Final answer:
A negative correlation coefficient indicates an inverse relationship between two variables, where one increases as the other decreases. This signifies that the slope of the regression line will be negative, not that the other options stated are correct.
Step-by-step explanation:
When discussing the correlation coefficient in statistics, it is important to understand its main components: direction and strength. The correlation coefficient, usually denoted as 'r,' is a measure that falls between -1 and +1, with the sign of 'r' (either positive or negative) indicating the direction of the relationship between two variables, and the magnitude indicating the strength.
A negative correlation coefficient means that there is an inverse relationship between the two variables; as one variable increases, the other tends to decrease and vice versa. This does not mean there is no correlation, nor does it imply the calculation was done incorrectly. Neither does it suggest that the regression line cannot be used for prediction or that the test statistic 't' cannot be calculated. Instead, it specifically means that the slope of the regression line is negative. Moreover, the strength of the relationship is determined by how close the correlation coefficient is to -1 or +1. A coefficient close to -1 implies a strong negative relationship, while a coefficient closer to 0 suggests a weaker relationship.
Keeping all this in mind, in the context of the provided question, if the correlation coefficient is negative, it means the slope of the regression line is negative.