Question

2. An economist wants to determine the relation between one’s FICO Credit scores x, and the interest rate of a 36-month auto loan y. Then given data represents the interest rate a bank would offer on a 36-month auto loan for various FICO scores.

Credit Score 545 595 640 675 705 750

Interest Rate 18.982 17.967 12.219 5.612 6.680 5.150

a) Find the linear regression line when r = −0.940, sx = 74.543 and sy = 6.254.

b) Find the residual for the Interset Rate of 5.612 and interpret what the result means.

Answer 1

a)

from above

least square line: y^ =62.5111-0.0789x

b)

residual =actual value-predicted value =5.612-(62.5111-0.0789*675)= -3.642

this tells us that actual interest rate for 675 credit score is 3.642 below than what is predicted from the linear model