The correlation coefficient ranges between:a.[-1,1]b.[0,1]c.(-∞ , ∞)d.(-1,0)Clear my choice

Step 1: Break Down the Problem

The question is asking about the range of the correlation coefficient, which is a statistical measure that expresses the extent to which two variables are linearly related.

Step 2: Relevant Concepts

The correlation coefficient, often denoted as $r$, indicates the strength and direction of a linear relationship between two variables. The value of $r$ can range from -1 to 1:

• $r = 1$ indicates a perfect positive linear correlation
• $r = -1$ indicates a perfect negative linear correlation
• $r = 0$ indicates no linear correlation

Step 3: Analysis and Detail

Given the provided options:

1. a. [-1, 1]: This includes both -1 and 1, which aligns well with the known range for correlation coefficients.
2. b. [0, 1]: This only covers non-negative correlations, which is not complete.
3. c. (-∞, ∞): This suggests that the correlation can take any value, which is incorrect.
4. d. (-1, 0): This only accounts for negative correlations and excludes positive ones.

Step 4: Verify and Summarize

The most accurate option representing the full range of the correlation coefficient is option a. [-1, 1].

Final Answer

The correlation coefficient ranges between [-1, 1].