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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 19 Nov 2007 15:52:29 -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/19/t11955124101j5rt61qfeig8c7.htm/, Retrieved Fri, 03 May 2024 11:41:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5789, Retrieved Fri, 03 May 2024 11:41:32 +0000

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Estimated Impact

169

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

-       [Multiple Regression] [Invloed olieprijs...] [2007-11-19 22:52:29] [9bb499d88394279c02e6a8b8cf177cf7] [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=5789&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=5789&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5789&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
Y[t] = + 102.5 + 0.75000000000001X[t] -0.0625000000000058M1[t] -0.275000000000011M2[t] -1.28750000000001M3[t] -0.700000000000012M4[t] -2.11250000000001M5[t] -1.52500000000001M6[t] -2.53750000000001M7[t] -1.15000000000001M8[t] -1.36250000000001M9[t] -2.17500000000001M10[t] -0.187500000000007M11[t] -0.187500000000000t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  102.5 +  0.75000000000001X[t] -0.0625000000000058M1[t] -0.275000000000011M2[t] -1.28750000000001M3[t] -0.700000000000012M4[t] -2.11250000000001M5[t] -1.52500000000001M6[t] -2.53750000000001M7[t] -1.15000000000001M8[t] -1.36250000000001M9[t] -2.17500000000001M10[t] -0.187500000000007M11[t] -0.187500000000000t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5789&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  102.5 +  0.75000000000001X[t] -0.0625000000000058M1[t] -0.275000000000011M2[t] -1.28750000000001M3[t] -0.700000000000012M4[t] -2.11250000000001M5[t] -1.52500000000001M6[t] -2.53750000000001M7[t] -1.15000000000001M8[t] -1.36250000000001M9[t] -2.17500000000001M10[t] -0.187500000000007M11[t] -0.187500000000000t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5789&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5789&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
Y[t] = + 102.5 + 0.75000000000001X[t] -0.0625000000000058M1[t] -0.275000000000011M2[t] -1.28750000000001M3[t] -0.700000000000012M4[t] -2.11250000000001M5[t] -1.52500000000001M6[t] -2.53750000000001M7[t] -1.15000000000001M8[t] -1.36250000000001M9[t] -2.17500000000001M10[t] -0.187500000000007M11[t] -0.187500000000000t + 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)	102.5	5.444203	18.8274	0	0
X	0.75000000000001	5.238687	0.1432	0.886785	0.443392
M1	-0.0625000000000058	6.502798	-0.0096	0.992373	0.496187
M2	-0.275000000000011	6.465765	-0.0425	0.966259	0.483129
M3	-1.28750000000001	6.432075	-0.2002	0.842231	0.421115
M4	-0.700000000000012	6.401781	-0.1093	0.913405	0.456702
M5	-2.11250000000001	6.374932	-0.3314	0.741865	0.370933
M6	-1.52500000000001	6.35157	-0.2401	0.811321	0.40566
M7	-2.53750000000001	6.331736	-0.4008	0.690453	0.345226
M8	-1.15000000000001	6.315461	-0.1821	0.85631	0.428155
M9	-1.36250000000001	6.302774	-0.2162	0.829807	0.414904
M10	-2.17500000000001	6.293696	-0.3456	0.731231	0.365615
M11	-0.187500000000007	6.288243	-0.0298	0.976342	0.488171
t	-0.187500000000000	0.151228	-1.2399	0.221318	0.110659

