Question

read the following description of a data set.
jasper manages the student health services department at yardley university. he suspects that the students poor breakfast habits are contributing to the schools academic decline. jasper surveyed several students asking how many times they ate breakfast in the past month. he also checked each students 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 = 0.145x + 0.702
what gpa does this line predict for a student who ate breakfast 26 times this past month?
round your answer to the nearest thousandth.

Explanation:

Step1: Substitute \(x = 26\) into the regression line equation

We have the equation \(y=0.145x + 0.702\). Substitute \(x = 26\) into it: \(y=0.145\times26+0.702\)

Step2: Calculate the value of \(0.145\times26\)

\(0.145\times26=(0.1 + 0.04+0.005)\times26=0.1\times26+0.04\times26 + 0.005\times26=2.6+1.04 + 0.13=3.77\)

Step3: Calculate the value of \(y\)

\(y=3.77+0.702=4.472\)

Answer:

\(4.472\)