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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 02 Dec 2007 04:37:30 -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/02/t1196594920e26p5rf3axsgwsr.htm/, Retrieved Sun, 28 Apr 2024 10:31:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2276, Retrieved Sun, 28 Apr 2024 10:31:30 +0000

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Original text written by user:

Multiple Linear Regression

IsPrivate?

No (this computation is public)

User-defined keywords

Multiple Linear Regression

Estimated Impact

277

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

-       [Multiple Regression] [Multiple Linear R...] [2007-12-02 11:37:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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100.6	115.9	59.7	125
96.1	112.9	58.2	121.7
110	126.3	75.3	134.3
108.2	116.8	69	124.3
106.9	112	66.1	119.1
117.2	129.7	77.5	137.8
105.2	113.6	69.3	120.5
106.3	115.7	70.2	122.7
95.9	119.5	70.2	127.2
107.5	125.8	78.2	133.2
113	129.6	85.4	136.3
111.4	128	82.4	134.9
95.5	112.8	61.2	120.9
90.3	101.6	52.2	109.4
110.8	123.9	85.3	129.6
107.1	118.8	79.9	124.7
101.4	109.1	72.2	114.6
112.9	130.6	85.7	137.4
98.5	112.4	75.5	117.9
100.1	111	69.2	117.4
93.4	116.2	77.6	122
104.4	119.8	85.3	124.8
101.8	117.2	77	123.3
107.9	127.3	89.9	132.8
91.3	107.7	60	115.1
86.6	97.5	54.3	104.2
111.4	120.1	84	125.5
98.4	110.6	69.9	116.8
102.2	111.3	75.1	116.8
103	119.8	81.7	125.5
95.8	105.5	69.9	110.9
96	108.7	68.3	114.9
95.7	128.7	77.3	136.4
106.4	119.5	77.4	125.8
112	121.1	85.3	126.5
116.2	128.4	91	134
93.9	108.8	60.6	116.1
100.5	107.5	57.6	115
112.5	125.6	93.8	130.3
101.2	102.9	78.7	106.5
107.8	107.5	80.3	111.6
114.3	120.4	89.8	125
99.6	104.3	77.5	108.3
98.6	100.6	71.7	105
93.6	121.9	83.2	127.4
99.6	112.7	86.2	116.6
113.1	124.9	100.7	128.6
110.7	123.9	100.8	127.5
88.1	102.2	57.1	108.4
93.1	104.9	62.5	110.8
107.4	109.8	79.7	114.2
99.5	98.9	80.3	101.8
105.6	107.3	92.4	109.8
108.3	112.6	91.8	115.9
99.2	104	85.8	106.9
99.3	110.6	84.2	114.6
107.1	100.8	93.1	105.4
106.9	103.8	101.2	108.1
115.4	117	100.6	118.4
99	108.4	106.7	112.7
100.1	95.5	64	98.4
96.2	96.9	67.5	99.6
96.9	103.9	101	103.9
96.2	101.1	95.5	101.5
91	100.6	97	100.8
99	104.3	103.8	104.5
99	98	95.2	98.2
107.2	99.5	86.7	99.9
110.8	97.4	93.5	97.5
111.1	105.6	102.5	105.7
104.6	117.5	112.3	117.7
94.3	107.4	105.5	107.4
90.7	97.8	75.4	98.4
88.8	91.5	70.4	92
90.9	107.7	108	107.7
90.5	100.1	100	100.2
95.5	96.6	93.3	96.7
103.1	106.8	111.1	106.8
100.6	98	101.1	98
103.1	98.6	98.1	98.6

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=2276&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=2276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2276&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
1[t] = + 53.2368533361207 + 0.761056250969949`2`[t] + 0.217444956801800`3`[t] -0.423766010526483`4 `[t] -0.115859441483030t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
1[t] =  +  53.2368533361207 +  0.761056250969949`2`[t] +  0.217444956801800`3`[t] -0.423766010526483`4
`[t] -0.115859441483030t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2276&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]1[t] =  +  53.2368533361207 +  0.761056250969949`2`[t] +  0.217444956801800`3`[t] -0.423766010526483`4
`[t] -0.115859441483030t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2276&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
1[t] = + 53.2368533361207 + 0.761056250969949`2`[t] + 0.217444956801800`3`[t] -0.423766010526483`4 `[t] -0.115859441483030t + 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)	53.2368533361207	11.310652	4.7068	1.1e-05	6e-06
`2`	0.761056250969949	0.849475	0.8959	0.373166	0.186583
`3`	0.217444956801800	0.104914	2.0726	0.041646	0.020823
`4 `	-0.423766010526483	0.769568	-0.5507	0.583507	0.291754
t	-0.115859441483030	0.072774	-1.592	0.11558	0.05779

