Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 19 Nov 2007 03:36:18 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/19/t1195468163gr10zjjpwbpdrb6.htm/, Retrieved Fri, 03 May 2024 04:58:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5675, Retrieved Fri, 03 May 2024 04:58:37 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

224

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

-       [Multiple Regression] [Ws6 T2] [2007-11-19 10:36:18] [6bae8369195607c4cbc8a8485fed7b2f] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=5675&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=5675&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5675&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] = + 94.8340828402367 + 2.50591715976330x[t] + 12.1943195266272M1[t] + 4.74118343195268M2[t] + 2.66118343195267M3[t] + 11.3011834319527M4[t] -12.2988165680473M5[t] -2.99881656804733M6[t] + 12.1611834319527M7[t] + 12.64M8[t] + 5.72000000000001M9[t] -0.639999999999997M10[t] -0.879999999999997M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  94.8340828402367 +  2.50591715976330x[t] +  12.1943195266272M1[t] +  4.74118343195268M2[t] +  2.66118343195267M3[t] +  11.3011834319527M4[t] -12.2988165680473M5[t] -2.99881656804733M6[t] +  12.1611834319527M7[t] +  12.64M8[t] +  5.72000000000001M9[t] -0.639999999999997M10[t] -0.879999999999997M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5675&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  94.8340828402367 +  2.50591715976330x[t] +  12.1943195266272M1[t] +  4.74118343195268M2[t] +  2.66118343195267M3[t] +  11.3011834319527M4[t] -12.2988165680473M5[t] -2.99881656804733M6[t] +  12.1611834319527M7[t] +  12.64M8[t] +  5.72000000000001M9[t] -0.639999999999997M10[t] -0.879999999999997M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5675&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5675&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] = + 94.8340828402367 + 2.50591715976330x[t] + 12.1943195266272M1[t] + 4.74118343195268M2[t] + 2.66118343195267M3[t] + 11.3011834319527M4[t] -12.2988165680473M5[t] -2.99881656804733M6[t] + 12.1611834319527M7[t] + 12.64M8[t] + 5.72000000000001M9[t] -0.639999999999997M10[t] -0.879999999999997M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	94.8340828402367	2.176328	43.5753	0	0
x	2.50591715976330	1.492364	1.6792	0.09962	0.04981
M1	12.1943195266272	2.159205	5.6476	1e-06	0
M2	4.74118343195268	2.259999	2.0979	0.041206	0.020603
M3	2.66118343195267	2.259999	1.1775	0.244795	0.122398
M4	11.3011834319527	2.259999	5.0005	8e-06	4e-06
M5	-12.2988165680473	2.259999	-5.442	2e-06	1e-06
M6	-2.99881656804733	2.259999	-1.3269	0.190816	0.095408
M7	12.1611834319527	2.259999	5.3811	2e-06	1e-06
M8	12.64	2.240203	5.6423	1e-06	0
M9	5.72000000000001	2.240203	2.5533	0.013902	0.006951
M10	-0.639999999999997	2.240203	-0.2857	0.776346	0.388173
M11	-0.879999999999997	2.240203	-0.3928	0.69619	0.348095

