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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 15 Nov 2007 04:28:14 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/15/t11951259101xrn65u80yhjogu.htm/, Retrieved Sat, 04 May 2024 07:42:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5427, Retrieved Sat, 04 May 2024 07:42:58 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q3, workshop 8, Rik, werkloosheid

Estimated Impact

287

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

-       [Multiple Regression] [Q3_WS8_Werklooshe...] [2007-11-15 11:28:14] [0ea70c1b491052c6d2a865ea09f80161] [Current]

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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=5427&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=5427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5427&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
<25[t] = + 145.357865871655 -1.33837687591762`ST/DL`[t] + 21.6262589242684Outc[t] -4.22921472041965M1[t] -11.7252604896346M2[t] -21.8230233049027M3[t] -26.3155591420747M4[t] -28.5825103953017M5[t] -31.3469398772365M6[t] -35.7216398798517M7[t] -39.5988616537590M8[t] -44.6427500943329M9[t] -44.1891603061991M10[t] -8.51250770541228M11[t] -0.289444892759341t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
<25[t] =  +  145.357865871655 -1.33837687591762`ST/DL`[t] +  21.6262589242684Outc[t] -4.22921472041965M1[t] -11.7252604896346M2[t] -21.8230233049027M3[t] -26.3155591420747M4[t] -28.5825103953017M5[t] -31.3469398772365M6[t] -35.7216398798517M7[t] -39.5988616537590M8[t] -44.6427500943329M9[t] -44.1891603061991M10[t] -8.51250770541228M11[t] -0.289444892759341t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5427&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]<25[t] =  +  145.357865871655 -1.33837687591762`ST/DL`[t] +  21.6262589242684Outc[t] -4.22921472041965M1[t] -11.7252604896346M2[t] -21.8230233049027M3[t] -26.3155591420747M4[t] -28.5825103953017M5[t] -31.3469398772365M6[t] -35.7216398798517M7[t] -39.5988616537590M8[t] -44.6427500943329M9[t] -44.1891603061991M10[t] -8.51250770541228M11[t] -0.289444892759341t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5427&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
<25[t] = + 145.357865871655 -1.33837687591762`ST/DL`[t] + 21.6262589242684Outc[t] -4.22921472041965M1[t] -11.7252604896346M2[t] -21.8230233049027M3[t] -26.3155591420747M4[t] -28.5825103953017M5[t] -31.3469398772365M6[t] -35.7216398798517M7[t] -39.5988616537590M8[t] -44.6427500943329M9[t] -44.1891603061991M10[t] -8.51250770541228M11[t] -0.289444892759341t + 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)	145.357865871655	3.345663	43.4467	0	0
`ST/DL`	-1.33837687591762	2.351273	-0.5692	0.571409	0.285704
Outc	21.6262589242684	2.90918	7.4338	0	0
M1	-4.22921472041965	4.032372	-1.0488	0.298614	0.149307
M2	-11.7252604896346	4.174553	-2.8087	0.006767	0.003383
M3	-21.8230233049027	4.478975	-4.8723	9e-06	4e-06
M4	-26.3155591420747	3.934067	-6.6891	0	0
M5	-28.5825103953017	3.934324	-7.2649	0	0
M6	-31.3469398772365	3.95506	-7.9258	0	0
M7	-35.7216398798517	4.258035	-8.3892	0	0
M8	-39.5988616537590	4.247708	-9.3224	0	0
M9	-44.6427500943329	4.238038	-10.5338	0	0
M10	-44.1891603061991	3.935521	-11.2283	0	0
M11	-8.51250770541228	3.928519	-2.1668	0.034367	0.017183
t	-0.289444892759341	0.053707	-5.3894	1e-06	1e-06

\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) & 145.357865871655 & 3.345663 & 43.4467 & 0 & 0 \tabularnewline
`ST/DL` & -1.33837687591762 & 2.351273 & -0.5692 & 0.571409 & 0.285704 \tabularnewline
Outc & 21.6262589242684 & 2.90918 & 7.4338 & 0 & 0 \tabularnewline
M1 & -4.22921472041965 & 4.032372 & -1.0488 & 0.298614 & 0.149307 \tabularnewline
