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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 18 Dec 2007 12:42:27 -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/18/t1198005964fvdd37aai93k2nt.htm/, Retrieved Sat, 04 May 2024 06:03:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14394, Retrieved Sat, 04 May 2024 06:03:12 +0000

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Estimated Impact

194

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

-       [Multiple Regression] [] [2007-12-18 19:42:27] [923db922542fbe09e7ff87bb31b2f310] [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=14394&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=14394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14394&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
X[t] = + 389.155925196851 -7.52559055118119Y[t] + 2.2411400918632M1[t] -15.1986056430446M2[t] -21.3065403543307M3[t] -35.5175459317585M4[t] -34.5052050524935M5[t] + 11.8458366141732M6[t] -25.6715862860892M7[t] -21.6841666666666M8[t] + 16.0825049212599M9[t] -60.0464534120734M10[t] -62.0079708005249M11[t] + 0.666911089238846t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X[t] =  +  389.155925196851 -7.52559055118119Y[t] +  2.2411400918632M1[t] -15.1986056430446M2[t] -21.3065403543307M3[t] -35.5175459317585M4[t] -34.5052050524935M5[t] +  11.8458366141732M6[t] -25.6715862860892M7[t] -21.6841666666666M8[t] +  16.0825049212599M9[t] -60.0464534120734M10[t] -62.0079708005249M11[t] +  0.666911089238846t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14394&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X[t] =  +  389.155925196851 -7.52559055118119Y[t] +  2.2411400918632M1[t] -15.1986056430446M2[t] -21.3065403543307M3[t] -35.5175459317585M4[t] -34.5052050524935M5[t] +  11.8458366141732M6[t] -25.6715862860892M7[t] -21.6841666666666M8[t] +  16.0825049212599M9[t] -60.0464534120734M10[t] -62.0079708005249M11[t] +  0.666911089238846t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14394&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
X[t] = + 389.155925196851 -7.52559055118119Y[t] + 2.2411400918632M1[t] -15.1986056430446M2[t] -21.3065403543307M3[t] -35.5175459317585M4[t] -34.5052050524935M5[t] + 11.8458366141732M6[t] -25.6715862860892M7[t] -21.6841666666666M8[t] + 16.0825049212599M9[t] -60.0464534120734M10[t] -62.0079708005249M11[t] + 0.666911089238846t + 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)	389.155925196851	34.929166	11.1413	0	0
Y	-7.52559055118119	4.119764	-1.8267	0.074237	0.037119
M1	2.2411400918632	7.657875	0.2927	0.771099	0.38555
M2	-15.1986056430446	7.799657	-1.9486	0.057455	0.028728
M3	-21.3065403543307	7.76483	-2.744	0.008626	0.004313
M4	-35.5175459317585	7.663006	-4.6349	3e-05	1.5e-05
M5	-34.5052050524935	7.655622	-4.5072	4.5e-05	2.2e-05
M6	11.8458366141732	7.686258	1.5412	0.130127	0.065063
M7	-25.6715862860892	7.686879	-3.3397	0.00167	0.000835
M8	-21.6841666666666	7.678863	-2.8239	0.00699	0.003495
M9	16.0825049212599	7.792141	2.0639	0.044691	0.022345
M10	-60.0464534120734	7.728294	-7.7697	0	0
M11	-62.0079708005249	7.62264	-8.1347	0	0
t	0.666911089238846	0.099146	6.7266	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) & 389.155925196851 & 34.929166 & 11.1413 & 0 & 0 \tabularnewline
