Question

Describe the relationship between two variables when the correlation coefficient r is one of the following. (a) near –1 strong positive linear correlation weak positive linear correlation strong negative linear correlation weak negative linear correlation weak or no linear correlation (b) near 0 strong negative linear correlation strong positive linear correlation weak negative linear correlation weak positive linear correlation weak or no linear correlation (c) near 1 weak positive linear correlation weak negative linear correlation weak or no linear correlation strong negative linear correlation strong positive linear correlation

Answer 1

Answer:

a) strong negative linear correlation.

b) Weak or no linear correlation.

c) strong positive linear correlation.

Step-by-step explanation:

The correlation coefficient r measures the strength and direction (positive or negative) of two variables. The correlation coefficient r is always between -1 and 1. When the coefficient r is negative then the direction of the correlation is downhill (negative) and when it's positive then it's an uphill correlation (positive). Similarly, as the coefficient is closer to -1 or 1 the correlation is stronger, with zero being a non linear relationship.

Now back to the question:

a) Near -1: as we said before, this means an strong negative (-1) linear correlation.

b) Near 0: weak or no linear correlation (we cannot say if its positive or negative because we don't know it it's near zero from the right (positive numbers) or the left (negative numbers)

c) Near 1: strong positive (close to +1) linear correlation