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Author

*Unverified author*

R Software Module

esteq.wasp

Title produced by software

Estimate Equation

Date of computation

Mon, 17 Dec 2007 23:44:26 -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/Dec/18/t11979595091h4psusstmvu7e3.htm/, Retrieved Sat, 04 May 2024 18:09:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4448, Retrieved Sat, 04 May 2024 18:09:08 +0000

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Original text written by user:

I used housing prices percent change, percent change in SP 500, and percent change in disposible income on a quarterly basis to predict the percent change in Automotive sales.

IsPrivate?

No (this computation is public)

User-defined keywords

Automotive, Sales, housing, SP 500, Disposible income, 2001-2007

Estimated Impact

221

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

-       [Estimate Equation] [Auto Sales Predic...] [2007-12-18 06:44:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

17.8	0.003223318	0.010452962	0.1
-9.8	-0.004242757	0.055172414	1.4
-15.1	0.027592008	-0.150326797	8.6
139.9	-0.014250825	0.103846154	-0.3
-41.2	0.027756602	-0.00087108	-0.2
-8.2	0.004675559	-0.137750654	0.3
25.6	-0.00391552	-0.175935288	-10.7
-23.9	0.000502945	0.078527607	-6.5
6.5	0.004286111	-0.035267349	1.1
-7	0.012381943	0.148584906	-2.7
5.9	0.015496311	0.021560575	-7.8
-12.2	0.004164104	0.116582915	27.4
19.6	0.00911028	0.01350135	0.7
-8	0.005866957	0.012433393	1.4
-8.1	0.007177785	-0.022807018	5.7
28	0.018297097	0.087073609	-0.3
-8.7	-0.008457126	-0.025598679	0.9
30.5	0.006316596	0.009322034	2.4
8.4	-0.003132332	0.031066331	1
-20.5	0.01609286	0.016286645	6
7.3	0.011908804	0.036858974	9.4
19.9	0.000527312	-0.018547141	5
-8.5	0.004300122	0.051181102	3
-6.1	0.015051583	0.062172285	-0.2
-1.7	0.013300904	0.001410437	2.9
5.5	-0.001948075	0.058450704	3.1
-31.9	0.010805033	0.015302728	3.3

Multiple Linear Regression - Estimated Regression Equation
Auto[t] = -1565.3792874194 DI[t] +53.421206920512 SP[t] -0.62142433994067 House[t] +15.003401042612 + e[t]

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

Auto[t] = -1565.3792874194 DI[t] +53.421206920512 SP[t] -0.62142433994067 House[t] +15.003401042612 + e[t] \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=4448&T=0

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

Auto[t] = -1565.3792874194 DI[t] +53.421206920512 SP[t] -0.62142433994067 House[t] +15.003401042612 + e[t][/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=4448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4448&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
Auto[t] = -1565.3792874194 DI[t] +53.421206920512 SP[t] -0.62142433994067 House[t] +15.003401042612 + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.E.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
DI[t]	-1565.379287	588.646635	-2.659285	0.014012	0.007006
SP[t]	53.421207	78.528681	0.680276	0.50312	0.25156
House[t]	-0.621424	0.882675	-0.704024	0.488485	0.244243
Constant	15.003401	7.094589	2.114767	0.045497	0.022748

Variable	Elasticity	S.E.^*	T-STATH0: \|elast\| = 1	2-tail p-value	1-tail p-value
%DI[t]	-2.752774	1.035155	1.693247	0.103911	0.051956
%SP[t]	0.186298	0.273856	-2.971277	0.006835	0.003418
%House[t]	-0.328638	0.466799	-1.438225	0.163839	0.08192
%Constant	3.895114	1.841865	1.571839	0.129645	0.064822
Variable	Stand. Coeff.	S.E.^*	T-STATH0: coeff = 0	2-tail p-value	1-tail p-value
S-DI[t]	-0.47772	0.179642	-2.659285	0.014012	0.007006
S-SP[t]	0.123714	0.181858	0.680276	0.50312	0.25156
S-House[t]	-0.128267	0.182191	-0.704024	0.488485	0.244243
S-Constant	0	0	0	1	0.5
^*Note	computed against deterministic endogenous series
Variable	Partial Correlation
DI[t]	-0.484937
SP[t]	0.140442
House[t]	-0.145243
Constant	0.403474
Critical Values (alpha = 5%)
1-tail CV at 5%	1.72
2-tail CV at 5%	2.07