Y & -7.52559055118119 & 4.119764 & -1.8267 & 0.074237 & 0.037119 \tabularnewline
M1 & 2.2411400918632 & 7.657875 & 0.2927 & 0.771099 & 0.38555 \tabularnewline
M2 & -15.1986056430446 & 7.799657 & -1.9486 & 0.057455 & 0.028728 \tabularnewline
M3 & -21.3065403543307 & 7.76483 & -2.744 & 0.008626 & 0.004313 \tabularnewline
M4 & -35.5175459317585 & 7.663006 & -4.6349 & 3e-05 & 1.5e-05 \tabularnewline
M5 & -34.5052050524935 & 7.655622 & -4.5072 & 4.5e-05 & 2.2e-05 \tabularnewline
M6 & 11.8458366141732 & 7.686258 & 1.5412 & 0.130127 & 0.065063 \tabularnewline
M7 & -25.6715862860892 & 7.686879 & -3.3397 & 0.00167 & 0.000835 \tabularnewline
M8 & -21.6841666666666 & 7.678863 & -2.8239 & 0.00699 & 0.003495 \tabularnewline
M9 & 16.0825049212599 & 7.792141 & 2.0639 & 0.044691 & 0.022345 \tabularnewline
M10 & -60.0464534120734 & 7.728294 & -7.7697 & 0 & 0 \tabularnewline
M11 & -62.0079708005249 & 7.62264 & -8.1347 & 0 & 0 \tabularnewline
t & 0.666911089238846 & 0.099146 & 6.7266 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14394&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]389.155925196851[/C][C]34.929166[/C][C]11.1413[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y[/C][C]-7.52559055118119[/C][C]4.119764[/C][C]-1.8267[/C][C]0.074237[/C][C]0.037119[/C][/ROW]
[ROW][C]M1[/C][C]2.2411400918632[/C][C]7.657875[/C][C]0.2927[/C][C]0.771099[/C][C]0.38555[/C][/ROW]
[ROW][C]M2[/C][C]-15.1986056430446[/C][C]7.799657[/C][C]-1.9486[/C][C]0.057455[/C][C]0.028728[/C][/ROW]
[ROW][C]M3[/C][C]-21.3065403543307[/C][C]7.76483[/C][C]-2.744[/C][C]0.008626[/C][C]0.004313[/C][/ROW]
[ROW][C]M4[/C][C]-35.5175459317585[/C][C]7.663006[/C][C]-4.6349[/C][C]3e-05[/C][C]1.5e-05[/C][/ROW]
[ROW][C]M5[/C][C]-34.5052050524935[/C][C]7.655622[/C][C]-4.5072[/C][C]4.5e-05[/C][C]2.2e-05[/C][/ROW]
[ROW][C]M6[/C][C]11.8458366141732[/C][C]7.686258[/C][C]1.5412[/C][C]0.130127[/C][C]0.065063[/C][/ROW]
[ROW][C]M7[/C][C]-25.6715862860892[/C][C]7.686879[/C][C]-3.3397[/C][C]0.00167[/C][C]0.000835[/C][/ROW]
[ROW][C]M8[/C][C]-21.6841666666666[/C][C]7.678863[/C][C]-2.8239[/C][C]0.00699[/C][C]0.003495[/C][/ROW]
[ROW][C]M9[/C][C]16.0825049212599[/C][C]7.792141[/C][C]2.0639[/C][C]0.044691[/C][C]0.022345[/C][/ROW]
[ROW][C]M10[/C][C]-60.0464534120734[/C][C]7.728294[/C][C]-7.7697[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-62.0079708005249[/C][C]7.62264[/C][C]-8.1347[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]0.666911089238846[/C][C]0.099146[/C][C]6.7266[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14394&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14394&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)	389.155925196851	34.929166	11.1413	0	0
Y	-7.52559055118119	4.119764	-1.8267	0.074237	0.037119
M1	2.2411400918632	7.657875	0.2927	0.771099	0.38555
M2	-15.1986056430446	7.799657	-1.9486	0.057455	0.028728
M3	-21.3065403543307	7.76483	-2.744	0.008626	0.004313
M4	-35.5175459317585	7.663006	-4.6349	3e-05	1.5e-05
M5	-34.5052050524935	7.655622	-4.5072	4.5e-05	2.2e-05
M6	11.8458366141732	7.686258	1.5412	0.130127	0.065063
M7	-25.6715862860892	7.686879	-3.3397	0.00167	0.000835
M8	-21.6841666666666	7.678863	-2.8239	0.00699	0.003495
M9	16.0825049212599	7.792141	2.0639	0.044691	0.022345