\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) & 94.8340828402367 & 2.176328 & 43.5753 & 0 & 0 \tabularnewline
x & 2.50591715976330 & 1.492364 & 1.6792 & 0.09962 & 0.04981 \tabularnewline
M1 & 12.1943195266272 & 2.159205 & 5.6476 & 1e-06 & 0 \tabularnewline
M2 & 4.74118343195268 & 2.259999 & 2.0979 & 0.041206 & 0.020603 \tabularnewline
M3 & 2.66118343195267 & 2.259999 & 1.1775 & 0.244795 & 0.122398 \tabularnewline
M4 & 11.3011834319527 & 2.259999 & 5.0005 & 8e-06 & 4e-06 \tabularnewline
M5 & -12.2988165680473 & 2.259999 & -5.442 & 2e-06 & 1e-06 \tabularnewline
M6 & -2.99881656804733 & 2.259999 & -1.3269 & 0.190816 & 0.095408 \tabularnewline
M7 & 12.1611834319527 & 2.259999 & 5.3811 & 2e-06 & 1e-06 \tabularnewline
M8 & 12.64 & 2.240203 & 5.6423 & 1e-06 & 0 \tabularnewline
M9 & 5.72000000000001 & 2.240203 & 2.5533 & 0.013902 & 0.006951 \tabularnewline
M10 & -0.639999999999997 & 2.240203 & -0.2857 & 0.776346 & 0.388173 \tabularnewline
M11 & -0.879999999999997 & 2.240203 & -0.3928 & 0.69619 & 0.348095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5675&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]94.8340828402367[/C][C]2.176328[/C][C]43.5753[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]2.50591715976330[/C][C]1.492364[/C][C]1.6792[/C][C]0.09962[/C][C]0.04981[/C][/ROW]
[ROW][C]M1[/C][C]12.1943195266272[/C][C]2.159205[/C][C]5.6476[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M2[/C][C]4.74118343195268[/C][C]2.259999[/C][C]2.0979[/C][C]0.041206[/C][C]0.020603[/C][/ROW]
[ROW][C]M3[/C][C]2.66118343195267[/C][C]2.259999[/C][C]1.1775[/C][C]0.244795[/C][C]0.122398[/C][/ROW]
[ROW][C]M4[/C][C]11.3011834319527[/C][C]2.259999[/C][C]5.0005[/C][C]8e-06[/C][C]4e-06[/C][/ROW]
[ROW][C]M5[/C][C]-12.2988165680473[/C][C]2.259999[/C][C]-5.442[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M6[/C][C]-2.99881656804733[/C][C]2.259999[/C][C]-1.3269[/C][C]0.190816[/C][C]0.095408[/C][/ROW]
[ROW][C]M7[/C][C]12.1611834319527[/C][C]2.259999[/C][C]5.3811[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M8[/C][C]12.64[/C][C]2.240203[/C][C]5.6423[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]5.72000000000001[/C][C]2.240203[/C][C]2.5533[/C][C]0.013902[/C][C]0.006951[/C][/ROW]
[ROW][C]M10[/C][C]-0.639999999999997[/C][C]2.240203[/C][C]-0.2857[/C][C]0.776346[/C][C]0.388173[/C][/ROW]
[ROW][C]M11[/C][C]-0.879999999999997[/C][C]2.240203[/C][C]-0.3928[/C][C]0.69619[/C][C]0.348095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5675&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5675&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)	94.8340828402367	2.176328	43.5753	0	0
x	2.50591715976330	1.492364	1.6792	0.09962	0.04981
M1	12.1943195266272	2.159205	5.6476	1e-06	0
M2	4.74118343195268	2.259999	2.0979	0.041206	0.020603
M3	2.66118343195267	2.259999	1.1775	0.244795	0.122398
M4	11.3011834319527	2.259999	5.0005	8e-06	4e-06
M5	-12.2988165680473	2.259999	-5.442	2e-06	1e-06
M6	-2.99881656804733	2.259999	-1.3269	0.190816	0.095408
M7	12.1611834319527	2.259999	5.3811	2e-06	1e-06
M8	12.64	2.240203	5.6423	1e-06	0
M9	5.72000000000001	2.240203	2.5533	0.013902	0.006951
M10	-0.639999999999997	2.240203	-0.2857	0.776346	0.388173
M11	-0.879999999999997	2.240203	-0.3928	0.69619	0.348095

Multiple Linear Regression - Regression Statistics
Multiple R	0.91994407847051
R-squared	0.846297107512956
Adjusted R-squared	0.807871384391195
F-TEST (value)	22.0242337361164
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	1.55431223447522e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.54207194571751
Sum Squared Residuals	602.221136094675

