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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 04 Dec 2007 08:10:23 -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/04/t1196781019jtp168vfdh4bcqq.htm/, Retrieved Wed, 01 May 2024 23:36:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2394, Retrieved Wed, 01 May 2024 23:36:53 +0000

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Paper regressie, alle variabelen

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222

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-       [Multiple Regression] [Paper] [2007-12-04 15:10:23] [3ab9003c9cd8f7bf2375584b9feecdee] [Current]

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106,7	97,3	0	104,8	93,5
110,2	101	0	105,6	94,7
125,9	113,2	0	118,3	112,9
100,1	101	0	89,9	99,2
106,4	105,7	0	90,2	105,6
114,8	113,9	0	107	113
81,3	86,4	0	64,5	83,1
87	96,5	0	92,6	81,1
104,2	103,3	0	95,8	96,9
108	114,9	0	94,3	104,3
105	105,8	0	91,2	97,7
94,5	94,2	0	86,3	102,6
92	98,4	0	77,6	89,9
95,9	99,4	0	82,5	96
108,8	108,8	0	97,7	112,7
103,4	112,6	0	83,3	107,1
102,1	104,4	0	84,2	106,2
110,1	112,2	0	92,8	121
83,2	81,1	0	77,4	101,2
82,7	97,1	0	72,5	83,2
106,8	112,6	0	88,8	105,1
113,7	113,8	0	93,4	113,3
102,5	107,8	0	92,6	99,1
96,6	103,2	0	90,7	100,3
92,1	103,3	0	81,6	93,5
95,6	101,2	0	84,1	98,8
102,3	107,7	0	88,1	106,2
98,6	110,4	0	85,3	98,3
98,2	101,9	0	82,9	102,1
104,5	115,9	0	84,8	117,1
84	89,9	0	71,2	101,5
73,8	88,6	0	68,9	80,5
103,9	117,2	0	94,3	105,9
106	123,9	0	97,6	109,5
97,2	100	0	85,6	97,2
102,6	103,6	0	91,9	114,5
89	94,1	0	75,8	93,5
93,8	98,7	0	79,8	100,9
116,7	119,5	0	99	121,1
106,8	112,7	0	88,5	116,5
98,5	104,4	0	86,7	109,3
118,7	124,7	0	97,9	118,1
90	89,1	0	94,3	108,3
91,9	97	0	72,9	105,4
113,3	121,6	0	91,8	116,2
113,1	118,8	0	93,2	111,2
104,1	114	0	86,5	105,8
108,7	111,5	0	98,9	122,7
96,7	97,2	0	77,2	99,5
101	102,5	0	79,4	107,9
116,9	113,4	0	90,4	124,6
105,8	109,8	0	81,4	115
99	104,9	0	85,8	110,3
129,4	126,1	0	103,6	132,7
83	80	0	73,6	99,7
88,9	96,8	0	75,7	96,5
115,9	117,2	1	99,2	118,7
104,2	112,3	1	88,7	112,9
113,4	117,3	1	94,6	130,5
112,2	111,1	1	98,7	137,9
100,8	102,2	1	84,2	115
107,3	104,3	1	87,7	116,8
126,6	122,9	1	103,3	140,9
102,9	107,6	1	88,2	120,7
117,9	121,3	1	93,4	134,2
128,8	131,5	1	106,3	147,3
87,5	89	1	73,1	112,4
93,8	104,4	1	78,6	107,1
122,7	128,9	1	101,6	128,4
126,2	135,9	1	101,4	137,7
124,6	133,3	1	98,5	135
116,7	121,3	1	99	151
115,2	120,5	1	89,5	137,4
111,1	120,4	1	83,5	132,4
129,9	137,9	1	97,4	161,3
113,3	126,1	1	87,8	139,8
118,5	133,2	1	90,4	146
133,5	146,6	1	97,1	154,6
102,1	103,4	1	79,4	142,1
102,4	117,2	1	85	120,5

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=2394&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=2394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2394&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
metaal[t] = + 20.8675860424059 + 1.12593999912943Totaal[t] + 1.60887221363666conjunctuur[t] -0.339736946221387elektrische[t] + 0.00158058220510757mac[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
