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esteq.wasp

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Estimate Equation

Date of computation

Sun, 02 Dec 2007 04:20:12 -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/02/t1196593809ispo5ldqkblkopa.htm/, Retrieved Sat, 27 Apr 2024 20:30:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2275, Retrieved Sat, 27 Apr 2024 20:30:03 +0000

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Multiple Linear Regression - B Estimated

Estimated Impact

308

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

-       [Estimate Equation] [Multiple Linear R...] [2007-12-02 11:20:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

100.6	115.9	59.7	125
96.1	112.9	58.2	121.7
110	126.3	75.3	134.3
108.2	116.8	69	124.3
106.9	112	66.1	119.1
117.2	129.7	77.5	137.8
105.2	113.6	69.3	120.5
106.3	115.7	70.2	122.7
95.9	119.5	70.2	127.2
107.5	125.8	78.2	133.2
113	129.6	85.4	136.3
111.4	128	82.4	134.9
95.5	112.8	61.2	120.9
90.3	101.6	52.2	109.4
110.8	123.9	85.3	129.6
107.1	118.8	79.9	124.7
101.4	109.1	72.2	114.6
112.9	130.6	85.7	137.4
98.5	112.4	75.5	117.9
100.1	111	69.2	117.4
93.4	116.2	77.6	122
104.4	119.8	85.3	124.8
101.8	117.2	77	123.3
107.9	127.3	89.9	132.8
91.3	107.7	60	115.1
86.6	97.5	54.3	104.2
111.4	120.1	84	125.5
98.4	110.6	69.9	116.8
102.2	111.3	75.1	116.8
103	119.8	81.7	125.5
95.8	105.5	69.9	110.9
96	108.7	68.3	114.9
95.7	128.7	77.3	136.4
106.4	119.5	77.4	125.8
112	121.1	85.3	126.5
116.2	128.4	91	134
93.9	108.8	60.6	116.1
100.5	107.5	57.6	115
112.5	125.6	93.8	130.3
101.2	102.9	78.7	106.5
107.8	107.5	80.3	111.6
114.3	120.4	89.8	125
99.6	104.3	77.5	108.3
98.6	100.6	71.7	105
93.6	121.9	83.2	127.4
99.6	112.7	86.2	116.6
113.1	124.9	100.7	128.6
110.7	123.9	100.8	127.5
88.1	102.2	57.1	108.4
93.1	104.9	62.5	110.8
107.4	109.8	79.7	114.2
99.5	98.9	80.3	101.8
105.6	107.3	92.4	109.8
108.3	112.6	91.8	115.9
99.2	104	85.8	106.9
99.3	110.6	84.2	114.6
107.1	100.8	93.1	105.4
106.9	103.8	101.2	108.1
115.4	117	100.6	118.4
99	108.4	106.7	112.7
100.1	95.5	64	98.4
96.2	96.9	67.5	99.6
96.9	103.9	101	103.9
96.2	101.1	95.5	101.5
91	100.6	97	100.8
99	104.3	103.8	104.5
99	98	95.2	98.2
107.2	99.5	86.7	99.9
110.8	97.4	93.5	97.5
111.1	105.6	102.5	105.7
104.6	117.5	112.3	117.7
94.3	107.4	105.5	107.4
90.7	97.8	75.4	98.4
88.8	91.5	70.4	92
90.9	107.7	108	107.7
90.5	100.1	100	100.2
95.5	96.6	93.3	96.7
103.1	106.8	111.1	106.8
100.6	98	101.1	98
103.1	98.6	98.1	98.6

Multiple Linear Regression - Estimated Regression Equation
1[t] = +0.24161924801945 2[t] +0.18147613954232 3[t] +0.1733150149762 4[t] +40.24610487899 + e[t]

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

1[t] = +0.24161924801945 2[t] +0.18147613954232 3[t] +0.1733150149762 4[t] +40.24610487899 + e[t] \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2275&T=0

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

1[t] = +0.24161924801945 2[t] +0.18147613954232 3[t] +0.1733150149762 4[t] +40.24610487899 + e[t][/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2275&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
1[t] = +0.24161924801945 2[t] +0.18147613954232 3[t] +0.1733150149762 4[t] +40.24610487899 + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.E.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
2[t]	0.241619	0.792198	0.304999	0.761201	0.3806
3[t]	0.181476	0.103482	1.753704	0.083513	0.041756
4[t]	0.173315	0.678748	0.255345	0.799146	0.399573
Constant	40.246105	7.911237	5.087207	3E-06	1E-06