M10	-60.0464534120734	7.728294	-7.7697	0	0
M11	-62.0079708005249	7.62264	-8.1347	0	0
t	0.666911089238846	0.099146	6.7266	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.933813178790619
R-squared	0.87200705288304
Adjusted R-squared	0.835835133045638
F-TEST (value)	24.1072925297536
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	3.33066907387547e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.9874974471114
Sum Squared Residuals	6610.20437204716

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.933813178790619 \tabularnewline
R-squared & 0.87200705288304 \tabularnewline
Adjusted R-squared & 0.835835133045638 \tabularnewline
F-TEST (value) & 24.1072925297536 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 3.33066907387547e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 11.9874974471114 \tabularnewline
Sum Squared Residuals & 6610.20437204716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14394&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.933813178790619[/C][/ROW]
[ROW][C]R-squared[/C][C]0.87200705288304[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.835835133045638[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]24.1072925297536[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]3.33066907387547e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]11.9874974471114[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]6610.20437204716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14394&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14394&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	0.933813178790619
R-squared	0.87200705288304
Adjusted R-squared	0.835835133045638
F-TEST (value)	24.1072925297536
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	3.33066907387547e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.9874974471114
Sum Squared Residuals	6610.20437204716

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	359	331.106692913387	27.8933070866129
2	304.6	312.82874015748	-8.22874015748024
3	297.7	308.140275590551	-10.4402755905512
4	303.3	295.34874015748	7.9512598425197
5	304.7	300.038228346457	4.66177165354334
6	331.3	347.808740157480	-16.5087401574803
7	318.8	310.205669291339	8.59433070866145
8	306.8	311.097204724409	-4.29720472440946
9	331.1	348.025669291339	-16.9256692913386
10	284.1	272.563622047244	11.5363779527559
11	259.7	269.763897637795	-10.0638976377952
12	335.8	333.943897637795	1.85610236220474
13	338.5	336.099389763779	2.40061023622085
14	310.3	317.821437007874	-7.52143700787398
15	322.1	312.380413385827	9.71958661417329
16	289.3	299.588877952756	-10.2888779527559
17	300.8	310.298838582677	-9.4988385826772
18	360.6	358.069350393701	2.53064960629918
19	327.3	320.466279527559	6.8337204724409
20	304.1	313.079665354331	-8.97966535433061
21	362	350.00812992126	11.9918700787402
22	287.8	274.546082677165	13.2539173228348
23	286.1	278.519389763779	7.58061023622051
24	358.2	342.699389763779	15.5006102362205
25	346	345.607440944882	0.392559055118447
26	329.9	326.576929133858	3.32307086614171
27	334.3	321.135905511811	13.164094488189
28	303.7	308.34437007874	-4.64437007874015
29	307.6	313.033858267717	-5.43385826771652
30	351.7	360.051811023622	-8.35181102362206