M2 & -11.7252604896346 & 4.174553 & -2.8087 & 0.006767 & 0.003383 \tabularnewline
M3 & -21.8230233049027 & 4.478975 & -4.8723 & 9e-06 & 4e-06 \tabularnewline
M4 & -26.3155591420747 & 3.934067 & -6.6891 & 0 & 0 \tabularnewline
M5 & -28.5825103953017 & 3.934324 & -7.2649 & 0 & 0 \tabularnewline
M6 & -31.3469398772365 & 3.95506 & -7.9258 & 0 & 0 \tabularnewline
M7 & -35.7216398798517 & 4.258035 & -8.3892 & 0 & 0 \tabularnewline
M8 & -39.5988616537590 & 4.247708 & -9.3224 & 0 & 0 \tabularnewline
M9 & -44.6427500943329 & 4.238038 & -10.5338 & 0 & 0 \tabularnewline
M10 & -44.1891603061991 & 3.935521 & -11.2283 & 0 & 0 \tabularnewline
M11 & -8.51250770541228 & 3.928519 & -2.1668 & 0.034367 & 0.017183 \tabularnewline
t & -0.289444892759341 & 0.053707 & -5.3894 & 1e-06 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5427&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]145.357865871655[/C][C]3.345663[/C][C]43.4467[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`ST/DL`[/C][C]-1.33837687591762[/C][C]2.351273[/C][C]-0.5692[/C][C]0.571409[/C][C]0.285704[/C][/ROW]
[ROW][C]Outc[/C][C]21.6262589242684[/C][C]2.90918[/C][C]7.4338[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-4.22921472041965[/C][C]4.032372[/C][C]-1.0488[/C][C]0.298614[/C][C]0.149307[/C][/ROW]
[ROW][C]M2[/C][C]-11.7252604896346[/C][C]4.174553[/C][C]-2.8087[/C][C]0.006767[/C][C]0.003383[/C][/ROW]
[ROW][C]M3[/C][C]-21.8230233049027[/C][C]4.478975[/C][C]-4.8723[/C][C]9e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]M4[/C][C]-26.3155591420747[/C][C]3.934067[/C][C]-6.6891[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-28.5825103953017[/C][C]3.934324[/C][C]-7.2649[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-31.3469398772365[/C][C]3.95506[/C][C]-7.9258[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]-35.7216398798517[/C][C]4.258035[/C][C]-8.3892[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-39.5988616537590[/C][C]4.247708[/C][C]-9.3224[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-44.6427500943329[/C][C]4.238038[/C][C]-10.5338[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-44.1891603061991[/C][C]3.935521[/C][C]-11.2283[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-8.51250770541228[/C][C]3.928519[/C][C]-2.1668[/C][C]0.034367[/C][C]0.017183[/C][/ROW]
[ROW][C]t[/C][C]-0.289444892759341[/C][C]0.053707[/C][C]-5.3894[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5427&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5427&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)	145.357865871655	3.345663	43.4467	0	0
`ST/DL`	-1.33837687591762	2.351273	-0.5692	0.571409	0.285704
Outc	21.6262589242684	2.90918	7.4338	0	0
M1	-4.22921472041965	4.032372	-1.0488	0.298614	0.149307
M2	-11.7252604896346	4.174553	-2.8087	0.006767	0.003383
M3	-21.8230233049027	4.478975	-4.8723	9e-06	4e-06
M4	-26.3155591420747	3.934067	-6.6891	0	0
M5	-28.5825103953017	3.934324	-7.2649	0	0
M6	-31.3469398772365	3.95506	-7.9258	0	0
M7	-35.7216398798517	4.258035	-8.3892	0	0
M8	-39.5988616537590	4.247708	-9.3224	0	0
M9	-44.6427500943329	4.238038	-10.5338	0	0
M10	-44.1891603061991	3.935521	-11.2283	0	0
M11	-8.51250770541228	3.928519	-2.1668	0.034367	0.017183
t	-0.289444892759341	0.053707	-5.3894	1e-06	1e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.93838584467497
R-squared	0.880567993486356
Adjusted R-squared	0.851739578120994
F-TEST (value)	30.5451403528884
F-TEST (DF numerator)	14
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.77324447055734
Sum Squared Residuals	2660.85675816027

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.93838584467497 \tabularnewline
R-squared & 0.880567993486356 \tabularnewline
