x | y\n0 | 0\n1 | 1\n4 | 4\n5 | 5\nwhat is the correlation coefficient for the data shown in the…

Explanation:

Step1: Analyze the relationship between x and y

Looking at the table, for each value of ( x ) (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 the correlation coefficient for perfect linear relationships

The correlation coefficient ( r ) measures the strength and direction of a linear relationship between two variables. For a perfect positive linear relationship (where all points lie exactly on a straight line with a positive slope), the correlation coefficient is 1. For a perfect negative linear relationship, it is -1, and for no linear relationship, it is 0. Since ( y = x ) here, it's a perfect positive linear relationship, so ( r = 1 ).

Answer:

1 (corresponding to the option "1")