High School

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation [tex]\varphi = 4.9x + 15.2[/tex], where [tex]x[/tex] represents the attendance (in thousands) and [tex]\varphi[/tex] is the predicted number of wins.

What is the predicted number of wins for a team that has an attendance of 17,000?

A. 99.9 wins
B. 98.5 wins
C. 258.4 wins
D. 263.3 wins

Answer :

To find the predicted number of wins for a baseball team with an attendance of 17,000, we use the provided regression equation:

[tex]\[ \rho = 4.9x + 15.2 \][/tex]

Here, [tex]\( x \)[/tex] is the attendance in thousands. Since the attendance is 17,000, we need to convert this to thousands by using [tex]\( x = 17 \)[/tex].

Substitute [tex]\( x = 17 \)[/tex] into the equation:

[tex]\[ \rho = 4.9 \times 17 + 15.2 \][/tex]

Now, calculate the expression:

1. Multiply 4.9 by 17:
[tex]\[ 4.9 \times 17 = 83.3 \][/tex]

2. Add 15.2 to the result:
[tex]\[ 83.3 + 15.2 = 98.5 \][/tex]

Therefore, the predicted number of wins for the team with an attendance of 17,000 is 98.5 wins.

The correct answer is 98.5 wins.