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: 74; 66; 83; 57; 73; 66; 52; 42; 62; 44; 60; 46; 38 Percent new: 6; 10; 8; 12; 12; 15; 16; 17; 18; 18; 22; 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? Use x to represent percent return. Round any calculated values to two decimal places. y=____ (b) Explain in words what the slope and y-intercept of the regression line tell us. Round your answer to two decimal places. The slope of the least squares line is________ . For each percentage increase in returning birds, the percentage of new birds in the colony decreases by__________ . The y-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 two decimal 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= __________ indicates a fairly strong correlation between returning and new percentages. (d) An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 65% 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 __________%
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: 74; 66; 83; 57; 73; 66; 52; 42; 62; 44; 60; 46; 38
Percent new: 6; 10; 8; 12; 12; 15; 16; 17; 18; 18; 22; 20; 20
Enter the data into your calculator and make a
(a) What is the equation of the least-squares regression line? Use x to represent percent return.
Round any calculated values to two decimal places.
y=____
(b) Explain in words what the slope and y-intercept of the regression line tell us.
Round your answer to two decimal places.
The slope of the least squares line is________ . For each percentage increase in returning birds, the percentage of new birds in the colony decreases by__________ .
The y-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 two decimal places.
The coefficient of determination indicates that ________% of the variation in the percent of new birds is explained by the model. The
(d) An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 65% 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 __________%
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