Question
A soccer coach is considering a strategy of having defensive players take more shots on goal. He evaluated a sample of his team's recent matches to see how players in defensive roles could contribute offensively.
In each match the coach tracked the number of shots on goal by his defenders, x. He also noted the difference between the number of goals that had been scored by his team and the opposing team, y.
The least squares regression line of this data set is:
y=0.344x+0.736
What goal difference does this line predict for a game in which the defenders had 5 shots on goal?
Round your answer to the nearest integer.
goals
In each match the coach tracked the number of shots on goal by his defenders, x. He also noted the difference between the number of goals that had been scored by his team and the opposing team, y.
The least squares regression line of this data set is:
y=0.344x+0.736
What goal difference does this line predict for a game in which the defenders had 5 shots on goal?
Round your answer to the nearest integer.
goals
Answers
GPT-4o mini
To predict the goal difference \( y \) for a game in which the defenders had 5 shots on goal \( x = 5 \), we can use the least squares regression line equation:
\[ y = 0.344x + 0.736 \]
Substituting \( x = 5 \) into the equation:
\[
y = 0.344(5) + 0.736
\]
Calculating \( 0.344 \times 5 \):
\[
0.344 \times 5 = 1.72
\]
Now, adding 0.736:
\[
y = 1.72 + 0.736 = 2.456
\]
Now, rounding \( 2.456 \) to the nearest integer gives:
\[
y \approx 2
\]
Therefore, the predicted goal difference for a game in which the defenders had 5 shots on goal is **2 goals**.
\[ y = 0.344x + 0.736 \]
Substituting \( x = 5 \) into the equation:
\[
y = 0.344(5) + 0.736
\]
Calculating \( 0.344 \times 5 \):
\[
0.344 \times 5 = 1.72
\]
Now, adding 0.736:
\[
y = 1.72 + 0.736 = 2.456
\]
Now, rounding \( 2.456 \) to the nearest integer gives:
\[
y \approx 2
\]
Therefore, the predicted goal difference for a game in which the defenders had 5 shots on goal is **2 goals**.