Question

the scatter plot shows the time spent studying, x, and the midterm score, y, for each of 24 students.
time spent studying (in hours)
use the equation of the line of best fit, y = 3.80x + 15.80, to answer the questions below.
give exact answers, not rounded approximations.
(a) what is the predicted midterm score for a student who doesnt spend any time studying?
(b) for an increase of one hour in the time spent studying, what is the predicted increase in the midterm score?
(c) what is the predicted midterm score for a student who studies for 12 hours?

Explanation:

Part (a)

To find the predicted midterm score for a student who doesn't spend any time studying, we set \( x = 0 \) in the equation \( y = 3.80x + 15.80 \).
Substituting \( x = 0 \) into the equation: \( y = 3.80(0) + 15.80 = 15.80 \).

Part (b)

The equation of the line of best fit is in the form \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y-intercept.
For the equation \( y = 3.80x + 15.80 \), the slope \( m = 3.80 \). This slope represents the predicted increase in the midterm score for an increase of one hour in the time spent studying. So the predicted increase is \( 3.80 \).

Part (c)

To find the predicted midterm score for a student who studies for 12 hours, we set \( x = 12 \) in the equation \( y = 3.80x + 15.80 \).
Substituting \( x = 12 \) into the equation: \( y = 3.80(12) + 15.80 \).
First, calculate \( 3.80(12) = 45.60 \).
Then, add \( 15.80 \): \( 45.60 + 15.80 = 61.40 \).

Answer:

(a) \( 15.80 \)
(b) \( 3.80 \)
(c) \( 61.40 \)