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

Sat, 17 Nov 2007 08:11:31 -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/17/t1195311975pxvi7fz7e8vpm9n.htm/, Retrieved Thu, 09 May 2024 01:15:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5535, Retrieved Thu, 09 May 2024 01:15:10 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

met maandseizonaliteit en LT-trend

IsPrivate?

No (this computation is public)

User-defined keywords

s0650921

Estimated Impact

271

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

-       [Multiple Regression] [multiple regressi...] [2007-11-17 15:11:31] [1232d415564adb2a600743f77b12553a] [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=5535&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=5535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5535&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] = + 109.038912048805 + 3.48261311642096x[t] -9.1558998474836M1[t] -11.3278139298424M2[t] + 0.94374936451449M3[t] -10.2481647178444M4[t] -10.9600788002033M5[t] -1.46851550584647M6[t] -14.6204295882054M7[t] -10.8923436705643M8[t] + 5.45574224707676M9[t] + 3.44382816471783M10[t] -1.72808591764109M11[t] + 0.251914082358923t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  109.038912048805 +  3.48261311642096x[t] -9.1558998474836M1[t] -11.3278139298424M2[t] +  0.94374936451449M3[t] -10.2481647178444M4[t] -10.9600788002033M5[t] -1.46851550584647M6[t] -14.6204295882054M7[t] -10.8923436705643M8[t] +  5.45574224707676M9[t] +  3.44382816471783M10[t] -1.72808591764109M11[t] +  0.251914082358923t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5535&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  109.038912048805 +  3.48261311642096x[t] -9.1558998474836M1[t] -11.3278139298424M2[t] +  0.94374936451449M3[t] -10.2481647178444M4[t] -10.9600788002033M5[t] -1.46851550584647M6[t] -14.6204295882054M7[t] -10.8923436705643M8[t] +  5.45574224707676M9[t] +  3.44382816471783M10[t] -1.72808591764109M11[t] +  0.251914082358923t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5535&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] = + 109.038912048805 + 3.48261311642096x[t] -9.1558998474836M1[t] -11.3278139298424M2[t] + 0.94374936451449M3[t] -10.2481647178444M4[t] -10.9600788002033M5[t] -1.46851550584647M6[t] -14.6204295882054M7[t] -10.8923436705643M8[t] + 5.45574224707676M9[t] + 3.44382816471783M10[t] -1.72808591764109M11[t] + 0.251914082358923t + 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)	109.038912048805	2.708965	40.2511	0	0
x	3.48261311642096	1.268821	2.7448	0.008608	0.004304
M1	-9.1558998474836	3.277355	-2.7937	0.007571	0.003786
M2	-11.3278139298424	3.272439	-3.4616	0.001171	0.000585
M3	0.94374936451449	3.273008	0.2883	0.774379	0.38719
M4	-10.2481647178444	3.266694	-3.1372	0.002973	0.001487
M5	-10.9600788002033	3.261557	-3.3604	0.001573	0.000787
M6	-1.46851550584647	3.270343	-0.449	0.655511	0.327756
M7	-14.6204295882054	3.263818	-4.4795	4.9e-05	2.5e-05
M8	-10.8923436705643	3.25847	-3.3428	0.001655	0.000828
M9	5.45574224707676	3.254305	1.6765	0.100431	0.050215
M10	3.44382816471783	3.251326	1.0592	0.295036	0.147518
M11	-1.72808591764109	3.249537	-0.5318	0.597427	0.298714
t	0.251914082358923	0.062255	4.0465	0.000197	9.8e-05

