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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 17 Dec 2007 11:55:22 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/17/t1197916821khev31dso1iy2mt.htm/, Retrieved Fri, 03 May 2024 21:39:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4406, Retrieved Fri, 03 May 2024 21:39:24 +0000

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Original text written by user:

zonder externe invloeden

IsPrivate?

No (this computation is public)

User-defined keywords

Multiple Regression

Estimated Impact

180

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-       [Multiple Regression] [Paper] [2007-12-17 18:55:22] [d06427f3e67cec1f6334fc93f511b0b4] [Current]

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103,1	98,6	98,1	98,6
100,6	98	101,1	98
103,1	106,8	111,1	106,8
95,5	96,6	93,3	96,7
90,5	100,1	100	100,2
90,9	107,7	108	107,7
88,8	91,5	70,4	92
90,7	97,8	75,4	98,4
94,3	107,4	105,5	107,4
104,6	117,5	112,3	117,7
111,1	105,6	102,5	105,7
110,8	97,4	93,5	97,5
107,2	99,5	86,7	99,9
99	98	95,2	98,2
99	104,3	103,8	104,5
91	100,6	97	100,8
96,2	101,1	95,5	101,5
96,9	103,9	101	103,9
96,2	96,9	67,5	99,6
100,1	95,5	64	98,4
99	108,4	106,7	112,7
115,4	117	100,6	118,4
106,9	103,8	101,2	108,1
107,1	100,8	93,1	105,4
99,3	110,6	84,2	114,6
99,2	104	85,8	106,9
108,3	112,6	91,8	115,9
105,6	107,3	92,4	109,8
99,5	98,9	80,3	101,8
107,4	109,8	79,7	114,2
93,1	104,9	62,5	110,8
88,1	102,2	57,1	108,4
110,7	123,9	100,8	127,5
113,1	124,9	100,7	128,6
99,6	112,7	86,2	116,6
93,6	121,9	83,2	127,4
98,6	100,6	71,7	105
99,6	104,3	77,5	108,3
114,3	120,4	89,8	125
107,8	107,5	80,3	111,6
101,2	102,9	78,7	106,5
112,5	125,6	93,8	130,3
100,5	107,5	57,6	115
93,9	108,8	60,6	116,1
116,2	128,4	91	134
112	121,1	85,3	126,5
106,4	119,5	77,4	125,8
95,7	128,7	77,3	136,4
96	108,7	68,3	114,9
95,8	105,5	69,9	110,9
103	119,8	81,7	125,5
102,2	111,3	75,1	116,8
98,4	110,6	69,9	116,8
111,4	120,1	84	125,5
86,6	97,5	54,3	104,2
91,3	107,7	60	115,1
107,9	127,3	89,9	132,8
101,8	117,2	77	123,3
104,4	119,8	85,3	124,8
93,4	116,2	77,6	122
100,1	111	69,2	117,4
98,5	112,4	75,5	117,9
112,9	130,6	85,7	137,4
101,4	109,1	72,2	114,6
107,1	118,8	79,9	124,7
110,8	123,9	85,3	129,6
90,3	101,6	52,2	109,4
95,5	112,8	61,2	120,9
111,4	128	82,4	134,9
113	129,6	85,4	136,3
107,5	125,8	78,2	133,2
95,9	119,5	70,2	127,2
106,3	115,7	70,2	122,7
105,2	113,6	69,3	120,5
117,2	129,7	77,5	137,8
106,9	112	66,1	119,1
108,2	116,8	69	124,3
110	126,3	75,3	134,3
96,1	112,9	58,2	121,7
100,6	115,9	59,7	125

