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A Fisheries Biologist Has Been Studying Horseshoe Crabs Using Categorical

Question 2

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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
Weighti = α+β × widthi + Ɛi
Where the deviations Ɛi 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:
 Variable  Estimate  Standard Error of  Estimate  Constant 2.30130.9788 Width 0.79630.0939\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.
The quantity s = 2.2018 is an estimate of the standard deviation, , of the deviations in the simple linear regression model. What is the degrees of freedom for s?


A) 100
B) 99
C) 98
D) 2

Correct Answer:

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