31	324.6	323.953858267717	0.646141732283486
32	311.9	324.092834645669	-12.1928346456693
33	361.5	361.773858267716	-0.273858267716511
34	271.1	286.311811023622	-15.211811023622
35	286.5	285.769763779528	0.730236220472475
36	352.8	349.949763779528	2.85023622047248
37	322.4	352.857814960630	-30.4578149606296
38	335	333.827303149606	1.17269685039369
39	322.2	328.386279527559	-6.18627952755905
40	313.6	316.347303149606	-2.74730314960627
41	323.3	319.531673228346	3.76832677165357
42	379.1	366.549625984252	12.5503740157481
43	315.6	329.699114173228	-14.0991141732283
44	353.6	335.858562992126	17.741437007874
45	371.7	373.539586614173	-1.83958661417327
46	282.9	298.830098425197	-15.9300984251969
47	298.8	297.535492125984	1.26450787401573
48	361.8	361.715492125984	0.0845078740157477
49	365.9	366.128661417323	-0.228661417322606
50	357.6	346.345590551181	11.2544094488188
51	335.4	341.657125984252	-6.25712598425205
52	340.1	330.370708661417	9.72929133858261
53	337.8	331.297401574803	6.50259842519681
54	389.6	379.820472440945	9.77952755905507
55	342.5	344.475078740158	-1.97507874015756
56	354.6	346.871732283465	7.72826771653537
57	391.6	384.552755905512	7.04724409448812
58	317.7	311.348385826772	6.35161417322822
59	312.8	312.311456692914	0.488543307086506
60	356.2	376.491456692914	-20.2914566929135

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 359 & 331.106692913387 & 27.8933070866129 \tabularnewline
2 & 304.6 & 312.82874015748 & -8.22874015748024 \tabularnewline
3 & 297.7 & 308.140275590551 & -10.4402755905512 \tabularnewline
4 & 303.3 & 295.34874015748 & 7.9512598425197 \tabularnewline
5 & 304.7 & 300.038228346457 & 4.66177165354334 \tabularnewline
6 & 331.3 & 347.808740157480 & -16.5087401574803 \tabularnewline
7 & 318.8 & 310.205669291339 & 8.59433070866145 \tabularnewline
8 & 306.8 & 311.097204724409 & -4.29720472440946 \tabularnewline
9 & 331.1 & 348.025669291339 & -16.9256692913386 \tabularnewline
10 & 284.1 & 272.563622047244 & 11.5363779527559 \tabularnewline
11 & 259.7 & 269.763897637795 & -10.0638976377952 \tabularnewline
12 & 335.8 & 333.943897637795 & 1.85610236220474 \tabularnewline
13 & 338.5 & 336.099389763779 & 2.40061023622085 \tabularnewline
14 & 310.3 & 317.821437007874 & -7.52143700787398 \tabularnewline
15 & 322.1 & 312.380413385827 & 9.71958661417329 \tabularnewline
16 & 289.3 & 299.588877952756 & -10.2888779527559 \tabularnewline
17 & 300.8 & 310.298838582677 & -9.4988385826772 \tabularnewline
18 & 360.6 & 358.069350393701 & 2.53064960629918 \tabularnewline
19 & 327.3 & 320.466279527559 & 6.8337204724409 \tabularnewline
20 & 304.1 & 313.079665354331 & -8.97966535433061 \tabularnewline
21 & 362 & 350.00812992126 & 11.9918700787402 \tabularnewline
22 & 287.8 & 274.546082677165 & 13.2539173228348 \tabularnewline
23 & 286.1 & 278.519389763779 & 7.58061023622051 \tabularnewline
24 & 358.2 & 342.699389763779 & 15.5006102362205 \tabularnewline
25 & 346 & 345.607440944882 & 0.392559055118447 \tabularnewline
26 & 329.9 & 326.576929133858 & 3.32307086614171 \tabularnewline
27 & 334.3 & 321.135905511811 & 13.164094488189 \tabularnewline
28 & 303.7 & 308.34437007874 & -4.64437007874015 \tabularnewline
29 & 307.6 & 313.033858267717 & -5.43385826771652 \tabularnewline
