Question

from unit 3 lesson 7
here is a scatter plot.
which of the following is the best estimate of the correlation coefficient for the data represented by the scatter plot?
a -0.9
b -0.4
c 0.4
d 0.9

Explanation:

Step1: Determine the sign of the correlation coefficient

Since the scatter plot shows a downward - trend (as \(x\) increases, \(y\) tends to decrease), the correlation coefficient \(r\) is negative. So we can eliminate options C (\(r = 0.4\)) and D (\(r=0.9\)).

Step2: Assess the strength of the negative correlation

The correlation coefficient \(r\) ranges from \(- 1\) to \(1\). A value of \(r=-1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship.
The points in the scatter - plot are not extremely close to forming a perfect straight line (a value of \(r=-0.9\) would mean the points are very close to a straight line), but they do show a noticeable linear trend. A value of \(r = - 0.4\) indicates a weaker negative linear relationship compared to \(r=-0.9\). The points are not scattered randomly (which would be closer to \(r = 0\)), but also not extremely tightly clustered around an imaginary line (as would be for \(r=-0.9\)).

Answer:

B. - 0.4