Question

PLEASE HELP

The scatter plot shows the time spent studying, X, and the midterm score, y, for each of 25students.
Time spent studying (in hours)
Use the equation of the line of best fit, y=3.84×+16.64, to answer the questions below.
Give exact answers, not rounded approximations.
(a) For an increase of one hour in the time spent studying,
what is the predicted increase in the midterm score?
(b) What is the predicted midterm score for a student who
doesn't spend any time studying?
(c) What is the predicted midterm score for a student who
studies for 12 hours?

Answer 1

The equation of the line of best fit is y = 3.84x + 16.64, where x is the time spent studying and y is the predicted midterm score.

(a) For an increase of one hour in the time spent studying, the predicted increase in the midterm score can be found by taking the derivative of the equation with respect to x:

dy/dx = 3.84

Therefore, for an increase of one hour in the time spent studying, the predicted increase in the midterm score is 3.84.

(b) To find the predicted midterm score for a student who doesn't spend any time studying, we can substitute x = 0 into the equation:

y = 3.84x + 16.64
y = 3.84(0) + 16.64
y = 16.64

Therefore, the predicted midterm score for a student who doesn't spend any time studying is 16.64.

(c) To find the predicted midterm score for a student who studies for 12 hours, we can substitute x = 12 into the equation:

y = 3.84x + 16.64
y = 3.84(12) + 16.64
y = 64.16

Therefore, the predicted midterm score for a student who studies for 12 hours is 64.16.