Adjusted R-squared & 0.851739578120994 \tabularnewline
F-TEST (value) & 30.5451403528884 \tabularnewline
F-TEST (DF numerator) & 14 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.77324447055734 \tabularnewline
Sum Squared Residuals & 2660.85675816027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5427&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.93838584467497[/C][/ROW]
[ROW][C]R-squared[/C][C]0.880567993486356[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.851739578120994[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]30.5451403528884[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]14[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/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]6.77324447055734[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2660.85675816027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5427&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5427&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	0.93838584467497
R-squared	0.880567993486356
Adjusted R-squared	0.851739578120994
F-TEST (value)	30.5451403528884
F-TEST (DF numerator)	14
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.77324447055734
Sum Squared Residuals	2660.85675816027

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	140	140.839206258476	-0.839206258476054
2	132	131.715338720584	0.284661279416025
3	117	121.328131012557	-4.32813101255654
4	114	117.884527158543	-3.88452715854283
5	113	115.328131012557	-2.32813101255654
6	110	112.274256637862	-2.27425663786241
7	107	106.271734866570	0.728265133429657
8	103	102.105068199904	0.894931800096396
9	98	96.7717348665703	1.22826513342974
10	98	98.2742566378624	-0.274256637862373
11	137	133.661464345890	3.33853565411012
12	148	140.546150282625	7.45384971737482
13	147	157.653749593715	-10.6537495937146
14	139	151.206635807658	-12.2066358076580
15	130	139.481051223713	-9.48105122371286
16	128	136.037447369699	-8.03744736969914
17	127	133.481051223713	-6.48105122371287
18	123	130.427176849019	-7.42717684901875
19	118	124.424655077727	-6.42465507772658
20	114	121.596365286978	-7.59636528697757
21	108	114.924655077727	-6.9246550777266
22	111	116.427176849019	-5.42717684901876
23	151	151.814384557046	-0.814384557046205
24	159	160.037447369699	-1.03744736969914
25	158	154.180410880603	3.81958911939748
26	148	146.394920218628	1.60507978137176
27	138	136.007712510601	1.99228748939922
28	137	132.564108656587	4.43589134341295
29	136	130.007712510601	5.99228748939922
30	133	126.953838135907	6.04616186409334
31	126	122.289693240532	3.71030675946787
32	120	116.784649697948	3.21535030205216
33	114	111.451316364615	2.54868363538549
34	116	112.953838135907	3.04616186409333
35	153	148.341045843934	4.65895415606589
36	162	156.564108656587	5.43589134341294
37	161	152.045449043408	8.95455095659194
38	149	144.259958381434	4.74004161856621
39	139	132.534373797489	6.46562620251131
40	135	129.090769943475	5.90923005652504
41	130	126.534373797489	3.46562620251131
42	127	123.480499422795	3.51950057720543
43	122	117.477977651502	4.52202234849759
44	117	113.311310984836	3.68868901516425
45	112	107.977977651502	4.02202234849757
46	113	109.480499422795	3.51950057720542
47	149	144.867707130822	4.13229286917798
48	157	153.090769943475	3.90923005652504
49	157	147.233733454378	9.76626654562166
50	147	139.448242792404	7.55175720759594
51	137	129.061035084377	7.9389649156234
52	132	125.617431230363	6.38256876963713
53	125	123.061035084377	1.9389649156234
54	123	118.668783833765	4.33121616623516
55	117	114.004638938390	2.99536106160969
56	114	109.837972271724	4.16202772827634
57	111	105.843015814308	5.15698418569204
58	112	104.668783833765	7.33121616623515
59	144	141.39436841771	2.60563158229006