metaal[t] =  +  20.8675860424059 +  1.12593999912943Totaal[t] +  1.60887221363666conjunctuur[t] -0.339736946221387elektrische[t] +  0.00158058220510757mac[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2394&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]metaal[t] =  +  20.8675860424059 +  1.12593999912943Totaal[t] +  1.60887221363666conjunctuur[t] -0.339736946221387elektrische[t] +  0.00158058220510757mac[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2394&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
metaal[t] = + 20.8675860424059 + 1.12593999912943Totaal[t] + 1.60887221363666conjunctuur[t] -0.339736946221387elektrische[t] + 0.00158058220510757mac[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)	20.8675860424059	6.164896	3.3849	0.001136	0.000568
Totaal	1.12593999912943	0.137513	8.1879	0	0
conjunctuur	1.60887221363666	2.003933	0.8029	0.424594	0.212297
elektrische	-0.339736946221387	0.117824	-2.8834	0.00513	0.002565
mac	0.00158058220510757	0.083851	0.0188	0.985011	0.492505

\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) & 20.8675860424059 & 6.164896 & 3.3849 & 0.001136 & 0.000568 \tabularnewline
Totaal & 1.12593999912943 & 0.137513 & 8.1879 & 0 & 0 \tabularnewline
conjunctuur & 1.60887221363666 & 2.003933 & 0.8029 & 0.424594 & 0.212297 \tabularnewline
elektrische & -0.339736946221387 & 0.117824 & -2.8834 & 0.00513 & 0.002565 \tabularnewline
mac & 0.00158058220510757 & 0.083851 & 0.0188 & 0.985011 & 0.492505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2394&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]20.8675860424059[/C][C]6.164896[/C][C]3.3849[/C][C]0.001136[/C][C]0.000568[/C][/ROW]
[ROW][C]Totaal[/C][C]1.12593999912943[/C][C]0.137513[/C][C]8.1879[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]conjunctuur[/C][C]1.60887221363666[/C][C]2.003933[/C][C]0.8029[/C][C]0.424594[/C][C]0.212297[/C][/ROW]
[ROW][C]elektrische[/C][C]-0.339736946221387[/C][C]0.117824[/C][C]-2.8834[/C][C]0.00513[/C][C]0.002565[/C][/ROW]
[ROW][C]mac[/C][C]0.00158058220510757[/C][C]0.083851[/C][C]0.0188[/C][C]0.985011[/C][C]0.492505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2394&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2394&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)	20.8675860424059	6.164896	3.3849	0.001136	0.000568
Totaal	1.12593999912943	0.137513	8.1879	0	0
conjunctuur	1.60887221363666	2.003933	0.8029	0.424594	0.212297
elektrische	-0.339736946221387	0.117824	-2.8834	0.00513	0.002565
mac	0.00158058220510757	0.083851	0.0188	0.985011	0.492505

Multiple Linear Regression - Regression Statistics
Multiple R	0.919833866017206
R-squared	0.846094341072158
Adjusted R-squared	0.837886039262674
F-TEST (value)	103.077879043687
F-TEST (DF numerator)	4
F-TEST (DF denominator)	75
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.31645716657112
Sum Squared Residuals	2119.85376029891

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.919833866017206 \tabularnewline
R-squared & 0.846094341072158 \tabularnewline
Adjusted R-squared & 0.837886039262674 \tabularnewline
F-TEST (value) & 103.077879043687 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 75 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.31645716657112 \tabularnewline
Sum Squared Residuals & 2119.85376029891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2394&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.919833866017206[/C][/ROW]