\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) & 109.038912048805 & 2.708965 & 40.2511 & 0 & 0 \tabularnewline
x & 3.48261311642096 & 1.268821 & 2.7448 & 0.008608 & 0.004304 \tabularnewline
M1 & -9.1558998474836 & 3.277355 & -2.7937 & 0.007571 & 0.003786 \tabularnewline
M2 & -11.3278139298424 & 3.272439 & -3.4616 & 0.001171 & 0.000585 \tabularnewline
M3 & 0.94374936451449 & 3.273008 & 0.2883 & 0.774379 & 0.38719 \tabularnewline
M4 & -10.2481647178444 & 3.266694 & -3.1372 & 0.002973 & 0.001487 \tabularnewline
M5 & -10.9600788002033 & 3.261557 & -3.3604 & 0.001573 & 0.000787 \tabularnewline
M6 & -1.46851550584647 & 3.270343 & -0.449 & 0.655511 & 0.327756 \tabularnewline
M7 & -14.6204295882054 & 3.263818 & -4.4795 & 4.9e-05 & 2.5e-05 \tabularnewline
M8 & -10.8923436705643 & 3.25847 & -3.3428 & 0.001655 & 0.000828 \tabularnewline
M9 & 5.45574224707676 & 3.254305 & 1.6765 & 0.100431 & 0.050215 \tabularnewline
M10 & 3.44382816471783 & 3.251326 & 1.0592 & 0.295036 & 0.147518 \tabularnewline
M11 & -1.72808591764109 & 3.249537 & -0.5318 & 0.597427 & 0.298714 \tabularnewline
t & 0.251914082358923 & 0.062255 & 4.0465 & 0.000197 & 9.8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5535&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]109.038912048805[/C][C]2.708965[/C][C]40.2511[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]3.48261311642096[/C][C]1.268821[/C][C]2.7448[/C][C]0.008608[/C][C]0.004304[/C][/ROW]
[ROW][C]M1[/C][C]-9.1558998474836[/C][C]3.277355[/C][C]-2.7937[/C][C]0.007571[/C][C]0.003786[/C][/ROW]
[ROW][C]M2[/C][C]-11.3278139298424[/C][C]3.272439[/C][C]-3.4616[/C][C]0.001171[/C][C]0.000585[/C][/ROW]
[ROW][C]M3[/C][C]0.94374936451449[/C][C]3.273008[/C][C]0.2883[/C][C]0.774379[/C][C]0.38719[/C][/ROW]
[ROW][C]M4[/C][C]-10.2481647178444[/C][C]3.266694[/C][C]-3.1372[/C][C]0.002973[/C][C]0.001487[/C][/ROW]
[ROW][C]M5[/C][C]-10.9600788002033[/C][C]3.261557[/C][C]-3.3604[/C][C]0.001573[/C][C]0.000787[/C][/ROW]
[ROW][C]M6[/C][C]-1.46851550584647[/C][C]3.270343[/C][C]-0.449[/C][C]0.655511[/C][C]0.327756[/C][/ROW]
[ROW][C]M7[/C][C]-14.6204295882054[/C][C]3.263818[/C][C]-4.4795[/C][C]4.9e-05[/C][C]2.5e-05[/C][/ROW]
[ROW][C]M8[/C][C]-10.8923436705643[/C][C]3.25847[/C][C]-3.3428[/C][C]0.001655[/C][C]0.000828[/C][/ROW]
[ROW][C]M9[/C][C]5.45574224707676[/C][C]3.254305[/C][C]1.6765[/C][C]0.100431[/C][C]0.050215[/C][/ROW]
[ROW][C]M10[/C][C]3.44382816471783[/C][C]3.251326[/C][C]1.0592[/C][C]0.295036[/C][C]0.147518[/C][/ROW]
[ROW][C]M11[/C][C]-1.72808591764109[/C][C]3.249537[/C][C]-0.5318[/C][C]0.597427[/C][C]0.298714[/C][/ROW]
[ROW][C]t[/C][C]0.251914082358923[/C][C]0.062255[/C][C]4.0465[/C][C]0.000197[/C][C]9.8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5535&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)	109.038912048805	2.708965	40.2511	0	0
x	3.48261311642096	1.268821	2.7448	0.008608	0.004304
M1	-9.1558998474836	3.277355	-2.7937	0.007571	0.003786
M2	-11.3278139298424	3.272439	-3.4616	0.001171	0.000585
M3	0.94374936451449	3.273008	0.2883	0.774379	0.38719
M4	-10.2481647178444	3.266694	-3.1372	0.002973	0.001487
M5	-10.9600788002033	3.261557	-3.3604	0.001573	0.000787
M6	-1.46851550584647	3.270343	-0.449	0.655511	0.327756
M7	-14.6204295882054	3.263818	-4.4795	4.9e-05	2.5e-05
M8	-10.8923436705643	3.25847	-3.3428	0.001655	0.000828
M9	5.45574224707676	3.254305	1.6765	0.100431	0.050215
M10	3.44382816471783	3.251326	1.0592	0.295036	0.147518
M11	-1.72808591764109	3.249537	-0.5318	0.597427	0.298714
t	0.251914082358923	0.062255	4.0465	0.000197	9.8e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.9113358675062
R-squared	0.830533063403278
Adjusted R-squared	0.78264023349551
F-TEST (value)	17.3414906783061
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	1.54098955817972e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.13702681040599
Sum Squared Residuals	1213.89604473818

