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*Unverified author*

R Software Module

esteq.wasp

Title produced by software

Estimate Equation

Date of computation

Wed, 05 Dec 2007 00:59:04 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/05/t1196840895l2n3sx0eizq6nce.htm/, Retrieved Thu, 02 May 2024 14:33:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2465, Retrieved Thu, 02 May 2024 14:33:52 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

edvanstee,test05122007,linreg

Estimated Impact

322

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

-     [Bivariate Kernel Density Estimation] [WS4 Q1] [2007-11-04 12:31:38] [96f19ddff91f3ea1f6a46c9c5521b568]
- RMPD    [Estimate Equation] [Lineaire Regressie] [2007-12-05 07:59:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D      [Estimate Equation] [Lineaire Regressi...] [2007-12-14 15:39:43] [74be16979710d4c4e7c6647856088456] 
-    D      [Estimate Equation] [testing blogging] [2008-03-12 06:55:49] [74be16979710d4c4e7c6647856088456] 

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Dataseries X:

Download CSV

Histogram

Boxplots

99.2	96.7	101.0
99.0	98.1	100.1
100.0	100.0	100.0
111.6	104.9	90.6
122.2	104.9	86.5
117.6	109.5	89.7
121.1	110.8	90.6
136.0	112.3	82.8
154.2	109.3	70.1
153.6	105.3	65.4
158.5	101.7	61.3
140.6	95.4	62.5
136.2	96.4	63.6
168.0	97.6	52.6
154.3	102.4	59.7
149.0	101.6	59.5
165.5	103.8	61.3

Multiple Linear Regression - Estimated Regression Equation
Cons[t] = +1.0617096285025 Inc[t] -1.3829854574122 Price[t] +130.70658748714 + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline

Cons[t] = +1.0617096285025 Inc[t] -1.3829854574122 Price[t] +130.70658748714 + e[t] \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2465&T=0

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW]

Cons[t] = +1.0617096285025 Inc[t] -1.3829854574122 Price[t] +130.70658748714 + e[t][/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2465&T=0

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
Cons[t] = +1.0617096285025 Inc[t] -1.3829854574122 Price[t] +130.70658748714 + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.E.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
Inc[t]	1.06171	0.266674	3.981302	0.001365	0.000683
Price[t]	-1.382985	0.083814	-16.500598	0	0
Constant	130.706587	27.094293	4.824137	0.00027	0.000135

Variable	Elasticity	S.E.^*	T-STATH0: \|elast\| = 1	2-tail p-value	1-tail p-value
%Inc[t]	0.812882	0.204175	-0.916462	0.374942	0.187471
%Price[t]	-0.784635	0.047552	-4.529043	0.000472	0.000236
%Constant	0.971754	0.201436	-0.140225	0.89048	0.44524
Variable	Stand. Coeff.	S.E.^*	T-STATH0: coeff = 0	2-tail p-value	1-tail p-value
S-Inc[t]	0.238708	0.059957	3.981302	0.001365	0.000683
S-Price[t]	-0.98933	0.059957	-16.500598	0	0
S-Constant	0	0	0	1	0.5
^*Note	computed against deterministic endogenous series
Variable	Partial Correlation
Inc[t]	0.728698
Price[t]	-0.975241
Constant	0.790181
Critical Values (alpha = 5%)
1-tail CV at 5%	1.77
2-tail CV at 5%	2.14

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ordinary Least Squares \tabularnewline

Variable

Parameter

S.E.

T-STATH0: parameter = 0

2-tail p-value

1-tail p-value \tabularnewline Inc[t]

1.06171

0.266674

3.981302

0.001365

0.000683 \tabularnewline Price[t]

-1.382985

0.083814

-16.500598

0 \tabularnewline Constant

130.706587

27.094293

4.824137

0.00027

0.000135 \tabularnewline \tabularnewline

Variable

Elasticity

S.E.^*

T-STATH0: |elast| = 1

2-tail p-value

1-tail p-value \tabularnewline %Inc[t]

0.812882

0.204175

-0.916462

0.374942

0.187471 \tabularnewline %Price[t]

-0.784635

0.047552

-4.529043

0.000472

0.000236 \tabularnewline %Constant

0.971754

0.201436

-0.140225

0.89048

0.44524 \tabularnewline

Variable

Stand. Coeff.

S.E.^*

T-STATH0: coeff = 0

2-tail p-value

1-tail p-value \tabularnewline S-Inc[t]

0.238708

0.059957

3.981302

0.001365

0.000683 \tabularnewline S-Price[t]

-0.98933

0.059957

-16.500598

0 \tabularnewline S-Constant

0.5 \tabularnewline ^*Note

computed against deterministic endogenous series \tabularnewline

Variable

Partial Correlation \tabularnewline Inc[t]

0.728698 \tabularnewline Price[t]

-0.975241 \tabularnewline Constant

0.790181 \tabularnewline Critical Values (alpha = 5%) \tabularnewline 1-tail CV at 5%

1.77 \tabularnewline 2-tail CV at 5%

2.14 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2465&T=1

[TABLE]

[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]

[ROW]

Variable[/C]

Parameter[/C]

S.E.[/C]

T-STATH0: parameter = 0[/C]

2-tail p-value[/C]

1-tail p-value[/C][/ROW] [ROW][C]Inc[t][/C]

1.06171[/C]

0.266674[/C]

3.981302[/C]

0.001365[/C]

0.000683[/C][/ROW] [ROW][C]Price[t][/C]

-1.382985[/C]

0.083814[/C]

-16.500598[/C]

0[/C]

0[/C][/ROW] [ROW][C]Constant[/C]

130.706587[/C]

27.094293[/C]

4.824137[/C]

0.00027[/C]

0.000135[/C][/ROW] [ROW][C][/C][/ROW] [ROW]

Variable[/C]

Elasticity[/C]

S.E.^*[/C]

T-STATH0: |elast| = 1[/C]

2-tail p-value[/C]

1-tail p-value[/C][/ROW] [ROW][C]%Inc[t][/C]

0.812882[/C]

0.204175[/C]

-0.916462[/C]

0.374942[/C]

0.187471[/C][/ROW] [ROW][C]%Price[t][/C]

-0.784635[/C]

0.047552[/C]

-4.529043[/C]

0.000472[/C]

0.000236[/C][/ROW] [ROW][C]%Constant[/C]

0.971754[/C]

0.201436[/C]

-0.140225[/C]

0.89048[/C]

0.44524[/C][/ROW] [ROW]

Variable[/C]

Stand. Coeff.[/C]

S.E.^*[/C]

T-STATH0: coeff = 0[/C]

2-tail p-value[/C]

1-tail p-value[/C][/ROW] [ROW][C]S-Inc[t][/C]

0.238708[/C]

0.059957[/C]

3.981302[/C]

0.001365[/C]

0.000683[/C][/ROW] [ROW][C]S-Price[t][/C]

-0.98933[/C]

0.059957[/C]

-16.500598[/C]

0[/C]

0[/C][/ROW] [ROW][C]S-Constant[/C]

0[/C]

1[/C]

0.5[/C][/ROW] [ROW][C]^*Note[/C]

computed against deterministic endogenous series[/C][/ROW] [ROW]

Variable[/C]

Partial Correlation[/C][/ROW] [ROW][C]Inc[t][/C]

0.728698[/C][/ROW] [ROW][C]Price[t][/C]

-0.975241[/C][/ROW] [ROW][C]Constant[/C]

0.790181[/C][/ROW] [ROW][C]Critical Values (alpha = 5%)[/C][/ROW] [ROW][C]1-tail CV at 5%[/C]

1.77[/C][/ROW] [ROW][C]2-tail CV at 5%[/C]

2.14[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2465&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 - Ordinary Least Squares
Variable	Parameter	S.E.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
Inc[t]	1.06171	0.266674	3.981302	0.001365	0.000683
Price[t]	-1.382985	0.083814	-16.500598	0	0
Constant	130.706587	27.094293	4.824137	0.00027	0.000135

Variable	Elasticity	S.E.^*	T-STATH0: \|elast\| = 1	2-tail p-value	1-tail p-value
%Inc[t]	0.812882	0.204175	-0.916462	0.374942	0.187471
%Price[t]	-0.784635	0.047552	-4.529043	0.000472	0.000236
%Constant	0.971754	0.201436	-0.140225	0.89048	0.44524
Variable	Stand. Coeff.	S.E.^*	T-STATH0: coeff = 0	2-tail p-value	1-tail p-value
S-Inc[t]	0.238708	0.059957	3.981302	0.001365	0.000683
S-Price[t]	-0.98933	0.059957	-16.500598	0	0
S-Constant	0	0	0	1	0.5
^*Note	computed against deterministic endogenous series
Variable	Partial Correlation
Inc[t]	0.728698
Price[t]	-0.975241
Constant	0.790181
Critical Values (alpha = 5%)
1-tail CV at 5%	1.77
2-tail CV at 5%	2.14

Multiple Linear Regression - Regression Statistics
Multiple R	0.975337
R-squared	0.951282
Adjusted R-squared	0.944322
F-TEST	136.683086
Observations	17
Degrees of Freedom	14
Multiple Linear Regression - Residual Statistics
Standard Error	5.563356
Sum Squared Errors	433.312979
Log Likelihood	-51.647054
Durbin-Watson	2.018549
Von Neumann Ratio	2.144708
# e[t] > 0	9
# e[t] < 0	8
# Runs	7
Runs Statistic	-1.242299

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Regression Statistics \tabularnewline

Multiple R

0.975337 \tabularnewline R-squared

0.951282 \tabularnewline Adjusted R-squared

0.944322 \tabularnewline F-TEST

136.683086 \tabularnewline Observations

17 \tabularnewline Degrees of Freedom

14 \tabularnewline Multiple Linear Regression - Residual Statistics \tabularnewline Standard Error

5.563356 \tabularnewline Sum Squared Errors

433.312979 \tabularnewline Log Likelihood

-51.647054 \tabularnewline Durbin-Watson

2.018549 \tabularnewline Von Neumann Ratio

2.144708 \tabularnewline # e[t] > 0

9 \tabularnewline # e[t] < 0

8 \tabularnewline # Runs

7 \tabularnewline Runs Statistic

-1.242299 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2465&T=2

[TABLE]

[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]

[ROW][C]Multiple R[/C]

0.975337[/C][/ROW] [ROW][C]R-squared[/C]

0.951282[/C][/ROW] [ROW][C]Adjusted R-squared[/C]

0.944322[/C][/ROW] [ROW][C]F-TEST[/C]

136.683086[/C][/ROW] [ROW][C]Observations[/C]

17[/C][/ROW] [ROW][C]Degrees of Freedom[/C]

14[/C][/ROW] [ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW] [ROW][C]Standard Error[/C]

5.563356[/C][/ROW] [ROW][C]Sum Squared Errors[/C]

433.312979[/C][/ROW] [ROW][C]Log Likelihood[/C]

-51.647054[/C][/ROW] [ROW][C]Durbin-Watson[/C]

2.018549[/C][/ROW] [ROW][C]Von Neumann Ratio[/C]

2.144708[/C][/ROW] [ROW][C]# e[t] > 0[/C]

9[/C][/ROW] [ROW][C]# e[t] < 0[/C]

8[/C][/ROW] [ROW][C]# Runs[/C]

7[/C][/ROW] [ROW][C]Runs Statistic[/C]

-1.242299[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2465&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2465&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 - Regression Statistics
Multiple R	0.975337
R-squared	0.951282
Adjusted R-squared	0.944322
F-TEST	136.683086
Observations	17
Degrees of Freedom	14
Multiple Linear Regression - Residual Statistics
Standard Error	5.563356
Sum Squared Errors	433.312979
Log Likelihood	-51.647054
Durbin-Watson	2.018549
Von Neumann Ratio	2.144708
# e[t] > 0	9
# e[t] < 0	8
# Runs	7
Runs Statistic	-1.242299

Multiple Linear Regression - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error	36.412855
Akaike (1973) Log Information Criterion	3.591188
Akaike (1974) Information Criterion	36.277152
Schwarz (1978) Log Criterion	3.738226
Schwarz (1978) Criterion	42.023365
Craven-Wahba (1979) Generalized Cross Validation	37.583269
Hannan-Quinn (1979) Criterion	36.811266
Rice (1984) Criterion	39.392089
Shibata (1981) Criterion	34.485116

