Ornithologists, scientists who study birds, tag sparrow hawks in 13 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; 81; 52; 73; 62; 52; 45; 62; 46; 60; 46; 38 Percent new:       5;   5;  8; 12;  13; 14; 16; 16; 18; 19; 19; 19; 21

Let Percent Return be the explanatory (independent) variable and Percent New be the response (dependent) variable.

(a) Enter the data into your calculator and make a scatter plot. Be sure that your TI-calculator WINDOW set-up for x-min, x-max, y-min, and y-max matches the given graphs.

A.       B.      

C.    

The correct scatter-plot is: Answer 1 Question 20 ABC

(b) Use your calculator's regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part (a). Be sure that your TI-calculator WINDOW set-up for x-min, x-max, y-min, and y-max matches the given graphs.

A.   

B.   

C.   

The correct scatter-plot is: Answer 2 Question 20 ABC

(c) Calculate the least-squares line. Put the equation in the form of ŷ = a + bx. (Round your answers to three decimal places.)

ŷ = Answer 3 Question 20 Answer 4 Question 20 +- Answer 5 Question 20 x

(d) Explain in words what the slope and y-intercept of the regression line tell us. (Round your answers to two decimal places.)

The y-intercept indicates that when there are no returning hawks, there will be Answer 6 Question 20% new hawks.

The slope indicates that for each percentage increase in returning hawks, the percentage of new hawks decreases by Answer 7 Question 20%.

(e) How well does the regression line fit the data? Explain your response. (Round your answer to two decimal places.)

The correlation coefficient is r =Answer 8 Question 20, which indicates a Answer 9 Question 20 negative and somewhat  weaknegative and somewhat strongpositive and somewhat weakpositive  and somewhat strong correlation between returning and new percentages.

(f) Which point from the data has the largest residual?

(x , y) = (Answer 10 Question 20, Answer 11 Question 20)

Explain what the residual means in context. Is this point an outlier? An influential point? Explain. (Round your answers to the nearest whole number.)

The residual means that when the observed return percentage is Answer 12 Question 20%, the observed new percentage will be Answer 13 Question 20% less than the predicted new percentage. Removing this data point Answer 14 Question 20 doesdoes not have a large effect on the regression line, so it Answer 15 Question 20 isis not an outlier, and it Answer 16 Question 20 isis not an influential point.

(g) An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 70% of the adults from the previous year have returned. What is the prediction? (Round your answer to two decimal places.)

ŷ (70%)= Answer 17 Question 20%\