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 cach 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 = -0.0505x + 2.9248. (a) Predict the grade-point average of a student who plays video garnet 8 hours per week. The predicted grade-point average is, (Round to the nearest hundredth as needed.) (b) Interpret the slope. For cach 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 grade-point average of a student who does not play video games it 2.924ft. O" The average number of video games played in a week by students is 2.9248. C. It cannot be interpreted without more information. (d) A student who plays video games 7 hours pet week has a grade-point average of 2.46. Is the student's grade-point average above or below average among all studenu who play video games 7 hours per week? The student's gradc-potnt average is average for those who play video games 7 hours per week.

Explanation / Answer

a)The predicted grade point average for student who plays video games 8 hours per week is:

Y^=-0.0505*8+2.9248

=2.5208

(b)For each additional hour that a student spends playing video games in a week the grade point average will decrease by 0.0505 points on average. This point -0.0505 is called the intercept.

(c) When x = 0, the corresponding y-value is the y-intercept, thus the correct choice is:

A.The grade point average of a student who does not play video games is 2.9248.

(d) The predicted grade point average for student who plays video games 8 hours per week is:

Y^=-0.0505*7+2.9248

=2.5713

Thus the student’s grade point average (2.46) is below average for those who play video games 7 hours per week.

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