The regression equation provided is [tex]\(\hat{y} = 4.9x + 15.2\)[/tex], where [tex]\(x\)[/tex] represents the game attendance (in thousands) and [tex]\(\hat{y}\)[/tex] is the predicted number of wins.
To understand the meaning of the [tex]\(y\)[/tex]-intercept:
1. The [tex]\(y\)[/tex]-intercept, given mathematically as the constant term in the regression equation, is 15.2.
2. The [tex]\(y\)[/tex]-intercept represents the value of [tex]\(\hat{y}\)[/tex] when [tex]\(x\)[/tex] is 0. That is, it tells us the predicted number of wins when the game attendance [tex]\(x\)[/tex] is 0.
When the attendance ([tex]\(x\)[/tex]) is 0, substituting [tex]\(x = 0\)[/tex] into the regression equation:
[tex]\[
\hat{y} = 4.9(0) + 15.2 = 15.2
\][/tex]
Therefore, when the attendance is 0 (meaning no one attends the game), the predicted number of wins ([tex]\(\hat{y}\)[/tex]) is 15.2.
Thus, the statement that best describes the meaning of the [tex]\(y\)[/tex]-intercept of the regression line is:
"When the attendance is 0, the predicted number of wins is 15.2."
