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 =-0.0512x + 2.9109. (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is 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 ponts, on average. (c) If appropriate, interpret the y-intercept. O A. The grade-point average of a student who does not play video games is 2.9109. O B. The average number of video games played in a week by students is 2.9109. O C. It cannot be interpreted without more information (d) A student who plays video games 7 hours per week has a grade-point average of 2.64. Is the student's grade-point average above or below average among all students who play video games 7 hours per week? The students grade-point average is | | average for those who play video games 7 hours per week.

Explanation / Answer

Solution:

y = -0.0512x + 2.9109

a) Plug in x = 8 :

y = -0.0512x + 2.9109

y = -0.0512(8) + 2.9109

y = 2.5013

y = 2.50 ---> ANSWER

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b) "decrease" by "0.0512" points

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c) When x = 0, y = 2.9109

x = 0 ---> student plays no video games
y = 2.9109 --> student who plays no video games during the week gets a GPA of 2.9109
Option B

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d)
When x = 7, y = 2.64

Lets use the equation

when x = 7 :

y = -0.0512(7) + 2.9109

y = 2.5525

So, since 2.5525 > 2.64

"The student's GPA is BELOW average.

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