Question
Read the following description of a data set. Seth 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, Seth 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. The least squares regression line of this data set is: y= – 49.801x+256.352 How long does this line predict it would take a band with 3 million followers to sell out a concert, on average? Round your answer to the nearest integer. hours
Answers
GPT-4o mini
To find how long it would take for a band with 3 million followers to sell out a concert using the least squares regression line given by the equation:
\[ y = -49.801x + 256.352 \]
we substitute \( x = 3 \) (for 3 million followers) into the equation:
\[
y = -49.801(3) + 256.352
\]
Now, calculate \( -49.801 \times 3 \):
\[
-49.801 \times 3 = -149.403
\]
Next, add this result to 256.352:
\[
y = -149.403 + 256.352 = 106.949
\]
Now, rounding 106.949 to the nearest integer gives us:
\[
\boxed{107}
\]
Therefore, the prediction is that it would take approximately 107 hours for a band with 3 million followers to sell out a concert, on average.
\[ y = -49.801x + 256.352 \]
we substitute \( x = 3 \) (for 3 million followers) into the equation:
\[
y = -49.801(3) + 256.352
\]
Now, calculate \( -49.801 \times 3 \):
\[
-49.801 \times 3 = -149.403
\]
Next, add this result to 256.352:
\[
y = -149.403 + 256.352 = 106.949
\]
Now, rounding 106.949 to the nearest integer gives us:
\[
\boxed{107}
\]
Therefore, the prediction is that it would take approximately 107 hours for a band with 3 million followers to sell out a concert, on average.