\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) & 102.5 & 5.444203 & 18.8274 & 0 & 0 \tabularnewline
X & 0.75000000000001 & 5.238687 & 0.1432 & 0.886785 & 0.443392 \tabularnewline
M1 & -0.0625000000000058 & 6.502798 & -0.0096 & 0.992373 & 0.496187 \tabularnewline
M2 & -0.275000000000011 & 6.465765 & -0.0425 & 0.966259 & 0.483129 \tabularnewline
M3 & -1.28750000000001 & 6.432075 & -0.2002 & 0.842231 & 0.421115 \tabularnewline
M4 & -0.700000000000012 & 6.401781 & -0.1093 & 0.913405 & 0.456702 \tabularnewline
M5 & -2.11250000000001 & 6.374932 & -0.3314 & 0.741865 & 0.370933 \tabularnewline
M6 & -1.52500000000001 & 6.35157 & -0.2401 & 0.811321 & 0.40566 \tabularnewline
M7 & -2.53750000000001 & 6.331736 & -0.4008 & 0.690453 & 0.345226 \tabularnewline
M8 & -1.15000000000001 & 6.315461 & -0.1821 & 0.85631 & 0.428155 \tabularnewline
M9 & -1.36250000000001 & 6.302774 & -0.2162 & 0.829807 & 0.414904 \tabularnewline
M10 & -2.17500000000001 & 6.293696 & -0.3456 & 0.731231 & 0.365615 \tabularnewline
M11 & -0.187500000000007 & 6.288243 & -0.0298 & 0.976342 & 0.488171 \tabularnewline
t & -0.187500000000000 & 0.151228 & -1.2399 & 0.221318 & 0.110659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5789&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]102.5[/C][C]5.444203[/C][C]18.8274[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.75000000000001[/C][C]5.238687[/C][C]0.1432[/C][C]0.886785[/C][C]0.443392[/C][/ROW]
[ROW][C]M1[/C][C]-0.0625000000000058[/C][C]6.502798[/C][C]-0.0096[/C][C]0.992373[/C][C]0.496187[/C][/ROW]
[ROW][C]M2[/C][C]-0.275000000000011[/C][C]6.465765[/C][C]-0.0425[/C][C]0.966259[/C][C]0.483129[/C][/ROW]
[ROW][C]M3[/C][C]-1.28750000000001[/C][C]6.432075[/C][C]-0.2002[/C][C]0.842231[/C][C]0.421115[/C][/ROW]
[ROW][C]M4[/C][C]-0.700000000000012[/C][C]6.401781[/C][C]-0.1093[/C][C]0.913405[/C][C]0.456702[/C][/ROW]
[ROW][C]M5[/C][C]-2.11250000000001[/C][C]6.374932[/C][C]-0.3314[/C][C]0.741865[/C][C]0.370933[/C][/ROW]
[ROW][C]M6[/C][C]-1.52500000000001[/C][C]6.35157[/C][C]-0.2401[/C][C]0.811321[/C][C]0.40566[/C][/ROW]
[ROW][C]M7[/C][C]-2.53750000000001[/C][C]6.331736[/C][C]-0.4008[/C][C]0.690453[/C][C]0.345226[/C][/ROW]
[ROW][C]M8[/C][C]-1.15000000000001[/C][C]6.315461[/C][C]-0.1821[/C][C]0.85631[/C][C]0.428155[/C][/ROW]
[ROW][C]M9[/C][C]-1.36250000000001[/C][C]6.302774[/C][C]-0.2162[/C][C]0.829807[/C][C]0.414904[/C][/ROW]
[ROW][C]M10[/C][C]-2.17500000000001[/C][C]6.293696[/C][C]-0.3456[/C][C]0.731231[/C][C]0.365615[/C][/ROW]
[ROW][C]M11[/C][C]-0.187500000000007[/C][C]6.288243[/C][C]-0.0298[/C][C]0.976342[/C][C]0.488171[/C][/ROW]
[ROW][C]t[/C][C]-0.187500000000000[/C][C]0.151228[/C][C]-1.2399[/C][C]0.221318[/C][C]0.110659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5789&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5789&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)	102.5	5.444203	18.8274	0	0
X	0.75000000000001	5.238687	0.1432	0.886785	0.443392
M1	-0.0625000000000058	6.502798	-0.0096	0.992373	0.496187
M2	-0.275000000000011	6.465765	-0.0425	0.966259	0.483129
M3	-1.28750000000001	6.432075	-0.2002	0.842231	0.421115
M4	-0.700000000000012	6.401781	-0.1093	0.913405	0.456702
M5	-2.11250000000001	6.374932	-0.3314	0.741865	0.370933
M6	-1.52500000000001	6.35157	-0.2401	0.811321	0.40566
M7	-2.53750000000001	6.331736	-0.4008	0.690453	0.345226
M8	-1.15000000000001	6.315461	-0.1821	0.85631	0.428155
M9	-1.36250000000001	6.302774	-0.2162	0.829807	0.414904
M10	-2.17500000000001	6.293696	-0.3456	0.731231	0.365615
M11	-0.187500000000007	6.288243	-0.0298	0.976342	0.488171
t	-0.187500000000000	0.151228	-1.2399	0.221318	0.110659

