Chapter 3.2, Problem 4AYU

If the Independent variable in a line of best fit $y=-0.008x+14$ is credit score, and the dependent variable is the interest rate on a used-car loan, then the slope is interpreted as follows: “If credit score increases by 1 point, the interest rate will __________ (increase/decrease) by ________ percent, on average.”

To determine

To fill: In the blanks of the given statement.

Answer to Problem 4AYU

Solution:

Decreases

$\underset{\_}{0.8\%}$

Explanation of Solution

Given:

The given statement is

“If the independent variable in a line of best fit $y=-0.008x+14$ is the credit score and the dependent variable is the interest rate on a used-car loan, then the slope is interpreted as follows: If the credit score increases by 1 point, the interest rate will ________ by ______ percent, on average.”

“If the independent variable in a line of best fit $y=-0.008x+14$ is the credit score and the dependent variable is the interest rate on a used-car loan, then the slope is interpreted as follows: If the credit score increases by 1 point, the interest rate will decreases by $0.8\%$ percent, on average.”

From the given equation, we can see that the slope of the line is negative $\left(-0.008\right)$; therefore, the interest rate will decrease by $0.008$units for each 1 unit increase in the credit score.

$0.008=\frac{100}{100}\times 0.008$

$\Rightarrow \frac{0.8}{100}=0.8\%$