Question

Read the following description of a data set.
Rosanne manages the student health services department at Westford University. She suspects that the students' poor breakfast habits are contributing to the school's academic decline. Rosanne surveyed several students asking how many times they ate breakfast in the past month. She 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.
The least squares regression line of this data set is:
y=0.028x+2.101
What GPA does this line predict for a student who ate breakfast 23 times this past month?
Round your answer to the nearest thousandth.

Answers

Answered by GPT-4o mini
To predict the GPA for a student who ate breakfast 23 times using the least squares regression line given by the equation \( y = 0.028x + 2.101 \), we will substitute \( x = 23 \) into the equation.

\[
y = 0.028(23) + 2.101
\]

Now, we calculate \( 0.028 \times 23 \):

\[
0.028 \times 23 = 0.644
\]

Now, add this value to 2.101:

\[
y = 0.644 + 2.101 = 2.745
\]

Thus, the predicted GPA for a student who ate breakfast 23 times in the past month is approximately \( \boxed{2.745} \) when rounded to the nearest thousandth.
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