Home > CC3MN > Chapter 7 > Lesson 7.3.2 > Problem7-104

7-104.

Marissa’s older sister was discussing purchasing a car with her summer job earnings.  Marissa collected data from her friends at her job.

Refer to problem 7-92 for help.

1. Marissa would like to know the typical age of her friends’ cars.  What kind of graphical display should she use?

A box plot shows center and spread of one-variable numerical data nicely.

1. Marissa wants to convince her dad that newer cars are more fuel-efficient.  What kind of graph(s) should Marissa make to convince her dad?

Marissa wants to show her dad an association between age and fuel efficiency.

1. Make a scatterplot of the data.

Use age as the $x$-axis and fuel efficiency as the $y$-axis.

1. Fully describe the association.

Weak, negative, linear association.

1. Draw a line of best fit on the data.  Find the equation of the line of best fit.

Remember that when drawing a line of best fit, about half the points should be above the line and about half should be below.

2. Use the equation to predict what the correct fuel efficiency for a $7$-year-old car should be.

You should get around $31$ mpg.

1. Interpret the slope and $y$-intercept in this situation.

A slope of $-0.7$ means that for each additional year old a car is, it is expected to go $0.7$ less miles per gallon.
What does the $y$-intercept say about a new car?

Age of
Car
(years)

Fuel Efficiency (mpg)

$9$

$34$

$2$

$30$

$5$

$30$

$1$

$35$

$4$

$34$

$10$

$28$

$9$

$27$

$3$

$40$

$8$

$29$