[ROW][C]R-squared[/C][C]0.846094341072158[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.837886039262674[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]103.077879043687[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]4[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]75[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.31645716657112[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2119.85376029891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2394&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2394&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	0.919833866017206
R-squared	0.846094341072158
Adjusted R-squared	0.837886039262674
F-TEST (value)	103.077879043687
F-TEST (DF numerator)	4
F-TEST (DF denominator)	75
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.31645716657112
Sum Squared Residuals	2119.85376029891

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	97.3	105.548736421692	-8.24873642169238
2	101	109.219633560315	-8.2196335603146
3	113.2	122.610998925768	-9.41099892576796
4	101	103.188622244706	-2.18862224470599
5	105.7	110.190238881468	-4.49023888146771
6	113.9	113.952250485953	-0.052250485953429
7	86.4	90.6248213215937	-4.22482132159366
8	96.5	87.4929099634003	9.00709003659976
9	103.3	105.796892919359	-2.49689291935876
10	114.9	110.596766643700	4.30323335629953
11	105.8	108.261699337045	-2.46169933704477
12	94.2	98.1117852354756	-3.91178523547554
13	98.4	98.2325732757732	0.16742672422684
14	99.4	100.968669787344	-1.56866978734431
15	108.8	110.355689916374	-1.55568991637421
16	112.6	109.158974686315	3.44102531368534
17	104.4	107.388066911863	-2.98806691186252
18	112.2	113.497241784030	-1.29724178402966
19	81.1	88.4101092515961	-7.31010925159615
20	97.1	89.4833998088243	7.6166001911757
21	112.6	111.115456314727	1.48454368527312
22	113.8	117.334613130183	-3.53461313018347
23	107.8	104.973430429598	2.8265695704016
24	103.2	98.9777813312015	4.22221866879851
25	103.3	96.991909586739	6.30809041326106
26	101.2	100.091734303826	1.10826569617444
27	107.7	106.288280821425	1.41171917857499
28	110.4	103.061079674646	7.33892032535437
29	101.9	103.432078558305	-1.53207855830461
30	115.9	109.903709088076	5.99629091192399
31	89.9	91.4177044921338	-1.51770449213382
32	88.6	80.6813192510155	7.91868074898446
33	117.2	105.982941578798	11.2170584212020
34	123.9	107.231973750378	16.6680262496224
35	100	101.381103951572	-1.38110395157241
36	103.6	105.348181257825	-1.74818125782496
37	94.1	95.4719698775218	-1.37196987752176
38	98.7	99.5292303967753	-0.829230396775268
39	119.5	118.822234769932	0.677765230068165
40	112.7	111.235396035732	1.46460396426849
41	104.4	102.490240354279	1.90975964572106
42	124.7	121.443083662419	3.2569163375811
43	89.1	90.3361689881911	-1.23616898819112
44	97	99.74124194728	-2.74124194727991
45	121.6	117.432399932881	4.16760006711928
46	118.8	116.723677297319	2.07632270268065
47	114	108.857919700930	5.14208029906984
48	111.5	109.851217403047	1.64878259695332
49	97.2	103.675559639339	-6.47555963933909
50	102.5	107.782957244432	-5.2829572444315
51	113.4	121.974692544980	-8.57469254497952
52	109.8	112.519217481466	-2.71921748146627
53	104.9	103.360554187648	1.53944581235199
54	126.1	131.577217559836	-5.47721755983652
55	80	89.4735507741039	-9.47355077410387
56	96.8	95.3980913188463	1.40190868115373
57	117.2	119.458614197728	-2.25861419772842
58	112.3	109.843186766449	2.45681323355101
