Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average,G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

Hours of Video Games per Week, h ………………………….. Grade-point Average, G

0 ……………………………………………………………………………. 3.49

0 ……………………………………………………………………………. 3.05

2 ……………………………………………………………………………. 3.24

3 ……………………………………………………………………………. 2.82

3 ……………………………………………………………………………. 3.19

5 ……………………………………………………………………………. 2.78

8 ……………………………………………………………………………. 2.31

8 ……………………………………………………………………………. 2.54

10 ……………………………………………………………………………. 2.03

12 ……………………………………………………………………………. 2.51

(a) Explain why the number of hours spent playing video games is the independent variable and cumulative grade point average is the dependent variable.

(b) Use a graphing utility to draw a scatter diagram.

(c) Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation.

(d) Interpret the slope.

(e) Predict the grade-point average of a student who plays video games for 8 hours each week.

(f) How many hours of video game playing do you think a student plays whose grade-point average is 2.40?