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= -0.0503x + 2.9235.

(a) Predict the grade-point average of a student who plays video games 8 hours per week. 
The predicted grade-point average is ?

(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, interpret the y-intercept.

A) The average number of video games played in a week by students is 2.9235

B) The grade-point average of a student who does not play video games is 2.9235

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 2.46. Is the students grade-point average above or below average among all students who play video games 7 hours per week?

Explanation / Answer

(a) Predict the grade-point average of a student who plays video games 8 hours per week.
The predicted grade-point average is ?

Answer : y(hat) = - 0.0503 * (Video game hours) + 2.9235

= - 0.0503 * 8 + 2.9235 = 2.5211 gpa

(b) Interpret the slope.

For each additional hour that a student spends playing video games in a week, the grade-point average will 1) decrease by 0.05 points, on average.

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

A) The average number of video games played in a week by students is 2.9235. NO

B) The grade-point average of a student who does not play video games is 2.9235. YES

C) It cannot be interpreted without more information. NO

(d) A student who plays video games 7 hours per week has a grade-point average of 2.46. Is the students grade-point average above or below average among all students who play video games 7 hours per week?

predict gpa yp = - 0.0503 * (Video game hours) + 2.9235

= -0.0503 * 7 + 2.9235 = 2.5714 gpa

so the studentgpa is below average among all students who play video games 7 Hours per week.

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