Question

(a) Present the regression output below noting the coefficients, assessing the adequacy of the model and the p-value of the model and the coefficients individually.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.19476248
R Square	0.037932424
Adjusted R Square	0.035147858
Standard Error	12.09940236
Observations	694
ANOVA
	df	SS	MS	F	Significance F
Regression	2	3988.511973	1994.255986	13.62238235	1.5759E-06
Residual	691	101159.3165	146.3955376
Total	693	105147.8284
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	27.88762549	0.747028382	37.33141358	7.6561E-168	26.42090772	29.35434326	26.42090772	29.35434326
Gender	-1.45054741	0.924086858	-1.569708948	0.116940613	-3.264902321	0.363807502	-3.264902321	0.363807502
Degree Type	4.662178098	0.975135895	4.781054748	2.13194E-06	2.747593355	6.576762841	2.747593355	6.576762841

Answer 1

Present the regression output below noting the coefficients, assessing the adequacy of the model and the p-value of the model and the coefficients individually.

since the p-value=1.5759E-06 of F of the regression is less than typical level of significance alpha=0.05, so we reject the null hypothesis that all the regression coefficients are zero and conclude that atleast one regression coefficeint is non-zero. since the R-square is 0.0379, which is very low, so taking consideration of this R-square we can say overall this model is not good.

we we go for individual regression coefficient,

p-value=0.0.1169 for Gender, so it is not significant and p-value=2.13194E-06 for Degree type is significant at alpha=0.05, so it can Gender can be remove from the model and reanalyze the data.