\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) & 53.2368533361207 & 11.310652 & 4.7068 & 1.1e-05 & 6e-06 \tabularnewline
`2` & 0.761056250969949 & 0.849475 & 0.8959 & 0.373166 & 0.186583 \tabularnewline
`3` & 0.217444956801800 & 0.104914 & 2.0726 & 0.041646 & 0.020823 \tabularnewline
`4
` & -0.423766010526483 & 0.769568 & -0.5507 & 0.583507 & 0.291754 \tabularnewline
t & -0.115859441483030 & 0.072774 & -1.592 & 0.11558 & 0.05779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2276&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]53.2368533361207[/C][C]11.310652[/C][C]4.7068[/C][C]1.1e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]`2`[/C][C]0.761056250969949[/C][C]0.849475[/C][C]0.8959[/C][C]0.373166[/C][C]0.186583[/C][/ROW]
[ROW][C]`3`[/C][C]0.217444956801800[/C][C]0.104914[/C][C]2.0726[/C][C]0.041646[/C][C]0.020823[/C][/ROW]
[ROW][C]`4
`[/C][C]-0.423766010526483[/C][C]0.769568[/C][C]-0.5507[/C][C]0.583507[/C][C]0.291754[/C][/ROW]
[ROW][C]t[/C][C]-0.115859441483030[/C][C]0.072774[/C][C]-1.592[/C][C]0.11558[/C][C]0.05779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2276&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2276&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)	53.2368533361207	11.310652	4.7068	1.1e-05	6e-06
`2`	0.761056250969949	0.849475	0.8959	0.373166	0.186583
`3`	0.217444956801800	0.104914	2.0726	0.041646	0.020823
`4 `	-0.423766010526483	0.769568	-0.5507	0.583507	0.291754
t	-0.115859441483030	0.072774	-1.592	0.11558	0.05779

Multiple Linear Regression - Regression Statistics
Multiple R	0.692089938519227
R-squared	0.478988482999547
Adjusted R-squared	0.451201202092857
F-TEST (value)	17.2376881569659
F-TEST (DF numerator)	4
F-TEST (DF denominator)	75
p-value	4.56730875342259e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.5816683947729
Sum Squared Residuals	2336.62665519050

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.692089938519227 \tabularnewline
R-squared & 0.478988482999547 \tabularnewline
Adjusted R-squared & 0.451201202092857 \tabularnewline
F-TEST (value) & 17.2376881569659 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 75 \tabularnewline
p-value & 4.56730875342259e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.5816683947729 \tabularnewline
Sum Squared Residuals & 2336.62665519050 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2276&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.692089938519227[/C][/ROW]
[ROW][C]R-squared[/C][C]0.478988482999547[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.451201202092857[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]17.2376881569659[/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]4.56730875342259e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.5816683947729[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2336.62665519050[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2276&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2276&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	0.692089938519227
R-squared	0.478988482999547
Adjusted R-squared	0.451201202092857
F-TEST (value)	17.2376881569659
F-TEST (DF numerator)	4
F-TEST (DF denominator)	75
p-value	4.56730875342259e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.5816683947729
Sum Squared Residuals	2336.62665519050

