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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 19 Nov 2007 03:48:25 -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/t1195468939cjkem217iiyqwhc.htm/, Retrieved Fri, 03 May 2024 06:53:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5689, Retrieved Fri, 03 May 2024 06:53:50 +0000

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Estimated Impact

204

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

-       [Multiple Regression] [Ws6 T3] [2007-11-19 10:48:25] [6bae8369195607c4cbc8a8485fed7b2f] [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=5689&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=5689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5689&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] = + 94.4102362204725 -0.0548228346456831`x `[t] + 12.1820554461943M1[t] + 5.05808727034122M2[t] + 2.89518208661418M3[t] + 11.4522769028871M4[t] -12.2306282808399M5[t] -3.01353346456693M6[t] + 12.0635613517060M7[t] + 12.9716207349081M8[t] + 5.96871555118111M9[t] -0.474189632545929M10[t] -0.797094816272964M11[t] + 0.082905183727034t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  94.4102362204725 -0.0548228346456831`x
`[t] +  12.1820554461943M1[t] +  5.05808727034122M2[t] +  2.89518208661418M3[t] +  11.4522769028871M4[t] -12.2306282808399M5[t] -3.01353346456693M6[t] +  12.0635613517060M7[t] +  12.9716207349081M8[t] +  5.96871555118111M9[t] -0.474189632545929M10[t] -0.797094816272964M11[t] +  0.082905183727034t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5689&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  94.4102362204725 -0.0548228346456831`x
`[t] +  12.1820554461943M1[t] +  5.05808727034122M2[t] +  2.89518208661418M3[t] +  11.4522769028871M4[t] -12.2306282808399M5[t] -3.01353346456693M6[t] +  12.0635613517060M7[t] +  12.9716207349081M8[t] +  5.96871555118111M9[t] -0.474189632545929M10[t] -0.797094816272964M11[t] +  0.082905183727034t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5689&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] = + 94.4102362204725 -0.0548228346456831`x `[t] + 12.1820554461943M1[t] + 5.05808727034122M2[t] + 2.89518208661418M3[t] + 11.4522769028871M4[t] -12.2306282808399M5[t] -3.01353346456693M6[t] + 12.0635613517060M7[t] + 12.9716207349081M8[t] + 5.96871555118111M9[t] -0.474189632545929M10[t] -0.797094816272964M11[t] + 0.082905183727034t + 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)	94.4102362204725	2.03525	46.3875	0	0
`x `	-0.0548228346456831	1.655082	-0.0331	0.973716	0.486858
M1	12.1820554461943	2.01388	6.049	0	0
M2	5.05808727034122	2.110797	2.3963	0.020594	0.010297
M3	2.89518208661418	2.109473	1.3725	0.176433	0.088216
M4	11.4522769028871	2.108548	5.4314	2e-06	1e-06
M5	-12.2306282808399	2.10802	-5.8019	1e-06	0
M6	-3.01353346456693	2.107892	-1.4296	0.159433	0.079717
M7	12.0635613517060	2.108162	5.7223	1e-06	0
M8	12.9716207349081	2.092638	6.1987	0	0
M9	5.96871555118111	2.091231	2.8542	0.0064	0.0032
M10	-0.474189632545929	2.090226	-0.2269	0.821516	0.410758
M11	-0.797094816272964	2.089623	-0.3815	0.704586	0.352293
