What does an rs value of -1 indicate about a data set?

What does an rs value of -1 indicate about a data set?

• A. The data set is consistently increasing
• B. The data set is not consistent in its trend
• C. The data set is monotonically decreasing
• D. The data set is perfectly positive

Answer: (C)

An rs value of -1 indicates a perfect negative correlation in the data set. This means that as one variable increases, the other variable consistently decreases in a linear manner. In other words, the relationship between the two variables is such that every increase in one variable corresponds to a specific, proportional decrease in the other variable. This attribute signifies that the data points lie perfectly along a straight line with a negative slope, demonstrating a strong monotonic decreasing trend. The concept of monotonicity refers to a consistently increasing or decreasing pattern without any fluctuations or reversals. In the case of a correlation of -1, the relationship is perfectly linear and strictly decreasing, confirming that the correct interpretation is that the data set is monotonically decreasing. Other possible values or statements about the data set would not accurately reflect this specific characteristic that a correlation of -1 entails.

An rs value of -1 indicates a perfect negative correlation in the data set. This means that as one variable increases, the other variable consistently decreases in a linear manner. In other words, the relationship between the two variables is such that every increase in one variable corresponds to a specific, proportional decrease in the other variable.

This attribute signifies that the data points lie perfectly along a straight line with a negative slope, demonstrating a strong monotonic decreasing trend. The concept of monotonicity refers to a consistently increasing or decreasing pattern without any fluctuations or reversals. In the case of a correlation of -1, the relationship is perfectly linear and strictly decreasing, confirming that the correct interpretation is that the data set is monotonically decreasing.

Other possible values or statements about the data set would not accurately reflect this specific characteristic that a correlation of -1 entails.