Problem-Solving and Data AnalysisEasy–MediumInterpreting the y-intercept of a model
Problem-Solving and Data Analysis practice question
The line of best fit for a scatterplot of a taxi's fare, y, in dollars, against the distance travelled, x, in miles, is y = 2.4x + 3. What does the number 3 most likely represent?
- A. The predicted fare, in dollars, for a trip of 0 miles.Correct
- B. The predicted increase in fare, in dollars, for each additional mile.
- C. The predicted distance, in miles, of a trip costing $2.40.
- D. The number of miles in a typical trip.
Answer: A. The predicted fare, in dollars, for a trip of 0 miles.
The 3 is the y-intercept: the value of y when x = 0. A trip of 0 miles is predicted to cost $3 — a base charge.
Why the other answers are wrong
- B. The predicted increase in fare, in dollars, for each additional mile.
- The per-mile increase is the slope, 2.4, not the intercept.
- C. The predicted distance, in miles, of a trip costing $2.40.
- The model predicts fare from distance, not the reverse, and 2.40 isn't a special value in it.
- D. The number of miles in a typical trip.
- Nothing in the equation describes a typical trip length; 3 is a fare, in dollars.
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