t	0.082905183727034	0.028991	2.8597	0.006306	0.003153

\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) & 94.4102362204725 & 2.03525 & 46.3875 & 0 & 0 \tabularnewline
`x
` & -0.0548228346456831 & 1.655082 & -0.0331 & 0.973716 & 0.486858 \tabularnewline
M1 & 12.1820554461943 & 2.01388 & 6.049 & 0 & 0 \tabularnewline
M2 & 5.05808727034122 & 2.110797 & 2.3963 & 0.020594 & 0.010297 \tabularnewline
M3 & 2.89518208661418 & 2.109473 & 1.3725 & 0.176433 & 0.088216 \tabularnewline
M4 & 11.4522769028871 & 2.108548 & 5.4314 & 2e-06 & 1e-06 \tabularnewline
M5 & -12.2306282808399 & 2.10802 & -5.8019 & 1e-06 & 0 \tabularnewline
M6 & -3.01353346456693 & 2.107892 & -1.4296 & 0.159433 & 0.079717 \tabularnewline
M7 & 12.0635613517060 & 2.108162 & 5.7223 & 1e-06 & 0 \tabularnewline
M8 & 12.9716207349081 & 2.092638 & 6.1987 & 0 & 0 \tabularnewline
M9 & 5.96871555118111 & 2.091231 & 2.8542 & 0.0064 & 0.0032 \tabularnewline
M10 & -0.474189632545929 & 2.090226 & -0.2269 & 0.821516 & 0.410758 \tabularnewline
M11 & -0.797094816272964 & 2.089623 & -0.3815 & 0.704586 & 0.352293 \tabularnewline
t & 0.082905183727034 & 0.028991 & 2.8597 & 0.006306 & 0.003153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5689&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]94.4102362204725[/C][C]2.03525[/C][C]46.3875[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`x
`[/C][C]-0.0548228346456831[/C][C]1.655082[/C][C]-0.0331[/C][C]0.973716[/C][C]0.486858[/C][/ROW]
[ROW][C]M1[/C][C]12.1820554461943[/C][C]2.01388[/C][C]6.049[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M2[/C][C]5.05808727034122[/C][C]2.110797[/C][C]2.3963[/C][C]0.020594[/C][C]0.010297[/C][/ROW]
[ROW][C]M3[/C][C]2.89518208661418[/C][C]2.109473[/C][C]1.3725[/C][C]0.176433[/C][C]0.088216[/C][/ROW]
[ROW][C]M4[/C][C]11.4522769028871[/C][C]2.108548[/C][C]5.4314[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M5[/C][C]-12.2306282808399[/C][C]2.10802[/C][C]-5.8019[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-3.01353346456693[/C][C]2.107892[/C][C]-1.4296[/C][C]0.159433[/C][C]0.079717[/C][/ROW]
[ROW][C]M7[/C][C]12.0635613517060[/C][C]2.108162[/C][C]5.7223[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]12.9716207349081[/C][C]2.092638[/C][C]6.1987[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]5.96871555118111[/C][C]2.091231[/C][C]2.8542[/C][C]0.0064[/C][C]0.0032[/C][/ROW]
[ROW][C]M10[/C][C]-0.474189632545929[/C][C]2.090226[/C][C]-0.2269[/C][C]0.821516[/C][C]0.410758[/C][/ROW]
[ROW][C]M11[/C][C]-0.797094816272964[/C][C]2.089623[/C][C]-0.3815[/C][C]0.704586[/C][C]0.352293[/C][/ROW]
[ROW][C]t[/C][C]0.082905183727034[/C][C]0.028991[/C][C]2.8597[/C][C]0.006306[/C][C]0.003153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5689&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5689&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)	94.4102362204725	2.03525	46.3875	0	0
`x `	-0.0548228346456831	1.655082	-0.0331	0.973716	0.486858
M1	12.1820554461943	2.01388	6.049	0	0
M2	5.05808727034122	2.110797	2.3963	0.020594	0.010297
M3	2.89518208661418	2.109473	1.3725	0.176433	0.088216
M4	11.4522769028871	2.108548	5.4314	2e-06	1e-06
M5	-12.2306282808399	2.10802	-5.8019	1e-06	0
M6	-3.01353346456693	2.107892	-1.4296	0.159433	0.079717
M7	12.0635613517060	2.108162	5.7223	1e-06	0
M8	12.9716207349081	2.092638	6.1987	0	0
M9	5.96871555118111	2.091231	2.8542	0.0064	0.0032
M10	-0.474189632545929	2.090226	-0.2269	0.821516	0.410758
M11	-0.797094816272964	2.089623	-0.3815	0.704586	0.352293
t	0.082905183727034	0.028991	2.8597	0.006306	0.003153

Multiple Linear Regression - Regression Statistics
Multiple R	0.932242951965714
R-squared	0.869076921489749
Adjusted R-squared	0.832864155093296
F-TEST (value)	23.9991861426772
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.30366613927501
Sum Squared Residuals	512.967868110237

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.932242951965714 \tabularnewline
R-squared & 0.869076921489749 \tabularnewline
Adjusted R-squared & 0.832864155093296 \tabularnewline
F-TEST (value) & 23.9991861426772 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 2.22044604925031e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.30366613927501 \tabularnewline
Sum Squared Residuals & 512.967868110237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5689&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.932242951965714[/C][/ROW]
[ROW][C]R-squared[/C][C]0.869076921489749[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.832864155093296[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]23.9991861426772[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]2.22044604925031e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.30366613927501[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]512.967868110237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5689&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5689&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	0.932242951965714
R-squared	0.869076921489749
Adjusted R-squared	0.832864155093296
F-TEST (value)	23.9991861426772
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.30366613927501
Sum Squared Residuals	512.967868110237

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	110.4	106.675196850394	3.72480314960639
2	96.4	99.6341338582677	-3.23413385826771
3	101.9	97.5541338582677	4.34586614173228
4	106.2	106.194133858268	0.00586614173226119
5	81	82.5941338582678	-1.59413385826775
6	94.7	91.8941338582677	2.80586614173227
7	101	107.054133858268	-6.05413385826772
8	109.4	107.990275590551	1.40972440944882
9	102.3	101.070275590551	1.22972440944882
10	90.7	94.7102755905512	-4.01027559055118
11	96.2	94.4702755905512	1.72972440944882
12	96.1	95.3502755905512	0.749724409448813
13	106	107.615236220472	-1.61523622047247
14	103.1	100.574173228346	2.52582677165353
15	102	98.4941732283465	3.50582677165355
16	104.7	107.134173228346	-2.43417322834645
17	86	83.5341732283465	2.46582677165354
18	92.1	92.8341732283465	-0.734173228346458
19	106.9	107.994173228346	-1.09417322834645
20	112.6	108.985137795276	3.6148622047244
21	101.7	102.065137795276	-0.365137795275590
22	92	95.7051377952756	-3.70513779527559
23	97.4	95.4651377952756	1.93486220472441
24	97	96.3451377952756	0.654862204724411
25	105.4	108.610098425197	-3.21009842519687
26	102.7	101.569035433071	1.13096456692913
27	98.1	99.4890354330709	-1.38903543307087
28	104.5	108.129035433071	-3.62903543307086
29	87.4	84.5290354330709	2.87096456692914
30	89.9	93.8290354330709	-3.92903543307086
31	109.8	108.989035433071	0.810964566929128
32	111.7	109.98	1.72000000000000
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	109.604960629921	3.09503937007872
38	102.9	102.563897637795	0.336102362204728
39	97.4	100.483897637795	-3.08389763779526
40	111.4	109.123897637795	2.27610236220473
41	87.4	85.5238976377953	1.87610236220473
42	96.8	94.8238976377953	1.97610236220473
43	114.1	109.983897637795	4.11610236220472
44	110.3	110.974862204724	-0.674862204724411
45	103.9	104.054862204724	-0.154862204724404
46	101.6	97.6948622047244	3.90513779527559
47	94.6	97.4548622047244	-2.85486220472441
48	95.9	98.3348622047244	-2.4348622047244
49	104.7	110.599822834646	-5.89982283464569
50	102.8	103.558759842520	-0.758759842519689
51	98.1	101.478759842520	-3.37875984251968
52	113.9	110.118759842520	3.78124015748032
53	80.9	86.5187598425197	-5.61875984251967
54	95.7	95.8187598425197	-0.118759842519676
55	113.2	110.978759842520	2.22124015748032
56	105.9	111.969724409449	-6.06972440944881
57	108.8	105.049724409449	3.75027559055118
58	102.3	98.6897244094488	3.61027559055118
59	99	98.4497244094488	0.550275590551184
60	100.7	99.3297244094488	1.37027559055119
61	115.5	111.59468503937	3.90531496062990

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 110.4 & 106.675196850394 & 3.72480314960639 \tabularnewline
2 & 96.4 & 99.6341338582677 & -3.23413385826771 \tabularnewline
3 & 101.9 & 97.5541338582677 & 4.34586614173228 \tabularnewline
4 & 106.2 & 106.194133858268 & 0.00586614173226119 \tabularnewline
5 & 81 & 82.5941338582678 & -1.59413385826775 \tabularnewline
6 & 94.7 & 91.8941338582677 & 2.80586614173227 \tabularnewline
7 & 101 & 107.054133858268 & -6.05413385826772 \tabularnewline
8 & 109.4 & 107.990275590551 & 1.40972440944882 \tabularnewline
9 & 102.3 & 101.070275590551 & 1.22972440944882 \tabularnewline
10 & 90.7 & 94.7102755905512 & -4.01027559055118 \tabularnewline
11 & 96.2 & 94.4702755905512 & 1.72972440944882 \tabularnewline
12 & 96.1 & 95.3502755905512 & 0.749724409448813 \tabularnewline
13 & 106 & 107.615236220472 & -1.61523622047247 \tabularnewline
14 & 103.1 & 100.574173228346 & 2.52582677165353 \tabularnewline
15 & 102 & 98.4941732283465 & 3.50582677165355 \tabularnewline
16 & 104.7 & 107.134173228346 & -2.43417322834645 \tabularnewline
17 & 86 & 83.5341732283465 & 2.46582677165354 \tabularnewline
18 & 92.1 & 92.8341732283465 & -0.734173228346458 \tabularnewline
19 & 106.9 & 107.994173228346 & -1.09417322834645 \tabularnewline
20 & 112.6 & 108.985137795276 & 3.6148622047244 \tabularnewline
21 & 101.7 & 102.065137795276 & -0.365137795275590 \tabularnewline
22 & 92 & 95.7051377952756 & -3.70513779527559 \tabularnewline
23 & 97.4 & 95.4651377952756 & 1.93486220472441 \tabularnewline
24 & 97 & 96.3451377952756 & 0.654862204724411 \tabularnewline
25 & 105.4 & 108.610098425197 & -3.21009842519687 \tabularnewline