Multiple Linear Regression - Regression Statistics
Multiple R	0.333175720431569
R-squared	0.111006060685095
Adjusted R-squared	-0.140231356947378
F-TEST (value)	0.441837293708704
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.944772506132533
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.93970955747483
Sum Squared Residuals	4544.7

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.333175720431569 \tabularnewline
R-squared & 0.111006060685095 \tabularnewline
Adjusted R-squared & -0.140231356947378 \tabularnewline
F-TEST (value) & 0.441837293708704 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.944772506132533 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9.93970955747483 \tabularnewline
Sum Squared Residuals & 4544.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5789&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.333175720431569[/C][/ROW]
[ROW][C]R-squared[/C][C]0.111006060685095[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.140231356947378[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.441837293708704[/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]0.944772506132533[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9.93970955747483[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4544.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5789&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5789&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	0.333175720431569
R-squared	0.111006060685095
Adjusted R-squared	-0.140231356947378
F-TEST (value)	0.441837293708704
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.944772506132533
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.93970955747483
Sum Squared Residuals	4544.7

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	99	102.25	-3.24999999999999
2	92	101.85	-9.84999999999999
3	91	100.65	-9.65
4	92	101.05	-9.05000000000001
5	93	99.45	-6.45
6	95	99.85	-4.85
7	98	98.65	-0.650000000000006
8	98	99.85	-1.85000000000000
9	97	99.45	-2.45
10	95	98.45	-3.45000000000000
11	93	100.25	-7.25
12	102	100.25	1.75000000000000
13	102	100	2.00000000000000
14	113	99.6	13.4
15	112	98.4	13.6
16	114	98.8	15.2
17	104	97.2	6.8
18	98	97.6	0.400000000000003
19	88	96.4	-8.4
20	93	97.6	-4.6
21	96	97.2	-1.20000000000000
22	101	96.2	4.8
23	107	98	9
24	104	98	6
25	96	98.5	-2.50000000000001
26	86	98.1	-12.1
27	83	96.9	-13.9
28	90	97.3	-7.3
29	95	95.7	-0.700000000000001
30	102	96.1	5.9
31	95	94.9	0.0999999999999981
32	98	96.1	1.90000000000000
33	95	95.7	-0.700000000000003
34	92	94.7	-2.7
35	94	96.5	-2.5
36	96	96.5	-0.50000000000001
37	109	96.25	12.75
38	117	95.85	21.15
39	118	94.65	23.35
40	107	95.05	11.95
41	104	93.45	10.55
42	101	93.85	7.15
43	110	92.65	17.35
44	101	93.85	7.15
45	101	93.45	7.55
46	98	92.45	5.55
47	99	94.25	4.75
48	92	94.25	-2.25000000000001
49	85	94	-9
50	81	93.6	-12.6
51	79	92.4	-13.4
52	82	92.8	-10.8
53	81	91.2	-10.2
54	83	91.6	-8.6
55	82	90.4	-8.4
56	89	91.6	-2.6
57	88	91.2	-3.20000000000000
58	86	90.2	-4.2
59	88	92	-4
60	87	92	-5

