Question

Your Fair Isaacs Corporation (FICO) credit score is used to determine your creditworthiness. It is used to help determine whether you qualify for a mortgage or credit and is even used to determine insurance rates. FICO scores have a range of 300 to 850, with a higher score indicating a better credit history. 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	545	595	640	675	705	750
Interest Rate (%)	18.982	17.967	12.218	8.612	6.680	5.150

4. (e) WITHOUT EXCEL Find the least-squares regression line using the explanatory and response variables determined in part (a). WITHOUT EXCEL

5. (f) WITHOUT EXCEL Draw the least-squares regression line on the scatter diagram in part (b). Label at least two points on the line.WITHOUT EXCEL

6. (g) WITHOUT EXCEL Suppose Bob has a FICO score of 680 and he is offered an interest rate of 8.3% on a 36-month auto loan. Is this a good offer? Explain.WITHOUT EXCEL

Answer 1

(e) the least square regression line y=a+bx=61.3687-0.0764x

a=(sum(y)*sum(x²)-sum(x)*sum(xy))/(n*sum(x²)-(sum(x))²)=61.3687

b=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x²)-(sum(x))²)=-0.0764

(f)

(g) for x=680, the estimated interest rate is y=61.3687-0.0764*680=9.4167,

offer of interest rate of 8.3% is a good offer as the estimated is 9.4167%

s.n.	Credit Score (x)	Interest Rate (y)	x2	y2	xy
1	545	18.982	297025	360.3163	10345.19
2	595	17.967	354025	322.8131	10690.37
3	640	12.218	409600	149.2795	7819.52
4	675	8.612	455625	74.16654	5813.1
5	705	6.68	497025	44.6224	4709.4
6	750	5.15	562500	26.5225	3862.5
sum=	3910	69.609	2575800	977.7204	43240.08