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=4406&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=4406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4406&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
Totale-Consumptiegoederen[t] = + 2.52721795203605 + 0.00505963680901596`Intermediaire-goederen`[t] + 0.117591019265851`Duurzame-consumptiegoederen`[t] + 0.85214723860919`Niet-duurzame-consumptiegoederen `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Totale-Consumptiegoederen[t] =  +  2.52721795203605 +  0.00505963680901596`Intermediaire-goederen`[t] +  0.117591019265851`Duurzame-consumptiegoederen`[t] +  0.85214723860919`Niet-duurzame-consumptiegoederen
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4406&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Totale-Consumptiegoederen[t] =  +  2.52721795203605 +  0.00505963680901596`Intermediaire-goederen`[t] +  0.117591019265851`Duurzame-consumptiegoederen`[t] +  0.85214723860919`Niet-duurzame-consumptiegoederen
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4406&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
Totale-Consumptiegoederen[t] = + 2.52721795203605 + 0.00505963680901596`Intermediaire-goederen`[t] + 0.117591019265851`Duurzame-consumptiegoederen`[t] + 0.85214723860919`Niet-duurzame-consumptiegoederen `[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)	2.52721795203605	1.293398	1.9539	0.054388	0.027194
`Intermediaire-goederen`	0.00505963680901596	0.016589	0.305	0.761201	0.3806
`Duurzame-consumptiegoederen`	0.117591019265851	0.007167	16.4063	0	0
`Niet-duurzame-consumptiegoederen `	0.85214723860919	0.010044	84.8444	0	0

\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) & 2.52721795203605 & 1.293398 & 1.9539 & 0.054388 & 0.027194 \tabularnewline
`Intermediaire-goederen` & 0.00505963680901596 & 0.016589 & 0.305 & 0.761201 & 0.3806 \tabularnewline
`Duurzame-consumptiegoederen` & 0.117591019265851 & 0.007167 & 16.4063 & 0 & 0 \tabularnewline
`Niet-duurzame-consumptiegoederen
` & 0.85214723860919 & 0.010044 & 84.8444 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4406&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]2.52721795203605[/C][C]1.293398[/C][C]1.9539[/C][C]0.054388[/C][C]0.027194[/C][/ROW]
[ROW][C]`Intermediaire-goederen`[/C][C]0.00505963680901596[/C][C]0.016589[/C][C]0.305[/C][C]0.761201[/C][C]0.3806[/C][/ROW]
[ROW][C]`Duurzame-consumptiegoederen`[/C][C]0.117591019265851[/C][C]0.007167[/C][C]16.4063[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Niet-duurzame-consumptiegoederen
`[/C][C]0.85214723860919[/C][C]0.010044[/C][C]84.8444[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4406&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4406&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)	2.52721795203605	1.293398	1.9539	0.054388	0.027194
`Intermediaire-goederen`	0.00505963680901596	0.016589	0.305	0.761201	0.3806
`Duurzame-consumptiegoederen`	0.117591019265851	0.007167	16.4063	0	0
`Niet-duurzame-consumptiegoederen `	0.85214723860919	0.010044	84.8444	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.996832156946681
R-squared	0.993674349122973
Adjusted R-squared	0.993424652377827
F-TEST (value)	3979.52463714607
F-TEST (DF numerator)	3
F-TEST (DF denominator)	76
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.815828659679967
Sum Squared Residuals	50.5838065485961

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996832156946681 \tabularnewline
R-squared & 0.993674349122973 \tabularnewline
Adjusted R-squared & 0.993424652377827 \tabularnewline
F-TEST (value) & 3979.52463714607 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 76 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.815828659679967 \tabularnewline
Sum Squared Residuals & 50.5838065485961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4406&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996832156946681[/C][/ROW]
[ROW][C]R-squared[/C][C]0.993674349122973[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.993424652377827[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3979.52463714607[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]76[/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]0.815828659679967[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]50.5838065485961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4406&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4406&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	0.996832156946681
R-squared	0.993674349122973
Adjusted R-squared	0.993424652377827
F-TEST (value)	3979.52463714607
F-TEST (DF numerator)	3
F-TEST (DF denominator)	76
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.815828659679967
Sum Squared Residuals	50.5838065485961

