Question

read the following description of a data set. jeremiah has trouble getting his math homework done on time, and his mother suspects it is due to lack of sleep. for the next few nights, jeremiahs mother notes the number of hours he sleeps, x, and the number of minutes it takes him to do his math homework the following day, y. the least squares regression line of this data set is: y = -20.445x + 300.767 co following sentence: sleeps for one extra hour at night, the least squares regression line pr will take him fewer minutes to do his math homework the next day.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the regression line \(y=-20.445x + 300.767\), \(x\) is the number of hours of sleep and \(y\) is the time to do homework.

Step2: Interpret the slope

The slope \(m=-20.445\). The slope represents the change in \(y\) (time to do homework) for a unit change in \(x\) (hours of sleep). When \(x\) (hours of sleep) increases by 1 (one extra hour of sleep), \(y\) (time to do homework) changes by \(m\).

Answer:

\(20.445\)