Boone 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.

Question

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=35618.514x–178,199.314
What number of visitors does this line predict for a park whose area is 11.01 square kilometers?
Round your answer to the nearest integer.

Answer 1

To predict the number of visitors for a park with an area of 11.01 square kilometers using the least squares regression line \( y = 35618.514x - 178199.314 \), simply substitute \( x = 11.01 \) into the equation.

\[ y = 35618.514(11.01) - 178199.314 \]

Calculating \( 35618.514 \times 11.01 \):

\[ 35618.514 \times 11.01 = 392,674.58614 \]

Now subtract \( 178199.314 \):

\[ y = 392674.58614 - 178199.314 = 214475.27114 \]

Rounding this to the nearest integer gives us:

\[ y \approx 214475 \]

Therefore, the predicted number of visitors for a park with an area of 11.01 square kilometers is 214475.