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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 18 Nov 2007 09:02:48 -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/18/t11954014147kb3e2i55bjtn7e.htm/, Retrieved Sun, 05 May 2024 01:03:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5593, Retrieved Sun, 05 May 2024 01:03:39 +0000

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User-defined keywords

Multiple Regression line

Estimated Impact

213

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

-       [Multiple Regression] [Workshop 6 Q3] [2007-11-18 16:02:48] [a2659e9a411aa0bcc5ca303430cc5df1] [Current]

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100,6	115,9	59,7
96,1	112,9	58,2
110	126,3	75,3
108,2	116,8	69
106,9	112	66,1
117,2	129,7	77,5
105,2	113,6	69,3
106,3	115,7	70,2
95,9	119,5	70,2
107,5	125,8	78,2
113	129,6	85,4
111,4	128	82,4
95,5	112,8	61,2
90,3	101,6	52,2
110,8	123,9	85,3
107,1	118,8	79,9
101,4	109,1	72,2
112,9	130,6	85,7
98,5	112,4	75,5
100,1	111	69,2
93,4	116,2	77,6
104,4	119,8	85,3
101,8	117,2	77
107,9	127,3	89,9
91,3	107,7	60
86,6	97,5	54,3
111,4	120,1	84
98,4	110,6	69,9
102,2	111,3	75,1
103	119,8	81,7
95,8	105,5	69,9
96	108,7	68,3
95,7	128,7	77,3
106,4	119,5	77,4
112	121,1	85,3
116,2	128,4	91
93,9	108,8	60,6
100,5	107,5	57,6
112,5	125,6	93,8
101,2	102,9	78,7
107,8	107,5	80,3
114,3	120,4	89,8
99,6	104,3	77,5
98,6	100,6	71,7
93,6	121,9	83,2
99,6	112,7	86,2
113,1	124,9	100,7
110,7	123,9	100,8
88,1	102,2	57,1
93,1	104,9	62,5
107,4	109,8	79,7
99,5	98,9	80,3
105,6	107,3	92,4
108,3	112,6	91,8
99,2	104	85,8
99,3	110,6	84,2
107,1	100,8	93,1
106,9	103,8	101,2
115,4	117	100,6
99	108,4	106,7
100,1	95,5	64
96,2	96,9	67,5
96,9	103,9	101
96,2	101,1	95,5
91	100,6	97
99	104,3	103,8
99	98	95,2
107,2	99,5	86,7
110,8	97,4	93,5
111,1	105,6	102,5
104,6	117,5	112,3
94,3	107,4	105,5
90,7	97,8	75,4
88,8	91,5	70,4
90,9	107,7	108
90,5	100,1	100
95,5	96,6	93,3
103,1	106,8	111,1
100,6	98	101,1
103,1	98,6	98,1

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=5593&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=5593&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5593&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
Int[t] = + 39.8313765615007 + 0.443260583766398Cons[t] + 0.157433989020551Duurzcons[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Int[t] =  +  39.8313765615007 +  0.443260583766398Cons[t] +  0.157433989020551Duurzcons[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5593&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Int[t] =  +  39.8313765615007 +  0.443260583766398Cons[t] +  0.157433989020551Duurzcons[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5593&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5593&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
Int[t] = + 39.8313765615007 + 0.443260583766398Cons[t] + 0.157433989020551Duurzcons[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)	39.8313765615007	7.695576	5.1759	2e-06	1e-06
Cons	0.443260583766398	0.062715	7.0679	0	0
Duurzcons	0.157433989020551	0.042671	3.6895	0.000417	0.000209

