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Question 8

6 points

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Ornithologists, scientists who study birds, tag sparrow hawks in 1313 different colonies to study their population. They gather data for the percent of new sparrow hawks in each colony and the percent of those that have returned from migration.

Percent return: 7575; 6666; 8181; 5757; 7373; 6262; 5252; 4343; 6363; 4242; 6060; 4646; 3838 Percent new: 77; 88; 88; 1515; 1212; 1515; 1616; 1717; 1818; 1818; 1919; 2020; 2020

Enter the data into your calculator and make a scatter plot. Use your calculator's regression function to find the equation of the least-squares regression line. Add this to your scatter plot.

(a) What is the equation of the least-squares regression line? Use xx to represent percent return. Round any calculated values to twodecimal places. y^=

b) Explain in words what the slope and yy-intercept of the regression line tell us. Round your answer to twodecimal places. The slope of the least squares line is . For each percentage increase in returning birds, the percentage of new birds in the colony increasesdecreasesClick for List by . The yy-intercept of the least squares line is . When there are no returning sparrow hawks, there will be almost new sparrow hawks.

(c) How well does the regression line fit the data? Explain your response. Round your answer to twodecimal places. The coefficient of determination indicates that %% of the variation in the percent of new birds is explained by the model. The correlation coefficient, r=r= indicates a fairly strongweakClick for List correlation between returning and new percentages.

(d) An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 67%67% of the adults from the previous year have returned. What is the prediction? Round your answer to the nearest integer. The predicted percent of new birds is %%.