32 & 48.1 & 91.575667351629 & -43.475667351629 \tabularnewline
33 & 58.8 & 90.2595155751762 & -31.4595155751762 \tabularnewline
34 & 70.4 & 92.7476454583751 & -22.3476454583751 \tabularnewline
35 & 71.9 & 95.170037009515 & -23.270037009515 \tabularnewline
36 & 73.3 & 96.1035408124506 & -22.8035408124506 \tabularnewline
37 & 83.5 & 97.5635901716008 & -14.0635901716008 \tabularnewline
38 & 90.1 & 95.5943399641415 & -5.49433996414148 \tabularnewline
39 & 101.3 & 93.0865638437968 & 8.2134361562032 \tabularnewline
40 & 98.3 & 88.0931310014309 & 10.2068689985691 \tabularnewline
41 & 106.7 & 84.7629457144882 & 21.9370542855118 \tabularnewline
42 & 109.9 & 82.2758179940267 & 27.6241820059733 \tabularnewline
43 & 111.1 & 95.9859752762085 & 15.1140247237915 \tabularnewline
44 & 119 & 95.1478461455247 & 23.8521538544753 \tabularnewline
45 & 120.7 & 93.1945759062183 & 27.5054240937816 \tabularnewline
46 & 104.5 & 95.5292607647982 & 8.97073923520178 \tabularnewline
47 & 121.6 & 99.0594158179136 & 22.5405841820863 \tabularnewline
48 & 129.6 & 98.3597358498266 & 31.2402641501734 \tabularnewline
49 & 124.5 & 98.1235734804263 & 26.3764265195737 \tabularnewline
50 & 130.1 & 98.0436573360269 & 32.0563426639731 \tabularnewline
51 & 142.3 & 94.2240150905146 & 48.0759849094854 \tabularnewline
52 & 140 & 91.6661329125765 & 48.3338670874235 \tabularnewline
53 & 143.3 & 86.316020671304 & 56.9839793286961 \tabularnewline
54 & 113.4 & 83.5941042704958 & 29.8058957295043 \tabularnewline
55 & 113.8 & 95.0646168868046 & 18.7353831131954 \tabularnewline
56 & 120.7 & 92.3023464427594 & 28.3976535572406 \tabularnewline
57 & 112.9 & 90.7750294390264 & 22.1249705609737 \tabularnewline
58 & 115.5 & 95.4817137024417 & 20.0182862975583 \tabularnewline
59 & 121.9 & 98.6060230920803 & 23.2939769079197 \tabularnewline
60 & 119.3 & 97.4289085734406 & 21.8710914265594 \tabularnewline
61 & 111 & 99.2694422037137 & 11.7305577962863 \tabularnewline
62 & 114.2 & 98.081172894224 & 16.1188271057760 \tabularnewline
63 & 113.5 & 93.7557639889007 & 19.7442360110993 \tabularnewline
64 & 94 & 91.3600451507558 & 2.63995484924417 \tabularnewline
65 & 83.2 & 86.2730402179489 & -3.07304021794885 \tabularnewline
66 & 82.8 & 84.9892884493454 & -2.18928844934544 \tabularnewline
67 & 85.8 & 93.9708365960246 & -8.17083659602456 \tabularnewline
68 & 88.7 & 96.1364101934678 & -7.43641019346775 \tabularnewline
69 & 105.3 & 95.890582861447 & 9.40941713855305 \tabularnewline
70 & 113.1 & 99.6317844536767 & 13.4682155463233 \tabularnewline
71 & 113.8 & 95.3404650831231 & 18.4595349168769 \tabularnewline
72 & 109.4 & 94.3062173727769 & 15.0937826272231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4420&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]85.6[/C][C]100.903779444029[/C][C]-15.3037794440286[/C][/ROW]
[ROW][C]2[/C][C]89[/C][C]99.9796480742283[/C][C]-10.9796480742283[/C][/ROW]
[ROW][C]3[/C][C]97.5[/C][C]94.3124166034401[/C][C]3.18758339655989[/C][/ROW]