59	117.3	118.225205022543	-0.925205022543493
60	111.1	115.492851852398	-4.39285185239828
61	102.2	107.547126250036	-5.34712625003588
62	104.3	113.679501980572	-9.37950198057154
63	122.9	130.148339633859	-7.24833963385904
64	107.6	108.561661781891	-0.96166178189127
65	121.3	123.705467508250	-2.4054675082505
66	131.5	131.616312519392	-0.116312519392342
67	89	96.3390948509386	-7.33909485093855
68	104.4	101.555586555549	2.84441344445074
69	128.9	126.314969168267	2.58503083173323
70	135.9	130.338405968972	5.56159403102844
71	133.3	129.517871542453	3.78212845754731
72	121.3	120.478366391501	0.82163360849878
73	120.5	121.995461463921	-1.49546146392078
74	120.4	119.409626233793	0.990373766207122
75	137.9	135.900633490677	1.99936650932344
76	126.1	120.437521671443	5.66247832855652
77	133.2	125.418893216413	7.7811067835874
78	146.6	140.045348670635	6.55465132936528
79	103.4	110.684419368525	-7.28441936852521
80	117.2	109.085533893794	8.11446610620604

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 97.3 & 105.548736421692 & -8.24873642169238 \tabularnewline
2 & 101 & 109.219633560315 & -8.2196335603146 \tabularnewline
3 & 113.2 & 122.610998925768 & -9.41099892576796 \tabularnewline
4 & 101 & 103.188622244706 & -2.18862224470599 \tabularnewline
5 & 105.7 & 110.190238881468 & -4.49023888146771 \tabularnewline
6 & 113.9 & 113.952250485953 & -0.052250485953429 \tabularnewline
7 & 86.4 & 90.6248213215937 & -4.22482132159366 \tabularnewline
8 & 96.5 & 87.4929099634003 & 9.00709003659976 \tabularnewline
9 & 103.3 & 105.796892919359 & -2.49689291935876 \tabularnewline
10 & 114.9 & 110.596766643700 & 4.30323335629953 \tabularnewline
11 & 105.8 & 108.261699337045 & -2.46169933704477 \tabularnewline
12 & 94.2 & 98.1117852354756 & -3.91178523547554 \tabularnewline
13 & 98.4 & 98.2325732757732 & 0.16742672422684 \tabularnewline
14 & 99.4 & 100.968669787344 & -1.56866978734431 \tabularnewline
15 & 108.8 & 110.355689916374 & -1.55568991637421 \tabularnewline
16 & 112.6 & 109.158974686315 & 3.44102531368534 \tabularnewline
17 & 104.4 & 107.388066911863 & -2.98806691186252 \tabularnewline
18 & 112.2 & 113.497241784030 & -1.29724178402966 \tabularnewline
19 & 81.1 & 88.4101092515961 & -7.31010925159615 \tabularnewline
20 & 97.1 & 89.4833998088243 & 7.6166001911757 \tabularnewline
21 & 112.6 & 111.115456314727 & 1.48454368527312 \tabularnewline
22 & 113.8 & 117.334613130183 & -3.53461313018347 \tabularnewline
23 & 107.8 & 104.973430429598 & 2.8265695704016 \tabularnewline
24 & 103.2 & 98.9777813312015 & 4.22221866879851 \tabularnewline
25 & 103.3 & 96.991909586739 & 6.30809041326106 \tabularnewline
26 & 101.2 & 100.091734303826 & 1.10826569617444 \tabularnewline
27 & 107.7 & 106.288280821425 & 1.41171917857499 \tabularnewline
28 & 110.4 & 103.061079674646 & 7.33892032535437 \tabularnewline
29 & 101.9 & 103.432078558305 & -1.53207855830461 \tabularnewline
30 & 115.9 & 109.903709088076 & 5.99629091192399 \tabularnewline
31 & 89.9 & 91.4177044921338 & -1.51770449213382 \tabularnewline
32 & 88.6 & 80.6813192510155 & 7.91868074898446 \tabularnewline
33 & 117.2 & 105.982941578798 & 11.2170584212020 \tabularnewline
34 & 123.9 & 107.231973750378 & 16.6680262496224 \tabularnewline
35 & 100 & 101.381103951572 & -1.38110395157241 \tabularnewline
36 & 103.6 & 105.348181257825 & -1.74818125782496 \tabularnewline