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 99 & 102.25 & -3.24999999999999 \tabularnewline
2 & 92 & 101.85 & -9.84999999999999 \tabularnewline
3 & 91 & 100.65 & -9.65 \tabularnewline
4 & 92 & 101.05 & -9.05000000000001 \tabularnewline
5 & 93 & 99.45 & -6.45 \tabularnewline
6 & 95 & 99.85 & -4.85 \tabularnewline
7 & 98 & 98.65 & -0.650000000000006 \tabularnewline
8 & 98 & 99.85 & -1.85000000000000 \tabularnewline
9 & 97 & 99.45 & -2.45 \tabularnewline
10 & 95 & 98.45 & -3.45000000000000 \tabularnewline
11 & 93 & 100.25 & -7.25 \tabularnewline
12 & 102 & 100.25 & 1.75000000000000 \tabularnewline
13 & 102 & 100 & 2.00000000000000 \tabularnewline
14 & 113 & 99.6 & 13.4 \tabularnewline
15 & 112 & 98.4 & 13.6 \tabularnewline
16 & 114 & 98.8 & 15.2 \tabularnewline
17 & 104 & 97.2 & 6.8 \tabularnewline
18 & 98 & 97.6 & 0.400000000000003 \tabularnewline
19 & 88 & 96.4 & -8.4 \tabularnewline
20 & 93 & 97.6 & -4.6 \tabularnewline
21 & 96 & 97.2 & -1.20000000000000 \tabularnewline
22 & 101 & 96.2 & 4.8 \tabularnewline
23 & 107 & 98 & 9 \tabularnewline
24 & 104 & 98 & 6 \tabularnewline
25 & 96 & 98.5 & -2.50000000000001 \tabularnewline
26 & 86 & 98.1 & -12.1 \tabularnewline
27 & 83 & 96.9 & -13.9 \tabularnewline
28 & 90 & 97.3 & -7.3 \tabularnewline
29 & 95 & 95.7 & -0.700000000000001 \tabularnewline
30 & 102 & 96.1 & 5.9 \tabularnewline
31 & 95 & 94.9 & 0.0999999999999981 \tabularnewline
32 & 98 & 96.1 & 1.90000000000000 \tabularnewline
33 & 95 & 95.7 & -0.700000000000003 \tabularnewline
34 & 92 & 94.7 & -2.7 \tabularnewline
35 & 94 & 96.5 & -2.5 \tabularnewline
36 & 96 & 96.5 & -0.50000000000001 \tabularnewline
37 & 109 & 96.25 & 12.75 \tabularnewline
38 & 117 & 95.85 & 21.15 \tabularnewline
39 & 118 & 94.65 & 23.35 \tabularnewline
40 & 107 & 95.05 & 11.95 \tabularnewline
41 & 104 & 93.45 & 10.55 \tabularnewline
42 & 101 & 93.85 & 7.15 \tabularnewline
43 & 110 & 92.65 & 17.35 \tabularnewline
44 & 101 & 93.85 & 7.15 \tabularnewline
45 & 101 & 93.45 & 7.55 \tabularnewline
46 & 98 & 92.45 & 5.55 \tabularnewline
47 & 99 & 94.25 & 4.75 \tabularnewline
48 & 92 & 94.25 & -2.25000000000001 \tabularnewline
49 & 85 & 94 & -9 \tabularnewline
50 & 81 & 93.6 & -12.6 \tabularnewline
51 & 79 & 92.4 & -13.4 \tabularnewline
52 & 82 & 92.8 & -10.8 \tabularnewline
53 & 81 & 91.2 & -10.2 \tabularnewline
54 & 83 & 91.6 & -8.6 \tabularnewline
55 & 82 & 90.4 & -8.4 \tabularnewline
56 & 89 & 91.6 & -2.6 \tabularnewline
57 & 88 & 91.2 & -3.20000000000000 \tabularnewline
58 & 86 & 90.2 & -4.2 \tabularnewline
59 & 88 & 92 & -4 \tabularnewline
