Final answer:
The true statement concerning the linear correlation coefficient is option a) It ranges from -1 to 1, as it indicates the strength and direction of a linear relationship between two variables. The correlation coefficient is weakest when it is closest to 0, meaning there is little or no linear correlation.
Step-by-step explanation:
The student has asked about the linear correlation coefficient, which is a statistical measure used to evaluate the strength and direction of a linear relationship between two variables. The statements provided in the question can be assessed as follows:
- a) It ranges from -1 to 1: This is true. The correlation coefficient (often denoted as r) indeed ranges from -1 to 1, where -1 indicates a perfect negative linear correlation, 0 indicates no linear correlation, and +1 indicates a perfect positive linear correlation.
- b) A value of 0 indicates a strong positive correlation: This is false. A value of 0 means there is no linear correlation between the variables, neither positive nor negative.
- c) It measures the strength of a nonlinear relationship: This is false. The linear correlation coefficient is specifically meant to measure the strength of a linear relationship. It does not accurately measure non-linear relationships.
- d) It is not affected by outliers: This is false. In reality, outliers can have a significant impact on the value of the correlation coefficient, potentially skewing the results.
The correlation coefficient indicates the weakest relationship when it is closest to 0. This means that when the absolute value of the correlation coefficient is near zero, the relationship between the variables is weak and changes in one variable do not reliably predict changes in the other.
Therefore, option a) is the correct answer to the student's question concerning properties of the linear correlation coefficient. Specifically, it is true that the correlation coefficient ranges from -1 to 1.