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Read the following description of a data set. $\newline$ Members of the popular band DrumSolo are concerned that the songs on their most recent album are too long. They decide to see if there was any relationship between song length and popularity of their previous albums.For every previously released album, they measure the average song length (in minutes), $x$ , and also note the number of albums sold, $y$ .The least squares regression line of this data set is: $y = -67,414.883x + 482,574.062$ $\newline$ Complete the following sentence: $\newline$ For each additional minute of average song length on an album, the least squares regression line predicts $\_\_$ fewer albums would sell.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Members of the popular band DrumSolo are concerned that the songs on their most recent album are too long. They decide to see if there was any relationship between song length and popularity of their previous albums.For every previously released album, they measure the average song length (in minutes),

x

, and also note the number of albums sold,

y

.The least squares regression line of this data set is:

y = -67,414.883x + 482,574.062

\newline

Complete the following sentence:

\newline

For each additional minute of average song length on an album, the least squares regression line predicts

\_\_

fewer albums would sell.

Identify slope: Identify the slope of the least squares regression line. The equation given is $y = -67,414.883x + 482,574.062$ . The slope of the least squares regression line is the coefficient of $x$ , which is $-67,414.883$ . This number represents the change in the number of albums sold ( $y$ ) for each one-minute increase in the average song length ( $x$ ).
Interpret slope: Interpret the slope. $\newline$ Since the slope is negative, it indicates that there is a decrease in the number of albums sold for each additional minute of average song length. Specifically, for each additional minute, the number of albums sold decreases by $67,414.883$ .

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