Section B Section B Checkpoint

Problem 1

A safety inspector records the speed of a car 30 times and how far the car travels until it comes to a complete stop. The results are summarized in the scatter plot.

Scatter plot showing stopping distance versus speed with a linear model graphed.

  1. Using the linear model y=3.1x−1y = 3.1x - 1, what does the slope mean in this situation? Does the vertical intercept make sense in this situation? Explain your thinking.
  2. Use the residuals to justify that this linear model is a good fit for the data at slow speeds.

Scatter plot showing residuals

Show Solution
Solution
Sample response: 
  1. The slope means that for every extra mile per hour of speed, the car takes about 3.1 feet longer to stop. The intercept does not make sense. If a car is going 0 miles per hour, according to the model it would stop in -1 feet, which is not possible.
  2. For speeds up to around 12 miles per hour, the residuals are relatively close to the axis and scattered on both sides.
Show Sample Response
Sample Response
Sample response: 
  1. The slope means that for every extra mile per hour of speed, the car takes about 3.1 feet longer to stop. The intercept does not make sense. If a car is going 0 miles per hour, according to the model it would stop in -1 feet, which is not possible.
  2. For speeds up to around 12 miles per hour, the residuals are relatively close to the axis and scattered on both sides.