\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) & 39.8313765615007 & 7.695576 & 5.1759 & 2e-06 & 1e-06 \tabularnewline
Cons & 0.443260583766398 & 0.062715 & 7.0679 & 0 & 0 \tabularnewline
Duurzcons & 0.157433989020551 & 0.042671 & 3.6895 & 0.000417 & 0.000209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5593&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]39.8313765615007[/C][C]7.695576[/C][C]5.1759[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]Cons[/C][C]0.443260583766398[/C][C]0.062715[/C][C]7.0679[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Duurzcons[/C][C]0.157433989020551[/C][C]0.042671[/C][C]3.6895[/C][C]0.000417[/C][C]0.000209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5593&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5593&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)	39.8313765615007	7.695576	5.1759	2e-06	1e-06
Cons	0.443260583766398	0.062715	7.0679	0	0
Duurzcons	0.157433989020551	0.042671	3.6895	0.000417	0.000209

Multiple Linear Regression - Regression Statistics
Multiple R	0.678910073141829
R-squared	0.460918887413444
Adjusted R-squared	0.446916780593014
F-TEST (value)	32.9178239621006
F-TEST (DF numerator)	2
F-TEST (DF denominator)	77
p-value	4.66319205472132e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.60341382082505
Sum Squared Residuals	2417.66497645081

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.678910073141829 \tabularnewline
R-squared & 0.460918887413444 \tabularnewline
Adjusted R-squared & 0.446916780593014 \tabularnewline
F-TEST (value) & 32.9178239621006 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 77 \tabularnewline
p-value & 4.66319205472132e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.60341382082505 \tabularnewline
Sum Squared Residuals & 2417.66497645081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5593&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.678910073141829[/C][/ROW]
[ROW][C]R-squared[/C][C]0.460918887413444[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.446916780593014[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]32.9178239621006[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]77[/C][/ROW]
[ROW][C]p-value[/C][C]4.66319205472132e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.60341382082505[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2417.66497645081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5593&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5593&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	0.678910073141829
R-squared	0.460918887413444
Adjusted R-squared	0.446916780593014
F-TEST (value)	32.9178239621006
F-TEST (DF numerator)	2
F-TEST (DF denominator)	77
p-value	4.66319205472132e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.60341382082505
Sum Squared Residuals	2417.66497645081

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	100.6	100.604087364553	-0.00408736455320509
2	96.1	99.0381546297231	-2.93815462972312
3	110	107.669967664444	2.33003233555573
4	108.2	102.467157987834	5.73284201216599
