Question

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 interst 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 reponse variable

b) interpret the and y-intercept, if appropriate, note: credit scores have a range of 300 to 850

c) predict the interest rate a person would pay if her FICO scores were the median score of 723.

Answer 1

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

	x	y	x*x	y*y	x*y
	545	18.982	297025	360.3163	10345.19
	595	17.967	354025	322.8131	10690.37
	640	12.218	409600	149.2795	7819.52
	675	8.612	455625	74.16654	5813.1
	705	6.68	497025	44.6224	4709.4
	750	5.51	562500	30.3601	4132.5
Total	3910	69.969	2575800	981.558	43510.08

The regression line is y=a+bx

= -0.0751

=69.969/6 - ( -0.0751)*3910/6 = 60.5984

The regression line is y=60.5984-0.0751*x

b)

Interpret the slope and y-intercept, if appropriate. Note: Credit scores have a range of 300 to 850.

When there is one unit increase in credit score, there is a decrease of 0.0751 in interest rate.

There is no meaning in interpreting the y-intercept.

c)

Predict the interest rate a person would pay if their FICO score were the median score of 723.

When x=723,

Predicted y =60.5984-0.0751*723

=6.3011

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