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	98.6	98.6062632238924	-0.00626322389244786
2	98	98.4350988465014	-0.435098846501362
3	106.8	107.122553830943	-0.322553830943246
4	96.6	96.3842933383098	0.215706661690198
5	100.1	100.129370318478	-0.0293703184780553
6	107.7	107.463226616897	0.236773383102613
7	91.5	89.6524674090382	1.84753259096183
8	97.8	95.7037781424034	2.09622185759662
9	107.4	106.930807662301	0.469192337699345
10	117.5	116.559657410116	0.940342589884038
11	105.6	105.214386197259	0.385613802741049
12	97.4	97.1669417762282	0.233058223771783
13	99.5	98.39426152537	1.10573847462996
14	98	97.9036458616602	0.0963541383397808
15	104.3	104.283456230584	0.0165437694155659
16	100.6	100.290415422251	0.309584577749482
17	101.1	100.736842071785	0.363157928214941
18	103.9	103.432287796176	0.467712203824399
19	96.9	95.8252137789838	1.07478622101625
20	95.5	94.4108011087774	1.08919889122258
21	108.4	111.612077543051	-3.21207754305075
22	117	115.834989629269	1.16501037073069
23	103.8	107.085420770278	-3.28542077027753
24	100.8	103.833147897341	-3.03314789734113
25	110.6	110.586877253969	0.0131227460307282
26	104	104.212983183823	-0.212983183822974
27	112.6	112.633897141863	-0.0338971418628386
28	107.3	107.492692578522	-0.192692578521939
29	98.9	99.2217995519966	-0.321799551996616
30	109.8	109.757841829982	0.0421581700177028
31	104.9	104.765622880969	0.134377119030528
32	102.2	102.060179820227	0.139820179773248
33	123.9	123.589267411464	0.31073258853628
34	124.9	124.527013400349	0.372986599651123
35	112.7	112.527871660762	0.172128339237950
36	121.9	121.347930959090	0.552069040910341
37	100.6	100.932834276732	-0.332834276731603
38	104.3	104.432007712693	-0.132007712692878
39	120.4	120.183612795529	0.216387204471160
40	107.5	107.614837475882	-0.114837475881511
41	102.9	103.047347325210	-0.147347325209777
42	125.6	125.161249890965	0.438750109035257
43	107.5	107.805886601112	-0.305886601112124
44	108.8	109.062628018440	-0.262628018440281
45	128.4	128.003660476068	0.3963395239323
46	121.1	120.921036902086	0.178963097914429
47	119.5	119.367230816728	0.132769183271583
48	128.7	128.334094330203	0.365905669797204
49	108.7	108.956127417755	-0.256127417755243
50	105.5	105.734672166782	-0.234672166782047
51	119.8	119.600025262838	0.199974737161828
52	111.3	111.406195850336	-0.106195850336388
53	110.6	110.775495930280	-0.175495930279706
54	120.1	119.912985556345	0.187014443654634
55	97.5	98.1443171089103	-0.644317108910251
56	107.7	108.126771112568	-0.426771112568134
57	127.3	126.809738683029	0.490261316970575
58	117.2	117.166551983178	0.0334480168223722
59	119.8	119.433933356701	0.366066643298577
60	116.2	116.086814235349	0.113185764650535
61	111	111.213071942534	-0.213071942534451
62	112.4	112.371873564319	0.0281264356805221
63	130.6	130.261031883760	0.338968116239801
64	109.1	109.186410260078	-0.0864102600779904
65	118.8	118.727388148189	0.0726118518107436
66	123.9	123.556621777603	0.343378222396777
67	101.6	102.347262265413	-0.747262265413116
68	112.8	113.231584794218	-0.431584794218335
69	128	127.735023968446	0.264976031553612
70	129.6	129.288898579191	0.311101420808759
71	125.8	125.772758798339	0.0272412016609843
72	119.5	119.660455425572	-0.160455425572493
73	115.7	115.878413074645	-0.178413074644901
74	113.6	113.892291631875	-0.292291631875506
75	129.7	129.659400859503	0.0405991404973276
76	112	112.331595618747	-0.331595618747232
77	116.8	117.110352743238	-0.310352743237714
78	126.3	126.381755896961	-0.0817558969607134
79	112.9	113.563565309394	-0.663565309393533
80	115.9	116.574806091343	-0.674806091343205