5	106.9	99.8829486175957	7.0170513824043
6	117.2	109.523408425095	7.67659157490478
7	105.2	101.095954316488	4.10404568351230
8	106.3	102.168492132516	4.13150786748436
9	95.9	103.852882350828	-7.95288235082795
10	107.5	107.904895940721	-0.404895940720662
11	113	110.722810879981	2.27718912001906
12	111.4	109.541291978893	1.85870802110695
13	95.5	99.4661305384081	-3.96613053840813
14	90.3	93.0847060990395	-2.78470609903952
15	110.8	108.180482153610	2.61951784638958
16	107.1	105.069709635691	2.03029036430918
17	101.4	99.5578402576985	1.84215974230149
18	112.9	111.213301660453	1.68669833954650
19	98.5	101.540132347895	-3.04013234789545
20	100.1	99.927733399793	0.172266600206973
21	93.4	103.555133943151	-10.1551339431509
22	104.4	106.363113760168	-1.96311376016818
23	101.8	103.903934133505	-2.10393413350499
24	107.9	110.411764487911	-2.51176448791070
25	91.3	97.0165807743748	-5.71658077437485
26	86.6	91.5979490825405	-4.99794908254045
27	111.4	106.291427749571	5.10857225042862
28	98.4	99.8606329586008	-1.46063295860084
29	102.2	100.989572110144	1.21042788985582
30	103	105.796351399694	-2.79635139969420
31	95.8	97.6000039813922	-1.80000398139222
32	96	98.7665434670118	-2.76654346701181
33	95.7	109.048661043525	-13.3486610435247
34	106.4	104.986407071776	1.41359292822409
35	112	106.939352519064	5.0606474809355
36	116.2	111.072528517976	5.12747148202365
37	93.9	97.5986278099302	-3.69862780993020
38	100.5	96.5500870839722	3.94991291602776
39	112.5	110.272214052688	2.22778594731203
40	101.2	97.8329455669804	3.36705443301957
41	107.8	100.123838634739	7.67616136526125
42	114.3	107.337523061021	6.96247693897949
43	99.6	98.2645895974287	1.33541040257127
44	98.6	95.7114083011739	2.88859169882613
45	93.6	106.963349609134	-13.3633496091345
46	99.6	103.357654205545	-3.75765420554527
47	113.1	111.048226168293	2.05177383170669
48	110.7	110.620708983429	0.079291016571046
49	88.1	94.1220889955	-6.02208899550006
50	93.1	96.1690361123803	-3.06903611238031
51	107.4	101.048877583989	6.35112241601088
52	99.5	96.3117976143477	3.18820238565228
53	105.6	101.940137785134	3.65986221486587
54	108.3	104.194958485684	4.10504151431630
55	99.2	99.4383135311694	-0.238313531169377
56	99.3	102.111939001595	-2.81193900159472
57	107.1	99.169147782967	7.93085221703307
58	106.9	101.774144845333	5.12585515466743
59	115.4	107.530724157637	7.8692758423633
60	99	104.679030470271	-5.67903047027104
61	100.1	92.238537608507	7.861462391493
62	96.2	93.4101213873519	2.78987861264812
63	96.9	101.786984105905	-4.88698410590511
64	96.2	99.6799675317462	-3.47996753174616
65	91	99.6944882233938	-8.6944882233938
66	99	102.405103508669	-3.40510350866921
67	99	98.2586295253642	0.741370474635829
68	107.2	97.585331494339	9.61466850566092
69	110.8	97.7250353937694	13.0749646062306
70	111.1	102.776678081839	8.32332191816118
71	104.6	109.594332121060	-4.99433212106035
72	94.3	104.04684909968	-9.74684909967999
73	90.7	95.052784426004	-4.35278442600398
74	88.8	91.473072803173	-2.67307280317293
75	90.9	104.573412247361	-13.6734122473613
76	90.5	99.9451598985722	-9.44515989857225