60 & 87 & 92 & -5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5789&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]99[/C][C]102.25[/C][C]-3.24999999999999[/C][/ROW]
[ROW][C]2[/C][C]92[/C][C]101.85[/C][C]-9.84999999999999[/C][/ROW]
[ROW][C]3[/C][C]91[/C][C]100.65[/C][C]-9.65[/C][/ROW]
[ROW][C]4[/C][C]92[/C][C]101.05[/C][C]-9.05000000000001[/C][/ROW]
[ROW][C]5[/C][C]93[/C][C]99.45[/C][C]-6.45[/C][/ROW]
[ROW][C]6[/C][C]95[/C][C]99.85[/C][C]-4.85[/C][/ROW]
[ROW][C]7[/C][C]98[/C][C]98.65[/C][C]-0.650000000000006[/C][/ROW]
[ROW][C]8[/C][C]98[/C][C]99.85[/C][C]-1.85000000000000[/C][/ROW]
[ROW][C]9[/C][C]97[/C][C]99.45[/C][C]-2.45[/C][/ROW]
[ROW][C]10[/C][C]95[/C][C]98.45[/C][C]-3.45000000000000[/C][/ROW]
[ROW][C]11[/C][C]93[/C][C]100.25[/C][C]-7.25[/C][/ROW]
[ROW][C]12[/C][C]102[/C][C]100.25[/C][C]1.75000000000000[/C][/ROW]
[ROW][C]13[/C][C]102[/C][C]100[/C][C]2.00000000000000[/C][/ROW]
[ROW][C]14[/C][C]113[/C][C]99.6[/C][C]13.4[/C][/ROW]
[ROW][C]15[/C][C]112[/C][C]98.4[/C][C]13.6[/C][/ROW]
[ROW][C]16[/C][C]114[/C][C]98.8[/C][C]15.2[/C][/ROW]
[ROW][C]17[/C][C]104[/C][C]97.2[/C][C]6.8[/C][/ROW]
[ROW][C]18[/C][C]98[/C][C]97.6[/C][C]0.400000000000003[/C][/ROW]
[ROW][C]19[/C][C]88[/C][C]96.4[/C][C]-8.4[/C][/ROW]
[ROW][C]20[/C][C]93[/C][C]97.6[/C][C]-4.6[/C][/ROW]
[ROW][C]21[/C][C]96[/C][C]97.2[/C][C]-1.20000000000000[/C][/ROW]
[ROW][C]22[/C][C]101[/C][C]96.2[/C][C]4.8[/C][/ROW]
[ROW][C]23[/C][C]107[/C][C]98[/C][C]9[/C][/ROW]
[ROW][C]24[/C][C]104[/C][C]98[/C][C]6[/C][/ROW]
[ROW][C]25[/C][C]96[/C][C]98.5[/C][C]-2.50000000000001[/C][/ROW]
[ROW][C]26[/C][C]86[/C][C]98.1[/C][C]-12.1[/C][/ROW]
[ROW][C]27[/C][C]83[/C][C]96.9[/C][C]-13.9[/C][/ROW]
[ROW][C]28[/C][C]90[/C][C]97.3[/C][C]-7.3[/C][/ROW]
[ROW][C]29[/C][C]95[/C][C]95.7[/C][C]-0.700000000000001[/C][/ROW]
[ROW][C]30[/C][C]102[/C][C]96.1[/C][C]5.9[/C][/ROW]
[ROW][C]31[/C][C]95[/C][C]94.9[/C][C]0.0999999999999981[/C][/ROW]
[ROW][C]32[/C][C]98[/C][C]96.1[/C][C]1.90000000000000[/C][/ROW]
[ROW][C]33[/C][C]95[/C][C]95.7[/C][C]-0.700000000000003[/C][/ROW]
[ROW][C]34[/C][C]92[/C][C]94.7[/C][C]-2.7[/C][/ROW]
[ROW][C]35[/C][C]94[/C][C]96.5[/C][C]-2.5[/C][/ROW]
[ROW][C]36[/C][C]96[/C][C]96.5[/C][C]-0.50000000000001[/C][/ROW]
[ROW][C]37[/C][C]109[/C][C]96.25[/C][C]12.75[/C][/ROW]
[ROW][C]38[/C][C]117[/C][C]95.85[/C][C]21.15[/C][/ROW]
[ROW][C]39[/C][C]118[/C][C]94.65[/C][C]23.35[/C][/ROW]
[ROW][C]40[/C][C]107[/C][C]95.05[/C][C]11.95[/C][/ROW]
[ROW][C]41[/C][C]104[/C][C]93.45[/C][C]10.55[/C][/ROW]
[ROW][C]42[/C][C]101[/C][C]93.85[/C][C]7.15[/C][/ROW]
