Question
or
Use the least squares regression line of this data set to predict a value.
A television sports commentator recently declared that basketball teams that rely on the three-point shot cannot win championships. To see if the commentator had a valid point, a sports analyst reviewed game statistics from several teams over the past season.
For each of the teams, the analyst calculated what percentage of attempted field goals had been three-pointers, x, and the number of wins in the season, y.
Percentage of shots taken from three-point range Number of wins in a season
23 34
24 25
26 31
27 46
28 46
The least squares regression line of this data set is:
y=3.419x–51.116
How many wins in a season does this line predict for a team that takes 25 percent of its shots from three-point range?
Round your answer to the nearest integer.
wins
Answers
GPT-4o mini
To predict the number of wins for a team that takes 25% of its shots from three-point range using the least squares regression line given by the equation \( y = 3.419x - 51.116 \), we can substitute \( x = 25 \) into the equation.
Substituting:
\[
y = 3.419(25) - 51.116
\]
Calculating \( 3.419 \times 25 \):
\[
3.419 \times 25 = 84.475
\]
Now substituting back into the equation:
\[
y = 84.475 - 51.116
\]
Calculating \( 84.475 - 51.116 \):
\[
y = 33.359
\]
Now, rounding to the nearest integer:
\[
y \approx 33
\]
Thus, the model predicts that a team that takes 25% of its shots from three-point range would win approximately **33** games in a season.
Substituting:
\[
y = 3.419(25) - 51.116
\]
Calculating \( 3.419 \times 25 \):
\[
3.419 \times 25 = 84.475
\]
Now substituting back into the equation:
\[
y = 84.475 - 51.116
\]
Calculating \( 84.475 - 51.116 \):
\[
y = 33.359
\]
Now, rounding to the nearest integer:
\[
y \approx 33
\]
Thus, the model predicts that a team that takes 25% of its shots from three-point range would win approximately **33** games in a season.