37 & 94.1 & 95.4719698775218 & -1.37196987752176 \tabularnewline
38 & 98.7 & 99.5292303967753 & -0.829230396775268 \tabularnewline
39 & 119.5 & 118.822234769932 & 0.677765230068165 \tabularnewline
40 & 112.7 & 111.235396035732 & 1.46460396426849 \tabularnewline
41 & 104.4 & 102.490240354279 & 1.90975964572106 \tabularnewline
42 & 124.7 & 121.443083662419 & 3.2569163375811 \tabularnewline
43 & 89.1 & 90.3361689881911 & -1.23616898819112 \tabularnewline
44 & 97 & 99.74124194728 & -2.74124194727991 \tabularnewline
45 & 121.6 & 117.432399932881 & 4.16760006711928 \tabularnewline
46 & 118.8 & 116.723677297319 & 2.07632270268065 \tabularnewline
47 & 114 & 108.857919700930 & 5.14208029906984 \tabularnewline
48 & 111.5 & 109.851217403047 & 1.64878259695332 \tabularnewline
49 & 97.2 & 103.675559639339 & -6.47555963933909 \tabularnewline
50 & 102.5 & 107.782957244432 & -5.2829572444315 \tabularnewline
51 & 113.4 & 121.974692544980 & -8.57469254497952 \tabularnewline
52 & 109.8 & 112.519217481466 & -2.71921748146627 \tabularnewline
53 & 104.9 & 103.360554187648 & 1.53944581235199 \tabularnewline
54 & 126.1 & 131.577217559836 & -5.47721755983652 \tabularnewline
55 & 80 & 89.4735507741039 & -9.47355077410387 \tabularnewline
56 & 96.8 & 95.3980913188463 & 1.40190868115373 \tabularnewline
57 & 117.2 & 119.458614197728 & -2.25861419772842 \tabularnewline
58 & 112.3 & 109.843186766449 & 2.45681323355101 \tabularnewline
59 & 117.3 & 118.225205022543 & -0.925205022543493 \tabularnewline
60 & 111.1 & 115.492851852398 & -4.39285185239828 \tabularnewline
61 & 102.2 & 107.547126250036 & -5.34712625003588 \tabularnewline
62 & 104.3 & 113.679501980572 & -9.37950198057154 \tabularnewline
63 & 122.9 & 130.148339633859 & -7.24833963385904 \tabularnewline
64 & 107.6 & 108.561661781891 & -0.96166178189127 \tabularnewline
65 & 121.3 & 123.705467508250 & -2.4054675082505 \tabularnewline
66 & 131.5 & 131.616312519392 & -0.116312519392342 \tabularnewline
67 & 89 & 96.3390948509386 & -7.33909485093855 \tabularnewline
68 & 104.4 & 101.555586555549 & 2.84441344445074 \tabularnewline
69 & 128.9 & 126.314969168267 & 2.58503083173323 \tabularnewline
70 & 135.9 & 130.338405968972 & 5.56159403102844 \tabularnewline
71 & 133.3 & 129.517871542453 & 3.78212845754731 \tabularnewline
72 & 121.3 & 120.478366391501 & 0.82163360849878 \tabularnewline
73 & 120.5 & 121.995461463921 & -1.49546146392078 \tabularnewline
74 & 120.4 & 119.409626233793 & 0.990373766207122 \tabularnewline
75 & 137.9 & 135.900633490677 & 1.99936650932344 \tabularnewline
76 & 126.1 & 120.437521671443 & 5.66247832855652 \tabularnewline
77 & 133.2 & 125.418893216413 & 7.7811067835874 \tabularnewline
78 & 146.6 & 140.045348670635 & 6.55465132936528 \tabularnewline
79 & 103.4 & 110.684419368525 & -7.28441936852521 \tabularnewline
80 & 117.2 & 109.085533893794 & 8.11446610620604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2394&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]97.3[/C][C]105.548736421692[/C][C]-8.24873642169238[/C][/ROW]
[ROW][C]2[/C][C]101[/C][C]109.219633560315[/C][C]-8.2196335603146[/C][/ROW]
[ROW][C]3[/C][C]113.2[/C][C]122.610998925768[/C][C]-9.41099892576796[/C][/ROW]
[ROW][C]4[/C][C]101[/C][C]103.188622244706[/C][C]-2.18862224470599[/C][/ROW]