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 98.6 & 98.6062632238924 & -0.00626322389244786 \tabularnewline
2 & 98 & 98.4350988465014 & -0.435098846501362 \tabularnewline
3 & 106.8 & 107.122553830943 & -0.322553830943246 \tabularnewline
4 & 96.6 & 96.3842933383098 & 0.215706661690198 \tabularnewline
5 & 100.1 & 100.129370318478 & -0.0293703184780553 \tabularnewline
6 & 107.7 & 107.463226616897 & 0.236773383102613 \tabularnewline
7 & 91.5 & 89.6524674090382 & 1.84753259096183 \tabularnewline
8 & 97.8 & 95.7037781424034 & 2.09622185759662 \tabularnewline
9 & 107.4 & 106.930807662301 & 0.469192337699345 \tabularnewline
10 & 117.5 & 116.559657410116 & 0.940342589884038 \tabularnewline
11 & 105.6 & 105.214386197259 & 0.385613802741049 \tabularnewline
12 & 97.4 & 97.1669417762282 & 0.233058223771783 \tabularnewline
13 & 99.5 & 98.39426152537 & 1.10573847462996 \tabularnewline
14 & 98 & 97.9036458616602 & 0.0963541383397808 \tabularnewline
15 & 104.3 & 104.283456230584 & 0.0165437694155659 \tabularnewline
16 & 100.6 & 100.290415422251 & 0.309584577749482 \tabularnewline
17 & 101.1 & 100.736842071785 & 0.363157928214941 \tabularnewline
18 & 103.9 & 103.432287796176 & 0.467712203824399 \tabularnewline
19 & 96.9 & 95.8252137789838 & 1.07478622101625 \tabularnewline
20 & 95.5 & 94.4108011087774 & 1.08919889122258 \tabularnewline
21 & 108.4 & 111.612077543051 & -3.21207754305075 \tabularnewline
22 & 117 & 115.834989629269 & 1.16501037073069 \tabularnewline
23 & 103.8 & 107.085420770278 & -3.28542077027753 \tabularnewline
24 & 100.8 & 103.833147897341 & -3.03314789734113 \tabularnewline
25 & 110.6 & 110.586877253969 & 0.0131227460307282 \tabularnewline
26 & 104 & 104.212983183823 & -0.212983183822974 \tabularnewline
27 & 112.6 & 112.633897141863 & -0.0338971418628386 \tabularnewline
28 & 107.3 & 107.492692578522 & -0.192692578521939 \tabularnewline
29 & 98.9 & 99.2217995519966 & -0.321799551996616 \tabularnewline
30 & 109.8 & 109.757841829982 & 0.0421581700177028 \tabularnewline
31 & 104.9 & 104.765622880969 & 0.134377119030528 \tabularnewline
32 & 102.2 & 102.060179820227 & 0.139820179773248 \tabularnewline
33 & 123.9 & 123.589267411464 & 0.31073258853628 \tabularnewline
34 & 124.9 & 124.527013400349 & 0.372986599651123 \tabularnewline
35 & 112.7 & 112.527871660762 & 0.172128339237950 \tabularnewline
36 & 121.9 & 121.347930959090 & 0.552069040910341 \tabularnewline
37 & 100.6 & 100.932834276732 & -0.332834276731603 \tabularnewline
38 & 104.3 & 104.432007712693 & -0.132007712692878 \tabularnewline
39 & 120.4 & 120.183612795529 & 0.216387204471160 \tabularnewline
40 & 107.5 & 107.614837475882 & -0.114837475881511 \tabularnewline
41 & 102.9 & 103.047347325210 & -0.147347325209777 \tabularnewline
42 & 125.6 & 125.161249890965 & 0.438750109035257 \tabularnewline
43 & 107.5 & 107.805886601112 & -0.305886601112124 \tabularnewline
44 & 108.8 & 109.062628018440 & -0.262628018440281 \tabularnewline
45 & 128.4 & 128.003660476068 & 0.3963395239323 \tabularnewline
46 & 121.1 & 120.921036902086 & 0.178963097914429 \tabularnewline
47 & 119.5 & 119.367230816728 & 0.132769183271583 \tabularnewline