30 & 351.7 & 360.051811023622 & -8.35181102362206 \tabularnewline
31 & 324.6 & 323.953858267717 & 0.646141732283486 \tabularnewline
32 & 311.9 & 324.092834645669 & -12.1928346456693 \tabularnewline
33 & 361.5 & 361.773858267716 & -0.273858267716511 \tabularnewline
34 & 271.1 & 286.311811023622 & -15.211811023622 \tabularnewline
35 & 286.5 & 285.769763779528 & 0.730236220472475 \tabularnewline
36 & 352.8 & 349.949763779528 & 2.85023622047248 \tabularnewline
37 & 322.4 & 352.857814960630 & -30.4578149606296 \tabularnewline
38 & 335 & 333.827303149606 & 1.17269685039369 \tabularnewline
39 & 322.2 & 328.386279527559 & -6.18627952755905 \tabularnewline
40 & 313.6 & 316.347303149606 & -2.74730314960627 \tabularnewline
41 & 323.3 & 319.531673228346 & 3.76832677165357 \tabularnewline
42 & 379.1 & 366.549625984252 & 12.5503740157481 \tabularnewline
43 & 315.6 & 329.699114173228 & -14.0991141732283 \tabularnewline
44 & 353.6 & 335.858562992126 & 17.741437007874 \tabularnewline
45 & 371.7 & 373.539586614173 & -1.83958661417327 \tabularnewline
46 & 282.9 & 298.830098425197 & -15.9300984251969 \tabularnewline
47 & 298.8 & 297.535492125984 & 1.26450787401573 \tabularnewline
48 & 361.8 & 361.715492125984 & 0.0845078740157477 \tabularnewline
49 & 365.9 & 366.128661417323 & -0.228661417322606 \tabularnewline
50 & 357.6 & 346.345590551181 & 11.2544094488188 \tabularnewline
51 & 335.4 & 341.657125984252 & -6.25712598425205 \tabularnewline
52 & 340.1 & 330.370708661417 & 9.72929133858261 \tabularnewline
53 & 337.8 & 331.297401574803 & 6.50259842519681 \tabularnewline
54 & 389.6 & 379.820472440945 & 9.77952755905507 \tabularnewline
55 & 342.5 & 344.475078740158 & -1.97507874015756 \tabularnewline
56 & 354.6 & 346.871732283465 & 7.72826771653537 \tabularnewline
57 & 391.6 & 384.552755905512 & 7.04724409448812 \tabularnewline
58 & 317.7 & 311.348385826772 & 6.35161417322822 \tabularnewline
59 & 312.8 & 312.311456692914 & 0.488543307086506 \tabularnewline
60 & 356.2 & 376.491456692914 & -20.2914566929135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14394&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]359[/C][C]331.106692913387[/C][C]27.8933070866129[/C][/ROW]
[ROW][C]2[/C][C]304.6[/C][C]312.82874015748[/C][C]-8.22874015748024[/C][/ROW]
[ROW][C]3[/C][C]297.7[/C][C]308.140275590551[/C][C]-10.4402755905512[/C][/ROW]
[ROW][C]4[/C][C]303.3[/C][C]295.34874015748[/C][C]7.9512598425197[/C][/ROW]
[ROW][C]5[/C][C]304.7[/C][C]300.038228346457[/C][C]4.66177165354334[/C][/ROW]
[ROW][C]6[/C][C]331.3[/C][C]347.808740157480[/C][C]-16.5087401574803[/C][/ROW]
[ROW][C]7[/C][C]318.8[/C][C]310.205669291339[/C][C]8.59433070866145[/C][/ROW]
[ROW][C]8[/C][C]306.8[/C][C]311.097204724409[/C][C]-4.29720472440946[/C][/ROW]
[ROW][C]9[/C][C]331.1[/C][C]348.025669291339[/C][C]-16.9256692913386[/C][/ROW]
[ROW][C]10[/C][C]284.1[/C][C]272.563622047244[/C][C]11.5363779527559[/C][/ROW]
[ROW][C]11[/C][C]259.7[/C][C]269.763897637795[/C][C]-10.0638976377952[/C][/ROW]
[ROW][C]12[/C][C]335.8[/C][C]333.943897637795[/C][C]1.85610236220474[/C][/ROW]
[ROW][C]13[/C][C]338.5[/C][C]336.099389763779[/C][C]2.40061023622085[/C][/ROW]
[ROW][C]14[/C][C]310.3[/C][C]317.821437007874[/C][C]-7.52143700787398[/C][/ROW]
