Question

You are given the following information about x and y.

x y
Independent Variable Dependent Variable
1 5
2 4
3 3
4 2
5 1

Refer to Exhibit 14-5. The sample correlation coefficient equals ______.

a. –.5
b. 1
c. –1
d. 0

Answer 1

The given data shows a perfect negative correlation between the independent variable x and the dependent variable y. For each one-unit increase in x, there is a consistent one-unit decrease in y, indicating a correlation coefficient of -1,

the answer is -1, which corresponds to choice c.

Step-by-step explanation:

The student is asked to identify the sample correlation coefficient based on the given data of an independent variable x and a dependent variable y. The correlation coefficient, often represented by 'r', indicates the strength and direction of a linear relationship between two variables. In this case, as x increases by 1, y decreases by 1 consistently. This indicates a perfect negative linear relationship between x and y, which is represented by a correlation coefficient of -1.

To calculate the correlation coefficient for this data set, here are the steps:

1. Assign each x and y value as pairs.
2. Observe the pattern that as x increases, y decreases consistently by the same amount.
3. Conclude that this represents a perfect negative correlation.