A Fisheries Biologist Has Been Studying Horseshoe Crabs Using Categorical

Multiple Choice

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.
Suppose we use statistical software to predict the weight for a horseshoe crab with width 2.25 centimeters, which yields the following:
​
$$\begin{array} { | c | c | c | c | } \hline \text { Predicted Weight } & \begin{array} { c } \text { Std Error } \\\text { Predict }\end{array} & \mathbf { 9 5 . 0 \% } \text { CI } & \mathbf { 9 5 . 0 \% } \text { PI } \\\hline 4.093 & 0.774 & ( 2.556,5.630 ) & ( - 0.539,8.725 ) \\\hline\end{array}$$ ​
What is a 95% interval for this prediction according to this output?

A) (2.556, 5.630)
B) (-0.539, 8.725)
C) 4.093 ± 1.9419
D) 4.093 ± 0.1863