60	150	149.617431230363	0.382568769637127
61	149	143.760394741266	5.23960525873376
62	134	135.974904079292	-1.97490407929197
63	123	125.587696371265	-2.58769637126451
64	116	120.805715641333	-4.80571564133316
65	117	119.587696371265	-2.58769637126451
66	111	115.195445120653	-4.19544512065275
67	105	110.531300225278	-5.53130022527822
68	102	106.364633558612	-4.36463355861158
69	95	101.031300225278	-6.03130022527824
70	93	101.195445120653	-8.19544512065276
71	124	137.921029704598	-13.9210297045978
72	130	146.144092517251	-16.1440925172508
73	124	140.287056028154	-16.2870560281542

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 140 & 140.839206258476 & -0.839206258476054 \tabularnewline
2 & 132 & 131.715338720584 & 0.284661279416025 \tabularnewline
3 & 117 & 121.328131012557 & -4.32813101255654 \tabularnewline
4 & 114 & 117.884527158543 & -3.88452715854283 \tabularnewline
5 & 113 & 115.328131012557 & -2.32813101255654 \tabularnewline
6 & 110 & 112.274256637862 & -2.27425663786241 \tabularnewline
7 & 107 & 106.271734866570 & 0.728265133429657 \tabularnewline
8 & 103 & 102.105068199904 & 0.894931800096396 \tabularnewline
9 & 98 & 96.7717348665703 & 1.22826513342974 \tabularnewline
10 & 98 & 98.2742566378624 & -0.274256637862373 \tabularnewline
11 & 137 & 133.661464345890 & 3.33853565411012 \tabularnewline
12 & 148 & 140.546150282625 & 7.45384971737482 \tabularnewline
13 & 147 & 157.653749593715 & -10.6537495937146 \tabularnewline
14 & 139 & 151.206635807658 & -12.2066358076580 \tabularnewline
15 & 130 & 139.481051223713 & -9.48105122371286 \tabularnewline
16 & 128 & 136.037447369699 & -8.03744736969914 \tabularnewline
17 & 127 & 133.481051223713 & -6.48105122371287 \tabularnewline
18 & 123 & 130.427176849019 & -7.42717684901875 \tabularnewline
19 & 118 & 124.424655077727 & -6.42465507772658 \tabularnewline
20 & 114 & 121.596365286978 & -7.59636528697757 \tabularnewline
21 & 108 & 114.924655077727 & -6.9246550777266 \tabularnewline
22 & 111 & 116.427176849019 & -5.42717684901876 \tabularnewline
23 & 151 & 151.814384557046 & -0.814384557046205 \tabularnewline
24 & 159 & 160.037447369699 & -1.03744736969914 \tabularnewline
25 & 158 & 154.180410880603 & 3.81958911939748 \tabularnewline
26 & 148 & 146.394920218628 & 1.60507978137176 \tabularnewline
27 & 138 & 136.007712510601 & 1.99228748939922 \tabularnewline
28 & 137 & 132.564108656587 & 4.43589134341295 \tabularnewline
29 & 136 & 130.007712510601 & 5.99228748939922 \tabularnewline
30 & 133 & 126.953838135907 & 6.04616186409334 \tabularnewline
31 & 126 & 122.289693240532 & 3.71030675946787 \tabularnewline
32 & 120 & 116.784649697948 & 3.21535030205216 \tabularnewline
33 & 114 & 111.451316364615 & 2.54868363538549 \tabularnewline
34 & 116 & 112.953838135907 & 3.04616186409333 \tabularnewline
35 & 153 & 148.341045843934 & 4.65895415606589 \tabularnewline
36 & 162 & 156.564108656587 & 5.43589134341294 \tabularnewline
37 & 161 & 152.045449043408 & 8.95455095659194 \tabularnewline
38 & 149 & 144.259958381434 & 4.74004161856621 \tabularnewline
39 & 139 & 132.534373797489 & 6.46562620251131 \tabularnewline
40 & 135 & 129.090769943475 & 5.90923005652504 \tabularnewline
41 & 130 & 126.534373797489 & 3.46562620251131 \tabularnewline
42 & 127 & 123.480499422795 & 3.51950057720543 \tabularnewline
43 & 122 & 117.477977651502 & 4.52202234849759 \tabularnewline
44 & 117 & 113.311310984836 & 3.68868901516425 \tabularnewline
45 & 112 & 107.977977651502 & 4.02202234849757 \tabularnewline
46 & 113 & 109.480499422795 & 3.51950057720542 \tabularnewline
47 & 149 & 144.867707130822 & 4.13229286917798 \tabularnewline
48 & 157 & 153.090769943475 & 3.90923005652504 \tabularnewline
49 & 157 & 147.233733454378 & 9.76626654562166 \tabularnewline