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	100.6	101.338125987312	-0.738125987312079
2	96.1	100.011358192454	-3.91135819245363
3	110	108.472509542645	1.52749045735504
4	108.2	103.994372594361	4.20562740563907
5	106.9	101.798436028235	5.10156397176537
6	117.2	109.707720339615	7.49227966038502
7	105.2	102.886958593849	2.31304140615083
8	106.3	103.632732517366	2.66726748263360
9	95.9	104.5019397822	-8.6019397822
10	107.5	108.377698313083	-0.877698313083153
11	113	111.405781681627	1.59421831837322
12	111.4	110.013169782924	1.38683021707649
13	95.5	99.6521463898699	-4.15214638986986
14	90.3	93.9287614473618	-3.62876144736176
15	110.8	109.421811060013	1.37818893998678
16	107.1	106.326815423433	0.773184576566506
17	101.4	101.434420886486	-0.0344208864855695
18	112.9	110.954912717677	1.94508728232308
19	98.5	103.033328154429	-4.53332815442889
20	100.1	100.693969739000	-0.59396973899984
21	93.4	104.412816791274	-11.0128167912738
22	104.4	107.524541191182	-3.12454119118232
23	101.8	104.260791371512	-2.46079137151222
24	107.9	110.610862907567	-2.71086290756729
25	91.3	96.5773551250182	-5.27735512501821
26	86.6	92.0783351846101	-5.47833518461011
27	111.4	106.594246207847	4.80575379215273
28	98.4	99.8691427828248	-1.46914278282476
29	102.2	101.41673649239	0.783263507609949
30	103	105.518227607463	-2.51822760746306
31	95.8	98.1403970405352	-2.34039704053519
32	96	98.4169416291672	-2.41694162916718
33	95.7	106.36824259198	-10.6682425919799
34	106.4	103.764329848834	2.63567015116573
35	112	106.287339360269	5.71266063973116
36	116.2	109.788381725688	6.41161827431192
37	93.9	95.7309046668434	-1.83090466684338
38	100.5	94.4394798402732	6.06052015972685
39	112.5	109.486626016516	3.01337398348386
40	101.2	98.8970018808384	2.30299811916159
41	107.8	100.468706471015	7.33129352898504
42	114.3	106.557735215606	7.7422647843935
43	99.6	98.5911895406374	1.00881045936258
44	98.6	95.7966690558525	2.80333094414747
45	93.6	104.899566127457	-11.2995661274569
46	99.6	103.010996961142	-3.41099696114175
47	113.1	110.247783528800	2.8522164711996
48	110.7	109.858754943607	0.841245056393281
49	88.1	91.819561044893	-3.71956104489298
50	93.1	93.915717822495	-0.815717822494978
51	107.4	99.8282828319656	7.57171716803441
52	99.5	96.8020757595196	2.6979242404804
53	105.6	102.320044719274	3.27995528072595
54	108.3	103.522343769639	4.77765623036088
55	99.2	99.370624923742	-0.170624923742072
56	99.3	100.666826526724	-1.36682652672391
57	107.1	98.926523238115	8.17347676188495
58	106.9	101.710968471215	5.18903152878507
59	115.4	107.145794660031	8.25420533996864
60	99	104.226731956699	-5.22673195669872
61	100.1	91.0682011727952	9.0317988272048
62	96.2	92.2703586188446	3.92964138115538
63	96.9	102.944105141748	-6.04410514174764
64	96.2	100.518379360402	-4.31837936040241
65	91	100.644795436006	-9.64479543600565
66	99	103.255535590416	-4.25553559041568
67	99	99.1447210056433	-0.144721005643339
68	107.2	97.601761589905	9.5982384100951
69	110.8	98.3833481529008	12.4166518470992
70	111.1	102.990273294270	8.10972670572962
71	104.6	108.976751689670	-4.37675168966958
72	94.3	104.060388315561	-9.7603883155606
73	90.7	93.9071897597702	-3.20718975977023
74	88.8	90.621553620537	-1.82155362053702
75	90.9	104.357609455249	-13.4576094552490
76	90.5	99.8964079309286	-9.39640793092863
77	95.5	97.1431514373214	-1.64315143732141
78	103.1	104.380549280486	-1.28054928048642
79	100.6	99.1220861550829	1.47791384491711
80	103.1	98.5562659874605	4.54373401253946