\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 DI[t]

-1565.379287

588.646635

-2.659285

0.014012

0.007006 \tabularnewline SP[t]

53.421207

78.528681

0.680276

0.50312

0.25156 \tabularnewline House[t]

-0.621424

0.882675

-0.704024

0.488485

0.244243 \tabularnewline Constant

15.003401

7.094589

2.114767

0.045497

0.022748 \tabularnewline \tabularnewline

Variable

Elasticity

S.E.^*

T-STATH0: |elast| = 1

2-tail p-value

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

-2.752774

1.035155

1.693247

0.103911

0.051956 \tabularnewline %SP[t]

0.186298

0.273856

-2.971277

0.006835

0.003418 \tabularnewline %House[t]

-0.328638

0.466799

-1.438225

0.163839

0.08192 \tabularnewline %Constant

3.895114

1.841865

1.571839

0.129645

0.064822 \tabularnewline

Variable

Stand. Coeff.

S.E.^*

T-STATH0: coeff = 0

2-tail p-value

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

-0.47772

0.179642

-2.659285

0.014012

0.007006 \tabularnewline S-SP[t]

0.123714

0.181858

0.680276

0.50312

0.25156 \tabularnewline S-House[t]

-0.128267

0.182191

-0.704024

0.488485

0.244243 \tabularnewline S-Constant

0.5 \tabularnewline ^*Note

computed against deterministic endogenous series \tabularnewline

Variable

Partial Correlation \tabularnewline DI[t]

-0.484937 \tabularnewline SP[t]

0.140442 \tabularnewline House[t]

-0.145243 \tabularnewline Constant

0.403474 \tabularnewline Critical Values (alpha = 5%) \tabularnewline 1-tail CV at 5%

1.72 \tabularnewline 2-tail CV at 5%

2.07 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=4448&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]DI[t][/C]

-1565.379287[/C]

588.646635[/C]

-2.659285[/C]

0.014012[/C]

0.007006[/C][/ROW] [ROW][C]SP[t][/C]

53.421207[/C]

78.528681[/C]

0.680276[/C]

0.50312[/C]

0.25156[/C][/ROW] [ROW][C]House[t][/C]

-0.621424[/C]

0.882675[/C]

-0.704024[/C]

0.488485[/C]

0.244243[/C][/ROW] [ROW][C]Constant[/C]

15.003401[/C]

7.094589[/C]

2.114767[/C]

0.045497[/C]

0.022748[/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]%DI[t][/C]

-2.752774[/C]

1.035155[/C]

1.693247[/C]

0.103911[/C]

0.051956[/C][/ROW] [ROW][C]%SP[t][/C]

0.186298[/C]

0.273856[/C]

-2.971277[/C]

0.006835[/C]

0.003418[/C][/ROW] [ROW][C]%House[t][/C]

-0.328638[/C]

0.466799[/C]

-1.438225[/C]

0.163839[/C]

0.08192[/C][/ROW] [ROW][C]%Constant[/C]

3.895114[/C]

1.841865[/C]

1.571839[/C]

0.129645[/C]

0.064822[/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-DI[t][/C]

-0.47772[/C]

0.179642[/C]

-2.659285[/C]

0.014012[/C]

0.007006[/C][/ROW] [ROW][C]S-SP[t][/C]

0.123714[/C]

0.181858[/C]

0.680276[/C]

0.50312[/C]

0.25156[/C][/ROW] [ROW][C]S-House[t][/C]

-0.128267[/C]

0.182191[/C]

-0.704024[/C]

0.488485[/C]

0.244243[/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]DI[t][/C]

-0.484937[/C][/ROW] [ROW][C]SP[t][/C]

0.140442[/C][/ROW] [ROW][C]House[t][/C]

-0.145243[/C][/ROW] [ROW][C]Constant[/C]

