At the end of a semester, a math teacher wonders if student attendance has an impact on final exam scores. Here is a scatterplot that shows the number of days absent and final exam score for a class of 25 students.
1. Identify which variable is the explanatory and which is the response.

2. Describe the relationship.

3. The line of best fit is y=90.9-3.5x, where x= number of days absent and y= final exam scores.
A) Interpret the slope of the line of best fit

B) Interpret the y-intercept of the line of best fit

1. In this scenario, the number of days absent would be considered the explanatory variable, as it is being used to explain or predict the final exam scores, which would be the response variable.

2. The relationship between the number of days absent and final exam scores appears to be negative, indicating that as the number of days absent increases, the final exam scores tend to decrease.

3.

A) The slope of the line of best fit, which is -3. 5, represents the rate of change in final exam scores for each additional day absent. In this case, it indicates that for every additional day a student is absent, their final exam score is expected to decrease by 3. 5 points.

B) The y-intercept of the line of best fit, which is 90. 9, represents the expected final exam score for a student who has not been absent (x = 0). In other words, if a student has not been absent, their predicted final exam score would be 90. 9.