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

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

(b) Use your calculator’s 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 which$60\%$ of the adults from the previous year return. What’s the prediction?

The given data is

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.

The given data is

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

The least-square regression line is $\hat{Y}=31.9-0.304X$.

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

The given data is

The least-squares regression line's equation is $\hat{Y}=31.9-0.304X$

The slope $b$of the above regression line represents the rate at which the expected response $Y$travels between the lines when the explanatory variable $X$changes$(-0.304)$. $b$is the expected change in $Y$when $X$is increased by one unit. If the per cent return increases by one unit, the number of new adult joins reduces by $0.304$units.

When the explanatory variable $x=0$, the anticipated response$Y$is 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" $31.9$new adults that enter the colony in the instance of bird colonies.

The given data is

The equation of the least-squares regression line is

$\hat{Y}=31.9-0.304X$

Let's take for $X=60\%$, the value of $Y$is

$\hat{Y}=31.9-0.304X$

$$\begin{gathered} =31.9-0.304\left(60\right) \\ =13.66 \end{gathered}$$

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