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.91994407847051 \tabularnewline
R-squared & 0.846297107512956 \tabularnewline
Adjusted R-squared & 0.807871384391195 \tabularnewline
F-TEST (value) & 22.0242337361164 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 1.55431223447522e-15 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.54207194571751 \tabularnewline
Sum Squared Residuals & 602.221136094675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5675&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.91994407847051[/C][/ROW]
[ROW][C]R-squared[/C][C]0.846297107512956[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.807871384391195[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]22.0242337361164[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]1.55431223447522e-15[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.54207194571751[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]602.221136094675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5675&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5675&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	0.91994407847051
R-squared	0.846297107512956
Adjusted R-squared	0.807871384391195
F-TEST (value)	22.0242337361164
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	1.55431223447522e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.54207194571751
Sum Squared Residuals	602.221136094675

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	110.4	107.028402366864	3.37159763313617
2	96.4	99.5752662721893	-3.17526627218933
3	101.9	97.4952662721894	4.40473372781065
4	106.2	106.135266272189	0.0647337278106297
5	81	82.5352662721894	-1.53526627218938
6	94.7	91.8352662721894	2.86473372781064
7	101	106.995266272189	-5.99526627218935
8	109.4	109.98	-0.580000000000001
9	102.3	103.06	-0.759999999999995
10	90.7	96.7	-6
11	96.2	96.46	-0.259999999999999
12	96.1	97.34	-1.24000000000000
13	106	109.534319526627	-3.53431952662724
14	103.1	102.081183431953	1.01881656804733
15	102	100.001183431953	1.99881656804734
16	104.7	108.641183431953	-3.94118343195266
17	86	85.0411834319527	0.958816568047336
18	92.1	94.3411834319527	-2.24118343195266
19	106.9	109.501183431953	-2.60118343195266
20	112.6	109.98	2.61999999999999
21	101.7	103.06	-1.36
22	92	96.7	-4.7
23	97.4	96.46	0.940000000000006
24	97	97.34	-0.339999999999997
25	105.4	109.534319526627	-4.13431952662723
26	102.7	102.081183431953	0.618816568047336
27	98.1	100.001183431953	-1.90118343195267
28	104.5	108.641183431953	-4.14118343195266
29	87.4	85.0411834319527	2.35881656804734
30	89.9	94.3411834319527	-4.44118343195265
31	109.8	109.501183431953	0.298816568047331
32	111.7	109.98	1.72
33	98.6	103.06	-4.46000000000001
34	96.9	96.7	0.200000000000006
35	95.1	96.46	-1.36000000000000
36	97	97.34	-0.339999999999997
37	112.7	109.534319526627	3.16568047337277
38	102.9	102.081183431953	0.818816568047338
39	97.4	100.001183431953	-2.60118343195265
40	111.4	108.641183431953	2.75881656804734
41	87.4	85.0411834319527	2.35881656804734
42	96.8	94.3411834319527	2.45881656804734
43	114.1	109.501183431953	4.59881656804733
44	110.3	109.98	0.319999999999996
45	103.9	103.06	0.840000000000005
46	101.6	96.7	4.90000000000000
47	94.6	96.46	-1.86000000000000
48	95.9	97.34	-1.43999999999999
49	104.7	109.534319526627	-4.83431952662723
50	102.8	102.081183431953	0.71881656804733
51	98.1	100.001183431953	-1.90118343195267
52	113.9	108.641183431953	5.25881656804734
53	80.9	85.0411834319527	-4.14118343195265
54	95.7	94.3411834319527	1.35881656804734
55	113.2	109.501183431953	3.69881656804734
56	105.9	109.98	-4.08000000000000
57	108.8	103.06	5.74
58	102.3	96.7	5.6
59	99	96.46	2.54
60	100.7	97.34	3.36000000000001
61	115.5	109.534319526627	5.96568047337276

