Question

Use the least squares regression line of this data set to predict a value.
Anthony manages the student health services department at Oxford University. He suspects that the students' poor breakfast habits are contributing to the school's academic decline. Anthony surveyed several students asking how many times they ate breakfast in the past month. He also checked each student's GPA.
The data shows the number of times each student ate breakfast in the past month, x, and his or her GPA, y.
Breakfasts GPA
4 2.2
8 2.1
13 1.8
23 3.4
29 3.8
The least squares regression line of this data set is:
y=0.075x+1.502
What GPA does this line predict for a student who ate breakfast 6 times this past month?
Round your answer to the nearest thousandth.

Answer 1

To predict the GPA for a student who ate breakfast 6 times using the least squares regression line \( y = 0.075x + 1.502 \), we can substitute \( x = 6 \) into the equation.

\[
y = 0.075(6) + 1.502
\]

Calculating it step-by-step:

1. Calculate \( 0.075 \times 6 \):
\[
0.075 \times 6 = 0.45
\]

2. Add this result to 1.502:
\[
y = 0.45 + 1.502 = 1.952
\]

Thus, the predicted GPA for a student who ate breakfast 6 times is:

\[
\boxed{1.952}
\]

Rounding to the nearest thousandth, the predicted GPA is 1.952.