What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? Both r and b always have values between −1 and 1. b is always larger than r. r is always larger than b. r and b have the same sign (+ or −). The slope b is always equal to the square of the correlation r.
Question
What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? Both r and b always have values between −1 and 1. b is always larger than r. r is always larger than b. r and b have the same sign (+ or −). The slope b is always equal to the square of the correlation r.
Solution
We can say that r and b always have values between −1 and 1. However, we cannot conclude that b is always larger than r or vice versa. The relationship between r and b depends on the specific data set and cannot be generalized. Additionally, r and b do not necessarily have the same sign. Lastly, the slope b is not always equal to the square of the correlation r.
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