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.9113358675062 \tabularnewline
R-squared & 0.830533063403278 \tabularnewline
Adjusted R-squared & 0.78264023349551 \tabularnewline
F-TEST (value) & 17.3414906783061 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 1.54098955817972e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.13702681040599 \tabularnewline
Sum Squared Residuals & 1213.89604473818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5535&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.9113358675062[/C][/ROW]
[ROW][C]R-squared[/C][C]0.830533063403278[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.78264023349551[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]17.3414906783061[/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]1.54098955817972e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.13702681040599[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1213.89604473818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5535&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5535&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	0.9113358675062
R-squared	0.830533063403278
Adjusted R-squared	0.78264023349551
F-TEST (value)	17.3414906783061
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	1.54098955817972e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.13702681040599
Sum Squared Residuals	1213.89604473818

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	99.9	100.134926283681	-0.234926283681134
2	98.2	98.2149262836808	-0.0149262836807459
3	104.5	110.738403660397	-6.23840366039651
4	100.8	99.7984036603965	1.0015963396035
5	101.5	99.3384036603965	2.16159633960349
6	103.9	109.081881037112	-5.18188103711232
7	99.6	96.1818810371124	3.41811896288764
8	98.4	100.161881037112	-1.76188103711232
9	112.7	116.761881037112	-4.06188103711233
10	118.4	115.001881037112	3.39811896288767
11	108.1	110.081881037112	-1.98188103711233
12	105.4	112.061881037112	-6.66188103711233
13	114.6	103.157895271988	11.4421047280123
14	106.9	101.237895271988	5.66210472801223
15	115.9	117.243985765125	-1.34398576512455
16	109.8	106.303985765125	3.49601423487545
17	101.8	105.843985765125	-4.04398576512455
18	114.2	119.070076258261	-4.87007625826131
19	110.8	106.170076258261	4.62992374173869
20	108.4	110.150076258261	-1.75007625826131
21	127.5	126.750076258261	0.749923741738689
22	128.6	124.990076258261	3.60992374173869
23	116.6	120.070076258261	-3.47007625826130
24	127.4	122.050076258261	5.34992374173869
25	105	113.146090493137	-8.14609049313666
26	108.3	111.226090493137	-2.92609049313676
27	125	123.749567869853	1.25043213014742
28	111.6	112.809567869853	-1.20956786985258
29	106.5	112.349567869853	-5.84956786985257
30	130.3	122.093045246568	8.20695475343162
31	115	109.193045246568	5.80695475343163
32	116.1	113.173045246568	2.92695475343161
33	134	129.773045246568	4.22695475343162
34	126.5	128.013045246568	-1.51304524656838
35	125.8	123.093045246568	2.70695475343162
36	136.4	125.073045246568	11.3269547534316
37	114.9	116.169059481444	-1.26905948144372
38	110.9	114.249059481444	-3.34905948144382
39	125.5	126.772536858160	-1.27253685815965
40	116.8	115.832536858160	0.967463141840352
41	116.8	115.372536858160	1.42746314184035
42	125.5	125.116014234875	0.383985765124540
43	104.2	112.216014234875	-8.01601423487544
44	115.1	116.196014234875	-1.09601423487546
45	132.8	132.796014234875	0.00398576512455416
46	123.3	131.036014234875	-7.73601423487546
47	124.8	126.116014234875	-1.31601423487545
48	122	128.096014234875	-6.09601423487546
49	117.4	119.192028469751	-1.79202846975079
50	117.9	117.272028469751	0.627971530249106
51	137.4	129.795505846467	7.60449415353328
52	114.6	118.855505846467	-4.25550584646672
53	124.7	118.395505846467	6.30449415353329
54	129.6	128.138983223183	1.46101677681746
55	109.4	115.238983223183	-5.83898322318251
56	120.9	119.218983223183	1.68101677681748
57	134.9	135.818983223183	-0.918983223182524
58	136.3	134.058983223183	2.24101677681748
59	133.2	129.138983223183	4.06101677681747
60	127.2	131.118983223183	-3.91898322318253

