$.$ Administrators at State University believes that decreases in the number of first year applications that they have experienced are directly related to tuition increases. They have collected the following enrollment and tuition data for the past decade

APPLICATION TUITION

$6,050$ $$3,600$

$4,0603,600$

$5,2004,000$

$4,4104,400$

$4,3804,500$

$4,1605,700$

$3,5606,000$

$2,9706,000$

$3,2807,500$

$3,4308,000$

a$)$ Develop a linear regression model for these data and forecast the number of applications for State University if tuition increases to $$9,000$ per year and if tuition is lowered to $$7,000$ per year.