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 y00556x + 2 9291 (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predictedrade-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 OA. The grade-point average of a student who does not play video games is 2.9291 OB. The average number of video games played in a week by students is 2.9291 ° 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 2.45. 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) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is

Plug in 8 into the equation (x)

y = -0.0556x + 2.9291

y = -0.0556*8 + 2.9291 =2.4843

(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 0.0556 points, on average.

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

a) The grade-point average of a student who does not play video games is 2.9291

(d) A student who plays video games 7 hours per week has a grade-point average of 2.45 Is the students grade-point average above or below average among all students who play video games 7 hours per week?

keeping 7 in x

y = -0.0556(8) + 2.9291 =2.5399

predicted y=2.5399 >observed y=2.45

The students grade-point average is below average for those who play video games 7 hours per week

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