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Read the following description of a data set. $\newline$ On most days Isabella takes her lunch break in the park near her office. While sitting on the park bench, she scatters seeds for the pigeons and wonders how many pigeons will come.She decided to keep track of both the number of seed packages she scatters for the pigeons, $x$ , and the number of pigeons that come, $y$ .The least squares regression line of this data set is: $y = 3.124x - 17.542$ $\newline$ Complete the following sentence: $\newline$ If Isabella scattered one additional seed package, the least squares regression line predicts that ___ additional pigeons would come.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

On most days Isabella takes her lunch break in the park near her office. While sitting on the park bench, she scatters seeds for the pigeons and wonders how many pigeons will come.She decided to keep track of both the number of seed packages she scatters for the pigeons,

x

, and the number of pigeons that come,

y

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

y = 3.124x - 17.542

\newline

Complete the following sentence:

\newline

If Isabella scattered one additional seed package, the least squares regression line predicts that ___ additional pigeons would come.

Identify Slope: Identify the slope of the least squares regression line from the given equation $y = 3.124x - 17.542$ . The slope is the coefficient of $x$ , which is $3.124$ .
Interpret Slope: Interpret the slope of the regression line. The slope of $3.124$ indicates that for each one unit increase in the number of seed packages scattered ( $x$ ), the number of pigeons that come ( $y$ ) is predicted to increase by $3.124$ .
Apply Slope: Apply the slope to the scenario of scattering one additional seed package. Since the slope is $3.124$ , if Isabella scatters one more seed package, the regression line predicts that $3.124$ more pigeons would come.

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