A student at a junior college conducted a survey of 20 rando

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=-0.0538x+2.9288.

(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.

Fore each additional hour that a student spends playing video games in a week, the grade-point average will (increase or decrease) by ______ points, on average.

(c) If appropriate, interpret the y-intercept.

    A. The average number of video games played in a week by students is 2.9288.

    B. The grade-point average of a student who does not play video games is 2.9288.

    C. It cannot be interpreted without more information.

(d) A student who plays video games 7 hour 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?

Solution

Sol)

The fitted Regression is ^y= - 0.0538x+2.9288.

a) Predict the grade-point average of a student who plays video games 8 hours per week.

ie when x=8 then

^y= - 0.0538(8)+2.9288.

The predicted grade point average is ^y= 2.498

B) Slpoe is -0.0538

Fore each additional hour that a student spends playing video games in a week, the grade-point average will decrease by 0.0538 points, on average.

C) If one unitin the change in hours that video game played it effeeccts -0.0538 change in grade point.

D) A student who plays video games 7 hour per week has a grade-point average of 2.64. then the student\'s grade-point average above average among all students who play video games 7 hours per week