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 100.6 & 101.338125987312 & -0.738125987312079 \tabularnewline
2 & 96.1 & 100.011358192454 & -3.91135819245363 \tabularnewline
3 & 110 & 108.472509542645 & 1.52749045735504 \tabularnewline
4 & 108.2 & 103.994372594361 & 4.20562740563907 \tabularnewline
5 & 106.9 & 101.798436028235 & 5.10156397176537 \tabularnewline
6 & 117.2 & 109.707720339615 & 7.49227966038502 \tabularnewline
7 & 105.2 & 102.886958593849 & 2.31304140615083 \tabularnewline
8 & 106.3 & 103.632732517366 & 2.66726748263360 \tabularnewline
9 & 95.9 & 104.5019397822 & -8.6019397822 \tabularnewline
10 & 107.5 & 108.377698313083 & -0.877698313083153 \tabularnewline
11 & 113 & 111.405781681627 & 1.59421831837322 \tabularnewline
12 & 111.4 & 110.013169782924 & 1.38683021707649 \tabularnewline
13 & 95.5 & 99.6521463898699 & -4.15214638986986 \tabularnewline
14 & 90.3 & 93.9287614473618 & -3.62876144736176 \tabularnewline
15 & 110.8 & 109.421811060013 & 1.37818893998678 \tabularnewline
16 & 107.1 & 106.326815423433 & 0.773184576566506 \tabularnewline
17 & 101.4 & 101.434420886486 & -0.0344208864855695 \tabularnewline
18 & 112.9 & 110.954912717677 & 1.94508728232308 \tabularnewline
19 & 98.5 & 103.033328154429 & -4.53332815442889 \tabularnewline
20 & 100.1 & 100.693969739000 & -0.59396973899984 \tabularnewline
21 & 93.4 & 104.412816791274 & -11.0128167912738 \tabularnewline
22 & 104.4 & 107.524541191182 & -3.12454119118232 \tabularnewline
23 & 101.8 & 104.260791371512 & -2.46079137151222 \tabularnewline
24 & 107.9 & 110.610862907567 & -2.71086290756729 \tabularnewline
25 & 91.3 & 96.5773551250182 & -5.27735512501821 \tabularnewline
26 & 86.6 & 92.0783351846101 & -5.47833518461011 \tabularnewline
27 & 111.4 & 106.594246207847 & 4.80575379215273 \tabularnewline
28 & 98.4 & 99.8691427828248 & -1.46914278282476 \tabularnewline
29 & 102.2 & 101.41673649239 & 0.783263507609949 \tabularnewline
30 & 103 & 105.518227607463 & -2.51822760746306 \tabularnewline
31 & 95.8 & 98.1403970405352 & -2.34039704053519 \tabularnewline
32 & 96 & 98.4169416291672 & -2.41694162916718 \tabularnewline
33 & 95.7 & 106.36824259198 & -10.6682425919799 \tabularnewline
34 & 106.4 & 103.764329848834 & 2.63567015116573 \tabularnewline
35 & 112 & 106.287339360269 & 5.71266063973116 \tabularnewline
36 & 116.2 & 109.788381725688 & 6.41161827431192 \tabularnewline
37 & 93.9 & 95.7309046668434 & -1.83090466684338 \tabularnewline
38 & 100.5 & 94.4394798402732 & 6.06052015972685 \tabularnewline
39 & 112.5 & 109.486626016516 & 3.01337398348386 \tabularnewline
40 & 101.2 & 98.8970018808384 & 2.30299811916159 \tabularnewline
41 & 107.8 & 100.468706471015 & 7.33129352898504 \tabularnewline
42 & 114.3 & 106.557735215606 & 7.7422647843935 \tabularnewline
43 & 99.6 & 98.5911895406374 & 1.00881045936258 \tabularnewline
44 & 98.6 & 95.7966690558525 & 2.80333094414747 \tabularnewline
45 & 93.6 & 104.899566127457 & -11.2995661274569 \tabularnewline
46 & 99.6 & 103.010996961142 & -3.41099696114175 \tabularnewline
47 & 113.1 & 110.247783528800 & 2.8522164711996 \tabularnewline
