Ornithologists, scientists who study birds, tag sparrow hawks in13different 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:78;66;85;53;73;65;52;42;66;44;60;46;38 Percent new:8;5;8;13;12;15;16;17;18;18;15;20;20

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? Usexto represent percent return. Round any calculated values to twodecimal places. y^=

(b) Explain in words what the slope andy-intercept of the regression line tell us. Round your answer to twodecimal places. The slope of the least-squares line is -0.25. For each percentage increase in returning birds, the percentage of new birds in the colon decreasesby ________________. They-intercept of the least-squares line is 29.11. 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=-0.769 indicates a fairlystrongcorrelation between returning and new percentages.

(d) An ecologist wants to predict how many birds will join another colony of sparrow hawks to which54%54%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 15.61%.