Question

Data for this problem are based on information from stats basketball scoreboard. It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls that were more than (i.e., over and above) the number of fouls made by the opposing team. Let y be the percentage of times the team with the larger number of fouls won the game. What is the relationship between x and y?

1) There is a positive relationship between x and y
2) There is a negative relationship between x and y
3) There is no relationship between x and y
4) The relationship between x and y cannot be determined

Answer 1

The relationship between x and y can be determined by analyzing the correlation coefficient between the two variables.

Step-by-step explanation:

The relationship between x and y can be determined by analyzing the correlation coefficient between the two variables. The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between x and y. If the correlation coefficient is positive, there is a positive relationship between x and y, meaning that as x increases, y also tends to increase. On the other hand, if the correlation coefficient is negative, there is a negative relationship between x and y, indicating that as x increases, y tends to decrease, and vice versa.

To determine the relationship between x and y, we can calculate the correlation coefficient and interpret its sign:

1. If the correlation coefficient is positive, the answer is 1) There is a positive relationship between x and y.
2. If the correlation coefficient is negative, the answer is 2) There is a negative relationship between x and y.
3. If the correlation coefficient is zero, the answer is 3) There is no relationship between x and y.

Therefore, once we have the correlation coefficient, we can determine the relationship between x and y.