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 99.9 & 100.134926283681 & -0.234926283681134 \tabularnewline
2 & 98.2 & 98.2149262836808 & -0.0149262836807459 \tabularnewline
3 & 104.5 & 110.738403660397 & -6.23840366039651 \tabularnewline
4 & 100.8 & 99.7984036603965 & 1.0015963396035 \tabularnewline
5 & 101.5 & 99.3384036603965 & 2.16159633960349 \tabularnewline
6 & 103.9 & 109.081881037112 & -5.18188103711232 \tabularnewline
7 & 99.6 & 96.1818810371124 & 3.41811896288764 \tabularnewline
8 & 98.4 & 100.161881037112 & -1.76188103711232 \tabularnewline
9 & 112.7 & 116.761881037112 & -4.06188103711233 \tabularnewline
10 & 118.4 & 115.001881037112 & 3.39811896288767 \tabularnewline
11 & 108.1 & 110.081881037112 & -1.98188103711233 \tabularnewline
12 & 105.4 & 112.061881037112 & -6.66188103711233 \tabularnewline
13 & 114.6 & 103.157895271988 & 11.4421047280123 \tabularnewline
14 & 106.9 & 101.237895271988 & 5.66210472801223 \tabularnewline
15 & 115.9 & 117.243985765125 & -1.34398576512455 \tabularnewline
16 & 109.8 & 106.303985765125 & 3.49601423487545 \tabularnewline
17 & 101.8 & 105.843985765125 & -4.04398576512455 \tabularnewline
18 & 114.2 & 119.070076258261 & -4.87007625826131 \tabularnewline
19 & 110.8 & 106.170076258261 & 4.62992374173869 \tabularnewline
20 & 108.4 & 110.150076258261 & -1.75007625826131 \tabularnewline
21 & 127.5 & 126.750076258261 & 0.749923741738689 \tabularnewline
22 & 128.6 & 124.990076258261 & 3.60992374173869 \tabularnewline
23 & 116.6 & 120.070076258261 & -3.47007625826130 \tabularnewline
24 & 127.4 & 122.050076258261 & 5.34992374173869 \tabularnewline
25 & 105 & 113.146090493137 & -8.14609049313666 \tabularnewline
26 & 108.3 & 111.226090493137 & -2.92609049313676 \tabularnewline
27 & 125 & 123.749567869853 & 1.25043213014742 \tabularnewline
28 & 111.6 & 112.809567869853 & -1.20956786985258 \tabularnewline
29 & 106.5 & 112.349567869853 & -5.84956786985257 \tabularnewline
30 & 130.3 & 122.093045246568 & 8.20695475343162 \tabularnewline
31 & 115 & 109.193045246568 & 5.80695475343163 \tabularnewline
32 & 116.1 & 113.173045246568 & 2.92695475343161 \tabularnewline
33 & 134 & 129.773045246568 & 4.22695475343162 \tabularnewline
34 & 126.5 & 128.013045246568 & -1.51304524656838 \tabularnewline
35 & 125.8 & 123.093045246568 & 2.70695475343162 \tabularnewline
36 & 136.4 & 125.073045246568 & 11.3269547534316 \tabularnewline
37 & 114.9 & 116.169059481444 & -1.26905948144372 \tabularnewline
38 & 110.9 & 114.249059481444 & -3.34905948144382 \tabularnewline
39 & 125.5 & 126.772536858160 & -1.27253685815965 \tabularnewline
40 & 116.8 & 115.832536858160 & 0.967463141840352 \tabularnewline
41 & 116.8 & 115.372536858160 & 1.42746314184035 \tabularnewline
42 & 125.5 & 125.116014234875 & 0.383985765124540 \tabularnewline
43 & 104.2 & 112.216014234875 & -8.01601423487544 \tabularnewline
44 & 115.1 & 116.196014234875 & -1.09601423487546 \tabularnewline