48 & 110.7 & 109.858754943607 & 0.841245056393281 \tabularnewline
49 & 88.1 & 91.819561044893 & -3.71956104489298 \tabularnewline
50 & 93.1 & 93.915717822495 & -0.815717822494978 \tabularnewline
51 & 107.4 & 99.8282828319656 & 7.57171716803441 \tabularnewline
52 & 99.5 & 96.8020757595196 & 2.6979242404804 \tabularnewline
53 & 105.6 & 102.320044719274 & 3.27995528072595 \tabularnewline
54 & 108.3 & 103.522343769639 & 4.77765623036088 \tabularnewline
55 & 99.2 & 99.370624923742 & -0.170624923742072 \tabularnewline
56 & 99.3 & 100.666826526724 & -1.36682652672391 \tabularnewline
57 & 107.1 & 98.926523238115 & 8.17347676188495 \tabularnewline
58 & 106.9 & 101.710968471215 & 5.18903152878507 \tabularnewline
59 & 115.4 & 107.145794660031 & 8.25420533996864 \tabularnewline
60 & 99 & 104.226731956699 & -5.22673195669872 \tabularnewline
61 & 100.1 & 91.0682011727952 & 9.0317988272048 \tabularnewline
62 & 96.2 & 92.2703586188446 & 3.92964138115538 \tabularnewline
63 & 96.9 & 102.944105141748 & -6.04410514174764 \tabularnewline
64 & 96.2 & 100.518379360402 & -4.31837936040241 \tabularnewline
65 & 91 & 100.644795436006 & -9.64479543600565 \tabularnewline
66 & 99 & 103.255535590416 & -4.25553559041568 \tabularnewline
67 & 99 & 99.1447210056433 & -0.144721005643339 \tabularnewline
68 & 107.2 & 97.601761589905 & 9.5982384100951 \tabularnewline
69 & 110.8 & 98.3833481529008 & 12.4166518470992 \tabularnewline
70 & 111.1 & 102.990273294270 & 8.10972670572962 \tabularnewline
71 & 104.6 & 108.976751689670 & -4.37675168966958 \tabularnewline
72 & 94.3 & 104.060388315561 & -9.7603883155606 \tabularnewline
73 & 90.7 & 93.9071897597702 & -3.20718975977023 \tabularnewline
74 & 88.8 & 90.621553620537 & -1.82155362053702 \tabularnewline
75 & 90.9 & 104.357609455249 & -13.4576094552490 \tabularnewline
76 & 90.5 & 99.8964079309286 & -9.39640793092863 \tabularnewline
77 & 95.5 & 97.1431514373214 & -1.64315143732141 \tabularnewline
78 & 103.1 & 104.380549280486 & -1.28054928048642 \tabularnewline
79 & 100.6 & 99.1220861550829 & 1.47791384491711 \tabularnewline
80 & 103.1 & 98.5562659874605 & 4.54373401253946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2276&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]101.338125987312[/C][C]-0.738125987312079[/C][/ROW]
[ROW][C]2[/C][C]96.1[/C][C]100.011358192454[/C][C]-3.91135819245363[/C][/ROW]
[ROW][C]3[/C][C]110[/C][C]108.472509542645[/C][C]1.52749045735504[/C][/ROW]
[ROW][C]4[/C][C]108.2[/C][C]103.994372594361[/C][C]4.20562740563907[/C][/ROW]
[ROW][C]5[/C][C]106.9[/C][C]101.798436028235[/C][C]5.10156397176537[/C][/ROW]
[ROW][C]6[/C][C]117.2[/C][C]109.707720339615[/C][C]7.49227966038502[/C][/ROW]
[ROW][C]7[/C][C]105.2[/C][C]102.886958593849[/C][C]2.31304140615083[/C][/ROW]
[ROW][C]8[/C][C]106.3[/C][C]103.632732517366[/C][C]2.66726748263360[/C][/ROW]
[ROW][C]9[/C][C]95.9[/C][C]104.5019397822[/C][C]-8.6019397822[/C][/ROW]
[ROW][C]10[/C][C]107.5[/C][C]108.377698313083[/C][C]-0.877698313083153[/C][/ROW]
[ROW][C]11[/C][C]113[/C][C]111.405781681627[/C][C]1.59421831837322[/C][/ROW]