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 110.4 & 107.028402366864 & 3.37159763313617 \tabularnewline
2 & 96.4 & 99.5752662721893 & -3.17526627218933 \tabularnewline
3 & 101.9 & 97.4952662721894 & 4.40473372781065 \tabularnewline
4 & 106.2 & 106.135266272189 & 0.0647337278106297 \tabularnewline
5 & 81 & 82.5352662721894 & -1.53526627218938 \tabularnewline
6 & 94.7 & 91.8352662721894 & 2.86473372781064 \tabularnewline
7 & 101 & 106.995266272189 & -5.99526627218935 \tabularnewline
8 & 109.4 & 109.98 & -0.580000000000001 \tabularnewline
9 & 102.3 & 103.06 & -0.759999999999995 \tabularnewline
10 & 90.7 & 96.7 & -6 \tabularnewline
11 & 96.2 & 96.46 & -0.259999999999999 \tabularnewline
12 & 96.1 & 97.34 & -1.24000000000000 \tabularnewline
13 & 106 & 109.534319526627 & -3.53431952662724 \tabularnewline
14 & 103.1 & 102.081183431953 & 1.01881656804733 \tabularnewline
15 & 102 & 100.001183431953 & 1.99881656804734 \tabularnewline
16 & 104.7 & 108.641183431953 & -3.94118343195266 \tabularnewline
17 & 86 & 85.0411834319527 & 0.958816568047336 \tabularnewline
18 & 92.1 & 94.3411834319527 & -2.24118343195266 \tabularnewline
19 & 106.9 & 109.501183431953 & -2.60118343195266 \tabularnewline
20 & 112.6 & 109.98 & 2.61999999999999 \tabularnewline
21 & 101.7 & 103.06 & -1.36 \tabularnewline
22 & 92 & 96.7 & -4.7 \tabularnewline
23 & 97.4 & 96.46 & 0.940000000000006 \tabularnewline
24 & 97 & 97.34 & -0.339999999999997 \tabularnewline
25 & 105.4 & 109.534319526627 & -4.13431952662723 \tabularnewline
26 & 102.7 & 102.081183431953 & 0.618816568047336 \tabularnewline
27 & 98.1 & 100.001183431953 & -1.90118343195267 \tabularnewline
28 & 104.5 & 108.641183431953 & -4.14118343195266 \tabularnewline
29 & 87.4 & 85.0411834319527 & 2.35881656804734 \tabularnewline
30 & 89.9 & 94.3411834319527 & -4.44118343195265 \tabularnewline
31 & 109.8 & 109.501183431953 & 0.298816568047331 \tabularnewline
32 & 111.7 & 109.98 & 1.72 \tabularnewline
33 & 98.6 & 103.06 & -4.46000000000001 \tabularnewline
34 & 96.9 & 96.7 & 0.200000000000006 \tabularnewline
35 & 95.1 & 96.46 & -1.36000000000000 \tabularnewline
36 & 97 & 97.34 & -0.339999999999997 \tabularnewline
37 & 112.7 & 109.534319526627 & 3.16568047337277 \tabularnewline
38 & 102.9 & 102.081183431953 & 0.818816568047338 \tabularnewline
39 & 97.4 & 100.001183431953 & -2.60118343195265 \tabularnewline
40 & 111.4 & 108.641183431953 & 2.75881656804734 \tabularnewline
41 & 87.4 & 85.0411834319527 & 2.35881656804734 \tabularnewline
42 & 96.8 & 94.3411834319527 & 2.45881656804734 \tabularnewline
43 & 114.1 & 109.501183431953 & 4.59881656804733 \tabularnewline
44 & 110.3 & 109.98 & 0.319999999999996 \tabularnewline
