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 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 represented in the following scatterplot, along with the least-squares regression line equation and the square of the correlation coefficient (R²) .
What is the value of the correlation coefficient describing the relationship between weight and tail-feather length?

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 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 represented in the following scatterplot, along with the least-squares regression line equation and the square of the correlation coefficient (R²) .

What is the value of the correlation coefficient describing the relationship between weight and tail-feather length?

Quizplus · Accepted Answer

The square of the correlation coefficient given in the question is R², which is approximately 0.46 when the square root is taken. Therefore, the correlation coefficient itself is approximately 0.68 (since the correlation coefficient is the square root of the coefficient of determination, which is 0.46).

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