Variable	Elasticity	S.E.^*	T-STATH0: \|elast\| = 1	2-tail p-value	1-tail p-value
%2[t]	0.263237	0.863077	-0.853647	0.395983	0.197992
%3[t]	0.145978	0.08324	-10.259753	0	0
%4[t]	0.196278	0.768676	-1.045594	0.299063	0.149531
%Constant	0.394507	0.077549	-7.807899	0	0
Variable	Stand. Coeff.	S.E.^*	T-STATH0: coeff = 0	2-tail p-value	1-tail p-value
S-2[t]	0.322637	1.05783	0.304999	0.761201	0.3806
S-3[t]	0.356155	0.203087	1.753704	0.083513	0.041756
S-4[t]	0.272278	1.066314	0.255345	0.799146	0.399573
S-Constant	0	0	0	1	0.5
^*Note	computed against deterministic endogenous series
Variable	Partial Correlation
2[t]	0.034964
3[t]	0.197213
4[t]	0.029278
Constant	0.504006
Critical Values (alpha = 5%)
1-tail CV at 5%	1.65
2-tail CV at 5%	1.96

\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 2[t]

0.241619

0.792198

0.304999

0.761201

0.3806 \tabularnewline 3[t]

0.181476

0.103482

1.753704

0.083513

0.041756 \tabularnewline 4[t]

0.173315

0.678748

0.255345

0.799146

0.399573 \tabularnewline Constant

40.246105

7.911237

5.087207

3E-06

1E-06 \tabularnewline \tabularnewline

Variable

Elasticity

S.E.^*

T-STATH0: |elast| = 1

2-tail p-value

1-tail p-value \tabularnewline %2[t]

0.263237

0.863077

-0.853647

0.395983

0.197992 \tabularnewline %3[t]

0.145978

0.08324

-10.259753

0 \tabularnewline %4[t]

0.196278

0.768676

-1.045594

0.299063

0.149531 \tabularnewline %Constant

0.394507

0.077549

-7.807899

0 \tabularnewline

Variable

Stand. Coeff.

S.E.^*

T-STATH0: coeff = 0

2-tail p-value

1-tail p-value \tabularnewline S-2[t]

0.322637

1.05783

0.304999

0.761201

0.3806 \tabularnewline S-3[t]

0.356155

0.203087

1.753704

0.083513

0.041756 \tabularnewline S-4[t]

0.272278

1.066314

0.255345

0.799146

0.399573 \tabularnewline S-Constant

0.5 \tabularnewline ^*Note

computed against deterministic endogenous series \tabularnewline

Variable

Partial Correlation \tabularnewline 2[t]

0.034964 \tabularnewline 3[t]

0.197213 \tabularnewline 4[t]

0.029278 \tabularnewline Constant

0.504006 \tabularnewline Critical Values (alpha = 5%) \tabularnewline 1-tail CV at 5%

1.65 \tabularnewline 2-tail CV at 5%

1.96 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2275&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]2[t][/C]

0.241619[/C]

0.792198[/C]

0.304999[/C]

0.761201[/C]

0.3806[/C][/ROW] [ROW][C]3[t][/C]

0.181476[/C]

0.103482[/C]

1.753704[/C]

0.083513[/C]

0.041756[/C][/ROW] [ROW][C]4[t][/C]

0.173315[/C]

0.678748[/C]

0.255345[/C]

0.799146[/C]

0.399573[/C][/ROW] [ROW][C]Constant[/C]

40.246105[/C]

7.911237[/C]

5.087207[/C]

3E-06[/C]

1E-06[/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]%2[t][/C]

0.263237[/C]

0.863077[/C]

-0.853647[/C]

0.395983[/C]

0.197992[/C][/ROW] [ROW][C]%3[t][/C]

0.145978[/C]

0.08324[/C]

-10.259753[/C]

0[/C]

0[/C][/ROW] [ROW][C]%4[t][/C]

0.196278[/C]

0.768676[/C]

-1.045594[/C]

0.299063[/C]

0.149531[/C][/ROW] [ROW][C]%Constant[/C]

0.394507[/C]

0.077549[/C]

-7.807899[/C]

0[/C]

0[/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-2[t][/C]

0.322637[/C]

1.05783[/C]

