Question

Read the following description of a data set.
Sophie is an aspiring journalist who writes a music blog. In her latest post, she examined how critical acclaim and commercial success were related for recently released albums. To judge critical acclaim, she looked up the albums on a site that combines ratings from multiple critics into a single number from 0 to 100.
Sophie recorded the score, x, and the sales, y, of each album.
The least squares regression line of this data set is:
y=1828.329x–79,367.619
How many sales does this line predict for an album whose score was 77?
Round your answer to the nearest integer.
sales

Answer 1

To predict the number of sales for an album with a score of 77 using the least squares regression line equation \( y = 1828.329x - 79,367.619 \), we can substitute \( x \) with 77 and calculate \( y \).

Substituting \( x = 77 \):

\[
y = 1828.329(77) - 79,367.619
\]

Calculating \( 1828.329 \times 77 \):

\[
1828.329 \times 77 = 140,211.353
\]

Now, substituting this back into the equation:

\[
y = 140,211.353 - 79,367.619
\]

Calculating \( 140,211.353 - 79,367.619 \):

\[
y = 60,843.734
\]

Rounding to the nearest integer, the predicted number of sales is:

\[
\text{Sales} \approx 60,844
\]

So, the predicted sales for an album with a score of 77 is **60,844**.