77	95.5	97.3389401289522	-1.83894012895216
78	103.1	104.662523087935	-1.56252308793523
79	100.6	99.1874900605854	1.41250993941458
80	103.1	98.9811444437836	4.11885555621639

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 100.6 & 100.604087364553 & -0.00408736455320509 \tabularnewline
2 & 96.1 & 99.0381546297231 & -2.93815462972312 \tabularnewline
3 & 110 & 107.669967664444 & 2.33003233555573 \tabularnewline
4 & 108.2 & 102.467157987834 & 5.73284201216599 \tabularnewline
5 & 106.9 & 99.8829486175957 & 7.0170513824043 \tabularnewline
6 & 117.2 & 109.523408425095 & 7.67659157490478 \tabularnewline
7 & 105.2 & 101.095954316488 & 4.10404568351230 \tabularnewline
8 & 106.3 & 102.168492132516 & 4.13150786748436 \tabularnewline
9 & 95.9 & 103.852882350828 & -7.95288235082795 \tabularnewline
10 & 107.5 & 107.904895940721 & -0.404895940720662 \tabularnewline
11 & 113 & 110.722810879981 & 2.27718912001906 \tabularnewline
12 & 111.4 & 109.541291978893 & 1.85870802110695 \tabularnewline
13 & 95.5 & 99.4661305384081 & -3.96613053840813 \tabularnewline
14 & 90.3 & 93.0847060990395 & -2.78470609903952 \tabularnewline
15 & 110.8 & 108.180482153610 & 2.61951784638958 \tabularnewline
16 & 107.1 & 105.069709635691 & 2.03029036430918 \tabularnewline
17 & 101.4 & 99.5578402576985 & 1.84215974230149 \tabularnewline
18 & 112.9 & 111.213301660453 & 1.68669833954650 \tabularnewline
19 & 98.5 & 101.540132347895 & -3.04013234789545 \tabularnewline
20 & 100.1 & 99.927733399793 & 0.172266600206973 \tabularnewline
21 & 93.4 & 103.555133943151 & -10.1551339431509 \tabularnewline
22 & 104.4 & 106.363113760168 & -1.96311376016818 \tabularnewline
23 & 101.8 & 103.903934133505 & -2.10393413350499 \tabularnewline
24 & 107.9 & 110.411764487911 & -2.51176448791070 \tabularnewline
25 & 91.3 & 97.0165807743748 & -5.71658077437485 \tabularnewline
26 & 86.6 & 91.5979490825405 & -4.99794908254045 \tabularnewline
27 & 111.4 & 106.291427749571 & 5.10857225042862 \tabularnewline
28 & 98.4 & 99.8606329586008 & -1.46063295860084 \tabularnewline
29 & 102.2 & 100.989572110144 & 1.21042788985582 \tabularnewline
30 & 103 & 105.796351399694 & -2.79635139969420 \tabularnewline
31 & 95.8 & 97.6000039813922 & -1.80000398139222 \tabularnewline
32 & 96 & 98.7665434670118 & -2.76654346701181 \tabularnewline
33 & 95.7 & 109.048661043525 & -13.3486610435247 \tabularnewline
34 & 106.4 & 104.986407071776 & 1.41359292822409 \tabularnewline
35 & 112 & 106.939352519064 & 5.0606474809355 \tabularnewline
36 & 116.2 & 111.072528517976 & 5.12747148202365 \tabularnewline
37 & 93.9 & 97.5986278099302 & -3.69862780993020 \tabularnewline
38 & 100.5 & 96.5500870839722 & 3.94991291602776 \tabularnewline
39 & 112.5 & 110.272214052688 & 2.22778594731203 \tabularnewline
40 & 101.2 & 97.8329455669804 & 3.36705443301957 \tabularnewline
41 & 107.8 & 100.123838634739 & 7.67616136526125 \tabularnewline
42 & 114.3 & 107.337523061021 & 6.96247693897949 \tabularnewline
43 & 99.6 & 98.2645895974287 & 1.33541040257127 \tabularnewline
44 & 98.6 & 95.7114083011739 & 2.88859169882613 \tabularnewline
