One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 13 colonies of sparrowhawks (a type of bird) and the software output:
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\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | l | l | l | } \hline \text { Percent return } & 74 & 66 & 81 & 52 & 73 & 62 & 52 & 45 & 62 & 46 & 60 & 46 & 38 \\\hline \text { New adults } & 5 & 6 & 8 & 11 & 12 & 15 & 16 & 17 & 18 & 18 & 19 & 20 & 20 \\\hline\end{array}

Simple linear regression results:
Dependent Variable: New adults
Independent Variable: percentage return
New adults

= 31.934259 - 0.30402295

percentage return
Sample size: 13

R

(correlation coefficient

) = - 0.7484673

\mathrm { R } - \mathrm { sq } = 0.5602033

Estimate of error standard deviation:

3.6668913

Parameter estimates:

\begin{array}{|l|r|r|r|r|r|r|}\hline \text { Parameter } & \text { Estimate } & \text { Std. Err. } & \text { Alternative } & \text { DF } & \text { T-Stat } & \text { P-value } \\\hline \text { Intercept } & 31.934259 & 4.8376164 & \neq 0 & 11 & 6.6012383 & <0.0001 \\\hline \text { Slope } & -0.30402295 & 0.081220034 & \neq 0 & 11 & -3.7432014 & 0.0032 \\\hline\end{array}

A scatterplot of the data shows that there is a linear relationship between the percent x of adult sparrowhawks that return to a colony from the previous year and the number y of new adult birds that join the colony.
An ecologist uses regression line, y = 31.934 - 0.304x to predict how many birds will join another colony when 50% of the adults from the previous year return. What is the prediction?
A)Approximately 14 new adults
B)Approximately 17 new adults
C)Approximately 32 new adults
D)We shouldn't make this prediction because it requires extrapolation.

What Can We Conclude If the Square of the Correlation

Multiple Choice

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