Question

Identify the relationship between two variables and the terminology used to describe that relationship if

a)$\rho >0$

b)$\rho =0$

c)$\rho <0$

Short answer

Part a) increase linearly

Part b) linearly uncorrelated

Part c) negatively linearly correlated,

Step-by-step solution

Step 1:Given information

The relationship between two variables

Step 2:Explaination Part a)

If $\rho >0$: The variables are positively linearly correlated, meaning that $y$tends to increase linearly as $x$increases (and vice versa), with the tendency being greater the closer that $\rho$is to $1$

Step 2:Explaination Part b)

If$\rho =0$ : The variables are linearly uncorrelated, meaning that there is no linear between the variables.

Step 2:Explaination Part c)

If $\rho <0$: The variables are negatively linearly correlated, meaning that $y$tends to decrease linearly as $x$increases (and vice versa), with the tendency being greater the closer that $\rho$is to $-1.$