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 y = -0.0503x + 2.9381.

(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 increase or decrease, by _ points, on average.

(c) If appropriate, interprety the y-intercept. A) The average number of video games played in a week by students is 2.9443 B) The grade-point average of a student who does not play video games is 2.9443 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 2.64. Is the students grade-point average above or below average among all students who play video games 7 hours per week? The students grade-point average is above or below average for those who play video games 7 hours per week.

Answer 1

y = -0.0503x + 2.9381

1) X= 8

2) To interpret slope,

For every additional unit of input, output value decreases by -.0503 units.

3) To interpret intercept -value: intercept= 2.9381

At zero hours per week, the output value grade point avearge will be 2.9381 units.

4) x= 7 and y= 2.64

Y'=-0.0503*X + 2.9381= -0.0503*7 + 2.9381= 2.586

Y= 2.64

Residual= Actual -Predication= 2.64- 2.586 = 0.054. Is below the avarage 2.64.