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ad Hoc Selection Test Statistics \tabularnewline

Akaike (1969) Final Prediction Error

36.412855 \tabularnewline Akaike (1973) Log Information Criterion

3.591188 \tabularnewline Akaike (1974) Information Criterion

36.277152 \tabularnewline Schwarz (1978) Log Criterion

3.738226 \tabularnewline Schwarz (1978) Criterion

42.023365 \tabularnewline Craven-Wahba (1979) Generalized Cross Validation

37.583269 \tabularnewline Hannan-Quinn (1979) Criterion

36.811266 \tabularnewline Rice (1984) Criterion

39.392089 \tabularnewline Shibata (1981) Criterion

34.485116 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2465&T=3

[TABLE]

[ROW][C]Multiple Linear Regression - Ad Hoc Selection Test Statistics[/C][/ROW]

[ROW][C]Akaike (1969) Final Prediction Error[/C]

36.412855[/C][/ROW] [ROW][C]Akaike (1973) Log Information Criterion[/C]

3.591188[/C][/ROW] [ROW][C]Akaike (1974) Information Criterion[/C]

36.277152[/C][/ROW] [ROW][C]Schwarz (1978) Log Criterion[/C]

3.738226[/C][/ROW] [ROW][C]Schwarz (1978) Criterion[/C]

42.023365[/C][/ROW] [ROW][C]Craven-Wahba (1979) Generalized Cross Validation[/C]

37.583269[/C][/ROW] [ROW][C]Hannan-Quinn (1979) Criterion[/C]

36.811266[/C][/ROW] [ROW][C]Rice (1984) Criterion[/C]

39.392089[/C][/ROW] [ROW][C]Shibata (1981) Criterion[/C]

34.485116[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2465&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2465&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 - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error	36.412855
Akaike (1973) Log Information Criterion	3.591188
Akaike (1974) Information Criterion	36.277152
Schwarz (1978) Log Criterion	3.738226
Schwarz (1978) Criterion	42.023365
Craven-Wahba (1979) Generalized Cross Validation	37.583269
Hannan-Quinn (1979) Criterion	36.811266
Rice (1984) Criterion	39.392089
Shibata (1981) Criterion	34.485116

Multiple Linear Regression - Analysis of Variance
ANOVA	DF	Sum of Squares	Mean Square
Regression	2	8460.936433	4230.468217
Residual	14	433.312979	30.950927
Total	16	8894.249412	555.89058823529
F-TEST	136.683086
p-value	0

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Analysis of Variance \tabularnewline

ANOVA & DF & Sum of Squares & Mean Square \tabularnewline

Regression

8460.936433

4230.468217 \tabularnewline Residual

433.312979

30.950927 \tabularnewline Total

8894.249412

555.89058823529 \tabularnewline F-TEST

136.683086 \tabularnewline p-value

0 \tabularnewline

\hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2465&T=4

[TABLE]

[ROW][C]Multiple Linear Regression - Analysis of Variance[/C][/ROW]

[ROW][C]ANOVA[/C][C]DF[/C][C]Sum of Squares[/C][C]Mean Square[/C][/ROW]

[ROW][C]Regression[/C]

2[/C]

8460.936433[/C]

4230.468217[/C][/ROW] [ROW][C]Residual[/C]

14[/C]

433.312979[/C]

30.950927[/C][/ROW] [ROW][C]Total[/C]

16[/C]

8894.249412[/C]

555.89058823529[/C][/ROW] [ROW][C]F-TEST[/C]

136.683086[/C][/ROW] [ROW][C]p-value[/C]

0[/C][/ROW]

[/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2465&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2465&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 - Analysis of Variance
ANOVA	DF	Sum of Squares	Mean Square
Regression	2	8460.936433	4230.468217
Residual	14	433.312979	30.950927
Total	16	8894.249412	555.89058823529
F-TEST	136.683086
p-value	0

Parameters (Session):

Parameters (R input):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code