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What's not true about a correlation coefficient \( r \) ? \( r<0 \) when scatter plot shows a falling trend. the closer \( r \) is to \( \pm 1 \), the more closely the scattered points line up. \( r>0 \) when scatter plot shows a rising trend \( r \) is the slope of the best-fit line. \( -1 \leq r \leq 1 \)

Ask by Hodges Lambert. in the United States
Mar 09,2025

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\( r \) is not the slope of the best-fit line.

Solución

1. The correlation coefficient \( r \) provides the strength and direction of a linear relationship between two variables. It does not represent the slope of the best-fit line. 2. The statement “\( r \) is the slope of the best-fit line” is not true. 3. The other statements are correct: - \( r < 0 \) when the scatter plot shows a falling trend. - \( r > 0 \) when the scatter plot shows a rising trend. - The value of \( r \) being closer to \( \pm 1 \) indicates that the points are more tightly clustered around a straight line. - \( r \) is always between \(-1\) and \(1\), so \( -1 \leq r \leq 1 \).

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Mind Expander

Did you know that while a correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables, it does not provide any information about causation? Just because two variables have a strong correlation does not mean that one causes the other to change. Spurious correlations can mislead you into thinking there’s a relationship when there isn’t! One common mistake many make is assuming that \( r \) is the same as the slope of the best-fit line. While they are related—both give insights into the relationship between variables—they represent different concepts. The slope indicates how much \( y \) changes for a given change in \( x \), while \( r \) only assesses strength and direction! So remember, they’re not interchangeable!

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