Question

Regression Statistics
Multiple R	0.710723
R Square	0.505127
Adjusted R Square	0.450141
Standard Error	1.216847
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	2	27.20518	13.60259	9.186487	0.00178
Residual	18	26.65291	1.480717
Total	20	53.8581
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	58.74307	12.66908	4.636728	0.000205	32.12632	85.35982	32.12632	85.35982
High School Grad	-0.00133	0.000311	-4.28236	0.000448	-0.00198	-0.00068	-0.00198	-0.00068
Bachelor's	-0.00016	5.46E-05	-3.00144	0.007661	-0.00028	-4.9E-05	-0.00028	-4.9E-05

In sentence form, describe the implications of your estimated beta coefficients (i.e. are they significant? what do they tell you about the relationship between that X and the Y?). Be sure to include beta-0, beta-1, and beta-2.

Answer 1

Sol:

For beta0,t=

t=4.636728

p=0.000205

p<0.05

beta0 is signiifcant at 5% level of significance

For beta1

t=-4.28236

p=0.000448

p<0.05

beta1 is significant at 5% level of significance

For beta2:

t=-3.00144

p=0.007661

p<0.05,beta2 is significant at 5% level of significance

From Global F test

Ho:

beta1=beta2=0

Ha:

Atleast one of the beta is different from zero

F=9.186487

p=0.00178

p<0.05

Regression model is significant that is there is a linear relationship between y and independent variables.

Intrepretation of beta1:

beta1=

-0.00133

for unit increase in High school grad, y decreases by 0.00133 on an average

beta2=

-0.00016

for unit increase in Bachelor's, y decreases by 0.00016 on an average