45 & 103.9 & 103.06 & 0.840000000000005 \tabularnewline
46 & 101.6 & 96.7 & 4.90000000000000 \tabularnewline
47 & 94.6 & 96.46 & -1.86000000000000 \tabularnewline
48 & 95.9 & 97.34 & -1.43999999999999 \tabularnewline
49 & 104.7 & 109.534319526627 & -4.83431952662723 \tabularnewline
50 & 102.8 & 102.081183431953 & 0.71881656804733 \tabularnewline
51 & 98.1 & 100.001183431953 & -1.90118343195267 \tabularnewline
52 & 113.9 & 108.641183431953 & 5.25881656804734 \tabularnewline
53 & 80.9 & 85.0411834319527 & -4.14118343195265 \tabularnewline
54 & 95.7 & 94.3411834319527 & 1.35881656804734 \tabularnewline
55 & 113.2 & 109.501183431953 & 3.69881656804734 \tabularnewline
56 & 105.9 & 109.98 & -4.08000000000000 \tabularnewline
57 & 108.8 & 103.06 & 5.74 \tabularnewline
58 & 102.3 & 96.7 & 5.6 \tabularnewline
59 & 99 & 96.46 & 2.54 \tabularnewline
60 & 100.7 & 97.34 & 3.36000000000001 \tabularnewline
61 & 115.5 & 109.534319526627 & 5.96568047337276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5675&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]110.4[/C][C]107.028402366864[/C][C]3.37159763313617[/C][/ROW]
[ROW][C]2[/C][C]96.4[/C][C]99.5752662721893[/C][C]-3.17526627218933[/C][/ROW]
[ROW][C]3[/C][C]101.9[/C][C]97.4952662721894[/C][C]4.40473372781065[/C][/ROW]
[ROW][C]4[/C][C]106.2[/C][C]106.135266272189[/C][C]0.0647337278106297[/C][/ROW]
[ROW][C]5[/C][C]81[/C][C]82.5352662721894[/C][C]-1.53526627218938[/C][/ROW]
[ROW][C]6[/C][C]94.7[/C][C]91.8352662721894[/C][C]2.86473372781064[/C][/ROW]
[ROW][C]7[/C][C]101[/C][C]106.995266272189[/C][C]-5.99526627218935[/C][/ROW]
[ROW][C]8[/C][C]109.4[/C][C]109.98[/C][C]-0.580000000000001[/C][/ROW]
[ROW][C]9[/C][C]102.3[/C][C]103.06[/C][C]-0.759999999999995[/C][/ROW]
[ROW][C]10[/C][C]90.7[/C][C]96.7[/C][C]-6[/C][/ROW]
[ROW][C]11[/C][C]96.2[/C][C]96.46[/C][C]-0.259999999999999[/C][/ROW]
[ROW][C]12[/C][C]96.1[/C][C]97.34[/C][C]-1.24000000000000[/C][/ROW]
[ROW][C]13[/C][C]106[/C][C]109.534319526627[/C][C]-3.53431952662724[/C][/ROW]
[ROW][C]14[/C][C]103.1[/C][C]102.081183431953[/C][C]1.01881656804733[/C][/ROW]
[ROW][C]15[/C][C]102[/C][C]100.001183431953[/C][C]1.99881656804734[/C][/ROW]
[ROW][C]16[/C][C]104.7[/C][C]108.641183431953[/C][C]-3.94118343195266[/C][/ROW]
[ROW][C]17[/C][C]86[/C][C]85.0411834319527[/C][C]0.958816568047336[/C][/ROW]
[ROW][C]18[/C][C]92.1[/C][C]94.3411834319527[/C][C]-2.24118343195266[/C][/ROW]
[ROW][C]19[/C][C]106.9[/C][C]109.501183431953[/C][C]-2.60118343195266[/C][/ROW]
[ROW][C]20[/C][C]112.6[/C][C]109.98[/C][C]2.61999999999999[/C][/ROW]
[ROW][C]21[/C][C]101.7[/C][C]103.06[/C][C]-1.36[/C][/ROW]
[ROW][C]22[/C][C]92[/C][C]96.7[/C][C]-4.7[/C][/ROW]
[ROW][C]23[/C][C]97.4[/C][C]96.46[/C][C]0.940000000000006[/C][/ROW]
