Write the regression equation. Discuss the statistical significance of the model using the appropriate regression statistic at...

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Statistics

Write the regression equation.
Discuss the statistical significance of the model using theappropriate regression statistic at a 95% level of confidence.
Discuss the statistical significance of the coefficient for theindependent variable using the appropriate regression statistic ata 95% level of confidence.
Interpret the coefficient for the independent variable.
What percentage of the observed variation in income isexplained by the model?
Predict the value of a personâ€™s income with 3 children, usingthis regression model.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.039342
R Square
0.001548
Adjusted R Square
0.000672
Standard Error
1.554036
Observations
1142
ANOVA
df
SS
MS
F
Significance F
Regression
1
4.267905
4.267905
1.767229
0.183991
Residual
1140
2753.131
2.415027
Total
1141
2757.398
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
1.621275
0.067736
23.93504
6.6E-103
1.488373
1.754177
1.488373
1.754177
X Variable 1
1.64E-06
1.23E-06
1.329372
0.183991
-7.8E-07
4.06E-06
-7.8E-07
4.06E-06

Answer & Explanation Solved by verified expert

4.4 Ratings (1002 Votes)

aThe sample regression equation toestimate the dependent variable income regressedon the independent variable children x1 1From the given summary outputSubstituting the parameter estimatesin equation 1 the regression equation is given as IbThe statistical significance of themodel is inferred from F statistic and the corresponding pvalueof the FstatisticWe test See Answer

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SUMMARY OUTPUT

Regression Statistics
Multiple R	0.039342
R Square	0.001548
Adjusted R Square	0.000672
Standard Error	1.554036
Observations	1142

ANOVA
	df	SS	MS	F	Significance F
Regression	1	4.267905	4.267905	1.767229	0.183991
Residual	1140	2753.131	2.415027
Total	1141	2757.398

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.621275	0.067736	23.93504	6.6E-103	1.488373	1.754177	1.488373	1.754177
X Variable 1	1.64E-06	1.23E-06	1.329372	0.183991	-7.8E-07	4.06E-06	-7.8E-07	4.06E-06