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Read the following description of a data set. $\newline$ Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any.Rod noted the age of each person he spoke with, $x$ , and the number of songs each could name, $y$ .The least squares regression line of this data set is: $y = 0.054x - 1.247$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that if a person is one year older, they will be able to name $\_\_$ more songs.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any.Rod noted the age of each person he spoke with,

x

, and the number of songs each could name,

y

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

y = 0.054x - 1.247

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that if a person is one year older, they will be able to name

\_\_

more songs.

Interpreting Coefficient of Age: To answer the question prompt, we need to look at the coefficient of the age variable $x$ in the least squares regression line equation, which is $y = 0.054x - 1.247$ . The coefficient of $x$ , which is $0.054$ , represents the slope of the line and indicates the change in the number of songs named ( $y$ ) for each additional year of age ( $x$ ).
Understanding Slope: Since the slope is $0.054$ , this means that for each additional year of age, the number of songs a person can name is predicted to increase by $0.054$ . This is the rate of change of $y$ with respect to $x$ .
Predicting Increase in Songs: Therefore, the least squares regression line predicts that if a person is one year older, they will be able to name $0.054$ more songs.

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