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Read the following description of a data set. $\newline$ Washington County's Parks and Recreation Department is considering establishing a new park. As part of the decision-making process, the department asked an intern to conduct a park usage study.The study considered the area (in square kilometers), $x$ , and the number of visitors last year, $y$ , of each county park.The least squares regression line of this data set is: $y = 10,444.674x - 172,509.926$ $\newline$ Complete the following sentence: $\newline$ If a park's area was one square kilometer larger, the least squares regression line predicts that it would have had ___ more visitors last year.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Washington County's Parks and Recreation Department is considering establishing a new park. As part of the decision-making process, the department asked an intern to conduct a park usage study.The study considered the area (in square kilometers),

x

, and the number of visitors last year,

y

, of each county park.The least squares regression line of this data set is:

y = 10,444.674x - 172,509.926

\newline

Complete the following sentence:

\newline

If a park's area was one square kilometer larger, the least squares regression line predicts that it would have had ___ more visitors last year.

Identify Coefficient of $x$ : To find out how many more visitors a park would have had if its area was one square kilometer larger, we need to look at the coefficient of $x$ in the regression equation, which represents the change in the number of visitors for each one square kilometer increase in park area.
Determine Regression Equation: The regression equation is $y = 10,444.674x - 172,509.926$ . The coefficient of $x$ is $10,444.674$ , which means for every increase of one square kilometer in park area, the number of visitors increases by $10,444.674$ .
Calculate Increase in Visitors: Therefore, if a park's area was one square kilometer larger, the regression line predicts that it would have had $10,444.674$ more visitors last year.

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