0.304999[/C]

0.761201[/C]

0.3806[/C][/ROW] [ROW][C]S-3[t][/C]

0.356155[/C]

0.203087[/C]

1.753704[/C]

0.083513[/C]

0.041756[/C][/ROW] [ROW][C]S-4[t][/C]

0.272278[/C]

1.066314[/C]

0.255345[/C]

0.799146[/C]

0.399573[/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]2[t][/C]

0.034964[/C][/ROW] [ROW][C]3[t][/C]

0.197213[/C][/ROW] [ROW][C]4[t][/C]

0.029278[/C][/ROW] [ROW][C]Constant[/C]

0.504006[/C][/ROW] [ROW][C]Critical Values (alpha = 5%)[/C][/ROW] [ROW][C]1-tail CV at 5%[/C]

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

1.96[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2275&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
2[t]	0.241619	0.792198	0.304999	0.761201	0.3806
3[t]	0.181476	0.103482	1.753704	0.083513	0.041756
4[t]	0.173315	0.678748	0.255345	0.799146	0.399573
Constant	40.246105	7.911237	5.087207	3E-06	1E-06

Variable	Elasticity	S.E.^*	T-STATH0: \|elast\| = 1	2-tail p-value	1-tail p-value
%2[t]	0.263237	0.863077	-0.853647	0.395983	0.197992
%3[t]	0.145978	0.08324	-10.259753	0	0
%4[t]	0.196278	0.768676	-1.045594	0.299063	0.149531
%Constant	0.394507	0.077549	-7.807899	0	0
Variable	Stand. Coeff.	S.E.^*	T-STATH0: coeff = 0	2-tail p-value	1-tail p-value
S-2[t]	0.322637	1.05783	0.304999	0.761201	0.3806
S-3[t]	0.356155	0.203087	1.753704	0.083513	0.041756
S-4[t]	0.272278	1.066314	0.255345	0.799146	0.399573
S-Constant	0	0	0	1	0.5
^*Note	computed against deterministic endogenous series
Variable	Partial Correlation
2[t]	0.034964
3[t]	0.197213
4[t]	0.029278
Constant	0.504006
Critical Values (alpha = 5%)
1-tail CV at 5%	1.65
2-tail CV at 5%	1.96

Multiple Linear Regression - Regression Statistics
Multiple R	0.67925
R-squared	0.461381
Adjusted R-squared	0.44012
F-TEST	21.700529
Observations	80
Degrees of Freedom	76
Multiple Linear Regression - Residual Statistics
Standard Error	5.63774
Sum Squared Errors	2415.592613
Log Likelihood	-249.822014
Durbin-Watson	1.286627
Von Neumann Ratio	1.302913
# e[t] > 0	42
# e[t] < 0	38
# Runs	28
Stand. Normal Runs Statistic	-2.910328

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Regression Statistics \tabularnewline

Multiple R

0.67925 \tabularnewline R-squared

0.461381 \tabularnewline Adjusted R-squared

0.44012 \tabularnewline F-TEST

21.700529 \tabularnewline Observations

80 \tabularnewline Degrees of Freedom

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

5.63774 \tabularnewline Sum Squared Errors

2415.592613 \tabularnewline Log Likelihood

-249.822014 \tabularnewline Durbin-Watson

1.286627 \tabularnewline Von Neumann Ratio

1.302913 \tabularnewline # e[t] > 0

42 \tabularnewline # e[t] < 0

38 \tabularnewline # Runs

28 \tabularnewline Stand. Normal Runs Statistic

-2.910328 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2275&T=2

[TABLE]

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

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

0.67925[/C][/ROW] [ROW][C]R-squared[/C]

0.461381[/C][/ROW] [ROW][C]Adjusted R-squared[/C]

0.44012[/C][/ROW] [ROW][C]F-TEST[/C]

21.700529[/C][/ROW] [ROW][C]Observations[/C]

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

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

5.63774[/C][/ROW] [ROW][C]Sum Squared Errors[/C]

2415.592613[/C][/ROW] [ROW][C]Log Likelihood[/C]

-249.822014[/C][/ROW] [ROW][C]Durbin-Watson[/C]

1.286627[/C][/ROW] [ROW][C]Von Neumann Ratio[/C]

1.302913[/C][/ROW] [ROW][C]# e[t] > 0[/C]

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

38[/C][/ROW] [ROW][C]# Runs[/C]