[ROW][C]4[/C][C]104[/C][C]92.7669836742388[/C][C]11.2330163257612[/C][/ROW]
[ROW][C]5[/C][C]99.4[/C][C]89.9064325937261[/C][C]9.4935674062739[/C][/ROW]
[ROW][C]6[/C][C]103.2[/C][C]84.7923699374314[/C][C]18.4076300625686[/C][/ROW]
[ROW][C]7[/C][C]103[/C][C]87.7093282360578[/C][C]15.2906717639422[/C][/ROW]
[ROW][C]8[/C][C]91.2[/C][C]93.1509758040077[/C][C]-1.95097580400765[/C][/ROW]
[ROW][C]9[/C][C]85.9[/C][C]92.5505360005159[/C][C]-6.65053600051587[/C][/ROW]
[ROW][C]10[/C][C]80.7[/C][C]94.1312074332206[/C][C]-13.4312074332205[/C][/ROW]
[ROW][C]11[/C][C]86.7[/C][C]94.9537496770423[/C][C]-8.25374967704227[/C][/ROW]
[ROW][C]12[/C][C]80.7[/C][C]97.5549310573292[/C][C]-16.8549310573292[/C][/ROW]
[ROW][C]13[/C][C]81.5[/C][C]101.351940997572[/C][C]-19.851940997572[/C][/ROW]
[ROW][C]14[/C][C]83.4[/C][C]96.2824253609686[/C][C]-12.8824253609686[/C][/ROW]
[ROW][C]15[/C][C]83.5[/C][C]94.364807754812[/C][C]-10.8648077548119[/C][/ROW]
[ROW][C]16[/C][C]89.5[/C][C]89.9455558317093[/C][C]-0.445555831709287[/C][/ROW]
[ROW][C]17[/C][C]85.8[/C][C]88.4078576683805[/C][C]-2.60785766838047[/C][/ROW]
[ROW][C]18[/C][C]77.4[/C][C]85.1953954579683[/C][C]-7.7953954579683[/C][/ROW]
[ROW][C]19[/C][C]67.5[/C][C]89.2631770919926[/C][C]-21.7631770919926[/C][/ROW]
[ROW][C]20[/C][C]63.7[/C][C]92.7839193104483[/C][C]-29.0839193104483[/C][/ROW]
[ROW][C]21[/C][C]59.4[/C][C]91.3279517112282[/C][C]-31.9279517112282[/C][/ROW]
[ROW][C]22[/C][C]62[/C][C]93.7640569533147[/C][C]-31.7640569533147[/C][/ROW]
[ROW][C]23[/C][C]62.4[/C][C]93.5260792769522[/C][C]-31.1260792769522[/C][/ROW]
[ROW][C]24[/C][C]58.1[/C][C]94.9590484214792[/C][C]-36.8590484214792[/C][/ROW]
[ROW][C]25[/C][C]58[/C][C]96.8447912606363[/C][C]-38.8447912606363[/C][/ROW]
[ROW][C]26[/C][C]56.3[/C][C]94.9569054251006[/C][C]-38.6569054251006[/C][/ROW]
[ROW][C]27[/C][C]61.4[/C][C]90.819721624944[/C][C]-29.4197216249440[/C][/ROW]
[ROW][C]28[/C][C]59.8[/C][C]87.8617292734322[/C][C]-28.0617292734322[/C][/ROW]
[ROW][C]29[/C][C]54.3[/C][C]86.314080440707[/C][C]-32.014080440707[/C][/ROW]
[ROW][C]30[/C][C]47[/C][C]80.4140939073591[/C][C]-33.4140939073591[/C][/ROW]
[ROW][C]31[/C][C]50.5[/C][C]93.4633076753063[/C][C]-42.9633076753063[/C][/ROW]
[ROW][C]32[/C][C]48.1[/C][C]91.575667351629[/C][C]-43.475667351629[/C][/ROW]
[ROW][C]33[/C][C]58.8[/C][C]90.2595155751762[/C][C]-31.4595155751762[/C][/ROW]
[ROW][C]34[/C][C]70.4[/C][C]92.7476454583751[/C][C]-22.3476454583751[/C][/ROW]
[ROW][C]35[/C][C]71.9[/C][C]95.170037009515[/C][C]-23.270037009515[/C][/ROW]
[ROW][C]36[/C][C]73.3[/C][C]96.1035408124506[/C][C]-22.8035408124506[/C][/ROW]
[ROW][C]37[/C][C]83.5[/C][C]97.5635901716008[/C][C]-14.0635901716008[/C][/ROW]
[ROW][C]38[/C][C]90.1[/C][C]95.5943399641415[/C][C]-5.49433996414148[/C][/ROW]
[ROW][C]39[/C][C]101.3[/C][C]93.0865638437968[/C][C]8.2134361562032[/C][/ROW]
[ROW][C]40[/C][C]98.3[/C][C]88.0931310014309[/C][C]10.2068689985691[/C][/ROW]
