Problem-Solving and Data AnalysisVery hardInterpreting the slope of a fitted line
Problem-Solving and Data Analysis practice question
A rental company fits the line c = 0.4m + 15 to data on the cost c, in dollars, of one-day van rentals driven m miles. Which of the following is the best interpretation of the number 0.4 in this context?
- A. Each additional mile driven is associated with an increase of about $0.40 in the cost of a rental.Correct
- B. A van driven 0 miles costs about $0.40 to rent.
- C. Each additional dollar of cost is associated with about 0.4 more miles.
- D. About 40% of the cost is due to distance driven.
Answer: A. Each additional mile driven is associated with an increase of about $0.40 in the cost of a rental.
The slope is the change in c per unit change in m: $0.40 per mile.
Why the other answers are wrong
- B. A van driven 0 miles costs about $0.40 to rent.
- The cost at 0 miles is the intercept, $15.
- C. Each additional dollar of cost is associated with about 0.4 more miles.
- This reverses the roles of the variables; the slope gives dollars per mile, not miles per dollar.
- D. About 40% of the cost is due to distance driven.
- 0.4 is a rate, not a proportion of the total cost.
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