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 = 3.84x + 15.64, to answer the questions below. give exact answers, not rounded approximations. (a) what is the predicted midterm score for a student who studies for 15 hours? (b) what is the predicted midterm score for a student who doesnt spend any time studying? (c) for an increase of one hour in the time spent studying, what is the predicted increase in the midterm score?

Explanation:

Step1: Substitute \(x = 15\) into the equation \(y=3.84x + 15.64\)

$$y=3.84\times15+15.64$$
$$y = 57.6+15.64$$

Step2: Calculate the sum

$$y=73.24$$

Step3: Substitute \(x = 0\) into the equation \(y=3.84x + 15.64\)

$$y=3.84\times0+15.64$$
$$y = 0 + 15.64$$

Step4: Calculate the sum

$$y=15.64$$

Step5: Analyze the slope - intercept form \(y=mx + b\) (where \(m\) is the slope)

For the equation \(y=3.84x + 15.64\), the slope \(m = 3.84\). In the context of the linear relationship \(y\) (mid - term score) and \(x\) (study time), the slope represents the change in \(y\) for a unit change in \(x\).

Answer:

(a) \(73.24\)
(b) \(15.64\)
(c) \(3.84\)