45 & 93.6 & 106.963349609134 & -13.3633496091345 \tabularnewline
46 & 99.6 & 103.357654205545 & -3.75765420554527 \tabularnewline
47 & 113.1 & 111.048226168293 & 2.05177383170669 \tabularnewline
48 & 110.7 & 110.620708983429 & 0.079291016571046 \tabularnewline
49 & 88.1 & 94.1220889955 & -6.02208899550006 \tabularnewline
50 & 93.1 & 96.1690361123803 & -3.06903611238031 \tabularnewline
51 & 107.4 & 101.048877583989 & 6.35112241601088 \tabularnewline
52 & 99.5 & 96.3117976143477 & 3.18820238565228 \tabularnewline
53 & 105.6 & 101.940137785134 & 3.65986221486587 \tabularnewline
54 & 108.3 & 104.194958485684 & 4.10504151431630 \tabularnewline
55 & 99.2 & 99.4383135311694 & -0.238313531169377 \tabularnewline
56 & 99.3 & 102.111939001595 & -2.81193900159472 \tabularnewline
57 & 107.1 & 99.169147782967 & 7.93085221703307 \tabularnewline
58 & 106.9 & 101.774144845333 & 5.12585515466743 \tabularnewline
59 & 115.4 & 107.530724157637 & 7.8692758423633 \tabularnewline
60 & 99 & 104.679030470271 & -5.67903047027104 \tabularnewline
61 & 100.1 & 92.238537608507 & 7.861462391493 \tabularnewline
62 & 96.2 & 93.4101213873519 & 2.78987861264812 \tabularnewline
63 & 96.9 & 101.786984105905 & -4.88698410590511 \tabularnewline
64 & 96.2 & 99.6799675317462 & -3.47996753174616 \tabularnewline
65 & 91 & 99.6944882233938 & -8.6944882233938 \tabularnewline
66 & 99 & 102.405103508669 & -3.40510350866921 \tabularnewline
67 & 99 & 98.2586295253642 & 0.741370474635829 \tabularnewline
68 & 107.2 & 97.585331494339 & 9.61466850566092 \tabularnewline
69 & 110.8 & 97.7250353937694 & 13.0749646062306 \tabularnewline
70 & 111.1 & 102.776678081839 & 8.32332191816118 \tabularnewline
71 & 104.6 & 109.594332121060 & -4.99433212106035 \tabularnewline
72 & 94.3 & 104.04684909968 & -9.74684909967999 \tabularnewline
73 & 90.7 & 95.052784426004 & -4.35278442600398 \tabularnewline
74 & 88.8 & 91.473072803173 & -2.67307280317293 \tabularnewline
75 & 90.9 & 104.573412247361 & -13.6734122473613 \tabularnewline
76 & 90.5 & 99.9451598985722 & -9.44515989857225 \tabularnewline
77 & 95.5 & 97.3389401289522 & -1.83894012895216 \tabularnewline
78 & 103.1 & 104.662523087935 & -1.56252308793523 \tabularnewline
79 & 100.6 & 99.1874900605854 & 1.41250993941458 \tabularnewline
80 & 103.1 & 98.9811444437836 & 4.11885555621639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5593&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]100.6[/C][C]100.604087364553[/C][C]-0.00408736455320509[/C][/ROW]
[ROW][C]2[/C][C]96.1[/C][C]99.0381546297231[/C][C]-2.93815462972312[/C][/ROW]
[ROW][C]3[/C][C]110[/C][C]107.669967664444[/C][C]2.33003233555573[/C][/ROW]
[ROW][C]4[/C][C]108.2[/C][C]102.467157987834[/C][C]5.73284201216599[/C][/ROW]
[ROW][C]5[/C][C]106.9[/C][C]99.8829486175957[/C][C]7.0170513824043[/C][/ROW]
[ROW][C]6[/C][C]117.2[/C][C]109.523408425095[/C][C]7.67659157490478[/C][/ROW]
[ROW][C]7[/C][C]105.2[/C][C]101.095954316488[/C][C]4.10404568351230[/C][/ROW]
[ROW][C]8[/C][C]106.3[/C][C]102.168492132516[/C][C]4.13150786748436[/C][/ROW]
[ROW][C]9[/C][C]95.9[/C][C]103.852882350828[/C][C]-7.95288235082795[/C][/ROW]