45 & 132.8 & 132.796014234875 & 0.00398576512455416 \tabularnewline
46 & 123.3 & 131.036014234875 & -7.73601423487546 \tabularnewline
47 & 124.8 & 126.116014234875 & -1.31601423487545 \tabularnewline
48 & 122 & 128.096014234875 & -6.09601423487546 \tabularnewline
49 & 117.4 & 119.192028469751 & -1.79202846975079 \tabularnewline
50 & 117.9 & 117.272028469751 & 0.627971530249106 \tabularnewline
51 & 137.4 & 129.795505846467 & 7.60449415353328 \tabularnewline
52 & 114.6 & 118.855505846467 & -4.25550584646672 \tabularnewline
53 & 124.7 & 118.395505846467 & 6.30449415353329 \tabularnewline
54 & 129.6 & 128.138983223183 & 1.46101677681746 \tabularnewline
55 & 109.4 & 115.238983223183 & -5.83898322318251 \tabularnewline
56 & 120.9 & 119.218983223183 & 1.68101677681748 \tabularnewline
57 & 134.9 & 135.818983223183 & -0.918983223182524 \tabularnewline
58 & 136.3 & 134.058983223183 & 2.24101677681748 \tabularnewline
59 & 133.2 & 129.138983223183 & 4.06101677681747 \tabularnewline
60 & 127.2 & 131.118983223183 & -3.91898322318253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5535&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]99.9[/C][C]100.134926283681[/C][C]-0.234926283681134[/C][/ROW]
[ROW][C]2[/C][C]98.2[/C][C]98.2149262836808[/C][C]-0.0149262836807459[/C][/ROW]
[ROW][C]3[/C][C]104.5[/C][C]110.738403660397[/C][C]-6.23840366039651[/C][/ROW]
[ROW][C]4[/C][C]100.8[/C][C]99.7984036603965[/C][C]1.0015963396035[/C][/ROW]
[ROW][C]5[/C][C]101.5[/C][C]99.3384036603965[/C][C]2.16159633960349[/C][/ROW]
[ROW][C]6[/C][C]103.9[/C][C]109.081881037112[/C][C]-5.18188103711232[/C][/ROW]
[ROW][C]7[/C][C]99.6[/C][C]96.1818810371124[/C][C]3.41811896288764[/C][/ROW]
[ROW][C]8[/C][C]98.4[/C][C]100.161881037112[/C][C]-1.76188103711232[/C][/ROW]
[ROW][C]9[/C][C]112.7[/C][C]116.761881037112[/C][C]-4.06188103711233[/C][/ROW]
[ROW][C]10[/C][C]118.4[/C][C]115.001881037112[/C][C]3.39811896288767[/C][/ROW]
[ROW][C]11[/C][C]108.1[/C][C]110.081881037112[/C][C]-1.98188103711233[/C][/ROW]
[ROW][C]12[/C][C]105.4[/C][C]112.061881037112[/C][C]-6.66188103711233[/C][/ROW]
[ROW][C]13[/C][C]114.6[/C][C]103.157895271988[/C][C]11.4421047280123[/C][/ROW]
[ROW][C]14[/C][C]106.9[/C][C]101.237895271988[/C][C]5.66210472801223[/C][/ROW]
[ROW][C]15[/C][C]115.9[/C][C]117.243985765125[/C][C]-1.34398576512455[/C][/ROW]
[ROW][C]16[/C][C]109.8[/C][C]106.303985765125[/C][C]3.49601423487545[/C][/ROW]
[ROW][C]17[/C][C]101.8[/C][C]105.843985765125[/C][C]-4.04398576512455[/C][/ROW]
[ROW][C]18[/C][C]114.2[/C][C]119.070076258261[/C][C]-4.87007625826131[/C][/ROW]
[ROW][C]19[/C][C]110.8[/C][C]106.170076258261[/C][C]4.62992374173869[/C][/ROW]
[ROW][C]20[/C][C]108.4[/C][C]110.150076258261[/C][C]-1.75007625826131[/C][/ROW]
[ROW][C]21[/C][C]127.5[/C][C]126.750076258261[/C][C]0.749923741738689[/C][/ROW]
[ROW][C]22[/C][C]128.6[/C][C]124.990076258261[/C][C]3.60992374173869[/C][/ROW]
[ROW][C]23[/C][C]116.6[/C][C]120.070076258261[/C][C]-3.47007625826130[/C][/ROW]