0.403474[/C][/ROW] [ROW][C]Critical Values (alpha = 5%)[/C][/ROW] [ROW][C]1-tail CV at 5%[/C]

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

2.07[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=4448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4448&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
DI[t]	-1565.379287	588.646635	-2.659285	0.014012	0.007006
SP[t]	53.421207	78.528681	0.680276	0.50312	0.25156
House[t]	-0.621424	0.882675	-0.704024	0.488485	0.244243
Constant	15.003401	7.094589	2.114767	0.045497	0.022748

Variable	Elasticity	S.E.^*	T-STATH0: \|elast\| = 1	2-tail p-value	1-tail p-value
%DI[t]	-2.752774	1.035155	1.693247	0.103911	0.051956
%SP[t]	0.186298	0.273856	-2.971277	0.006835	0.003418
%House[t]	-0.328638	0.466799	-1.438225	0.163839	0.08192
%Constant	3.895114	1.841865	1.571839	0.129645	0.064822
Variable	Stand. Coeff.	S.E.^*	T-STATH0: coeff = 0	2-tail p-value	1-tail p-value
S-DI[t]	-0.47772	0.179642	-2.659285	0.014012	0.007006
S-SP[t]	0.123714	0.181858	0.680276	0.50312	0.25156
S-House[t]	-0.128267	0.182191	-0.704024	0.488485	0.244243
S-Constant	0	0	0	1	0.5
^*Note	computed against deterministic endogenous series
Variable	Partial Correlation
DI[t]	-0.484937
SP[t]	0.140442
House[t]	-0.145243
Constant	0.403474
Critical Values (alpha = 5%)
1-tail CV at 5%	1.72
2-tail CV at 5%	2.07

Multiple Linear Regression - Regression Statistics
Multiple R	0.529636
R-squared	0.280514
Adjusted R-squared	0.186668
F-TEST	2.989087
Observations	27
Degrees of Freedom	23
Multiple Linear Regression - Residual Statistics
Standard Error	29.320765
Sum Squared Errors	19773.267097
Log Likelihood	-127.360706
Durbin-Watson	2.280227
Von Neumann Ratio	2.367928
# e[t] > 0	12
# e[t] < 0	15
# Runs	20
Stand. Normal Runs Statistic	2.253226

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Regression Statistics \tabularnewline

Multiple R

0.529636 \tabularnewline R-squared

0.280514 \tabularnewline Adjusted R-squared

0.186668 \tabularnewline F-TEST

2.989087 \tabularnewline Observations

27 \tabularnewline Degrees of Freedom

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

29.320765 \tabularnewline Sum Squared Errors

19773.267097 \tabularnewline Log Likelihood

-127.360706 \tabularnewline Durbin-Watson

2.280227 \tabularnewline Von Neumann Ratio

2.367928 \tabularnewline # e[t] > 0

12 \tabularnewline # e[t] < 0

15 \tabularnewline # Runs

20 \tabularnewline Stand. Normal Runs Statistic

2.253226 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=4448&T=2

[TABLE]

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

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

0.529636[/C][/ROW] [ROW][C]R-squared[/C]

0.280514[/C][/ROW] [ROW][C]Adjusted R-squared[/C]

0.186668[/C][/ROW] [ROW][C]F-TEST[/C]

2.989087[/C][/ROW] [ROW][C]Observations[/C]

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

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

29.320765[/C][/ROW] [ROW][C]Sum Squared Errors[/C]

19773.267097[/C][/ROW] [ROW][C]Log Likelihood[/C]

-127.360706[/C][/ROW] [ROW][C]Durbin-Watson[/C]

2.280227[/C][/ROW] [ROW][C]Von Neumann Ratio[/C]

2.367928[/C][/ROW] [ROW][C]# e[t] > 0[/C]

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

15[/C][/ROW] [ROW][C]# Runs[/C]

20[/C][/ROW] [ROW][C]Stand. Normal Runs Statistic[/C]

2.253226[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=4448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4448&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	0.529636
R-squared	0.280514
Adjusted R-squared	0.186668
F-TEST	2.989087
Observations	27
Degrees of Freedom	23
Multiple Linear Regression - Residual Statistics
Standard Error	29.320765
Sum Squared Errors	19773.267097
Log Likelihood	-127.360706
Durbin-Watson	2.280227
Von Neumann Ratio	2.367928
# e[t] > 0	12
# e[t] < 0	15
# Runs	20
Stand. Normal Runs Statistic	2.253226