[ROW][C]10[/C][C]107.5[/C][C]107.904895940721[/C][C]-0.404895940720662[/C][/ROW]
[ROW][C]11[/C][C]113[/C][C]110.722810879981[/C][C]2.27718912001906[/C][/ROW]
[ROW][C]12[/C][C]111.4[/C][C]109.541291978893[/C][C]1.85870802110695[/C][/ROW]
[ROW][C]13[/C][C]95.5[/C][C]99.4661305384081[/C][C]-3.96613053840813[/C][/ROW]
[ROW][C]14[/C][C]90.3[/C][C]93.0847060990395[/C][C]-2.78470609903952[/C][/ROW]
[ROW][C]15[/C][C]110.8[/C][C]108.180482153610[/C][C]2.61951784638958[/C][/ROW]
[ROW][C]16[/C][C]107.1[/C][C]105.069709635691[/C][C]2.03029036430918[/C][/ROW]
[ROW][C]17[/C][C]101.4[/C][C]99.5578402576985[/C][C]1.84215974230149[/C][/ROW]
[ROW][C]18[/C][C]112.9[/C][C]111.213301660453[/C][C]1.68669833954650[/C][/ROW]
[ROW][C]19[/C][C]98.5[/C][C]101.540132347895[/C][C]-3.04013234789545[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]99.927733399793[/C][C]0.172266600206973[/C][/ROW]
[ROW][C]21[/C][C]93.4[/C][C]103.555133943151[/C][C]-10.1551339431509[/C][/ROW]
[ROW][C]22[/C][C]104.4[/C][C]106.363113760168[/C][C]-1.96311376016818[/C][/ROW]
[ROW][C]23[/C][C]101.8[/C][C]103.903934133505[/C][C]-2.10393413350499[/C][/ROW]
[ROW][C]24[/C][C]107.9[/C][C]110.411764487911[/C][C]-2.51176448791070[/C][/ROW]
[ROW][C]25[/C][C]91.3[/C][C]97.0165807743748[/C][C]-5.71658077437485[/C][/ROW]
[ROW][C]26[/C][C]86.6[/C][C]91.5979490825405[/C][C]-4.99794908254045[/C][/ROW]
[ROW][C]27[/C][C]111.4[/C][C]106.291427749571[/C][C]5.10857225042862[/C][/ROW]
[ROW][C]28[/C][C]98.4[/C][C]99.8606329586008[/C][C]-1.46063295860084[/C][/ROW]
[ROW][C]29[/C][C]102.2[/C][C]100.989572110144[/C][C]1.21042788985582[/C][/ROW]
[ROW][C]30[/C][C]103[/C][C]105.796351399694[/C][C]-2.79635139969420[/C][/ROW]
[ROW][C]31[/C][C]95.8[/C][C]97.6000039813922[/C][C]-1.80000398139222[/C][/ROW]
[ROW][C]32[/C][C]96[/C][C]98.7665434670118[/C][C]-2.76654346701181[/C][/ROW]
[ROW][C]33[/C][C]95.7[/C][C]109.048661043525[/C][C]-13.3486610435247[/C][/ROW]
[ROW][C]34[/C][C]106.4[/C][C]104.986407071776[/C][C]1.41359292822409[/C][/ROW]
[ROW][C]35[/C][C]112[/C][C]106.939352519064[/C][C]5.0606474809355[/C][/ROW]
[ROW][C]36[/C][C]116.2[/C][C]111.072528517976[/C][C]5.12747148202365[/C][/ROW]
[ROW][C]37[/C][C]93.9[/C][C]97.5986278099302[/C][C]-3.69862780993020[/C][/ROW]
[ROW][C]38[/C][C]100.5[/C][C]96.5500870839722[/C][C]3.94991291602776[/C][/ROW]
[ROW][C]39[/C][C]112.5[/C][C]110.272214052688[/C][C]2.22778594731203[/C][/ROW]
[ROW][C]40[/C][C]101.2[/C][C]97.8329455669804[/C][C]3.36705443301957[/C][/ROW]
[ROW][C]41[/C][C]107.8[/C][C]100.123838634739[/C][C]7.67616136526125[/C][/ROW]
[ROW][C]42[/C][C]114.3[/C][C]107.337523061021[/C][C]6.96247693897949[/C][/ROW]
[ROW][C]43[/C][C]99.6[/C][C]98.2645895974287[/C][C]1.33541040257127[/C][/ROW]
[ROW][C]44[/C][C]98.6[/C][C]95.7114083011739[/C][C]2.88859169882613[/C][/ROW]
[ROW][C]45[/C][C]93.6[/C][C]106.963349609134[/C][C]-13.3633496091345[/C][/ROW]
[ROW][C]46[/C][C]99.6[/C][C]103.357654205545[/C][C]-3.75765420554527[/C][/ROW]
[ROW][C]47[/C][C]113.1[/C][C]111.048226168293[/C][C]2.05177383170669[/C][/ROW]
[ROW][C]48[/C][C]110.7[/C][C]110.620708983429[/C][C]0.079291016571046[/C][/ROW]
