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Bird colonies Exercise 6examined the relationship between the number of new birds y and per cent of returning birds xfor 13sparrowhawk colonies. Here are the data once again

(a) Enter the data into your calculator and make a scatterplot.

(b) Use your calculator鈥檚 regression function to find the equation of the least-squares regression line. Add this line to your scatterplot from (a).

(c) Explain in words what the slope and y-intercept of the regression line tell us.

(d) An ecologist uses the line to predict how many birds will join another colony of sparrowhawks and to which60% of the adults from the previous year return. What鈥檚 the prediction?

Short Answer

Expert verified

(a)

(b) The equation of the least-squares regression line is Y^=31.9-0.304X

(c) The rate at which the predicted response Ymoves among the lines as the explanatory variable Xchanges is the slope bof the aforementioned regression line (-0.304).

When the explanatory variable x=0, the anticipated response Yis the y-intercept of the above regression line 31.9.

(d) This indicates that 13.66birds will join another sparrow hawk colony, to which 60%of the adults from the previous year will return.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

From the given data

On the horizontal axis, we plotted per cent return (the explanatory variable), and on the vertical axis, we plotted new adults (the response variable).

The resultant scatterplot for the given data is shown below.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

Using the MINITAB, the expression for the least-squares regression line would be displayed below:

The least-square regression line is Y^=31.9-0.304X.

Look at the data scatter plot above with the regression line added.

05

Part (c) Step 1: Given information

The given data is

06

Part (c) Step 2: Explanation

The least-squares regression line's equation is Y^=31.9-0.304X

The slope bof the above regression line represents the rate at which the expected response Ytravels between the lines when the explanatory variable Xchanges(-0.304). bis the expected change in Ywhen Xis increased by one unit. If the per cent return increases by one unit, the number of new adult joins reduces by 0.304units.

When the explanatory variable x=0, the anticipated responseYis the y-intercept of the above regression line 31.9. This demonstrates if the per cent return of adult birds in a colony that return from the previous year is localid="1653038213492" 31.9new adults that enter the colony in the instance of bird colonies.

07

Part (d) Step 1: Given information

The given data is

08

Part (d) Step 2: Explanation

The equation of the least-squares regression line is

Y^=31.9-0.304X

Let's take for X=60%, the value of Yis

Y^=31.9-0.304X

=31.9-0.304(60)=13.66

This indicates that 13.66 birds will join another sparrow hawk colony, to which 60% of the adults from the previous year will return.

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