26 & 102.7 & 101.569035433071 & 1.13096456692913 \tabularnewline
27 & 98.1 & 99.4890354330709 & -1.38903543307087 \tabularnewline
28 & 104.5 & 108.129035433071 & -3.62903543307086 \tabularnewline
29 & 87.4 & 84.5290354330709 & 2.87096456692914 \tabularnewline
30 & 89.9 & 93.8290354330709 & -3.92903543307086 \tabularnewline
31 & 109.8 & 108.989035433071 & 0.810964566929128 \tabularnewline
32 & 111.7 & 109.98 & 1.72000000000000 \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 & 109.604960629921 & 3.09503937007872 \tabularnewline
38 & 102.9 & 102.563897637795 & 0.336102362204728 \tabularnewline
39 & 97.4 & 100.483897637795 & -3.08389763779526 \tabularnewline
40 & 111.4 & 109.123897637795 & 2.27610236220473 \tabularnewline
41 & 87.4 & 85.5238976377953 & 1.87610236220473 \tabularnewline
42 & 96.8 & 94.8238976377953 & 1.97610236220473 \tabularnewline
43 & 114.1 & 109.983897637795 & 4.11610236220472 \tabularnewline
44 & 110.3 & 110.974862204724 & -0.674862204724411 \tabularnewline
45 & 103.9 & 104.054862204724 & -0.154862204724404 \tabularnewline
46 & 101.6 & 97.6948622047244 & 3.90513779527559 \tabularnewline
47 & 94.6 & 97.4548622047244 & -2.85486220472441 \tabularnewline
48 & 95.9 & 98.3348622047244 & -2.4348622047244 \tabularnewline
49 & 104.7 & 110.599822834646 & -5.89982283464569 \tabularnewline
50 & 102.8 & 103.558759842520 & -0.758759842519689 \tabularnewline
51 & 98.1 & 101.478759842520 & -3.37875984251968 \tabularnewline
52 & 113.9 & 110.118759842520 & 3.78124015748032 \tabularnewline
53 & 80.9 & 86.5187598425197 & -5.61875984251967 \tabularnewline
54 & 95.7 & 95.8187598425197 & -0.118759842519676 \tabularnewline
55 & 113.2 & 110.978759842520 & 2.22124015748032 \tabularnewline
56 & 105.9 & 111.969724409449 & -6.06972440944881 \tabularnewline
57 & 108.8 & 105.049724409449 & 3.75027559055118 \tabularnewline
58 & 102.3 & 98.6897244094488 & 3.61027559055118 \tabularnewline
59 & 99 & 98.4497244094488 & 0.550275590551184 \tabularnewline
60 & 100.7 & 99.3297244094488 & 1.37027559055119 \tabularnewline
61 & 115.5 & 111.59468503937 & 3.90531496062990 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5689&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]106.675196850394[/C][C]3.72480314960639[/C][/ROW]
[ROW][C]2[/C][C]96.4[/C][C]99.6341338582677[/C][C]-3.23413385826771[/C][/ROW]
[ROW][C]3[/C][C]101.9[/C][C]97.5541338582677[/C][C]4.34586614173228[/C][/ROW]
[ROW][C]4[/C][C]106.2[/C][C]106.194133858268[/C][C]0.00586614173226119[/C][/ROW]
[ROW][C]5[/C][C]81[/C][C]82.5941338582678[/C][C]-1.59413385826775[/C][/ROW]
[ROW][C]6[/C][C]94.7[/C][C]91.8941338582677[/C][C]2.80586614173227[/C][/ROW]
[ROW][C]7[/C][C]101[/C][C]107.054133858268[/C][C]-6.05413385826772[/C][/ROW]
[ROW][C]8[/C][C]109.4[/C][C]107.990275590551[/C][C]1.40972440944882[/C][/ROW]
[ROW][C]9[/C][C]102.3[/C][C]101.070275590551[/C][C]1.22972440944882[/C][/ROW]
[ROW][C]10[/C][C]90.7[/C][C]94.7102755905512[/C][C]-4.01027559055118[/C][/ROW]
[ROW][C]11[/C][C]96.2[/C][C]94.4702755905512[/C][C]1.72972440944882[/C][/ROW]
[ROW][C]12[/C][C]96.1[/C][C]95.3502755905512[/C][C]0.749724409448813[/C][/ROW]
