The problem asks to determine the direction (positive or negative) and magnitude of the given correlation coefficients. The correlation coefficients are: a. $0.71$ b. $-0.40$ c. $-0.15$ d. $0.09$ e. $-0.89$

1. Problem Description

The problem asks to determine the direction (positive or negative) and magnitude of the given correlation coefficients. The correlation coefficients are:

a. $0.71$

b. $-0.40$

c. $-0.15$

d. $0.09$

e. $-0.89$

2. Solution Steps

The direction of a correlation coefficient is determined by its sign. A positive correlation coefficient indicates a positive (direct) relationship, while a negative correlation coefficient indicates a negative (inverse) relationship. The magnitude of a correlation coefficient is its absolute value, which indicates the strength of the relationship. The closer the absolute value is to 1, the stronger the relationship. The closer to 0, the weaker the relationship.

a. $0.71$: Direction is positive. Magnitude is $|0.71| = 0.71$.

b. $-0.40$: Direction is negative. Magnitude is $|-0.40| = 0.40$.

c. $-0.15$: Direction is negative. Magnitude is $|-0.15| = 0.15$.

d. $0.09$: Direction is positive. Magnitude is $|0.09| = 0.09$.

e. $-0.89$: Direction is negative. Magnitude is $|-0.89| = 0.89$.

3. Final Answer

a. Direction: Positive, Magnitude: 0.71

b. Direction: Negative, Magnitude: 0.40

c. Direction: Negative, Magnitude: 0.15

d. Direction: Positive, Magnitude: 0.09

e. Direction: Negative, Magnitude: 0.89