48 & 128.7 & 128.334094330203 & 0.365905669797204 \tabularnewline
49 & 108.7 & 108.956127417755 & -0.256127417755243 \tabularnewline
50 & 105.5 & 105.734672166782 & -0.234672166782047 \tabularnewline
51 & 119.8 & 119.600025262838 & 0.199974737161828 \tabularnewline
52 & 111.3 & 111.406195850336 & -0.106195850336388 \tabularnewline
53 & 110.6 & 110.775495930280 & -0.175495930279706 \tabularnewline
54 & 120.1 & 119.912985556345 & 0.187014443654634 \tabularnewline
55 & 97.5 & 98.1443171089103 & -0.644317108910251 \tabularnewline
56 & 107.7 & 108.126771112568 & -0.426771112568134 \tabularnewline
57 & 127.3 & 126.809738683029 & 0.490261316970575 \tabularnewline
58 & 117.2 & 117.166551983178 & 0.0334480168223722 \tabularnewline
59 & 119.8 & 119.433933356701 & 0.366066643298577 \tabularnewline
60 & 116.2 & 116.086814235349 & 0.113185764650535 \tabularnewline
61 & 111 & 111.213071942534 & -0.213071942534451 \tabularnewline
62 & 112.4 & 112.371873564319 & 0.0281264356805221 \tabularnewline
63 & 130.6 & 130.261031883760 & 0.338968116239801 \tabularnewline
64 & 109.1 & 109.186410260078 & -0.0864102600779904 \tabularnewline
65 & 118.8 & 118.727388148189 & 0.0726118518107436 \tabularnewline
66 & 123.9 & 123.556621777603 & 0.343378222396777 \tabularnewline
67 & 101.6 & 102.347262265413 & -0.747262265413116 \tabularnewline
68 & 112.8 & 113.231584794218 & -0.431584794218335 \tabularnewline
69 & 128 & 127.735023968446 & 0.264976031553612 \tabularnewline
70 & 129.6 & 129.288898579191 & 0.311101420808759 \tabularnewline
71 & 125.8 & 125.772758798339 & 0.0272412016609843 \tabularnewline
72 & 119.5 & 119.660455425572 & -0.160455425572493 \tabularnewline
73 & 115.7 & 115.878413074645 & -0.178413074644901 \tabularnewline
74 & 113.6 & 113.892291631875 & -0.292291631875506 \tabularnewline
75 & 129.7 & 129.659400859503 & 0.0405991404973276 \tabularnewline
76 & 112 & 112.331595618747 & -0.331595618747232 \tabularnewline
77 & 116.8 & 117.110352743238 & -0.310352743237714 \tabularnewline
78 & 126.3 & 126.381755896961 & -0.0817558969607134 \tabularnewline
79 & 112.9 & 113.563565309394 & -0.663565309393533 \tabularnewline
80 & 115.9 & 116.574806091343 & -0.674806091343205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4406&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]98.6[/C][C]98.6062632238924[/C][C]-0.00626322389244786[/C][/ROW]
[ROW][C]2[/C][C]98[/C][C]98.4350988465014[/C][C]-0.435098846501362[/C][/ROW]
[ROW][C]3[/C][C]106.8[/C][C]107.122553830943[/C][C]-0.322553830943246[/C][/ROW]
[ROW][C]4[/C][C]96.6[/C][C]96.3842933383098[/C][C]0.215706661690198[/C][/ROW]
[ROW][C]5[/C][C]100.1[/C][C]100.129370318478[/C][C]-0.0293703184780553[/C][/ROW]
[ROW][C]6[/C][C]107.7[/C][C]107.463226616897[/C][C]0.236773383102613[/C][/ROW]
[ROW][C]7[/C][C]91.5[/C][C]89.6524674090382[/C][C]1.84753259096183[/C][/ROW]
[ROW][C]8[/C][C]97.8[/C][C]95.7037781424034[/C][C]2.09622185759662[/C][/ROW]
[ROW][C]9[/C][C]107.4[/C][C]106.930807662301[/C][C]0.469192337699345[/C][/ROW]
[ROW][C]10[/C][C]117.5[/C][C]116.559657410116[/C][C]0.940342589884038[/C][/ROW]
[ROW][C]11[/C][C]105.6[/C][C]105.214386197259[/C][C]0.385613802741049[/C][/ROW]