[ROW][C]12[/C][C]111.4[/C][C]110.013169782924[/C][C]1.38683021707649[/C][/ROW]
[ROW][C]13[/C][C]95.5[/C][C]99.6521463898699[/C][C]-4.15214638986986[/C][/ROW]
[ROW][C]14[/C][C]90.3[/C][C]93.9287614473618[/C][C]-3.62876144736176[/C][/ROW]
[ROW][C]15[/C][C]110.8[/C][C]109.421811060013[/C][C]1.37818893998678[/C][/ROW]
[ROW][C]16[/C][C]107.1[/C][C]106.326815423433[/C][C]0.773184576566506[/C][/ROW]
[ROW][C]17[/C][C]101.4[/C][C]101.434420886486[/C][C]-0.0344208864855695[/C][/ROW]
[ROW][C]18[/C][C]112.9[/C][C]110.954912717677[/C][C]1.94508728232308[/C][/ROW]
[ROW][C]19[/C][C]98.5[/C][C]103.033328154429[/C][C]-4.53332815442889[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]100.693969739000[/C][C]-0.59396973899984[/C][/ROW]
[ROW][C]21[/C][C]93.4[/C][C]104.412816791274[/C][C]-11.0128167912738[/C][/ROW]
[ROW][C]22[/C][C]104.4[/C][C]107.524541191182[/C][C]-3.12454119118232[/C][/ROW]
[ROW][C]23[/C][C]101.8[/C][C]104.260791371512[/C][C]-2.46079137151222[/C][/ROW]
[ROW][C]24[/C][C]107.9[/C][C]110.610862907567[/C][C]-2.71086290756729[/C][/ROW]
[ROW][C]25[/C][C]91.3[/C][C]96.5773551250182[/C][C]-5.27735512501821[/C][/ROW]
[ROW][C]26[/C][C]86.6[/C][C]92.0783351846101[/C][C]-5.47833518461011[/C][/ROW]
[ROW][C]27[/C][C]111.4[/C][C]106.594246207847[/C][C]4.80575379215273[/C][/ROW]
[ROW][C]28[/C][C]98.4[/C][C]99.8691427828248[/C][C]-1.46914278282476[/C][/ROW]
[ROW][C]29[/C][C]102.2[/C][C]101.41673649239[/C][C]0.783263507609949[/C][/ROW]
[ROW][C]30[/C][C]103[/C][C]105.518227607463[/C][C]-2.51822760746306[/C][/ROW]
[ROW][C]31[/C][C]95.8[/C][C]98.1403970405352[/C][C]-2.34039704053519[/C][/ROW]
[ROW][C]32[/C][C]96[/C][C]98.4169416291672[/C][C]-2.41694162916718[/C][/ROW]
[ROW][C]33[/C][C]95.7[/C][C]106.36824259198[/C][C]-10.6682425919799[/C][/ROW]
[ROW][C]34[/C][C]106.4[/C][C]103.764329848834[/C][C]2.63567015116573[/C][/ROW]
[ROW][C]35[/C][C]112[/C][C]106.287339360269[/C][C]5.71266063973116[/C][/ROW]
[ROW][C]36[/C][C]116.2[/C][C]109.788381725688[/C][C]6.41161827431192[/C][/ROW]
[ROW][C]37[/C][C]93.9[/C][C]95.7309046668434[/C][C]-1.83090466684338[/C][/ROW]
[ROW][C]38[/C][C]100.5[/C][C]94.4394798402732[/C][C]6.06052015972685[/C][/ROW]
[ROW][C]39[/C][C]112.5[/C][C]109.486626016516[/C][C]3.01337398348386[/C][/ROW]
[ROW][C]40[/C][C]101.2[/C][C]98.8970018808384[/C][C]2.30299811916159[/C][/ROW]
[ROW][C]41[/C][C]107.8[/C][C]100.468706471015[/C][C]7.33129352898504[/C][/ROW]
[ROW][C]42[/C][C]114.3[/C][C]106.557735215606[/C][C]7.7422647843935[/C][/ROW]
[ROW][C]43[/C][C]99.6[/C][C]98.5911895406374[/C][C]1.00881045936258[/C][/ROW]
[ROW][C]44[/C][C]98.6[/C][C]95.7966690558525[/C][C]2.80333094414747[/C][/ROW]
[ROW][C]45[/C][C]93.6[/C][C]104.899566127457[/C][C]-11.2995661274569[/C][/ROW]
[ROW][C]46[/C][C]99.6[/C][C]103.010996961142[/C][C]-3.41099696114175[/C][/ROW]
[ROW][C]47[/C][C]113.1[/C][C]110.247783528800[/C][C]2.8522164711996[/C][/ROW]
[ROW][C]48[/C][C]110.7[/C][C]109.858754943607[/C][C]0.841245056393281[/C][/ROW]
[ROW][C]49[/C][C]88.1[/C][C]91.819561044893[/C][C]-3.71956104489298[/C][/ROW]
