Question

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

Explanation:

Step1: Analyze the relationship between x and y

Looking at the data: when \( x = 0 \), \( y = 0 \); \( x = 1 \), \( y = 1 \); \( x = 4 \), \( y = 4 \); \( x = 5 \), \( y = 5 \). So \( y = x \) for all data points.

Step2: Recall the correlation coefficient

A correlation coefficient of 1 means a perfect positive linear relationship, where \( y \) increases linearly with \( x \) and all points lie on the line \( y = x \) (or a line with positive slope). Since here \( y = x \) for all points, the correlation coefficient is 1.

Answer:

B. 1