Question
Adrianna gathered data on different schools' winning percentages and the average yearly salary of their head coaches (in millions of dollars) in the years
\[2000\]-
\[2011\]. She then created the following scatterplot and regression line.
The fitted line has a
\[y\]-intercept of
\[39\].
What is the best interpretation of this
\[y\]-intercept?
Choose 1 answer:
Choose 1 answer:
(Choice A) The average winning percentage was
\[39 \%\].
A
The average winning percentage was
\[39 \%\].
(Choice B) On average, each
\[1\] million dollar increase in salary was associated with a
\[39 \%\] increase in winning percentage.
B
On average, each
\[1\] million dollar increase in salary was associated with a
\[39 \%\] increase in winning percentage.
(Choice C) The average salary was
\[39\] million dollars.
C
The average salary was
\[39\] million dollars.
(Choice D) The model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
D
The model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
\[2000\]-
\[2011\]. She then created the following scatterplot and regression line.
The fitted line has a
\[y\]-intercept of
\[39\].
What is the best interpretation of this
\[y\]-intercept?
Choose 1 answer:
Choose 1 answer:
(Choice A) The average winning percentage was
\[39 \%\].
A
The average winning percentage was
\[39 \%\].
(Choice B) On average, each
\[1\] million dollar increase in salary was associated with a
\[39 \%\] increase in winning percentage.
B
On average, each
\[1\] million dollar increase in salary was associated with a
\[39 \%\] increase in winning percentage.
(Choice C) The average salary was
\[39\] million dollars.
C
The average salary was
\[39\] million dollars.
(Choice D) The model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
D
The model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
Answers
GPT-4o mini
The best interpretation of the \(y\)-intercept in this context is:
(Choice D) The model indicates that teams with coaches who had a salary of \(0\) million dollars will average a winning percentage of \(39 \%\).
In a regression model, the \(y\)-intercept represents the expected value of the dependent variable (winning percentage, in this case) when the independent variable (salary) is zero. Therefore, when a coach's salary is \(0\) million dollars, the expected average winning percentage would be \(39\%\).
(Choice D) The model indicates that teams with coaches who had a salary of \(0\) million dollars will average a winning percentage of \(39 \%\).
In a regression model, the \(y\)-intercept represents the expected value of the dependent variable (winning percentage, in this case) when the independent variable (salary) is zero. Therefore, when a coach's salary is \(0\) million dollars, the expected average winning percentage would be \(39\%\).