[ROW][C]50[/C][C]93.1[/C][C]93.915717822495[/C][C]-0.815717822494978[/C][/ROW]
[ROW][C]51[/C][C]107.4[/C][C]99.8282828319656[/C][C]7.57171716803441[/C][/ROW]
[ROW][C]52[/C][C]99.5[/C][C]96.8020757595196[/C][C]2.6979242404804[/C][/ROW]
[ROW][C]53[/C][C]105.6[/C][C]102.320044719274[/C][C]3.27995528072595[/C][/ROW]
[ROW][C]54[/C][C]108.3[/C][C]103.522343769639[/C][C]4.77765623036088[/C][/ROW]
[ROW][C]55[/C][C]99.2[/C][C]99.370624923742[/C][C]-0.170624923742072[/C][/ROW]
[ROW][C]56[/C][C]99.3[/C][C]100.666826526724[/C][C]-1.36682652672391[/C][/ROW]
[ROW][C]57[/C][C]107.1[/C][C]98.926523238115[/C][C]8.17347676188495[/C][/ROW]
[ROW][C]58[/C][C]106.9[/C][C]101.710968471215[/C][C]5.18903152878507[/C][/ROW]
[ROW][C]59[/C][C]115.4[/C][C]107.145794660031[/C][C]8.25420533996864[/C][/ROW]
[ROW][C]60[/C][C]99[/C][C]104.226731956699[/C][C]-5.22673195669872[/C][/ROW]
[ROW][C]61[/C][C]100.1[/C][C]91.0682011727952[/C][C]9.0317988272048[/C][/ROW]
[ROW][C]62[/C][C]96.2[/C][C]92.2703586188446[/C][C]3.92964138115538[/C][/ROW]
[ROW][C]63[/C][C]96.9[/C][C]102.944105141748[/C][C]-6.04410514174764[/C][/ROW]
[ROW][C]64[/C][C]96.2[/C][C]100.518379360402[/C][C]-4.31837936040241[/C][/ROW]
[ROW][C]65[/C][C]91[/C][C]100.644795436006[/C][C]-9.64479543600565[/C][/ROW]
[ROW][C]66[/C][C]99[/C][C]103.255535590416[/C][C]-4.25553559041568[/C][/ROW]
[ROW][C]67[/C][C]99[/C][C]99.1447210056433[/C][C]-0.144721005643339[/C][/ROW]
[ROW][C]68[/C][C]107.2[/C][C]97.601761589905[/C][C]9.5982384100951[/C][/ROW]
[ROW][C]69[/C][C]110.8[/C][C]98.3833481529008[/C][C]12.4166518470992[/C][/ROW]
[ROW][C]70[/C][C]111.1[/C][C]102.990273294270[/C][C]8.10972670572962[/C][/ROW]
[ROW][C]71[/C][C]104.6[/C][C]108.976751689670[/C][C]-4.37675168966958[/C][/ROW]
[ROW][C]72[/C][C]94.3[/C][C]104.060388315561[/C][C]-9.7603883155606[/C][/ROW]
[ROW][C]73[/C][C]90.7[/C][C]93.9071897597702[/C][C]-3.20718975977023[/C][/ROW]
[ROW][C]74[/C][C]88.8[/C][C]90.621553620537[/C][C]-1.82155362053702[/C][/ROW]
[ROW][C]75[/C][C]90.9[/C][C]104.357609455249[/C][C]-13.4576094552490[/C][/ROW]
[ROW][C]76[/C][C]90.5[/C][C]99.8964079309286[/C][C]-9.39640793092863[/C][/ROW]
[ROW][C]77[/C][C]95.5[/C][C]97.1431514373214[/C][C]-1.64315143732141[/C][/ROW]
[ROW][C]78[/C][C]103.1[/C][C]104.380549280486[/C][C]-1.28054928048642[/C][/ROW]
[ROW][C]79[/C][C]100.6[/C][C]99.1220861550829[/C][C]1.47791384491711[/C][/ROW]
[ROW][C]80[/C][C]103.1[/C][C]98.5562659874605[/C][C]4.54373401253946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2276&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2276&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	101.338125987312	-0.738125987312079
2	96.1	100.011358192454	-3.91135819245363
3	110	108.472509542645	1.52749045735504
4	108.2	103.994372594361	4.20562740563907
5	106.9	101.798436028235	5.10156397176537
6	117.2	109.707720339615	7.49227966038502
7	105.2	102.886958593849	2.31304140615083
8	106.3	103.632732517366	2.66726748263360
9	95.9	104.5019397822	-8.6019397822
10	107.5	108.377698313083	-0.877698313083153
11	113	111.405781681627	1.59421831837322
12	111.4	110.013169782924	1.38683021707649
