Question

Read the following description of a data set.
Johnson 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=12986.642x–6,396.832
What number of visitors does this line predict for a park whose area is 14.27 square kilometers?
Round your answer to the nearest integer.
visitors

Answer 1

To predict the number of visitors for a park with an area of 14.27 square kilometers using the given least squares regression line equation:

\[ y = 12986.642x - 6396.832 \]

we will plug in \( x = 14.27 \):

\[
y = 12986.642(14.27) - 6396.832
\]

Now, calculate \( 12986.642 \times 14.27 \):

\[
12986.642 \times 14.27 \approx 184,655.66394
\]

Next, subtract \( 6396.832 \):

\[
y \approx 184,655.66394 - 6396.832 \approx 178,258.83194
\]

Rounding this to the nearest integer, we get:

\[
y \approx 178,259
\]

Therefore, the predicted number of visitors for a park with an area of 14.27 square kilometers is **178,259**.