50 & 147 & 139.448242792404 & 7.55175720759594 \tabularnewline
51 & 137 & 129.061035084377 & 7.9389649156234 \tabularnewline
52 & 132 & 125.617431230363 & 6.38256876963713 \tabularnewline
53 & 125 & 123.061035084377 & 1.9389649156234 \tabularnewline
54 & 123 & 118.668783833765 & 4.33121616623516 \tabularnewline
55 & 117 & 114.004638938390 & 2.99536106160969 \tabularnewline
56 & 114 & 109.837972271724 & 4.16202772827634 \tabularnewline
57 & 111 & 105.843015814308 & 5.15698418569204 \tabularnewline
58 & 112 & 104.668783833765 & 7.33121616623515 \tabularnewline
59 & 144 & 141.39436841771 & 2.60563158229006 \tabularnewline
60 & 150 & 149.617431230363 & 0.382568769637127 \tabularnewline
61 & 149 & 143.760394741266 & 5.23960525873376 \tabularnewline
62 & 134 & 135.974904079292 & -1.97490407929197 \tabularnewline
63 & 123 & 125.587696371265 & -2.58769637126451 \tabularnewline
64 & 116 & 120.805715641333 & -4.80571564133316 \tabularnewline
65 & 117 & 119.587696371265 & -2.58769637126451 \tabularnewline
66 & 111 & 115.195445120653 & -4.19544512065275 \tabularnewline
67 & 105 & 110.531300225278 & -5.53130022527822 \tabularnewline
68 & 102 & 106.364633558612 & -4.36463355861158 \tabularnewline
69 & 95 & 101.031300225278 & -6.03130022527824 \tabularnewline
70 & 93 & 101.195445120653 & -8.19544512065276 \tabularnewline
71 & 124 & 137.921029704598 & -13.9210297045978 \tabularnewline
72 & 130 & 146.144092517251 & -16.1440925172508 \tabularnewline
73 & 124 & 140.287056028154 & -16.2870560281542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5427&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]140[/C][C]140.839206258476[/C][C]-0.839206258476054[/C][/ROW]
[ROW][C]2[/C][C]132[/C][C]131.715338720584[/C][C]0.284661279416025[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]121.328131012557[/C][C]-4.32813101255654[/C][/ROW]
[ROW][C]4[/C][C]114[/C][C]117.884527158543[/C][C]-3.88452715854283[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]115.328131012557[/C][C]-2.32813101255654[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]112.274256637862[/C][C]-2.27425663786241[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]106.271734866570[/C][C]0.728265133429657[/C][/ROW]
[ROW][C]8[/C][C]103[/C][C]102.105068199904[/C][C]0.894931800096396[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]96.7717348665703[/C][C]1.22826513342974[/C][/ROW]
[ROW][C]10[/C][C]98[/C][C]98.2742566378624[/C][C]-0.274256637862373[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]133.661464345890[/C][C]3.33853565411012[/C][/ROW]
[ROW][C]12[/C][C]148[/C][C]140.546150282625[/C][C]7.45384971737482[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]157.653749593715[/C][C]-10.6537495937146[/C][/ROW]
[ROW][C]14[/C][C]139[/C][C]151.206635807658[/C][C]-12.2066358076580[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]139.481051223713[/C][C]-9.48105122371286[/C][/ROW]
[ROW][C]16[/C][C]128[/C][C]136.037447369699[/C][C]-8.03744736969914[/C][/ROW]
[ROW][C]17[/C][C]127[/C][C]133.481051223713[/C][C]-6.48105122371287[/C][/ROW]
[ROW][C]18[/C][C]123[/C][C]130.427176849019[/C][C]-7.42717684901875[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]124.424655077727[/C][C]-6.42465507772658[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]121.596365286978[/C][C]-7.59636528697757[/C][/ROW]
[ROW][C]21[/C][C]108[/C][C]114.924655077727[/C][C]-6.9246550777266[/C][/ROW]
[ROW][C]22[/C][C]111[/C][C]116.427176849019[/C][C]-5.42717684901876[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]151.814384557046[/C][C]-0.814384557046205[/C][/ROW]
[ROW][C]24[/C][C]159[/C][C]160.037447369699[/C][C]-1.03744736969914[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]154.180410880603[/C][C]3.81958911939748[/C][/ROW]
