Question

read the following description of a data set.
mona is a pr agent for an up - and - coming band. she wants to convince the band members that being active on social media is good for their careers. she claims that a large social media following typically translates into ticket sales. to prove her point, mona looked up information about several successful bands.
she compared the number of social media followers (in millions), ( x ), to the average number of hours it takes these bands to sell out a concert, ( y ).
the least squares regression line of this data set is:
( y=-1.724x + 62.933 )
complete the following sentence:
the least squares regression line predicts that for each additional million followers on social media, a band sells out a concert (\boxed{}) hours faster on average.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the regression line \(y=-1.724x + 62.933\), \(x\) is the number of social - media followers (in millions) and \(y\) is the average number of hours to sell out a concert.

Step2: Interpret the slope

The slope \(m=-1.724\). The slope represents the change in \(y\) (average number of hours to sell out a concert) for a unit change in \(x\) (number of social - media followers). When \(x\) (number of followers) increases by 1 (one million more followers), \(y\) (time to sell out) changes by \(m\). Since \(y=-1.724x + 62.933\), when \(x\) becomes \(x + 1\), \(y_{new}=-1.724(x + 1)+62.933=-1.724x-1.724 + 62.933\). The change in \(y\) is \(y_{new}-y=(-1.724x-1.724 + 62.933)-(-1.724x + 62.933)=-1.724\). A negative change in \(y\) means that \(y\) (time) decreases.

Answer:

\(1.724\)