[ROW][C]49[/C][C]88.1[/C][C]94.1220889955[/C][C]-6.02208899550006[/C][/ROW]
[ROW][C]50[/C][C]93.1[/C][C]96.1690361123803[/C][C]-3.06903611238031[/C][/ROW]
[ROW][C]51[/C][C]107.4[/C][C]101.048877583989[/C][C]6.35112241601088[/C][/ROW]
[ROW][C]52[/C][C]99.5[/C][C]96.3117976143477[/C][C]3.18820238565228[/C][/ROW]
[ROW][C]53[/C][C]105.6[/C][C]101.940137785134[/C][C]3.65986221486587[/C][/ROW]
[ROW][C]54[/C][C]108.3[/C][C]104.194958485684[/C][C]4.10504151431630[/C][/ROW]
[ROW][C]55[/C][C]99.2[/C][C]99.4383135311694[/C][C]-0.238313531169377[/C][/ROW]
[ROW][C]56[/C][C]99.3[/C][C]102.111939001595[/C][C]-2.81193900159472[/C][/ROW]
[ROW][C]57[/C][C]107.1[/C][C]99.169147782967[/C][C]7.93085221703307[/C][/ROW]
[ROW][C]58[/C][C]106.9[/C][C]101.774144845333[/C][C]5.12585515466743[/C][/ROW]
[ROW][C]59[/C][C]115.4[/C][C]107.530724157637[/C][C]7.8692758423633[/C][/ROW]
[ROW][C]60[/C][C]99[/C][C]104.679030470271[/C][C]-5.67903047027104[/C][/ROW]
[ROW][C]61[/C][C]100.1[/C][C]92.238537608507[/C][C]7.861462391493[/C][/ROW]
[ROW][C]62[/C][C]96.2[/C][C]93.4101213873519[/C][C]2.78987861264812[/C][/ROW]
[ROW][C]63[/C][C]96.9[/C][C]101.786984105905[/C][C]-4.88698410590511[/C][/ROW]
[ROW][C]64[/C][C]96.2[/C][C]99.6799675317462[/C][C]-3.47996753174616[/C][/ROW]
[ROW][C]65[/C][C]91[/C][C]99.6944882233938[/C][C]-8.6944882233938[/C][/ROW]
[ROW][C]66[/C][C]99[/C][C]102.405103508669[/C][C]-3.40510350866921[/C][/ROW]
[ROW][C]67[/C][C]99[/C][C]98.2586295253642[/C][C]0.741370474635829[/C][/ROW]
[ROW][C]68[/C][C]107.2[/C][C]97.585331494339[/C][C]9.61466850566092[/C][/ROW]
[ROW][C]69[/C][C]110.8[/C][C]97.7250353937694[/C][C]13.0749646062306[/C][/ROW]
[ROW][C]70[/C][C]111.1[/C][C]102.776678081839[/C][C]8.32332191816118[/C][/ROW]
[ROW][C]71[/C][C]104.6[/C][C]109.594332121060[/C][C]-4.99433212106035[/C][/ROW]
[ROW][C]72[/C][C]94.3[/C][C]104.04684909968[/C][C]-9.74684909967999[/C][/ROW]
[ROW][C]73[/C][C]90.7[/C][C]95.052784426004[/C][C]-4.35278442600398[/C][/ROW]
[ROW][C]74[/C][C]88.8[/C][C]91.473072803173[/C][C]-2.67307280317293[/C][/ROW]
[ROW][C]75[/C][C]90.9[/C][C]104.573412247361[/C][C]-13.6734122473613[/C][/ROW]
[ROW][C]76[/C][C]90.5[/C][C]99.9451598985722[/C][C]-9.44515989857225[/C][/ROW]
[ROW][C]77[/C][C]95.5[/C][C]97.3389401289522[/C][C]-1.83894012895216[/C][/ROW]
[ROW][C]78[/C][C]103.1[/C][C]104.662523087935[/C][C]-1.56252308793523[/C][/ROW]
[ROW][C]79[/C][C]100.6[/C][C]99.1874900605854[/C][C]1.41250993941458[/C][/ROW]
[ROW][C]80[/C][C]103.1[/C][C]98.9811444437836[/C][C]4.11885555621639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5593&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5593&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	100.6	100.604087364553	-0.00408736455320509
2	96.1	99.0381546297231	-2.93815462972312
3	110	107.669967664444	2.33003233555573
4	108.2	102.467157987834	5.73284201216599
5	106.9	99.8829486175957	7.0170513824043
6	117.2	109.523408425095	7.67659157490478
7	105.2	101.095954316488	4.10404568351230
8	106.3	102.168492132516	4.13150786748436
9	95.9	103.852882350828	-7.95288235082795