[ROW][C]5[/C][C]105.7[/C][C]110.190238881468[/C][C]-4.49023888146771[/C][/ROW]
[ROW][C]6[/C][C]113.9[/C][C]113.952250485953[/C][C]-0.052250485953429[/C][/ROW]
[ROW][C]7[/C][C]86.4[/C][C]90.6248213215937[/C][C]-4.22482132159366[/C][/ROW]
[ROW][C]8[/C][C]96.5[/C][C]87.4929099634003[/C][C]9.00709003659976[/C][/ROW]
[ROW][C]9[/C][C]103.3[/C][C]105.796892919359[/C][C]-2.49689291935876[/C][/ROW]
[ROW][C]10[/C][C]114.9[/C][C]110.596766643700[/C][C]4.30323335629953[/C][/ROW]
[ROW][C]11[/C][C]105.8[/C][C]108.261699337045[/C][C]-2.46169933704477[/C][/ROW]
[ROW][C]12[/C][C]94.2[/C][C]98.1117852354756[/C][C]-3.91178523547554[/C][/ROW]
[ROW][C]13[/C][C]98.4[/C][C]98.2325732757732[/C][C]0.16742672422684[/C][/ROW]
[ROW][C]14[/C][C]99.4[/C][C]100.968669787344[/C][C]-1.56866978734431[/C][/ROW]
[ROW][C]15[/C][C]108.8[/C][C]110.355689916374[/C][C]-1.55568991637421[/C][/ROW]
[ROW][C]16[/C][C]112.6[/C][C]109.158974686315[/C][C]3.44102531368534[/C][/ROW]
[ROW][C]17[/C][C]104.4[/C][C]107.388066911863[/C][C]-2.98806691186252[/C][/ROW]
[ROW][C]18[/C][C]112.2[/C][C]113.497241784030[/C][C]-1.29724178402966[/C][/ROW]
[ROW][C]19[/C][C]81.1[/C][C]88.4101092515961[/C][C]-7.31010925159615[/C][/ROW]
[ROW][C]20[/C][C]97.1[/C][C]89.4833998088243[/C][C]7.6166001911757[/C][/ROW]
[ROW][C]21[/C][C]112.6[/C][C]111.115456314727[/C][C]1.48454368527312[/C][/ROW]
[ROW][C]22[/C][C]113.8[/C][C]117.334613130183[/C][C]-3.53461313018347[/C][/ROW]
[ROW][C]23[/C][C]107.8[/C][C]104.973430429598[/C][C]2.8265695704016[/C][/ROW]
[ROW][C]24[/C][C]103.2[/C][C]98.9777813312015[/C][C]4.22221866879851[/C][/ROW]
[ROW][C]25[/C][C]103.3[/C][C]96.991909586739[/C][C]6.30809041326106[/C][/ROW]
[ROW][C]26[/C][C]101.2[/C][C]100.091734303826[/C][C]1.10826569617444[/C][/ROW]
[ROW][C]27[/C][C]107.7[/C][C]106.288280821425[/C][C]1.41171917857499[/C][/ROW]
[ROW][C]28[/C][C]110.4[/C][C]103.061079674646[/C][C]7.33892032535437[/C][/ROW]
[ROW][C]29[/C][C]101.9[/C][C]103.432078558305[/C][C]-1.53207855830461[/C][/ROW]
[ROW][C]30[/C][C]115.9[/C][C]109.903709088076[/C][C]5.99629091192399[/C][/ROW]
[ROW][C]31[/C][C]89.9[/C][C]91.4177044921338[/C][C]-1.51770449213382[/C][/ROW]
[ROW][C]32[/C][C]88.6[/C][C]80.6813192510155[/C][C]7.91868074898446[/C][/ROW]
[ROW][C]33[/C][C]117.2[/C][C]105.982941578798[/C][C]11.2170584212020[/C][/ROW]
[ROW][C]34[/C][C]123.9[/C][C]107.231973750378[/C][C]16.6680262496224[/C][/ROW]
[ROW][C]35[/C][C]100[/C][C]101.381103951572[/C][C]-1.38110395157241[/C][/ROW]
[ROW][C]36[/C][C]103.6[/C][C]105.348181257825[/C][C]-1.74818125782496[/C][/ROW]
[ROW][C]37[/C][C]94.1[/C][C]95.4719698775218[/C][C]-1.37196987752176[/C][/ROW]
[ROW][C]38[/C][C]98.7[/C][C]99.5292303967753[/C][C]-0.829230396775268[/C][/ROW]
[ROW][C]39[/C][C]119.5[/C][C]118.822234769932[/C][C]0.677765230068165[/C][/ROW]
[ROW][C]40[/C][C]112.7[/C][C]111.235396035732[/C][C]1.46460396426849[/C][/ROW]
[ROW][C]41[/C][C]104.4[/C][C]102.490240354279[/C][C]1.90975964572106[/C][/ROW]
[ROW][C]42[/C][C]124.7[/C][C]121.443083662419[/C][C]3.2569163375811[/C][/ROW]
[ROW][C]43[/C][C]89.1[/C][C]90.3361689881911[/C][C]-1.23616898819112[/C][/ROW]
[ROW][C]44[/C][C]97[/C][C]99.74124194728[/C][C]-2.74124194727991[/C][/ROW]
[ROW][C]45[/C][C]121.6[/C][C]117.432399932881[/C][C]4.16760006711928[/C][/ROW]
[ROW][C]46[/C][C]118.8[/C][C]116.723677297319[/C][C]2.07632270268065[/C][/ROW]
