Question

use the equation of the line of best fit, ( y = 3.79x + 15.84 ), 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:

Step1: Find the predicted midterm score for a student who doesn't study

When \(x = 0\) (no time spent studying), substitute \(x = 0\) into the equation \(y=3.79x + 15.84\).
\(y=3.79\times0+15.84\)

Step2: Find the increase in midterm score for an increase of one - hour study time

The equation of the line is in the form \(y = mx + b\), where \(m\) is the slope. For the line \(y = 3.79x+15.84\), the slope \(m = 3.79\).

Step3: Find the predicted midterm score for a student who studies 12 hours

Substitute \(x = 12\) into the equation \(y=3.79x + 15.84\).
\(y=3.79\times12+15.84\)
First, calculate \(3.79\times12=(3 + 0.79)\times12=3\times12+0.79\times12=36+9.48 = 45.48\).
Then \(y=45.48+15.84\)

Answer:

(a) \(15.84\)
(b) \(3.79\)
(c) \(61.32\)