A fisheries biologist has been studying horseshoe crabs using categorical variables, but she has decided that reporting the data as continuous variables would be more useful. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters) . The proposed regression equation is
Weight_i = α+β × width_i + Ɛ_i
Where the deviations Ɛ_i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software:
$\begin{array} { | l | c | c | } \hline { \text { Variable } } & \text { Estimate } & \begin{array} { c } \text { Standard Error of } \\\text { Estimate }\end{array} \\\hline \text { Constant } & 2.3013 & 0.9788 \\\text { Width } & 0.7963 & 0.0939 \\\hline\end{array}$ r² = 0.423, s = 2.2018.
Based on the sample data, what is the correlation between the width and weight of horseshoe crabs?

Question

A fisheries biologist has been studying horseshoe crabs using categorical variables, but she has decided that reporting the data as continuous variables would be more useful. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters) . The proposed regression equation is
Weight_i = α+β × width_i + Ɛ_i
Where the deviations Ɛ_i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software:

\begin{array} { | l | c | c | } \hline { \text { Variable } } & \text { Estimate } & \begin{array} { c } \text { Standard Error of } \\\text { Estimate }\end{array} \\\hline \text { Constant } & 2.3013 & 0.9788 \\\text { Width } & 0.7963 & 0.0939 \\\hline\end{array}

r² = 0.423, s = 2.2018.
Based on the sample data, what is the correlation between the width and weight of horseshoe crabs?

Quizplus · Accepted Answer

The correlation coefficient (r) is the square root of the coefficient of determination (r²) when the relationship is positive. Since r² = 0.423, the correlation is √0.423 = 0.650.

A Fisheries Biologist Has Been Studying Horseshoe Crabs Using Categorical