[ROW][C]12[/C][C]97.4[/C][C]97.1669417762282[/C][C]0.233058223771783[/C][/ROW]
[ROW][C]13[/C][C]99.5[/C][C]98.39426152537[/C][C]1.10573847462996[/C][/ROW]
[ROW][C]14[/C][C]98[/C][C]97.9036458616602[/C][C]0.0963541383397808[/C][/ROW]
[ROW][C]15[/C][C]104.3[/C][C]104.283456230584[/C][C]0.0165437694155659[/C][/ROW]
[ROW][C]16[/C][C]100.6[/C][C]100.290415422251[/C][C]0.309584577749482[/C][/ROW]
[ROW][C]17[/C][C]101.1[/C][C]100.736842071785[/C][C]0.363157928214941[/C][/ROW]
[ROW][C]18[/C][C]103.9[/C][C]103.432287796176[/C][C]0.467712203824399[/C][/ROW]
[ROW][C]19[/C][C]96.9[/C][C]95.8252137789838[/C][C]1.07478622101625[/C][/ROW]
[ROW][C]20[/C][C]95.5[/C][C]94.4108011087774[/C][C]1.08919889122258[/C][/ROW]
[ROW][C]21[/C][C]108.4[/C][C]111.612077543051[/C][C]-3.21207754305075[/C][/ROW]
[ROW][C]22[/C][C]117[/C][C]115.834989629269[/C][C]1.16501037073069[/C][/ROW]
[ROW][C]23[/C][C]103.8[/C][C]107.085420770278[/C][C]-3.28542077027753[/C][/ROW]
[ROW][C]24[/C][C]100.8[/C][C]103.833147897341[/C][C]-3.03314789734113[/C][/ROW]
[ROW][C]25[/C][C]110.6[/C][C]110.586877253969[/C][C]0.0131227460307282[/C][/ROW]
[ROW][C]26[/C][C]104[/C][C]104.212983183823[/C][C]-0.212983183822974[/C][/ROW]
[ROW][C]27[/C][C]112.6[/C][C]112.633897141863[/C][C]-0.0338971418628386[/C][/ROW]
[ROW][C]28[/C][C]107.3[/C][C]107.492692578522[/C][C]-0.192692578521939[/C][/ROW]
[ROW][C]29[/C][C]98.9[/C][C]99.2217995519966[/C][C]-0.321799551996616[/C][/ROW]
[ROW][C]30[/C][C]109.8[/C][C]109.757841829982[/C][C]0.0421581700177028[/C][/ROW]
[ROW][C]31[/C][C]104.9[/C][C]104.765622880969[/C][C]0.134377119030528[/C][/ROW]
[ROW][C]32[/C][C]102.2[/C][C]102.060179820227[/C][C]0.139820179773248[/C][/ROW]
[ROW][C]33[/C][C]123.9[/C][C]123.589267411464[/C][C]0.31073258853628[/C][/ROW]
[ROW][C]34[/C][C]124.9[/C][C]124.527013400349[/C][C]0.372986599651123[/C][/ROW]
[ROW][C]35[/C][C]112.7[/C][C]112.527871660762[/C][C]0.172128339237950[/C][/ROW]
[ROW][C]36[/C][C]121.9[/C][C]121.347930959090[/C][C]0.552069040910341[/C][/ROW]
[ROW][C]37[/C][C]100.6[/C][C]100.932834276732[/C][C]-0.332834276731603[/C][/ROW]
[ROW][C]38[/C][C]104.3[/C][C]104.432007712693[/C][C]-0.132007712692878[/C][/ROW]
[ROW][C]39[/C][C]120.4[/C][C]120.183612795529[/C][C]0.216387204471160[/C][/ROW]
[ROW][C]40[/C][C]107.5[/C][C]107.614837475882[/C][C]-0.114837475881511[/C][/ROW]
[ROW][C]41[/C][C]102.9[/C][C]103.047347325210[/C][C]-0.147347325209777[/C][/ROW]
[ROW][C]42[/C][C]125.6[/C][C]125.161249890965[/C][C]0.438750109035257[/C][/ROW]
[ROW][C]43[/C][C]107.5[/C][C]107.805886601112[/C][C]-0.305886601112124[/C][/ROW]
[ROW][C]44[/C][C]108.8[/C][C]109.062628018440[/C][C]-0.262628018440281[/C][/ROW]
[ROW][C]45[/C][C]128.4[/C][C]128.003660476068[/C][C]0.3963395239323[/C][/ROW]
[ROW][C]46[/C][C]121.1[/C][C]120.921036902086[/C][C]0.178963097914429[/C][/ROW]
[ROW][C]47[/C][C]119.5[/C][C]119.367230816728[/C][C]0.132769183271583[/C][/ROW]
[ROW][C]48[/C][C]128.7[/C][C]128.334094330203[/C][C]0.365905669797204[/C][/ROW]
[ROW][C]49[/C][C]108.7[/C][C]108.956127417755[/C][C]-0.256127417755243[/C][/ROW]
[ROW][C]50[/C][C]105.5[/C][C]105.734672166782[/C][C]-0.234672166782047[/C][/ROW]