[ROW][C]13[/C][C]106[/C][C]107.615236220472[/C][C]-1.61523622047247[/C][/ROW]
[ROW][C]14[/C][C]103.1[/C][C]100.574173228346[/C][C]2.52582677165353[/C][/ROW]
[ROW][C]15[/C][C]102[/C][C]98.4941732283465[/C][C]3.50582677165355[/C][/ROW]
[ROW][C]16[/C][C]104.7[/C][C]107.134173228346[/C][C]-2.43417322834645[/C][/ROW]
[ROW][C]17[/C][C]86[/C][C]83.5341732283465[/C][C]2.46582677165354[/C][/ROW]
[ROW][C]18[/C][C]92.1[/C][C]92.8341732283465[/C][C]-0.734173228346458[/C][/ROW]
[ROW][C]19[/C][C]106.9[/C][C]107.994173228346[/C][C]-1.09417322834645[/C][/ROW]
[ROW][C]20[/C][C]112.6[/C][C]108.985137795276[/C][C]3.6148622047244[/C][/ROW]
[ROW][C]21[/C][C]101.7[/C][C]102.065137795276[/C][C]-0.365137795275590[/C][/ROW]
[ROW][C]22[/C][C]92[/C][C]95.7051377952756[/C][C]-3.70513779527559[/C][/ROW]
[ROW][C]23[/C][C]97.4[/C][C]95.4651377952756[/C][C]1.93486220472441[/C][/ROW]
[ROW][C]24[/C][C]97[/C][C]96.3451377952756[/C][C]0.654862204724411[/C][/ROW]
[ROW][C]25[/C][C]105.4[/C][C]108.610098425197[/C][C]-3.21009842519687[/C][/ROW]
[ROW][C]26[/C][C]102.7[/C][C]101.569035433071[/C][C]1.13096456692913[/C][/ROW]
[ROW][C]27[/C][C]98.1[/C][C]99.4890354330709[/C][C]-1.38903543307087[/C][/ROW]
[ROW][C]28[/C][C]104.5[/C][C]108.129035433071[/C][C]-3.62903543307086[/C][/ROW]
[ROW][C]29[/C][C]87.4[/C][C]84.5290354330709[/C][C]2.87096456692914[/C][/ROW]
[ROW][C]30[/C][C]89.9[/C][C]93.8290354330709[/C][C]-3.92903543307086[/C][/ROW]
[ROW][C]31[/C][C]109.8[/C][C]108.989035433071[/C][C]0.810964566929128[/C][/ROW]
[ROW][C]32[/C][C]111.7[/C][C]109.98[/C][C]1.72000000000000[/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]109.604960629921[/C][C]3.09503937007872[/C][/ROW]
[ROW][C]38[/C][C]102.9[/C][C]102.563897637795[/C][C]0.336102362204728[/C][/ROW]
[ROW][C]39[/C][C]97.4[/C][C]100.483897637795[/C][C]-3.08389763779526[/C][/ROW]
[ROW][C]40[/C][C]111.4[/C][C]109.123897637795[/C][C]2.27610236220473[/C][/ROW]
[ROW][C]41[/C][C]87.4[/C][C]85.5238976377953[/C][C]1.87610236220473[/C][/ROW]
[ROW][C]42[/C][C]96.8[/C][C]94.8238976377953[/C][C]1.97610236220473[/C][/ROW]
[ROW][C]43[/C][C]114.1[/C][C]109.983897637795[/C][C]4.11610236220472[/C][/ROW]
[ROW][C]44[/C][C]110.3[/C][C]110.974862204724[/C][C]-0.674862204724411[/C][/ROW]
[ROW][C]45[/C][C]103.9[/C][C]104.054862204724[/C][C]-0.154862204724404[/C][/ROW]
[ROW][C]46[/C][C]101.6[/C][C]97.6948622047244[/C][C]3.90513779527559[/C][/ROW]
[ROW][C]47[/C][C]94.6[/C][C]97.4548622047244[/C][C]-2.85486220472441[/C][/ROW]
[ROW][C]48[/C][C]95.9[/C][C]98.3348622047244[/C][C]-2.4348622047244[/C][/ROW]
[ROW][C]49[/C][C]104.7[/C][C]110.599822834646[/C][C]-5.89982283464569[/C][/ROW]
[ROW][C]50[/C][C]102.8[/C][C]103.558759842520[/C][C]-0.758759842519689[/C][/ROW]
[ROW][C]51[/C][C]98.1[/C][C]101.478759842520[/C][C]-3.37875984251968[/C][/ROW]
[ROW][C]52[/C][C]113.9[/C][C]110.118759842520[/C][C]3.78124015748032[/C][/ROW]
[ROW][C]53[/C][C]80.9[/C][C]86.5187598425197[/C][C]-5.61875984251967[/C][/ROW]
[ROW][C]54[/C][C]95.7[/C][C]95.8187598425197[/C][C]-0.118759842519676[/C][/ROW]
[ROW][C]55[/C][C]113.2[/C][C]110.978759842520[/C][C]2.22124015748032[/C][/ROW]
[ROW][C]56[/C][C]105.9[/C][C]111.969724409449[/C][C]-6.06972440944881[/C][/ROW]
