Homework Sourse20 A student at a junior college conducted a survey of 20 ra
20) 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 = -0.0585 + 2.9443.
(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 1) increase or decrease, by _ points, on average.
(c) If appropriate, interprety the y-intercept.
A) The average number of video games played in a week by students is 2.9443
B) The grade-point average of a student who does not play video games is 2.9443
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 students grade-point average above or below average among all students who play video games 7 hours per week?
The students grade-point average is above or below average for those who play video games 7 hours per week.
Solution
20) 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 = -0.0585 + 2.9443.
(a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is 2.48 (round to the nearest hundredth as needed.)
y = -0.0585x + 2.9443
y = -0.0585*8 + 2.9443 =2.4763
(b) Interpret the slope.
For each additional hour that a student spends playing video games in a week, the grade-point average will decrease, by 0.0585 points, on average.
(c) If appropriate, interprety the y-intercept.
A) The average number of video games played in a week by students is 2.9443
B) The grade-point average of a student who does not play video games is 2.9443
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 students grade-point average above or below average among all students who play video games 7 hours per week?
y = -0.0585*7 + 2.9443 =2.5738
predicted y=2.5738 < observed y=2.64
The students grade-point average is above average for those who play video games 7 hours per week.
