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 model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
C
The model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
(Choice D) The average salary was
\[39\] million dollars.
D
The average salary was
\[39\] million dollars.
\[2000\]-
\[2011\]. 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 model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
C
The model indicates that teams with coaches who had a salary of
\[0\] million dollars will average a winning percentage of
\[39 \%\].
(Choice D) The average salary was
\[39\] million dollars.
D
The average salary was
\[39\] million dollars.
Answers
GPT-4o mini
The best interpretation of the \(y\)-intercept of \(39\) in this context is:
**(Choice C)** The model indicates that teams with coaches who had a salary of \(0\) million dollars will average a winning percentage of \(39\%\).
The \(y\)-intercept represents the predicted value of the dependent variable (winning percentage) when the independent variable (salary) is zero. In this case, the interpretation reflects the winning percentage when the salary is \(0\) million dollars.
**(Choice C)** The model indicates that teams with coaches who had a salary of \(0\) million dollars will average a winning percentage of \(39\%\).
The \(y\)-intercept represents the predicted value of the dependent variable (winning percentage) when the independent variable (salary) is zero. In this case, the interpretation reflects the winning percentage when the salary is \(0\) million dollars.