Section B Section B Checkpoint

Problem 1

The scatter plot shows the height and diameter of a kind of bush that grows naturally in an area with 2 possible linear models.

The solid line has the equation y=45x+3.5y=\frac{4}{5}x+3.5, and the dashed line has the equation y=710x+3.8y=\frac{7}{10}x+3.8.

  1. Which linear model fits the data better? Explain your reasoning.
  2. What is the slope of the model you chose and what does it mean in this situation?

  3. Does this data show a positive, negative, or no association? Explain your reasoning.

  4. Add a point to the graph that would be considered an outlier.
Show Solution
Solution
  1. The dashed line fits better. Sample reasoning: It goes through the middle of the data and follows the trend better than the solid line.
  2. The slope is 710\frac{7}{10}. This means that, for every extra inch in diameter for one of these bushes, the height is expected to be 710\frac{7}{10} of an inch taller.
  3. It shows a positive association because as the diameter increases, the height tends to also increase.
  4. Any point far away from the other points in the scatter plot.
Show Sample Response
Sample Response
  1. The dashed line fits better. Sample reasoning: It goes through the middle of the data and follows the trend better than the solid line.
  2. The slope is 710\frac{7}{10}. This means that, for every extra inch in diameter for one of these bushes, the height is expected to be 710\frac{7}{10} of an inch taller.
  3. It shows a positive association because as the diameter increases, the height tends to also increase.
  4. Any point far away from the other points in the scatter plot.

Problem 2

  1. Do these data show a linear or non-linear association?

    Explain your reasoning.

    scatter plot

  2. Circle any clusters that appear to be present in the data.
Show Solution
Solution
  1. The data show a non-linear association. Sample reasoning: The points do not follow a steadily increasing or decreasing trend. They appear to go up and down as the xx-coordinate increases.
  2. A cluster is present for points with xx-values between 5 and 20 and another cluster for points with xx-values between 30 and 45.
Show Sample Response
Sample Response
  1. The data show a non-linear association. Sample reasoning: The points do not follow a steadily increasing or decreasing trend. They appear to go up and down as the xx-coordinate increases.
  2. A cluster is present for points with xx-values between 5 and 20 and another cluster for points with xx-values between 30 and 45.