[ROW][C]47[/C][C]114[/C][C]108.857919700930[/C][C]5.14208029906984[/C][/ROW]
[ROW][C]48[/C][C]111.5[/C][C]109.851217403047[/C][C]1.64878259695332[/C][/ROW]
[ROW][C]49[/C][C]97.2[/C][C]103.675559639339[/C][C]-6.47555963933909[/C][/ROW]
[ROW][C]50[/C][C]102.5[/C][C]107.782957244432[/C][C]-5.2829572444315[/C][/ROW]
[ROW][C]51[/C][C]113.4[/C][C]121.974692544980[/C][C]-8.57469254497952[/C][/ROW]
[ROW][C]52[/C][C]109.8[/C][C]112.519217481466[/C][C]-2.71921748146627[/C][/ROW]
[ROW][C]53[/C][C]104.9[/C][C]103.360554187648[/C][C]1.53944581235199[/C][/ROW]
[ROW][C]54[/C][C]126.1[/C][C]131.577217559836[/C][C]-5.47721755983652[/C][/ROW]
[ROW][C]55[/C][C]80[/C][C]89.4735507741039[/C][C]-9.47355077410387[/C][/ROW]
[ROW][C]56[/C][C]96.8[/C][C]95.3980913188463[/C][C]1.40190868115373[/C][/ROW]
[ROW][C]57[/C][C]117.2[/C][C]119.458614197728[/C][C]-2.25861419772842[/C][/ROW]
[ROW][C]58[/C][C]112.3[/C][C]109.843186766449[/C][C]2.45681323355101[/C][/ROW]
[ROW][C]59[/C][C]117.3[/C][C]118.225205022543[/C][C]-0.925205022543493[/C][/ROW]
[ROW][C]60[/C][C]111.1[/C][C]115.492851852398[/C][C]-4.39285185239828[/C][/ROW]
[ROW][C]61[/C][C]102.2[/C][C]107.547126250036[/C][C]-5.34712625003588[/C][/ROW]
[ROW][C]62[/C][C]104.3[/C][C]113.679501980572[/C][C]-9.37950198057154[/C][/ROW]
[ROW][C]63[/C][C]122.9[/C][C]130.148339633859[/C][C]-7.24833963385904[/C][/ROW]
[ROW][C]64[/C][C]107.6[/C][C]108.561661781891[/C][C]-0.96166178189127[/C][/ROW]
[ROW][C]65[/C][C]121.3[/C][C]123.705467508250[/C][C]-2.4054675082505[/C][/ROW]
[ROW][C]66[/C][C]131.5[/C][C]131.616312519392[/C][C]-0.116312519392342[/C][/ROW]
[ROW][C]67[/C][C]89[/C][C]96.3390948509386[/C][C]-7.33909485093855[/C][/ROW]
[ROW][C]68[/C][C]104.4[/C][C]101.555586555549[/C][C]2.84441344445074[/C][/ROW]
[ROW][C]69[/C][C]128.9[/C][C]126.314969168267[/C][C]2.58503083173323[/C][/ROW]
[ROW][C]70[/C][C]135.9[/C][C]130.338405968972[/C][C]5.56159403102844[/C][/ROW]
[ROW][C]71[/C][C]133.3[/C][C]129.517871542453[/C][C]3.78212845754731[/C][/ROW]
[ROW][C]72[/C][C]121.3[/C][C]120.478366391501[/C][C]0.82163360849878[/C][/ROW]
[ROW][C]73[/C][C]120.5[/C][C]121.995461463921[/C][C]-1.49546146392078[/C][/ROW]
[ROW][C]74[/C][C]120.4[/C][C]119.409626233793[/C][C]0.990373766207122[/C][/ROW]
[ROW][C]75[/C][C]137.9[/C][C]135.900633490677[/C][C]1.99936650932344[/C][/ROW]
[ROW][C]76[/C][C]126.1[/C][C]120.437521671443[/C][C]5.66247832855652[/C][/ROW]
[ROW][C]77[/C][C]133.2[/C][C]125.418893216413[/C][C]7.7811067835874[/C][/ROW]
[ROW][C]78[/C][C]146.6[/C][C]140.045348670635[/C][C]6.55465132936528[/C][/ROW]
[ROW][C]79[/C][C]103.4[/C][C]110.684419368525[/C][C]-7.28441936852521[/C][/ROW]
[ROW][C]80[/C][C]117.2[/C][C]109.085533893794[/C][C]8.11446610620604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2394&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2394&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	97.3	105.548736421692	-8.24873642169238
2	101	109.219633560315	-8.2196335603146
3	113.2	122.610998925768	-9.41099892576796
4	101	103.188622244706	-2.18862224470599
5	105.7	110.190238881468	-4.49023888146771
6	113.9	113.952250485953	-0.052250485953429
7	86.4	90.6248213215937	-4.22482132159366
8	96.5	87.4929099634003	9.00709003659976
9	103.3	105.796892919359	-2.49689291935876
10	114.9	110.596766643700	4.30323335629953
