Question

8.4.3 test (cst): data and mathematical modeling
which graph has a correlation coefficient, r, closest to - 0.95?
a
b
c
d
a. graph a
previous

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. A value of \(r = - 0.95\) indicates a strong negative linear relationship.

Step2: Analyze each graph

• Graph A: The points are scattered randomly. There is no clear linear pattern (neither positive nor negative), so \(r\) is close to \(0\).
• Graph B: The points show a strong negative linear trend. As one variable increases, the other decreases in a fairly consistent linear - like fashion.
• Graph C: The points show a weak positive linear trend. \(r\) is close to a small positive value (e.g., \(r\approx0.2 - 0.3\)).
• Graph D: The points are scattered with no clear linear trend (similar to Graph A in terms of lack of a defined linear relationship), so \(r\) is close to \(0\).

Answer:

B. Graph B