Question

X

0
1
4
5
y
0
1
4
5
What is the correlation coefficient for the data shown in the table?
A. 0
B. 1
C. 4
D. 5

Answer 1

The correlation coefficient of the given data is 1, indicating a perfect positive relationship between x and y. A value of 1 implies that as x increases, y increases in a directly proportional manner.

Step-by-step explanation:

The correlation coefficient is a statistic that measures the degree to which two variables move in relation to each other. In the given table, both x and y increase at the same rate. When x is 0, y is 0; when x is 1, y is 1, and so on.

This perfect one-to-one relationship means that the correlation coefficient is 1. If we had to calculate it, we would use the Pearson correlation formula, which involves taking the covariance of the variables and dividing it by the product of their standard deviations.

Now, addressing some of the references:

1. The correlation coefficient indicates the weakest relationship when it is closest to 0.
2. All the given options, y = -3x, y = 0.2 +0.74x, and y=-9.4 - 2x, are linear equations, as they can be written in the form y = mx + b.
3. A correlation coefficient of 1 or -1 indicates the strongest relationship between two variables; -0.90 reflects a strong negative correlation, while -0.50 is a moderate negative correlation.