Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of 5 wild male long-tailed finches. Here are the data:
$$\begin{array} { c c }
\text { weight } ( \mathrm { g } ) & \text { tail length } ( \mathrm { mm } ) \
20.8 & 82.5 \
19.1 & 82.5 \
15.9 & 67.0 \
16.7 & 70.5 \
15.7 & 73.5
\end{array}$$ Using appropriate software, what percentage of variation in tail-feather length can be explained by weight among male long-tailed finches in the wild?

Question

Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of 5 wild male long-tailed finches. Here are the data:
$$\begin{array} { c c } 
\text { weight } ( \mathrm { g } ) & \text { tail length } ( \mathrm { mm } ) \
20.8 & 82.5 \
19.1 & 82.5 \
15.9 & 67.0 \
16.7 & 70.5 \
15.7 & 73.5
\end{array}$$ Using appropriate software, what percentage of variation in tail-feather length can be explained by weight among male long-tailed finches in the wild?

Quizplus · Accepted Answer

The percentage of variation in tail-feather length that can be explained by weight among male long-tailed finches in the wild is referred to as the coefficient of determination (R-squared). Using appropriate software to analyze the data, we get an R-squared value of 0.79, which means that 79% of the variation in tail-feather length can be explained by weight among male long-tailed finches in the wild. Therefore, the correct answer is B) 79%.

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