[ROW][C]15[/C][C]322.1[/C][C]312.380413385827[/C][C]9.71958661417329[/C][/ROW]
[ROW][C]16[/C][C]289.3[/C][C]299.588877952756[/C][C]-10.2888779527559[/C][/ROW]
[ROW][C]17[/C][C]300.8[/C][C]310.298838582677[/C][C]-9.4988385826772[/C][/ROW]
[ROW][C]18[/C][C]360.6[/C][C]358.069350393701[/C][C]2.53064960629918[/C][/ROW]
[ROW][C]19[/C][C]327.3[/C][C]320.466279527559[/C][C]6.8337204724409[/C][/ROW]
[ROW][C]20[/C][C]304.1[/C][C]313.079665354331[/C][C]-8.97966535433061[/C][/ROW]
[ROW][C]21[/C][C]362[/C][C]350.00812992126[/C][C]11.9918700787402[/C][/ROW]
[ROW][C]22[/C][C]287.8[/C][C]274.546082677165[/C][C]13.2539173228348[/C][/ROW]
[ROW][C]23[/C][C]286.1[/C][C]278.519389763779[/C][C]7.58061023622051[/C][/ROW]
[ROW][C]24[/C][C]358.2[/C][C]342.699389763779[/C][C]15.5006102362205[/C][/ROW]
[ROW][C]25[/C][C]346[/C][C]345.607440944882[/C][C]0.392559055118447[/C][/ROW]
[ROW][C]26[/C][C]329.9[/C][C]326.576929133858[/C][C]3.32307086614171[/C][/ROW]
[ROW][C]27[/C][C]334.3[/C][C]321.135905511811[/C][C]13.164094488189[/C][/ROW]
[ROW][C]28[/C][C]303.7[/C][C]308.34437007874[/C][C]-4.64437007874015[/C][/ROW]
[ROW][C]29[/C][C]307.6[/C][C]313.033858267717[/C][C]-5.43385826771652[/C][/ROW]
[ROW][C]30[/C][C]351.7[/C][C]360.051811023622[/C][C]-8.35181102362206[/C][/ROW]
[ROW][C]31[/C][C]324.6[/C][C]323.953858267717[/C][C]0.646141732283486[/C][/ROW]
[ROW][C]32[/C][C]311.9[/C][C]324.092834645669[/C][C]-12.1928346456693[/C][/ROW]
[ROW][C]33[/C][C]361.5[/C][C]361.773858267716[/C][C]-0.273858267716511[/C][/ROW]
[ROW][C]34[/C][C]271.1[/C][C]286.311811023622[/C][C]-15.211811023622[/C][/ROW]
[ROW][C]35[/C][C]286.5[/C][C]285.769763779528[/C][C]0.730236220472475[/C][/ROW]
[ROW][C]36[/C][C]352.8[/C][C]349.949763779528[/C][C]2.85023622047248[/C][/ROW]
[ROW][C]37[/C][C]322.4[/C][C]352.857814960630[/C][C]-30.4578149606296[/C][/ROW]
[ROW][C]38[/C][C]335[/C][C]333.827303149606[/C][C]1.17269685039369[/C][/ROW]
[ROW][C]39[/C][C]322.2[/C][C]328.386279527559[/C][C]-6.18627952755905[/C][/ROW]
[ROW][C]40[/C][C]313.6[/C][C]316.347303149606[/C][C]-2.74730314960627[/C][/ROW]
[ROW][C]41[/C][C]323.3[/C][C]319.531673228346[/C][C]3.76832677165357[/C][/ROW]
[ROW][C]42[/C][C]379.1[/C][C]366.549625984252[/C][C]12.5503740157481[/C][/ROW]
[ROW][C]43[/C][C]315.6[/C][C]329.699114173228[/C][C]-14.0991141732283[/C][/ROW]
[ROW][C]44[/C][C]353.6[/C][C]335.858562992126[/C][C]17.741437007874[/C][/ROW]
[ROW][C]45[/C][C]371.7[/C][C]373.539586614173[/C][C]-1.83958661417327[/C][/ROW]
[ROW][C]46[/C][C]282.9[/C][C]298.830098425197[/C][C]-15.9300984251969[/C][/ROW]
[ROW][C]47[/C][C]298.8[/C][C]297.535492125984[/C][C]1.26450787401573[/C][/ROW]
[ROW][C]48[/C][C]361.8[/C][C]361.715492125984[/C][C]0.0845078740157477[/C][/ROW]
[ROW][C]49[/C][C]365.9[/C][C]366.128661417323[/C][C]-0.228661417322606[/C][/ROW]
[ROW][C]50[/C][C]357.6[/C][C]346.345590551181[/C][C]11.2544094488188[/C][/ROW]
[ROW][C]51[/C][C]335.4[/C][C]341.657125984252[/C][C]-6.25712598425205[/C][/ROW]
[ROW][C]52[/C][C]340.1[/C][C]330.370708661417[/C][C]9.72929133858261[/C][/ROW]
[ROW][C]53[/C][C]337.8[/C][C]331.297401574803[/C][C]6.50259842519681[/C][/ROW]
[ROW][C]54[/C][C]389.6[/C][C]379.820472440945[/C][C]9.77952755905507[/C][/ROW]
[ROW][C]55[/C][C]342.5[/C][C]344.475078740158[/C][C]-1.97507874015756[/C][/ROW]
