Question

lisa is not sure if m causes n, n causes m, or neither. in an attempt to come to a conclusion, she first plotted m on the x - axis, n on the y - axis, and used the linear regression feature of her graphing calculator. when she did this, she got a correlation coefficient (r) of 0.962 and a line with a slope of 2.3. she then plotted n on the x - axis, m on the y - axis, and used the linear regression feature of her graphing calculator. when she did this, she got a correlation coefficient (r) of 0.962 and a line with a slope of 0.4. which conclusion is the most valid?
a m causes n
b n causes m
c m might cause n, or n might cause m
d m doesnt cause n, and n doesnt cause m

Explanation:

Correlation coefficient (\(r\)) measures the strength and direction of a linear relationship between two variables, but it does not imply causation. Here, both regressions have the same \(r = 0.962\), showing a strong linear association between \(m\) and \(n\), but this association alone doesn't prove which causes which (or if there's a third variable causing both). So we can only say \(m\) might cause \(n\), or \(n\) might cause \(m\).

Answer:

C. \(m\) might cause \(n\), or \(n\) might cause \(m\)