13	95.5	99.6521463898699	-4.15214638986986
14	90.3	93.9287614473618	-3.62876144736176
15	110.8	109.421811060013	1.37818893998678
16	107.1	106.326815423433	0.773184576566506
17	101.4	101.434420886486	-0.0344208864855695
18	112.9	110.954912717677	1.94508728232308
19	98.5	103.033328154429	-4.53332815442889
20	100.1	100.693969739000	-0.59396973899984
21	93.4	104.412816791274	-11.0128167912738
22	104.4	107.524541191182	-3.12454119118232
23	101.8	104.260791371512	-2.46079137151222
24	107.9	110.610862907567	-2.71086290756729
25	91.3	96.5773551250182	-5.27735512501821
26	86.6	92.0783351846101	-5.47833518461011
27	111.4	106.594246207847	4.80575379215273
28	98.4	99.8691427828248	-1.46914278282476
29	102.2	101.41673649239	0.783263507609949
30	103	105.518227607463	-2.51822760746306
31	95.8	98.1403970405352	-2.34039704053519
32	96	98.4169416291672	-2.41694162916718
33	95.7	106.36824259198	-10.6682425919799
34	106.4	103.764329848834	2.63567015116573
35	112	106.287339360269	5.71266063973116
36	116.2	109.788381725688	6.41161827431192
37	93.9	95.7309046668434	-1.83090466684338
38	100.5	94.4394798402732	6.06052015972685
39	112.5	109.486626016516	3.01337398348386
40	101.2	98.8970018808384	2.30299811916159
41	107.8	100.468706471015	7.33129352898504
42	114.3	106.557735215606	7.7422647843935
43	99.6	98.5911895406374	1.00881045936258
44	98.6	95.7966690558525	2.80333094414747
45	93.6	104.899566127457	-11.2995661274569
46	99.6	103.010996961142	-3.41099696114175
47	113.1	110.247783528800	2.8522164711996
48	110.7	109.858754943607	0.841245056393281
49	88.1	91.819561044893	-3.71956104489298
50	93.1	93.915717822495	-0.815717822494978
51	107.4	99.8282828319656	7.57171716803441
52	99.5	96.8020757595196	2.6979242404804
53	105.6	102.320044719274	3.27995528072595
54	108.3	103.522343769639	4.77765623036088
55	99.2	99.370624923742	-0.170624923742072
56	99.3	100.666826526724	-1.36682652672391
57	107.1	98.926523238115	8.17347676188495
58	106.9	101.710968471215	5.18903152878507
59	115.4	107.145794660031	8.25420533996864
60	99	104.226731956699	-5.22673195669872
61	100.1	91.0682011727952	9.0317988272048
62	96.2	92.2703586188446	3.92964138115538
63	96.9	102.944105141748	-6.04410514174764
64	96.2	100.518379360402	-4.31837936040241
65	91	100.644795436006	-9.64479543600565
66	99	103.255535590416	-4.25553559041568
67	99	99.1447210056433	-0.144721005643339
68	107.2	97.601761589905	9.5982384100951
69	110.8	98.3833481529008	12.4166518470992
70	111.1	102.990273294270	8.10972670572962
71	104.6	108.976751689670	-4.37675168966958
72	94.3	104.060388315561	-9.7603883155606
73	90.7	93.9071897597702	-3.20718975977023
74	88.8	90.621553620537	-1.82155362053702
75	90.9	104.357609455249	-13.4576094552490
76	90.5	99.8964079309286	-9.39640793092863
77	95.5	97.1431514373214	-1.64315143732141
78	103.1	104.380549280486	-1.28054928048642
79	100.6	99.1220861550829	1.47791384491711
80	103.1	98.5562659874605	4.54373401253946

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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 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code