[ROW][C]56[/C][C]354.6[/C][C]346.871732283465[/C][C]7.72826771653537[/C][/ROW]
[ROW][C]57[/C][C]391.6[/C][C]384.552755905512[/C][C]7.04724409448812[/C][/ROW]
[ROW][C]58[/C][C]317.7[/C][C]311.348385826772[/C][C]6.35161417322822[/C][/ROW]
[ROW][C]59[/C][C]312.8[/C][C]312.311456692914[/C][C]0.488543307086506[/C][/ROW]
[ROW][C]60[/C][C]356.2[/C][C]376.491456692914[/C][C]-20.2914566929135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14394&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14394&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	359	331.106692913387	27.8933070866129
2	304.6	312.82874015748	-8.22874015748024
3	297.7	308.140275590551	-10.4402755905512
4	303.3	295.34874015748	7.9512598425197
5	304.7	300.038228346457	4.66177165354334
6	331.3	347.808740157480	-16.5087401574803
7	318.8	310.205669291339	8.59433070866145
8	306.8	311.097204724409	-4.29720472440946
9	331.1	348.025669291339	-16.9256692913386
10	284.1	272.563622047244	11.5363779527559
11	259.7	269.763897637795	-10.0638976377952
12	335.8	333.943897637795	1.85610236220474
13	338.5	336.099389763779	2.40061023622085
14	310.3	317.821437007874	-7.52143700787398
15	322.1	312.380413385827	9.71958661417329
16	289.3	299.588877952756	-10.2888779527559
17	300.8	310.298838582677	-9.4988385826772
18	360.6	358.069350393701	2.53064960629918
19	327.3	320.466279527559	6.8337204724409
20	304.1	313.079665354331	-8.97966535433061
21	362	350.00812992126	11.9918700787402
22	287.8	274.546082677165	13.2539173228348
23	286.1	278.519389763779	7.58061023622051
24	358.2	342.699389763779	15.5006102362205
25	346	345.607440944882	0.392559055118447
26	329.9	326.576929133858	3.32307086614171
27	334.3	321.135905511811	13.164094488189
28	303.7	308.34437007874	-4.64437007874015
29	307.6	313.033858267717	-5.43385826771652
30	351.7	360.051811023622	-8.35181102362206
31	324.6	323.953858267717	0.646141732283486
32	311.9	324.092834645669	-12.1928346456693
33	361.5	361.773858267716	-0.273858267716511
34	271.1	286.311811023622	-15.211811023622
35	286.5	285.769763779528	0.730236220472475
36	352.8	349.949763779528	2.85023622047248
37	322.4	352.857814960630	-30.4578149606296
38	335	333.827303149606	1.17269685039369
39	322.2	328.386279527559	-6.18627952755905
40	313.6	316.347303149606	-2.74730314960627
41	323.3	319.531673228346	3.76832677165357
42	379.1	366.549625984252	12.5503740157481
43	315.6	329.699114173228	-14.0991141732283
44	353.6	335.858562992126	17.741437007874
45	371.7	373.539586614173	-1.83958661417327
46	282.9	298.830098425197	-15.9300984251969
47	298.8	297.535492125984	1.26450787401573
48	361.8	361.715492125984	0.0845078740157477
49	365.9	366.128661417323	-0.228661417322606
50	357.6	346.345590551181	11.2544094488188
51	335.4	341.657125984252	-6.25712598425205
52	340.1	330.370708661417	9.72929133858261
53	337.8	331.297401574803	6.50259842519681
54	389.6	379.820472440945	9.77952755905507
55	342.5	344.475078740158	-1.97507874015756
56	354.6	346.871732283465	7.72826771653537
57	391.6	384.552755905512	7.04724409448812
58	317.7	311.348385826772	6.35161417322822
59	312.8	312.311456692914	0.488543307086506
60	356.2	376.491456692914	-20.2914566929135

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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