[ROW][C]24[/C][C]127.4[/C][C]122.050076258261[/C][C]5.34992374173869[/C][/ROW]
[ROW][C]25[/C][C]105[/C][C]113.146090493137[/C][C]-8.14609049313666[/C][/ROW]
[ROW][C]26[/C][C]108.3[/C][C]111.226090493137[/C][C]-2.92609049313676[/C][/ROW]
[ROW][C]27[/C][C]125[/C][C]123.749567869853[/C][C]1.25043213014742[/C][/ROW]
[ROW][C]28[/C][C]111.6[/C][C]112.809567869853[/C][C]-1.20956786985258[/C][/ROW]
[ROW][C]29[/C][C]106.5[/C][C]112.349567869853[/C][C]-5.84956786985257[/C][/ROW]
[ROW][C]30[/C][C]130.3[/C][C]122.093045246568[/C][C]8.20695475343162[/C][/ROW]
[ROW][C]31[/C][C]115[/C][C]109.193045246568[/C][C]5.80695475343163[/C][/ROW]
[ROW][C]32[/C][C]116.1[/C][C]113.173045246568[/C][C]2.92695475343161[/C][/ROW]
[ROW][C]33[/C][C]134[/C][C]129.773045246568[/C][C]4.22695475343162[/C][/ROW]
[ROW][C]34[/C][C]126.5[/C][C]128.013045246568[/C][C]-1.51304524656838[/C][/ROW]
[ROW][C]35[/C][C]125.8[/C][C]123.093045246568[/C][C]2.70695475343162[/C][/ROW]
[ROW][C]36[/C][C]136.4[/C][C]125.073045246568[/C][C]11.3269547534316[/C][/ROW]
[ROW][C]37[/C][C]114.9[/C][C]116.169059481444[/C][C]-1.26905948144372[/C][/ROW]
[ROW][C]38[/C][C]110.9[/C][C]114.249059481444[/C][C]-3.34905948144382[/C][/ROW]
[ROW][C]39[/C][C]125.5[/C][C]126.772536858160[/C][C]-1.27253685815965[/C][/ROW]
[ROW][C]40[/C][C]116.8[/C][C]115.832536858160[/C][C]0.967463141840352[/C][/ROW]
[ROW][C]41[/C][C]116.8[/C][C]115.372536858160[/C][C]1.42746314184035[/C][/ROW]
[ROW][C]42[/C][C]125.5[/C][C]125.116014234875[/C][C]0.383985765124540[/C][/ROW]
[ROW][C]43[/C][C]104.2[/C][C]112.216014234875[/C][C]-8.01601423487544[/C][/ROW]
[ROW][C]44[/C][C]115.1[/C][C]116.196014234875[/C][C]-1.09601423487546[/C][/ROW]
[ROW][C]45[/C][C]132.8[/C][C]132.796014234875[/C][C]0.00398576512455416[/C][/ROW]
[ROW][C]46[/C][C]123.3[/C][C]131.036014234875[/C][C]-7.73601423487546[/C][/ROW]
[ROW][C]47[/C][C]124.8[/C][C]126.116014234875[/C][C]-1.31601423487545[/C][/ROW]
[ROW][C]48[/C][C]122[/C][C]128.096014234875[/C][C]-6.09601423487546[/C][/ROW]
[ROW][C]49[/C][C]117.4[/C][C]119.192028469751[/C][C]-1.79202846975079[/C][/ROW]
[ROW][C]50[/C][C]117.9[/C][C]117.272028469751[/C][C]0.627971530249106[/C][/ROW]
[ROW][C]51[/C][C]137.4[/C][C]129.795505846467[/C][C]7.60449415353328[/C][/ROW]
[ROW][C]52[/C][C]114.6[/C][C]118.855505846467[/C][C]-4.25550584646672[/C][/ROW]
[ROW][C]53[/C][C]124.7[/C][C]118.395505846467[/C][C]6.30449415353329[/C][/ROW]
[ROW][C]54[/C][C]129.6[/C][C]128.138983223183[/C][C]1.46101677681746[/C][/ROW]
[ROW][C]55[/C][C]109.4[/C][C]115.238983223183[/C][C]-5.83898322318251[/C][/ROW]
[ROW][C]56[/C][C]120.9[/C][C]119.218983223183[/C][C]1.68101677681748[/C][/ROW]
[ROW][C]57[/C][C]134.9[/C][C]135.818983223183[/C][C]-0.918983223182524[/C][/ROW]
[ROW][C]58[/C][C]136.3[/C][C]134.058983223183[/C][C]2.24101677681748[/C][/ROW]
[ROW][C]59[/C][C]133.2[/C][C]129.138983223183[/C][C]4.06101677681747[/C][/ROW]