[ROW][C]51[/C][C]119.8[/C][C]119.600025262838[/C][C]0.199974737161828[/C][/ROW]
[ROW][C]52[/C][C]111.3[/C][C]111.406195850336[/C][C]-0.106195850336388[/C][/ROW]
[ROW][C]53[/C][C]110.6[/C][C]110.775495930280[/C][C]-0.175495930279706[/C][/ROW]
[ROW][C]54[/C][C]120.1[/C][C]119.912985556345[/C][C]0.187014443654634[/C][/ROW]
[ROW][C]55[/C][C]97.5[/C][C]98.1443171089103[/C][C]-0.644317108910251[/C][/ROW]
[ROW][C]56[/C][C]107.7[/C][C]108.126771112568[/C][C]-0.426771112568134[/C][/ROW]
[ROW][C]57[/C][C]127.3[/C][C]126.809738683029[/C][C]0.490261316970575[/C][/ROW]
[ROW][C]58[/C][C]117.2[/C][C]117.166551983178[/C][C]0.0334480168223722[/C][/ROW]
[ROW][C]59[/C][C]119.8[/C][C]119.433933356701[/C][C]0.366066643298577[/C][/ROW]
[ROW][C]60[/C][C]116.2[/C][C]116.086814235349[/C][C]0.113185764650535[/C][/ROW]
[ROW][C]61[/C][C]111[/C][C]111.213071942534[/C][C]-0.213071942534451[/C][/ROW]
[ROW][C]62[/C][C]112.4[/C][C]112.371873564319[/C][C]0.0281264356805221[/C][/ROW]
[ROW][C]63[/C][C]130.6[/C][C]130.261031883760[/C][C]0.338968116239801[/C][/ROW]
[ROW][C]64[/C][C]109.1[/C][C]109.186410260078[/C][C]-0.0864102600779904[/C][/ROW]
[ROW][C]65[/C][C]118.8[/C][C]118.727388148189[/C][C]0.0726118518107436[/C][/ROW]
[ROW][C]66[/C][C]123.9[/C][C]123.556621777603[/C][C]0.343378222396777[/C][/ROW]
[ROW][C]67[/C][C]101.6[/C][C]102.347262265413[/C][C]-0.747262265413116[/C][/ROW]
[ROW][C]68[/C][C]112.8[/C][C]113.231584794218[/C][C]-0.431584794218335[/C][/ROW]
[ROW][C]69[/C][C]128[/C][C]127.735023968446[/C][C]0.264976031553612[/C][/ROW]
[ROW][C]70[/C][C]129.6[/C][C]129.288898579191[/C][C]0.311101420808759[/C][/ROW]
[ROW][C]71[/C][C]125.8[/C][C]125.772758798339[/C][C]0.0272412016609843[/C][/ROW]
[ROW][C]72[/C][C]119.5[/C][C]119.660455425572[/C][C]-0.160455425572493[/C][/ROW]
[ROW][C]73[/C][C]115.7[/C][C]115.878413074645[/C][C]-0.178413074644901[/C][/ROW]
[ROW][C]74[/C][C]113.6[/C][C]113.892291631875[/C][C]-0.292291631875506[/C][/ROW]
[ROW][C]75[/C][C]129.7[/C][C]129.659400859503[/C][C]0.0405991404973276[/C][/ROW]
[ROW][C]76[/C][C]112[/C][C]112.331595618747[/C][C]-0.331595618747232[/C][/ROW]
[ROW][C]77[/C][C]116.8[/C][C]117.110352743238[/C][C]-0.310352743237714[/C][/ROW]
[ROW][C]78[/C][C]126.3[/C][C]126.381755896961[/C][C]-0.0817558969607134[/C][/ROW]
[ROW][C]79[/C][C]112.9[/C][C]113.563565309394[/C][C]-0.663565309393533[/C][/ROW]
[ROW][C]80[/C][C]115.9[/C][C]116.574806091343[/C][C]-0.674806091343205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4406&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4406&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	98.6	98.6062632238924	-0.00626322389244786
2	98	98.4350988465014	-0.435098846501362
3	106.8	107.122553830943	-0.322553830943246
4	96.6	96.3842933383098	0.215706661690198
5	100.1	100.129370318478	-0.0293703184780553
6	107.7	107.463226616897	0.236773383102613
7	91.5	89.6524674090382	1.84753259096183
8	97.8	95.7037781424034	2.09622185759662
9	107.4	106.930807662301	0.469192337699345
10	117.5	116.559657410116	0.940342589884038
11	105.6	105.214386197259	0.385613802741049
12	97.4	97.1669417762282	0.233058223771783
