An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The given data represent the interest rate (in percent) a bank would offer on a 36-month auto loan for various FICO scores.
Credit Score, x .... Interest Rate (percent), y
545 ......... 18.982
595 ......... 17.967
640 ......... 12.218
675 ......... 8.612
705 ......... 6.680
750 ......... 5.150
(a) Find the least-squares regression line treating the FICO score, x, as the explanatory variable and the interest rate, y, as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Predict the interest rate a person would pay if her FICO scores were the median score of 723.
(d) Suppose Bob has a FICO score of 680 and he is offered an interest rate of 8.3%. Is this a good offer? Why?