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Read the following description of a data set. $\newline$ Pike 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: $y = 24,417.569x - 58,522.969$ $\newline$ 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

Pike 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 = 24,417.569x - 58,522.969

\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.

Regression Line Equation: The least squares regression line provided is $y = 24,417.569x - 58,522.969$ . This equation predicts the number of visitors, $y$ , based on the area of the park, $x$ , in square kilometers. To find out how many more visitors a park would have if its area was one square kilometer larger, we need to look at the coefficient of $x$ , which represents the change in the number of visitors for each one square kilometer increase in park area.
Coefficient of $x$ : The coefficient of $x$ in the regression equation is $24,417.569$ . This means that for every additional square kilometer of park area, the model predicts an increase of $24,417.569$ visitors.
Predicted Increase in Visitors: Therefore, if a park's area was $1\,\text{square kilometer}$ larger, the least squares regression line predicts that it would have had $24,417.569$ more visitors last year.

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