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

-2.910328[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2275&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	0.67925
R-squared	0.461381
Adjusted R-squared	0.44012
F-TEST	21.700529
Observations	80
Degrees of Freedom	76
Multiple Linear Regression - Residual Statistics
Standard Error	5.63774
Sum Squared Errors	2415.592613
Log Likelihood	-249.822014
Durbin-Watson	1.286627
Von Neumann Ratio	1.302913
# e[t] > 0	42
# e[t] < 0	38
# Runs	28
Stand. Normal Runs Statistic	-2.910328

Multiple Linear Regression - Ad Hoc Selection Test Statistics
Akaike (1969) Final Prediction Error	33.373319
Akaike (1973) Log Information Criterion	3.507673
Akaike (1974) Information Criterion	33.370534
Schwarz (1978) Log Criterion	3.626775
Schwarz (1978) Criterion	37.591374
Craven-Wahba (1979) Generalized Cross Validation	33.456961
Hannan-Quinn (1979) Criterion	35.002673
Rice (1984) Criterion	33.549897
Shibata (1981) Criterion	33.214398

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Ad Hoc Selection Test Statistics \tabularnewline

Akaike (1969) Final Prediction Error

33.373319 \tabularnewline Akaike (1973) Log Information Criterion

3.507673 \tabularnewline Akaike (1974) Information Criterion

33.370534 \tabularnewline Schwarz (1978) Log Criterion

3.626775 \tabularnewline Schwarz (1978) Criterion

37.591374 \tabularnewline Craven-Wahba (1979) Generalized Cross Validation

33.456961 \tabularnewline Hannan-Quinn (1979) Criterion

35.002673 \tabularnewline Rice (1984) Criterion

33.549897 \tabularnewline Shibata (1981) Criterion

33.214398 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2275&T=3

[TABLE]

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

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

33.373319[/C][/ROW] [ROW][C]Akaike (1973) Log Information Criterion[/C]

3.507673[/C][/ROW] [ROW][C]Akaike (1974) Information Criterion[/C]

33.370534[/C][/ROW] [ROW][C]Schwarz (1978) Log Criterion[/C]

3.626775[/C][/ROW] [ROW][C]Schwarz (1978) Criterion[/C]

37.591374[/C][/ROW] [ROW][C]Craven-Wahba (1979) Generalized Cross Validation[/C]

33.456961[/C][/ROW] [ROW][C]Hannan-Quinn (1979) Criterion[/C]

35.002673[/C][/ROW] [ROW][C]Rice (1984) Criterion[/C]

33.549897[/C][/ROW] [ROW][C]Shibata (1981) Criterion[/C]

33.214398[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2275&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2275&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	33.373319
Akaike (1973) Log Information Criterion	3.507673
Akaike (1974) Information Criterion	33.370534
Schwarz (1978) Log Criterion	3.626775
Schwarz (1978) Criterion	37.591374
Craven-Wahba (1979) Generalized Cross Validation	33.456961
Hannan-Quinn (1979) Criterion	35.002673
Rice (1984) Criterion	33.549897
Shibata (1981) Criterion	33.214398

Multiple Linear Regression - Analysis of Variance
ANOVA	DF	Sum of Squares	Mean Square
Regression	3	2069.196262	689.732087
Residual	76	2415.592613	31.784113
Total	79	4484.788875	56.76947943038
F-TEST	21.700529
p-value	0

\begin{tabular}{lllllllll}
\hline

Multiple Linear Regression - Analysis of Variance \tabularnewline

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

Regression

2069.196262

689.732087 \tabularnewline Residual

2415.592613

31.784113 \tabularnewline Total

4484.788875

56.76947943038 \tabularnewline F-TEST

21.700529 \tabularnewline p-value

0 \tabularnewline

\hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2275&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]

2069.196262[/C]

689.732087[/C][/ROW] [ROW][C]Residual[/C]

76[/C]

2415.592613[/C]

31.784113[/C][/ROW] [ROW][C]Total[/C]

79[/C]

4484.788875[/C]

56.76947943038[/C][/ROW] [ROW][C]F-TEST[/C]

21.700529[/C][/ROW] [ROW][C]p-value[/C]

0[/C][/ROW]

[/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2275&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2275&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	2069.196262	689.732087
Residual	76	2415.592613	31.784113
Total	79	4484.788875	56.76947943038
F-TEST	21.700529
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