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Chapter 3, Problem 18AYU

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QUESTION:

(Refer to Problem 26, Section 4.1.). 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.

\(\begin{array}{cc}
\text { Credit Score, } \boldsymbol{x} & \text { Interest Rate (percent), } \boldsymbol{y} \\
\hline 545 & 18.982 \\
\hline 595 & 17.967 \\
\hline 640 & 12.218 \\
\hline 675 & 8.612 \\
\hline 705 & 6.680 \\
\hline 750 & 5.150 \\
\hline \text { Source: www.myfico.com } &
\end{array}\)

(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. 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.

(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?

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QUESTION:

(Refer to Problem 26, Section 4.1.). 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.

\(\begin{array}{cc}
\text { Credit Score, } \boldsymbol{x} & \text { Interest Rate (percent), } \boldsymbol{y} \\
\hline 545 & 18.982 \\
\hline 595 & 17.967 \\
\hline 640 & 12.218 \\
\hline 675 & 8.612 \\
\hline 705 & 6.680 \\
\hline 750 & 5.150 \\
\hline \text { Source: www.myfico.com } &
\end{array}\)

(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. 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.

(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?

ANSWER:

Step 1 of 6

The least-squares regression line is a statistical method used to find the best-fitting line through a set of data points. It is commonly employed in regression analysis, where the goal is to model the relationship between a dependent variable (also known as the response variable) and one or more independent variables (predictors).

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