13	99.5	98.39426152537	1.10573847462996
14	98	97.9036458616602	0.0963541383397808
15	104.3	104.283456230584	0.0165437694155659
16	100.6	100.290415422251	0.309584577749482
17	101.1	100.736842071785	0.363157928214941
18	103.9	103.432287796176	0.467712203824399
19	96.9	95.8252137789838	1.07478622101625
20	95.5	94.4108011087774	1.08919889122258
21	108.4	111.612077543051	-3.21207754305075
22	117	115.834989629269	1.16501037073069
23	103.8	107.085420770278	-3.28542077027753
24	100.8	103.833147897341	-3.03314789734113
25	110.6	110.586877253969	0.0131227460307282
26	104	104.212983183823	-0.212983183822974
27	112.6	112.633897141863	-0.0338971418628386
28	107.3	107.492692578522	-0.192692578521939
29	98.9	99.2217995519966	-0.321799551996616
30	109.8	109.757841829982	0.0421581700177028
31	104.9	104.765622880969	0.134377119030528
32	102.2	102.060179820227	0.139820179773248
33	123.9	123.589267411464	0.31073258853628
34	124.9	124.527013400349	0.372986599651123
35	112.7	112.527871660762	0.172128339237950
36	121.9	121.347930959090	0.552069040910341
37	100.6	100.932834276732	-0.332834276731603
38	104.3	104.432007712693	-0.132007712692878
39	120.4	120.183612795529	0.216387204471160
40	107.5	107.614837475882	-0.114837475881511
41	102.9	103.047347325210	-0.147347325209777
42	125.6	125.161249890965	0.438750109035257
43	107.5	107.805886601112	-0.305886601112124
44	108.8	109.062628018440	-0.262628018440281
45	128.4	128.003660476068	0.3963395239323
46	121.1	120.921036902086	0.178963097914429
47	119.5	119.367230816728	0.132769183271583
48	128.7	128.334094330203	0.365905669797204
49	108.7	108.956127417755	-0.256127417755243
50	105.5	105.734672166782	-0.234672166782047
51	119.8	119.600025262838	0.199974737161828
52	111.3	111.406195850336	-0.106195850336388
53	110.6	110.775495930280	-0.175495930279706
54	120.1	119.912985556345	0.187014443654634
55	97.5	98.1443171089103	-0.644317108910251
56	107.7	108.126771112568	-0.426771112568134
57	127.3	126.809738683029	0.490261316970575
58	117.2	117.166551983178	0.0334480168223722
59	119.8	119.433933356701	0.366066643298577
60	116.2	116.086814235349	0.113185764650535
61	111	111.213071942534	-0.213071942534451
62	112.4	112.371873564319	0.0281264356805221
63	130.6	130.261031883760	0.338968116239801
64	109.1	109.186410260078	-0.0864102600779904
65	118.8	118.727388148189	0.0726118518107436
66	123.9	123.556621777603	0.343378222396777
67	101.6	102.347262265413	-0.747262265413116
68	112.8	113.231584794218	-0.431584794218335
69	128	127.735023968446	0.264976031553612
70	129.6	129.288898579191	0.311101420808759
71	125.8	125.772758798339	0.0272412016609843
72	119.5	119.660455425572	-0.160455425572493
73	115.7	115.878413074645	-0.178413074644901
74	113.6	113.892291631875	-0.292291631875506
75	129.7	129.659400859503	0.0405991404973276
76	112	112.331595618747	-0.331595618747232
77	116.8	117.110352743238	-0.310352743237714
78	126.3	126.381755896961	-0.0817558969607134
79	112.9	113.563565309394	-0.663565309393533
80	115.9	116.574806091343	-0.674806091343205

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 = 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