Final answer:
Among the options provided, a correlation coefficient of 0.9 (D) represents the strongest linear relationship in a data set, as it is the closest to 1, demonstrating a highly predictable pattern in the changing relationship between two variables.
Step-by-step explanation:
Out of the given options for correlation coefficients, a strong linear relationship is represented by the coefficient that is closest to 1 or -1, be it positive or negative. The sign indicates the direction of the relationship, with positive indicating that as one variable increases, the other variable also increases, and negative indicating that as one variable increases, the other decreases. However, the strength of the relationship is determined by the absolute value of the correlation coefficient.
Therefore, among the given options, 0.9 (D) would correspond to the strongest linear relationship in a data set because it is closest to 1. This means that as one variable changes, the other variable is likely to change in the same direction in a highly predictable pattern. A correlation coefficient of 0.8 (A) also indicates a strong linear relationship but not as strong as 0.9. Option B (0) indicates no linear relationship, and option C (0.2) indicates a very weak linear relationship.