A student in Arch Hall would like to know the impact years of Education (YED) has on a graduate's yearly starting salary $000's. Recently, data associating YED with yearly starting salary in $000's (Y) was collected and summarized. The results are given below:

Multiple R	0.840220581
R Square	0.705970625
Adjusted R Square	0.676567688
Standard Error	0.48459412
Observations	12

ANOVA
	df		SS	MS	F	Significance F
Regression		1	5.63835206	5.638352	24.0102073	0.000623096
Residual		10	2.348314607	0.234831
Total		11	7.986666667

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	37.98089888	0.480493108	79.04567	2.5653E-15	36.91029351	39.0515042
YED	0.435955056	0.088970035	4.900021	0.0006231	0.237717463	0.63419265

Conduct a hypothesis test at the 0.01 level of significance to determine if a significant relationship exists between years of education and a graduate's yearly starting salary. Comment on the necessity of the independent variable in this regression model and explain why it may or may not be necessary.