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Read the following description of a data set. $\newline$ Diana owns a car wash and has noticed that her business fluctuates throughout the year. She is curious to know whether these fluctuations are related to changes in the local pigeon population.Over several mornings, Diana counted the number of pigeons that were sitting on power lines in her neighborhood each day, $x$ , and the number of car washes that were purchased during that day, $y$ .The least squares regression line of this data set is: $y = 2.082x - 26.073$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line from Diana's analysis predicts an increase of ___ car washes for each additional pigeon she counts.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Diana owns a car wash and has noticed that her business fluctuates throughout the year. She is curious to know whether these fluctuations are related to changes in the local pigeon population.Over several mornings, Diana counted the number of pigeons that were sitting on power lines in her neighborhood each day,

x

, and the number of car washes that were purchased during that day,

y

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

y = 2.082x - 26.073

\newline

Complete the following sentence:

\newline

The least squares regression line from Diana's analysis predicts an increase of ___ car washes for each additional pigeon she counts.

Calculate Slope Interpretation: To find out how many additional car washes are predicted for each additional pigeon, we need to look at the slope of the least squares regression line. The slope represents the change in the dependent variable $y$ , the number of car washes) for each unit increase in the independent variable $x$ , the number of pigeons).
Determine Regression Line Slope: The slope of the regression line is the coefficient of $x$ in the equation $y = 2.082x - 26.073$ . This means that for each additional pigeon counted, the number of car washes is predicted to increase by $2.082$ .

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