10	107.5	107.904895940721	-0.404895940720662
11	113	110.722810879981	2.27718912001906
12	111.4	109.541291978893	1.85870802110695
13	95.5	99.4661305384081	-3.96613053840813
14	90.3	93.0847060990395	-2.78470609903952
15	110.8	108.180482153610	2.61951784638958
16	107.1	105.069709635691	2.03029036430918
17	101.4	99.5578402576985	1.84215974230149
18	112.9	111.213301660453	1.68669833954650
19	98.5	101.540132347895	-3.04013234789545
20	100.1	99.927733399793	0.172266600206973
21	93.4	103.555133943151	-10.1551339431509
22	104.4	106.363113760168	-1.96311376016818
23	101.8	103.903934133505	-2.10393413350499
24	107.9	110.411764487911	-2.51176448791070
25	91.3	97.0165807743748	-5.71658077437485
26	86.6	91.5979490825405	-4.99794908254045
27	111.4	106.291427749571	5.10857225042862
28	98.4	99.8606329586008	-1.46063295860084
29	102.2	100.989572110144	1.21042788985582
30	103	105.796351399694	-2.79635139969420
31	95.8	97.6000039813922	-1.80000398139222
32	96	98.7665434670118	-2.76654346701181
33	95.7	109.048661043525	-13.3486610435247
34	106.4	104.986407071776	1.41359292822409
35	112	106.939352519064	5.0606474809355
36	116.2	111.072528517976	5.12747148202365
37	93.9	97.5986278099302	-3.69862780993020
38	100.5	96.5500870839722	3.94991291602776
39	112.5	110.272214052688	2.22778594731203
40	101.2	97.8329455669804	3.36705443301957
41	107.8	100.123838634739	7.67616136526125
42	114.3	107.337523061021	6.96247693897949
43	99.6	98.2645895974287	1.33541040257127
44	98.6	95.7114083011739	2.88859169882613
45	93.6	106.963349609134	-13.3633496091345
46	99.6	103.357654205545	-3.75765420554527
47	113.1	111.048226168293	2.05177383170669
48	110.7	110.620708983429	0.079291016571046
49	88.1	94.1220889955	-6.02208899550006
50	93.1	96.1690361123803	-3.06903611238031
51	107.4	101.048877583989	6.35112241601088
52	99.5	96.3117976143477	3.18820238565228
53	105.6	101.940137785134	3.65986221486587
54	108.3	104.194958485684	4.10504151431630
55	99.2	99.4383135311694	-0.238313531169377
56	99.3	102.111939001595	-2.81193900159472
57	107.1	99.169147782967	7.93085221703307
58	106.9	101.774144845333	5.12585515466743
59	115.4	107.530724157637	7.8692758423633
60	99	104.679030470271	-5.67903047027104
61	100.1	92.238537608507	7.861462391493
62	96.2	93.4101213873519	2.78987861264812
63	96.9	101.786984105905	-4.88698410590511
64	96.2	99.6799675317462	-3.47996753174616
65	91	99.6944882233938	-8.6944882233938
66	99	102.405103508669	-3.40510350866921
67	99	98.2586295253642	0.741370474635829
68	107.2	97.585331494339	9.61466850566092
69	110.8	97.7250353937694	13.0749646062306
70	111.1	102.776678081839	8.32332191816118
71	104.6	109.594332121060	-4.99433212106035
72	94.3	104.04684909968	-9.74684909967999
73	90.7	95.052784426004	-4.35278442600398
74	88.8	91.473072803173	-2.67307280317293
75	90.9	104.573412247361	-13.6734122473613
76	90.5	99.9451598985722	-9.44515989857225
77	95.5	97.3389401289522	-1.83894012895216
78	103.1	104.662523087935	-1.56252308793523
79	100.6	99.1874900605854	1.41250993941458
80	103.1	98.9811444437836	4.11885555621639

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