[ROW][C]41[/C][C]106.7[/C][C]84.7629457144882[/C][C]21.9370542855118[/C][/ROW]
[ROW][C]42[/C][C]109.9[/C][C]82.2758179940267[/C][C]27.6241820059733[/C][/ROW]
[ROW][C]43[/C][C]111.1[/C][C]95.9859752762085[/C][C]15.1140247237915[/C][/ROW]
[ROW][C]44[/C][C]119[/C][C]95.1478461455247[/C][C]23.8521538544753[/C][/ROW]
[ROW][C]45[/C][C]120.7[/C][C]93.1945759062183[/C][C]27.5054240937816[/C][/ROW]
[ROW][C]46[/C][C]104.5[/C][C]95.5292607647982[/C][C]8.97073923520178[/C][/ROW]
[ROW][C]47[/C][C]121.6[/C][C]99.0594158179136[/C][C]22.5405841820863[/C][/ROW]
[ROW][C]48[/C][C]129.6[/C][C]98.3597358498266[/C][C]31.2402641501734[/C][/ROW]
[ROW][C]49[/C][C]124.5[/C][C]98.1235734804263[/C][C]26.3764265195737[/C][/ROW]
[ROW][C]50[/C][C]130.1[/C][C]98.0436573360269[/C][C]32.0563426639731[/C][/ROW]
[ROW][C]51[/C][C]142.3[/C][C]94.2240150905146[/C][C]48.0759849094854[/C][/ROW]
[ROW][C]52[/C][C]140[/C][C]91.6661329125765[/C][C]48.3338670874235[/C][/ROW]
[ROW][C]53[/C][C]143.3[/C][C]86.316020671304[/C][C]56.9839793286961[/C][/ROW]
[ROW][C]54[/C][C]113.4[/C][C]83.5941042704958[/C][C]29.8058957295043[/C][/ROW]
[ROW][C]55[/C][C]113.8[/C][C]95.0646168868046[/C][C]18.7353831131954[/C][/ROW]
[ROW][C]56[/C][C]120.7[/C][C]92.3023464427594[/C][C]28.3976535572406[/C][/ROW]
[ROW][C]57[/C][C]112.9[/C][C]90.7750294390264[/C][C]22.1249705609737[/C][/ROW]
[ROW][C]58[/C][C]115.5[/C][C]95.4817137024417[/C][C]20.0182862975583[/C][/ROW]
[ROW][C]59[/C][C]121.9[/C][C]98.6060230920803[/C][C]23.2939769079197[/C][/ROW]
[ROW][C]60[/C][C]119.3[/C][C]97.4289085734406[/C][C]21.8710914265594[/C][/ROW]
[ROW][C]61[/C][C]111[/C][C]99.2694422037137[/C][C]11.7305577962863[/C][/ROW]
[ROW][C]62[/C][C]114.2[/C][C]98.081172894224[/C][C]16.1188271057760[/C][/ROW]
[ROW][C]63[/C][C]113.5[/C][C]93.7557639889007[/C][C]19.7442360110993[/C][/ROW]
[ROW][C]64[/C][C]94[/C][C]91.3600451507558[/C][C]2.63995484924417[/C][/ROW]
[ROW][C]65[/C][C]83.2[/C][C]86.2730402179489[/C][C]-3.07304021794885[/C][/ROW]
[ROW][C]66[/C][C]82.8[/C][C]84.9892884493454[/C][C]-2.18928844934544[/C][/ROW]
[ROW][C]67[/C][C]85.8[/C][C]93.9708365960246[/C][C]-8.17083659602456[/C][/ROW]
[ROW][C]68[/C][C]88.7[/C][C]96.1364101934678[/C][C]-7.43641019346775[/C][/ROW]
[ROW][C]69[/C][C]105.3[/C][C]95.890582861447[/C][C]9.40941713855305[/C][/ROW]
[ROW][C]70[/C][C]113.1[/C][C]99.6317844536767[/C][C]13.4682155463233[/C][/ROW]
[ROW][C]71[/C][C]113.8[/C][C]95.3404650831231[/C][C]18.4595349168769[/C][/ROW]
[ROW][C]72[/C][C]109.4[/C][C]94.3062173727769[/C][C]15.0937826272231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4420&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4420&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	85.6	100.903779444029	-15.3037794440286
2	89	99.9796480742283	-10.9796480742283
3	97.5	94.3124166034401	3.18758339655989
4	104	92.7669836742388	11.2330163257612
5	99.4	89.9064325937261	9.4935674062739
6	103.2	84.7923699374314	18.4076300625686
7	103	87.7093282360578	15.2906717639422
