A study was done to investigate the relationship between student absences per semester and semester grades. The correlating linear model is shown below, where x represents the number of absences per semester, and y represents the semester grade [in points out of 100]. Interpret the slope.

Question

A.
Zero absences is associated with a grade of 62.
B.
An additional absence is associated with a grade decrease of 1.4.
C.
An additional 1.4 absences is associated with a grade decrease of 1.
D.
Zero absences is associated with a grade of 87.

Answer 1

To interpret the slope of a linear model that relates student absences (x) to semester grades (y), we focus on the coefficient of the x variable in the equation of the line. The slope indicates how much the semester grade (y) changes for each additional absence (x).

In this case, if the slope is negative (which is common in such studies), it means that for each additional absence, the semester grade decreases by a certain amount.

Given the options provided, the correct interpretation of the slope is:

B. An additional absence is associated with a grade decrease of 1.4.

This indicates that with each absence a student accumulates, their expected semester grade decreases by 1.4 points. The other options either misstate the relationship or do not directly relate to the slope of the linear model.