13)
A school compared students' absences to their course grades. The school determined the correlation coefficient of each student's absences to course grades was r = −92
(3 points)
There is ___ relationship between the number of absences and the course grades
The graph represents a ____ relationship between x and y
The slope of the graph is ____
There is a negative relationship between the number of absences and the course grades.
The graph represents a negative relationship between x and y.
The slope of the graph is negative.
The graph represents a ____ relationship between x and y
A. linear
B. exponential
C. quadratic
The graph represents a linear relationship between x and y.
To determine the relationship between absences and course grades based on the correlation coefficient of -92, we can follow these steps:
1. Determine the magnitude of the correlation coefficient: The correlation coefficient, denoted by "r," ranges from -1 to 1. The closer the value is to -1 or 1, the stronger the relationship. In this case, the coefficient is -92, which is very close to -1. Therefore, the relationship between the number of absences and the course grades is a strong negative relationship.
2. Interpret the relationship: Since the correlation coefficient is negative, it means that as the number of absences increases, the course grades tend to decrease. The relationship is negative, indicating that more absences are associated with lower grades.
3. Determine the type of relationship: Since the coefficient is negative, it indicates a negative or inverse relationship. This means that as the number of absences increases, the course grades decrease. A negative relationship is represented by a downward sloping line when graphed.
4. Determine the slope: The slope of the relationship line can be calculated using the formula: slope = r * (standard deviation of y / standard deviation of x). However, since the correlation coefficient (-92) already represents the slope, we can directly conclude that the slope of the graph is -92.
In summary:
- There is a strong, negative relationship between the number of absences and course grades.
- The graph represents a negative relationship between absences (x-axis) and course grades (y-axis).
- The slope of the graph is -92, indicating a decrease of course grades for each additional absence.