[ROW][C]57[/C][C]108.8[/C][C]105.049724409449[/C][C]3.75027559055118[/C][/ROW]
[ROW][C]58[/C][C]102.3[/C][C]98.6897244094488[/C][C]3.61027559055118[/C][/ROW]
[ROW][C]59[/C][C]99[/C][C]98.4497244094488[/C][C]0.550275590551184[/C][/ROW]
[ROW][C]60[/C][C]100.7[/C][C]99.3297244094488[/C][C]1.37027559055119[/C][/ROW]
[ROW][C]61[/C][C]115.5[/C][C]111.59468503937[/C][C]3.90531496062990[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5689&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5689&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	106.675196850394	3.72480314960639
2	96.4	99.6341338582677	-3.23413385826771
3	101.9	97.5541338582677	4.34586614173228
4	106.2	106.194133858268	0.00586614173226119
5	81	82.5941338582678	-1.59413385826775
6	94.7	91.8941338582677	2.80586614173227
7	101	107.054133858268	-6.05413385826772
8	109.4	107.990275590551	1.40972440944882
9	102.3	101.070275590551	1.22972440944882
10	90.7	94.7102755905512	-4.01027559055118
11	96.2	94.4702755905512	1.72972440944882
12	96.1	95.3502755905512	0.749724409448813
13	106	107.615236220472	-1.61523622047247
14	103.1	100.574173228346	2.52582677165353
15	102	98.4941732283465	3.50582677165355
16	104.7	107.134173228346	-2.43417322834645
17	86	83.5341732283465	2.46582677165354
18	92.1	92.8341732283465	-0.734173228346458
19	106.9	107.994173228346	-1.09417322834645
20	112.6	108.985137795276	3.6148622047244
21	101.7	102.065137795276	-0.365137795275590
22	92	95.7051377952756	-3.70513779527559
23	97.4	95.4651377952756	1.93486220472441
24	97	96.3451377952756	0.654862204724411
25	105.4	108.610098425197	-3.21009842519687
26	102.7	101.569035433071	1.13096456692913
27	98.1	99.4890354330709	-1.38903543307087
28	104.5	108.129035433071	-3.62903543307086
29	87.4	84.5290354330709	2.87096456692914
30	89.9	93.8290354330709	-3.92903543307086
31	109.8	108.989035433071	0.810964566929128
32	111.7	109.98	1.72000000000000
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	109.604960629921	3.09503937007872
38	102.9	102.563897637795	0.336102362204728
39	97.4	100.483897637795	-3.08389763779526
40	111.4	109.123897637795	2.27610236220473
41	87.4	85.5238976377953	1.87610236220473
42	96.8	94.8238976377953	1.97610236220473
43	114.1	109.983897637795	4.11610236220472
44	110.3	110.974862204724	-0.674862204724411
45	103.9	104.054862204724	-0.154862204724404
46	101.6	97.6948622047244	3.90513779527559
47	94.6	97.4548622047244	-2.85486220472441
48	95.9	98.3348622047244	-2.4348622047244
49	104.7	110.599822834646	-5.89982283464569
50	102.8	103.558759842520	-0.758759842519689
51	98.1	101.478759842520	-3.37875984251968
52	113.9	110.118759842520	3.78124015748032
53	80.9	86.5187598425197	-5.61875984251967
54	95.7	95.8187598425197	-0.118759842519676
55	113.2	110.978759842520	2.22124015748032
56	105.9	111.969724409449	-6.06972440944881
57	108.8	105.049724409449	3.75027559055118
58	102.3	98.6897244094488	3.61027559055118
59	99	98.4497244094488	0.550275590551184
60	100.7	99.3297244094488	1.37027559055119
61	115.5	111.59468503937	3.90531496062990

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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