[ROW][C]26[/C][C]148[/C][C]146.394920218628[/C][C]1.60507978137176[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]136.007712510601[/C][C]1.99228748939922[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]132.564108656587[/C][C]4.43589134341295[/C][/ROW]
[ROW][C]29[/C][C]136[/C][C]130.007712510601[/C][C]5.99228748939922[/C][/ROW]
[ROW][C]30[/C][C]133[/C][C]126.953838135907[/C][C]6.04616186409334[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]122.289693240532[/C][C]3.71030675946787[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]116.784649697948[/C][C]3.21535030205216[/C][/ROW]
[ROW][C]33[/C][C]114[/C][C]111.451316364615[/C][C]2.54868363538549[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]112.953838135907[/C][C]3.04616186409333[/C][/ROW]
[ROW][C]35[/C][C]153[/C][C]148.341045843934[/C][C]4.65895415606589[/C][/ROW]
[ROW][C]36[/C][C]162[/C][C]156.564108656587[/C][C]5.43589134341294[/C][/ROW]
[ROW][C]37[/C][C]161[/C][C]152.045449043408[/C][C]8.95455095659194[/C][/ROW]
[ROW][C]38[/C][C]149[/C][C]144.259958381434[/C][C]4.74004161856621[/C][/ROW]
[ROW][C]39[/C][C]139[/C][C]132.534373797489[/C][C]6.46562620251131[/C][/ROW]
[ROW][C]40[/C][C]135[/C][C]129.090769943475[/C][C]5.90923005652504[/C][/ROW]
[ROW][C]41[/C][C]130[/C][C]126.534373797489[/C][C]3.46562620251131[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]123.480499422795[/C][C]3.51950057720543[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]117.477977651502[/C][C]4.52202234849759[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]113.311310984836[/C][C]3.68868901516425[/C][/ROW]
[ROW][C]45[/C][C]112[/C][C]107.977977651502[/C][C]4.02202234849757[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]109.480499422795[/C][C]3.51950057720542[/C][/ROW]
[ROW][C]47[/C][C]149[/C][C]144.867707130822[/C][C]4.13229286917798[/C][/ROW]
[ROW][C]48[/C][C]157[/C][C]153.090769943475[/C][C]3.90923005652504[/C][/ROW]
[ROW][C]49[/C][C]157[/C][C]147.233733454378[/C][C]9.76626654562166[/C][/ROW]
[ROW][C]50[/C][C]147[/C][C]139.448242792404[/C][C]7.55175720759594[/C][/ROW]
[ROW][C]51[/C][C]137[/C][C]129.061035084377[/C][C]7.9389649156234[/C][/ROW]
[ROW][C]52[/C][C]132[/C][C]125.617431230363[/C][C]6.38256876963713[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]123.061035084377[/C][C]1.9389649156234[/C][/ROW]
[ROW][C]54[/C][C]123[/C][C]118.668783833765[/C][C]4.33121616623516[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]114.004638938390[/C][C]2.99536106160969[/C][/ROW]
[ROW][C]56[/C][C]114[/C][C]109.837972271724[/C][C]4.16202772827634[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]105.843015814308[/C][C]5.15698418569204[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]104.668783833765[/C][C]7.33121616623515[/C][/ROW]
[ROW][C]59[/C][C]144[/C][C]141.39436841771[/C][C]2.60563158229006[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]149.617431230363[/C][C]0.382568769637127[/C][/ROW]
[ROW][C]61[/C][C]149[/C][C]143.760394741266[/C][C]5.23960525873376[/C][/ROW]
[ROW][C]62[/C][C]134[/C][C]135.974904079292[/C][C]-1.97490407929197[/C][/ROW]
[ROW][C]63[/C][C]123[/C][C]125.587696371265[/C][C]-2.58769637126451[/C][/ROW]
[ROW][C]64[/C][C]116[/C][C]120.805715641333[/C][C]-4.80571564133316[/C][/ROW]
[ROW][C]65[/C][C]117[/C][C]119.587696371265[/C][C]-2.58769637126451[/C][/ROW]
[ROW][C]66[/C][C]111[/C][C]115.195445120653[/C][C]-4.19544512065275[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]110.531300225278[/C][C]-5.53130022527822[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]106.364633558612[/C][C]-4.36463355861158[/C][/ROW]
