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 = - 0.0541x + 2.9327.

(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 (Increase or Decrease), by ___ points, on average. (Select the correct answer and fill in the blank)

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

A) The average number of video games played in a week by students is 2.9327.

B) The grade-point average of a student who does not play video games is 2.9327

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 2.44. 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

y = -0.0552 x + 2.9352

a.
x = 8
The predicted grade point average is
y = -0.0552*8 + 2.9352
= 2.4936

b.
slope of regression line is -0.0552
For each additional hour that a student spends playing video games in a week the grade point average will decrease by 0.0552.

c.
intercept = 2.9352
at x=0, y = 2.9352
a. The grade point average of a student who does not play video games is 2.9352

d.
x = 7
The predicted grade point average is
y = -0.0552*7 + 2.9352
= 2.5488

actual grade point average is 2.66
The student