To determine whether the correlation coefficient [tex]\( R \)[/tex] can ever be equal to 154, let's consider the properties of the correlation coefficient.
The correlation coefficient, denoted as [tex]\( R \)[/tex], measures the strength and direction of the linear relationship between two variables. The value of [tex]\( R \)[/tex] lies within a specific range:
[tex]\[ -1 \leq R \leq 1 \][/tex]
- If [tex]\( R = 1 \)[/tex], it indicates a perfect positive linear relationship.
- If [tex]\( R = -1 \)[/tex], it indicates a perfect negative linear relationship.
- If [tex]\( R = 0 \)[/tex], it indicates no linear relationship.
Given the defined range, it is clear that 154 lies far beyond the maximum possible value of 1 and the minimum possible value of -1. Therefore, it is impossible for the correlation coefficient [tex]\( R \)[/tex] to ever be equal to 154.
Hence, the statement "The correlation coefficient [tex]\( R \)[/tex] can never be equal to 154" is True.