[ROW][C]24[/C][C]97[/C][C]97.34[/C][C]-0.339999999999997[/C][/ROW]
[ROW][C]25[/C][C]105.4[/C][C]109.534319526627[/C][C]-4.13431952662723[/C][/ROW]
[ROW][C]26[/C][C]102.7[/C][C]102.081183431953[/C][C]0.618816568047336[/C][/ROW]
[ROW][C]27[/C][C]98.1[/C][C]100.001183431953[/C][C]-1.90118343195267[/C][/ROW]
[ROW][C]28[/C][C]104.5[/C][C]108.641183431953[/C][C]-4.14118343195266[/C][/ROW]
[ROW][C]29[/C][C]87.4[/C][C]85.0411834319527[/C][C]2.35881656804734[/C][/ROW]
[ROW][C]30[/C][C]89.9[/C][C]94.3411834319527[/C][C]-4.44118343195265[/C][/ROW]
[ROW][C]31[/C][C]109.8[/C][C]109.501183431953[/C][C]0.298816568047331[/C][/ROW]
[ROW][C]32[/C][C]111.7[/C][C]109.98[/C][C]1.72[/C][/ROW]
[ROW][C]33[/C][C]98.6[/C][C]103.06[/C][C]-4.46000000000001[/C][/ROW]
[ROW][C]34[/C][C]96.9[/C][C]96.7[/C][C]0.200000000000006[/C][/ROW]
[ROW][C]35[/C][C]95.1[/C][C]96.46[/C][C]-1.36000000000000[/C][/ROW]
[ROW][C]36[/C][C]97[/C][C]97.34[/C][C]-0.339999999999997[/C][/ROW]
[ROW][C]37[/C][C]112.7[/C][C]109.534319526627[/C][C]3.16568047337277[/C][/ROW]
[ROW][C]38[/C][C]102.9[/C][C]102.081183431953[/C][C]0.818816568047338[/C][/ROW]
[ROW][C]39[/C][C]97.4[/C][C]100.001183431953[/C][C]-2.60118343195265[/C][/ROW]
[ROW][C]40[/C][C]111.4[/C][C]108.641183431953[/C][C]2.75881656804734[/C][/ROW]
[ROW][C]41[/C][C]87.4[/C][C]85.0411834319527[/C][C]2.35881656804734[/C][/ROW]
[ROW][C]42[/C][C]96.8[/C][C]94.3411834319527[/C][C]2.45881656804734[/C][/ROW]
[ROW][C]43[/C][C]114.1[/C][C]109.501183431953[/C][C]4.59881656804733[/C][/ROW]
[ROW][C]44[/C][C]110.3[/C][C]109.98[/C][C]0.319999999999996[/C][/ROW]
[ROW][C]45[/C][C]103.9[/C][C]103.06[/C][C]0.840000000000005[/C][/ROW]
[ROW][C]46[/C][C]101.6[/C][C]96.7[/C][C]4.90000000000000[/C][/ROW]
[ROW][C]47[/C][C]94.6[/C][C]96.46[/C][C]-1.86000000000000[/C][/ROW]
[ROW][C]48[/C][C]95.9[/C][C]97.34[/C][C]-1.43999999999999[/C][/ROW]
[ROW][C]49[/C][C]104.7[/C][C]109.534319526627[/C][C]-4.83431952662723[/C][/ROW]
[ROW][C]50[/C][C]102.8[/C][C]102.081183431953[/C][C]0.71881656804733[/C][/ROW]
[ROW][C]51[/C][C]98.1[/C][C]100.001183431953[/C][C]-1.90118343195267[/C][/ROW]
[ROW][C]52[/C][C]113.9[/C][C]108.641183431953[/C][C]5.25881656804734[/C][/ROW]
[ROW][C]53[/C][C]80.9[/C][C]85.0411834319527[/C][C]-4.14118343195265[/C][/ROW]
[ROW][C]54[/C][C]95.7[/C][C]94.3411834319527[/C][C]1.35881656804734[/C][/ROW]
[ROW][C]55[/C][C]113.2[/C][C]109.501183431953[/C][C]3.69881656804734[/C][/ROW]
[ROW][C]56[/C][C]105.9[/C][C]109.98[/C][C]-4.08000000000000[/C][/ROW]
[ROW][C]57[/C][C]108.8[/C][C]103.06[/C][C]5.74[/C][/ROW]
[ROW][C]58[/C][C]102.3[/C][C]96.7[/C][C]5.6[/C][/ROW]
[ROW][C]59[/C][C]99[/C][C]96.46[/C][C]2.54[/C][/ROW]
