Question

a. Write the regression equation.

b. Discuss the statistical significance of the model using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income using this regression model with 16 years of education.

	SUMMARY OUTPUT
	Regression Statistics
	Multiple R	0.414957
	R Square	0.17219
	Adjusted R Square	0.171463
	Standard Error	2.762937
	Observations	1142
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	1810.183	1810.183	237.1268	9.42E-49
	Residual	1140	8702.553	7.633818
	Total	1141	10512.74
		Coefficients	Standard Error	t Stat	P-value	Lower 95%
	Intercept	12.60511	0.120429	104.668	0	12.36882
	X Variable 1	3.38E-05	2.19E-06	15.39892	9.42E-49	2.95E-05

Answer 1

a. Write the regression equation.

Answer :

Here the regressinon equation is

Y = 12.60511 + 3.38 * 10^-5 X

b. Discuss the statistical significance of the model using the appropriate regression statistic at a 95% level of confidence.

Answer : Here apprpriate statistic is F statistic which is 237.13 which is less than F(critical value) and also significance F value which is equals to 9.42 x 10^-49 which is less than 0.05 significance level so we reject the null hypothesis is that model is significant and conclude that the model is statistically significant.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

Answer : Here the appropriate statistic is t statistic which is 15.40 and which is less than F(critical) and also p value which is equals to 9.42 x 10^-49 which is less than 0.05 significance level so we reject the null hypothesis is that the coefficient for the independent variable is significant and conclude that the coefficient for the independent variable is significant here.

d. Interpret the coefficient for the independent variable.

Answer : Here the interpration of coefficient is that if we increaase the x variable by 1 unit than there would be an increase of 3.38 x 10^-5 units in the value of y.

e. What percentage of the observed variation in income is explained by the model?

Answer : here R² = 0.1722 so here there is 17.22% percent variation is explained by the model.

f. Predict the value of a person’s income using this regression model with 16 years of education.

Here eduction level = 16 years

Y = 12.60511 + 3.38 * 10^-5 * 16 = 12.60565