12.5 Exercise 16

Ornithologists (scientists who study birds) tag sparrow hawks in 13 different colonies to study their population. They gather data for the percentage of new sparrow hawks in each colony and the percentage of those that have returned from migration.

Percent return: 74, 66, 81, 52, 73, 62, 52, 45, 62, 46, 60, 46, 38
Percent new: 5, 6, 8, 11, 12, 15, 16, 17, 18, 18, 19, 20, 20

1. Enter the data into a calculator and make a scatter plot.
2. Use the calculator’s regression function to find the equation of the least-squares regression line. Add this to your scatter plot from Part A.
3. Explain what the slope and y-intercept of the regression line tell us.
4. How well does the regression line fit the data? Explain your response.
5. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.
6. An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 70 percent of the adults from the previous year have returned. What is the prediction?