[ROW][C]69[/C][C]95[/C][C]101.031300225278[/C][C]-6.03130022527824[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]101.195445120653[/C][C]-8.19544512065276[/C][/ROW]
[ROW][C]71[/C][C]124[/C][C]137.921029704598[/C][C]-13.9210297045978[/C][/ROW]
[ROW][C]72[/C][C]130[/C][C]146.144092517251[/C][C]-16.1440925172508[/C][/ROW]
[ROW][C]73[/C][C]124[/C][C]140.287056028154[/C][C]-16.2870560281542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5427&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5427&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	140	140.839206258476	-0.839206258476054
2	132	131.715338720584	0.284661279416025
3	117	121.328131012557	-4.32813101255654
4	114	117.884527158543	-3.88452715854283
5	113	115.328131012557	-2.32813101255654
6	110	112.274256637862	-2.27425663786241
7	107	106.271734866570	0.728265133429657
8	103	102.105068199904	0.894931800096396
9	98	96.7717348665703	1.22826513342974
10	98	98.2742566378624	-0.274256637862373
11	137	133.661464345890	3.33853565411012
12	148	140.546150282625	7.45384971737482
13	147	157.653749593715	-10.6537495937146
14	139	151.206635807658	-12.2066358076580
15	130	139.481051223713	-9.48105122371286
16	128	136.037447369699	-8.03744736969914
17	127	133.481051223713	-6.48105122371287
18	123	130.427176849019	-7.42717684901875
19	118	124.424655077727	-6.42465507772658
20	114	121.596365286978	-7.59636528697757
21	108	114.924655077727	-6.9246550777266
22	111	116.427176849019	-5.42717684901876
23	151	151.814384557046	-0.814384557046205
24	159	160.037447369699	-1.03744736969914
25	158	154.180410880603	3.81958911939748
26	148	146.394920218628	1.60507978137176
27	138	136.007712510601	1.99228748939922
28	137	132.564108656587	4.43589134341295
29	136	130.007712510601	5.99228748939922
30	133	126.953838135907	6.04616186409334
31	126	122.289693240532	3.71030675946787
32	120	116.784649697948	3.21535030205216
33	114	111.451316364615	2.54868363538549
34	116	112.953838135907	3.04616186409333
35	153	148.341045843934	4.65895415606589
36	162	156.564108656587	5.43589134341294
37	161	152.045449043408	8.95455095659194
38	149	144.259958381434	4.74004161856621
39	139	132.534373797489	6.46562620251131
40	135	129.090769943475	5.90923005652504
41	130	126.534373797489	3.46562620251131
42	127	123.480499422795	3.51950057720543
43	122	117.477977651502	4.52202234849759
44	117	113.311310984836	3.68868901516425
45	112	107.977977651502	4.02202234849757
46	113	109.480499422795	3.51950057720542
47	149	144.867707130822	4.13229286917798
48	157	153.090769943475	3.90923005652504
49	157	147.233733454378	9.76626654562166
50	147	139.448242792404	7.55175720759594
51	137	129.061035084377	7.9389649156234
52	132	125.617431230363	6.38256876963713
53	125	123.061035084377	1.9389649156234
54	123	118.668783833765	4.33121616623516
55	117	114.004638938390	2.99536106160969
56	114	109.837972271724	4.16202772827634
57	111	105.843015814308	5.15698418569204
58	112	104.668783833765	7.33121616623515
59	144	141.39436841771	2.60563158229006
60	150	149.617431230363	0.382568769637127
61	149	143.760394741266	5.23960525873376
62	134	135.974904079292	-1.97490407929197
63	123	125.587696371265	-2.58769637126451
64	116	120.805715641333	-4.80571564133316
65	117	119.587696371265	-2.58769637126451
66	111	115.195445120653	-4.19544512065275
67	105	110.531300225278	-5.53130022527822
68	102	106.364633558612	-4.36463355861158
69	95	101.031300225278	-6.03130022527824
70	93	101.195445120653	-8.19544512065276
71	124	137.921029704598	-13.9210297045978
72	130	146.144092517251	-16.1440925172508
73	124	140.287056028154	-16.2870560281542

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 7

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Figure 8

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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