[ROW][C]43[/C][C]110[/C][C]92.65[/C][C]17.35[/C][/ROW]
[ROW][C]44[/C][C]101[/C][C]93.85[/C][C]7.15[/C][/ROW]
[ROW][C]45[/C][C]101[/C][C]93.45[/C][C]7.55[/C][/ROW]
[ROW][C]46[/C][C]98[/C][C]92.45[/C][C]5.55[/C][/ROW]
[ROW][C]47[/C][C]99[/C][C]94.25[/C][C]4.75[/C][/ROW]
[ROW][C]48[/C][C]92[/C][C]94.25[/C][C]-2.25000000000001[/C][/ROW]
[ROW][C]49[/C][C]85[/C][C]94[/C][C]-9[/C][/ROW]
[ROW][C]50[/C][C]81[/C][C]93.6[/C][C]-12.6[/C][/ROW]
[ROW][C]51[/C][C]79[/C][C]92.4[/C][C]-13.4[/C][/ROW]
[ROW][C]52[/C][C]82[/C][C]92.8[/C][C]-10.8[/C][/ROW]
[ROW][C]53[/C][C]81[/C][C]91.2[/C][C]-10.2[/C][/ROW]
[ROW][C]54[/C][C]83[/C][C]91.6[/C][C]-8.6[/C][/ROW]
[ROW][C]55[/C][C]82[/C][C]90.4[/C][C]-8.4[/C][/ROW]
[ROW][C]56[/C][C]89[/C][C]91.6[/C][C]-2.6[/C][/ROW]
[ROW][C]57[/C][C]88[/C][C]91.2[/C][C]-3.20000000000000[/C][/ROW]
[ROW][C]58[/C][C]86[/C][C]90.2[/C][C]-4.2[/C][/ROW]
[ROW][C]59[/C][C]88[/C][C]92[/C][C]-4[/C][/ROW]
[ROW][C]60[/C][C]87[/C][C]92[/C][C]-5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5789&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5789&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	99	102.25	-3.24999999999999
2	92	101.85	-9.84999999999999
3	91	100.65	-9.65
4	92	101.05	-9.05000000000001
5	93	99.45	-6.45
6	95	99.85	-4.85
7	98	98.65	-0.650000000000006
8	98	99.85	-1.85000000000000
9	97	99.45	-2.45
10	95	98.45	-3.45000000000000
11	93	100.25	-7.25
12	102	100.25	1.75000000000000
13	102	100	2.00000000000000
14	113	99.6	13.4
15	112	98.4	13.6
16	114	98.8	15.2
17	104	97.2	6.8
18	98	97.6	0.400000000000003
19	88	96.4	-8.4
20	93	97.6	-4.6
21	96	97.2	-1.20000000000000
22	101	96.2	4.8
23	107	98	9
24	104	98	6
25	96	98.5	-2.50000000000001
26	86	98.1	-12.1
27	83	96.9	-13.9
28	90	97.3	-7.3
29	95	95.7	-0.700000000000001
30	102	96.1	5.9
31	95	94.9	0.0999999999999981
32	98	96.1	1.90000000000000
33	95	95.7	-0.700000000000003
34	92	94.7	-2.7
35	94	96.5	-2.5
36	96	96.5	-0.50000000000001
37	109	96.25	12.75
38	117	95.85	21.15
39	118	94.65	23.35
40	107	95.05	11.95
41	104	93.45	10.55
42	101	93.85	7.15
43	110	92.65	17.35
44	101	93.85	7.15
45	101	93.45	7.55
46	98	92.45	5.55
47	99	94.25	4.75
48	92	94.25	-2.25000000000001
49	85	94	-9
50	81	93.6	-12.6
51	79	92.4	-13.4
52	82	92.8	-10.8
53	81	91.2	-10.2
54	83	91.6	-8.6
55	82	90.4	-8.4
56	89	91.6	-2.6
57	88	91.2	-3.20000000000000
58	86	90.2	-4.2
59	88	92	-4
60	87	92	-5

Figure 1

PNG link

Postscript link

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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 = 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