[ROW][C]60[/C][C]127.2[/C][C]131.118983223183[/C][C]-3.91898322318253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5535&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5535&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	99.9	100.134926283681	-0.234926283681134
2	98.2	98.2149262836808	-0.0149262836807459
3	104.5	110.738403660397	-6.23840366039651
4	100.8	99.7984036603965	1.0015963396035
5	101.5	99.3384036603965	2.16159633960349
6	103.9	109.081881037112	-5.18188103711232
7	99.6	96.1818810371124	3.41811896288764
8	98.4	100.161881037112	-1.76188103711232
9	112.7	116.761881037112	-4.06188103711233
10	118.4	115.001881037112	3.39811896288767
11	108.1	110.081881037112	-1.98188103711233
12	105.4	112.061881037112	-6.66188103711233
13	114.6	103.157895271988	11.4421047280123
14	106.9	101.237895271988	5.66210472801223
15	115.9	117.243985765125	-1.34398576512455
16	109.8	106.303985765125	3.49601423487545
17	101.8	105.843985765125	-4.04398576512455
18	114.2	119.070076258261	-4.87007625826131
19	110.8	106.170076258261	4.62992374173869
20	108.4	110.150076258261	-1.75007625826131
21	127.5	126.750076258261	0.749923741738689
22	128.6	124.990076258261	3.60992374173869
23	116.6	120.070076258261	-3.47007625826130
24	127.4	122.050076258261	5.34992374173869
25	105	113.146090493137	-8.14609049313666
26	108.3	111.226090493137	-2.92609049313676
27	125	123.749567869853	1.25043213014742
28	111.6	112.809567869853	-1.20956786985258
29	106.5	112.349567869853	-5.84956786985257
30	130.3	122.093045246568	8.20695475343162
31	115	109.193045246568	5.80695475343163
32	116.1	113.173045246568	2.92695475343161
33	134	129.773045246568	4.22695475343162
34	126.5	128.013045246568	-1.51304524656838
35	125.8	123.093045246568	2.70695475343162
36	136.4	125.073045246568	11.3269547534316
37	114.9	116.169059481444	-1.26905948144372
38	110.9	114.249059481444	-3.34905948144382
39	125.5	126.772536858160	-1.27253685815965
40	116.8	115.832536858160	0.967463141840352
41	116.8	115.372536858160	1.42746314184035
42	125.5	125.116014234875	0.383985765124540
43	104.2	112.216014234875	-8.01601423487544
44	115.1	116.196014234875	-1.09601423487546
45	132.8	132.796014234875	0.00398576512455416
46	123.3	131.036014234875	-7.73601423487546
47	124.8	126.116014234875	-1.31601423487545
48	122	128.096014234875	-6.09601423487546
49	117.4	119.192028469751	-1.79202846975079
50	117.9	117.272028469751	0.627971530249106
51	137.4	129.795505846467	7.60449415353328
52	114.6	118.855505846467	-4.25550584646672
53	124.7	118.395505846467	6.30449415353329
54	129.6	128.138983223183	1.46101677681746
55	109.4	115.238983223183	-5.83898322318251
56	120.9	119.218983223183	1.68101677681748
57	134.9	135.818983223183	-0.918983223182524
58	136.3	134.058983223183	2.24101677681748
59	133.2	129.138983223183	4.06101677681747
60	127.2	131.118983223183	-3.91898322318253

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 = 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