Question

The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration.

GPA	Monthly Salary ($)
2.6	3,600
3.4	3,900
3.6	4,300
3.2	3,700
3.5	4,200
2.9	2,200

The estimated regression equation for these data is  = -414.9 + 1,270.3x and MSE =425,236

A) Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).

B) Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).

C) Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).

Answer 1

a)

Point estimate =-414.9+1,270.3*3 =3396.0

b)

std error of CI=s*√(1/n+(x0-x̅)2/Sxx)=		306.3634
for 95 % CI value of t=		2.776
margin of error E=t*std error=		850.601
lower confidence bound=xo-E=		2545.40
Upper confidence bound=xo+E=		4246.60

95% confidence interval for the mean starting salary =(2545.40 ; 4246.60)

c)

std error of PI=s*√(1+1/n+(x0-x̅)2/Sxx)=		720.4825
for 95 % CI value of t=		2.776
margin of error E=t*std error=		2000.380
lower confidence bound=xo-E=		1395.62
Upper confidence bound=xo+E=		5396.38

95% prediction interval for Ryan Dailey =(1395.62 , 5396.38)