what is the correlation coefficient for the data shown in the table?\n0 15\n5 10\n10 5\n15 0\n1\n-1\n5\n10

Explanation:

Step1: Recall correlation - coefficient concept

The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. If the relationship is perfectly linear and negative (as $x$ increases, $y$ decreases in a straight - line fashion), $r=-1$. If it is perfectly linear and positive (as $x$ increases, $y$ increases in a straight - line fashion), $r = 1$.

Step2: Analyze the data

In the given table, as $x$ increases from $0$ to $15$, $y$ decreases from $15$ to $0$ in a linear fashion. For example, when $x = 0,y = 15$; when $x=5,y = 10$; when $x = 10,y = 5$; when $x=15,y = 0$. This is a perfect negative linear relationship.

Answer:

-1