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 ModifyingAbove y with caret equals negative 0.0592 x plus 2.9306y=−0.0592x+2.9306. ​(a) Predict the​ grade-point average of a student who plays video games 8 hours per week. The predicted​ grade-point average is 2.462.46. ​(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 decrease by . 0592.0592 ​points, on average. ​(c) If​ appropriate, interpret the​ y-intercept.

Answer 1

Explanation:

given that 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.

x=number of hours of video game playing each​ week

y= grade-point average,

The regression line found out using least squares method is

`y=-0.0592x+2.9306`

a) The grade-point average of a student who plays video games 8 hours per week.

=
`y(8) = -0.0592(8)+2.9306\\ \\=2.45844\\`

2.45844 is the answer.

Round off to 2.46

b) Slope = -0.0592 means For each additional hour that a student spends playing video games in a​ week, the​ grade-point average will decrease by . 0592. ​points, on average