11	105.8	108.261699337045	-2.46169933704477
12	94.2	98.1117852354756	-3.91178523547554
13	98.4	98.2325732757732	0.16742672422684
14	99.4	100.968669787344	-1.56866978734431
15	108.8	110.355689916374	-1.55568991637421
16	112.6	109.158974686315	3.44102531368534
17	104.4	107.388066911863	-2.98806691186252
18	112.2	113.497241784030	-1.29724178402966
19	81.1	88.4101092515961	-7.31010925159615
20	97.1	89.4833998088243	7.6166001911757
21	112.6	111.115456314727	1.48454368527312
22	113.8	117.334613130183	-3.53461313018347
23	107.8	104.973430429598	2.8265695704016
24	103.2	98.9777813312015	4.22221866879851
25	103.3	96.991909586739	6.30809041326106
26	101.2	100.091734303826	1.10826569617444
27	107.7	106.288280821425	1.41171917857499
28	110.4	103.061079674646	7.33892032535437
29	101.9	103.432078558305	-1.53207855830461
30	115.9	109.903709088076	5.99629091192399
31	89.9	91.4177044921338	-1.51770449213382
32	88.6	80.6813192510155	7.91868074898446
33	117.2	105.982941578798	11.2170584212020
34	123.9	107.231973750378	16.6680262496224
35	100	101.381103951572	-1.38110395157241
36	103.6	105.348181257825	-1.74818125782496
37	94.1	95.4719698775218	-1.37196987752176
38	98.7	99.5292303967753	-0.829230396775268
39	119.5	118.822234769932	0.677765230068165
40	112.7	111.235396035732	1.46460396426849
41	104.4	102.490240354279	1.90975964572106
42	124.7	121.443083662419	3.2569163375811
43	89.1	90.3361689881911	-1.23616898819112
44	97	99.74124194728	-2.74124194727991
45	121.6	117.432399932881	4.16760006711928
46	118.8	116.723677297319	2.07632270268065
47	114	108.857919700930	5.14208029906984
48	111.5	109.851217403047	1.64878259695332
49	97.2	103.675559639339	-6.47555963933909
50	102.5	107.782957244432	-5.2829572444315
51	113.4	121.974692544980	-8.57469254497952
52	109.8	112.519217481466	-2.71921748146627
53	104.9	103.360554187648	1.53944581235199
54	126.1	131.577217559836	-5.47721755983652
55	80	89.4735507741039	-9.47355077410387
56	96.8	95.3980913188463	1.40190868115373
57	117.2	119.458614197728	-2.25861419772842
58	112.3	109.843186766449	2.45681323355101
59	117.3	118.225205022543	-0.925205022543493
60	111.1	115.492851852398	-4.39285185239828
61	102.2	107.547126250036	-5.34712625003588
62	104.3	113.679501980572	-9.37950198057154
63	122.9	130.148339633859	-7.24833963385904
64	107.6	108.561661781891	-0.96166178189127
65	121.3	123.705467508250	-2.4054675082505
66	131.5	131.616312519392	-0.116312519392342
67	89	96.3390948509386	-7.33909485093855
68	104.4	101.555586555549	2.84441344445074
69	128.9	126.314969168267	2.58503083173323
70	135.9	130.338405968972	5.56159403102844
71	133.3	129.517871542453	3.78212845754731
72	121.3	120.478366391501	0.82163360849878
73	120.5	121.995461463921	-1.49546146392078
74	120.4	119.409626233793	0.990373766207122
75	137.9	135.900633490677	1.99936650932344
76	126.1	120.437521671443	5.66247832855652
77	133.2	125.418893216413	7.7811067835874
78	146.6	140.045348670635	6.55465132936528
79	103.4	110.684419368525	-7.28441936852521
80	117.2	109.085533893794	8.11446610620604

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Figure 3

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Figure 4

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Figure 9

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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