Question

As part of a bear population study, data were gath-ered on a sample of black bears inthewesternUnitedStates to examine the relationship between the bear’sneck girth (distance around the neck) and the weight ofthe bear. A scatterplot of the data reveals a straight-linepattern. The $r^2$-value from a least-squares regression anal-ysis was determined to be $r^2$0.963. Which one of thefollowing is the correct value and corresponding interpre-tation for the correlation?

(a) The corrlation is $0.963$, and $96.3\%$of the variationin a bear’s weight can be explained by the least squaresregression line using neck girth as the explanatory variable.

(b) The correlation is $0.963$. There is a strong positive lin-ear relationship between a bear’s neck girth and its weight.

(c) The correlation is 0.981, and 98.1% of the variation ina bear’s weight can be explained by the least-squares regres-sion line using neck girth as the explanatory variable.

(d) The correlation is0.981. There is a strong negative lin-ear relationship between a bear’s neck girth and its weight.

(e) The correlation is 0.981. There is a strong positive lin-ear relationship between a bear’s neck girth and its weight.

Short answer

Result is:

$\text{The correlation is}0.981\text{. There is a strong positive linear relationship between a bear's neck girth and it's weight.}$

Step-by-step solution

Given information

we have been given five options from which we have to find the correct one.

Explanation

$\text{They want you to interpret the correlation}$

$r^2=0.963\Rightarrow \left|r\right|=0.981$

remember doing the squares

$r=0.981$

Hence, (e) part is correct.