Question

tariqs math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. what does the slope of the line represent?
answer
a students expected quiz score if they spent no time on their homework.
the change in expected quiz score for every additional one hour students spend on their homework.
a prediction of a students quiz score if they spent 1 hour on their homework.
the change in a students actual quiz score for every additional one hour that student spent on their homework.

Explanation:

Step1: Recall the concept of slope in regression line

The slope of a regression line (line of best fit) in a scatter - plot of \(y\) (quiz score) against \(x\) (time spent on homework) is calculated as \(m=\frac{\Delta y}{\Delta x}\).

Step2: Interpret the slope formula

In the context of \(y\) (quiz score) and \(x\) (time spent on homework), \(\Delta y\) is the change in the quiz score and \(\Delta x\) is the change in the time spent on homework. When \(\Delta x = 1\) (an additional one - hour of homework), the slope \(m\) gives the change in the expected quiz score.

Answer:

The change in expected quiz score for every additional one hour students spend on their homework.