Multiple Linear Regression - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error	987.071304
Akaike (1973) Log Information Criterion	6.892546
Akaike (1974) Information Criterion	984.905392
Schwarz (1978) Log Criterion	7.084521
Schwarz (1978) Criterion	1193.351985
Craven-Wahba (1979) Generalized Cross Validation	1009.221572
Hannan-Quinn (1979) Criterion	1042.763904
Rice (1984) Criterion	1040.698268
Shibata (1981) Criterion	949.333811

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ad Hoc Selection Test Statistics \tabularnewline

Akaike (1969) Final Prediction Error

987.071304 \tabularnewline Akaike (1973) Log Information Criterion

6.892546 \tabularnewline Akaike (1974) Information Criterion

984.905392 \tabularnewline Schwarz (1978) Log Criterion

7.084521 \tabularnewline Schwarz (1978) Criterion

1193.351985 \tabularnewline Craven-Wahba (1979) Generalized Cross Validation

1009.221572 \tabularnewline Hannan-Quinn (1979) Criterion

1042.763904 \tabularnewline Rice (1984) Criterion

1040.698268 \tabularnewline Shibata (1981) Criterion

949.333811 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=4448&T=3

[TABLE]

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

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

987.071304[/C][/ROW] [ROW][C]Akaike (1973) Log Information Criterion[/C]

6.892546[/C][/ROW] [ROW][C]Akaike (1974) Information Criterion[/C]

984.905392[/C][/ROW] [ROW][C]Schwarz (1978) Log Criterion[/C]

7.084521[/C][/ROW] [ROW][C]Schwarz (1978) Criterion[/C]

1193.351985[/C][/ROW] [ROW][C]Craven-Wahba (1979) Generalized Cross Validation[/C]

1009.221572[/C][/ROW] [ROW][C]Hannan-Quinn (1979) Criterion[/C]

1042.763904[/C][/ROW] [ROW][C]Rice (1984) Criterion[/C]

1040.698268[/C][/ROW] [ROW][C]Shibata (1981) Criterion[/C]

949.333811[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=4448&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4448&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	987.071304
Akaike (1973) Log Information Criterion	6.892546
Akaike (1974) Information Criterion	984.905392
Schwarz (1978) Log Criterion	7.084521
Schwarz (1978) Criterion	1193.351985
Craven-Wahba (1979) Generalized Cross Validation	1009.221572
Hannan-Quinn (1979) Criterion	1042.763904
Rice (1984) Criterion	1040.698268
Shibata (1981) Criterion	949.333811

Multiple Linear Regression - Analysis of Variance
ANOVA	DF	Sum of Squares	Mean Square
Regression	3	7709.22031	2569.740103
Residual	23	19773.267097	859.707265
Total	26	27482.487407	1057.0187464387
F-TEST	2.989087
p-value	0.051953

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Analysis of Variance \tabularnewline

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

Regression

7709.22031

2569.740103 \tabularnewline Residual

19773.267097

859.707265 \tabularnewline Total

27482.487407

1057.0187464387 \tabularnewline F-TEST

2.989087 \tabularnewline p-value

0.051953 \tabularnewline

\hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=4448&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]

3[/C]

7709.22031[/C]

2569.740103[/C][/ROW] [ROW][C]Residual[/C]

23[/C]

19773.267097[/C]

859.707265[/C][/ROW] [ROW][C]Total[/C]

26[/C]

27482.487407[/C]

1057.0187464387[/C][/ROW] [ROW][C]F-TEST[/C]

2.989087[/C][/ROW] [ROW][C]p-value[/C]

0.051953[/C][/ROW]

[/TABLE] Source: https://freestatistics.org/blog/index.php?pk=4448&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4448&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	3	7709.22031	2569.740103
Residual	23	19773.267097	859.707265
Total	26	27482.487407	1057.0187464387
F-TEST	2.989087
p-value	0.051953

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