Question

x | y
0 | 0
1 | 1
4 | 4
5 | 5
what is the correlation coefficient for the data shown in the table?
0
1
4
5

Explanation:

Step1: Analyze the data pattern

Looking at the table, for each \( x \) value (0, 1, 4, 5), the corresponding \( y \) value is the same as \( x \) (0, 1, 4, 5). This means \( y = x \), which is a perfect positive linear relationship.

Step2: Recall correlation coefficient meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship. A perfect positive linear relationship (all points lie on a straight line with positive slope) has \( r = 1 \). Since \( y = x \) here, the points lie exactly on the line \( y = x \), so the correlation coefficient is 1.

Answer:

1 (the option with "1")