Question

An economist wants to determine the relation between one’s FICO score and interest rate of a 36-month auto loan. The data represent the interest rate (in percent) a bank might offer on a 36-month auto loan for various FICO scores. Credit Score, x: 550;600;640;670;700;750 Interest Rate, y: 19;18;12;8;6;5 a) Calculate the least regression line y=b0+b1x b) Calculate a 99% Confidence Interval about the slope of the least regression line c) Calculate a 99% Prediction Interval about the slope of the least regression line when x=650

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable Independent Variable: x y 64.353172 0.081360366 x Sample size: 6 R (correlation coefficient)0.95922457 R-sq0.92011178 Estimate of error standard deviation: 1.913516 Parameter estimates: Std. Err. DF 99% L. Limit 99% U. Limit ParameterEstimate Intercept Slope 64.353172 7.8503757 4 28.209283 0.081360366 0.01198682 40.13654884-0.026171888 100.49706 Analysis of variance table for regression model Source DF Model1 168.68716 168.68716 46.069959 0.0025 Error 4 14.646174 3.6615435 Total F-stat p-value MS 5 183.33333 Predicted values: X value Pred. Y s.e.(Pred. y) 99% c.1, for mean 99% P.I. for new 650 11.468934 0.781445057.8710853, 15.066783) (1.952588, 20.98528)

Hence,

a) Least square line:

y = 64.353 - 0.081 x

b) 99% confidence interval for slope:

(-0.1365, -0.0262)

c) 99% prediction interval:

(1.9526, 20.9853)