In the 2014 - 2015 season of the English Premier League, there were 20 soccer teams, and each team played a total of 38 matches. The scatter plot below shows the average number of goals each team scored per match, and how many total matches each team won. Each dot on the scatter plot represents a team. A line was fit to the data to model the relationship between scoring goals and winning games.
Answers
Answer:
Step-by-step explanation:
Answer:
Finding the equation of the line
We need the slope and the yyy-intercept to find the equation of the linear model.
This line goes through (0.25,0)(0.25,0)left parenthesis, 0, point, 25, comma, 0, right parenthesis and (0.75,7)(0.75,7)left parenthesis, 0, point, 75, comma, 7, right parenthesis, so the slope is \dfrac{7-0}{0.75-0.25} = 14
0.75−0.25
7−0
=14start fraction, 7, minus, 0, divided by, 0, point, 75, minus, 0, point, 25, end fraction, equals, 14.
We can use this slope along with the fact that the line passes through (1,10.5)(1,10.5)left parenthesis, 1, comma, 10, point, 5, right parenthesis to determine that the line passes through (0,-3.5)(0,−3.5)left parenthesis, 0, comma, minus, 3, point, 5, right parenthesis, so the yyy-intercept is -3.5−3.5minus, 3, point, 5.
The equation that best describes the model is \hat y=14x-3.5
y
^
=14x−3.5.
Hint #22 / 3
Using the line to make a prediction
To estimate the number of wins for a team that scores 222 goals per match, we can plug in 222 for xxx in the equation like this:
\begin{aligned}\hat y&=14x-3.5\\ \hat y&=\left(14\right)(2)-3.5\\ \hat y&=28-3.5\\ \hat y&=24.5\end{aligned}
y
^
y
^
y
^
y
^
=14x−3.5
=(14)(2)−3.5
=28−3.5
=24.5
Hint #33 / 3
The answers
The equation of the model shown is \hat y=14x-3.5
y
^
=14x−3.5.
Based on this equation, we estimate a team that scores 222 goals per match to have 24.524.524, point, 5 wins.
Step-by-step explanation: