Question

read the following description of a data set.
carson wonders how many times he has played his favorite songs on his computer. to investigate, he looked up information stored by his music playing software.
carson determined how long he had owned each song (in months), x. he also counted how many times each song had been played, y.
the least squares regression line of this data set is:
y = 4.595x + 14.015
if carson owned a song for 5 months, how times does this line predict he would have played it?
round your answer to the nearest integer.
plays
save answer

Explanation:

Step1: Substitute \(x = 5\) into the regression equation

Given the regression line \(y=4.595x + 14.015\), when \(x = 5\), we have \(y=4.595\times5+14.015\).
First, calculate \(4.595\times5\): \(4.595\times5=(4 + 0.595)\times5=4\times5+0.595\times5=20+2.975 = 22.975\).
Then, add \(14.015\) to the result: \(y=22.975+14.015\).

Step2: Calculate the sum

\(y=22.975 + 14.015=36.99\).

Step3: Round to the nearest integer

Since \(36.99\approx37\) (because the decimal part \(0.99\gt0.5\)).

Answer:

37