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 exactly the same as \( x \) (0, 1, 4, 5). This means \( y = x \), a perfect positive linear relationship.

Step2: Recall correlation coefficient meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship. For a perfect positive linear relationship (all points lie exactly on a straight line with positive slope), \( r = 1 \). Values like 0 (no linear relationship), 4, or 5 are not valid correlation coefficients (correlation coefficient ranges between -1 and 1).

Answer:

1 (the option with value 1, as the data has a perfect positive linear correlation where \( y = x \), so the correlation coefficient is 1)