Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females of the same species. Researchers studied the relationship between tail-feather length (measuring the R1 central tail feather) and weight in a sample of 20 male long-tailed finches raised in an aviary. The data are displayed in the scatterplot below, followed with software output about the least-squares regression model of feather length as a function of weight.

$$\begin{array}{l}
\begin{array} { l l r }
\hline &\text {Coefficients }&\text {Standard Error }\
\hline\text {Intercept }&35.7379 & 21.0523 \
\text { Bird-weight}&2.8299 & 1.2811\
\hline\text {R Square }&0.2133\
\text {Standard Error }&\ 10.5270\
\end{array}
\end{array}$$ What is the margin of error for a 95% confidence interval for the true population slope β in this linear regression model?

Question

Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females of the same species. Researchers studied the relationship between tail-feather length (measuring the R1 central tail feather) and weight in a sample of 20 male long-tailed finches raised in an aviary. The data are displayed in the scatterplot below, followed with software output about the least-squares regression model of feather length as a function of weight.
 ​
​
$$\begin{array}{l}
\begin{array} { l  l r } 
\hline &\text {Coefficients }&\text {Standard Error }\
\hline\text {Intercept }&35.7379 & 21.0523 \
\text { Bird-weight}&2.8299 & 1.2811\
\hline\text {R Square }&0.2133\
\text {Standard Error }&\ 10.5270\
\end{array}
\end{array}$$ What is the margin of error for a 95% confidence interval for the true population slope β in this linear regression model?

Quizplus · Accepted Answer

The Answer of Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females of the same species. Researchers studied the relationship between tail-feather length (measuring the R1 central tail feather) and weight in a sample of 20 male long-tailed finches raised in an aviary. The data are displayed in the scatterplot below, followed with software output about the least-squares regression model of feather length as a function of weight.
 ​
​
$$\begin{array}{l}
\begin{array} { l  l r } 
\hline &\text {Coefficients }&\text {Standard Error }\
\hline\text {Intercept }&35.7379 & 21.0523 \
\text { Bird-weight}&2.8299 & 1.2811\
\hline\text {R Square }&0.2133\
\text {Standard Error }&\ 10.5270\
\end{array}
\end{array}$$ What is the margin of error for a 95% confidence interval for the true population slope β in this linear regression model?

Tail-Feather Length in Birds Is Sometimes a Sexually Dimorphic Trait;