Final answer:
The correlation coefficient of -1 between the number of sales managers and net income indicates a perfect inverse correlation, meaning they move in opposite directions. This is a direct reflection of the strength and predictability of their relationship, and not causation.
Step-by-step explanation:
When analyzing the relationship between variables, regression analysis is often employed to determine the nature and strength of the correlation. In this specific case, the correlation coefficient between the number of sales managers in a territory and the net income for that territory is -1.
This value is indicative of a perfect inverse correlation, meaning that as the number of sales managers increases, the net income decreases, and vice versa. This correlation coefficient demonstrates a perfectly predictable relationship in the opposite direction.
It is essential to understand what the correlation coefficient represents to make accurate interpretations. A correlation coefficient of +1 implies a perfect positive correlation, whereas a correlation coefficient of -1 indicates a perfect negative correlation.
A coefficient of 0 would mean there is no correlation between the variables. Additionally, the sign of the correlation coefficient (positive or negative) dictates the direction of the relationship. Within this context, a negative coefficient such as -1 is a clear indication of variables moving in opposite directions.
Based on the given data, the best description of the situation would be c) perfect inverse correlation. This conclusion is drawn directly from the value of the correlation coefficient. It's also important to note that a strong correlation does not imply causation.
Thus, while the number of sales managers and net income are inversely related, this does not necessarily mean that hiring more sales managers will cause a decrease in net income. It is merely an association observed from the given data.