Question

the scatter - plot shows the time spent studying, x, and the midterm score, y, for each of 23 students. use the equation of the line of best fit, y = 3.91x + 14.36, 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: Identify the equation

The equation of the line of best - fit is $y = 3.91x+14.36$, where $y$ is the mid - term score and $x$ is the time spent studying.

Step2: Answer part (a)

For a student who doesn't study ($x = 0$), substitute $x = 0$ into the equation.
$y=3.91\times0 + 14.36=14.36$

Step3: Answer part (b)

The slope of the line $y = mx + b$ is $m$. In the equation $y = 3.91x+14.36$, the slope $m = 3.91$. The increase in the mid - term score for an increase of one hour in the time spent studying is equal to the slope of the line. So the increase is $3.91$.

Step4: Answer part (c)

Substitute $x = 12$ into the equation $y = 3.91x+14.36$.
$y=3.91\times12 + 14.36=46.92+14.36 = 61.28$

Answer:

(a) $14.36$
(b) $3.91$
(c) $61.28$