8	91.2	93.1509758040077	-1.95097580400765
9	85.9	92.5505360005159	-6.65053600051587
10	80.7	94.1312074332206	-13.4312074332205
11	86.7	94.9537496770423	-8.25374967704227
12	80.7	97.5549310573292	-16.8549310573292
13	81.5	101.351940997572	-19.851940997572
14	83.4	96.2824253609686	-12.8824253609686
15	83.5	94.364807754812	-10.8648077548119
16	89.5	89.9455558317093	-0.445555831709287
17	85.8	88.4078576683805	-2.60785766838047
18	77.4	85.1953954579683	-7.7953954579683
19	67.5	89.2631770919926	-21.7631770919926
20	63.7	92.7839193104483	-29.0839193104483
21	59.4	91.3279517112282	-31.9279517112282
22	62	93.7640569533147	-31.7640569533147
23	62.4	93.5260792769522	-31.1260792769522
24	58.1	94.9590484214792	-36.8590484214792
25	58	96.8447912606363	-38.8447912606363
26	56.3	94.9569054251006	-38.6569054251006
27	61.4	90.819721624944	-29.4197216249440
28	59.8	87.8617292734322	-28.0617292734322
29	54.3	86.314080440707	-32.014080440707
30	47	80.4140939073591	-33.4140939073591
31	50.5	93.4633076753063	-42.9633076753063
32	48.1	91.575667351629	-43.475667351629
33	58.8	90.2595155751762	-31.4595155751762
34	70.4	92.7476454583751	-22.3476454583751
35	71.9	95.170037009515	-23.270037009515
36	73.3	96.1035408124506	-22.8035408124506
37	83.5	97.5635901716008	-14.0635901716008
38	90.1	95.5943399641415	-5.49433996414148
39	101.3	93.0865638437968	8.2134361562032
40	98.3	88.0931310014309	10.2068689985691
41	106.7	84.7629457144882	21.9370542855118
42	109.9	82.2758179940267	27.6241820059733
43	111.1	95.9859752762085	15.1140247237915
44	119	95.1478461455247	23.8521538544753
45	120.7	93.1945759062183	27.5054240937816
46	104.5	95.5292607647982	8.97073923520178
47	121.6	99.0594158179136	22.5405841820863
48	129.6	98.3597358498266	31.2402641501734
49	124.5	98.1235734804263	26.3764265195737
50	130.1	98.0436573360269	32.0563426639731
51	142.3	94.2240150905146	48.0759849094854
52	140	91.6661329125765	48.3338670874235
53	143.3	86.316020671304	56.9839793286961
54	113.4	83.5941042704958	29.8058957295043
55	113.8	95.0646168868046	18.7353831131954
56	120.7	92.3023464427594	28.3976535572406
57	112.9	90.7750294390264	22.1249705609737
58	115.5	95.4817137024417	20.0182862975583
59	121.9	98.6060230920803	23.2939769079197
60	119.3	97.4289085734406	21.8710914265594
61	111	99.2694422037137	11.7305577962863
62	114.2	98.081172894224	16.1188271057760
63	113.5	93.7557639889007	19.7442360110993
64	94	91.3600451507558	2.63995484924417
65	83.2	86.2730402179489	-3.07304021794885
66	82.8	84.9892884493454	-2.18928844934544
67	85.8	93.9708365960246	-8.17083659602456
68	88.7	96.1364101934678	-7.43641019346775
69	105.3	95.890582861447	9.40941713855305
70	113.1	99.6317844536767	13.4682155463233
71	113.8	95.3404650831231	18.4595349168769
72	109.4	94.3062173727769	15.0937826272231

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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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