[ROW][C]60[/C][C]100.7[/C][C]97.34[/C][C]3.36000000000001[/C][/ROW]
[ROW][C]61[/C][C]115.5[/C][C]109.534319526627[/C][C]5.96568047337276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5675&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5675&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	110.4	107.028402366864	3.37159763313617
2	96.4	99.5752662721893	-3.17526627218933
3	101.9	97.4952662721894	4.40473372781065
4	106.2	106.135266272189	0.0647337278106297
5	81	82.5352662721894	-1.53526627218938
6	94.7	91.8352662721894	2.86473372781064
7	101	106.995266272189	-5.99526627218935
8	109.4	109.98	-0.580000000000001
9	102.3	103.06	-0.759999999999995
10	90.7	96.7	-6
11	96.2	96.46	-0.259999999999999
12	96.1	97.34	-1.24000000000000
13	106	109.534319526627	-3.53431952662724
14	103.1	102.081183431953	1.01881656804733
15	102	100.001183431953	1.99881656804734
16	104.7	108.641183431953	-3.94118343195266
17	86	85.0411834319527	0.958816568047336
18	92.1	94.3411834319527	-2.24118343195266
19	106.9	109.501183431953	-2.60118343195266
20	112.6	109.98	2.61999999999999
21	101.7	103.06	-1.36
22	92	96.7	-4.7
23	97.4	96.46	0.940000000000006
24	97	97.34	-0.339999999999997
25	105.4	109.534319526627	-4.13431952662723
26	102.7	102.081183431953	0.618816568047336
27	98.1	100.001183431953	-1.90118343195267
28	104.5	108.641183431953	-4.14118343195266
29	87.4	85.0411834319527	2.35881656804734
30	89.9	94.3411834319527	-4.44118343195265
31	109.8	109.501183431953	0.298816568047331
32	111.7	109.98	1.72
33	98.6	103.06	-4.46000000000001
34	96.9	96.7	0.200000000000006
35	95.1	96.46	-1.36000000000000
36	97	97.34	-0.339999999999997
37	112.7	109.534319526627	3.16568047337277
38	102.9	102.081183431953	0.818816568047338
39	97.4	100.001183431953	-2.60118343195265
40	111.4	108.641183431953	2.75881656804734
41	87.4	85.0411834319527	2.35881656804734
42	96.8	94.3411834319527	2.45881656804734
43	114.1	109.501183431953	4.59881656804733
44	110.3	109.98	0.319999999999996
45	103.9	103.06	0.840000000000005
46	101.6	96.7	4.90000000000000
47	94.6	96.46	-1.86000000000000
48	95.9	97.34	-1.43999999999999
49	104.7	109.534319526627	-4.83431952662723
50	102.8	102.081183431953	0.71881656804733
51	98.1	100.001183431953	-1.90118343195267
52	113.9	108.641183431953	5.25881656804734
53	80.9	85.0411834319527	-4.14118343195265
54	95.7	94.3411834319527	1.35881656804734
55	113.2	109.501183431953	3.69881656804734
56	105.9	109.98	-4.08000000000000
57	108.8	103.06	5.74
58	102.3	96.7	5.6
59	99	96.46	2.54
60	100.7	97.34	3.36000000000001
61	115.5	109.534319526627	5.96568047337276

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

Postscript link

PDF link

Figure 9

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code