Question

Use the least squares regression line of this data set to predict a value.
Clayton is a PR agent for an up-and-coming band. He wants to convince the band members that being active on social media is good for their careers. He claims that a large social media following typically translates into ticket sales. To prove his point, Clayton looked up information about several successful bands.
He 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.
Followers (in millions) Hours
2.70 138
3.79 147
4.07 129
5.18 131
9.84 106
The least squares regression line of this data set is:
y=
–
4.971x+155.629
How long does this line predict it would take a band with 7.02 million followers to sell out a concert, on average?
Round your answer to the nearest integer.
hours

Answer 1

To use the least squares regression line to predict the average number of hours it would take a band with 7.02 million followers to sell out a concert, we can plug the value of \( x = 7.02 \) into the regression equation:

\[
y = -4.971x + 155.629
\]

Substituting \( x \) with 7.02:

\[
y = -4.971(7.02) + 155.629
\]

Calculating step by step:

1. Multiply \(-4.971\) by \(7.02\):

\[
-4.971 \times 7.02 \approx -34.95242
\]

2. Add \(155.629\):

\[
y \approx -34.95242 + 155.629 \approx 120.67658
\]

Rounding \(y\) to the nearest integer gives us:

\[
y \approx 121 \text{ hours}
\]

Therefore, the regression line predicts it would take a band with 7.02 million followers approximately **121 hours** to sell out a concert.