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 = -0.0524x + 2.9418. (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 points, on average. (c) If appropriate, interpret the y-intercept. A. The average number of video games played in a week by students is 2.9418. B. The grade-point average of a student who does not play video games is 2.9418. 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 student's grade-point average above or below average among all students who play video games 7 hours per week? The student's grade-point average is average for those who play video games 7 hours per week.

Explanation / Answer

a) y^ = 2.9418 - 0.0524*x

when x = 8

y^ = 2.9418 -0.0524 * 8 = 2.5226 = 2.52

b)

decrease , 0.0524

c)

option B) is correct

d)

y^ = 2.9418 -0.0524 * 7 =    2.5226

since 2.46 < 2.5226

hence    smaller /lower

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