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 0.0559 x plus 2.9289.

(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

decrease / increase / nothing

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 is

2.92892.9289.

B.The average number of video games played in a week by students is

2.92892.9289.

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

2.632.63. 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

above/ below

average for those who play video games 7 hours per week.

Answer 1

Given regression equation is y = - 0.0559x + 2.9289.

(A) grade-point average of a student who plays video games 8 hours per week, i.e. put x = 8 in the regression equation

this implies

= - 0.0559*8 + 2.9289.

= -0.4472 + 2.9289

= 2.48

(B) Slope is -0.0559, negative sign indicates decrease in dependent variable with increase in independent variable

So,

For each additional hour that a student spends playing video games in a​ week, the​ grade-point average will

decrease by __-0.0559__​points, on average

(C) Intercept is denote the value of dependent variable y when independent variable x is 0

So, correct answer is option A

The​ grade-point average of a student who does not play video games is 2.9289.

(D) grade-point average of a student who plays video games 7 hours per week, i.e. put x = 7 in the regression equation

this implies

= - 0.0559*7 + 2.9289.

= -0.3913 + 2.9289

= 2.54

So, it is clear that average grade point for playing 7 hours video game is 2.54, which is less than 2.63

The​ student's grade-point average is above average for those who play video games 7 hours per week.