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Read the following description of a data set. $\newline$ Neil 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.Neil 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: $y = 1.184x + 25.609$ $\newline$ Complete the following sentence: $\newline$ For each additional month owning the song, the least squares regression line predicts that it would have played ___ more times.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

Neil 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.Neil 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 = 1.184x + 25.609

\newline

Complete the following sentence:

\newline

For each additional month owning the song, the least squares regression line predicts that it would have played ___ more times.

Understand Equation: To solve this problem, we need to understand the equation of the least squares regression line, which is given by $y = 1.184x + 25.609$ . In this equation, $y$ represents the number of times the song has been played, and $x$ represents the number of months the song has been owned. The coefficient of $x$ ( $1.184$ ) represents the slope of the line, which indicates the change in the number of times played for each additional month the song is owned.
Interpret Slope: We can interpret the slope of the regression line ( $1.184$ ) as the predicted increase in the number of times the song is played for each additional month of ownership. Therefore, for each additional month owning the song, the least squares regression line predicts that it would have been played $1.184$ more times.

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