A student at a junior college conducted a survey of 20 randomly selected full-ti

Question

A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is y^Hat = - 0.0589x + 2.9406. (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is 2.47. (Round to the nearest hundredth as needed.) (b) Interpret the slope. For each additional hour that a student spends playing video games in a week, the grade-point average will by points, on average.

Explanation / Answer

Given regression relation:

y' = -0.0589*x + 2.9406

(a)

Put x = 8 in the above relation, we get:

y' = -0.0589*8 + 2.9406 = 2.4694 = 2.47

(b)

From the above relation, we have:

slope = dy'/dx = -0.0589

Putting dx = 1, we get:

dy' = -0.0589

Thus, for rach additional hour of video game played, the GPA decreases by 0.0589 points, on average.

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.